Finite Group Databasebeta

← C2×#23777764 #35195914

Subgroups — C2×#23777764 #35195914

Order 20224.

8046 conjugacy classes of subgroups.

The subgroup lattice has 1440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777764C2132yesmaximal, direct product factor
2C2×#19099303C212yesmaximal, complemented
3C2×#19099302C212yesmaximal, complemented
4C2×#19099284C211yesmaximal, characteristic, complemented
5C2×#19099263C211yesmaximal, characteristic, complemented
6C2×#19099259C211yesmaximal, characteristic, complemented
7C2×#19099232C211yesmaximal, characteristic, complemented
8C2×#19099231C212yesmaximal, complemented
9C2×#19099213C211yesmaximal, characteristic, complemented
10C2×#19099206C211yesmaximal, characteristic, complemented
11C2×#19099203C212yesmaximal, complemented
12C2×D4×C22⋊D79C211yesmaximal, characteristic, complemented
13C2×#19099181C212yesmaximal, complemented
14C2×#19099151C212yesmaximal, complemented
15C2×#19099145C212yesmaximal, complemented
16C2×#19099143C211yesmaximal, characteristic, complemented
17C2×#19099141C211yesmaximal, characteristic, complemented
18C2×#19099130C211yesmaximal, characteristic, complemented
19C2×#19099129C211yesmaximal, characteristic, complemented
20C2×#19099128C212yesmaximal, complemented
21C2×#19099110C211yesmaximal, characteristic, complemented
22C2×#19099110C211yesmaximal, characteristic, complemented
23C2×#19099092C211yesmaximal, characteristic, complemented
24C2×#546×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic, complemented
26C22×#11929624C2212yescomplemented
27C22×#11929624C2211yescharacteristic, complemented
28C22×#11929624C2211yescharacteristic, complemented
29C22×#11929623C2212yescomplemented
30C23×C22⋊D79C2212yes—
31C22×D4×D79C2211yescharacteristic
32#19099303C22132yescomplemented
33#19099302C22132yescomplemented
34#19099284C22116yescomplemented
35#19099263C22116yescomplemented
36#19099259C22116yescomplemented
37#19099232C22116yescomplemented
38#19099231C22132yescomplemented
39#19099213C22116yescomplemented
40#19099206C22116yescomplemented
41#19099203C22132yescomplemented
42D4×C22⋊D79C22116yescomplemented
43#19099181C22132yescomplemented
44#19099151C22132yescomplemented
45#19099145C22132yescomplemented
46#19099143C22116yescomplemented
47#19099141C22116yescomplemented
48#19099130C22116yescomplemented
49#19099129C22116yescomplemented
50#19099128C22132yescomplemented
51#19099110C22116yescomplemented
52#19099110C22116yescomplemented
53C2×#14579160C2211yescharacteristic, complemented
54C2×#14579160C2211yescharacteristic, complemented
55C2×#14579157C2211yescharacteristic
56C2×#14579157C2211yescharacteristic
57C2×#14579157C2212yescomplemented
58C2×#14579157C2212yescomplemented
59C2×#14579157C2212yescomplemented
60#19099092C22116yescomplemented
61C2×#14579156C2212yescomplemented
62C2×#14579156C2212yescomplemented
63C2×#14579154C2212yescomplemented
64C2×#14579154C2212yescomplemented
65C2×#14579154C2212yescomplemented
66C2×#14579153C2211yescharacteristic, complemented
67C2×#14579148C2212yescomplemented
68C2×#14579147C2212yes—
69C2×#14579147C2212yescomplemented
70C2×#14579147C2212yescomplemented
71C2×#14579147C2211yescharacteristic, complemented
72C2×#14579147C2211yescharacteristic, complemented
73C2×#14579144C2212yescomplemented
74C2×#14579143C2212yescomplemented
75C2×#14579143C2212yescomplemented
76C2×#14579143C2212yescomplemented
77C2×#14579143C2212yescomplemented
78C2×#14579142C2212yescomplemented
79C2×#14579140C2212yescomplemented
80C2×#14579139C2212yescomplemented
81C2×#14579138C2212yescomplemented
82C2×#14579137C2211yescharacteristic, complemented
83C2×#14579137C2211yescharacteristic, complemented
84C2×#14579136C2212yescomplemented
85C2×#14579136C2211yescharacteristic, complemented
86C2×#14579136C2211yescharacteristic, complemented
87C2×#14579135C2211yescharacteristic
88C2×#14579135C2212yescomplemented
89C2×#14579135C2211yescharacteristic, complemented
90C2×#14579135C2212yescomplemented
91C2×#14579134C2211yescharacteristic
92C2×#14579134C2212yescomplemented
93C2×#14579134C2212yescomplemented
94C2×#14579134C2211yescharacteristic, complemented
95C2×#14579134C2212yescomplemented
96C2×#14579134C2212yescomplemented
97C2×#14579134C2212yescomplemented
98C2×#14579133C2212yes—
99C2×#14579133C2212yescomplemented
100C2×#14579133C2212yescomplemented
101C2×#14579133C2212yescomplemented
102C2×#14579132C2211yescharacteristic
103C2×#14579132C2211yescharacteristic
104C2×#14579132C2211yescharacteristic
105C2×#14579132C2211yescharacteristic, complemented
106C2×#14579132C2212yescomplemented
107C2×#14579132C2211yescharacteristic, complemented
108C2×#14579132C2211yescharacteristic, complemented
109C2×#14579131C2212yescomplemented
110C2×#14579131C2212yescomplemented
111C2×#14579130C2212yes—
112C2×#14579130C2212yescomplemented
113C2×#14579130C2212yescomplemented
114C2×#14579129C2212yes—
115C2×#14579129C2212yescomplemented
116C2×Q8×Dic79C2211yescharacteristic, complemented
117C2×#14579126C2212yescomplemented
118C2×C4×D316C2211yescharacteristic, complemented
119C2×C4×D316C2211yescharacteristic, complemented
