Finite Group Databasebeta

← C2×#21459630 #30588337

Subgroups — C2×#21459630 #30588337

Order 15616.

7478 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459630C2132yesmaximal, direct product factor
2C2×#16840492C212yesmaximal, complemented
3C2×#16840490C211yesmaximal, characteristic, complemented
4C2×#16840487C211yesmaximal, characteristic, complemented
5C2×#16840471C212yesmaximal, complemented
6C2×#16840466C214yesmaximal, complemented
7C2×D4×Dic122C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D61C212yesmaximal, complemented
9C2×#16840425C212yesmaximal, complemented
10C2×#16840391C214yesmaximal, complemented
11C2×#16840389C212yesmaximal, complemented
12C2×#16840316C211yesmaximal, characteristic, complemented
13C2×#16840314C212yesmaximal, complemented
14C22×#14519775C212yesmaximal, complemented
15C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
16C2×#16840241C212yesmaximal
17C2×C4×#11758224C211yesmaximal, characteristic
18C2×D4×Q8×C61C211yesmaximal, characteristic, complemented
19C22×#11758224C2211yescharacteristic
20C23×Dic122C2212yes—
21C22×Q8×D61C2212yes—
22#16840492C22132yescomplemented
23#16840490C22116yescomplemented
24#16840487C22116yescomplemented
25#16840471C22132yescomplemented
26#16840466C22164yescomplemented
27D4×Dic122C22116yescomplemented
28Q8×C22⋊D61C22132yescomplemented
29#16840425C22132yescomplemented
30#16840391C22164yescomplemented
31#16840389C22132yescomplemented
32#16840316C22116yescomplemented
33#16840314C22132yescomplemented
34C2×#14519777C2211yescharacteristic
35C2×#14519776C2212yes—
36C2×#14519776C2212yes—
37C2×#14519776C2214yes—
38C2×#14519776C2212yes—
39C2×#14519776C2211yescharacteristic
40C2×#14519775C2214yes—
41C2×#14519775C2214yes—
42C2×#14519775C2212yes—
43C2×#14519775C2212yes—
44C2×#14519775C2214yes—
45C2×#14519775C2212yes—
46C2×#14519775C2211yescharacteristic
47C2×#14519775C22132yescomplemented
48C4⋊Q8×D61C22116yescomplemented
49C2×#14519769C2212yes—
50C2×#14519768C2212yes—
51C2×#14519767C2214yes—
52C2×#14519767C2212yes—
53C2×#14519767C2214yes—
54C2×#14519767C2214yes—
55C2×#14519757C2211yescharacteristic
56C2×#14519756C2214yes—
57C2×#14519756C2212yes—
58C2×#14519755C2214yes—
59C2×#14519755C2212yes—
60C2×#14519754C2214yes—
61C2×#14519754C2214yes—
62C2×#14519754C2214yes—
63C2×#14519753C2214yes—
64C2×#14519753C2211yescharacteristic
65#16840241C22132yes—
66C4×#11758224C22116yes—
67C2×Q8×Dic61C2212yes—
68C2×C4×Dic122C2211yescharacteristic
69C2×C4×Dic122C2212yes—
70C2×C4×Dic122C2211yescharacteristic
71C2×C4×Dic122C2212yes—
72C2×#14519742C2211yescharacteristic
