Finite Group Databasebeta

← #35152942

Subgroups — #35152942

Order 20224.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23776962C211yesmaximal, characteristic
2#23772420C211yesmaximal, characteristic, complemented
3#23772416C211yesmaximal, characteristic, complemented
4#23772406C211yesmaximal, characteristic, complemented
5#23772398C211yesmaximal, characteristic, complemented
6#23772398C212yesmaximal, complemented
7#23772397C212yesmaximal, complemented
8#23772385C212yesmaximal, complemented
9#23772379C212yesmaximal, complemented
10#23772375C211yesmaximal, characteristic, complemented
11#23772374C211yesmaximal, characteristic, complemented
12#23772363C211yesmaximal, characteristic, complemented
13#23772348C211yesmaximal, characteristic, complemented
14#23772331C211yesmaximal, characteristic, complemented
15#23772136C211yesmaximal, characteristic, complemented
16#23772123C212yesmaximal, complemented
17#23772098C212yesmaximal, complemented
18#436×D79C211yesmaximal, characteristic, complemented
19#23772061C211yesmaximal, characteristic, complemented
20#23772053C212yesmaximal, complemented
21C4×#14579167C211yesmaximal, characteristic, complemented
22#23771817C212yesmaximal, complemented
23C79×#2965C211yesmaximal, characteristic, complemented
24C2×#14579167C2211yescharacteristic
25C2×#14579167C2211yescharacteristic
26C2×M16×D79C2212yes—
27C2×M16×D79C2212yes—
28#19099285C411yescharacteristic
29#19099276C411yescharacteristic
30#19099272C411yescharacteristic
31#19099262C412yes—
32#19099254C411yescharacteristic
33#19099252C411yescharacteristic
34#19099246C412yes—
35#19099242C412yes—
36#19099237C412yes—
37#19099212C411yescharacteristic
38#19099208C411yescharacteristic
39#19099201C411yescharacteristic
40#19099117C2211yescharacteristic
41#19099100C2211yescharacteristic
42#19099097C2211yescharacteristic
43#19099097C2212yes—
44#19099093C2212yes—
45#19099072C2212yes—
46C4×#11929624C2211yescharacteristic
47C4×#11929623C2211yescharacteristic
48C4×D4×D79C2211yescharacteristic
49C2×#14579118C2212yes—
50#19098693C2211yescharacteristic, complemented
51#19098691C2212yescomplemented
52#19098691C2212yescomplemented
53#19098690C2211yescharacteristic, complemented
54#19098690C2212yescomplemented
55Q8×C79⋊C8C2211yescharacteristic, complemented
56Q8×C79⋊C8C2211yescharacteristic, complemented
57C8×Dic158C2211yescharacteristic, complemented
58#19098687C2211yescharacteristic, complemented
59#19098687C2212yescomplemented
60#19098642C2211yescharacteristic
61#19098641C2211yescharacteristic
62#19098641C2211yescharacteristic
63#19098641C2212yescomplemented
64#19098641C2212yescomplemented
65#19098640C2211yescharacteristic
66#19098640C2212yescomplemented
67#19098639C2212yes—
68#19098639C2212yescomplemented
69#19098638C2212yes—
70#19098638C2212yescomplemented
71#19098638C2212yescomplemented
72#19098637C2212yes—
73#19098637C2212yescomplemented
74#19098637C2212yescomplemented
75#19098636C2212yescomplemented
76#19098636C2212yescomplemented
77#19098634C2212yescomplemented
78#19098632C2212yes—
79#19098632C2212yescomplemented
80C8×D316C2211yescharacteristic
81#19098628C2211yescharacteristic
82#19098628C2212yescomplemented
83C8×C22⋊D79C2212yescomplemented
84#19098623C2212yescomplemented
85#19098623C2212yescomplemented
86#19098622C2212yescomplemented
87#19098622C2212yescomplemented
88#19098622C2212yescomplemented
89#19098621C2212yescomplemented
90#19098620C2212yescomplemented
91#19098620C2211yescharacteristic, complemented
92#19098619C2211yescharacteristic, complemented
93#19098617C2212yescomplemented
94#19098615C2211yescharacteristic, complemented
95#19098613C2212yescomplemented
96#19098588C2212yes—
97#19098588C2212yes—
98#19098585C2211yescharacteristic
