Finite Group Databasebeta

← C2×#21459633 #30588342

Subgroups — C2×#21459633 #30588342

Order 15616.

7478 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459633C2132yesmaximal, direct product factor
2C2×Q8×Dic122C211yesmaximal, characteristic, complemented
3C2×#16840492C211yesmaximal, characteristic, complemented
4C2×#16840489C212yesmaximal, complemented
5C2×#16840470C212yesmaximal, complemented
6C2×#16840469C211yesmaximal, characteristic, complemented
7C2×#16840467C212yesmaximal, complemented
8C2×D4×Dic122C212yesmaximal, complemented
9C2×#16840425C214yesmaximal, complemented
10C2×#16840392C212yesmaximal, complemented
11C2×#16840391C214yesmaximal, complemented
12C2×#16840316C211yesmaximal, characteristic, complemented
13C2×#16840314C212yesmaximal, complemented
14C22×#14519776C212yesmaximal, complemented
15C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
16C2×#16840241C212yesmaximal
17C2×C4×#11758224C211yesmaximal, characteristic
18C2×C61×#554C211yesmaximal, characteristic, complemented
19C22×#11758224C2211yescharacteristic
20C23×Dic122C2214yes—
21C22×Q8×D61C2212yes—
22Q8×Dic122C22116yescomplemented
23#16840492C22116yescomplemented
24#16840489C22132yescomplemented
25#16840470C22132yescomplemented
26#16840469C22116yescomplemented
27#16840467C22132yescomplemented
28D4×Dic122C22132yescomplemented
29#16840425C22164yescomplemented
30#16840392C22132yescomplemented
31#16840391C22164yescomplemented
32#16840316C22116yescomplemented
33#16840314C22132yescomplemented
34C2×#14519777C2212yes—
35C2×#14519777C2211yescharacteristic
36C2×#14519776C2214yes—
37C2×#14519776C2214yes—
38C2×#14519776C2212yes—
39C2×#14519776C2214yes—
40C2×#14519776C2212yes—
41C2×#14519776C2212yes—
42C2×#14519776C2212yes—
43C2×#14519776C2211yescharacteristic
44C2×#14519776C2212yes—
45C2×#14519776C22132yescomplemented
46C2×#14519775C2212yes—
47C2×#14519775C2214yes—
48C2×#14519775C2211yescharacteristic
49C4⋊Q8×D61C22116yescomplemented
50C2×#14519768C2212yes—
51C2×#14519767C2212yes—
52C2×#14519767C2214yes—
53C2×#14519767C2214yes—
54C2×#14519767C2214yes—
55C2×#14519757C2214yes—
56C2×#14519757C2211yescharacteristic
57C2×#14519756C2214yes—
58C2×#14519756C2212yes—
59C2×#14519755C2214yes—
60C2×#14519755C2212yes—
61C2×#14519754C2214yes—
62C2×#14519754C2214yes—
63C2×#14519754C2214yes—
64C2×#14519753C2211yescharacteristic
65#16840241C22132yes—
66C4×#11758224C22116yes—
67C2×Q8×Dic61C2212yes—
68C2×C4×Dic122C2211yescharacteristic
69C2×C4×Dic122C2212yes—
70C2×C4×Dic122C2212yes—
71C2×C4×Dic122C2211yescharacteristic
72C2×#14519742C2211yescharacteristic
73C2×#14519742C2212yes—
74C2×#14519742C2214yes—
75C2×#14519742C2212yes—
