Finite Group Databasebeta

← C2×#21448693 #29839255

Subgroups — C2×#21448693 #29839255

Order 15616.

3094 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D61C211yesmaximal, characteristic
2#21448693C2116yesmaximal, direct product factor
3C2×#16839659C211yesmaximal, characteristic, complemented
4C2×#16839657C211yesmaximal, characteristic, complemented
5C2×#16839648C211yesmaximal, characteristic, complemented
6C2×#16839647C211yesmaximal, characteristic, complemented
7C2×#16839645C211yesmaximal, characteristic, complemented
8C2×#16839621C211yesmaximal, characteristic
9C2×#16839621C211yesmaximal, characteristic
10C2×#16839619C211yesmaximal, characteristic
11C2×C4×#11758196C211yesmaximal, characteristic, complemented
12C2×#16839613C211yesmaximal, characteristic, complemented
13C2×C4×#11758198C211yesmaximal, characteristic
14C2×#16839609C211yesmaximal, characteristic
15C2×#16839609C211yesmaximal, characteristic
16C2×C61×#387C211yesmaximal, characteristic, complemented
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C2×C4⋊C4×D61C4116yescomplemented
29C2×C4⋊C4×D61C2218yes—
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839659C2218yescomplemented
40#16839657C2218yescomplemented
41#16839648C2218yescomplemented
42#16839647C2218yescomplemented
43#16839645C2218yescomplemented
44#16839621C2218yes—
45#16839621C2218yes—
46#16839619C2218yes—
47C4×#11758196C2218yescomplemented
48#16839613C2218yescomplemented
49C4×#11758198C2218yes—
50#16839609C2218yes—
51#16839609C2218yes—
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C42×C61C2211yescharacteristic
63C61×#387C2218yescomplemented
64C2×#95×C61C2211yescharacteristic
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C24×D61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C22×C4×D61—24no—
77C22×C4×D61—24no—
78C22×C4×D61—42no—
79C22×C4×D61—42no—
80C22×C4×D61—42no—
81C22×C4×D61—42no—
82C22×C4×D61C2×C418yes—
83C22×C4×D61C2×C418yes—
84C22×C4×D61C2×C418yes—
85C22×C4×D61C2314yes—
86C22×C4×D61C2314yes—
87C22×C4×D61C2314yes—
88C2×C4⋊Dic61—42no—
89C2×C4⋊Dic61C2×C418yes—
90C2×C4⋊Dic61C2314yes—
91C2×C4⋊Dic61C2314yes—
92C2×#11758196—24no—
93C2×#11758196—24no—
94C2×#11758196—42no—
95C2×#11758196—42no—
96C2×#11758196C2×C418yes—
97C2×#11758196C2×C418yes—
98C2×#11758196C2314yes—
99C2×#11758196C2314yes—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C4⋊C4×D61C2×C4164yescomplemented
105C2×#11758198—24no—
106C2×#11758198—24no—
107C2×#11758198—24no—
108C2×#11758198Q818yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×C4×Dic61—24no—
114C2×C4×Dic61—24no—
115C2×C4×Dic61—42no—
116C2×C4×Dic61—42no—
117C2×C4×Dic61—42no—
118C2×C4×Dic61C2314yes—
119C2×C4×Dic61C2314yes—
120C2×C4×Dic61C2314yes—
121C2×C4×Dic61C2314yes—
122C2×C4×Dic61C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61—42no—
139C2×C4⋊C4×C61C2×C418yes—
140C2×C4⋊C4×C61C2314yes—
141C2×C4⋊C4×C61C2314yes—
142C2×C42×C61—42no—
143C2×C42×C61C2314yes—
144#95×C61C2314yes—
145#95×C61C2314yes—
146#95×C61C2314yes—
147#95×C61C2314yes—
148C24×C61C2411yescharacteristic
149C23×D61—22no—
150C23×D61—22no—
151C23×D61—22no—
152C23×D61—22no—
153C23×D61C22×C414yes—
154C23×D61C2×Q814yes—
155C23×D61#4114yes—
156C23×D61C2412yes—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61C22×C414yes—
175C22×C4×C61C22×C414yes—
176C22×C4×C61C22×C414yes—
177C22×C4×C61C2×Q814yes—
178C22×C4×C61C2412yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61C22×C414yes—
