Finite Group Databasebeta

← C2×#21459642 #30588493

Subgroups — C2×#21459642 #30588493

Order 15616.

6958 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459642C2132yesmaximal, direct product factor
2C2×#16840489C212yesmaximal, complemented
3C2×#16840487C212yesmaximal, complemented
4C2×#16840473C212yesmaximal, complemented
5C2×#16840470C214yesmaximal, complemented
6C2×#16840468C212yesmaximal, complemented
7C2×#16840466C214yesmaximal, complemented
8C2×#16840392C212yesmaximal, complemented
9C2×#16840390C211yesmaximal, characteristic, complemented
10C2×#16840389C212yesmaximal, complemented
11C2×#16840317C212yesmaximal, complemented
12C2×#16840315C211yesmaximal, characteristic, complemented
13C22×#14519768C211yesmaximal, characteristic, complemented
14C2×#125×D61C212yesmaximal, complemented
15C2×#16840243C211yesmaximal, characteristic
16C2×#16840242C211yesmaximal, characteristic
17C2×#16840230C211yesmaximal, characteristic
18C2×C61×#544C211yesmaximal, characteristic, complemented
19C22×#11758222C2211yescharacteristic
20#16840489C22132yescomplemented
21#16840487C22132yescomplemented
22#16840473C22132yescomplemented
23#16840470C22164yescomplemented
24#16840468C22132yescomplemented
25#16840466C22164yescomplemented
26#16840392C22132yescomplemented
27#16840390C22116yescomplemented
28#16840389C22132yescomplemented
29#16840317C22132yescomplemented
30#16840315C22116yescomplemented
31C2×#14519777C2212yes—
32C2×#14519776C2211yescharacteristic
33C2×#14519776C2212yes—
34C2×#14519776C2211yescharacteristic
35C2×#14519776C2214yes—
36C2×#14519775C2214yes—
37C2×#14519769C2212yes—
38C2×#14519768C2212yes—
39C2×#14519768C2212yes—
40C2×#14519768C2211yescharacteristic
41C2×#14519768C2212yes—
42C2×#14519768C2212yes—
43C2×#14519768C2212yes—
44C2×#14519768C2211yescharacteristic
45C2×#14519768C22116yescomplemented
46C2×#14519767C2214yes—
47C2×#14519767C2214yes—
48C2×#14519767C2214yes—
49C2×#14519767C2214yes—
50#125×D61C22132yescomplemented
51C2×#14519757C2214yes—
52C2×#14519757C2214yes—
53C2×#14519755C2214yes—
54C2×#14519755C2214yes—
55C2×#14519754C2214yes—
56C2×#14519754C2212yes—
57C2×#14519754C2212yes—
58C2×#14519753C2214yes—
59C2×#14519753C2214yes—
60#16840243C22116yes—
61#16840242C22116yes—
62#16840230C22116yes—
63C2×Q8×Dic61C2214yes—
64C2×C4×Dic122C2212yes—
65C2×C4×Dic122C2212yes—
66C2×C4×Dic122C2212yes—
67C2×#14519742C2211yescharacteristic
68C2×#14519742C2211yescharacteristic
69C2×#14519742C2212yes—
70C2×#14519742C2214yes—
71C2×C4×D244C2212yes—
72C2×#14519739C2211yescharacteristic
73C2×#14519739C2211yescharacteristic
74C2×#14519739C2212yes—
75C2×C4×C22⋊D61C2214yes—
76C2×#14519737C2212yes—
77C2×#14519737C2212yes—
78C2×#14519737C2214yes—
79C2×#14519736C2211yescharacteristic
80C2×#14519735C2212yes—
81C2×#14519735C2212yes—
82C2×#14519734C2212yes—
83C22×C4⋊Dic61C2211yescharacteristic
84C22×C4⋊Dic61C2212yes—