76C2×D4×Dic61C2211yescharacteristic
77C2×D4×Dic61C2212yes—
78C2×C4×C22⋊D61C2212yes—
79C2×C4×C22⋊D61C2214yes—
80C2×#14519737C2212yes—
81C2×#14519737C2214yes—
82C2×#14519735C2211yescharacteristic
83C2×#14519734C2212yes—
84C2×#14519733C2212yes—
85C2×#14519733C2214yes—
86C22×C4⋊Dic61C2212yes—
87C22×#11758196C2214yes—
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C22×C4×Dic61C2212yes—
91C2×C42×D61C2211yescharacteristic
92C61×#554C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×#125×C61C2212yes—
95C2×C22⋊Q8×C61C2214yes—
96C2×C22⋊Q8×C61C2212yes—
97C2×C4×Q8×C61C2211yescharacteristic
98C2×C4×D4×C61C2211yescharacteristic
99C2×C4×D4×C61C2212yes—
100C22×C4⋊C4×C61C2212yes—
101C2×#11758224Q8116yescomplemented
102C2×#11758224C2318yes—
103C22×Dic122—416no—
104C22×Dic122C2311yescharacteristic
105C22×Dic122C2314yes—
106C22×Dic122C2312yes—
107C22×Dic122C2312yes—
108C22×Dic122C2314yes—
109C22×Dic122C2314yes—
110C22×Dic122C23132yes—
111C22×Dic122C2311yescharacteristic
112C2×Q8×D61—48no—
113C2×Q8×D61C23116yes—
114C22×C22⋊D61C2312yes—
115C23×Dic61C2312yes—
116C23×Dic61C2314yes—
117C23×Dic61C2312yes—
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2314yes—
121C22×C4×D61C2311yescharacteristic
122#14519777C2318yes—
123#14519777C23116yes—
124#14519776C23116yes—
125#14519776C23116yes—
126#14519776C23116yes—
127#14519776C23132yes—
128#14519776C23116yes—
129#14519776C23132yes—
130#14519776C23116yes—
131#14519776C2318yes—
132#14519776C23132yes—
133#14519775C23132yes—
134#14519775C23116yes—
135#14519775C2318yes—
136#14519768C23116yes—
137#14519767C23132yes—
138#14519767C23132yes—
139#14519767C23132yes—
140#14519767C23116yes—
141#14519757C2318yes—
142#14519757C23132yes—
143#14519756C23116yes—
144#14519756C23132yes—
145#14519755C23132yes—
146#14519755C23116yes—
147#14519754C23132yes—
148#14519754C23132yes—
149#14519754C23132yes—
150#14519753C2318yes—
151Q8×Dic61C23116yes—
152C4×Dic122C2318yes—
153C4×Dic122C2318yes—
154C4×Dic122C23116yes—
155C4×Dic122C23116yes—
156#14519742C23116yes—
157#14519742C2318yes—
158#14519742C23116yes—
159#14519742C23132yes—
160D4×Dic61C23116yes—
161D4×Dic61C2318yes—
162C4×C22⋊D61C23116yes—
163C4×C22⋊D61C23132yes—
164#14519737C23132yes—
165#14519737C23116yes—
166#14519735C2318yes—
167#14519734C23116yes—
168#14519733C23116yes—
169#14519733C23132yes—
170C2×C4⋊Dic61C2312yes—
171C2×C4⋊Dic61C2312yes—
172C2×C4⋊Dic61C2311yescharacteristic
173C2×C4⋊Dic61C23116yes—
174C2×C4⋊Dic61C2314yes—
175C2×C4⋊Dic61C2311yescharacteristic
176C2×C4⋊Dic61C2312yes—
177C2×C4⋊Dic61C2314yes—
178C2×#11758196C2314yes—
179C2×#11758196C2314yes—
180C2×#11758196C2312yes—
181C2×#11758196C2314yes—
182C2×#11758196C2314yes—
