Finite Group Databasebeta

← C2×#21449642 #29847769

Subgroups — C2×#21449642 #29847769

Order 15616.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519755C211yesmaximal, characteristic, complemented
2C22×C4×D244C211yesmaximal, characteristic
3#21449642C2116yesmaximal, direct product factor
4C2×#16839704C211yesmaximal, characteristic, complemented
5C2×#16839696C211yesmaximal, characteristic, complemented
6C2×#16839684C211yesmaximal, characteristic, complemented
7C2×#16839675C211yesmaximal, characteristic, complemented
8C2×#16839668C211yesmaximal, characteristic, complemented
9C2×#16839640C211yesmaximal, characteristic
10C2×#16839640C211yesmaximal, characteristic
11C2×#16839636C211yesmaximal, characteristic, complemented
12C2×#16839633C211yesmaximal, characteristic, complemented
13C2×#16839633C211yesmaximal, characteristic, complemented
14C2×#16839621C211yesmaximal, characteristic, complemented
15C2×#95×D61C211yesmaximal, characteristic, complemented
16C2×C61×#387C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C2×#14519755—28no—
24C2×#14519755C2218yescomplemented
25C2×C4×D244—28no—
26C2×C4×D244C2218yes—
27C22×C4⋊Dic61C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41#16839704C2218yescomplemented
42#16839696C2218yescomplemented
43#16839684C2218yescomplemented
44#16839675C2218yescomplemented
45#16839668C2218yescomplemented
46#16839640C2218yes—
47#16839640C2218yes—
48#16839636C2218yescomplemented
49#16839633C2218yescomplemented
50#16839633C2218yescomplemented
51#16839621C2218yescomplemented
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60#95×D61C2218yescomplemented
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C42×C61C2211yescharacteristic
64C61×#387C2218yescomplemented
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C24×D61C2311yescharacteristic
71C22×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122—42no—
74C22×Dic122C2314yes—
75C22×D244—24no—
76C22×D244—24no—
77C22×D244Q818yescomplemented
78C22×D244C2314yes—
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C22×C4×D61—24no—
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—24no—
89C22×C4×D61—24no—
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61—42no—
93C22×C4×D61—42no—
94C22×C4×D61—42no—
95C22×C4×D61—42no—
96C22×C4×D61—42no—
97C22×C4×D61C2314yes—
98C22×C4×D61C2314yes—
99C22×C4×D61C2314yes—
100C22×C4×D61C2314yes—
101#14519755—232no—
102C4×D244—232no—
103C2×C4⋊Dic61—24no—
104C2×C4⋊Dic61—42no—
105C2×C4⋊Dic61C2314yes—
106C2×C4⋊Dic61C2314yes—
107C2×#11758196—24no—
108C2×#11758196—24no—
109C2×#11758196—42no—
110C2×#11758196—42no—
111C2×#11758196C2314yes—
112C2×#11758196C2314yes—
113C2×#11758196C2314yes—
114C2×#11758196C2314yes—
115C2×#11758198—24no—
116C2×#11758198—24no—
117C2×#11758198—24no—
118C2×#11758198—24no—
119C2×#11758198—42no—
120C2×#11758198—42no—
121C2×#11758198—42no—
122C2×#11758198D418yes—
123C2×#11758198C2314yes—
124C2×#11758198C2314yes—
125C2×#11758198C2314yes—
126C2×#11758198C2314yes—
127C2×#11758198C2314yes—
128C2×#11758198C2314yes—
129C2×#11758198C2314yes—
130C2×#11758198C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137#14519684C2314yes—
138#14519684C2314yes—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61—24no—
147C2×C4⋊C4×C61—24no—
148C2×C4⋊C4×C61C2314yes—
149C2×C4⋊C4×C61C2314yes—
150C2×C42×C61—24no—
151C2×C42×C61C2314yes—
152#95×C61C2314yes—
153#95×C61C2314yes—
154#95×C61C2314yes—
155#95×C61C2314yes—
156C24×C61C2411yescharacteristic
157C23×D61—22no—
158C23×D61—22no—
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61C2×D414yes—
168C23×D61C2×Q814yes—
169C23×D61C2×Q814yes—
170C23×D61#4114yes—
171C23×D61C2412yes—
172C23×D61C2412yes—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61C2×D414yes—