85C22×#11758196C2212yes—
86C2×C4⋊C4×D61C2212yes—
87C2×C4⋊C4×D61C2212yes—
88C2×C4⋊C4×D61C2214yes—
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×Dic122C2314yes—
104C22×Dic122C2312yes—
105C22×Dic122C2312yes—
106C22×Dic122C2311yescharacteristic
107C22×D244C2311yescharacteristic
108C22×C22⋊D61C2312yes—
109C23×Dic61C2311yescharacteristic
110C23×Dic61C2311yescharacteristic
111C23×Dic61C2312yes—
112C22×C4×D61C2312yes—
113C22×C4×D61C2312yes—
114C22×C4×D61C2314yes—
115C22×C4×D61C2314yes—
116C22×C4×D61C2312yes—
117#14519777C23116yes—
118#14519776C23116yes—
119#14519776C23132yes—
120#14519776C2318yes—
121#14519776C2318yes—
122#14519775C23132yes—
123#14519769C23116yes—
124#14519768C23116yes—
125#14519768C23116yes—
126#14519768C23116yes—
127#14519768C2318yes—
128#14519768C23116yes—
129#14519768C23116yes—
130#14519768C2318yes—
131#14519767C23132yes—
132#14519767C23132yes—
133#14519767C23132yes—
134#14519767C23132yes—
135#14519757C23132yes—
136#14519757C23132yes—
137#14519755C23132yes—
138#14519755C23132yes—
139#14519754C23116yes—
140#14519754C23132yes—
141#14519754C23116yes—
142#14519753C23132yes—
143#14519753C23132yes—
144Q8×Dic61C23132yes—
145C4×Dic122C23116yes—
146C4×Dic122C23116yes—
147C4×Dic122C23116yes—
148#14519742C23132yes—
149#14519742C2318yes—
150#14519742C2318yes—
151#14519742C23116yes—
152C4×D244C23116yes—
153#14519739C2318yes—
154#14519739C23116yes—
155#14519739C2318yes—
156C4×C22⋊D61C23132yes—
157#14519737C23116yes—
158#14519737C23132yes—
159#14519737C23116yes—
160#14519736C2318yes—
161#14519735C23116yes—
162#14519735C23116yes—
163#14519734C23116yes—
164C2×C4⋊Dic61C2311yescharacteristic
165C2×C4⋊Dic61C2312yes—
166C2×C4⋊Dic61C2312yes—
167C2×C4⋊Dic61C2314yes—
168C2×C4⋊Dic61C23116yes—
169C2×C4⋊Dic61C2312yes—
170C2×C4⋊Dic61C2318yes—
171C2×C4⋊Dic61C2314yes—
172C2×C4⋊Dic61C2311yescharacteristic
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2314yes—
175C2×#11758196C23116yes—
176C2×#11758196C2312yes—
177C2×#11758196C2314yes—
178C2×#11758196C2314yes—
179C2×#11758196C2314yes—
180C2×#11758196C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C2314yes—
183C2×#11758196C2312yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2312yes—
188C4⋊C4×D61C23132yes—
189C4⋊C4×D61C23132yes—
190C4⋊C4×D61C23116yes—
191C4⋊C4×D61C23116yes—
192C2×C22⋊Dic61C2312yes—
193C2×#11758198C2312yes—
194C2×#11758198C2312yes—
195C2×#11758198C2314yes—
196C2×#11758198C2314yes—
197C2×C4×Dic61C2311yescharacteristic
198C2×C4×Dic61C2312yes—
199C2×C4×Dic61C2312yes—
200C2×C4×Dic61C2311yescharacteristic
201C2×C4×Dic61C2311yescharacteristic
202C2×C4×Dic61C2311yescharacteristic
203C2×C4×Dic61C2318yes—
204C2×C4×Dic61C2314yes—
205C2×C4×Dic61C2314yes—
206C2×C4×Dic61C2312yes—
207C42×D61C23116yes—
208C22×Q8×C61C2314yes—
209C23×C4×C61C2312yes—
210C23×C4×C61C2311yescharacteristic
211C4⋊Q8×C61C23116yes—
