Finite Group Databasebeta

← #35152938

Subgroups — #35152938

Order 20224.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23776967C211yesmaximal, characteristic
2#23772413C212yesmaximal, complemented
3#23772406C212yesmaximal, complemented
4#23772393C212yesmaximal, complemented
5#23772393C212yesmaximal, complemented
6#23772384C212yesmaximal, complemented
7#23772384C212yesmaximal, complemented
8#23772374C212yesmaximal, complemented
9#23772365C212yesmaximal, complemented
10#23772349C211yesmaximal, characteristic, complemented
11#23772135C211yesmaximal, characteristic, complemented
12#23772124C211yesmaximal, characteristic, complemented
13#23772124C211yesmaximal, characteristic, complemented
14#23772105C211yesmaximal, characteristic, complemented
15#23772096C211yesmaximal, characteristic, complemented
16C2×#19098636C211yesmaximal, characteristic, complemented
17#23772068C211yesmaximal, characteristic, complemented
18#23772057C211yesmaximal, characteristic, complemented
19#23772057C211yesmaximal, characteristic, complemented
20#23771825C211yesmaximal, characteristic, complemented
21#23771816C211yesmaximal, characteristic, complemented
22#405×D79C211yesmaximal, characteristic, complemented
23C79×#2961C211yesmaximal, characteristic, complemented
24C2×#14579167C2211yescharacteristic
25C2×#14579167C2211yescharacteristic
26C22×#11929607C2211yescharacteristic
27C2×M16×D79C2211yescharacteristic
28C2×M16×D79C2211yescharacteristic
29C22×C8×D79C2211yescharacteristic
30#19099287C411yescharacteristic
31#19099279C411yescharacteristic
32#19099274C411yescharacteristic
33#19099266C411yescharacteristic
34#19099266C411yescharacteristic
35#19099255C412yes—
36#19099251C411yescharacteristic
37#19099251C411yescharacteristic
38#19099240C412yes—
39#19099240C412yes—
40#19099216C411yescharacteristic
41#19099204C412yes—
42#19099100C2212yes—
43#19099100C2212yes—
44#19099100C2212yes—
45#19099075C2211yescharacteristic
46#19099075C2211yescharacteristic
47C4×#11929625C2212yes—
48C4×#11929624C2211yescharacteristic
49C2×C4×D316C2211yescharacteristic
50#117×D79C2211yescharacteristic
51#117×D79C2211yescharacteristic
52#19098694C2212yescomplemented
53#19098694C2212yescomplemented
54#19098694C2212yescomplemented
55Q8×C79⋊C8C2212yescomplemented
56#19098642C2212yescomplemented
57#19098642C2212yescomplemented
58#19098640C2212yes—
59#19098640C2212yescomplemented
60#19098640C2212yescomplemented
61#19098636C2211yescharacteristic
62#19098636C2211yescharacteristic
63#19098636C2211yescharacteristic
64#19098636C2211yescharacteristic
65#19098636C2211yescharacteristic
66#19098636C2211yescharacteristic
67#19098636C2211yescharacteristic
68#19098636C2211yescharacteristic
69#19098636C2212yescomplemented
70#19098636C2212yescomplemented
71#19098636C2212yescomplemented
72#19098636C2212yescomplemented
73#19098633C2212yes—
74#19098633C2212yes—
75#19098633C2212yescomplemented
76#19098633C2212yescomplemented
77#19098633C2212yescomplemented
78#19098633C2212yescomplemented
79C8×D316C2212yescomplemented
80C8×D316C2212yescomplemented
81#19098628C2212yes—
82#19098628C2212yescomplemented
83#19098628C2212yescomplemented
84#19098623C2212yescomplemented
85#19098623C2212yescomplemented
86#19098623C2212yescomplemented
87#19098623C2212yescomplemented
88#19098623C2212yescomplemented
89#19098623C2212yescomplemented
90#19098619C2212yescomplemented
91#19098619C2212yescomplemented
92#19098619C2212yescomplemented
93#19098615C2212yescomplemented
94#19098615C2212yescomplemented
95#19098615C2212yescomplemented
96#19098590C2211yescharacteristic
97#19098590C2211yescharacteristic
98C2×C4⋊(C79⋊C8)C2211yescharacteristic
99#19098531C2211yescharacteristic
100#19098531C2211yescharacteristic
101#19098526C2211yescharacteristic
102#19098526C2211yescharacteristic