99C4⋊C8×D79C2211yescharacteristic
100#19098528C2212yes—
101#19098525C2212yes—
102C22⋊C8×D79C2212yes—
103#19098520C2212yes—
104#19098520C2212yes—
105#19098520C2212yescomplemented
106#19098520C2212yescomplemented
107#19098518C2211yescharacteristic, complemented
108#19098518C2211yescharacteristic, complemented
109#19098517C2211yescharacteristic
110#19098517C2212yes—
111#19098517C2211yescharacteristic
112#19098517C2212yescomplemented
113#19098517C2212yescomplemented
114#19098517C2211yescharacteristic, complemented
115#19098517C2211yescharacteristic, complemented
116C4×#11929608C2212yescomplemented
117C4×#11929608C2211yescharacteristic, complemented
118M16×Dic79C2212yescomplemented
119M16×Dic79C2212yescomplemented
120C4×#11929607C2211yescharacteristic
121C4×#11929607C2211yescharacteristic, complemented
122C4×C8×D79C2211yescharacteristic
123C4×C8×D79C2211yescharacteristic, complemented
124C4×#41×C79C2211yescharacteristic
125#446×C79C2211yescharacteristic, complemented
126#446×C79C2211yescharacteristic, complemented
127#436×C79C2211yescharacteristic
128#436×C79C2211yescharacteristic
129#435×C79C2212yescomplemented
130#435×C79C2212yescomplemented
131#431×C79C2212yescomplemented
132#431×C79C2211yescharacteristic, complemented
133C4×M16×C79C2212yescomplemented
134C2×C4×C8×C79C2211yescharacteristic, complemented
135C2×#11929624C2311yescharacteristic
136C2×#11929623C2×C411yescharacteristic
137C2×D4×D79C2×C411yescharacteristic
138C22×C4×D79C2312yes—
139#14579167—24no—
140#14579167—24no—
141C2×#11929608C2312yes—
142C2×#11929608C2311yescharacteristic
143C2×#11929608C2312yes—
144C2×#11929608C2311yescharacteristic
145C2×#11929607C2312yes—
146C2×#11929607C2311yescharacteristic
147C2×#11929607C2312yes—
148C2×#11929607C2311yescharacteristic
149C2×#11929607C2311yescharacteristic
150C2×#11929607C2312yes—
151C2×#11929607C2311yescharacteristic
152M16×D79—28no—
153M16×D79—28no—
154C2×C8×D79C2312yes—
155C2×C8×D79C2312yes—
156C2×C8×D79C2311yescharacteristic
157C2×C8×D79C2311yescharacteristic
158C2×C8×D79C2311yescharacteristic
159C2×C8×D79C2312yes—
160C2×C8×D79C2311yescharacteristic
161#14579160C2×C411yescharacteristic
162#14579159C2×C411yescharacteristic
163#14579156C2×C412yes—
164#14579156C2×C412yes—
165#14579155C2×C412yes—
166#14579155C2×C412yes—
167#14579155C2×C412yes—
168#14579154C2×C412yes—
169#14579153C2×C412yes—
170#14579153C2×C411yescharacteristic
171#14579152C2×C411yescharacteristic
172#14579151C2×C412yes—
173#14579151C2×C412yes—
174#14579150C2×C411yescharacteristic
175#14579149C2×C411yescharacteristic
176#14579149C2×C412yes—
177#14579147C2×C412yes—
178#14579146C2×C412yes—
179#14579146C2×C412yes—
180#14579145C2×C412yes—
181#14579144C2×C412yes—
182#14579144C2×C412yes—
183#14579144C2×C412yes—
184#14579143C2×C412yes—
185#14579142C2×C412yes—
186#14579141C2×C411yescharacteristic
187#14579140C2×C411yescharacteristic
188#14579140C2×C412yes—
189#14579139C2×C412yes—
190#14579139C2×C412yes—
191#14579138C2×C412yes—
192#14579138C2×C412yes—
193#14579137C2×C411yescharacteristic
194#14579137C2×C411yescharacteristic
195#14579136C2×C411yescharacteristic
196#14579135C2×C411yescharacteristic
197#14579135C2×C412yes—
198#14579134C2×C412yes—
199#14579133C2×C412yes—
200#14579133C2×C412yes—
201#14579131C2×C412yes—
202#14579129C2×C412yes—
203C4×Dic158C2×C411yescharacteristic
204C4×Dic158C2×C411yescharacteristic
205C4×Dic158C2311yescharacteristic
206C4×Dic158C2312yes—
207#14579126C2×C411yescharacteristic
208C4×D316C2×C411yescharacteristic
209C4×D316C2×C411yescharacteristic
210C4×D316C2311yescharacteristic
211C4×D316C2312yes—
212D4×Dic79C2×C411yescharacteristic
213D4×Dic79C2×C411yescharacteristic
214#14579123C2×C411yescharacteristic
