Finite Group Databasebeta

← #29840192

Subgroups — #29840192

Order 15616.

2470 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758222C211yesmaximal, characteristic
2#21448771C212yesmaximal, complemented
3#21448745C212yesmaximal, complemented
4#21448744C212yesmaximal, complemented
5C4⋊C4×C22⋊D61C212yesmaximal, complemented
6#21448699C212yesmaximal, complemented
7#21448675C212yesmaximal, complemented
8#21448672C212yesmaximal, complemented
9#21448646C212yesmaximal
10#21448467C212yesmaximal, complemented
11#21448455C212yesmaximal, complemented
12#21448453C212yesmaximal, complemented
13#21448225C211yesmaximal, characteristic, complemented
14#21448217C211yesmaximal, characteristic, complemented
15#21448212C211yesmaximal, characteristic, complemented
16#21448212C211yesmaximal, characteristic, complemented
17#382×D61C211yesmaximal, characteristic, complemented
18#21448177C212yesmaximal, complemented
19C2×C61×#382C211yesmaximal, characteristic, complemented
20C22×#11758222C2211yescharacteristic
21C4×#11758222C4116yescomplemented
22C2×C4×Dic122C2211yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×C4×C22⋊D61C2214yes—
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×#14519736C2211yescharacteristic
32C2×#14519735C2212yes—
33C2×#14519734C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35C2×C4⋊C4×D61C2212yes—
36C2×C42×D61C2211yescharacteristic
37C2×C42×D61C2211yescharacteristic
38#16839666C2214yes—
39#16839657C2214yes—
40#16839652C2214yes—
41#16839651C2214yes—
42#16839647C2214yes—
43#16839645C2214yes—
44#16839644C2214yes—
45#16839643C2214yes—
46#16839641C2214yes—
47#16839640C2214yes—
48#16839635C2214yes—
49#16839633C2214yes—
50#16839631C2212yes—
51#16839630C2212yes—
52#16839629C2212yes—
53#16839629C2212yes—
54#16839628C2211yescharacteristic
55#16839628C2211yescharacteristic
56#16839627C2212yes—
57#16839626C2212yes—
58#16839626C2212yes—
59#16839625C2212yes—
60#16839624C2212yes—
61#16839624C2212yes—
62#16839622C2212yes—
63#16839621C2212yes—
64#16839621C2212yes—
65#16839619C2212yes—
66#16839619C2212yes—
67C4⋊C4×Dic61C2212yes—
68C4⋊C4×Dic61C2212yes—
69C4×C4⋊Dic61C2212yes—
70#16839613C2212yes—
71#16839613C2212yes—
72#16839613C2214yes—
73C4×C22⋊Dic61C2212yes—
74C4×C22⋊Dic61C2214yes—
75#16839609C2212yes—
76#16839609C2212yes—
77#16839609C2214yes—
78#16839608C2212yes—
79#16839607C2212yes—
80#16839607C2212yes—
81#95×D61C2212yes—
82#95×D61C2212yes—
83C22×C4⋊C4×C61C2212yes—
84C22×C42×C61C2211yescharacteristic
85C61×#382C2212yes—
86C61×#382C2211yescharacteristic
87C61×#382C2211yescharacteristic
88C61×#382C2212yes—
89C61×#382C2212yes—
90C2×#95×C61C2212yes—
91C2×#95×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×D61C2311yescharacteristic
102C22×C4×D61C2314yes—
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105C4×Dic122C2×C418yescomplemented
106C4×Dic122C2×C418yescomplemented
107C4×D244C2×C418yescomplemented
108C4×D244C2×C418yescomplemented
109C4×C22⋊D61—216no—
110C4×C22⋊D61C2×C418yes—
111C4×C22⋊D61C2×C418yes—
112C4×C22⋊D61C2×C418yescomplemented
113C4×C22⋊D61C2×C418yescomplemented
114#14519736C2×C418yescomplemented
115#14519735—44no—
116#14519734C2×C418yescomplemented
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—44no—
