Finite Group Databasebeta

← C2×#21456489 #30549883

Subgroups — C2×#21456489 #30549883

Order 15616.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840383C211yesmaximal, characteristic
2#21456489C2116yesmaximal, direct product factor
3C2×#16840172C211yesmaximal, characteristic, complemented
4C2×#16840154C211yesmaximal, characteristic, complemented
5C2×#16840119C211yesmaximal, characteristic, complemented
6C2×#16840112C211yesmaximal, characteristic, complemented
7C2×#16840018C211yesmaximal, characteristic, complemented
8C2×#16840010C211yesmaximal, characteristic
9C2×#16840001C211yesmaximal, characteristic, complemented
10C2×#16839993C211yesmaximal, characteristic
11C2×#16839867C211yesmaximal, characteristic, complemented
12C2×#16839860C211yesmaximal, characteristic, complemented
13C2×C4×#11758202C211yesmaximal, characteristic, complemented
14C2×C4×#11758201C211yesmaximal, characteristic, complemented
15C2×#16839718C211yesmaximal, characteristic, complemented
16C2×C61×#541C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22C23×#92418C2211yescharacteristic
23#16840383—24no—
24#16840383C2218yes—
25C2×#14519777C2211yescharacteristic
26C2×#14519772—21no—
27C2×#14519765C2211yescharacteristic
28C2×#14519763—21no—
29C2×#14519759—21no—
30C2×#14519756C2211yescharacteristic
31C2×#14519755—21no—
32C2×#14519751C2211yescharacteristic
33C2×C4×Dic122C2211yescharacteristic
34C2×C4×D244C2211yescharacteristic
35#16840172C2218yescomplemented
36#16840154C2218yescomplemented
37#16840119C2218yescomplemented
38#16840112C2218yescomplemented
39#16840018C2218yescomplemented
40#16840010C2218yes—
41#16840001C2218yescomplemented
42#16839993C2218yes—
43#16839867C2218yescomplemented
44#16839860C2218yescomplemented
45C4×#11758202C2218yescomplemented
46C4×#11758201C2218yescomplemented
47C2×#14519710C2211yescharacteristic
48C2×#14519710C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×#14519708C2211yescharacteristic
51C2×#14519701C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519701C2211yescharacteristic
55C2×#14519700C2211yescharacteristic
56C2×#14519700C2211yescharacteristic
57C2×#14519697C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59#16839718C2218yescomplemented
60C2×#14519688C2211yescharacteristic
61C2×#14519688C2211yescharacteristic
62C2×C4×#92418C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#541—24no—
65C61×#541C2218yescomplemented
66C2×C4⋊Q8×C61C2211yescharacteristic
67C2×#126×C61—21no—
68C2×#126×C61—21no—
69C2×#125×C61—21no—
70C2×#125×C61—21no—
71C2×#125×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×C22⋊Q8×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×Q8×C61C2211yescharacteristic
76C2×#117×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C4×D61—21no—
82C2×#11758202—24no—
83C2×#11758202—24no—
84C2×#11758202C2314yes—
85C2×#11758202C2314yes—
86C2×#11758201—24no—
87C2×#11758201—24no—
88C2×#11758201C2314yes—
89C2×#11758201C2314yes—
90C2×#11758194—24no—
91C2×#11758194C2314yes—
92C22×#92418—24no—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C22×#92418C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98#14519777—22no—
99#14519777C2314yes—
100#14519772—28no—
101#14519765—22no—
102#14519765C2314yes—
103#14519763—28no—
104#14519759—28no—
105#14519756—22no—
106#14519756C2314yes—
107#14519755—28no—
108#14519751—22no—
109#14519751C2314yes—
110C4×Dic122—22no—
111C4×Dic122C2314yes—
112C4×D244—22no—
113C4×D244C2314yes—
114C2×C4⋊Dic61—21no—
115C2×C4⋊Dic61C2311yescharacteristic
116C2×C4⋊Dic61C2311yescharacteristic
117C2×#11758196—21no—
118C2×#11758196—21no—
119C2×C22⋊Dic61—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×C4×Dic61—21no—
