Finite Group Databasebeta

← #35155880

Subgroups — #35155880

Order 20224.

2178 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#23776804C211yesmaximal, characteristic, complemented
2#518×D79C211yesmaximal, characteristic
3#23773234C211yesmaximal, characteristic, complemented
4#23773233C211yesmaximal, characteristic, complemented
5#23773232C211yesmaximal, characteristic, complemented
6#23773231C211yesmaximal, characteristic, complemented
7#23773230C212yesmaximal, complemented
8#23773229C211yesmaximal, characteristic, complemented
9#23773228C212yesmaximal, complemented
10#23773227C211yesmaximal, characteristic, complemented
11#23773226C212yesmaximal, complemented
12#23773225C211yesmaximal, characteristic, complemented
13#23773224C212yesmaximal, complemented
14#23773198C212yesmaximal, complemented
15#23773195C212yesmaximal, complemented
16#23773195C212yesmaximal, complemented
17#23773192C212yesmaximal, complemented
18#23771988C211yesmaximal, characteristic, complemented
19#23771987C211yesmaximal, characteristic, complemented
20#23771961C211yesmaximal, characteristic, complemented
21C2×#19098566C211yesmaximal, characteristic
22#418×D79C211yesmaximal, characteristic
23C79×#3081C211yesmaximal, characteristic, complemented
24C22×D4×D79C2211yescharacteristic
25C22×#11929607C2211yescharacteristic
26C2×M16×D79C2211yescharacteristic
27#19099194C2211yescharacteristic, complemented
28#19099193—21no—
29#19099193C2212yescomplemented
30#19099191C2211yescharacteristic, complemented
31#19099191C2211yescharacteristic, complemented
32#19099190—21no—
33#19099190C2212yescomplemented
34#19099188—22no—
35#19099119—21no—
36#19099119C2212yescomplemented
37#19099118—21no—
38#19099118C2212yescomplemented
39#19099115—22no—
40#19099038C2211yescharacteristic
41#19099037C2211yescharacteristic
42#19099037C2211yescharacteristic
43#19099036—22no—
44#19099035—21no—
45#19099035—21no—
46#19099035C2212yes—
47#19099035C2212yes—
48C4×D4×D79—21no—
49C4×D4×D79—21no—
50C4×D4×D79C2212yes—
51C4×D4×D79C2212yes—
52C2×#14579119C2211yescharacteristic
53#117×D79C2211yescharacteristic
54#117×D79C2211yescharacteristic
55#117×D79C2211yescharacteristic
56C2×C22⋊C4×D79—22no—
57#19098866C2212yescomplemented
58#19098866C2212yescomplemented
59#19098865C2212yescomplemented
60#19098865C2212yescomplemented
61#19098864C2212yescomplemented
62#19098864C2212yescomplemented
63#19098863C2212yescomplemented
64#19098863C2212yescomplemented
65#19098862C2212yescomplemented
66#19098862C2212yescomplemented
67#19098861C2212yescomplemented
68#19098861C2212yescomplemented
69#19098860C2212yescomplemented
70#19098860C2212yescomplemented
71#19098854C2212yescomplemented
72#19098853C2212yescomplemented
73#19098852C2212yescomplemented
74#19098852C2212yescomplemented
75#19098851C2212yescomplemented
76#19098851C2212yescomplemented
77#19098850C2212yescomplemented
78#19098844C2212yescomplemented
79#19098843C2212yescomplemented
80#19098842C2212yescomplemented
81#19098842C2212yescomplemented
82#19098841C2212yescomplemented
83#19098841C2212yescomplemented
84#19098840C2212yescomplemented
85#19098606C2211yescharacteristic, complemented
86#19098605C2211yescharacteristic, complemented
87#19098604C2211yescharacteristic, complemented
88#19098604C2212yescomplemented
89#19098604C2211yescharacteristic, complemented
90#19098604C2211yescharacteristic, complemented
91#19098604C2211yescharacteristic, complemented
92#19098603C2211yescharacteristic, complemented
93#19098602C2211yescharacteristic, complemented
94#19098602C2212yescomplemented
95#19098602C2211yescharacteristic, complemented
96#19098602C2211yescharacteristic, complemented
97#19098602C2211yescharacteristic, complemented
98#19098601C2211yescharacteristic, complemented
99#19098600C2212yescomplemented
100#19098599C2211yescharacteristic, complemented
101#19098599C2211yescharacteristic, complemented
102#19098598C2212yescomplemented