212C4⋊Q8×C61C23116yes—
213#125×C61C23116yes—
214#125×C61C23116yes—
215C22⋊Q8×C61C23132yes—
216#117×C61C2318yes—
217#117×C61C2318yes—
218C2×C4⋊C4×C61C2311yescharacteristic
219C2×C4⋊C4×C61C2311yescharacteristic
220C2×C4⋊C4×C61C2312yes—
221C2×C4⋊C4×C61C2314yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2314yes—
224C2×C4⋊C4×C61C2318yes—
225C2×C4⋊C4×C61C2311yescharacteristic
226C2×C4⋊C4×C61C2314yes—
227C2×C4⋊C4×C61C2311yescharacteristic
228C2×C22⋊C4×C61C2312yes—
229C2×C22⋊C4×C61C2312yes—
230C2×C42×C61C2312yes—
231C2×C42×C61C2312yes—
232C24×C61C2411yescharacteristic
233C23×D61C2412yes—
234C2×Q8×C61—48no—
235C2×Q8×C61C24116yes—
236C22×C4×C61—44no—
237C22×C4×C61C2×Q818yes—
238C22×C4×C61C2412yes—
239C22×C4×C61C2412yes—
240C22×C4×C61C2412yes—
241C22×C4×C61C2414yes—
242C22×C4×C61C2412yes—
243C22×C4×C61C2418yes—
244C22×C4×C61C2411yescharacteristic
245C22×C4×C61C2411yescharacteristic
246C22×C4×C61C2414yes—
247C2×C22⋊D61C2×Q8116yes—
248C2×C22⋊D61C2418yes—
249C22×Dic61—42no—
250C22×Dic61—42no—
251C22×Dic61—44no—
252C22×Dic61C2411yescharacteristic
253C22×Dic61C2411yescharacteristic
254C22×Dic61C2412yes—
255C22×Dic61C2414yes—
256C22×Dic61C2411yescharacteristic
257C22×Dic61C2411yescharacteristic
258C22×Dic61C2412yes—
259C22×Dic61C2414yes—
260C22×Dic61C2414yes—
261C22×Dic61C2418yes—
262C22×Dic61C2412yes—
263#11758222C2×Q8164yescomplemented
264C2×D244C2×Q818yes—
265C2×D244C2414yes—
266C2×C4×D61—48no—
267C2×C4×D61—48no—
268C2×C4×D61—44no—
269C2×C4×D61—44no—
270C2×C4×D61C2×Q8116yes—
271C2×C4×D61C2418yes—
272C2×C4×D61C2418yes—
273C2×C4×D61C24116yes—
274C2×C4×D61C24116yes—
275C2×C4×D61C2418yes—
276C2×Dic122—44no—
277C2×Dic122—48no—
278C2×Dic122—44no—
279C2×Dic122C2×Q818yes—
280C2×Dic122C24116yes—
281C2×Dic122C2418yes—
282C2×Dic122C2418yes—
283C2×Dic122C2414yes—
284C4⋊C4×C61C2418yes—
285C4⋊C4×C61C2418yes—
286C4⋊C4×C61C2414yes—
287C4⋊C4×C61C2414yes—
288C4⋊C4×C61C2414yes—
289C4⋊C4×C61C2414yes—
290C4⋊C4×C61C24116yes—
291C4⋊C4×C61C24116yes—
292C4⋊C4×C61C24116yes—
293C22⋊C4×C61C2418yes—
294C22⋊C4×C61C2418yes—
295C42×C61C2418yes—
296C42×C61C2418yes—
297C22⋊Dic61C2418yes—
298#11758198C2418yes—
299#11758198C2418yes—
300#11758198C24116yes—
301#11758198C24116yes—
302C4⋊Dic61C2414yes—
303C4⋊Dic61C2418yes—
304C4⋊Dic61C2418yes—
305C4⋊Dic61C24116yes—
306C4⋊Dic61C2418yes—
307C4⋊Dic61C24116yes—
308C4⋊Dic61C2414yes—
309C4⋊Dic61C2418yes—
310C4⋊Dic61C24116yes—
311#11758196C2418yes—
312#11758196C24116yes—
313#11758196C24116yes—
314#11758196C24116yes—
315#11758196C24116yes—
316#11758196C24116yes—
317#11758196C24116yes—
318#11758196C2418yes—
319#11758196C2418yes—
320#11758196C2418yes—
321#11758196C2418yes—
322#11758196C2418yes—
323C4×Dic61C2414yes—
324C4×Dic61C2418yes—
325C4×Dic61C2418yes—
326C4×Dic61C2414yes—
327C4×Dic61C2414yes—
328C4×Dic61C2414yes—
329C4×Dic61C24116yes—
330C4×Dic61C24116yes—