120C2×D4×Dic79C2211yescharacteristic
121C2×C4×C22⋊D79C2211yescharacteristic
122C2×C4×C22⋊D79C2212yescomplemented
123C2×C4×C22⋊D79C2211yescharacteristic, complemented
124C2×C4×C22⋊D79C2212yescomplemented
125C2×C4×C22⋊D79C2212yescomplemented
126C2×(C22⋊D79)⋊C4C2212yescomplemented
127C2×(C22⋊D79)⋊C4C2212yescomplemented
128C2×#14579120C2211yescharacteristic, complemented
129C2×#14579119C2211yescharacteristic, complemented
130C2×#14579117C2212yescomplemented
131C22×C4⋊Dic79C2211yescharacteristic, complemented
132C2×C4⋊C4×D79C2211yescharacteristic, complemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C42×D79C2211yescharacteristic, complemented
135C22×#41×C79C2211yescharacteristic, complemented
136C23×D4×C79C2211yescharacteristic
137#546×C79C22116yescomplemented
138C2×#124×C79C2211yescharacteristic
139C2×#123×C79C2212yescomplemented
140C2×C22⋊Q8×C79C2211yescharacteristic, complemented
141C2×#121×C79C2211yescharacteristic
142C2×#121×C79C2212yescomplemented
143C2×#120×C79C2212yescomplemented
144C2×C4×D4×C79C2211yescharacteristic, complemented
145C2×C4×D4×C79C2211yescharacteristic, complemented
146C22×C22⋊C4×C79C2212yescomplemented
147C24×D79C2312yes—
148C2×#11929625—44no—
149C2×#11929625C2318yescomplemented
150C2×#11929624—44no—
151C2×#11929624—44no—
152C2×#11929624—48no—
153C2×#11929624C2318yescomplemented
154C2×#11929624C2318yescomplemented
155C2×#11929624C23116yescomplemented
156C2×#11929623—48no—
157C2×#11929623C23116yescomplemented
158C22×Dic158C2312yes—
159C22×Dic158C2311yescharacteristic
160C22×Dic158C2311yescharacteristic
161C22×D316C2311yescharacteristic
162C22×D316C2311yescharacteristic
163C22×D316C2311yescharacteristic
164C22×D316C2312yes—
165C22×D316C2312yes—
166C22×D316C2311yescharacteristic
167C22×C22⋊D79—48no—
168C22×C22⋊D79C2311yescharacteristic
169C22×C22⋊D79C2312yes—
170C22×C22⋊D79C2311yescharacteristic
171C22×C22⋊D79C23116yes—
172C22×C22⋊D79C2312yes—
173C22×C22⋊D79C2312yes—
174C22×C22⋊D79C2312yes—
175C22×C22⋊D79C2312yes—
176C22×C22⋊D79C2312yes—
177C22×C22⋊D79C2311yescharacteristic
178C22×C22⋊D79C2312yes—
179C22×C22⋊D79C2312yes—
180C22×C22⋊D79C2311yescharacteristic
181C22×C22⋊D79C2311yescharacteristic
182C22×C22⋊D79C2312yes—
183C22×C22⋊D79C2312yes—
184C22×C22⋊D79C2311yescharacteristic
185C2×D4×D79—44no—
186C2×D4×D79C2318yes—
187C23×Dic79C2312yes—
188C23×Dic79C2312yes—
189C22×C4×D79C2311yescharacteristic
190C22×C4×D79C2311yescharacteristic
191C22×C4×D79C2311yescharacteristic
192C22×C4×D79C2311yescharacteristic
193C22×C4×D79C2311yescharacteristic
194C22×C4×D79C2312yes—
195C22×C4×D79C2312yes—
196C22×C4×D79C2312yes—
197#14579160C2318yescomplemented
198#14579160C2318yescomplemented
199#14579157C2318yes—
200#14579157C2318yes—
201#14579157C23116yescomplemented
202#14579157C23116yescomplemented
203#14579157C23116yescomplemented
204#14579156C23116yescomplemented
205#14579156C23116yescomplemented
206#14579154C23116yescomplemented
207#14579154C23116yescomplemented
208#14579154C23116yescomplemented
209#14579153C2318yescomplemented
210#14579148C23116yescomplemented
211#14579147C23116yes—
212#14579147C2318yescomplemented
213#14579147C2318yescomplemented
214#14579147C23116yescomplemented
215#14579147C23116yescomplemented
216#14579144C23116yescomplemented
217#14579143C23116yescomplemented
218#14579143C23116yescomplemented
219#14579143C23116yescomplemented
220#14579143C23116yescomplemented
221#14579142C23116yescomplemented
222#14579140C23116yescomplemented
223#14579139C23116yescomplemented
224#14579138C23116yescomplemented
225#14579137C2318yescomplemented
226#14579137C2318yescomplemented
227#14579136C23116yescomplemented
228#14579136C2318yescomplemented
229#14579136C2318yescomplemented
230#14579135C2318yes—
231#14579135C23116yescomplemented
232#14579135C23116yescomplemented
233#14579135C2318yescomplemented
234#14579134C2318yes—
235#14579134C23116yescomplemented
236#14579134C23116yescomplemented
237#14579134C23116yescomplemented
238#14579134C2318yescomplemented
239#14579134C23116yescomplemented
240#14579134C23116yescomplemented
241#14579133C23116yes—
242#14579133C23116yescomplemented
243#14579133C23116yescomplemented
244#14579133C23116yescomplemented
245#14579132C2318yes—
246#14579132C2318yes—
247#14579132C2318yes—
248#14579132C2318yescomplemented
249#14579132C23116yescomplemented
250#14579132C2318yescomplemented
251#14579132C2318yescomplemented
252#14579131C23116yescomplemented
253#14579131C23116yescomplemented
254#14579130C23116yes—
255#14579130C23116yescomplemented
256#14579130C23116yescomplemented
257#14579129C23116yes—
258#14579129C23116yescomplemented
259Q8×Dic79C2318yescomplemented
260#14579126C23116yescomplemented
261C4×D316C2318yescomplemented
262C4×D316C2318yescomplemented
263D4×Dic79C2318yes—
264C4×C22⋊D79C2318yes—
265C4×C22⋊D79C23116yescomplemented
266C4×C22⋊D79C23116yescomplemented
267C4×C22⋊D79C23116yescomplemented
268C4×C22⋊D79C2318yescomplemented
269(C22⋊D79)⋊C4C23116yescomplemented
270(C22⋊D79)⋊C4C23116yescomplemented
271#14579120C2318yescomplemented
272#14579119C2318yescomplemented
273#14579117C23116yescomplemented
274C2×C4⋊Dic79C2311yescharacteristic
