Finite Group Databasebeta

← #30548455

Subgroups — #30548455

Order 15616.

2148 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic, complemented
2C2×#16840230C211yesmaximal, characteristic
3#21455976C214yesmaximal, complemented
4#21455946C212yesmaximal, complemented
5#21455915C212yesmaximal, complemented
6#21455885C214yesmaximal, complemented
7#21455855C212yesmaximal, complemented
8#21455824C212yesmaximal, complemented
9#21455767C211yesmaximal, characteristic, complemented
10#21455632C212yesmaximal, complemented
11#21455305C212yesmaximal, complemented
12#21455081C211yesmaximal, characteristic
13#21455077C211yesmaximal, characteristic
14#21454637C212yesmaximal, complemented
15#21454634C212yesmaximal, complemented
16#21454448C211yesmaximal, characteristic, complemented
17C61×#3095C211yesmaximal, characteristic, complemented
18C22×#11758222C2211yescharacteristic
19C2×#14519810C2212yes—
20C2×#14519808C2212yes—
21#16840314—21no—
22#16840314—21no—
23#16840314—21no—
24#16840314—21no—
25#16840314C2212yes—
26#16840314C2212yes—
27#16840314C2212yescomplemented
28#16840314C2212yescomplemented
29C2×#14519776C2211yescharacteristic, complemented
30C2×#14519775C2211yescharacteristic, complemented
31C2×#14519767—21no—
32C2×#14519756C2211yescharacteristic
33C2×#14519754—21no—
34#16840230—21no—
35#16840230—21no—
36#16840230—21no—
37#16840230—21no—
38#16840230C2212yes—
39#16840230C2212yes—
40#16840230C2212yes—
41#16840230C2212yes—
42C2×Q8×Dic61C2211yescharacteristic, complemented
43C2×#14519742—21no—
44C2×#14519742C2211yescharacteristic
45C2×#14519742C2211yescharacteristic
46C2×#14519742C2211yescharacteristic, complemented
47C2×#14519739C2211yescharacteristic
48C2×#14519739C2211yescharacteristic
49C2×#14519737—21no—
50C2×#14519737—21no—
51C2×#14519734—21no—
52C2×#14519733—21no—
53C22×C4×Dic61C2211yescharacteristic
54C2×C42×D61—21no—
55#16840103C2214yescomplemented
56#16840097C2212yes—
57#16840092C2212yes—
58#16840056C2214yescomplemented
59#16840051C2214yescomplemented
60#16840046C2214yescomplemented
61#16840041C2214yescomplemented
62#16839971C2214yescomplemented
63#16839971C2214yescomplemented
64#16839966C2214yescomplemented
65#16839966C2214yescomplemented
66#16839926C2214yes—
67#16839922C2214yes—
68#16839920C2212yes—
69#16839917C2212yes—
70#16839915C2212yes—
71#16839912C2212yes—
72#16839868C2214yescomplemented
73#16839866C2214yescomplemented
74#16839865C2214yescomplemented
75#16839861C2214yescomplemented
76#16839856C2214yescomplemented
77#16839854C2214yescomplemented
78#16839849C2214yescomplemented
79#16839847C2214yescomplemented
80#16839816C2212yes—
81#16839816C2212yescomplemented
82#16839812C2212yes—
83#16839812C2212yescomplemented
84#16839805C2212yescomplemented
85#16839785C2212yescomplemented
86#16839770C2212yescomplemented