192C22×C4×C61C2×Q814yes—
193C22×C4×C61#4114yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61C2×D414yes—
218C22×Dic61#4114yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C2×D244—232no—
226C2×D244—28no—
227C2×D244—28no—
228C2×D244C2×Q8116yescomplemented
229C2×C4×D61—28no—
230C2×C4×D61—28no—
231C2×C4×D61—28no—
232C2×C4×D61—28no—
233C2×C4×D61—28no—
234C2×C4×D61—28no—
235C2×C4×D61—28no—
236C2×C4×D61—44no—
237C2×C4×D61—44no—
238C2×C4×D61—44no—
239C2×C4×D61—44no—
240C2×C4×D61—44no—
241C2×C4×D61—416no—
242C2×C4×D61—416no—
243C2×C4×D61—416no—
244C2×C4×D61—416no—
245C2×Dic122—28no—
246C2×Dic122—28no—
247C2×Dic122—44no—
248C2×Dic122—416no—
249C4⋊C4×C61—28no—
250C4⋊C4×C61—28no—
251C42×C61—28no—
252#11758198—28no—
253#11758198—28no—
254#11758198—28no—
255#11758198—28no—
256#11758198—44no—
257#11758198—44no—
258#11758198—44no—
259#11758198C2×D4116yes—
260C4⋊Dic61—28no—
261C4⋊Dic61—44no—
262#11758196—28no—
263#11758196—28no—
264#11758196—44no—
265#11758196—44no—
266C23×C61C22×D412yes—
267C23×C61C22×Q812yes—
268C23×C61C2×#4112yes—
269C23×C61C2×#4112yes—
270C23×C61C2×#4112yes—
271C23×C61H(5,𝔽2)12yes—
272C23×C61H(5,𝔽2)12yes—
273C23×C61C2511yescharacteristic
274C22×D61—28no—
275C22×D61—28no—
276C22×D61—28no—
277C22×D61—28no—
278C22×D61—28no—
279C22×D61—28no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—28no—
285C22×D61—28no—
286C22×D61—28no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—44no—
294C22×D61—44no—
295C22×D61—44no—
296C22×D61—44no—
297C22×D61C22⋊Q8116yes—
298C22×D61C22×D414yes—
299C22×D61C22×Q814yes—
300C22×D61C22×Q814yes—
301C22×D61C2×#4114yes—
302C2×C4×C61—28no—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—22no—
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×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—44no—
324C2×C4×C61—44no—
325C2×C4×C61—44no—
326C2×C4×C61—44no—
327C2×C4×C61C22×D414yes—
328C2×C4×C61C22×Q814yes—
329C2×C4×C61C2×#4114yes—
330C2×Dic61—28no—
331C2×Dic61—28no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—44no—
349C2×Dic61—44no—
350C2×Dic61—44no—
351C2×Dic61—44no—
352C2×Dic61C22×D414yes—
353C2×Dic61C2×#4114yes—
354D244—232no—
355C4×D61—416no—
356C4×D61—416no—
357C4×D61—416no—
358C4×D61—416no—
359Dic122—416no—
360C2×#2450—611nomaximal, Sylow
361C22×C61C2×C22⋊Q814yes—
362C22×C61#52914yes—
363C22×C61#53814yes—
364C22×C61#54614yes—
365C22×C61#54614yes—
366C22×C61#55414yes—
367C22×C61#55414yes—
368C22×C61C23×D411yescharacteristic
369C22×C61C23×Q811yescharacteristic
370C22×C61C22×#4111yescharacteristic
371C22×C61C22×#4111yescharacteristic
372C22×C61C22×#4111yescharacteristic
373C22×C61C2×H(5,𝔽2)11yescharacteristic
374C22×C61C2×H(5,𝔽2)11yescharacteristic
375C2×D61—24no—
376C2×D61—24no—
377C2×D61—24no—
378C2×D61—24no—
379C2×D61—24no—
380C2×D61—24no—
381C2×D61—232no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—24no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—416no—
390C2×D61C2×C22⋊Q818yes—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—24no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61—42no—
397C4×C61—42no—
398Dic61—24no—
399Dic61—24no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61—42no—
404C22×C22⋊Q8—611no—
405C22×C4×D4—611no—
406#2450—6116no—
407C2×#400—611no—
408C2×#398—611no—
409C2×#396—611no—
410C2×#393—611no—
411C2×#391—611no—
412C2×#387D6111yescharacteristic, complemented
413C2×#386—611no—
414C2×#386—611no—
415C2×#385—611no—
416C2×#385—611no—
417C2×#385—611no—
418C2×#380—611no—
419C22×#95—611no—
420C2×C61#245018yescomplemented
421C2×C61C22×C22⋊Q811yescharacteristic
422C2×C61C2×#52911yescharacteristic
423C2×C61C2×#53811yescharacteristic
424C2×C61C2×#54611yescharacteristic
