Finite Group Databasebeta

← #35196818

Subgroups — #35196818

Order 20224.

11346 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099400C211yesmaximal, characteristic, complemented
2C2×#19099398C211yesmaximal, characteristic, complemented
3#23777193C211yesmaximal, characteristic, complemented
4#23777190C213yesmaximal, complemented
5#23777187C213yesmaximal, complemented
6#23777182C213yesmaximal, complemented
7#23777181C211yesmaximal, characteristic, complemented
8#23777175C213yesmaximal, complemented
9#23777174C211yesmaximal, characteristic, complemented
10#23777168C214yesmaximal, complemented
11#23777160C2112yesmaximal, complemented
12#23776889C214yesmaximal, complemented
13#23776884C2112yesmaximal, complemented
14#23776732C213yesmaximal, complemented
15#23776731C213yesmaximal, complemented
16C2×#19099112C213yesmaximal, complemented
17#532×D79C213yesmaximal, complemented
18C4×#41×D79C211yesmaximal, characteristic, complemented
19C79×#3500C211yesmaximal, characteristic, complemented
20#19099400—216no—
21#19099398—216no—
22C2×#14579209C2212yescomplemented
23C2×#14579209C2213yescomplemented
24C2×#14579208C2212yescomplemented
25C2×#14579208C2211yescharacteristic, complemented
26C2×#14579208C2213yescomplemented
27C2×#14579207C2216yescomplemented
28C2×#14579207C2211yescharacteristic, complemented
29C2×#14579207C2213yescomplemented
30C2×#14579206C2216yescomplemented
31C2×#14579206C2213yescomplemented
32C22×#11929625C2212yescomplemented
33C22×#11929625C2213yescomplemented
34C22×#11929623C2216yescomplemented
35C22×#11929623C2213yescomplemented
36C2×#41×D79C2211yescharacteristic
37C2×#41×D79C2216yescomplemented
38C2×#41×D79C2212yescomplemented
39C2×#41×D79C2213yescomplemented
40C2×#41×D79C2213yescomplemented
41#19099232C2214yescomplemented
42#19099231C22112yescomplemented
43Q8×C22⋊D79C2214yescomplemented
44#19099226C22112yescomplemented
45#19099225C2214yescomplemented
46#19099222C22112yescomplemented
47#19099221C22112yescomplemented
48#19099215C22112yescomplemented
49#19099212C22112yescomplemented
50#19099211C22124yescomplemented
51#19099209C22112yescomplemented
52#19099208C22112yescomplemented
53#19099206C22112yescomplemented
54#19099203C22124yescomplemented
55#19099202C22124yescomplemented
56#19099197C22112yescomplemented
57D4×C22⋊D79C22112yescomplemented
58#19099195C22124yescomplemented
59#19099143C22112yescomplemented
60#19099142C22112yescomplemented
61#19099139C2213yescomplemented
62#19099138C2216yescomplemented
63#19099137C2213yescomplemented
64#19099134C2213yescomplemented
65#19099133C2216yescomplemented
66#19099132C2213yescomplemented
67#19099131C2216yescomplemented
68#19099130C2213yescomplemented
69#19099127C2213yescomplemented
70#19099126C2216yescomplemented
71#19099124C22112yescomplemented
72#19099123C22112yescomplemented
73#19099114C2213yescomplemented
74#19099113C2213yescomplemented
75#19099112C22112yescomplemented
76#19099112C22112yescomplemented
77#19099112C2216yescomplemented
78#19099112C2216yescomplemented
79#19099112C2211yescharacteristic, complemented
80#19099112C2213yescomplemented
81#19099112C2216yescomplemented
82#19099111C2213yescomplemented
83#19099110C22112yescomplemented
84#19099109C2213yescomplemented
85#19099109C2213yescomplemented
86#19099108C22112yescomplemented
87C2×#14579159C2213yescomplemented
88C4⋊Q8×D79C2213yescomplemented
89C2×#14579157C2213yescomplemented
90#127×D79C2213yescomplemented
91C2×#14579149C2213yescomplemented
92#124×D79C2213yescomplemented
93#124×D79C2213yescomplemented
94#19099076C22112yescomplemented
95#19099073C22112yescomplemented
96#19099071C22112yescomplemented
97#19099069C22112yescomplemented
98C2×#14579134C22112yescomplemented
99#121×D79C22112yescomplemented
100#41×Dic79C2211yescharacteristic, complemented
101C4×#11929625C2212yescomplemented
