Finite Group Databasebeta

← C2×#21459798 #30588121

Subgroups — C2×#21459798 #30588121

Order 15616.

7142 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#21459798C2132yesmaximal, direct product factor
2C2×#16840491C211yesmaximal, characteristic, complemented
3C2×#16840473C211yesmaximal, characteristic, complemented
4C2×#16840460C212yesmaximal, complemented
5C2×#16840454C214yesmaximal, complemented
6C2×#16840454C212yesmaximal, complemented
7C2×#16840450C212yesmaximal, complemented
8C2×#16840416C212yesmaximal, complemented
9C2×#16840416C211yesmaximal, characteristic, complemented
10C2×#16840375C212yesmaximal, complemented
11C2×#16840361C214yesmaximal, complemented
12C2×#16840317C211yesmaximal, characteristic, complemented
13C2×#16840299C211yesmaximal, characteristic, complemented
14C2×#16840298C212yesmaximal, complemented
15C22×#14519768C212yesmaximal, complemented
16C2×#16840241C212yesmaximal, complemented
17C2×C4×#11758224C211yesmaximal, characteristic, complemented
18C2×C61×#554C211yesmaximal, characteristic, complemented
19C22×#11758224C2211yescharacteristic
20C22×#11758224C2212yes—
21#16840491C22116yescomplemented
22#16840473C22116yescomplemented
23#16840460C22132yescomplemented
24#16840454C22132yescomplemented
25#16840454C22164yescomplemented
26#16840450C22132yescomplemented
27#16840416C22132yescomplemented
28#16840416C22116yescomplemented
29#16840375C22132yescomplemented
30#16840361C22164yescomplemented
31#16840317C22116yescomplemented
32C2×#14519777C2211yescharacteristic
33C2×#14519777C2212yes—
34#16840299C22116yescomplemented
35#16840298C22132yescomplemented
36C2×#14519772C2214yes—
37C2×#14519772C2212yes—
38C2×#14519772C2214yes—
39C2×#14519772C2214yes—
40C2×#14519768C2211yescharacteristic
41C2×#14519768C2214yes—
42C2×#14519768C2212yes—
43C2×#14519768C2212yes—
44C2×#14519768C2212yes—
45C2×#14519768C2214yes—
46C2×#14519768C2214yes—
47C2×#14519768C2214yes—
48C2×#14519768C22132yescomplemented
49C2×#14519766C2211yescharacteristic
50C2×#14519762C2214yes—
51C2×#14519762C2212yes—
52C2×#14519761C2214yes—
53C2×#14519761C2214yes—
54C2×#14519761C2214yes—
55C2×#14519757C2212yes—
56C2×#14519757C2212yes—
57C2×#14519757C2212yes—
58C2×#14519753C2211yescharacteristic
59C2×#14519753C2214yes—
60C2×#14519753C2212yes—
61C2×#14519752C2211yescharacteristic
62C2×#14519751C2212yes—
63C2×#14519751C2214yes—
64#16840241C22132yescomplemented
65C4×#11758224C22116yescomplemented
66C2×Q8×Dic61C2212yes—
67C2×Q8×Dic61C2212yes—
68C2×C4×Dic122C2211yescharacteristic
69C2×C4×Dic122C2212yes—
70C2×#14519742C2211yescharacteristic
71C2×#14519742C2212yes—
72C2×C4×D244C2212yes—
73C2×C4×D244C2211yescharacteristic
74C2×D4×Dic61C2211yescharacteristic
75C2×#14519739C2212yes—
76C2×C4×C22⋊D61C2212yes—
77C2×C4×C22⋊D61C2214yes—
78C2×#14519737C2212yes—
79C2×#14519737C2214yes—
80C2×#14519735C2211yescharacteristic
81C2×#14519735C2214yes—
