Finite Group Databasebeta

← C2×#21458379 #30558691

Subgroups — C2×#21458379 #30558691

Order 15616.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic
2#21458379C2116yesmaximal, direct product factor
3C2×#16840161C211yesmaximal, characteristic, complemented
4C2×#16840080C211yesmaximal, characteristic, complemented
5C2×#16840100C211yesmaximal, characteristic, complemented
6C2×#16840086C211yesmaximal, characteristic, complemented
7C2×#16840090C211yesmaximal, characteristic, complemented
8C2×#16840069C211yesmaximal, characteristic, complemented
9C2×#16840059C211yesmaximal, characteristic, complemented
10C2×#16840010C211yesmaximal, characteristic, complemented
11C2×#16840010C211yesmaximal, characteristic, complemented
12C2×C4×#11758201C211yesmaximal, characteristic, complemented
13C2×#16839840C211yesmaximal, characteristic, complemented
14C2×#16839805C211yesmaximal, characteristic, complemented
15C2×#16839802C211yesmaximal, characteristic, complemented
16C2×C61×#552C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20#16840458—24no—
21#16840458C2218yes—
22C2×#14519772—21no—
23C2×#14519769C2211yescharacteristic
24C2×#14519759—21no—
25C2×#14519751C2211yescharacteristic
26C2×#14519751C2211yescharacteristic
27C2×#14519749—21no—
28C2×C4×D244C2211yescharacteristic
29C2×#14519737—21no—
30C2×#14519736C2211yescharacteristic
31C22×C4⋊Dic61C2211yescharacteristic
32#16840161C2218yescomplemented
33#16840100C2218yescomplemented
34#16840090C2218yescomplemented
35#16840086C2218yescomplemented
36#16840080C2218yescomplemented
37#16840069C2218yescomplemented
38#16840059C2218yescomplemented
39#16840010C2218yescomplemented
40#16840010C2218yescomplemented
41C4×#11758201C2218yescomplemented
42#16839840C2218yescomplemented
43#16839805C2218yescomplemented
44#16839802C2218yescomplemented
45C2×#14519710C2211yescharacteristic
46C2×#14519710C2211yescharacteristic
47C2×#14519710C2211yescharacteristic
48C2×#14519710C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×#14519708C2211yescharacteristic
51C2×#14519708C2211yescharacteristic
52C2×#14519708C2211yescharacteristic
53C2×#14519708C2211yescharacteristic
54C2×C4⋊#92418C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519701C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#552—24no—
65C61×#552C2218yescomplemented
66C2×#126×C61—21no—
67C2×#125×C61—21no—
68C2×#125×C61C2211yescharacteristic
69C2×#123×C61—21no—
70C2×C22⋊Q8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×D4×C61C2211yescharacteristic
74C2×#117×C61—21no—
75C2×#117×C61C2211yescharacteristic
76C22×C4⋊C4×C61C2211yescharacteristic
77C22×D244C2311yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C23×Dic61—21no—
81C22×C4×D61—21no—
82C2×#11758201—24no—
83C2×#11758201C2314yes—
84C2×#11758194—24no—
85C2×#11758194—24no—
86C2×#11758194C2314yes—
87C2×#11758194C2314yes—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519772—28no—
93#14519769—22no—
94#14519769C2314yes—
95#14519759—28no—
96#14519751—22no—
97#14519751—22no—
98#14519751C2314yes—
99#14519751C2314yes—
100#14519749—28no—
101C4×D244—22no—
102C4×D244C2314yes—
103#14519737—28no—
104#14519736—22no—
105#14519736C2314yes—
106C2×C4⋊Dic61—22no—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61C2314yes—
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×C4×Dic61—21no—
119#14519710C2314yes—
120#14519710C2314yes—
121#14519710C2314yes—
122#14519710C2314yes—
123#14519708C2314yes—
124#14519708C2314yes—
125#14519708C2314yes—
126#14519708C2314yes—
127#14519708C2314yes—
128C4⋊#92418C2314yes—
129#14519701C2314yes—
130#14519701C2314yes—
131#14519701C2314yes—
132#14519697C2314yes—
133#14519697C2314yes—