102C4×#11929624C2213yescomplemented
103#19099031C2213yescomplemented
104C4×#11929623C2216yescomplemented
105C4×Q8×D79C2212yescomplemented
106C2×(C22⋊D79)⋊C4C22112yescomplemented
107C4×D4×D79C2216yescomplemented
108C4×D4×D79C22112yescomplemented
109#117×D79C2213yescomplemented
110C2×C42×D79C2213yescomplemented
111C2×2−1+4×C79C2211yescharacteristic, complemented
112C2×H(5,𝔽2)×C79C2211yescharacteristic, complemented
113#548×C79C2214yescomplemented
114#546×C79C22112yescomplemented
115#536×C79C2213yescomplemented
116#535×C79C2213yescomplemented
117#532×C79C2213yescomplemented
118C2×#124×C79C2213yescomplemented
119C4×#41×C79C2211yescharacteristic, complemented
120#14579209—224no—
121#14579209—216no—
122#14579208—28no—
123#14579208—224no—
124#14579208—216no—
125#14579207—28no—
126#14579207—224no—
127#14579207—248no—
128#14579206—224no—
129#14579206—248no—
130C2×#11929625—216no—
131C2×#11929625—224no—
132C2×#11929625C2316yes—
133C2×#11929625C2316yes—
134C2×#11929625C2316yes—
135C2×#11929625C2312yes—
136C2×#11929625C2316yes—
137C2×#11929625C2313yes—
138C2×#11929625C2311yescharacteristic
139C2×#11929625C2311yescharacteristic
140C2×#11929624C2313yes—
141C2×#11929624C2316yes—
142C2×#11929624C2316yes—
143C2×#11929624C2313yes—
144C2×#11929624C2316yes—
145C2×#11929624C23112yes—
146C2×#11929624C2316yes—
147C2×#11929624C2313yes—
148C2×#11929623—248no—
149C2×#11929623—224no—
150C2×#11929623C2316yes—
151C2×#11929623C23112yes—
152C2×#11929623C2316yes—
153C2×#11929623C2316yes—
154C2×#11929623C2316yes—
155C2×#11929623C2316yes—
156C2×#11929623C2316yes—
157C2×#11929623C2316yes—
158C2×#11929623C2311yescharacteristic
159C2×#11929623C2313yes—
160C2×#11929623C2313yes—
161#41×D79—216no—
162#41×D79—248no—
163#41×D79—224no—
164#41×D79—224no—
165#41×D79D4116yescomplemented
166C22×Dic158C2313yes—
167C22×Dic158C2316yes—
168C2×Q8×D79C2313yes—
169C2×Q8×D79C2312yes—
170C2×Q8×D79C2316yes—
171C2×Q8×D79C2313yes—
172C2×Q8×D79C2311yescharacteristic
173C22×D316C2316yes—
174C22×D316C2316yes—
175C22×D316C2313yes—
176C22×C22⋊D79C23112yes—
177C22×C22⋊D79C2316yes—
178C22×C22⋊D79C23112yes—
179C2×D4×D79C2316yes—
180C2×D4×D79C2316yes—
181C2×D4×D79C2313yes—
182C2×D4×D79C23112yes—
183C2×D4×D79C2316yes—
184C2×D4×D79C2316yes—
185C2×D4×D79C2313yes—
186C2×D4×D79C23112yes—
187C2×D4×D79C2313yes—
188C23×Dic79C2316yes—
189C22×C4×D79C2316yes—
190C22×C4×D79C2316yes—
191C22×C4×D79C2316yes—
192C22×C4×D79C2316yes—
193C22×C4×D79C2313yes—
194#14579161C2313yes—
195#14579160C23112yes—
196#14579159C2316yes—
197#14579159C23112yes—
198#14579159C2311yescharacteristic
199#14579159C2313yes—
200#14579158C2313yes—
201#14579157C23112yes—
202#14579157C23112yes—
203#14579157C2311yescharacteristic
204#14579157C2313yes—
205#14579157C2316yes—
206#14579150C2313yes—
207#14579150C2313yes—
208#14579149C2316yes—
209#14579149C23112yes—
210#14579149C2311yescharacteristic
211#14579149C2313yes—
212#14579148C2313yes—
213#14579148C2313yes—
214#14579147C23112yes—
215#14579147C23112yes—
216#14579146C23124yes—
217#14579145C23112yes—
218#14579144C23112yes—
219#14579143C23124yes—
220#14579142C23112yes—
221#14579141C23112yes—
222#14579140C23112yes—
223#14579139C23124yes—
224#14579138C23124yes—
225#14579137C23112yes—
226#14579136C23112yes—
227#14579136C23112yes—
228#14579135C23112yes—
229#14579135C23112yes—
230#14579134C23124yes—
231#14579134C23124yes—
232#14579134C23124yes—
233#14579134C23124yes—
234#14579134C2314yes—
235#14579134C23112yes—
236#14579133C23124yes—
237#14579133C23112yes—
238#14579133C23112yes—
239#14579132C23112yes—
240#14579132C23112yes—
241#14579131C23112yes—
242#14579131C23124yes—
243#14579130C23112yes—
244#14579129C23124yes—
245#14579129C23112yes—
246Q8×Dic79C2312yes—
247C4×Dic158C2316yes—
248#14579126C2316yes—
249C4×D316C2316yes—
250C4×D316C23112yes—
251D4×Dic79C2316yes—
