Finite Group Databasebeta

← C2×#21458259 #30558544

Subgroups — C2×#21458259 #30558544

Order 15616.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840416C211yesmaximal, characteristic
2#21458259C2116yesmaximal, direct product factor
3C2×#16840172C211yesmaximal, characteristic, complemented
4C2×#16840095C211yesmaximal, characteristic, complemented
5C2×#16840086C211yesmaximal, characteristic, complemented
6C2×#16840090C211yesmaximal, characteristic, complemented
7C2×#16840075C211yesmaximal, characteristic, complemented
8C2×#16840057C211yesmaximal, characteristic, complemented
9C2×#16840059C211yesmaximal, characteristic, complemented
10C2×#16840010C211yesmaximal, characteristic, complemented
11C2×#16839993C211yesmaximal, characteristic, complemented
12C2×#16839860C211yesmaximal, characteristic, complemented
13C2×#16839834C211yesmaximal, characteristic, complemented
14C2×#16839805C211yesmaximal, characteristic, complemented
15C22×#14519710C211yesmaximal, characteristic, complemented
16C2×C61×#552C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758201C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C23×#92418C2211yescharacteristic
21#16840416—24no—
22#16840416C2218yes—
23C2×#14519777C2211yescharacteristic
24C2×#14519761—21no—
25C2×#14519761—21no—
26C2×#14519757—21no—
27C2×#14519751C2211yescharacteristic
28C2×#14519751C2211yescharacteristic
29C2×C4×D244C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C22×C4⋊Dic61C2211yescharacteristic
32#16840172C2218yescomplemented
33#16840095C2218yescomplemented
34#16840090C2218yescomplemented
35#16840086C2218yescomplemented
36#16840075C2218yescomplemented
37#16840059C2218yescomplemented
38#16840057C2218yescomplemented
39#16840010C2218yescomplemented
40#16839993C2218yescomplemented
41#16839860C2218yescomplemented
42#16839834C2218yescomplemented
43#16839805C2218yescomplemented
44C2×#14519710C2211yescharacteristic
45C2×#14519710C2211yescharacteristic
46C2×#14519710C2211yescharacteristic
47C2×#14519710C2211yescharacteristic
48C2×#14519710C2211yescharacteristic
49C2×#14519710C2211yescharacteristic
50C2×#14519710C2218yescomplemented
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×#14519688C2211yescharacteristic
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
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C2×#11758201—24no—
87C2×#11758201C2314yes—
88C2×#11758194—24no—
89C2×#11758194C2314yes—
90C22×#92418—24no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2314yes—
95C22×#92418C2311yescharacteristic
96#14519777—22no—
97#14519777C2314yes—
98#14519761—28no—
99#14519761—28no—
100#14519757—28no—
101#14519751—22no—
102#14519751—22no—
103#14519751C2314yes—
104#14519751C2314yes—
105C4×D244—22no—
106C4×D244C2314yes—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61—22no—
110C2×C4⋊Dic61—22no—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×C4⋊Dic61C2314yes—
116C2×C4⋊Dic61C2314yes—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120#14519710C2314yes—
121#14519710C2314yes—
122#14519710C2314yes—
123#14519710C2314yes—
124#14519710C2314yes—
125#14519710C2314yes—
126#14519708C2314yes—
127#14519708C2314yes—
128#14519708C2314yes—
129C4⋊#92418C2314yes—
130#14519701C2314yes—
131#14519701C2314yes—
132#14519701C2314yes—
133#14519697C2314yes—
134#14519697C2314yes—
135#14519697C2314yes—
136C22⋊#92418C2314yes—
137C22⋊#92418C2314yes—
138#14519688C2314yes—
139C22×Q8×C61C2311yescharacteristic
140C22×D4×C61D411yescharacteristic
141C23×C4×C61—21no—
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144#126×C61—28no—
145#125×C61—28no—
146#125×C61—22no—
147#125×C61C2314yes—