87#16839764C2212yes—
88#16839761C2212yes—
89#16839726C2211yescharacteristic
90M16×Dic61C2212yescomplemented
91C2×C22⋊Q8×C61C2211yescharacteristic
92C2×#117×C61C2211yescharacteristic
93C61×#485C2214yescomplemented
94C61×#484C2212yes—
95C61×#483C2212yes—
96C61×#428C2212yescomplemented
97C61×#419C2212yescomplemented
98C61×#407C2211yescharacteristic
99C2×#11758222—21no—
100C2×#11758222—21no—
101C2×#11758222—28no—
102C2×#11758222C2312yes—
103C2×#11758222C2312yes—
104C22×Dic122—21no—
105C22×Dic122C2311yescharacteristic
106C22×Dic122C2311yescharacteristic
107C22×D244C2311yescharacteristic
108C22×C22⋊D61—21no—
109C23×Dic61D411yescharacteristic
110C23×Dic61D411yescharacteristic
111C22×C4×D61—21no—
112C22×C4×D61—21no—
113C22×C4×D61—21no—
114#14519810—28no—
115#14519808—28no—
116C2×Dic244C2314yes—
117C2×#11758202C2314yes—
118C2×#11758190C2314yes—
119C2×#11758201C2314yes—
120C2×#11758194C2312yes—
121#14519776—21no—
122#14519776—21no—
123#14519776C2312yes—
124#14519776C2312yes—
125#14519775—21no—
126#14519775—21no—
127#14519775C2312yes—
128#14519775C2312yes—
129#14519767—22no—
130#14519767—22no—
131#14519767—22no—
132#14519767—22no—
133#14519756—21no—
134#14519756—21no—
135#14519756C2312yes—
136#14519756C2312yes—
137#14519754—22no—
138#14519754—22no—
139#14519754—22no—
140#14519754—22no—
141Q8×Dic61—21no—
142Q8×Dic61—21no—
143Q8×Dic61C2312yes—
144Q8×Dic61C2312yes—
145#14519742—22no—
146#14519742—22no—
147#14519742—22no—
148#14519742—22no—
149#14519742—21no—
150#14519742—21no—
151#14519742—21no—
152#14519742—21no—
153#14519742—21no—
154#14519742—21no—
155#14519742C2312yes—
156#14519742C2312yes—
157#14519742C2312yes—
158#14519742C2312yes—
159#14519742C2312yes—
160#14519742C2312yes—
161#14519739—21no—
162#14519739—21no—
163#14519739—21no—
164#14519739—21no—
165#14519739C2312yes—
166#14519739C2312yes—
167#14519739C2312yes—
168#14519739C2312yes—
169#14519737—22no—
170#14519737—22no—
171#14519737—22no—
172#14519737—22no—
173#14519737—22no—
174#14519737—22no—
175#14519737—22no—
176#14519737—22no—
177#14519734—22no—
178#14519734—22no—
179#14519734—22no—
180#14519734—22no—
181#14519733—22no—
182#14519733—22no—
183#14519733—22no—
184#14519733—22no—
185C2×C4⋊Dic61—21no—
186C2×C4⋊Dic61C2311yescharacteristic
187C2×#11758196—21no—
188C2×#11758196—21no—
189C2×#11758196—21no—
190C2×#11758196—21no—
191C2×#11758196—21no—
192C2×#11758196—21no—
193C2×#11758196—21no—
194C2×C22⋊Dic61—21no—
195C2×#11758198—21no—
196C2×#11758198—21no—
197C2×C4×Dic61—21no—
198C2×C4×Dic61—21no—
199C2×C4×Dic61—21no—
200C2×C4×Dic61—21no—
201C2×C4×Dic61D411yescharacteristic
202C2×C4×Dic61D411yescharacteristic
203C2×C4×Dic61D411yescharacteristic
204C2×C4×Dic61D411yescharacteristic
205C2×C4×Dic61D411yescharacteristic
206C2×C4×Dic61D411yescharacteristic
207C2×C4×Dic61C2311yescharacteristic
