Finite Group Databasebeta

← C2×#23777268 #35196621

Subgroups — C2×#23777268 #35196621

Order 20224.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777268C2132yesmaximal, direct product factor
2C2×#19099297C212yesmaximal, complemented
3C2×#19099296C211yesmaximal, characteristic, complemented
4C2×#19099295C211yesmaximal, characteristic, complemented
5C2×#19099232C211yesmaximal, characteristic, complemented
6C2×#19099231C211yesmaximal, characteristic, complemented
7C2×#19099231C212yesmaximal, complemented
8C2×#19099209C211yesmaximal, characteristic, complemented
9C2×#19099207C211yesmaximal, characteristic, complemented
10C2×#19099204C211yesmaximal, characteristic, complemented
11C2×#19099203C212yesmaximal, complemented
12C2×#19099200C212yesmaximal, complemented
13C2×#19099165C212yesmaximal, complemented
14C2×#19099163C212yesmaximal, complemented
15C2×#19099128C212yesmaximal, complemented
16C2×#19099115C211yesmaximal, characteristic, complemented
17C2×#19099112C211yesmaximal, characteristic, complemented
18C2×#19099110C211yesmaximal, characteristic, complemented
19C2×#19099109C211yesmaximal, characteristic, complemented
20C2×#19099108C211yesmaximal, characteristic, complemented
21C22×#14579157C211yesmaximal, characteristic, complemented
22C2×#19099036C212yesmaximal, complemented
23C2×C4×#11929623C211yesmaximal, characteristic, complemented
24C2×#546×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic, complemented
26C22×#11929624C2212yescomplemented
27C22×#11929624C2211yescharacteristic, complemented
28C22×#11929623C2211yescharacteristic
29C22×#11929623C2212yescomplemented
30C22×#11929623C2211yescharacteristic, complemented
31C23×D316C2211yescharacteristic
32C23×C22⋊D79C2212yes—
33C23×C22⋊D79C2212yes—
34#19099297C22132yescomplemented
35#19099296C22116yescomplemented
36#19099295C22116yescomplemented
37#19099232C22116yescomplemented
38#19099231C22132yescomplemented
39#19099231C22116yescomplemented
40#19099209C22116yescomplemented
41#19099207C22116yescomplemented
42#19099204C22116yescomplemented
43#19099203C22132yescomplemented
44#19099200C22132yescomplemented
45#19099165C22132yescomplemented
46#19099163C22132yescomplemented
47#19099128C22132yescomplemented
48#19099115C22116yescomplemented
49#19099112C22116yescomplemented
50#19099110C22116yescomplemented
51#19099109C22116yescomplemented
52#19099108C22116yescomplemented
53C2×#14579160C2211yescharacteristic, complemented
54C2×#14579159C2211yescharacteristic, complemented
55C2×#14579157C2211yescharacteristic
56C2×#14579157C2212yes—
57C2×#14579157C2211yescharacteristic
58C2×#14579157C2211yescharacteristic
59C2×#14579157C2211yescharacteristic
60C2×#14579157C2212yes—
61C2×#14579157C22116yescomplemented
62C2×#14579157C2212yescomplemented
63C2×#14579157C2212yescomplemented
64C2×#14579151C2212yescomplemented
65C2×#14579150C2211yescharacteristic, complemented
66C2×#14579149C2211yescharacteristic, complemented
67C2×#14579148C2211yescharacteristic, complemented
68C2×#14579147C2212yescomplemented
69C2×#14579147C2212yescomplemented
70C2×#14579147C2212yescomplemented
71C2×#14579147C2212yescomplemented
72C2×#14579146C2212yescomplemented
73C2×#14579146C2212yescomplemented
74C2×#14579145C2212yescomplemented
75C2×#14579144C2212yescomplemented
76C2×#14579143C2212yescomplemented
77C2×#14579143C2212yescomplemented
78C2×#14579142C2212yescomplemented
79C2×#14579140C2211yescharacteristic
80C2×#14579138C2212yes—
81C2×#14579136C2211yescharacteristic, complemented
82C2×#14579136C2212yescomplemented
83C2×#14579135C2212yescomplemented
84C2×#14579135C2211yescharacteristic, complemented
85C2×#14579134C2212yescomplemented
86C2×#14579134C2212yescomplemented
87C2×#14579134C2212yescomplemented
88C2×#14579134C2212yescomplemented
89C2×#14579134C2212yescomplemented
90C2×#14579133C2212yescomplemented
91C2×#14579133C2212yescomplemented
92C2×#14579133C2212yescomplemented
93C2×#14579133C2212yescomplemented
94C2×#14579133C2212yescomplemented
95C2×#14579132C2212yescomplemented
96C2×#14579132C2211yescharacteristic, complemented
97C2×#14579131C2212yes—
98C2×#14579130C2212yes—
99C2×#14579129C2212yes—
100#19099036C22132yescomplemented
101C4×#11929623C22116yescomplemented
102C2×Q8×Dic79C2211yescharacteristic, complemented
103C2×C4×Dic158C2211yescharacteristic, complemented
104C2×#14579126C2211yescharacteristic, complemented
105C2×#14579126C2211yescharacteristic, complemented
106C2×#14579126C2212yescomplemented
107C2×C4×D316C2211yescharacteristic, complemented
108C2×D4×Dic79C2211yescharacteristic
109C2×D4×Dic79C2211yescharacteristic, complemented
110C2×#14579123C2211yescharacteristic, complemented
111C2×C4×C22⋊D79C2211yescharacteristic
112C2×C4×C22⋊D79C2211yescharacteristic, complemented
113C2×C4×C22⋊D79C2212yescomplemented
114C2×C4×C22⋊D79C2212yescomplemented
115C2×C4×C22⋊D79C2212yescomplemented
116C2×C4×C22⋊D79C2212yescomplemented
117C2×C4×C22⋊D79C2212yescomplemented
118C2×(C22⋊D79)⋊C4C2211yescharacteristic