252D4×Dic79C23112yes—
253#14579123C2316yes—
254#14579123C23112yes—
255C4×C22⋊D79C23112yes—
256C4×C22⋊D79C23112yes—
257C4×C22⋊D79C23112yes—
258(C22⋊D79)⋊C4C23112yes—
259(C22⋊D79)⋊C4C23124yes—
260(C22⋊D79)⋊C4C23124yes—
261(C22⋊D79)⋊C4C2314yes—
262(C22⋊D79)⋊C4C23112yes—
263(C22⋊D79)⋊C4C23124yes—
264#14579120C2313yes—
265#14579119C2316yes—
266#14579118C2316yes—
267#14579117C2316yes—
268C2×Dic79⋊C4C23112yes—
269C4⋊C4×D79C2316yes—
270C4⋊C4×D79C23112yes—
271C2×(C2×D79)⋊C4C23112yes—
272C22⋊C4×D79C23112yes—
273C22⋊C4×D79C23112yes—
274C22⋊C4×D79C2316yes—
275C2×C4×Dic79C2316yes—
276C2×C4×Dic79C2313yes—
277C42×D79C2311yescharacteristic
278C42×D79C2313yes—
279C42×D79C2316yes—
280C42×D79C2316yes—
281C42×D79C2313yes—
282C42×D79C2313yes—
2832−1+4×C79—28no—
284H(5,𝔽2)×C79—28no—
285C2×#41×C79C2316yes—
286C2×#41×C79C2313yes—
287C2×#41×C79C2312yes—
288C2×#41×C79C2313yes—
289C2×#41×C79C2311yescharacteristic
290C22×Q8×C79C2313yes—
291C22×Q8×C79C2312yes—
292C22×D4×C79C2316yes—
293C22×D4×C79C2313yes—
294C4⋊Q8×C79C2313yes—
295#127×C79C2313yes—
296#124×C79C23112yes—
297#124×C79C2313yes—
298#124×C79C2316yes—
299#124×C79C2311yescharacteristic
300#123×C79C23112yes—
301C22⋊Q8×C79C23112yes—
302#121×C79C23112yes—
303#121×C79C23112yes—
304#120×C79C23112yes—
305C4×Q8×C79C2312yes—
306C4×D4×C79C2316yes—
307C4×D4×C79C23112yes—
308#117×C79C2313yes—
309C2×C22⋊C4×C79C23112yes—
310C2×C42×C79C2313yes—
311C23×D79C2416yes—
312C23×D79C2416yes—
313C23×D79C2416yes—
314C23×D79C2413yes—
315#11929625—224no—
316#11929625—24no—
317#11929625—224no—
318#11929625—212no—
319#11929625—224no—
320#11929625—224no—
321#11929625—28no—
322#11929625C2×D418yescomplemented
323#11929624—224no—
324#11929624—224no—
325#11929624—224no—
326#11929624—224no—
327#11929624—212no—
328#11929624—212no—
329#11929624—248no—
330#11929624C2×D4124yescomplemented
331#11929623—224no—
332#11929623—224no—
333#11929623—24no—
334#11929623—224no—
335#11929623—212no—
336#11929623—224no—
337#11929623—224no—
338#11929623—224no—
339#11929623—224no—
340#11929623—248no—
341#11929623C2×D4124yescomplemented
342C2×Dic158—224no—
343C2×Dic158—212no—
344C2×Dic158C2416yes—
345C2×Dic158C2411yescharacteristic
346C2×Dic158C2416yes—
347C2×Dic158C2416yes—
348C2×Dic158C2413yes—
349C2×Dic158C2413yes—
350Q8×D79—212no—
351Q8×D79—212no—
352Q8×D79—224no—
353Q8×D79—28no—
354Q8×D79C2×D418yescomplemented
355C2×D316—224no—
356C2×D316—224no—
357C2×D316—212no—
358C2×D316C2412yes—
359C2×D316C2411yescharacteristic
360C2×D316C24112yes—
361C2×D316C2416yes—
362C2×D316C2416yes—
363C2×D316C2413yes—
364C2×D316C24112yes—
365C2×D316C2413yes—
366C2×C22⋊D79—224no—
367C2×C22⋊D79—248no—
368C2×C22⋊D79—424no—
369C2×C22⋊D79C24112yes—
370C2×C22⋊D79C2416yes—
371C2×C22⋊D79C2416yes—
372C2×C22⋊D79C2416yes—
373C2×C22⋊D79C2416yes—
374C2×C22⋊D79C2412yes—
375C2×C22⋊D79C2416yes—
376C2×C22⋊D79C24112yes—
377C2×C22⋊D79C2414yes—
378C2×C22⋊D79C24124yes—
379C2×C22⋊D79C2416yes—
380D4×D79—224no—
381D4×D79—212no—
382D4×D79—212no—
383D4×D79—224no—
384D4×D79—224no—
385D4×D79—224no—
386D4×D79—248no—
387D4×D79—424no—
388D4×D79C2×D4124yescomplemented
389C22×Dic79—224no—
390C22×Dic79C2416yes—
391C22×Dic79C24112yes—
392C22×Dic79C2416yes—
393C22×Dic79C2412yes—
394C22×Dic79C2416yes—
395C22×Dic79C2413yes—
396C2×C4×D79—224no—
397C2×C4×D79—224no—
398C2×C4×D79—224no—
399C2×C4×D79—412no—
400C2×C4×D79C2×D4124yescomplemented
401C2×C4×D79C2416yes—
402C2×C4×D79C2416yes—
403C2×C4×D79C2416yes—
404C2×C4×D79C24112yes—
405C2×C4×D79C2416yes—
406C2×C4×D79C2412yes—
407C2×C4×D79C2416yes—
408C2×C4×D79C2412yes—
409C2×C4×D79C2416yes—
410C2×C4×D79C2416yes—
411C2×C4×D79C2416yes—
412C2×C4×D79C2413yes—
413C2×C4×D79C2413yes—
414C2×C4×D79C2411yescharacteristic
415C2×C4×D79C2413yes—
416C4⋊Dic79C2416yes—
417C4⋊Dic79C24112yes—
418Dic79⋊C4C2414yes—
419Dic79⋊C4C24112yes—
420Dic79⋊C4C24112yes—