425C2×C61C2×#54611yescharacteristic
426C2×C61C2×#55411yescharacteristic
427C2×C61C2×#55411yescharacteristic
428D61—28no—
429D61—44no—
430C23×Q8—611no—
431C23×D4—611no—
432C24×C4—611no—
433C24×C4—611no—
434C24×C4—611no—
435C24×C4—611no—
436C2×C22⋊Q8—618no—
437C2×C22⋊Q8—1228no—
438C2×C4×D4—618no—
439C2×C4×D4—1228no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—611no—
446C22×C4⋊C4C2×D6111yescharacteristic
447C22×C4⋊C4C2×D6111yescharacteristic
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4—611no—
456C22×C42C2×D6111yescharacteristic
457#400—618no—
458#398—618no—
459#396—618no—
460#393—618no—
461#391—618no—
462#387C2×D6118yescomplemented
463#386—618no—
464#386—618no—
465#385—618no—
466#385—618no—
467#385—618no—
468#380—618no—
469C2×#95—611no—
470C2×#95—611no—
471C2×#95—611no—
472C2×#95—611no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—618no—
478C2×#95C2×D6111yescharacteristic
479C2×#95C2×D6111yescharacteristic
480C2×#95C2×D6111yescharacteristic
481C2×#95C2×D6111yescharacteristic
482C61C2×#245011yescharacteristic, complemented, Sylow
483C25—611no—
484C25—611no—
485C22×Q8—614no—
486C22×Q8—1224no—
487C22×Q8—1224no—
488C22×Q8—2442no—
489C22×D4—618no—
490C22×D4—614no—
491C22×D4—1224no—
492C22×D4—1224no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—614no—
500C23×C4—614no—
501C23×C4—614no—
502C23×C4—614no—
503C23×C4—1224no—
504C23×C4—1224no—
505C23×C4—1224no—
506C23×C4—1224no—
507C23×C4—1224no—
508C23×C4—1224no—
509C23×C4—1224no—
510C23×C4—2442no—
511C23×C4—2442no—
512C23×C4—2442no—
513C23×C4—2442no—
514C23×C4—2442no—
515C23×C4C22×D6111yescharacteristic
516C23×C4C22×D6111yescharacteristic
517C23×C4C22×D6111yescharacteristic
518C23×C4C22×D6111yescharacteristic
519C23×C4C22×D6111yescharacteristic
520C23×C4C22×D6111yescharacteristic
521C23×C4C22×D6111yescharacteristic
522C22⋊Q8—12232no—
523C4×D4—12232no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—614no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—614no—
531C2×C4⋊C4—614no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—1224no—
535C2×C4⋊C4—2442no—
536C2×C4⋊C4—2442no—
537C2×C4⋊C4—2442no—
538C2×C4⋊C4C22×D6114yes—
539C2×C4⋊C4C22×D6114yes—
540C2×C22⋊C4—618no—
541C2×C22⋊C4—614no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—614no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4—614no—
549C2×C22⋊C4—1224no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—1224no—
552C2×C22⋊C4—1224no—
553C2×C22⋊C4—2442no—
554C2×C22⋊C4—2442no—
555C2×C22⋊C4—2442no—
556C2×C42—24no—
557C2×C42C22×D6114yes—
558#95—614no—
559#95—614no—
560#95—614no—
561#95—614no—
562#95—614no—
563#95—614no—
564#95—614no—
565#95—614no—
566#95C22×D6114yes—
567#95C22×D6114yes—
568#95C22×D6114yes—
569#95C22×D6114yes—
570C24—614no—
571C24—614no—
572C24—614no—
573C24—612no—
574C24—614no—
575C24—612no—
576C24—1222no—
577C24—1222no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24—1222no—
585C24—1222no—
586C24C23×D6111yescharacteristic
587C2×Q8—1228no—
588C2×Q8—1228no—
589C2×Q8—2444no—
590C2×Q8—24416no—
591C2×D4—6116no—
592C2×D4—1228no—
593C2×D4—12232no—
594C2×D4—1228no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—1228no—
622C22×C4—1228no—
623C22×C4—1228no—
624C22×C4—1228no—
625C22×C4—1228no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1228no—
643C22×C4—1228no—
644C22×C4—2444no—
645C22×C4—2444no—
646C22×C4—2444no—
647C22×C4—2444no—
648C22×C4—2444no—
649C22×C4—24416no—
650C22×C4—24416no—
651C22×C4—24416no—
652C22×C4—24416no—
653C22×C4#1175822214yes—
654C22×C4D4×D6114yes—
655C22×C4Q8×D6114yes—
656C22×C4C23×D6112yes—
657C22×C4C23×D6112yes—
658C22×C4C23×D6112yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6112yes—
661C22×C4C23×D6112yes—