183C2×#11758196C23132yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2312yes—
188C2×#11758196C2314yes—
189C2×#11758196C2314yes—
190C2×#11758196C2312yes—
191C2×#11758196C2312yes—
192C4⋊C4×D61C23116yes—
193C4⋊C4×D61C23116yes—
194C2×C22⋊Dic61C2314yes—
195C2×C22⋊Dic61C2312yes—
196C2×#11758198C2312yes—
197C2×#11758198C2312yes—
198C2×#11758198C2312yes—
199C2×C4×Dic61C2311yescharacteristic
200C2×C4×Dic61C2311yescharacteristic
201C2×C4×Dic61C2311yescharacteristic
202C2×C4×Dic61C2312yes—
203C2×C4×Dic61C2312yes—
204C2×C4×Dic61C2312yes—
205C2×C4×Dic61C23116yes—
206C2×C4×Dic61C2314yes—
207C2×C4×Dic61C2314yes—
208C2×C4×Dic61C2312yes—
209C42×D61C2318yes—
210C22×Q8×C61C2311yescharacteristic
211C22×Q8×C61C2312yes—
212C22×D4×C61C2311yescharacteristic
213C23×C4×C61C2312yes—
214C23×C4×C61C2314yes—
215C4⋊Q8×C61C2318yes—
216#125×C61C23116yes—
217C22⋊Q8×C61C23116yes—
218C22⋊Q8×C61C23132yes—
219C4×Q8×C61C2318yes—
220C4×D4×C61C2318yes—
221C4×D4×C61C23116yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2312yes—
224C2×C4⋊C4×C61C23116yes—
225C2×C4⋊C4×C61C2311yescharacteristic
226C2×C4⋊C4×C61C2314yes—
227C2×C4⋊C4×C61C2314yes—
228C2×C4⋊C4×C61C2312yes—
229C2×C4⋊C4×C61C2311yescharacteristic
230C2×C22⋊C4×C61C2312yes—
231C2×C22⋊C4×C61C2314yes—
232C2×C42×C61C2311yescharacteristic
233C2×C42×C61C2312yes—
234C24×C61C2412yes—
235C23×D61C2411yescharacteristic
236C2×Q8×C61—24no—
237C2×Q8×C61—44no—
238C2×Q8×C61C2414yes—
239C2×Q8×C61C2418yes—
240C2×D4×C61C2×Q818yescomplemented
241C2×D4×C61C2414yes—
242C22×C4×C61—28no—
243C22×C4×C61—48no—
244C22×C4×C61C2411yescharacteristic
245C22×C4×C61C2414yes—
246C22×C4×C61C2412yes—
247C22×C4×C61C2412yes—
248C22×C4×C61C2412yes—
249C22×C4×C61C2418yes—
250C22×C4×C61C24116yes—
251C22×C4×C61C2411yescharacteristic
252C22×C4×C61C2411yescharacteristic
253C2×C22⋊D61C2×Q8116yescomplemented
254C2×C22⋊D61C2418yes—
255C22×Dic61—28no—
256C22×Dic61—48no—
257C22×Dic61C2×Q8116yescomplemented
258C22×Dic61C2414yes—
259C22×Dic61C2411yescharacteristic
260C22×Dic61C2412yes—
261C22×Dic61C2412yes—
262C22×Dic61C2418yes—
263C22×Dic61C2412yes—
264C22×Dic61C24116yes—
265C22×Dic61C2411yescharacteristic
266C22×Dic61C2412yes—
267C22×Dic61C2418yes—
268C22×Dic61C2411yescharacteristic
269Q8×D61—432no—
270#11758224C2×Q8164yescomplemented
271C2×C4×D61—24no—
272C2×C4×D61—24no—
273C2×C4×D61—48no—
274C2×C4×D61C2×Q818yescomplemented
275C2×C4×D61C2414yes—
276C2×C4×D61C2414yes—
277C2×C4×D61C24116yes—
278C2×C4×D61C2414yes—
279C2×Dic122—24no—
280C2×Dic122—216no—
281C2×Dic122—28no—
282C2×Dic122—464no—
283C2×Dic122—44no—
284C2×Dic122—48no—
285C2×Dic122—48no—
286C2×Dic122C2×Q818yescomplemented
287C2×Dic122C24116yes—
288C2×Dic122C2418yes—
