Finite Group Databasebeta

← #30547556

Subgroups — #30547556

Order 15616.

2130 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic, complemented
2C4×#41×D61C211yesmaximal, characteristic
3#21455640C212yesmaximal, complemented
4#21455639C212yesmaximal, complemented
5#21455635C211yesmaximal, characteristic, complemented
6#21455634C211yesmaximal, characteristic, complemented
7#21455628C211yesmaximal, characteristic, complemented
8#21455625C212yesmaximal, complemented
9#21455619C212yesmaximal, complemented
10#21455617C212yesmaximal, complemented
11#21455611C212yesmaximal, complemented
12#21455610C212yesmaximal, complemented
13#21455608C212yesmaximal, complemented
14#21455602C212yesmaximal, complemented
15#21455600C212yesmaximal, complemented
16#21454406C212yesmaximal, complemented
17#423×D61C211yesmaximal, characteristic, complemented
18#21454335C212yesmaximal
19C61×#3079C211yesmaximal, characteristic, complemented
20C2×#41×D61C2211yescharacteristic
21C2×M16×D61C2212yes—
22#16840317—21no—
23#16840317—21no—
24#16840317—21no—
25#16840317—21no—
26#16840317C2212yes—
27#16840317C2212yes—
28#16840317C2212yescomplemented
29#16840317C2212yescomplemented
30C2×#14519777C2211yescharacteristic, complemented
31C2×#14519768C2212yescomplemented
32C2×#14519757—21no—
33C2×#14519753—21no—
34#41×Dic61C2211yescharacteristic
35C4×#11758226C2211yescharacteristic
36C4×#11758226C2211yescharacteristic
37C4×#11758222—21no—
38C4×#11758222C2211yescharacteristic
39#16840230—21no—
40#16840230C2211yescharacteristic
41C4×#11758224—21no—
42C4×#11758224—21no—
43C4×#11758224C2211yescharacteristic
44C4×#11758224C2211yescharacteristic
45C2×Q8×Dic61—21no—
46C2×#14519742—21no—
47C4×Q8×D61C2211yescharacteristic
48C4×Q8×D61C2211yescharacteristic
49C4×D4×D61—21no—
50C4×D4×D61—21no—
51C4×D4×D61C2211yescharacteristic
52C4×D4×D61C2211yescharacteristic
53C2×#14519735C2212yes—
54#117×D61—21no—
55#117×D61C2211yescharacteristic
56C2×C42×D61—21no—
57C2×C42×D61C2211yescharacteristic
58#16840072C2214yescomplemented
59#16840071C2214yescomplemented
60#16840068C2214yescomplemented
61#16840067C2214yescomplemented
62#16840065C2214yescomplemented
63#16840064C2214yescomplemented
64#16840061C2214yescomplemented
65#16840060C2214yescomplemented
66#16840058C2212yescomplemented
67#16840057C2212yescomplemented
68#16840054C2212yescomplemented
69#16840053C2212yescomplemented
70#16840052C2212yescomplemented
71#16840049C2212yescomplemented
72#16840048C2212yescomplemented
73#16840047C2212yescomplemented
74#16840044C2212yescomplemented
75#16840043C2212yescomplemented
76#16840042C2212yescomplemented
77#16840039C2212yescomplemented
78#16839805C2212yescomplemented
79#16839804C2212yescomplemented
80#16839803C2214yes—
81#16839802C2212yescomplemented
82#16839801C2214yes—
83#16839799C2214yescomplemented
84#16839797C2214yescomplemented
85#16839786C2211yescharacteristic, complemented
86#16839785C2212yescomplemented
87#16839784C2212yes—
88#16839784C2212yes—
89C4⋊C8×D61C2212yescomplemented
90C4⋊C8×D61C2212yescomplemented
91#16839769C2214yes—
92#16839765C2214yes—
93#16839764C2212yes—
94#16839763C2212yes—
95#16839761C2212yes—
96#16839757C2214yes—
97#16839755C2214yes—
98C2×C4⋊Q8×C61C2211yescharacteristic, complemented
99C4×#41×C61C2211yescharacteristic
100C61×#477C2212yescomplemented
101C61×#476C2212yescomplemented