103#19098591C2211yescharacteristic, complemented
104#19098590C2211yescharacteristic, complemented
105#19098589C2211yescharacteristic, complemented
106#19098588C2212yescomplemented
107#19098588C2212yescomplemented
108#19098585C2212yescomplemented
109#19098585C2212yescomplemented
110#19098569C2211yescharacteristic
111#19098568C2211yescharacteristic
112#19098567C2211yescharacteristic
113#19098566C2212yes—
114#19098566C2212yes—
115#19098566C2212yes—
116#19098566C2212yes—
117#19098566C2212yes—
118#19098566C2212yes—
119C2×#14579083C2211yescharacteristic
120C2×#14579082C2211yescharacteristic
121C2×#14579081C2211yescharacteristic
122#102×D79C2212yes—
123#102×D79C2212yes—
124#544×C79C2211yescharacteristic, complemented
125#518×C79C2211yescharacteristic
126#478×C79C2212yescomplemented
127#478×C79C2212yescomplemented
128#476×C79C2212yescomplemented
129#474×C79C2212yescomplemented
130#428×C79C2211yescharacteristic, complemented
131#427×C79C2211yescharacteristic, complemented
132#424×C79C2211yescharacteristic, complemented
133#418×C79C2211yescharacteristic
134C2×#102×C79C2211yescharacteristic
135C24×D79—21no—
136C22×D316C2311yescharacteristic
137C22×C22⋊D79—21no—
138C2×D4×D79—21no—
139C2×D4×D79—21no—
140C2×D4×D79—24no—
141C2×D4×D79Q818yescomplemented
142C2×D4×D79C2312yes—
143C2×D4×D79C2312yes—
144C22×C4×D79—22no—
145C22×C4×D79—22no—
146C22×C4×D79C2311yescharacteristic
147C2×#11929608C2311yescharacteristic
148C2×#11929607—24no—
149C2×#11929607C2312yes—
150C2×#11929607C2311yescharacteristic
151C2×#11929607C2311yescharacteristic
152C2×#11929607C2311yescharacteristic
153C2×#11929607C2311yescharacteristic
154M16×D79—24no—
155C22×C79⋊C8C2311yescharacteristic
156C2×C8×D79C2312yes—
157#14579161—21no—
158#14579161C2312yescomplemented
159#14579160—21no—
160#14579160—21no—
161#14579160—22no—
162#14579160C2312yescomplemented
163#14579160C2312yescomplemented
164#14579159—22no—
165#14579153—21no—
166#14579153C2312yescomplemented
167#14579152—21no—
168#14579152—21no—
169#14579152C2312yescomplemented
170#14579152C2312yescomplemented
171#14579151—22no—
172#14579151—22no—
173#14579141—22no—
174#14579141—22no—
175#14579140—22no—
176#14579139—22no—
177#14579139—22no—
178#14579139—22no—
179#14579139—22no—
180#14579138—22no—
181#14579138—22no—
182#14579137—22no—
183#14579137—22no—
184Q8×Dic79—22no—
185#14579126—22no—
186#14579126—22no—
187#14579126—22no—
188C4×D316—21no—
189C4×D316—21no—
190C4×D316C2312yes—
191C4×D316C2312yes—
192D4×Dic79—21no—
193D4×Dic79—21no—
194D4×Dic79C2312yes—
195D4×Dic79C2312yes—
196#14579123—21no—
197#14579123—21no—
198#14579123C2312yes—
199#14579123C2312yes—
200C4×C22⋊D79—22no—
201C4×C22⋊D79—22no—
202C4×C22⋊D79—22no—
203C4×C22⋊D79—22no—
204(C22⋊D79)⋊C4—22no—
205(C22⋊D79)⋊C4—22no—
206(C22⋊D79)⋊C4—22no—
207(C22⋊D79)⋊C4—22no—
208#14579120C2311yescharacteristic
209#14579120C2311yescharacteristic
210#14579120C2311yescharacteristic
211#14579119—21no—
212#14579119—21no—
213#14579119D411yescharacteristic
214#14579119D411yescharacteristic
215#14579119C2312yes—
216#14579119C2311yescharacteristic
217#14579119C2311yescharacteristic
218#14579119C2311yescharacteristic
219#14579119C2311yescharacteristic
220#14579119C2312yes—
221#14579118—21no—
222#14579118—21no—
223#14579118C2312yes—
224#14579117—21no—
225#14579117—21no—
226#14579117D412yes—
227C2×C4⋊Dic79C2311yescharacteristic
228C4⋊C4×D79D411yescharacteristic
229C4⋊C4×D79D411yescharacteristic
230C4⋊C4×D79C2311yescharacteristic
231C4⋊C4×D79C2311yescharacteristic
232C4⋊C4×D79C2311yescharacteristic
233C4⋊C4×D79C2311yescharacteristic
234C2×C22⋊Dic79—22no—
235C2×(C2×D79)⋊C4—21no—
236C2×(C2×D79)⋊C4—22no—
237C2×(C2×D79)⋊C4—22no—
238C22⋊C4×D79—22no—
239C22⋊C4×D79—21no—
240C22⋊C4×D79—21no—
241C22⋊C4×D79—22no—
242C22⋊C4×D79—22no—
243C22⋊C4×D79—22no—
244C22⋊C4×D79—22no—
245C22⋊C4×D79—22no—
246C22⋊C4×D79D412yes—
247C2×C4×Dic79—21no—
248C42×D79—21no—
249C42×D79—21no—