275C2×C4⋊Dic79C2311yescharacteristic
276C2×C4⋊Dic79C2312yes—
277C2×C4⋊Dic79C2311yescharacteristic
278C2×C4⋊Dic79C2311yescharacteristic
279C2×C4⋊Dic79C2312yes—
280C2×C4⋊Dic79C2318yescomplemented
281C2×Dic79⋊C4C2312yes—
282C2×Dic79⋊C4C2312yes—
283C2×Dic79⋊C4C2312yes—
284C2×Dic79⋊C4C2312yes—
285C2×Dic79⋊C4C2311yescharacteristic
286C2×Dic79⋊C4C2311yescharacteristic
287C2×Dic79⋊C4C2312yes—
288C2×Dic79⋊C4C2312yes—
289C4⋊C4×D79C2318yescomplemented
290C2×C22⋊Dic79C2312yes—
291C2×C22⋊Dic79C2312yes—
292C2×C22⋊Dic79C2312yes—
293C2×C22⋊Dic79C2311yescharacteristic
294C2×C22⋊Dic79C2312yes—
295C2×C22⋊Dic79C2312yes—
296C2×C22⋊Dic79C2312yes—
297C2×C22⋊Dic79C2311yescharacteristic
298C2×C22⋊Dic79C2312yes—
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2311yescharacteristic
305C2×(C2×D79)⋊C4C2311yescharacteristic
306C2×(C2×D79)⋊C4C2312yes—
307C2×(C2×D79)⋊C4C2312yes—
308C2×(C2×D79)⋊C4C2311yescharacteristic
309C2×(C2×D79)⋊C4C2312yes—
310C22⋊C4×D79C23116yescomplemented
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2311yescharacteristic
313C2×C4×Dic79C2311yescharacteristic
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2312yes—
316C2×C4×Dic79C2312yes—
317C42×D79C2318yescomplemented
318C25×C79C2312yes—
319C2×#41×C79—44no—
320C2×#41×C79C2318yescomplemented
321C22×Q8×C79C2311yescharacteristic
322C22×D4×C79—44no—
323C22×D4×C79C2311yescharacteristic
324C22×D4×C79C2311yescharacteristic
325C22×D4×C79C2318yes—
326C22×D4×C79C2311yescharacteristic
327C22×D4×C79C2312yes—
328C22×D4×C79C2312yes—
329C22×D4×C79C2312yes—
330C23×C4×C79C2311yescharacteristic
331C23×C4×C79C2311yescharacteristic
332C23×C4×C79C2312yes—
333C23×C4×C79C2312yes—
334#124×C79C2318yes—
335#123×C79C23116yescomplemented
336C22⋊Q8×C79C2318yescomplemented
337#121×C79C2318yes—
338#121×C79C23116yescomplemented
339#120×C79C23116yescomplemented
340C4×D4×C79C2318yescomplemented
341C4×D4×C79C2318yescomplemented
342C2×C4⋊C4×C79C2311yescharacteristic
343C2×C4⋊C4×C79C2311yescharacteristic
344C2×C4⋊C4×C79C2312yes—
345C2×C22⋊C4×C79C2311yescharacteristic
346C2×C22⋊C4×C79C2312yes—
347C2×C22⋊C4×C79C2312yes—
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2311yescharacteristic
351C2×C22⋊C4×C79C2312yes—
352C2×C22⋊C4×C79C23116yescomplemented
353C2×C42×C79C2311yescharacteristic
354C23×D79—44no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79C2411yescharacteristic
358C23×D79C2412yes—
359C23×D79C2411yescharacteristic
360C23×D79C2411yescharacteristic
361C23×D79C2418yes—
362#11929625—416no—
363#11929624—432no—
364#11929624—416no—
365#11929624—416no—
366#11929623—432no—
367C2×Dic158—28no—
368C2×Dic158—42no—
369C2×Dic158—42no—
370C2×Dic158C2418yes—
371C2×Dic158C2414yes—
372C2×Dic158C2414yes—
373C2×D316—24no—
374C2×D316—44no—
375C2×D316—42no—
376C2×D316—42no—
377C2×D316—44no—
378C2×D316—42no—
379C2×D316C2414yes—
380C2×D316C2414yes—
381C2×D316C2418yes—
382C2×D316C2414yes—
383C2×D316C2418yes—
384C2×D316C2414yes—
385C2×C22⋊D79—24no—
386C2×C22⋊D79—28no—
387C2×C22⋊D79—24no—
388C2×C22⋊D79—432no—
389C2×C22⋊D79—44no—
390C2×C22⋊D79—44no—
391C2×C22⋊D79—42no—
392C2×C22⋊D79—42no—
393C2×C22⋊D79—42no—
394C2×C22⋊D79—42no—
395C2×C22⋊D79—44no—
396C2×C22⋊D79—44no—
397C2×C22⋊D79—44no—
398C2×C22⋊D79—44no—
399C2×C22⋊D79—44no—
400C2×C22⋊D79—44no—
401C2×C22⋊D79—44no—
402C2×C22⋊D79C2414yes—
403C2×C22⋊D79C2418yes—
404C2×C22⋊D79C2414yes—
405C2×C22⋊D79C2418yes—
406C2×C22⋊D79C2414yes—
407C2×C22⋊D79C2414yes—
408C2×C22⋊D79C2414yes—
409C2×C22⋊D79C2418yes—
410C2×C22⋊D79C2414yes—
411C2×C22⋊D79C2418yes—
412C2×C22⋊D79C2418yes—
413C2×C22⋊D79C2418yes—
414C2×C22⋊D79C2418yes—
415C2×C22⋊D79C2418yes—
416C2×C22⋊D79C2418yes—
417C2×C22⋊D79C2418yes—
418D4×D79—416no—
419C22×Dic79—28no—
420C22×Dic79—44no—
421C22×Dic79C2411yescharacteristic
422C22×Dic79C2411yescharacteristic
423C22×Dic79C2412yes—
424C22×Dic79C2411yescharacteristic
425C22×Dic79C2418yes—
426C22×Dic79C2412yes—
427C22×Dic79C2411yescharacteristic
428C22×Dic79C2412yes—
429C22×Dic79C2418yes—
430C22×Dic79C2411yescharacteristic
431C2×C4×D79—24no—
432C2×C4×D79—24no—
433C2×C4×D79—24no—
434C2×C4×D79—24no—
435C2×C4×D79—44no—
436C2×C4×D79—44no—
437C2×C4×D79—44no—
438C2×C4×D79—42no—
439C2×C4×D79C2414yes—
440C2×C4×D79C2414yes—
441C2×C4×D79C2414yes—
442C2×C4×D79C2414yes—
443C2×C4×D79C2418yes—
444C2×C4×D79C2418yes—
445C2×C4×D79C2418yes—
446C2×C4×D79C2414yes—
447C4⋊Dic79C2414yes—
448C4⋊Dic79C2414yes—
449C4⋊Dic79C2418yes—
450C4⋊Dic79C2414yes—
451C4⋊Dic79C2414yes—
452C4⋊Dic79C2418yes—
453Dic79⋊C4C2418yes—
454Dic79⋊C4C2418yes—
455Dic79⋊C4C2418yes—
456Dic79⋊C4C2418yes—
457Dic79⋊C4C2414yes—
458Dic79⋊C4C2414yes—
459Dic79⋊C4C2418yes—
460Dic79⋊C4C2418yes—
461C22⋊Dic79C2418yes—
462C22⋊Dic79C2418yes—
463C22⋊Dic79C2418yes—
464C22⋊Dic79C2414yes—
465C22⋊Dic79C2418yes—
466C22⋊Dic79C2418yes—
467C22⋊Dic79C2418yes—
468C22⋊Dic79C2414yes—
469C22⋊Dic79C2418yes—
470(C2×D79)⋊C4C2414yes—
471(C2×D79)⋊C4C2418yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2418yes—
475(C2×D79)⋊C4C2414yes—
476(C2×D79)⋊C4C2414yes—
477(C2×D79)⋊C4C2418yes—
478(C2×D79)⋊C4C2418yes—
479(C2×D79)⋊C4C2414yes—
480(C2×D79)⋊C4C2418yes—
481C4×Dic79C2414yes—