102C61×#475C2212yescomplemented
103C61×#474C2212yescomplemented
104C61×#428C2212yescomplemented
105C61×#423C2211yescharacteristic, complemented
106C61×#417C2212yes—
107C2×#11758226C2311yescharacteristic
108C2×#11758222—21no—
109C2×#11758222C2311yescharacteristic
110C2×#11758224—21no—
111C2×#11758224C2311yescharacteristic
112#41×D61—24no—
113#41×D61Q818yescomplemented
114C22×Dic122—21no—
115C2×Q8×D61C2311yescharacteristic
116C2×D4×D61—21no—
117C2×D4×D61C2311yescharacteristic
118C22×C4×D61—21no—
119C22×C4×D61—21no—
120C22×C4×D61—21no—
121C22×C4×D61D411yescharacteristic
122C22×C4×D61D411yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C2×#11758194C2312yes—
125C2×#11758189C2314yes—
126M16×D61—28no—
127C2×C8×D61C2314yes—
128#14519777—21no—
129#14519777—21no—
130#14519777C2312yes—
131#14519777C2312yes—
132#14519768—22no—
133#14519768—22no—
134#14519768C2314yes—
135#14519768C2314yes—
136#14519757—22no—
137#14519757—22no—
138#14519757—22no—
139#14519757—22no—
140#14519753—22no—
141#14519753—22no—
142#14519753—22no—
143#14519753—22no—
144Q8×Dic61—22no—
145Q8×Dic61—22no—
146Q8×Dic61—22no—
147Q8×Dic61—22no—
148Q8×Dic61C2311yescharacteristic
149Q8×Dic61C2311yescharacteristic
150C4×Dic122—21no—
151C4×Dic122—21no—
152C4×Dic122C2311yescharacteristic
153C4×Dic122C2311yescharacteristic
154#14519742—21no—
155#14519742—21no—
156#14519742—22no—
157#14519742—22no—
158#14519742—22no—
159#14519742—22no—
160#14519742C2311yescharacteristic
161#14519742C2311yescharacteristic
162C4×D244—21no—
163C4×D244—21no—
164C4×D244C2311yescharacteristic
165C4×D244C2311yescharacteristic
166D4×Dic61—21no—
167D4×Dic61—21no—
168D4×Dic61C2311yescharacteristic
169D4×Dic61C2311yescharacteristic
170#14519739—21no—
171#14519739—21no—
172#14519739C2311yescharacteristic
173#14519739C2311yescharacteristic
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176C4×C22⋊D61—21no—
177C4×C22⋊D61—21no—
178C4×C22⋊D61—21no—
179C4×C22⋊D61—21no—
180#14519737—21no—
181#14519737—21no—
182#14519737—21no—
183#14519737—21no—
184#14519737—21no—
185#14519737—21no—
186#14519736—21no—
187#14519736C2311yescharacteristic
188#14519735—22no—
189#14519735—22no—
190#14519735—21no—
191#14519735—21no—
192#14519735C2311yescharacteristic
193#14519735C2311yescharacteristic
194#14519735C2314yes—
195#14519735C2314yes—
196#14519734—21no—
197#14519734—21no—
198#14519734—21no—
199#14519733—21no—
200#14519733—21no—
201#14519733—21no—
202C2×C4⋊Dic61—21no—
203C2×C4⋊Dic61—22no—
204C2×C4⋊Dic61C2312yes—
205C2×#11758196—22no—
206C4⋊C4×D61—21no—
207C4⋊C4×D61—21no—
208C4⋊C4×D61C2311yescharacteristic
209C4⋊C4×D61C2311yescharacteristic
210C2×#11758198—22no—
211C22⋊C4×D61—21no—
212C22⋊C4×D61—21no—
213C22⋊C4×D61—21no—
214C2×C4×Dic61—22no—
215C2×C4×Dic61—21no—
216C2×C4×Dic61—21no—
217C2×C4×Dic61—21no—
218C2×C4×Dic61D411yescharacteristic
219C2×C4×Dic61D411yescharacteristic
220C2×C4×Dic61C2311yescharacteristic
221C42×D61—21no—
222C42×D61—21no—
223C42×D61—21no—
224C42×D61—21no—
225C42×D61—21no—
226C42×D61—21no—
227C42×D61—21no—
228C42×D61D411yescharacteristic
229C42×D61D411yescharacteristic
230C42×D61D411yescharacteristic
231C42×D61D411yescharacteristic
232C42×D61C2311yescharacteristic
233C42×D61C2311yescharacteristic
234C42×D61C2311yescharacteristic
235C42×D61C2311yescharacteristic
236#14519711C2314yes—
237#14519710C2314yes—
