Finite Group Databasebeta

← #35152847

Subgroups — #35152847

Order 20224.

1996 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23776694C211yesmaximal, characteristic
2#23772405C211yesmaximal, characteristic, complemented
3#23772404C211yesmaximal, characteristic, complemented
4#23772398C211yesmaximal, characteristic, complemented
5#23772392C212yesmaximal, complemented
6#23772390C212yesmaximal, complemented
7#23772365C211yesmaximal, characteristic, complemented
8#23772363C211yesmaximal, characteristic, complemented
9#23772363C212yesmaximal, complemented
10#23772360C212yesmaximal, complemented
11C8×#11929625C211yesmaximal, characteristic, complemented
12C8×#11929623C211yesmaximal, characteristic, complemented
13#23772348C211yesmaximal, characteristic, complemented
14#23772342C211yesmaximal, characteristic, complemented
15#23772145C211yesmaximal, characteristic, complemented
16#23772139C211yesmaximal, characteristic, complemented
17#23772129C212yesmaximal, complemented
18#23772123C212yesmaximal, complemented
19#23772041C212yesmaximal, complemented
20#431×D79C211yesmaximal, characteristic, complemented
21#23771822C212yesmaximal, complemented
22C4×M16×D79C211yesmaximal, characteristic, complemented
23C79×#2969C211yesmaximal, characteristic, complemented
24C2×#14579169C2212yes—
25C2×#14579167C2212yes—
26C2×M16×D79C2211yescharacteristic
27C2×M16×D79C2211yescharacteristic
28#19099119C411yescharacteristic
29#19099117C2211yescharacteristic
30#19099115C411yescharacteristic
31#19099112C411yescharacteristic
32#19099110C2211yescharacteristic
33#19099108C411yescharacteristic
34#19099098C411yescharacteristic
35#19099097C2211yescharacteristic
36#19099096C412yes—
37#19099096C412yes—
38#19099092C411yescharacteristic
39#19099091C2212yes—
40#19099090C412yes—
41#19099076C411yescharacteristic
42#19099073C411yescharacteristic
43#19099072C2212yes—
44#19099071C412yes—
45C4×#11929625C2211yescharacteristic
46#19099031C2212yes—
47C4×#11929623C2211yescharacteristic
48C4×#11929623C2212yes—
49C2×C42×D79C2211yescharacteristic
50#19098694C2211yescharacteristic, complemented
51#19098693C2212yescomplemented
52#19098693C2211yescharacteristic, complemented
53#19098692C2212yescomplemented
54#19098691C2212yescomplemented
55#19098690C2212yescomplemented
56#19098690C2211yescharacteristic, complemented
57Q8×C79⋊C8C2211yescharacteristic, complemented
58C8×Dic158C2211yescharacteristic, complemented
59#19098687C2211yescharacteristic, complemented
60#19098642C2211yescharacteristic, complemented
61#19098641C2212yes—
62#19098641C2211yescharacteristic, complemented
63#19098640C2211yescharacteristic, complemented
64#19098639C2212yes—
65#19098638C2212yes—
66#19098637C2212yes—
67#19098637C2212yes—
68#19098637C2212yescomplemented
69#19098636C2212yes—
70#19098635C2212yes—
71#19098634C2212yescomplemented
72#19098633C2212yes—
73#19098632C2212yes—
74#19098632C2212yes—
75#19098632C2212yescomplemented
76#19098631C2212yescomplemented
77C8×D316C2212yes—
78C8×D316C2211yescharacteristic, complemented
79D4×C79⋊C8C2211yescharacteristic, complemented
80#19098628C2212yes—
81#19098628C2211yescharacteristic, complemented
82C8×C22⋊D79C2212yes—
83(C22⋊D79)⋊C8C2212yes—
84#19098625C2212yescomplemented
85#19098624C2212yescomplemented
86#19098622C2212yescomplemented
87#19098616C2211yescharacteristic
88#19098615C2211yescharacteristic
89#19098615C2211yescharacteristic
90#19098615C2212yescomplemented
91#19098615C2212yescomplemented
92#19098614C2212yes—
93#19098613C2212yes—
94#19098613C2212yescomplemented
95#19098613C2212yescomplemented
96#19098588C2212yes—
97#19098588C2212yes—
98C4⋊C8×D79C2211yescharacteristic
99C4⋊C8×D79C2211yescharacteristic
100#19098528C2212yes—
101#19098528C2212yes—
