Finite Group Databasebeta

← #29695852

Subgroups — #29695852

Order 15616.

1506 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519798C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3C2×#16839842C211yesmaximal, characteristic, complemented
4#21448648C211yesmaximal, characteristic, complemented
5#21448644C211yesmaximal, characteristic, complemented
6#21446679C211yesmaximal, characteristic, complemented
7#21446677C211yesmaximal, characteristic, complemented
8#21446155C211yesmaximal, characteristic, complemented
9#21446154C211yesmaximal, characteristic, complemented
10#21446152C211yesmaximal, characteristic, complemented
11#21445847C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1877C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C2×#14519798—24no—
19C2×#14519798—24no—
20C2×#14519798C418yescomplemented
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×C8×D61C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×#14519739C2211yescharacteristic
28C4×#11758199—24no—
29#16839842—24no—
30C2×#14519710C2211yescharacteristic
31C2×#14519710C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41#16839669C2211yescharacteristic
42#16839668C2211yescharacteristic
43#16839667C2211yescharacteristic
44#16839641—21no—
45#16839640—21no—
46#16839640—21no—
47#16839639—21no—
48#16839624—21no—
49#16839623—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52C4×#11758198C2211yescharacteristic
53C2×#14519684—21no—
54#95×D61—21no—
55#16839525C2211yescharacteristic
56#16839516C2211yescharacteristic
57C22×SD16×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#391C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yescomplemented
70C2×#11758224—22no—
71C2×#11758224—22no—
72C2×#11758224—22no—
73C2×#11758224—41no—
74C2×#11758224—41no—
75C2×#11758224C2×C414yescomplemented
76C22×Dic122C2311yescharacteristic
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C23×Dic61—21no—
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86#14519798—232no—
87C2×#11758202—22no—
88C2×#11758202—22no—
89C2×#11758202C2×C414yescomplemented
90C2×#11758190—22no—
91C2×#11758190—22no—
92C2×#11758190C2×C414yescomplemented
93C2×#11758199C2×C414yes—
94C2×#11758199D414yes—
95C2×#11758199D414yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C2×C8×D61—22no—
99C2×C8×D61—22no—
100C2×C8×D61C2×C414yescomplemented
101C4×D244—22no—
102C4×D244—41no—
103D4×Dic61—22no—
104D4×Dic61—41no—
105#14519739—22no—
106#14519739—41no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C22⋊Dic61—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198D411yescharacteristic
115C2×#11758198D411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117#14519710—22no—
118#14519710—22no—
119#14519702—41no—
120#14519701—41no—
121#14519700—41no—
122#14519699—22no—
123#14519698—22no—
124#14519697—22no—
125#14519689—22no—
126C4×#92418—22no—
127C8×Dic61—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684D411yescharacteristic
137#14519684D411yescharacteristic
138C22×Q8×C61C2311yescharacteristic
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C2×SD16×C61—22no—
142C2×SD16×C61—22no—
143C2×SD16×C61C2×C414yescomplemented
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C4×D4×C61—22no—
147C4×D4×C61—41no—
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151C2×C42×C61C2311yescharacteristic
152#103×C61—41no—
153#102×C61—22no—
154#95×C61—21no—
155#95×C61—21no—
156C24×C61—21no—
157C23×D61—21no—
158C23×D61C2×D411yescharacteristic
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61C22×C412yes—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61C22×C412yes—
169C2×D4×C61C2×D412yes—