289C2×Dic122C2414yes—
290C2×Dic122C2418yes—
291C2×Dic122C24116yes—
292C2×Dic122C24116yes—
293C2×Dic122C2414yes—
294C4⋊C4×C61C2414yes—
295C4⋊C4×C61C24116yes—
296C4⋊C4×C61C2418yes—
297C4⋊C4×C61C2414yes—
298C4⋊C4×C61C2418yes—
299C4⋊C4×C61C2418yes—
300C4⋊C4×C61C24116yes—
301C22⋊C4×C61C24116yes—
302C22⋊C4×C61C2418yes—
303C42×C61C2418yes—
304C42×C61C2414yes—
305C22⋊Dic61C24116yes—
306C22⋊Dic61C2418yes—
307#11758198C2418yes—
308#11758198C2418yes—
309#11758198C2418yes—
310C4⋊Dic61C2418yes—
311C4⋊Dic61C2418yes—
312C4⋊Dic61C2414yes—
313C4⋊Dic61C24116yes—
314C4⋊Dic61C2414yes—
315C4⋊Dic61C2418yes—
316C4⋊Dic61C24116yes—
317#11758196C24116yes—
318#11758196C24116yes—
319#11758196C2418yes—
320#11758196C24116yes—
321#11758196C24116yes—
322#11758196C2418yes—
323#11758196C2418yes—
324#11758196C2418yes—
325#11758196C2418yes—
326#11758196C24116yes—
327#11758196C24116yes—
328#11758196C2418yes—
329#11758196C2418yes—
330C4×Dic61C2414yes—
331C4×Dic61C2414yes—
332C4×Dic61C2414yes—
333C4×Dic61C2418yes—
334C4×Dic61C2418yes—
335C4×Dic61C2418yes—
336C4×Dic61C24116yes—
337C4×Dic61C24116yes—
338C4×Dic61C2418yes—
339C23×C61—24no—
340C23×C61—24no—
341C23×C61C22×Q818yes—
342C23×C61C2514yes—
343C23×C61C2511yescharacteristic
344C22×D61—22no—
345C22×D61—22no—
346C22×D61C22×Q814yes—
347C22×D61C2512yes—
348Q8×C61—28no—
349Q8×C61—48no—
350D4×C61C22×Q8116yescomplemented
351C2×C4×C61—24no—
352C2×C4×C61—28no—
353C2×C4×C61—22no—
354C2×C4×C61—24no—
355C2×C4×C61—24no—
356C2×C4×C61—216no—
357C2×C4×C61—416no—
358C2×C4×C61C22×Q814yes—
359C2×C4×C612−1+414yes—
360C2×C4×C61C2514yes—
361C2×C4×C61C2514yes—
362C2×C4×C61C2512yes—
363C2×C4×C61C2518yes—
364C2×C4×C61C2514yes—
365C2×C4×C61C2512yes—
366C2×C4×C61C2512yes—
367C22⋊D61C22×Q8132yescomplemented
368C2×Dic61—28no—
369C2×Dic61—24no—
370C2×Dic61—24no—
371C2×Dic61—24no—
372C2×Dic61—22no—
373C2×Dic61—216no—
374C2×Dic61—416no—
375C2×Dic61C22×Q818yes—
376C2×Dic61C22×Q814yes—
377C2×Dic61C22×Q8132yescomplemented
378C2×Dic61H(5,𝔽2)14yes—
379C2×Dic61C2514yes—
380C2×Dic61C2512yes—
381C2×Dic61C2514yes—
382C2×Dic61C2514yes—
383C2×Dic61C2518yes—
384C2×Dic61C2514yes—
385C2×Dic61C2512yes—
386C2×Dic61C2512yes—
387C4×D61—28no—
388C4×D61—28no—
389C4×D61—416no—
390C4×D61C22×Q8116yescomplemented
391Dic122—28no—
392Dic122—216no—
393Dic122—232no—
394Dic122—416no—
395Dic122—416no—
396Dic122—48no—
397Dic122C22×Q8116yescomplemented
398C2×#3503—611nomaximal, Sylow
399C22×C61—24no—
400C22×C61—24no—
401C22×C61—216no—
402C22×C61C23×Q818yes—
403C22×C61C23×Q812yes—
404C22×C61C2×H(5,𝔽2)12yes—
405C22×C61C2×2−1+412yes—
406C22×C61C2611yescharacteristic
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—28no—
410C2×D61C23×Q814yes—
