Finite Group Databasebeta

← #35197390

Subgroups — #35197390

Order 20224.

6806 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777226C211yesmaximal, characteristic, complemented
2#23777225C212yesmaximal, complemented
3#23777223C213yesmaximal, complemented
4#23777222C211yesmaximal, characteristic, complemented
5#23777221C213yesmaximal, complemented
6#23777220C216yesmaximal, complemented
7#23777218C212yesmaximal, complemented
8#23777216C213yesmaximal, complemented
9#23777215C213yesmaximal, complemented
10#23777213C211yesmaximal, characteristic, complemented
11#23777211C216yesmaximal, complemented
12#23777209C212yesmaximal, complemented
13#23777207C212yesmaximal, complemented
14#23777199C216yesmaximal, complemented
15#23777195C216yesmaximal, complemented
16#23776804C213yesmaximal, complemented
17#23776803C213yesmaximal, complemented
18C2×#19099190C213yesmaximal, complemented
19#544×D79C213yesmaximal, complemented
20#23776600C211yesmaximal, characteristic
21#23776599C211yesmaximal, characteristic
22#520×D79C211yesmaximal, characteristic
23C79×#3503C211yesmaximal, characteristic, complemented
24C2×#41×D79C2211yescharacteristic
25Q8×Dic158C2212yescomplemented
26#19099293C2216yescomplemented
27#19099293C2216yescomplemented
28#19099292C2212yescomplemented
29#19099291C2216yescomplemented
30#19099291C2216yescomplemented
31#19099290C2216yescomplemented
32#19099290C2216yescomplemented
33#19099289C2212yescomplemented
34#19099289C2212yescomplemented
35#19099289C2212yescomplemented
36#19099289C2212yescomplemented
37#19099288C2216yescomplemented
38#19099288C2216yescomplemented
39#19099274C2216yescomplemented
40#19099274C2216yescomplemented
41#19099273C2216yescomplemented
42#19099273C2216yescomplemented
43#19099272C2216yescomplemented
44#19099272C2216yescomplemented
45#19099272C2216yescomplemented
46#19099272C2216yescomplemented
47#19099271C22112yescomplemented
48#19099270C2216yescomplemented
49#19099269C2216yescomplemented
50#19099269C2216yescomplemented
51#19099268C22112yescomplemented
52#19099267C22112yescomplemented
53#19099267C22112yescomplemented
54#19099267C22112yescomplemented
55#19099267C22112yescomplemented
56D4×Dic158C2216yescomplemented
57#19099228C2216yescomplemented
58#19099228C2216yescomplemented
59Q8×C22⋊D79C22112yescomplemented
60#19099226C22112yescomplemented
61#19099194C2213yescomplemented
62#19099194C2213yescomplemented
63#19099193C2213yes—
64#19099193C2216yes—
65#19099193C2213yes—
66#19099193C2213yescomplemented
67#19099193C2213yescomplemented
68#19099193C2216yescomplemented
69#19099192C22112yescomplemented
70#19099192C2216yescomplemented
71#19099192C2216yescomplemented
72#19099191C2213yescomplemented
73#19099191C2213yescomplemented
74#19099191C2213yescomplemented
75#19099191C2213yescomplemented
76#19099190C2216yes—
77#19099190C2216yes—
78#19099190C2213yes—
79#19099190C2216yes—
80#19099190C2216yes—
81#19099190C2211yescharacteristic
82#19099190C2216yescomplemented
83#19099190C2216yescomplemented
84#19099190C2216yescomplemented
85#19099190C2216yescomplemented
86#19099190C2213yescomplemented
87#19099190C2213yescomplemented
88#19099190C2216yescomplemented
89#19099188C2216yes—
90#19099188C2216yes—
91#19099188C22112yes—
92#19099120C2213yescomplemented
93#19099119C2216yes—
94#19099119C2216yescomplemented
95#19099118C2216yes—
96#19099118C2216yescomplemented
97#19099117C2216yes—
98#19099117C2216yes—
99#19099117C2216yescomplemented
100#19099117C2216yescomplemented
101#19099116C2213yescomplemented
102#19099116C2213yescomplemented
103#19099115C22112yescomplemented
104C2×#14579160C2213yescomplemented
105C2×#14579159C2216yescomplemented
106C4⋊Q8×D79C2216yescomplemented
107C4⋊Q8×D79C2216yescomplemented
108C2×#14579153C2213yescomplemented
109C2×#14579152C2213yescomplemented
110C2×#14579151C2216yescomplemented
111#125×D79C2216yescomplemented
112#125×D79C2216yescomplemented
113C2×#14579139C2216yes—
114C2×#14579137C2216yes—
115C22⋊Q8×D79C22112yes—
