Finite Group Databasebeta

← C2×#23777761 #35195905

Subgroups — C2×#23777761 #35195905

Order 20224.

8046 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777761C2132yesmaximal, direct product factor
2C2×#19099302C212yesmaximal, complemented
3C2×#19099301C212yesmaximal, complemented
4C2×#19099282C211yesmaximal, characteristic, complemented
5C2×#19099256C212yesmaximal, complemented
6C2×#19099233C211yesmaximal, characteristic, complemented
7C2×#19099233C211yesmaximal, characteristic, complemented
8C2×#19099232C211yesmaximal, characteristic, complemented
9C2×#19099212C211yesmaximal, characteristic, complemented
10C2×#19099207C211yesmaximal, characteristic, complemented
11C2×#19099206C211yesmaximal, characteristic, complemented
12C2×#19099200C212yesmaximal, complemented
13C2×D4×C22⋊D79C211yesmaximal, characteristic, complemented
14C2×#19099184C211yesmaximal, characteristic, complemented
15C2×#19099182C211yesmaximal, characteristic, complemented
16C2×#19099148C212yesmaximal, complemented
17C2×#19099145C212yesmaximal, complemented
18C2×#19099140C212yesmaximal, complemented
19C2×#19099128C212yesmaximal, complemented
20C2×#19099126C211yesmaximal, characteristic, complemented
21C2×#19099112C211yesmaximal, characteristic, complemented
22C2×#19099111C211yesmaximal, characteristic, complemented
23C2×#19099091C211yesmaximal, characteristic, complemented
24C2×#535×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic, complemented
26C22×#11929623C2212yescomplemented
27C22×#11929623C2211yescharacteristic, complemented
28C22×#11929623C2211yescharacteristic, complemented
29C22×#11929623C2212yescomplemented
30C23×C22⋊D79C2212yes—
31C22×D4×D79C2211yescharacteristic
32#19099302C22132yescomplemented
33#19099301C22132yescomplemented
34#19099282C22116yescomplemented
35#19099256C22132yescomplemented
36#19099233C22116yescomplemented
37#19099233C22116yescomplemented
38#19099232C22116yescomplemented
39#19099212C22116yescomplemented
40#19099207C22116yescomplemented
41#19099206C22116yescomplemented
42#19099200C22132yescomplemented
43D4×C22⋊D79C22116yescomplemented
44#19099184C22116yescomplemented
45#19099182C22116yescomplemented
46#19099148C22132yescomplemented
47#19099145C22132yescomplemented
48#19099140C22132yescomplemented
49#19099128C22132yescomplemented
50#19099126C22116yescomplemented
51#19099112C22116yescomplemented
52#19099111C22116yescomplemented
53C2×#14579161C2211yescharacteristic, complemented
54C2×#14579159C2211yescharacteristic, complemented
55C2×#14579157C2211yescharacteristic
56C2×#14579157C2211yescharacteristic, complemented
57C2×#14579157C2212yescomplemented
58C2×#14579157C2212yescomplemented
59#19099091C22116yescomplemented
60C2×#14579156C2212yescomplemented
61C2×#14579156C2211yescharacteristic, complemented
62C2×#14579154C2212yescomplemented
63C2×#14579154C2211yescharacteristic, complemented
64C2×#14579154C2212yescomplemented
65C2×#14579154C2212yescomplemented
66C2×#14579151C2211yescharacteristic, complemented
67C2×#14579149C2211yescharacteristic, complemented
68C2×#14579148C2211yescharacteristic
69C2×#14579148C2212yescomplemented
70C2×#14579147C2211yescharacteristic
71C2×#14579147C2212yescomplemented
72C2×#14579147C2212yescomplemented
73C2×#14579146C2211yescharacteristic, complemented
74C2×#14579145C2212yescomplemented
75C2×#14579144C2212yescomplemented
76C2×#14579143C2212yescomplemented
77C2×#14579143C2212yescomplemented
78C2×#14579143C2211yescharacteristic, complemented
79C2×#14579142C2212yescomplemented
80C2×#14579142C2212yescomplemented
81C2×#14579140C2211yescharacteristic, complemented
82C2×#14579139C2212yescomplemented
83C2×#14579139C2211yescharacteristic, complemented
84C2×#14579138C2212yescomplemented
85C2×#14579138C2212yescomplemented
86C2×#14579137C2211yescharacteristic, complemented
87C2×#14579135C2211yescharacteristic
88C2×#14579135C2212yescomplemented
89C2×#14579134C2211yescharacteristic
90C2×#14579134C2212yescomplemented
91C2×#14579134C2212yescomplemented
92C2×#14579134C2212yescomplemented
93C2×#14579133C2212yes—
94C2×#14579133C2212yes—
95C2×#14579133C2212yescomplemented
96C2×#14579133C2212yescomplemented
97C2×#14579133C2212yescomplemented
98C2×#14579133C2212yescomplemented
99C2×#14579133C2212yescomplemented
100C2×#14579133C2212yescomplemented
101C2×#14579133C2212yescomplemented
102C2×#14579132C2211yescharacteristic
103C2×#14579132C2211yescharacteristic
104C2×#14579132C2212yescomplemented
105C2×#14579132C2211yescharacteristic, complemented
106C2×#14579132C2212yescomplemented
107C2×#14579132C2212yescomplemented
108C2×#14579131C2212yescomplemented
109C2×#14579130C2212yes—
110C2×#14579130C2212yescomplemented
111C2×#14579129C2212yes—
112C2×#14579129C2212yescomplemented
113C2×#14579129C2212yescomplemented
114C2×Q8×Dic79C2211yescharacteristic, complemented
115C2×C4×Dic158C2211yescharacteristic, complemented
116C2×C4×Dic158C2211yescharacteristic, complemented
117C2×C4×D316C2211yescharacteristic, complemented
118C2×C4×D316C2211yescharacteristic, complemented