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×Dic61C2314yes—
141C2×C4×Dic61C2314yes—
142C2×C4×Dic61C2314yes—
143C2×C4×Dic61C2314yes—
144C2×C4×Dic61C2311yescharacteristic
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149C2×C4×Dic61C2311yescharacteristic
150C42×D61C2×C418yescomplemented
151C42×D61C2×C418yescomplemented
152#14519684C2312yes—
153#14519684C2312yes—
154#14519684C2314yes—
155#14519684C2314yes—
156#14519684C2312yes—
157#14519684C2314yes—
158#14519684C2312yes—
159#14519684C2314yes—
160#14519684C2314yes—
161#14519684C2314yes—
162#14519684C2314yes—
163#14519684C2314yes—
164C23×C4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2314yes—
167C23×C4×C61C2311yescharacteristic
168C2×C4⋊C4×C61—44no—
169C2×C4⋊C4×C61C2312yes—
170C2×C4⋊C4×C61C2312yes—
171C2×C4⋊C4×C61C2314yes—
172C2×C42×C61C2×C418yescomplemented
173C2×C42×C61C2311yescharacteristic
174C2×C42×C61C2311yescharacteristic
175C2×C42×C61C2311yescharacteristic
176C2×C42×C61C2311yescharacteristic
177#95×C61C2312yes—
178#95×C61C2312yes—
179#95×C61C2312yes—
180#95×C61C2312yes—
181#95×C61C2314yes—
182#95×C61C2314yes—
183C24×C61C2411yescharacteristic
184C23×D61C2411yescharacteristic
185C23×D61C2411yescharacteristic
186C22×C4×C61—24no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—28no—
190C22×C4×C61—42no—
191C22×C4×C61—44no—
192C22×C4×C61—44no—
193C22×C4×C61C22×C414yes—
194C22×C4×C61C22×C414yes—
195C22×C4×C61C22×C414yes—
196C22×C4×C61C2414yes—
197C22×C4×C61C2414yes—
198C22×C4×C61C2411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C22×C4×C61C2411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61C22×C414yes—
206C2×C22⋊D61C22×C414yes—
207C2×C22⋊D61#4118yes—
208C22×Dic61C2414yes—
209C22×Dic61C2414yes—
210C22×Dic61C2411yescharacteristic
211C22×Dic61C2411yescharacteristic
212C22×Dic61C2411yescharacteristic
213C22×Dic61C2411yescharacteristic
214C22×Dic61C2411yescharacteristic
215C22×Dic61C2411yescharacteristic
216#11758222—232no—
217C2×D244—24no—
218C2×D244C22×C414yes—
219C2×C4×D61—24no—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—24no—
225C2×C4×D61—28no—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×C4×D61C22×C414yes—
231C2×C4×D61C22×C414yes—
232C2×C4×D61C22×C414yes—
233C2×C4×D61C22×C414yes—
234C2×C4×D61C22×C414yes—
235C2×C4×D61C22×C414yes—
236C2×Dic122—24no—
237C2×Dic122C22×C414yes—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—44no—
241C42×C61C22×C414yes—
242C42×C61C22×C414yes—
243C42×C61C22×C414yes—
244C42×C61C22×C414yes—
245C22⋊Dic61—28no—
246C22⋊Dic61C22×C414yes—
247C22⋊Dic61C22×C414yes—
248#11758198—28no—
249#11758198—44no—
250#11758198—44no—
251#11758198C22×C414yes—
252#11758198C22×C414yes—
253#11758198C22×C414yes—
254#11758198C22×C414yes—
255C4⋊Dic61—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61C22×C414yes—
258C4⋊Dic61C22×C414yes—
259#11758196—28no—
260#11758196—44no—
261#11758196—44no—
262#11758196C22×C414yes—
263#11758196C22×C414yes—
264#11758196C22×C414yes—
265#11758196C22×C414yes—
266C4×Dic61—28no—
267C4×Dic61—44no—
268C4×Dic61—44no—
269C4×Dic61—44no—
270C4×Dic61C22×C414yes—
271C4×Dic61C22×C414yes—
272C4×Dic61C22×C414yes—
273C4×Dic61C22×C414yes—
274C4×Dic61C22×C414yes—
275C4×Dic61C22×C414yes—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—22no—