331C4×Dic61C2418yes—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61C22×Q814yes—
335C23×C61C2512yes—
336C23×C61C2511yescharacteristic
337C22×D61—24no—
338C22×D61—24no—
339C22×D61C22×Q818yes—
340C22×D61C2514yes—
341Q8×C61—416no—
342C2×C4×C61—24no—
343C2×C4×C61—24no—
344C2×C4×C61—24no—
345C2×C4×C61—28no—
346C2×C4×C61—24no—
347C2×C4×C61—48no—
348C2×C4×C61C22×Q814yes—
349C2×C4×C61C22×Q814yes—
350C2×C4×C61C22×Q8116yes—
351C2×C4×C61C2514yes—
352C2×C4×C61C2514yes—
353C2×C4×C61C2518yes—
354C2×C4×C61C2514yes—
355C2×C4×C61C2514yes—
356C2×C4×C61C2512yes—
357C2×C4×C61C2512yes—
358C22⋊D61C22×Q8132yes—
359C2×Dic61—24no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—24no—
363C2×Dic61—28no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—44no—
367C2×Dic61—44no—
368C2×Dic61—48no—
369C2×Dic61C22×Q818yes—
370C2×Dic61C2512yes—
371C2×Dic61C2512yes—
372C2×Dic61C2514yes—
373C2×Dic61C2512yes—
374C2×Dic61C2512yes—
375C2×Dic61C2514yes—
376C2×Dic61C2518yes—
377C2×Dic61C2514yes—
378D244C22×Q8116yes—
379C4×D61—416no—
380C4×D61—416no—
381C4×D61—48no—
382C4×D61—48no—
383C4×D61C22×Q8132yes—
384Dic122—48no—
385Dic122—416no—
386Dic122—48no—
387Dic122C22×Q8116yes—
388C2×#3504—611nomaximal, Sylow
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—28no—
392C22×C61C23×Q814yes—
393C22×C61C23×Q812yes—
394C22×C61#58512yes—
395C22×C61#58512yes—
396C22×C61C2611yescharacteristic
397C2×D61—24no—
398C2×D61—24no—
399C2×D61—216no—
400C2×D61C23×Q818yes—
401C4×C61—24no—
402C4×C61—24no—
403C4×C61—24no—
404C4×C61—28no—
405C4×C61—24no—
406C4×C61C23×Q814yes—
407C4×C61C23×Q814yes—
408Dic61—24no—
409Dic61—22no—
410Dic61—22no—
411Dic61—24no—
412Dic61—28no—
413Dic61—22no—
414Dic61—22no—
415Dic61C23×Q818yes—
416#3504—6132no—
417C2×#557—612no—
418C2×#557—612no—
419C2×#554—612no—
420C2×#554—612no—
421C2×#554—614no—
422C2×#554—614no—
423C2×#544—612no—
424C2×#544—612no—
425C2×#544—611no—
426C2×#544D6111yescharacteristic, complemented
427C2×#533—612no—
428C2×#533—611no—
429C22×#125—612no—
430C22×#125—611no—
431C2×#520—611no—
432C2×#520—611no—
433C2×C4×#41—611no—
434C2×C61—24no—
435C2×C61#350414yescomplemented
436C2×C61C24×Q811yescharacteristic
437C2×C61C2×#58511yescharacteristic
438C2×C61C2×#58511yescharacteristic
439D61—28no—
440C22×#41—611no—
441#557—6132no—
442#557—6132no—
443#554—6132no—
444#554—6132no—
445#554—6164no—
446#554—6164no—
447#544—6132no—
448#544—6132no—
449#544—6116no—
450#544C2×D61116yescomplemented
451#533—6132no—
452#533—6116no—
453C2×C4⋊Q8—614no—
454C2×C4⋊Q8—611no—
455C2×C4⋊Q8—611no—
456C2×C4⋊Q8—614no—
457C2×C4⋊Q8—612no—
458C2×C4⋊Q8—612no—
459C2×C4⋊Q8C2×D6112yes—
460C2×C4⋊Q8C2×D6112yes—
461C2×#125—6132no—
462C2×#125—614no—
463C2×#125—614no—
464C2×#125—614no—
465C2×#125—614no—
466C2×#125—611no—
467C2×#125—612no—
468C2×#125—612no—
469C2×#125—612no—
470C2×#125—612no—
471C2×#125—611no—
472C2×#125—612no—
473C2×#125—6116no—
474C2×#125—612no—
