Finite Group Databasebeta

← C2×#21459572 #30588445

Subgroups — C2×#21459572 #30588445

Order 15616.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459572C2132yesmaximal, direct product factor
2C2×#16840480C212yesmaximal, complemented
3C2×#16840467C212yesmaximal, complemented
4C2×#16840452C214yesmaximal, complemented
5C2×#16840451C212yesmaximal, complemented
6C2×#16840447C212yesmaximal, complemented
7C2×#16840441C214yesmaximal, complemented
8C2×#16840393C211yesmaximal, characteristic, complemented
9C2×#16840377C212yesmaximal, complemented
10C2×#16840370C212yesmaximal, complemented
11C2×#16840333C211yesmaximal, characteristic, complemented
12C2×#16840316C212yesmaximal, complemented
13C2×#16840294C212yesmaximal, complemented
14C2×#16840269C211yesmaximal, characteristic
15C22×#14519757C211yesmaximal, characteristic, complemented
16C2×#16840239C211yesmaximal, characteristic, complemented
17C2×#117×D61C211yesmaximal, characteristic, complemented
18C2×C61×#520C211yesmaximal, characteristic, complemented
19C23×Dic122C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21#16840480C22132yescomplemented
22#16840467C22132yescomplemented
23#16840452C22164yescomplemented
24#16840451C22132yescomplemented
25#16840447C22132yescomplemented
26#16840441C22164yescomplemented
27#16840393C22116yescomplemented
28#16840377C22132yescomplemented
29#16840370C22132yescomplemented
30#16840333C22116yescomplemented
31#16840316C22132yescomplemented
32C2×#14519776C2212yescomplemented
33C2×#14519776C2212yescomplemented
34C2×#14519775C2212yescomplemented
35#16840294C22132yescomplemented
36C2×#14519772C2214yes—
37C2×#14519771C2214yes—
38C2×#14519770C2214yescomplemented
39C2×#14519770C2214yescomplemented
40C2×#14519769C2214yescomplemented
41C2×#14519768C2212yescomplemented
42C2×#14519768C2212yescomplemented
43C2×#14519767C2214yescomplemented
44C2×#14519767C2214yescomplemented
45C2×#14519764C2212yescomplemented
46C2×#14519763C2214yes—
47#16840269C22116yes—
48C2×#14519760C2214yes—
49C2×#14519759C2214yes—
50C2×#14519758C2212yes—
51C2×#14519758C2214yes—
52C2×#14519757C2212yes—
53C2×#14519757C2212yes—
54C2×#14519757C2212yes—
55C2×#14519757C2212yes—
56C2×#14519757C22116yescomplemented
57C2×#14519756C2214yes—
58C2×#14519756C2212yescomplemented
59C2×#14519756C2214yescomplemented
60C2×#14519756C2212yescomplemented
61C2×#14519755C2214yes—
62C2×#14519753C2211yescharacteristic
63C2×#14519753C2211yescharacteristic
64C2×#14519748C2211yescharacteristic
65C2×#14519748C2211yescharacteristic
66C2×#14519745C2212yes—
67#16840239C22116yescomplemented
68C2×C4×Dic122C2212yescomplemented
69C2×C4×Dic122C2212yescomplemented
70C2×C4×Dic122C2214yescomplemented
71C2×#14519742C2212yescomplemented
72C2×#14519742C2212yescomplemented
73C2×C4×C22⋊D61C2212yes—
74C2×C4×C22⋊D61C2212yes—
75C2×C4×C22⋊D61C2214yes—
76C2×#14519736C2211yescharacteristic
77C2×#14519736C2211yescharacteristic
78C2×#14519736C2214yescomplemented