102C22⋊C8×D79C2212yes—
103#19098520C2212yes—
104#19098520C2212yescomplemented
105#19098519C2212yescomplemented
106#19098517C2212yes—
107#19098517C2212yescomplemented
108C4×#11929608C2211yescharacteristic
109#19098515C2211yescharacteristic
110#19098515C2211yescharacteristic
111#19098515C2212yescomplemented
112M16×Dic79C2211yescharacteristic
113M16×Dic79C2211yescharacteristic
114M16×Dic79C2212yescomplemented
115C4×#11929607C2211yescharacteristic
116C4×#11929607C2211yescharacteristic
117#97×D79C2211yescharacteristic
118#97×D79C2211yescharacteristic
119C2×C8×Dic79C2212yescomplemented
120C4×C8×D79C2212yes—
121C4×C8×D79C2211yescharacteristic
122C4×C8×D79C2211yescharacteristic
123C4×C8×D79C2212yescomplemented
124#529×C79C2211yescharacteristic
125#446×C79C2211yescharacteristic, complemented
126C8×Q8×C79C2211yescharacteristic, complemented
127#436×C79C2212yes—
128#436×C79C2211yescharacteristic, complemented
129#435×C79C2212yes—
130C8×D4×C79C2211yescharacteristic, complemented
131#433×C79C2212yescomplemented
132#431×C79C2211yescharacteristic
133#405×C79C2212yescomplemented
134C4×M16×C79C2211yescharacteristic
135C2×#11929625C2×C411yescharacteristic
136C2×#11929624C2312yes—
137C2×#11929623C2×C411yescharacteristic
138C2×#11929623C2×C412yes—
139C22×C4×D79C2×C411yescharacteristic
140C22×C4×D79C2×C411yescharacteristic
141C22×C4×D79C2311yescharacteristic
142#14579169—28no—
143#14579167—28no—
144C2×#11929608C2311yescharacteristic
145C2×#11929608C2311yescharacteristic
146C2×#11929608C2312yes—
147C2×#11929607C2312yes—
148C2×#11929607C2312yes—
149C2×#11929607C2311yescharacteristic
150C2×#11929607C2311yescharacteristic
151C2×#11929607C2311yescharacteristic
152C2×#11929607C2311yescharacteristic
153M16×D79—24no—
154M16×D79—24no—
155C22×C79⋊C8C2312yes—
156C2×C8×D79C2311yescharacteristic
157C2×C8×D79C2311yescharacteristic
158C2×C8×D79C2311yescharacteristic
159C2×C8×D79C2312yes—
160C2×C8×D79C2311yescharacteristic
161C2×C8×D79C2312yes—
162C2×C8×D79C2312yes—
163C2×C8×D79C2312yes—
164#14579160C2×C411yescharacteristic
165#14579160C2×C411yescharacteristic
166#14579159C2×C411yescharacteristic
167#14579157C2×C411yescharacteristic
168#14579156C2×C412yes—
169#14579155C2×C412yes—
170#14579154C2×C412yes—
171#14579153C2×C411yescharacteristic
172#14579151C2×C412yes—
173#14579151C2×C412yes—
174#14579149C2×C411yescharacteristic
175#14579147C2×C412yes—
176#14579147C2×C412yes—
177#14579146C2×C412yes—
178#14579146C2×C412yes—
179#14579144C2×C412yes—
180#14579143C2×C412yes—
181#14579143C2×C412yes—
182#14579141C2×C411yescharacteristic
183#14579140C2×C411yescharacteristic
184#14579139C2×C412yes—
185#14579139C2×C412yes—
186#14579139C2×C412yes—
187#14579138C2×C412yes—
188#14579137C2×C411yescharacteristic
189#14579136C2×C411yescharacteristic
190#14579135C2×C411yescharacteristic
191#14579134C2×C412yes—
192#14579134C2×C412yes—
193#14579134C2×C412yes—
194#14579133C2×C412yes—
195#14579132C2×C411yescharacteristic
196#14579131C2×C412yes—
197#14579129C2×C412yes—
198Q8×Dic79C2×C411yescharacteristic
199C4×Dic158C2311yescharacteristic
200C4×Dic158C2312yes—
201#14579126C2×C412yes—
202#14579126C2×C411yescharacteristic
203#14579126C2×C412yes—
204#14579126C2×C412yes—
205C4×D316C2312yes—
206C4×D316C2311yescharacteristic
207D4×Dic79C2×C412yes—
208D4×Dic79C2×C411yescharacteristic
209#14579123C2×C412yes—
210#14579123C2×C412yes—
211#14579123C2×C412yes—
212#14579123C2×C411yescharacteristic
213C4×C22⋊D79C2312yes—
214C4×C22⋊D79C2312yes—
215C4×C22⋊D79C2312yes—
216(C22⋊D79)⋊C4C2×C412yes—
217(C22⋊D79)⋊C4C2×C412yes—
218(C22⋊D79)⋊C4C2×C412yes—
219(C22⋊D79)⋊C4C2×C412yes—
220(C22⋊D79)⋊C4C2×C412yes—
221(C22⋊D79)⋊C4C2×C412yes—
222(C22⋊D79)⋊C4C2×C412yes—
223#14579119C2×C411yescharacteristic
224#14579119C2×C412yes—