662C22×C4C23×D6112yes—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—1228no—
666C4⋊C4—1228no—
667C4⋊C4—1228no—
668C4⋊C4—2444no—
669C4⋊C4—2444no—
670C4⋊C4—2444no—
671C22⋊C4—6116no—
672C22⋊C4—1228no—
673C22⋊C4—1228no—
674C22⋊C4—1228no—
675C22⋊C4—1228no—
676C22⋊C4—2444no—
677C22⋊C4—2444no—
678C22⋊C4—2444no—
679C42—28no—
680C23—6116no—
681C23—614no—
682C23—614no—
683C23—614no—
684C23—614no—
685C23—1228no—
686C23—1228no—
687C23—1228no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1228no—
693C23—1228no—
694C23—1228no—
695C23—1228no—
696C23—1228no—
697C23—1228no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—2444no—
705C23—2444no—
706C23—2444no—
707C23—2444no—
708C23C2×D4×D6112yes—
709C23C2×Q8×D6112yes—
710C23#41×D6112yes—
711C23#41×D6112yes—
712C23C2×#1175822212yes—
713C23#1451982312yes—
714C23#1451982312yes—
715C23C24×D6111yescharacteristic
716Q8—24416no—
717D4—12232no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—614no—
744C2×C4—614no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1228no—
750C2×C4—1228no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—24416no—
764C2×C4—24416no—
765C2×C4—24416no—
766C2×C4—24416no—
767C2×C4—2444no—
768C2×C4—2444no—
769C2×C4—2444no—
770C2×C4—2444no—
771C2×C4C2×D4×D6114yes—
772C2×C4C2×Q8×D6114yes—
773C2×C4C2×#1175822214yes—
774C22—618no—
775C22—1224no—
776C22—1224no—
777C22—1224no—
778C22—1224no—
779C22—1224no—
780C22—12232no—
781C22—1224no—
782C22—1224no—
783C22—1224no—
784C22—1224no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—24416no—
789C22—2442no—
790C22C22⋊Q8×D6114yes—
791C22#1684029014yes—
792C22#1684035114yes—
793C22#1684040414yes—
794C22#1684040814yes—
795C22#1684046814yes—
796C22#1684047214yes—
797C22C22×D4×D6111yescharacteristic
798C22C22×Q8×D6111yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C2×#41×D6111yescharacteristic
801C22C22×#1175822211yescharacteristic
802C22C2×#1451982311yescharacteristic
803C22C2×#1451982311yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—1224no—
812C4—1224no—
813C4—2442no—
814C4—2442no—
815C4—2442no—
816C4—2442no—
817C2—1228no—
818C2—2444no—
819C2#2144964218yesdirect product factor
820C2C2×C22⋊Q8×D6111yescharacteristic
821C2C2×#1684029011yescharacteristic
822C2C2×#1684035111yescharacteristic
823C2C2×#1684040411yescharacteristic
824C2C2×#1684040811yescharacteristic
825C2C2×#1684046811yescharacteristic
826C2C2×#1684047211yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#387C2
socleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×#387D61
hypocenterC61C2×#2450
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#14519755C2semidirect
3. #21449642C2direct (N × H)
4. C2×#16839704C2semidirect
5. C2×#16839696C2semidirect
6. C2×#16839684C2semidirect
7. C2×#16839675C2semidirect
8. C2×#16839668C2semidirect
11. C2×#16839636C2semidirect
12. C2×#16839633C2semidirect
13. C2×#16839633C2semidirect
14. C2×#16839621C2semidirect
15. C2×#95×D61C2semidirect
16. C2×C61×#387C2semidirect
24. C2×#14519755C22semidirect
41. #16839704C22semidirect
42. #16839696C22semidirect
43. #16839684C22semidirect
44. #16839675C22semidirect
45. #16839668C22semidirect
48. #16839636C22semidirect
49. #16839633C22semidirect
50. #16839633C22semidirect
51. #16839621C22semidirect
60. #95×D61C22semidirect
64. C61×#387C22semidirect
77. C22×D244Q8semidirect
228. C2×D244C2×Q8semidirect
412. C2×#387D61semidirect
420. C2×C61#2450semidirect
462. #387C2×D61semidirect
482. C61C2×#2450semidirect
819. C2#21449642direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197552
C22×C4×D2442
#214496422
C2×#168397042
C2×#168396962
C2×#168396842
C2×#168396752
C2×#168396682
C2×#168396402
C2×#168396362
C2×#168396332
C2×#168396212
C2×#95×D612
C2×C61×#3872
C2×#245061