82C2×#14519735C2212yes—
83C2×#14519734C2212yes—
84C2×#14519733C2212yes—
85C2×#14519733C2214yes—
86C22×C4⋊Dic61C2214yes—
87C22×C4⋊Dic61C2212yes—
88C22×#11758196C2214yes—
89C2×C4⋊C4×D61C2212yes—
90C22×C4×Dic61C2212yes—
91C2×C42×D61C2211yescharacteristic
92C61×#554C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×#125×C61C2212yes—
95C2×C22⋊Q8×C61C2212yes—
96C2×C22⋊Q8×C61C2214yes—
97C2×C4×Q8×C61C2211yescharacteristic
98C2×C4×D4×C61C2211yescharacteristic
99C2×C4×D4×C61C2212yes—
100C22×C4⋊C4×C61C2212yes—
101C2×#11758224—28no—
102C2×#11758224—216no—
103C2×#11758224C2318yes—
104C2×#11758224C23116yes—
105C22×Dic122C2311yescharacteristic
106C22×Dic122C2312yes—
107C22×D244C2311yescharacteristic
108C22×D244C2312yes—
109C22×C22⋊D61C2312yes—
110C22×C22⋊D61C2314yes—
111C23×Dic61C2312yes—
112C23×Dic61C2314yes—
113C23×Dic61C2312yes—
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2312yes—
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2314yes—
119#14519777C2318yes—
120#14519777C23116yes—
121#14519772C23132yes—
122#14519772C23116yes—
123#14519772C23132yes—
124#14519772C23132yes—
125#14519768C23132yes—
126#14519768C23132yes—
127#14519768C23116yes—
128#14519768C23132yes—
129#14519768C23116yes—
130#14519768C2318yes—
131#14519768C23116yes—
132#14519768C23132yes—
133#14519766C2318yes—
134#14519762C23132yes—
135#14519762C23116yes—
136#14519761C23132yes—
137#14519761C23132yes—
138#14519761C23132yes—
139#14519757C23116yes—
140#14519757C23116yes—
141#14519757C23116yes—
142#14519753C2318yes—
143#14519753C23132yes—
144#14519753C23116yes—
145#14519752C2318yes—
146#14519751C23116yes—
147#14519751C23132yes—
148Q8×Dic61C23116yes—
149Q8×Dic61C23116yes—
150C4×Dic122C23116yes—
151C4×Dic122C2318yes—
152#14519742C2318yes—
153#14519742C23116yes—
154C4×D244C23116yes—
155C4×D244C2318yes—
156D4×Dic61C2318yes—
157#14519739C23116yes—
158C4×C22⋊D61C23116yes—
159C4×C22⋊D61C23132yes—
160#14519737C23116yes—
161#14519737C23132yes—
162#14519735C2318yes—
163#14519735C23132yes—
164#14519735C23116yes—
165#14519734C23116yes—
166#14519733C23116yes—
167#14519733C23132yes—
168C2×C4⋊Dic61C23116yes—
169C2×C4⋊Dic61C23132yes—
170C2×C4⋊Dic61C2311yescharacteristic
171C2×C4⋊Dic61C2311yescharacteristic
172C2×C4⋊Dic61C2312yes—
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2314yes—
175C2×C4⋊Dic61C2314yes—
176C2×C4⋊Dic61C2314yes—
177C2×C4⋊Dic61C2314yes—
178C2×C4⋊Dic61C2312yes—
179C2×C4⋊Dic61C2314yes—
180C2×#11758196C2314yes—
181C2×#11758196C2312yes—
182C2×#11758196C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C23132yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2312yes—
188C4⋊C4×D61C23116yes—
189C2×C22⋊Dic61C2312yes—
190C2×#11758198C2312yes—
191C2×#11758198C2312yes—
192C2×#11758198C2312yes—
193C2×#11758198C2312yes—
194C2×#11758198C2314yes—
195C2×#11758198C2314yes—
196C2×#11758198C2314yes—
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—