170C2×D4×C61C2×D412yes—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—81no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—24no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—42no—
183C22×Dic61—21no—
184C22×Dic61—24no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61—42no—
190C22×Dic61—42no—
191C22×Dic61—81no—
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195#11758226—28no—
196#11758226—44no—
197#11758226—44no—
198#11758226—44no—
199#11758224—28no—
200#11758224—44no—
201#11758224—44no—
202#11758224—44no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—24no—
207C2×D244—42no—
208C2×D244—42no—
209C2×D244C22×C412yes—
210C2×D244C2×D412yes—
211C2×D244C2×D412yes—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—24no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61—42no—
223C2×C4×D61—81no—
224C2×C4×D61—81no—
225C2×C4×D61C22×C412yes—
226C2×C4×D61#4112yes—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122C22×C412yes—
233SD16×C61—28no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61C22×C412yes—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C22⋊C4×C61—42no—
245C42×C61—21no—
246C42×C61—21no—
247C22⋊Dic61—42no—
248#11758202—28no—
249#11758199C22⋊C4116yescomplemented
250#11758198—22no—
251#11758198—22no—
252#11758198—42no—
253#11758198—42no—
254#11758198—81no—
255#11758198—81no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418C22×C412yes—
266C2×#92418C2×D412yes—
267C2×#92418C2×D412yes—
268#11758190—28no—
269C8×D61—28no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61C22×D411yescharacteristic
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61C4×D412yes—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—41no—
295Q8×C61—41no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61C2×C22⋊C414yes—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—84no—
315C2×C4×C61#13512yescomplemented
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C22⋊D61—48no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—22no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—48no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—84no—
341C2×Dic61C4×D412yes—
342C2×Dic61#13512yescomplemented
343D244—22no—
344D244—22no—
345D244—22no—
346D244—48no—
347D244C2×C22⋊C414yes—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—48no—
353C4×D61—84no—
354C4×D61—84no—
355Dic122—22no—
356Dic122—22no—
357Dic122—41no—
358Dic122—41no—
359C8×C61—22no—
360C8×C61—41no—
361#92418—41no—
362#92418C2×C22⋊C414yes—
363#22448—611nomaximal, Sylow
364C22×C61—24no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61C2×C4×D411yescharacteristic
372C22×C61D4211yescharacteristic
373C22×C61D4211yescharacteristic
374C22×C61C2×#13511yescharacteristic
375C22×C61C2×#13511yescharacteristic
376C22×C61#57611yescharacteristic
377C22×C61#57811yescharacteristic
378C2×D61—22no—
379C2×D61—24no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—42no—
391C2×D61—42no—
392C4×C61—22no—
393C4×C61—42no—
394C4×C61—41no—
395C4×C61—81no—
396C4×C61—81no—
397C4×C61C22×C22⋊C411yescharacteristic
398C4×C61#51811yescharacteristic
399C4×C61#54611yescharacteristic
400C4×C61#54611yescharacteristic
401Dic61—22no—
402Dic61—22no—
403Dic61—42no—
404Dic61—41no—
405Dic61—81no—
406Dic61—81no—
407C22×#135—611no—
408C2×C4×D8—611no—
409C2×C4×D8—611no—
410#2339—611no—
411#2339—611no—
412#1969—611no—
413#1969—611no—
414#1877—611no—
415#1877—611no—
416#1877—611no—
417#1877D6111yescharacteristic, complemented
418#1808—611no—
419#1788—611no—
420#1788—611no—
421C8×C22⋊C4—611no—
422C2×C61—44no—
423C2×C61D4×C22⋊C411yescharacteristic
424C2×C61C4×#13511yescharacteristic
425C2×C61#295111yescharacteristic
426C2×C61#328011yescharacteristic
427C2×C61#328011yescharacteristic
428C2×C61#328311yescharacteristic
