Finite Group Databasebeta

← C2×#21454814 #30544487

Subgroups — C2×#21454814 #30544487

Order 15616.

2026 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840292C211yesmaximal, characteristic
2#21454814C2116yesmaximal, direct product factor
3C2×#16839890C211yesmaximal, characteristic, complemented
4C2×#16839889C211yesmaximal, characteristic, complemented
5C2×#16839831C211yesmaximal, characteristic, complemented
6C2×#16839830C211yesmaximal, characteristic, complemented
7C2×#16839830C211yesmaximal, characteristic, complemented
8C2×D4×#92418C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
10C2×#16839822C211yesmaximal, characteristic, complemented
11C2×#16839820C211yesmaximal, characteristic, complemented
12C2×#16839812C211yesmaximal, characteristic, complemented
13C2×#16839720C211yesmaximal, characteristic, complemented
14C2×#16839719C211yesmaximal, characteristic, complemented
15C22×#14519687C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840292C418yes—
22#16840292C2218yes—
23C2×#14519772C411yescharacteristic
24C2×#14519770C411yescharacteristic
25C2×#14519767C411yescharacteristic
26C2×#14519763C411yescharacteristic
27C2×#14519761C411yescharacteristic
28C2×#14519758C411yescharacteristic
29C2×#14519754C411yescharacteristic
30C2×#14519749C411yescharacteristic
31C2×C4×Dic122C2211yescharacteristic
32C2×C4×C22⋊D61C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519736C2211yescharacteristic
35C2×#14519734C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839890C2218yescomplemented
38#16839889C2218yescomplemented
39#16839831C2218yescomplemented
40#16839830C2218yescomplemented
41#16839830C2218yescomplemented
42D4×#92418C2218yescomplemented
43C8×C22⋊D61C2218yescomplemented
44#16839822C2218yescomplemented
45#16839820C2218yescomplemented
46#16839812C2218yescomplemented
47C2×C4⋊#92418C2211yescharacteristic
48C2×#14519706C2211yescharacteristic
49C2×#14519706C2211yescharacteristic
50C2×#14519706C2211yescharacteristic
51C2×#14519706C2211yescharacteristic
52C2×C22⋊#92418C2211yescharacteristic
53C2×C22⋊#92418C2211yescharacteristic
54C2×#14519689C2211yescharacteristic
55C2×#14519689C2211yescharacteristic
56#16839720C2218yescomplemented
57#16839719C2218yescomplemented
58C2×#14519687C2211yescharacteristic
59C2×#14519687C2211yescharacteristic
60C2×#14519687C2211yescharacteristic
61C2×#14519687C2211yescharacteristic
62C2×#14519687C2211yescharacteristic
63C2×#14519687C2218yescomplemented
64C2×C4×#92418C2211yescharacteristic
65C2×C8×Dic61C2211yescharacteristic
66C2×C8×Dic61C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C22×M16×C61C2211yescharacteristic
69C23×C8×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#435C2218yescomplemented
72C2×C4⋊C8×C61C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C23×Dic61C2×C411yescharacteristic
80C23×Dic61C2×C411yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C2×#11758189—24no—
83C2×#11758189C2314yes—
84C22×#92418—24no—
85C22×#92418—24no—
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2314yes—
90C22×#92418C2314yes—
91C22×#92418C2311yescharacteristic
92C2×C8×D61—24no—
93C2×C8×D61C2314yes—
94#14519772C2×C418yes—
95#14519770C2×C418yes—
96#14519767C2×C418yes—
97#14519763C2×C418yes—
98#14519761C2×C418yes—
99#14519758C2×C418yes—
100#14519754C2×C418yes—
101#14519749C2×C418yes—