238#14519710C2314yes—
239#14519709C2314yes—
240#14519708C2314yes—
241#14519708C2314yes—
242C4⋊#92418C2312yes—
243C4⋊#92418C2312yes—
244#14519706C2314yes—
245#14519706C2314yes—
246#14519702C2314yes—
247#14519701C2314yes—
248#14519700C2314yes—
249#14519699C2314yes—
250#14519698C2314yes—
251#14519697C2314yes—
252C2×#41×C61C2311yescharacteristic
253C22×Q8×C61—21no—
254C2×M16×C61C2312yes—
255C4⋊Q8×C61—21no—
256C4⋊Q8×C61—21no—
257C4⋊Q8×C61C2312yes—
258C4⋊Q8×C61C2312yes—
259C4×Q8×C61C2311yescharacteristic
260C4×Q8×C61C2311yescharacteristic
261C4×D4×C61—21no—
262C4×D4×C61—21no—
263C4×D4×C61C2311yescharacteristic
264C4×D4×C61C2311yescharacteristic
265#117×C61—21no—
266#117×C61C2311yescharacteristic
267C2×C4⋊C4×C61—21no—
268C2×C4⋊C4×C61C2312yes—
269C2×C42×C61—21no—
270C2×C42×C61C2311yescharacteristic
271#107×C61C2314yes—
272#106×C61C2314yes—
273C4⋊C8×C61C2312yes—
274C4⋊C8×C61C2312yes—
275#103×C61C2314yes—
276#102×C61C2314yes—
277C23×D61—21no—
278C23×D61C2×D411yescharacteristic
279#41×C61—22no—
280#41×C61C2×Q814yes—
281C2×Q8×C61—22no—
282C2×Q8×C61—22no—
283C2×Q8×C61—44no—
284C2×Q8×C61C2411yescharacteristic
285C2×D4×C61—21no—
286C2×D4×C61C2411yescharacteristic
287C22×C4×C61—21no—
288C22×C4×C61—22no—
289C22×C4×C61—21no—
290C22×C4×C61—21no—
291C22×C4×C61C2×D411yescharacteristic
292C22×C4×C61C2×D411yescharacteristic
293C22×C4×C61C2411yescharacteristic
294C2×C22⋊D61—21no—
295C2×C22⋊D61—21no—
296C2×C22⋊D61—21no—
297C22×Dic61—21no—
298C22×Dic61—22no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61C2×D411yescharacteristic
302C22×Dic61C2×D411yescharacteristic
303C22×Dic61C2×D411yescharacteristic
304#11758226—22no—
305#11758226C2×Q814yescomplemented
306Q8×D61—22no—
307Q8×D61C2×Q814yescomplemented
308#11758224—28no—
309#11758224—22no—
310#11758224C2×Q814yescomplemented
311D4×D61—28no—
312D4×D61—22no—
313D4×D61C2×Q814yescomplemented
314#11758222—22no—
315#11758222—28no—
316#11758222C2×Q814yes—
317C2×D244—21no—
318C2×D244C2411yescharacteristic
319C2×C4×D61—21no—
320C2×C4×D61—21no—
321C2×C4×D61—21no—
322C2×C4×D61—28no—
323C2×C4×D61—21no—
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—42no—
330C2×C4×D61—42no—
331C2×C4×D61—44no—
332C2×C4×D61—44no—
333C2×C4×D61C2×D411yescharacteristic
334C2×C4×D61C2×D411yescharacteristic
335C2×C4×D61C2×D411yescharacteristic
336C2×C4×D61C2×D411yescharacteristic
337C2×C4×D61C2×D411yescharacteristic
338C2×C4×D61C2×D411yescharacteristic
339C2×C4×D61C2×D411yescharacteristic
340C2×C4×D61C2×D411yescharacteristic
341C2×C4×D61C2×D411yescharacteristic
342C2×C4×D61C2×D411yescharacteristic
343C2×C4×D61C2×Q814yes—
344C2×C4×D61#4114yes—
345C2×C4×D61C2411yescharacteristic
346C2×C4×D61C2411yescharacteristic
347C2×Dic122—21no—
348C2×Dic122—22no—
349C2×Dic122—22no—
350C2×Dic122—44no—
351C2×Dic122C2411yescharacteristic
352M16×C61—24no—
353C2×C8×C61C2414yes—
354C4⋊C4×C61—22no—
355C4⋊C4×C61—22no—
356C4⋊C4×C61—22no—
357C4⋊C4×C61—21no—
358C4⋊C4×C61—21no—
359C4⋊C4×C61C2414yes—
360C4⋊C4×C61C2411yescharacteristic
361C4⋊C4×C61C2411yescharacteristic
362C22⋊C4×C61—21no—
363C22⋊C4×C61—21no—
364C22⋊C4×C61—21no—
365C42×C61—21no—
366C42×C61—21no—
367C42×C61—21no—
368C42×C61C2×D411yescharacteristic
369C42×C61C2×D411yescharacteristic
370C42×C61C2411yescharacteristic
371C42×C61C2411yescharacteristic
372C22⋊Dic61—21no—
373C22⋊Dic61—21no—