250C42×D79C2312yes—
251#14579095C2311yescharacteristic, complemented
252#14579095C2312yescomplemented
253#14579095C2311yescharacteristic, complemented
254#14579094C2311yescharacteristic, complemented
255#14579094C2312yescomplemented
256#14579094C2311yescharacteristic, complemented
257#14579094C2311yescharacteristic, complemented
258#14579094C2312yescomplemented
259#14579094C2311yescharacteristic, complemented
260#14579093C2311yescharacteristic, complemented
261#14579093C2312yescomplemented
262#14579093C2311yescharacteristic, complemented
263#14579092C2311yescharacteristic, complemented
264#14579092C2312yescomplemented
265#14579092C2311yescharacteristic, complemented
266#14579092C2311yescharacteristic, complemented
267#14579092C2312yescomplemented
268#14579092C2311yescharacteristic, complemented
269C4⋊(C79⋊C8)C2312yescomplemented
270C4⋊(C79⋊C8)C2312yescomplemented
271Dic79⋊C8C2312yescomplemented
272Dic79⋊C8C2312yescomplemented
273Dic79⋊C8C2312yescomplemented
274Dic79⋊C8C2312yescomplemented
275#14579083C2312yes—
276#14579083C2312yes—
277#14579083C2312yes—
278#14579083C2312yes—
279#14579082C2312yes—
280#14579082C2312yes—
281#14579082C2312yes—
282#14579082C2312yes—
283#14579081C2312yes—
284#14579081C2312yes—
285#14579081C2312yes—
286#14579081C2312yes—
287C22×D4×C79C2311yescharacteristic
288C2×M16×C79C2311yescharacteristic
289C22×C8×C79C2311yescharacteristic
290C4⋊Q8×C79—21no—
291C4⋊Q8×C79C2312yescomplemented
292#125×C79—21no—
293#125×C79C2312yescomplemented
294C22⋊Q8×C79—22no—
295C4×D4×C79—21no—
296C4×D4×C79—21no—
297C4×D4×C79C2312yes—
298C4×D4×C79C2312yes—
299#117×C79C2311yescharacteristic
300#117×C79C2311yescharacteristic
301#117×C79C2311yescharacteristic
302C2×C4⋊C4×C79C2311yescharacteristic
303C2×C22⋊C4×C79—22no—
304#107×C79C2311yescharacteristic, complemented
305#107×C79C2311yescharacteristic, complemented
306#107×C79C2312yescomplemented
307#106×C79C2311yescharacteristic, complemented
308#106×C79C2311yescharacteristic, complemented
309#106×C79C2312yescomplemented
310C4⋊C8×C79C2312yescomplemented
311C4⋊C8×C79C2312yescomplemented
312#102×C79C2312yes—
313#102×C79C2312yes—
314#102×C79C2312yes—
315#102×C79C2312yes—
316C23×D79—21no—
317C23×D79—22no—
318C23×D79—28no—
319C23×D79—22no—
320C23×D79—82no—
321C23×D79—82no—
322C23×D79C2×D411yescharacteristic
323C2×Dic158—22no—
324C2×Dic158—22no—
325C2×Dic158—22no—
326C2×D316—21no—
327C2×D316—22no—
328C2×D316C2×Q814yes—
329C2×D316C2412yes—
330C2×C22⋊D79—28no—
331C2×C22⋊D79—22no—
332C2×C22⋊D79—22no—
333D4×D79—28no—
334D4×D79—28no—
335D4×D79—24no—
336D4×D79—24no—
337D4×D79C2×Q818yes—
338D4×D79C2×Q818yes—
339C22×Dic79—22no—
340C22×Dic79—22no—
341C22×Dic79—21no—
342C22×Dic79C2×D411yescharacteristic
343C2×C4×D79—22no—
344C2×C4×D79—22no—
345C2×C4×D79—21no—
346C2×C4×D79—21no—
347C2×C4×D79—21no—
348C2×C4×D79—21no—
349C2×C4×D79—22no—
350C2×C4×D79—22no—
351C2×C4×D79—84no—
352C2×C4×D79—84no—
353C2×C4×D79C2×D412yes—
354C2×C4×D79C2×D412yes—
355C2×C4×D79C2×D411yescharacteristic
356C2×C4×D79C2×D411yescharacteristic
357C2×C4×D79C2×Q814yes—
358C2×C4×D79#4114yes—
359C2×C4×D79C2411yescharacteristic
360C2×C4×D79C2411yescharacteristic
361#11929608—22no—
362#11929607—24no—
363#11929607—22no—
364#11929607—22no—
365#11929607—22no—
366#11929607—22no—
367C2×C79⋊C8—22no—
368C2×C79⋊C8C2412yes—
369C2×C79⋊C8C2411yescharacteristic
370C2×C79⋊C8C2411yescharacteristic
371C8×D79—24no—
372C4⋊Dic79—22no—
373C4⋊Dic79—22no—
374C4⋊Dic79—21no—
375C4⋊Dic79—22no—
376C4⋊Dic79C2×D411yescharacteristic
377C4⋊Dic79C2×D411yescharacteristic
378C4⋊Dic79C2411yescharacteristic
379C4⋊Dic79C2411yescharacteristic
380C4⋊Dic79C2412yes—
381C4⋊Dic79C2411yescharacteristic
382C4⋊Dic79C2411yescharacteristic
383Dic79⋊C4—21no—
384Dic79⋊C4—21no—
385Dic79⋊C4—21no—
386Dic79⋊C4—21no—
387Dic79⋊C4—22no—
388Dic79⋊C4—22no—
389Dic79⋊C4—22no—
390Dic79⋊C4—22no—
391Dic79⋊C4—22no—
392Dic79⋊C4—22no—
393Dic79⋊C4C2×D412yes—