215C4×C22⋊D79C2×C411yescharacteristic
216C4×C22⋊D79C2×C411yescharacteristic
217C4×C22⋊D79C2×C411yescharacteristic
218C4×C22⋊D79C2×C411yescharacteristic
219C4×C22⋊D79C2312yes—
220C4×C22⋊D79C2312yes—
221C4×C22⋊D79C2312yes—
222(C22⋊D79)⋊C4C2×C412yes—
223(C22⋊D79)⋊C4C2×C412yes—
224#14579120C2311yescharacteristic
225#14579119C2×C411yescharacteristic
226#14579118C2×C412yes—
227#14579118C2×C412yes—
228#14579118C2×C412yes—
229#14579118C2×C412yes—
230#14579118C2311yescharacteristic
231#14579118C2312yes—
232#14579118C2312yes—
233#14579118C2312yes—
234#14579118C2311yescharacteristic
235#14579117C2×C412yes—
236C2×Dic79⋊C4C2×C412yes—
237C2×Dic79⋊C4C2×C412yes—
238C4⋊C4×D79C2×C411yescharacteristic
239C2×(C2×D79)⋊C4C2×C412yes—
240C2×(C2×D79)⋊C4C2×C412yes—
241C22⋊C4×D79C2×C412yes—
242C2×C4×Dic79C2312yes—
243C42×D79C2311yescharacteristic
244C42×D79C2311yescharacteristic
245C4⋊(C79⋊C8)C2311yescharacteristic
246C4⋊(C79⋊C8)C2312yes—
247C4⋊(C79⋊C8)C2312yes—
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#14579071C2312yes—
271#14579071C2311yescharacteristic
272#14579071C2311yescharacteristic
273#14579071C2312yes—
274C4×C79⋊C8C2311yescharacteristic
275C4×C79⋊C8C2312yes—
276C4×C79⋊C8C2311yescharacteristic
277C4×C79⋊C8C2312yes—
278C8×Dic79C2312yes—
279C8×Dic79C2311yescharacteristic
280C8×Dic79C2312yes—
281C8×Dic79C2311yescharacteristic
282C8×Dic79C2311yescharacteristic
283C8×Dic79C2311yescharacteristic
284C8×Dic79C2312yes—
285C2×#41×C79C2×C411yescharacteristic
286C2×M16×C79C2312yes—
287C2×M16×C79C2312yes—
288C22×C8×C79C2311yescharacteristic
289C22×C8×C79C2311yescharacteristic
290C4×Q8×C79C2×C411yescharacteristic
291C4×Q8×C79C2311yescharacteristic
292C4×D4×C79C2×C411yescharacteristic
293C4×D4×C79C2×C412yes—
294C4×D4×C79C2311yescharacteristic
295C4×D4×C79C2312yes—
296#117×C79C2×C412yes—
297#117×C79C2×C411yescharacteristic
298C2×C42×C79C2312yes—
299C2×C42×C79C2311yescharacteristic
300C4⋊C8×C79C2311yescharacteristic
301C4⋊C8×C79C2312yes—
302C4⋊C8×C79C2311yescharacteristic
303C4⋊C8×C79C2312yes—
304C22⋊C8×C79C2312yes—
305C22⋊C8×C79C2312yes—
306C22⋊C8×C79C2312yes—
307#97×C79C2312yes—
308#97×C79C2312yes—
309C4×C8×C79C2311yescharacteristic
310C4×C8×C79C2311yescharacteristic
311C4×C8×C79C2312yes—
312C4×C8×C79C2311yescharacteristic
313C4×C8×C79C2311yescharacteristic
314C23×D79C22×C412yes—
315#11929624—22no—
316#11929624—22no—
317#11929623—42no—
318C2×Dic158C22×C411yescharacteristic
319C2×Dic158C22×C411yescharacteristic
320C2×Dic158C22×C412yes—
321C2×D316C22×C411yescharacteristic
322C2×D316C22×C411yescharacteristic
323C2×D316C22×C412yes—
324C2×C22⋊D79C22×C411yescharacteristic
325C2×C22⋊D79C22×C411yescharacteristic
326C2×C22⋊D79C22×C412yes—
327C2×C22⋊D79C22×C412yes—
328C2×C22⋊D79C22×C412yes—
329D4×D79—42no—
330C22×Dic79C22×C412yes—
331C22×Dic79C22×C412yes—
332C22×Dic79C22×C412yes—
333C2×C4×D79—24no—
334C2×C4×D79—24no—
335C2×C4×D79C22×C411yescharacteristic
336C2×C4×D79C22×C411yescharacteristic
337C2×C4×D79C22×C412yes—
338C2×C4×D79C22×C412yes—
339C2×C4×D79C22×C411yescharacteristic
340C2×C4×D79C22×C411yescharacteristic
341C2×C4×D79C2411yescharacteristic
342C2×C4×D79C2412yes—
343C2×C4×D79C2411yescharacteristic
344#11929608—24no—
345#11929608—24no—
346#11929608—22no—
347#11929608—22no—
348#11929607—24no—
349#11929607—22no—
350#11929607—24no—
351#11929607—22no—
352#11929607—24no—
353#11929607—22no—
354#11929607#4114yescomplemented
355C2×C79⋊C8C2412yes—
356C2×C79⋊C8C2411yescharacteristic
357C2×C79⋊C8C2411yescharacteristic
358C2×C79⋊C8C2412yes—
359C2×C79⋊C8C2411yescharacteristic
360C2×C79⋊C8C2411yescharacteristic
361C8×D79—24no—
362C8×D79—22no—
363C8×D79—24no—
364C8×D79—22no—
365C8×D79—24no—
366C8×D79—22no—
367C8×D79#4114yescomplemented