482C4×Dic79C2414yes—
483C4×Dic79C2414yes—
484C4×Dic79C2418yes—
485C4×Dic79C2418yes—
486C4×Dic79C2418yes—
487C24×C79—44no—
488C24×C79—44no—
489C24×C79—44no—
490C24×C79C2412yes—
491C24×C79C2411yescharacteristic
492C24×C79C2412yes—
493C24×C79C2411yescharacteristic
494C24×C79C2418yes—
495#41×C79—416no—
496C2×Q8×C79—24no—
497C2×Q8×C79C2414yes—
498C2×D4×C79—24no—
499C2×D4×C79—24no—
500C2×D4×C79—416no—
501C2×D4×C79—44no—
502C2×D4×C79—44no—
503C2×D4×C79—42no—
504C2×D4×C79—44no—
505C2×D4×C79C2414yes—
506C2×D4×C79C2414yes—
507C2×D4×C79C2418yes—
508C2×D4×C79C2414yes—
509C2×D4×C79C2418yes—
510C2×D4×C79C2418yes—
511C22×C4×C79—24no—
512C22×C4×C79—24no—
513C22×C4×C79—44no—
514C22×C4×C79—44no—
515C22×C4×C79C2412yes—
516C22×C4×C79C2411yescharacteristic
517C22×C4×C79C2411yescharacteristic
518C22×C4×C79C2414yes—
519C22×C4×C79C2414yes—
520C22×C4×C79C2411yescharacteristic
521C22×C4×C79C2411yescharacteristic
522C22×C4×C79C2412yes—
523C22×C4×C79C2418yes—
524C22×C4×C79C2418yes—
525C22×C4×C79C2411yescharacteristic
526C4⋊C4×C79C2414yes—
527C4⋊C4×C79C2414yes—
528C4⋊C4×C79C2418yes—
529C22⋊C4×C79C2414yes—
530C22⋊C4×C79C2418yes—
531C22⋊C4×C79C2418yes—
532C22⋊C4×C79C2418yes—
533C22⋊C4×C79C2418yes—
534C22⋊C4×C79C2414yes—
535C22⋊C4×C79C2418yes—
536C42×C79C2414yes—
537C23×C79—24no—
538C23×C79—22no—
539C23×C79—24no—
540C23×C79—22no—
541C23×C79—22no—
542C23×C79—22no—
543C23×C79—24no—
544C23×C79—24no—
545C23×C79—22no—
546C23×C79—24no—
547C23×C79—24no—
548C23×C79—22no—
549C23×C79—48no—
550C23×C79—48no—
551C23×C79—48no—
552C23×C79—816no—
553C23×C79C2514yes—
554C23×C79C2512yes—
555C23×C79C2514yes—
556C23×C79C2512yes—
557C23×C79C2511yescharacteristic
558C22×D79—22no—
559C22×D79—22no—
560C22×D79—22no—
561C22×D79—22no—
562C22×D79—22no—
563C22×D79—24no—
564C22×D79—24no—
565C22×D79—22no—
566C22×D79—22no—
567C22×D79—22no—
568C22×D79—24no—
569C22×D79—22no—
570C22×D79—48no—
571C22×D79—48no—
572C22×D79—48no—
573C22×D79—816no—
574C22×D79C2512yes—
575C22×D79C2514yes—
576C22×D79C2512yes—
577C22×D79C2512yes—
578Q8×C79—28no—
579D4×C79—28no—
580D4×C79—28no—
581D4×C79—48no—
582D4×C79—48no—
583D4×C79—44no—
584D4×C79—48no—
585C2×C4×C79—22no—
586C2×C4×C79—24no—
587C2×C4×C79—24no—
588C2×C4×C79—22no—
589C2×C4×C79—22no—
590C2×C4×C79—22no—
591C2×C4×C79—28no—
592C2×C4×C79—28no—
593C2×C4×C79—48no—
594C2×C4×C79—48no—
595C2×C4×C79H(5,𝔽2)14yes—
596C2×C4×C79C2512yes—
597C2×C4×C79C2512yes—
598C2×C4×C79C2514yes—
599C2×C4×C79C2512yes—
600C2×C4×C79C2514yes—
601C2×C4×C79C2512yes—
602C2×C4×C79C2512yes—
603C22⋊D79—28no—
604C22⋊D79—216no—
605C22⋊D79—28no—
606C22⋊D79—48no—
607C22⋊D79—48no—
608C22⋊D79—48no—
609C22⋊D79—48no—
610C22⋊D79—48no—
611C22⋊D79—48no—
612C22⋊D79—48no—
613C22⋊D79—48no—
614C22⋊D79—44no—
615C22⋊D79—48no—
616C22⋊D79—44no—
617C22⋊D79—44no—
618C22⋊D79—44no—
619C2×Dic79—22no—
620C2×Dic79—22no—
621C2×Dic79—22no—
622C2×Dic79—24no—
623C2×Dic79—24no—
624C2×Dic79—22no—
625C2×Dic79—24no—
626C2×Dic79—216no—
627C2×Dic79—48no—
628C2×Dic79H(5,𝔽2)14yes—
629C2×Dic79C2514yes—
630C2×Dic79C2512yes—
631C2×Dic79C2512yes—
632C2×Dic79C2512yes—
633C2×Dic79C2514yes—
634C2×Dic79C2514yes—
635C2×Dic79C2512yes—
636C2×Dic79C2512yes—
637D316—28no—
638D316—44no—
639D316—44no—
640D316—44no—
641D316—48no—
642D316—48no—
643C4×D79—28no—
644C4×D79—28no—
645C4×D79—28no—
646C4×D79—28no—
647C4×D79—44no—
648C4×D79—48no—
649C4×D79—48no—
650C4×D79—48no—
651Dic158—216no—
652Dic158—44no—
653Dic158—44no—
654C22×C79—24no—
655C22×C79—22no—
656C22×C79—22no—
657C22×C79—22no—
658C22×C79—22no—
659C22×C79—24no—
660C22×C79—24no—
661C22×C79—24no—
662C22×C79—22no—
663C22×C79—24no—
664C22×C79—24no—
665C22×C79—22no—
666C22×C79—48no—
667C22×C79—44no—
668C22×C79—48no—
669C22×C79—44no—
670C22×C79—816no—
671C22×C79C2×H(5,𝔽2)12yes—
672C22×C79C2×H(5,𝔽2)12yes—
673C22×C79#58512yes—
674C22×C79C2611yescharacteristic
675C2×D79—22no—
676C2×D79—22no—
677C2×D79—24no—
678C2×D79—22no—
679C2×D79—22no—
680C2×D79—22no—
681C2×D79—24no—
682C2×D79—22no—
683C2×D79—24no—
684C2×D79—22no—
685C2×D79—22no—
686C2×D79—22no—
687C2×D79—44no—
688C2×D79—44no—
689C2×D79—48no—
690C2×D79—44no—
691C2×D79—816no—
692C4×C79—22no—
693C4×C79—22no—
694C4×C79—22no—
695C4×C79—24no—
696C4×C79—24no—
697C4×C79—22no—
698C4×C79C2×H(5,𝔽2)14yes—
699Dic79—22no—
700Dic79—24no—
701Dic79—22no—
702Dic79—24no—
703Dic79—22no—
704Dic79—24no—
705Dic79—22no—
706Dic79C2×H(5,𝔽2)14yes—
707C2×#3546—791nomaximal, Sylow
708C2×C79—44no—
709C2×C79—42no—
710C2×C79—44no—
711C2×C79—42no—
712C2×C79#354614yescomplemented
713C2×C79C22×H(5,𝔽2)11yescharacteristic
714C2×C79C22×H(5,𝔽2)11yescharacteristic
715C2×C79C2×#58511yescharacteristic
716D79—42no—
717D79—42no—
718D79—44no—
719D79—42no—
720#3546—7932no—
721C2×#560—792no—
722C2×#560—792no—
723C2×#556—791no—
724C2×#553—791no—
725C2×#553—791no—
726C2×#550—791no—
727C2×#550—792no—
728C2×#547—791no—
729C2×#546—791no—
730C2×#546—792no—
731C2×#546D7911yescharacteristic, complemented
732C2×D42—791no—
733C2×#542—792no—
734C2×#538—792no—
735C2×#538—792no—
736C2×#537—791no—
737C2×#537—791no—
738C2×#535—791no—
739C2×#535—791no—
740C2×#535—792no—
741C2×#532—791no—
742C2×#532—791no—
743C2×#529—791no—