208C42×D61C2318yes—
209C22×Q8×C61C2311yescharacteristic
210C22×Q8×C61C2312yes—
211C22×D4×C61C2311yescharacteristic
212C23×C4×C61C2312yes—
213C23×C4×C61C2314yes—
214C4⋊Q8×C61C2318yes—
215#125×C61C23116yes—
216C22⋊Q8×C61C23116yes—
217C22⋊Q8×C61C23132yes—
218C4×Q8×C61C2318yes—
219C4×D4×C61C2318yes—
220C4×D4×C61C23116yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C23116yes—
224C2×C4⋊C4×C61C2311yescharacteristic
225C2×C4⋊C4×C61C2314yes—
226C2×C4⋊C4×C61C2311yescharacteristic
227C2×C4⋊C4×C61C2314yes—
228C2×C4⋊C4×C61C2312yes—
229C2×C22⋊C4×C61C2312yes—
230C2×C22⋊C4×C61C2314yes—
231C2×C42×C61C2311yescharacteristic
232C2×C42×C61C2312yes—
233C24×C61C2412yes—
234C23×D61C2411yescharacteristic
235C23×D61C2412yes—
236C2×Q8×C61—24no—
237C2×Q8×C61—44no—
238C2×Q8×C61C2414yes—
239C2×Q8×C61C2418yes—
240C2×D4×C61#4118yes—
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⋊D61—28no—
254C2×C22⋊D61—216no—
255C2×C22⋊D61C2418yes—
256C2×C22⋊D61C24116yes—
257C22×Dic61—28no—
258C22×Dic61—216no—
259C22×Dic61—44no—
260C22×Dic61C2412yes—
261C22×Dic61C2411yescharacteristic
262C22×Dic61C2411yescharacteristic
263C22×Dic61C2412yes—
264C22×Dic61C2411yescharacteristic
265C22×Dic61C2412yes—
266C22×Dic61C2414yes—
267C22×Dic61C2418yes—
268C22×Dic61C24116yes—
269C22×Dic61C2418yes—
270#11758224—232no—
271#11758224—264no—
272C2×D244—24no—
273C2×D244—44no—
274C2×D244C2414yes—
275C2×D244C2418yes—
276C2×C4×D61—24no—
277C2×C4×D61—28no—
278C2×C4×D61—24no—
279C2×C4×D61—48no—
280C2×C4×D61—42no—
281C2×C4×D61C2414yes—
282C2×C4×D61C2418yes—
283C2×C4×D61C2414yes—
284C2×C4×D61C2414yes—
285C2×C4×D61C24116yes—
286C2×Dic122—24no—
287C2×Dic122—28no—
288C2×Dic122C2414yes—
289C2×Dic122C2418yes—
290C4⋊C4×C61C2414yes—
291C4⋊C4×C61C24116yes—
292C4⋊C4×C61C2418yes—
293C4⋊C4×C61C2414yes—
294C4⋊C4×C61C2418yes—
295C4⋊C4×C61C2418yes—
296C4⋊C4×C61C24116yes—
297C22⋊C4×C61C24116yes—
298C22⋊C4×C61C2418yes—
299C42×C61C2418yes—
300C42×C61C2414yes—
301C22⋊Dic61C2418yes—
302#11758198C2418yes—
303#11758198C2418yes—
304#11758198C2418yes—
305#11758198C2418yes—
306#11758198C24116yes—
307#11758198C24116yes—
308#11758198C24116yes—
309#11758198C2418yes—
310#11758198C2418yes—
311C4⋊Dic61C2414yes—
312C4⋊Dic61C2414yes—
313C4⋊Dic61C2418yes—
314C4⋊Dic61C2418yes—
315C4⋊Dic61C24116yes—
316C4⋊Dic61C24116yes—
317C4⋊Dic61C24116yes—
318C4⋊Dic61C24116yes—
319C4⋊Dic61C2418yes—
320C4⋊Dic61C24116yes—
321#11758196C24116yes—
322#11758196C2418yes—
323#11758196C24116yes—
324#11758196C24116yes—
325#11758196C2418yes—
326#11758196C2418yes—
327#11758196C2418yes—
328C4×Dic61C2414yes—
329C4×Dic61C2414yes—
330C4×Dic61C2414yes—
331C4×Dic61C2418yes—
332C4×Dic61C2418yes—
333C4×Dic61C2418yes—
334C4×Dic61C24116yes—
335C4×Dic61C24116yes—
336C23×C61—24no—
337C23×C61—24no—
338C23×C61C2×#4118yes—
339C23×C61C2514yes—
340C23×C61C2511yescharacteristic
341C22×D61—22no—
342C22×D61—24no—
343C22×D61—22no—