421Dic79⋊C4C24124yes—
422C22⋊Dic79C2416yes—
423C22⋊Dic79C24112yes—
424C22⋊Dic79C24112yes—
425(C2×D79)⋊C4C2414yes—
426(C2×D79)⋊C4C24112yes—
427(C2×D79)⋊C4C24112yes—
428(C2×D79)⋊C4C24112yes—
429(C2×D79)⋊C4C24112yes—
430(C2×D79)⋊C4C24124yes—
431C4×Dic79C2412yes—
432C4×Dic79C2411yescharacteristic
433C4×Dic79C2416yes—
434C4×Dic79C2413yes—
435C4×Dic79C2416yes—
436C4×Dic79C2416yes—
437C4×Dic79C2416yes—
438C24×C79C2416yes—
439#41×C79—28no—
440#41×C79—224no—
441#41×C79—212no—
442#41×C79—212no—
443#41×C79C2×D418yescomplemented
444C2×Q8×C79—28no—
445C2×Q8×C79—212no—
446C2×Q8×C79C2411yescharacteristic
447C2×Q8×C79C2416yes—
448C2×Q8×C79C2413yes—
449C2×Q8×C79C2411yescharacteristic
450C2×D4×C79—224no—
451C2×D4×C79—212no—
452C2×D4×C79C2416yes—
453C2×D4×C79C2416yes—
454C2×D4×C79C2413yes—
455C2×D4×C79C2416yes—
456C2×D4×C79C2411yescharacteristic
457C2×D4×C79C24112yes—
458C2×D4×C79C2413yes—
459C22×C4×C79C2416yes—
460C22×C4×C79C2416yes—
461C22×C4×C79C2416yes—
462C22×C4×C79C2416yes—
463C22×C4×C79C2413yes—
464C4⋊C4×C79C2416yes—
465C4⋊C4×C79C24112yes—
466C22⋊C4×C79C24112yes—
467C22⋊C4×C79C24124yes—
468C22⋊C4×C79C2416yes—
469C22⋊C4×C79C2414yes—
470C42×C79C2411yescharacteristic
471C42×C79C2413yes—
472C42×C79C2416yes—
473C23×C79—212no—
474C23×C79—412no—
475C23×C79C2512yes—
476C23×C79C2516yes—
477C23×C79C2513yes—
478C22×D79—212no—
479C22×D79—212no—
480C22×D79—212no—
481C22×D79—46no—
482C22×D79—412no—
483C22×D79—412no—
484C22×D79—412no—
485C22×D79C22×D4112yes—
486C22×D79C2512yes—
487C22×D79C2516yes—
488C22×D79C2513yes—
489C22×D79C2511yescharacteristic
490Q8×C79—22no—
491Q8×C79—212no—
492Q8×C79—26no—
493Q8×C79C22×D414yes—
494D4×C79—212no—
495D4×C79—212no—
496D4×C79—22no—
497D4×C79—212no—
498D4×C79—26no—
499D4×C79—412no—
500D4×C79C22×D4112yes—
501C2×C4×C79—212no—
502C2×C4×C79—212no—
503C2×C4×C79—212no—
504C2×C4×C79—46no—
505C2×C4×C79C22×D4112yes—
506C2×C4×C79C2512yes—
507C2×C4×C79C2516yes—
508C2×C4×C79C2512yes—
509C2×C4×C79C2516yes—
510C2×C4×C79C2511yescharacteristic
511C2×C4×C79C2513yes—
512C22⋊D79—212no—
513C22⋊D79—212no—
514C22⋊D79—24no—
515C22⋊D79—212no—
516C22⋊D79—224no—
517C22⋊D79—212no—
518C22⋊D79—212no—
519C22⋊D79—28no—
520C22⋊D79—224no—
521C22⋊D79—424no—
522C22⋊D79C22×D4124yes—
523C2×Dic79—212no—
524C2×Dic79—24no—
525C2×Dic79—212no—
526C2×Dic79—224no—
527C2×Dic79—212no—
528C2×Dic79C22×D4112yes—
529C2×Dic79C2516yes—
530C2×Dic79C2516yes—
531C2×Dic79C2512yes—
532C2×Dic79C2511yescharacteristic
533C2×Dic79C2513yes—
534C2×Dic79C2512yes—
535D316—24no—
536D316—212no—
537D316—224no—
538D316—22no—
539D316—212no—
540D316—26no—
541D316—412no—
542D316C22×D4112yes—
543C4×D79—212no—
544C4×D79—212no—
545C4×D79—212no—
546C4×D79—212no—
547C4×D79—24no—
548C4×D79—212no—
549C4×D79—224no—
550C4×D79—24no—
551C4×D79—212no—
552C4×D79—46no—
553C4×D79—46no—
554C4×D79C22×D4112yes—
555C4×D79C22×D414yes—
556C4×D79C22×D4112yes—
557C4×D79C22×D4112yes—
558Dic158—22no—
559Dic158—212no—
560Dic158—26no—
561Dic158—212no—
562Dic158—212no—
563Dic158C22×D4112yes—
564C22×C79—26no—
565C22×C79—22no—
566C22×C79—26no—
567C22×C79—212no—
568C22×C79—24no—
569C22×C79—812no—
570C22×C79C23×D416yes—
571C22×C79C2611yescharacteristic
572C2×D79—26no—
573C2×D79—22no—
574C2×D79—22no—
575C2×D79—26no—
576C2×D79—212no—
577C2×D79—24no—
578C2×D79—412no—
579C2×D79—812no—
580C2×D79—812no—
581C2×D79—812no—
582C2×D79C23×D412yes—
583C2×D79C23×D416yes—
584C4×C79—22no—
585C4×C79—26no—
586C4×C79—22no—
587C4×C79—26no—
588C4×C79C23×D416yes—
589C4×C79C23×D412yes—
590Dic79—22no—
591Dic79—26no—
592Dic79—26no—
593Dic79C23×D416yes—
594Dic79C23×D412yes—
595Dic79#58514yescomplemented
596#62812—791nomaximal, Sylow
597C2×C79—26no—
598C2×C79—42no—
599C2×C79—46no—
600C2×C79C24×D411yescharacteristic
601C2×C79C2×#58512yes—
602D79—22no—
603D79—26no—
604D79—42no—
605D79—46no—
606C2×#585—791no—
607C2×#585—791no—