103C2×(C2×D79)⋊C8C2211yescharacteristic
104C2×(C2×D79)⋊C8C2211yescharacteristic
105#19098521C2211yescharacteristic
106#19098521C2211yescharacteristic
107#19098520C2212yescomplemented
108#19098520C2212yescomplemented
109#19098520C2212yescomplemented
110#19098520C2212yescomplemented
111#19098519C2211yescharacteristic
112#19098519C2211yescharacteristic
113#19098518C2211yescharacteristic
114#19098518C2211yescharacteristic
115#19098517C2212yescomplemented
116#19098517C2212yescomplemented
117C4×#11929608C2211yescharacteristic
118#19098515C2212yescomplemented
119#19098515C2212yescomplemented
120C4×#11929607C2212yescomplemented
121#97×D79C2212yescomplemented
122#97×D79C2212yescomplemented
123C4×C8×D79C2212yescomplemented
124#533×C79C2211yescharacteristic
125#446×C79C2212yescomplemented
126#446×C79C2212yescomplemented
127#446×C79C2212yescomplemented
128#446×C79C2212yescomplemented
129#424×C79C2211yescharacteristic
130#424×C79C2211yescharacteristic
131#423×C79C2211yescharacteristic
132#405×C79C2211yescharacteristic
133#405×C79C2211yescharacteristic
134C2×#97×C79C2211yescharacteristic
135C2×#11929625C2×C412yes—
136C2×#11929624C2311yescharacteristic
137C22×D316C2×C411yescharacteristic
138C22×C4×D79C2311yescharacteristic
139C22×C4×D79C2311yescharacteristic
140#14579167—24no—
141#14579167—24no—
142C2×#11929608C2311yescharacteristic
143C2×#11929608C2311yescharacteristic
144C2×#11929607—24no—
145C2×#11929607C2312yes—
146C2×#11929607C2312yes—
147C2×#11929607C2312yes—
148C2×#11929607C2311yescharacteristic
149C2×#11929607C2311yescharacteristic
150C2×#11929607C2311yescharacteristic
151C2×#11929607C2311yescharacteristic
152C2×#11929607C2312yes—
153M16×D79—24no—
154M16×D79—24no—
155C22×C79⋊C8C2311yescharacteristic
156C22×C79⋊C8C2311yescharacteristic
157C2×C8×D79—24no—
158C2×C8×D79C2312yes—
159C2×C8×D79C2312yes—
160C2×C8×D79C2312yes—
161C2×C8×D79C2311yescharacteristic
162C2×C8×D79C2311yescharacteristic
163C2×C8×D79C2312yes—
164C2×C8×D79C2311yescharacteristic
165C2×C8×D79C2311yescharacteristic
166#14579156C2×C412yes—
167#14579156C2×C412yes—
168#14579156C2×C412yes—
169#14579156C2×C412yes—
170#14579156C2×C412yes—
171#14579156C2×C412yes—
172#14579152C2×C412yes—
173#14579152C2×C412yes—
174#14579152C2×C412yes—
175#14579150C2×C412yes—
176#14579150C2×C412yes—
177#14579150C2×C412yes—
178#14579146C2×C412yes—
179#14579146C2×C412yes—
180#14579146C2×C412yes—
181#14579146C2×C412yes—
182#14579146C2×C412yes—
183#14579146C2×C412yes—
184#14579145C2×C412yes—
185#14579145C2×C412yes—
186#14579141C2×C411yescharacteristic
187#14579141C2×C411yescharacteristic
188#14579141C2×C411yescharacteristic
189#14579141C2×C411yescharacteristic
190#14579137C2×C412yes—
191#14579137C2×C412yes—
192#14579137C2×C412yes—
193#14579136C2×C412yes—
194#14579136C2×C412yes—
195#14579136C2×C412yes—
196#14579136C2×C411yescharacteristic
197#14579136C2×C411yescharacteristic
198#14579136C2×C411yescharacteristic
199#14579136C2×C411yescharacteristic
200#14579131C2×C412yes—
201#14579131C2×C412yes—
202Q8×Dic79C2×C412yes—
203C4×Dic158C2×C411yescharacteristic
204C4×Dic158C2×C411yescharacteristic
205C4×D316C2×C411yescharacteristic
206C4×D316C2×C411yescharacteristic
207C4×D316C2×C411yescharacteristic
208C4×D316C2×C411yescharacteristic
209C4×D316C2×C411yescharacteristic
210C4×D316C2×C411yescharacteristic
211C4×D316C2311yescharacteristic
212C4×D316C2312yes—
213C4×D316C2312yes—
214C4×D316C2312yes—
215C4×D316C2311yescharacteristic
216C4×D316C2311yescharacteristic
217C4×D316C2312yes—
218C4×D316C2311yescharacteristic
219#14579123C2×C412yes—
220#14579123C2×C412yes—
221#14579123C2×C412yes—
222C4×C22⋊D79C2×C412yes—
223C4×C22⋊D79C2×C412yes—
224#14579120C2311yescharacteristic
225#14579119C2×C412yes—
226#14579119C2×C412yes—
227#14579119C2×C411yescharacteristic
228#14579119C2×C411yescharacteristic