344C22×D61—24no—
345C22×D61—24no—
346C22×D61—22no—
347C22×D61C2512yes—
348C22×D61C2514yes—
349Q8×C61—28no—
350Q8×C61—48no—
351D4×C61C2×#41116yes—
352C2×C4×C61—24no—
353C2×C4×C61—24no—
354C2×C4×C61—28no—
355C2×C4×C61—22no—
356C2×C4×C61—24no—
357C2×C4×C61—216no—
358C2×C4×C61—416no—
359C2×C4×C61C2×#4114yes—
360C2×C4×C612−1+414yes—
361C2×C4×C61C2514yes—
362C2×C4×C61C2514yes—
363C2×C4×C61C2512yes—
364C2×C4×C61C2518yes—
365C2×C4×C61C2514yes—
366C2×C4×C61C2512yes—
367C2×C4×C61C2512yes—
368C22⋊D61—216no—
369C22⋊D61—232no—
370C2×Dic61—24no—
371C2×Dic61—28no—
372C2×Dic61—22no—
373C2×Dic61—24no—
374C2×Dic61—216no—
375C2×Dic61—232no—
376C2×Dic61—22no—
377C2×Dic61—24no—
378C2×Dic61—22no—
379C2×Dic61—48no—
380C2×Dic61C2512yes—
381C2×Dic61C2512yes—
382C2×Dic61C2514yes—
383C2×Dic61C2512yes—
384C2×Dic61C2514yes—
385C2×Dic61C2518yes—
386C2×Dic61C2514yes—
387D244—28no—
388D244—48no—
389C4×D61—28no—
390C4×D61—216no—
391C4×D61—28no—
392C4×D61—416no—
393C4×D61—44no—
394Dic122—28no—
395Dic122—216no—
396C2×#3515—611nomaximal, Sylow
397C22×C61—24no—
398C22×C61—24no—
399C22×C61—216no—
400C22×C61C22×#4118yes—
401C22×C61C22×#4112yes—
402C22×C61C2×2−1+412yes—
403C22×C61#58512yes—
404C22×C61C2611yescharacteristic
405C2×D61—22no—
406C2×D61—24no—
407C2×D61—22no—
408C2×D61—24no—
409C2×D61—24no—
410C2×D61—22no—
411C2×D61—44no—
412C2×D61—48no—
413C4×C61—24no—
414C4×C61—24no—
415C4×C61—28no—
416C4×C61—22no—
417C4×C61—24no—
418C4×C61C22×#4114yes—
419C4×C61C2×2−1+414yes—
420Dic61—24no—
421Dic61—28no—
422Dic61—22no—
423Dic61—24no—
424Dic61—22no—
425Dic61—24no—
426Dic61—22no—
427#3515—6132no—
428C2×#557—611no—
429C2×#554—611no—
430C2×#554D6111yescharacteristic, complemented
431C2×#553—612no—
432C2×#552—612no—
433C2×#552—614no—
434C2×#552—612no—
435C2×#547—612no—
436C2×#547—611no—
437C2×#541—612no—
438C2×#539—614no—
439C2×#533—611no—
440C2×#529—612no—
441C2×#529—611no—
442C22×#125—612no—
443C2×#520—612no—
444C2×C4×#41—611no—
445C2×C61—28no—
446C2×C61#351514yescomplemented
447C2×C61C23×#4111yescharacteristic
448C2×C61C22×2−1+411yescharacteristic
449C2×C61C2×#58511yescharacteristic
450D61—42no—
451D61—44no—
452C22×#41—611no—
453C22×#41—612no—
454#557—6116no—
455#554—6116no—
456#554C2×D61116yescomplemented
457#553—6132no—
458#552—6132no—
459#552—6164no—
460#552—6132no—
461#547—6132no—
462#547—6116no—
463#541—6132no—
464#539—6164no—
465#533—6116no—
466C2×C4⋊Q8—611no—
467C2×C4⋊Q8—612no—
468C2×C4⋊Q8C2×D6111yescharacteristic
469#529—6132no—
470#529—6116no—
471C2×#126—614no—
472C2×#126—612no—
473C2×#126—614no—
474C2×#126—614no—
475C2×#125—611no—
476C2×#125—612no—
477C2×#125—614no—
478C2×#125—614no—
479C2×#125—612no—
480C2×#125—612no—
481C2×#125—614no—
482C2×#125—614no—
483C2×#125—6132no—
484C2×#125C2×D6112yes—
485C2×#124—611no—
486C2×#123—612no—
487C2×#123—614no—
488C2×#123—614no—
489C2×#123—614no—
490C2×#123—614no—
491C2×C22⋊Q8—611no—
