Finite Group Databasebeta

← #29695643

Subgroups — #29695643

Order 15616.

1466 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840423C211yesmaximal, characteristic
2C2×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4C2×#16839771C211yesmaximal, characteristic, complemented
5#21448741C211yesmaximal, characteristic, complemented
6#21446748C211yesmaximal, characteristic, complemented
7#21446627C211yesmaximal, characteristic, complemented
8#21446255C211yesmaximal, characteristic, complemented
9#21446249C211yesmaximal, characteristic, complemented
10#21446139C211yesmaximal, characteristic, complemented
11#21446123C211yesmaximal, characteristic, complemented
12#21445832C211yesmaximal, characteristic, complemented
13#21445758C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C61×#1787C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19#16840423—24no—
20#16840423C418yescomplemented
21C2×#14519766—21no—
22C2×#14519766C2211yescharacteristic
23C2×#14519753—21no—
24C2×#14519753C2211yescharacteristic
25C2×#14519751—21no—
26C2×#14519751C2211yescharacteristic
27C2×Q8×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519736C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839837—24no—
33C2×#14519706C2211yescharacteristic
34#16839771—24no—
35#16839762—24no—
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46#16839650—21no—
47#16839644—21no—
48#16839638—21no—
49#16839627C2211yescharacteristic
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic
52#16839609—21no—
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C23×Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yes—
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×#11758194—22no—
78C2×#11758194—22no—
79C2×#11758194—41no—
80C2×#11758189—22no—
81C2×#11758189—22no—
82C2×#11758189—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519766—28no—
86#14519766—22no—
87#14519766C2×C414yescomplemented
88#14519753—22no—
89#14519753—28no—
90#14519753C2×C414yes—
91#14519751—22no—
92#14519751—28no—
93#14519751C2×C414yescomplemented
94Q8×Dic61—22no—
95Q8×Dic61C2×C414yescomplemented
96C4×C22⋊D61—28no—
97C4×C22⋊D61C2×C414yes—
98C4×C22⋊D61D414yes—
99#14519736—22no—
100#14519736—41no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196D411yescharacteristic
108C4⋊C4×D61—22no—
109C4⋊C4×D61—41no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61D411yescharacteristic
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198D411yescharacteristic
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519706—22no—
123#14519701—22no—
124#14519701—22no—
125#14519701—22no—
126#14519701D414yescomplemented
127#14519699—22no—
128#14519699—41no—
129#14519697—22no—
130#14519697—41no—
131#14519689—22no—
132C8×Dic61—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C22×Q8×C61—21no—
138C22×Q8×C61—22no—
139C22×Q8×C61—22no—
140C22×Q8×C61—22no—
141C22×Q8×C61—41no—
142C22×Q8×C61—41no—
143C22×Q8×C61C2×C414yescomplemented
144C22×Q8×C61C2311yescharacteristic
145C22×Q8×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153#103×C61—22no—
154#103×C61—22no—
155#103×C61—41no—
156#103×C61—41no—
157C22⋊C8×C61—22no—
158#95×C61—21no—
159C24×C61C2×D411yescharacteristic
160C23×D61—21no—
161C23×D61C2×D411yescharacteristic
162C2×Q8×C61—24no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—28no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—42no—
173C2×Q8×C61—42no—
174C2×Q8×C61—44no—
175C2×Q8×C61—44no—
176C2×Q8×C61—44no—
177C2×Q8×C61C22×C412yes—
178C2×Q8×C61C22×C412yes—
179C2×Q8×C61C2×D412yes—
180C2×Q8×C61#4112yes—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—24no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61C22×C412yes—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—24no—
197C2×C22⋊D61—41no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61C22⋊C414yes—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208#11758226—28no—
209#11758226—44no—
210#11758226—44no—
211#11758226—44no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—24no—
217C2×D244—21no—
218C2×D244—42no—
219C2×D244—42no—
220C2×D244C22×C412yes—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—24no—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61—81no—
231C2×C4×D61C22×C412yes—
232C2×C4×D61C2×D412yes—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C22⋊C4×C61—81no—
244C22⋊Dic61—42no—
245C22⋊Dic61C22⋊C414yes—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198—42no—
251#11758198C22⋊C414yes—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C22×C412yes—
258C4⋊Dic61C2×D412yes—
259#11758196—24no—
260#11758196—42no—
261#11758196C22⋊C414yes—
262C4×Dic61—24no—
263C4×Dic61—42no—
264C4×Dic61—81no—