119C2×(C22⋊D79)⋊C4C2211yescharacteristic, complemented
120C2×(C22⋊D79)⋊C4C2212yescomplemented
121C2×(C22⋊D79)⋊C4C2212yescomplemented
122C2×(C22⋊D79)⋊C4C2212yescomplemented
123C2×(C22⋊D79)⋊C4C2212yescomplemented
124C2×(C22⋊D79)⋊C4C2212yescomplemented
125C2×#14579119C2211yescharacteristic, complemented
126C2×#14579117C2211yescharacteristic
127C2×#14579117C2212yes—
128C2×#14579117C2211yescharacteristic, complemented
129C22×C22⋊Dic79C2212yes—
130C2×C22⋊C4×D79C2212yes—
131C2×C22⋊C4×D79C2212yes—
132C22×C4×Dic79C2211yescharacteristic
133C22×C4×Dic79C2211yescharacteristic, complemented
134C2×C42×D79C2211yescharacteristic, complemented
135C22×#41×C79C2211yescharacteristic, complemented
136C23×D4×C79C2211yescharacteristic
137#546×C79C22116yescomplemented
138C2×#124×C79C2211yescharacteristic, complemented
139C2×#123×C79C2212yescomplemented
140C2×C22⋊Q8×C79C2211yescharacteristic
141C2×#121×C79C2211yescharacteristic, complemented
142C2×#121×C79C2212yescomplemented
143C2×#120×C79C2212yes—
144C2×C4×D4×C79C2211yescharacteristic
145C2×C4×D4×C79C2211yescharacteristic, complemented
146C22×C22⋊C4×C79C2212yes—
147C24×D79C2312yes—
148C2×#11929625—44no—
149C2×#11929625C2318yescomplemented
150C2×#11929624—48no—
151C2×#11929624—44no—
152C2×#11929624C23116yescomplemented
153C2×#11929624C2318yescomplemented
154C2×#11929623—28no—
155C2×#11929623—44no—
156C2×#11929623—48no—
157C2×#11929623C2318yes—
158C2×#11929623C23116yescomplemented
159C2×#11929623C2318yescomplemented
160C22×Dic158C2311yescharacteristic
161C22×Dic158C2312yes—
162C22×Dic158C2311yescharacteristic
163C22×D316—44no—
164C22×D316C2311yescharacteristic
165C22×D316C2311yescharacteristic
166C22×D316C2318yes—
167C22×D316C2312yes—
168C22×D316C2312yes—
169C22×D316C2312yes—
170C22×C22⋊D79—216no—
171C22×C22⋊D79—48no—
172C22×C22⋊D79C2311yescharacteristic
173C22×C22⋊D79C2312yes—
174C22×C22⋊D79C2312yes—
175C22×C22⋊D79C2311yescharacteristic
176C22×C22⋊D79C2312yes—
177C22×C22⋊D79C2312yes—
178C22×C22⋊D79C2312yes—
179C22×C22⋊D79C2312yes—
180C22×C22⋊D79C23116yes—
181C22×C22⋊D79C23116yes—
182C22×C22⋊D79C2312yes—
183C22×C22⋊D79C2312yes—
184C22×C22⋊D79C2312yes—
185C22×C22⋊D79C2312yes—
186C22×C22⋊D79C2312yes—
187C22×C22⋊D79C2312yes—
188C23×Dic79C2311yescharacteristic
189C23×Dic79C2311yescharacteristic
190C23×Dic79C2311yescharacteristic
191C23×Dic79C2312yes—
192C23×Dic79C2312yes—
193C23×Dic79C2311yescharacteristic
194C22×C4×D79C2311yescharacteristic
195C22×C4×D79C2311yescharacteristic
196C22×C4×D79C2311yescharacteristic
197C22×C4×D79C2312yes—
198C22×C4×D79C2312yes—
199C22×C4×D79C2312yes—
200C22×C4×D79C2312yes—
201#14579160C2318yescomplemented
202#14579159C2318yescomplemented
203#14579157C23116yes—
204#14579157C2318yes—
205#14579157C23116yes—
206#14579157C2318yes—
207#14579157C2318yes—
208#14579157C2318yes—
209#14579157C23116yescomplemented
210#14579157C23116yescomplemented
211#14579151C23116yescomplemented
212#14579150C2318yescomplemented
213#14579149C2318yescomplemented
214#14579148C2318yescomplemented
215#14579147C23116yescomplemented
216#14579147C23116yescomplemented
217#14579147C23116yescomplemented
218#14579147C23116yescomplemented
219#14579146C23116yescomplemented
220#14579146C23116yescomplemented
221#14579145C23116yescomplemented
222#14579144C23116yescomplemented
223#14579143C23116yescomplemented
224#14579143C23116yescomplemented
225#14579142C23116yescomplemented
226#14579140C2318yes—
227#14579138C23116yes—
228#14579136C23116yescomplemented
229#14579136C2318yescomplemented
230#14579135C23116yescomplemented
231#14579135C2318yescomplemented
232#14579134C23116yescomplemented
233#14579134C23116yescomplemented
234#14579134C23116yescomplemented
235#14579134C23116yescomplemented
236#14579134C23116yescomplemented
237#14579133C23116yescomplemented
238#14579133C23116yescomplemented
239#14579133C23116yescomplemented
240#14579133C23116yescomplemented
241#14579133C23116yescomplemented
242#14579132C23116yescomplemented
243#14579132C2318yescomplemented
244#14579131C23116yes—
245#14579130C23116yes—
246#14579129C23116yes—
247Q8×Dic79C2318yescomplemented
248C4×Dic158C2318yescomplemented
249#14579126C2318yescomplemented
250#14579126C23116yescomplemented
251#14579126C2318yescomplemented
252C4×D316C2318yescomplemented
253D4×Dic79C2318yes—
254D4×Dic79C2318yescomplemented
255#14579123C2318yescomplemented
256C4×C22⋊D79C2318yes—
257C4×C22⋊D79C23116yescomplemented
258C4×C22⋊D79C23116yescomplemented
259C4×C22⋊D79C23116yescomplemented
260C4×C22⋊D79C2318yescomplemented
261C4×C22⋊D79C23116yescomplemented
262C4×C22⋊D79C23116yescomplemented
263(C22⋊D79)⋊C4C2318yes—
264(C22⋊D79)⋊C4C23116yescomplemented
265(C22⋊D79)⋊C4C23116yescomplemented
266(C22⋊D79)⋊C4C23116yescomplemented
267(C22⋊D79)⋊C4C2318yescomplemented
268(C22⋊D79)⋊C4C23116yescomplemented
269(C22⋊D79)⋊C4C23116yescomplemented
270#14579119C2318yescomplemented
271#14579117C2318yes—
272#14579117C23116yes—
273#14579117C2318yescomplemented
274C2×C4⋊Dic79C2311yescharacteristic