79C2×#14519735C2211yescharacteristic
80C2×#14519735C2211yescharacteristic
81C2×#14519734C2212yes—
82C2×#14519734C2214yes—
83C2×#14519733C2212yes—
84C2×#14519733C2214yes—
85#117×D61C22116yescomplemented
86C22×C4⋊Dic61C2212yes—
87C2×C4⋊C4×D61C2211yescharacteristic
88C2×C4⋊C4×D61C2211yescharacteristic
89C22×#11758198C2212yes—
90C2×C22⋊C4×D61C2212yes—
91C2×C42×D61C2212yes—
92C22×#41×C61C2211yescharacteristic
93C61×#520C22116yescomplemented
94C2×C4×Q8×C61C2212yescomplemented
95C2×C4×D4×C61C2214yes—
96C2×C4×D4×C61C2212yescomplemented
97C2×#117×C61C2211yescharacteristic
98C2×#117×C61C2212yescomplemented
99C22×C4⋊C4×C61C2211yescharacteristic
100C22×C4⋊C4×C61C2212yescomplemented
101C24×D61C2311yescharacteristic
102C22×Dic122—28no—
103C22×Dic122C2312yes—
104C22×Dic122C2312yes—
105C22×Dic122C2318yes—
106C22×Dic122C2314yes—
107C22×C22⋊D61C2312yes—
108C22×C22⋊D61C2312yes—
109C23×Dic61C2312yes—
110C23×Dic61C2311yescharacteristic
111C22×C4×D61—28no—
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2312yes—
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2318yes—
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2312yes—
119#14519776C23116yescomplemented
120#14519776C23116yescomplemented
121#14519775C23116yescomplemented
122#14519772C23132yes—
123#14519771C23132yes—
124#14519770C23132yescomplemented
125#14519770C23132yescomplemented
126#14519769C23132yescomplemented
127#14519768C23116yescomplemented
128#14519768C23116yescomplemented
129#14519767C23132yescomplemented
130#14519767C23132yescomplemented
131#14519764C23116yescomplemented
132#14519763C23132yes—
133#14519760C23132yes—
134#14519759C23132yes—
135#14519758C23116yes—
136#14519758C23132yes—
137#14519757C23116yes—
138#14519757C23116yes—
139#14519757C23116yes—
140#14519757C23116yes—
141#14519756C23132yes—
142#14519756C23116yescomplemented
143#14519756C23132yescomplemented
144#14519756C23116yescomplemented
145#14519755C23132yes—
146#14519753C2318yes—
147#14519753C2318yes—
148#14519748C2318yes—
149#14519748C2318yes—
150#14519745C23116yes—
151C4×Dic122C23132yescomplemented
152C4×Dic122C23116yescomplemented
153C4×Dic122C23116yescomplemented
154#14519742C23116yescomplemented
155#14519742C23116yescomplemented
156C4×C22⋊D61C23116yes—
157C4×C22⋊D61C23132yes—
158C4×C22⋊D61C23116yes—
159#14519736C2318yes—
160#14519736C2318yes—
161#14519736C23132yescomplemented
162#14519735C2318yes—
163#14519735C2318yes—
164#14519734C23132yes—
165#14519734C23116yes—
166#14519733C23116yes—
167#14519733C23132yes—
168C2×C4⋊Dic61C23116yes—
169C2×C4⋊Dic61C2311yescharacteristic
170C2×C4⋊Dic61C2311yescharacteristic
171C2×C4⋊Dic61C2314yes—
172C2×C4⋊Dic61C2314yes—
173C2×C4⋊Dic61C2311yescharacteristic
174C2×C4⋊Dic61C2311yescharacteristic
175C2×C4⋊Dic61C2314yes—
176C2×#11758196C2312yes—
177C2×#11758196C2312yes—
178C2×#11758196C2314yes—
179C2×#11758196C2314yes—
180C2×#11758196C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C2312yes—
183C2×#11758196C2312yes—