116#19099046C2211yescharacteristic
117#19099046C2211yescharacteristic
118#19099045C2212yes—
119#19099045C2211yescharacteristic
120#19099045C2211yescharacteristic
121#19099044C2213yes—
122#19099044C2213yes—
123#19099043C2213yes—
124#19099043C2213yes—
125#19099042C2216yes—
126#19099042C2213yes—
127#19099042C2213yes—
128#19099039C2211yescharacteristic
129#19099039C2211yescharacteristic
130#19099039C2212yes—
131#19099035C2213yes—
132#19099035C2213yes—
133#19099035C2216yes—
134#41×Dic79C2211yescharacteristic
135C4×#11929625C2212yes—
136C4×#11929624C2213yes—
137#19099031C2213yes—
138C4×#11929623C2216yes—
139C4×Q8×D79C2212yes—
140C4×D4×D79C2216yes—
141C2×#14579119C2213yes—
142C2×#14579118C2213yes—
143#117×D79C2213yes—
144#117×D79C2213yes—
145#117×D79C2213yes—
146C2×C4⋊C4×D79C2213yes—
147Q82×C79C2212yescomplemented
148#557×C79C2212yescomplemented
149#554×C79C2216yescomplemented
150D4×Q8×C79C2216yescomplemented
151#544×C79C2213yescomplemented
152#544×C79C2213yescomplemented
153#533×C79C2213yescomplemented
154C2×C4⋊Q8×C79C2213yescomplemented
155#520×C79C2211yescharacteristic
156#520×C79C2211yescharacteristic
157C4×#41×C79C2211yescharacteristic
158C2×#11929625C2311yescharacteristic
159C2×#11929624C2313yes—
160C2×#11929623C2313yes—
161#41×D79Q8116yescomplemented
162C22×Dic158C2316yes—
163C2×Q8×D79C23112yes—
164C2×Q8×D79C2311yescharacteristic
165C2×D4×D79C2313yes—
166C22×C4×D79C2316yes—
167C22×C4×D79C2313yes—
168#14579161C2313yes—
169#14579161C2313yes—
170#14579161C2316yes—
171#14579161C2316yes—
172#14579160C2313yes—
173#14579160C2316yes—
174#14579160C2316yes—
175#14579160C2316yes—
176#14579160C2316yes—
177#14579160C2311yescharacteristic
178#14579160C2313yes—
179#14579160C2313yes—
180#14579160C2316yes—
181#14579160C2316yes—
182#14579160C2316yes—
183#14579160C2316yes—
184#14579160C23112yes—
185#14579160C2316yes—
186#14579160C2316yes—
187#14579160C2316yes—
188#14579159C23112yes—
189#14579159C2316yes—
190#14579159C23112yes—
191#14579159C23112yes—
192#14579159C2312yes—
193#14579159C23112yes—
194#14579159C2316yes—
195#14579159C2316yes—
196#14579153C2313yes—
197#14579153C2311yescharacteristic
198#14579153C2316yes—
199#14579153C2316yes—
200#14579153C2316yes—
201#14579153C2316yes—
202#14579153C2316yes—
203#14579152C2313yes—
204#14579152C2316yes—
205#14579152C2316yes—
206#14579152C2316yes—
207#14579152C2311yescharacteristic
208#14579152C2316yes—
209#14579152C2313yes—
210#14579152C2316yes—
211#14579152C2313yes—
212#14579152C2316yes—
213#14579152C2316yes—
214#14579151C2316yes—
215#14579151C23112yes—
216#14579151C23112yes—
217#14579151C23112yes—
218#14579151C2312yes—
219#14579151C23112yes—
220#14579151C2316yes—
221#14579151C2316yes—
222#14579151C2316yes—
223#14579151C2316yes—
224#14579151C23112yes—
225#14579151C2316yes—
226#14579151C2316yes—
227#14579141C2316yes—
228#14579141C2316yes—
229#14579141C2316yes—
230#14579141C23112yes—
231#14579141C2316yes—
232#14579140C2316yes—
233#14579140C2316yes—
234#14579140C23112yes—
235#14579140C23112yes—
236#14579139C2312yes—
237#14579139C2316yes—
238#14579139C2316yes—
239#14579139C2316yes—
240#14579139C23112yes—
241#14579139C23112yes—
242#14579139C2316yes—
243#14579139C2316yes—
244#14579139C2316yes—
245#14579139C2316yes—
246#14579139C23112yes—
247#14579139C23112yes—
248#14579139C23112yes—
249#14579138C23112yes—
250#14579138C23112yes—
251#14579138C2316yes—
252#14579138C2316yes—
253#14579138C2316yes—
254#14579138C2316yes—
255#14579138C23112yes—
256#14579138C23112yes—
257#14579137C2312yes—
258#14579137C23112yes—
259#14579137C2316yes—
260#14579137C2316yes—
261#14579137C23112yes—
262#14579137C2316yes—
263#14579137C23112yes—
264#14579137C23112yes—
265Q8×Dic79C23112yes—
266Q8×Dic79C2312yes—
267Q8×Dic79C2312yes—
268Q8×Dic79C2311yescharacteristic
269Q8×Dic79C2311yescharacteristic
270C4×Dic158C2316yes—
271C4×Dic158C2316yes—
272C4×Dic158C2316yes—
273C4×Dic158C2316yes—
274C4×Dic158C2316yes—
275C4×Dic158C2316yes—
276C4×Dic158C2316yes—
277C4×Dic158C2316yes—