744C79C2×#354611yescharacteristic, complemented, Sylow
745C22×#41—791no—
746C22×#41—792no—
747C22×#41—791no—
748C22×#41—791no—
749C22×#41—792no—
750C22×#41C2×D7911yescharacteristic, complemented
751C23×D4—792no—
752C23×D4—791no—
753C23×D4C2×D7911yescharacteristic
754#560—7932no—
755#560—7932no—
756#556—7916no—
757#553—7916no—
758#553—7916no—
759#550—7916no—
760#550—7932no—
761#547—7916no—
762#546—7916no—
763#546—7932no—
764#546C2×D79116yescomplemented
765D42—7916no—
766#542—7932no—
767#538—7932no—
768#538—7932no—
769#537—7916no—
770#537—7916no—
771#535—7916no—
772#535—7916no—
773#535—7932no—
774#532—7916no—
775#532—7916no—
776C2×C4⋊Q8—791no—
777C2×C4⋊Q8—791no—
778C2×#127—791no—
779C2×#127—791no—
780C2×#127—792no—
781C2×#127—792no—
782C2×#127—792no—
783#529—7916no—
784C2×#126—792no—
785C2×#126—792no—
786C2×#126—792no—
787C2×#126—792no—
788C2×#126—792no—
789C2×#125—791no—
790C2×#124—792no—
791C2×#124—792no—
792C2×#124—791no—
793C2×#124—791no—
794C2×#124—792no—
795C2×#124—792no—
796C2×#124C2×D7911yescharacteristic
797C2×#123—792no—
798C2×#123—792no—
799C2×#123—792no—
800C2×#123—792no—
801C2×#123—792no—
802C2×#123—792no—
803C2×#123C2×D7912yescomplemented
804C2×C22⋊Q8—791no—
805C2×C22⋊Q8—791no—
806C2×C22⋊Q8—792no—
807C2×C22⋊Q8—792no—
808C2×C22⋊Q8—792no—
809C2×C22⋊Q8C2×D7911yescharacteristic, complemented
810C2×#121—791no—
811C2×#121—791no—
812C2×#121—791no—
813C2×#121—792no—
814C2×#121—791no—
815C2×#121—791no—
816C2×#121—792no—
817C2×#121—791no—
818C2×#121—792no—
819C2×#121—792no—
820C2×#121—792no—
821C2×#121—791no—
822C2×#121—791no—
823C2×#121—792no—
824C2×#121—792no—
825C2×#121—791no—
826C2×#121—791no—
827C2×#121—792no—
828C2×#121—791no—
829C2×#121—791no—
830C2×#121—792no—
831C2×#121—792no—
832C2×#121—792no—
833C2×#121—792no—
834C2×#121—792no—
835C2×#121C2×D7911yescharacteristic
836C2×#121C2×D7912yescomplemented
837C2×#120—792no—
838C2×#120—792no—
839C2×#120—792no—
840C2×#120—792no—
841C2×#120—792no—
842C2×#120—792no—
843C2×#120—792no—
844C2×#120C2×D7912yescomplemented
845C2×C4×Q8—791no—
846C2×C4×Q8—792no—
847C2×C4×D4—791no—
848C2×C4×D4—792no—
849C2×C4×D4—791no—
850C2×C4×D4—791no—
851C2×C4×D4—792no—
852C2×C4×D4—792no—
853C2×C4×D4—792no—
854C2×C4×D4—792no—
855C2×C4×D4—791no—
856C2×C4×D4—791no—
857C2×C4×D4C2×D7911yescharacteristic, complemented
858C2×C4×D4C2×D7911yescharacteristic, complemented
859C2×#117—791no—
860C2×#117—791no—
861C2×#117—792no—
862C22×C4⋊C4—791no—
863C22×C4⋊C4—791no—
864C22×C22⋊C4—792no—
865C22×C22⋊C4C2×D7912yescomplemented
866C22×C42—791no—
867C25—792no—
868C25C22×D7912yes—
869C2×#41—44no—
870C2×#41—3164no—
871C2×#41—3164no—
872C2×#41—3168no—
873C2×#41—3168no—
874C2×#41—3164no—
875C2×#41—798no—
876C2×#41—7916no—
877C2×#41—798no—
878C2×#41—798no—
879C2×#41—7916no—
880C2×#41C22×D7918yescomplemented
881C22×Q8—791no—
882C22×Q8—791no—
883C22×Q8—792no—
884C22×Q8C22×D7911yescharacteristic
885C22×D4—44no—
886C22×D4—3164no—
887C22×D4—3168no—
888C22×D4—792no—
889C22×D4—792no—
890C22×D4—792no—
891C22×D4—792no—
892C22×D4—791no—
893C22×D4—792no—
894C22×D4—791no—
895C22×D4—791no—
896C22×D4—792no—
897C22×D4—792no—
898C22×D4—792no—
899C22×D4—792no—
900C22×D4—791no—
901C22×D4—7916no—
902C22×D4—798no—
903C22×D4—791no—
904C22×D4—792no—
905C22×D4—791no—
906C22×D4—791no—
907C22×D4—791no—
908C22×D4—792no—
909C22×D4—792no—
910C22×D4—791no—
911C22×D4—791no—
912C22×D4C22×D7911yescharacteristic
913C22×D4C22×D7911yescharacteristic
914C22×D4C22×D7911yescharacteristic
915C22×D4C22×D7912yes—
916C22×D4C22×D7912yes—
917C22×D4C22×D7912yes—
918C22×D4C22×D7918yes—
919C23×C4—792no—
920C23×C4—792no—
921C23×C4—792no—
922C23×C4—792no—
923C23×C4—791no—
924C23×C4—792no—
925C23×C4—791no—
926C23×C4—791no—
927C23×C4—791no—
928C23×C4—791no—
929C23×C4C22×D7911yescharacteristic
930C23×C4C22×D7911yescharacteristic
931C23×C4C22×D7912yes—
932C23×C4C22×D7912yes—
933C4⋊Q8—798no—
934C4⋊Q8—798no—
935#127—798no—
936#127—798no—
937#127—7916no—
938#127—7916no—
939#127—7916no—
940#126—7916no—
941#126—7916no—
942#126—7916no—
943#126—7916no—
944#126—7916no—
945#125—798no—
946#124—7916no—
947#124—7916no—
948#124—798no—
949#124—798no—
950#124—7916no—
951#124—7916no—
952#124C22×D7918yes—
953#123—7916no—
954#123—7916no—
955#123—7916no—
956#123—7916no—
957#123—7916no—
958#123—7916no—
959#123C22×D79116yescomplemented
960C22⋊Q8—798no—
961C22⋊Q8—798no—
962C22⋊Q8—7916no—
963C22⋊Q8—7916no—
964C22⋊Q8—7916no—
965C22⋊Q8C22×D7918yescomplemented
966#121—798no—
967#121—798no—
968#121—798no—
969#121—7916no—
970#121—798no—
971#121—798no—
972#121—7916no—
973#121—798no—
974#121—7916no—
975#121—7916no—
976#121—7916no—
977#121—798no—
978#121—798no—
979#121—7916no—
980#121—7916no—
981#121—798no—
982#121—798no—
983#121—7916no—
984#121—798no—
985#121—798no—
986#121—7916no—
987#121—7916no—
988#121—7916no—
989#121—7916no—
990#121—7916no—
991#121C22×D7918yes—
992#121C22×D79116yescomplemented
993#120—7916no—
994#120—7916no—
995#120—7916no—
996#120—7916no—
997#120—7916no—
998#120—7916no—
999#120—7916no—
1000#120C22×D79116yescomplemented
1001C4×Q8—798no—
1002C4×Q8—7916no—
1003C4×D4—798no—
1004C4×D4—7916no—
1005C4×D4—798no—
1006C4×D4—798no—