201C22×Dic61C22×C414yes—
202C22×Dic61C22×C414yes—
203C22×Dic61C2×Q814yes—
204C22×Dic61#4114yes—
205C22×Dic61#4114yes—
206C22×Dic61C2412yes—
207C22×Dic61C2412yes—
208C22×Dic61C2412yes—
209C22×Dic61C2412yes—
210C22×Dic61C2412yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C2×C4×D61—232no—
214C2×C4×D61—28no—
215C2×C4×D61—28no—
216C2×C4×D61—416no—
217C2×C4×D61—416no—
218C2×C4×D61—44no—
219C2×C4×D61—44no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C2×C4×D61C22×C4116yes—
223C2×C4×D61C22×C4116yes—
224C2×C4×D61C22×C4116yes—
225C4⋊C4×C61—44no—
226C4⋊C4×C61C22×C4116yes—
227C42×C61—44no—
228#11758198—28no—
229#11758198—28no—
230#11758198—28no—
231#11758198C2×Q8116yes—
232C4⋊Dic61—44no—
233C4⋊Dic61C22×C4116yes—
234#11758196—28no—
235#11758196—28no—
236#11758196—44no—
237#11758196—44no—
238#11758196C22×C4116yes—
239#11758196C22×C4116yes—
240C4×Dic61—28no—
241C4×Dic61—28no—
242C4×Dic61—44no—
243C4×Dic61—44no—
244C4×Dic61—44no—
245C23×C61C23×C412yes—
246C23×C61C22×Q812yes—
247C23×C61C2×#4112yes—
248C23×C61C2×#4112yes—
249C23×C61C2×#4112yes—
250C23×C61H(5,𝔽2)12yes—
251C23×C61H(5,𝔽2)12yes—
252C23×C61C2511yescharacteristic
253C22×D61—28no—
254C22×D61—28no—
255C22×D61—28no—
256C22×D61—28no—
257C22×D61—28no—
258C22×D61—28no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61C4×Q8116yes—
264C22×D61C23×C414yes—
265C22×D61C22×Q814yes—
266C22×D61C2×#4114yes—
267C2×C4×C61—28no—
268C2×C4×C61—28no—
269C2×C4×C61—28no—
270C2×C4×C61—28no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—44no—
289C2×C4×C61—44no—
290C2×C4×C61—44no—
291C2×C4×C61C23×C414yes—
292C2×C4×C61C23×C414yes—
293C2×C4×C61C23×C414yes—
294C2×C4×C61C22×Q814yes—
295C2×Dic61—28no—
296C2×Dic61—28no—
297C2×Dic61—28no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—44no—
314C2×Dic61—44no—
315C2×Dic61—44no—
316C2×Dic61#117116yes—
317C2×Dic61C23×C414yes—
318C2×Dic61C23×C414yes—
319C2×Dic61C23×C414yes—
320C2×Dic61C22×Q814yes—
321C2×Dic61C2×#4114yes—
322C2×Dic61C2×#4114yes—
323C4×D61—232no—
324C4×D61—416no—
325C4×D61—416no—
326C2×#2345—611nomaximal, Sylow
327C22×C61C2×#11714yes—
328C22×C61C2×C4×Q814yes—
329C22×C61#51814yes—
330C22×C61#55314yes—
331C22×C61#55314yes—
332C22×C61#55414yes—
333C22×C61#55414yes—
334C22×C61C24×C411yescharacteristic
335C22×C61C23×Q811yescharacteristic
336C22×C61C22×#4111yescharacteristic
337C22×C61C22×#4111yescharacteristic
338C22×C61C22×#4111yescharacteristic
339C22×C61C2×H(5,𝔽2)11yescharacteristic
340C22×C61C2×H(5,𝔽2)11yescharacteristic
341C2×D61—232no—
342C2×D61—24no—
343C2×D61—24no—
344C2×D61—24no—
345C2×D61—24no—
346C2×D61—24no—
347C2×D61—24no—
348C2×D61C2×C4×Q818yes—
349C4×C61—24no—
350C4×C61—24no—
351C4×C61—24no—
352C4×C61—24no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61—42no—
356Dic61—24no—
357Dic61—24no—
358Dic61—24no—
359Dic61—42no—
360Dic61—42no—
361Dic61—42no—
362Dic61C2×#11718yes—
363C23×C4⋊C4—611no—
364#2345—6116no—
365C2×#389—611no—
366C2×#389—611no—
367C2×#387—611no—
368C2×#387—611no—
369C2×#387—611no—
370C2×#387D6111yescharacteristic, complemented
371C2×#380—611no—
372C2×#380—611no—
373C2×#380—611no—
374C2×C4×C4⋊C4—611no—
375C2×C4×C4⋊C4—611no—
376C2×C4×C22⋊C4—611no—
377C2×C4×C22⋊C4—611no—
378C2×C4×C22⋊C4—611no—
379C2×C61#234518yescomplemented
380C2×C61C22×#11711yescharacteristic
381C2×C61C22×C4×Q811yescharacteristic
382C2×C61C2×#51811yescharacteristic
383C2×C61C2×#55311yescharacteristic