278C4×Dic158C2313yes—
279C4×Dic158C2313yes—
280#14579126C23112yes—
281#14579126C23112yes—
282#14579126C23112yes—
283#14579126C2316yes—
284#14579126C2316yes—
285#14579126C2313yes—
286#14579126C2313yes—
287C4×D316C2313yes—
288C4×D316C2316yes—
289C4×D316C2316yes—
290C4×D316C2313yes—
291D4×Dic79C2313yes—
292D4×Dic79C2316yes—
293D4×Dic79C2313yes—
294D4×Dic79C2316yes—
295#14579123C2316yes—
296#14579123C2313yes—
297#14579123C2316yes—
298#14579123C2313yes—
299C4×C22⋊D79C23112yes—
300C4×C22⋊D79C2316yes—
301C4×C22⋊D79C23112yes—
302C4×C22⋊D79C2316yes—
303(C22⋊D79)⋊C4C2316yes—
304(C22⋊D79)⋊C4C23112yes—
305(C22⋊D79)⋊C4C23112yes—
306(C22⋊D79)⋊C4C2316yes—
307#14579120C2313yes—
308#14579120C2313yes—
309#14579120C2313yes—
310#14579119C2313yes—
311#14579119C2313yes—
312#14579119C2316yes—
313#14579119C2311yescharacteristic
314#14579119C2316yes—
315#14579119C2316yes—
316#14579119C2313yes—
317#14579119C2313yes—
318#14579119C2313yes—
319#14579118C2311yescharacteristic
320#14579118C2313yes—
321#14579118C2313yes—
322#14579118C2313yes—
323#14579118C2316yes—
324#14579118C2313yes—
325#14579118C2313yes—
326#14579118C2313yes—
327#14579118C2313yes—
328#14579118C2316yes—
329#14579117C2316yes—
330#14579117C2316yes—
331#14579117C2316yes—
332C2×C4⋊Dic79C2313yes—
333C2×C4⋊Dic79C2313yes—
334C2×C4⋊Dic79C2316yes—
335C2×Dic79⋊C4C2316yes—
336C2×Dic79⋊C4C2313yes—
337C2×Dic79⋊C4C2313yes—
338C2×Dic79⋊C4C2316yes—
339C2×Dic79⋊C4C2316yes—
340C2×Dic79⋊C4C2316yes—
341C2×Dic79⋊C4C2316yes—
342C4⋊C4×D79C2313yes—
343C4⋊C4×D79C2316yes—
344C4⋊C4×D79C2311yescharacteristic
345C4⋊C4×D79C2316yes—
346C4⋊C4×D79C2316yes—
347C4⋊C4×D79C2313yes—
348C4⋊C4×D79C2313yes—
349C4⋊C4×D79C2313yes—
350C4⋊C4×D79C2313yes—
351C4⋊C4×D79C23112yes—
352C4⋊C4×D79C23112yes—
353C4⋊C4×D79C23112yes—
354C2×(C2×D79)⋊C4C2313yes—
355C2×(C2×D79)⋊C4C2313yes—
356C2×(C2×D79)⋊C4C2316yes—
357C22⋊C4×D79C2316yes—
358C22⋊C4×D79C2316yes—
359C22⋊C4×D79C2316yes—
360C2×C4×Dic79C2313yes—
361C2×C4×Dic79C2316yes—
362C42×D79C2316yes—
363C42×D79C2316yes—
364C42×D79C2316yes—
365C2×#41×C79C2311yescharacteristic
366C22×Q8×C79C2316yes—
367C4⋊Q8×C79C2313yes—
368C4⋊Q8×C79C2311yescharacteristic
369C4⋊Q8×C79C2316yes—
370C4⋊Q8×C79C2316yes—
371C4⋊Q8×C79C2316yes—
372C4⋊Q8×C79C2316yes—
373C4⋊Q8×C79C2316yes—
374#125×C79C2313yes—
375#125×C79C2313yes—
376#125×C79C2316yes—
377#125×C79C2316yes—
378C22⋊Q8×C79C2316yes—
379C22⋊Q8×C79C2316yes—
380C22⋊Q8×C79C23112yes—
381C22⋊Q8×C79C23112yes—
382C4×Q8×C79C2311yescharacteristic
383C4×Q8×C79C2311yescharacteristic
384C4×Q8×C79C2312yes—
385C4×Q8×C79C2312yes—
386C4×Q8×C79C2316yes—
387C4×Q8×C79C2316yes—
388C4×D4×C79C2316yes—
389C4×D4×C79C2313yes—
390C4×D4×C79C2313yes—
391C4×D4×C79C2316yes—
392#117×C79C2313yes—
393#117×C79C2313yes—
394#117×C79C2313yes—
395C2×C4⋊C4×C79C2313yes—
396C2×C4⋊C4×C79C2313yes—
397C2×C4⋊C4×C79C2316yes—
398C2×C42×C79C2313yes—
399C23×D79C2413yes—
400#11929625C2×Q818yescomplemented
401#11929624C2×Q8124yescomplemented
402#11929623C2×Q8124yescomplemented
403C2×Dic158—86no—
404C2×Dic158C2416yes—
405C2×Dic158C2416yes—
406C2×Dic158C24112yes—
407C2×Dic158C2416yes—
408C2×Dic158C2416yes—
409C2×Dic158C2416yes—
410C2×Dic158C2412yes—
411C2×Dic158C2413yes—
412Q8×D79—812no—
413Q8×D79C2×Q818yescomplemented
414C2×D316C2413yes—
415C2×C22⋊D79C2416yes—
416D4×D79C2×Q8124yescomplemented
417C22×Dic79C2413yes—
418C22×Dic79C2416yes—
419C22×Dic79C2413yes—
420C22×Dic79C2416yes—
421C22×Dic79C2413yes—
422C2×C4×D79—86no—
423C2×C4×D79C2×Q8124yescomplemented
424C2×C4×D79C2416yes—
425C2×C4×D79C2416yes—
426C2×C4×D79C24112yes—
427C2×C4×D79C2412yes—
428C2×C4×D79C2416yes—
429C2×C4×D79C2416yes—
430C2×C4×D79C2416yes—
431C2×C4×D79C2413yes—
432C2×C4×D79C2413yes—
433C2×C4×D79C2413yes—
434C2×C4×D79C2411yescharacteristic
435C4⋊Dic79C2413yes—
436C4⋊Dic79C2411yescharacteristic
437C4⋊Dic79C2416yes—
438C4⋊Dic79C2416yes—
439C4⋊Dic79C2416yes—
440C4⋊Dic79C2413yes—
441C4⋊Dic79C24112yes—
442C4⋊Dic79C2411yescharacteristic
443C4⋊Dic79C2413yes—
444C4⋊Dic79C2413yes—
445C4⋊Dic79C2416yes—