1007C4×D4—7916no—
1008C4×D4—7916no—
1009C4×D4—7916no—
1010C4×D4—7916no—
1011C4×D4—798no—
1012C4×D4—798no—
1013C4×D4C22×D7918yescomplemented
1014C4×D4C22×D7918yescomplemented
1015#117—798no—
1016#117—798no—
1017#117—7916no—
1018C2×C4⋊C4—791no—
1019C2×C4⋊C4—791no—
1020C2×C4⋊C4—792no—
1021C2×C4⋊C4—792no—
1022C2×C4⋊C4—798no—
1023C2×C4⋊C4—791no—
1024C2×C4⋊C4—792no—
1025C2×C4⋊C4—792no—
1026C2×C4⋊C4—791no—
1027C2×C4⋊C4—792no—
1028C2×C4⋊C4—791no—
1029C2×C4⋊C4—792no—
1030C2×C4⋊C4—791no—
1031C2×C4⋊C4—792no—
1032C2×C4⋊C4—792no—
1033C2×C4⋊C4—798no—
1034C2×C4⋊C4C22×D7911yescharacteristic
1035C2×C4⋊C4C22×D7911yescharacteristic
1036C2×C4⋊C4C22×D7912yes—
1037C2×C22⋊C4—792no—
1038C2×C22⋊C4—792no—
1039C2×C22⋊C4—792no—
1040C2×C22⋊C4—791no—
1041C2×C22⋊C4—792no—
1042C2×C22⋊C4—792no—
1043C2×C22⋊C4—792no—
1044C2×C22⋊C4—792no—
1045C2×C22⋊C4—791no—
1046C2×C22⋊C4—791no—
1047C2×C22⋊C4—792no—
1048C2×C22⋊C4—792no—
1049C2×C22⋊C4—791no—
1050C2×C22⋊C4—791no—
1051C2×C22⋊C4—792no—
1052C2×C22⋊C4—792no—
1053C2×C22⋊C4—792no—
1054C2×C22⋊C4—792no—
1055C2×C22⋊C4—792no—
1056C2×C22⋊C4—791no—
1057C2×C22⋊C4—7916no—
1058C2×C22⋊C4C22×D7912yes—
1059C2×C22⋊C4C22×D7911yescharacteristic
1060C2×C22⋊C4C22×D7912yes—
1061C2×C22⋊C4C22×D7912yes—
1062C2×C22⋊C4C22×D7912yes—
1063C2×C22⋊C4C22×D7911yescharacteristic
1064C2×C22⋊C4C22×D7912yes—
1065C2×C22⋊C4C22×D79116yescomplemented
1066C2×C42—791no—
1067C2×C42—792no—
1068C2×C42—792no—
1069C2×C42—792no—
1070C2×C42—791no—
1071C2×C42—791no—
1072C2×C42—798no—
1073C2×C42C22×D7911yescharacteristic
1074C24—44no—
1075C24—44no—
1076C24—44no—
1077C24—3164no—
1078C24—3164no—
1079C24—3164no—
1080C24—798no—
1081C24—791no—
1082C24—792no—
1083C24—791no—
1084C24—791no—
1085C24C23×D7912yes—
1086C24C23×D7911yescharacteristic
1087C24C23×D7912yes—
1088C24C23×D7911yescharacteristic
1089C24C23×D7918yes—
1090#41—416no—
1091#41—31616no—
1092#41—31616no—
1093#41—31632no—
1094#41—31632no—
1095#41—31616no—
1096C2×Q8—24no—
1097C2×Q8—3162no—
1098C2×Q8—3162no—
1099C2×Q8—794no—
1100C2×Q8—794no—
1101C2×Q8—798no—
1102C2×Q8—1588no—
1103C2×Q8C23×D7914yes—
1104C2×D4—24no—
1105C2×D4—24no—
1106C2×D4—416no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—42no—
1111C2×D4—3162no—
1112C2×D4—3164no—
1113C2×D4—3162no—
1114C2×D4—3162no—
1115C2×D4—3164no—
1116C2×D4—31616no—
1117C2×D4—3164no—
1118C2×D4—3164no—
1119C2×D4—3164no—
1120C2×D4—3164no—
1121C2×D4—3164no—
1122C2×D4—3164no—
1123C2×D4—3164no—
1124C2×D4—3164no—
1125C2×D4—3164no—
1126C2×D4—3162no—
1127C2×D4—3162no—
1128C2×D4—3162no—
1129C2×D4—3162no—
1130C2×D4—31632no—
1131C2×D4—798no—
1132C2×D4—798no—
1133C2×D4—798no—
1134C2×D4—798no—
1135C2×D4—794no—
1136C2×D4—798no—
1137C2×D4—794no—
1138C2×D4—794no—
1139C2×D4—798no—
1140C2×D4—798no—
1141C2×D4—798no—
1142C2×D4—798no—
1143C2×D4—794no—
1144C2×D4—794no—
1145C2×D4—798no—
1146C2×D4—794no—
1147C2×D4—794no—
1148C2×D4—794no—
1149C2×D4—798no—
1150C2×D4—798no—
1151C2×D4—794no—
1152C2×D4—794no—
1153C2×D4—1584no—
1154C2×D4—1588no—
1155C2×D4—1584no—
1156C2×D4—1584no—
1157C2×D4C23×D7914yes—
1158C2×D4C23×D7914yes—
1159C2×D4C23×D7914yes—
1160C2×D4C23×D7918yes—
1161C2×D4C23×D7918yes—
1162C2×D4C23×D7918yes—
1163C22×C4—24no—
1164C22×C4—24no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—3162no—
1168C22×C4—3164no—
1169C22×C4—3164no—
1170C22×C4—3164no—
1171C22×C4—3164no—
1172C22×C4—798no—
1173C22×C4—794no—
1174C22×C4—798no—
1175C22×C4—798no—
1176C22×C4—798no—
1177C22×C4—791no—
1178C22×C4—798no—
1179C22×C4—792no—
1180C22×C4—791no—
1181C22×C4—791no—
1182C22×C4—791no—
1183C22×C4—792no—
1184C22×C4—791no—
1185C22×C4—792no—
1186C22×C4—794no—
1187C22×C4—794no—
1188C22×C4—794no—
1189C22×C4—794no—
1190C22×C4—1584no—
1191C22×C4—1588no—
1192C22×C4—1584no—
1193C22×C4—1584no—
1194C22×C4—1584no—
1195C22×C4C23×D7914yes—
1196C22×C4C23×D7914yes—
1197C22×C4C23×D7911yescharacteristic
1198C22×C4C23×D7911yescharacteristic
1199C22×C4C23×D7911yescharacteristic
1200C22×C4C23×D7912yes—
1201C22×C4C23×D7912yes—
1202C22×C4C23×D7911yescharacteristic
1203C22×C4C23×D7918yes—
1204C22×C4C23×D7918yes—
1205C22×C4C23×D7911yescharacteristic
1206C4⋊C4—798no—
1207C4⋊C4—798no—
1208C4⋊C4—798no—
1209C4⋊C4—794no—
1210C4⋊C4—798no—
1211C4⋊C4—794no—
1212C4⋊C4—798no—
1213C4⋊C4—798no—
1214C4⋊C4—794no—
1215C4⋊C4—794no—
1216C4⋊C4—798no—
1217C4⋊C4—794no—
1218C4⋊C4—794no—
1219C4⋊C4—798no—
1220C4⋊C4C23×D7914yes—
1221C4⋊C4C23×D7914yes—
1222C4⋊C4C23×D7918yes—
1223C22⋊C4—798no—
1224C22⋊C4—798no—
1225C22⋊C4—798no—
1226C22⋊C4—794no—
1227C22⋊C4—798no—
1228C22⋊C4—798no—
1229C22⋊C4—798no—
1230C22⋊C4—798no—
1231C22⋊C4—794no—
1232C22⋊C4—794no—
1233C22⋊C4—798no—
1234C22⋊C4—798no—
1235C22⋊C4—794no—
1236C22⋊C4—794no—
1237C22⋊C4—798no—
1238C22⋊C4—798no—
1239C22⋊C4—798no—
1240C22⋊C4—798no—
1241C22⋊C4—798no—
1242C22⋊C4—794no—
1243C22⋊C4C23×D7918yes—
1244C22⋊C4C23×D7914yes—
1245C22⋊C4C23×D7918yes—
1246C22⋊C4C23×D7918yes—
1247C22⋊C4C23×D7918yes—
1248C22⋊C4C23×D7914yes—
1249C22⋊C4C23×D7918yes—
1250C42—794no—
1251C42—794no—
1252C42—794no—
1253C42—798no—
1254C42—798no—
1255C42—798no—
1256C42C23×D7914yes—
1257C23—24no—
1258C23—22no—
1259C23—24no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—24no—