279C23×C61C23×C412yes—
280C23×C61C2×#4114yes—
281C23×C61C2511yescharacteristic
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—22no—
289C22×D61C23×C412yes—
290C22×D61C23×C412yes—
291C22×D61C2×#4114yes—
292C2×C4×C61—28no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—28no—
300C2×C4×C61—24no—
301C2×C4×C61—24no—
302C2×C4×C61—24no—
303C2×C4×C61—24no—
304C2×C4×C61—24no—
305C2×C4×C61—24no—
306C2×C4×C61—44no—
307C2×C4×C61—88no—
308C2×C4×C61C23×C412yes—
309C2×C4×C61C23×C412yes—
310C2×C4×C61C23×C412yes—
311C2×C4×C61C23×C412yes—
312C2×C4×C61C23×C412yes—
313C2×C4×C61C23×C412yes—
314C2×C4×C61H(5,𝔽2)12yes—
315C2×C4×C612−1+412yes—
316C22⋊D61—28no—
317C22⋊D61#117116yescomplemented
318C2×Dic61—22no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—24no—
326C2×Dic61—24no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—24no—
331C2×Dic61C23×C412yes—
332C2×Dic61C23×C412yes—
333C2×Dic61C23×C412yes—
334C2×Dic61C23×C412yes—
335C2×Dic61C23×C412yes—
336C2×Dic61C23×C412yes—
337C2×Dic61C2×#4114yes—
338D244—28no—
339C4×D61—28no—
340C4×D61—28no—
341C4×D61—28no—
342C4×D61—28no—
343C4×D61—44no—
344C4×D61—44no—
345C4×D61—88no—
346Dic122—28no—
347#34191—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—24no—
351C22×C61—24no—
352C22×C61C2×#11714yes—
353C22×C61C24×C411yescharacteristic
354C22×C61C22×#4112yes—
355C22×C61C2×H(5,𝔽2)11yescharacteristic
356C22×C61C2×2−1+411yescharacteristic
357C22×C61#58512yes—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—24no—
361C2×D61—24no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61C2×#11714yes—
368C4×C61—22no—
369C4×C61—22no—
370C4×C61—22no—
371C4×C61—22no—
372C4×C61—22no—
373C4×C61—44no—
374C4×C61—44no—
375C4×C61#52014yes—
376Dic61—22no—
377Dic61—22no—
378Dic61—22no—
379Dic61—22no—
380Dic61—22no—
381Dic61—44no—
382Dic61—44no—
383Dic61C2×#11714yes—
384C2×C4×#41—611no—
385#2355—612no—
386#2352—612no—
387#2352—612no—
388D4×C4⋊C4—612no—
389#2346—612no—
390#2343—612no—
391#2343—612no—
392#2339—612no—
393#2320—612no—
394#2318—612no—
395#2318—612no—
396#2285—611no—
397#2283—611no—
398#2283—611no—
399#2283—611no—
400C2×#382—611no—
401C2×#382D6111yescharacteristic, complemented
402#2275—612no—
403C2×C61—24no—
404C2×C61C22×#11711yescharacteristic
405C2×C61C2×#52011yescharacteristic
406C2×C61#342811yescharacteristic
407C2×C61#351412yes—
408C2×C61#351512yes—
409D61—24no—
410D61—42no—
411C22×#41—611no—
412C4×#41—6116no—
413C2×C4×Q8—611no—
414C2×C4×Q8—611no—
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×C4×D4—611no—
419C2×C4×D4—614no—
420C2×C4×D4—611no—
421C2×C4×D4—611no—
422C2×#117—611no—
423C2×#117—612no—
424C2×#117—611no—
425C2×#117—611no—
426C22×C4⋊C4—612no—
427C22×C4⋊C4C2×D6112yes—
428C22×C42—611no—
429C22×C42—611no—
430C22×C42C2×D6111yescharacteristic
431#391—614no—
432#389—614no—
433#388—614no—
434#388—614no—
435#387—614no—
436#387—614no—
437#387—614no—
438#387—614no—
439#386—614no—
440#386—614no—
441#385—614no—
442#385—614no—
443#384—612no—
444#383—612no—
445#383—612no—
446#383—612no—
447#382—612no—
448#382—611no—
449#382—611no—
450#382—612no—
451#382—612no—
452#382C2×D6112yes—
453#382C2×D6112yes—
454#382C2×D6112yes—
455#382C2×D6111yescharacteristic
456#382C2×D6111yescharacteristic
