Finite Group Databasebeta

← C2×#21459797 #30588127

Subgroups — C2×#21459797 #30588127

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#21459797C2132yesmaximal, direct product factor
2C2×#16840490C211yesmaximal, characteristic, complemented
3C2×#16840472C211yesmaximal, characteristic, complemented
4C2×#16840469C211yesmaximal, characteristic, complemented
5C2×#16840458C212yesmaximal, complemented
6C2×#16840452C212yesmaximal, complemented
7C2×#16840451C212yesmaximal, complemented
8C2×#16840445C214yesmaximal, complemented
9C2×#16840416C211yesmaximal, characteristic, complemented
10C2×#16840411C212yesmaximal, complemented
11C2×#16840370C212yesmaximal, complemented
12C2×#16840354C214yesmaximal, complemented
13C2×#16840319C211yesmaximal, characteristic, complemented
14C2×#16840296C211yesmaximal, characteristic, complemented
15C2×#16840296C212yesmaximal, complemented
16C22×#14519769C212yesmaximal, complemented
17C2×#16840241C212yesmaximal, complemented
18C2×C4×#41×C61C211yesmaximal, characteristic, complemented
19C22×#11758224C2212yes—
20#16840490C22116yescomplemented
21#16840472C22116yescomplemented
22#16840469C22116yescomplemented
23#16840458C22132yescomplemented
24#16840452C22132yescomplemented
25#16840451C22132yescomplemented
26#16840445C22164yescomplemented
27#16840416C22116yescomplemented
28#16840411C22132yescomplemented
29#16840370C22132yescomplemented
30#16840354C22164yescomplemented
31#16840319C22116yescomplemented
32C2×#14519777C2211yescharacteristic
33C2×#14519777C2211yescharacteristic
34C2×#14519775C2212yes—
35#16840296C22132yescomplemented
36#16840296C22116yescomplemented
37C2×#14519772C2214yes—
38C2×#14519771C2212yes—
39C2×#14519771C2214yes—
40C2×#14519770C2214yes—
41C2×#14519769C2214yes—
42C2×#14519769C2211yescharacteristic
43C2×#14519769C2212yes—
44C2×#14519769C2212yes—
45C2×#14519769C2212yes—
46C2×#14519769C2214yes—
47C2×#14519769C22132yescomplemented
48C2×#14519768C2212yes—
49C2×#14519767C2214yes—
50C2×#14519767C2214yes—
51C2×#14519765C2211yescharacteristic
52C2×#14519761C2214yes—
53C2×#14519760C2214yes—
54C2×#14519760C2212yes—
55C2×#14519759C2214yes—
56C2×#14519758C2214yes—
57C2×#14519757C2212yes—
58C2×#14519756C2212yes—
59C2×#14519756C2211yescharacteristic
60C2×#14519756C2212yes—
61C2×#14519756C2212yes—
62C2×#14519755C2214yes—
63C2×#14519754C2214yes—
64C2×#14519753C2212yes—
65C2×#14519751C2212yes—
66C2×#14519751C2211yescharacteristic
67C2×#14519749C2214yes—
68#16840241C22132yescomplemented
69C2×C4×Dic122C2212yes—
70C2×C4×Dic122C2212yes—