374C22⋊Dic61—21no—
375#11758198—21no—
376#11758198—21no—
377#11758198—24no—
378#11758198—24no—
379#11758198—21no—
380#11758198—21no—
381#11758198—21no—
382#11758198—21no—
383C4⋊Dic61—22no—
384C4⋊Dic61—22no—
385C4⋊Dic61—22no—
386C4⋊Dic61—21no—
387C4⋊Dic61—21no—
388C4⋊Dic61—24no—
389C4⋊Dic61—24no—
390C4⋊Dic61C2414yes—
391C4⋊Dic61C2411yescharacteristic
392C4⋊Dic61C2411yescharacteristic
393#11758196—21no—
394#11758196—21no—
395#11758196—21no—
396#11758196—21no—
397#11758196—21no—
398#11758196—21no—
399#11758196—24no—
400#11758196—24no—
401C4×Dic61—21no—
402C4×Dic61—21no—
403C4×Dic61—21no—
404C4×Dic61—21no—
405C4×Dic61—21no—
406C4×Dic61—21no—
407C4×Dic61—21no—
408C4×Dic61—21no—
409C4×Dic61—21no—
410C4×Dic61—24no—
411C4×Dic61—24no—
412C4×Dic61C2×D411yescharacteristic
413C4×Dic61C2×D411yescharacteristic
414C4×Dic61C2×D411yescharacteristic
415C4×Dic61C2×D411yescharacteristic
416C4×Dic61C2×D411yescharacteristic
417C4×Dic61C2×D411yescharacteristic
418C4×Dic61C2×D411yescharacteristic
419C4×Dic61C2×D411yescharacteristic
420C4×Dic61C2×D411yescharacteristic
421C4×Dic61C2×D411yescharacteristic
422C4×Dic61C2411yescharacteristic
423C4×Dic61C2411yescharacteristic
424#11758194—24no—
425C2×#92418C2414yes—
426#11758189—28no—
427C8×D61—28no—
428C23×C61—21no—
429C23×C61C22×D411yescharacteristic
430C22×D61—21no—
431C22×D61—24no—
432C22×D61—41no—
433C22×D61—41no—
434C22×D61—42no—
435C22×D61—42no—
436C22×D61C22⋊Q814yes—
437C22×D61C22×D411yescharacteristic
438C22×D61C22×D411yescharacteristic
439Q8×C61—21no—
440Q8×C61—44no—
441Q8×C61—44no—
442Q8×C61C22×Q812yes—
443D4×C61—24no—
444D4×C61—21no—
445D4×C61C22×Q812yes—
446C2×C4×C61—21no—
447C2×C4×C61—24no—
448C2×C4×C61—22no—
449C2×C4×C61—22no—
450C2×C4×C61—24no—
451C2×C4×C61—21no—
452C2×C4×C61—21no—
453C2×C4×C61—44no—
454C2×C4×C61—42no—
455C2×C4×C61—42no—
456C2×C4×C61C22×D411yescharacteristic
457C2×C4×C61C22×D411yescharacteristic
458C2×C4×C61C22×D411yescharacteristic
459C2×C4×C61C22×D411yescharacteristic
460C2×C4×C61C22×D411yescharacteristic
461C2×C4×C61C22×Q812yes—
462C2×C4×C61C2×#4112yes—
463C2×C4×C61C2511yescharacteristic
464C22⋊D61—24no—
465C22⋊D61—24no—
466C22⋊D61—24no—
467C2×Dic61—21no—
468C2×Dic61—24no—
469C2×Dic61—21no—
470C2×Dic61—21no—
471C2×Dic61—24no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—42no—
475C2×Dic61—42no—
476C2×Dic61—44no—
477C2×Dic61C22⋊Q814yes—
478C2×Dic61C22×D411yescharacteristic
479C2×Dic61C22×D411yescharacteristic
480C2×Dic61C22×D411yescharacteristic
481C2×Dic61C22×D411yescharacteristic
482C2×Dic61C22×D411yescharacteristic
483C2×Dic61C22×D411yescharacteristic
484D244—24no—
485D244—21no—
486D244C22×Q812yes—
487C4×D61—24no—
488C4×D61—24no—
489C4×D61—22no—
490C4×D61—22no—
491C4×D61—22no—
492C4×D61—22no—
493C4×D61—24no—
494C4×D61—41no—
495C4×D61—41no—
496C4×D61—41no—
497C4×D61—41no—
498C4×D61—42no—
499C4×D61—42no—
500C4×D61—42no—
501C4×D61—42no—
502C4×D61—42no—
503C4×D61—42no—
504C4×D61C22⋊Q814yes—
505C4×D61C22⋊Q814yes—
506C4×D61C22×Q812yes—
507C4×D61C22×Q812yes—
508C4×D61C2×#4112yes—
509C4×D61C2×#4112yes—
510Dic122—21no—
511Dic122—24no—
512Dic122—44no—
513Dic122—44no—
514Dic122C22×Q812yes—
515C8×C61—24no—
516#92418—24no—
517#60484—611nomaximal, Sylow
518C22×C61—21no—
519C22×C61—21no—
520C22×C61—22no—
521C22×C61—41no—
522C22×C61—41no—
523C22×C61C2×C22⋊Q812yes—
524C22×C61C23×D411yescharacteristic