229#14579119C2×C412yes—
230#14579119C2×C411yescharacteristic
231#14579119C2×C411yescharacteristic
232#14579118C2312yes—
233#14579118C2312yes—
234#14579118C2312yes—
235#14579117C2×C412yes—
236#14579117C2×C412yes—
237C2×C4⋊Dic79C2×C411yescharacteristic
238C4⋊C4×D79C2×C411yescharacteristic
239C4⋊C4×D79C2×C411yescharacteristic
240C4⋊C4×D79C2×C411yescharacteristic
241C4⋊C4×D79C2×C411yescharacteristic
242C2×(C2×D79)⋊C4C2×C411yescharacteristic
243C2×(C2×D79)⋊C4C2×C411yescharacteristic
244C22⋊C4×D79C2×C412yes—
245C22⋊C4×D79C2×C412yes—
246C42×D79C2312yes—
247C42×D79C2312yes—
248C42×D79C2312yes—
249C4⋊(C79⋊C8)C2312yes—
250C4⋊(C79⋊C8)C2312yes—
251C4⋊(C79⋊C8)C2311yescharacteristic
252C4⋊(C79⋊C8)C2311yescharacteristic
253C4⋊(C79⋊C8)C2311yescharacteristic
254C4⋊(C79⋊C8)C2311yescharacteristic
255C4⋊(C79⋊C8)C2312yes—
256C4⋊(C79⋊C8)C2312yes—
257(C2×D79)⋊C8C2312yes—
258(C2×D79)⋊C8C2312yes—
259(C2×D79)⋊C8C2311yescharacteristic
260(C2×D79)⋊C8C2311yescharacteristic
261(C2×D79)⋊C8C2312yes—
262(C2×D79)⋊C8C2312yes—
263(C2×D79)⋊C8C2312yes—
264(C2×D79)⋊C8C2312yes—
265(C2×D79)⋊C8C2312yes—
266(C2×D79)⋊C8C2311yescharacteristic
267(C2×D79)⋊C8C2311yescharacteristic
268(C2×D79)⋊C8C2311yescharacteristic
269(C2×D79)⋊C8C2311yescharacteristic
270(C2×D79)⋊C8C2312yes—
271(C2×D79)⋊C8C2311yescharacteristic
272(C2×D79)⋊C8C2311yescharacteristic
273#14579072C2312yes—
274#14579072C2312yes—
275#14579072C2312yes—
276#14579071C2312yes—
277#14579071C2312yes—
278#14579071C2312yes—
279#14579071C2312yes—
280C4×C79⋊C8C2312yes—
281C4×C79⋊C8C2312yes—
282C4×C79⋊C8C2312yes—
283C8×Dic79C2312yes—
284C8×Dic79C2312yes—
285C8×Dic79C2312yes—
286C8×Dic79C2312yes—
287C2×M16×C79C2311yescharacteristic
288C2×M16×C79C2311yescharacteristic
289C22×C8×C79C2311yescharacteristic
290C22×C8×C79C2311yescharacteristic
291C4⋊Q8×C79C2×C411yescharacteristic
292C4⋊Q8×C79C2×C411yescharacteristic
293#125×C79C2×C411yescharacteristic
294#125×C79C2×C411yescharacteristic
295C22⋊Q8×C79C2×C412yes—
296C22⋊Q8×C79C2×C412yes—
297C4×Q8×C79C2312yes—
298C4×Q8×C79C2312yes—
299#117×C79C2311yescharacteristic
300#117×C79C2311yescharacteristic
301C2×C42×C79C2311yescharacteristic
302C4⋊C8×C79C2312yes—
303C4⋊C8×C79C2312yes—
304C4⋊C8×C79C2312yes—
305C4⋊C8×C79C2312yes—
306C4⋊C8×C79C2312yes—
307C4⋊C8×C79C2312yes—
308#97×C79C2311yescharacteristic
309#97×C79C2311yescharacteristic
310#97×C79C2311yescharacteristic
311#97×C79C2311yescharacteristic
312#97×C79C2312yes—
313#97×C79C2312yes—
314C4×C8×C79C2312yes—
315C4×C8×C79C2312yes—
316C23×D79C22×C411yescharacteristic
317C23×D79C22×C411yescharacteristic
318#11929625—44no—
319#11929624—22no—
320#11929624—22no—
321C2×Dic158C22×C411yescharacteristic
322C2×D316—42no—
323C2×D316C22×C411yescharacteristic
324C2×D316C22×C411yescharacteristic
325C2×D316C22×C412yes—
326C2×D316C22×C411yescharacteristic
327C2×D316C22×C412yes—
328C2×D316C22×C411yescharacteristic
329C2×D316C22×C411yescharacteristic
330C2×D316C22×C412yes—
331C2×D316C22×C412yes—
332C2×C22⋊D79C22×C412yes—
333C22×Dic79C22×C411yescharacteristic
334C22×Dic79C22×C411yescharacteristic
335C2×C4×D79—22no—
336C2×C4×D79—22no—
337C2×C4×D79—22no—
338C2×C4×D79—22no—
339C2×C4×D79C22×C412yes—
340C2×C4×D79C22×C411yescharacteristic
341C2×C4×D79C22×C411yescharacteristic
342C2×C4×D79C22×C411yescharacteristic
343C2×C4×D79C22×C411yescharacteristic
344C2×C4×D79C22×C412yes—
345C2×C4×D79C22×C412yes—
346C2×C4×D79C22×C412yes—
347C2×C4×D79C22×C412yes—
348C2×C4×D79C22×C412yes—
349C2×C4×D79C2412yes—
350C2×C4×D79C2411yescharacteristic
351C2×C4×D79C2411yescharacteristic
352C2×C4×D79C2411yescharacteristic
353C2×C4×D79C2411yescharacteristic
354#11929608—22no—
355#11929608#4114yescomplemented
356#11929607—22no—
357#11929607—22no—
358#11929607—22no—
359#11929607—22no—
360#11929607—24no—
361#11929607—24no—
362#11929607—24no—
