Finite Group Databasebeta

← #29838714

Subgroups — #29838714

Order 15616.

2458 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758222C211yesmaximal, characteristic
2#21448467C212yesmaximal, complemented
3#21448461C212yesmaximal, complemented
4#21448455C212yesmaximal, complemented
5#21448454C212yesmaximal, complemented
6#21448440C212yesmaximal, complemented
7#21448427C212yesmaximal, complemented
8#21448426C212yesmaximal, complemented
9#21448408C212yesmaximal
10#21448295C212yesmaximal, complemented
11#21448278C212yesmaximal, complemented
12#21448260C212yesmaximal, complemented
13#21448256C212yesmaximal, complemented
14#21448223C211yesmaximal, characteristic, complemented
15#21448217C211yesmaximal, characteristic, complemented
16#21448215C211yesmaximal, characteristic, complemented
17C4×#14519735C211yesmaximal, characteristic, complemented
18C4×C4⋊C4×D61C211yesmaximal, characteristic, complemented
19C61×#2285C211yesmaximal, characteristic, complemented
20C22×#11758222C2211yescharacteristic
21C4×#11758222C4116yescomplemented
22C2×C4×Dic122C2211yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×C4×C22⋊D61C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519736C2211yescharacteristic
31C2×#14519735C2212yes—
32C2×#14519734C2212yes—
33C2×#14519734C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35C2×C4⋊C4×D61C2212yes—
36C2×C42×D61C2212yes—
37C2×C42×D61C2211yescharacteristic
38C2×C42×D61C2211yescharacteristic
39#16839666C2214yes—
40#16839662C2214yes—
41#16839657C2214yes—
42#16839657C2214yes—
43#16839656C2214yes—
44#16839652C2214yes—
45#16839652C2214yes—
46#16839650C2214yes—
47#16839647C2214yes—
48#16839645C2214yes—
49#16839643C2214yes—
50#16839643C2214yes—
51#16839640C2214yes—
52#16839638C2214yes—
53#16839633C2214yes—
54#16839633C2214yes—
55#16839631C2212yes—
56#16839630C2212yes—
57#16839629C2212yes—
58#16839628C2212yes—
59#16839627C2212yes—
60#16839626C2212yes—
61#16839625C2212yes—
62#16839624C2212yes—
63#16839622C2212yes—
64#16839621C2212yes—
65#16839619C2212yes—
66#16839619C2212yes—
67C4⋊C4×Dic61C2212yes—
68C4⋊C4×Dic61C2212yes—
69C4×#11758196C2212yes—
70C4×#11758196C2212yes—
71C4×C4⋊Dic61C2211yescharacteristic
72C4×C4⋊Dic61C2211yescharacteristic
73#16839613C2212yes—
74C4×#11758198C2212yes—
75C4×#11758198C2212yes—
76C4×C22⋊Dic61C2212yes—
77#16839609C2212yes—
78#16839608C2212yes—
79#16839608C2212yes—
80#16839607C2212yes—
81#95×D61C2212yes—
82C42×Dic61C2212yes—
83C2×#117×C61C2212yes—
84C22×C42×C61C2211yescharacteristic
85C61×#384C2212yes—
86C61×#382C2212yes—
87C61×#380C2212yes—
88C61×#380C2212yes—
89C4×C4⋊C4×C61C2211yescharacteristic
90C4×C4⋊C4×C61C2211yescharacteristic
91C4×C4⋊C4×C61C2212yes—
92C2×#11758222—28no—
93C2×#11758222C2×C418yes—
94C22×Dic122C2311yescharacteristic
95C22×D244C2311yescharacteristic
96C22×C22⋊D61C2311yescharacteristic
97C22×C22⋊D61C2311yescharacteristic
98C22×C4×D61C2311yescharacteristic
99C22×C4×D61C2311yescharacteristic
100C22×C4×D61C2311yescharacteristic
101C22×C4×D61C2314yes—
102C22×C4×D61C2311yescharacteristic
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105C4×Dic122C2×C418yescomplemented
106C4×Dic122C2×C418yescomplemented
107C4×D244C2×C418yes—
108C4×D244C2×C418yes—
109C4×C22⋊D61C2×C418yes—
110C4×C22⋊D61C2×C418yes—
111C4×C22⋊D61C2×C418yescomplemented
112C4×C22⋊D61C2×C418yescomplemented
113#14519736C2×C418yescomplemented
114#14519735—28no—
115#14519734—44no—
116#14519734C2×C418yes—
117#14519734C2×C418yescomplemented