102C4×Dic122C2×C414yes—
103C4×Dic122C2314yes—
104C4×C22⋊D61C2×C414yes—
105C4×C22⋊D61C2×C414yes—
106C4×C22⋊D61C2314yes—
107C4×C22⋊D61C2314yes—
108#14519736C2×C414yes—
109#14519736C2314yes—
110#14519734C2×C414yes—
111#14519734C2314yes—
112C2×C4⋊Dic61C2×C411yescharacteristic
113C2×C4⋊Dic61C2×C411yescharacteristic
114C2×C4⋊Dic61C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×C22⋊Dic61C2×C411yescharacteristic
122C2×C22⋊Dic61C2×C411yescharacteristic
123C2×C22⋊Dic61C2×C411yescharacteristic
124C2×C22⋊Dic61C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×C4×Dic61C2×C411yescharacteristic
130C2×C4×Dic61C2×C411yescharacteristic
131C2×C4×Dic61C2×C414yes—
132C2×C4×Dic61C2311yescharacteristic
133C2×C4×Dic61C2311yescharacteristic
134C2×C4×Dic61C2314yes—
135C2×C4×Dic61C2311yescharacteristic
136C4⋊#92418C2314yes—
137#14519706C2314yes—
138#14519706C2314yes—
139#14519706C2314yes—
140#14519706C2314yes—
141C22⋊#92418C2314yes—
142C22⋊#92418C2314yes—
143#14519689C2314yes—
144#14519689C2314yes—
145#14519687C2314yes—
146#14519687C2314yes—
147#14519687C2314yes—
148#14519687C2314yes—
149#14519687C2314yes—
150C4×#92418C2314yes—
151C8×Dic61C2314yes—
152C8×Dic61C2314yes—
153C8×Dic61C2314yes—
154C22×D4×C61C2×C411yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C2×M16×C61—24no—
158C2×M16×C61C2314yes—
159C22×C8×C61—24no—
160C22×C8×C61C2311yescharacteristic
161C22×C8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2314yes—
164C22×C8×C61C2311yescharacteristic
165C4×D4×C61C2×C414yes—
166C4×D4×C61C2314yes—
167C2×C4⋊C4×C61C2×C411yescharacteristic
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C22⋊C4×C61C2×C411yescharacteristic
170C2×C42×C61C2311yescharacteristic
171C4⋊C8×C61C2314yes—
172C22⋊C8×C61C2314yes—
173C22⋊C8×C61C2314yes—
174#97×C61C2314yes—
175C24×C61C22×C411yescharacteristic
176C24×C61C22×C411yescharacteristic
177C23×D61C22×C411yescharacteristic
178C2×D4×C61—24no—
179C2×D4×C61C22×C414yes—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C22×C412yes—
189C22×C4×C61C22×C412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2411yescharacteristic
193C2×C22⋊D61—24no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61C22×C414yes—
196C2×C22⋊D61C22×C414yes—
197C22×Dic61—24no—
198C22×Dic61—42no—
199C22×Dic61C22×C411yescharacteristic
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C22×Dic61C22×C411yescharacteristic
203C22×Dic61C22×C411yescharacteristic
204C22×Dic61C22×C414yes—
205C22×Dic61C22×C411yescharacteristic
206C22×Dic61C22×C411yescharacteristic
207C22×Dic61C22×C414yes—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61C22×C412yes—
211C2×C4×D61C2412yes—
212C2×Dic122—42no—
213C2×Dic122C22×C414yes—
214M16×C61—28no—
215C2×C8×C61—22no—
216C2×C8×C61—22no—
217C2×C8×C61—22no—
218C2×C8×C61—28no—
219C2×C8×C61#4114yes—
220C2×C8×C61C2412yes—
221C2×C8×C61C2412yes—
222C2×C8×C61C2412yes—
223C2×C8×C61C2412yes—
224C4⋊C4×C61C22×C414yes—
225C22⋊C4×C61C22×C414yes—
226C22⋊C4×C61C22×C414yes—
227C42×C61C22×C412yes—
228C42×C61C2412yes—
229C22⋊Dic61C22×C414yes—
230C22⋊Dic61C22×C414yes—
231C22⋊Dic61C22×C414yes—
232C22⋊Dic61C22×C414yes—
233#11758198C22×C414yes—
234#11758198C22×C414yes—
235#11758198C22×C414yes—
236#11758198C22×C414yes—
237C4⋊Dic61C22×C414yes—
238C4⋊Dic61C22×C414yes—
239C4⋊Dic61C22×C414yes—
240#11758196C22×C414yes—
241#11758196C22×C414yes—
