Finite Group Databasebeta

← C2×#21454803 #30544475

Subgroups — C2×#21454803 #30544475

Order 15616.

1970 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×#16840299C211yesmaximal, characteristic
2#21454803C2116yesmaximal, direct product factor
3C2×#16839893C211yesmaximal, characteristic, complemented
4C2×#16839841C211yesmaximal, characteristic, complemented
5C2×#16839839C211yesmaximal, characteristic, complemented
6C2×#16839835C211yesmaximal, characteristic, complemented
7C2×#16839835C211yesmaximal, characteristic, complemented
8C2×#16839832C211yesmaximal, characteristic, complemented
9C2×#16839832C211yesmaximal, characteristic, complemented
10C2×#16839822C211yesmaximal, characteristic, complemented
11C2×#16839822C211yesmaximal, characteristic, complemented
12C2×#16839818C211yesmaximal, characteristic, complemented
13C2×#16839719C211yesmaximal, characteristic, complemented
14C2×#16839716C211yesmaximal, characteristic, complemented
15C2×#16839714C211yesmaximal, characteristic, complemented
16C2×C61×#446C211yesmaximal, characteristic, complemented
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840299C418yes—
24#16840299C2218yes—
25C2×#14519772C411yescharacteristic
26C2×#14519772C411yescharacteristic
27C2×#14519768C411yescharacteristic
28C2×#14519766C411yescharacteristic
29C2×#14519762C411yescharacteristic
30C2×#14519762C411yescharacteristic
31C2×#14519753C411yescharacteristic
32C2×#14519752C411yescharacteristic
33C2×C4×D244C2211yescharacteristic
34C2×C4×D244C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×#14519734C2211yescharacteristic
37C2×#14519734C2211yescharacteristic
38C2×C42×D61C2211yescharacteristic
39#16839893C2218yescomplemented
40#16839841C2218yescomplemented
41#16839839C2218yescomplemented
42#16839835C2218yescomplemented
43#16839835C2218yescomplemented
44#16839832C2218yescomplemented
45#16839832C2218yescomplemented
46#16839822C2218yescomplemented
47#16839822C2218yescomplemented
48#16839818C2218yescomplemented
49C2×C4⋊#92418C2211yescharacteristic
50C2×C4⋊#92418C2211yescharacteristic
51C2×C4⋊#92418C2211yescharacteristic
52C2×#14519689C2211yescharacteristic
53C2×#14519689C2211yescharacteristic
54C2×#14519689C2211yescharacteristic
55C2×#14519689C2211yescharacteristic
56C2×#14519689C2211yescharacteristic
57C2×#14519689C2211yescharacteristic
58#16839719C2218yescomplemented
59#16839716C2218yescomplemented
60#16839714C2218yescomplemented
61C2×#14519688C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×#14519687C2211yescharacteristic
64C2×#14519687C2211yescharacteristic
65C2×C4×#92418C2211yescharacteristic
66C2×C8×Dic61C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C4×Q8×C61C2211yescharacteristic
69C61×#446C2218yescomplemented
70C2×C4⋊C8×C61C2211yescharacteristic
71C2×C4⋊C8×C61C2211yescharacteristic
72C2×C4⋊C8×C61C2211yescharacteristic
73C2×#97×C61C2211yescharacteristic
74C2×#97×C61C2211yescharacteristic
75C2×C4×C8×C61C2211yescharacteristic
76C22×D244C2×C411yescharacteristic
77C22×D244C2×C411yescharacteristic
78C22×D244C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C2×#11758189—24no—
85C2×#11758189—24no—
86C2×#11758189—24no—
87C2×#11758189—24no—
88C2×#11758189C2314yes—
89C2×#11758189C2314yes—
90C2×#11758189C2314yes—
91C2×#11758189C2314yes—
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C2×C8×D61—24no—
97C2×C8×D61—24no—
98C2×C8×D61C2314yes—
99C2×C8×D61C2314yes—
100#14519772C2×C418yes—
101#14519772C2×C418yes—
102#14519768C2×C418yes—
103#14519766C2×C418yes—
104#14519762C2×C418yes—
105#14519762C2×C418yes—
106#14519753C2×C418yes—
107#14519752C2×C418yes—
108C4×D244C2×C414yes—
109C4×D244C2×C414yes—
110C4×D244C2×C414yes—
111C4×D244C2314yes—
112C4×D244C2314yes—
113C4×D244C2314yes—
114#14519734C2×C414yes—
115#14519734C2×C414yes—