1264C23—24no—
1265C23—22no—
1266C23—22no—
1267C23—24no—
1268C23—24no—
1269C23—48no—
1270C23—48no—
1271C23—48no—
1272C23—816no—
1273C23—3168no—
1274C23—3168no—
1275C23—3168no—
1276C23—792no—
1277C23—794no—
1278C23—792no—
1279C23—792no—
1280C23—63216no—
1281C23—1582no—
1282C23—1584no—
1283C23—1582no—
1284C23—1582no—
1285C23—1584no—
1286C23—1582no—
1287C23—1582no—
1288C23—1582no—
1289C23—1582no—
1290C23—1582no—
1291C23—1584no—
1292C23—1582no—
1293C23C24×D7914yes—
1294C23C24×D7912yes—
1295C23C24×D7914yes—
1296C23C24×D7912yes—
1297C23C24×D7911yescharacteristic
1298Q8—28no—
1299Q8—3164no—
1300Q8—3164no—
1301Q8—15816no—
1302D4—28no—
1303D4—28no—
1304D4—48no—
1305D4—44no—
1306D4—48no—
1307D4—48no—
1308D4—3168no—
1309D4—3164no—
1310D4—3164no—
1311D4—3168no—
1312D4—3164no—
1313D4—3168no—
1314D4—3168no—
1315D4—3168no—
1316D4—3168no—
1317D4—3168no—
1318D4—3168no—
1319D4—3168no—
1320D4—3168no—
1321D4—3168no—
1322D4—3164no—
1323D4—3164no—
1324D4—3164no—
1325D4—3164no—
1326D4—1588no—
1327D4—15816no—
1328D4—1588no—
1329D4—1588no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—28no—
1337C2×C4—28no—
1338C2×C4—48no—
1339C2×C4—48no—
1340C2×C4—3168no—
1341C2×C4—3168no—
1342C2×C4—3168no—
1343C2×C4—3164no—
1344C2×C4—3168no—
1345C2×C4—794no—
1346C2×C4—792no—
1347C2×C4—794no—
1348C2×C4—792no—
1349C2×C4—792no—
1350C2×C4—792no—
1351C2×C4—794no—
1352C2×C4—792no—
1353C2×C4—794no—
1354C2×C4—1588no—
1355C2×C4—15816no—
1356C2×C4—1584no—
1357C2×C4—1584no—
1358C2×C4—1582no—
1359C2×C4—1582no—
1360C2×C4—1582no—
1361C2×C4—1582no—
1362C2×C4—1584no—
1363C2×C4—1588no—
1364C2×C4—1588no—
1365C2×C4—1588no—
1366C2×C4#1457920614yes—
1367C2×C4C24×D7912yes—
1368C2×C4C24×D7912yes—
1369C2×C4C24×D7912yes—
1370C2×C4C24×D7914yes—
1371C2×C4C24×D7914yes—
1372C2×C4C24×D7912yes—
1373C2×C4C24×D7912yes—
1374C22—24no—
1375C22—22no—
1376C22—24no—
1377C22—22no—
1378C22—22no—
1379C22—22no—
1380C22—24no—
1381C22—24no—
1382C22—22no—
1383C22—22no—
1384C22—24no—
1385C22—24no—
1386C22—44no—
1387C22—48no—
1388C22—48no—
1389C22—44no—
1390C22—816no—
1391C22—3164no—
1392C22—3168no—
1393C22—3164no—
1394C22—3164no—
1395C22—63216no—
1396C22—1582no—
1397C22—1584no—
1398C22—1582no—
1399C22—1582no—
1400C22—1584no—
1401C22—1582no—
1402C22—1582no—
1403C22—1582no—
1404C22—1582no—
1405C22—1582no—
1406C22—1584no—
1407C22—1582no—
1408C22H(5,𝔽2)×D7912yes—
1409C22C2×#1457920612yes—
1410C22#1909939912yes—
1411C22C25×D7911yescharacteristic
1412C4—22no—
1413C4—24no—
1414C4—22no—
1415C4—22no—
1416C4—24no—
1417C4—22no—
1418C4—794no—
1419C4—1584no—
1420C4—1584no—
1421C4—1582no—
1422C4—1582no—
1423C4—1582no—
1424C4—1582no—
1425C4—1584no—
1426C4C2×#1457920614yes—
1427C2—42no—
1428C2—44no—
1429C2—44no—
1430C2—42no—
1431C2—3162no—
1432C2—3164no—
1433C2—3162no—
1434C2—3162no—
1435C2#2377776414yesdirect product factor
1436C2C2×H(5,𝔽2)×D7911yescharacteristic
1437C2C22×#1457920611yescharacteristic
1438C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#546×C79C2
socleC23×C79C25
hypercenterC2×#546D79
hypocenterC79C2×#3546
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777764C2direct (N × H)
2. C2×#19099303C2semidirect
3. C2×#19099302C2semidirect
4. C2×#19099284C2semidirect
5. C2×#19099263C2semidirect
6. C2×#19099259C2semidirect
7. C2×#19099232C2semidirect
8. C2×#19099231C2semidirect
9. C2×#19099213C2semidirect
10. C2×#19099206C2semidirect
11. C2×#19099203C2semidirect
12. C2×D4×C22⋊D79C2semidirect
13. C2×#19099181C2semidirect
14. C2×#19099151C2semidirect
15. C2×#19099145C2semidirect
16. C2×#19099143C2semidirect
17. C2×#19099141C2semidirect
18. C2×#19099130C2semidirect
19. C2×#19099129C2semidirect
20. C2×#19099128C2semidirect
21. C2×#19099110C2semidirect
22. C2×#19099110C2semidirect
23. C2×#19099092C2semidirect
24. C2×#546×C79C2semidirect
25. C22×#11929625C22semidirect
26. C22×#11929624C22semidirect
27. C22×#11929624C22semidirect
28. C22×#11929624C22semidirect
29. C22×#11929623C22semidirect
32. #19099303C22semidirect
33. #19099302C22semidirect
34. #19099284C22semidirect
35. #19099263C22semidirect
36. #19099259C22semidirect
37. #19099232C22semidirect
38. #19099231C22semidirect
39. #19099213C22semidirect
40. #19099206C22semidirect
41. #19099203C22semidirect
42. D4×C22⋊D79C22semidirect
43. #19099181C22semidirect
44. #19099151C22semidirect
45. #19099145C22semidirect
46. #19099143C22semidirect
47. #19099141C22semidirect
48. #19099130C22semidirect
49. #19099129C22semidirect
50. #19099128C22semidirect
51. #19099110C22semidirect
52. #19099110C22semidirect
53. C2×#14579160C22semidirect
54. C2×#14579160C22semidirect
57. C2×#14579157C22semidirect
58. C2×#14579157C22semidirect
59. C2×#14579157C22semidirect
60. #19099092C22semidirect
61. C2×#14579156C22semidirect
62. C2×#14579156C22semidirect
63. C2×#14579154C22semidirect
64. C2×#14579154C22semidirect
65. C2×#14579154C22semidirect
66. C2×#14579153C22semidirect
67. C2×#14579148C22semidirect
69. C2×#14579147C22semidirect
70. C2×#14579147C22semidirect
71. C2×#14579147C22semidirect
72. C2×#14579147C22semidirect
73. C2×#14579144C22semidirect
74. C2×#14579143C22semidirect
75. C2×#14579143C22semidirect