525C2×D61—21no—
526C2×D61—21no—
527C2×D61—21no—
528C2×D61—21no—
529C2×D61—22no—
530C2×D61—44no—
531C2×D61—48no—
532C2×D61—41no—
533C2×D61—41no—
534C2×D61C2×C22⋊Q812yes—
535C2×D61C2×C22⋊Q812yes—
536C4×C61—22no—
537C4×C61—21no—
538C4×C61—21no—
539C4×C61—41no—
540C4×C61—41no—
541C4×C61—44no—
542C4×C61C2×C22⋊Q812yes—
543C4×C61#57512yes—
544C4×C61#57512yes—
545C4×C61C23×Q811yescharacteristic
546C4×C61C22×#4111yescharacteristic
547Dic61—22no—
548Dic61—21no—
549Dic61—21no—
550Dic61—21no—
551Dic61—21no—
552Dic61—44no—
553Dic61—41no—
554Dic61—41no—
555Dic61C2×C22⋊Q812yes—
556Dic61C2×C22⋊Q812yes—
557C2×#533—611no—
558C2×C4×#41—611no—
559#3080—612no—
560#3080—612no—
561#3079—611no—
562#3079—611no—
563#3079—611no—
564#3079D6111yescharacteristic, complemented
565#3078—612no—
566#3078—612no—
567#3077—612no—
568#3077—612no—
569#3076—612no—
570#3076—612no—
571#3076—612no—
572#3076—612no—
573#2911—612no—
574C2×#423—611no—
575#2896—612no—
576C2×C61—22no—
577C2×C61—42no—
578C2×C61C22×C22⋊Q811yescharacteristic
579C2×C61C2×#57511yescharacteristic
580C2×C61C2×#57511yescharacteristic
581D61—22no—
582D61—22no—
583D61—42no—
584C22×#41—611no—
585C22×M16—612no—
586#533—612no—
587#533—612no—
588#533—612no—
589#533—612no—
590#533—1221no—
591#533—1221no—
592#533—1221no—
593#533—1221no—
594C2×C4⋊Q8—611no—
595C2×C4⋊Q8C2×D6111yescharacteristic, complemented
596C2×#125—612no—
597C2×C22⋊Q8—1221no—
598C2×C22⋊Q8—1221no—
599C4×#41—611no—
600C4×#41—611no—
601C4×#41—611no—
602C4×#41—611no—
603C4×#41—611no—
604C4×#41—611no—
605C4×#41—611no—
606C4×#41—1221no—
607C4×#41—1221no—
608C4×#41—1221no—
609C4×#41—1221no—
610C4×#41C2×D6111yescharacteristic
611C2×C4×Q8—611no—
612C2×C4×Q8—611no—
613C2×C4×Q8—1221no—
614C2×C4×Q8—1221no—
615C2×C4×D4—611no—
616C2×C4×D4—611no—
617C2×C4×D4—1221no—
618C2×C4×D4—1221no—
619C2×#117—611no—
620C2×#117—612no—
621C2×#117—1221no—
622C22×C42—611no—
623C22×C42—1221no—
624#479—614no—
625#479—614no—
626#479—614no—
627#479—614no—
628#478—614no—
629#478—614no—
630#478—614no—
631#478—614no—
632#477—612no—
633#477—612no—
634#477—612no—
635#477C2×D6112yescomplemented
636#476—612no—
637#476—612no—
638#476—612no—
639#476C2×D6112yescomplemented
640#475—612no—
641#475—612no—
642#475—612no—
643#475C2×D6112yescomplemented
644#474—612no—
645#474—612no—
646#474—612no—
647#474C2×D6112yescomplemented
648#428—612no—
649#428—612no—
650#428—612no—
651#428—614no—
652#428—614no—
653#428C2×D6112yescomplemented
654#427—614no—
655#427—614no—
656#423—612no—
657#423—611no—
658#423—612no—
659#423—612no—
660#423C2×D6111yescharacteristic, complemented
661C2×C4⋊C8—612no—
662C2×C4⋊C8—612no—
663#419—614no—
664#418—614no—
665#417—612no—
666#417—612no—
667#417—612no—
668#417C2×D6112yes—
669#416—614no—
670#416—614no—
671C61#6048411yescharacteristic, complemented, Sylow
672C2×#41—618no—
673C2×#41—611no—
674C2×#41—611no—
675C2×#41—611no—
676C2×#41—1221no—
677C2×#41—1221no—
678C2×#41—1224no—
679C2×#41C22×D6111yescharacteristic
680C22×Q8—21no—
681C22×Q8—611no—
682C22×Q8—1221no—
683C22×D4—611no—
684C22×D4—1221no—
685C23×C4—611no—
686C23×C4—611no—
687C23×C4—611no—
688C23×C4—1221no—
689C23×C4—1221no—
690C23×C4—1221no—
691C2×M16—612no—
692C2×M16—614no—
693C2×M16—1228no—
694C2×M16C22×D6112yes—
695C22×C8—614no—
696C4⋊Q8—21no—
697C4⋊Q8—21no—
698C4⋊Q8—612no—
699C4⋊Q8—612no—
700C4⋊Q8—1221no—
