Finite Group Databasebeta

← #29647166

Subgroups — #29647166

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3#376×D61C211yesmaximal, characteristic, complemented
4#21444329C212yesmaximal, complemented
5#21444325C212yesmaximal, complemented
6#21444322C212yesmaximal, complemented
7#21444320C212yesmaximal, complemented
8#21444306C211yesmaximal, characteristic, complemented
9#21444305C211yesmaximal, characteristic, complemented
10#21444303C211yesmaximal, characteristic, complemented
11C61×#1500C211yesmaximal, characteristic, complemented
12#16840318C411yescharacteristic, complemented
13#16840316C411yescharacteristic, complemented
14#16840314C2211yescharacteristic
15#16840311C411yescharacteristic, complemented
16#16840309C411yescharacteristic, complemented
17#16840307C2211yescharacteristic
18#16840297C411yescharacteristic, complemented
19#16840296C2211yescharacteristic
20#16840295—21no—
21#16840295—21no—
22#16840291C411yescharacteristic, complemented
23#16840290—21no—
24#16840289—21no—
25#16840275C2211yescharacteristic
26#16840272C2211yescharacteristic
27#16840271—21no—
28#16840270—21no—
29C4×#11758226C411yescharacteristic, complemented
30#16840230—21no—
31C4×#11758224—21no—
32C4×#11758224C411yescharacteristic, complemented
33C2×C42×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16839818—21no—
36#16839816C2212yes—
37#16839815C2211yescharacteristic
38#16839813—21no—
39#16839784—21no—
40#16839724C2212yes—
41C4×#11758189—21no—
42#16839608—21no—
43#16839608C2211yescharacteristic
44#16839607—21no—
45#16839607C2212yes—
46#95×D61—21no—
47#95×D61C2212yes—
48#16839500C2212yes—
49#16839499C2212yes—
50#16839498C2212yes—
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#529C2211yescharacteristic
55C61×#431C2211yescharacteristic
56C61×#376C2211yescharacteristic
57C61×#328C2212yes—
58C61×#327C2212yes—
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758224—21no—
62C2×#11758224C2×C411yescharacteristic
63C22×C4×D61—22no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758189—22no—
68#14519776C2×C411yescharacteristic, complemented
69#14519776C2×C411yescharacteristic, complemented
70#14519775C2×C411yescharacteristic, complemented
71#14519773C2×C411yescharacteristic, complemented
72#14519772—21no—
73#14519771—21no—
74#14519770—21no—
75#14519769C2×C411yescharacteristic, complemented
76#14519767—21no—
77#14519767—21no—
78#14519765C2×C411yescharacteristic, complemented
79#14519763—21no—
80#14519763—21no—
81#14519762—21no—
82#14519762—21no—
83#14519760—21no—
84#14519759—21no—
85#14519759—21no—
86#14519757C2×C411yescharacteristic
87#14519756C2311yescharacteristic
88#14519755—21no—
89#14519755—21no—
90#14519755—21no—
91#14519754—21no—
92#14519753C2×C411yescharacteristic
93#14519752C2×C411yescharacteristic
94#14519751C2311yescharacteristic
95#14519750—21no—
96#14519750—21no—
97#14519750—21no—
98#14519749—21no—
99#14519748C2×C411yescharacteristic
100#14519747—21no—
101#14519745—21no—
102Q8×Dic61C2×C411yescharacteristic, complemented
103C4×Dic122—21no—
104C4×Dic122C2×C411yescharacteristic, complemented
105#14519742—21no—
106#14519742—21no—
107#14519742—21no—
108#14519742C2×C411yescharacteristic, complemented
109C4×D244—21no—
110C4×D244C2×C411yescharacteristic, complemented
111D4×Dic61—21no—
112D4×Dic61C2×C411yescharacteristic, complemented
113#14519739—21no—
114#14519739—21no—
115#14519739—21no—
116#14519739C2×C411yescharacteristic, complemented
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519735—21no—
128#14519735—21no—
129#14519735C2×C411yescharacteristic
130#14519735C2×C411yescharacteristic
131#14519734—21no—
132#14519734—21no—
133#14519733—21no—
134#14519733—21no—