225#14579119C2×C411yescharacteristic
226#14579119C2×C412yes—
227#14579118C2312yes—
228#14579118C2312yes—
229#14579117C2×C412yes—
230#14579117C2×C412yes—
231#14579117C2×C412yes—
232C2×C4×Dic79C2×C411yescharacteristic
233C2×C4×Dic79C2×C411yescharacteristic
234C2×C4×Dic79C2311yescharacteristic
235C2×C4×Dic79C2312yes—
236C42×D79C2×C411yescharacteristic
237C42×D79C2×C411yescharacteristic
238C42×D79C2×C411yescharacteristic
239C42×D79C2×C411yescharacteristic
240C42×D79C2311yescharacteristic
241C42×D79C2311yescharacteristic
242C42×D79C2311yescharacteristic
243C42×D79C2311yescharacteristic
244C42×D79C2312yes—
245C4⋊(C79⋊C8)C2312yes—
246C4⋊(C79⋊C8)C2312yes—
247C4⋊(C79⋊C8)C2311yescharacteristic
248C4⋊(C79⋊C8)C2311yescharacteristic
249Dic79⋊C8C2312yes—
250Dic79⋊C8C2312yes—
251Dic79⋊C8C2312yes—
252Dic79⋊C8C2312yes—
253Dic79⋊C8C2312yes—
254Dic79⋊C8C2312yes—
255C22⋊(C79⋊C8)C2312yes—
256C22⋊(C79⋊C8)C2312yes—
257C22⋊(C79⋊C8)C2312yes—
258(C2×D79)⋊C8C2312yes—
259(C2×D79)⋊C8C2312yes—
260(C2×D79)⋊C8C2312yes—
261(C2×D79)⋊C8C2312yes—
262(C2×D79)⋊C8C2312yes—
263(C2×D79)⋊C8C2312yes—
264#14579072C2311yescharacteristic
265#14579072C2312yes—
266#14579072C2311yescharacteristic
267#14579071C2311yescharacteristic
268#14579071C2312yes—
269#14579071C2311yescharacteristic
270#14579071C2311yescharacteristic
271#14579071C2312yes—
272#14579071C2311yescharacteristic
273C4×C79⋊C8C2312yes—
274C4×C79⋊C8C2312yes—
275C4×C79⋊C8C2311yescharacteristic
276C4×C79⋊C8C2311yescharacteristic
277C8×Dic79C2312yes—
278C8×Dic79C2312yes—
279C8×Dic79C2311yescharacteristic
280C8×Dic79C2312yes—
281C8×Dic79C2311yescharacteristic
282C8×Dic79C2311yescharacteristic
283C8×Dic79C2311yescharacteristic
284C8×Dic79C2312yes—
285C2×M16×C79C2311yescharacteristic
286C2×M16×C79C2312yes—
287C2×M16×C79C2311yescharacteristic
288C22×C8×C79C2312yes—
289#126×C79C2×C412yes—
290#125×C79C2×C411yescharacteristic
291#124×C79C2×C411yescharacteristic
292#123×C79C2×C412yes—
293C22⋊Q8×C79C2×C411yescharacteristic
294#121×C79C2×C411yescharacteristic
295C4×Q8×C79C2311yescharacteristic
296C4×D4×C79C2311yescharacteristic
297C4×D4×C79C2312yes—
298#117×C79C2312yes—
299C2×C42×C79C2311yescharacteristic
300C4⋊C8×C79C2312yes—
301C4⋊C8×C79C2311yescharacteristic
302C4⋊C8×C79C2312yes—
303C4⋊C8×C79C2311yescharacteristic
304C22⋊C8×C79C2312yes—
305C22⋊C8×C79C2312yes—
306C22⋊C8×C79C2312yes—
307#97×C79C2311yescharacteristic
308#97×C79C2312yes—
309#97×C79C2311yescharacteristic
310C4×C8×C79C2312yes—
311C4×C8×C79C2311yescharacteristic
312C4×C8×C79C2312yes—
313C4×C8×C79C2311yescharacteristic
314C23×D79C22×C411yescharacteristic
315#11929625—24no—
316#11929624—24no—
317#11929624—24no—
318#11929623—24no—
319#11929623—44no—
320C2×Dic158C22×C411yescharacteristic
321C2×Dic158C22×C412yes—
322C2×Dic158C22×C412yes—
323C2×D316C22×C412yes—
324C2×D316C22×C412yes—
325C2×D316C22×C411yescharacteristic
326C2×C22⋊D79C22×C412yes—
327C2×C22⋊D79C22×C412yes—
328C2×C22⋊D79C22×C412yes—
329C2×C22⋊D79C22×C412yes—
330C2×C22⋊D79C22×C412yes—
331C22×Dic79C22×C411yescharacteristic
332C22×Dic79C22×C412yes—
333C22×Dic79C22×C412yes—
334C22×Dic79C22×C411yescharacteristic
335C22×Dic79C22×C411yescharacteristic
336C2×C4×D79—24no—
337C2×C4×D79—22no—
338C2×C4×D79—22no—
339C2×C4×D79—42no—
340C2×C4×D79C22×C412yes—
341C2×C4×D79C22×C412yes—
342C2×C4×D79C22×C411yescharacteristic
343C2×C4×D79C22×C411yescharacteristic
344C2×C4×D79C22×C411yescharacteristic
345C2×C4×D79C22×C411yescharacteristic
346C2×C4×D79C22×C411yescharacteristic
347C2×C4×D79C22×C411yescharacteristic
348C2×C4×D79C22×C411yescharacteristic
349C2×C4×D79C22×C411yescharacteristic
350C2×C4×D79C22×C411yescharacteristic
351C2×C4×D79C22×C411yescharacteristic
352C2×C4×D79C2412yes—
353C2×C4×D79C2411yescharacteristic