71C2×C4×Dic122C2212yes—
72C2×C4×Dic122C2211yescharacteristic
73C2×#14519742C2212yes—
74C2×C4×D244C2211yescharacteristic
75C2×C4×D244C2212yes—
76C2×D4×Dic61C2212yes—
77C2×C4×C22⋊D61C2214yes—
78C2×C4×C22⋊D61C2212yes—
79C2×#14519737C2214yes—
80C2×#14519736C2212yes—
81C2×#14519734C2212yes—
82C2×#14519734C2214yes—
83C2×#14519733C2214yes—
84C22×C4⋊Dic61C2212yes—
85C22×C4⋊Dic61C2212yes—
86C22×#11758196C2214yes—
87C22×#11758196C2214yes—
88C2×C4⋊C4×D61C2212yes—
89C22×#41×C61C2211yescharacteristic
90C4×#41×C61C22116yescomplemented
91C2×C4×Q8×C61C2211yescharacteristic
92C2×C4×Q8×C61C2211yescharacteristic
93C2×C4×D4×C61C2211yescharacteristic
94C2×C4×D4×C61C2211yescharacteristic
95C2×C4×D4×C61C2212yes—
96C2×C4×D4×C61C2212yes—
97C2×#117×C61C2212yes—
98C2×#117×C61C2211yescharacteristic
99C22×C42×C61C2212yes—
100C22×C42×C61C2211yescharacteristic
101C2×#11758224—216no—
102C2×#11758224C23116yes—
103C22×Dic122C2312yes—
104C22×Dic122C2311yescharacteristic
105C22×Dic122C2312yes—
106C22×D244C2311yescharacteristic
107C22×C22⋊D61C2314yes—
108C22×C22⋊D61C2312yes—
109C23×Dic61C2314yes—
110C23×Dic61C2314yes—
111C22×C4×D61C2312yes—
112C22×C4×D61C2314yes—
113#14519777C2318yes—
114#14519777C2318yes—
115#14519775C23116yes—
116#14519772C23132yes—
117#14519771C23132yes—
118#14519771C23116yes—
119#14519770C23132yes—
120#14519769C23132yes—
121#14519769C23116yes—
122#14519769C23116yes—
123#14519769C2318yes—
124#14519769C23116yes—
125#14519769C23132yes—
126#14519768C23116yes—
127#14519767C23132yes—
128#14519767C23132yes—
129#14519765C2318yes—
130#14519761C23132yes—
131#14519760C23116yes—
132#14519760C23132yes—
133#14519759C23132yes—
134#14519758C23132yes—
135#14519757C23116yes—
136#14519756C23116yes—
137#14519756C2318yes—
138#14519756C23116yes—
139#14519756C23116yes—
140#14519755C23132yes—
141#14519754C23132yes—
142#14519753C23116yes—
143#14519751C2318yes—
144#14519751C23116yes—
145#14519749C23132yes—
146C4×Dic122C23116yes—
147C4×Dic122C2318yes—
148C4×Dic122C23116yes—
149C4×Dic122C23116yes—
150#14519742C23116yes—
151C4×D244C23116yes—
152C4×D244C2318yes—
153D4×Dic61C23116yes—
154C4×C22⋊D61C23116yes—
155C4×C22⋊D61C23132yes—
156#14519737C23132yes—
157#14519736C23116yes—
158#14519734C23132yes—
159#14519734C23116yes—
160#14519733C23132yes—
161C2×C4⋊Dic61C23116yes—
162C2×C4⋊Dic61C23116yes—
163C2×C4⋊Dic61C2312yes—
164C2×C4⋊Dic61C2311yescharacteristic
165C2×C4⋊Dic61C2311yescharacteristic
166C2×C4⋊Dic61C2312yes—
167C2×C4⋊Dic61C2312yes—
168C2×C4⋊Dic61C2314yes—
169C2×C4⋊Dic61C2314yes—
170C2×C4⋊Dic61C2312yes—
171C2×#11758196C2314yes—