368C4⋊Dic79C22×C411yescharacteristic
369C4⋊Dic79C22×C411yescharacteristic
370C4⋊Dic79C22×C411yescharacteristic
371C4⋊Dic79C22×C411yescharacteristic
372C4⋊Dic79C22×C412yes—
373C4⋊Dic79C22×C412yes—
374Dic79⋊C4C22×C412yes—
375Dic79⋊C4C22×C411yescharacteristic
376Dic79⋊C4C22×C411yescharacteristic
377Dic79⋊C4C22×C412yes—
378Dic79⋊C4C22×C412yes—
379Dic79⋊C4C22×C412yes—
380Dic79⋊C4C22×C412yes—
381Dic79⋊C4C22×C412yes—
382Dic79⋊C4C22×C412yes—
383Dic79⋊C4C22×C412yes—
384Dic79⋊C4C22×C412yes—
385Dic79⋊C4C22×C411yescharacteristic
386Dic79⋊C4C22×C411yescharacteristic
387Dic79⋊C4C22×C412yes—
388Dic79⋊C4C22×C412yes—
389Dic79⋊C4C22×C412yes—
390C22⋊Dic79C22×C412yes—
391C22⋊Dic79C22×C412yes—
392C22⋊Dic79C22×C411yescharacteristic
393C22⋊Dic79C22×C411yescharacteristic
394C22⋊Dic79C22×C412yes—
395(C2×D79)⋊C4C22×C412yes—
396(C2×D79)⋊C4C22×C412yes—
397(C2×D79)⋊C4C22×C411yescharacteristic
398(C2×D79)⋊C4C22×C411yescharacteristic
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×C411yescharacteristic
406(C2×D79)⋊C4C22×C411yescharacteristic
407(C2×D79)⋊C4C22×C412yes—
408(C2×D79)⋊C4C22×C412yes—
409(C2×D79)⋊C4C22×C412yes—
410(C2×D79)⋊C4C22×C412yes—
411C4×Dic79C22×C411yescharacteristic
412C4×Dic79C22×C411yescharacteristic
413C4×Dic79C22×C411yescharacteristic
414C4×Dic79C22×C411yescharacteristic
415C4×Dic79C22×C412yes—
416C4×Dic79C22×C412yes—
417C4×Dic79C2411yescharacteristic
418C4×Dic79C2411yescharacteristic
419C4×Dic79C2412yes—
420#41×C79—42no—
421C2×Q8×C79C22×C411yescharacteristic
422C2×D4×C79C22×C411yescharacteristic
423C2×D4×C79C22×C412yes—
424C22×C4×C79C22×C411yescharacteristic
425C22×C4×C79C22×C412yes—
426C22×C4×C79C22×C412yes—
427C22×C4×C79C22×C411yescharacteristic
428C22×C4×C79C2411yescharacteristic
429C22×C4×C79C2412yes—
430M16×C79—24no—
431M16×C79—24no—
432C2×C8×C79—22no—
433C2×C8×C79—22no—
434C2×C8×C79C2411yescharacteristic
435C2×C8×C79C2411yescharacteristic
436C2×C8×C79C2412yes—
437C2×C8×C79C2412yes—
438C2×C8×C79C2411yescharacteristic
439C2×C8×C79C2411yescharacteristic
440C4⋊C4×C79C22×C411yescharacteristic
441C4⋊C4×C79C22×C412yes—
442C4⋊C4×C79C22×C411yescharacteristic
443C4⋊C4×C79C22×C412yes—
444C22⋊C4×C79C22×C412yes—
445C22⋊C4×C79C22×C412yes—
446C22⋊C4×C79C22×C412yes—
447C42×C79C22×C412yes—
448C42×C79C22×C411yescharacteristic
449C42×C79C22×C412yes—
450C42×C79C22×C411yescharacteristic
451C42×C79C2411yescharacteristic
452C42×C79C2411yescharacteristic
453C42×C79C2412yes—
454C23×C79C23×C411yescharacteristic
455C23×C79C23×C412yes—
456C22×D79—24no—
457C22×D79—42no—
458C22×D79—42no—
459C22×D79C23×C412yes—
460C22×D79C23×C411yescharacteristic
461C22×D79C23×C411yescharacteristic
462Q8×C79—22no—
463D4×C79—22no—
464D4×C79—42no—
465C2×C4×C79—22no—
466C2×C4×C79—22no—
467C2×C4×C79—22no—
468C2×C4×C79—21no—
469C2×C4×C79—21no—
470C2×C4×C79—42no—
471C2×C4×C79—41no—
472C2×C4×C79—42no—
473C2×C4×C79C23×C412yes—
474C2×C4×C79C23×C411yescharacteristic
475C2×C4×C79C23×C411yescharacteristic
476C2×C4×C79C23×C411yescharacteristic
477C2×C4×C79C23×C412yes—
478C2×C4×C79C23×C411yescharacteristic
479C2×C4×C79C23×C412yes—
480C2×C4×C79C23×C411yescharacteristic
481C2×C4×C79C2511yescharacteristic
482C22⋊D79—22no—
483C22⋊D79—22no—
484C22⋊D79—42no—
485C22⋊D79—42no—
486C22⋊D79—42no—
487C2×Dic79—24no—
488C2×Dic79—42no—
489C2×Dic79—42no—
490C2×Dic79C23×C411yescharacteristic
491C2×Dic79C23×C411yescharacteristic
492C2×Dic79C23×C411yescharacteristic
493C2×Dic79C23×C411yescharacteristic
494C2×Dic79C23×C412yes—
495C2×Dic79C23×C412yes—
496C2×Dic79C23×C411yescharacteristic
497C2×Dic79C23×C412yes—
498C2×Dic79C23×C411yescharacteristic
499D316—22no—
500D316—22no—
501D316—42no—
502C4×D79—24no—
503C4×D79—22no—
504C4×D79—22no—
505C4×D79—22no—
506C4×D79—21no—
507C4×D79—21no—
508C4×D79—22no—