429C2×C61#328311yescharacteristic
430D61—42no—
431D61—44no—
432C22×#41—611no—
433C22×#41—611no—
434C2×#135—618no—
435C2×#135—1224no—
436C2×#135—1224no—
437C22×Q16—611no—
438C22×SD16—611no—
439C22×SD16C2×D6111yescharacteristic
440C22×D8—611no—
441C23×C8—611no—
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445C2×C4×D4C2×D6111yescharacteristic
446C4×D8—1224no—
447C4×D8—1224no—
448C2×#107—611no—
449C2×#107—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103C2×D6111yescharacteristic
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102C2×D6111yescharacteristic
458C2×C22⋊C8—611no—
459C2×C4×C8—611no—
460C2×C4×C8—611no—
461#391—611no—
462#391—611no—
463#391—611no—
464#391C2×D6111yescharacteristic
465#386—1221no—
466#386—1221no—
467#386—1221no—
468#386—1221no—
469#381—1221no—
470#381—1221no—
471#380—611no—
472#380—611no—
473C4×C22⋊C4—611no—
474C2×#95—1221no—
475C2×#95—1221no—
476#340—611no—
477#340C2×D6111yescharacteristic
478#336—611no—
479#336C2×D6111yescharacteristic
480C61#2244811yescharacteristic, complemented, Sylow
481C2×#41—614no—
482C2×#41—614no—
483C2×#41—1222no—
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—1222no—
489C2×#41—2441no—
490C2×#41—2441no—
491C2×#41—2441no—
492C2×#41—2441no—
493C22×Q8—611no—
494C22×Q8C22×D6111yescharacteristic
495C22×D4—611no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4C22×D6111yescharacteristic
499C23×C4—21no—
500C23×C4—611no—
501C23×C4—1221no—
502C23×C4—1221no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4—1221no—
506#135—12232no—
507C2×Q16—614no—
508C2×Q16—1222no—
509C2×Q16—1222no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—614no—
513C2×SD16—1222no—
514C2×SD16—1222no—
515C2×SD16C4×D6114yescomplemented
516C2×D8—614no—
517C2×D8—614no—
518C2×D8—614no—
519C22×C8—611no—
520C22×C8—614no—
521C22×C8—611no—
522C22×C8—1222no—
523C22×C8—1222no—
524C22×C8C22×D6111yescharacteristic
525C22×C8C22×D6111yescharacteristic
526C4×D4—22no—
527C4×D4—41no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—2441no—
532C4×D4—2441no—
533C4×D4—2441no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4C22×D6111yescharacteristic
537C2×C4⋊C4C22×D6111yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C42—611no—
547C2×C42C22×D6111yescharacteristic
548#107—1222no—
549#107—1222no—
550#103—41no—
551#103—2441no—
552#103—2441no—
553#103—2441no—
554#102—22no—
555#102—1222no—
556#102—1222no—
557#102—1222no—
558C22⋊C8—1222no—
559C4×C8—1222no—
560C4×C8—1222no—
561#95—21no—
562#95—21no—
563#95—611no—
564#95—611no—
565#95—1221no—
566#95—1221no—
567#95—1221no—
568#95—1221no—
569#95—1221no—
570#95—1221no—
571#95—1221no—
572#95—1221no—
573C24—21no—
574C24—611no—
575C24—1221no—
576#41—1228no—
577#41—1228no—
578#41—2444no—
579#41—2444no—
580#41—2444no—
581#41—2444no—
582#41—2444no—
583#41—2444no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—612no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8C2×C4×D6112yes—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—612no—
600C2×D4—612no—
601C2×D4—612no—
602C2×D4—1224no—
603C2×D4—1224no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—2442no—
608C2×D4—2442no—
609C2×D4—2442no—
610C2×D4—2442no—
611C2×D4C2×C4×D6112yes—
612C2×D4D4×D6112yes—
613C2×D4D4×D6112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—81no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—611no—
625C22×C4—1224no—
626C22×C4—1224no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—4881no—
635C22×C4—4881no—
636C22×C4—4881no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650Q16—1228no—
651SD16—28no—
652SD16—1228no—
653D8—6116no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—612no—
660C2×C8—612no—
661C2×C8—612no—
