Finite Group Databasebeta

← C2×#21459634 #30588343

Subgroups — C2×#21459634 #30588343

Order 15616.

7478 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459634C2132yesmaximal, direct product factor
2C2×#16840492C212yesmaximal, complemented
3C2×#16840489C212yesmaximal, complemented
4C2×#16840468C212yesmaximal, complemented
5C2×#16840466C214yesmaximal, complemented
6C2×#16840427C212yesmaximal, complemented
7C2×#16840425C214yesmaximal, complemented
8C2×#16840392C212yesmaximal, complemented
9C2×#16840390C211yesmaximal, characteristic, complemented
10C2×#16840389C212yesmaximal, complemented
11C2×#16840318C212yesmaximal, complemented
12C2×#16840315C211yesmaximal, characteristic, complemented
13C22×#14519776C211yesmaximal, characteristic, complemented
14C2×C4⋊Q8×D61C212yesmaximal, complemented
15C2×#16840243C211yesmaximal, characteristic
16C2×#16840242C211yesmaximal, characteristic
17C2×#16840230C211yesmaximal, characteristic
18C2×C61×#544C211yesmaximal, characteristic, complemented
19C22×#11758222C2211yescharacteristic
20C23×Dic122C2212yes—
21C22×Q8×D61C2214yes—
22#16840492C22132yescomplemented
23#16840489C22132yescomplemented
24#16840468C22132yescomplemented
25#16840466C22164yescomplemented
26#16840427C22132yescomplemented
27#16840425C22164yescomplemented
28#16840392C22132yescomplemented
29#16840390C22116yescomplemented
30#16840389C22132yescomplemented
31#16840318C22132yescomplemented
32#16840315C22116yescomplemented
33C2×#14519777C2212yes—
34C2×#14519776C2212yes—
35C2×#14519776C2212yes—
36C2×#14519776C2214yes—
37C2×#14519776C2214yes—
38C2×#14519776C2212yes—
39C2×#14519776C2211yescharacteristic
40C2×#14519776C2212yes—
41C2×#14519776C2212yes—
42C2×#14519776C2211yescharacteristic
43C2×#14519776C22116yescomplemented
44C2×#14519775C2214yes—
45C2×#14519775C2214yes—
46C4⋊Q8×D61C22132yescomplemented
47C2×#14519769C2212yes—
48C2×#14519768C2211yescharacteristic
49C2×#14519768C2212yes—
50C2×#14519768C2211yescharacteristic
51C2×#14519767C2214yes—
52C2×#14519767C2214yes—
53C2×#14519757C2214yes—
54C2×#14519755C2214yes—
55C2×#14519755C2214yes—
56C2×#14519755C2214yes—
57C2×#14519755C2214yes—
58C2×#14519754C2214yes—
59C2×#14519754C2212yes—
60C2×#14519754C2212yes—
61C2×#14519753C2214yes—
62#16840243C22116yes—
63#16840242C22116yes—
64#16840230C22116yes—
65C2×C4×Dic122C2212yes—
66C2×C4×Dic122C2212yes—
67C2×C4×Dic122C2212yes—
68C2×#14519742C2211yescharacteristic
69C2×#14519742C2211yescharacteristic
70C2×#14519742C2212yes—
71C2×#14519742C2214yes—
72C2×#14519742C2214yes—
73C2×C4×D244C2212yes—
74C2×#14519739C2211yescharacteristic
75C2×#14519739C2211yescharacteristic
76C2×#14519739C2212yes—