125#14519710C2314yes—
126#14519710C2314yes—
127#14519708C2314yes—
128#14519708C2314yes—
129#14519701C2314yes—
130#14519701C2314yes—
131#14519701C2314yes—
132#14519701C2314yes—
133#14519700C2314yes—
134#14519700C2314yes—
135#14519697C2314yes—
136#14519697C2314yes—
137#14519688C2314yes—
138#14519688C2314yes—
139C4×#92418C2314yes—
140C4×#92418C2314yes—
141C22×Q8×C61C2311yescharacteristic
142C22×Q8×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C4⋊Q8×C61—22no—
145C4⋊Q8×C61C2314yes—
146#126×C61—28no—
147#126×C61—28no—
148#125×C61—28no—
149#125×C61—28no—
150#125×C61—22no—
151#125×C61C2314yes—
152C22⋊Q8×C61—22no—
153C22⋊Q8×C61—22no—
154C22⋊Q8×C61C2314yes—
155C22⋊Q8×C61C2314yes—
156C4×Q8×C61—22no—
157C4×Q8×C61—22no—
158C4×Q8×C61C2314yes—
159C4×Q8×C61C2314yes—
160#117×C61D414yes—
161#117×C61C2314yes—
162C2×C4⋊C4×C61—21no—
163C2×C4⋊C4×C61—21no—
164C2×C4⋊C4×C61—21no—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61D411yescharacteristic
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61D411yescharacteristic
177C2×C22⋊C4×C61D411yescharacteristic
178C2×C42×C61—21no—
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2311yescharacteristic
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61C2412yes—
191C2×Q8×C61C2412yes—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2412yes—
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61—82no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C2×D244—22no—
212C2×D244—22no—
213C2×D244—21no—
214C2×D244C2412yes—
215C2×C4×D61—24no—
216C2×C4×D61—82no—
217C2×Dic122—22no—
218C2×Dic122—22no—
219C2×Dic122—21no—
220C2×Dic122—24no—
221C2×Dic122—82no—
222C2×Dic122C2412yes—
223C4⋊C4×C61—24no—
224C4⋊C4×C61—24no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—24no—
228C4⋊C4×C61—24no—
229C4⋊C4×C61—24no—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61C2×D414yes—
234C4⋊C4×C61C2×D414yes—
235C4⋊C4×C61C2412yes—
236C4⋊C4×C61C2412yes—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C22⋊C4×C61C2×D414yes—
240C22⋊C4×C61C2×D414yes—
241C42×C61—24no—
242C42×C61—24no—
243C42×C61C2×D412yes—
244C42×C61C2×D412yes—
245C42×C61C2412yes—
246C42×C61C2412yes—
247C22⋊Dic61—24no—
248#11758202—28no—
249#11758202—28no—
250#11758201—28no—
251#11758201—28no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261#11758196—24no—
262#11758196—24no—
263C4×Dic61—24no—
264#11758194—28no—
265C2×#92418—22no—
266C2×#92418—22no—
267C2×#92418—28no—
268C2×#92418#4114yes—
269C2×#92418#4114yes—
270C2×#92418C2412yes—
271C2×#92418C2412yes—
272C2×#92418C2412yes—
273C2×#92418C2412yes—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61C22×D412yes—
278C23×C61C22×D411yescharacteristic
279C22×D61—22no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—22no—
287Q8×C61—42no—
288Q8×C61—42no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—24no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D412yes—
307C2×C4×C61C22×D412yes—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2×#4112yes—
313C2×C4×C61C2511yescharacteristic
314C22⋊D61—84no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321D244—22no—
322D244—22no—
323D244—42no—
324C4×D61—84no—
325Dic122—22no—
326Dic122—22no—
327Dic122—42no—
328Dic122—84no—
329#92418—22no—
330#92418—22no—
331#92418C2×#4114yes—
332#92418C2×#4114yes—
333C2×#3178—611nomaximal, Sylow
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—44no—
338C22×C61#53212yes—
339C22×C61#57712yes—
340C22×C61#57812yes—
341C22×C61C23×D411yescharacteristic
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—84no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61#53212yes—
356C4×C61C22×#4111yescharacteristic
357C4×C61C22×#4111yescharacteristic