394Dic79⋊C4C2×D412yes—
395C22⋊Dic79—22no—
396C22⋊Dic79—22no—
397C22⋊Dic79—21no—
398C22⋊Dic79—21no—
399C22⋊Dic79C2×D412yes—
400(C2×D79)⋊C4—22no—
401(C2×D79)⋊C4—22no—
402(C2×D79)⋊C4—21no—
403(C2×D79)⋊C4—21no—
404(C2×D79)⋊C4—21no—
405(C2×D79)⋊C4—21no—
406(C2×D79)⋊C4—22no—
407(C2×D79)⋊C4—22no—
408(C2×D79)⋊C4—22no—
409(C2×D79)⋊C4—22no—
410(C2×D79)⋊C4C2×D412yes—
411(C2×D79)⋊C4C2×D412yes—
412C4×Dic79—21no—
413C4×Dic79—21no—
414C4×Dic79—21no—
415C4×Dic79—21no—
416C4×Dic79—22no—
417C4×Dic79—22no—
418C4×Dic79—21no—
419C4×Dic79—21no—
420C4×Dic79C2×D412yes—
421C4×Dic79C2×D412yes—
422C4×Dic79C2412yes—
423C24×C79—21no—
424C2×Q8×C79—22no—
425C2×D4×C79—21no—
426C2×D4×C79—22no—
427C2×D4×C79C2×Q814yes—
428C2×D4×C79C2412yes—
429C22×C4×C79—21no—
430C22×C4×C79—22no—
431C22×C4×C79—22no—
432C22×C4×C79C2411yescharacteristic
433M16×C79—22no—
434C2×C8×C79—22no—
435C2×C8×C79C2411yescharacteristic
436C2×C8×C79C2412yes—
437C2×C8×C79C2411yescharacteristic
438C4⋊C4×C79—21no—
439C4⋊C4×C79—22no—
440C4⋊C4×C79—22no—
441C4⋊C4×C79—22no—
442C4⋊C4×C79C2×D411yescharacteristic
443C4⋊C4×C79C2×D411yescharacteristic
444C4⋊C4×C79C2412yes—
445C4⋊C4×C79C2411yescharacteristic
446C4⋊C4×C79C2411yescharacteristic
447C4⋊C4×C79C2411yescharacteristic
448C4⋊C4×C79C2411yescharacteristic
449C22⋊C4×C79—21no—
450C22⋊C4×C79—21no—
451C22⋊C4×C79—22no—
452C22⋊C4×C79—22no—
453C22⋊C4×C79C2×D412yes—
454C42×C79—21no—
455C42×C79—21no—
456C42×C79C2412yes—
457C23×C79—22no—
458C23×C79—24no—
459C23×C79—81no—
460C23×C79—81no—
461C23×C79C22×D411yescharacteristic
462C22×D79—22no—
463C22×D79—24no—
464C22×D79—28no—
465C22×D79—28no—
466C22×D79—41no—
467C22×D79—41no—
468C22×D79—44no—
469C22×D79—44no—
470C22×D79—82no—
471C22×D79—82no—
472C22×D79—816no—
473C22×D79—81no—
474C22×D79—81no—
475C22×D79C22⋊Q814yes—
476C22×D79C22×D411yescharacteristic
477C22×D79C22×D411yescharacteristic
478Q8×C79—82no—
479D4×C79—24no—
480D4×C79—22no—
481D4×C79C22×Q814yes—
482C2×C4×C79—22no—
483C2×C4×C79—21no—
484C2×C4×C79—21no—
485C2×C4×C79—21no—
486C2×C4×C79—21no—
487C2×C4×C79—82no—
488C2×C4×C79—82no—
489C2×C4×C79—81no—
490C2×C4×C79C22×D412yes—
491C2×C4×C79C22×D412yes—
492C2×C4×C79C22×D411yescharacteristic
493C2×C4×C79C22×Q812yes—
494C2×C4×C79C2×#4112yes—
495C2×C4×C79C2511yescharacteristic
496C22⋊D79—28no—
497C22⋊D79—28no—
498C2×Dic79—21no—
499C2×Dic79—21no—
500C2×Dic79—22no—
501C2×Dic79—21no—
502C2×Dic79—21no—
503C2×Dic79—82no—
504C2×Dic79—82no—
505C2×Dic79—81no—
506C2×Dic79C22⋊Q814yes—
507C2×Dic79C22×D412yes—
508C2×Dic79C22×D412yes—
509C2×Dic79C22×D411yescharacteristic
510C2×Dic79C22×D411yescharacteristic
511D316—24no—
512D316—22no—
513D316C22×Q814yes—
514C4×D79—42no—
515C4×D79—42no—
516C4×D79—42no—
517C4×D79—42no—
518C4×D79—82no—
519C4×D79—82no—
520C4×D79—82no—
521C4×D79—82no—
522C4×D79—81no—
523C4×D79—81no—
524C4×D79C22⋊Q814yes—
525C4×D79C22⋊Q814yes—
526C4×D79C22×Q812yes—
527C4×D79C22×Q812yes—
528C4×D79C2×#4112yes—
529C4×D79C2×#4112yes—
530Dic158—82no—
531Dic158—82no—
532Dic158—82no—
533C8×C79—22no—
534C8×C79—21no—
535C8×C79—21no—
536C79⋊C8—22no—
537C79⋊C8—21no—
538C79⋊C8—21no—
539C22×C79—21no—
540C22×C79—21no—
541C22×C79—24no—
542C22×C79—42no—
543C22×C79—42no—
544C22×C79—84no—
545C22×C79C2×C22⋊Q812yes—
546C22×C79C23×D411yescharacteristic
547C2×D79—21no—
548C2×D79—21no—
549C2×D79—21no—
550C2×D79—21no—
551C2×D79—24no—
552C2×D79—44no—
553C2×D79—416no—
554C2×D79—42no—
555C2×D79—42no—
556C2×D79—88no—
557C2×D79—84no—
558C2×D79C2×C22⋊Q812yes—
559C2×D79C2×C22⋊Q812yes—
560C4×C79—22no—
561C4×C79—22no—
562C4×C79—41no—
563C4×C79—41no—
564C4×C79—42no—
565C4×C79—41no—
566C4×C79—41no—
567C4×C79C2×C22⋊Q812yes—
568C4×C79C23×Q811yescharacteristic
569C4×C79C22×#4111yescharacteristic
570Dic79—22no—
571Dic79—22no—
572Dic79—41no—
573Dic79—41no—
574Dic79—42no—
575Dic79—41no—
576Dic79—41no—
577Dic79C2×C22⋊Q812yes—
578Dic79C2×C22⋊Q812yes—
579#60490—791nomaximal, Sylow
580C2×C79—22no—
581C2×C79—44no—