509C4×D79—24no—
510C4×D79—41no—
511C4×D79—41no—
512C4×D79C2×#4112yes—
513C4×D79C2×#4112yes—
514Dic158—22no—
515Dic158—22no—
516Dic158—42no—
517C8×C79—21no—
518C8×C79—22no—
519C8×C79—22no—
520C8×C79—21no—
521C8×C79C2×#4112yes—
522C8×C79C2×#4112yes—
523C79⋊C8—22no—
524C79⋊C8—21no—
525C79⋊C8—22no—
526C79⋊C8—21no—
527C79⋊C8C2×#4112yes—
528C79⋊C8C2×#4112yes—
529C22×C79—21no—
530C22×C79—22no—
531C22×C79—22no—
532C22×C79—21no—
533C22×C79—21no—
534C22×C79—22no—
535C22×C79C24×C411yescharacteristic
536C2×D79—21no—
537C2×D79—21no—
538C2×D79—21no—
539C2×D79—22no—
540C2×D79—21no—
541C2×D79—22no—
542C2×D79—22no—
543C2×D79—21no—
544C2×D79—84no—
545C2×D79C4×#4112yes—
546C4×C79—21no—
547C4×C79—22no—
548C4×C79—21no—
549C4×C79—22no—
550C4×C79—21no—
551C4×C79—22no—
552C4×C79—21no—
553C4×C79#56812yes—
554C4×C79C22×#4111yescharacteristic
555C4×C79C22×#4111yescharacteristic
556Dic79—21no—
557Dic79—22no—
558Dic79—21no—
559Dic79—22no—
560Dic79—21no—
561Dic79—22no—
562Dic79—21no—
563Dic79—21no—
564Dic79C4×#4112yes—
565#60217—791nomaximal, Sylow
566C2×C79—42no—
567C2×C79—41no—
568C2×C79C2×C4×#4111yescharacteristic
569C2×C79C2×#56811yescharacteristic
570C2×C79#357311yescharacteristic
571D79—22no—
572D79—41no—
573D79—42no—
574#3475—791no—
575#2971—791no—
576#2971—791no—
577#2969—791no—
578#2969—792no—
579#2969—791no—
580#2969—792no—
581#2967—792no—
582#2967—792no—
583#2966—791no—
584#2966—791no—
585#2965—791no—
586#2965D7911yescharacteristic, complemented
587#2962—791no—
588#2960—791no—
589D4×M16—791no—
590#2933—792no—
591#2930—792no—
592C2×#436—791no—
593#2925—791no—
594#2924—792no—
595C4×#131—791no—
596#2873—792no—
597C79#6021711yescharacteristic, complemented, Sylow
598C2×#131—791no—
599C2×#131—791no—
600C22×M16—792no—
601C22×M16—792no—
602#556—791no—
603#555—791no—
604#554—791no—
605#553—792no—
606#552—791no—
607#552—792no—
608#552—791no—
609#551—792no—
610#551—792no—
611#547—791no—
612#546—791no—
613#546—791no—
614#533—791no—
615#529—791no—
616#529—792no—
617#529—791no—
618#529—792no—
619#525—792no—
620C4×#41—791no—
621C4×#41—791no—
622C4×#41C2×D7911yescharacteristic
623C2×C4×D4—791no—
624C2×#117—792no—
625#446—791no—
626#446—792no—
627#446—792no—
628#446—792no—
629#446—791no—
630#446C2×D7911yescharacteristic, complemented
631#446C2×D7911yescharacteristic, complemented
632C8×Q8—791no—
633C8×Q8—791no—
634C8×Q8—792no—
635C8×Q8—791no—
636C8×Q8—791no—
637#436—792no—
638#436—792no—
639#436—791no—
640#436—791no—
641#436—792no—
642#436—792no—
643#436—791no—
644#436—792no—
645#436—792no—
646#436—792no—
647#436—792no—
648#436—791no—
649#436C2×D7911yescharacteristic
650#436C2×D7911yescharacteristic
651#435—792no—
652#435—792no—
653#435—792no—
654#435—792no—
655#435—792no—
656#435—792no—
657#435—792no—
658#435—792no—
659#435C2×D7912yescomplemented
660#435C2×D7912yescomplemented
661C8×D4—792no—
662C8×D4—791no—
663C8×D4—792no—
664C8×D4—791no—
665#433—792no—
666#433—792no—
667#433—792no—
668#433—792no—
669#433—792no—
670#433—792no—
671#432—792no—
672#432—791no—
673#432—791no—
674#432—792no—
675#431—791no—
676#431—792no—
677#431C2×D7912yescomplemented
678#431C2×D7911yescharacteristic, complemented
679#424—792no—
680#424—792no—
681#423—791no—
682C2×C4⋊C8—791no—
683#408—792no—
684#407—792no—
685C2×C22⋊C8—792no—
686#405—791no—
687#405—791no—
688#405—792no—
689#405—792no—
690#405—792no—
691#405—792no—
692#405—791no—
693#405—792no—
694#405—792no—
695#405—792no—
696#405—791no—
697#405—791no—
698#405—791no—
699C4×M16—792no—
700C4×M16—792no—
701C4×M16—792no—
702C4×M16—791no—
703C4×M16—791no—
704C4×M16—791no—
705C4×M16C2×D7912yescomplemented
706C2×C4×C8—791no—
707C2×C4×C8—791no—
708C2×C4×C8C2×D7911yescharacteristic, complemented
709C2×#41—791no—