184C2×#11758196C2314yes—
185C2×#11758196C2314yes—
186C4⋊C4×D61C2318yes—
187C4⋊C4×D61C2318yes—
188C2×C22⋊Dic61C2312yes—
189C2×C22⋊Dic61C2312yes—
190C2×C22⋊Dic61C2312yes—
191C2×C22⋊Dic61C2314yes—
192C2×C22⋊Dic61C2312yes—
193C2×C22⋊Dic61C2314yes—
194C2×#11758198C2312yes—
195C2×#11758198C2312yes—
196C2×#11758198C2314yes—
197C2×#11758198C2314yes—
198C2×#11758198C23116yes—
199C2×#11758198C2312yes—
200C2×#11758198C2312yes—
201C22⋊C4×D61C23116yes—
202C2×C4×Dic61C2312yes—
203C2×C4×Dic61C2312yes—
204C2×C4×Dic61C2312yes—
205C2×C4×Dic61C2314yes—
206C2×C4×Dic61C2314yes—
207C2×C4×Dic61C2312yes—
208C42×D61C23116yes—
209C2×#41×C61—28no—
210C2×#41×C61C2318yes—
211C22×Q8×C61C2311yescharacteristic
212C22×D4×C61C2312yes—
213C22×D4×C61C2311yescharacteristic
214C23×C4×C61C2312yes—
215C23×C4×C61C2312yes—
216C23×C4×C61C2314yes—
217C23×C4×C61C2311yescharacteristic
218C4×Q8×C61C23116yescomplemented
219C4×D4×C61C23132yes—
220C4×D4×C61C23116yescomplemented
221#117×C61C2318yes—
222#117×C61C23116yescomplemented
223C2×C4⋊C4×C61C2311yescharacteristic
224C2×C4⋊C4×C61C2311yescharacteristic
225C2×C4⋊C4×C61C2314yes—
226C2×C4⋊C4×C61C2312yes—
227C2×C4⋊C4×C61C2312yes—
228C2×C4⋊C4×C61C2318yes—
229C2×C4⋊C4×C61C23116yescomplemented
230C2×C22⋊C4×C61C2312yes—
231C2×C22⋊C4×C61C2314yes—
232C2×C42×C61C2312yes—
233C2×C42×C61C2314yes—
234C24×C61C2412yes—
235C24×C61C2411yescharacteristic
236C23×D61—24no—
237C23×D61—24no—
238C23×D61—42no—
239C23×D61C2411yescharacteristic
240C23×D61C2414yes—
241C23×D61C2411yescharacteristic
242#41×C61—232no—
243C2×Q8×C61—24no—
244C2×Q8×C61C2414yes—
245C2×D4×C61—28no—
246C2×D4×C61—24no—
247C2×D4×C61C2418yes—
248C2×D4×C61C2414yes—
249C22×C4×C61—28no—
250C22×C4×C61—44no—
251C22×C4×C61—48no—
252C22×C4×C61#4118yes—
253C22×C4×C61C2412yes—
254C22×C4×C61C2412yes—
255C22×C4×C61C2414yes—
256C22×C4×C61C2412yes—
257C22×C4×C61C2418yes—
258C22×C4×C61C2418yes—
259C22×C4×C61C24116yes—
260C22×C4×C61C2411yescharacteristic
261C22×C4×C61C2411yescharacteristic
262C22×C4×C61C2414yes—
263C2×C22⋊D61—28no—
264C2×C22⋊D61—44no—
265C2×C22⋊D61C2418yes—
266C2×C22⋊D61C2418yes—
267C22×Dic61—24no—
268C22×Dic61—28no—
269C22×Dic61C2411yescharacteristic
270C22×Dic61C2411yescharacteristic
271C22×Dic61C2414yes—
272C22×Dic61C2412yes—
273C22×Dic61C2412yes—
274C22×Dic61C2414yes—
275C22×Dic61C2418yes—
276C22×Dic61C2412yes—
277C22×Dic61C2412yes—
278C2×C4×D61—28no—
279C2×C4×D61—24no—
280C2×C4×D61—24no—
281C2×C4×D61—24no—
282C2×C4×D61—24no—
283C2×C4×D61—232no—
284C2×C4×D61—44no—
285C2×C4×D61C2414yes—
286C2×C4×D61C2414yes—
287C2×C4×D61C2414yes—
288C2×C4×D61C2414yes—
289C2×C4×D61C2418yes—
290C2×C4×D61C2418yes—
291C2×Dic122—28no—
292C2×Dic122—28no—
293C2×Dic122—232no—
294C2×Dic122—48no—
295C2×Dic122C2418yes—
296C2×Dic122C2418yes—
297C2×Dic122C24116yes—
298C4⋊C4×C61C2418yes—
299C4⋊C4×C61C2418yes—
300C4⋊C4×C61C2414yes—
301C4⋊C4×C61C24116yes—
302C4⋊C4×C61C2414yes—
303C22⋊C4×C61C2418yes—
304C22⋊C4×C61C24116yes—
305C42×C61C2418yes—