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#542—611no—
362C2×#541D6111yescharacteristic, complemented
363#3178—6116no—
364C2×#501—611no—
365C2×#497—611no—
366C2×#488—611no—
367C2×#487—611no—
368C2×#470—611no—
369C2×#468—611no—
370C2×#467—611no—
371C2×#465—611no—
372C2×#441—611no—
373C2×#440—611no—
374C2×C4×Q16—611no—
375C2×C4×SD16—611no—
376C2×#405—611no—
377C2×C61—42no—
378C2×C61#317814yescomplemented
379C2×C61C2×#53211yescharacteristic
380C2×C61C2×#57711yescharacteristic
381C2×C61C2×#57811yescharacteristic
382D61—82no—
383C22×Q16—611no—
384C22×Q16—611no—
385C22×SD16—611no—
386C22×SD16—611no—
387C22×M16—611no—
388C23×C8—611no—
389#542—618no—
390#542—1224no—
391#541—24no—
392#541C2×D6118yescomplemented
393C2×C4⋊Q8—611no—
394C2×C4⋊Q8C2×D6111yescharacteristic
395C2×#126—21no—
396C2×#126—21no—
397C2×#126—1221no—
398C2×#125—21no—
399C2×#125—21no—
400C2×#125C2×D6111yescharacteristic
401C2×#124—611no—
402C2×#124—1221no—
403C2×#123—1221no—
404C2×C22⋊Q8—611no—
405C2×C22⋊Q8—1221no—
406C2×C22⋊Q8C2×D6111yescharacteristic
407C2×C22⋊Q8C2×D6111yescharacteristic
408C2×#121—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8C2×D6111yescharacteristic
411C2×C4×Q8C2×D6111yescharacteristic
412C2×C4×D4—611no—
413C2×#117C2×D6111yescharacteristic
414#501—618no—
415#497—618no—
416#488—618no—
417#487—618no—
418#470—618no—
419#468—618no—
420#467—618no—
421#465—618no—
422#441—618no—
423#440—618no—
424C4×Q16—618no—
425C4×SD16—618no—
426C2×#107—611no—
427C2×#107—611no—
428C2×#106—611no—
429C2×#106—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#102—611no—
437C2×#102—611no—
438#405—618no—
439C2×#97—611no—
440C2×#97—611no—
441C2×C4×C8—611no—
442C2×C4×C8—611no—
443C61C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—611no—
445C22×Q8—1221no—
446C22×Q8C22×D6111yescharacteristic
447C22×Q8C22×D6111yescharacteristic
448C22×D4—611no—
449C22×D4—1221no—
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C2×Q16—614no—
453C2×Q16—614no—
454C2×Q16—1224no—
455C2×Q16—1224no—
456C2×SD16—614no—
457C2×SD16—614no—
458C2×SD16—1224no—
459C2×SD16—1224no—
460C2×M16—614no—
461C2×M16—1224no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—614no—
466C22×C8—611no—
467C22×C8—1224no—
468C4⋊Q8—22no—
469C4⋊Q8—614no—
470C4⋊Q8—1222no—
471C4⋊Q8C22×D6114yes—
472#126—28no—
473#126—28no—
474#126—1228no—
475#125—28no—
476#125—28no—
477#125—22no—
478#125C22×D6114yes—
479#124—614no—
480#124—1228no—
481#124—1222no—
482#123—1228no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—614no—
486C22⋊Q8—1222no—
487C22⋊Q8—1228no—
488C22⋊Q8C22×D6114yes—
489C22⋊Q8C22×D6114yes—
490#121—614no—
491#121—1222no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—614no—
495C4×Q8—1222no—
496C4×Q8C22×D6114yes—
497C4×Q8C22×D6114yes—
498C4×D4—614no—
499C4×D4—1222no—
500#117C22⋊D6114yes—
501#117C22×D6114yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4C22⋊D6111yescharacteristic
516C2×C4⋊C4C22⋊D6111yescharacteristic
517C2×C4⋊C4C22×D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4C22⋊D6111yescharacteristic
527C2×C22⋊C4C22⋊D6111yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—1221no—
531C2×C42C22×D6111yescharacteristic
532C2×C42C22×D6111yescharacteristic
533#107—614no—
534#107—614no—
535#106—614no—
536#106—614no—
537#103—614no—
538#103—614no—
539#103—614no—
540#103—614no—
541#103—614no—
542#103—614no—
543#102—614no—
544#102—614no—
545#97—614no—
546#97—614no—
547C4×C8—614no—
548C4×C8—614no—
549C24—1221no—
550C24C2×C22⋊D6111yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—612no—
558C2×Q8—1224no—
559C2×Q8—1221no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—4882no—
563C2×Q8C23×D6112yes—
564C2×Q8C23×D6112yes—