582C2×C79C22×C22⋊Q811yescharacteristic
583C2×C79#358511yescharacteristic
584C2×C79#358511yescharacteristic
585D79—22no—
586D79—22no—
587D79—44no—
588#3458—791no—
589C2×#518—791no—
590#3081—792no—
591#3081—792no—
592#3081—792no—
593#3081—792no—
594#3081—791no—
595#3081—791no—
596#3081—791no—
597#3081—791no—
598#3081—791no—
599#3081—791no—
600#3081—791no—
601#3081D7911yescharacteristic, complemented
602#3077—792no—
603#3077—792no—
604#3077—792no—
605#3077—792no—
606#2911—791no—
607#2911—791no—
608#2905—791no—
609C2×#418—791no—
610C2×#418—791no—
611C79#6049011yescharacteristic, complemented, Sylow
612C23×D4—791no—
613C22×M16—791no—
614C22×M16—791no—
615#544—792no—
616#544—792no—
617#544—791no—
618#544—791no—
619#544—791no—
620#544—1581no—
621#544—1581no—
622#544C2×D7911yescharacteristic, complemented
623#543—1582no—
624#533—792no—
625#533—792no—
626#533—1582no—
627#533—1581no—
628#533—1581no—
629#518—791no—
630#518—792no—
631#518—792no—
632#518—791no—
633#518—791no—
634#518—1582no—
635#518—1581no—
636#518—1581no—
637#518C2×D7911yescharacteristic
638C2×C4×D4—792no—
639C2×C4×D4—792no—
640C2×C4×D4—1581no—
641C2×C4×D4—1581no—
642C2×#117—791no—
643C2×#117—791no—
644C2×#117—791no—
645C2×#117—791no—
646C22×C22⋊C4—1582no—
647#478—792no—
648#478—792no—
649#478—792no—
650#478—792no—
651#478—792no—
652#478—792no—
653#478—792no—
654#478—792no—
655#478—792no—
656#478—792no—
657#478—792no—
658#478—792no—
659#478—792no—
660#478—792no—
661#478C2×D7912yescomplemented
662#478C2×D7912yescomplemented
663#476—792no—
664#476—792no—
665#476—792no—
666#476—792no—
667#476—792no—
668#476—792no—
669#476—792no—
670#476C2×D7912yescomplemented
671#474—792no—
672#474—792no—
673#474—792no—
674#474—792no—
675#474—792no—
676#474—792no—
677#474—792no—
678#474C2×D7912yescomplemented
679#428—791no—
680#428—791no—
681#428—791no—
682#428—792no—
683#428—791no—
684#428—791no—
685#428—791no—
686#428—791no—
687#428—792no—
688#428—791no—
689#428—791no—
690#428—791no—
691#428—791no—
692#428C2×D7911yescharacteristic, complemented
693#427—791no—
694#427—791no—
695#427—791no—
696#427—792no—
697#427—792no—
698#427C2×D7911yescharacteristic, complemented
699#424—791no—
700#424—791no—
701#424—791no—
702#424—792no—
703#424—792no—
704#424C2×D7911yescharacteristic, complemented
705#423—792no—
706#423—792no—
707#418—791no—
708#418—791no—
709#418—791no—
710#418—792no—
711#418—792no—
712#418—792no—
713#418—792no—
714#418—792no—
715#418—792no—
716#418C2×D7911yescharacteristic
717C2×#102—791no—
718C2×#102—791no—
719C2×#102—791no—
720C2×#102—792no—
721C2×#102—792no—
722C2×#102C2×D7911yescharacteristic
723C25—1581no—
724C22×D4—798no—
725C22×D4—792no—
726C22×D4—792no—
727C22×D4—791no—
728C22×D4—1581no—
729C22×D4—1581no—
730C22×D4—1584no—
731C22×D4—1581no—
732C22×D4C22×D7911yescharacteristic
733C23×C4—791no—
734C23×C4—1582no—
735C23×C4—1582no—
736C2×M16—791no—
737C2×M16—791no—
738C2×M16—792no—
739C2×M16—791no—
740C2×M16—791no—
741C2×M16—791no—
742C2×M16—1584no—
743C2×M16—1584no—
744C2×M16C22×D7911yescharacteristic
745C22×C8—791no—
746C22×C8—792no—
747C22×C8C22×D7911yescharacteristic
748C4⋊Q8—21no—
749C4⋊Q8—792no—
750C4⋊Q8—792no—
751C4⋊Q8—792no—
752C4⋊Q8—1581no—
753C4⋊Q8—1582no—
754C4⋊Q8—1581no—
755C4⋊Q8—1582no—
756C4⋊Q8—1581no—
757C4⋊Q8C22×D7912yescomplemented
758#125—21no—
759#125—792no—
760#125—792no—
761#125—792no—
762#125—1581no—
763#125—1582no—
764#125—1582no—
765#125—1581no—
766#125—1581no—
767#125C22×D7912yescomplemented
768C22⋊Q8—22no—
769C22⋊Q8—1582no—
770C22⋊Q8—1582no—
771C22⋊Q8—1582no—
772C22⋊Q8—1582no—
773C22⋊Q8—1582no—
774C22⋊Q8—1582no—
775C22⋊Q8—1582no—
776C22⋊Q8—1582no—
777C22⋊Q8—1582no—
778C22⋊Q8—1582no—
779C22⋊Q8—1582no—
780C4×Q8—1582no—
781C4×Q8—1582no—
782C4×Q8—1582no—
783C4×Q8—1582no—
784C4×D4—21no—
785C4×D4—21no—
786C4×D4—792no—
787C4×D4—792no—
788C4×D4—792no—
789C4×D4—792no—
790C4×D4—792no—
791C4×D4—792no—
792C4×D4—1581no—
793C4×D4—1581no—