306C42×C61C24116yes—
307C22⋊Dic61C2418yes—
308C22⋊Dic61C2418yes—
309C22⋊Dic61C2418yes—
310C22⋊Dic61C24116yes—
311C22⋊Dic61C2418yes—
312C22⋊Dic61C24116yes—
313#11758198C2418yes—
314#11758198C2418yes—
315#11758198C24116yes—
316#11758198C24116yes—
317#11758198C2418yes—
318#11758198C2418yes—
319C4⋊Dic61C2414yes—
320C4⋊Dic61C2414yes—
321C4⋊Dic61C24116yes—
322C4⋊Dic61C24116yes—
323C4⋊Dic61C2414yes—
324C4⋊Dic61C2414yes—
325C4⋊Dic61C24116yes—
326#11758196C2418yes—
327#11758196C2418yes—
328#11758196C24116yes—
329#11758196C24116yes—
330#11758196C24116yes—
331#11758196C24116yes—
332#11758196C2418yes—
333#11758196C2418yes—
334#11758196C24116yes—
335#11758196C24116yes—
336C4×Dic61C2418yes—
337C4×Dic61C2418yes—
338C4×Dic61C2418yes—
339C4×Dic61C24116yes—
340C4×Dic61C24116yes—
341C4×Dic61C2418yes—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—24no—
345C23×C61—24no—
346C23×C61—24no—
347C23×C61C2×#4114yes—
348C23×C61C2514yes—
349C23×C61C2512yes—
350C23×C61C2511yescharacteristic
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—28no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—28no—
358C22×D61—44no—
359C22×D61—416no—
360C22×D612−1+414yes—
361C22×D61C2512yes—
362C22×D61C2512yes—
363Q8×C61—28no—
364D4×C61—216no—
365D4×C61—28no—
366C2×C4×C61—24no—
367C2×C4×C61—24no—
368C2×C4×C61—28no—
369C2×C4×C61—24no—
370C2×C4×C61—216no—
371C2×C4×C61—48no—
372C2×C4×C61—416no—
373C2×C4×C61C2×#4114yes—
374C2×C4×C61C2×#4114yes—
375C2×C4×C61C2×#41116yes—
376C2×C4×C61C2514yes—
377C2×C4×C61C2514yes—
378C2×C4×C61C2514yes—
379C2×C4×C61C2518yes—
380C2×C4×C61C2512yes—
381C2×C4×C61C2512yes—
382C22⋊D61—216no—
383C22⋊D61—48no—
384C2×Dic61—216no—
385C2×Dic61—28no—
386C2×Dic61—28no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—24no—
390C2×Dic61—24no—
391C2×Dic61—24no—
392C2×Dic61—24no—
393C2×Dic61C2512yes—
394C2×Dic61C2514yes—
395C2×Dic61C2514yes—
396C2×Dic61C2514yes—
397C2×Dic61C2514yes—
398C2×Dic61C2518yes—
399C2×Dic61C2512yes—
400C4×D61—216no—
401C4×D61—28no—
402C4×D61—28no—
403C4×D61—28no—
404C4×D61—28no—
405C4×D61—48no—
406Dic122—216no—
407Dic122—216no—
408Dic122—416no—
409C2×#3495—611nomaximal, Sylow
410C22×C61—22no—
411C22×C61—22no—
412C22×C61—28no—
413C22×C61—24no—
414C22×C61—24no—
415C22×C61—24no—
416C22×C61—48no—
417C22×C61C22×#4114yes—
418C22×C61C22×#4112yes—
419C22×C61C2×2−1+412yes—
420C22×C61#58512yes—
421C22×C61C2611yescharacteristic
422C2×D61—22no—
423C2×D61—22no—
424C2×D61—28no—
425C2×D61—22no—
426C2×D61—22no—
427C2×D61—22no—
428C2×D61—416no—
429C2×D61—44no—
430C2×D61C2×2−1+414yes—
431C4×C61—24no—
432C4×C61—24no—
433C4×C61—28no—
434C4×C61—24no—
435C4×C61C22×#4114yes—
436C4×C61C22×#4114yes—
437Dic61—28no—
438Dic61—22no—
439Dic61—22no—
440Dic61—24no—
441Dic61—24no—
442Dic61—24no—
443Dic61—24no—
444#3495—6132no—
445C2×#556—612no—
446C2×#554—612no—
447C2×#552—614no—
448C2×#552—612no—
449C2×#552—612no—
450C2×#551—614no—
451C2×#544—611no—
452C2×#542—612no—
453C2×#541—612no—
454C2×#536—611no—