384C2×C61C2×#55311yescharacteristic
385C2×C61C2×#55411yescharacteristic
386C2×C61C2×#55411yescharacteristic
387D61—28no—
388C24×C4—611no—
389C24×C4—611no—
390C24×C4—611no—
391C22×C4⋊C4—611no—
392C22×C4⋊C4—611no—
393C22×C4⋊C4—611no—
394C22×C4⋊C4—6116no—
395C22×C4⋊C4—618no—
396C22×C4⋊C4—611no—
397C22×C4⋊C4—611no—
398C22×C4⋊C4—611no—
399C22×C4⋊C4—611no—
400C22×C4⋊C4—611no—
401C22×C4⋊C4C2×D6111yescharacteristic
402C22×C4⋊C4C2×D6111yescharacteristic
403C22×C22⋊C4—611no—
404C22×C22⋊C4—611no—
405C22×C22⋊C4—611no—
406C22×C22⋊C4—611no—
407C22×C42—611no—
408C22×C42—611no—
409C22×C42—611no—
410C22×C42—611no—
411C22×C42—611no—
412C22×C42C2×D6111yescharacteristic
413#389—618no—
414#389—618no—
415#387—618no—
416#387—618no—
417#387—618no—
418#387C2×D6118yescomplemented
419#380—618no—
420#380—618no—
421#380—618no—
422C4×C4⋊C4—618no—
423C4×C4⋊C4—618no—
424C4×C22⋊C4—618no—
425C4×C22⋊C4—618no—
426C4×C22⋊C4—618no—
427C2×#95—611no—
428C2×#95—611no—
429C2×#95—611no—
430C2×#95—611no—
431C2×#95—611no—
432C2×#95—611no—
433C2×#95—611no—
434C2×#95—611no—
435C2×#95C2×D6111yescharacteristic
436C2×#95C2×D6111yescharacteristic
437C2×#95C2×D6111yescharacteristic
438C2×#95C2×D6111yescharacteristic
439C61C2×#234511yescharacteristic, complemented, Sylow
440C25—611no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—618no—
446C23×C4—614no—
447C23×C4—618no—
448C23×C4—618no—
449C23×C4—614no—
450C23×C4—614no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—1224no—
455C23×C4—1224no—
456C23×C4—2442no—
457C23×C4—2442no—
458C23×C4—2442no—
459C23×C4—2442no—
460C23×C4C22×D6111yescharacteristic
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C2×C4⋊C4—42no—
468C2×C4⋊C4—618no—
469C2×C4⋊C4—618no—
470C2×C4⋊C4—618no—
471C2×C4⋊C4—614no—
472C2×C4⋊C4—614no—
473C2×C4⋊C4—614no—
474C2×C4⋊C4—6164no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—614no—
480C2×C4⋊C4—1224no—
481C2×C4⋊C4—1224no—
482C2×C4⋊C4—2442no—
483C2×C4⋊C4—2442no—
484C2×C4⋊C4—2442no—
485C2×C4⋊C4C4×D6118yes—
486C2×C4⋊C4C22×D6114yes—
487C2×C4⋊C4C22×D6114yes—
488C2×C22⋊C4—618no—
489C2×C22⋊C4—614no—
490C2×C22⋊C4—614no—
491C2×C22⋊C4—614no—
492C2×C22⋊C4—614no—
493C2×C22⋊C4—1224no—
494C2×C22⋊C4—1224no—
495C2×C22⋊C4—1224no—
496C2×C42—42no—
497C2×C42—614no—
498C2×C42—614no—
499C2×C42—614no—
500C2×C42—614no—
501C2×C42—614no—
502C2×C42—1224no—
503C2×C42—1224no—
504C2×C42—2442no—
505C2×C42—2442no—
506C2×C42—2442no—
507C2×C42C22×D6114yes—
508#95—614no—
509#95—614no—
510#95—614no—
511#95—614no—
512#95—614no—
513#95—614no—
514#95—614no—
515#95—614no—
516#95C22×D6114yes—
517#95C22×D6114yes—
518#95C22×D6114yes—
519#95C22×D6114yes—
520C24—614no—
521C24—614no—
522C24—614no—
523C24—612no—
524C24—1222no—
525C24—1222no—
526C24—1222no—
527C24—1222no—
528C24C23×D6111yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—614no—
547C22×C4—614no—
548C22×C4—614no—
549C22×C4—612no—
550C22×C4—614no—
551C22×C4—614no—
552C22×C4—614no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—6116no—
557C22×C4—6116no—
558C22×C4—6116no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—12232no—
563C22×C4—1228no—
564C22×C4—1228no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—24416no—
581C22×C4—24416no—
582C22×C4—2444no—
583C22×C4—2444no—
584C22×C4—2444no—
585C22×C4—2444no—
586C22×C4C2×C4×D6114yes—
587C22×C4C2×C4×D6114yes—
588C22×C4C2×C4×D6114yes—
589C22×C4Q8×D6114yes—
590C22×C4C23×D6112yes—
591C22×C4C23×D6112yes—
592C22×C4C23×D6112yes—