475C2×#125C2×D6112yes—
476C2×#125C2×D6112yes—
477C2×C22⋊Q8—614no—
478C2×C22⋊Q8—614no—
479C2×C22⋊Q8—614no—
480C2×C22⋊Q8—614no—
481C2×C22⋊Q8—614no—
482C2×C22⋊Q8—614no—
483C2×C22⋊Q8—612no—
484C2×C22⋊Q8—612no—
485C2×C22⋊Q8—614no—
486C2×C22⋊Q8C2×D6114yes—
487#520—6116no—
488#520—6116no—
489C4×#41—6116no—
490C2×C4×Q8—614no—
491C2×C4×Q8—611no—
492C2×C4×Q8—611no—
493C2×C4×Q8—612no—
494C2×C4×Q8—614no—
495C2×C4×Q8—612no—
496C2×C4×Q8—612no—
497C2×C4×Q8—612no—
498C2×C4×D4—614no—
499C2×C4×D4—611no—
500C2×C4×D4—611no—
501C2×C4×D4—612no—
502C2×C4×D4—612no—
503C2×C4×D4—612no—
504C2×C4×D4—614no—
505C2×C4×D4—612no—
506C2×#117—611no—
507C2×#117—612no—
508C2×#117—612no—
509C2×#117—612no—
510C2×#117C2×D6111yescharacteristic
511C2×#117C2×D6111yescharacteristic
512C22×C4⋊C4—612no—
513C22×C4⋊C4—611no—
514C22×C4⋊C4—612no—
515C22×C4⋊C4—612no—
516C22×C4⋊C4—612no—
517C22×C4⋊C4—614no—
518C22×C4⋊C4—614no—
519C22×C4⋊C4C2×D6111yescharacteristic
520C22×C42—611no—
521C22×C42—612no—
522C61C2×#350411yescharacteristic, complemented, Sylow
523C2×#41—6116no—
524C2×#41—618no—
525C22×Q8—611no—
526C22×Q8—612no—
527C22×Q8—614no—
528C22×Q8—612no—
529C22×Q8C22×D6114yes—
530C22×D4—612no—
531C22×D4—611no—
532C23×C4—612no—
533C23×C4—612no—
534C23×C4—611no—
535C23×C4—611no—
536C23×C4—614no—
537C23×C4—614no—
538C23×C4—612no—
539C23×C4—612no—
540C23×C4C22×D6112yes—
541C23×C4C22×D6111yescharacteristic
542C4⋊Q8—6132no—
543C4⋊Q8—618no—
544C4⋊Q8—618no—
545C4⋊Q8—6132no—
546C4⋊Q8—6116no—
547C4⋊Q8—6116no—
548C4⋊Q8C22×D61116yes—
549C4⋊Q8C22×D61116yes—
550#125—618no—
551#125—6116no—
552#125—6116no—
553#125—6132no—
554#125—6132no—
555#125—6116no—
556#125—6116no—
557#125—618no—
558#125—6132no—
559#125—6132no—
560#125—6116no—
561#125—6116no—
562#125C22×D61116yes—
563#125C22×D61116yes—
564C22⋊Q8—6132no—
565C22⋊Q8—6132no—
566C22⋊Q8—6132no—
567C22⋊Q8—6132no—
568C22⋊Q8—6132no—
569C22⋊Q8—6132no—
570C22⋊Q8—6116no—
571C22⋊Q8—6116no—
572C22⋊Q8—6132no—
573C22⋊Q8C22×D61132yes—
574C4×Q8—6132no—
575C4×Q8—618no—
576C4×Q8—618no—
577C4×Q8—6116no—
578C4×Q8—6132no—
579C4×Q8—6116no—
580C4×Q8—6116no—
581C4×Q8—6116no—
582C4×D4—6132no—
583C4×D4—618no—
584C4×D4—618no—
585C4×D4—6116no—
586C4×D4—6116no—
587C4×D4—6116no—
588C4×D4—6132no—
589C4×D4—6116no—
590#117—618no—
591#117—6116no—
592#117—6116no—
593#117—6116no—
594#117C22×D6118yes—
595#117C22×D6118yes—
596C2×C4⋊C4—612no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—614no—
599C2×C4⋊C4—612no—
600C2×C4⋊C4—614no—
601C2×C4⋊C4—612no—
602C2×C4⋊C4—614no—
603C2×C4⋊C4—614no—
604C2×C4⋊C4—612no—
605C2×C4⋊C4—618no—
606C2×C4⋊C4—614no—
607C2×C4⋊C4—614no—
608C2×C4⋊C4—614no—
609C2×C4⋊C4—614no—
610C2×C4⋊C4—6116no—
611C2×C4⋊C4—6116no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—612no—
614C2×C4⋊C4—612no—
615C2×C4⋊C4—612no—
616C2×C4⋊C4—612no—
617C2×C4⋊C4—612no—
618C2×C4⋊C4—612no—
619C2×C4⋊C4—614no—
620C2×C4⋊C4—6116no—
