Finite Group Databasebeta

← #29695600

Subgroups — #29695600

Order 15616.

1458 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840421C211yesmaximal, characteristic
2C2×#16839772C211yesmaximal, characteristic, complemented
3C2×#16839759C211yesmaximal, characteristic, complemented
4#21448768C211yesmaximal, characteristic, complemented
5#21446749C211yesmaximal, characteristic, complemented
6#21446635C211yesmaximal, characteristic, complemented
7#21446257C211yesmaximal, characteristic, complemented
8#21446242C211yesmaximal, characteristic, complemented
9#21446139C211yesmaximal, characteristic, complemented
10#21446129C211yesmaximal, characteristic, complemented
11#21445825C211yesmaximal, characteristic, complemented
12#21445760C211yesmaximal, characteristic, complemented
13#21445755C211yesmaximal, characteristic, complemented
14#21445650C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×Dic122C2211yescharacteristic
18#16840421—24no—
19#16840421C418yescomplemented
20C2×#14519765C2211yescharacteristic
21C2×#14519763—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519755—21no—
24C2×#14519751C2211yescharacteristic
25C2×#14519749—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519737—21no—
28C2×#14519736C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30#16839772—24no—
31#16839759—24no—
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519702C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44#16839665—21no—
45#16839655—21no—
46#16839655—21no—
47#16839632C2211yescharacteristic
48#16839622C2211yescharacteristic
49#16839622C2211yescharacteristic
50C4⋊C4×Dic61—21no—
51C4×C4⋊Dic61C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839525C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C61×#435—24no—
60C2×C4⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C2×#97×C61C2211yescharacteristic
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222C2×C414yes—
70C22×Dic122—22no—
71C22×Dic122—22no—
72C22×Dic122—21no—
73C22×Dic122—22no—
74C22×Dic122—41no—
75C22×Dic122—41no—
76C22×Dic122C2×C414yes—
77C22×Dic122C2311yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84#14519765—22no—
85#14519765C2×C414yes—
86#14519763—28no—
87#14519756—22no—
88#14519756C2×C414yes—
89#14519755—28no—
90#14519751—22no—
91#14519751C2×C414yes—
92#14519749—28no—
93C4×Dic122—22no—
94C4×Dic122C2×C414yes—
95#14519737—28no—
96#14519736—22no—
97#14519736—22no—
98#14519736—41no—
99#14519736—41no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121#14519702—22no—
122#14519702—22no—
123#14519702—22no—
124#14519702—22no—
125#14519702—22no—
126#14519702—41no—
127#14519702—41no—
128#14519702D414yescomplemented
129#14519699—22no—
130#14519699—22no—
131#14519699—41no—
132#14519699—41no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C22×D4×C61D411yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C2×M16×C61—22no—
140C2×M16×C61—22no—
141C2×M16×C61—41no—
142C22×C8×C61—22no—
143C22×C8×C61—22no—
144C22×C8×C61—41no—
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C4×D4×C61C2×C414yes—
150C4×D4×C61D414yes—
151C2×C4⋊C4×C61D411yescharacteristic
152C2×C22⋊C4×C61D411yescharacteristic
153C2×C22⋊C4×C61D411yescharacteristic
154C2×C42×C61C2311yescharacteristic
155C4⋊C8×C61—22no—
156C22⋊C8×C61—22no—
157C22⋊C8×C61—22no—
158#97×C61—22no—
159C24×C61C2×D411yescharacteristic
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
164C2×D4×C61C22⋊C414yes—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C22×C412yes—
174C22×C4×C61C22×C412yes—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D412yes—
180C22×C4×C61C2×D412yes—
181C22×C4×C61C2411yescharacteristic
182C2×C22⋊D61—24no—
183C2×C22⋊D61—24no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—42no—
188C22×Dic61—21no—
189C22×Dic61—24no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—42no—
197C22×Dic61—42no—
198#11758222—28no—
199#11758222—44no—
200#11758222—44no—
201#11758222—44no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244C22×C412yes—
208C2×C4×D61—24no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—28no—
219C2×Dic122—24no—
220C2×Dic122—21no—
221C2×Dic122—44no—
222C2×Dic122—44no—
223C2×Dic122—44no—
224C2×Dic122—42no—
225C2×Dic122—42no—
226C2×Dic122C22×C412yes—
227C2×Dic122C22×C412yes—
228C2×Dic122C2×D412yes—
229C2×Dic122#4112yes—
230M16×C61—44no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—44no—
243C2×C8×C61C2×D412yes—
244C4⋊C4×C61C22⋊C414yes—
245C22⋊C4×C61C22⋊C414yes—
246C22⋊C4×C61C22⋊C414yes—
247C42×C61C22×C412yes—
248C42×C61C2×D412yes—
249C22⋊Dic61—24no—
250C22⋊Dic61—42no—