148#123×C61—28no—
149C22⋊Q8×C61—22no—
150C22⋊Q8×C61—22no—
151C22⋊Q8×C61C2314yes—
152C22⋊Q8×C61C2314yes—
153C4×Q8×C61—22no—
154C4×Q8×C61C2314yes—
155C4×D4×C61D414yes—
156C4×D4×C61C2314yes—
157#117×C61—22no—
158#117×C61—28no—
159#117×C61C2314yes—
160C2×C4⋊C4×C61—22no—
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×C61—21no—
167C2×C4⋊C4×C61D411yescharacteristic
168C2×C4⋊C4×C61C2314yes—
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61D411yescharacteristic
176C2×C22⋊C4×C61D411yescharacteristic
177C2×C42×C61—21no—
178C2×C42×C61—21no—
179C2×C42×C61C2311yescharacteristic
180C24×C61C2×D411yescharacteristic
181C24×C61C2×D411yescharacteristic
182C23×D61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—22no—
185C2×Q8×C61—22no—
186C2×Q8×C61C2412yes—
187C2×D4×C61—24no—
188C2×D4×C61C2×D414yes—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—24no—
198C22×C4×C61—44no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2412yes—
206C22×C4×C61C2412yes—
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—44no—
211C2×C22⋊D61—44no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—24no—
217C22×Dic61—44no—
218C22×Dic61—44no—
219#11758224—432no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—21no—
223C2×D244C2412yes—
224C2×C4×D61—24no—
225C2×C4×D61—44no—
226C2×Dic122—24no—
227C2×Dic122—44no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—24no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C2×D414yes—
238C4⋊C4×C61C2412yes—
239C4⋊C4×C61C2412yes—
240C4⋊C4×C61C2412yes—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61C2×D414yes—
245C22⋊C4×C61C2×D414yes—
246C42×C61—24no—
247C42×C61—24no—
248C42×C61C2×D412yes—
249C42×C61C2412yes—
250#11758201—28no—
251#11758198—24no—
252#11758198—24no—
253#11758198—24no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61—24no—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263#11758194—28no—
264C2×#92418—22no—
265C2×#92418—22no—
266C2×#92418—22no—
267C2×#92418—28no—
268C2×#92418#4114yescomplemented
269C2×#92418C2412yes—
270C2×#92418C2412yes—
271C2×#92418C2412yes—
272C2×#92418C2412yes—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61AGL(1,ℤ/8)14yes—
279C23×C61C22×D412yes—
280C23×C61C22×D412yes—
281C23×C61C22×D411yescharacteristic
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286Q8×C61—22no—
287Q8×C61—22no—
288Q8×C61—42no—
289D4×C61—28no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—24no—
295C2×C4×C61—24no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—42no—
305C2×C4×C61—48no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D412yes—
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4112yes—
315C2×C4×C612−1+412yes—
316C2×C4×C61C2511yescharacteristic
317C22⋊D61—48no—
318C22⋊D61—48no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—48no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—48no—
327D244—22no—
328D244—22no—
329D244—42no—
330C4×D61—48no—
331Dic122—48no—
332#92418—22no—
333#92418—22no—
334#92418—22no—
335#92418C2×#4114yescomplemented
336C2×#3343—611nomaximal, Sylow
337C22×C61—28no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—44no—
344C22×C61#54712yes—
345C22×C61C2×AGL(1,ℤ/8)14yes—
346C22×C61C2×AGL(1,ℤ/8)12yes—
347C22×C61#57812yes—
348C22×C61C23×D411yescharacteristic
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—84no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61#54712yes—
362C4×C61C22×#4111yescharacteristic
363C4×C61C2×2−1+411yescharacteristic
364Dic61—42no—
365Dic61—42no—
366Dic61—42no—
367C2×#552D6111yescharacteristic, complemented
368C2×#547—611no—
369#3343—6116no—
370C2×#501—611no—
371C2×#484—611no—