275C2×C4⋊Dic79C2311yescharacteristic
276C2×C4⋊Dic79C2312yes—
277C2×Dic79⋊C4C2311yescharacteristic
278C2×Dic79⋊C4C2311yescharacteristic
279C2×Dic79⋊C4C2312yes—
280C2×Dic79⋊C4C2312yes—
281C2×Dic79⋊C4C2311yescharacteristic
282C2×Dic79⋊C4C2311yescharacteristic
283C2×Dic79⋊C4C2312yes—
284C2×Dic79⋊C4C2312yes—
285C2×Dic79⋊C4C2312yes—
286C2×C22⋊Dic79C23116yes—
287C2×C22⋊Dic79C2311yescharacteristic
288C2×C22⋊Dic79C2312yes—
289C2×C22⋊Dic79C2312yes—
290C2×C22⋊Dic79C2312yes—
291C2×C22⋊Dic79C2311yescharacteristic
292C2×C22⋊Dic79C2312yes—
293C2×C22⋊Dic79C2312yes—
294C2×(C2×D79)⋊C4C2312yes—
295C2×(C2×D79)⋊C4C2312yes—
296C2×(C2×D79)⋊C4C2312yes—
297C2×(C2×D79)⋊C4C2312yes—
298C2×(C2×D79)⋊C4C2311yescharacteristic
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2312yes—
304C22⋊C4×D79C23116yes—
305C22⋊C4×D79C23116yes—
306C2×C4×Dic79C2311yescharacteristic
307C2×C4×Dic79C2311yescharacteristic
308C2×C4×Dic79C2311yescharacteristic
309C2×C4×Dic79C2311yescharacteristic
310C2×C4×Dic79C2311yescharacteristic
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2318yes—
313C2×C4×Dic79C2311yescharacteristic
314C2×C4×Dic79C2311yescharacteristic
315C2×C4×Dic79C2311yescharacteristic
316C2×C4×Dic79C2312yes—
317C2×C4×Dic79C2312yes—
318C2×C4×Dic79C2318yescomplemented
319C42×D79C2318yescomplemented
320C25×C79C2312yes—
321C2×#41×C79—44no—
322C2×#41×C79C2318yescomplemented
323C22×Q8×C79C2311yescharacteristic
324C22×D4×C79—44no—
325C22×D4×C79C2311yescharacteristic
326C22×D4×C79C2311yescharacteristic
327C22×D4×C79C2311yescharacteristic
328C22×D4×C79C2318yes—
329C22×D4×C79C2312yes—
330C22×D4×C79C2312yes—
331C22×D4×C79C2312yes—
332C23×C4×C79C2311yescharacteristic
333C23×C4×C79C2311yescharacteristic
334C23×C4×C79C2312yes—
335C23×C4×C79C2312yes—
336#124×C79C2318yescomplemented
337#123×C79C23116yescomplemented
338C22⋊Q8×C79C2318yes—
339#121×C79C23116yescomplemented
340#121×C79C2318yescomplemented
341#120×C79C23116yes—
342C4×D4×C79C2318yes—
343C4×D4×C79C2318yescomplemented
344C2×C4⋊C4×C79C2311yescharacteristic
345C2×C4⋊C4×C79C2311yescharacteristic
346C2×C4⋊C4×C79C2312yes—
347C2×C22⋊C4×C79C23116yes—
348C2×C22⋊C4×C79C2311yescharacteristic
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2312yes—
351C2×C22⋊C4×C79C2312yes—
352C2×C22⋊C4×C79C2311yescharacteristic
353C2×C22⋊C4×C79C2312yes—
354C2×C22⋊C4×C79C2312yes—
355C2×C42×C79C2311yescharacteristic
356C23×D79—28no—
357C23×D79—44no—
358C23×D79—44no—
359C23×D79C2412yes—
360C23×D79C2412yes—
361C23×D79C2411yescharacteristic
362C23×D79C2418yes—
363#11929625—416no—
364#11929624—432no—
365#11929624—416no—
366#11929623—232no—
367#11929623—432no—
368#11929623—416no—
369C2×Dic158—24no—
370C2×Dic158—28no—
371C2×Dic158—24no—
372C2×Dic158C2414yes—
373C2×Dic158C2418yes—
374C2×Dic158C2414yes—
375C2×D316—24no—
376C2×D316—24no—
377C2×D316—44no—
378C2×D316—44no—
379C2×D316—44no—
380C2×D316—416no—
381C2×D316C2414yes—
382C2×D316C2414yes—
383C2×D316C2418yes—
384C2×D316C2418yes—
385C2×D316C2418yes—
386C2×C22⋊D79—24no—
387C2×C22⋊D79—28no—
388C2×C22⋊D79—28no—
389C2×C22⋊D79—28no—
390C2×C22⋊D79—28no—
391C2×C22⋊D79—264no—
392C2×C22⋊D79—28no—
393C2×C22⋊D79—28no—
394C2×C22⋊D79—24no—
395C2×C22⋊D79—432no—
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⋊D79C2414yes—
404C2×C22⋊D79C2418yes—
405C2×C22⋊D79C2418yes—
406C2×C22⋊D79C2418yes—
407C2×C22⋊D79C2418yes—
408C2×C22⋊D79C2418yes—
409C2×C22⋊D79C2418yes—
410C2×C22⋊D79C2418yes—
411C2×C22⋊D79C2418yes—
412C2×C22⋊D79C2418yes—
413C2×C22⋊D79C2418yes—
414C2×C22⋊D79C2418yes—
415C2×C22⋊D79C2418yes—
416C22×Dic79—24no—
417C22×Dic79—24no—
418C22×Dic79—24no—
419C22×Dic79—44no—
420C22×Dic79—44no—
421C22×Dic79#4118yescomplemented
422C22×Dic79C2411yescharacteristic
423C22×Dic79C2412yes—
424C22×Dic79C2412yes—
425C22×Dic79C2414yes—
426C22×Dic79C2414yes—
427C22×Dic79C2411yescharacteristic
428C22×Dic79C2411yescharacteristic
429C22×Dic79C2411yescharacteristic
430C22×Dic79C2414yes—
431C22×Dic79C2418yes—
432C22×Dic79C2418yes—
433C22×Dic79C2411yescharacteristic
434C22×Dic79C2411yescharacteristic
435C22×Dic79C2414yes—
436C22×Dic79C2411yescharacteristic
437C2×C4×D79—24no—
438C2×C4×D79—24no—
439C2×C4×D79—24no—
440C2×C4×D79—44no—
441C2×C4×D79—44no—
442C2×C4×D79—44no—
443C2×C4×D79—44no—
444C2×C4×D79C2414yes—
445C2×C4×D79C2414yes—
446C2×C4×D79C2414yes—
447C2×C4×D79C2418yes—
448C2×C4×D79C2418yes—
449C2×C4×D79C2418yes—
450C2×C4×D79C2418yes—
451C4⋊Dic79C2414yes—
452C4⋊Dic79C2414yes—
453C4⋊Dic79C2418yes—
454Dic79⋊C4C2414yes—
455Dic79⋊C4C2414yes—
456Dic79⋊C4C2418yes—
457Dic79⋊C4C2418yes—
458Dic79⋊C4C2414yes—
459Dic79⋊C4C2414yes—
460Dic79⋊C4C2418yes—
461Dic79⋊C4C2418yes—
462Dic79⋊C4C2418yes—
463C22⋊Dic79C2414yes—
464C22⋊Dic79C2418yes—
465C22⋊Dic79C2418yes—
466C22⋊Dic79C2418yes—
467C22⋊Dic79C2414yes—
468C22⋊Dic79C2418yes—
469C22⋊Dic79C2418yes—
470(C2×D79)⋊C4C2418yes—
471(C2×D79)⋊C4C2418yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2414yes—
475(C2×D79)⋊C4C2414yes—
476(C2×D79)⋊C4C2418yes—
477(C2×D79)⋊C4C2418yes—