135#14519733—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—22no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61D411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142C42×D61—28no—
143C42×D61—21no—
144C42×D61C2×C411yescharacteristic
145C42×D61C2×C411yescharacteristic
146C42×D61C2×C411yescharacteristic
147C42×D61C2×C411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C4⋊#92418—21no—
153#14519706—22no—
154C22⋊#92418C2312yes—
155#14519689—22no—
156#14519687—22no—
157C4×#92418—21no—
158#14519684—21no—
159#14519684—22no—
160#14519684—22no—
161#14519684C2312yes—
162#126×C61—21no—
163#125×C61C2×C411yescharacteristic, complemented
164#124×C61C2×C411yescharacteristic, complemented
165#123×C61—21no—
166C22⋊Q8×C61C2311yescharacteristic
167#121×C61C2311yescharacteristic
168C4×Q8×C61C2×C411yescharacteristic, complemented
169C4×D4×C61—21no—
170C4×D4×C61C2×C411yescharacteristic, complemented
171#117×C61—21no—
172C2×C42×C61—21no—
173C2×C42×C61C2311yescharacteristic
174C4⋊C8×C61—21no—
175C22⋊C8×C61C2312yes—
176C4×C8×C61—21no—
177#95×C61—21no—
178#95×C61C2312yes—
179C23×D61C2×D411yescharacteristic
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C22×C4×C61—22no—
184C22×C4×C61—21no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C22×Dic61—22no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199#11758226—42no—
200#11758224—42no—
201#11758224—44no—
202#11758222—44no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244C22×C411yescharacteristic
206C2×C4×D61—24no—
207C2×C4×D61—28no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22×C411yescharacteristic
224C2×C4×D61C22×C411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122C22×C411yescharacteristic
230C2×C8×C61—22no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C22×C411yescharacteristic
236C4⋊C4×C61C22×C411yescharacteristic
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C42×C61—24no—
243C42×C61—21no—
244C42×C61C22×C411yescharacteristic
245C42×C61C22×C411yescharacteristic
246C42×C61C2×D411yescharacteristic
247C42×C61C2×D411yescharacteristic
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C22×C411yescharacteristic
264C4⋊Dic61C22×C411yescharacteristic
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275C4×Dic61—28no—
276C4×Dic61—24no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—21no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22⋊C411yescharacteristic
287C4×Dic61C22⋊C411yescharacteristic
288C4×Dic61C22⋊C411yescharacteristic
289C4×Dic61C22⋊C411yescharacteristic
290C4×Dic61C22×C411yescharacteristic
291C4×Dic61C22×C411yescharacteristic
292C4×Dic61C2×D411yescharacteristic
293C4×Dic61C2×D411yescharacteristic
294C2×#92418—22no—
295#11758189—44no—
296C23×C61—21no—
297C23×C61C22×D411yescharacteristic
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—21no—
302C22×D61C2×C22⋊C411yescharacteristic
303C22×D61C2×C22⋊C411yescharacteristic
304Q8×C61—41no—
305D4×C61—41no—
306D4×C61—42no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—41no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C23×C411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C22⋊D61—42no—
324C22⋊D61—42no—
325C22⋊D61—42no—
326C22⋊D61—42no—
327C22⋊D61—42no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—24no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—41no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C2×C22⋊C411yescharacteristic
345D244—41no—
346D244—42no—
347D244—42no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—416no—
362C4×D61—42no—
363C4×D61#10414yes—
364Dic122—42no—
365Dic122—42no—
366Dic122—41no—
367C8×C61—42no—
368#92418—42no—
369#17541—611nomaximal, Sylow
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61C22×C22⋊C411yescharacteristic
376C22×C61#57512yes—
377C2×D61—28no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61#41012yes—