77C2×C4×C22⋊D61C2214yes—
78C2×#14519737C2212yes—
79C2×#14519737C2212yes—
80C2×#14519737C2214yes—
81C2×#14519736C2211yescharacteristic
82C2×#14519735C2212yes—
83C2×#14519735C2212yes—
84C2×#14519734C2212yes—
85C22×C4⋊Dic61C2211yescharacteristic
86C22×#11758196C2212yes—
87C2×C4⋊C4×D61C2212yes—
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2214yes—
90C22×C4×Dic61C2211yescharacteristic
91C2×C42×D61C2212yes—
92C61×#544C22116yescomplemented
93C2×C4⋊Q8×C61C2212yes—
94C2×C4⋊Q8×C61C2212yes—
95C2×#125×C61C2212yes—
96C2×#125×C61C2212yes—
97C2×C22⋊Q8×C61C2214yes—
98C2×#117×C61C2211yescharacteristic
99C2×#117×C61C2211yescharacteristic
100C22×C4⋊C4×C61C2211yescharacteristic
101C2×#11758222Q8116yescomplemented
102C2×#11758222C2318yes—
103C22×Dic122—48no—
104C22×Dic122C2312yes—
105C22×Dic122C2314yes—
106C22×Dic122C2312yes—
107C22×Dic122C2314yes—
108C22×Dic122C2314yes—
109C22×Dic122C23116yes—
110C22×Dic122C2311yescharacteristic
111C2×Q8×D61—416no—
112C2×Q8×D61C23132yes—
113C22×D244C2311yescharacteristic
114C22×C22⋊D61C2312yes—
115C23×Dic61C2311yescharacteristic
116C23×Dic61C2311yescharacteristic
117C23×Dic61C2312yes—
118C22×C4×D61C2312yes—
119C22×C4×D61C2312yes—
120C22×C4×D61C2314yes—
121C22×C4×D61C2314yes—
122C22×C4×D61C2312yes—
123#14519777C23116yes—
124#14519776C23116yes—
125#14519776C23132yes—
126#14519776C23116yes—
127#14519776C23116yes—
128#14519776C23132yes—
129#14519776C2318yes—
130#14519776C23116yes—
131#14519776C23116yes—
132#14519776C2318yes—
133#14519775C23132yes—
134#14519775C23132yes—
135#14519769C23116yes—
136#14519768C23116yes—
137#14519768C2318yes—
138#14519768C2318yes—
139#14519767C23132yes—
140#14519767C23132yes—
141#14519757C23132yes—
142#14519755C23132yes—
143#14519755C23132yes—
144#14519755C23132yes—
145#14519755C23132yes—
146#14519754C23116yes—
147#14519754C23132yes—
148#14519754C23116yes—
149#14519753C23132yes—
150C4×Dic122C23116yes—
151C4×Dic122C23116yes—
152C4×Dic122C23116yes—
153#14519742C23132yes—
154#14519742C2318yes—
155#14519742C2318yes—
156#14519742C23116yes—
157#14519742C23132yes—
158C4×D244C23116yes—
159#14519739C2318yes—
160#14519739C23116yes—
161#14519739C2318yes—
162C4×C22⋊D61C23132yes—
163#14519737C23116yes—
164#14519737C23132yes—
165#14519737C23116yes—
166#14519736C2318yes—
167#14519735C23116yes—
168#14519735C23116yes—
169#14519734C23116yes—
170C2×C4⋊Dic61C2311yescharacteristic
171C2×C4⋊Dic61C2312yes—
172C2×C4⋊Dic61C2314yes—
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2318yes—
175C2×C4⋊Dic61C2311yescharacteristic
176C2×C4⋊Dic61C2312yes—
177C2×C4⋊Dic61C2312yes—
178C2×#11758196C23116yes—
179C2×#11758196C2312yes—