446C4⋊Dic79C2416yes—
447C4⋊Dic79C2412yes—
448C4⋊Dic79C2416yes—
449C4⋊Dic79C2416yes—
450Dic79⋊C4C2416yes—
451Dic79⋊C4C2413yes—
452Dic79⋊C4C2413yes—
453Dic79⋊C4C24112yes—
454Dic79⋊C4C2416yes—
455Dic79⋊C4C2416yes—
456Dic79⋊C4C24112yes—
457Dic79⋊C4C24112yes—
458Dic79⋊C4C24112yes—
459Dic79⋊C4C24112yes—
460Dic79⋊C4C2412yes—
461Dic79⋊C4C2416yes—
462Dic79⋊C4C2416yes—
463Dic79⋊C4C2411yescharacteristic
464Dic79⋊C4C2411yescharacteristic
465Dic79⋊C4C2416yes—
466Dic79⋊C4C2416yes—
467Dic79⋊C4C2416yes—
468Dic79⋊C4C2416yes—
469Dic79⋊C4C2413yes—
470Dic79⋊C4C2413yes—
471Dic79⋊C4C2413yes—
472Dic79⋊C4C2413yes—
473Dic79⋊C4C2416yes—
474Dic79⋊C4C2416yes—
475Dic79⋊C4C2412yes—
476Dic79⋊C4C2412yes—
477Dic79⋊C4C2412yes—
478Dic79⋊C4C2412yes—
479C22⋊Dic79C2416yes—
480C22⋊Dic79C2416yes—
481C22⋊Dic79C2416yes—
482(C2×D79)⋊C4C2412yes—
483(C2×D79)⋊C4C2413yes—
484(C2×D79)⋊C4C2413yes—
485(C2×D79)⋊C4C2416yes—
486(C2×D79)⋊C4C2416yes—
487(C2×D79)⋊C4C2416yes—
488(C2×D79)⋊C4C2411yescharacteristic
489(C2×D79)⋊C4C2411yescharacteristic
490(C2×D79)⋊C4C2413yes—
491(C2×D79)⋊C4C2413yes—
492(C2×D79)⋊C4C2413yes—
493(C2×D79)⋊C4C2413yes—
494(C2×D79)⋊C4C24112yes—
495C4×Dic79C2412yes—
496C4×Dic79C2413yes—
497C4×Dic79C2416yes—
498C4×Dic79C2416yes—
499C4×Dic79C2416yes—
500C4×Dic79C2416yes—
501C4×Dic79C2416yes—
502C4×Dic79C2416yes—
503C4×Dic79C2416yes—
504C4×Dic79C2411yescharacteristic
505C4×Dic79C2413yes—
506C4×Dic79C2413yes—
507C4×Dic79C24112yes—
508#41×C79C2×Q818yescomplemented
509C2×Q8×C79—86no—
510C2×Q8×C79C24112yes—
511C2×Q8×C79C2412yes—
512C2×Q8×C79C2416yes—
513C2×Q8×C79C2411yescharacteristic
514C2×D4×C79C2413yes—
515C22×C4×C79C2416yes—
516C22×C4×C79C2413yes—
517C22×C4×C79C2413yes—
518C22×C4×C79C2416yes—
519C22×C4×C79C2413yes—
520C4⋊C4×C79C2413yes—
521C4⋊C4×C79C2413yes—
522C4⋊C4×C79C2416yes—
523C4⋊C4×C79C2416yes—
524C4⋊C4×C79C2416yes—
525C4⋊C4×C79C24112yes—
526C4⋊C4×C79C2411yescharacteristic
527C4⋊C4×C79C2411yescharacteristic
528C4⋊C4×C79C2413yes—
529C4⋊C4×C79C2413yes—
530C4⋊C4×C79C2412yes—
531C4⋊C4×C79C2416yes—
532C4⋊C4×C79C2416yes—
533C4⋊C4×C79C2416yes—
534C4⋊C4×C79C2416yes—
535C22⋊C4×C79C2416yes—
536C22⋊C4×C79C2416yes—
537C22⋊C4×C79C2416yes—
538C42×C79C2411yescharacteristic
539C42×C79C2413yes—
540C42×C79C2413yes—
541C42×C79C2413yes—
542C42×C79C2416yes—
543C42×C79C2416yes—
544C23×C79C2513yes—
545C22×D79—43no—
546C22×D79—43no—
547C22×D79C22×Q8112yes—
548C22×D79C2511yescharacteristic
549C22×D79C2513yes—
550Q8×C79—412no—
551Q8×C79—46no—
552Q8×C79—42no—
553Q8×C79C22×Q814yes—
554D4×C79C22×Q8112yes—
555C2×C4×C79—46no—
556C2×C4×C79—46no—
557C2×C4×C79—43no—
558C2×C4×C79—43no—
559C2×C4×C79C22×Q8112yes—
560C2×C4×C79C2512yes—
561C2×C4×C79C2516yes—
562C2×C4×C79C2513yes—
563C2×C4×C79C2513yes—
564C2×C4×C79C2512yes—
565C2×C4×C79C2516yes—
566C2×C4×C79C2511yescharacteristic
567C2×C4×C79C2511yescharacteristic
568C2×C4×C79C2513yes—
569C2×C4×C79C2511yescharacteristic
570C22⋊D79C22×Q8124yes—
571C2×Dic79—46no—
572C2×Dic79—43no—
573C2×Dic79—46no—
574C2×Dic79—43no—
575C2×Dic79C22×Q8112yes—
576C2×Dic79C2512yes—
577C2×Dic79C2511yescharacteristic
578C2×Dic79C2511yescharacteristic
579C2×Dic79C2516yes—
580C2×Dic79C2513yes—
581C2×Dic79C2513yes—
582C2×Dic79C2512yes—
583C2×Dic79C2516yes—
584C2×Dic79C2513yes—
585C2×Dic79C2511yescharacteristic
586D316C22×Q8112yes—
587C4×D79—46no—
588C4×D79—412no—
589C4×D79—42no—
590C4×D79—46no—
591C4×D79—46no—
592C4×D79—46no—
593C4×D79—46no—
594C4×D79C22×Q814yes—
595C4×D79C22×Q8112yes—
596C4×D79C22×Q8112yes—
597C4×D79C22×Q8112yes—
598Dic158—46no—
599Dic158—46no—
600Dic158—412no—
601Dic158—46no—
602Dic158—46no—
603Dic158—42no—
604Dic158—46no—
605Dic158C22×Q8112yes—
606C22×C79—23no—
607C22×C79—23no—
608C22×C79C23×Q816yes—
609C22×C79C2611yescharacteristic
610C2×D79—21no—
611C2×D79—23no—
612C2×D79—21no—
613C2×D79—23no—
614C2×D79—412no—
615C2×D79C23×Q816yes—
616C2×D79C23×Q812yes—
617C4×C79—21no—
618C4×C79—26no—
619C4×C79—26no—
620C4×C79—23no—
621C4×C79—21no—
622C4×C79—23no—
623C4×C79—22no—
624C4×C79—22no—