478(C2×D79)⋊C4C2418yes—
479(C2×D79)⋊C4C2418yes—
480C4×Dic79C2414yes—
481C4×Dic79C2414yes—
482C4×Dic79C2414yes—
483C4×Dic79C2414yes—
484C4×Dic79C2414yes—
485C4×Dic79C2414yes—
486C4×Dic79C2414yes—
487C4×Dic79C2414yes—
488C4×Dic79C2414yes—
489C4×Dic79C2418yes—
490C4×Dic79C2418yes—
491C24×C79—28no—
492C24×C79—44no—
493C24×C79—44no—
494C24×C79C2412yes—
495C24×C79C2412yes—
496C24×C79C2411yescharacteristic
497C24×C79C2411yescharacteristic
498C24×C79C2418yes—
499#41×C79—416no—
500C2×Q8×C79—24no—
501C2×Q8×C79C2414yes—
502C2×D4×C79—24no—
503C2×D4×C79—24no—
504C2×D4×C79—24no—
505C2×D4×C79—416no—
506C2×D4×C79—44no—
507C2×D4×C79—44no—
508C2×D4×C79—44no—
509C2×D4×C79C2414yes—
510C2×D4×C79C2414yes—
511C2×D4×C79C2414yes—
512C2×D4×C79C2418yes—
513C2×D4×C79C2418yes—
514C2×D4×C79C2418yes—
515C22×C4×C79—24no—
516C22×C4×C79—24no—
517C22×C4×C79—44no—
518C22×C4×C79—44no—
519C22×C4×C79C2411yescharacteristic
520C22×C4×C79C2412yes—
521C22×C4×C79C2414yes—
522C22×C4×C79C2411yescharacteristic
523C22×C4×C79C2411yescharacteristic
524C22×C4×C79C2412yes—
525C22×C4×C79C2411yescharacteristic
526C22×C4×C79C2414yes—
527C22×C4×C79C2418yes—
528C22×C4×C79C2418yes—
529C22×C4×C79C2411yescharacteristic
530C4⋊C4×C79C2414yes—
531C4⋊C4×C79C2414yes—
532C4⋊C4×C79C2418yes—
533C22⋊C4×C79C2414yes—
534C22⋊C4×C79C2418yes—
535C22⋊C4×C79C2418yes—
536C22⋊C4×C79C2418yes—
537C22⋊C4×C79C2414yes—
538C22⋊C4×C79C2418yes—
539C22⋊C4×C79C2418yes—
540C42×C79C2414yes—
541C23×C79—22no—
542C23×C79—22no—
543C23×C79—22no—
544C23×C79—24no—
545C23×C79—24no—
546C23×C79—22no—
547C23×C79—24no—
548C23×C79—24no—
549C23×C79—24no—
550C23×C79—22no—
551C23×C79—24no—
552C23×C79—216no—
553C23×C79—48no—
554C23×C79—48no—
555C23×C79—816no—
556C23×C79C2×#4114yes—
557C23×C79C2514yes—
558C23×C79C2514yes—
559C23×C79C2512yes—
560C23×C79C2512yes—
561C23×C79C2511yescharacteristic
562C22×D79—22no—
563C22×D79—24no—
564C22×D79—24no—
565C22×D79—22no—
566C22×D79—22no—
567C22×D79—24no—
568C22×D79—24no—
569C22×D79—24no—
570C22×D79—24no—
571C22×D79—216no—
572C22×D79—48no—
573C22×D79—48no—
574C22×D79—816no—
575C22×D79C2514yes—
576C22×D79C2514yes—
577C22×D79C2512yes—
578Q8×C79—28no—
579D4×C79—28no—
580D4×C79—28no—
581D4×C79—28no—
582D4×C79—48no—
583D4×C79—48no—
584D4×C79—48no—
585C2×C4×C79—22no—
586C2×C4×C79—22no—
587C2×C4×C79—22no—
588C2×C4×C79—24no—
589C2×C4×C79—24no—
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×C79C2512yes—
599C2×C4×C79C2514yes—
600C2×C4×C79C2512yes—
601C2×C4×C79C2514yes—
602C2×C4×C79C2512yes—
603C22⋊D79—28no—
604C22⋊D79—216no—
605C22⋊D79—216no—
606C22⋊D79—216no—
607C22⋊D79—216no—
608C22⋊D79—28no—
609C22⋊D79—216no—
610C22⋊D79—216no—
611C22⋊D79—48no—
612C22⋊D79—48no—
613C22⋊D79—48no—
614C22⋊D79—48no—
615C22⋊D79—48no—
616C22⋊D79—48no—
617C2×Dic79—22no—
618C2×Dic79—22no—
619C2×Dic79—22no—
620C2×Dic79—24no—
621C2×Dic79—24no—
622C2×Dic79—22no—
623C2×Dic79—28no—
624C2×Dic79—28no—
625C2×Dic79—28no—
626C2×Dic79—48no—
627C2×Dic79—48no—
628C2×Dic79C2×#4114yes—
629C2×Dic79C2×#4114yes—
630C2×Dic79C2×#41116yescomplemented
631C2×Dic79H(5,𝔽2)14yes—
632C2×Dic79C2512yes—
633C2×Dic79C2512yes—
634C2×Dic79C2512yes—
635C2×Dic79C2512yes—
636C2×Dic79C2514yes—
637C2×Dic79C2514yes—
638C2×Dic79C2512yes—
639C2×Dic79C2512yes—
640C2×Dic79C2512yes—
641D316—28no—
642D316—28no—
643D316—48no—
644D316—48no—
645D316—48no—
646C4×D79—28no—
647C4×D79—28no—
648C4×D79—28no—
649C4×D79—48no—
650C4×D79—48no—
651C4×D79—48no—
652C4×D79—48no—
653Dic158—28no—
654Dic158—28no—
655Dic158—216no—
656C22×C79—22no—
657C22×C79—22no—
658C22×C79—28no—
659C22×C79—24no—
660C22×C79—24no—
661C22×C79—22no—
662C22×C79—24no—
663C22×C79—24no—
664C22×C79—22no—
665C22×C79—22no—
666C22×C79—24no—
667C22×C79—24no—
668C22×C79—44no—
669C22×C79—48no—
670C22×C79—48no—
671C22×C79—816no—
672C22×C79C22×#4114yes—
673C22×C79C22×#4112yes—
674C22×C79C2×H(5,𝔽2)12yes—
675C22×C79C2×H(5,𝔽2)12yes—
676C22×C79C2611yescharacteristic
677C2×D79—24no—
678C2×D79—24no—
679C2×D79—22no—
680C2×D79—24no—
681C2×D79—24no—
682C2×D79—22no—
683C2×D79—22no—
684C2×D79—24no—
685C2×D79—24no—
686C2×D79—44no—
687C2×D79—48no—
688C2×D79—48no—
689C2×D79—816no—
690C4×C79—22no—
691C4×C79—22no—
692C4×C79—22no—
693C4×C79—22no—
694C4×C79—24no—
695C4×C79—24no—
696C4×C79C2×H(5,𝔽2)14yes—
697Dic79—22no—
698Dic79—22no—
699Dic79—24no—
700Dic79—24no—
701Dic79—22no—
702Dic79—22no—
703Dic79C22×#4114yes—
704Dic79C22×#4114yes—
705Dic79C2×H(5,𝔽2)14yes—
706C2×#3508—791nomaximal, Sylow
707C2×C79—24no—
708C2×C79—42no—
709C2×C79—44no—
710C2×C79—44no—
711C2×C79#350814yescomplemented
712C2×C79C23×#4111yescharacteristic
713C2×C79C22×H(5,𝔽2)11yescharacteristic
714C2×C79C22×H(5,𝔽2)11yescharacteristic
715D79—42no—
716D79—44no—
717D79—44no—
718#3508—7932no—
719C2×#559—791no—
720C2×#559—792no—
721C2×#559—791no—
722C2×#550—791no—
723C2×#550—791no—
724C2×#550—792no—
725C2×#546—791no—
726C2×#546—791no—
727C2×#546—792no—
728C2×#546—791no—
729C2×#546—792no—
730C2×#546D7911yescharacteristic, complemented
731C2×#540—792no—
732C2×#540—792no—