172C2×#11758196C2312yes—
173C2×#11758196C2312yes—
174C2×#11758196C2314yes—
175C2×#11758196C2314yes—
176C2×#11758196C2314yes—
177C2×#11758196C23132yes—
178C2×#11758196C2314yes—
179C2×#11758196C2314yes—
180C2×#11758196C23132yes—
181C2×#11758196C2312yes—
182C2×#11758196C2314yes—
183C2×#11758196C2312yes—
184C2×#11758196C2314yes—
185C4⋊C4×D61C23116yes—
186C2×C22⋊Dic61C2314yes—
187C2×C22⋊Dic61C2314yes—
188C2×C22⋊Dic61C2312yes—
189C2×#11758198C2312yes—
190C2×#11758198C2312yes—
191C2×#11758198C2312yes—
192C2×#11758198C2314yes—
193C2×#11758198C2314yes—
194C2×#11758198C2312yes—
195C2×C4×Dic61C2314yes—
196C2×C4×Dic61C2314yes—
197C2×C4×Dic61C2312yes—
198C2×#41×C61—28no—
199C2×#41×C61C2318yes—
200C22×Q8×C61C2311yescharacteristic
201C22×D4×C61C2312yes—
202C22×D4×C61C2311yescharacteristic
203C23×C4×C61C2312yes—
204C23×C4×C61C2312yes—
205C23×C4×C61C2311yescharacteristic
206C23×C4×C61C2311yescharacteristic
207C23×C4×C61C2312yes—
208C23×C4×C61C2311yescharacteristic
209C4×Q8×C61C2318yes—
210C4×Q8×C61C2318yes—
211C4×D4×C61C23116yes—
212C4×D4×C61C2318yes—
213C4×D4×C61C2318yes—
214C4×D4×C61C23116yes—
215#117×C61C2318yes—
216#117×C61C23116yes—
217C2×C4⋊C4×C61C2311yescharacteristic
218C2×C4⋊C4×C61C2312yes—
219C2×C4⋊C4×C61C2311yescharacteristic
220C2×C4⋊C4×C61C2312yes—
221C2×C22⋊C4×C61C2312yes—
222C2×C22⋊C4×C61C2312yes—
223C2×C22⋊C4×C61C2312yes—
224C2×C42×C61C2311yescharacteristic
225C2×C42×C61C2312yes—
226C2×C42×C61C2312yes—
227C2×C42×C61C2311yescharacteristic
228C2×C42×C61C2311yescharacteristic
229C2×C42×C61C2311yescharacteristic
230C2×C42×C61C2312yes—
231C2×C42×C61C23116yes—
232C2×C42×C61C2318yes—
233C24×C61C2411yescharacteristic
234C24×C61C2412yes—
235C23×D61C2412yes—
236#41×C61—232no—
237C2×Q8×C61—24no—
238C2×Q8×C61C2414yes—
239C2×D4×C61—28no—
240C2×D4×C61#4118yes—
241C2×D4×C61C2418yes—
242C2×D4×C61C2414yes—
243C22×C4×C61—28no—
244C22×C4×C61—24no—
245C22×C4×C61—28no—
246C22×C4×C61—24no—
247C22×C4×C61—42no—
248C22×C4×C61—44no—
249C22×C4×C61C2412yes—
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2411yescharacteristic
252C22×C4×C61C2411yescharacteristic
253C22×C4×C61C2411yescharacteristic
254C22×C4×C61C2412yes—
255C22×C4×C61C2412yes—
256C22×C4×C61C2418yes—
257C22×C4×C61C2414yes—
258C22×C4×C61C2418yes—
259C22×C4×C61C2414yes—
260C22×C4×C61C2418yes—
261C22×C4×C61C2414yes—
262C22×C4×C61C2411yescharacteristic
263C22×C4×C61C2411yescharacteristic
264C2×C22⋊D61—216no—
265C2×C22⋊D61—44no—
266C2×C22⋊D61C24116yes—
267C2×C22⋊D61C2418yes—
268C22×Dic61—216no—
269C22×Dic61—48no—
270C22×Dic61C2412yes—