363#11929607—24no—
364C2×C79⋊C8—22no—
365C2×C79⋊C8—22no—
366C2×C79⋊C8C2411yescharacteristic
367C2×C79⋊C8C2411yescharacteristic
368C2×C79⋊C8C2412yes—
369C2×C79⋊C8C2411yescharacteristic
370C2×C79⋊C8C2411yescharacteristic
371C2×C79⋊C8C2412yes—
372C8×D79—22no—
373C8×D79—22no—
374C8×D79—22no—
375C8×D79—22no—
376C8×D79—24no—
377C8×D79—24no—
378C8×D79—24no—
379C8×D79—24no—
380C4⋊Dic79C22×C411yescharacteristic
381C4⋊Dic79C22×C411yescharacteristic
382C4⋊Dic79C22×C411yescharacteristic
383C4⋊Dic79C22×C411yescharacteristic
384C4⋊Dic79C22×C411yescharacteristic
385C4⋊Dic79C22×C411yescharacteristic
386C4⋊Dic79C22×C412yes—
387C4⋊Dic79C22×C412yes—
388C4⋊Dic79C22×C412yes—
389C4⋊Dic79C22×C412yes—
390Dic79⋊C4C22×C412yes—
391Dic79⋊C4C22×C412yes—
392Dic79⋊C4C22×C412yes—
393Dic79⋊C4C22×C412yes—
394Dic79⋊C4C22×C412yes—
395Dic79⋊C4C22×C412yes—
396C22⋊Dic79C22×C412yes—
397(C2×D79)⋊C4C22×C412yes—
398(C2×D79)⋊C4C22×C412yes—
399(C2×D79)⋊C4C22×C412yes—
400(C2×D79)⋊C4C22×C412yes—
401(C2×D79)⋊C4C22×C411yescharacteristic
402(C2×D79)⋊C4C22×C411yescharacteristic
403(C2×D79)⋊C4C22×C411yescharacteristic
404(C2×D79)⋊C4C22×C411yescharacteristic
405(C2×D79)⋊C4C22×C411yescharacteristic
406(C2×D79)⋊C4C22×C411yescharacteristic
407(C2×D79)⋊C4C22×C411yescharacteristic
408(C2×D79)⋊C4C22×C411yescharacteristic
409(C2×D79)⋊C4C22×C412yes—
410(C2×D79)⋊C4C22×C412yes—
411(C2×D79)⋊C4C22×C412yes—
412(C2×D79)⋊C4C22×C412yes—
413(C2×D79)⋊C4C22×C412yes—
414(C2×D79)⋊C4C22×C412yes—
415(C2×D79)⋊C4C22×C412yes—
416(C2×D79)⋊C4C22×C412yes—
417(C2×D79)⋊C4C22×C412yes—
418(C2×D79)⋊C4C22×C412yes—
419C4×Dic79C22×C412yes—
420C4×Dic79C22×C412yes—
421C4×Dic79C22×C412yes—
422C4×Dic79C22×C412yes—
423C4×Dic79C22×C412yes—
424C4×Dic79C22×C412yes—
425C4×Dic79C2412yes—
426C2×Q8×C79C22×C412yes—
427C2×Q8×C79C22×C412yes—
428C22×C4×C79C22×C411yescharacteristic
429C22×C4×C79C22×C411yescharacteristic
430C22×C4×C79C2411yescharacteristic
431M16×C79—22no—
432M16×C79—22no—
433C2×C8×C79—22no—
434C2×C8×C79#4114yescomplemented
435C2×C8×C79C2412yes—
436C2×C8×C79C2412yes—
437C2×C8×C79C2411yescharacteristic
438C2×C8×C79C2411yescharacteristic
439C2×C8×C79C2411yescharacteristic
440C2×C8×C79C2411yescharacteristic
441C4⋊C4×C79C22×C411yescharacteristic
442C4⋊C4×C79C22×C411yescharacteristic
443C4⋊C4×C79C22×C411yescharacteristic
444C4⋊C4×C79C22×C411yescharacteristic
445C4⋊C4×C79C22×C412yes—
446C4⋊C4×C79C22×C412yes—
447C4⋊C4×C79C22×C412yes—
448C4⋊C4×C79C22×C412yes—
449C4⋊C4×C79C22×C412yes—
450C4⋊C4×C79C22×C412yes—
451C22⋊C4×C79C22×C412yes—
452C22⋊C4×C79C22×C412yes—
453C42×C79C22×C411yescharacteristic
454C42×C79C22×C411yescharacteristic
455C42×C79C2412yes—
456C42×C79C2412yes—
457C42×C79C2411yescharacteristic
458C42×C79C2411yescharacteristic
459C23×C79C23×C411yescharacteristic
460C22×D79—22no—
461C22×D79—22no—
462C22×D79—22no—
463C22×D79—41no—
464C22×D79—41no—
465C22×D79—41no—
466C22×D79C23×C411yescharacteristic
467C22×D79C23×C411yescharacteristic
468C22×D79C23×C412yes—
469C22×D79C23×C411yescharacteristic
470C22×D79C23×C411yescharacteristic
471Q8×C79—42no—
472Q8×C79—42no—
473C2×C4×C79—41no—
474C2×C4×C79—41no—
475C2×C4×C79C23×C411yescharacteristic
476C2×C4×C79C23×C411yescharacteristic
477C2×C4×C79C23×C412yes—
478C2×C4×C79C23×C412yes—
479C2×C4×C79C23×C412yes—
480C2×C4×C79C23×C412yes—
481C2×C4×C79C23×C411yescharacteristic
482C2×C4×C79C23×C411yescharacteristic
483C2×C4×C79C23×C411yescharacteristic
484C2×C4×C79C2×#4112yes—
485C2×C4×C79C2×#4112yes—
486C2×C4×C79C2511yescharacteristic
487C22⋊D79—24no—
488C2×Dic79—22no—
489C2×Dic79—22no—
490C2×Dic79C23×C411yescharacteristic
491C2×Dic79C23×C411yescharacteristic
492C2×Dic79C23×C412yes—
493C2×Dic79C23×C412yes—
494C2×Dic79C23×C412yes—
495C2×Dic79C23×C411yescharacteristic
496C2×Dic79C23×C411yescharacteristic
497D316—22no—
498D316—22no—
499D316—24no—