733C2×#535—792no—
734C2×#533—791no—
735C2×#532—791no—
736C2×#532—791no—
737C2×#532—791no—
738C2×#532—791no—
739C22×#127—791no—
740C2×#518—792no—
741C2×C4×#41—791no—
742C79C2×#350811yescharacteristic, complemented, Sylow
743C22×#41—791no—
744C22×#41—791no—
745C22×#41—792no—
746C22×#41—791no—
747C22×#41—791no—
748C22×#41—792no—
749C22×#41C2×D7911yescharacteristic, complemented
750C23×D4—792no—
751C23×D4—792no—
752C23×D4—791no—
753C23×D4C2×D7911yescharacteristic
754#559—7916no—
755#559—7932no—
756#559—7916no—
757#550—7916no—
758#550—7916no—
759#550—7932no—
760#546—7916no—
761#546—7916no—
762#546—7932no—
763#546—7916no—
764#546—7932no—
765#546C2×D79116yescomplemented
766#540—7932no—
767#540—7932no—
768#535—7932no—
769#533—7916no—
770#532—7916no—
771#532—7916no—
772#532—7916no—
773#532—7916no—
774C2×C4⋊Q8—791no—
775C2×C4⋊Q8—791no—
776C2×#127—791no—
777C2×#127—791no—
778C2×#127—792no—
779C2×#127—791no—
780C2×#127—791no—
781C2×#127—792no—
782C2×#127—7916no—
783C2×#127—792no—
784C2×#127—792no—
785C2×#125—792no—
786C2×#124—791no—
787C2×#124—791no—
788C2×#124—792no—
789C2×#124—792no—
790C2×#124—792no—
791C2×#124—792no—
792C2×#124—791no—
793C2×#124C2×D7911yescharacteristic, complemented
794C2×#123—792no—
795C2×#123—792no—
796C2×#123—792no—
797C2×#123—792no—
798C2×#123—792no—
799C2×#123—792no—
800C2×#123—792no—
801C2×#123C2×D7912yescomplemented
802C2×C22⋊Q8—791no—
803C2×C22⋊Q8—792no—
804C2×C22⋊Q8C2×D7911yescharacteristic
805C2×#121—792no—
806C2×#121—792no—
807C2×#121—791no—
808C2×#121—792no—
809C2×#121—792no—
810C2×#121—792no—
811C2×#121—792no—
812C2×#121—791no—
813C2×#121—792no—
814C2×#121—791no—
815C2×#121—792no—
816C2×#121—792no—
817C2×#121—792no—
818C2×#121—792no—
819C2×#121—792no—
820C2×#121—792no—
821C2×#121C2×D7911yescharacteristic, complemented
822C2×#121C2×D7912yescomplemented
823C2×#120—792no—
824C2×#120—792no—
825C2×#120—792no—
826C2×#120C2×D7912yes—
827#518—7932no—
828C4×#41—7916no—
829C2×C4×Q8—791no—
830C2×C4×Q8—791no—
831C2×C4×Q8—792no—
832C2×C4×Q8—791no—
833C2×C4×Q8—791no—
834C2×C4×D4—791no—
835C2×C4×D4—791no—
836C2×C4×D4—791no—
837C2×C4×D4—791no—
838C2×C4×D4—792no—
839C2×C4×D4—792no—
840C2×C4×D4—792no—
841C2×C4×D4—792no—
842C2×C4×D4—792no—
843C2×C4×D4—791no—
844C2×C4×D4—791no—
845C2×C4×D4—791no—
846C2×C4×D4—792no—
847C2×C4×D4—792no—
848C2×C4×D4—792no—
849C2×C4×D4—792no—
850C2×C4×D4—792no—
851C2×C4×D4—791no—
852C2×C4×D4C2×D7911yescharacteristic
853C2×C4×D4C2×D7911yescharacteristic, complemented
854C2×#117—791no—
855C2×#117—791no—
856C2×#117—791no—
857C2×#117—792no—
858C22×C22⋊C4—792no—
859C22×C22⋊C4—792no—
860C22×C22⋊C4—792no—
861C22×C22⋊C4C2×D7912yes—
862C22×C42—791no—
863C22×C42—791no—
864C22×C42—791no—
865C25—792no—
866C25C22×D7912yes—
867C2×#41—44no—
868C2×#41—3164no—
869C2×#41—3168no—
870C2×#41—3164no—
871C2×#41—3168no—
872C2×#41—3164no—
873C2×#41—798no—
874C2×#41—798no—
875C2×#41—7916no—
876C2×#41—798no—
877C2×#41—798no—
878C2×#41—7916no—
879C2×#41—1588no—
880C2×#41C22×D7918yescomplemented
881C22×Q8—791no—
882C22×Q8—792no—
883C22×Q8—791no—
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—792no—
893C22×D4—792no—
894C22×D4—7916no—
895C22×D4—791no—
896C22×D4—792no—
897C22×D4—792no—
898C22×D4—792no—
899C22×D4—792no—
900C22×D4—791no—
901C22×D4—792no—
902C22×D4—792no—
903C22×D4—7916no—
904C22×D4—792no—
905C22×D4—792no—
906C22×D4—792no—
907C22×D4—798no—
908C22×D4—791no—
909C22×D4—791no—
910C22×D4—15816no—
911C22×D4C22×D7911yescharacteristic
912C22×D4C22×D7911yescharacteristic
913C22×D4C22×D7911yescharacteristic
914C22×D4C22×D7912yes—
915C22×D4C22×D7912yes—
916C22×D4C22×D7912yes—
917C22×D4C22×D7918yes—
918C23×C4—792no—
919C23×C4—792no—
920C23×C4—792no—
921C23×C4—792no—
922C23×C4—792no—
923C23×C4—792no—
924C23×C4—791no—
925C23×C4—791no—
926C23×C4—791no—
927C23×C4—791no—
928C23×C4—791no—
929C23×C4—791no—
930C23×C4—791no—
931C23×C4C22×D7911yescharacteristic
932C23×C4C22×D7911yescharacteristic
933C23×C4C22×D7912yes—
934C23×C4C22×D7912yes—
935C4⋊Q8—798no—
936C4⋊Q8—798no—
937#127—798no—
938#127—798no—
939#127—7916no—
940#127—798no—
941#127—798no—
942#127—7916no—
943#127—7916no—
944#127—7916no—
945#125—7916no—
946#124—798no—
947#124—798no—
948#124—7916no—
949#124—7916no—
950#124—7916no—
951#124—7916no—
952#124—798no—
953#124C22×D7918yescomplemented
954#123—7916no—
955#123—7916no—
956#123—7916no—
957#123—7916no—
958#123—7916no—
959#123—7916no—
960#123—7916no—
961#123C22×D79116yescomplemented
962C22⋊Q8—798no—
963C22⋊Q8—7916no—
964C22⋊Q8C22×D7918yes—
965#121—7916no—
966#121—7916no—
967#121—798no—
968#121—7916no—
969#121—7916no—
970#121—7916no—
971#121—7916no—
972#121—798no—
973#121—7916no—
974#121—798no—
975#121—7916no—
976#121—7916no—
977#121—7916no—
978#121—7916no—
979#121—7916no—
980#121—7916no—
981#121C22×D7918yescomplemented
982#121C22×D79116yescomplemented
983#120—7916no—
984#120—7916no—
985#120—7916no—
986#120C22×D79116yes—
987C4×Q8—798no—
988C4×Q8—798no—
989C4×Q8—7916no—
990C4×Q8—798no—
991C4×Q8—798no—