134#14519697C2314yes—
135C22⋊#92418C2314yes—
136C22⋊#92418C2314yes—
137C4×#92418C2314yes—
138C22×Q8×C61C2311yescharacteristic
139C22×D4×C61D411yescharacteristic
140C23×C4×C61—21no—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143#126×C61—28no—
144#125×C61—28no—
145#125×C61—22no—
146#125×C61C2314yes—
147#123×C61—28no—
148C22⋊Q8×C61—22no—
149C22⋊Q8×C61—22no—
150C22⋊Q8×C61C2314yes—
151C22⋊Q8×C61C2314yes—
152C4×Q8×C61—22no—
153C4×Q8×C61C2314yes—
154C4×D4×C61D414yes—
155C4×D4×C61C2314yes—
156#117×C61—22no—
157#117×C61—28no—
158#117×C61C2314yes—
159C2×C4⋊C4×C61—22no—
160C2×C4⋊C4×C61—21no—
161C2×C4⋊C4×C61—21no—
162C2×C4⋊C4×C61—21no—
163C2×C4⋊C4×C61—21no—
164C2×C4⋊C4×C61—21no—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61D411yescharacteristic
167C2×C4⋊C4×C61C2314yes—
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61—21no—
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61D411yescharacteristic
175C2×C22⋊C4×C61D411yescharacteristic
176C2×C42×C61—21no—
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C24×C61C2×D411yescharacteristic
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61C2412yes—
186C2×D4×C61—42no—
187C2×D4×C61C2×D414yes—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—24no—
197C22×C4×C61—44no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2412yes—
205C22×C4×C61C2412yes—
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—44no—
210C2×C22⋊D61—82no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—82no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244C2412yes—
220C2×C4×D61—24no—
221C2×C4×D61—82no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
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—21no—
231C4⋊C4×C61C2×D414yes—
232C4⋊C4×C61C2412yes—
233C4⋊C4×C61C2412yes—
234C4⋊C4×C61C2412yes—
235C22⋊C4×C61—24no—
236C22⋊C4×C61—24no—
237C22⋊C4×C61—24no—
238C22⋊C4×C61C2×D414yes—
239C22⋊C4×C61C2×D414yes—
240C42×C61—24no—
241C42×C61—24no—
242C42×C61C2×D412yes—
243C42×C61C2412yes—
244C22⋊Dic61—24no—
245#11758201—28no—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—24no—
252C4⋊Dic61—21no—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255C4⋊Dic61C2412yes—
256#11758196—24no—
257#11758196—24no—
258C4×Dic61—24no—
259#11758194—28no—
260#11758194—28no—
261C2×#92418—22no—
262C2×#92418—22no—
263C2×#92418—22no—
264C2×#92418#4114yes—
265C2×#92418C2412yes—
266C2×#92418C2412yes—
267C2×#92418C2412yes—
268C2×#92418C2412yes—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61C22×D412yes—
276C23×C61C22×D412yes—
277C23×C61C22×D411yescharacteristic
278C22×D61—22no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—42no—
285D4×C61—44no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—48no—
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×D411yescharacteristic
310C2×C4×C61C2×#4112yes—
311C2×C4×C612−1+412yes—
312C2×C4×C61C2511yescharacteristic
313C22⋊D61—48no—
314C22⋊D61—84no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—84no—
322D244—22no—
323D244—22no—
324D244—42no—
325C4×D61—84no—
326#92418—22no—
327#92418—22no—
328#92418—22no—
329#92418C2×#4114yes—
330C2×#3351—611nomaximal, Sylow
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—44no—
338C22×C61—44no—
339C22×C61#54712yes—
340C22×C61#57512yes—
341C22×C61#57712yes—
342C22×C61C23×D411yescharacteristic
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—84no—
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#54712yes—
356C4×C61C22×#4111yescharacteristic
357C4×C61C2×2−1+411yescharacteristic
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#553—611no—
362C2×#552D6111yescharacteristic, complemented
363#3351—6116no—
364C2×#499—611no—