411C4×C61—24no—
412C4×C61—28no—
413C4×C61—22no—
414C4×C61—24no—
415C4×C61—24no—
416C4×C61C23×Q814yes—
417C4×C61C2×2−1+414yes—
418Dic61—28no—
419Dic61—24no—
420Dic61—24no—
421Dic61—24no—
422Dic61—22no—
423Dic61C23×Q818yes—
424Dic61C23×Q814yes—
425Dic61C2×H(5,𝔽2)14yes—
426#3503—6132no—
427C2×Q82—611no—
428C2×Q82—611no—
429C2×#557—612no—
430C2×#554—612no—
431C2×#554—611no—
432C2×#554—612no—
433C2×#554D6111yescharacteristic, complemented
434C2×D4×Q8—614no—
435C2×D4×Q8—612no—
436C2×#544—612no—
437C2×#544—614no—
438C2×#533—612no—
439C2×#533—611no—
440C22×C4⋊Q8—611no—
441C22×C4⋊Q8—612no—
442C2×#520—612no—
443C2×C4×#41—611no—
444C2×C61—28no—
445C2×C61#350314yescomplemented
446C2×C61C24×Q811yescharacteristic
447C2×C61C22×H(5,𝔽2)11yescharacteristic
448C2×C61C22×2−1+411yescharacteristic
449D61—24no—
450C22×#41—611no—
451C23×Q8—612no—
452C23×Q8—614no—
453Q82—6116no—
454Q82—6116no—
455#557—6132no—
456#554—6132no—
457#554—6116no—
458#554—6132no—
459#554C2×D61116yescomplemented
460D4×Q8—6164no—
461D4×Q8—6132no—
462#544—6132no—
463#544—6164no—
464#533—6132no—
465#533—6116no—
466C2×C4⋊Q8—612no—
467C2×C4⋊Q8—611no—
468C2×C4⋊Q8—614no—
469C2×C4⋊Q8—6116no—
470C2×C4⋊Q8—612no—
471C2×C4⋊Q8—611no—
472C2×C4⋊Q8—614no—
473C2×C4⋊Q8—614no—
474C2×C4⋊Q8—612no—
475C2×C4⋊Q8—612no—
476C2×C4⋊Q8—612no—
477C2×C4⋊Q8—6132no—
478C2×C4⋊Q8—614no—
479C2×C4⋊Q8—612no—
480C2×C4⋊Q8—611no—
481C2×C4⋊Q8—612no—
482C2×C4⋊Q8C2×D6111yescharacteristic
483C2×#125—612no—
484C2×#125—614no—
485C2×#125—614no—
486C2×#125—614no—
487C2×#125—612no—
488C2×#125C2×D6112yes—
489C2×C22⋊Q8—611no—
490C2×C22⋊Q8—612no—
491C2×C22⋊Q8—614no—
492C2×C22⋊Q8—612no—
493C2×C22⋊Q8—614no—
494C2×C22⋊Q8—611no—
495C2×C22⋊Q8—614no—
496C2×C22⋊Q8—614no—
497C2×C22⋊Q8—614no—
498C2×C22⋊Q8—614no—
499C2×C22⋊Q8C2×D6112yes—
500C2×C22⋊Q8C2×D6114yes—
501#520—6132no—
502C4×#41—6116no—
503C2×C4×Q8—612no—
504C2×C4×Q8—611no—
505C2×C4×Q8—612no—
506C2×C4×Q8—614no—
507C2×C4×Q8—612no—
508C2×C4×Q8—611no—
509C2×C4×Q8—612no—
510C2×C4×Q8—612no—
511C2×C4×Q8—611no—
512C2×C4×Q8C2×D6111yescharacteristic
513C2×C4×D4—611no—
514C2×C4×D4—612no—
515C2×C4×D4—612no—
516C2×C4×D4—614no—
517C2×C4×D4—612no—
518C2×C4×D4—614no—
519C2×C4×D4C2×D6111yescharacteristic
520C2×C4×D4C2×D6112yes—
521C2×#117—611no—
522C2×#117—612no—
523C2×#117—614no—
524C2×#117—612no—
525C22×C4⋊C4—614no—
526C22×C4⋊C4—612no—
527C22×C4⋊C4—612no—
528C22×C4⋊C4—612no—
529C22×C4⋊C4C2×D6112yes—
530C22×C42—612no—
531C22×C42—611no—
532C61C2×#350311yescharacteristic, complemented, Sylow
533C2×#41—6116no—
534C2×#41—618no—
535C22×Q8—6116no—
536C22×Q8—611no—
537C22×Q8—611no—
538C22×Q8—614no—
539C22×Q8—612no—
540C22×Q8—614no—
541C22×Q8—614no—