992C4×D4—798no—
993C4×D4—798no—
994C4×D4—798no—
995C4×D4—798no—
996C4×D4—7916no—
997C4×D4—7916no—
998C4×D4—7916no—
999C4×D4—7916no—
1000C4×D4—7916no—
1001C4×D4—798no—
1002C4×D4—798no—
1003C4×D4—798no—
1004C4×D4—7916no—
1005C4×D4—7916no—
1006C4×D4—7916no—
1007C4×D4—7916no—
1008C4×D4—7916no—
1009C4×D4—798no—
1010C4×D4C22×D7918yes—
1011C4×D4C22×D7918yescomplemented
1012#117—798no—
1013#117—798no—
1014#117—798no—
1015#117—7916no—
1016C2×C4⋊C4—791no—
1017C2×C4⋊C4—791no—
1018C2×C4⋊C4—792no—
1019C2×C4⋊C4—792no—
1020C2×C4⋊C4—791no—
1021C2×C4⋊C4—791no—
1022C2×C4⋊C4—791no—
1023C2×C4⋊C4—792no—
1024C2×C4⋊C4—791no—
1025C2×C4⋊C4—792no—
1026C2×C4⋊C4—792no—
1027C2×C4⋊C4—792no—
1028C2×C4⋊C4C22×D7911yescharacteristic
1029C2×C4⋊C4C22×D7911yescharacteristic
1030C2×C4⋊C4C22×D7912yes—
1031C2×C22⋊C4—791no—
1032C2×C22⋊C4—792no—
1033C2×C22⋊C4—792no—
1034C2×C22⋊C4—792no—
1035C2×C22⋊C4—7916no—
1036C2×C22⋊C4—791no—
1037C2×C22⋊C4—792no—
1038C2×C22⋊C4—792no—
1039C2×C22⋊C4—792no—
1040C2×C22⋊C4—792no—
1041C2×C22⋊C4—792no—
1042C2×C22⋊C4—792no—
1043C2×C22⋊C4—791no—
1044C2×C22⋊C4—791no—
1045C2×C22⋊C4—792no—
1046C2×C22⋊C4—792no—
1047C2×C22⋊C4—792no—
1048C2×C22⋊C4—792no—
1049C2×C22⋊C4—7916no—
1050C2×C22⋊C4—7916no—
1051C2×C22⋊C4C22×D7911yescharacteristic
1052C2×C22⋊C4C22×D7912yes—
1053C2×C22⋊C4C22×D7912yes—
1054C2×C22⋊C4C22×D7912yes—
1055C2×C22⋊C4C22×D79116yes—
1056C2×C22⋊C4C22×D7911yescharacteristic
1057C2×C22⋊C4C22×D7912yes—
1058C2×C22⋊C4C22×D7912yes—
1059C2×C42—791no—
1060C2×C42—791no—
1061C2×C42—791no—
1062C2×C42—792no—
1063C2×C42—792no—
1064C2×C42—791no—
1065C2×C42—791no—
1066C2×C42—791no—
1067C2×C42—791no—
1068C2×C42—791no—
1069C2×C42—798no—
1070C2×C42—798no—
1071C2×C42—791no—
1072C2×C42—798no—
1073C2×C42C22×D7911yescharacteristic
1074C24—28no—
1075C24—44no—
1076C24—44no—
1077C24—3164no—
1078C24—3164no—
1079C24—798no—
1080C24—792no—
1081C24—792no—
1082C24—791no—
1083C24—1588no—
1084C24C23×D7912yes—
1085C24C23×D7912yes—
1086C24C23×D7911yescharacteristic
1087C24C23×D7911yescharacteristic
1088C24C23×D7918yes—
1089#41—416no—
1090#41—31616no—
1091#41—31632no—
1092#41—31616no—
1093#41—31632no—
1094#41—31616no—
1095#41—15832no—
1096C2×Q8—24no—
1097C2×Q8—794no—
1098C2×Q8—798no—
1099C2×Q8—794no—
1100C2×Q8—1588no—
1101C2×Q8—1584no—
1102C2×Q8—1584no—
1103C2×Q8C23×D7914yes—
1104C2×D4—24no—
1105C2×D4—24no—
1106C2×D4—24no—
1107C2×D4—416no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—3164no—
1112C2×D4—3164no—
1113C2×D4—3164no—
1114C2×D4—31616no—
1115C2×D4—3164no—
1116C2×D4—3164no—
1117C2×D4—3164no—
1118C2×D4—3164no—
1119C2×D4—3164no—
1120C2×D4—3164no—
1121C2×D4—31632no—
1122C2×D4—798no—
1123C2×D4—798no—
1124C2×D4—798no—
1125C2×D4—798no—
1126C2×D4—798no—
1127C2×D4—798no—
1128C2×D4—794no—
1129C2×D4—798no—
1130C2×D4—798no—
1131C2×D4—798no—
1132C2×D4—798no—
1133C2×D4—794no—
1134C2×D4—798no—
1135C2×D4—798no—
1136C2×D4—798no—
1137C2×D4—798no—
1138C2×D4—798no—
1139C2×D4—794no—
1140C2×D4—794no—
1141C2×D4—1588no—
1142C2×D4—1588no—
1143C2×D4—1588no—
1144C2×D4—1588no—
1145C2×D4—1588no—
1146C2×D4—1588no—
1147C2×D4—15864no—
1148C2×D4—1584no—
1149C2×D4—1584no—
1150C2×D4—1584no—
1151C2×D4—1584no—
1152C2×D4C23×D7914yes—
1153C2×D4C23×D7914yes—
1154C2×D4C23×D7914yes—
1155C2×D4C23×D7918yes—
1156C2×D4C23×D7918yes—
1157C2×D4C23×D7918yes—
1158C22×C4—24no—
1159C22×C4—24no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—3164no—
1163C22×C4—3164no—
1164C22×C4—3164no—
1165C22×C4—3164no—
1166C22×C4—3164no—
1167C22×C4—3164no—
1168C22×C4—798no—
1169C22×C4—798no—
1170C22×C4—798no—
1171C22×C4—798no—
1172C22×C4—798no—
1173C22×C4—798no—
1174C22×C4—798no—
1175C22×C4—794no—
1176C22×C4—791no—
1177C22×C4—791no—
1178C22×C4—791no—
1179C22×C4—794no—
1180C22×C4—794no—
1181C22×C4—794no—
1182C22×C4—791no—
1183C22×C4—791no—
1184C22×C4—791no—
1185C22×C4—791no—
1186C22×C4—792no—
1187C22×C4—792no—
1188C22×C4—794no—
1189C22×C4—794no—
1190C22×C4—794no—
1191C22×C4—1584no—
1192C22×C4—1584no—
1193C22×C4—1584no—
1194C22×C4—1584no—
1195C22×C4—1584no—
1196C22×C4—1584no—
1197C22×C4C23×D7914yes—
1198C22×C4C23×D7914yes—
1199C22×C4C23×D7911yescharacteristic
1200C22×C4C23×D7911yescharacteristic
1201C22×C4C23×D7911yescharacteristic
1202C22×C4C23×D7911yescharacteristic
1203C22×C4C23×D7912yes—
1204C22×C4C23×D7912yes—
1205C22×C4C23×D7918yes—
1206C22×C4C23×D7918yes—
1207C22×C4C23×D7911yescharacteristic
1208C4⋊C4—794no—
1209C4⋊C4—794no—
1210C4⋊C4—798no—
1211C4⋊C4—798no—
1212C4⋊C4—794no—
1213C4⋊C4—794no—
1214C4⋊C4—798no—
1215C4⋊C4—798no—
1216C4⋊C4—798no—
1217C4⋊C4—794no—
1218C4⋊C4—794no—
1219C4⋊C4—798no—
1220C4⋊C4C23×D7914yes—
1221C4⋊C4C23×D7914yes—
1222C4⋊C4C23×D7918yes—
1223C22⋊C4—794no—
1224C22⋊C4—798no—
1225C22⋊C4—798no—
1226C22⋊C4—798no—
1227C22⋊C4—794no—
1228C22⋊C4—798no—
1229C22⋊C4—798no—
1230C22⋊C4—798no—
1231C22⋊C4—798no—
1232C22⋊C4—798no—
1233C22⋊C4—798no—
1234C22⋊C4—794no—
1235C22⋊C4—794no—
1236C22⋊C4—798no—
1237C22⋊C4—798no—
1238C22⋊C4—798no—
1239C22⋊C4—798no—
1240C22⋊C4C23×D7914yes—
1241C22⋊C4C23×D7918yes—