116#14519734C2314yes—
117#14519734C2314yes—
118C2×C4⋊Dic61C2×C411yescharacteristic
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×C4⋊Dic61C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×C4×Dic61C2×C411yescharacteristic
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61C2311yescharacteristic
138C42×D61C2×C414yes—
139C42×D61C2314yes—
140C4⋊#92418C2314yes—
141C4⋊#92418C2314yes—
142C4⋊#92418C2314yes—
143#14519689C2314yes—
144#14519689C2314yes—
145#14519689C2314yes—
146#14519689C2314yes—
147#14519689C2314yes—
148#14519689C2314yes—
149#14519688C2314yes—
150#14519688C2314yes—
151#14519687C2314yes—
152#14519687C2314yes—
153C4×#92418C2314yes—
154C8×Dic61C2314yes—
155C8×Dic61C2314yes—
156C22×Q8×C61C2×C411yescharacteristic
157C22×C8×C61C2311yescharacteristic
158C22×C8×C61C2311yescharacteristic
159C22×C8×C61C2311yescharacteristic
160C22×C8×C61C2311yescharacteristic
161C4×Q8×C61C2×C414yes—
162C4×Q8×C61C2314yes—
163C2×C4⋊C4×C61C2×C411yescharacteristic
164C2×C4⋊C4×C61C2×C411yescharacteristic
165C2×C4⋊C4×C61C2×C411yescharacteristic
166C2×C42×C61C2311yescharacteristic
167C2×C42×C61C2311yescharacteristic
168C2×C42×C61C2311yescharacteristic
169C4⋊C8×C61C2314yes—
170C4⋊C8×C61C2314yes—
171C4⋊C8×C61C2314yes—
172#97×C61C2314yes—
173#97×C61C2314yes—
174C4×C8×C61C2314yes—
175C23×D61C22×C411yescharacteristic
176C23×D61C22×C411yescharacteristic
177C23×D61C22×C411yescharacteristic
178C2×Q8×C61—42no—
179C2×Q8×C61C22×C414yes—
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C2×D244—42no—
193C2×D244—42no—
194C2×D244—42no—
195C2×D244C22×C414yes—
196C2×D244C22×C414yes—
197C2×D244C22×C414yes—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61C22×C412yes—
207C2×C4×D61C22×C412yes—
208C2×C4×D61C22×C412yes—
209C2×C4×D61C22×C414yes—
210C2×C4×D61C22×C414yes—
211C2×C4×D61C2412yes—
212C2×C4×D61C2412yes—
213C2×C4×D61C2412yes—
214C2×C8×C61—22no—
215C2×C8×C61—22no—
216C2×C8×C61—22no—
217C2×C8×C61#4114yes—
218C2×C8×C61C2412yes—
219C2×C8×C61C2412yes—
220C2×C8×C61C2412yes—
221C2×C8×C61C2412yes—
222C4⋊C4×C61C22×C414yes—
223C4⋊C4×C61C22×C414yes—
224C4⋊C4×C61C22×C414yes—
225C42×C61C22×C412yes—
226C42×C61C22×C412yes—
227C42×C61C22×C412yes—
228C42×C61C2412yes—
229C42×C61C2412yes—
230C42×C61C2412yes—
231#11758198C22×C414yes—
232#11758198C22×C414yes—
233#11758198C22×C414yes—
234#11758198C22×C414yes—
235#11758198C22×C414yes—
236#11758198C22×C414yes—
237#11758198C22×C414yes—
238#11758198C22×C414yes—
239#11758198C22×C414yes—
240#11758198C22×C414yes—
241C4⋊Dic61C22×C414yes—
242C4⋊Dic61C22×C414yes—
243C4⋊Dic61C22×C414yes—
244#11758196C22×C414yes—
245#11758196C22×C414yes—
246#11758196C22×C414yes—
247#11758196C22×C414yes—
248C4×Dic61C22×C412yes—
249C4×Dic61C22×C414yes—
250C4×Dic61C22×C414yes—
251C4×Dic61C2412yes—
252C2×#92418—22no—
253C2×#92418—22no—
254C2×#92418—22no—
255C2×#92418#4114yes—
256C2×#92418C2412yes—
257C2×#92418C2412yes—
258C2×#92418C2412yes—
259C2×#92418C2412yes—
260#11758189—28no—
261#11758189—28no—
262#11758189—28no—
263#11758189—28no—
264C8×D61—28no—
265C8×D61—28no—
266C23×C61C23×C411yescharacteristic
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61C23×C412yes—
277C22×D61C23×C412yes—
278C22×D61C23×C412yes—
279Q8×C61—44no—
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×C61C23×C412yes—
287C2×C4×C61C23×C412yes—
288C2×C4×C61C23×C412yes—
289C2×C4×C61C23×C412yes—
290C2×C4×C61C23×C412yes—
291C2×C4×C61C23×C412yes—
292C2×C4×C61C23×C411yescharacteristic
293C2×C4×C61C2×#4112yes—
294C2×C4×C61C2×#4112yes—
295C2×C4×C61C2511yescharacteristic
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61C23×C412yes—
302C2×Dic61C23×C412yes—
303C2×Dic61C23×C412yes—
304C2×Dic61C23×C412yes—
305C2×Dic61C23×C412yes—
306D244—44no—
307D244—44no—
308D244—44no—
309C4×D61—24no—
310C4×D61—24no—