208C2×C4×Dic61C2311yescharacteristic
209C2×C4×Dic61C2311yescharacteristic
210C2×C4×Dic61C2311yescharacteristic
211C2×C4×Dic61C2311yescharacteristic
212C2×C4×Dic61C2311yescharacteristic
213C42×D61—22no—
214C42×D61—22no—
215C42×D61—22no—
216C42×D61—22no—
217#14519710C2314yes—
218#14519708C2314yes—
219#14519706C2314yes—
220#14519706C2314yes—
221#14519702C2314yes—
222#14519700C2314yes—
223#14519700C2314yes—
224#14519700C2314yes—
225#14519699C2314yes—
226#14519697C2314yes—
227C22⋊#92418C2312yes—
228C22⋊#92418C2312yes—
229#14519687C2314yes—
230C8×Dic61C2314yes—
231C22×Q8×C61C2311yescharacteristic
232C23×C4×C61C2311yescharacteristic
233C2×M16×C61C2312yes—
234C22⋊Q8×C61—21no—
235C22⋊Q8×C61—21no—
236C22⋊Q8×C61C2312yes—
237C22⋊Q8×C61C2312yes—
238#117×C61—21no—
239#117×C61—21no—
240#117×C61C2312yes—
241#117×C61C2312yes—
242C2×C4⋊C4×C61—21no—
243C2×C4⋊C4×C61C2311yescharacteristic
244C2×C4⋊C4×C61C2311yescharacteristic
245C2×C4⋊C4×C61C2311yescharacteristic
246C2×C22⋊C4×C61—21no—
247C2×C22⋊C4×C61—21no—
248C2×C42×C61—21no—
249#107×C61C2314yes—
250#106×C61C2314yes—
251#103×C61C2314yes—
252#103×C61C2314yes—
253C22⋊C8×C61C2312yes—
254C22⋊C8×C61C2312yes—
255C24×C61C2×D411yescharacteristic
256C23×D61—21no—
257C2×Q8×C61—21no—
258C2×Q8×C61—24no—
259C2×Q8×C61C2412yes—
260C22×C4×C61—24no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2411yescharacteristic
269C22×C4×C61C2411yescharacteristic
270C22×C4×C61C2411yescharacteristic
271C2×C22⋊D61—28no—
272C2×C22⋊D61—22no—
273C2×C22⋊D61—22no—
274C22×Dic61—21no—
275C22×Dic61—24no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—42no—
279C22×Dic61C2×D411yescharacteristic
280C22×Dic61C2×D411yescharacteristic
281C22×Dic61C2×D411yescharacteristic
282C22×Dic61C2×D411yescharacteristic
283C22×Dic61C2×D411yescharacteristic
284C22×Dic61C2×D411yescharacteristic
285C22×Dic61C2×D411yescharacteristic
286C22×Dic61C2×D411yescharacteristic
287C22×Dic61C2×D411yescharacteristic
288C22×Dic61C2×D411yescharacteristic
289C22×Dic61C2×D411yescharacteristic
290C22×Dic61C2×D411yescharacteristic
291#11758222—28no—
292#11758222—28no—
293#11758222—24no—
294#11758222—24no—
295#11758222—24no—
296#11758222#4118yes—
297C2×D244—21no—
298C2×D244—24no—
299C2×D244C2412yes—
300C2×C4×D61—28no—
301C2×C4×D61—22no—
302C2×C4×D61—22no—
303C2×C4×D61—22no—
304C2×C4×D61—22no—
305C2×C4×D61—22no—
306C2×C4×D61—22no—
307C2×C4×D61—44no—
308C2×C4×D61—44no—
309C2×Dic122—21no—
310C2×Dic122—24no—
311C2×Dic122—24no—
312C2×Dic122—21no—
313C2×Dic122—22no—
314C2×Dic122—22no—
315C2×Dic122—44no—
316C2×Dic122C2412yes—
317C2×Dic122C2412yes—
318M16×C61—24no—
319C2×C8×C61C2414yes—
320C4⋊C4×C61—22no—
321C4⋊C4×C61—22no—
322C4⋊C4×C61—21no—
323C4⋊C4×C61—21no—
324C4⋊C4×C61—21no—
325C4⋊C4×C61C2412yes—
326C4⋊C4×C61C2412yes—
327C4⋊C4×C61C2412yes—
328C22⋊C4×C61—22no—