354C2×C4×D79C2411yescharacteristic
355#11929608—22no—
356#11929608—22no—
357#11929608—24no—
358#11929607—22no—
359#11929607—22no—
360#11929607—24no—
361#11929607—24no—
362#11929607#4114yescomplemented
363#11929607#4114yescomplemented
364C2×C79⋊C8—24no—
365C2×C79⋊C8C2412yes—
366C2×C79⋊C8C2411yescharacteristic
367C2×C79⋊C8C2411yescharacteristic
368C2×C79⋊C8C2412yes—
369C2×C79⋊C8C2411yescharacteristic
370C2×C79⋊C8C2411yescharacteristic
371C8×D79—24no—
372C8×D79—24no—
373C8×D79—22no—
374C8×D79—22no—
375C8×D79—24no—
376C8×D79—22no—
377C8×D79—22no—
378C8×D79—24no—
379C4⋊Dic79C22×C411yescharacteristic
380C4⋊Dic79C22×C412yes—
381C4⋊Dic79C22×C411yescharacteristic
382C4⋊Dic79C22×C412yes—
383Dic79⋊C4C22×C412yes—
384Dic79⋊C4C22×C412yes—
385Dic79⋊C4C22×C412yes—
386Dic79⋊C4C22×C412yes—
387Dic79⋊C4C22×C412yes—
388Dic79⋊C4C22×C412yes—
389Dic79⋊C4C22×C412yes—
390Dic79⋊C4C22×C412yes—
391Dic79⋊C4C22×C412yes—
392Dic79⋊C4C22×C412yes—
393C22⋊Dic79C22×C412yes—
394C22⋊Dic79C22×C412yes—
395C22⋊Dic79C22×C412yes—
396(C2×D79)⋊C4C22×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×C412yes—
402(C2×D79)⋊C4C22×C412yes—
403(C2×D79)⋊C4C22×C412yes—
404(C2×D79)⋊C4C22×C412yes—
405(C2×D79)⋊C4C22×C412yes—
406C4×Dic79C22×C411yescharacteristic
407C4×Dic79C22×C411yescharacteristic
408C4×Dic79C22×C411yescharacteristic
409C4×Dic79C22×C411yescharacteristic
410C4×Dic79C22×C411yescharacteristic
411C4×Dic79C22×C411yescharacteristic
412C4×Dic79C22×C411yescharacteristic
413C4×Dic79C22×C411yescharacteristic
414C4×Dic79C22×C411yescharacteristic
415C4×Dic79C22×C411yescharacteristic
416C4×Dic79C22×C412yes—
417C4×Dic79C22×C412yes—
418C4×Dic79C22×C412yes—
419C4×Dic79C22×C412yes—
420C4×Dic79C2411yescharacteristic
421C4×Dic79C2412yes—
422C4×Dic79C2411yescharacteristic
423C2×Q8×C79C22×C411yescharacteristic
424C2×D4×C79C22×C411yescharacteristic
425C2×D4×C79C22×C412yes—
426C22×C4×C79C22×C411yescharacteristic
427C22×C4×C79C22×C411yescharacteristic
428C22×C4×C79C2412yes—
429C22×C4×C79C2411yescharacteristic
430M16×C79—22no—
431M16×C79—22no—
432M16×C79—24no—
433C2×C8×C79—24no—
434C2×C8×C79C2412yes—
435C2×C8×C79C2411yescharacteristic
436C2×C8×C79C2412yes—
437C2×C8×C79C2411yescharacteristic
438C2×C8×C79C2411yescharacteristic
439C2×C8×C79C2411yescharacteristic
440C4⋊C4×C79C22×C412yes—
441C4⋊C4×C79C22×C412yes—
442C4⋊C4×C79C22×C411yescharacteristic
443C4⋊C4×C79C22×C412yes—
444C4⋊C4×C79C22×C411yescharacteristic
445C4⋊C4×C79C22×C412yes—
446C22⋊C4×C79C22×C412yes—
447C22⋊C4×C79C22×C412yes—
448C22⋊C4×C79C22×C412yes—
449C22⋊C4×C79C22×C412yes—
450C22⋊C4×C79C22×C412yes—
451C42×C79C22×C411yescharacteristic
452C42×C79C22×C411yescharacteristic
453C42×C79C2411yescharacteristic
454C42×C79C2411yescharacteristic
455C42×C79C2412yes—
456C23×C79C23×C411yescharacteristic
457C23×C79C23×C412yes—
458C22×D79—22no—
459C22×D79—22no—
460C22×D79—41no—
461C22×D79C23×C412yes—
462C22×D79C23×C411yescharacteristic
463C22×D79C23×C411yescharacteristic
464Q8×C79—22no—
465D4×C79—22no—
466D4×C79—42no—
467C2×C4×C79—22no—
468C2×C4×C79—22no—
469C2×C4×C79—21no—
470C2×C4×C79—21no—
471C2×C4×C79—22no—
472C2×C4×C79—41no—
473C2×C4×C79C23×C411yescharacteristic
474C2×C4×C79C23×C411yescharacteristic
475C2×C4×C79C23×C411yescharacteristic
476C2×C4×C79C23×C411yescharacteristic
477C2×C4×C79C23×C412yes—
478C2×C4×C79C23×C412yes—
479C2×C4×C79C23×C412yes—
480C2×C4×C79C23×C411yescharacteristic
481C2×C4×C79C2511yescharacteristic
482C22⋊D79—24no—
483C22⋊D79—24no—
484C22⋊D79—24no—
485C22⋊D79—42no—
486C22⋊D79—42no—
487C2×Dic79—22no—
488C2×Dic79—22no—
489C2×Dic79—24no—
490C2×Dic79—22no—
491C2×Dic79—24no—
492C2×Dic79C23×C411yescharacteristic
493C2×Dic79C23×C411yescharacteristic
494C2×Dic79C23×C411yescharacteristic
495C2×Dic79C23×C412yes—