73C2×#14519742C2212yes—
74C2×#14519742C2212yes—
75C2×#14519742C2214yes—
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×#11758196C2214yes—
87C22×#11758196C2214yes—
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C22×C4×Dic61C2212yes—
91C2×C42×D61C2211yescharacteristic
92C23×Q8×C61C2212yes—
93D4×Q8×C61C22116yescomplemented
94C2×C4⋊Q8×C61C2212yes—
95C2×C4⋊Q8×C61C2211yescharacteristic
96C2×C22⋊Q8×C61C2214yes—
97C2×C22⋊Q8×C61C2212yes—
98C2×C4×Q8×C61C2211yescharacteristic
99C2×C4×D4×C61C2211yescharacteristic
100C2×C4×D4×C61C2212yes—
101C2×#11758224Q8116yescomplemented
102C2×#11758224C2318yes—
103C22×Dic122—48no—
104C22×Dic122C2312yes—
105C22×Dic122C2312yes—
106C22×Dic122C2311yescharacteristic
107C22×Dic122C2314yes—
108C22×Dic122C2314yes—
109C22×Dic122C23116yes—
110C22×Dic122C2311yescharacteristic
111C2×Q8×D61—48no—
112C2×Q8×D61C23116yes—
113C22×C22⋊D61C2312yes—
114C23×Dic61C2312yes—
115C23×Dic61C2314yes—
116C23×Dic61C2312yes—
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2314yes—
120C22×C4×D61C2311yescharacteristic
121#14519777C2318yes—
122#14519776C23116yes—
123#14519776C23116yes—
124#14519776C23132yes—
125#14519776C23116yes—
126#14519776C2318yes—
127#14519775C23132yes—
128#14519775C23116yes—
129#14519775C23116yes—
130#14519775C23132yes—
131#14519775C23116yes—
132#14519775C2318yes—
133#14519775C23132yes—
134#14519769C23116yes—
135#14519768C23116yes—
136#14519767C23132yes—
137#14519767C23132yes—
138#14519767C23132yes—
139#14519767C23116yes—
140#14519757C2318yes—
141#14519756C23132yes—
142#14519756C23116yes—
143#14519755C23116yes—
144#14519755C23132yes—
145#14519754C23132yes—
146#14519754C23132yes—
147#14519754C23132yes—
148#14519753C23132yes—
149#14519753C2318yes—
150Q8×Dic61C23116yes—
151C4×Dic122C23116yes—
152C4×Dic122C2318yes—
153C4×Dic122C2318yes—
154C4×Dic122C23116yes—
155#14519742C23132yes—
156#14519742C2318yes—
157#14519742C23116yes—
158#14519742C23116yes—
159D4×Dic61C2318yes—
160D4×Dic61C23116yes—
161C4×C22⋊D61C23132yes—
162C4×C22⋊D61C23116yes—
163#14519737C23116yes—
164#14519737C23132yes—
165#14519735C2318yes—
166#14519734C23116yes—
167#14519733C23116yes—
168#14519733C23132yes—
169C2×C4⋊Dic61C2312yes—
170C2×C4⋊Dic61C2312yes—
171C2×C4⋊Dic61C2311yescharacteristic
172C2×C4⋊Dic61C2311yescharacteristic
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2314yes—
175C2×#11758196C23132yes—
176C2×#11758196C2314yes—
177C2×#11758196C2314yes—
178C2×#11758196C2312yes—
179C2×#11758196C2312yes—
180C2×#11758196C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C23132yes—
183C2×#11758196C2314yes—