119C2×D4×Dic79C2211yescharacteristic
120C2×D4×Dic79C2211yescharacteristic, complemented
121C2×D4×Dic79C2212yescomplemented
122C2×D4×Dic79C2211yescharacteristic, complemented
123C2×D4×Dic79C2212yescomplemented
124C2×C4×C22⋊D79C2211yescharacteristic
125C2×C4×C22⋊D79C2211yescharacteristic, complemented
126C2×C4×C22⋊D79C2212yescomplemented
127C2×(C22⋊D79)⋊C4C2212yescomplemented
128C2×(C22⋊D79)⋊C4C2212yescomplemented
129C2×#14579118C2211yescharacteristic, complemented
130C2×#14579117C2212yescomplemented
131C22×Dic79⋊C4C2212yescomplemented
132C22×C22⋊Dic79C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C42×D79C2211yescharacteristic, complemented
135C22×#41×C79C2211yescharacteristic, complemented
136C23×D4×C79C2211yescharacteristic
137#535×C79C22116yescomplemented
138C2×#127×C79C2211yescharacteristic
139C2×#127×C79C2211yescharacteristic, complemented
140C2×#124×C79C2211yescharacteristic
141C2×#124×C79C2211yescharacteristic, complemented
142C2×#121×C79C2212yescomplemented
143C2×#121×C79C2212yescomplemented
144C2×#120×C79C2212yescomplemented
145C2×#120×C79C2212yescomplemented
146C2×#117×C79C2211yescharacteristic, complemented
147C24×D79C2312yes—
148C2×#11929625—44no—
149C2×#11929625C2318yescomplemented
150C2×#11929623—48no—
151C2×#11929623—44no—
152C2×#11929623—44no—
153C2×#11929623—48no—
154C2×#11929623C23116yescomplemented
155C2×#11929623C23116yescomplemented
156C2×#11929623C2318yescomplemented
157C2×#11929623C2318yescomplemented
158C22×Dic158C2311yescharacteristic
159C22×Dic158C2311yescharacteristic
160C22×Dic158C2312yes—
161C22×D316C2311yescharacteristic
162C22×D316C2311yescharacteristic
163C22×D316C2312yes—
164C22×C22⋊D79—48no—
165C22×C22⋊D79C2312yes—
166C22×C22⋊D79C2311yescharacteristic
167C22×C22⋊D79C23116yes—
168C22×C22⋊D79C2312yes—
169C22×C22⋊D79C2312yes—
170C22×C22⋊D79C2311yescharacteristic
171C22×C22⋊D79C2312yes—
172C22×C22⋊D79C2312yes—
173C22×C22⋊D79C2312yes—
174C22×C22⋊D79C2312yes—
175C22×C22⋊D79C2312yes—
176C22×C22⋊D79C2312yes—
177C22×C22⋊D79C2312yes—
178C22×C22⋊D79C2312yes—
179C2×D4×D79—44no—
180C2×D4×D79C2318yes—
181C23×Dic79C2312yes—
182C23×Dic79C2312yes—
183C23×Dic79C2312yes—
184C23×Dic79C2312yes—
185C23×Dic79C2312yes—
186C22×C4×D79C2311yescharacteristic
187C22×C4×D79C2311yescharacteristic
188C22×C4×D79C2311yescharacteristic
189C22×C4×D79C2311yescharacteristic
190C22×C4×D79C2312yes—
191C22×C4×D79C2312yes—
192#14579161C2318yescomplemented
193#14579159C2318yescomplemented
194#14579157C2318yes—
195#14579157C2318yescomplemented
196#14579157C23116yescomplemented
197#14579157C23116yescomplemented
198#14579156C2318yescomplemented
199#14579156C23116yescomplemented
200#14579154C23116yescomplemented
201#14579154C2318yescomplemented
202#14579154C23116yescomplemented
203#14579154C23116yescomplemented
204#14579151C2318yescomplemented
205#14579149C2318yescomplemented
206#14579148C2318yes—
207#14579148C23116yescomplemented
208#14579147C2318yes—
209#14579147C23116yescomplemented
210#14579147C23116yescomplemented
211#14579146C2318yescomplemented
212#14579145C23116yescomplemented
213#14579144C23116yescomplemented
214#14579143C23116yescomplemented
215#14579143C23116yescomplemented
216#14579143C2318yescomplemented
217#14579142C23116yescomplemented
218#14579142C23116yescomplemented
219#14579140C2318yescomplemented
220#14579139C2318yescomplemented
221#14579139C23116yescomplemented
222#14579138C23116yescomplemented
223#14579138C23116yescomplemented
224#14579137C2318yescomplemented
225#14579135C2318yes—
226#14579135C23116yescomplemented
227#14579134C2318yes—
228#14579134C23116yescomplemented
229#14579134C23116yescomplemented
230#14579134C23116yescomplemented
231#14579133C23116yes—
232#14579133C23116yes—
233#14579133C23116yescomplemented
234#14579133C23116yescomplemented
235#14579133C23116yescomplemented
236#14579133C23116yescomplemented
237#14579133C23116yescomplemented
238#14579133C23116yescomplemented
239#14579133C23116yescomplemented
240#14579132C2318yes—
241#14579132C2318yes—
242#14579132C23116yescomplemented
243#14579132C23116yescomplemented
244#14579132C2318yescomplemented
245#14579132C23116yescomplemented
246#14579131C23116yescomplemented
247#14579130C23116yes—
248#14579130C23116yescomplemented
249#14579129C23116yes—
250#14579129C23116yescomplemented
251#14579129C23116yescomplemented
252Q8×Dic79C2318yescomplemented
253C4×Dic158C2318yescomplemented
254C4×Dic158C2318yescomplemented
255C4×D316C2318yescomplemented
256C4×D316C2318yescomplemented
257D4×Dic79C2318yes—
258D4×Dic79C23116yescomplemented
259D4×Dic79C2318yescomplemented
260D4×Dic79C23116yescomplemented
261D4×Dic79C2318yescomplemented
262C4×C22⋊D79C2318yes—
263C4×C22⋊D79C23116yescomplemented
264C4×C22⋊D79C2318yescomplemented
265(C22⋊D79)⋊C4C23116yescomplemented
266(C22⋊D79)⋊C4C23116yescomplemented
267#14579118C2318yescomplemented
268#14579117C23116yescomplemented
269C2×C4⋊Dic79C2311yescharacteristic
270C2×C4⋊Dic79C2311yescharacteristic
271C2×C4⋊Dic79C2311yescharacteristic
272C2×C4⋊Dic79C2312yes—
273C2×C4⋊Dic79C2311yescharacteristic