492C2×C22⋊Q8—612no—
493C2×C22⋊Q8—614no—
494C2×C22⋊Q8—612no—
495C2×C22⋊Q8—612no—
496C2×C22⋊Q8—612no—
497C2×C22⋊Q8C2×D6112yes—
498C2×C22⋊Q8C2×D6114yes—
499C2×#121—612no—
500C2×#121—614no—
501C2×#121—611no—
502#520—6132no—
503C4×#41—6116no—
504C2×C4×Q8—612no—
505C2×C4×Q8—612no—
506C2×C4×Q8—611no—
507C2×C4×Q8—612no—
508C2×C4×Q8—611no—
509C2×C4×Q8—612no—
510C2×C4×Q8C2×D6111yescharacteristic
511C2×C4×D4—611no—
512C2×C4×D4—612no—
513C2×C4×D4—614no—
514C2×C4×D4—612no—
515C2×C4×D4—612no—
516C2×C4×D4—614no—
517C2×C4×D4—612no—
518C2×C4×D4—611no—
519C2×C4×D4C2×D6111yescharacteristic
520C2×C4×D4C2×D6112yes—
521C2×#117—611no—
522C2×#117—614no—
523C2×#117—612no—
524C2×#117—612no—
525C2×#117—614no—
526C2×#117—612no—
527C22×C4⋊C4—614no—
528C22×C4⋊C4—612no—
529C22×C4⋊C4—614no—
530C22×C4⋊C4—612no—
531C22×C4⋊C4C2×D6112yes—
532C22×C42—612no—
533C22×C42—611no—
534C61C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—618no—
536C2×#41—6116no—
537C2×#41—1228no—
538C2×#41—12216no—
539C22×Q8—611no—
540C22×Q8—612no—
541C22×Q8C22×D6111yescharacteristic
542C22×Q8C22×D6112yes—
543C22×D4—612no—
544C22×D4—614no—
545C22×D4—611no—
546C22×D4—612no—
547C22×D4C22×D6111yescharacteristic
548C23×C4—614no—
549C23×C4—612no—
550C23×C4—612no—
551C23×C4—612no—
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—614no—
555C23×C4—611no—
556C23×C4C22×D6112yes—
557C23×C4C22×D6114yes—
558C4⋊Q8—618no—
559C4⋊Q8—6116no—
560C4⋊Q8C22×D6118yes—
561#126—6132no—
562#126—6116no—
563#126—6132no—
564#126—6132no—
565#125—618no—
566#125—6116no—
567#125—6132no—
568#125—6132no—
569#125—6116no—
570#125—6116no—
571#125—6132no—
572#125—6132no—
573#125C22×D61116yes—
574#124—618no—
575#123—6116no—
576#123—6132no—
577#123—6132no—
578#123—6132no—
579#123—6132no—
580C22⋊Q8—618no—
581C22⋊Q8—6116no—
582C22⋊Q8—6132no—
583C22⋊Q8—6116no—
584C22⋊Q8—6116no—
585C22⋊Q8—6116no—
586C22⋊Q8C22×D61116yes—
587C22⋊Q8C22×D61132yes—
588#121—6116no—
589#121—6132no—
590#121—618no—
591C4×Q8—6116no—
592C4×Q8—6116no—
593C4×Q8—618no—
594C4×Q8—6116no—
595C4×Q8—618no—
596C4×Q8—6116no—
597C4×Q8C22×D6118yes—
598C4×D4—618no—
599C4×D4—6116no—
600C4×D4—6132no—
601C4×D4—6116no—
602C4×D4—6116no—
603C4×D4—6132no—
604C4×D4—6116no—
605C4×D4—618no—
606C4×D4C22×D6118yes—
607C4×D4C22×D61116yes—
608#117—618no—
609#117—6132no—
610#117—6116no—
611#117—6116no—
612#117—6132no—
613#117—6116no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—614no—
616C2×C4⋊C4—612no—
617C2×C4⋊C4—611no—
618C2×C4⋊C4—612no—
619C2×C4⋊C4—612no—
620C2×C4⋊C4—614no—
621C2×C4⋊C4—614no—
622C2×C4⋊C4—614no—
623C2×C4⋊C4—6132no—
624C2×C4⋊C4—614no—
625C2×C4⋊C4—614no—
626C2×C4⋊C4—614no—
627C2×C4⋊C4—6116no—
628C2×C4⋊C4—6132no—
629C2×C4⋊C4—612no—
630C2×C4⋊C4—612no—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—612no—
633C2×C4⋊C4—614no—
634C2×C4⋊C4—6116no—
635C2×C4⋊C4C22×D6112yes—
636C2×C4⋊C4C22×D6111yescharacteristic
637C2×C4⋊C4C22×D6112yes—