455C2×#533—612no—
456C2×#529—612no—
457C2×#525—611no—
458C22×C22⋊Q8—611no—
459C2×#520D6111yescharacteristic, complemented
460C2×#519—611no—
461C22×#117—611no—
462C2×C61—24no—
463C2×C61—44no—
464C2×C61#349514yescomplemented
465C2×C61C23×#4111yescharacteristic
466C2×C61C22×2−1+411yescharacteristic
467C2×C61C2×#58511yescharacteristic
468D61—24no—
469D61—42no—
470C22×#41C2×D6111yescharacteristic
471C23×Q8—611no—
472C24×C4—611no—
473#556—6132no—
474#554—6132no—
475#552—6164no—
476#552—6132no—
477#552—6132no—
478#551—6164no—
479#544—6116no—
480#542—6132no—
481#541—6132no—
482#536—6116no—
483#533—6132no—
484C2×C4⋊Q8—612no—
485C2×C4⋊Q8—612no—
486C2×C4⋊Q8—612no—
487#529—6132no—
488C2×#126—614no—
489C2×#126—614no—
490C2×#126—614no—
491C2×#126—614no—
492C2×#125—614no—
493C2×#125—614no—
494C2×#125—612no—
495C2×#125—612no—
496C2×#125—614no—
497C2×#124—612no—
498C2×#124—614no—
499#525—6116no—
500C2×#123—612no—
501C2×#123—614no—
502C2×#123—614no—
503C2×#123—614no—
504C2×C22⋊Q8—611no—
505C2×C22⋊Q8—611no—
506C2×C22⋊Q8—614no—
507C2×C22⋊Q8—612no—
508C2×C22⋊Q8—612no—
509C2×C22⋊Q8—614no—
510C2×C22⋊Q8—614no—
511C2×C22⋊Q8—612no—
512C2×C22⋊Q8—612no—
513C2×C22⋊Q8—612no—
514C2×C22⋊Q8—612no—
515C2×C22⋊Q8—6116no—
516C2×#121—611no—
517C2×#121—611no—
518C2×#120—612no—
519#520C2×D61116yescomplemented
520#519—6116no—
521C2×C4×Q8—612no—
522C2×C4×Q8—612no—
523C2×C4×Q8—612no—
524C2×C4×Q8—612no—
525C2×C4×Q8—614no—
526C2×C4×Q8C2×D6112yescomplemented
527C2×C4×D4—612no—
528C2×C4×D4—612no—
529C2×C4×D4—614no—
530C2×C4×D4C2×D6114yes—
531C2×C4×D4C2×D6112yescomplemented
532C2×#117—611no—
533C2×#117—611no—
534C2×#117—614no—
535C2×#117—6116no—
536C2×#117—611no—
537C2×#117—611no—
538C2×#117—612no—
539C2×#117—614no—
540C2×#117—612no—
541C2×#117—614no—
542C2×#117C2×D6111yescharacteristic
543C2×#117C2×D6112yescomplemented
544C22×C4⋊C4—612no—
545C22×C4⋊C4—611no—
546C22×C4⋊C4—611no—
547C22×C4⋊C4C2×D6111yescharacteristic
548C22×C4⋊C4C2×D6112yescomplemented
549C22×C22⋊C4—612no—
550C22×C22⋊C4—612no—
551C22×C42—612no—
552C61C2×#349511yescharacteristic, complemented, Sylow
553C25—611no—
554C2×#41—28no—
555C2×#41C22×D6118yes—
556C22×Q8—612no—
557C22×Q8—612no—
558C22×Q8—618no—
559C22×Q8—614no—
560C22×Q8—1228no—
561C22×Q8C22×D6111yescharacteristic
562C22×D4—612no—
563C22×D4—612no—
564C22×D4C22×D6112yes—
565C22×D4C22×D6111yescharacteristic
566C23×C4—612no—
567C23×C4—611no—
568C23×C4—612no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—618no—
573C23×C4—611no—
574C23×C4—612no—
575C23×C4—1228no—
576C23×C4C22×D6112yes—
577C23×C4C22×D6112yes—
578C23×C4C22×D6114yes—
579C23×C4C22×D6111yescharacteristic
580C4⋊Q8—6116no—
581C4⋊Q8—6116no—
582C4⋊Q8—6116no—
583#126—6132no—
584#126—6132no—
585#126—6132no—
586#126—6132no—
587#125—6116no—
588#125—6132no—
589#125—6132no—
590#125—6116no—
591#125—6132no—
592#124—6116no—
593#124—6132no—
594#123—6116no—
595#123—6132no—
596#123—6132no—
597#123—6132no—
598C22⋊Q8—618no—
599C22⋊Q8—618no—