274C2×C4⋊Dic79C2312yes—
275C2×Dic79⋊C4C2311yescharacteristic
276C2×Dic79⋊C4C2312yes—
277C2×Dic79⋊C4C2312yes—
278C2×Dic79⋊C4C2312yes—
279C2×Dic79⋊C4C2311yescharacteristic
280C2×Dic79⋊C4C2311yescharacteristic
281C2×Dic79⋊C4C2311yescharacteristic
282C2×Dic79⋊C4C2312yes—
283C2×Dic79⋊C4C2311yescharacteristic
284C2×Dic79⋊C4C2312yes—
285C2×Dic79⋊C4C2311yescharacteristic
286C2×Dic79⋊C4C23116yescomplemented
287C2×C22⋊Dic79C2312yes—
288C2×C22⋊Dic79C2311yescharacteristic
289C2×C22⋊Dic79C2312yes—
290C2×C22⋊Dic79C2312yes—
291C2×C22⋊Dic79C2312yes—
292C2×C22⋊Dic79C2311yescharacteristic
293C2×C22⋊Dic79C2312yes—
294C2×C22⋊Dic79C2312yes—
295C2×C22⋊Dic79C2312yes—
296C2×C22⋊Dic79C2312yes—
297C2×C22⋊Dic79C2312yes—
298C2×C22⋊Dic79C23116yescomplemented
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2311yescharacteristic
302C2×(C2×D79)⋊C4C2311yescharacteristic
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2312yes—
305C2×(C2×D79)⋊C4C2311yescharacteristic
306C2×(C2×D79)⋊C4C2312yes—
307C2×(C2×D79)⋊C4C2311yescharacteristic
308C2×(C2×D79)⋊C4C2312yes—
309C2×(C2×D79)⋊C4C2311yescharacteristic
310C22⋊C4×D79C23116yescomplemented
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2311yescharacteristic
313C2×C4×Dic79C2311yescharacteristic
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2312yes—
316C2×C4×Dic79C2311yescharacteristic
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×C79C2311yescharacteristic
326C22×D4×C79C2318yes—
327C22×D4×C79C2312yes—
328C22×D4×C79C2312yes—
329C22×D4×C79C2312yes—
330C22×D4×C79C2312yes—
331C22×D4×C79C2312yes—
332C22×D4×C79C2312yes—
333C23×C4×C79C2311yescharacteristic
334C23×C4×C79C2312yes—
335#127×C79C2318yes—
336#127×C79C2318yescomplemented
337#124×C79C2318yes—
338#124×C79C2318yescomplemented
339#121×C79C23116yescomplemented
340#121×C79C23116yescomplemented
341#120×C79C23116yescomplemented
342#120×C79C23116yescomplemented
343#117×C79C2318yescomplemented
344C2×C4⋊C4×C79C2311yescharacteristic
345C2×C4⋊C4×C79C2311yescharacteristic
346C2×C22⋊C4×C79C2311yescharacteristic
347C2×C22⋊C4×C79C2311yescharacteristic
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2312yes—
351C2×C22⋊C4×C79C2312yes—
352C2×C42×C79C2311yescharacteristic
353C2×C42×C79C2311yescharacteristic
354C23×D79—44no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79C2411yescharacteristic
358C23×D79C2412yes—
359C23×D79C2411yescharacteristic
360C23×D79C2418yes—
361#11929625—416no—
362#11929623—432no—
363#11929623—416no—
364#11929623—416no—
365#11929623—432no—
366C2×Dic158—24no—
367C2×Dic158—24no—
368C2×Dic158—44no—
369C2×Dic158C2414yes—
370C2×Dic158C2414yes—
371C2×Dic158C2418yes—
372C2×D316—24no—
373C2×D316—44no—
374C2×D316—42no—
375C2×D316C2414yes—
376C2×D316C2418yes—
377C2×D316C2414yes—
378C2×C22⋊D79—28no—
379C2×C22⋊D79—24no—
380C2×C22⋊D79—432no—
381C2×C22⋊D79—44no—
382C2×C22⋊D79—44no—
383C2×C22⋊D79—44no—
384C2×C22⋊D79—44no—
385C2×C22⋊D79—44no—
386C2×C22⋊D79—44no—
387C2×C22⋊D79—44no—
388C2×C22⋊D79—44no—
389C2×C22⋊D79—42no—
390C2×C22⋊D79—44no—
391C2×C22⋊D79—44no—
392C2×C22⋊D79C2418yes—
393C2×C22⋊D79C2414yes—
394C2×C22⋊D79C2418yes—
395C2×C22⋊D79C2418yes—
396C2×C22⋊D79C2418yes—
397C2×C22⋊D79C2418yes—
398C2×C22⋊D79C2418yes—
399C2×C22⋊D79C2418yes—
400C2×C22⋊D79C2418yes—
401C2×C22⋊D79C2414yes—
402C2×C22⋊D79C2418yes—
403C2×C22⋊D79C2418yes—
404C2×C22⋊D79C2418yes—
405D4×D79—416no—
406C22×Dic79—28no—
407C22×Dic79—28no—
408C22×Dic79—44no—
409C22×Dic79—44no—
410C22×Dic79—44no—
411C22×Dic79C2412yes—
412C22×Dic79C2412yes—
413C22×Dic79C2411yescharacteristic
414C22×Dic79C2412yes—
415C22×Dic79C2418yes—
416C22×Dic79C2418yes—
417C22×Dic79C2411yescharacteristic
418C22×Dic79C2411yescharacteristic
419C22×Dic79C2411yescharacteristic
420C22×Dic79C2411yescharacteristic
421C22×Dic79C2418yes—
422C22×Dic79C2418yes—
423C22×Dic79C2418yes—
424C22×Dic79C2411yescharacteristic
425C2×C4×D79—24no—
426C2×C4×D79—24no—
427C2×C4×D79—24no—
428C2×C4×D79—44no—
429C2×C4×D79—44no—
430C2×C4×D79—42no—
431C2×C4×D79C2414yes—
432C2×C4×D79C2414yes—
433C2×C4×D79C2414yes—
434C2×C4×D79C2418yes—
435C2×C4×D79C2418yes—
436C2×C4×D79C2414yes—
437C4⋊Dic79C2414yes—
438C4⋊Dic79C2414yes—
439C4⋊Dic79C2414yes—
440C4⋊Dic79C2418yes—
441C4⋊Dic79C2414yes—
442C4⋊Dic79C2418yes—
443Dic79⋊C4C2414yes—
444Dic79⋊C4C2418yes—
445Dic79⋊C4C2418yes—
446Dic79⋊C4C2418yes—
447Dic79⋊C4C2414yes—
448Dic79⋊C4C2414yes—
449Dic79⋊C4C2414yes—
450Dic79⋊C4C2418yes—
451Dic79⋊C4C2414yes—
452Dic79⋊C4C2418yes—
453Dic79⋊C4C2414yes—
454C22⋊Dic79C2418yes—
455C22⋊Dic79C2414yes—
456C22⋊Dic79C2418yes—
457C22⋊Dic79C2418yes—
458C22⋊Dic79C2418yes—
459C22⋊Dic79C2414yes—
460C22⋊Dic79C2418yes—
461C22⋊Dic79C2418yes—
462C22⋊Dic79C2418yes—
463C22⋊Dic79C2418yes—
464C22⋊Dic79C2418yes—
465(C2×D79)⋊C4C2414yes—
466(C2×D79)⋊C4C2418yes—
467(C2×D79)⋊C4C2414yes—
468(C2×D79)⋊C4C2414yes—
469(C2×D79)⋊C4C2418yes—
470(C2×D79)⋊C4C2418yes—
471(C2×D79)⋊C4C2414yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2414yes—
474(C2×D79)⋊C4C2418yes—
475(C2×D79)⋊C4C2414yes—
476C4×Dic79C2414yes—
477C4×Dic79C2414yes—