794C4×D4—1582no—
795C4×D4—1582no—
796C4×D4—1582no—
797C4×D4—1582no—
798C4×D4—1582no—
799C4×D4—1582no—
800C4×D4—1582no—
801C4×D4—1582no—
802C4×D4—1581no—
803C4×D4—1581no—
804C4×D4—1581no—
805C4×D4—1581no—
806C4×D4C22×D7912yes—
807C4×D4C22×D7912yes—
808#117—791no—
809#117—791no—
810#117—791no—
811#117—792no—
812#117—792no—
813#117—791no—
814#117—791no—
815#117—791no—
816#117—791no—
817#117—791no—
818#117—791no—
819#117—792no—
820#117—792no—
821#117—1581no—
822#117—1581no—
823#117—1581no—
824#117—1581no—
825#117—1581no—
826#117—1581no—
827#117C22×D7911yescharacteristic
828#117C22×D7911yescharacteristic
829#117C22×D7911yescharacteristic
830C2×C4⋊C4—791no—
831C2×C4⋊C4—791no—
832C2×C4⋊C4—791no—
833C2×C4⋊C4—791no—
834C2×C4⋊C4—791no—
835C2×C4⋊C4—791no—
836C2×C4⋊C4—791no—
837C2×C4⋊C4C22×D7911yescharacteristic
838C2×C22⋊C4—22no—
839C2×C22⋊C4—792no—
840C2×C22⋊C4—1582no—
841C2×C22⋊C4—1582no—
842C2×C22⋊C4—1582no—
843C2×C22⋊C4—1582no—
844C2×C22⋊C4—1582no—
845C2×C22⋊C4—1581no—
846C2×C22⋊C4—1581no—
847C2×C22⋊C4—1582no—
848C2×C22⋊C4—1582no—
849C2×C22⋊C4—1582no—
850C2×C22⋊C4—1581no—
851C2×C22⋊C4—1582no—
852C2×C42—792no—
853C2×C42—1581no—
854C2×C42—1581no—
855C2×C42—1581no—
856#107—792no—
857#107—791no—
858#107—791no—
859#107—791no—
860#107—792no—
861#107—791no—
862#107—791no—
863#107—791no—
864#107—792no—
865#107C22×D7912yescomplemented
866#107C22×D7911yescharacteristic, complemented
867#107C22×D7911yescharacteristic, complemented
868#106—791no—
869#106—791no—
870#106—792no—
871#106—792no—
872#106—791no—
873#106—791no—
874#106—791no—
875#106—791no—
876#106—792no—
877#106C22×D7912yescomplemented
878#106C22×D7911yescharacteristic, complemented
879#106C22×D7911yescharacteristic, complemented
880C4⋊C8—792no—
881C4⋊C8—792no—
882C4⋊C8—792no—
883C4⋊C8—792no—
884C4⋊C8—792no—
885C4⋊C8—792no—
886C4⋊C8C22×D7912yescomplemented
887C4⋊C8C22×D7912yescomplemented
888#102—792no—
889#102—792no—
890#102—792no—
891#102—792no—
892#102—792no—
893#102—792no—
894#102—792no—
895#102—792no—
896#102—792no—
897#102—792no—
898#102—792no—
899#102—792no—
900#102C22×D7912yes—
901#102C22×D7912yes—
902#102C22×D7912yes—
903#102C22×D7912yes—
904C24—21no—
905C24—791no—
906C24—6322no—
907C24—6322no—
908C24—1582no—
909C24—1582no—
910C24—1588no—
911C24—1581no—
912C2×Q8—22no—
913C2×Q8—1582no—
914C2×Q8—1582no—
915C2×Q8—1582no—
916C2×D4—22no—
917C2×D4—21no—
918C2×D4—798no—
919C2×D4—798no—
920C2×D4—794no—
921C2×D4—792no—
922C2×D4—1588no—
923C2×D4—1588no—
924C2×D4—1584no—
925C2×D4—1584no—
926C2×D4—1582no—
927C2×D4—1582no—
928C2×D4—1588no—
929C2×D4—1582no—
930C2×D4—1581no—
931C2×D4Q8×D7914yes—
932C2×D4C23×D7912yes—
933C22×C4—21no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—792no—
937C22×C4—792no—
938C22×C4—791no—
939C22×C4—794no—
940C22×C4—794no—
941C22×C4—791no—
942C22×C4—791no—
943C22×C4—791no—
944C22×C4—791no—
945C22×C4—6324no—
946C22×C4—6324no—
947C22×C4—1581no—
948C22×C4—1581no—
949C22×C4—1582no—
950C22×C4—1582no—
951C22×C4—1581no—
952C22×C4—1581no—
953C22×C4—1582no—
954C22×C4—1582no—
955C22×C4—1581no—
956C22×C4—1582no—
957C22×C4—1582no—
958C22×C4C23×D7911yescharacteristic
959M16—22no—
960M16—1582no—
961M16—1582no—
962M16—1582no—
963M16—1582no—
964M16—1584no—
965M16—1582no—
966C2×C8—22no—
967C2×C8—792no—
968C2×C8—791no—
969C2×C8—791no—
970C2×C8—1584no—
971C2×C8—1582no—
972C2×C8C23×D7911yescharacteristic
973C2×C8C23×D7912yes—
974C2×C8C23×D7911yescharacteristic
975C4⋊C4—21no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—792no—
980C4⋊C4—792no—
981C4⋊C4—791no—
982C4⋊C4—791no—
983C4⋊C4—791no—
984C4⋊C4—791no—
985C4⋊C4—792no—
986C4⋊C4—791no—
987C4⋊C4—791no—
988C4⋊C4—1581no—
989C4⋊C4—1581no—
990C4⋊C4—1581no—
991C4⋊C4—1581no—
992C4⋊C4—1582no—
993C4⋊C4—1582no—
994C4⋊C4—1582no—
995C4⋊C4—1582no—
996C4⋊C4—1582no—
997C4⋊C4—1582no—
998C4⋊C4—1582no—
999C4⋊C4—1582no—
1000C4⋊C4—1581no—
1001C4⋊C4—1582no—
1002C4⋊C4D4×D7911yescharacteristic