457#381—612no—
458#381—612no—
459#381—612no—
460#380—612no—
461#380—612no—
462#380—612no—
463#380—612no—
464#380—612no—
465C4×C4⋊C4—612no—
466C4×C4⋊C4—612no—
467C4×C4⋊C4—612no—
468C4×C4⋊C4—612no—
469C4×C4⋊C4—612no—
470C4×C4⋊C4—614no—
471C4×C22⋊C4—612no—
472C4×C22⋊C4—614no—
473C4×C22⋊C4—612no—
474C4×C22⋊C4—612no—
475C4×C22⋊C4—614no—
476#376—612no—
477#376—612no—
478#376—612no—
479C2×#95—612no—
480C2×#95—612no—
481C2×#95C2×D6112yes—
482C2×#95C2×D6112yes—
483C61#3419111yescharacteristic, complemented, Sylow
484C2×#41—618no—
485C2×#41—1228no—
486C22×Q8—611no—
487C22×D4—611no—
488C22×D4—611no—
489C22×D4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—614no—
497C23×C4C22×D6111yescharacteristic
498C23×C4C22×D6111yescharacteristic
499C23×C4C22×D6114yes—
500C23×C4C22×D6111yescharacteristic
501C4×Q8—618no—
502C4×Q8—618no—
503C4×D4—618no—
504C4×D4—618no—
505C4×D4—618no—
506C4×D4—618no—
507C4×D4—618no—
508C4×D4—618no—
509C4×D4—12216no—
510#117—618no—
511#117—618no—
512#117—618no—
513#117—2444no—
514C2×C4⋊C4—44no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—612no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—612no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—2444no—
527C2×C4⋊C4C22×D6112yes—
528C2×C4⋊C4C22×D6112yes—
529C2×C4⋊C4C22×D6114yes—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—614no—
537C2×C22⋊C4—614no—
538C2×C22⋊C4—614no—
539C2×C22⋊C4—614no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—611no—
543C2×C42—611no—
544C2×C42—611no—
545C2×C42—611no—
546C2×C42—618no—
547C2×C42—618no—
548C2×C42—614no—
549C2×C42—614no—
550C2×C42—614no—
551C2×C42—614no—
552C2×C42C4×D6118yescomplemented
553C2×C42C22×D6111yescharacteristic
554C2×C42C22×D6111yescharacteristic
555C2×C42C22×D6111yescharacteristic
556C2×C42C22×D6111yescharacteristic
557#95—612no—
558#95—612no—
559#95—614no—
560#95—614no—
561#95—612no—
562#95—614no—
563#95—612no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95—614no—
568#95—614no—
569#95C22×D6112yes—
570#95C22×D6112yes—
571#95C22×D6112yes—
572#95C22×D6112yes—
573#95C22×D6114yes—
574#95C22×D6114yes—
575C24—611no—
576C24—611no—
577C24C23×D6111yescharacteristic
578#41—12232no—
579C2×Q8—614no—
580C2×Q8—1224no—
581C2×D4—614no—
582C2×D4—618no—
583C2×D4—614no—
584C2×D4—614no—
585C2×D4—1224no—
586C2×D4—1224no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—614no—
601C22×C4—614no—
602C22×C4—614no—
603C22×C4—614no—
604C22×C4—614no—
605C22×C4—614no—
606C22×C4—614no—
607C22×C4—614no—
608C22×C4—1224no—
609C22×C4—1224no—
610C22×C4—1228no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—2444no—
616C22×C4—2444no—
617C22×C4—2442no—
618C22×C4—2442no—
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—614no—
634C4⋊C4—614no—
635C4⋊C4—614no—
636C4⋊C4—614no—
637C4⋊C4—614no—
638C4⋊C4—614no—
639C4⋊C4—1228no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—2444no—
643C4⋊C4—2444no—
644C22⋊C4—614no—
645C22⋊C4—614no—
646C22⋊C4—614no—
647C22⋊C4—614no—
648C22⋊C4—614no—
649C22⋊C4—614no—
650C22⋊C4—1228no—
651C22⋊C4—1228no—
652C22⋊C4—2444no—
653C22⋊C4—2444no—
654C42—614no—
655C42—614no—
656C42—614no—
657C42—614no—
658C42—614no—
659C42—614no—
660C42—1228no—
661C42—2444no—
662C42—2444no—
663C42—2444no—