496C2×Dic79C23×C412yes—
497C2×Dic79C23×C412yes—
498C2×Dic79C23×C411yescharacteristic
499C2×Dic79C23×C411yescharacteristic
500C2×Dic79C23×C411yescharacteristic
501D316—24no—
502D316—24no—
503D316—22no—
504C4×D79—22no—
505C4×D79—22no—
506C4×D79—22no—
507C4×D79—21no—
508C4×D79—21no—
509C4×D79—22no—
510C4×D79—22no—
511C4×D79—22no—
512C4×D79—22no—
513C4×D79—24no—
514C4×D79—22no—
515C4×D79—22no—
516C4×D79—24no—
517C4×D79—41no—
518C4×D79—41no—
519C4×D79#13114yescomplemented
520C4×D79C2×#4112yes—
521C4×D79C2×#4112yes—
522Dic158—22no—
523Dic158—24no—
524Dic158—42no—
525C8×C79—22no—
526C8×C79—22no—
527C8×C79—21no—
528C8×C79—21no—
529C8×C79C2×#4112yes—
530C8×C79C2×#4112yes—
531C79⋊C8—22no—
532C79⋊C8—22no—
533C79⋊C8—21no—
534C79⋊C8—21no—
535C79⋊C8C2×#4112yes—
536C79⋊C8C2×#4112yes—
537C22×C79—22no—
538C22×C79—21no—
539C22×C79—22no—
540C22×C79—21no—
541C22×C79—21no—
542C22×C79—22no—
543C22×C79C24×C411yescharacteristic
544C2×D79—21no—
545C2×D79—21no—
546C2×D79—21no—
547C2×D79—21no—
548C2×D79—22no—
549C2×D79—22no—
550C2×D79—22no—
551C2×D79—44no—
552C2×D79C4×#4112yes—
553C2×D79C2×#13112yes—
554C4×C79—22no—
555C4×C79—21no—
556C4×C79—21no—
557C4×C79—22no—
558C4×C79—21no—
559C4×C79—21no—
560C4×C79—22no—
561C4×C79C2×#13112yes—
562C4×C79C22×#4111yescharacteristic
563C4×C79C22×#4111yescharacteristic
564Dic79—22no—
565Dic79—21no—
566Dic79—22no—
567Dic79—21no—
568Dic79—21no—
569Dic79—22no—
570Dic79C4×#4112yes—
571Dic79C2×#13112yes—
572Dic79#56812yes—
573#60210—791nomaximal, Sylow
574C2×C79—41no—
575C2×C79—42no—
576C2×C79C2×C4×#4111yescharacteristic
577C2×C79C22×#13111yescharacteristic
578C2×C79C2×#56811yescharacteristic
579D79—22no—
580D79—22no—
581D79—42no—
582#3444—791no—
583#2969—791no—
584#2969—791no—
585#2969—791no—
586#2969D7911yescharacteristic, complemented
587#2968—792no—
588#2968—792no—
589#2965—791no—
590#2965—792no—
591#2965—791no—
592#2965—792no—
593C8×#41—791no—
594C8×#41—791no—
595#2962—791no—
596#2962—791no—
597#2935—791no—
598#2935—791no—
599#2933—792no—
600#2933—792no—
601#2922—792no—
602C2×#431—791no—
603C4×#131—792no—
604C2×C4×M16—791no—
605C79#6021011yescharacteristic, complemented, Sylow
606C2×#131—792no—
607C2×#131—792no—
608C22×M16—791no—
609C22×M16—791no—
610#533—791no—
611#533—791no—
612#533—791no—
613#532—791no—
614#532—791no—
615#532—791no—
616#529—792no—
617#529—792no—
618#529—791no—
619#529—791no—
620#529—792no—
621#529—792no—
622#529—791no—
623#529C2×D7911yescharacteristic
624#525—792no—
625#525—791no—
626#525—791no—
627#525—792no—
628C4×#41—791no—
629C4×#41—791no—
630C4×#41—792no—
631C4×#41—792no—
632C22×C42—791no—
633#446—791no—
634#446—792no—
635#446—791no—
636#446—792no—
637#446—792no—
638#446—792no—
639#446—791no—
640#446C2×D7911yescharacteristic, complemented
641C8×Q8—791no—
642C8×Q8—791no—
643C8×Q8—791no—
644C8×Q8C2×D7911yescharacteristic, complemented
645#436—792no—
646#436—792no—
647#436—791no—
648#436—791no—
649#436—792no—
650#436—791no—
651#436C2×D7912yes—
652#436C2×D7911yescharacteristic, complemented
653#435—792no—
654#435—792no—
655#435—792no—
656#435—792no—
657#435—792no—
658#435—792no—
659#435—792no—
660#435—792no—
661#435—792no—
662#435—792no—
663#435—792no—
664#435C2×D7912yes—
665C8×D4—792no—
666C8×D4—791no—
667C8×D4—792no—
668C8×D4—791no—
669C8×D4—792no—
670C8×D4—792no—
671C8×D4—791no—
672C8×D4C2×D7911yescharacteristic, complemented
673#433—792no—
674#433—792no—
675#433—792no—
676#433C2×D7912yescomplemented
677#431—791no—
678#431—791no—
679#431—791no—
680#431—792no—
681#431—792no—
682#431—792no—
683#431—792no—
684#431—792no—
685#431—792no—
686#431C2×D7911yescharacteristic
687#424—792no—
688#424—792no—
689C2×C4⋊C8—791no—
690C2×C4⋊C8—791no—
691#408—792no—
692#408—792no—
693C2×C22⋊C8—792no—