1003C4⋊C4D4×D7911yescharacteristic
1004C4⋊C4C23×D7911yescharacteristic
1005C4⋊C4C23×D7911yescharacteristic
1006C4⋊C4C23×D7912yes—
1007C4⋊C4C23×D7911yescharacteristic
1008C4⋊C4C23×D7911yescharacteristic
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—792no—
1014C22⋊C4—792no—
1015C22⋊C4—792no—
1016C22⋊C4—1582no—
1017C22⋊C4—1582no—
1018C22⋊C4—1581no—
1019C22⋊C4—1581no—
1020C22⋊C4—1581no—
1021C22⋊C4—1581no—
1022C22⋊C4—1582no—
1023C22⋊C4—1582no—
1024C22⋊C4—1582no—
1025C22⋊C4—1582no—
1026C22⋊C4—1581no—
1027C22⋊C4—1581no—
1028C22⋊C4—1582no—
1029C22⋊C4—1582no—
1030C22⋊C4D4×D7912yes—
1031C42—21no—
1032C42—21no—
1033C42—792no—
1034C42—792no—
1035C42—792no—
1036C42—1581no—
1037C42—1581no—
1038C42—1581no—
1039C42—1581no—
1040C42—1582no—
1041C42—1582no—
1042C42—1581no—
1043C42—1581no—
1044C42C23×D7912yes—
1045C23—22no—
1046C23—24no—
1047C23—81no—
1048C23—81no—
1049C23—3161no—
1050C23—3161no—
1051C23—3164no—
1052C23—3164no—
1053C23—794no—
1054C23—791no—
1055C23—791no—
1056C23—6321no—
1057C23—6321no—
1058C23—6322no—
1059C23—6322no—
1060C23—63216no—
1061C23—1588no—
1062C23—1588no—
1063C23—1582no—
1064C23—1584no—
1065C23C2×D4×D7911yescharacteristic
1066Q8—82no—
1067Q8—6322no—
1068Q8—6322no—
1069Q8—6322no—
1070D4—24no—
1071D4—22no—
1072D4—794no—
1073D4—1588no—
1074D4—1588no—
1075D4—1584no—
1076D4—1582no—
1077D4C2×Q8×D7914yes—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—82no—
1084C2×C4—82no—
1085C2×C4—81no—
1086C2×C4—3162no—
1087C2×C4—3162no—
1088C2×C4—3162no—
1089C2×C4—3162no—
1090C2×C4—794no—
1091C2×C4—791no—
1092C2×C4—791no—
1093C2×C4—794no—
1094C2×C4—794no—
1095C2×C4—792no—
1096C2×C4—792no—
1097C2×C4—792no—
1098C2×C4—792no—
1099C2×C4—792no—
1100C2×C4—792no—
1101C2×C4—6322no—
1102C2×C4—6322no—
1103C2×C4—6321no—
1104C2×C4—6321no—
1105C2×C4—6322no—
1106C2×C4—6322no—
1107C2×C4—6321no—
1108C2×C4—6322no—
1109C2×C4—6322no—
1110C2×C4—1581no—
1111C2×C4—1581no—
1112C2×C4—1581no—
1113C2×C4—1582no—
1114C2×C4—1581no—
1115C2×C4C2×D4×D7912yes—
1116C2×C4C2×D4×D7912yes—
1117C2×C4C2×D4×D7911yescharacteristic
1118C2×C4C2×Q8×D7912yes—
1119C2×C4#41×D7912yes—
1120C2×C4C24×D7911yescharacteristic
1121C8—21no—
1122C8—21no—
1123C8—22no—
1124C8—1582no—
1125C8—1581no—
1126C8—1581no—
1127C22—21no—
1128C22—21no—
1129C22—24no—
1130C22—42no—
1131C22—42no—
1132C22—84no—
1133C22—3164no—
1134C22—31616no—
1135C22—3162no—
1136C22—3162no—
1137C22—792no—
1138C22—792no—
1139C22—6324no—
1140C22—6328no—
1141C22—1584no—
1142C22—1581no—
1143C22—1581no—
1144C22—1581no—
1145C22—1581no—
1146C22C22⋊Q8×D7912yes—
1147C22C22×D4×D7911yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—41no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—3161no—
1156C4—3161no—
1157C4—3161no—
1158C4—3161no—
1159C4—3162no—
1160C4—792no—
1161C4—792no—
1162C4—1582no—
1163C4—1582no—
1164C4C22⋊Q8×D7912yes—
1165C4C22×Q8×D7911yescharacteristic
1166C4C2×#41×D7911yescharacteristic
1167C2—22no—
1168C2—44no—
1169C2—3164no—
1170C2—1582no—
1171C2—1582no—
1172C2C2×C22⋊Q8×D7911yescharacteristic
1173C2#2377817511yescharacteristic
1174C2#2377817811yescharacteristic
subgroupG/H
centerC22C22×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC79×#3081C2
socleC22×C79C23×D4
prime radicalC22×D4×D79C22
hypercenter#3081D79
hypocenterC79#60490
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #3081

Complements

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

NH ≅ G/Ntype
1. #23776804C2semidirect
3. #23773234C2semidirect
4. #23773233C2semidirect
5. #23773232C2semidirect
6. #23773231C2semidirect
7. #23773230C2semidirect
8. #23773229C2semidirect
9. #23773228C2semidirect
10. #23773227C2semidirect
11. #23773226C2semidirect
12. #23773225C2semidirect
13. #23773224C2semidirect
14. #23773198C2semidirect
15. #23773195C2semidirect
16. #23773195C2semidirect
17. #23773192C2semidirect
18. #23771988C2semidirect
19. #23771987C2semidirect
20. #23771961C2semidirect
23. C79×#3081C2semidirect