184C2×#11758196C2314yes—
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×C61—48no—
211C22×Q8×C61C2312yes—
212C22×Q8×C61C2311yescharacteristic
213C22×Q8×C61C2314yes—
214C22×Q8×C61C23116yes—
215C22×D4×C61C2311yescharacteristic
216C23×C4×C61C2312yes—
217C23×C4×C61C2314yes—
218C4⋊Q8×C61C2318yes—
219C4⋊Q8×C61C23116yes—
220C22⋊Q8×C61C23132yes—
221C22⋊Q8×C61C23116yes—
222C4×Q8×C61C2318yes—
223C4×D4×C61C23116yes—
224C4×D4×C61C2318yes—
225C2×C4⋊C4×C61C2312yes—
226C2×C4⋊C4×C61C2311yescharacteristic
227C2×C4⋊C4×C61C2312yes—
228C2×C4⋊C4×C61C2314yes—
229C2×C4⋊C4×C61C2311yescharacteristic
230C2×C4⋊C4×C61C2312yes—
231C2×C22⋊C4×C61C2314yes—
232C2×C22⋊C4×C61C2312yes—
233C2×C42×C61C2311yescharacteristic
234C2×C42×C61C2312yes—
235C24×C61C2412yes—
236C23×D61C2411yescharacteristic
237C2×Q8×C61—28no—
238C2×Q8×C61—24no—
239C2×Q8×C61—48no—
240C2×Q8×C61—432no—
241C2×Q8×C61C2418yes—
242C2×Q8×C61C2414yes—
243C2×Q8×C61C24116yes—
244C2×D4×C61C2×Q818yescomplemented
245C2×D4×C61C2414yes—
246C22×C4×C61—28no—
247C22×C4×C61—48no—
248C22×C4×C61C2414yes—
249C22×C4×C61C2411yescharacteristic
250C22×C4×C61C2412yes—
251C22×C4×C61C2418yes—
252C22×C4×C61C2412yes—
253C22×C4×C61C2412yes—
254C22×C4×C61C24116yes—
255C22×C4×C61C2411yescharacteristic
256C22×C4×C61C2411yescharacteristic
257C2×C22⋊D61C2×Q8116yescomplemented
258C2×C22⋊D61C2418yes—
259C22×Dic61—28no—
260C22×Dic61—48no—
261C22×Dic61C2×Q8116yescomplemented
262C22×Dic61C2414yes—
263C22×Dic61C2411yescharacteristic
264C22×Dic61C2412yes—
265C22×Dic61C2412yes—
266C22×Dic61C2418yes—
267C22×Dic61C2412yes—
268C22×Dic61C24116yes—
269C22×Dic61C2411yescharacteristic
270C22×Dic61C2412yes—
271C22×Dic61C2418yes—
272C22×Dic61C2411yescharacteristic
273Q8×D61—432no—
274#11758224C2×Q8164yescomplemented
275C2×C4×D61—24no—
276C2×C4×D61—24no—
277C2×C4×D61—48no—
278C2×C4×D61C2×Q818yescomplemented
279C2×C4×D61C2414yes—
280C2×C4×D61C2414yes—
281C2×C4×D61C24116yes—
282C2×C4×D61C2414yes—
283C2×Dic122—28no—
284C2×Dic122—24no—
285C2×Dic122—28no—
286C2×Dic122—432no—
287C2×Dic122—48no—
288C2×Dic122—48no—
289C2×Dic122C2×Q818yescomplemented
290C2×Dic122C2418yes—
291C2×Dic122C2414yes—
292C2×Dic122C2418yes—
293C2×Dic122C24116yes—
294C2×Dic122C24116yes—
295C2×Dic122C2414yes—
296C4⋊C4×C61C2418yes—
297C4⋊C4×C61C2414yes—
298C4⋊C4×C61C2414yes—
299C4⋊C4×C61C2418yes—
300C4⋊C4×C61C2418yes—
301C4⋊C4×C61C24116yes—
302C22⋊C4×C61C24116yes—
303C22⋊C4×C61C2418yes—
304C42×C61C2414yes—
305C42×C61C2418yes—
306C22⋊Dic61C24116yes—
307C22⋊Dic61C2418yes—
308#11758198C2418yes—
309#11758198C2418yes—
310#11758198C2418yes—
311C4⋊Dic61C2418yes—