701C4⋊Q8—1221no—
702C4⋊Q8C22×D6112yes—
703C4⋊Q8C22×D6112yes—
704#125—614no—
705#125—614no—
706#125—1222no—
707#125—1222no—
708C22⋊Q8—1222no—
709C22⋊Q8—1222no—
710C22⋊Q8—1222no—
711C22⋊Q8—1222no—
712C22⋊Q8—1222no—
713C22⋊Q8—1222no—
714C22⋊Q8—1222no—
715C22⋊Q8—1222no—
716C4×Q8—611no—
717C4×Q8—611no—
718C4×Q8—611no—
719C4×Q8—611no—
720C4×Q8—611no—
721C4×Q8—611no—
722C4×Q8—1221no—
723C4×Q8—1221no—
724C4×Q8—1221no—
725C4×Q8—1221no—
726C4×Q8—1222no—
727C4×Q8—1222no—
728C4×Q8—1222no—
729C4×Q8—1222no—
730C4×Q8—1222no—
731C4×Q8—1222no—
732C4×Q8—1222no—
733C4×Q8—1222no—
734C4×Q8C22×D6111yescharacteristic
735C4×Q8C22×D6111yescharacteristic
736C4×D4—21no—
737C4×D4—21no—
738C4×D4—611no—
739C4×D4—611no—
740C4×D4—611no—
741C4×D4—611no—
742C4×D4—611no—
743C4×D4—611no—
744C4×D4—1221no—
745C4×D4—1221no—
746C4×D4—1221no—
747C4×D4—1221no—
748C4×D4—1221no—
749C4×D4—1221no—
750C4×D4—1221no—
751C4×D4—1221no—
752C4×D4—1221no—
753C4×D4—1221no—
754C4×D4—1221no—
755C4×D4—1221no—
756C4×D4—1221no—
757C4×D4—1221no—
758C4×D4—1221no—
759C4×D4—1221no—
760C4×D4—1221no—
761C4×D4—1221no—
762C4×D4C22×D6111yescharacteristic
763C4×D4C22×D6111yescharacteristic
764#117—21no—
765#117—611no—
766#117—611no—
767#117—611no—
768#117—614no—
769#117—614no—
770#117—1221no—
771#117—1221no—
772#117—1221no—
773#117—1221no—
774#117—1221no—
775#117—1221no—
776#117—1221no—
777#117—1221no—
778#117—1222no—
779#117—1222no—
780#117—1221no—
781#117C22×D6111yescharacteristic
782C2×C4⋊C4—21no—
783C2×C4⋊C4—612no—
784C2×C4⋊C4—611no—
785C2×C4⋊C4—611no—
786C2×C4⋊C4—1221no—
787C2×C4⋊C4—1221no—
788C2×C4⋊C4—1222no—
789C2×C4⋊C4—1222no—
790C2×C4⋊C4—1221no—
791C2×C4⋊C4C22×D6112yes—
792C2×C22⋊C4—1221no—
793C2×C22⋊C4—1221no—
794C2×C22⋊C4—1221no—
795C2×C22⋊C4—1222no—
796C2×C42—21no—
797C2×C42—611no—
798C2×C42—611no—
799C2×C42—611no—
800C2×C42—611no—
801C2×C42—611no—
802C2×C42—611no—
803C2×C42—611no—
804C2×C42—611no—
805C2×C42—611no—
806C2×C42—611no—
807C2×C42—611no—
808C2×C42—1221no—
809C2×C42—1221no—
810C2×C42—1221no—
811C2×C42—1221no—
812C2×C42—1221no—
813C2×C42—1221no—
814C2×C42—1221no—
815C2×C42—1221no—
816C2×C42—1221no—
817C2×C42—1222no—
818C2×C42—1221no—
819C2×C42C22×D6111yescharacteristic
820#107—614no—
821#107—614no—
822#107—614no—
823#107C22×D6114yes—
824#106—614no—
825#106—614no—
826#106—614no—
827#106C22×D6114yes—
828C4⋊C8—614no—
829C4⋊C8—614no—
830C4⋊C8—612no—
831C4⋊C8—612no—
832C4⋊C8C22×D6112yes—
833C4⋊C8C22×D6112yes—
834#103—614no—
835#103—614no—
836#103—614no—
837#103C22×D6114yes—
838#102—614no—
839#102—614no—
840#102—614no—
841#102C22×D6114yes—
842C24—611no—
843C24—1221no—
844#41—22no—
845#41—614no—
846#41—614no—
847#41—614no—
848#41—1228no—
849#41—1228no—
850#41—1222no—
851#41—1222no—
852#41—1222no—
853#41Q8×D6114yes—
854C2×Q8—22no—
855C2×Q8—22no—
856C2×Q8—44no—
857C2×Q8—614no—
858C2×Q8—611no—
859C2×Q8—1221no—
860C2×Q8—1222no—
861C2×Q8—1222no—
862C2×Q8—1222no—
863C2×Q8—2444no—
864C2×Q8C23×D6111yescharacteristic
865C2×D4—21no—
866C2×D4—614no—
867C2×D4—611no—
868C2×D4—1221no—
869C2×D4—1222no—
870C2×D4—1221no—
871C2×D4—1228no—
872C2×D4—1221no—
873C2×D4—1221no—
874C2×D4C23×D6111yescharacteristic
875C22×C4—21no—
876C22×C4—22no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—611no—
880C22×C4—611no—
881C22×C4—611no—
882C22×C4—614no—
883C22×C4—614no—
884C22×C4—611no—
885C22×C4—611no—