118C2×C4⋊Dic61C2312yes—
119C2×C4⋊Dic61C2312yes—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196C2314yes—
123C2×#11758196C2314yes—
124C2×#11758196C2314yes—
125C2×#11758196C2311yescharacteristic
126C2×#11758196C2311yescharacteristic
127C2×#11758196C2311yescharacteristic
128C2×#11758196C2311yescharacteristic
129C4⋊C4×D61—28no—
130C2×C22⋊Dic61C2314yes—
131C2×C22⋊Dic61C2311yescharacteristic
132C2×C22⋊Dic61C2311yescharacteristic
133C2×#11758198C2314yes—
134C2×#11758198C2314yes—
135C2×#11758198C2314yes—
136C2×#11758198C2311yescharacteristic
137C2×#11758198C2311yescharacteristic
138C2×#11758198C2311yescharacteristic
139C2×#11758198C2311yescharacteristic
140C2×C4×Dic61C2312yes—
141C2×C4×Dic61C2314yes—
142C2×C4×Dic61C2312yes—
143C2×C4×Dic61C2314yes—
144C2×C4×Dic61C2314yes—
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149C2×C4×Dic61C2311yescharacteristic
150C2×C4×Dic61C2311yescharacteristic
151C42×D61—44no—
152C42×D61C2×C418yes—
153C42×D61C2×C418yescomplemented
154#14519684C2312yes—
155#14519684C2314yes—
156#14519684C2312yes—
157#14519684C2314yes—
158#14519684C2314yes—
159#14519684C2314yes—
160#14519684C2314yes—
161#14519684C2314yes—
162#14519684C2314yes—
163#14519684C2314yes—
164#14519684C2314yes—
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168#117×C61—44no—
169C2×C4⋊C4×C61C2312yes—
170C2×C4⋊C4×C61C2312yes—
171C2×C4⋊C4×C61C2314yes—
172C2×C4⋊C4×C61C2314yes—
173C2×C22⋊C4×C61C2314yes—
174C2×C42×C61C2×C418yescomplemented
175C2×C42×C61C2312yes—
176C2×C42×C61C2312yes—
177C2×C42×C61C2311yescharacteristic
178C2×C42×C61C2311yescharacteristic
179C2×C42×C61C2311yescharacteristic
180C2×C42×C61C2311yescharacteristic
181#95×C61C2312yes—
182#95×C61C2312yes—
183#95×C61C2314yes—
184C24×C61C2411yescharacteristic
185C23×D61C2411yescharacteristic
186C23×D61C2411yescharacteristic
187C22×C4×C61—24no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—42no—
191C22×C4×C61C22×C414yes—
192C22×C4×C61C22×C414yes—
193C22×C4×C61C22×C414yes—
194C22×C4×C61C2414yes—
195C22×C4×C61C2414yes—
196C22×C4×C61C2411yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61C22×C414yes—
205C2×C22⋊D61C22×C414yes—
206C22×Dic61C2414yes—
207C22×Dic61C2414yes—
208C22×Dic61C2411yescharacteristic
209C22×Dic61C2411yescharacteristic
210C22×Dic61C2411yescharacteristic
211C22×Dic61C2411yescharacteristic
212C22×Dic61C2411yescharacteristic
213C22×Dic61C2411yescharacteristic
214#11758222—232no—
215C2×D244—24no—
216C2×D244C22×C414yes—
217C2×C4×D61—24no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—28no—
223C2×C4×D61—42no—
224C2×C4×D61—42no—
225C2×C4×D61—44no—
226C2×C4×D61—44no—
227C2×C4×D61C22×C414yes—
228C2×C4×D61C22×C414yes—
229C2×C4×D61C22×C414yes—
230C2×C4×D61C22×C414yes—
231C2×C4×D61C22×C414yes—
232C2×C4×D61C22×C414yes—
233C2×C4×D61#4118yes—
234C2×Dic122—24no—
235C2×Dic122C22×C414yes—
236C4⋊C4×C61—24no—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—44no—
239C4⋊C4×C61—44no—
240C22⋊C4×C61—44no—
241C42×C61—24no—
242C42×C61—24no—
243C42×C61C22×C414yes—
244C42×C61C22×C414yes—
245C42×C61C22×C414yes—
246C42×C61C22×C414yes—
247C22⋊Dic61—44no—
248C22⋊Dic61C22×C414yes—
249C22⋊Dic61C22×C414yes—
250#11758198—28no—
251#11758198—44no—
252#11758198—44no—
253#11758198C22×C414yes—
254#11758198C22×C414yes—
255#11758198C22×C414yes—
256#11758198C22×C414yes—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61C22×C414yes—
260C4⋊Dic61C22×C414yes—
261#11758196—28no—
262#11758196—44no—
263#11758196—44no—