662C2×C8—1228no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8C2×C4×D6112yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C22⋊C4—42no—
676C22⋊C4—1222no—
677C22⋊C4—1222no—
678C22⋊C4—4881no—
679C22⋊C4—4881no—
680C22⋊C4—2442no—
681C22⋊C4—2442no—
682C22⋊C4—2442no—
683C42—21no—
684C42—21no—
685C42—1221no—
686C42—1221no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—612no—
695C23—1222no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23—1221no—
700C23—1222no—
701C23—1221no—
702C23—1222no—
703C23—1221no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23C2×D4×D6111yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713Q8—1222no—
714Q8—1222no—
715Q8—2441no—
716Q8—2441no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—614no—
721D4—1222no—
722D4—1222no—
723D4—1222no—
724D4—2448no—
725D4—2448no—
726D4C22⋊C4×D6114yes—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—84no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—4884no—
757C2×C4—4884no—
758C2×C4—4884no—
759C2×C4—2448no—
760C2×C4—2448no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4#1451979812yescomplemented
770C2×C4C22×C4×D6111yescharacteristic
771C2×C4C2×D4×D6111yescharacteristic
772C2×C4C2×D4×D6111yescharacteristic
773C2×C4#41×D6111yescharacteristic
774C2×C4#1451982211yescharacteristic
775C2×C4#1451982311yescharacteristic
776C8—22no—
777C8—41no—
778C8—614no—
779C8—2441no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—1222no—
788C22—1222no—
789C22—1224no—
790C22—1222no—
791C22—2442no—
792C22—2441no—
793C22—2442no—
794C22—2441no—
795C22—2442no—
796C22—2441no—
797C22—2442no—
798C22—2441no—
799C22—2442no—
800C22—2442no—
801C22C4×D4×D6111yescharacteristic
802C22#1684039411yescharacteristic
803C22#1684039611yescharacteristic
804C22#135×D6111yescharacteristic
805C22C2×#1451979811yescharacteristic
806C22#1684056611yescharacteristic
807C22#1684057811yescharacteristic
808C4—22no—
809C4—41no—
810C4—42no—
811C4—81no—
812C4—81no—
813C4—1222no—
814C4—1222no—
815C4—4881no—
816C4—4881no—
817C4—2441no—
818C4—2442no—
819C4C2×C22⋊C4×D6111yescharacteristic
820C4#1684023411yescharacteristic
821C4#1684040111yescharacteristic
822C4#1684040411yescharacteristic
823C2—44no—
824C2—2442no—
825C2—2444no—
826C2#2144863711yescharacteristic
827C2C4×#1451979811yescharacteristic
828C2#2145469111yescharacteristic
829C2#2145749711yescharacteristic
830C2#2145749911yescharacteristic
831C2#2145753411yescharacteristic
832C2#2145753611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1877C2
socleC23×C61C22×D4
prime radicalC22×#14519798C2
cosocleC22×C4×C61C24
hypercenter#1877D61
hypocenterC61#22448
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758199C2semidirect
3. C2×#16839842C2semidirect
4. #21448648C2semidirect
5. #21448644C2semidirect
6. #21446679C2semidirect
7. #21446677C2semidirect
8. #21446155C2semidirect
9. #21446154C2semidirect
10. #21446152C2semidirect
11. #21445847C2semidirect
12. #21445758C2semidirect
13. #21445756C2semidirect
14. #21445589C2semidirect
15. C61×#1877C2semidirect
20. C2×#14519798C4semidirect
69. C2×#11758226C2×C4semidirect
75. C2×#11758224C2×C4semidirect
89. C2×#11758202C2×C4semidirect
92. C2×#11758190C2×C4semidirect
100. C2×C8×D61C2×C4semidirect
143. C2×SD16×C61C2×C4semidirect
249. #11758199C22⋊C4semidirect
315. C2×C4×C61#135semidirect
342. C2×Dic61#135semidirect
417. #1877D61semidirect
480. C61#22448semidirect
515. C2×SD16C4×D61semidirect
769. C2×C4#14519798semidirect

Maximal subgroups

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

subgroupindex
C22×#145197982
C2×C4×#117581992
C2×#168398422
#214486482
#214486442
#214466792
#214466772
#214461552
#214461542
#214461522
#214458472
#214457582
#214457562
#214455892
C61×#18772
#2244861