500D316—22no—
501D316—41no—
502D316—41no—
503D316—42no—
504D316—42no—
505D316—42no—
506C4×D79—24no—
507C4×D79—22no—
508C4×D79—22no—
509C4×D79—22no—
510C4×D79—22no—
511C4×D79—21no—
512C4×D79—21no—
513C4×D79—21no—
514C4×D79—21no—
515C4×D79—22no—
516C4×D79—22no—
517C4×D79—21no—
518C4×D79—21no—
519C4×D79—21no—
520C4×D79—21no—
521C4×D79—42no—
522C4×D79—42no—
523C4×D79—42no—
524C4×D79—42no—
525C4×D79—42no—
526Dic158—22no—
527C8×C79—21no—
528C8×C79—22no—
529C8×C79—22no—
530C8×C79—21no—
531C8×C79C2×#4112yes—
532C8×C79C2×#4112yes—
533C79⋊C8—21no—
534C79⋊C8—21no—
535C79⋊C8—22no—
536C79⋊C8—21no—
537C79⋊C8—21no—
538C79⋊C8C2×#4114yes—
539C22×C79—21no—
540C22×C79—21no—
541C22×C79C4×#4112yes—
542C22×C79C24×C411yescharacteristic
543C2×D79—21no—
544C2×D79—21no—
545C2×D79—22no—
546C2×D79—21no—
547C2×D79—21no—
548C2×D79—21no—
549C2×D79—21no—
550C2×D79—21no—
551C2×D79—21no—
552C2×D79—22no—
553C2×D79—21no—
554C2×D79—21no—
555C2×D79—21no—
556C2×D79—22no—
557C2×D79—44no—
558C2×D79—82no—
559C2×D79#56812yes—
560C4×C79—21no—
561C4×C79—21no—
562C4×C79—22no—
563C4×C79—22no—
564C4×C79—21no—
565C4×C79—21no—
566C4×C79—22no—
567C4×C79—22no—
568C4×C79C4×#4112yes—
569C4×C79C22×#4111yescharacteristic
570C4×C79C22×#4111yescharacteristic
571Dic79—22no—
572Dic79—21no—
573Dic79—21no—
574Dic79—21no—
575Dic79—21no—
576Dic79—22no—
577Dic79—22no—
578#60216—791nomaximal, Sylow
579C2×C79—22no—
580C2×C79C2×C4×#4111yescharacteristic
581C2×C79C2×#56811yescharacteristic
582C2×C79#357311yescharacteristic
583D79—22no—
584D79—42no—
585D79—41no—
586D79—41no—
587D79—41no—
588#3475—791no—
589#2970—792no—
590#2969—792no—
591#2968—792no—
592#2968—792no—
593#2967—792no—
594#2967—792no—
595#2966—792no—
596#2965—792no—
597#2962—791no—
598#2961D7911yescharacteristic, complemented
599D4×M16—791no—
600#2933—791no—
601#2933—791no—
602#2930—791no—
603#2929—791no—
604C2×#435—791no—
605#2925—791no—
606#2924—791no—
607#2924—791no—
608#2875—791no—
609#2873—791no—
610C2×#405—791no—
611C79#6021611yescharacteristic, complemented, Sylow
612C2×#131—791no—
613C2×#131—791no—
614C22×M16—791no—
615C22×M16—791no—
616C22×M16—791no—
617C23×C8—791no—
618#556—791no—
619#555—791no—
620#554—791no—
621#553—791no—
622#553—791no—
623#552—791no—
624#552—791no—
625#552—792no—
626#551—792no—
627#551—792no—
628#547—791no—
629#546—792no—
630#533C2×D7911yescharacteristic
631#529—792no—
632#529—792no—
633#529—792no—
634#525—791no—
635#525—791no—
636C4×#41—792no—
637C4×#41—791no—
638C2×C4×D4—791no—
639C2×#117—791no—
640C2×#117—791no—
641#446—792no—
642#446—792no—
643#446—792no—
644#446C2×D7912yescomplemented
645#446C2×D7912yescomplemented
646#446C2×D7912yescomplemented
647#446C2×D7912yescomplemented
648C8×Q8—792no—
649#436—792no—
650#436—792no—
651#436—792no—
652#436—792no—
653#436—792no—
654#435—792no—
655#435—792no—
656#435—792no—
657#435—792no—
658#435—792no—
659#435—792no—
660#435—791no—
661#435—791no—
662#435—791no—
663#435—791no—
664#435—791no—
665#435—791no—
666#435—791no—
667#435—791no—
668#435—792no—
669#435—792no—
670#435—792no—
671#435—792no—
672C8×D4—792no—
673C8×D4—792no—
674C8×D4—792no—
675C8×D4—792no—
676C8×D4—792no—
677#433—792no—
678#433—792no—
679#433—792no—
680#433—792no—
681#433—792no—
682#433—792no—
683#432—792no—
684#432—792no—
685#432—792no—
686#431—792no—
687#431—792no—
688#431—792no—
689#424—791no—
690#424—791no—
691#424C2×D7911yescharacteristic
692#424C2×D7911yescharacteristic
693#423C2×D7911yescharacteristic
694C2×C4⋊C8—791no—
695#408—791no—
696#408—791no—
697#407—791no—
698#407—791no—
699C2×C22⋊C8—791no—
700C2×C22⋊C8—791no—
701#405—791no—
702#405—791no—
703#405—791no—
704#405—791no—
705#405—791no—
706#405—791no—
707#405—792no—
708#405—792no—
709#405—792no—
710#405—792no—
711#405—792no—
712#405—792no—
713#405C2×D7911yescharacteristic
714#405C2×D7911yescharacteristic