386C2×D61C2×#10412yes—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—44no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61C2×#10412yes—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—21no—
402Dic61—44no—
403Dic61—41no—
404Dic61—41no—
405Dic61—41no—
406Dic61C2×#10412yes—
407#3444—611no—
408#2920—611no—
409C2×#376—611no—
410#1506—612no—
411#1505—612no—
412#1504—612no—
413#1504—612no—
414#1500—611no—
415#1500—611no—
416#1500—611no—
417#1500D6111yescharacteristic, complemented
418C2×C61—22no—
419C2×C61—81no—
420C2×C61C2×#41011yescharacteristic
421C2×C61#289611yescharacteristic
422C2×C61C22×#10411yescharacteristic
423D61—22no—
424D61—22no—
425D61—81no—
426#533—611no—
427#533—611no—
428#533—611no—
429#532—611no—
430#532—611no—
431#532—611no—
432#529—611no—
433#529—611no—
434#529—611no—
435#529—1221no—
436#529—1221no—
437#529—1221no—
438#529—1221no—
439#529C2×D6111yescharacteristic
440#525—611no—
441#525—611no—
442#525—1221no—
443#525—1221no—
444C4×#41—611no—
445C4×#41—611no—
446C4×#41—1221no—
447C4×#41—1221no—
448C22×C42—611no—
449C22×C42—1221no—
450#432—612no—
451#432—1221no—
452#431—611no—
453#431—1221no—
454#431C2×D6111yescharacteristic
455#423—1221no—
456#407—612no—
457C4×M16—1221no—
458#376—611no—
459#376—612no—
460#376—1221no—
461#376—1221no—
462#376C2×D6111yescharacteristic
463C2×#95—612no—
464C2×#95—1221no—
465#328—612no—
466#328—612no—
467#328—612no—
468#328C2×D6112yes—
469#327—612no—
470#327—612no—
471#327—612no—
472#327C2×D6112yes—
473C61#1754111yescharacteristic, complemented, Sylow
474C2×#41—611no—
475C2×#41—611no—
476C2×#41—1221no—
477C2×#41—1221no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—1222no—
482C2×M16—1222no—
483C4⋊Q8—611no—
484C4⋊Q8—611no—
485C4⋊Q8—611no—
486#127—611no—
487#126—21no—
488#126—1221no—
489#126—1221no—
490#126—1221no—
491#125—611no—
492#125—1221no—
493#125—1221no—
494#125C4×D6111yescharacteristic, complemented
495#124—611no—
496#124—1221no—
497#124—1221no—
498#124C4×D6111yescharacteristic, complemented
499#123—21no—
500#123—1221no—
501#123—1221no—
502#123—1221no—
503#123—1221no—
504#123—1221no—
505C22⋊Q8—611no—
506C22⋊Q8—611no—
507C22⋊Q8—611no—
508C22⋊Q8—1221no—
509C22⋊Q8—1221no—
510C22⋊Q8—1221no—
511C22⋊Q8—1221no—
512C22⋊Q8C22×D6111yescharacteristic
513#121—611no—
514#121—611no—
515#121—611no—
516#121—1221no—
517#121—1221no—
518#121—1221no—
519#121—1221no—
520#121C22×D6111yescharacteristic
521#120—1221no—
522#120—1221no—
523C4×Q8—611no—
524C4×Q8—611no—
525C4×Q8—611no—
526C4×Q8—1221no—
527C4×Q8—1221no—
528C4×Q8—1221no—
529C4×Q8—1221no—
530C4×Q8C4×D6111yescharacteristic, complemented
531C4×D4—21no—
532C4×D4—611no—
533C4×D4—611no—
534C4×D4—611no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4—1221no—
549C4×D4—1221no—
550C4×D4C4×D6111yescharacteristic, complemented
551#117—21no—
552#117—611no—
553#117—611no—
554#117—1221no—
555#117—1221no—
556#117—1221no—
557#117—1221no—
558#117—1221no—
559#117—1221no—
560#117—1221no—
561C2×C42—21no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—1221no—
574C2×C42—1228no—
575C2×C42—1221no—
576C2×C42—1222no—
577C2×C42—1221no—
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—21no—
580C4⋊C8—1222no—
581C4⋊C8—1221no—
582C22⋊C8—612no—
583C22⋊C8—1222no—
584C22⋊C8C22×D6112yes—
585#97—1222no—
586C4×C8—21no—
587C4×C8—1221no—
588#95—21no—
589#95—612no—
590#95—1222no—
591#95—1222no—
592#95—1221no—
593#95C22×D6112yes—
594C24—611no—
595#41—2444no—
596#41—2444no—
597#41—2442no—
598#41—2442no—
599C2×Q8—611no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8C2×C4×D6111yescharacteristic
603C2×D4—21no—
604C2×D4—611no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4C2×C4×D6111yescharacteristic
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—1224no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1228no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1222no—