600C22⋊Q8—6116no—
601C22⋊Q8—6116no—
602C22⋊Q8—6132no—
603C22⋊Q8—6132no—
604C22⋊Q8—6116no—
605C22⋊Q8—6116no—
606C22⋊Q8—6116no—
607C22⋊Q8—6116no—
608C22⋊Q8—6132no—
609#121—618no—
610#121—618no—
611#120—6116no—
612C4×Q8—6116no—
613C4×Q8—6116no—
614C4×Q8—6116no—
615C4×Q8—6116no—
616C4×Q8—6132no—
617C4×Q8C22×D61116yescomplemented
618C4×D4—6116no—
619C4×D4—6116no—
620C4×D4—6132no—
621C4×D4C22×D61132yes—
622C4×D4C22×D61116yescomplemented
623#117—618no—
624#117—618no—
625#117—6132no—
626#117—618no—
627#117—618no—
628#117—6116no—
629#117—6132no—
630#117—6116no—
631#117—6132no—
632#117C22×D6118yes—
633#117C22×D61116yescomplemented
634C2×C4⋊C4—612no—
635C2×C4⋊C4—611no—
636C2×C4⋊C4—611no—
637C2×C4⋊C4—612no—
638C2×C4⋊C4—614no—
639C2×C4⋊C4—614no—
640C2×C4⋊C4—6116no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—614no—
644C2×C4⋊C4—614no—
645C2×C4⋊C4—614no—
646C2×C4⋊C4—614no—
647C2×C4⋊C4—614no—
648C2×C4⋊C4—612no—
649C2×C4⋊C4—612no—
650C2×C4⋊C4—614no—
651C2×C4⋊C4—614no—
652C2×C4⋊C4—618no—
653C2×C4⋊C4—618no—
654C2×C4⋊C4C22×D6111yescharacteristic
655C2×C4⋊C4C22×D6111yescharacteristic
656C2×C4⋊C4C22×D6112yes—
657C2×C4⋊C4C22×D6112yes—
658C2×C4⋊C4C22×D6118yes—
659C2×C4⋊C4C22×D6114yes—
660C2×C4⋊C4C22×D61116yescomplemented
661C2×C22⋊C4—612no—
662C2×C22⋊C4—612no—
663C2×C22⋊C4—612no—
664C2×C22⋊C4—614no—
665C2×C22⋊C4—612no—
666C2×C22⋊C4—614no—
667C2×C22⋊C4—612no—
668C2×C22⋊C4—612no—
669C2×C22⋊C4—614no—
670C2×C22⋊C4—614no—
671C2×C22⋊C4—6116no—
672C2×C22⋊C4—612no—
673C2×C22⋊C4—612no—
674C2×C22⋊C4—6116no—
675C2×C22⋊C4C22×D6112yes—
676C2×C22⋊C4C22×D6114yes—
677C2×C42—612no—
678C2×C42—614no—
679C2×C42—614no—
680C2×C42—612no—
681C2×C42—612no—
682C2×C42—612no—
683C2×C42—6116no—
684C2×C42C22×D6112yes—
685C2×C42C22×D6114yes—
686C24—611no—
687C24—611no—
688C24—614no—
689C24—1224no—
690C24—1224no—
691C24—2442no—
692C24C23×D6112yes—
693C24C23×D6111yescharacteristic
694#41—232no—
695C2×Q8—24no—
696C2×Q8—618no—
697C2×Q8—618no—
698C2×Q8—6116no—
699C2×Q8—1228no—
700C2×Q8—1228no—
701C2×Q8—12232no—
702C2×Q8—2448no—
703C2×Q8C23×D6114yes—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—618no—
707C2×D4—618no—
708C2×D4—1228no—
709C2×D4—2444no—
710C2×D4C23×D6118yes—
711C2×D4C23×D6114yes—
712C22×C4—28no—
713C22×C4—48no—
714C22×C4—44no—
715C22×C4—618no—
716C22×C4—614no—
717C22×C4—611no—
718C22×C4—612no—
719C22×C4—612no—
720C22×C4—612no—
721C22×C4—614no—
722C22×C4—612no—
723C22×C4—611no—
724C22×C4—614no—
725C22×C4—618no—
726C22×C4—614no—
727C22×C4—614no—
728C22×C4—614no—
729C22×C4—618no—
730C22×C4—1228no—
731C22×C4—1224no—
732C22×C4—1228no—
733C22×C4—1224no—
734C22×C4—1224no—
735C22×C4—1224no—
736C22×C4—1224no—
737C22×C4—12232no—
738C22×C4—2444no—
739C22×C4#1175822218yes—
740C22×C4C23×D6118yes—
741C22×C4C23×D6112yes—
742C22×C4C23×D6112yes—
743C22×C4C23×D6112yes—
744C22×C4C23×D6114yes—
745C22×C4C23×D6118yes—
746C22×C4C23×D61116yes—
747C22×C4C23×D6114yes—
748C22×C4C23×D6111yescharacteristic
749C22×C4C23×D6111yescharacteristic