311C4×D61—24no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—44no—
319C4×D61—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×#2967—611nomaximal, Sylow
329C22×C61C4×#4112yes—
330C22×C61#56812yes—
331C22×C61#56812yes—
332C22×C61C24×C411yescharacteristic
333C2×D61—22no—
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—44no—
343C2×D61—44no—
344C2×D61—44no—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61C4×#4112yes—
352C4×C61C22×#4111yescharacteristic
353C4×C61C22×#4111yescharacteristic
354Dic61—22no—
355Dic61—22no—
356Dic61—22no—
357Dic61—22no—
358Dic61—22no—
359C2×#529—611no—
360#2967—6116no—
361C2×#446—611no—
362C2×#446D6111yescharacteristic, complemented
363C2×#436—611no—
364C2×#436—611no—
365C2×#435—611no—
366C2×#435—611no—
367C2×#435—611no—
368C2×#435—611no—
369C2×#433—611no—
370C2×#433—611no—
371C2×#432—611no—
372C2×#405—611no—
373C2×#405—611no—
374C2×C4×M16—611no—
375C2×C61#296714yescomplemented
376C2×C61C2×C4×#4111yescharacteristic
377C2×C61C2×#56811yescharacteristic
378C2×C61C2×#56811yescharacteristic
379D61—42no—
380D61—42no—
381D61—42no—
382C22×M16—611no—
383C22×M16—611no—
384C22×M16—611no—
385C22×M16—611no—
386C23×C8—611no—
387C23×C8—611no—
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×Q8C2×D6111yescharacteristic
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×#117—611no—
403C2×#117—611no—
404C22×C42—611no—
405#446—618no—
406#446C2×D6118yescomplemented
407#436—618no—
408#436—618no—
409#435—618no—
410#435—618no—
411#435—618no—
412#435—618no—
413#433—618no—
414#433—618no—
415#432—618no—
416C2×C4⋊C8—611no—
417C2×C4⋊C8—611no—
418C2×C4⋊C8—611no—
419C2×C4⋊C8C2×D6111yescharacteristic
420C2×C4⋊C8C2×D6111yescharacteristic
421C2×C4⋊C8C2×D6111yescharacteristic
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C2×C22⋊C8—611no—
428#405—618no—
429#405—618no—
430C4×M16—618no—
431C2×#97—611no—
432C2×#97—611no—
433C2×#97—611no—
434C2×#97—611no—
435C2×#97C2×D6111yescharacteristic
436C2×#97C2×D6111yescharacteristic
437C2×C4×C8—611no—
438C2×C4×C8—611no—
439C2×C4×C8—611no—
440C2×C4×C8C2×D6111yescharacteristic
441C61C2×#296711yescharacteristic, complemented, Sylow
442C22×Q8C4×D6111yescharacteristic
443C22×D4—611no—
444C22×D4—611no—
445C22×D4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C2×M16—614no—
452C2×M16—614no—
453C2×M16—614no—
454C2×M16—614no—
455C2×M16—1224no—
456C2×M16—1224no—
457C2×M16—1224no—
458C2×M16—1224no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—614no—
464C22×C8—614no—
465C22×C8—1224no—
466C22×C8—1224no—
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×Q8C4×D6114yes—
480C4×Q8C22×D6114yes—
481C4×D4—614no—
482C4×D4—614no—
483C4×D4—614no—
484C4×D4—614no—
485C4×D4—614no—
486C4×D4—614no—
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⋊C4C4×D6111yescharacteristic
499C2×C4⋊C4C4×D6111yescharacteristic
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⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C42—611no—
512C2×C42—611no—
513C2×C42—611no—
514C2×C42—614no—
515C2×C42—614no—
516C2×C42C22×D6111yescharacteristic
517C2×C42C22×D6111yescharacteristic
518C2×C42C22×D6111yescharacteristic
519C4⋊C8—614no—
520C4⋊C8—614no—
521C4⋊C8—614no—
522C4⋊C8C22×D6114yes—
523C4⋊C8C22×D6114yes—
524C4⋊C8C22×D6114yes—
525C22⋊C8—614no—
526C22⋊C8—614no—
527C22⋊C8—614no—
528C22⋊C8—614no—
529C22⋊C8—614no—
530C22⋊C8—614no—
531#97—614no—
532#97—614no—
533#97—614no—
534#97—614no—
535#97C22×D6114yes—
536#97C22×D6114yes—
537C4×C8—614no—
538C4×C8—614no—
539C4×C8—614no—
540C4×C8C22×D6114yes—
541C24—611no—
542C24—611no—
543C24—611no—
544C2×Q8—42no—
545C2×Q8C2×C4×D6114yes—
546C2×D4—614no—
547C2×D4—614no—
548C2×D4—614no—
549C2×D4—2442no—
550C2×D4—2442no—
551C2×D4—2442no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—614no—