251C22⋊Dic61—42no—
252C22⋊Dic61—81no—
253C22⋊Dic61—81no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—42no—
266C4⋊Dic61—81no—
267C4⋊Dic61C22×C412yes—
268C4⋊Dic61C2×D412yes—
269#11758196—24no—
270#11758196—24no—
271C4×Dic61—24no—
272C4×Dic61—42no—
273C4×Dic61—42no—
274C4×Dic61—42no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61C2×C22⋊C412yes—
288C23×C61C2×C22⋊C412yes—
289C23×C61C22×D411yescharacteristic
290C22×D61—22no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297D4×C61—44no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61C2×C22⋊C412yes—
315C2×C4×C61C2×C22⋊C412yes—
316C2×C4×C61C2×C22⋊C412yes—
317C2×C4×C61C2×C22⋊C412yes—
318C2×C4×C61C23×C411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×C4×C61H(5,𝔽2)11yescharacteristic
324C22⋊D61—48no—
325C22⋊D61—48no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—48no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348D244—22no—
349D244—22no—
350D244—41no—
351D244—41no—
352C4×D61—48no—
353Dic122—22no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—48no—
359Dic122—41no—
360Dic122—41no—
361Dic122C4×D414yes—
362C8×C61—22no—
363C8×C61—41no—
364C8×C61—41no—
365C8×C61—41no—
366#22426—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61C22×C22⋊C411yescharacteristic
382C22×C61D4211yescharacteristic
383C22×C61#54611yescharacteristic
384C22×C61#57511yescharacteristic
385C22×C61#57511yescharacteristic
386C22×C61#57711yescharacteristic
387C22×C61#57811yescharacteristic
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—81no—
392C2×D61—81no—
393C2×D61—81no—
394C2×D61—81no—
395C4×C61—22no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61C2×C4×D411yescharacteristic
400C4×C61#51811yescharacteristic
401C4×C61D4211yescharacteristic
402C4×C61#54611yescharacteristic
403Dic61—24no—
404Dic61—42no—
405Dic61—42no—
406Dic61—42no—
407Dic61—81no—
408Dic61—81no—
409Dic61—81no—
410C2×#548—611no—
411C2×#435D6111yescharacteristic, complemented
412C2×#419—611no—
413C2×#416—611no—
414#2354—611no—
415#1983—611no—
416#1959—611no—
417#1895—611no—
418#1892—611no—
419#1875—611no—
420#1873—611no—
421#1803—611no—
422#1788—611no—
423#1787—611no—
424#1763—611no—
425C2×C61—42no—
426C2×C61—42no—
427C2×C61D4×C22⋊C411yescharacteristic
428C2×C61#289611yescharacteristic
429C2×C61#289811yescharacteristic
430C2×C61#326911yescharacteristic
431C2×C61#327111yescharacteristic
432C2×C61#331311yescharacteristic
433C2×C61#332111yescharacteristic
434D61—82no—
435C22×#41—611no—
436C23×Q8—611no—
437C22×M16C2×D6111yescharacteristic
438C23×C8C2×D6111yescharacteristic
439#548—618no—
440#548—1224no—
441C2×#124—611no—
442C2×#124—1221no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8—1221no—
445C2×#121—611no—
446C2×#121—1221no—
447C2×C4×Q8—611no—
448C2×C4×D4—1221no—
449C2×C4×D4C2×D6111yescharacteristic
450C2×#117—611no—
451C2×#117—611no—
452#435—24no—
453C2×C4⋊C8C2×D6111yescharacteristic
454#419—1224no—
455#416—1224no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×C22⋊C8C2×D6111yescharacteristic
469C2×C22⋊C8C2×D6111yescharacteristic
470C2×#97C2×D6111yescharacteristic
471#390—1221no—
472#388—1221no—
473#388—1221no—
474#384—611no—
475#380—611no—
476#380—611no—
477C4×C4⋊C4—611no—
478C4×C4⋊C4—1221no—
479#340—611no—
480#340—611no—
481#340—611no—
482#340—611no—
483C61#2242611yescharacteristic, complemented, Sylow
484C2×#41—614no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—2441no—
489C2×#41—2441no—
490C22×Q8—614no—
491C22×Q8—611no—
492C22×Q8—611no—
493C22×Q8—1222no—
494C22×Q8—1222no—
495C22×Q8—1221no—
496C22×Q8—1222no—
497C22×Q8—2441no—
498C22×Q8—2441no—
499C22×D4—611no—
500C22×D4—1221no—
501C22×D4—1221no—
502C22×D4D24411yescharacteristic
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C22×D6111yescharacteristic
514C22×C8C22×D6111yescharacteristic
515C22×C8C22×D6111yescharacteristic
516C22×C8C22×D6111yescharacteristic
517#124—614no—
518#124—1228no—
519#124—1222no—
520C22⋊Q8—614no—
521C22⋊Q8—1222no—
522C22⋊Q8—1228no—
523#121—614no—
524#121—1228no—
525#121—1222no—
526C4×Q8—614no—
527C4×Q8—1222no—
528C4×D4—1228no—
529C4×D4C4×D6114yes—
530C4×D4C22⋊D6114yes—
531#117—1222no—
532#117—1222no—
533#117—2441no—
534#117—2441no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4D24411yescharacteristic
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4D24411yescharacteristic
554C2×C22⋊C4D24411yescharacteristic
555C2×C42—1221no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42—1221no—
559C2×C42C22×D6111yescharacteristic
560C4⋊C8—22no—
561#103—614no—
562#103—1222no—
563#103—1222no—
564#103—1222no—
565#103—1222no—