710C2×#41—791no—
711C2×#41C4×D7911yescharacteristic
712C22×D4—791no—
713C23×C4—792no—
714#131—1584no—
715#131—1584no—
716C2×M16—792no—
717C2×M16—792no—
718C2×M16—791no—
719C2×M16—791no—
720C2×M16—791no—
721C2×M16—792no—
722C2×M16—792no—
723C2×M16—792no—
724C2×M16—791no—
725C2×M16—791no—
726C2×M16—791no—
727C2×M16—1588no—
728C2×M16—1588no—
729C2×M16C22×D7912yes—
730C2×M16C22×D7912yes—
731C22×C8—791no—
732C22×C8—792no—
733C22×C8—792no—
734C22×C8—792no—
735C22×C8—791no—
736C22×C8—791no—
737C22×C8—791no—
738C22×C8C22×D7911yescharacteristic
739C22×C8C22×D7911yescharacteristic
740C4⋊Q8—791no—
741C4⋊Q8—791no—
742#126—792no—
743#126—792no—
744#126—792no—
745#126—792no—
746#126—792no—
747#126—792no—
748#125—792no—
749#125—791no—
750#125—792no—
751#125—792no—
752#125—791no—
753#124—791no—
754#124—792no—
755#124—791no—
756#124—792no—
757#123—792no—
758#123—792no—
759#123—792no—
760#123—792no—
761#123—792no—
762#123—792no—
763#123—792no—
764#123—792no—
765C22⋊Q8—791no—
766C22⋊Q8—791no—
767C22⋊Q8—791no—
768C22⋊Q8—792no—
769C22⋊Q8—792no—
770C22⋊Q8—791no—
771C22⋊Q8—792no—
772C22⋊Q8—792no—
773C22⋊Q8—792no—
774#121—792no—
775#121—792no—
776#121—792no—
777#121—791no—
778#121—791no—
779#121—792no—
780#120—792no—
781#120—792no—
782C4×Q8—791no—
783C4×Q8—791no—
784C4×Q8—791no—
785C4×Q8—791no—
786C4×Q8—792no—
787C4×Q8C4×D7911yescharacteristic
788C4×Q8C22×D7911yescharacteristic
789C4×D4—791no—
790C4×D4—791no—
791C4×D4—791no—
792C4×D4—791no—
793C4×D4—791no—
794C4×D4—791no—
795C4×D4—792no—
796C4×D4—792no—
797C4×D4—792no—
798C4×D4—791no—
799C4×D4—792no—
800C4×D4—792no—
801C4×D4—791no—
802C4×D4—791no—
803C4×D4—791no—
804C4×D4—792no—
805C4×D4C4×D7911yescharacteristic
806C4×D4C4×D7912yes—
807C4×D4C22×D7911yescharacteristic
808C4×D4C22×D7912yes—
809#117—791no—
810#117—791no—
811#117—792no—
812#117—792no—
813#117—792no—
814#117—792no—
815#117—792no—
816#117—791no—
817#117—792no—
818#117—792no—
819#117—792no—
820#117—791no—
821#117C4×D7912yes—
822#117C4×D7911yescharacteristic
823C2×C4⋊C4—792no—
824C2×C4⋊C4—792no—
825C2×C4⋊C4—791no—
826C2×C22⋊C4—792no—
827C2×C22⋊C4—792no—
828C2×C22⋊C4—792no—
829C2×C42—792no—
830C2×C42—791no—
831C2×C42—791no—
832C2×C42C22×D7912yes—
833C2×C42C22×D7911yescharacteristic
834C4⋊C8—792no—
835C4⋊C8—792no—
836C4⋊C8—792no—
837C4⋊C8—792no—
838C4⋊C8—792no—
839C4⋊C8—792no—
840C4⋊C8—791no—
841C4⋊C8—791no—
842C4⋊C8—792no—
843C4⋊C8—792no—
844C4⋊C8C22×D7911yescharacteristic
845C4⋊C8C22×D7911yescharacteristic
846C4⋊C8C22×D7912yes—
847C4⋊C8C22×D7912yes—
848C22⋊C8—792no—
849C22⋊C8—792no—
850C22⋊C8—792no—
851C22⋊C8—792no—
852C22⋊C8—792no—
853C22⋊C8—792no—
854C22⋊C8—792no—
855C22⋊C8—792no—
856C22⋊C8—792no—
857C22⋊C8C22×D7912yes—
858C22⋊C8C22×D7912yes—
859C22⋊C8C22×D7912yes—
860#97—791no—
861#97—792no—
862#97—791no—
863#97—792no—
864#97—791no—
865#97—791no—
866#97—792no—
867#97—791no—
868#97—792no—
869#97—791no—
870#97C22×D7912yes—
871#97C22×D7912yes—
872C4×C8—791no—
873C4×C8—791no—
874C4×C8—791no—
875C4×C8—791no—
876C4×C8—792no—
877C4×C8—792no—
878C4×C8—792no—
879C4×C8—791no—
880C4×C8—791no—
881C4×C8—792no—
882C4×C8—792no—
883C4×C8C22×D7911yescharacteristic
884C4×C8C22×D7911yescharacteristic
885C4×C8C22×D7911yescharacteristic
886C4×C8C22×D7911yescharacteristic
887C4×C8C22×D7912yes—
888C24—792no—
889#41—42no—
890#41—3162no—
891#41—1582no—
892#41—1582no—
893C2×Q8—792no—
894C2×Q8—791no—
895C2×Q8—791no—
896C2×Q8C2×C4×D7911yescharacteristic
897C2×D4—3162no—
898C2×D4—792no—
899C2×D4—792no—
900C2×D4—792no—
901C2×D4—791no—
902C2×D4—791no—
903C2×D4—792no—
904C2×D4—791no—
905C2×D4—791no—
906C2×D4C2×C4×D7911yescharacteristic
907C2×D4C2×C4×D7912yes—
908C22×C4—792no—
909C22×C4—792no—
910C22×C4—791no—
911C22×C4—791no—
912C22×C4—791no—
913C22×C4—792no—