625C4×C79C23×Q812yes—
626C4×C79C23×Q816yes—
627Dic79—22no—
628Dic79—23no—
629Dic79—21no—
630Dic79—26no—
631Dic79—22no—
632Dic79—23no—
633Dic79—26no—
634Dic79—21no—
635Dic79C23×Q816yes—
636Dic79C23×Q812yes—
637#62854—791nomaximal, Sylow
638C2×C79—26no—
639C2×C79C24×Q811yescharacteristic
640C2×C79H(7,𝔽2)11yescharacteristic
641C2×C792−1+611yescharacteristic
642D79—22no—
643D79—26no—
644#3504—792no—
645#3504—796no—
646#3504—793no—
647#3504—793no—
648#3504—791no—
649#3504—791no—
650#3503—792no—
651#3503—796no—
652#3503—793no—
653#3503—793no—
654#3503—791no—
655#3503D7911yescharacteristic, complemented
656#3502—792no—
657#3502—792no—
658#3501—796no—
659#3501—796no—
660#3458—793no—
661#3458—793no—
662C2×#544—793no—
663C2×#544—793no—
664#3428—791no—
665#3428—791no—
666C2×#520—791no—
667C79#6285411yescharacteristic, complemented, Sylow
668C22×#41—791no—
669Q82—796no—
670Q82—796no—
671Q82—792no—
672Q82C2×D7912yescomplemented
673#557—796no—
674#557—796no—
675#557—796no—
676#557—796no—
677#557—792no—
678#557—792no—
679#557—792no—
680#557—792no—
681#557—796no—
682#557—796no—
683#557—792no—
684#557C2×D7912yescomplemented
685#554—796no—
686#554—796no—
687#554—796no—
688#554—796no—
689#554—7912no—
690#554—7912no—
691#554—7912no—
692#554—7912no—
693#554—7912no—
694#554—796no—
695#554—796no—
696#554—796no—
697#554—796no—
698#554—796no—
699#554—796no—
700#554—796no—
701#554—7912no—
702#554C2×D7916yescomplemented
703D4×Q8—7912no—
704D4×Q8—796no—
705D4×Q8—796no—
706D4×Q8—7912no—
707D4×Q8—796no—
708D4×Q8C2×D7916yescomplemented
709#544—796no—
710#544—793no—
711#544—796no—
712#544—796no—
713#544—796no—
714#544—791no—
715#544—796no—
716#544—796no—
717#544—796no—
718#544—796no—
719#544—796no—
720#544—793no—
721#544—793no—
722#544—793no—
723#544—796no—
724#544—793no—
725#544—793no—
726#544—796no—
727#544—793no—
728#544—7912no—
729#544—796no—
730#544—796no—
731#544—793no—
732#544—793no—
733#544—793no—
734#544—793no—
735#544—793no—
736#544—793no—
737#544C2×D7913yescomplemented
738#544C2×D7913yescomplemented
739#543—7912no—
740#543—796no—
741#543—796no—
742#533—796no—
743#533—796no—
744#533—796no—
745#533—796no—
746#533—7912no—
747#533—796no—
748#533—796no—
749#533—796no—
750#533—796no—
751#533—793no—
752#533—793no—
753#533—793no—
754#533C2×D7913yescomplemented
755C2×C4⋊Q8—796no—
756C2×C4⋊Q8—796no—
757C2×C4⋊Q8—796no—
758C2×C4⋊Q8—793no—
759C2×C4⋊Q8C2×D7913yescomplemented
760C2×#125—796no—
761C2×#125—796no—
762C2×#125—796no—
763C2×#125—793no—
764C2×#125—793no—
765C2×C22⋊Q8—796no—
766C2×C22⋊Q8—7912no—
767C2×C22⋊Q8—796no—
768#520—791no—
769#520—791no—
770#520—792no—
771#520—791no—
772#520—791no—
773#520—796no—
774#520—793no—
775#520—793no—
776#520—793no—
777#520—793no—
778#520—793no—
779#520—793no—
780#520C2×D7911yescharacteristic
781#520C2×D7911yescharacteristic
782#519—792no—
783#519—791no—
784#519—791no—
785#518—793no—
786#518—796no—
787#518—793no—
788C4×#41—791no—
789C4×#41—792no—
790C4×#41—796no—
791C4×#41—793no—
792C4×#41—793no—
793C4×#41C2×D7911yescharacteristic
794C2×C4×Q8—792no—
795C2×C4×D4—796no—
796C2×#117—793no—
797C2×#117—793no—
798C2×#117—793no—
799C2×#117—793no—
800C2×#117—793no—
801C22×C4⋊C4—793no—
802C2×#41—7916no—
803C2×#41—791no—
804C2×#41—793no—
805C2×#41—793no—
806C2×#41C22×D7911yescharacteristic
807C22×Q8—791no—
808C22×Q8—7912no—
809C22×Q8—796no—
810C22×Q8C22×D7916yes—
811C22×D4—793no—
812C23×C4—793no—
813C23×C4—796no—
814C4⋊Q8—7912no—
815C4⋊Q8—796no—
816C4⋊Q8—7912no—
817C4⋊Q8—7912no—
818C4⋊Q8—7912no—
819C4⋊Q8—792no—
820C4⋊Q8—796no—
821C4⋊Q8—796no—
822C4⋊Q8—796no—
823C4⋊Q8—796no—
824C4⋊Q8—793no—
825C4⋊Q8—793no—
826C4⋊Q8—7912no—
827C4⋊Q8—796no—
828C4⋊Q8—796no—
829C4⋊Q8—796no—
830C4⋊Q8—796no—
831C4⋊Q8—796no—
832C4⋊Q8—793no—
833C4⋊Q8—791no—
834C4⋊Q8—796no—
835C4⋊Q8—796no—
836C4⋊Q8—796no—
837C4⋊Q8—796no—
838C4⋊Q8—793no—
839C4⋊Q8—796no—
840C4⋊Q8—793no—
841C4⋊Q8—796no—
842C4⋊Q8C22×D7916yes—
843C4⋊Q8C22×D7916yes—
844C4⋊Q8C22×D7913yes—
845C4⋊Q8C22×D7916yes—