593C22×C4C23×D6112yes—
594C22×C4C23×D6112yes—
595C22×C4C23×D6112yes—
596C22×C4C23×D6112yes—
597C4⋊C4—44no—
598C4⋊C4—6116no—
599C4⋊C4—6116no—
600C4⋊C4—6116no—
601C4⋊C4—1228no—
602C4⋊C4—1228no—
603C4⋊C4—2444no—
604C4⋊C4—2444no—
605C4⋊C4—2444no—
606C4⋊C4C2×C4×D61116yes—
607C22⋊C4—6116no—
608C22⋊C4—1228no—
609C22⋊C4—1228no—
610C22⋊C4—1228no—
611C42—44no—
612C42—1228no—
613C42—1228no—
614C42—2444no—
615C42—2444no—
616C42—2444no—
617C23—6116no—
618C23—614no—
619C23—614no—
620C23—614no—
621C23—1228no—
622C23—1228no—
623C23—1228no—
624C23—1228no—
625C23—1228no—
626C23—1228no—
627C23—1222no—
628C23—1222no—
629C23—1222no—
630C23—1222no—
631C23C22×C4×D6112yes—
632C23C2×Q8×D6112yes—
633C23#41×D6112yes—
634C23#41×D6112yes—
635C23#41×D6112yes—
636C23#1451982212yes—
637C23#1451982312yes—
638C23C24×D6111yescharacteristic
639C2×C4—28no—
640C2×C4—28no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—6116no—
664C2×C4—614no—
665C2×C4—614no—
666C2×C4—614no—
667C2×C4—614no—
668C2×C4—614no—
669C2×C4—614no—
670C2×C4—12232no—
671C2×C4—1228no—
672C2×C4—1228no—
673C2×C4—1228no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—24416no—
690C2×C4—24416no—
691C2×C4—2444no—
692C2×C4—2444no—
693C2×C4—2444no—
694C2×C4C22×C4×D6114yes—
695C2×C4C22×C4×D6114yes—
696C2×C4C22×C4×D6114yes—
697C2×C4C2×Q8×D6114yes—
698C22—618no—
699C22—1224no—
700C22—1224no—
701C22—1224no—
702C22—1224no—
703C22—1224no—
704C22—1224no—
705C22—12232no—
706C22#117×D6114yes—
707C22C4×Q8×D6114yes—
708C22#1684023414yes—
709C22#1684045714yes—
710C22#1684046314yes—
711C22#1684046614yes—
712C22#1684046814yes—
713C22C23×C4×D6111yescharacteristic
714C22C22×Q8×D6111yescharacteristic
715C22C2×#41×D6111yescharacteristic
716C22C2×#41×D6111yescharacteristic
717C22C2×#41×D6111yescharacteristic
718C22C2×#1451982211yescharacteristic
719C22C2×#1451982311yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—618no—
728C4—1224no—
729C4—1224no—
730C4—1224no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C2—1228no—
735C2#2144869318yesdirect product factor
736C2C2×#117×D6111yescharacteristic
737C2C2×C4×Q8×D6111yescharacteristic
738C2C2×#1684023411yescharacteristic
739C2C2×#1684045711yescharacteristic
740C2C2×#1684046311yescharacteristic
741C2C2×#1684046611yescharacteristic
742C2C2×#1684046811yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#387C2
socleC24×C61C24
prime radicalC24×D61C23
cosocleC23×C61C25
hypercenterC2×#387D61
hypocenterC61C2×#2345
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #21448693C2direct (N × H)
3. C2×#16839659C2semidirect
4. C2×#16839657C2semidirect
5. C2×#16839648C2semidirect
6. C2×#16839647C2semidirect
7. C2×#16839645C2semidirect
11. C2×C4×#11758196C2semidirect
12. C2×#16839613C2semidirect
16. C2×C61×#387C2semidirect
28. C2×C4⋊C4×D61C4semidirect
39. #16839659C22semidirect
40. #16839657C22semidirect
41. #16839648C22semidirect
42. #16839647C22semidirect
43. #16839645C22semidirect
47. C4×#11758196C22semidirect
48. #16839613C22semidirect
63. C61×#387C22semidirect
104. C4⋊C4×D61C2×C4semidirect
370. C2×#387D61semidirect
379. C2×C61#2345semidirect
418. #387C2×D61semidirect
439. C61C2×#2345semidirect
735. C2#21448693direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D612
#214486932
C2×#168396592
C2×#168396572
C2×#168396482
C2×#168396472
C2×#168396452
C2×#168396212
C2×#168396192
C2×C4×#117581962
C2×#168396132
C2×C4×#117581982
C2×#168396092
C2×C61×#3872
C2×#234561