372C2×#482—611no—
373C2×#483—611no—
374C2×#480—611no—
375C2×#477—611no—
376C2×#478—611no—
377C2×#468—611no—
378C2×#465—611no—
379C2×#440—611no—
380C2×#435—611no—
381C2×#428—611no—
382C22×#107—611no—
383C2×C61—24no—
384C2×C61—42no—
385C2×C61#334314yescomplemented
386C2×C61C2×#54711yescharacteristic
387C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C61C2×#57811yescharacteristic
389D61—82no—
390C22×#41—1221no—
391C22×SD16—611no—
392C22×M16—611no—
393C23×C8—611no—
394#552—24no—
395#552C2×D6118yescomplemented
396#547—618no—
397#547—1224no—
398C2×C4⋊Q8—611no—
399C2×#126—21no—
400C2×#125—21no—
401C2×#125C2×D6111yescharacteristic
402C2×#123—21no—
403C2×#123—1221no—
404C2×#123—1221no—
405C2×C22⋊Q8—1221no—
406C2×C22⋊Q8C2×D6111yescharacteristic
407C2×C22⋊Q8C2×D6111yescharacteristic
408C2×#121—611no—
409C2×#121—611no—
410C2×C4×Q8C2×D6111yescharacteristic
411C2×C4×D4—611no—
412C2×C4×D4C2×D6111yescharacteristic
413C2×#117—21no—
414C2×#117C2×D6111yescharacteristic
415C22×C4⋊C4—611no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4C2×D6111yescharacteristic
418#501—618no—
419#484—618no—
420#483—618no—
421#482—618no—
422#480—618no—
423#478—618no—
424#477—618no—
425#468—618no—
426#465—618no—
427#440—618no—
428#435—618no—
429#428—618no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#107—611no—
434C2×#107—618no—
435C2×#107—611no—
436C2×#107—611no—
437C2×#106—611no—
438C2×#106—611no—
439C2×#106—611no—
440C2×C4⋊C8—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×#97—611no—
450C61C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1228no—
452C2×#41—2448no—
453C22×Q8—1221no—
454C22×Q8C22×D6111yescharacteristic
455C22×D4—611no—
456C22×D4—1221no—
457C22×D4—1221no—
458C22×D4C22⋊D6111yescharacteristic
459C23×C4—21no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C2×SD16—614no—
466C2×SD16—1224no—
467C2×M16—614no—
468C2×M16—1224no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—614no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—1224no—
475C4⋊Q8—614no—
476C4⋊Q8—1222no—
477#126—28no—
478#125—28no—
479#125—22no—
480#125C22×D6114yes—
481#123—28no—
482#123—1228no—
483#123—1228no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—1228no—
487C22⋊Q8C22×D6114yes—
488C22⋊Q8C22×D6114yes—
489#121—614no—
490#121—614no—
491#121—1222no—
492#121—1222no—
493C4×Q8—22no—
494C4×Q8C22×D6114yes—
495C4×D4—614no—
496C4×D4—1222no—
497C4×D4C22⋊D6114yes—
498C4×D4C22×D6114yes—
499#117—22no—
500#117—28no—
501#117C22×D6114yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—614no—
513C2×C4⋊C4—614no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4C22⋊D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6114yes—
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4C22⋊D6111yescharacteristic
531C2×C22⋊C4C22⋊D6111yescharacteristic
532C2×C42—21no—
533C2×C42—21no—
534C2×C42C22×D6111yescharacteristic
535#107—614no—
536#107—614no—
537#107—614no—
538#107—614no—
539#107—614no—
540#107—614no—
541#106—614no—
542#106—614no—
543#106—614no—
544C4⋊C8—614no—
545#103—614no—
546#103—614no—
547#103—614no—
548#102—614no—
549#102—614no—
550#102—614no—
551C22⋊C8—614no—
552C22⋊C8—614no—
553#97—614no—
554C24—1221no—
555C24C2×C22⋊D6111yescharacteristic
556C24C2×C22⋊D6111yescharacteristic
557#41—24432no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—1224no—
562C2×Q8—2444no—
563C2×Q8C23×D6112yes—
564C2×D4—24no—
565C2×D4—612no—
566C2×D4—1224no—
567C2×D4—1224no—
568C2×D4—1221no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—2444no—
572C2×D4—2444no—
573C2×D4C2×C22⋊D6114yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1224no—
590C22×C4—2444no—