329C22⋊C4×C61—22no—
330C22⋊C4×C61—22no—
331C22⋊C4×C61—22no—
332C42×C61—22no—
333C42×C61—22no—
334C22⋊Dic61—22no—
335C22⋊Dic61—22no—
336#11758202—28no—
337#11758201—28no—
338#11758198—22no—
339#11758198—22no—
340#11758198—22no—
341#11758198—22no—
342C4⋊Dic61—21no—
343C4⋊Dic61—22no—
344C4⋊Dic61—22no—
345C4⋊Dic61C2412yes—
346#11758196—22no—
347#11758196—22no—
348#11758196—22no—
349#11758196—22no—
350#11758196—22no—
351#11758196—22no—
352#11758196—22no—
353#11758196—22no—
354#11758196—22no—
355#11758196—22no—
356#11758196—22no—
357#11758196—22no—
358#11758196—22no—
359#11758196—22no—
360C4×Dic61—22no—
361C4×Dic61—22no—
362C4×Dic61—22no—
363C4×Dic61—22no—
364C4×Dic61—22no—
365C4×Dic61—22no—
366C4×Dic61—22no—
367C4×Dic61—22no—
368C4×Dic61C2×D411yescharacteristic
369C4×Dic61C2×D411yescharacteristic
370C4×Dic61C2×D411yescharacteristic
371C4×Dic61C2×D411yescharacteristic
372C4×Dic61C2×D411yescharacteristic
373C4×Dic61C2×D411yescharacteristic
374C4×Dic61C2×D411yescharacteristic
375C4×Dic61C2×D411yescharacteristic
376C4×Dic61C2×D411yescharacteristic
377C4×Dic61C2×D411yescharacteristic
378C4×Dic61C2×D411yescharacteristic
379C4×Dic61C2×D411yescharacteristic
380C4×Dic61C2411yescharacteristic
381C4×Dic61C2411yescharacteristic
382C4×Dic61C2411yescharacteristic
383C4×Dic61C2411yescharacteristic
384#11758194—24no—
385C2×#92418C2414yes—
386Dic244—28no—
387#11758190—28no—
388C23×C61—22no—
389C23×C61—22no—
390C23×C61—41no—
391C23×C61C22×D411yescharacteristic
392C23×C61C22×D411yescharacteristic
393C23×C61C22×D411yescharacteristic
394C22×D61—24no—
395C22×D61—22no—
396C22×D61—42no—
397C22×D61—42no—
398Q8×C61—24no—
399Q8×C61—42no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—42no—
410C2×C4×C61—42no—
411C2×C4×C61—42no—
412C2×C4×C61—42no—
413C2×C4×C61C22×D411yescharacteristic
414C2×C4×C61C22×D411yescharacteristic
415C2×C4×C61C22×D411yescharacteristic
416C2×C4×C61C2×#4114yes—
417C2×C4×C61C2511yescharacteristic
418C22⋊D61—28no—
419C22⋊D61—28no—
420C2×Dic61—24no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—42no—
436C2×Dic61—42no—
437C2×Dic61#13714yescomplemented
438C2×Dic61C22×D411yescharacteristic
439C2×Dic61C22×D411yescharacteristic
440C2×Dic61C22×D411yescharacteristic
441C2×Dic61C22×D411yescharacteristic
442C2×Dic61C22×D411yescharacteristic
443C2×Dic61C22×D411yescharacteristic
444C2×Dic61C22×D411yescharacteristic
445C2×Dic61C22×D411yescharacteristic
446D244—24no—
447D244—22no—
448D244C2×#4114yes—
449C4×D61—28no—
450C4×D61—28no—
451C4×D61—44no—
452C4×D61—44no—
453C4×D61—44no—
454C4×D61—44no—
455Dic122—24no—
456Dic122—22no—
457Dic122—24no—
458Dic122—44no—
459Dic122—42no—
460Dic122—44no—
461Dic122C2×#4114yes—
462C8×C61—24no—
463#92418—24no—
464#60562—611nomaximal, Sylow
465C22×C61—21no—
466C22×C61—21no—