715C4×M16—791no—
716C4×M16—792no—
717C4×M16—792no—
718C4×M16—792no—
719C2×#97—792no—
720C2×#97—792no—
721C2×#97C2×D7911yescharacteristic
722C2×C4×C8—792no—
723C2×#41—792no—
724C2×#41—791no—
725C22×D4—791no—
726C23×C4—791no—
727C23×C4—791no—
728#131—1584no—
729#131—1584no—
730C2×M16—791no—
731C2×M16—791no—
732C2×M16—791no—
733C2×M16—792no—
734C2×M16—791no—
735C2×M16—791no—
736C2×M16—792no—
737C2×M16—791no—
738C2×M16—792no—
739C2×M16—792no—
740C2×M16—1584no—
741C2×M16—1584no—
742C2×M16—1584no—
743C2×M16C22×D7911yescharacteristic
744C2×M16C22×D7911yescharacteristic
745C22×C8—791no—
746C22×C8—791no—
747C22×C8—791no—
748C22×C8—791no—
749C22×C8—791no—
750C22×C8—791no—
751C22×C8—792no—
752C22×C8—792no—
753C22×C8—792no—
754C22×C8—792no—
755C22×C8—1584no—
756C22×C8C22×D7911yescharacteristic
757C22×C8C22×D7911yescharacteristic
758C4⋊Q8C4×D7911yescharacteristic
759C4⋊Q8C4×D7911yescharacteristic
760#126—792no—
761#126—792no—
762#126—792no—
763#126—792no—
764#126—792no—
765#126—792no—
766#125—792no—
767#125—792no—
768#125—792no—
769#125C4×D7911yescharacteristic
770#125C4×D7911yescharacteristic
771#124—792no—
772#124—792no—
773#124—792no—
774#123—792no—
775#123—792no—
776#123—792no—
777#123—792no—
778#123—792no—
779#123—792no—
780#123—792no—
781#123—792no—
782C22⋊Q8—792no—
783C22⋊Q8—792no—
784C22⋊Q8—792no—
785C22⋊Q8—791no—
786C22⋊Q8—791no—
787C22⋊Q8—791no—
788C22⋊Q8—791no—
789C22⋊Q8C4×D7912yes—
790C22⋊Q8C4×D7912yes—
791#121—791no—
792#121—791no—
793#121—791no—
794#121—791no—
795#121—792no—
796#121—792no—
797#121—792no—
798#120—792no—
799#120—792no—
800C4×Q8—792no—
801C4×Q8—791no—
802C4×Q8—791no—
803C4×Q8C22×D7912yes—
804C4×Q8C22×D7912yes—
805C4×D4—792no—
806C4×D4—792no—
807C4×D4—792no—
808C4×D4—792no—
809C4×D4—792no—
810C4×D4—791no—
811C4×D4—791no—
812C4×D4—791no—
813C4×D4—791no—
814C4×D4—791no—
815C4×D4—791no—
816C4×D4—791no—
817C4×D4—791no—
818C4×D4—791no—
819C4×D4—791no—
820C4×D4—792no—
821C4×D4—792no—
822C4×D4—792no—
823C4×D4—792no—
824#117—791no—
825#117—791no—
826#117—791no—
827#117—791no—
828#117—791no—
829#117—792no—
830#117—792no—
831#117—792no—
832#117—792no—
833#117—792no—
834#117—792no—
835#117—792no—
836#117—792no—
837#117C22×D7911yescharacteristic
838#117C22×D7911yescharacteristic
839C2×C4⋊C4—791no—
840C2×C4⋊C4—791no—
841C2×C4⋊C4—791no—
842C2×C4⋊C4—791no—
843C2×C4⋊C4—791no—
844C2×C22⋊C4—791no—
845C2×C22⋊C4—791no—
846C2×C22⋊C4—792no—
847C2×C22⋊C4—792no—
848C2×C42—792no—
849C2×C42—792no—
850C2×C42—792no—
851C2×C42C22×D7911yescharacteristic
852C4⋊C8—791no—
853C4⋊C8—791no—
854C4⋊C8—791no—
855C4⋊C8—791no—
856C4⋊C8—792no—
857C4⋊C8—792no—
858C4⋊C8—792no—
859C4⋊C8—792no—
860C4⋊C8C22×D7912yes—
861C4⋊C8C22×D7912yes—
862C4⋊C8C22×D7912yes—
863C4⋊C8C22×D7912yes—
864C4⋊C8C22×D7912yes—
865C4⋊C8C22×D7912yes—
866C22⋊C8—791no—
867C22⋊C8—791no—
868C22⋊C8—791no—
869C22⋊C8—791no—
870C22⋊C8—791no—
871C22⋊C8—791no—
872C22⋊C8—791no—
873C22⋊C8—791no—
874C22⋊C8—792no—
875C22⋊C8—792no—
876C22⋊C8—792no—
877C22⋊C8—792no—
878C22⋊C8—792no—
879C22⋊C8—792no—
880C22⋊C8—792no—
881C22⋊C8—792no—
882#97—792no—
883#97—792no—
884#97—792no—
885#97—792no—
886#97—792no—
887#97—792no—
888#97—792no—
889#97C22×D7911yescharacteristic
890#97C22×D7912yes—
891#97C22×D7911yescharacteristic
892#97C22×D7911yescharacteristic
893#97C22×D7911yescharacteristic
894#97C22×D7912yes—
895C4×C8—792no—
896C4×C8—792no—
897C4×C8—792no—
898C4×C8—792no—
899C4×C8—792no—
900C4×C8—792no—
901C4×C8—792no—
902C4×C8C22×D7912yes—
903C4×C8C22×D7912yes—
904C24—791no—
905C24—791no—
906#41—3164no—
907#41—1582no—
908#41—1582no—
909C2×Q8—791no—
910C2×Q8C2×C4×D7912yes—
911C2×Q8C2×C4×D7912yes—
912C2×D4—3162no—
913C2×D4—792no—
914C2×D4—792no—
915C2×D4—791no—
916C2×D4—791no—
917C2×D4—792no—
918C2×D4—792no—
919C2×D4—791no—
920C2×D4—792no—
921C2×D4—791no—