637C22×C4—1221no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2444no—
641C22×C4—2444no—
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4C23×D6111yescharacteristic
645M16—2444no—
646C2×C8—22no—
647C2×C8—1222no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—611no—
653C4⋊C4—611no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4C2×C4×D6111yescharacteristic
667C4⋊C4C2×C4×D6111yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C42—24no—
687C42—21no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—1221no—
701C42—1221no—
702C42—1221no—
703C42—1221no—
704C42—1224no—
705C42—1228no—
706C42—1221no—
707C42C2×C4×D6111yescharacteristic
708C42C2×C4×D6111yescharacteristic
709C42D4×D6111yescharacteristic
710C42D4×D6111yescharacteristic
711C23—21no—
712C23—611no—
713C23—611no—
714C23—1222no—
715C23—1222no—
716C23—1222no—
717C23—1221no—
718C23C2×D4×D6111yescharacteristic
719Q8—41no—
720Q8—2441no—
721Q8—2442no—
722Q8—2442no—
723D4—41no—
724D4—42no—
725D4—2441no—
726D4—2442no—
727D4—2442no—
728D4—2442no—
729D4—2442no—
730D4—2442no—
731D4—2442no—
732D4—2442no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—611no—
744C2×C4—614no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1224no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4—24416no—
770C2×C4—2441no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22⋊C4×D6111yescharacteristic
778C2×C4C22⋊C4×D6111yescharacteristic
779C2×C4C22⋊C4×D6111yescharacteristic
780C2×C4C22×C4×D6111yescharacteristic
781C2×C4C2×D4×D6111yescharacteristic
782C8—42no—
783C8—2442no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—612no—
790C22—612no—
791C22—1228no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—1221no—
796C22—2441no—
797C22—2441no—
798C22—2441no—
799C22C2×C22⋊C4×D6111yescharacteristic
800C22#1684055912yes—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—44no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—612no—
811C4—1221no—
812C4—1221no—
813C4—1221no—
814C4—1221no—
815C4—1221no—
816C4—2444no—
817C4—2441no—
818C4—2441no—
819C4—2441no—
820C4#104×D6112yes—
821C2—22no—
822C2—81no—
823C2—1222no—
824C2—1222no—
825C2—4881no—
826C2#410×D6111yescharacteristic
827C2#2145433411yescharacteristic
828C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1500C2
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC22×C4×C61C24
hypercenter#1500D61
hypocenterC61#17541
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #376×D61C2semidirect
4. #21444329C2semidirect
5. #21444325C2semidirect
6. #21444322C2semidirect
7. #21444320C2semidirect
8. #21444306C2semidirect
9. #21444305C2semidirect
10. #21444303C2semidirect
11. C61×#1500C2semidirect
12. #16840318C4semidirect
13. #16840316C4semidirect
15. #16840311C4semidirect
16. #16840309C4semidirect
18. #16840297C4semidirect
22. #16840291C4semidirect
29. C4×#11758226C4semidirect
32. C4×#11758224C4semidirect
68. #14519776C2×C4semidirect
69. #14519776C2×C4semidirect
70. #14519775C2×C4semidirect
71. #14519773C2×C4semidirect
75. #14519769C2×C4semidirect
78. #14519765C2×C4semidirect
102. Q8×Dic61C2×C4semidirect
104. C4×Dic122C2×C4semidirect
108. #14519742C2×C4semidirect
110. C4×D244C2×C4semidirect
112. D4×Dic61C2×C4semidirect
116. #14519739C2×C4semidirect
163. #125×C61C2×C4semidirect
164. #124×C61C2×C4semidirect
168. C4×Q8×C61C2×C4semidirect
170. C4×D4×C61C2×C4semidirect
417. #1500D61semidirect
473. C61#17541semidirect
494. #125C4×D61semidirect
498. #124C4×D61semidirect
530. C4×Q8C4×D61semidirect
550. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214591132
#214544472
#376×D612
#214443292
#214443252
#214443222
#214443202
#214443062
#214443052
#214443032
C61×#15002
#1754161