265C4×Dic61C22×C412yes—
266C4×Dic61C2×D412yes—
267#11758194—44no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418C2×D412yes—
274#11758189—44no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61C2×C22⋊C412yes—
282C23×C61C22×D411yescharacteristic
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—22no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61C2×C22⋊C412yes—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—48no—
303Q8×C61—41no—
304Q8×C61—41no—
305Q8×C61C4×D414yes—
306C2×C4×C61—22no—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—48no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61C2×C22⋊C412yes—
326C2×C4×C61C23×C411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61H(5,𝔽2)11yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C22⋊D61—44no—
333C22⋊D61—48no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61C2×C22⋊C412yes—
350C2×Dic61C2×C22⋊C412yes—
351C2×Dic61C2×C22⋊C412yes—
352D244—22no—
353D244—22no—
354D244—48no—
355D244—41no—
356D244—41no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—48no—
362C4×D61—84no—
363C8×C61—41no—
364C8×C61—41no—
365#92418—22no—
366#92418—41no—
367#22429—611nomaximal, Sylow
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61C22×C22⋊C411yescharacteristic
376C22×C61D4211yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61#57511yescharacteristic
379C22×C61#57511yescharacteristic
380C22×C61#57711yescharacteristic
381C22×C61#57811yescharacteristic
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—81no—
393C2×D61—81no—
394C2×D61—81no—
395C2×D61—81no—
396C4×C61—24no—
397C4×C61—22no—
398C4×C61—42no—
399C4×C61—81no—
400C4×C61—81no—
401C4×C61C2×C4×D411yescharacteristic
402C4×C61#51811yescharacteristic
403C4×C61D4211yescharacteristic
404C4×C61#54611yescharacteristic
405Dic61—22no—
406Dic61—22no—
407Dic61—22no—
408Dic61—42no—
409Dic61—42no—
410Dic61—81no—
411C2×#548—611no—
412C2×#436—611no—
413C2×#417—611no—
414C2×#419—611no—
415#2352—611no—
416#1983—611no—
417#1958—611no—
418#1895—611no—
419#1894—611no—
420#1875—611no—
421#1872—611no—
422#1805—611no—
423#1788—611no—
424#1787D6111yescharacteristic, complemented
425C4×#103—611no—
426C2×C61—42no—
427C2×C61D4×C22⋊C411yescharacteristic
428C2×C61#289611yescharacteristic
429C2×C61#289811yescharacteristic
430C2×C61#327511yescharacteristic
431C2×C61#327711yescharacteristic
432C2×C61#332611yescharacteristic
433C2×C61#332711yescharacteristic
434D61—42no—
435D61—82no—
436C22×#41—611no—
437C23×Q8C2×D6111yescharacteristic
438C22×M16—611no—
439C22×M16—611no—
440#548—618no—
441#548—1224no—
442C2×#124—611no—
443C2×#124—1221no—
444C2×C22⋊Q8—611no—
445C2×C22⋊Q8—1221no—
446C2×#121—611no—
447C2×#121—1221no—
448C2×C4×Q8—611no—
449C2×C4×D4—611no—
450C2×C4×D4—1221no—
451C2×#117—611no—
452C22×C4⋊C4—611no—
453#436—1224no—
454C2×C4⋊C8—611no—
455#419—1224no—
456#417—1224no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103C2×D6111yescharacteristic
462C2×#103C2×D6111yescharacteristic
463C2×#103C2×D6111yescharacteristic
464C2×#103C2×D6111yescharacteristic
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×C22⋊C8—611no—
470C2×C22⋊C8C2×D6111yescharacteristic
471C2×C4×C8—611no—
472#388—1221no—
473#387—1221no—
474#386—1221no—
475#382—611no—
476#380—611no—
477#380C2×D6111yescharacteristic
478C4×C4⋊C4—611no—
479C4×C22⋊C4—1221no—
480#340—611no—
481#340—611no—
482#340—611no—
483#340—611no—
484C61#2242911yescharacteristic, complemented, Sylow
485C2×#41—614no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—1222no—
489C2×#41—2441no—
490C2×#41—2441no—
491C22×Q8—21no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8C4×D6114yescomplemented
498C22×Q8C22×D6111yescharacteristic
499C22×Q8C22×D6111yescharacteristic
500C22×D4—611no—
501C22×D4—611no—
502C22×D4—1221no—
503C22×D4—1221no—
504C23×C4—21no—
505C23×C4—611no—
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4C22×D6111yescharacteristic
509C2×M16—1222no—
510C2×M16—1222no—
511C2×M16—1222no—
512C2×M16—1222no—
513C2×M16—2441no—
514C2×M16—2441no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8C22×D6111yescharacteristic
518C22×C8C22×D6111yescharacteristic
519#124—614no—
520#124—1222no—
521#124—1228no—
522C22⋊Q8—614no—
523C22⋊Q8—1228no—
524C22⋊Q8—1222no—
525#121—614no—
526#121—1228no—
527#121—1222no—
528C4×Q8—614no—
529C4×Q8—1222no—
530C4×D4—614no—
531C4×D4—614no—
532C4×D4—1228no—
533#117—1222no—
534#117—2441no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1222no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—2441no—
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C42—611no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42—1221no—
559C4⋊C8—1222no—
560#103—22no—
561#103—22no—
562#103—41no—