180C2×#11758196C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2314yes—
188C2×#11758196C2314yes—
189C2×#11758196C2312yes—
190C2×#11758196C2312yes—
191C4⋊C4×D61C23132yes—
192C4⋊C4×D61C23116yes—
193C4⋊C4×D61C23116yes—
194C2×C22⋊Dic61C2312yes—
195C2×#11758198C2312yes—
196C2×#11758198C2312yes—
197C2×#11758198C2314yes—
198C2×#11758198C2314yes—
199C2×C4×Dic61C2311yescharacteristic
200C2×C4×Dic61C2312yes—
201C2×C4×Dic61C2312yes—
202C2×C4×Dic61C2311yescharacteristic
203C2×C4×Dic61C2311yescharacteristic
204C2×C4×Dic61C2311yescharacteristic
205C2×C4×Dic61C2318yes—
206C2×C4×Dic61C2314yes—
207C2×C4×Dic61C2314yes—
208C2×C4×Dic61C2312yes—
209C42×D61C23116yes—
210C22×Q8×C61C2314yes—
211C23×C4×C61C2312yes—
212C23×C4×C61C2311yescharacteristic
213C4⋊Q8×C61C23116yes—
214C4⋊Q8×C61C23116yes—
215#125×C61C23116yes—
216#125×C61C23116yes—
217C22⋊Q8×C61C23132yes—
218#117×C61C2318yes—
219#117×C61C2318yes—
220C2×C4⋊C4×C61C2311yescharacteristic
221C2×C4⋊C4×C61C2311yescharacteristic
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2314yes—
224C2×C4⋊C4×C61C2312yes—
225C2×C4⋊C4×C61C2314yes—
226C2×C4⋊C4×C61C2318yes—
227C2×C4⋊C4×C61C2311yescharacteristic
228C2×C4⋊C4×C61C2311yescharacteristic
229C2×C4⋊C4×C61C2314yes—
230C2×C22⋊C4×C61C2312yes—
231C2×C22⋊C4×C61C2312yes—
232C2×C42×C61C2312yes—
233C2×C42×C61C2312yes—
234C24×C61C2411yescharacteristic
235C23×D61C2412yes—
236C2×Q8×C61—48no—
237C2×Q8×C61C24116yes—
238C22×C4×C61—44no—
239C22×C4×C61C2×Q818yescomplemented
240C22×C4×C61C2412yes—
241C22×C4×C61C2412yes—
242C22×C4×C61C2414yes—
243C22×C4×C61C2412yes—
244C22×C4×C61C2412yes—
245C22×C4×C61C2418yes—
246C22×C4×C61C2411yescharacteristic
247C22×C4×C61C2411yescharacteristic
248C22×C4×C61C2414yes—
249C2×C22⋊D61C2×Q8116yescomplemented
250C2×C22⋊D61C2418yes—
251C22×Dic61—24no—
252C22×Dic61—24no—
253C22×Dic61—44no—
254C22×Dic61C2412yes—
255C22×Dic61C2414yes—
256C22×Dic61C2411yescharacteristic
257C22×Dic61C2414yes—
258C22×Dic61C2411yescharacteristic
259C22×Dic61C2414yes—
260C22×Dic61C2412yes—
261C22×Dic61C2418yes—
262C22×Dic61C2412yes—
263C22×Dic61C2411yescharacteristic
264C22×Dic61C2411yescharacteristic
265Q8×D61—464no—
266#11758222C2×Q8164yescomplemented
267C2×D244C2×Q818yescomplemented
268C2×D244C2414yes—
269C2×C4×D61—28no—
270C2×C4×D61—28no—
271C2×C4×D61—48no—
272C2×C4×D61—48no—
273C2×C4×D61C2×Q8116yescomplemented
274C2×C4×D61C2418yes—
275C2×C4×D61C2418yes—
276C2×C4×D61C24116yes—
277C2×C4×D61C24116yes—
278C2×C4×D61C2418yes—
279C2×Dic122—28no—
280C2×Dic122—216no—
281C2×Dic122—28no—
282C2×Dic122—432no—
283C2×Dic122—48no—
284C2×Dic122—48no—
285C2×Dic122C2×Q818yescomplemented
286C2×Dic122C2418yes—
287C2×Dic122C24116yes—
288C2×Dic122C2418yes—