542C22×Q8—612no—
543C22×Q8—6132no—
544C22×Q8—24416no—
545C22×Q8—2448no—
546C22×Q8C22×D6111yescharacteristic
547C22×Q8C22×D6112yes—
548C22×D4—612no—
549C22×D4C22×D6111yescharacteristic
550C23×C4—612no—
551C23×C4—611no—
552C23×C4—612no—
553C23×C4—614no—
554C23×C4—611no—
555C23×C4—611no—
556C23×C4—614no—
557C23×C4C22×D6112yes—
558C23×C4C22×D6114yes—
559C4⋊Q8—6116no—
560C4⋊Q8—618no—
561C4⋊Q8—6132no—
562C4⋊Q8—6116no—
563C4⋊Q8—618no—
564C4⋊Q8—6132no—
565C4⋊Q8—6132no—
566C4⋊Q8—6116no—
567C4⋊Q8—6116no—
568C4⋊Q8—6116no—
569C4⋊Q8—6132no—
570C4⋊Q8—6116no—
571C4⋊Q8—618no—
572C4⋊Q8—6116no—
573C4⋊Q8C22×D6118yes—
574#125—6116no—
575#125—6132no—
576#125—6132no—
577#125—6132no—
578#125—6116no—
579#125C22×D61116yes—
580C22⋊Q8—618no—
581C22⋊Q8—6116no—
582C22⋊Q8—6132no—
583C22⋊Q8—6116no—
584C22⋊Q8—618no—
585C22⋊Q8—6132no—
586C22⋊Q8—6132no—
587C22⋊Q8—6132no—
588C22⋊Q8—6132no—
589C22⋊Q8—6132no—
590C22⋊Q8C22×D61116yes—
591C22⋊Q8C22×D61132yes—
592C4×Q8—6116no—
593C4×Q8—618no—
594C4×Q8—6116no—
595C4×Q8—6132no—
596C4×Q8—6116no—
597C4×Q8—618no—
598C4×Q8—6116no—
599C4×Q8—6116no—
600C4×Q8—618no—
601C4×Q8C22×D6118yes—
602C4×D4—618no—
603C4×D4—6116no—
604C4×D4—6116no—
605C4×D4—6132no—
606C4×D4—6116no—
607C4×D4—6132no—
608C4×D4C22×D6118yes—
609C4×D4C22×D61116yes—
610#117—618no—
611#117—6116no—
612#117—6132no—
613#117—6116no—
614C2×C4⋊C4—614no—
615C2×C4⋊C4—612no—
616C2×C4⋊C4—611no—
617C2×C4⋊C4—612no—
618C2×C4⋊C4—614no—
619C2×C4⋊C4—614no—
620C2×C4⋊C4—612no—
621C2×C4⋊C4—6132no—
622C2×C4⋊C4—614no—
623C2×C4⋊C4—614no—
624C2×C4⋊C4—6116no—
625C2×C4⋊C4—612no—
626C2×C4⋊C4—612no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—612no—
630C2×C4⋊C4—614no—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—612no—
633C2×C4⋊C4—614no—
634C2×C4⋊C4—612no—
635C2×C4⋊C4—614no—
636C2×C4⋊C4—6116no—
637C2×C4⋊C4—6116no—
638C2×C4⋊C4C22×D6112yes—
639C2×C4⋊C4C22×D6112yes—
640C2×C4⋊C4C22×D6111yescharacteristic
641C2×C4⋊C4C22×D6114yes—
642C2×C4⋊C4C22×D61116yes—
643C2×C4⋊C4C22×D6111yescharacteristic
644C2×C4⋊C4C22×D6114yes—
645C2×C4⋊C4C22×D6112yes—
646C2×C22⋊C4—614no—
647C2×C22⋊C4—612no—
648C2×C22⋊C4—612no—
649C2×C22⋊C4—612no—
650C2×C22⋊C4—612no—
651C2×C22⋊C4C22×D6114yes—
652C2×C22⋊C4C22×D6112yes—
653C2×C42—611no—
654C2×C42—612no—
655C2×C42—614no—
656C2×C42—614no—
657C2×C42—612no—
658C2×C42—612no—
659C2×C42—612no—
660C2×C42—611no—
661C2×C42—6116no—
662C2×C42—611no—
663C2×C42—618no—
664C2×C42C22×D6112yes—
665C2×C42C22×D6111yescharacteristic
666C24—611no—
667C24C23×D6112yes—
668#41—6164no—
669C2×Q8—24no—
670C2×Q8—44no—
671C2×Q8—618no—
672C2×Q8—614no—
673C2×Q8—614no—
674C2×Q8—6116no—
675C2×Q8—618no—
676C2×Q8—6116no—
677C2×Q8—6116no—
678C2×Q8—618no—