365C2×#481—611no—
366C2×#485—611no—
367C2×#482—611no—
368C2×#483—611no—
369C2×#479—611no—
370C2×#478—611no—
371C2×#468—611no—
372C2×#468—611no—
373C2×C4×SD16—611no—
374C2×#436—611no—
375C2×#428—611no—
376C2×#428—611no—
377C2×C61—42no—
378C2×C61—42no—
379C2×C61#335114yescomplemented
380C2×C61C2×#54711yescharacteristic
381C2×C61C2×#57511yescharacteristic
382C2×C61C2×#57711yescharacteristic
383D61—82no—
384C22×SD16—611no—
385C22×M16—611no—
386C22×M16—611no—
387#553—618no—
388#553—1224no—
389#552—24no—
390#552C2×D6118yescomplemented
391C2×#126—21no—
392C2×#126—1221no—
393C2×#125—21no—
394C2×#125—611no—
395C2×#125C2×D6111yescharacteristic
396C2×#123—21no—
397C2×#123—1221no—
398C2×C22⋊Q8C2×D6111yescharacteristic
399C2×C22⋊Q8C2×D6111yescharacteristic
400C2×#121—611no—
401C2×#121—611no—
402C2×#121—1221no—
403C2×C4×Q8C2×D6111yescharacteristic
404C2×C4×D4—611no—
405C2×C4×D4—1221no—
406C2×C4×D4C2×D6111yescharacteristic
407C2×#117—21no—
408C2×#117—611no—
409C2×#117C2×D6111yescharacteristic
410C22×C4⋊C4—611no—
411C22×C4⋊C4C2×D6111yescharacteristic
412#499—618no—
413#485—618no—
414#483—618no—
415#482—618no—
416#481—618no—
417#479—618no—
418#478—618no—
419#468—618no—
420#468—618no—
421C4×SD16—618no—
422#436—618no—
423#428—618no—
424#428—618no—
425C2×#107—611no—
426C2×#107—611no—
427C2×#107—611no—
428C2×#107—611no—
429C2×#106—611no—
430C2×#106—611no—
431C2×#106—611no—
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C4×C8—611no—
444C61C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8C22×D6111yescharacteristic
446C22×D4—611no—
447C22×D4—1221no—
448C22×D4—1221no—
449C22×D4C22⋊D6111yescharacteristic
450C23×C4—21no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4C22×D6111yescharacteristic
454C23×C4C22×D6111yescharacteristic
455C2×SD16—614no—
456C2×SD16—1224no—
457C2×M16—614no—
458C2×M16—614no—
459C2×M16—1224no—
460C2×M16—1224no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465#126—28no—
466#126—1228no—
467#125—28no—
468#125—22no—
469#125—614no—
470#125—1222no—
471#125C22×D6114yes—
472#123—28no—
473#123—1228no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8C22×D6114yes—
477C22⋊Q8C22×D6114yes—
478#121—614no—
479#121—614no—
480#121—1228no—
481#121—1222no—
482#121—1222no—
483C4×Q8—22no—
484C4×Q8C22×D6114yes—
485C4×D4—614no—
486C4×D4—1228no—
487C4×D4—1222no—
488C4×D4C22⋊D6114yes—
489C4×D4C22×D6114yes—
490#117—22no—
491#117—28no—
492#117—614no—
493#117—1222no—
494#117C22×D6114yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—614no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1222no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4C22⋊D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6114yes—
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4C22⋊D6111yescharacteristic
523C2×C22⋊C4C22⋊D6111yescharacteristic
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—1221no—
527C2×C42C22×D6111yescharacteristic
528#107—614no—
529#107—614no—
530#107—614no—
531#107—614no—
532#106—614no—
533#106—614no—
534#106—614no—
535#106—614no—
536#106—614no—
537C4⋊C8—614no—
538#103—614no—
539#103—614no—
540#103—614no—
541#102—614no—
542#102—614no—
543#102—614no—
544C22⋊C8—614no—
545C22⋊C8—614no—
546C4×C8—614no—
547C24—1221no—
548C24C2×C22⋊D6111yescharacteristic
549C24C2×C22⋊D6111yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D6112yes—
554C2×D4—42no—
555C2×D4—612no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—1221no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—4882no—
562C2×D4—2444no—
563C2×D4C2×C22⋊D6114yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—44no—
574C22×C4—1224no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1224no—