289C2×Dic122C24116yes—
290C2×Dic122C24116yes—
291C2×Dic122C2414yes—
292C4⋊C4×C61C2418yes—
293C4⋊C4×C61C2418yes—
294C4⋊C4×C61C2414yes—
295C4⋊C4×C61C2414yes—
296C4⋊C4×C61C2414yes—
297C4⋊C4×C61C2414yes—
298C4⋊C4×C61C24116yes—
299C4⋊C4×C61C24116yes—
300C4⋊C4×C61C24116yes—
301C22⋊C4×C61C2418yes—
302C22⋊C4×C61C2418yes—
303C42×C61C2418yes—
304C42×C61C2418yes—
305C22⋊Dic61C2418yes—
306#11758198C2418yes—
307#11758198C2418yes—
308#11758198C24116yes—
309#11758198C24116yes—
310C4⋊Dic61C2414yes—
311C4⋊Dic61C2418yes—
312C4⋊Dic61C24116yes—
313C4⋊Dic61C2418yes—
314C4⋊Dic61C2414yes—
315C4⋊Dic61C2418yes—
316C4⋊Dic61C2418yes—
317#11758196C2418yes—
318#11758196C24116yes—
319#11758196C24116yes—
320#11758196C24116yes—
321#11758196C24116yes—
322#11758196C2418yes—
323#11758196C2418yes—
324#11758196C2418yes—
325#11758196C24116yes—
326#11758196C24116yes—
327#11758196C2418yes—
328#11758196C2418yes—
329C4×Dic61C2414yes—
330C4×Dic61C2418yes—
331C4×Dic61C2418yes—
332C4×Dic61C2414yes—
333C4×Dic61C2414yes—
334C4×Dic61C2414yes—
335C4×Dic61C24116yes—
336C4×Dic61C24116yes—
337C4×Dic61C2418yes—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61C22×Q814yes—
341C23×C61C2512yes—
342C23×C61C2511yescharacteristic
343C22×D61—24no—
344C22×D61—24no—
345C22×D61C22×Q818yes—
346C22×D61C2514yes—
347Q8×C61—416no—
348C2×C4×C61—28no—
349C2×C4×C61—24no—
350C2×C4×C61—24no—
351C2×C4×C61—24no—
352C2×C4×C61—24no—
353C2×C4×C61—48no—
354C2×C4×C61C22×Q814yes—
355C2×C4×C61C22×Q814yes—
356C2×C4×C61C22×Q8116yescomplemented
357C2×C4×C61C2514yes—
358C2×C4×C61C2514yes—
359C2×C4×C61C2514yes—
360C2×C4×C61C2518yes—
361C2×C4×C61C2514yes—
362C2×C4×C61C2512yes—
363C2×C4×C61C2512yes—
364C22⋊D61C22×Q8132yescomplemented
365C2×Dic61—24no—
366C2×Dic61—28no—
367C2×Dic61—22no—
368C2×Dic61—24no—
369C2×Dic61—22no—
370C2×Dic61—28no—
371C2×Dic61—28no—
372C2×Dic61—48no—
373C2×Dic61C22×Q818yes—
374C2×Dic61H(5,𝔽2)14yes—
375C2×Dic612−1+414yes—
376C2×Dic61C2514yes—
377C2×Dic61C2512yes—
378C2×Dic61C2512yes—
379C2×Dic61C2518yes—
380C2×Dic61C2514yes—
381C2×Dic61C2514yes—
382C2×Dic61C2512yes—
383C2×Dic61C2512yes—
384D244C22×Q8116yescomplemented
385C4×D61—216no—
386C4×D61—216no—
387C4×D61—416no—
388C4×D61—416no—
389C4×D61C22×Q8132yescomplemented
390Dic122—232no—
391Dic122—216no—
392Dic122—216no—
393Dic122—416no—
394Dic122—416no—
395Dic122C22×Q8116yescomplemented
396C2×#3503—611nomaximal, Sylow
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—28no—
400C22×C61C23×Q814yes—
401C22×C61C23×Q812yes—
402C22×C61C2×H(5,𝔽2)12yes—
403C22×C61C2×2−1+412yes—
404C22×C61C2611yescharacteristic
405C2×D61—24no—
406C2×D61—24no—
407C2×D61—216no—
408C2×D61C23×Q818yes—
409C4×C61—28no—