478C4×Dic79C2414yes—
479C4×Dic79C2418yes—
480C4×Dic79C2418yes—
481C4×Dic79C2414yes—
482C24×C79—44no—
483C24×C79—44no—
484C24×C79—44no—
485C24×C79C2412yes—
486C24×C79C2411yescharacteristic
487C24×C79C2412yes—
488C24×C79C2412yes—
489C24×C79C2418yes—
490#41×C79—416no—
491C2×Q8×C79—24no—
492C2×Q8×C79C2414yes—
493C2×D4×C79—24no—
494C2×D4×C79—24no—
495C2×D4×C79—24no—
496C2×D4×C79—416no—
497C2×D4×C79—44no—
498C2×D4×C79—44no—
499C2×D4×C79—44no—
500C2×D4×C79—44no—
501C2×D4×C79—44no—
502C2×D4×C79—44no—
503C2×D4×C79C2414yes—
504C2×D4×C79C2414yes—
505C2×D4×C79C2414yes—
506C2×D4×C79C2418yes—
507C2×D4×C79C2418yes—
508C2×D4×C79C2418yes—
509C2×D4×C79C2418yes—
510C2×D4×C79C2418yes—
511C2×D4×C79C2418yes—
512C22×C4×C79—24no—
513C22×C4×C79—44no—
514C22×C4×C79C2411yescharacteristic
515C22×C4×C79C2411yescharacteristic
516C22×C4×C79C2411yescharacteristic
517C22×C4×C79C2411yescharacteristic
518C22×C4×C79C2412yes—
519C22×C4×C79C2411yescharacteristic
520C22×C4×C79C2414yes—
521C22×C4×C79C2418yes—
522C22×C4×C79C2411yescharacteristic
523C4⋊C4×C79C2414yes—
524C4⋊C4×C79C2414yes—
525C22⋊C4×C79C2414yes—
526C22⋊C4×C79C2414yes—
527C22⋊C4×C79C2418yes—
528C22⋊C4×C79C2418yes—
529C22⋊C4×C79C2418yes—
530C22⋊C4×C79C2418yes—
531C42×C79C2414yes—
532C42×C79C2414yes—
533C23×C79—24no—
534C23×C79—24no—
535C23×C79—24no—
536C23×C79—24no—
537C23×C79—24no—
538C23×C79—22no—
539C23×C79—24no—
540C23×C79—22no—
541C23×C79—24no—
542C23×C79—24no—
543C23×C79—22no—
544C23×C79—24no—
545C23×C79—48no—
546C23×C79—48no—
547C23×C79—48no—
548C23×C79—816no—
549C23×C79C2514yes—
550C23×C79C2512yes—
551C23×C79C2514yes—
552C23×C79C2514yes—
553C23×C79C2511yescharacteristic
554C22×D79—22no—
555C22×D79—22no—
556C22×D79—22no—
557C22×D79—24no—
558C22×D79—24no—
559C22×D79—22no—
560C22×D79—22no—
561C22×D79—24no—
562C22×D79—22no—
563C22×D79—48no—
564C22×D79—48no—
565C22×D79—48no—
566C22×D79—816no—
567C22×D79C2512yes—
568C22×D79C2514yes—
569C22×D79C2512yes—
570Q8×C79—28no—
571D4×C79—28no—
572D4×C79—28no—
573D4×C79—28no—
574D4×C79—48no—
575D4×C79—48no—
576D4×C79—48no—
577D4×C79—48no—
578D4×C79—48no—
579D4×C79—48no—
580C2×C4×C79—22no—
581C2×C4×C79—22no—
582C2×C4×C79—24no—
583C2×C4×C79—22no—
584C2×C4×C79—22no—
585C2×C4×C79—22no—
586C2×C4×C79—28no—
587C2×C4×C79—48no—
588C2×C4×C79H(5,𝔽2)14yes—
589C2×C4×C79C2512yes—
590C2×C4×C79C2512yes—
591C2×C4×C79C2512yes—
592C2×C4×C79C2514yes—
593C2×C4×C79C2512yes—
594C2×C4×C79C2512yes—
595C2×C4×C79C2512yes—
596C22⋊D79—28no—
597C22⋊D79—216no—
598C22⋊D79—48no—
599C22⋊D79—48no—
600C22⋊D79—48no—
601C22⋊D79—48no—
602C22⋊D79—44no—
603C22⋊D79—48no—
604C22⋊D79—48no—
605C22⋊D79—48no—
606C22⋊D79—48no—
607C22⋊D79—48no—
608C22⋊D79—48no—
609C2×Dic79—22no—
610C2×Dic79—22no—
611C2×Dic79—24no—
612C2×Dic79—24no—
613C2×Dic79—22no—
614C2×Dic79—24no—
615C2×Dic79—22no—
616C2×Dic79—22no—
617C2×Dic79—216no—
618C2×Dic79—216no—
619C2×Dic79—48no—
620C2×Dic79—48no—
621C2×Dic79—48no—
622C2×Dic79H(5,𝔽2)14yes—
623C2×Dic79C2512yes—
624C2×Dic79C2512yes—
625C2×Dic79C2512yes—
626C2×Dic79C2514yes—
627C2×Dic79C2514yes—
628C2×Dic79C2512yes—
629C2×Dic79C2514yes—
630C2×Dic79C2512yes—
631C2×Dic79C2512yes—
632D316—28no—
633D316—44no—
634D316—48no—
635C4×D79—28no—
636C4×D79—28no—
637C4×D79—28no—
638C4×D79—44no—
639C4×D79—48no—
640C4×D79—48no—
641Dic158—28no—
642Dic158—28no—
643Dic158—48no—
644C22×C79—22no—
645C22×C79—24no—
646C22×C79—24no—
647C22×C79—24no—
648C22×C79—24no—
649C22×C79—24no—
650C22×C79—24no—
651C22×C79—22no—
652C22×C79—24no—
653C22×C79—24no—
654C22×C79—22no—
655C22×C79—24no—
656C22×C79—48no—
657C22×C79—48no—
658C22×C79—48no—
659C22×C79—44no—
660C22×C79—816no—
661C22×C79C2×H(5,𝔽2)12yes—
662C22×C79C2×H(5,𝔽2)12yes—
663C22×C79#58512yes—
664C22×C79C2611yescharacteristic
665C2×D79—22no—
666C2×D79—24no—
667C2×D79—22no—
668C2×D79—22no—
669C2×D79—22no—
670C2×D79—24no—
671C2×D79—24no—
672C2×D79—22no—
673C2×D79—22no—
674C2×D79—44no—
675C2×D79—48no—
676C2×D79—44no—
677C2×D79—816no—
678C4×C79—22no—
679C4×C79—24no—
680C4×C79—22no—
681C4×C79—22no—
682C4×C79—22no—
683C4×C79—22no—
684C4×C79C2×H(5,𝔽2)14yes—
685Dic79—24no—
686Dic79—22no—
687Dic79—24no—
688Dic79—22no—
689Dic79—24no—
690Dic79—22no—
691Dic79—22no—
692Dic79—22no—
693Dic79C2×H(5,𝔽2)14yes—
694C2×#3546—791nomaximal, Sylow
695C2×C79—44no—
696C2×C79—44no—
697C2×C79—44no—
698C2×C79—42no—
699C2×C79#354614yescomplemented
700C2×C79C22×H(5,𝔽2)11yescharacteristic
701C2×C79C22×H(5,𝔽2)11yescharacteristic
702C2×C79C2×#58511yescharacteristic
703D79—42no—
704D79—44no—
705D79—42no—
706#3546—7932no—
707C2×#560—792no—
708C2×#560—792no—
709C2×#556—791no—
710C2×#553—792no—
711C2×#550—791no—
712C2×#550—791no—
713C2×#550—791no—
714C2×#547—791no—
715C2×#546—791no—
716C2×#546—791no—
717C2×#546—792no—
718C2×D42—791no—
719C2×#542—791no—
720C2×#542—791no—
721C2×#538—792no—
722C2×#538—792no—
723C2×#537—792no—
724C2×#535—791no—
725C2×#535—792no—
726C2×#535D7911yescharacteristic, complemented
727C2×#532—791no—
728C2×#532—791no—
729C2×#529—791no—
730C79C2×#354611yescharacteristic, complemented, Sylow
731C22×#41—791no—
732C22×#41—792no—