914C22×C4—791no—
915C22×C4—792no—
916C22×C4—791no—
917C22×C4—791no—
918C22×C4—792no—
919C22×C4—792no—
920C22×C4—1584no—
921C22×C4—1584no—
922C22×C4C2×C4×D7911yescharacteristic
923C22×C4C2×C4×D7912yes—
924C22×C4C2×C4×D7912yes—
925C22×C4C2×C4×D7911yescharacteristic
926C22×C4C23×D7912yes—
927C22×C4C23×D7911yescharacteristic
928M16—24no—
929M16—24no—
930M16—794no—
931M16—1584no—
932M16—1582no—
933M16—1584no—
934M16—1582no—
935M16—1584no—
936M16—1584no—
937M16—1582no—
938M16—1582no—
939M16—1584no—
940M16—1582no—
941C2×C8—22no—
942C2×C8—22no—
943C2×C8—791no—
944C2×C8—791no—
945C2×C8—794no—
946C2×C8—791no—
947C2×C8—791no—
948C2×C8—792no—
949C2×C8—792no—
950C2×C8—1584no—
951C2×C8—1582no—
952C2×C8—1584no—
953C2×C8—1582no—
954C2×C8—1584no—
955C2×C8—1582no—
956C2×C8C23×D7911yescharacteristic
957C2×C8C23×D7912yes—
958C2×C8C23×D7912yes—
959C2×C8C23×D7911yescharacteristic
960C2×C8C23×D7911yescharacteristic
961C2×C8C23×D7911yescharacteristic
962C4⋊C4—791no—
963C4⋊C4—791no—
964C4⋊C4—792no—
965C4⋊C4—792no—
966C4⋊C4—792no—
967C4⋊C4—792no—
968C4⋊C4—792no—
969C4⋊C4—792no—
970C4⋊C4—792no—
971C4⋊C4—791no—
972C4⋊C4—792no—
973C4⋊C4—792no—
974C4⋊C4—791no—
975C4⋊C4—792no—
976C4⋊C4—792no—
977C4⋊C4—792no—
978C4⋊C4—791no—
979C4⋊C4—791no—
980C4⋊C4—791no—
981C4⋊C4—791no—
982C4⋊C4—792no—
983C4⋊C4—792no—
984C4⋊C4C2×C4×D7911yescharacteristic
985C4⋊C4C2×C4×D7912yes—
986C4⋊C4C2×C4×D7911yescharacteristic
987C4⋊C4C2×C4×D7912yes—
988C22⋊C4—792no—
989C22⋊C4—792no—
990C22⋊C4—791no—
991C22⋊C4—791no—
992C22⋊C4—792no—
993C22⋊C4—791no—
994C22⋊C4—791no—
995C22⋊C4—792no—
996C22⋊C4—792no—
997C22⋊C4—792no—
998C22⋊C4—792no—
999C22⋊C4—792no—
1000C22⋊C4—792no—
1001C22⋊C4—792no—
1002C22⋊C4—792no—
1003C22⋊C4—791no—
1004C22⋊C4—792no—
1005C22⋊C4—791no—
1006C22⋊C4—792no—
1007C22⋊C4—792no—
1008C22⋊C4—792no—
1009C22⋊C4C2×C4×D7912yes—
1010C22⋊C4C2×C4×D7912yes—
1011C22⋊C4C2×C4×D7912yes—
1012C42—791no—
1013C42—791no—
1014C42—792no—
1015C42—792no—
1016C42—792no—
1017C42—791no—
1018C42—791no—
1019C42—791no—
1020C42—791no—
1021C42C2×C4×D7912yes—
1022C42C2×C4×D7912yes—
1023C42C2×C4×D7911yescharacteristic
1024C42C2×C4×D7911yescharacteristic
1025C42C23×D7911yescharacteristic
1026C42C23×D7912yes—
1027C42C23×D7911yescharacteristic
1028C23—3162no—
1029C23—3162no—
1030C23—791no—
1031C23—792no—
1032C23—791no—
1033C23—1584no—
1034C23C22×C4×D7911yescharacteristic
1035C23C22×C4×D7912yes—
1036Q8—22no—
1037Q8—3162no—
1038Q8—1582no—
1039Q8—1582no—
1040D4—22no—
1041D4—42no—
1042D4—3162no—
1043D4—3162no—
1044D4—3162no—
1045D4—3162no—
1046D4—1582no—
1047D4—1582no—
1048D4—1582no—
1049D4—1582no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—41no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—3161no—
1059C2×C4—3161no—
1060C2×C4—3162no—
1061C2×C4—3162no—
1062C2×C4—791no—
1063C2×C4—792no—
1064C2×C4—792no—
1065C2×C4—791no—
1066C2×C4—791no—
1067C2×C4—791no—
1068C2×C4—792no—
1069C2×C4—792no—
1070C2×C4—791no—
1071C2×C4—791no—
1072C2×C4—792no—
1073C2×C4—1584no—
1074C2×C4—1584no—
1075C2×C4—1584no—
1076C2×C4—1582no—
1077C2×C4—1582no—
1078C2×C4—1582no—
1079C2×C4—1581no—
1080C2×C4—1581no—
1081C2×C4—1582no—
1082C2×C4C22×C4×D7912yes—
1083C2×C4C22×C4×D7911yescharacteristic
1084C2×C4C22×C4×D7911yescharacteristic
1085C2×C4C22×C4×D7911yescharacteristic
1086C2×C4C22×C4×D7911yescharacteristic
1087C2×C4C22×C4×D7912yes—
1088C2×C4C22×C4×D7912yes—
1089C2×C4C22×C4×D7911yescharacteristic
1090C2×C4C24×D7911yescharacteristic
1091C8—21no—
1092C8—21no—
1093C8—22no—
1094C8—22no—
1095C8—792no—
1096C8—792no—
1097C8—1582no—
1098C8—1581no—
1099C8—1582no—
1100C8—1581no—
1101C8#41×D7912yes—
1102C8#41×D7912yes—
1103C22—21no—
1104C22—22no—
1105C22—22no—
1106C22—21no—
1107C22—22no—
1108C22—21no—
1109C22—792no—