410C4×C61—24no—
411C4×C61—24no—
412C4×C61—24no—
413C4×C61—24no—
414C4×C61C23×Q814yes—
415C4×C61C23×Q814yes—
416Dic61—24no—
417Dic61—28no—
418Dic61—22no—
419Dic61—24no—
420Dic61—22no—
421Dic61C23×Q818yes—
422Dic61C2×H(5,𝔽2)14yes—
423Dic61C2×2−1+414yes—
424#3503—6132no—
425C2×Q82—612no—
426C2×#557—612no—
427C2×#554—612no—
428C2×#554—614no—
429C2×D4×Q8—612no—
430C2×D4×Q8—614no—
431C2×#544—612no—
432C2×#544—612no—
433C2×#544—611no—
434C2×#544D6111yescharacteristic, complemented
435C2×#533—612no—
436C2×#533—611no—
437C22×C4⋊Q8—612no—
438C22×C4⋊Q8—611no—
439C2×#520—611no—
440C2×#520—611no—
441C2×C4×#41—611no—
442C2×C61—24no—
443C2×C61#350314yescomplemented
444C2×C61C24×Q811yescharacteristic
445C2×C61C22×H(5,𝔽2)11yescharacteristic
446C2×C61C22×2−1+411yescharacteristic
447D61—28no—
448C22×#41—611no—
449C23×Q8—614no—
450C23×Q8—612no—
451Q82—6132no—
452#557—6132no—
453#554—6132no—
454#554—6164no—
455D4×Q8—6132no—
456D4×Q8—6164no—
457#544—6132no—
458#544—6132no—
459#544—6116no—
460#544C2×D61116yescomplemented
461#533—6132no—
462#533—6116no—
463C2×C4⋊Q8—614no—
464C2×C4⋊Q8—614no—
465C2×C4⋊Q8—6132no—
466C2×C4⋊Q8—611no—
467C2×C4⋊Q8—612no—
468C2×C4⋊Q8—612no—
469C2×C4⋊Q8—614no—
470C2×C4⋊Q8—612no—
471C2×C4⋊Q8—612no—
472C2×C4⋊Q8—6116no—
473C2×C4⋊Q8—611no—
474C2×C4⋊Q8—614no—
475C2×C4⋊Q8—612no—
476C2×C4⋊Q8—612no—
477C2×C4⋊Q8C2×D6112yes—
478C2×C4⋊Q8C2×D6112yes—
479C2×#125—614no—
480C2×#125—614no—
481C2×#125—611no—
482C2×#125—611no—
483C2×#125—612no—
484C2×#125—612no—
485C2×#125C2×D6112yes—
486C2×#125C2×D6112yes—
487C2×C22⋊Q8—614no—
488C2×C22⋊Q8—614no—
489C2×C22⋊Q8—614no—
490C2×C22⋊Q8—614no—
491C2×C22⋊Q8—614no—
492C2×C22⋊Q8—614no—
493C2×C22⋊Q8—612no—
494C2×C22⋊Q8—612no—
495C2×C22⋊Q8—614no—
496C2×C22⋊Q8C2×D6114yes—
497#520—6116no—
498#520—6116no—
499C4×#41—6116no—
500C2×C4×Q8—611no—
501C2×C4×Q8—611no—
502C2×C4×Q8—612no—
503C2×C4×Q8—614no—
504C2×C4×Q8—614no—
505C2×C4×Q8—612no—
506C2×C4×Q8—612no—
507C2×C4×Q8—612no—
508C2×C4×D4—614no—
509C2×C4×D4—611no—
510C2×C4×D4—611no—
511C2×C4×D4—612no—
512C2×C4×D4—612no—
513C2×C4×D4—612no—
514C2×C4×D4—614no—
515C2×C4×D4—612no—
516C2×#117—611no—
517C2×#117—612no—
518C2×#117—612no—
519C2×#117—612no—
520C2×#117C2×D6111yescharacteristic
521C2×#117C2×D6111yescharacteristic
522C22×C4⋊C4—612no—
523C22×C4⋊C4—611no—
524C22×C4⋊C4—612no—
525C22×C4⋊C4—612no—
526C22×C4⋊C4—614no—
527C22×C4⋊C4C2×D6111yescharacteristic
528C22×C42—611no—
529C22×C42—612no—
530C61C2×#350311yescharacteristic, complemented, Sylow
531C2×#41—6116no—
532C2×#41—618no—
533C22×Q8—6132no—
534C22×Q8—611no—
535C22×Q8—612no—
536C22×Q8—614no—
537C22×Q8—612no—
538C22×Q8—614no—
539C22×Q8—614no—
540C22×Q8—6116no—