922C2×D4—791no—
923C22×C4—792no—
924C22×C4—792no—
925C22×C4—792no—
926C22×C4—792no—
927C22×C4—792no—
928C22×C4—791no—
929C22×C4—791no—
930C22×C4—791no—
931C22×C4—791no—
932C22×C4—792no—
933C22×C4—791no—
934C22×C4—791no—
935C22×C4—792no—
936C22×C4—791no—
937C22×C4—791no—
938C22×C4—791no—
939C22×C4—791no—
940C22×C4—1582no—
941C22×C4—1582no—
942C22×C4—1582no—
943C22×C4—1582no—
944C22×C4C2×C4×D7911yescharacteristic
945C22×C4C2×C4×D7911yescharacteristic
946C22×C4C23×D7911yescharacteristic
947M16—22no—
948M16—22no—
949M16—794no—
950M16—1584no—
951M16—1584no—
952M16—1584no—
953M16—1582no—
954M16—1582no—
955M16—1582no—
956M16—1582no—
957M16—1582no—
958M16—1584no—
959C2×C8—22no—
960C2×C8—792no—
961C2×C8—791no—
962C2×C8—791no—
963C2×C8—792no—
964C2×C8—791no—
965C2×C8—791no—
966C2×C8—1584no—
967C2×C8—1584no—
968C2×C8—1584no—
969C2×C8—1582no—
970C2×C8—1582no—
971C2×C8—1582no—
972C2×C8—1582no—
973C2×C8—1582no—
974C2×C8—1582no—
975C2×C8—1584no—
976C2×C8#1192962514yescomplemented
977C2×C8C23×D7911yescharacteristic
978C2×C8C23×D7912yes—
979C2×C8C23×D7912yes—
980C2×C8C23×D7911yescharacteristic
981C2×C8C23×D7911yescharacteristic
982C2×C8C23×D7911yescharacteristic
983C4⋊C4—792no—
984C4⋊C4—792no—
985C4⋊C4—792no—
986C4⋊C4—792no—
987C4⋊C4—792no—
988C4⋊C4—792no—
989C4⋊C4—791no—
990C4⋊C4—791no—
991C4⋊C4—791no—
992C4⋊C4—791no—
993C4⋊C4—791no—
994C4⋊C4—791no—
995C4⋊C4—792no—
996C4⋊C4—792no—
997C4⋊C4—792no—
998C4⋊C4—792no—
999C4⋊C4C2×C4×D7911yescharacteristic
1000C4⋊C4C2×C4×D7911yescharacteristic
1001C4⋊C4C2×C4×D7911yescharacteristic
1002C4⋊C4C2×C4×D7911yescharacteristic
1003C4⋊C4C2×C4×D7912yes—
1004C4⋊C4C2×C4×D7912yes—
1005C4⋊C4C2×C4×D7912yes—
1006C4⋊C4C2×C4×D7912yes—
1007C4⋊C4C2×C4×D7912yes—
1008C4⋊C4C2×C4×D7912yes—
1009C22⋊C4—792no—
1010C22⋊C4—791no—
1011C22⋊C4—791no—
1012C22⋊C4—792no—
1013C22⋊C4—792no—
1014C22⋊C4—792no—
1015C22⋊C4—792no—
1016C22⋊C4—791no—
1017C22⋊C4—791no—
1018C22⋊C4—791no—
1019C22⋊C4—791no—
1020C22⋊C4—791no—
1021C22⋊C4—791no—
1022C22⋊C4—792no—
1023C22⋊C4—792no—
1024C22⋊C4—792no—
1025C22⋊C4—792no—
1026C22⋊C4—792no—
1027C22⋊C4—792no—
1028C22⋊C4—792no—
1029C22⋊C4—792no—
1030C22⋊C4—792no—
1031C22⋊C4—792no—
1032C22⋊C4C2×C4×D7912yes—
1033C22⋊C4C2×C4×D7912yes—
1034C42—792no—
1035C42—792no—
1036C42—792no—
1037C42—792no—
1038C42—792no—
1039C42—792no—
1040C42—792no—
1041C42C2×C4×D7911yescharacteristic
1042C42C2×C4×D7911yescharacteristic
1043C42C23×D7911yescharacteristic
1044C42C23×D7912yes—
1045C42C23×D7912yes—
1046C42C23×D7911yescharacteristic
1047C23—3161no—
1048C23—3161no—
1049C23—3161no—
1050C23—791no—
1051C23—791no—
1052C23—791no—
1053C23—792no—
1054C23—791no—
1055C23—1582no—
1056C23—1582no—
1057C23—1582no—
1058C23C22×C4×D7911yescharacteristic
1059Q8—42no—
1060Q8—42no—
1061Q8—1582no—
1062D4—3161no—
1063D4—3161no—
1064D4—3162no—
1065D4—3162no—
1066D4—3162no—
1067D4—1582no—
1068D4—1582no—
1069D4—1584no—
1070D4—1584no—
1071D4—1582no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—3162no—
1075C2×C4—3162no—
1076C2×C4—3162no—
1077C2×C4—3162no—
1078C2×C4—3162no—
1079C2×C4—792no—
1080C2×C4—792no—
1081C2×C4—791no—
1082C2×C4—791no—
1083C2×C4—792no—
1084C2×C4—791no—
1085C2×C4—791no—
1086C2×C4—1584no—
1087C2×C4—1582no—
1088C2×C4—1582no—
1089C2×C4—1582no—
1090C2×C4—1582no—
1091C2×C4—1582no—
1092C2×C4—1582no—
1093C2×C4—1581no—
1094C2×C4—1581no—
1095C2×C4—1582no—
1096C2×C4—1581no—
1097C2×C4—1581no—
1098C2×C4—1581no—
1099C2×C4—1581no—
1100C2×C4—1582no—
1101C2×C4—1581no—
1102C2×C4—1581no—
1103C2×C4C22×C4×D7911yescharacteristic
1104C2×C4C22×C4×D7911yescharacteristic
1105C2×C4C22×C4×D7912yes—
1106C2×C4C22×C4×D7912yes—
1107C2×C4C22×C4×D7912yes—
1108C2×C4C22×C4×D7912yes—
1109C2×C4C22×C4×D7911yescharacteristic
1110C2×C4C22×C4×D7911yescharacteristic
1111C2×C4C22×C4×D7911yescharacteristic
1112C2×C4#41×D7912yes—