679C2×Q8—1228no—
680C2×Q8—12216no—
681C2×Q8—1224no—
682C2×Q8—2448no—
683C2×Q8—2448no—
684C2×Q8—2444no—
685C2×Q8—24464no—
686C2×Q8—24432no—
687C2×Q8C23×D6114yes—
688C2×Q8C23×D6118yes—
689C2×D4—6116no—
690C2×D4—618no—
691C2×D4Q8×D6118yescomplemented
692C2×D4C23×D6114yes—
693C22×C4—28no—
694C22×C4—48no—
695C22×C4—6116no—
696C22×C4—618no—
697C22×C4—612no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—618no—
701C22×C4—614no—
702C22×C4—618no—
703C22×C4—612no—
704C22×C4—611no—
705C22×C4—612no—
706C22×C4—614no—
707C22×C4—612no—
708C22×C4—6116no—
709C22×C4—614no—
710C22×C4—614no—
711C22×C4—6116no—
712C22×C4—1224no—
713C22×C4—1228no—
714C22×C4—1224no—
715C22×C4—2448no—
716C22×C4—2448no—
717C22×C4C23×D6118yes—
718C22×C4C23×D6112yes—
719C22×C4C23×D6112yes—
720C22×C4C23×D6111yescharacteristic
721C22×C4C23×D6114yes—
722C22×C4C23×D6112yes—
723C22×C4C23×D61116yes—
724C22×C4C23×D6111yescharacteristic
725C22×C4C23×D6111yescharacteristic
726C4⋊C4—6116no—
727C4⋊C4—618no—
728C4⋊C4—614no—
729C4⋊C4—618no—
730C4⋊C4—6116no—
731C4⋊C4—6116no—
732C4⋊C4—6116no—
733C4⋊C4—618no—
734C4⋊C4—6116no—
735C4⋊C4—618no—
736C4⋊C4—618no—
737C4⋊C4—618no—
738C4⋊C4—618no—
739C4⋊C4—6116no—
740C4⋊C4—618no—
741C4⋊C4—6116no—
742C4⋊C4—618no—
743C4⋊C4—614no—
744C4⋊C4—618no—
745C4⋊C4—6116no—
746C4⋊C4C23×D6118yes—
747C4⋊C4C23×D6118yes—
748C4⋊C4C23×D6114yes—
749C4⋊C4C23×D61116yes—
750C4⋊C4C23×D6114yes—
751C4⋊C4C23×D61116yes—
752C4⋊C4C23×D6118yes—
753C22⋊C4—6116no—
754C22⋊C4—618no—
755C22⋊C4—618no—
756C22⋊C4—618no—
757C22⋊C4—618no—
758C22⋊C4C23×D61116yes—
759C22⋊C4C23×D6118yes—
760C42—614no—
761C42—614no—
762C42—618no—
763C42—618no—
764C42—618no—
765C42—614no—
766C42—6116no—
767C42—6116no—
768C42—618no—
769C42C23×D6114yes—
770C42C23×D6118yes—
771C23—24no—
772C23—24no—
773C23—614no—
774C23—612no—
775C23—1222no—
776C23—1222no—
777C23C2×Q8×D6118yes—
778C23C24×D6114yes—
779C23C24×D6111yescharacteristic
780Q8—28no—
781Q8—48no—
782Q8—6116no—
783Q8—12216no—
784Q8—12232no—
785Q8—1228no—
786Q8—24416no—
787Q8—24416no—
788Q8—2448no—
789D4—6132no—
790D4C2×Q8×D61116yescomplemented
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—216no—
797C2×C4—416no—
798C2×C4—614no—
799C2×C4—618no—
800C2×C4—6132no—
801C2×C4—614no—
802C2×C4—614no—
803C2×C4—612no—
804C2×C4—612no—
805C2×C4—6116no—
806C2×C4—614no—
807C2×C4—612no—
808C2×C4—614no—
809C2×C4—614no—
810C2×C4—618no—
811C2×C4—1228no—
812C2×C4—12216no—
813C2×C4—1224no—
814C2×C4—1228no—
815C2×C4—1224no—
816C2×C4—1222no—
817C2×C4—1224no—
818C2×C4—1228no—
819C2×C4—24416no—
820C2×C4—24416no—
821C2×C4C2×Q8×D6114yes—
822C2×C4#1451982414yes—
823C2×C4C24×D6114yes—
824C2×C4C24×D6114yes—
825C2×C4C24×D6112yes—
826C2×C4C24×D6118yes—