541C22×Q8—2448no—
542C22×Q8—24416no—
543C22×Q8C22×D6114yes—
544C22×D4—612no—
545C22×D4—611no—
546C23×C4—612no—
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—612no—
550C23×C4—612no—
551C23×C4—612no—
552C23×C4—614no—
553C23×C4—614no—
554C23×C4C22×D6112yes—
555C23×C4C22×D6111yescharacteristic
556C4⋊Q8—6132no—
557C4⋊Q8—6132no—
558C4⋊Q8—618no—
559C4⋊Q8—6116no—
560C4⋊Q8—6116no—
561C4⋊Q8—6132no—
562C4⋊Q8—6116no—
563C4⋊Q8—6116no—
564C4⋊Q8—618no—
565C4⋊Q8—6132no—
566C4⋊Q8—6116no—
567C4⋊Q8—6116no—
568C4⋊Q8C22×D61116yes—
569C4⋊Q8C22×D61116yes—
570#125—618no—
571#125—618no—
572#125—6132no—
573#125—6132no—
574#125—6116no—
575#125—6116no—
576#125C22×D61116yes—
577#125C22×D61116yes—
578C22⋊Q8—6132no—
579C22⋊Q8—6132no—
580C22⋊Q8—6132no—
581C22⋊Q8—6132no—
582C22⋊Q8—6132no—
583C22⋊Q8—6132no—
584C22⋊Q8—6116no—
585C22⋊Q8—6116no—
586C22⋊Q8—6132no—
587C22⋊Q8C22×D61132yes—
588C4×Q8—618no—
589C4×Q8—618no—
590C4×Q8—6116no—
591C4×Q8—6132no—
592C4×Q8—6132no—
593C4×Q8—6116no—
594C4×Q8—6116no—
595C4×Q8—6116no—
596C4×D4—6132no—
597C4×D4—618no—
598C4×D4—618no—
599C4×D4—6116no—
600C4×D4—6116no—
601C4×D4—6116no—
602C4×D4—6132no—
603C4×D4—6116no—
604#117—618no—
605#117—6116no—
606#117—6116no—
607#117—6116no—
608#117C22×D6118yes—
609#117C22×D6118yes—
610C2×C4⋊C4—612no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—614no—
613C2×C4⋊C4—612no—
614C2×C4⋊C4—614no—
615C2×C4⋊C4—614no—
616C2×C4⋊C4—612no—
617C2×C4⋊C4—618no—
618C2×C4⋊C4—614no—
619C2×C4⋊C4—614no—
620C2×C4⋊C4—6116no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—612no—
623C2×C4⋊C4—612no—
624C2×C4⋊C4—612no—
625C2×C4⋊C4—614no—
626C2×C4⋊C4—612no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—612no—
629C2×C4⋊C4—614no—
630C2×C4⋊C4—612no—
631C2×C4⋊C4—6116no—
632C2×C4⋊C4—6116no—
633C2×C4⋊C4—6132no—
634C2×C4⋊C4C22×D6111yescharacteristic
635C2×C4⋊C4C22×D6112yes—
636C2×C4⋊C4C22×D6114yes—
637C2×C4⋊C4C22×D6112yes—
638C2×C4⋊C4C22×D6118yes—
639C2×C4⋊C4C22×D6111yescharacteristic
640C2×C4⋊C4C22×D6111yescharacteristic
641C2×C4⋊C4C22×D6111yescharacteristic
642C2×C4⋊C4C22×D6114yes—
643C2×C4⋊C4C22×D6114yes—
644C2×C22⋊C4—612no—
645C2×C22⋊C4—614no—
646C2×C22⋊C4—612no—
647C2×C22⋊C4—612no—
648C2×C22⋊C4—614no—
649C2×C22⋊C4C22×D6112yes—
650C2×C22⋊C4C22×D6112yes—
651C2×C42—611no—
652C2×C42—614no—
653C2×C42—614no—
654C2×C42—612no—
655C2×C42—612no—
656C2×C42—612no—
657C2×C42—611no—
658C2×C42—611no—
659C2×C42—618no—
660C2×C42—611no—
661C2×C42—6116no—
662C2×C42C22×D6112yes—
663C2×C42C22×D6112yes—
664C24—612no—
665C24C23×D6111yescharacteristic
666#41—6164no—
667C2×Q8—48no—
668C2×Q8—618no—
669C2×Q8—614no—
670C2×Q8—618no—
671C2×Q8—6116no—
672C2×Q8—618no—
673C2×Q8—6116no—