1113C2×C4C2×#1192962512yes—
1114C2×C4C24×D7911yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—22no—
1118C8—22no—
1119C8—794no—
1120C8—1581no—
1121C8—1581no—
1122C8—1581no—
1123C8—1581no—
1124C8—1582no—
1125C8C2×#1192962512yes—
1126C8C2×#1192962512yes—
1127C22—21no—
1128C22—21no—
1129C22—3164no—
1130C22—792no—
1131C22—6322no—
1132C22—1581no—
1133C22—1582no—
1134C22—1581no—
1135C22—1581no—
1136C22—1581no—
1137C22—1582no—
1138C22—1581no—
1139C22—1581no—
1140C22—1581no—
1141C22—1581no—
1142C22—1581no—
1143C22—1582no—
1144C22—1581no—
1145C22—1581no—
1146C22C4×#1192962512yes—
1147C22C23×C4×D7911yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—22no—
1152C4—21no—
1153C4—21no—
1154C4—22no—
1155C4—22no—
1156C4—1582no—
1157C4—1582no—
1158C4—1581no—
1159C4—1581no—
1160C4—1581no—
1161C4—1581no—
1162C4—1582no—
1163C4C4×#1192962512yes—
1164C4C2×#41×D7911yescharacteristic
1165C4C22×#1192962511yescharacteristic
1166C2—22no—
1167C2—3161no—
1168C2—3161no—
1169C2—3161no—
1170C2—3162no—
1171C2—1582no—
1172C2C2×C4×#1192962511yescharacteristic
1173C2#568×D7911yescharacteristic
1174C2#2377811311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D79
commutator, socleC22×C79C24×C4
FittingC79×#2961C2
prime radical#23776967C2
cosocleC2×C4×C79C25
hypercenter#2961D79
hypocenterC79#60216
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #23772413C2semidirect
3. #23772406C2semidirect
4. #23772393C2semidirect
5. #23772393C2semidirect
6. #23772384C2semidirect
7. #23772384C2semidirect
8. #23772374C2semidirect
9. #23772365C2semidirect
10. #23772349C2semidirect
11. #23772135C2semidirect
12. #23772124C2semidirect
13. #23772124C2semidirect
14. #23772105C2semidirect
15. #23772096C2semidirect
16. C2×#19098636C2semidirect
17. #23772068C2semidirect
18. #23772057C2semidirect
19. #23772057C2semidirect
20. #23771825C2semidirect
21. #23771816C2semidirect
22. #405×D79C2semidirect
23. C79×#2961C2semidirect
52. #19098694C22semidirect
53. #19098694C22semidirect
54. #19098694C22semidirect
55. Q8×C79⋊C8C22semidirect
56. #19098642C22semidirect
57. #19098642C22semidirect
59. #19098640C22semidirect
60. #19098640C22semidirect
69. #19098636C22semidirect
70. #19098636C22semidirect
71. #19098636C22semidirect
72. #19098636C22semidirect
75. #19098633C22semidirect
76. #19098633C22semidirect
77. #19098633C22semidirect
78. #19098633C22semidirect
79. C8×D316C22semidirect
80. C8×D316C22semidirect
82. #19098628C22semidirect
83. #19098628C22semidirect
84. #19098623C22semidirect
85. #19098623C22semidirect
86. #19098623C22semidirect
87. #19098623C22semidirect
88. #19098623C22semidirect
89. #19098623C22semidirect
90. #19098619C22semidirect
91. #19098619C22semidirect
92. #19098619C22semidirect
93. #19098615C22semidirect
94. #19098615C22semidirect
95. #19098615C22semidirect
107. #19098520C22semidirect
108. #19098520C22semidirect
109. #19098520C22semidirect
110. #19098520C22semidirect
115. #19098517C22semidirect
116. #19098517C22semidirect
118. #19098515C22semidirect
119. #19098515C22semidirect
120. C4×#11929607C22semidirect
121. #97×D79C22semidirect
122. #97×D79C22semidirect
123. C4×C8×D79C22semidirect
125. #446×C79C22semidirect
126. #446×C79C22semidirect
127. #446×C79C22semidirect
128. #446×C79C22semidirect
355. #11929608#41semidirect
434. C2×C8×C79#41semidirect
598. #2961D79semidirect
611. C79#60216semidirect
644. #446C2×D79semidirect
645. #446C2×D79semidirect
646. #446C2×D79semidirect
647. #446C2×D79semidirect
976. C2×C8#11929625semidirect

Maximal subgroups

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

subgroupindex
#237769672
#237724132
#237724062
#237723932
#237723842
#237723742
#237723652
#237723492
#237721352
#237721242
#237721052
#237720962
C2×#190986362
#237720682
#237720572
#237718252
#237718162
#405×D792
C79×#29612
#6021679