886C22×C4—611no—
887C22×C4—611no—
888C22×C4—611no—
889C22×C4—611no—
890C22×C4—611no—
891C22×C4—611no—
892C22×C4—611no—
893C22×C4—611no—
894C22×C4—611no—
895C22×C4—611no—
896C22×C4—1221no—
897C22×C4—1228no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1221no—
907C22×C4—1222no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—2442no—
911C22×C4—2442no—
912C22×C4—2444no—
913C22×C4—2444no—
914C22×C4D4×D6111yescharacteristic
915C22×C4D4×D6111yescharacteristic
916C22×C4C23×D6111yescharacteristic
917M16—24no—
918M16—1228no—
919M16—1224no—
920C2×C8—614no—
921C2×C8—1228no—
922C2×C8C23×D6114yes—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—22no—
928C4⋊C4—614no—
929C4⋊C4—611no—
930C4⋊C4—611no—
931C4⋊C4—1221no—
932C4⋊C4—1221no—
933C4⋊C4—1221no—
934C4⋊C4—1221no—
935C4⋊C4—1224no—
936C4⋊C4—1224no—
937C4⋊C4—1221no—
938C4⋊C4—1221no—
939C4⋊C4—1224no—
940C4⋊C4—1224no—
941C4⋊C4—1222no—
942C4⋊C4—1221no—
943C4⋊C4—1221no—
944C4⋊C4—1222no—
945C4⋊C4—1222no—
946C4⋊C4C23×D6114yes—
947C4⋊C4C23×D6111yescharacteristic
948C4⋊C4C23×D6111yescharacteristic
949C22⋊C4—21no—
950C22⋊C4—21no—
951C22⋊C4—21no—
952C22⋊C4—1221no—
953C22⋊C4—1221no—
954C22⋊C4—1221no—
955C22⋊C4—1221no—
956C22⋊C4—1224no—
957C22⋊C4—1224no—
958C22⋊C4—1221no—
959C22⋊C4—1221no—
960C22⋊C4—1221no—
961C22⋊C4—1221no—
962C22⋊C4—1221no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—611no—
967C42—611no—
968C42—611no—
969C42—611no—
970C42—611no—
971C42—611no—
972C42—611no—
973C42—611no—
974C42—611no—
975C42—611no—
976C42—611no—
977C42—611no—
978C42—1221no—
979C42—1221no—
980C42—1221no—
981C42—1221no—
982C42—1221no—
983C42—1221no—
984C42—1224no—
985C42—1224no—
986C42—1221no—
987C42—1221no—
988C42—1221no—
989C42D4×D6111yescharacteristic
990C42D4×D6111yescharacteristic
991C42C23×D6111yescharacteristic
992C42C23×D6111yescharacteristic
993C23—21no—
994C23—611no—
995C23—611no—
996C23—614no—
997C23—1224no—
998C23—1221no—
999C23—2441no—
1000C23—2441no—
1001C23—2442no—
1002C23—2442no—
1003C23C2×D4×D6111yescharacteristic
1004Q8—21no—
1005Q8—44no—
1006Q8—44no—
1007Q8—612no—
1008Q8—1224no—
1009Q8—1221no—
1010Q8—2444no—
1011Q8—2444no—
1012Q8C2×Q8×D6112yes—
1013D4—24no—
1014D4—21no—
1015D4—612no—
1016D4—1224no—
1017D4—1224no—
1018D4—1224no—
1019D4—1224no—
1020D4—1221no—
1021D4C2×Q8×D6112yes—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—24no—
1029C2×C4—44no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—614no—
1033C2×C4—611no—
1034C2×C4—611no—
1035C2×C4—614no—
1036C2×C4—614no—
1037C2×C4—612no—
1038C2×C4—612no—
1039C2×C4—612no—
1040C2×C4—612no—
1041C2×C4—611no—
1042C2×C4—611no—
1043C2×C4—611no—
1044C2×C4—611no—
1045C2×C4—1224no—
1046C2×C4—1224no—
1047C2×C4—1224no—
1048C2×C4—1221no—
1049C2×C4—1224no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1221no—
1055C2×C4—1221no—
1056C2×C4—1224no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2442no—
1062C2×C4—2442no—
1063C2×C4—2442no—
1064C2×C4—2442no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2442no—
1068C2×C4—2442no—
1069C2×C4—2444no—
1070C2×C4—2442no—
1071C2×C4—2442no—
1072C2×C4C2×D4×D6111yescharacteristic
1073C2×C4C2×D4×D6111yescharacteristic
1074C2×C4C2×D4×D6111yescharacteristic
1075C2×C4C2×D4×D6111yescharacteristic
1076C2×C4C2×D4×D6111yescharacteristic
1077C2×C4C2×Q8×D6112yes—
1078C2×C4#41×D6112yes—
1079C2×C4C24×D6111yescharacteristic