827C2×C4C24×D6114yes—
828C2×C4C24×D6112yes—
829C2×C4C24×D6112yes—
830C22—24no—
831C22—24no—
832C22—216no—
833C22—614no—
834C22—1222no—
835C22—1222no—
836C22—1228no—
837C22C22×Q8×D6118yes—
838C22C22×Q8×D6112yes—
839C22H(5,𝔽2)×D6112yes—
840C22C2×#1451982412yes—
841C22C25×D6111yescharacteristic
842C4—24no—
843C4—28no—
844C4—22no—
845C4—24no—
846C4—24no—
847C4—614no—
848C4—618no—
849C4—614no—
850C4—1224no—
851C4—1228no—
852C4—1224no—
853C4—1222no—
854C4—1224no—
855C4C22×Q8×D6114yes—
856C4C2×#1451982414yes—
857C2—28no—
858C2—1224no—
859C2#2145963314yesdirect product factor
860C2C23×Q8×D6111yescharacteristic
861C2C2×H(5,𝔽2)×D6111yescharacteristic
862C2C22×#1451982411yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#554C2
socleC23×C61C25
prime radicalC22×#11758224C22
hypercenterC2×#554D61
hypocenterC61C2×#3503
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #21459633C2direct (N × H)
2. C2×Q8×Dic122C2semidirect
3. C2×#16840492C2semidirect
4. C2×#16840489C2semidirect
5. C2×#16840470C2semidirect
6. C2×#16840469C2semidirect
7. C2×#16840467C2semidirect
8. C2×D4×Dic122C2semidirect
9. C2×#16840425C2semidirect
10. C2×#16840392C2semidirect
11. C2×#16840391C2semidirect
12. C2×#16840316C2semidirect
13. C2×#16840314C2semidirect
14. C22×#14519776C2semidirect
15. C2×C4⋊Q8×D61C2semidirect
18. C2×C61×#554C2semidirect
22. Q8×Dic122C22semidirect
23. #16840492C22semidirect
24. #16840489C22semidirect
25. #16840470C22semidirect
26. #16840469C22semidirect
27. #16840467C22semidirect
28. D4×Dic122C22semidirect
29. #16840425C22semidirect
30. #16840392C22semidirect
31. #16840391C22semidirect
32. #16840316C22semidirect
33. #16840314C22semidirect
45. C2×#14519776C22semidirect
49. C4⋊Q8×D61C22semidirect
92. C61×#554C22semidirect
101. C2×#11758224Q8semidirect
240. C2×D4×C61C2×Q8semidirect
253. C2×C22⋊D61C2×Q8semidirect
257. C22×Dic61C2×Q8semidirect
270. #11758224C2×Q8semidirect
274. C2×C4×D61C2×Q8semidirect
286. C2×Dic122C2×Q8semidirect
350. D4×C61C22×Q8semidirect
367. C22⋊D61C22×Q8semidirect
377. C2×Dic61C22×Q8semidirect
390. C4×D61C22×Q8semidirect
397. Dic122C22×Q8semidirect
433. C2×#554D61semidirect
445. C2×C61#3503semidirect
459. #554C2×D61semidirect
532. C61C2×#3503semidirect
691. C2×D4Q8×D61semidirect
790. D4C2×Q8×D61semidirect
859. C2#21459633direct (N × H)

Maximal subgroups

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

subgroupindex
#214596332
C2×Q8×Dic1222
C2×#168404922
C2×#168404892
C2×#168404702
C2×#168404692
C2×#168404672
C2×D4×Dic1222
C2×#168404252
C2×#168403922
C2×#168403912
C2×#168403162
C2×#168403142
C22×#145197762
C2×C4⋊Q8×D612
C2×#168402412
C2×C4×#117582242
C2×C61×#5542
C2×#350361