846C4⋊Q8C22×D7916yes—
847C4⋊Q8C22×D7916yes—
848C4⋊Q8C22×D7911yescharacteristic
849#125—7912no—
850#125—796no—
851#125—796no—
852#125—793no—
853#125—796no—
854#125—793no—
855#125—7912no—
856#125—7912no—
857#125—7912no—
858#125—7912no—
859#125—796no—
860#125—796no—
861#125—796no—
862#125—796no—
863#125—796no—
864#125—792no—
865#125—791no—
866#125—793no—
867#125—796no—
868#125—796no—
869#125—796no—
870#125—796no—
871#125—796no—
872#125—796no—
873#125—796no—
874#125—793no—
875#125—796no—
876#125—796no—
877#125—796no—
878#125—791no—
879#125—796no—
880#125C22×D7913yes—
881#125C22×D7916yes—
882#125C22×D7913yes—
883#125C22×D7916yes—
884C22⋊Q8—7912no—
885C22⋊Q8—796no—
886C22⋊Q8—7912no—
887C22⋊Q8—7912no—
888C22⋊Q8—792no—
889C22⋊Q8—7912no—
890C22⋊Q8—796no—
891C22⋊Q8—796no—
892C22⋊Q8—7912no—
893C22⋊Q8—7912no—
894C22⋊Q8—796no—
895C22⋊Q8—796no—
896C22⋊Q8—796no—
897C22⋊Q8—7912no—
898C22⋊Q8—796no—
899C22⋊Q8—796no—
900C22⋊Q8—7912no—
901C22⋊Q8—7912no—
902C22⋊Q8—796no—
903C22⋊Q8—792no—
904C22⋊Q8—796no—
905C22⋊Q8—7912no—
906C22⋊Q8—796no—
907C22⋊Q8—796no—
908C22⋊Q8—796no—
909C22⋊Q8—7912no—
910C22⋊Q8—796no—
911C22⋊Q8—796no—
912C22⋊Q8—796no—
913C22⋊Q8—7912no—
914C22⋊Q8—7912no—
915C22⋊Q8—7912no—
916C22⋊Q8—796no—
917C22⋊Q8—796no—
918C22⋊Q8—7912no—
919C22⋊Q8—796no—
920C22⋊Q8—7912no—
921C22⋊Q8—796no—
922C22⋊Q8C22×D79112yes—
923C22⋊Q8C22×D79112yes—
924C22⋊Q8C22×D7916yes—
925C22⋊Q8C22×D7916yes—
926C4×Q8—792no—
927C4×Q8—791no—
928C4×Q8—792no—
929C4×Q8—791no—
930C4×Q8—7912no—
931C4×Q8—796no—
932C4×Q8—793no—
933C4×Q8—793no—
934C4×Q8—796no—
935C4×Q8—7912no—
936C4×Q8—7912no—
937C4×Q8—7912no—
938C4×Q8—796no—
939C4×Q8—796no—
940C4×Q8—793no—
941C4×Q8—793no—
942C4×Q8—796no—
943C4×Q8—796no—
944C4×Q8—796no—
945C4×Q8—796no—
946C4×Q8—796no—
947C4×Q8—796no—
948C4×Q8C22×D7912yes—
949C4×Q8C22×D7912yes—
950C4×Q8C22×D7911yescharacteristic
951C4×Q8C22×D7911yescharacteristic
952C4×Q8C22×D7916yes—
953C4×Q8C22×D7916yes—
954C4×D4—796no—
955C4×D4—793no—
956C4×D4—793no—
957C4×D4—796no—
958C4×D4—7912no—
959C4×D4—7912no—
960C4×D4—796no—
961C4×D4—796no—
962C4×D4—796no—
963C4×D4—793no—
964C4×D4—796no—
965C4×D4—793no—
966C4×D4—7912no—
967C4×D4—796no—
968C4×D4—7912no—
969C4×D4—796no—
970C4×D4—796no—
971C4×D4—793no—
972C4×D4—796no—
973C4×D4—793no—
974C4×D4C22×D7916yes—
975C4×D4C22×D7916yes—
976C4×D4C22×D7913yes—
977C4×D4C22×D7913yes—
978#117—793no—
979#117—793no—
980#117—793no—
981#117—793no—
982#117—791no—
983#117—796no—
984#117—793no—
985#117—796no—
986#117—793no—
987#117—793no—
988#117—796no—
989#117—793no—
990#117—796no—
991#117—796no—
992#117—796no—
993#117—793no—
994#117—791no—
995#117—793no—
996#117—793no—
997#117—796no—
998#117—793no—
999#117—793no—
1000#117—796no—
1001#117—793no—
1002#117—793no—
1003#117C22×D7913yes—
1004#117C22×D7913yes—
1005#117C22×D7913yes—
1006C2×C4⋊C4—796no—
1007C2×C4⋊C4—793no—
1008C2×C4⋊C4—793no—
1009C2×C4⋊C4—793no—
1010C2×C4⋊C4—793no—
1011C2×C4⋊C4—796no—
1012C2×C4⋊C4—796no—
1013C2×C4⋊C4—796no—
1014C2×C4⋊C4—796no—
1015C2×C4⋊C4—796no—
1016C2×C4⋊C4—793no—
1017C2×C4⋊C4—796no—
1018C2×C4⋊C4—796no—
1019C2×C4⋊C4—796no—
1020C2×C4⋊C4—791no—
1021C2×C4⋊C4—793no—
1022C2×C4⋊C4—793no—
1023C2×C4⋊C4—793no—
1024C2×C4⋊C4—793no—
1025C2×C4⋊C4—7912no—
1026C2×C4⋊C4—7912no—
1027C2×C4⋊C4—7912no—
1028C2×C4⋊C4C22×D7913yes—
1029C2×C4⋊C4C22×D7913yes—
1030C2×C4⋊C4C22×D7916yes—
1031C2×C22⋊C4—796no—
1032C2×C22⋊C4—793no—
1033C2×C22⋊C4—793no—
1034C2×C22⋊C4—796no—
1035C2×C22⋊C4—796no—
1036C2×C22⋊C4—796no—
1037C2×C42—793no—
1038C2×C42—796no—
1039C2×C42—796no—
1040C2×C42—796no—
1041C2×C42—796no—
1042C2×C42C22×D7913yes—
1043C24—793no—
1044#41—798no—
1045#41—7924no—
1046#41—7924no—
1047#41Q8×D7918yescomplemented
1048C2×Q8—86no—
1049C2×Q8—798no—
1050C2×Q8—796no—
1051C2×Q8—792no—
1052C2×Q8—796no—
1053C2×Q8—796no—
1054C2×Q8—7912no—
1055C2×Q8—796no—
1056C2×Q8—796no—
1057C2×Q8—793no—
1058C2×Q8—6326no—
1059C2×Q8—63212no—
1060C2×Q8C23×D79112yes—
1061C2×Q8C23×D7912yes—
1062C2×Q8C23×D7916yes—
1063C2×Q8C23×D7911yescharacteristic