312C4⋊Dic61C2418yes—
313C4⋊Dic61C2414yes—
314C4⋊Dic61C2414yes—
315C4⋊Dic61C2418yes—
316C4⋊Dic61C24116yes—
317#11758196C24116yes—
318#11758196C24116yes—
319#11758196C2418yes—
320#11758196C2418yes—
321#11758196C24116yes—
322#11758196C24116yes—
323#11758196C24116yes—
324#11758196C24116yes—
325#11758196C2418yes—
326#11758196C2418yes—
327#11758196C2418yes—
328#11758196C24116yes—
329#11758196C24116yes—
330#11758196C2418yes—
331#11758196C2418yes—
332C4×Dic61C2414yes—
333C4×Dic61C2414yes—
334C4×Dic61C2414yes—
335C4×Dic61C2418yes—
336C4×Dic61C2418yes—
337C4×Dic61C2418yes—
338C4×Dic61C24116yes—
339C4×Dic61C24116yes—
340C4×Dic61C2418yes—
341C23×C61—24no—
342C23×C61—24no—
343C23×C61C22×Q818yes—
344C23×C61C2514yes—
345C23×C61C2511yescharacteristic
346C22×D61—22no—
347C22×D61—22no—
348C22×D61C22×Q814yes—
349C22×D61C2512yes—
350Q8×C61—216no—
351Q8×C61—28no—
352Q8×C61—416no—
353D4×C61C22×Q8116yescomplemented
354C2×C4×C61—24no—
355C2×C4×C61—28no—
356C2×C4×C61—24no—
357C2×C4×C61—24no—
358C2×C4×C61—22no—
359C2×C4×C61—216no—
360C2×C4×C61—416no—
361C2×C4×C61C22×Q814yes—
362C2×C4×C61H(5,𝔽2)14yes—
363C2×C4×C61C2514yes—
364C2×C4×C61C2514yes—
365C2×C4×C61C2512yes—
366C2×C4×C61C2518yes—
367C2×C4×C61C2514yes—
368C2×C4×C61C2512yes—
369C2×C4×C61C2512yes—
370C22⋊D61C22×Q8132yescomplemented
371C2×Dic61—28no—
372C2×Dic61—24no—
373C2×Dic61—22no—
374C2×Dic61—24no—
375C2×Dic61—24no—
376C2×Dic61—216no—
377C2×Dic61—416no—
378C2×Dic61C22×Q818yes—
379C2×Dic61C22×Q814yes—
380C2×Dic61C22×Q8132yescomplemented
381C2×Dic612−1+414yes—
382C2×Dic61C2514yes—
383C2×Dic61C2514yes—
384C2×Dic61C2512yes—
385C2×Dic61C2514yes—
386C2×Dic61C2518yes—
387C2×Dic61C2514yes—
388C2×Dic61C2512yes—
389C2×Dic61C2512yes—
390C4×D61—28no—
391C4×D61—28no—
392C4×D61—416no—
393C4×D61C22×Q8116yescomplemented
394Dic122—28no—
395Dic122—216no—
396Dic122—216no—
397Dic122—416no—
398Dic122—416no—
399Dic122C22×Q8116yescomplemented
400C2×#3503—611nomaximal, Sylow
401C22×C61—24no—
402C22×C61—24no—
403C22×C61—216no—
404C22×C61C23×Q818yes—
405C22×C61C23×Q812yes—
406C22×C61C2×H(5,𝔽2)12yes—
407C22×C61C2×2−1+412yes—
408C22×C61C2611yescharacteristic
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—28no—
412C2×D61C23×Q814yes—
413C4×C61—24no—
414C4×C61—28no—
415C4×C61—24no—
416C4×C61—24no—
417C4×C61—22no—
418C4×C61C23×Q814yes—
419C4×C61C2×H(5,𝔽2)14yes—
420Dic61—28no—
421Dic61—24no—
422Dic61—22no—
423Dic61—24no—
424Dic61—24no—
425Dic61C23×Q818yes—
426Dic61C23×Q814yes—
427Dic61C2×2−1+414yes—
428#3503—6132no—
429C2×Q82—612no—
430C2×#557—611no—
431C2×#557—611no—
432C2×#554—614no—
433C2×#554—612no—