467C22×C61—21no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—44no—
473C22×C61#52512yes—
474C22×C61C2×#13712yes—
475C22×C61C23×D411yescharacteristic
476C2×D61—24no—
477C2×D61—48no—
478C2×D61—42no—
479C2×D61—42no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—42no—
483C4×C61—42no—
484C4×C61—42no—
485C4×C61—42no—
486C4×C61#52512yes—
487C4×C61C22×#4112yes—
488Dic61—24no—
489Dic61—21no—
490Dic61—21no—
491Dic61—21no—
492Dic61—21no—
493Dic61—21no—
494Dic61—42no—
495Dic61—42no—
496Dic61C2×#13712yes—
497Dic61C2×#13712yes—
498Dic61#57512yes—
499C2×#533—611no—
500C2×C4×#41—611no—
501#3116—614no—
502#3113—612no—
503#3110—612no—
504#3107—614no—
505#3104—612no—
506#3101—612no—
507#3095—611no—
508#3095D6111yescharacteristic, complemented
509#3079—612no—
510#3039—612no—
511#3007—611no—
512#3007—611no—
513C4×#137—612no—
514C4×#137—612no—
515#2920—611no—
516C2×C61—22no—
517C2×C61—22no—
518C2×C61—41no—
519C2×C61C2×#52511yescharacteristic
520C2×C61C22×#13711yescharacteristic
521C2×C61C2×#57511yescharacteristic
522D61—44no—
523C22×#41—611no—
524C2×#137—612no—
525C2×#137—612no—
526#533—612no—
527#533—612no—
528#533—612no—
529#533—612no—
530#533—1221no—
531#533—1221no—
532#533—1221no—
533#533—1221no—
534C2×C4⋊Q8—611no—
535C2×C4⋊Q8—611no—
536C2×#125—1221no—
537C2×C22⋊Q8—611no—
538C2×C22⋊Q8—1221no—
539C2×C22⋊Q8C2×D6111yescharacteristic
540C4×#41—612no—
541C4×#41—612no—
542C4×#41—612no—
543C4×#41—612no—
544C4×#41—1221no—
545C4×#41—1221no—
546C4×#41—1221no—
547C4×#41—1221no—
548C2×C4×Q8—611no—
549C2×C4×Q8—611no—
550C2×C4×Q8—611no—
551C2×C4×Q8—611no—
552C2×C4×Q8—1221no—
553C2×C4×D4—611no—
554C2×C4×D4—611no—
555C2×C4×D4—1221no—
556C2×C4×D4—1221no—
557C2×#117—1221no—
558C2×#117—1221no—
559C2×#117C2×D6111yescharacteristic
560C22×C42—611no—
561C22×C42—1221no—
562#485—614no—
563#485C2×D6114yescomplemented
564#484—612no—
565#484C2×D6112yes—
566#483—612no—
567#483C2×D6112yes—
568#477—614no—
569#476—614no—
570#475—614no—
571#474—614no—
572#462—614no—
573#462—614no—
574#461—614no—
575#461—614no—
576#452—614no—
577#452—614no—
578#451—612no—
579#451—612no—
580#450—612no—
581#450—612no—
582#441—614no—
583#441—614no—
584#440—614no—
585#440—614no—
586C4×Q16—614no—
587C4×Q16—614no—
588C4×SD16—614no—
589C4×SD16—614no—
590#432—612no—
591#432—612no—
592#431—612no—
593#431—612no—
594#428—612no—
595#428C2×D6112yescomplemented
596#423—612no—
597#419—612no—
598#419C2×D6112yescomplemented
599#417—612no—
600#417—612no—
601#407—611no—
602#407C2×D6111yescharacteristic
603C4×M16—612no—
604C61#6056211yescharacteristic, complemented, Sylow
605C2×#41—612no—
606C2×#41—612no—
607C2×#41—1228no—
608C2×#41—1221no—
609C2×#41—1221no—
610C22×Q8—611no—
611C22×Q8—611no—
612C22×Q8—1221no—
613C22×Q8C22×D6111yescharacteristic
614C22×D4—611no—
615C22×D4—1221no—
616C23×C4—611no—
617C23×C4—611no—