242#11758196C22×C414yes—
243#11758196C22×C414yes—
244#11758196C22×C414yes—
245#11758196C22×C414yes—
246C4×Dic61C22×C412yes—
247C4×Dic61C22×C412yes—
248C4×Dic61C22×C414yes—
249C4×Dic61C22×C414yes—
250C4×Dic61C22×C412yes—
251C4×Dic61C2412yes—
252C4×Dic61C2412yes—
253C4×Dic61C2412yes—
254C2×#92418—22no—
255C2×#92418—22no—
256C2×#92418—22no—
257C2×#92418—28no—
258C2×#92418—28no—
259C2×#92418#4114yes—
260C2×#92418C2412yes—
261C2×#92418C2412yes—
262C2×#92418C2412yes—
263C2×#92418C2412yes—
264#11758189—28no—
265C8×D61—28no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61#13114yes—
272C23×C61C23×C412yes—
273C23×C61C23×C412yes—
274C23×C61C23×C411yescharacteristic
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61C23×C412yes—
279D4×C61—28no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61C23×C412yes—
291C2×C4×C61C23×C412yes—
292C2×C4×C61C23×C412yes—
293C2×C4×C61C23×C412yes—
294C2×C4×C61C23×C411yescharacteristic
295C2×C4×C61C2×#4112yes—
296C2×C4×C61C2×#4112yes—
297C2×C4×C61C2511yescharacteristic
298C22⋊D61—28no—
299C22⋊D61—44no—
300C2×Dic61—22no—
301C2×Dic61—28no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—44no—
309C2×Dic61C23×C412yes—
310C2×Dic61C23×C412yes—
311C2×Dic61C23×C412yes—
312C2×Dic61C23×C412yes—
313C2×Dic61C23×C412yes—
314C2×Dic61C23×C412yes—
315C2×Dic61C23×C412yes—
316C4×D61—24no—
317C4×D61—22no—
318C4×D61—22no—
319Dic122—44no—
320C8×C61—22no—
321C8×C61—22no—
322C8×C61—22no—
323C8×C61C2×#4114yes—
324#92418—22no—
325#92418—22no—
326#92418—22no—
327#92418C2×#4114yes—
328C2×#2968—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—28no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—44no—
336C22×C61C4×#4112yes—
337C22×C61C2×#13114yes—
338C22×C61C2×#13112yes—
339C22×C61#56812yes—
340C22×C61C24×C411yescharacteristic
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—44no—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61C4×#4112yes—
350C4×C61C22×#4111yescharacteristic
351C4×C61C22×#4111yescharacteristic
352Dic61—22no—
353Dic61—22no—
354Dic61—22no—
355Dic61—22no—
356Dic61—22no—
357Dic61—22no—
358Dic61—22no—
359C2×#529—611no—
360#2968—6116no—
361C2×#446—611no—
362C2×#446—611no—
363C2×#435—611no—
364C2×#435—611no—
365C2×#435—611no—
366C2×#435D6111yescharacteristic, complemented
367C2×C8×D4—611no—
368C2×C8×D4—611no—
369C2×#433—611no—
370C2×#433—611no—
371C2×#431—611no—
372C2×#405—611no—
373C2×#405—611no—
374C22×#97—611no—
375C2×C61—24no—
376C2×C61—42no—
377C2×C61#296814yescomplemented
378C2×C61C2×C4×#4111yescharacteristic
379C2×C61C22×#13111yescharacteristic
380C2×C61C2×#56811yescharacteristic
381D61—42no—
382C22×M16—611no—
383C22×M16C2×D6111yescharacteristic
384C23×C8—611no—
385C23×C8—611no—
386C23×C8—611no—
387C23×C8C2×D6111yescharacteristic
388#529—618no—
389#529—618no—
390C2×#126—611no—
391C2×#126—611no—
392C2×#125—611no—
393C2×#124—611no—
394C2×#123—611no—
395C2×#123—611no—
396C2×C22⋊Q8—611no—
397C2×#121—611no—
398C2×C4×Q8—611no—
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401C2×C4×D4C2×D6111yescharacteristic
402C2×#117—611no—
403C2×#117—611no—
404C22×C42—611no—
405#446—618no—
406#446—618no—
407#435—618no—
408#435—618no—
409#435—618no—
410#435C2×D6118yescomplemented
411C8×D4—618no—
412C8×D4—618no—
413#433—618no—
414#433—618no—
415#431—618no—
416C2×C4⋊C8—611no—
417C2×C4⋊C8—611no—
418C2×C4⋊C8—611no—