434C2×D4×Q8—612no—
435C2×D4×Q8—612no—
436C2×D4×Q8—611no—
437C2×D4×Q8D6111yescharacteristic, complemented
438C2×#544—612no—
439C2×#544—614no—
440C2×#533—612no—
441C2×#533—611no—
442C22×C4⋊Q8—612no—
443C22×C4⋊Q8—611no—
444C2×#520—612no—
445C2×C4×#41—611no—
446C2×C61—28no—
447C2×C61#350314yescomplemented
448C2×C61C24×Q811yescharacteristic
449C2×C61C22×H(5,𝔽2)11yescharacteristic
450C2×C61C22×2−1+411yescharacteristic
451D61—24no—
452C22×#41—611no—
453C23×Q8—612no—
454C23×Q8—612no—
455C23×Q8C2×D6112yes—
456Q82—6132no—
457#557—6116no—
458#557—6116no—
459#554—6164no—
460#554—6132no—
461D4×Q8—6132no—
462D4×Q8—6132no—
463D4×Q8—6116no—
464D4×Q8C2×D61116yescomplemented
465#544—6132no—
466#544—6164no—
467#533—6132no—
468#533—6116no—
469C2×C4⋊Q8—612no—
470C2×C4⋊Q8—611no—
471C2×C4⋊Q8—614no—
472C2×C4⋊Q8—612no—
473C2×C4⋊Q8—612no—
474C2×C4⋊Q8—614no—
475C2×C4⋊Q8—614no—
476C2×C4⋊Q8—6132no—
477C2×C4⋊Q8—6116no—
478C2×C4⋊Q8—612no—
479C2×C4⋊Q8—612no—
480C2×C4⋊Q8—611no—
481C2×C4⋊Q8—614no—
482C2×C4⋊Q8—612no—
483C2×C4⋊Q8—611no—
484C2×C4⋊Q8C2×D6111yescharacteristic
485C2×C4⋊Q8C2×D6112yes—
486C2×#125—614no—
487C2×#125—612no—
488C2×#125—614no—
489C2×#125—614no—
490C2×#125—612no—
491C2×#125—612no—
492C2×C22⋊Q8—611no—
493C2×C22⋊Q8—614no—
494C2×C22⋊Q8—612no—
495C2×C22⋊Q8—614no—
496C2×C22⋊Q8—612no—
497C2×C22⋊Q8—614no—
498C2×C22⋊Q8—611no—
499C2×C22⋊Q8—614no—
500C2×C22⋊Q8—614no—
501C2×C22⋊Q8—614no—
502C2×C22⋊Q8C2×D6112yes—
503C2×C22⋊Q8C2×D6114yes—
504#520—6132no—
505C4×#41—6116no—
506C2×C4×Q8—612no—
507C2×C4×Q8—611no—
508C2×C4×Q8—612no—
509C2×C4×Q8—612no—
510C2×C4×Q8—614no—
511C2×C4×Q8—611no—
512C2×C4×Q8—612no—
513C2×C4×Q8—611no—
514C2×C4×Q8—612no—
515C2×C4×Q8C2×D6111yescharacteristic
516C2×C4×D4—611no—
517C2×C4×D4—612no—
518C2×C4×D4—612no—
519C2×C4×D4—614no—
520C2×C4×D4—612no—
521C2×C4×D4—614no—
522C2×C4×D4C2×D6111yescharacteristic
523C2×C4×D4C2×D6112yes—
524C2×#117—611no—
525C2×#117—612no—
526C2×#117—614no—
527C2×#117—612no—
528C22×C4⋊C4—614no—
529C22×C4⋊C4—614no—
530C22×C4⋊C4—612no—
531C22×C4⋊C4—612no—
532C22×C42—612no—
533C22×C42—611no—
534C61C2×#350311yescharacteristic, complemented, Sylow
535C2×#41—6116no—
536C2×#41—618no—
537C22×Q8—48no—
538C22×Q8—6116no—
539C22×Q8—611no—
540C22×Q8—612no—
541C22×Q8—612no—
542C22×Q8—611no—
543C22×Q8—614no—
544C22×Q8—614no—
545C22×Q8—6116no—
546C22×Q8—2448no—
547C22×Q8—2448no—
548C22×Q8C22×D6112yes—
549C22×Q8C22×D6111yescharacteristic
550C22×Q8C22×D6114yes—
551C22×Q8C22×D61116yes—
552C22×D4—612no—
553C22×D4C22×D6111yescharacteristic
554C23×C4—612no—
555C23×C4—611no—
556C23×C4—612no—