638C2×C4⋊C4C22×D6114yes—
639C2×C4⋊C4C22×D61116yes—
640C2×C4⋊C4C22×D6111yescharacteristic
641C2×C4⋊C4C22×D6114yes—
642C2×C4⋊C4C22×D6112yes—
643C2×C22⋊C4—612no—
644C2×C22⋊C4—612no—
645C2×C22⋊C4—612no—
646C2×C22⋊C4—612no—
647C2×C22⋊C4—612no—
648C2×C22⋊C4—614no—
649C2×C22⋊C4—614no—
650C2×C22⋊C4—614no—
651C2×C22⋊C4—612no—
652C2×C22⋊C4—612no—
653C2×C22⋊C4C22×D6114yes—
654C2×C22⋊C4C22×D6112yes—
655C2×C42—612no—
656C2×C42—611no—
657C2×C42—614no—
658C2×C42—614no—
659C2×C42—611no—
660C2×C42—612no—
661C2×C42—612no—
662C2×C42—6116no—
663C2×C42—611no—
664C2×C42—618no—
665C2×C42C22×D6112yes—
666C2×C42C22×D6111yescharacteristic
667C24—611no—
668C24—612no—
669C24C23×D6112yes—
670#41—12232no—
671#41—12264no—
672C2×Q8—24no—
673C2×Q8—44no—
674C2×Q8—614no—
675C2×Q8—618no—
676C2×Q8—1224no—
677C2×Q8—1228no—
678C2×Q8C23×D6114yes—
679C2×Q8C23×D6118yes—
680C2×D4—618no—
681C2×D4—6116no—
682C2×D4—614no—
683C2×D4—618no—
684C2×D4—1228no—
685C2×D4—12216no—
686C2×D4—1224no—
687C2×D4—2444no—
688C2×D4#1175822618yes—
689C2×D4C23×D6114yes—
690C22×C4—28no—
691C22×C4—48no—
692C22×C4—618no—
693C22×C4—6116no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—612no—
697C22×C4—611no—
698C22×C4—614no—
699C22×C4—612no—
700C22×C4—612no—
701C22×C4—618no—
702C22×C4—614no—
703C22×C4—614no—
704C22×C4—618no—
705C22×C4—614no—
706C22×C4—6116no—
707C22×C4—12216no—
708C22×C4—1228no—
709C22×C4—1228no—
710C22×C4—1224no—
711C22×C4—1224no—
712C22×C4—2448no—
713C22×C4—2442no—
714C22×C4—2444no—
715C22×C4C23×D6118yes—
716C22×C4C23×D6112yes—
717C22×C4C23×D6112yes—
718C22×C4C23×D6111yescharacteristic
719C22×C4C23×D6114yes—
720C22×C4C23×D6112yes—
721C22×C4C23×D61116yes—
722C22×C4C23×D6111yescharacteristic
723C22×C4C23×D6111yescharacteristic
724C4⋊C4—6116no—
725C4⋊C4—618no—
726C4⋊C4—614no—
727C4⋊C4—614no—
728C4⋊C4—618no—
729C4⋊C4—6116no—
730C4⋊C4—6116no—
731C4⋊C4—618no—
732C4⋊C4—6116no—
733C4⋊C4—6116no—
734C4⋊C4—6116no—
735C4⋊C4—6116no—
736C4⋊C4—618no—
737C4⋊C4—618no—
738C4⋊C4—618no—
739C4⋊C4—618no—
740C4⋊C4—6116no—
741C4⋊C4C23×D6118yes—
742C4⋊C4C23×D6114yes—
743C4⋊C4C23×D6118yes—
744C4⋊C4C23×D61116yes—
745C4⋊C4C23×D6114yes—
746C4⋊C4C23×D61116yes—
747C4⋊C4C23×D6118yes—
748C22⋊C4—618no—
749C22⋊C4—618no—
750C22⋊C4—618no—
751C22⋊C4—618no—
752C22⋊C4—618no—
753C22⋊C4—6116no—
754C22⋊C4—6116no—
755C22⋊C4—6116no—
756C22⋊C4—618no—
757C22⋊C4—618no—
758C22⋊C4C23×D61116yes—
759C22⋊C4C23×D6118yes—
760C42—614no—
761C42—618no—
762C42—614no—
763C42—614no—
764C42—618no—
765C42—618no—
766C42—6116no—
767C42—6116no—
768C42C23×D6114yes—
769C42C23×D6118yes—
770C23—24no—
771C23—24no—
772C23—612no—
773C23—614no—
774C23—1222no—
775C23—1224no—
776C23—1222no—
777C23—1224no—
778C23—1224no—
779C23—1222no—
780C23C2×#1175822618yes—
781C23C24×D6114yes—
782C23C24×D6111yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—1228no—
786Q8—12216no—
787D4—12216no—
788D4—12232no—
789D4—1228no—
790D4—2448no—