618C23×C4—1221no—
619C23×C4—1221no—
620C23×C4—1221no—
621C23×C4C22×D6111yescharacteristic
622#137—1228no—
623#137—1228no—
624C2×Q16—614no—
625C2×Q16—614no—
626C2×SD16—614no—
627C2×SD16—614no—
628C2×M16—612no—
629C2×M16C22×D6112yes—
630C4⋊Q8—612no—
631C4⋊Q8—612no—
632C4⋊Q8—612no—
633C4⋊Q8—612no—
634C4⋊Q8—1221no—
635C4⋊Q8—1221no—
636C4⋊Q8—1221no—
637C4⋊Q8—1221no—
638#125—1222no—
639#125—1222no—
640#125—1222no—
641#125—1222no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—612no—
645C22⋊Q8—612no—
646C22⋊Q8—1222no—
647C22⋊Q8—1222no—
648C22⋊Q8—1222no—
649C22⋊Q8—1222no—
650C22⋊Q8—1221no—
651C22⋊Q8—1221no—
652C22⋊Q8C22×D6112yes—
653C22⋊Q8C22×D6112yes—
654C4×Q8—612no—
655C4×Q8—612no—
656C4×Q8—612no—
657C4×Q8—612no—
658C4×Q8—612no—
659C4×Q8—612no—
660C4×Q8—612no—
661C4×Q8—612no—
662C4×Q8—1221no—
663C4×Q8—1221no—
664C4×Q8—1221no—
665C4×Q8—1221no—
666C4×Q8—1221no—
667C4×Q8—1221no—
668C4×Q8—1222no—
669C4×Q8—1222no—
670C4×Q8—1222no—
671C4×Q8—1222no—
672C4×Q8—1221no—
673C4×Q8—1221no—
674C4×D4—612no—
675C4×D4—612no—
676C4×D4—612no—
677C4×D4—612no—
678C4×D4—1221no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4—1221no—
682C4×D4—1222no—
683C4×D4—1222no—
684C4×D4—1222no—
685C4×D4—1222no—
686C4×D4—1222no—
687C4×D4—1222no—
688C4×D4—1222no—
689C4×D4—1222no—
690#117—21no—
691#117—21no—
692#117—1222no—
693#117—1222no—
694#117—1222no—
695#117—1222no—
696#117—1222no—
697#117—1222no—
698#117—1222no—
699#117—1222no—
700#117C22×D6112yes—
701#117C22×D6112yes—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—611no—
704C2×C4⋊C4—1221no—
705C2×C4⋊C4—1221no—
706C2×C4⋊C4—1221no—
707C2×C4⋊C4—1221no—
708C2×C4⋊C4—1221no—
709C2×C4⋊C4—1221no—
710C2×C4⋊C4—1221no—
711C2×C4⋊C4—1221no—
712C2×C4⋊C4C22×D6111yescharacteristic
713C2×C4⋊C4C22×D6111yescharacteristic
714C2×C4⋊C4C22×D6111yescharacteristic
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—1221no—
718C2×C22⋊C4—1221no—
719C2×C22⋊C4—1221no—
720C2×C42—21no—
721C2×C42—611no—
722C2×C42—611no—
723C2×C42—611no—
724C2×C42—611no—
725C2×C42—611no—
726C2×C42—611no—
727C2×C42—611no—
728C2×C42—611no—
729C2×C42—611no—
730C2×C42—611no—
731C2×C42—611no—
732C2×C42—611no—
733C2×C42—1222no—
734C2×C42—1222no—
735C2×C42—1222no—
736C2×C42—1222no—
737C2×C42—1221no—
738C2×C42—1221no—
739C2×C42—1221no—
740C2×C42—1221no—
741#107—614no—
742#107C22×D6114yes—
743#106—614no—
744#106C22×D6114yes—
745C4⋊C8—614no—
746C4⋊C8—614no—
747#103—614no—
748#103—614no—
749#103—614no—
750#103—614no—
751#103C22×D6114yes—
752#103C22×D6114yes—
753#102—614no—
754#102—614no—
755C22⋊C8—612no—
756C22⋊C8—612no—
757C22⋊C8C22×D6112yes—
758C22⋊C8C22×D6112yes—
759#97—614no—
760C4×C8—614no—
761C24—1221no—
762C24D4×D6111yescharacteristic
763#41—618no—
764#41—1224no—
765#41—1224no—
766#41—1228no—
767#41—1228no—
768#41—1224no—
769C2×Q8—21no—
770C2×Q8—24no—