1080C8—24no—
1081C8—1224no—
1082C22—21no—
1083C22—21no—
1084C22—22no—
1085C22—41no—
1086C22—41no—
1087C22—612no—
1088C22—612no—
1089C22—1221no—
1090C22—1221no—
1091C22—1221no—
1092C22—1221no—
1093C22—1222no—
1094C22—2444no—
1095C22—2448no—
1096C22—2441no—
1097C22—2441no—
1098C22C22⋊Q8×D6112yes—
1099C22C22×D4×D6111yescharacteristic
1100C4—21no—
1101C4—21no—
1102C4—22no—
1103C4—41no—
1104C4—44no—
1105C4—41no—
1106C4—612no—
1107C4—612no—
1108C4—1221no—
1109C4—1221no—
1110C4—1221no—
1111C4—1221no—
1112C4—1222no—
1113C4—2441no—
1114C4—2441no—
1115C4—2444no—
1116C4C22⋊Q8×D6112yes—
1117C4#1684055812yes—
1118C4#1684056112yes—
1119C4C22×Q8×D6111yescharacteristic
1120C4C2×#41×D6111yescharacteristic
1121C2—22no—
1122C2—42no—
1123C2—1222no—
1124C2—1222no—
1125C2—2442no—
1126C2C2×C22⋊Q8×D6111yescharacteristic
1127C2C2×#1684055811yescharacteristic
1128C2C2×#1684056111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3079C2
socleC22×C61C23×D4
prime radicalC2×#41×D61C22
hypercenter#3079D61
hypocenterC61#60484
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. C2×#16840317C2semidirect
3. #21455640C2semidirect
4. #21455639C2semidirect
5. #21455635C2semidirect
6. #21455634C2semidirect
7. #21455628C2semidirect
8. #21455625C2semidirect
9. #21455619C2semidirect
10. #21455617C2semidirect
11. #21455611C2semidirect
12. #21455610C2semidirect
13. #21455608C2semidirect
14. #21455602C2semidirect
15. #21455600C2semidirect
16. #21454406C2semidirect
17. #423×D61C2semidirect
19. C61×#3079C2semidirect
28. #16840317C22semidirect
29. #16840317C22semidirect
30. C2×#14519777C22semidirect
31. C2×#14519768C22semidirect
58. #16840072C22semidirect
59. #16840071C22semidirect
60. #16840068C22semidirect
61. #16840067C22semidirect
62. #16840065C22semidirect
63. #16840064C22semidirect
64. #16840061C22semidirect
65. #16840060C22semidirect
66. #16840058C22semidirect
67. #16840057C22semidirect
68. #16840054C22semidirect
69. #16840053C22semidirect
70. #16840052C22semidirect
71. #16840049C22semidirect
72. #16840048C22semidirect
73. #16840047C22semidirect
74. #16840044C22semidirect
75. #16840043C22semidirect
76. #16840042C22semidirect
77. #16840039C22semidirect
78. #16839805C22semidirect
79. #16839804C22semidirect
81. #16839802C22semidirect
83. #16839799C22semidirect
84. #16839797C22semidirect
85. #16839786C22semidirect
86. #16839785C22semidirect
89. C4⋊C8×D61C22semidirect
90. C4⋊C8×D61C22semidirect
98. C2×C4⋊Q8×C61C22semidirect
100. C61×#477C22semidirect
101. C61×#476C22semidirect
102. C61×#475C22semidirect
103. C61×#474C22semidirect
104. C61×#428C22semidirect
105. C61×#423C22semidirect
113. #41×D61Q8semidirect
305. #11758226C2×Q8semidirect
307. Q8×D61C2×Q8semidirect
310. #11758224C2×Q8semidirect
313. D4×D61C2×Q8semidirect
564. #3079D61semidirect
595. C2×C4⋊Q8C2×D61semidirect
635. #477C2×D61semidirect
639. #476C2×D61semidirect
643. #475C2×D61semidirect
647. #474C2×D61semidirect
653. #428C2×D61semidirect
660. #423C2×D61semidirect
671. C61#60484semidirect

Maximal subgroups

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

subgroupindex
C2×#168403172
C4×#41×D612
#214556402
#214556392
#214556352
#214556342
#214556282
#214556252
#214556192
#214556172
#214556112
#214556102
#214556082
#214556022
#214556002
#214544062
#423×D612
#214543352
C61×#30792
#6048461