591C22×C4—2444no—
592C22×C4—2444no—
593C22×C4C2×C22⋊D6112yes—
594C22×C4C2×C22⋊D6112yes—
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C23×D6112yes—
600C22×C4C23×D6112yes—
601C22×C4C23×D6111yescharacteristic
602SD16—1228no—
603M16—1228no—
604C2×C8—614no—
605C2×C8—612no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—1228no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8—1222no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—612no—
623C4⋊C4—612no—
624C4⋊C4—612no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4C2×C22⋊D6114yes—
632C4⋊C4C23×D6112yes—
633C4⋊C4C23×D6112yes—
634C4⋊C4C23×D6112yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C22⋊C4—1224no—
641C22⋊C4C2×C22⋊D6114yes—
642C22⋊C4C2×C22⋊D6114yes—
643C42—24no—
644C42—24no—
645C42C2×C22⋊D6112yes—
646C42C23×D6112yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1222no—
653C23—2442no—
654C23—2442no—
655C23—2442no—
656C23#1451980214yes—
657C23C22×C22⋊D6112yes—
658C23C22×C22⋊D6112yes—
659C23C22×C22⋊D6111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—2448no—
664D4—28no—
665D4—1222no—
666D4—1222no—
667D4—2448no—
668D4—2448no—
669D4—2442no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—2448no—
693C2×C4—2448no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4—2448no—
698C2×C4C22×C22⋊D6112yes—
699C2×C4C22×C22⋊D6112yes—
700C2×C4C22×C22⋊D6112yes—
701C2×C4C22×C22⋊D6112yes—
702C2×C4C22×C22⋊D6111yescharacteristic
703C2×C4#41×D6112yes—
704C2×C4#1451982412yes—
705C2×C4C24×D6111yescharacteristic
706C8—614no—
707C8—1222no—
708C8—1222no—
709C8—1222no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—4884no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22#1684041112yes—
722C22C2×#1451980214yes—
723C22C2×#1451980212yes—
724C22#1684057712yes—
725C22C23×C22⋊D6111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—2442no—
735C4—2442no—
736C4—2442no—
737C4#1684041112yes—
738C4C2×#41×D6111yescharacteristic
739C4C2×#1451982411yescharacteristic
740C2—24no—
741C2—42no—
742C2—4882no—
743C2#2145825914yesdirect product factor
744C2C2×#1684041111yescharacteristic
745C2C22×#1451980211yescharacteristic
746C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#552C2
socleC23×C61C22×D4
prime radicalC2×#16840416C2
hypercenterC2×#552D61
hypocenterC61C2×#3343
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. #21458259C2direct (N × H)
3. C2×#16840172C2semidirect
4. C2×#16840095C2semidirect
5. C2×#16840086C2semidirect
6. C2×#16840090C2semidirect
7. C2×#16840075C2semidirect
8. C2×#16840057C2semidirect
9. C2×#16840059C2semidirect
10. C2×#16840010C2semidirect
11. C2×#16839993C2semidirect
12. C2×#16839860C2semidirect
13. C2×#16839834C2semidirect
14. C2×#16839805C2semidirect
15. C22×#14519710C2semidirect
16. C2×C61×#552C2semidirect
32. #16840172C22semidirect
33. #16840095C22semidirect
34. #16840090C22semidirect
35. #16840086C22semidirect
36. #16840075C22semidirect
37. #16840059C22semidirect
38. #16840057C22semidirect
39. #16840010C22semidirect
40. #16839993C22semidirect
41. #16839860C22semidirect
42. #16839834C22semidirect
43. #16839805C22semidirect
50. C2×#14519710C22semidirect
65. C61×#552C22semidirect
268. C2×#92418#41semidirect
335. #92418C2×#41semidirect
367. C2×#552D61semidirect
385. C2×C61#3343semidirect
395. #552C2×D61semidirect
450. C61C2×#3343semidirect
743. C2#21458259direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404162
#214582592
C2×#168401722
C2×#168400952
C2×#168400862
C2×#168400902
C2×#168400752
C2×#168400572
C2×#168400592
C2×#168400102
C2×#168399932
C2×#168398602
C2×#168398342
C2×#168398052
C22×#145197102
C2×C61×#5522
C2×#334361