557C23×C4—614no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—614no—
561C23×C4C22×D6112yes—
562C23×C4C22×D6114yes—
563C4⋊Q8—6116no—
564C4⋊Q8—618no—
565C4⋊Q8—6132no—
566C4⋊Q8—6116no—
567C4⋊Q8—6116no—
568C4⋊Q8—6132no—
569C4⋊Q8—6132no—
570C4⋊Q8—6116no—
571C4⋊Q8—6116no—
572C4⋊Q8—618no—
573C4⋊Q8—6132no—
574C4⋊Q8—6116no—
575C4⋊Q8—618no—
576C4⋊Q8C22×D6118yes—
577C4⋊Q8C22×D61116yes—
578#125—6132no—
579#125—6116no—
580#125—6132no—
581#125—6132no—
582#125—6116no—
583#125—6116no—
584C22⋊Q8—618no—
585C22⋊Q8—6132no—
586C22⋊Q8—6116no—
587C22⋊Q8—6132no—
588C22⋊Q8—618no—
589C22⋊Q8—6116no—
590C22⋊Q8—6132no—
591C22⋊Q8—6132no—
592C22⋊Q8—6132no—
593C22⋊Q8—6132no—
594C22⋊Q8C22×D61116yes—
595C22⋊Q8C22×D61132yes—
596C4×Q8—6116no—
597C4×Q8—618no—
598C4×Q8—6116no—
599C4×Q8—6116no—
600C4×Q8—6132no—
601C4×Q8—618no—
602C4×Q8—6116no—
603C4×Q8—618no—
604C4×Q8—6116no—
605C4×Q8C22×D6118yes—
606C4×D4—618no—
607C4×D4—6116no—
608C4×D4—6116no—
609C4×D4—6132no—
610C4×D4—6116no—
611C4×D4—6132no—
612C4×D4C22×D6118yes—
613C4×D4C22×D61116yes—
614#117—618no—
615#117—6116no—
616#117—6132no—
617#117—6116no—
618C2×C4⋊C4—614no—
619C2×C4⋊C4—612no—
620C2×C4⋊C4—614no—
621C2×C4⋊C4—612no—
622C2×C4⋊C4—614no—
623C2×C4⋊C4—614no—
624C2×C4⋊C4—612no—
625C2×C4⋊C4—6132no—
626C2×C4⋊C4—614no—
627C2×C4⋊C4—614no—
628C2×C4⋊C4—612no—
629C2×C4⋊C4—6132no—
630C2×C4⋊C4—612no—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—612no—
634C2×C4⋊C4—611no—
635C2×C4⋊C4—612no—
636C2×C4⋊C4—614no—
637C2×C4⋊C4—614no—
638C2×C4⋊C4—612no—
639C2×C4⋊C4—614no—
640C2×C4⋊C4—612no—
641C2×C4⋊C4—6116no—
642C2×C4⋊C4—6116no—
643C2×C4⋊C4C22×D6112yes—
644C2×C4⋊C4C22×D6112yes—
645C2×C4⋊C4C22×D6111yescharacteristic
646C2×C4⋊C4C22×D6111yescharacteristic
647C2×C4⋊C4C22×D6114yes—
648C2×C4⋊C4C22×D6112yes—
649C2×C22⋊C4—614no—
650C2×C22⋊C4—612no—
651C2×C22⋊C4—612no—
652C2×C22⋊C4—612no—
653C2×C22⋊C4—612no—
654C2×C22⋊C4C22×D6114yes—
655C2×C22⋊C4C22×D6112yes—
656C2×C42—612no—
657C2×C42—611no—
658C2×C42—614no—
659C2×C42—614no—
660C2×C42—612no—
661C2×C42—612no—
662C2×C42—612no—
663C2×C42—611no—
664C2×C42—6116no—
665C2×C42—611no—
666C2×C42—618no—
667C2×C42C22×D6112yes—
668C2×C42C22×D6111yescharacteristic
669C24—611no—
670C24C23×D6112yes—
671#41—6164no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—48no—
675C2×Q8—432no—
676C2×Q8—618no—
677C2×Q8—614no—
678C2×Q8—618no—
679C2×Q8—618no—
680C2×Q8—614no—
681C2×Q8—6116no—
682C2×Q8—6116no—
683C2×Q8—1228no—
684C2×Q8—1228no—
685C2×Q8—1224no—
686C2×Q8—2448no—
687C2×Q8—2448no—
688C2×Q8—24432no—
689C2×Q8—24432no—
690C2×Q8C23×D6118yes—
691C2×Q8C23×D6114yes—
692C2×Q8C23×D61116yes—