694#405—792no—
695#405—792no—
696#405—792no—
697#405—792no—
698#405—792no—
699#405C2×D7912yescomplemented
700C4×M16—791no—
701C4×M16—791no—
702C4×M16—792no—
703C4×M16—791no—
704C4×M16—791no—
705C4×M16—791no—
706C4×M16—792no—
707C4×M16—791no—
708C4×M16—791no—
709C4×M16C2×D7911yescharacteristic
710C2×#97—791no—
711C2×#97—791no—
712C2×C4×C8—792no—
713C2×C4×C8—791no—
714C2×C4×C8—791no—
715C2×C4×C8—792no—
716C2×C4×C8—792no—
717C2×#41—791no—
718C2×#41—792no—
719C2×#41—791no—
720C2×#41—792no—
721C23×C4—791no—
722C23×C4—791no—
723C23×C4—791no—
724#131—1588no—
725#131—1588no—
726C2×M16—791no—
727C2×M16—791no—
728C2×M16—792no—
729C2×M16—791no—
730C2×M16—791no—
731C2×M16—791no—
732C2×M16—791no—
733C2×M16—792no—
734C2×M16—792no—
735C2×M16—1584no—
736C2×M16—1584no—
737C2×M16C22×D7911yescharacteristic
738C2×M16C22×D7911yescharacteristic
739C2×M16C22×D7912yes—
740C22×C8—792no—
741C22×C8—791no—
742C22×C8—791no—
743C22×C8—791no—
744C22×C8—791no—
745C22×C8—792no—
746C22×C8—792no—
747C22×C8—792no—
748C22×C8—792no—
749C22×C8C22×D7912yes—
750C4⋊Q8—791no—
751C4⋊Q8—791no—
752C4⋊Q8—791no—
753#127—791no—
754#126—792no—
755#126—792no—
756#126—792no—
757#126C4×D7912yes—
758#125—792no—
759#125—792no—
760#125—791no—
761#125C4×D7911yescharacteristic
762#124—792no—
763#124—792no—
764#124—791no—
765#124C4×D7911yescharacteristic
766#123—792no—
767#123—792no—
768#123—792no—
769#123—792no—
770#123—792no—
771#123C4×D7912yes—
772C22⋊Q8—791no—
773C22⋊Q8—791no—
774C22⋊Q8—792no—
775C22⋊Q8—792no—
776C22⋊Q8—792no—
777C22⋊Q8—791no—
778C22⋊Q8—792no—
779C22⋊Q8C4×D7911yescharacteristic
780#121—791no—
781#121—792no—
782#121—791no—
783#121—791no—
784#121—792no—
785#121—792no—
786#121—792no—
787#121C4×D7911yescharacteristic
788#120—792no—
789#120—792no—
790C4×Q8—791no—
791C4×Q8—792no—
792C4×Q8—792no—
793C4×Q8—792no—
794C4×Q8—791no—
795C4×Q8—791no—
796C4×Q8—792no—
797C4×Q8C22×D7911yescharacteristic
798C4×D4—792no—
799C4×D4—791no—
800C4×D4—792no—
801C4×D4—792no—
802C4×D4—792no—
803C4×D4—792no—
804C4×D4—792no—
805C4×D4—792no—
806C4×D4—791no—
807C4×D4—792no—
808C4×D4—792no—
809C4×D4—792no—
810C4×D4—792no—
811C4×D4—792no—
812C4×D4—792no—
813C4×D4—792no—
814C4×D4—792no—
815C4×D4—791no—
816C4×D4C22×D7912yes—
817C4×D4C22×D7911yescharacteristic
818#117—791no—
819#117—791no—
820#117—792no—
821#117—792no—
822#117—792no—
823#117—792no—
824#117—792no—
825#117—792no—
826#117—792no—
827#117C22×D7912yes—
828C2×C42—791no—
829C2×C42—791no—
830C2×C42—792no—
831C2×C42—791no—
832C2×C42—791no—
833C2×C42—791no—
834C2×C42—791no—
835C2×C42—791no—
836C2×C42—792no—
837C2×C42—791no—
838C2×C42—791no—
839C2×C42—791no—
840C2×C42—791no—
841C2×C42C22×D7911yescharacteristic
842C4⋊C8—792no—
843C4⋊C8—792no—
844C4⋊C8—792no—
845C4⋊C8—792no—
846C4⋊C8—792no—
847C4⋊C8—792no—
848C4⋊C8—791no—
849C4⋊C8—791no—
850C4⋊C8—792no—
851C4⋊C8—792no—
852C4⋊C8C22×D7911yescharacteristic
853C4⋊C8C22×D7911yescharacteristic
854C4⋊C8C22×D7912yes—
855C4⋊C8C22×D7912yes—
856C22⋊C8—792no—
857C22⋊C8—792no—
858C22⋊C8—792no—
859C22⋊C8—792no—
860C22⋊C8—792no—
861C22⋊C8—792no—
862C22⋊C8—792no—
863C22⋊C8—792no—
864C22⋊C8—792no—
865C22⋊C8C22×D7912yes—
866C22⋊C8C22×D7912yes—
867C22⋊C8C22×D7912yes—
868#97—791no—
869#97—791no—
870#97—791no—
871#97—791no—
872#97—792no—
873#97—792no—
874#97—791no—
875#97—791no—
876#97—792no—
877#97C22×D7911yescharacteristic
878#97C22×D7911yescharacteristic
879#97C22×D7912yes—
880C4×C8—791no—
881C4×C8—791no—
882C4×C8—792no—
883C4×C8—791no—
884C4×C8—791no—
885C4×C8—792no—
886C4×C8—792no—
887C4×C8—792no—
888C4×C8—791no—
889C4×C8—791no—
890C4×C8—792no—
891C4×C8—792no—
892C4×C8C22×D7911yescharacteristic
893C4×C8C22×D7911yescharacteristic
894C4×C8C22×D7912yes—
895C4×C8C22×D7912yes—
896C24—791no—
897#41—3164no—