1064C2×D4—796no—
1065C2×D4—7924no—
1066C2×D4—793no—
1067C2×D4C23×D7913yes—
1068C22×C4—793no—
1069C22×C4—796no—
1070C22×C4—793no—
1071C22×C4—796no—
1072C22×C4—792no—
1073C22×C4—796no—
1074C22×C4—796no—
1075C22×C4—796no—
1076C22×C4—796no—
1077C22×C4—796no—
1078C22×C4—7912no—
1079C22×C4—793no—
1080C22×C4—7924no—
1081C22×C4—793no—
1082C22×C4—793no—
1083C22×C4—793no—
1084C22×C4—791no—
1085C22×C4—6326no—
1086C22×C4C23×D7916yes—
1087C22×C4C23×D7913yes—
1088C22×C4C23×D7913yes—
1089C22×C4C23×D7916yes—
1090C22×C4C23×D7913yes—
1091C4⋊C4—796no—
1092C4⋊C4—793no—
1093C4⋊C4—791no—
1094C4⋊C4—793no—
1095C4⋊C4—791no—
1096C4⋊C4—7912no—
1097C4⋊C4—7912no—
1098C4⋊C4—796no—
1099C4⋊C4—796no—
1100C4⋊C4—796no—
1101C4⋊C4—7912no—
1102C4⋊C4—796no—
1103C4⋊C4—7912no—
1104C4⋊C4—796no—
1105C4⋊C4—7912no—
1106C4⋊C4—796no—
1107C4⋊C4—792no—
1108C4⋊C4—793no—
1109C4⋊C4—796no—
1110C4⋊C4—793no—
1111C4⋊C4—796no—
1112C4⋊C4—793no—
1113C4⋊C4—793no—
1114C4⋊C4—792no—
1115C4⋊C4—792no—
1116C4⋊C4—796no—
1117C4⋊C4—792no—
1118C4⋊C4—796no—
1119C4⋊C4—792no—
1120C4⋊C4—793no—
1121C4⋊C4—793no—
1122C4⋊C4—791no—
1123C4⋊C4—796no—
1124C4⋊C4—7912no—
1125C4⋊C4—796no—
1126C4⋊C4—796no—
1127C4⋊C4—796no—
1128C4⋊C4—791no—
1129C4⋊C4—793no—
1130C4⋊C4—796no—
1131C4⋊C4—793no—
1132C4⋊C4—796no—
1133C4⋊C4—796no—
1134C4⋊C4—792no—
1135C4⋊C4C23×D7913yes—
1136C4⋊C4C23×D7911yescharacteristic
1137C4⋊C4C23×D7916yes—
1138C4⋊C4C23×D7916yes—
1139C4⋊C4C23×D7916yes—
1140C4⋊C4C23×D7913yes—
1141C4⋊C4C23×D79112yes—
1142C4⋊C4C23×D7911yescharacteristic
1143C4⋊C4C23×D7913yes—
1144C4⋊C4C23×D7913yes—
1145C4⋊C4C23×D7916yes—
1146C4⋊C4C23×D7916yes—
1147C4⋊C4C23×D7916yes—
1148C4⋊C4C23×D7916yes—
1149C4⋊C4C23×D7912yes—
1150C22⋊C4—796no—
1151C22⋊C4—796no—
1152C22⋊C4—796no—
1153C22⋊C4—796no—
1154C22⋊C4—793no—
1155C22⋊C4—791no—
1156C22⋊C4—793no—
1157C22⋊C4—792no—
1158C22⋊C4—791no—
1159C22⋊C4—796no—
1160C22⋊C4—7912no—
1161C22⋊C4—793no—
1162C22⋊C4—793no—
1163C22⋊C4—793no—
1164C22⋊C4—793no—
1165C22⋊C4—796no—
1166C22⋊C4C23×D7916yes—
1167C22⋊C4C23×D7916yes—
1168C22⋊C4C23×D7916yes—
1169C42—796no—
1170C42—792no—
1171C42—793no—
1172C42—791no—
1173C42—796no—
1174C42—7912no—
1175C42—796no—
1176C42—796no—
1177C42—796no—
1178C42—796no—
1179C42—796no—
1180C42—793no—
1181C42—793no—
1182C42C23×D7913yes—
1183C42C23×D7916yes—
1184C42C23×D7916yes—
1185C42C23×D7911yescharacteristic
1186C42C23×D7913yes—
1187C42C23×D7913yes—
1188C23—3163no—
1189C23—3163no—
1190C23—7912no—
1191C23—791no—
1192C23—793no—
1193C23C24×D7913yes—
1194Q8—46no—
1195Q8—412no—
1196Q8—42no—
1197Q8—3166no—
1198Q8—3166no—
1199Q8—31612no—
1200Q8—3166no—
1201Q8—3166no—
1202Q8—3162no—
1203Q8—3166no—
1204Q8—7912no—
1205Q8C2×Q8×D7914yes—
1206D4—7924no—
1207D4—7912no—
1208D4C2×Q8×D79112yes—
1209C2×C4—46no—
1210C2×C4—43no—
1211C2×C4—43no—
1212C2×C4—46no—
1213C2×C4—3166no—
1214C2×C4—31612no—
1215C2×C4—3166no—
1216C2×C4—3166no—
1217C2×C4—3166no—
1218C2×C4—3166no—
1219C2×C4—3162no—
1220C2×C4—3166no—
1221C2×C4—3163no—
1222C2×C4—3163no—
1223C2×C4—3166no—
1224C2×C4—793no—
1225C2×C4—791no—
1226C2×C4—7912no—
1227C2×C4—794no—
1228C2×C4—7912no—
1229C2×C4—7912no—
1230C2×C4—7912no—
1231C2×C4—792no—
1232C2×C4—793no—
1233C2×C4—796no—
1234C2×C4—791no—
1235C2×C4—792no—
1236C2×C4—793no—
1237C2×C4—791no—
1238C2×C4—796no—
1239C2×C4C2×Q8×D79112yes—
1240C2×C4C24×D7912yes—
1241C2×C4C24×D7916yes—
1242C2×C4C24×D7913yes—
1243C2×C4C24×D7913yes—
1244C2×C4C24×D7912yes—
1245C2×C4C24×D7916yes—
1246C2×C4C24×D7911yescharacteristic
1247C2×C4C24×D7911yescharacteristic
1248C2×C4C24×D7913yes—
1249C2×C4C24×D7911yescharacteristic
1250C22—23no—
1251C22—23no—
1252C22—31612no—
1253C22—792no—
1254C22—796no—
1255C22—1583no—
1256C22—1581no—
1257C22—1583no—
1258C22—1581no—
1259C22C22×Q8×D7916yes—
1260C22C25×D7911yescharacteristic
1261C4—21no—
1262C4—26no—
1263C4—26no—
1264C4—23no—
1265C4—21no—
1266C4—23no—
1267C4—22no—
1268C4—22no—
1269C4—792no—
1270C4—796no—
1271C4—1586no—
1272C4—1582no—
1273C4—1583no—
1274C4—1581no—
1275C4—1583no—
1276C4—1586no—
1277C4—1581no—