750C4⋊C4—618no—
751C4⋊C4—618no—
752C4⋊C4—614no—
753C4⋊C4—614no—
754C4⋊C4—6116no—
755C4⋊C4—6116no—
756C4⋊C4—6116no—
757C4⋊C4—6116no—
758C4⋊C4—6116no—
759C4⋊C4—6116no—
760C4⋊C4—618no—
761C4⋊C4—618no—
762C4⋊C4—6116no—
763C4⋊C4—6116no—
764C4⋊C4—614no—
765C4⋊C4—614no—
766C4⋊C4—6116no—
767C4⋊C4C23×D6114yes—
768C4⋊C4C23×D6114yes—
769C4⋊C4C23×D6118yes—
770C4⋊C4C23×D6118yes—
771C4⋊C4C23×D61116yes—
772C22⋊C4—618no—
773C22⋊C4—618no—
774C22⋊C4—618no—
775C22⋊C4—6116no—
776C22⋊C4—618no—
777C22⋊C4—6116no—
778C22⋊C4—618no—
779C22⋊C4—618no—
780C22⋊C4—6116no—
781C22⋊C4—6116no—
782C22⋊C4—618no—
783C22⋊C4—618no—
784C22⋊C4C23×D6118yes—
785C22⋊C4C23×D61116yes—
786C42—618no—
787C42—618no—
788C42—618no—
789C42—6116no—
790C42—6116no—
791C42—618no—
792C42C23×D6118yes—
793C42C23×D61116yes—
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—614no—
800C23—612no—
801C23—612no—
802C23—1228no—
803C23—1222no—
804C23—1222no—
805C23—1228no—
806C23—1222no—
807C23—1222no—
808C23—1222no—
809C23—2444no—
810C23—24416no—
811C23C2×#1175822214yes—
812C23C24×D6114yes—
813C23C24×D6112yes—
814C23C24×D6111yescharacteristic
815Q8—28no—
816Q8—12216no—
817Q8—12216no—
818Q8—24416no—
819D4—216no—
820D4—28no—
821D4—12216no—
822D4—2448no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—28no—
827C2×C4—216no—
828C2×C4—416no—
829C2×C4—48no—
830C2×C4—612no—
831C2×C4—614no—
832C2×C4—614no—
833C2×C4—614no—
834C2×C4—618no—
835C2×C4—614no—
836C2×C4—612no—
837C2×C4—12216no—
838C2×C4—1228no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—12216no—
842C2×C4—1228no—
843C2×C4—1224no—
844C2×C4—1224no—
845C2×C4—1224no—
846C2×C4—1224no—
847C2×C4—1228no—
848C2×C4—1228no—
849C2×C4—1228no—
850C2×C4—1228no—
851C2×C4—2448no—
852C2×C4C2×#1175822214yes—
853C2×C4C2×#1175822214yes—
854C2×C4C2×#11758222116yes—
855C2×C4C24×D6114yes—
856C2×C4C24×D6114yes—
857C2×C4C24×D6114yes—
858C2×C4C24×D6118yes—
859C2×C4C24×D6112yes—
860C2×C4C24×D6112yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—614no—
869C22—1228no—
870C22—1222no—
871C22—1222no—
872C22—1222no—
873C22—1222no—
874C22—1222no—
875C22—24416no—
876C22—2444no—
877C22C22×#1175822214yes—
878C22C22×#1175822212yes—
879C222−1+4×D6112yes—
880C22#1684059712yes—
881C22C25×D6111yescharacteristic
882C4—24no—
883C4—24no—
884C4—24no—
885C4—28no—
886C4—1222no—
887C4—1222no—
888C4—1228no—
889C4—1224no—
890C4—1224no—
891C4—1224no—
892C4—1224no—
893C4C22×#1175822214yes—
894C4C22×#1175822214yes—
895C2—24no—
896C2—44no—
897C2—1224no—
898C2—2442no—
899C2#2145957214yesdirect product factor
900C2C23×#1175822211yescharacteristic
901C2C2×2−1+4×D6111yescharacteristic
902C2C2×#1684059711yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#520C2
socleC23×C61C25
prime radicalC2×#16840269C2
hypercenterC2×#520D61
hypocenterC61C2×#3495
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #21459572C2direct (N × H)
2. C2×#16840480C2semidirect
3. C2×#16840467C2semidirect
4. C2×#16840452C2semidirect