608#3500—793no—
609#3500—793no—
610#3500—791no—
611#3500D7911yescharacteristic, complemented
612#3499—791no—
613#3499—793no—
614#3498—791no—
615#3498—793no—
616#3497—794no—
617#3496—7912no—
618D4×#41—794no—
619D4×#41—7912no—
620#3449—793no—
621#3449—793no—
622C2×#532—793no—
623C2×#532—793no—
624C2×C4×#41—791no—
625C79#6281211yescharacteristic, complemented, Sylow
626#585—15816no—
627#585—15816no—
628C2×2−1+4—792no—
629C2×2−1+4—793no—
630C2×2−1+4—791no—
631C2×2−1+4—792no—
632C2×2−1+4—793no—
633C2×2−1+4C2×D7911yescharacteristic, complemented
634C2×H(5,𝔽2)—796no—
635C2×H(5,𝔽2)—793no—
636C2×H(5,𝔽2)—791no—
637C2×H(5,𝔽2)—796no—
638C2×H(5,𝔽2)—793no—
639C2×H(5,𝔽2)C2×D7911yescharacteristic, complemented
640C22×#41—791no—
641C22×#41—793no—
642C22×#41—793no—
643C22×#41—792no—
644C22×#41—796no—
645C22×#41—793no—
646C22×#41—792no—
647C22×#41—793no—
648C22×#41—796no—
649#550—794no—
650#550—7912no—
651D4×Q8—794no—
652D4×Q8—7912no—
653#548—7912no—
654#548—794no—
655#548—7912no—
656#548C2×D7914yescomplemented
657#547—7912no—
658#547—7924no—
659#547—7912no—
660#546—7912no—
661#546—7924no—
662#546—7912no—
663#546—7912no—
664#546—7924no—
665#546C2×D79112yescomplemented
666D42—7912no—
667D42—7912no—
668D42—7924no—
669#537—7912no—
670#537—7912no—
671#536—793no—
672#536—793no—
673#536—796no—
674#536—796no—
675#536—793no—
676#536C2×D7913yescomplemented
677#535—793no—
678#535—793no—
679#535—796no—
680#535—796no—
681#535—793no—
682#535C2×D7913yescomplemented
683#534—7912no—
684#534—7912no—
685#532—793no—
686#532—793no—
687#532—793no—
688#532—793no—
689#532—791no—
690#532—793no—
691#532—796no—
692#532—7912no—
693#532—7912no—
694#532—796no—
695#532—796no—
696#532—7912no—
697#532—7912no—
698#532—793no—
699#532C2×D7913yescomplemented
700C2×C4⋊Q8—793no—
701C2×C4⋊Q8—793no—
702C2×#127—793no—
703C2×#127—793no—
704C2×#124—793no—
705C2×#124—793no—
706C2×#124—793no—
707C2×#124C2×D7913yescomplemented
708#525—7912no—
709#525—7912no—
710#525—7912no—
711#525—7912no—
712C2×#121—7912no—
713C2×#121—7912no—
714C4×#41—791no—
715C4×#41—792no—
716C4×#41—796no—
717C4×#41—793no—
718C4×#41—793no—
719C4×#41C2×D7911yescharacteristic, complemented
720C2×C4×Q8—792no—
721C2×C4×D4—796no—
722C2×C4×D4—7912no—
723C2×C4×D4—7912no—
724C2×#117—793no—
725C22×C42—793no—
7262−1+4—28no—
7272−1+4—15816no—
7282−1+4—15824no—
7292−1+4—15816no—
7302−1+4—15824no—
7312−1+4—1588no—
732H(5,𝔽2)—28no—
733H(5,𝔽2)—15848no—
734H(5,𝔽2)—15824no—
735H(5,𝔽2)—15848no—
736H(5,𝔽2)—15824no—
737H(5,𝔽2)—1588no—
738C2×#41—7916no—
739C2×#41—791no—
740C2×#41—796no—
741C2×#41—791no—
742C2×#41—793no—
743C2×#41—796no—
744C2×#41—796no—
745C2×#41—796no—
746C2×#41—792no—
747C2×#41—793no—
748C2×#41—796no—
749C2×#41—796no—
750C2×#41—796no—
751C2×#41—791no—
752C2×#41—793no—
753C2×#41—796no—
754C2×#41—796no—
755C2×#41—796no—
756C2×#41—7912no—
757C2×#41—796no—
758C2×#41—793no—
759C2×#41—793no—
760C2×#41—793no—
761C2×#41—796no—
762C2×#41—796no—
763C2×#41—796no—
764C2×#41—7912no—
765C2×#41—796no—
766C2×#41—15824no—
767C2×#41—15824no—
768C2×#41—15824no—
769C2×#41—15824no—
770C2×#41—15848no—
771C2×#41—15816no—
772C2×#41—15816no—
773C2×#41—15848no—
774C2×#41C22×D7913yes—
775C2×#41C22×D7913yes—
776C2×#41C22×D7916yes—
777C2×#41C22×D7912yes—
778C2×#41C22×D7911yescharacteristic
779C22×Q8—791no—
780C22×Q8—793no—
781C22×Q8—793no—
782C22×Q8—796no—
783C22×Q8—792no—
784C22×Q8—793no—
785C22×Q8—796no—
786C22×Q8C22×D7913yes—
787C22×Q8C22×D7912yes—
788C22×D4—7912no—
789C22×D4—7912no—
790C22×D4—793no—
791C22×D4—796no—
792C22×D4—7912no—
793C22×D4—796no—
794C22×D4—796no—
795C22×D4—793no—
796C22×D4—793no—
797C22×D4—7912no—
798C22×D4—796no—
799C22×D4—796no—
800C22×D4—796no—
801C22×D4—793no—
802C22×D4—796no—
803C22×D4C22×D7913yes—
804C22×D4C22×D7916yes—
805C23×C4—796no—
806C23×C4—793no—
807C23×C4—796no—
808C23×C4—796no—