76. C2×#14579143C22semidirect
77. C2×#14579143C22semidirect
78. C2×#14579142C22semidirect
79. C2×#14579140C22semidirect
80. C2×#14579139C22semidirect
81. C2×#14579138C22semidirect
82. C2×#14579137C22semidirect
83. C2×#14579137C22semidirect
84. C2×#14579136C22semidirect
85. C2×#14579136C22semidirect
86. C2×#14579136C22semidirect
88. C2×#14579135C22semidirect
89. C2×#14579135C22semidirect
90. C2×#14579135C22semidirect
92. C2×#14579134C22semidirect
93. C2×#14579134C22semidirect
94. C2×#14579134C22semidirect
95. C2×#14579134C22semidirect
96. C2×#14579134C22semidirect
97. C2×#14579134C22semidirect
99. C2×#14579133C22semidirect
100. C2×#14579133C22semidirect
101. C2×#14579133C22semidirect
105. C2×#14579132C22semidirect
106. C2×#14579132C22semidirect
107. C2×#14579132C22semidirect
108. C2×#14579132C22semidirect
109. C2×#14579131C22semidirect
110. C2×#14579131C22semidirect
112. C2×#14579130C22semidirect
113. C2×#14579130C22semidirect
115. C2×#14579129C22semidirect
116. C2×Q8×Dic79C22semidirect
117. C2×#14579126C22semidirect
118. C2×C4×D316C22semidirect
119. C2×C4×D316C22semidirect
122. C2×C4×C22⋊D79C22semidirect
123. C2×C4×C22⋊D79C22semidirect
124. C2×C4×C22⋊D79C22semidirect
125. C2×C4×C22⋊D79C22semidirect
126. C2×(C22⋊D79)⋊C4C22semidirect
127. C2×(C22⋊D79)⋊C4C22semidirect
128. C2×#14579120C22semidirect
129. C2×#14579119C22semidirect
130. C2×#14579117C22semidirect
131. C22×C4⋊Dic79C22semidirect
132. C2×C4⋊C4×D79C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C2×C42×D79C22semidirect
135. C22×#41×C79C22semidirect
137. #546×C79C22semidirect
139. C2×#123×C79C22semidirect
140. C2×C22⋊Q8×C79C22semidirect
142. C2×#121×C79C22semidirect
143. C2×#120×C79C22semidirect
144. C2×C4×D4×C79C22semidirect
145. C2×C4×D4×C79C22semidirect
146. C22×C22⋊C4×C79C22semidirect
149. C2×#11929625C23semidirect
153. C2×#11929624C23semidirect
154. C2×#11929624C23semidirect
155. C2×#11929624C23semidirect
157. C2×#11929623C23semidirect
197. #14579160C23semidirect
198. #14579160C23semidirect
201. #14579157C23semidirect
202. #14579157C23semidirect
203. #14579157C23semidirect
204. #14579156C23semidirect
205. #14579156C23semidirect
206. #14579154C23semidirect
207. #14579154C23semidirect
208. #14579154C23semidirect
209. #14579153C23semidirect
210. #14579148C23semidirect
212. #14579147C23semidirect
213. #14579147C23semidirect
214. #14579147C23semidirect
215. #14579147C23semidirect
216. #14579144C23semidirect
217. #14579143C23semidirect
218. #14579143C23semidirect
219. #14579143C23semidirect
220. #14579143C23semidirect
221. #14579142C23semidirect
222. #14579140C23semidirect
223. #14579139C23semidirect
224. #14579138C23semidirect
225. #14579137C23semidirect
226. #14579137C23semidirect
227. #14579136C23semidirect
228. #14579136C23semidirect
229. #14579136C23semidirect
231. #14579135C23semidirect
232. #14579135C23semidirect
233. #14579135C23semidirect
235. #14579134C23semidirect
236. #14579134C23semidirect
237. #14579134C23semidirect
238. #14579134C23semidirect
239. #14579134C23semidirect
240. #14579134C23semidirect
242. #14579133C23semidirect
243. #14579133C23semidirect
244. #14579133C23semidirect
248. #14579132C23semidirect
249. #14579132C23semidirect
250. #14579132C23semidirect
251. #14579132C23semidirect
252. #14579131C23semidirect
253. #14579131C23semidirect
255. #14579130C23semidirect
256. #14579130C23semidirect
258. #14579129C23semidirect
259. Q8×Dic79C23semidirect
260. #14579126C23semidirect
261. C4×D316C23semidirect
262. C4×D316C23semidirect
265. C4×C22⋊D79C23semidirect
266. C4×C22⋊D79C23semidirect
267. C4×C22⋊D79C23semidirect
268. C4×C22⋊D79C23semidirect
269. (C22⋊D79)⋊C4C23semidirect
270. (C22⋊D79)⋊C4C23semidirect
271. #14579120C23semidirect
272. #14579119C23semidirect
273. #14579117C23semidirect
280. C2×C4⋊Dic79C23semidirect
289. C4⋊C4×D79C23semidirect
310. C22⋊C4×D79C23semidirect
317. C42×D79C23semidirect
320. C2×#41×C79C23semidirect
335. #123×C79C23semidirect
336. C22⋊Q8×C79C23semidirect
338. #121×C79C23semidirect
339. #120×C79C23semidirect
340. C4×D4×C79C23semidirect
341. C4×D4×C79C23semidirect
352. C2×C22⋊C4×C79C23semidirect
712. C2×C79#3546semidirect
731. C2×#546D79semidirect
744. C79C2×#3546semidirect
750. C22×#41C2×D79semidirect
764. #546C2×D79semidirect
803. C2×#123C2×D79semidirect
809. C2×C22⋊Q8C2×D79semidirect
836. C2×#121C2×D79semidirect
844. C2×#120C2×D79semidirect
857. C2×C4×D4C2×D79semidirect
858. C2×C4×D4C2×D79semidirect
865. C22×C22⋊C4C2×D79semidirect
880. C2×#41C22×D79semidirect
959. #123C22×D79semidirect
965. C22⋊Q8C22×D79semidirect
992. #121C22×D79semidirect
1000. #120C22×D79semidirect
1013. C4×D4C22×D79semidirect
1014. C4×D4C22×D79semidirect
1065. C2×C22⋊C4C22×D79semidirect
1435. C2#23777764direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237777642
C2×#190993032
C2×#190993022
C2×#190992842
C2×#190992632
C2×#190992592
C2×#190992322
C2×#190992312
C2×#190992132
C2×#190992062
C2×#190992032
C2×D4×C22⋊D792
C2×#190991812
C2×#190991512
C2×#190991452
C2×#190991432
C2×#190991412
C2×#190991302
C2×#190991292
C2×#190991282
C2×#190991102
C2×#190990922
C2×#546×C792
C2×#354679