1110C22—6324no—
1111C22—1581no—
1112C22—1582no—
1113C22—1581no—
1114C22—1582no—
1115C22—1582no—
1116C22—1581no—
1117C22—1581no—
1118C22—1581no—
1119C22C23×C4×D7911yescharacteristic
1120C4—21no—
1121C4—22no—
1122C4—21no—
1123C4—21no—
1124C4—22no—
1125C4—22no—
1126C4—21no—
1127C4—792no—
1128C4—1581no—
1129C4—1582no—
1130C4—1581no—
1131C4—1581no—
1132C4—1582no—
1133C4—1581no—
1134C4—1582no—
1135C4—1581no—
1136C4#1909932912yes—
1137C4C2×#41×D7911yescharacteristic
1138C4C2×#41×D7911yescharacteristic
1139C2—42no—
1140C2—41no—
1141C2—3162no—
1142C2—3161no—
1143C2—1582no—
1144C2C4×#41×D7911yescharacteristic
1145C2C2×#1909932911yescharacteristic
1146C2#2377811111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D79
commutator, socleC22×C79C24×C4
FittingC79×#2965C2
prime radical#23776962C2
cosocleC2×C4×C79C25
hypercenter#2965D79
hypocenterC79#60217
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #23772420C2semidirect
3. #23772416C2semidirect
4. #23772406C2semidirect
5. #23772398C2semidirect
6. #23772398C2semidirect
7. #23772397C2semidirect
8. #23772385C2semidirect
9. #23772379C2semidirect
10. #23772375C2semidirect
11. #23772374C2semidirect
12. #23772363C2semidirect
13. #23772348C2semidirect
14. #23772331C2semidirect
15. #23772136C2semidirect
16. #23772123C2semidirect
17. #23772098C2semidirect
18. #436×D79C2semidirect
19. #23772061C2semidirect
20. #23772053C2semidirect
21. C4×#14579167C2semidirect
22. #23771817C2semidirect
23. C79×#2965C2semidirect
50. #19098693C22semidirect
51. #19098691C22semidirect
52. #19098691C22semidirect
53. #19098690C22semidirect
54. #19098690C22semidirect
55. Q8×C79⋊C8C22semidirect
56. Q8×C79⋊C8C22semidirect
57. C8×Dic158C22semidirect
58. #19098687C22semidirect
59. #19098687C22semidirect
63. #19098641C22semidirect
64. #19098641C22semidirect
66. #19098640C22semidirect
68. #19098639C22semidirect
70. #19098638C22semidirect
71. #19098638C22semidirect
73. #19098637C22semidirect
74. #19098637C22semidirect
75. #19098636C22semidirect
76. #19098636C22semidirect
77. #19098634C22semidirect
79. #19098632C22semidirect
82. #19098628C22semidirect
83. C8×C22⋊D79C22semidirect
84. #19098623C22semidirect
85. #19098623C22semidirect
86. #19098622C22semidirect
87. #19098622C22semidirect
88. #19098622C22semidirect
89. #19098621C22semidirect
90. #19098620C22semidirect
91. #19098620C22semidirect
92. #19098619C22semidirect
93. #19098617C22semidirect
94. #19098615C22semidirect
95. #19098613C22semidirect
105. #19098520C22semidirect
106. #19098520C22semidirect
107. #19098518C22semidirect
108. #19098518C22semidirect
112. #19098517C22semidirect
113. #19098517C22semidirect
114. #19098517C22semidirect
115. #19098517C22semidirect
116. C4×#11929608C22semidirect
117. C4×#11929608C22semidirect
118. M16×Dic79C22semidirect
119. M16×Dic79C22semidirect
121. C4×#11929607C22semidirect
123. C4×C8×D79C22semidirect
125. #446×C79C22semidirect
126. #446×C79C22semidirect
129. #435×C79C22semidirect
130. #435×C79C22semidirect
131. #431×C79C22semidirect
132. #431×C79C22semidirect
133. C4×M16×C79C22semidirect
134. C2×C4×C8×C79C22semidirect
354. #11929607#41semidirect
367. C8×D79#41semidirect
586. #2965D79semidirect
597. C79#60217semidirect
630. #446C2×D79semidirect
631. #446C2×D79semidirect
659. #435C2×D79semidirect
660. #435C2×D79semidirect
677. #431C2×D79semidirect
678. #431C2×D79semidirect
705. C4×M16C2×D79semidirect
708. C2×C4×C8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237769622
#237724202
#237724162
#237724062
#237723982
#237723972
#237723852
#237723792
#237723752
#237723742
#237723632
#237723482
#237723312
#237721362
#237721232
#237720982
#436×D792
#237720612
#237720532
C4×#145791672
#237718172
C79×#29652
#6021779