419C2×C4⋊C8—611no—
420C2×C4⋊C8—611no—
421C2×C4⋊C8C2×D6111yescharacteristic
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8C2×D6111yescharacteristic
427C2×C22⋊C8C2×D6111yescharacteristic
428#405—618no—
429#405—618no—
430C2×#97—611no—
431C2×#97—611no—
432C2×#97—611no—
433C2×#97—611no—
434C2×#97—611no—
435C2×#97—618no—
436C2×#97C2×D6111yescharacteristic
437C2×C4×C8—611no—
438C2×C4×C8—611no—
439C2×C4×C8—611no—
440C2×C4×C8—611no—
441C61C2×#296811yescharacteristic, complemented, Sylow
442C22×Q8—611no—
443C22×D4—611no—
444C22×D4—611no—
445C22×D4C4×D6111yescharacteristic
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4C22×D6111yescharacteristic
450C23×C4C22×D6111yescharacteristic
451C2×M16—24no—
452C2×M16—614no—
453C2×M16—1224no—
454C2×M16C22×D6114yes—
455C22×C8—24no—
456C22×C8—611no—
457C22×C8—614no—
458C22×C8—614no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8—614no—
463C22×C8—1224no—
464C22×C8—1224no—
465C22×C8—1224no—
466C22×C8C22×D6114yes—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6111yescharacteristic
470C22×C8C22×D6111yescharacteristic
471#126—618no—
472#126—618no—
473#125—618no—
474#124—618no—
475#123—618no—
476#123—618no—
477C22⋊Q8—618no—
478#121—618no—
479C4×Q8—614no—
480C4×Q8—614no—
481C4×D4—614no—
482C4×D4—614no—
483C4×D4—614no—
484C4×D4—614no—
485C4×D4C4×D6114yes—
486C4×D4C22×D6114yes—
487#117—614no—
488#117—614no—
489#117—614no—
490#117—614no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4C4×D6111yescharacteristic
501C2×C22⋊C4—611no—
502C2×C22⋊C4—611no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4—611no—
509C2×C22⋊C4C4×D6111yescharacteristic
510C2×C22⋊C4C4×D6111yescharacteristic
511C2×C42—611no—
512C2×C42—611no—
513C2×C42—614no—
514C2×C42—614no—
515C2×C42—611no—
516C2×C42—611no—
517C2×C42—611no—
518C2×C42C22×D6111yescharacteristic
519C4⋊C8—614no—
520C4⋊C8—614no—
521C4⋊C8—614no—
522C4⋊C8—614no—
523C4⋊C8—614no—
524C4⋊C8C22×D6114yes—
525C22⋊C8—614no—
526C22⋊C8—614no—
527C22⋊C8—614no—
528C22⋊C8—614no—
529C22⋊C8C22×D6114yes—
530C22⋊C8C22×D6114yes—
531#97—614no—
532#97—614no—
533#97—614no—
534#97—614no—
535#97—614no—
536#97C22×D6114yes—
537C4×C8—614no—
538C4×C8—614no—
539C4×C8—614no—
540C4×C8—614no—
541C24—611no—
542C24C2×C4×D6111yescharacteristic
543C24C2×C4×D6111yescharacteristic
544C2×Q8—614no—
545C2×Q8—2442no—
546C2×D4—24no—
547C2×D4—614no—
548C2×D4—614no—
549C2×D4—1224no—
550C2×D4—2442no—
551C2×D4C2×C4×D6114yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—614no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—614no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—1224no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—2442no—
571C22×C4C2×C4×D6111yescharacteristic
572C22×C4C2×C4×D6112yes—
573C22×C4C2×C4×D6111yescharacteristic
574C22×C4C2×C4×D6111yescharacteristic
575C22×C4C2×C4×D6111yescharacteristic
576C22×C4C2×C4×D6112yes—
577C22×C4C23×D6112yes—
578C22×C4C23×D6112yes—
579C22×C4C23×D6111yescharacteristic
580M16—28no—
581M16—1228no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8—614no—
587C2×C8—612no—
588C2×C8—612no—
589C2×C8—612no—
590C2×C8—612no—
591C2×C8—1228no—
592C2×C8—1228no—
593C2×C8—1222no—
594C2×C8—1222no—
595C2×C8—1222no—
596C2×C8—1228no—
597C2×C8#1175822414yes—
598C2×C8C23×D6112yes—
599C2×C8C23×D6112yes—
600C2×C8C23×D6112yes—
601C2×C8C23×D6112yes—