809C23×C4—796no—
810C23×C4—796no—
811C4⋊Q8—791no—
812C4⋊Q8—793no—
813C4⋊Q8—796no—
814C4⋊Q8—7912no—
815C4⋊Q8—7912no—
816C4⋊Q8—793no—
817C4⋊Q8C22×D7913yes—
818#127—791no—
819#127—793no—
820#127—796no—
821#127—7912no—
822#127—7912no—
823#127—793no—
824#127C22×D7913yes—
825#124—793no—
826#124—793no—
827#124—793no—
828#124—793no—
829#124—7912no—
830#124—7912no—
831#124—791no—
832#124—793no—
833#124—796no—
834#124—7912no—
835#124C22×D7911yescharacteristic
836#124C22×D7913yes—
837#124C22×D7916yes—
838#124C22×D79112yes—
839#123—7912no—
840#123—7912no—
841#123—7924no—
842#123—7924no—
843#123—7912no—
844#123C22×D79112yes—
845C22⋊Q8—7912no—
846C22⋊Q8—7912no—
847C22⋊Q8—7924no—
848C22⋊Q8—7912no—
849C22⋊Q8—7924no—
850C22⋊Q8C22×D79112yes—
851#121—7912no—
852#121—7912no—
853#121—7912no—
854#121—7912no—
855#121—7924no—
856#121—7912no—
857#121—7912no—
858#121—7912no—
859#121—7912no—
860#121—794no—
861#121—7912no—
862#121—7924no—
863#121—7924no—
864#121—7924no—
865#121—7924no—
866#121C22×D79112yes—
867#121C22×D79112yes—
868#120—7912no—
869#120—7912no—
870#120—7924no—
871#120—7924no—
872#120—7912no—
873#120C22×D79112yes—
874C4×Q8—792no—
875C4×Q8—796no—
876C4×Q8—796no—
877C4×Q8C22×D7912yes—
878C4×D4—796no—
879C4×D4—7912no—
880C4×D4—7912no—
881C4×D4—7912no—
882C4×D4—7912no—
883C4×D4—796no—
884C4×D4—7912no—
885C4×D4—794no—
886C4×D4—7912no—
887C4×D4—7912no—
888C4×D4—7924no—
889C4×D4—7924no—
890C4×D4—7924no—
891C4×D4—796no—
892C4×D4—7912no—
893C4×D4C22×D7916yes—
894C4×D4C22×D79112yes—
895#117—793no—
896#117—796no—
897#117—796no—
898#117—796no—
899#117C22×D7913yes—
900C2×C4⋊C4—7912no—
901C2×C4⋊C4—796no—
902C2×C4⋊C4—7912no—
903C2×C22⋊C4—7912no—
904C2×C22⋊C4—796no—
905C2×C22⋊C4—7912no—
906C2×C22⋊C4—7912no—
907C2×C22⋊C4C22×D79112yes—
908C2×C42—796no—
909C2×C42—793no—
910C2×C42—793no—
911C2×C42—796no—
912C2×C42—796no—
913C2×C42—793no—
914C2×C42—793no—
915C2×C42—791no—
916C2×C42C22×D7913yes—
917C24—793no—
918C24—796no—
919C24—796no—
920C24—796no—
921C24C23×D7916yes—
922#41—28no—
923#41—224no—
924#41—212no—
925#41—212no—
926#41—798no—
927#41—7924no—
928#41—7924no—
929#41—15824no—
930#41—15824no—
931#41—15848no—
932#41—15824no—
933#41—15824no—
934#41—15824no—
935#41—15824no—
936#41—15812no—
937#41—1584no—
938#41—15824no—
939#41—15824no—
940#41—15824no—
941#41—15812no—
942#41—1584no—
943#41—15824no—
944#41—15824no—
945#41—15824no—
946#41—15848no—
947#41—15824no—
948#41—15824no—
949#41—1588no—
950#41—15824no—
951#41—15812no—
952#41—15812no—
953#41D4×D7918yescomplemented
954C2×Q8—28no—
955C2×Q8—212no—
956C2×Q8—798no—
957C2×Q8—793no—
958C2×Q8—796no—
959C2×Q8—796no—
960C2×Q8—796no—
961C2×Q8—791no—
962C2×Q8—793no—
963C2×Q8—15824no—
964C2×Q8—15812no—
965C2×Q8—15812no—
966C2×Q8—15824no—
967C2×Q8—1588no—
968C2×Q8—15812no—
969C2×Q8C23×D7916yes—
970C2×Q8C23×D7911yescharacteristic
971C2×Q8C23×D7913yes—
972C2×Q8C23×D7911yescharacteristic
973C2×D4—224no—
974C2×D4—212no—
975C2×D4—31624no—
976C2×D4—31624no—
977C2×D4—7924no—
978C2×D4—796no—
979C2×D4—7924no—
980C2×D4—794no—
981C2×D4—7912no—
982C2×D4—7912no—
983C2×D4—796no—
984C2×D4—796no—
985C2×D4—792no—
986C2×D4—796no—
987C2×D4—796no—
988C2×D4—796no—
989C2×D4—7912no—
990C2×D4—793no—
991C2×D4—7912no—
992C2×D4—792no—
993C2×D4—796no—
994C2×D4—796no—
995C2×D4—791no—
996C2×D4—793no—
997C2×D4—15824no—
998C2×D4—15824no—
999C2×D4—15812no—
1000C2×D4—15812no—
1001C2×D4—15848no—
1002C2×D4—15824no—
1003C2×D4—15824no—
1004C2×D4—15824no—
1005C2×D4—15848no—
1006C2×D4—15824no—
1007C2×D4—15824no—
1008C2×D4—15812no—
1009C2×D4C23×D7916yes—
1010C2×D4C23×D7916yes—
1011C2×D4C23×D7916yes—
1012C2×D4C23×D7911yescharacteristic
1013C2×D4C23×D7913yes—
1014C2×D4C23×D79112yes—
1015C2×D4C23×D7913yes—
1016C22×C4—31612no—
1017C22×C4—796no—
1018C22×C4—796no—
1019C22×C4—793no—
1020C22×C4—791no—
1021C22×C4—793no—
1022C22×C4—793no—