1242C22⋊C4C23×D7918yes—
1243C22⋊C4C23×D7918yes—
1244C22⋊C4C23×D7914yes—
1245C22⋊C4C23×D7918yes—
1246C22⋊C4C23×D7918yes—
1247C42—794no—
1248C42—794no—
1249C42—794no—
1250C42—794no—
1251C42—794no—
1252C42—794no—
1253C42—794no—
1254C42—794no—
1255C42—794no—
1256C42—798no—
1257C42—798no—
1258C42C23×D7914yes—
1259C23—22no—
1260C23—22no—
1261C23—24no—
1262C23—24no—
1263C23—22no—
1264C23—22no—
1265C23—24no—
1266C23—24no—
1267C23—22no—
1268C23—24no—
1269C23—24no—
1270C23—216no—
1271C23—48no—
1272C23—48no—
1273C23—816no—
1274C23—3168no—
1275C23—3168no—
1276C23—794no—
1277C23—794no—
1278C23—792no—
1279C23—63216no—
1280C23—1584no—
1281C23—1584no—
1282C23—1582no—
1283C23—1584no—
1284C23—1584no—
1285C23—1582no—
1286C23—1582no—
1287C23—1584no—
1288C23—1584no—
1289C23—15816no—
1290C23#41×D7914yes—
1291C23C24×D7914yes—
1292C23C24×D7914yes—
1293C23C24×D7912yes—
1294C23C24×D7912yes—
1295C23C24×D7911yescharacteristic
1296Q8—28no—
1297Q8—15816no—
1298Q8—1588no—
1299Q8—1588no—
1300D4—28no—
1301D4—28no—
1302D4—28no—
1303D4—48no—
1304D4—48no—
1305D4—48no—
1306D4—3168no—
1307D4—3168no—
1308D4—3168no—
1309D4—3168no—
1310D4—3168no—
1311D4—3168no—
1312D4—3168no—
1313D4—3168no—
1314D4—3168no—
1315D4—15816no—
1316D4—15816no—
1317D4—15816no—
1318D4—15816no—
1319D4—15816no—
1320D4—15816no—
1321D4—1588no—
1322D4—1588no—
1323D4—1588no—
1324D4—1588no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—28no—
1332C2×C4—28no—
1333C2×C4—48no—
1334C2×C4—48no—
1335C2×C4—3168no—
1336C2×C4—3168no—
1337C2×C4—3168no—
1338C2×C4—3168no—
1339C2×C4—3168no—
1340C2×C4—3168no—
1341C2×C4—794no—
1342C2×C4—792no—
1343C2×C4—792no—
1344C2×C4—792no—
1345C2×C4—794no—
1346C2×C4—794no—
1347C2×C4—7916no—
1348C2×C4—792no—
1349C2×C4—792no—
1350C2×C4—792no—
1351C2×C4—792no—
1352C2×C4—794no—
1353C2×C4—794no—
1354C2×C4—1588no—
1355C2×C4—1588no—
1356C2×C4—1588no—
1357C2×C4—1588no—
1358C2×C4—1588no—
1359C2×C4—1582no—
1360C2×C4—1584no—
1361C2×C4—1582no—
1362C2×C4—1582no—
1363C2×C4—1584no—
1364C2×C4—1582no—
1365C2×C4—1588no—
1366C2×C4#1457920614yes—
1367C2×C4C24×D7912yes—
1368C2×C4C24×D7912yes—
1369C2×C4C24×D7912yes—
1370C2×C4C24×D7912yes—
1371C2×C4C24×D7914yes—
1372C2×C4C24×D7914yes—
1373C2×C4C24×D7912yes—
1374C22—22no—
1375C22—22no—
1376C22—28no—
1377C22—22no—
1378C22—24no—
1379C22—24no—
1380C22—24no—
1381C22—24no—
1382C22—22no—
1383C22—22no—
1384C22—24no—
1385C22—24no—
1386C22—48no—
1387C22—48no—
1388C22—44no—
1389C22—816no—
1390C22—3168no—
1391C22—3168no—
1392C22—3164no—
1393C22—63216no—
1394C22—1582no—
1395C22—1584no—
1396C22—1584no—
1397C22—1584no—
1398C22—1584no—
1399C22—1582no—
1400C22—1584no—
1401C22—1584no—
1402C22—1582no—
1403C22C2×#41×D7914yes—
1404C22C2×#41×D7912yes—
1405C22H(5,𝔽2)×D7912yes—
1406C22C2×#1457920612yes—
1407C22C25×D7911yescharacteristic
1408C4—22no—
1409C4—22no—
1410C4—24no—
1411C4—22no—
1412C4—22no—
1413C4—24no—
1414C4—794no—
1415C4—794no—
1416C4—794no—
1417C4—1582no—
1418C4—1582no—
1419C4—1584no—
1420C4—1582no—
1421C4—1582no—
1422C4—1584no—
1423C4C2×#1457920614yes—
1424C2—24no—
1425C2—44no—
1426C2—44no—
1427C2—42no—
1428C2—3164no—
1429C2—3164no—
1430C2—3162no—
1431C2#2377726814yesdirect product factor
1432C2C22×#41×D7911yescharacteristic
1433C2C2×H(5,𝔽2)×D7911yescharacteristic
1434C2C22×#1457920611yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#546×C79C2
socleC23×C79C25
hypercenterC2×#546D79
hypocenterC79C2×#3508
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. #23777268C2direct (N × H)
2. C2×#19099297C2semidirect
3. C2×#19099296C2semidirect
4. C2×#19099295C2semidirect
5. C2×#19099232C2semidirect
6. C2×#19099231C2semidirect
7. C2×#19099231C2semidirect
8. C2×#19099209C2semidirect
9. C2×#19099207C2semidirect
10. C2×#19099204C2semidirect
11. C2×#19099203C2semidirect
12. C2×#19099200C2semidirect
13. C2×#19099165C2semidirect
14. C2×#19099163C2semidirect
15. C2×#19099128C2semidirect
16. C2×#19099115C2semidirect
17. C2×#19099112C2semidirect
18. C2×#19099110C2semidirect
19. C2×#19099109C2semidirect
20. C2×#19099108C2semidirect
21. C22×#14579157C2semidirect
22. C2×#19099036C2semidirect
23. C2×C4×#11929623C2semidirect
24. C2×#546×C79C2semidirect
25. C22×#11929625C22semidirect
26. C22×#11929624C22semidirect
27. C22×#11929624C22semidirect
29. C22×#11929623C22semidirect
30. C22×#11929623C22semidirect
34. #19099297C22semidirect
35. #19099296C22semidirect
36. #19099295C22semidirect
37. #19099232C22semidirect
38. #19099231C22semidirect
39. #19099231C22semidirect
40. #19099209C22semidirect
41. #19099207C22semidirect
42. #19099204C22semidirect
43. #19099203C22semidirect
44. #19099200C22semidirect
45. #19099165C22semidirect
46. #19099163C22semidirect
47. #19099128C22semidirect
48. #19099115C22semidirect
49. #19099112C22semidirect
50. #19099110C22semidirect
51. #19099109C22semidirect
52. #19099108C22semidirect
53. C2×#14579160C22semidirect
54. C2×#14579159C22semidirect
61. C2×#14579157C22semidirect
62. C2×#14579157C22semidirect
63. C2×#14579157C22semidirect