733C22×#41—791no—
734C22×#41—791no—
735C22×#41—792no—
736C22×#41C2×D7911yescharacteristic, complemented
737C23×D4—792no—
738C23×D4—791no—
739C23×D4C2×D7911yescharacteristic
740#560—7932no—
741#560—7932no—
742#556—7916no—
743#553—7932no—
744#550—7916no—
745#550—7916no—
746#550—7916no—
747#547—7916no—
748#546—7916no—
749#546—7916no—
750#546—7932no—
751D42—7916no—
752#542—7916no—
753#542—7916no—
754#538—7932no—
755#538—7932no—
756#537—7932no—
757#535—7916no—
758#535—7932no—
759#535C2×D79116yescomplemented
760#532—7916no—
761#532—7916no—
762C2×C4⋊Q8—791no—
763C2×C4⋊Q8—791no—
764C2×#127—791no—
765C2×#127—791no—
766C2×#127—792no—
767C2×#127—792no—
768C2×#127C2×D7911yescharacteristic
769C2×#127C2×D7911yescharacteristic, complemented
770#529—7916no—
771C2×#126—791no—
772C2×#126—792no—
773C2×#126—791no—
774C2×#126—792no—
775C2×#126—792no—
776C2×#126—792no—
777C2×#125—791no—
778C2×#124—792no—
779C2×#124—791no—
780C2×#124—791no—
781C2×#124—792no—
782C2×#124—792no—
783C2×#124—791no—
784C2×#124C2×D7911yescharacteristic
785C2×#124C2×D7911yescharacteristic, complemented
786C2×#123—792no—
787C2×#123—792no—
788C2×#123—792no—
789C2×#123—791no—
790C2×#123—791no—
791C2×#123—792no—
792C2×#123—792no—
793C2×#123—792no—
794C2×C22⋊Q8—791no—
795C2×C22⋊Q8—791no—
796C2×C22⋊Q8—791no—
797C2×C22⋊Q8—792no—
798C2×C22⋊Q8—792no—
799C2×C22⋊Q8—792no—
800C2×#121—791no—
801C2×#121—791no—
802C2×#121—792no—
803C2×#121—792no—
804C2×#121—792no—
805C2×#121—792no—
806C2×#121—792no—
807C2×#121—792no—
808C2×#121—792no—
809C2×#121—792no—
810C2×#121—792no—
811C2×#121—792no—
812C2×#121—792no—
813C2×#121—792no—
814C2×#121—791no—
815C2×#121—792no—
816C2×#121—791no—
817C2×#121—791no—
818C2×#121—792no—
819C2×#121—792no—
820C2×#121—792no—
821C2×#121C2×D7912yescomplemented
822C2×#121C2×D7912yescomplemented
823C2×#120—792no—
824C2×#120—792no—
825C2×#120—792no—
826C2×#120—792no—
827C2×#120—792no—
828C2×#120—792no—
829C2×#120C2×D7912yescomplemented
830C2×#120C2×D7912yescomplemented
831C2×C4×Q8—791no—
832C2×C4×Q8—791no—
833C2×C4×Q8—791no—
834C2×C4×D4—791no—
835C2×C4×D4—792no—
836C2×C4×D4—791no—
837C2×C4×D4—792no—
838C2×C4×D4—791no—
839C2×C4×D4—791no—
840C2×C4×D4—791no—
841C2×C4×D4—792no—
842C2×C4×D4—792no—
843C2×C4×D4—792no—
844C2×C4×D4—791no—
845C2×C4×D4—791no—
846C2×#117—792no—
847C2×#117—791no—
848C2×#117C2×D7911yescharacteristic, complemented
849C22×C4⋊C4—792no—
850C22×C22⋊C4—792no—
851C22×C22⋊C4—792no—
852C22×C42—791no—
853C25—792no—
854C25C22×D7912yes—
855C2×#41—44no—
856C2×#41—3164no—
857C2×#41—3164no—
858C2×#41—3168no—
859C2×#41—3164no—
860C2×#41—3168no—
861C2×#41—798no—
862C2×#41—7916no—
863C2×#41—798no—
864C2×#41—798no—
865C2×#41—7916no—
866C2×#41C22×D7918yescomplemented
867C22×Q8—792no—
868C22×Q8—791no—
869C22×Q8—791no—
870C22×Q8C22×D7911yescharacteristic
871C22×D4—44no—
872C22×D4—3164no—
873C22×D4—3168no—
874C22×D4—792no—
875C22×D4—791no—
876C22×D4—792no—
877C22×D4—792no—
878C22×D4—792no—
879C22×D4—792no—
880C22×D4—792no—
881C22×D4—792no—
882C22×D4—792no—
883C22×D4—792no—
884C22×D4—792no—
885C22×D4—7916no—
886C22×D4—798no—
887C22×D4—791no—
888C22×D4—792no—
889C22×D4—791no—
890C22×D4—792no—
891C22×D4—791no—
892C22×D4C22×D7911yescharacteristic
893C22×D4C22×D7911yescharacteristic
894C22×D4C22×D7911yescharacteristic
895C22×D4C22×D7912yes—
896C22×D4C22×D7912yes—
897C22×D4C22×D7912yes—
898C22×D4C22×D7912yes—
899C22×D4C22×D7912yes—
900C22×D4C22×D7912yes—
901C22×D4C22×D7918yes—
902C23×C4—792no—
903C23×C4—792no—
904C23×C4—792no—
905C23×C4—792no—
906C23×C4—792no—
907C23×C4—791no—
908C23×C4—792no—
909C23×C4—792no—
910C23×C4—791no—
911C23×C4—791no—
912C23×C4—791no—
913C23×C4C22×D7911yescharacteristic
914C23×C4C22×D7912yes—
915C4⋊Q8—798no—
916C4⋊Q8—798no—
917#127—798no—
918#127—798no—
919#127—7916no—
920#127—7916no—
921#127C22×D7918yes—
922#127C22×D7918yescomplemented
923#126—798no—
924#126—7916no—
925#126—798no—
926#126—7916no—
927#126—7916no—
928#126—7916no—
929#125—798no—
930#124—7916no—
931#124—798no—
932#124—798no—
933#124—7916no—
934#124—7916no—
935#124—798no—
936#124C22×D7918yes—
937#124C22×D7918yescomplemented
938#123—7916no—
939#123—7916no—
940#123—7916no—
941#123—798no—
942#123—798no—
943#123—7916no—
944#123—7916no—
945#123—7916no—
946C22⋊Q8—798no—
947C22⋊Q8—798no—
948C22⋊Q8—798no—
949C22⋊Q8—7916no—
950C22⋊Q8—7916no—
951C22⋊Q8—7916no—
952#121—798no—
953#121—798no—
954#121—7916no—
955#121—7916no—
956#121—7916no—
957#121—7916no—
958#121—7916no—
959#121—7916no—
960#121—7916no—
961#121—7916no—
962#121—7916no—
963#121—7916no—
964#121—7916no—
965#121—7916no—
966#121—798no—
967#121—7916no—
968#121—798no—
969#121—798no—
970#121—7916no—
971#121—7916no—
972#121—7916no—
973#121C22×D79116yescomplemented
974#121C22×D79116yescomplemented
975#120—7916no—
976#120—7916no—
977#120—7916no—
978#120—7916no—
979#120—7916no—
980#120—7916no—
981#120C22×D79116yescomplemented
982#120C22×D79116yescomplemented
983C4×Q8—798no—
984C4×Q8—798no—
985C4×Q8—798no—
986C4×D4—798no—
987C4×D4—7916no—
988C4×D4—798no—
989C4×D4—7916no—
990C4×D4—798no—