898#41—1584no—
899#41—1584no—
900#41—1584no—
901#41—1584no—
902C2×Q8—792no—
903C2×Q8—792no—
904C2×Q8—791no—
905C2×Q8C2×C4×D7911yescharacteristic
906C2×D4—792no—
907C2×D4—792no—
908C2×D4—792no—
909C2×D4—792no—
910C2×D4—792no—
911C2×D4—792no—
912C2×D4—792no—
913C2×D4—791no—
914C2×D4C2×C4×D7911yescharacteristic
915C2×D4C2×C4×D7912yes—
916C22×C4—3162no—
917C22×C4—791no—
918C22×C4—791no—
919C22×C4—791no—
920C22×C4—791no—
921C22×C4—791no—
922C22×C4—791no—
923C22×C4—791no—
924C22×C4—792no—
925C22×C4—792no—
926C22×C4—791no—
927C22×C4—792no—
928C22×C4—791no—
929C22×C4—791no—
930C22×C4—791no—
931C22×C4—791no—
932C22×C4—791no—
933C22×C4—791no—
934C22×C4—791no—
935C22×C4—792no—
936C22×C4—792no—
937C22×C4—1582no—
938C22×C4—1582no—
939C22×C4—1584no—
940C22×C4C2×C4×D7911yescharacteristic
941C22×C4C2×C4×D7911yescharacteristic
942C22×C4C23×D7911yescharacteristic
943C22×C4C23×D7912yes—
944M16—22no—
945M16—22no—
946M16—24no—
947M16—794no—
948M16—794no—
949M16—1584no—
950M16—1582no—
951M16—1582no—
952M16—1582no—
953M16—1582no—
954M16—1584no—
955M16—1584no—
956C2×C8—24no—
957C2×C8—791no—
958C2×C8—791no—
959C2×C8—792no—
960C2×C8—791no—
961C2×C8—791no—
962C2×C8—792no—
963C2×C8—1582no—
964C2×C8—1582no—
965C2×C8—1584no—
966C2×C8—1584no—
967C2×C8—1584no—
968C2×C8—1584no—
969C2×C8—1582no—
970C2×C8—1582no—
971C2×C8—1584no—
972C2×C8C23×D7912yes—
973C2×C8C23×D7911yescharacteristic
974C2×C8C23×D7911yescharacteristic
975C2×C8C23×D7912yes—
976C2×C8C23×D7911yescharacteristic
977C2×C8C23×D7911yescharacteristic
978C4⋊C4—792no—
979C4⋊C4—792no—
980C4⋊C4—792no—
981C4⋊C4—792no—
982C4⋊C4—792no—
983C4⋊C4—792no—
984C4⋊C4—792no—
985C4⋊C4—792no—
986C4⋊C4—792no—
987C4⋊C4—792no—
988C4⋊C4—791no—
989C4⋊C4—791no—
990C4⋊C4—792no—
991C4⋊C4—792no—
992C4⋊C4C2×C4×D7911yescharacteristic
993C4⋊C4C2×C4×D7912yes—
994C4⋊C4C2×C4×D7911yescharacteristic
995C4⋊C4C2×C4×D7912yes—
996C4⋊C4C2×C4×D7912yes—
997C4⋊C4C2×C4×D7912yes—
998C22⋊C4—792no—
999C22⋊C4—792no—
1000C22⋊C4—792no—
1001C22⋊C4—792no—
1002C22⋊C4—792no—
1003C22⋊C4—792no—
1004C22⋊C4—792no—
1005C22⋊C4—792no—
1006C22⋊C4—792no—
1007C22⋊C4—792no—
1008C22⋊C4—792no—
1009C22⋊C4—792no—
1010C22⋊C4—792no—
1011C22⋊C4C2×C4×D7912yes—
1012C22⋊C4C2×C4×D7912yes—
1013C22⋊C4C2×C4×D7912yes—
1014C22⋊C4C2×C4×D7912yes—
1015C22⋊C4C2×C4×D7912yes—
1016C42—791no—
1017C42—792no—
1018C42—791no—
1019C42—791no—
1020C42—791no—
1021C42—791no—
1022C42—791no—
1023C42—791no—
1024C42—791no—
1025C42—791no—
1026C42—791no—
1027C42—791no—
1028C42—791no—
1029C42—792no—
1030C42—792no—
1031C42—792no—
1032C42—792no—
1033C42C2×C4×D7911yescharacteristic
1034C42C2×C4×D7911yescharacteristic
1035C42C23×D7911yescharacteristic
1036C42C23×D7911yescharacteristic
1037C42C23×D7912yes—
1038C23—3161no—
1039C23—791no—
1040C23—791no—
1041C23—792no—
1042C23—1582no—
1043C23—1582no—
1044C23C22×C4×D7912yes—
1045C23C22×C4×D7911yescharacteristic
1046Q8—22no—
1047Q8—3162no—
1048Q8—1584no—
1049Q8—1582no—
1050D4—22no—
1051D4—42no—
1052D4—3162no—
1053D4—3162no—
1054D4—1584no—
1055D4—1584no—
1056D4—1584no—
1057D4—1584no—
1058D4—1584no—
1059D4—1582no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—41no—
1066C2×C4—3161no—
1067C2×C4—3161no—
1068C2×C4—791no—
1069C2×C4—791no—
1070C2×C4—791no—
1071C2×C4—794no—
1072C2×C4—792no—
1073C2×C4—792no—
1074C2×C4—791no—
1075C2×C4—791no—
1076C2×C4—791no—
1077C2×C4—792no—
1078C2×C4—792no—
1079C2×C4—792no—
1080C2×C4—1582no—
1081C2×C4—1582no—
1082C2×C4—1582no—
1083C2×C4—1582no—
1084C2×C4—1584no—
1085C2×C4—1584no—
1086C2×C4—1582no—
1087C2×C4—1582no—
1088C2×C4—1582no—
1089C2×C4—1582no—
1090C2×C4—1582no—
1091C2×C4—1584no—
1092C2×C4—1584no—
1093C2×C4—1582no—
1094C2×C4—1581no—
1095C2×C4—1581no—
1096C2×C4—1582no—
1097C2×C4—1582no—
1098C2×C4C22×C4×D7911yescharacteristic