563#103—41no—
564#103—614no—
565#103—1222no—
566#103—1222no—
567#103—1222no—
568#102—1222no—
569#102—1222no—
570#102—2441no—
571#102—2441no—
572C22⋊C8—22no—
573C22⋊C8—1222no—
574C4×C8—1222no—
575#95—21no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580C24—611no—
581C24—1221no—
582C24D4×D6111yescharacteristic
583#41—1228no—
584#41—2444no—
585#41—2444no—
586#41—2444no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—24no—
592C2×Q8—28no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—42no—
598C2×Q8—42no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8C2×C4×D6112yes—
603C2×Q8C2×C4×D6112yes—
604C2×Q8D4×D6112yes—
605C2×Q8#1175822412yes—
606C2×D4—614no—
607C2×D4—612no—
608C2×D4—1224no—
609C2×D4—1224no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—2442no—
616C2×D4—2442no—
617C2×D4—2441no—
618C2×D4—2441no—
619C2×D4—2442no—
620C2×D4—2442no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—1224no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—4881no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4—2442no—
650C22×C4C2×C4×D6112yes—
651C22×C4D4×D6112yes—
652C22×C4D4×D6111yescharacteristic
653C22×C4C23×D6111yescharacteristic
654M16—2444no—
655M16—2444no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—612no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—614no—
673C4⋊C4—612no—
674C4⋊C4—612no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—2442no—
682C22⋊C4—81no—
683C22⋊C4—614no—
684C22⋊C4—614no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—2442no—
690C22⋊C4—2442no—
691C42—612no—
692C42—612no—
693C42—1224no—
694C42—4881no—
695C42—2442no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—612no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1222no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23—2441no—
716C23C22⋊C4×D6112yes—
717C23C2×D4×D6111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—48no—
724Q8—41no—
725Q8—41no—
726Q8#1451973714yes—
727D4—1222no—
728D4—1222no—
729D4—2448no—
730D4—2444no—
731D4—2448no—
732D4—2441no—
733D4—2441no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—48no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—612no—
754C2×C4—612no—
755C2×C4—612no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—4884no—
769C2×C4—2448no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4C22⋊C4×D6112yes—
778C2×C4C22×C4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C2×C4C2×#1175822411yescharacteristic
782C2×C4#1451982211yescharacteristic
783C2×C4#1451982211yescharacteristic
784C8—41no—
785C8—41no—
786C8—1222no—
787C8—2441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—1222no—
796C22—1222no—
797C22—1222no—
798C22—4881no—
799C22—4881no—
800C22—4881no—
801C22—4881no—
802C22—2442no—
803C22—2442no—
804C22—2442no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22C2×C22⋊C4×D6111yescharacteristic
810C22#1684039411yescharacteristic
811C22#1684039911yescharacteristic
812C22#1684056111yescharacteristic
813C22#1684056111yescharacteristic
814C22#1684056811yescharacteristic
815C22#1684057511yescharacteristic
816C4—22no—
817C4—24no—
818C4—42no—
819C4—81no—
820C4—81no—
821C4—1222no—
822C4—1222no—
823C4—1222no—
824C4—4881no—
825C4—2442no—
826C4—2442no—
827C4C2×#1451973711yescharacteristic
828C4#1684023511yescharacteristic
829C4#1684039411yescharacteristic
830C4#1684039911yescharacteristic
831C2—42no—
832C2—4882no—
833C2—2442no—
834C2#2144863511yescharacteristic
835C2#2145433711yescharacteristic
836C2#2145434711yescharacteristic
837C2#2145745311yescharacteristic
838C2#2145747611yescharacteristic
839C2#2145807611yescharacteristic
840C2#2145809111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1787C2
socleC23×C61C22×D4
prime radicalC2×#16840423C2
cosocleC22×C4×C61C24
hypercenter#1787D61
hypocenterC61#22429
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#16839837C2semidirect
3. C2×#16839762C2semidirect
4. C2×#16839771C2semidirect
5. #21448741C2semidirect
6. #21446748C2semidirect
7. #21446627C2semidirect
8. #21446255C2semidirect
9. #21446249C2semidirect
10. #21446139C2semidirect
11. #21446123C2semidirect
12. #21445832C2semidirect
13. #21445758C2semidirect
14. #103×Dic61C2semidirect
15. C61×#1787C2semidirect
20. #16840423C4semidirect
87. #14519766C2×C4semidirect
93. #14519751C2×C4semidirect
95. Q8×Dic61C2×C4semidirect
126. #14519701D4semidirect
143. C22×Q8×C61C2×C4semidirect
424. #1787D61semidirect
484. C61#22429semidirect
497. C22×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404232
C2×#168398372
C2×#168397622
C2×#168397712
#214487412
#214467482
#214466272
#214462552
#214462492
#214461392
#214461232
#214458322
#214457582
#103×Dic612
C61×#17872
#2242961