991C4×D4—798no—
992C4×D4—798no—
993C4×D4—7916no—
994C4×D4—7916no—
995C4×D4—7916no—
996C4×D4—798no—
997C4×D4—798no—
998#117—7916no—
999#117—798no—
1000#117C22×D7918yescomplemented
1001C2×C4⋊C4—791no—
1002C2×C4⋊C4—792no—
1003C2×C4⋊C4—792no—
1004C2×C4⋊C4—792no—
1005C2×C4⋊C4—7916no—
1006C2×C4⋊C4—791no—
1007C2×C4⋊C4—791no—
1008C2×C4⋊C4—791no—
1009C2×C4⋊C4—791no—
1010C2×C4⋊C4—791no—
1011C2×C4⋊C4—791no—
1012C2×C4⋊C4—791no—
1013C2×C4⋊C4—792no—
1014C2×C4⋊C4—792no—
1015C2×C4⋊C4—792no—
1016C2×C4⋊C4—792no—
1017C2×C4⋊C4—791no—
1018C2×C4⋊C4—791no—
1019C2×C4⋊C4C22×D7911yescharacteristic
1020C2×C4⋊C4C22×D7911yescharacteristic
1021C2×C22⋊C4—791no—
1022C2×C22⋊C4—792no—
1023C2×C22⋊C4—792no—
1024C2×C22⋊C4—792no—
1025C2×C22⋊C4—7916no—
1026C2×C22⋊C4—792no—
1027C2×C22⋊C4—792no—
1028C2×C22⋊C4—792no—
1029C2×C22⋊C4—791no—
1030C2×C22⋊C4—792no—
1031C2×C22⋊C4—792no—
1032C2×C22⋊C4—792no—
1033C2×C22⋊C4—791no—
1034C2×C22⋊C4—792no—
1035C2×C22⋊C4—791no—
1036C2×C22⋊C4—791no—
1037C2×C22⋊C4—791no—
1038C2×C22⋊C4—792no—
1039C2×C22⋊C4—792no—
1040C2×C22⋊C4—792no—
1041C2×C22⋊C4—792no—
1042C2×C22⋊C4—791no—
1043C2×C22⋊C4—791no—
1044C2×C22⋊C4—7916no—
1045C2×C22⋊C4C22×D7912yes—
1046C2×C22⋊C4C22×D7912yes—
1047C2×C22⋊C4C22×D7911yescharacteristic
1048C2×C22⋊C4C22×D7911yescharacteristic
1049C2×C22⋊C4C22×D7912yes—
1050C2×C22⋊C4C22×D7912yes—
1051C2×C42—791no—
1052C2×C42—792no—
1053C2×C42—792no—
1054C2×C42—791no—
1055C2×C42—791no—
1056C2×C42—791no—
1057C2×C42—798no—
1058C2×C42C22×D7911yescharacteristic
1059C2×C42C22×D7911yescharacteristic
1060C24—44no—
1061C24—44no—
1062C24—44no—
1063C24—3164no—
1064C24—3164no—
1065C24—3164no—
1066C24—798no—
1067C24—791no—
1068C24—792no—
1069C24—791no—
1070C24C23×D7912yes—
1071C24C23×D7911yescharacteristic
1072C24C23×D7912yes—
1073C24C23×D7912yes—
1074C24C23×D7918yes—
1075#41—416no—
1076#41—31616no—
1077#41—31616no—
1078#41—31632no—
1079#41—31616no—
1080#41—31632no—
1081C2×Q8—24no—
1082C2×Q8—3164no—
1083C2×Q8—798no—
1084C2×Q8—794no—
1085C2×Q8—794no—
1086C2×Q8—1584no—
1087C2×Q8—1584no—
1088C2×Q8C23×D7914yes—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—416no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—3162no—
1100C2×D4—3164no—
1101C2×D4—31616no—
1102C2×D4—3164no—
1103C2×D4—3164no—
1104C2×D4—3164no—
1105C2×D4—3164no—
1106C2×D4—3164no—
1107C2×D4—3162no—
1108C2×D4—3164no—
1109C2×D4—3164no—
1110C2×D4—3164no—
1111C2×D4—3164no—
1112C2×D4—3164no—
1113C2×D4—31632no—
1114C2×D4—798no—
1115C2×D4—794no—
1116C2×D4—798no—
1117C2×D4—798no—
1118C2×D4—798no—
1119C2×D4—798no—
1120C2×D4—798no—
1121C2×D4—798no—
1122C2×D4—798no—
1123C2×D4—798no—
1124C2×D4—798no—
1125C2×D4—794no—
1126C2×D4—798no—
1127C2×D4—794no—
1128C2×D4—798no—
1129C2×D4—794no—
1130C2×D4—1584no—
1131C2×D4—1588no—
1132C2×D4—1584no—
1133C2×D4C23×D7914yes—
1134C2×D4C23×D7914yes—
1135C2×D4C23×D7914yes—
1136C2×D4C23×D7918yes—
1137C2×D4C23×D7918yes—
1138C2×D4C23×D7918yes—
1139C2×D4C23×D7918yes—
1140C2×D4C23×D7918yes—
1141C2×D4C23×D7918yes—
1142C22×C4—24no—
1143C22×C4—44no—
1144C22×C4—3162no—
1145C22×C4—3164no—
1146C22×C4—3164no—
1147C22×C4—3164no—
1148C22×C4—3164no—
1149C22×C4—3164no—
1150C22×C4—798no—
1151C22×C4—798no—
1152C22×C4—798no—
1153C22×C4—794no—
1154C22×C4—798no—
1155C22×C4—798no—
1156C22×C4—791no—
1157C22×C4—798no—
1158C22×C4—798no—
1159C22×C4—791no—
1160C22×C4—791no—
1161C22×C4—791no—
1162C22×C4—792no—
1163C22×C4—791no—
1164C22×C4—792no—
1165C22×C4—792no—
1166C22×C4—791no—
1167C22×C4—794no—
1168C22×C4—794no—
1169C22×C4—794no—
1170C22×C4—1584no—
1171C22×C4—1588no—
1172C22×C4—1588no—
1173C22×C4—1584no—
1174C22×C4—1584no—
1175C22×C4C23×D7914yes—
1176C22×C4C23×D7911yescharacteristic
1177C22×C4C23×D7911yescharacteristic
1178C22×C4C23×D7911yescharacteristic
1179C22×C4C23×D7912yes—
1180C22×C4C23×D7911yescharacteristic
1181C22×C4C23×D7911yescharacteristic
1182C22×C4C23×D7918yes—
1183C22×C4C23×D7911yescharacteristic
1184C4⋊C4—794no—
1185C4⋊C4—798no—
1186C4⋊C4—798no—
1187C4⋊C4—798no—
1188C4⋊C4—794no—
1189C4⋊C4—794no—
1190C4⋊C4—794no—
1191C4⋊C4—794no—
1192C4⋊C4—798no—
1193C4⋊C4—798no—
1194C4⋊C4—794no—
1195C4⋊C4—794no—
1196C4⋊C4—794no—
1197C4⋊C4—794no—
1198C4⋊C4—798no—
1199C4⋊C4—798no—
1200C4⋊C4—794no—
1201C4⋊C4C23×D7914yes—
1202C4⋊C4C23×D7914yes—
1203C22⋊C4—794no—
1204C22⋊C4—798no—
1205C22⋊C4—798no—
1206C22⋊C4—798no—
1207C22⋊C4—798no—
1208C22⋊C4—798no—
1209C22⋊C4—798no—
1210C22⋊C4—794no—
1211C22⋊C4—798no—
1212C22⋊C4—798no—
1213C22⋊C4—798no—
1214C22⋊C4—794no—
1215C22⋊C4—798no—
1216C22⋊C4—794no—
1217C22⋊C4—794no—
1218C22⋊C4—794no—
1219C22⋊C4—798no—
1220C22⋊C4—798no—
1221C22⋊C4—798no—
1222C22⋊C4—798no—
1223C22⋊C4—794no—
1224C22⋊C4—794no—
1225C22⋊C4C23×D7918yes—
1226C22⋊C4C23×D7918yes—
1227C22⋊C4C23×D7914yes—
1228C22⋊C4C23×D7914yes—
1229C22⋊C4C23×D7918yes—
1230C22⋊C4C23×D7918yes—
1231C42—794no—
1232C42—794no—
1233C42—794no—
1234C42—794no—
1235C42—798no—
1236C42—798no—
1237C42C23×D7914yes—
1238C42C23×D7914yes—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23—22no—
1243C23—22no—
1244C23—24no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—24no—