1023C22×C4—793no—
1024C22×C4—7924no—
1025C22×C4—796no—
1026C22×C4—796no—
1027C22×C4—792no—
1028C22×C4—796no—
1029C22×C4—7912no—
1030C22×C4—792no—
1031C22×C4—796no—
1032C22×C4—796no—
1033C22×C4—796no—
1034C22×C4—792no—
1035C22×C4—796no—
1036C22×C4—7912no—
1037C22×C4—796no—
1038C22×C4—796no—
1039C22×C4—15824no—
1040C22×C4—15824no—
1041C22×C4—15824no—
1042C22×C4—15824no—
1043C22×C4C23×D7916yes—
1044C22×C4C23×D7916yes—
1045C22×C4C23×D7916yes—
1046C22×C4C23×D7916yes—
1047C22×C4C23×D7913yes—
1048C4⋊C4—794no—
1049C4⋊C4—7912no—
1050C4⋊C4—7912no—
1051C4⋊C4—7924no—
1052C4⋊C4—796no—
1053C4⋊C4—7912no—
1054C4⋊C4C23×D7916yes—
1055C4⋊C4C23×D79112yes—
1056C22⋊C4—796no—
1057C22⋊C4—7912no—
1058C22⋊C4—7912no—
1059C22⋊C4—794no—
1060C22⋊C4—7912no—
1061C22⋊C4—7912no—
1062C22⋊C4—7912no—
1063C22⋊C4—7912no—
1064C22⋊C4—7924no—
1065C22⋊C4C23×D7914yes—
1066C22⋊C4C23×D79112yes—
1067C22⋊C4C23×D7916yes—
1068C22⋊C4C23×D79124yes—
1069C42—792no—
1070C42—791no—
1071C42—796no—
1072C42—793no—
1073C42—796no—
1074C42—796no—
1075C42—796no—
1076C42C23×D7911yescharacteristic
1077C42C23×D7913yes—
1078C42C23×D7916yes—
1079C23—212no—
1080C23—412no—
1081C23—3166no—
1082C23—31612no—
1083C23—31612no—
1084C23—31612no—
1085C23—7912no—
1086C23—793no—
1087C23—791no—
1088C23—796no—
1089C23—792no—
1090C23—15812no—
1091C23—15812no—
1092C23—15812no—
1093C23C24×D7912yes—
1094C23C24×D7916yes—
1095C23C24×D7913yes—
1096Q8—212no—
1097Q8—26no—
1098Q8—22no—
1099Q8—7912no—
1100Q8—15812no—
1101Q8—15812no—
1102Q8—15812no—
1103Q8—1582no—
1104Q8—1586no—
1105Q8C2×D4×D7914yes—
1106D4—212no—
1107D4—212no—
1108D4—212no—
1109D4—26no—
1110D4—22no—
1111D4—412no—
1112D4—31612no—
1113D4—31624no—
1114D4—7924no—
1115D4—7912no—
1116D4—1584no—
1117D4—15812no—
1118D4—15824no—
1119D4—1588no—
1120D4—15824no—
1121D4—15812no—
1122D4—15812no—
1123D4—1584no—
1124D4—15812no—
1125D4—15824no—
1126D4—15812no—
1127D4—15812no—
1128D4—15812no—
1129D4—1582no—
1130D4—1586no—
1131D4C2×D4×D79112yes—
1132C2×C4—212no—
1133C2×C4—212no—
1134C2×C4—212no—
1135C2×C4—46no—
1136C2×C4—3166no—
1137C2×C4—3166no—
1138C2×C4—792no—
1139C2×C4—791no—
1140C2×C4—793no—
1141C2×C4—7912no—
1142C2×C4—794no—
1143C2×C4—7912no—
1144C2×C4—7912no—
1145C2×C4—7912no—
1146C2×C4—796no—
1147C2×C4—792no—
1148C2×C4—796no—
1149C2×C4—1584no—
1150C2×C4—15812no—
1151C2×C4—1584no—
1152C2×C4—15812no—
1153C2×C4—15824no—
1154C2×C4—15812no—
1155C2×C4—15812no—
1156C2×C4—15812no—
1157C2×C4—1584no—
1158C2×C4—15812no—
1159C2×C4—15824no—
1160C2×C4—15812no—
1161C2×C4—15812no—
1162C2×C4—15812no—
1163C2×C4C2×D4×D79112yes—
1164C2×C4C24×D7912yes—
1165C2×C4C24×D7916yes—
1166C2×C4C24×D7912yes—
1167C2×C4C24×D7916yes—
1168C2×C4C24×D7911yescharacteristic
1169C2×C4C24×D7913yes—
1170C22—26no—
1171C22—22no—
1172C22—26no—
1173C22—24no—
1174C22—212no—
1175C22—812no—
1176C22—31612no—
1177C22—792no—
1178C22—796no—
1179C22—63212no—
1180C22—63212no—
1181C22—63212no—
1182C22—1586no—
1183C22—1582no—
1184C22—1584no—
1185C22—15812no—
1186C22—1582no—
1187C22—1586no—
1188C22C22×D4×D7916yes—
1189C22C25×D7911yescharacteristic
1190C4—22no—
1191C4—26no—
1192C4—22no—
1193C4—26no—
1194C4—792no—
1195C4—796no—
1196C4—794no—
1197C4—1582no—
1198C4—1586no—
1199C4—1586no—
1200C4C22×D4×D7916yes—
1201C4C22×D4×D7912yes—
1202C2—26no—
1203C2—46no—
1204C2—42no—
1205C2—3166no—
1206C2—3162no—
1207C2—1582no—
1208C2—1586no—
1209C2C23×D4×D7911yescharacteristic
1210C2#585×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3500C2
hypercenter#3500D79
hypocenterC79#62812
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. C2×#19099400C2semidirect
2. C2×#19099398C2semidirect
3. #23777193C2semidirect
4. #23777190C2semidirect
5. #23777187C2semidirect
6. #23777182C2semidirect
7. #23777181C2semidirect
8. #23777175C2semidirect
9. #23777174C2semidirect
10. #23777168C2semidirect
11. #23777160C2semidirect