1099C2×C4C22×C4×D7911yescharacteristic
1100C2×C4C22×C4×D7911yescharacteristic
1101C2×C4C22×C4×D7911yescharacteristic
1102C2×C4C22×C4×D7912yes—
1103C2×C4C22×C4×D7912yes—
1104C2×C4C22×C4×D7912yes—
1105C2×C4C22×C4×D7911yescharacteristic
1106C2×C4C24×D7911yescharacteristic
1107C8—22no—
1108C8—21no—
1109C8—21no—
1110C8—22no—
1111C8—792no—
1112C8—792no—
1113C8—1582no—
1114C8—1582no—
1115C8—1581no—
1116C8—1581no—
1117C8#41×D7912yes—
1118C8#41×D7912yes—
1119C22—21no—
1120C22—22no—
1121C22—21no—
1122C22—22no—
1123C22—21no—
1124C22—22no—
1125C22—3164no—
1126C22—792no—
1127C22—792no—
1128C22—1582no—
1129C22—1582no—
1130C22—1582no—
1131C22—1581no—
1132C22—1581no—
1133C22—1581no—
1134C22—1581no—
1135C22C23×C4×D7911yescharacteristic
1136C4—21no—
1137C4—22no—
1138C4—21no—
1139C4—21no—
1140C4—22no—
1141C4—21no—
1142C4—22no—
1143C4—792no—
1144C4—792no—
1145C4—792no—
1146C4—1581no—
1147C4—1582no—
1148C4—1581no—
1149C4—1582no—
1150C4—1581no—
1151C4—1582no—
1152C4#131×D7912yes—
1153C4C2×#41×D7911yescharacteristic
1154C4C2×#41×D7911yescharacteristic
1155C2—41no—
1156C2—42no—
1157C2—3162no—
1158C2—1582no—
1159C2—1582no—
1160C2C4×#41×D7911yescharacteristic
1161C2C2×#131×D7911yescharacteristic
1162C2#568×D7911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D79
commutator, socleC22×C79C24×C4
FittingC79×#2969C2
prime radical#23776694C2
cosocleC2×C4×C79C25
hypercenter#2969D79
hypocenterC79#60210
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #23772405C2semidirect
3. #23772404C2semidirect
4. #23772398C2semidirect
5. #23772392C2semidirect
6. #23772390C2semidirect
7. #23772365C2semidirect
8. #23772363C2semidirect
9. #23772363C2semidirect
10. #23772360C2semidirect
11. C8×#11929625C2semidirect
12. C8×#11929623C2semidirect
13. #23772348C2semidirect
14. #23772342C2semidirect
15. #23772145C2semidirect
16. #23772139C2semidirect
17. #23772129C2semidirect
18. #23772123C2semidirect
19. #23772041C2semidirect
20. #431×D79C2semidirect
21. #23771822C2semidirect
22. C4×M16×D79C2semidirect
23. C79×#2969C2semidirect
50. #19098694C22semidirect
51. #19098693C22semidirect
52. #19098693C22semidirect
53. #19098692C22semidirect
54. #19098691C22semidirect
55. #19098690C22semidirect
56. #19098690C22semidirect
57. Q8×C79⋊C8C22semidirect
58. C8×Dic158C22semidirect
59. #19098687C22semidirect
60. #19098642C22semidirect
62. #19098641C22semidirect
63. #19098640C22semidirect
68. #19098637C22semidirect
71. #19098634C22semidirect
75. #19098632C22semidirect
76. #19098631C22semidirect
78. C8×D316C22semidirect
79. D4×C79⋊C8C22semidirect
81. #19098628C22semidirect
84. #19098625C22semidirect
85. #19098624C22semidirect
86. #19098622C22semidirect
90. #19098615C22semidirect
91. #19098615C22semidirect
94. #19098613C22semidirect
95. #19098613C22semidirect
104. #19098520C22semidirect
105. #19098519C22semidirect
107. #19098517C22semidirect
111. #19098515C22semidirect
114. M16×Dic79C22semidirect
119. C2×C8×Dic79C22semidirect
123. C4×C8×D79C22semidirect
125. #446×C79C22semidirect
126. C8×Q8×C79C22semidirect
128. #436×C79C22semidirect
130. C8×D4×C79C22semidirect
131. #433×C79C22semidirect
133. #405×C79C22semidirect
362. #11929607#41semidirect
363. #11929607#41semidirect
519. C4×D79#131semidirect
586. #2969D79semidirect
605. C79#60210semidirect
640. #446C2×D79semidirect
644. C8×Q8C2×D79semidirect
652. #436C2×D79semidirect
672. C8×D4C2×D79semidirect
676. #433C2×D79semidirect
699. #405C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237766942
#237724052
#237724042
#237723982
#237723922
#237723902
#237723652
#237723632
#237723602
C8×#119296252
C8×#119296232
#237723482
#237723422
#237721452
#237721392
#237721292
#237721232
#237720412
#431×D792
#237718222
C4×M16×D792
C79×#29692
#6021079