1249C23—24no—
1250C23—22no—
1251C23—48no—
1252C23—48no—
1253C23—48no—
1254C23—816no—
1255C23—3168no—
1256C23—3168no—
1257C23—3168no—
1258C23—792no—
1259C23—794no—
1260C23—792no—
1261C23—63216no—
1262C23—1584no—
1263C23—1582no—
1264C23—1582no—
1265C23—1584no—
1266C23—1582no—
1267C23—1582no—
1268C23—1582no—
1269C23—1584no—
1270C23—1582no—
1271C23C24×D7914yes—
1272C23C24×D7912yes—
1273C23C24×D7914yes—
1274C23C24×D7914yes—
1275C23C24×D7911yescharacteristic
1276Q8—28no—
1277Q8—3168no—
1278Q8—1588no—
1279Q8—1588no—
1280D4—28no—
1281D4—28no—
1282D4—28no—
1283D4—48no—
1284D4—48no—
1285D4—48no—
1286D4—48no—
1287D4—48no—
1288D4—48no—
1289D4—3168no—
1290D4—3164no—
1291D4—3168no—
1292D4—3168no—
1293D4—3168no—
1294D4—3168no—
1295D4—3168no—
1296D4—3164no—
1297D4—3168no—
1298D4—3168no—
1299D4—3168no—
1300D4—3168no—
1301D4—3168no—
1302D4—1588no—
1303D4—15816no—
1304D4—1588no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—28no—
1312C2×C4—48no—
1313C2×C4—3168no—
1314C2×C4—3168no—
1315C2×C4—3164no—
1316C2×C4—3168no—
1317C2×C4—3168no—
1318C2×C4—3168no—
1319C2×C4—794no—
1320C2×C4—792no—
1321C2×C4—792no—
1322C2×C4—792no—
1323C2×C4—792no—
1324C2×C4—794no—
1325C2×C4—792no—
1326C2×C4—794no—
1327C2×C4—794no—
1328C2×C4—792no—
1329C2×C4—1588no—
1330C2×C4—15816no—
1331C2×C4—15816no—
1332C2×C4—1584no—
1333C2×C4—1582no—
1334C2×C4—1584no—
1335C2×C4—1582no—
1336C2×C4—1582no—
1337C2×C4—1584no—
1338C2×C4—1582no—
1339C2×C4—1582no—
1340C2×C4—1588no—
1341C2×C4—1588no—
1342C2×C4#1457920614yes—
1343C2×C4C24×D7912yes—
1344C2×C4C24×D7912yes—
1345C2×C4C24×D7912yes—
1346C2×C4C24×D7914yes—
1347C2×C4C24×D7912yes—
1348C2×C4C24×D7912yes—
1349C2×C4C24×D7912yes—
1350C22—24no—
1351C22—24no—
1352C22—24no—
1353C22—22no—
1354C22—22no—
1355C22—24no—
1356C22—24no—
1357C22—24no—
1358C22—24no—
1359C22—24no—
1360C22—24no—
1361C22—22no—
1362C22—44no—
1363C22—48no—
1364C22—48no—
1365C22—48no—
1366C22—816no—
1367C22—3164no—
1368C22—3168no—
1369C22—3164no—
1370C22—63216no—
1371C22—1584no—
1372C22—1582no—
1373C22—1582no—
1374C22—1584no—
1375C22—1582no—
1376C22—1582no—
1377C22—1582no—
1378C22—1584no—
1379C22—1582no—
1380C22H(5,𝔽2)×D7912yes—
1381C22C2×#1457920612yes—
1382C22#1909939812yes—
1383C22C25×D7911yescharacteristic
1384C4—22no—
1385C4—22no—
1386C4—22no—
1387C4—24no—
1388C4—22no—
1389C4—22no—
1390C4—794no—
1391C4—1584no—
1392C4—1582no—
1393C4—1584no—
1394C4—1582no—
1395C4—1582no—
1396C4—1584no—
1397C4—1582no—
1398C4—1582no—
1399C4C2×#1457920614yes—
1400C2—42no—
1401C2—44no—
1402C2—44no—
1403C2—44no—
1404C2—3162no—
1405C2—3164no—
1406C2—3162no—
1407C2#2377776114yesdirect product factor
1408C2C2×H(5,𝔽2)×D7911yescharacteristic
1409C2C22×#1457920611yescharacteristic
1410C2C2×#1909939811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#535×C79C2
socleC23×C79C25
hypercenterC2×#535D79
hypocenterC79C2×#3546
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. #23777761C2direct (N × H)
2. C2×#19099302C2semidirect
3. C2×#19099301C2semidirect
4. C2×#19099282C2semidirect
5. C2×#19099256C2semidirect
6. C2×#19099233C2semidirect
7. C2×#19099233C2semidirect
8. C2×#19099232C2semidirect
9. C2×#19099212C2semidirect
10. C2×#19099207C2semidirect
11. C2×#19099206C2semidirect
12. C2×#19099200C2semidirect
13. C2×D4×C22⋊D79C2semidirect
14. C2×#19099184C2semidirect
15. C2×#19099182C2semidirect
16. C2×#19099148C2semidirect
17. C2×#19099145C2semidirect
18. C2×#19099140C2semidirect
19. C2×#19099128C2semidirect
20. C2×#19099126C2semidirect
21. C2×#19099112C2semidirect
22. C2×#19099111C2semidirect
23. C2×#19099091C2semidirect
24. C2×#535×C79C2semidirect
25. C22×#11929625C22semidirect
26. C22×#11929623C22semidirect
27. C22×#11929623C22semidirect
28. C22×#11929623C22semidirect
29. C22×#11929623C22semidirect
32. #19099302C22semidirect
33. #19099301C22semidirect
34. #19099282C22semidirect
35. #19099256C22semidirect
36. #19099233C22semidirect
37. #19099233C22semidirect
38. #19099232C22semidirect
39. #19099212C22semidirect
40. #19099207C22semidirect
41. #19099206C22semidirect
42. #19099200C22semidirect
43. D4×C22⋊D79C22semidirect
44. #19099184C22semidirect
45. #19099182C22semidirect
46. #19099148C22semidirect
47. #19099145C22semidirect
48. #19099140C22semidirect
49. #19099128C22semidirect
50. #19099126C22semidirect
51. #19099112C22semidirect
52. #19099111C22semidirect
53. C2×#14579161C22semidirect
54. C2×#14579159C22semidirect
56. C2×#14579157C22semidirect
57. C2×#14579157C22semidirect
58. C2×#14579157C22semidirect
59. #19099091C22semidirect
60. C2×#14579156C22semidirect
61. C2×#14579156C22semidirect
62. C2×#14579154C22semidirect
63. C2×#14579154C22semidirect
64. C2×#14579154C22semidirect
65. C2×#14579154C22semidirect
66. C2×#14579151C22semidirect
67. C2×#14579149C22semidirect
69. C2×#14579148C22semidirect
71. C2×#14579147C22semidirect
72. C2×#14579147C22semidirect
73. C2×#14579146C22semidirect
74. C2×#14579145C22semidirect
75. C2×#14579144C22semidirect
76. C2×#14579143C22semidirect
77. C2×#14579143C22semidirect
78. C2×#14579143C22semidirect