1278C4—1582no—
1279C4C22×Q8×D7912yes—
1280C4C22×Q8×D7916yes—
1281C2—26no—
1282C2—1582no—
1283C2—1586no—
1284C2C23×Q8×D7911yescharacteristic
1285C2#2377821011yescharacteristic
1286C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3503C2
prime radicalC2×#41×D79C22
hypercenter#3503D79
hypocenterC79#62854
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #23777226C2semidirect
2. #23777225C2semidirect
3. #23777223C2semidirect
4. #23777222C2semidirect
5. #23777221C2semidirect
6. #23777220C2semidirect
7. #23777218C2semidirect
8. #23777216C2semidirect
9. #23777215C2semidirect
10. #23777213C2semidirect
11. #23777211C2semidirect
12. #23777209C2semidirect
13. #23777207C2semidirect
14. #23777199C2semidirect
15. #23777195C2semidirect
16. #23776804C2semidirect
17. #23776803C2semidirect
18. C2×#19099190C2semidirect
19. #544×D79C2semidirect
23. C79×#3503C2semidirect
25. Q8×Dic158C22semidirect
26. #19099293C22semidirect
27. #19099293C22semidirect
28. #19099292C22semidirect
29. #19099291C22semidirect
30. #19099291C22semidirect
31. #19099290C22semidirect
32. #19099290C22semidirect
33. #19099289C22semidirect
34. #19099289C22semidirect
35. #19099289C22semidirect
36. #19099289C22semidirect
37. #19099288C22semidirect
38. #19099288C22semidirect
39. #19099274C22semidirect
40. #19099274C22semidirect
41. #19099273C22semidirect
42. #19099273C22semidirect
43. #19099272C22semidirect
44. #19099272C22semidirect
45. #19099272C22semidirect
46. #19099272C22semidirect
47. #19099271C22semidirect
48. #19099270C22semidirect
49. #19099269C22semidirect
50. #19099269C22semidirect
51. #19099268C22semidirect
52. #19099267C22semidirect
53. #19099267C22semidirect
54. #19099267C22semidirect
55. #19099267C22semidirect
56. D4×Dic158C22semidirect
57. #19099228C22semidirect
58. #19099228C22semidirect
59. Q8×C22⋊D79C22semidirect
60. #19099226C22semidirect
61. #19099194C22semidirect
62. #19099194C22semidirect
66. #19099193C22semidirect
67. #19099193C22semidirect
68. #19099193C22semidirect
69. #19099192C22semidirect
70. #19099192C22semidirect
71. #19099192C22semidirect
72. #19099191C22semidirect
73. #19099191C22semidirect
74. #19099191C22semidirect
75. #19099191C22semidirect
82. #19099190C22semidirect
83. #19099190C22semidirect
84. #19099190C22semidirect
85. #19099190C22semidirect
86. #19099190C22semidirect
87. #19099190C22semidirect
88. #19099190C22semidirect
92. #19099120C22semidirect
94. #19099119C22semidirect
96. #19099118C22semidirect
99. #19099117C22semidirect
100. #19099117C22semidirect
101. #19099116C22semidirect
102. #19099116C22semidirect
103. #19099115C22semidirect
104. C2×#14579160C22semidirect
105. C2×#14579159C22semidirect
106. C4⋊Q8×D79C22semidirect
107. C4⋊Q8×D79C22semidirect
108. C2×#14579153C22semidirect
109. C2×#14579152C22semidirect
110. C2×#14579151C22semidirect
111. #125×D79C22semidirect
112. #125×D79C22semidirect
147. Q82×C79C22semidirect
148. #557×C79C22semidirect
149. #554×C79C22semidirect
150. D4×Q8×C79C22semidirect
151. #544×C79C22semidirect
152. #544×C79C22semidirect
153. #533×C79C22semidirect
154. C2×C4⋊Q8×C79C22semidirect
161. #41×D79Q8semidirect
400. #11929625C2×Q8semidirect
401. #11929624C2×Q8semidirect
402. #11929623C2×Q8semidirect
413. Q8×D79C2×Q8semidirect
416. D4×D79C2×Q8semidirect
423. C2×C4×D79C2×Q8semidirect
508. #41×C79C2×Q8semidirect
655. #3503D79semidirect
667. C79#62854semidirect
672. Q82C2×D79semidirect
684. #557C2×D79semidirect
702. #554C2×D79semidirect
708. D4×Q8C2×D79semidirect
737. #544C2×D79semidirect
738. #544C2×D79semidirect
754. #533C2×D79semidirect
759. C2×C4⋊Q8C2×D79semidirect
1047. #41Q8×D79semidirect

Maximal subgroups

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

subgroupindex
#237772262
#237772252
#237772232
#237772222
#237772212
#237772202
#237772182
#237772162
#237772152
#237772132
#237772112
#237772092
#237772072
#237771992
#237771952
#237768042
#237768032
C2×#190991902
#544×D792
#237766002
#237765992
#520×D792
C79×#35032
#6285479