693C2×D4—6116no—
694C2×D4—618no—
695C2×D4Q8×D6118yescomplemented
696C2×D4C23×D6114yes—
697C22×C4—28no—
698C22×C4—48no—
699C22×C4—6116no—
700C22×C4—618no—
701C22×C4—612no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—618no—
705C22×C4—614no—
706C22×C4—618no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—611no—
710C22×C4—614no—
711C22×C4—612no—
712C22×C4—6116no—
713C22×C4—614no—
714C22×C4—614no—
715C22×C4—6116no—
716C22×C4—1224no—
717C22×C4—1228no—
718C22×C4—1224no—
719C22×C4—2448no—
720C22×C4—2448no—
721C22×C4C23×D6118yes—
722C22×C4C23×D6112yes—
723C22×C4C23×D6112yes—
724C22×C4C23×D6111yescharacteristic
725C22×C4C23×D6114yes—
726C22×C4C23×D6112yes—
727C22×C4C23×D61116yes—
728C22×C4C23×D6111yescharacteristic
729C22×C4C23×D6111yescharacteristic
730C4⋊C4—6116no—
731C4⋊C4—618no—
732C4⋊C4—6116no—
733C4⋊C4—618no—
734C4⋊C4—6116no—
735C4⋊C4—6116no—
736C4⋊C4—6116no—
737C4⋊C4—6116no—
738C4⋊C4—618no—
739C4⋊C4—618no—
740C4⋊C4—618no—
741C4⋊C4—618no—
742C4⋊C4—618no—
743C4⋊C4—618no—
744C4⋊C4—6116no—
745C4⋊C4—618no—
746C4⋊C4—6116no—
747C4⋊C4—614no—
748C4⋊C4—614no—
749C4⋊C4—6116no—
750C4⋊C4—618no—
751C4⋊C4C23×D6118yes—
752C4⋊C4C23×D6118yes—
753C4⋊C4C23×D6114yes—
754C4⋊C4C23×D6114yes—
755C4⋊C4C23×D61116yes—
756C4⋊C4C23×D6118yes—
757C22⋊C4—6116no—
758C22⋊C4—618no—
759C22⋊C4—618no—
760C22⋊C4—618no—
761C22⋊C4—618no—
762C22⋊C4C23×D61116yes—
763C22⋊C4C23×D6118yes—
764C42—614no—
765C42—618no—
766C42—614no—
767C42—618no—
768C42—618no—
769C42—614no—
770C42—6116no—
771C42—6116no—
772C42—618no—
773C42C23×D6114yes—
774C42C23×D6118yes—
775C23—24no—
776C23—24no—
777C23—614no—
778C23—612no—
779C23—1222no—
780C23—1222no—
781C23C2×Q8×D6118yes—
782C23C24×D6114yes—
783C23C24×D6111yescharacteristic
784Q8—28no—
785Q8—216no—
786Q8—416no—
787Q8—6116no—
788Q8—12216no—
789Q8—1228no—
790Q8—12216no—
791Q8—24416no—
792Q8—24416no—
793D4—6132no—
794D4C2×Q8×D61116yescomplemented
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—216no—
801C2×C4—416no—
802C2×C4—614no—
803C2×C4—618no—
804C2×C4—6132no—
805C2×C4—614no—
806C2×C4—614no—
807C2×C4—612no—
808C2×C4—612no—
809C2×C4—6116no—
810C2×C4—614no—
811C2×C4—614no—
812C2×C4—612no—
813C2×C4—614no—
814C2×C4—618no—
815C2×C4—1228no—
816C2×C4—12216no—
817C2×C4—1222no—
818C2×C4—1228no—
819C2×C4—1224no—
820C2×C4—1224no—
821C2×C4—1224no—
822C2×C4—1228no—
823C2×C4—24416no—
824C2×C4—24416no—
825C2×C4C2×Q8×D6114yes—
826C2×C4#1451982214yes—
827C2×C4C24×D6114yes—
828C2×C4C24×D6114yes—
829C2×C4C24×D6112yes—
830C2×C4C24×D6118yes—
831C2×C4C24×D6114yes—
832C2×C4C24×D6112yes—
833C2×C4C24×D6112yes—
834C22—24no—
835C22—24no—