79. C2×#14579142C22semidirect
80. C2×#14579142C22semidirect
81. C2×#14579140C22semidirect
82. C2×#14579139C22semidirect
83. C2×#14579139C22semidirect
84. C2×#14579138C22semidirect
85. C2×#14579138C22semidirect
86. C2×#14579137C22semidirect
88. C2×#14579135C22semidirect
90. C2×#14579134C22semidirect
91. C2×#14579134C22semidirect
92. C2×#14579134C22semidirect
95. C2×#14579133C22semidirect
96. C2×#14579133C22semidirect
97. C2×#14579133C22semidirect
98. C2×#14579133C22semidirect
99. C2×#14579133C22semidirect
100. C2×#14579133C22semidirect
101. C2×#14579133C22semidirect
104. C2×#14579132C22semidirect
105. C2×#14579132C22semidirect
106. C2×#14579132C22semidirect
107. C2×#14579132C22semidirect
108. C2×#14579131C22semidirect
110. C2×#14579130C22semidirect
112. C2×#14579129C22semidirect
113. C2×#14579129C22semidirect
114. C2×Q8×Dic79C22semidirect
115. C2×C4×Dic158C22semidirect
116. C2×C4×Dic158C22semidirect
117. C2×C4×D316C22semidirect
118. C2×C4×D316C22semidirect
120. C2×D4×Dic79C22semidirect
121. C2×D4×Dic79C22semidirect
122. C2×D4×Dic79C22semidirect
123. C2×D4×Dic79C22semidirect
125. C2×C4×C22⋊D79C22semidirect
126. C2×C4×C22⋊D79C22semidirect
127. C2×(C22⋊D79)⋊C4C22semidirect
128. C2×(C22⋊D79)⋊C4C22semidirect
129. C2×#14579118C22semidirect
130. C2×#14579117C22semidirect
131. C22×Dic79⋊C4C22semidirect
132. C22×C22⋊Dic79C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C2×C42×D79C22semidirect
135. C22×#41×C79C22semidirect
137. #535×C79C22semidirect
139. C2×#127×C79C22semidirect
141. C2×#124×C79C22semidirect
142. C2×#121×C79C22semidirect
143. C2×#121×C79C22semidirect
144. C2×#120×C79C22semidirect
145. C2×#120×C79C22semidirect
146. C2×#117×C79C22semidirect
149. C2×#11929625C23semidirect
154. C2×#11929623C23semidirect
155. C2×#11929623C23semidirect
156. C2×#11929623C23semidirect
157. C2×#11929623C23semidirect
192. #14579161C23semidirect
193. #14579159C23semidirect
195. #14579157C23semidirect
196. #14579157C23semidirect
197. #14579157C23semidirect
198. #14579156C23semidirect
199. #14579156C23semidirect
200. #14579154C23semidirect
201. #14579154C23semidirect
202. #14579154C23semidirect
203. #14579154C23semidirect
204. #14579151C23semidirect
205. #14579149C23semidirect
207. #14579148C23semidirect
209. #14579147C23semidirect
210. #14579147C23semidirect
211. #14579146C23semidirect
212. #14579145C23semidirect
213. #14579144C23semidirect
214. #14579143C23semidirect
215. #14579143C23semidirect
216. #14579143C23semidirect
217. #14579142C23semidirect
218. #14579142C23semidirect
219. #14579140C23semidirect
220. #14579139C23semidirect
221. #14579139C23semidirect
222. #14579138C23semidirect
223. #14579138C23semidirect
224. #14579137C23semidirect
226. #14579135C23semidirect
228. #14579134C23semidirect
229. #14579134C23semidirect
230. #14579134C23semidirect
233. #14579133C23semidirect
234. #14579133C23semidirect
235. #14579133C23semidirect
236. #14579133C23semidirect
237. #14579133C23semidirect
238. #14579133C23semidirect
239. #14579133C23semidirect
242. #14579132C23semidirect
243. #14579132C23semidirect
244. #14579132C23semidirect
245. #14579132C23semidirect
246. #14579131C23semidirect
248. #14579130C23semidirect
250. #14579129C23semidirect
251. #14579129C23semidirect
252. Q8×Dic79C23semidirect
253. C4×Dic158C23semidirect
254. C4×Dic158C23semidirect
255. C4×D316C23semidirect
256. C4×D316C23semidirect
258. D4×Dic79C23semidirect
259. D4×Dic79C23semidirect
260. D4×Dic79C23semidirect
261. D4×Dic79C23semidirect
263. C4×C22⋊D79C23semidirect
264. C4×C22⋊D79C23semidirect
265. (C22⋊D79)⋊C4C23semidirect
266. (C22⋊D79)⋊C4C23semidirect
267. #14579118C23semidirect
268. #14579117C23semidirect
286. C2×Dic79⋊C4C23semidirect
298. C2×C22⋊Dic79C23semidirect
310. C22⋊C4×D79C23semidirect
317. C42×D79C23semidirect
320. C2×#41×C79C23semidirect
336. #127×C79C23semidirect
338. #124×C79C23semidirect
339. #121×C79C23semidirect
340. #121×C79C23semidirect
341. #120×C79C23semidirect
342. #120×C79C23semidirect
343. #117×C79C23semidirect
699. C2×C79#3546semidirect
726. C2×#535D79semidirect
730. C79C2×#3546semidirect
736. C22×#41C2×D79semidirect
759. #535C2×D79semidirect
769. C2×#127C2×D79semidirect
785. C2×#124C2×D79semidirect
821. C2×#121C2×D79semidirect
822. C2×#121C2×D79semidirect
829. C2×#120C2×D79semidirect
830. C2×#120C2×D79semidirect
848. C2×#117C2×D79semidirect
866. C2×#41C22×D79semidirect
922. #127C22×D79semidirect
937. #124C22×D79semidirect
973. #121C22×D79semidirect
974. #121C22×D79semidirect
981. #120C22×D79semidirect
982. #120C22×D79semidirect
1000. #117C22×D79semidirect
1407. C2#23777761direct (N × H)

Maximal subgroups

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

subgroupindex
#237777612
C2×#190993022
C2×#190993012
C2×#190992822
C2×#190992562
C2×#190992332
C2×#190992322
C2×#190992122
C2×#190992072
C2×#190992062
C2×#190992002
C2×D4×C22⋊D792
C2×#190991842
C2×#190991822
C2×#190991482
C2×#190991452
C2×#190991402
C2×#190991282
C2×#190991262
C2×#190991122
C2×#190991112
C2×#190990912
C2×#535×C792
C2×#354679