5. C2×#16840451C2semidirect
6. C2×#16840447C2semidirect
7. C2×#16840441C2semidirect
8. C2×#16840393C2semidirect
9. C2×#16840377C2semidirect
10. C2×#16840370C2semidirect
11. C2×#16840333C2semidirect
12. C2×#16840316C2semidirect
13. C2×#16840294C2semidirect
15. C22×#14519757C2semidirect
16. C2×#16840239C2semidirect
17. C2×#117×D61C2semidirect
18. C2×C61×#520C2semidirect
21. #16840480C22semidirect
22. #16840467C22semidirect
23. #16840452C22semidirect
24. #16840451C22semidirect
25. #16840447C22semidirect
26. #16840441C22semidirect
27. #16840393C22semidirect
28. #16840377C22semidirect
29. #16840370C22semidirect
30. #16840333C22semidirect
31. #16840316C22semidirect
32. C2×#14519776C22semidirect
33. C2×#14519776C22semidirect
34. C2×#14519775C22semidirect
35. #16840294C22semidirect
38. C2×#14519770C22semidirect
39. C2×#14519770C22semidirect
40. C2×#14519769C22semidirect
41. C2×#14519768C22semidirect
42. C2×#14519768C22semidirect
43. C2×#14519767C22semidirect
44. C2×#14519767C22semidirect
45. C2×#14519764C22semidirect
56. C2×#14519757C22semidirect
58. C2×#14519756C22semidirect
59. C2×#14519756C22semidirect
60. C2×#14519756C22semidirect
67. #16840239C22semidirect
68. C2×C4×Dic122C22semidirect
69. C2×C4×Dic122C22semidirect
70. C2×C4×Dic122C22semidirect
71. C2×#14519742C22semidirect
72. C2×#14519742C22semidirect
78. C2×#14519736C22semidirect
85. #117×D61C22semidirect
93. C61×#520C22semidirect
94. C2×C4×Q8×C61C22semidirect
96. C2×C4×D4×C61C22semidirect
98. C2×#117×C61C22semidirect
100. C22×C4⋊C4×C61C22semidirect
119. #14519776C23semidirect
120. #14519776C23semidirect
121. #14519775C23semidirect
124. #14519770C23semidirect
125. #14519770C23semidirect
126. #14519769C23semidirect
127. #14519768C23semidirect
128. #14519768C23semidirect
129. #14519767C23semidirect
130. #14519767C23semidirect
131. #14519764C23semidirect
142. #14519756C23semidirect
143. #14519756C23semidirect
144. #14519756C23semidirect
151. C4×Dic122C23semidirect
152. C4×Dic122C23semidirect
153. C4×Dic122C23semidirect
154. #14519742C23semidirect
155. #14519742C23semidirect
161. #14519736C23semidirect
218. C4×Q8×C61C23semidirect
220. C4×D4×C61C23semidirect
222. #117×C61C23semidirect
229. C2×C4⋊C4×C61C23semidirect
459. C2×#520D61semidirect
464. C2×C61#3495semidirect
519. #520C2×D61semidirect
526. C2×C4×Q8C2×D61semidirect
531. C2×C4×D4C2×D61semidirect
543. C2×#117C2×D61semidirect
548. C22×C4⋊C4C2×D61semidirect
552. C61C2×#3495semidirect
617. C4×Q8C22×D61semidirect
622. C4×D4C22×D61semidirect
633. #117C22×D61semidirect
660. C2×C4⋊C4C22×D61semidirect
899. C2#21459572direct (N × H)

Maximal subgroups

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

subgroupindex
#214595722
C2×#168404802
C2×#168404672
C2×#168404522
C2×#168404512
C2×#168404472
C2×#168404412
C2×#168403932
C2×#168403772
C2×#168403702
C2×#168403332
C2×#168403162
C2×#168402942
C2×#168402692
C22×#145197572
C2×#168402392
C2×#117×D612
C2×C61×#5202
C2×#349561