771C2×Q8—612no—
772C2×Q8—612no—
773C2×Q8—1222no—
774C2×Q8—1222no—
775C2×Q8—1224no—
776C2×Q8—1221no—
777C2×Q8—1221no—
778C2×Q8—1224no—
779C2×Q8—2444no—
780C2×Q8C23×D6112yes—
781C2×D4—612no—
782C2×D4—1224no—
783C2×D4—1228no—
784C2×D4—1222no—
785C2×D4—1222no—
786C2×D4—1221no—
787C22×C4—24no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—1222no—
805C22×C4—1222no—
806C22×C4—1222no—
807C22×C4—1222no—
808C22×C4—1228no—
809C22×C4—1224no—
810C22×C4—1221no—
811C22×C4—1222no—
812C22×C4—1222no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—2444no—
816C22×C4—2444no—
817C22×C4—2442no—
818C22×C4D4×D6111yescharacteristic
819C22×C4D4×D6111yescharacteristic
820C22×C4D4×D6111yescharacteristic
821C22×C4C23×D6111yescharacteristic
822C22×C4C23×D6111yescharacteristic
823C22×C4C23×D6111yescharacteristic
824Q16—1228no—
825Q16—1228no—
826SD16—1228no—
827SD16—1228no—
828M16—24no—
829M16—1224no—
830C2×C8—614no—
831C2×C8C23×D6114yes—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—612no—
838C4⋊C4—1222no—
839C4⋊C4—1222no—
840C4⋊C4—1222no—
841C4⋊C4—1222no—
842C4⋊C4—1222no—
843C4⋊C4—1222no—
844C4⋊C4—1222no—
845C4⋊C4—1222no—
846C4⋊C4—1222no—
847C4⋊C4—1222no—
848C4⋊C4—1222no—
849C4⋊C4—1222no—
850C4⋊C4—1222no—
851C4⋊C4—1222no—
852C4⋊C4—1221no—
853C4⋊C4—1222no—
854C4⋊C4—1222no—
855C4⋊C4C23×D6112yes—
856C4⋊C4C23×D6112yes—
857C4⋊C4C23×D6112yes—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—1222no—
863C22⋊C4—1222no—
864C22⋊C4—1222no—
865C22⋊C4—1222no—
866C22⋊C4—1222no—
867C22⋊C4—1222no—
868C42—22no—
869C42—22no—
870C42—611no—
871C42—611no—
872C42—611no—
873C42—611no—
874C42—611no—
875C42—611no—
876C42—611no—
877C42—611no—
878C42—611no—
879C42—611no—
880C42—611no—
881C42—611no—
882C42—611no—
883C42—611no—
884C42—611no—
885C42—611no—
886C42—1222no—
887C42—1222no—
888C42—1222no—
889C42—1222no—
890C42—1222no—
891C42—1222no—
892C42—1222no—
893C42—1222no—
894C23—22no—
895C23—22no—
896C23—41no—
897C23—1224no—
898C23—1222no—
899C23—2442no—
900C23—2442no—
901C23C2×D4×D6111yescharacteristic
902C23C2×D4×D6111yescharacteristic
903C23C2×D4×D6111yescharacteristic
904Q8—24no—
905Q8—42no—
906Q8—614no—
907Q8—1224no—
908Q8—1222no—
909Q8—1224no—
910Q8—2444no—
911Q8—2444no—
912Q8—2442no—
913D4—614no—
914D4—1224no—
915D4—1228no—
916D4—1228no—
917D4—1222no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—614no—
932C2×C4—611no—
933C2×C4—611no—
934C2×C4—611no—
935C2×C4—611no—
936C2×C4—611no—
937C2×C4—611no—
938C2×C4—611no—
939C2×C4—611no—
940C2×C4—1228no—
941C2×C4—1222no—
942C2×C4—1222no—
943C2×C4—1222no—
944C2×C4—1222no—
945C2×C4—1222no—
946C2×C4—1222no—
947C2×C4—1222no—
948C2×C4—1224no—
949C2×C4—1222no—
950C2×C4—1222no—
951C2×C4—1228no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—2444no—
955C2×C4—2444no—
956C2×C4—2444no—
957C2×C4—2444no—