836C22—216no—
837C22—614no—
838C22—1222no—
839C22—1222no—
840C22—1228no—
841C22C22×Q8×D6118yes—
842C22C22×Q8×D6112yes—
843C22C2×#1451982212yes—
844C222−1+4×D6112yes—
845C22C25×D6111yescharacteristic
846C4—24no—
847C4—24no—
848C4—28no—
849C4—22no—
850C4—24no—
851C4—614no—
852C4—618no—
853C4—614no—
854C4—1222no—
855C4—1228no—
856C4—1224no—
857C4—1224no—
858C4—1224no—
859C4C22×Q8×D6114yes—
860C4C2×#1451982214yes—
861C2—28no—
862C2—1224no—
863C2#2145963014yesdirect product factor
864C2C23×Q8×D6111yescharacteristic
865C2C22×#1451982211yescharacteristic
866C2C2×2−1+4×D6111yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×D4×Q8×C61C2
socleC23×C61C25
prime radicalC22×#11758224C22
hypercenterC2×D4×Q8D61
hypocenterC61C2×#3503
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #21459630C2direct (N × H)
2. C2×#16840492C2semidirect
3. C2×#16840490C2semidirect
4. C2×#16840487C2semidirect
5. C2×#16840471C2semidirect
6. C2×#16840466C2semidirect
7. C2×D4×Dic122C2semidirect
8. C2×Q8×C22⋊D61C2semidirect
9. C2×#16840425C2semidirect
10. C2×#16840391C2semidirect
11. C2×#16840389C2semidirect
12. C2×#16840316C2semidirect
13. C2×#16840314C2semidirect
14. C22×#14519775C2semidirect
15. C2×C4⋊Q8×D61C2semidirect
18. C2×D4×Q8×C61C2semidirect
22. #16840492C22semidirect
23. #16840490C22semidirect
24. #16840487C22semidirect
25. #16840471C22semidirect
26. #16840466C22semidirect
27. D4×Dic122C22semidirect
28. Q8×C22⋊D61C22semidirect
29. #16840425C22semidirect
30. #16840391C22semidirect
31. #16840389C22semidirect
32. #16840316C22semidirect
33. #16840314C22semidirect
47. C2×#14519775C22semidirect
48. C4⋊Q8×D61C22semidirect
93. D4×Q8×C61C22semidirect
101. C2×#11758224Q8semidirect
244. C2×D4×C61C2×Q8semidirect
257. C2×C22⋊D61C2×Q8semidirect
261. C22×Dic61C2×Q8semidirect
274. #11758224C2×Q8semidirect
278. C2×C4×D61C2×Q8semidirect
289. C2×Dic122C2×Q8semidirect
353. D4×C61C22×Q8semidirect
370. C22⋊D61C22×Q8semidirect
380. C2×Dic61C22×Q8semidirect
393. C4×D61C22×Q8semidirect
399. Dic122C22×Q8semidirect
437. C2×D4×Q8D61semidirect
447. C2×C61#3503semidirect
464. D4×Q8C2×D61semidirect
534. C61C2×#3503semidirect
695. C2×D4Q8×D61semidirect
794. D4C2×Q8×D61semidirect
863. C2#21459630direct (N × H)

Maximal subgroups

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

subgroupindex
#214596302
C2×#168404922
C2×#168404902
C2×#168404872
C2×#168404712
C2×#168404662
C2×D4×Dic1222
C2×Q8×C22⋊D612
C2×#168404252
C2×#168403912
C2×#168403892
C2×#168403162
C2×#168403142
C22×#145197752
C2×C4⋊Q8×D612
C2×#168402412
C2×C4×#117582242
C2×D4×Q8×C612
C2×#350361