602C4⋊C4—614no—
603C4⋊C4—614no—
604C4⋊C4—614no—
605C4⋊C4—614no—
606C4⋊C4—614no—
607C4⋊C4—614no—
608C4⋊C4—614no—
609C4⋊C4—614no—
610C4⋊C4—614no—
611C4⋊C4C2×C4×D6114yes—
612C22⋊C4—614no—
613C22⋊C4—614no—
614C22⋊C4—614no—
615C22⋊C4—614no—
616C22⋊C4—614no—
617C22⋊C4—614no—
618C22⋊C4—614no—
619C22⋊C4—614no—
620C22⋊C4C2×C4×D6114yes—
621C22⋊C4C2×C4×D6114yes—
622C42—612no—
623C42—612no—
624C42—614no—
625C42—614no—
626C42—612no—
627C42—612no—
628C42—612no—
629C42—612no—
630C42C2×C4×D6112yes—
631C42C23×D6112yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—612no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23#1451978514yes—
642C23C22×C4×D6112yes—
643C23C22×C4×D6112yes—
644C23C22×C4×D6111yescharacteristic
645Q8—2444no—
646D4—28no—
647D4—1228no—
648D4—2444no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—1222no—
667C2×C4—1228no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1224no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—2444no—
678C2×C4C22×C4×D6112yes—
679C2×C4C22×C4×D6112yes—
680C2×C4C22×C4×D6112yes—
681C2×C4C22×C4×D6112yes—
682C2×C4C22×C4×D6111yescharacteristic
683C2×C4#41×D6112yes—
684C2×C4C2×#1175822412yes—
685C2×C4C24×D6111yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—614no—
690C8—1222no—
691C8—1222no—
692C8—1222no—
693C8C2×#1175822414yes—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—2444no—
705C22C4×#1175822412yes—
706C22C2×#1451978514yes—
707C22C2×#1451978512yes—
708C22#1684052712yes—
709C22C23×C4×D6111yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—1222no—
715C4—1222no—
716C4—1222no—
717C4—1222no—
718C4—1222no—
719C4—1222no—
720C4—1222no—
721C4C4×#1175822412yes—
722C4C2×#41×D6111yescharacteristic
723C4C22×#1175822411yescharacteristic
724C2—24no—
725C2—42no—
726C2—2442no—
727C2#2145481414yesdirect product factor
728C2C2×C4×#1175822411yescharacteristic
729C2C22×#1451978511yescharacteristic
730C2C2×#1684052711yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C23×C4
prime radicalC2×#14519749C4
cosocleC2×C4×C61C25
hypercenterC2×#435D61
hypocenterC61C2×#2968
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #21454814C2direct (N × H)
3. C2×#16839890C2semidirect
4. C2×#16839889C2semidirect
5. C2×#16839831C2semidirect
6. C2×#16839830C2semidirect
7. C2×#16839830C2semidirect
8. C2×D4×#92418C2semidirect
9. C2×C8×C22⋊D61C2semidirect
10. C2×#16839822C2semidirect
11. C2×#16839820C2semidirect
12. C2×#16839812C2semidirect
13. C2×#16839720C2semidirect
14. C2×#16839719C2semidirect
15. C22×#14519687C2semidirect
16. C2×C61×#435C2semidirect
37. #16839890C22semidirect
38. #16839889C22semidirect
39. #16839831C22semidirect
40. #16839830C22semidirect
41. #16839830C22semidirect
42. D4×#92418C22semidirect
43. C8×C22⋊D61C22semidirect
44. #16839822C22semidirect
45. #16839820C22semidirect
46. #16839812C22semidirect
56. #16839720C22semidirect
57. #16839719C22semidirect
63. C2×#14519687C22semidirect
71. C61×#435C22semidirect
366. C2×#435D61semidirect
377. C2×C61#2968semidirect
410. #435C2×D61semidirect
441. C61C2×#2968semidirect
727. C2#21454814direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402922
#214548142
C2×#168398902
C2×#168398892
C2×#168398312
C2×#168398302
C2×D4×#924182
C2×C8×C22⋊D612
C2×#168398222
C2×#168398202
C2×#168398122
C2×#168397202
C2×#168397192
C22×#145196872
C2×C61×#4352
C2×#296861