12. #23776889C2semidirect
13. #23776884C2semidirect
14. #23776732C2semidirect
15. #23776731C2semidirect
16. C2×#19099112C2semidirect
17. #532×D79C2semidirect
18. C4×#41×D79C2semidirect
19. C79×#3500C2semidirect
22. C2×#14579209C22semidirect
23. C2×#14579209C22semidirect
24. C2×#14579208C22semidirect
25. C2×#14579208C22semidirect
26. C2×#14579208C22semidirect
27. C2×#14579207C22semidirect
28. C2×#14579207C22semidirect
29. C2×#14579207C22semidirect
30. C2×#14579206C22semidirect
31. C2×#14579206C22semidirect
32. C22×#11929625C22semidirect
33. C22×#11929625C22semidirect
34. C22×#11929623C22semidirect
35. C22×#11929623C22semidirect
37. C2×#41×D79C22semidirect
38. C2×#41×D79C22semidirect
39. C2×#41×D79C22semidirect
40. C2×#41×D79C22semidirect
41. #19099232C22semidirect
42. #19099231C22semidirect
43. Q8×C22⋊D79C22semidirect
44. #19099226C22semidirect
45. #19099225C22semidirect
46. #19099222C22semidirect
47. #19099221C22semidirect
48. #19099215C22semidirect
49. #19099212C22semidirect
50. #19099211C22semidirect
51. #19099209C22semidirect
52. #19099208C22semidirect
53. #19099206C22semidirect
54. #19099203C22semidirect
55. #19099202C22semidirect
56. #19099197C22semidirect
57. D4×C22⋊D79C22semidirect
58. #19099195C22semidirect
59. #19099143C22semidirect
60. #19099142C22semidirect
61. #19099139C22semidirect
62. #19099138C22semidirect
63. #19099137C22semidirect
64. #19099134C22semidirect
65. #19099133C22semidirect
66. #19099132C22semidirect
67. #19099131C22semidirect
68. #19099130C22semidirect
69. #19099127C22semidirect
70. #19099126C22semidirect
71. #19099124C22semidirect
72. #19099123C22semidirect
73. #19099114C22semidirect
74. #19099113C22semidirect
75. #19099112C22semidirect
76. #19099112C22semidirect
77. #19099112C22semidirect
78. #19099112C22semidirect
79. #19099112C22semidirect
80. #19099112C22semidirect
81. #19099112C22semidirect
82. #19099111C22semidirect
83. #19099110C22semidirect
84. #19099109C22semidirect
85. #19099109C22semidirect
86. #19099108C22semidirect
87. C2×#14579159C22semidirect
88. C4⋊Q8×D79C22semidirect
89. C2×#14579157C22semidirect
90. #127×D79C22semidirect
91. C2×#14579149C22semidirect
92. #124×D79C22semidirect
93. #124×D79C22semidirect
94. #19099076C22semidirect
95. #19099073C22semidirect
96. #19099071C22semidirect
97. #19099069C22semidirect
98. C2×#14579134C22semidirect
99. #121×D79C22semidirect
100. #41×Dic79C22semidirect
101. C4×#11929625C22semidirect
102. C4×#11929624C22semidirect
103. #19099031C22semidirect
104. C4×#11929623C22semidirect
105. C4×Q8×D79C22semidirect
106. C2×(C22⋊D79)⋊C4C22semidirect
107. C4×D4×D79C22semidirect
108. C4×D4×D79C22semidirect
109. #117×D79C22semidirect
110. C2×C42×D79C22semidirect
111. C2×2−1+4×C79C22semidirect
112. C2×H(5,𝔽2)×C79C22semidirect
113. #548×C79C22semidirect
114. #546×C79C22semidirect
115. #536×C79C22semidirect
116. #535×C79C22semidirect
117. #532×C79C22semidirect
118. C2×#124×C79C22semidirect
119. C4×#41×C79C22semidirect
165. #41×D79D4semidirect
322. #11929625C2×D4semidirect
330. #11929624C2×D4semidirect
341. #11929623C2×D4semidirect
354. Q8×D79C2×D4semidirect
388. D4×D79C2×D4semidirect
400. C2×C4×D79C2×D4semidirect
443. #41×C79C2×D4semidirect
595. Dic79#585semidirect
611. #3500D79semidirect
625. C79#62812semidirect
633. C2×2−1+4C2×D79semidirect
639. C2×H(5,𝔽2)C2×D79semidirect
656. #548C2×D79semidirect
665. #546C2×D79semidirect
676. #536C2×D79semidirect
682. #535C2×D79semidirect
699. #532C2×D79semidirect
707. C2×#124C2×D79semidirect
719. C4×#41C2×D79semidirect
953. #41D4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190994002
C2×#190993982
#237771932
#237771902
#237771872
#237771822
#237771812
#237771752
#237771742
#237771682
#237771602
#237768892
#237768842
#237767322
#237767312
C2×#190991122
#532×D792
C4×#41×D792
C79×#35002
#6281279