674C2×Q8—6116no—
675C2×Q8—1228no—
676C2×Q8—12216no—
677C2×Q8—1228no—
678C2×Q8—2448no—
679C2×Q8—2448no—
680C2×Q8—24432no—
681C2×Q8—24464no—
682C2×Q8C23×D61116yes—
683C2×D4—6116no—
684C2×D4—618no—
685C2×D4—618no—
686C2×D4—614no—
687C22×C4—44no—
688C22×C4—612no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—6116no—
692C22×C4—618no—
693C22×C4—614no—
694C22×C4—614no—
695C22×C4—612no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—612no—
699C22×C4—614no—
700C22×C4—618no—
701C22×C4—618no—
702C22×C4—618no—
703C22×C4—6116no—
704C22×C4—6116no—
705C22×C4—1228no—
706C22×C4—1228no—
707C22×C4—1224no—
708C22×C4—1224no—
709C22×C4—2448no—
710C22×C4—2448no—
711C22×C4—2444no—
712C22×C4Q8×D6118yescomplemented
713C22×C4C23×D6112yes—
714C22×C4C23×D6112yes—
715C22×C4C23×D6112yes—
716C22×C4C23×D6114yes—
717C22×C4C23×D6112yes—
718C22×C4C23×D6118yes—
719C22×C4C23×D6111yescharacteristic
720C22×C4C23×D6111yescharacteristic
721C22×C4C23×D6114yes—
722C4⋊C4—6116no—
723C4⋊C4—618no—
724C4⋊C4—618no—
725C4⋊C4—614no—
726C4⋊C4—6116no—
727C4⋊C4—6116no—
728C4⋊C4—6116no—
729C4⋊C4—618no—
730C4⋊C4—6116no—
731C4⋊C4—618no—
732C4⋊C4—618no—
733C4⋊C4—618no—
734C4⋊C4—6116no—
735C4⋊C4—618no—
736C4⋊C4—618no—
737C4⋊C4—6116no—
738C4⋊C4—614no—
739C4⋊C4—618no—
740C4⋊C4—618no—
741C4⋊C4C23×D6114yes—
742C4⋊C4C23×D6118yes—
743C4⋊C4C23×D61116yes—
744C4⋊C4C23×D6118yes—
745C4⋊C4C23×D6114yes—
746C4⋊C4C23×D6114yes—
747C4⋊C4C23×D6114yes—
748C4⋊C4C23×D61116yes—
749C4⋊C4C23×D61116yes—
750C22⋊C4—618no—
751C22⋊C4—6116no—
752C22⋊C4—618no—
753C22⋊C4—618no—
754C22⋊C4—6116no—
755C22⋊C4C23×D6118yes—
756C22⋊C4C23×D6118yes—
757C42—614no—
758C42—614no—
759C42—618no—
760C42—618no—
761C42—614no—
762C42—614no—
763C42—6116no—
764C42—6116no—
765C42—618no—
766C42C23×D6118yes—
767C42C23×D6118yes—
768C23—22no—
769C23—22no—
770C23—618no—
771C23—614no—
772C23—1224no—
773C23—1224no—
774C23C2×Q8×D6114yes—
775C23C24×D6112yes—
776C23C24×D6111yescharacteristic
777Q8—416no—
778Q8—6116no—
779Q8—12216no—
780Q8—12232no—
781Q8—12216no—
782Q8—24416no—
783Q8—24416no—
784D4—6132no—
785D4—6116no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—48no—
792C2×C4—618no—
793C2×C4—614no—
794C2×C4—614no—
795C2×C4—614no—
796C2×C4—612no—
797C2×C4—612no—
798C2×C4—6132no—
799C2×C4—614no—
800C2×C4—612no—
801C2×C4—612no—
802C2×C4—618no—
803C2×C4—614no—
804C2×C4—12216no—
805C2×C4—12216no—
806C2×C4—1228no—
807C2×C4—1228no—
808C2×C4—1222no—
809C2×C4—1224no—
810C2×C4—1228no—
811C2×C4—1222no—
812C2×C4—1224no—
813C2×C4—24416no—
814C2×C4—24416no—
815C2×C4—2448no—
816C2×C4C2×Q8×D6114yes—
817C2×C4C2×Q8×D6114yes—
818C2×C4C2×Q8×D61116yescomplemented
819C2×C4C24×D6114yes—