621C2×C4⋊C4—6116no—
622C2×C4⋊C4—6132no—
623C2×C4⋊C4—6132no—
624C2×C4⋊C4C22×D6111yescharacteristic
625C2×C4⋊C4C22×D6112yes—
626C2×C4⋊C4C22×D6114yes—
627C2×C4⋊C4C22×D6114yes—
628C2×C4⋊C4C22×D6112yes—
629C2×C4⋊C4C22×D6118yes—
630C2×C4⋊C4C22×D6111yescharacteristic
631C2×C4⋊C4C22×D6111yescharacteristic
632C2×C4⋊C4C22×D6111yescharacteristic
633C2×C4⋊C4C22×D6114yes—
634C2×C22⋊C4—612no—
635C2×C22⋊C4—614no—
636C2×C22⋊C4—612no—
637C2×C22⋊C4—612no—
638C2×C22⋊C4—614no—
639C2×C22⋊C4C22×D6112yes—
640C2×C22⋊C4C22×D6112yes—
641C2×C42—611no—
642C2×C42—614no—
643C2×C42—614no—
644C2×C42—612no—
645C2×C42—612no—
646C2×C42—612no—
647C2×C42—611no—
648C2×C42—611no—
649C2×C42—618no—
650C2×C42—611no—
651C2×C42—6116no—
652C2×C42C22×D6112yes—
653C2×C42C22×D6112yes—
654C24—612no—
655C24C23×D6111yescharacteristic
656#41—6164no—
657C2×Q8—48no—
658C2×Q8—618no—
659C2×Q8—614no—
660C2×Q8—618no—
661C2×Q8—6116no—
662C2×Q8—618no—
663C2×Q8—2444no—
664C2×Q8—2444no—
665C2×Q8—2448no—
666C2×Q8C23×D61116yes—
667C2×D4—6116no—
668C2×D4—618no—
669C2×D4—618no—
670C2×D4—614no—
671C22×C4—44no—
672C22×C4—612no—
673C22×C4—6116no—
674C22×C4—618no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—612no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—612no—
681C22×C4—614no—
682C22×C4—614no—
683C22×C4—614no—
684C22×C4—618no—
685C22×C4—618no—
686C22×C4—618no—
687C22×C4—6116no—
688C22×C4—6116no—
689C22×C4—2448no—
690C22×C4—2444no—
691C22×C4—2448no—
692C22×C4—2444no—
693C22×C4—2442no—
694C22×C4—2442no—
695C22×C4—2444no—
696C22×C4Q8×D6118yes—
697C22×C4C23×D6112yes—
698C22×C4C23×D6112yes—
699C22×C4C23×D6112yes—
700C22×C4C23×D6114yes—
701C22×C4C23×D6112yes—
702C22×C4C23×D6118yes—
703C22×C4C23×D6114yes—
704C22×C4C23×D6111yescharacteristic
705C22×C4C23×D6111yescharacteristic
706C4⋊C4—6116no—
707C4⋊C4—618no—
708C4⋊C4—618no—
709C4⋊C4—614no—
710C4⋊C4—6116no—
711C4⋊C4—618no—
712C4⋊C4—6116no—
713C4⋊C4—6116no—
714C4⋊C4—6116no—
715C4⋊C4—6116no—
716C4⋊C4—6116no—
717C4⋊C4—618no—
718C4⋊C4—6116no—
719C4⋊C4—618no—
720C4⋊C4—618no—
721C4⋊C4—618no—
722C4⋊C4—618no—
723C4⋊C4—618no—
724C4⋊C4—614no—
725C4⋊C4—618no—
726C4⋊C4—6116no—
727C4⋊C4C23×D6114yes—
728C4⋊C4C23×D6118yes—
729C4⋊C4C23×D61116yes—
730C4⋊C4C23×D61116yes—
731C4⋊C4C23×D6118yes—
732C4⋊C4C23×D6114yes—
733C4⋊C4C23×D6114yes—
734C4⋊C4C23×D6114yes—
735C4⋊C4C23×D61116yes—
736C22⋊C4—618no—
737C22⋊C4—6116no—
738C22⋊C4—618no—
739C22⋊C4—618no—
740C22⋊C4—6116no—
741C22⋊C4C23×D6118yes—
742C22⋊C4C23×D6118yes—
743C42—614no—
744C42—614no—
745C42—618no—
746C42—618no—
747C42—614no—
748C42—614no—
749C42—6116no—
750C42—6116no—
751C42—618no—
752C42C23×D6118yes—
753C42C23×D6118yes—
754C23—22no—
755C23—22no—
756C23—618no—
757C23—614no—
758C23—1224no—
759C23—1224no—
760C23C2×Q8×D6114yes—
761C23C24×D6112yes—
762C23C24×D6111yescharacteristic
763Q8—416no—
764Q8—6116no—
765Q8—2448no—
766Q8—2448no—
767Q8—24416no—