664C42C2×C4×D6114yes—
665C42C2×C4×D6114yes—
666C42C2×C4×D6114yes—
667C42C2×C4×D6114yes—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—612no—
672C23—614no—
673C23—612no—
674C23—1221no—
675C23—1221no—
676C23—1222no—
677C23—1222no—
678C23—1221no—
679C23—1221no—
680C23—1222no—
681C23C22×C4×D6112yes—
682C23#41×D6114yes—
683C23C24×D6111yescharacteristic
684Q8—1228no—
685D4—6116no—
686D4—1228no—
687D4—1228no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—44no—
703C2×C4—88no—
704C2×C4—612no—
705C2×C4—614no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—612no—
711C2×C4—1228no—
712C2×C4—1228no—
713C2×C4—1222no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1228no—
721C2×C4—1228no—
722C2×C4—1224no—
723C2×C4—1224no—
724C2×C4—1224no—
725C2×C4—1224no—
726C2×C4—1224no—
727C2×C4—1224no—
728C2×C4—4888no—
729C2×C4—2444no—
730C2×C4—2444no—
731C2×C4C22×C4×D6112yes—
732C2×C4C22×C4×D6112yes—
733C2×C4C22×C4×D6112yes—
734C2×C4C22×C4×D6112yes—
735C2×C4C22×C4×D6112yes—
736C2×C4C22×C4×D6112yes—
737C2×C4#1451982212yes—
738C2×C4#1451982512yes—
739C22—24no—
740C22—22no—
741C22—22no—
742C22—24no—
743C22—614no—
744C22—1224no—
745C22—1222no—
746C22—1222no—
747C22—1224no—
748C22—1222no—
749C22—1222no—
750C22—1222no—
751C22—2442no—
752C22—2442no—
753C22#117×D6114yes—
754C22C23×C4×D6111yescharacteristic
755C22C2×#41×D6112yes—
756C22C2×#1451982211yescharacteristic
757C22C2×#1451982511yescharacteristic
758C22#1684059812yes—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—44no—
765C4—44no—
766C4—614no—
767C4—1222no—
768C4—1222no—
769C4—1222no—
770C4—1222no—
771C4—1222no—
772C4—2444no—
773C4—2444no—
774C4#1684024314yes—
775C2—24no—
776C2—1224no—
777C2—2442no—
778C2C2×#117×D6111yescharacteristic
779C2C2×#1684024311yescharacteristic
780C2#2145902011yescharacteristic
781C2#2145977412yes—
782C2#2145979112yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC2×C61×#382C2
socle, cosocleC23×C61C25
prime radicalC22×#11758222C22
hypercenterC2×#382D61
hypocenterC61#34191
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #21448771C2semidirect
3. #21448745C2semidirect
4. #21448744C2semidirect
5. C4⋊C4×C22⋊D61C2semidirect
6. #21448699C2semidirect
7. #21448675C2semidirect
8. #21448672C2semidirect
10. #21448467C2semidirect
11. #21448455C2semidirect
12. #21448453C2semidirect
13. #21448225C2semidirect
14. #21448217C2semidirect
15. #21448212C2semidirect
16. #21448212C2semidirect
17. #382×D61C2semidirect
18. #21448177C2semidirect
19. C2×C61×#382C2semidirect
21. C4×#11758222C4semidirect
105. C4×Dic122C2×C4semidirect
106. C4×Dic122C2×C4semidirect
107. C4×D244C2×C4semidirect
108. C4×D244C2×C4semidirect
112. C4×C22⋊D61C2×C4semidirect
113. C4×C22⋊D61C2×C4semidirect
114. #14519736C2×C4semidirect
116. #14519734C2×C4semidirect
117. #14519734C2×C4semidirect
150. C42×D61C2×C4semidirect
151. C42×D61C2×C4semidirect
172. C2×C42×C61C2×C4semidirect
317. C22⋊D61#117semidirect
401. C2×#382D61semidirect
483. C61#34191semidirect
552. 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
#214487712
#214487452
#214487442
C4⋊C4×C22⋊D612
#214486992
#214486752
#214486722
#214486462
#214484672
#214484552
#214484532
#214482252
#214482172
#214482122
#382×D612
#214481772
C2×C61×#3822
#3419161