958C2×C4—2441no—
959C2×C4—2441no—
960C2×C4—2441no—
961C2×C4—2442no—
962C2×C4—2442no—
963C2×C4C2×D4×D6111yescharacteristic
964C2×C4C2×D4×D6111yescharacteristic
965C2×C4C2×D4×D6111yescharacteristic
966C2×C4#41×D6114yes—
967C2×C4C24×D6111yescharacteristic
968C8—24no—
969C8—1224no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—21no—
977C22—44no—
978C22—1224no—
979C22—2448no—
980C22—2442no—
981C22—2442no—
982C22#1684027012yes—
983C22#137×D6112yes—
984C22C22×D4×D6111yescharacteristic
985C4—21no—
986C4—21no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—612no—
992C4—612no—
993C4—612no—
994C4—1221no—
995C4—1221no—
996C4—1221no—
997C4—1221no—
998C4—1221no—
999C4—1224no—
1000C4—2442no—
1001C4—2442no—
1002C4#1684027012yes—
1003C4C2×#41×D6112yes—
1004C2—22no—
1005C2—22no—
1006C2—41no—
1007C2—2444no—
1008C2C2×#1684027011yescharacteristic
1009C2C2×#137×D6111yescharacteristic
1010C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3095C2
socleC22×C61C23×D4
prime radicalC22×#11758222C22
hypercenter#3095D61
hypocenterC61#60562
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
1. C2×#16840314C2semidirect
3. #21455976C2semidirect
4. #21455946C2semidirect
5. #21455915C2semidirect
6. #21455885C2semidirect
7. #21455855C2semidirect
8. #21455824C2semidirect
9. #21455767C2semidirect
10. #21455632C2semidirect
11. #21455305C2semidirect
14. #21454637C2semidirect
15. #21454634C2semidirect
16. #21454448C2semidirect
17. C61×#3095C2semidirect
27. #16840314C22semidirect
28. #16840314C22semidirect
29. C2×#14519776C22semidirect
30. C2×#14519775C22semidirect
42. C2×Q8×Dic61C22semidirect
46. C2×#14519742C22semidirect
55. #16840103C22semidirect
58. #16840056C22semidirect
59. #16840051C22semidirect
60. #16840046C22semidirect
61. #16840041C22semidirect
62. #16839971C22semidirect
63. #16839971C22semidirect
64. #16839966C22semidirect
65. #16839966C22semidirect
72. #16839868C22semidirect
73. #16839866C22semidirect
74. #16839865C22semidirect
75. #16839861C22semidirect
76. #16839856C22semidirect
77. #16839854C22semidirect
78. #16839849C22semidirect
79. #16839847C22semidirect
81. #16839816C22semidirect
83. #16839812C22semidirect
84. #16839805C22semidirect
85. #16839785C22semidirect
86. #16839770C22semidirect
90. M16×Dic61C22semidirect
93. C61×#485C22semidirect
96. C61×#428C22semidirect
97. C61×#419C22semidirect
437. C2×Dic61#137semidirect
508. #3095D61semidirect
563. #485C2×D61semidirect
595. #428C2×D61semidirect
598. #419C2×D61semidirect
604. C61#60562semidirect

Maximal subgroups

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

subgroupindex
C2×#168403142
C2×#168402302
#214559762
#214559462
#214559152
#214558852
#214558552
#214558242
#214557672
#214556322
#214553052
#214550812
#214550772
#214546372
#214546342
#214544482
C61×#30952
#6056261