64. C2×#14579151C22semidirect
65. C2×#14579150C22semidirect
66. C2×#14579149C22semidirect
67. C2×#14579148C22semidirect
68. C2×#14579147C22semidirect
69. C2×#14579147C22semidirect
70. C2×#14579147C22semidirect
71. C2×#14579147C22semidirect
72. C2×#14579146C22semidirect
73. C2×#14579146C22semidirect
74. C2×#14579145C22semidirect
75. C2×#14579144C22semidirect
76. C2×#14579143C22semidirect
77. C2×#14579143C22semidirect
78. C2×#14579142C22semidirect
81. C2×#14579136C22semidirect
82. C2×#14579136C22semidirect
83. C2×#14579135C22semidirect
84. C2×#14579135C22semidirect
85. C2×#14579134C22semidirect
86. C2×#14579134C22semidirect
87. C2×#14579134C22semidirect
88. C2×#14579134C22semidirect
89. C2×#14579134C22semidirect
90. C2×#14579133C22semidirect
91. C2×#14579133C22semidirect
92. C2×#14579133C22semidirect
93. C2×#14579133C22semidirect
94. C2×#14579133C22semidirect
95. C2×#14579132C22semidirect
96. C2×#14579132C22semidirect
100. #19099036C22semidirect
101. C4×#11929623C22semidirect
102. C2×Q8×Dic79C22semidirect
103. C2×C4×Dic158C22semidirect
104. C2×#14579126C22semidirect
105. C2×#14579126C22semidirect
106. C2×#14579126C22semidirect
107. C2×C4×D316C22semidirect
109. C2×D4×Dic79C22semidirect
110. C2×#14579123C22semidirect
112. C2×C4×C22⋊D79C22semidirect
113. C2×C4×C22⋊D79C22semidirect
114. C2×C4×C22⋊D79C22semidirect
115. C2×C4×C22⋊D79C22semidirect
116. C2×C4×C22⋊D79C22semidirect
117. C2×C4×C22⋊D79C22semidirect
119. C2×(C22⋊D79)⋊C4C22semidirect
120. C2×(C22⋊D79)⋊C4C22semidirect
121. C2×(C22⋊D79)⋊C4C22semidirect
122. C2×(C22⋊D79)⋊C4C22semidirect
123. C2×(C22⋊D79)⋊C4C22semidirect
124. C2×(C22⋊D79)⋊C4C22semidirect
125. C2×#14579119C22semidirect
128. C2×#14579117C22semidirect
133. C22×C4×Dic79C22semidirect
134. C2×C42×D79C22semidirect
135. C22×#41×C79C22semidirect
137. #546×C79C22semidirect
138. C2×#124×C79C22semidirect
139. C2×#123×C79C22semidirect
141. C2×#121×C79C22semidirect
142. C2×#121×C79C22semidirect
145. C2×C4×D4×C79C22semidirect
149. C2×#11929625C23semidirect
152. C2×#11929624C23semidirect
153. C2×#11929624C23semidirect
158. C2×#11929623C23semidirect
159. C2×#11929623C23semidirect
201. #14579160C23semidirect
202. #14579159C23semidirect
209. #14579157C23semidirect
210. #14579157C23semidirect
211. #14579151C23semidirect
212. #14579150C23semidirect
213. #14579149C23semidirect
214. #14579148C23semidirect
215. #14579147C23semidirect
216. #14579147C23semidirect
217. #14579147C23semidirect
218. #14579147C23semidirect
219. #14579146C23semidirect
220. #14579146C23semidirect
221. #14579145C23semidirect
222. #14579144C23semidirect
223. #14579143C23semidirect
224. #14579143C23semidirect
225. #14579142C23semidirect
228. #14579136C23semidirect
229. #14579136C23semidirect
230. #14579135C23semidirect
231. #14579135C23semidirect
232. #14579134C23semidirect
233. #14579134C23semidirect
234. #14579134C23semidirect
235. #14579134C23semidirect
236. #14579134C23semidirect
237. #14579133C23semidirect
238. #14579133C23semidirect
239. #14579133C23semidirect
240. #14579133C23semidirect
241. #14579133C23semidirect
242. #14579132C23semidirect
243. #14579132C23semidirect
247. Q8×Dic79C23semidirect
248. C4×Dic158C23semidirect
249. #14579126C23semidirect
250. #14579126C23semidirect
251. #14579126C23semidirect
252. C4×D316C23semidirect
254. D4×Dic79C23semidirect
255. #14579123C23semidirect
257. C4×C22⋊D79C23semidirect
258. C4×C22⋊D79C23semidirect
259. C4×C22⋊D79C23semidirect
260. C4×C22⋊D79C23semidirect
261. C4×C22⋊D79C23semidirect
262. C4×C22⋊D79C23semidirect
264. (C22⋊D79)⋊C4C23semidirect
265. (C22⋊D79)⋊C4C23semidirect
266. (C22⋊D79)⋊C4C23semidirect
267. (C22⋊D79)⋊C4C23semidirect
268. (C22⋊D79)⋊C4C23semidirect
269. (C22⋊D79)⋊C4C23semidirect
270. #14579119C23semidirect
273. #14579117C23semidirect
318. C2×C4×Dic79C23semidirect
319. C42×D79C23semidirect
322. C2×#41×C79C23semidirect
336. #124×C79C23semidirect
337. #123×C79C23semidirect
339. #121×C79C23semidirect
340. #121×C79C23semidirect
343. C4×D4×C79C23semidirect
421. C22×Dic79#41semidirect
630. C2×Dic79C2×#41semidirect
711. C2×C79#3508semidirect
730. C2×#546D79semidirect
742. C79C2×#3508semidirect
749. C22×#41C2×D79semidirect
765. #546C2×D79semidirect
793. C2×#124C2×D79semidirect
801. C2×#123C2×D79semidirect
821. C2×#121C2×D79semidirect
822. C2×#121C2×D79semidirect
853. C2×C4×D4C2×D79semidirect
880. C2×#41C22×D79semidirect
953. #124C22×D79semidirect
961. #123C22×D79semidirect
981. #121C22×D79semidirect
982. #121C22×D79semidirect
1011. C4×D4C22×D79semidirect
1431. C2#23777268direct (N × H)

Maximal subgroups

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

subgroupindex
#237772682
C2×#190992972
C2×#190992962
C2×#190992952
C2×#190992322
C2×#190992312
C2×#190992092
C2×#190992072
C2×#190992042
C2×#190992032
C2×#190992002
C2×#190991652
C2×#190991632
C2×#190991282
C2×#190991152
C2×#190991122
C2×#190991102
C2×#190991092
C2×#190991082
C22×#145791572
C2×#190990362
C2×C4×#119296232
C2×#546×C792
C2×#350879