27. #19099194C22semidirect
29. #19099193C22semidirect
30. #19099191C22semidirect
31. #19099191C22semidirect
33. #19099190C22semidirect
36. #19099119C22semidirect
38. #19099118C22semidirect
57. #19098866C22semidirect
58. #19098866C22semidirect
59. #19098865C22semidirect
60. #19098865C22semidirect
61. #19098864C22semidirect
62. #19098864C22semidirect
63. #19098863C22semidirect
64. #19098863C22semidirect
65. #19098862C22semidirect
66. #19098862C22semidirect
67. #19098861C22semidirect
68. #19098861C22semidirect
69. #19098860C22semidirect
70. #19098860C22semidirect
71. #19098854C22semidirect
72. #19098853C22semidirect
73. #19098852C22semidirect
74. #19098852C22semidirect
75. #19098851C22semidirect
76. #19098851C22semidirect
77. #19098850C22semidirect
78. #19098844C22semidirect
79. #19098843C22semidirect
80. #19098842C22semidirect
81. #19098842C22semidirect
82. #19098841C22semidirect
83. #19098841C22semidirect
84. #19098840C22semidirect
85. #19098606C22semidirect
86. #19098605C22semidirect
87. #19098604C22semidirect
88. #19098604C22semidirect
89. #19098604C22semidirect
90. #19098604C22semidirect
91. #19098604C22semidirect
92. #19098603C22semidirect
93. #19098602C22semidirect
94. #19098602C22semidirect
95. #19098602C22semidirect
96. #19098602C22semidirect
97. #19098602C22semidirect
98. #19098601C22semidirect
99. #19098600C22semidirect
100. #19098599C22semidirect
101. #19098599C22semidirect
102. #19098598C22semidirect
103. #19098591C22semidirect
104. #19098590C22semidirect
105. #19098589C22semidirect
106. #19098588C22semidirect
107. #19098588C22semidirect
108. #19098585C22semidirect
109. #19098585C22semidirect
124. #544×C79C22semidirect
126. #478×C79C22semidirect
127. #478×C79C22semidirect
128. #476×C79C22semidirect
129. #474×C79C22semidirect
130. #428×C79C22semidirect
131. #427×C79C22semidirect
132. #424×C79C22semidirect
141. C2×D4×D79Q8semidirect
158. #14579161C23semidirect
162. #14579160C23semidirect
163. #14579160C23semidirect
166. #14579153C23semidirect
169. #14579152C23semidirect
170. #14579152C23semidirect
251. #14579095C23semidirect
252. #14579095C23semidirect
253. #14579095C23semidirect
254. #14579094C23semidirect
255. #14579094C23semidirect
256. #14579094C23semidirect
257. #14579094C23semidirect
258. #14579094C23semidirect
259. #14579094C23semidirect
260. #14579093C23semidirect
261. #14579093C23semidirect
262. #14579093C23semidirect
263. #14579092C23semidirect
264. #14579092C23semidirect
265. #14579092C23semidirect
266. #14579092C23semidirect
267. #14579092C23semidirect
268. #14579092C23semidirect
269. C4⋊(C79⋊C8)C23semidirect
270. C4⋊(C79⋊C8)C23semidirect
271. Dic79⋊C8C23semidirect
272. Dic79⋊C8C23semidirect
273. Dic79⋊C8C23semidirect
274. Dic79⋊C8C23semidirect
291. C4⋊Q8×C79C23semidirect
293. #125×C79C23semidirect
304. #107×C79C23semidirect
305. #107×C79C23semidirect
306. #107×C79C23semidirect
307. #106×C79C23semidirect
308. #106×C79C23semidirect
309. #106×C79C23semidirect
310. C4⋊C8×C79C23semidirect
311. C4⋊C8×C79C23semidirect
601. #3081D79semidirect
611. C79#60490semidirect
622. #544C2×D79semidirect
661. #478C2×D79semidirect
662. #478C2×D79semidirect
670. #476C2×D79semidirect
678. #474C2×D79semidirect
692. #428C2×D79semidirect
698. #427C2×D79semidirect
704. #424C2×D79semidirect
757. C4⋊Q8C22×D79semidirect
767. #125C22×D79semidirect
865. #107C22×D79semidirect
866. #107C22×D79semidirect
867. #107C22×D79semidirect
877. #106C22×D79semidirect
878. #106C22×D79semidirect
879. #106C22×D79semidirect
886. C4⋊C8C22×D79semidirect
887. C4⋊C8C22×D79semidirect

Maximal subgroups

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

subgroupindex
#237768042
#518×D792
#237732342
#237732332
#237732322
#237732312
#237732302
#237732292
#237732282
#237732272
#237732262
#237732252
#237732242
#237731982
#237731952
#237731922
#237719882
#237719872
#237719612
C2×#190985662
#418×D792
C79×#30812
#6049079