264#11758196C22×C414yes—
265#11758196C22×C414yes—
266#11758196C22×C414yes—
267#11758196C22×C414yes—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61—28no—
271C4×Dic61—44no—
272C4×Dic61—44no—
273C4×Dic61C22×C414yes—
274C4×Dic61C22×C414yes—
275C4×Dic61C22×C414yes—
276C4×Dic61C22×C414yes—
277C4×Dic61C22×C414yes—
278C4×Dic61C22×C414yes—
279C23×C61—22no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—22no—
283C23×C61C23×C412yes—
284C23×C61C2511yescharacteristic
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—22no—
292C22×D61C23×C412yes—
293C22×D61C23×C412yes—
294C22×D61C2×#4114yes—
295C2×C4×C61—22no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—28no—
301C2×C4×C61—28no—
302C2×C4×C61—24no—
303C2×C4×C61—24no—
304C2×C4×C61—24no—
305C2×C4×C61—24no—
306C2×C4×C61—24no—
307C2×C4×C61—24no—
308C2×C4×C61—44no—
309C2×C4×C61C23×C412yes—
310C2×C4×C61C23×C412yes—
311C2×C4×C61C23×C412yes—
312C2×C4×C61C23×C412yes—
313C2×C4×C61C23×C412yes—
314C2×C4×C61C23×C412yes—
315C2×C4×C61C2×#4114yes—
316C2×C4×C61H(5,𝔽2)12yes—
317C2×C4×C612−1+412yes—
318C22⋊D61—28no—
319C22⋊D61—28no—
320C2×Dic61—22no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—24no—
333C2×Dic61C23×C412yes—
334C2×Dic61C23×C412yes—
335C2×Dic61C23×C412yes—
336C2×Dic61C23×C412yes—
337C2×Dic61C23×C412yes—
338C2×Dic61C23×C412yes—
339C2×Dic61C2×#4114yes—
340D244—28no—
341C4×D61—28no—
342C4×D61—28no—
343C4×D61—28no—
344C4×D61—44no—
345C4×D61—44no—
346C4×D61—416no—
347C4×D61#117116yescomplemented
348Dic122—28no—
349#34060—611nomaximal, Sylow
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61C24×C411yescharacteristic
356C22×C61C22×#4112yes—
357C22×C61C2×H(5,𝔽2)11yescharacteristic
358C22×C61C2×2−1+411yescharacteristic
359C22×C61#58512yes—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—24no—
363C2×D61—24no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61C2×#11714yes—
370C4×C61—22no—
371C4×C61—22no—
372C4×C61—22no—
373C4×C61—22no—
374C4×C61—44no—
375C4×C61—44no—
376C4×C61C2×#11714yes—
377C4×C61#52014yes—
378Dic61—22no—
379Dic61—22no—
380Dic61—22no—
381Dic61—22no—
382Dic61—22no—
383Dic61—44no—
384Dic61—44no—
385Dic61C2×#11714yes—
386C2×C4×#41—611no—
387#2320—612no—
388#2319—612no—
389#2318—612no—
390#2318—612no—
391#2317—612no—
392#2314—612no—
393#2314—612no—
394#2311—612no—
395#2295—612no—
396#2293—612no—
397#2290—612no—
398#2290—612no—
399#2285—611no—
400#2285D6111yescharacteristic, complemented
401#2283—611no—
402#2283—611no—
403C4×#117—611no—
404C2×C4×C4⋊C4—611no—
405C2×C61—42no—
406C2×C61C22×#11711yescharacteristic
407C2×C61C2×#52011yescharacteristic
408C2×C61#342811yescharacteristic
409C2×C61#346012yes—
410C2×C61#346112yes—
411D61—24no—
412D61—42no—
413C22×#41—611no—
414C4×#41—6116no—
415C2×C4×Q8—611no—
416C2×C4×Q8—611no—
417C2×C4×D4—611no—
418C2×C4×D4—611no—
419C2×C4×D4—611no—
420C2×C4×D4—611no—
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×#117—611no—
424C2×#117—612no—
425C2×#117—611no—
426C2×#117—611no—
427C2×#117—612no—
428C2×#117C2×D6112yes—
429C22×C4⋊C4—612no—
430C22×C42—611no—
431C22×C42—611no—
432C22×C42—612no—
433C22×C42C2×D6111yescharacteristic
434#391—614no—
435#390—614no—
436#389—614no—
437#389—614no—
438#388—614no—
439#388—614no—
440#388—614no—
441#388—614no—
442#387—614no—
443#387—614no—
444#387—614no—
445#387—614no—
446#386—614no—
447#386—614no—
448#385—614no—
449#385—614no—
450#384—612no—
451#384C2×D6112yes—
452#383—612no—
453#383—612no—
454#382—612no—
455#382—612no—