791D4C2×#11758226116yes—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—216no—
798C2×C4—416no—
799C2×C4—612no—
800C2×C4—612no—
801C2×C4—612no—
802C2×C4—614no—
803C2×C4—614no—
804C2×C4—618no—
805C2×C4—614no—
806C2×C4—1222no—
807C2×C4—1224no—
808C2×C4—1228no—
809C2×C4—1224no—
810C2×C4—12216no—
811C2×C4—12232no—
812C2×C4—1222no—
813C2×C4—1224no—
814C2×C4—1222no—
815C2×C4—1228no—
816C2×C4—12216no—
817C2×C4—1228no—
818C2×C4—24416no—
819C2×C4—2444no—
820C2×C4—2448no—
821C2×C4C2×#1175822614yes—
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—216no—
831C22—24no—
832C22—24no—
833C22—1222no—
834C22—1224no—
835C22—1222no—
836C22—1224no—
837C22—1224no—
838C22—1222no—
839C22—2444no—
840C22—2448no—
841C22C22×#1175822618yes—
842C22C22×#1175822612yes—
843C22C2×#1451982412yes—
844C22#1684059712yes—
845C22C25×D6111yescharacteristic
846C4—24no—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—22no—
851C4—1222no—
852C4—1224no—
853C4—1224no—
854C4—1228no—
855C4—1222no—
856C4—1224no—
857C4—1222no—
858C4C22×#1175822614yes—
859C4C2×#1451982414yes—
860C2—28no—
861C2—2442no—
862C2—2444no—
863C2#2145979814yesdirect product factor
864C2C23×#1175822611yescharacteristic
865C2C22×#1451982411yescharacteristic
866C2C2×#1684059711yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#554C2
socleC23×C61C25
hypercenterC2×#554D61
hypocenterC61C2×#3515
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #21459798C2direct (N × H)
2. C2×#16840491C2semidirect
3. C2×#16840473C2semidirect
4. C2×#16840460C2semidirect
5. C2×#16840454C2semidirect
6. C2×#16840454C2semidirect
7. C2×#16840450C2semidirect
8. C2×#16840416C2semidirect
9. C2×#16840416C2semidirect
10. C2×#16840375C2semidirect
11. C2×#16840361C2semidirect
12. C2×#16840317C2semidirect
13. C2×#16840299C2semidirect
14. C2×#16840298C2semidirect
15. C22×#14519768C2semidirect
16. C2×#16840241C2semidirect
17. C2×C4×#11758224C2semidirect
18. C2×C61×#554C2semidirect
21. #16840491C22semidirect
22. #16840473C22semidirect
23. #16840460C22semidirect
24. #16840454C22semidirect
25. #16840454C22semidirect
26. #16840450C22semidirect
27. #16840416C22semidirect
28. #16840416C22semidirect
29. #16840375C22semidirect
30. #16840361C22semidirect
31. #16840317C22semidirect
34. #16840299C22semidirect
35. #16840298C22semidirect
48. C2×#14519768C22semidirect
64. #16840241C22semidirect
65. C4×#11758224C22semidirect
92. C61×#554C22semidirect
430. C2×#554D61semidirect
446. C2×C61#3515semidirect
456. #554C2×D61semidirect
534. C61C2×#3515semidirect
863. C2#21459798direct (N × H)

Maximal subgroups

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

subgroupindex
#214597982
C2×#168404912
C2×#168404732
C2×#168404602
C2×#168404542
C2×#168404502
C2×#168404162
C2×#168403752
C2×#168403612
C2×#168403172
C2×#168402992
C2×#168402982
C22×#145197682
C2×#168402412
C2×C4×#117582242
C2×C61×#5542
C2×#351561