564C22×C4—614no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4C2×C4×D6111yescharacteristic
574C22×C4C2×C4×D6111yescharacteristic
575C22×C4C2×C4×D6111yescharacteristic
576C22×C4C2×C4×D6111yescharacteristic
577C22×C4C2×C4×D6111yescharacteristic
578C22×C4C2×C4×D6111yescharacteristic
579C22×C4C23×D6111yescharacteristic
580M16—1228no—
581M16—1228no—
582M16—1228no—
583M16—1228no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—614no—
588C2×C8—612no—
589C2×C8—612no—
590C2×C8—612no—
591C2×C8—612no—
592C2×C8—1228no—
593C2×C8—1222no—
594C2×C8—1222no—
595C2×C8—1222no—
596C2×C8—1228no—
597C2×C8#1175822614yes—
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⋊C4C2×C4×D6114yes—
610C4⋊C4C2×C4×D6114yes—
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⋊C4—614no—
621C22⋊C4—614no—
622C42—612no—
623C42—614no—
624C42—614no—
625C42—612no—
626C42C2×C4×D6112yes—
627C42C2×C4×D6112yes—
628C42C2×C4×D6112yes—
629C42C23×D6112yes—
630C42C23×D6112yes—
631C42C23×D6112yes—
632C23—612no—
633C23—612no—
634C23—612no—
635C23—1222no—
636C23—1222no—
637C23—1222no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23C22×C4×D6111yescharacteristic
645Q8—44no—
646D4—2444no—
647D4—2444no—
648D4—2444no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—612no—
656C2×C4—612no—
657C2×C4—612no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1224no—
666C2×C4—1224no—
667C2×C4—1224no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—2444no—
675C2×C4—2444no—
676C2×C4C22×C4×D6112yes—
677C2×C4C22×C4×D6112yes—
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×#1175822612yes—
685C2×C4C24×D6111yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—614no—
690C8—1222no—
691C8—1222no—
692C8—1222no—
693C8C2×#1175822614yes—
694C22—1222no—
695C22—1222no—
696C22—1222no—
697C22—1222no—
698C22—1222no—
699C22—1222no—
700C22—1222no—
701C22—1222no—
702C22—1222no—
703C22—2444no—
704C22—2444no—
705C22—2444no—
706C22C4×#1175822612yes—
707C22#1684052712yes—
708C22#1684052812yes—
709C22C23×C4×D6111yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—1222no—
717C4—1222no—
718C4—1222no—
719C4—1222no—
720C4—1222no—
721C4C4×#1175822612yes—
722C4C2×#41×D6111yescharacteristic
723C4C22×#1175822611yescharacteristic
724C2—2442no—
725C2—2442no—
726C2—2442no—
727C2#2145480314yesdirect product factor
728C2C2×C4×#1175822611yescharacteristic
729C2C2×#1684052711yescharacteristic
730C2C2×#1684052811yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#446C2
socleC23×C61C23×C4
prime radicalC2×#14519752C4
cosocleC2×C4×C61C25
hypercenterC2×#446D61
hypocenterC61C2×#2967
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #21454803C2direct (N × H)
3. C2×#16839893C2semidirect
4. C2×#16839841C2semidirect
5. C2×#16839839C2semidirect
6. C2×#16839835C2semidirect
7. C2×#16839835C2semidirect
8. C2×#16839832C2semidirect
9. C2×#16839832C2semidirect
10. C2×#16839822C2semidirect
11. C2×#16839822C2semidirect
12. C2×#16839818C2semidirect
13. C2×#16839719C2semidirect
14. C2×#16839716C2semidirect
15. C2×#16839714C2semidirect
16. C2×C61×#446C2semidirect
39. #16839893C22semidirect
40. #16839841C22semidirect
41. #16839839C22semidirect
42. #16839835C22semidirect
43. #16839835C22semidirect
44. #16839832C22semidirect
45. #16839832C22semidirect
46. #16839822C22semidirect
47. #16839822C22semidirect
48. #16839818C22semidirect
58. #16839719C22semidirect
59. #16839716C22semidirect
60. #16839714C22semidirect
69. C61×#446C22semidirect
362. C2×#446D61semidirect
375. C2×C61#2967semidirect
406. #446C2×D61semidirect
441. C61C2×#2967semidirect
727. C2#21454803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402992
#214548032
C2×#168398932
C2×#168398412
C2×#168398392
C2×#168398352
C2×#168398322
C2×#168398222
C2×#168398182
C2×#168397192
C2×#168397162
C2×#168397142
C2×C61×#4462
C2×#296761