768D4—6132no—
769D4—6116no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—618no—
777C2×C4—614no—
778C2×C4—6132no—
779C2×C4—612no—
780C2×C4—612no—
781C2×C4—614no—
782C2×C4—612no—
783C2×C4—612no—
784C2×C4—614no—
785C2×C4—618no—
786C2×C4—1222no—
787C2×C4—1224no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1228no—
791C2×C4—1222no—
792C2×C4—1224no—
793C2×C4—24416no—
794C2×C4—2448no—
795C2×C4—24416no—
796C2×C4—2448no—
797C2×C4—2444no—
798C2×C4—2444no—
799C2×C4—2448no—
800C2×C4C2×Q8×D6114yes—
801C2×C4C2×Q8×D6114yes—
802C2×C4C2×Q8×D61116yes—
803C2×C4C24×D6114yes—
804C2×C4C24×D6114yes—
805C2×C4C24×D6114yes—
806C2×C4C24×D6118yes—
807C2×C4C24×D6114yes—
808C2×C4C24×D6112yes—
809C2×C4C24×D6112yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—618no—
814C22—1224no—
815C22—1224no—
816C22—12216no—
817C22C22×Q8×D6114yes—
818C22C22×Q8×D6112yes—
819C22#1684059712yes—
820C22#1684059912yes—
821C22C25×D6111yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—618no—
828C4—1222no—
829C4—1224no—
830C4—1222no—
831C4—1222no—
832C4—1228no—
833C4—1222no—
834C4—1224no—
835C4C22×Q8×D6114yes—
836C4C22×Q8×D6114yes—
837C2—24no—
838C2—1228no—
839C2#2145964214yesdirect product factor
840C2C23×Q8×D6111yescharacteristic
841C2C2×#1684059711yescharacteristic
842C2C2×#1684059911yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#544C2
socleC23×C61C25
prime radicalC22×#11758222C22
hypercenterC2×#544D61
hypocenterC61C2×#3504
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #21459642C2direct (N × H)
2. C2×#16840489C2semidirect
3. C2×#16840487C2semidirect
4. C2×#16840473C2semidirect
5. C2×#16840470C2semidirect
6. C2×#16840468C2semidirect
7. C2×#16840466C2semidirect
8. C2×#16840392C2semidirect
9. C2×#16840390C2semidirect
10. C2×#16840389C2semidirect
11. C2×#16840317C2semidirect
12. C2×#16840315C2semidirect
13. C22×#14519768C2semidirect
14. C2×#125×D61C2semidirect
18. C2×C61×#544C2semidirect
20. #16840489C22semidirect
21. #16840487C22semidirect
22. #16840473C22semidirect
23. #16840470C22semidirect
24. #16840468C22semidirect
25. #16840466C22semidirect
26. #16840392C22semidirect
27. #16840390C22semidirect
28. #16840389C22semidirect
29. #16840317C22semidirect
30. #16840315C22semidirect
45. C2×#14519768C22semidirect
50. #125×D61C22semidirect
92. C61×#544C22semidirect
101. C2×#11758222Q8semidirect
263. #11758222C2×Q8semidirect
426. C2×#544D61semidirect
435. C2×C61#3504semidirect
450. #544C2×D61semidirect
522. C61C2×#3504semidirect
839. C2#21459642direct (N × H)

Maximal subgroups

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

subgroupindex
#214596422
C2×#168404892
C2×#168404872
C2×#168404732
C2×#168404702
C2×#168404682
C2×#168404662
C2×#168403922
C2×#168403902
C2×#168403892
C2×#168403172
C2×#168403152
C22×#145197682
C2×#125×D612
C2×#168402432
C2×#168402422
C2×#168402302
C2×C61×#5442
C2×#350461