566#103—1222no—
567#103—2441no—
568#103—2441no—
569#102—1222no—
570#102—1222no—
571#102—2441no—
572#102—2441no—
573C22⋊C8—22no—
574C22⋊C8—22no—
575#97—22no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579C24—1221no—
580C24C2×D24411yescharacteristic
581C24C2×D24411yescharacteristic
582#41—1228no—
583#41—2444no—
584#41—2444no—
585#41—2444no—
586C2×Q8—612no—
587C2×Q8—612no—
588C2×Q8—612no—
589C2×Q8—612no—
590C2×Q8—1228no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1224no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—2442no—
601C2×Q8—2442no—
602C2×Q8—2444no—
603C2×Q8—2444no—
604C2×Q8—2444no—
605C2×D4—41no—
606C2×D4—41no—
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—2442no—
618C2×D4—2442no—
619C2×D4#1175819814yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1224no—
633C22×C4—1224no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4C2×C4×D6112yes—
642C22×C4C2×C4×D6112yes—
643C22×C4C2×D24411yescharacteristic
644C22×C4C2×D24411yescharacteristic
645C22×C4C2×D24411yescharacteristic
646C22×C4C2×D24411yescharacteristic
647C22×C4C2×C22⋊D6112yes—
648C22×C4C2×C22⋊D6112yes—
649C22×C4C23×D6111yescharacteristic
650M16—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—44no—
663C2×C8D4×D6112yes—
664C4⋊C4—612no—
665C4⋊C4—612no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1224no—
669C4⋊C4—1224no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—4881no—
677C4⋊C4—2442no—
678C4⋊C4#1175819814yes—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—4881no—
684C22⋊C4—4881no—
685C22⋊C4—2442no—
686C22⋊C4—2442no—
687C22⋊C4#1175819814yes—
688C22⋊C4#1175819814yes—
689C42—1224no—
690C42—2442no—
691C42—2442no—
692C42—2442no—
693C42C2×C4×D6112yes—
694C42C2×C22⋊D6112yes—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—1222no—
708C23—2441no—
709C23—2441no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23C2×#1175819812yes—
715C23C2×#1175819812yes—
716C23C22×D24411yescharacteristic
717Q8—614no—
718Q8—1222no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—1222no—
723Q8—2448no—
724Q8—2441no—
725Q8—2441no—
726D4—44no—
727D4—1222no—
728D4—1222no—
729D4—2448no—
730D4—2448no—
731D4—2441no—
732D4—2441no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—2448no—
756C2×C4—2448no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
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—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4C2×#1175819812yes—
773C2×C4C2×#1175819812yes—
774C2×C4C2×#1175819812yes—
775C2×C4C2×#1175819812yes—
776C2×C4C22×C4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C22×C22⋊D6111yescharacteristic
779C2×C4#41×D6111yescharacteristic
780C2×C4#1451982211yescharacteristic
781C2×C4#1451982311yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—4881no—
801C22—4881no—
802C22—4881no—
803C22—4881no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22C22×#1175819811yescharacteristic
808C22D4×D24411yescharacteristic
809C22#1684040711yescharacteristic
810C22#1684056211yescharacteristic
811C22#1684056211yescharacteristic
812C22#1684057411yescharacteristic
813C22#1684057911yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—1224no—
819C4—4881no—
820C4—4881no—
821C4—4881no—
822C4—2442no—
823C4—2442no—
824C4—2442no—
825C4C4×D4×D6111yescharacteristic
826C4#1684023411yescharacteristic
827C4D4×C22⋊D6111yescharacteristic
828C4#1684040011yescharacteristic
829C2—42no—
830C2—42no—
831C2—4882no—
832C2D4×#1175819811yescharacteristic
833C2#2145433911yescharacteristic
834C2#2145435311yescharacteristic
835C2#2145737911yescharacteristic
836C2#2145740911yescharacteristic
837C2#2145788711yescharacteristic
838C2#2145800711yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC2×#16840421C2
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22426
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#16839772C2semidirect
3. C2×#16839759C2semidirect
4. #21448768C2semidirect
5. #21446749C2semidirect
6. #21446635C2semidirect
7. #21446257C2semidirect
8. #21446242C2semidirect
9. #21446139C2semidirect
10. #21446129C2semidirect
11. #21445825C2semidirect
12. #21445760C2semidirect
13. #21445755C2semidirect
14. #21445650C2semidirect
15. C2×C61×#435C2semidirect
19. #16840421C4semidirect
128. #14519702D4semidirect
411. C2×#435D61semidirect
483. C61#22426semidirect

Maximal subgroups

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

subgroupindex
C2×#168404212
C2×#168397722
C2×#168397592
#214487682
#214467492
#214466352
#214462572
#214462422
#214461392
#214461292
#214458252
#214457602
#214457552
#214456502
C2×C61×#4352
#2242661