579C22×C4—4882no—
580C22×C4—4882no—
581C22×C4C2×C22⋊D6112yes—
582C22×C4C2×C22⋊D6112yes—
583C22×C4C2×C22⋊D6111yescharacteristic
584C22×C4C2×C22⋊D6111yescharacteristic
585C22×C4C2×C22⋊D6111yescharacteristic
586C22×C4C2×C22⋊D6111yescharacteristic
587C22×C4C23×D6112yes—
588C22×C4C23×D6112yes—
589C22×C4C23×D6111yescharacteristic
590SD16—1228no—
591M16—1228no—
592M16—1228no—
593C2×C8—614no—
594C2×C8—612no—
595C2×C8—612no—
596C2×C8—612no—
597C2×C8—612no—
598C2×C8—1222no—
599C2×C8—1222no—
600C2×C8—1222no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—612no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1224no—
616C4⋊C4—1221no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4C2×C22⋊D6114yes—
620C4⋊C4C23×D6112yes—
621C4⋊C4C23×D6112yes—
622C4⋊C4C23×D6112yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4C2×C22⋊D6114yes—
631C22⋊C4C2×C22⋊D6114yes—
632C42—24no—
633C42—24no—
634C42—1224no—
635C42C2×C22⋊D6112yes—
636C42C23×D6112yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—1222no—
644C23—2442no—
645C23—2442no—
646C23—2442no—
647C23C22×C22⋊D6112yes—
648C23C22×C22⋊D6112yes—
649C23C22×C22⋊D6111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—44no—
654D4—1222no—
655D4—1222no—
656D4—4884no—
657D4—2448no—
658D4—2442no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—48no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—4884no—
682C2×C4—4884no—
683C2×C4—2442no—
684C2×C4—2442no—
685C2×C4—2442no—
686C2×C4C22×C22⋊D6112yes—
687C2×C4C22×C22⋊D6112yes—
688C2×C4C22×C22⋊D6112yes—
689C2×C4C22×C22⋊D6112yes—
690C2×C4C22×C22⋊D6111yescharacteristic
691C2×C4#41×D6112yes—
692C2×C4#1451982412yes—
693C2×C4C24×D6111yescharacteristic
694C8—614no—
695C8—1222no—
696C8—1222no—
697C8—1222no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—4884no—
707C22—2442no—
708C22—2442no—
709C22—2442no—
710C22#1684041112yes—
711C22#1684056012yes—
712C22#1684057012yes—
713C22C23×C22⋊D6111yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4#1684041112yes—
726C4C2×#41×D6111yescharacteristic
727C4C2×#1451982411yescharacteristic
728C2—42no—
729C2—42no—
730C2—4882no—
731C2#2145837914yesdirect product factor
732C2C2×#1684041111yescharacteristic
733C2C2×#1684056011yescharacteristic
734C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#552C2
socleC23×C61C22×D4
prime radicalC2×#16840458C2
hypercenterC2×#552D61
hypocenterC61C2×#3351
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #21458379C2direct (N × H)
3. C2×#16840161C2semidirect
4. C2×#16840080C2semidirect
5. C2×#16840100C2semidirect
6. C2×#16840086C2semidirect
7. C2×#16840090C2semidirect
8. C2×#16840069C2semidirect
9. C2×#16840059C2semidirect
10. C2×#16840010C2semidirect
11. C2×#16840010C2semidirect
12. C2×C4×#11758201C2semidirect
13. C2×#16839840C2semidirect
14. C2×#16839805C2semidirect
15. C2×#16839802C2semidirect
16. C2×C61×#552C2semidirect
32. #16840161C22semidirect
33. #16840100C22semidirect
34. #16840090C22semidirect
35. #16840086C22semidirect
36. #16840080C22semidirect
37. #16840069C22semidirect
38. #16840059C22semidirect
39. #16840010C22semidirect
40. #16840010C22semidirect
41. C4×#11758201C22semidirect
42. #16839840C22semidirect
43. #16839805C22semidirect
44. #16839802C22semidirect
65. C61×#552C22semidirect
362. C2×#552D61semidirect
379. C2×C61#3351semidirect
390. #552C2×D61semidirect
444. C61C2×#3351semidirect
731. C2#21458379direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404582
#214583792
C2×#168401612
C2×#168400802
C2×#168401002
C2×#168400862
C2×#168400902
C2×#168400692
C2×#168400592
C2×#168400102
C2×C4×#117582012
C2×#168398402
C2×#168398052
C2×#168398022
C2×C61×#5522
C2×#335161