565C2×D4—612no—
566C2×D4—1224no—
567C2×D4—1221no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—4882no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1224no—
581C22×C4—4882no—
582C22×C4C2×C22⋊D6112yes—
583C22×C4C2×C22⋊D6111yescharacteristic
584C22×C4C2×C22⋊D6111yescharacteristic
585C22×C4C2×C22⋊D6111yescharacteristic
586C22×C4C2×C22⋊D6111yescharacteristic
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C23×D6112yes—
589C22×C4C23×D6111yescharacteristic
590Q16—1228no—
591Q16—1228no—
592SD16—1228no—
593SD16—1228no—
594M16—1228no—
595C2×C8—614no—
596C2×C8—614no—
597C2×C8—612no—
598C2×C8—612no—
599C2×C8—612no—
600C2×C8—612no—
601C2×C8—1228no—
602C2×C8—1222no—
603C2×C8—1222no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—612no—
615C4⋊C4—612no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4C2×C22⋊D6114yes—
622C4⋊C4C2×C22⋊D6114yes—
623C4⋊C4C23×D6112yes—
624C4⋊C4C23×D6112yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C22⋊C4C2×C22⋊D6114yes—
633C22⋊C4C2×C22⋊D6114yes—
634C42—24no—
635C42—24no—
636C42—1224no—
637C42C2×C22⋊D6112yes—
638C42C2×C22⋊D6112yes—
639C42C23×D6112yes—
640C42C23×D6112yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—1222no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23C22×C22⋊D6112yes—
649C23C22×C22⋊D6111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—1222no—
657Q8—1222no—
658Q8—4884no—
659Q8—2442no—
660D4—1222no—
661D4—1222no—
662D4—4884no—
663D4—2442no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—4884no—
684C2×C4—2442no—
685C2×C4—2442no—
686C2×C4—2442no—
687C2×C4C22×C22⋊D6112yes—
688C2×C4C22×C22⋊D6112yes—
689C2×C4C22×C22⋊D6112yes—
690C2×C4C22×C22⋊D6112yes—
691C2×C4C22×C22⋊D6112yes—
692C2×C4C22×C22⋊D6111yescharacteristic
693C2×C4#41×D6112yes—
694C2×C4#41×D6112yes—
695C2×C4C24×D6111yescharacteristic
696C8—614no—
697C8—614no—
698C8—1222no—
699C8—1222no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—4884no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22#1684030812yes—
709C22#1684057012yes—
710C22#1684057712yes—
711C22C23×C22⋊D6111yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4#1684030812yes—
725C4C2×#41×D6111yescharacteristic
726C4C2×#41×D6111yescharacteristic
727C2—42no—
728C2—4882no—
729C2#2145648914yesdirect product factor
730C2C2×#1684030811yescharacteristic
731C2C2×#1684057011yescharacteristic
732C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#541C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterC2×#541D61
hypocenterC61C2×#3178
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #21456489C2direct (N × H)
3. C2×#16840172C2semidirect
4. C2×#16840154C2semidirect
5. C2×#16840119C2semidirect
6. C2×#16840112C2semidirect
7. C2×#16840018C2semidirect
9. C2×#16840001C2semidirect
11. C2×#16839867C2semidirect
12. C2×#16839860C2semidirect
13. C2×C4×#11758202C2semidirect
14. C2×C4×#11758201C2semidirect
15. C2×#16839718C2semidirect
16. C2×C61×#541C2semidirect
35. #16840172C22semidirect
36. #16840154C22semidirect
37. #16840119C22semidirect
38. #16840112C22semidirect
39. #16840018C22semidirect
41. #16840001C22semidirect
43. #16839867C22semidirect
44. #16839860C22semidirect
45. C4×#11758202C22semidirect
46. C4×#11758201C22semidirect
59. #16839718C22semidirect
65. C61×#541C22semidirect
362. C2×#541D61semidirect
378. C2×C61#3178semidirect
392. #541C2×D61semidirect
443. C61C2×#3178semidirect
729. C2#21456489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403832
#214564892
C2×#168401722
C2×#168401542
C2×#168401192
C2×#168401122
C2×#168400182
C2×#168400102
C2×#168400012
C2×#168399932
C2×#168398672
C2×#168398602
C2×C4×#117582022
C2×C4×#117582012
C2×#168397182
C2×C61×#5412
C2×#317861