456#382—612no—
457#382C2×D6112yes—
458#381—612no—
459#381—612no—
460#380—612no—
461#380—612no—
462#380—612no—
463#380—612no—
464#380C2×D6112yes—
465#380C2×D6112yes—
466C4×C4⋊C4—612no—
467C4×C4⋊C4—612no—
468C4×C4⋊C4—611no—
469C4×C4⋊C4—611no—
470C4×C4⋊C4—612no—
471C4×C4⋊C4—612no—
472C4×C4⋊C4—612no—
473C4×C4⋊C4C2×D6111yescharacteristic
474C4×C4⋊C4C2×D6111yescharacteristic
475C4×C4⋊C4C2×D6112yes—
476C4×C22⋊C4—612no—
477C4×C22⋊C4—612no—
478C4×C22⋊C4—612no—
479C4×C22⋊C4—612no—
480#376—612no—
481#376—612no—
482#376—612no—
483C2×#95—612no—
484C43—612no—
485C61#3406011yescharacteristic, complemented, Sylow
486C2×#41—618no—
487C2×#41—1228no—
488C22×Q8—611no—
489C22×D4—611no—
490C22×D4—611no—
491C22×D4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—614no—
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C23×C4C22×D6111yescharacteristic
502C4×Q8—618no—
503C4×Q8—618no—
504C4×D4—618no—
505C4×D4—618no—
506C4×D4—618no—
507C4×D4—618no—
508C4×D4—618no—
509C4×D4—618no—
510#117—44no—
511#117—618no—
512#117—618no—
513#117—618no—
514#117—1228no—
515#117—2444no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—612no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—612no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—1228no—
528C2×C4⋊C4C22×D6112yes—
529C2×C4⋊C4C22×D6112yes—
530C2×C4⋊C4C22×D6114yes—
531C2×C4⋊C4C22×D6114yes—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—614no—
539C2×C22⋊C4—614no—
540C2×C22⋊C4—614no—
541C2×C22⋊C4—614no—
542C2×C22⋊C4C22×D6114yes—
543C2×C42—611no—
544C2×C42—611no—
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—611no—
548C2×C42—611no—
549C2×C42—618no—
550C2×C42—618no—
551C2×C42—614no—
552C2×C42—612no—
553C2×C42—612no—
554C2×C42—614no—
555C2×C42—614no—
556C2×C42—2444no—
557C2×C42C4×D6118yescomplemented
558C2×C42C22×D6112yes—
559C2×C42C22×D6112yes—
560C2×C42C22×D6111yescharacteristic
561C2×C42C22×D6111yescharacteristic
562C2×C42C22×D6111yescharacteristic
563C2×C42C22×D6111yescharacteristic
564#95—612no—
565#95—614no—
566#95—612no—
567#95—614no—
568#95—614no—
569#95—614no—
570#95—614no—
571#95—614no—
572#95—614no—
573#95—614no—
574#95—614no—
575#95C22×D6112yes—
576#95C22×D6112yes—
577#95C22×D6114yes—
578C24—611no—
579C24—611no—
580C24C23×D6111yescharacteristic
581#41—12232no—
582C2×Q8—614no—
583C2×Q8—1224no—
584C2×D4—614no—
585C2×D4—614no—
586C2×D4—614no—
587C2×D4—1224no—
588C2×D4—1224no—
589C2×D4—1224no—
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—42no—
594C22×C4—611no—
595C22×C4—614no—
596C22×C4—618no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—614no—
603C22×C4—614no—
604C22×C4—614no—
605C22×C4—614no—
606C22×C4—614no—
607C22×C4—614no—
608C22×C4—614no—
609C22×C4—1228no—
610C22×C4—1224no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—2444no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2444no—
619C22×C4C2×C4×D6114yes—
620C22×C4C2×C4×D6114yes—
621C22×C4C2×C4×D6114yes—
622C22×C4C23×D6114yes—
623C22×C4C23×D6114yes—
624C22×C4C23×D6111yescharacteristic
625C22×C4C23×D6111yescharacteristic
626C22×C4C23×D6111yescharacteristic
627C22×C4C23×D6111yescharacteristic
628C22×C4C23×D6111yescharacteristic
629C22×C4C23×D6111yescharacteristic
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—614no—
635C4⋊C4—614no—
636C4⋊C4—614no—
637C4⋊C4—614no—
638C4⋊C4—614no—
639C4⋊C4—614no—
640C4⋊C4—1228no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—2444no—
644C4⋊C4—2444no—
645C22⋊C4—44no—
646C22⋊C4—614no—