820C2×C4C24×D6114yes—
821C2×C4C24×D6114yes—
822C2×C4C24×D6118yes—
823C2×C4C24×D6114yes—
824C2×C4C24×D6112yes—
825C2×C4C24×D6112yes—
826C22—22no—
827C22—22no—
828C22—28no—
829C22—618no—
830C22—1224no—
831C22—1224no—
832C22—12216no—
833C22C22×Q8×D6114yes—
834C22C22×Q8×D6112yes—
835C22H(5,𝔽2)×D6112yes—
836C222−1+4×D6112yes—
837C22C25×D6111yescharacteristic
838C4—28no—
839C4—24no—
840C4—24no—
841C4—24no—
842C4—24no—
843C4—618no—
844C4—614no—
845C4—614no—
846C4—1222no—
847C4—1224no—
848C4—1228no—
849C4—1222no—
850C4—1224no—
851C4C22×Q8×D6114yes—
852C4C22×Q8×D6114yes—
853C2—24no—
854C2—1228no—
855C2#2145963414yesdirect product factor
856C2C23×Q8×D6111yescharacteristic
857C2C2×H(5,𝔽2)×D6111yescharacteristic
858C2C2×2−1+4×D6111yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#544C2
socleC23×C61C25
prime radicalC22×#11758222C22
hypercenterC2×#544D61
hypocenterC61C2×#3503
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #21459634C2direct (N × H)
2. C2×#16840492C2semidirect
3. C2×#16840489C2semidirect
4. C2×#16840468C2semidirect
5. C2×#16840466C2semidirect
6. C2×#16840427C2semidirect
7. C2×#16840425C2semidirect
8. C2×#16840392C2semidirect
9. C2×#16840390C2semidirect
10. C2×#16840389C2semidirect
11. C2×#16840318C2semidirect
12. C2×#16840315C2semidirect
13. C22×#14519776C2semidirect
14. C2×C4⋊Q8×D61C2semidirect
18. C2×C61×#544C2semidirect
22. #16840492C22semidirect
23. #16840489C22semidirect
24. #16840468C22semidirect
25. #16840466C22semidirect
26. #16840427C22semidirect
27. #16840425C22semidirect
28. #16840392C22semidirect
29. #16840390C22semidirect
30. #16840389C22semidirect
31. #16840318C22semidirect
32. #16840315C22semidirect
43. C2×#14519776C22semidirect
46. C4⋊Q8×D61C22semidirect
92. C61×#544C22semidirect
101. C2×#11758222Q8semidirect
239. C22×C4×C61C2×Q8semidirect
249. C2×C22⋊D61C2×Q8semidirect
266. #11758222C2×Q8semidirect
267. C2×D244C2×Q8semidirect
273. C2×C4×D61C2×Q8semidirect
285. C2×Dic122C2×Q8semidirect
356. C2×C4×C61C22×Q8semidirect
364. C22⋊D61C22×Q8semidirect
384. D244C22×Q8semidirect
389. C4×D61C22×Q8semidirect
395. Dic122C22×Q8semidirect
434. C2×#544D61semidirect
443. C2×C61#3503semidirect
460. #544C2×D61semidirect
530. C61C2×#3503semidirect
712. C22×C4Q8×D61semidirect
818. C2×C4C2×Q8×D61semidirect
855. C2#21459634direct (N × H)

Maximal subgroups

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

subgroupindex
#214596342
C2×#168404922
C2×#168404892
C2×#168404682
C2×#168404662
C2×#168404272
C2×#168404252
C2×#168403922
C2×#168403902
C2×#168403892
C2×#168403182
C2×#168403152
C22×#145197762
C2×C4⋊Q8×D612
C2×#168402432
C2×#168402422
C2×#168402302
C2×C61×#5442
C2×#350361