647C22⋊C4—614no—
648C22⋊C4—614no—
649C22⋊C4—614no—
650C22⋊C4—614no—
651C22⋊C4—614no—
652C22⋊C4—1228no—
653C22⋊C4—2444no—
654C22⋊C4—2444no—
655C22⋊C4—2444no—
656C42—24no—
657C42—24no—
658C42—614no—
659C42—614no—
660C42—614no—
661C42—614no—
662C42—614no—
663C42—614no—
664C42—1228no—
665C42—1224no—
666C42—1224no—
667C42—2444no—
668C42—2444no—
669C42C2×C4×D6114yes—
670C42C2×C4×D6114yes—
671C42C2×C4×D6114yes—
672C42C2×C4×D6114yes—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—612no—
678C23—614no—
679C23—612no—
680C23—1221no—
681C23—1221no—
682C23—1222no—
683C23—1222no—
684C23—1221no—
685C23—1221no—
686C23—1222no—
687C23C22×C4×D6112yes—
688C23C24×D6111yescharacteristic
689Q8—1228no—
690D4—1228no—
691D4—1228no—
692D4—1228no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—44no—
707C2×C4—612no—
708C2×C4—614no—
709C2×C4—6116no—
710C2×C4—612no—
711C2×C4—612no—
712C2×C4—612no—
713C2×C4—612no—
714C2×C4—612no—
715C2×C4—1222no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1228no—
723C2×C4—1228no—
724C2×C4—1228no—
725C2×C4—1224no—
726C2×C4—1224no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—2444no—
732C2×C4—2444no—
733C2×C4—24416no—
734C2×C4C22×C4×D6112yes—
735C2×C4C22×C4×D6112yes—
736C2×C4C22×C4×D6112yes—
737C2×C4C22×C4×D6112yes—
738C2×C4C22×C4×D6112yes—
739C2×C4C22×C4×D6112yes—
740C2×C4#41×D6114yes—
741C2×C4#1451982212yes—
742C2×C4#1451982512yes—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—42no—
747C22—42no—
748C22—614no—
749C22—1224no—
750C22—1224no—
751C22—1222no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—2442no—
757C22—2442no—
758C22C23×C4×D6111yescharacteristic
759C22C2×#41×D6112yes—
760C22C2×#1451982211yescharacteristic
761C22C2×#1451982511yescharacteristic
762C22#1684059812yes—
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—44no—
768C4—44no—
769C4—614no—
770C4—1222no—
771C4—1222no—
772C4—1222no—
773C4—1222no—
774C4—1222no—
775C4—2444no—
776C4—2444no—
777C4#117×D6114yes—
778C4#1684024314yes—
779C2—42no—
780C2—1224no—
781C2—2442no—
782C2C2×#117×D6111yescharacteristic
783C2C2×#1684024311yescharacteristic
784C2#2145902011yescharacteristic
785C2#2145923312yes—
786C2#2145925012yes—
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC61×#2285C2
socle, cosocleC23×C61C25
prime radicalC22×#11758222C22
hypercenter#2285D61
hypocenterC61#34060
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #21448467C2semidirect
3. #21448461C2semidirect
4. #21448455C2semidirect
5. #21448454C2semidirect
6. #21448440C2semidirect
7. #21448427C2semidirect
8. #21448426C2semidirect
10. #21448295C2semidirect
11. #21448278C2semidirect
12. #21448260C2semidirect
13. #21448256C2semidirect
14. #21448223C2semidirect
15. #21448217C2semidirect
16. #21448215C2semidirect
17. C4×#14519735C2semidirect
18. C4×C4⋊C4×D61C2semidirect
19. C61×#2285C2semidirect
21. C4×#11758222C4semidirect
105. C4×Dic122C2×C4semidirect
106. C4×Dic122C2×C4semidirect
111. C4×C22⋊D61C2×C4semidirect
112. C4×C22⋊D61C2×C4semidirect
113. #14519736C2×C4semidirect
117. #14519734C2×C4semidirect
153. C42×D61C2×C4semidirect
174. C2×C42×C61C2×C4semidirect
347. C4×D61#117semidirect
400. #2285D61semidirect
485. C61#34060semidirect
557. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582222
#214484672
#214484612
#214484552
#214484542
#214484402
#214484272
#214484262
#214484082
#214482952
#214482782
#214482602
#214482562
#214482232
#214482172
#214482152
C4×#145197352
C4×C4⋊C4×D612
C61×#22852
#3406061