271C22×Dic61C2414yes—
272C22×Dic61C2412yes—
273C22×Dic61C2414yes—
274C22×Dic61C24116yes—
275C22×Dic61C2412yes—
276C22×Dic61C24116yes—
277#11758224—264no—
278C2×D244—24no—
279C2×D244C2414yes—
280C2×C4×D61—28no—
281C2×C4×D61—48no—
282C2×C4×D61C2418yes—
283C2×C4×D61C24116yes—
284C2×Dic122—28no—
285C2×Dic122—24no—
286C2×Dic122—44no—
287C2×Dic122C2418yes—
288C2×Dic122C2414yes—
289C2×Dic122C2418yes—
290C4⋊C4×C61C2414yes—
291C4⋊C4×C61C2418yes—
292C4⋊C4×C61C2414yes—
293C4⋊C4×C61C2418yes—
294C22⋊C4×C61C2418yes—
295C22⋊C4×C61C2418yes—
296C22⋊C4×C61C2418yes—
297C42×C61C2414yes—
298C42×C61C2418yes—
299C42×C61C2414yes—
300C42×C61C2414yes—
301C42×C61C2418yes—
302C42×C61C2414yes—
303C42×C61C2418yes—
304C22⋊Dic61C24116yes—
305C22⋊Dic61C24116yes—
306C22⋊Dic61C2418yes—
307#11758198C2418yes—
308#11758198C2418yes—
309#11758198C2418yes—
310#11758198C24116yes—
311#11758198C24116yes—
312#11758198C2418yes—
313C4⋊Dic61C2418yes—
314C4⋊Dic61C2414yes—
315C4⋊Dic61C2414yes—
316C4⋊Dic61C2418yes—
317C4⋊Dic61C2418yes—
318C4⋊Dic61C24116yes—
319C4⋊Dic61C24116yes—
320C4⋊Dic61C2418yes—
321#11758196C24116yes—
322#11758196C2418yes—
323#11758196C2418yes—
324#11758196C24116yes—
325#11758196C24116yes—
326#11758196C24116yes—
327#11758196C24116yes—
328#11758196C24116yes—
329#11758196C2418yes—
330#11758196C24116yes—
331#11758196C2418yes—
332#11758196C24116yes—
333C4×Dic61C24116yes—
334C4×Dic61C24116yes—
335C4×Dic61C2418yes—
336C23×C61—24no—
337C23×C61—24no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61C2×#4118yes—
342C23×C61C2512yes—
343C23×C61C2514yes—
344C23×C61C2511yescharacteristic
345C22×D61—24no—
346C22×D61—24no—
347C22×D61—24no—
348C22×D61C2514yes—
349Q8×C61—28no—
350D4×C61—216no—
351D4×C61C2×#41116yes—
352C2×C4×C61—22no—
353C2×C4×C61—24no—
354C2×C4×C61—216no—
355C2×C4×C61—22no—
356C2×C4×C61—24no—
357C2×C4×C61—22no—
358C2×C4×C61—24no—
359C2×C4×C61—22no—
360C2×C4×C61—28no—
361C2×C4×C61—216no—
362C2×C4×C61—28no—
363C2×C4×C61—44no—
364C2×C4×C61—48no—
365C2×C4×C61C2×#4114yes—
366C2×C4×C612−1+414yes—
367C2×C4×C61C2512yes—
368C2×C4×C61C2514yes—
369C2×C4×C61C2512yes—
370C2×C4×C61C2512yes—
371C2×C4×C61C2514yes—
372C2×C4×C61C2514yes—
373C2×C4×C61C2512yes—
374C2×C4×C61C2512yes—
375C2×C4×C61C2512yes—
376C22⋊D61—232no—
377C22⋊D61—48no—
378C2×Dic61—28no—
379C2×Dic61—24no—
380C2×Dic61—232no—
381C2×Dic61—24no—
382C2×Dic61—28no—
383C2×Dic61—24no—
384C2×Dic61—416no—
385C2×Dic61C2514yes—
386C2×Dic61C2518yes—
387C2×Dic61C2514yes—
388C2×Dic61C2518yes—
389C2×Dic61C2514yes—
390D244—28no—
391C4×D61—216no—
392C4×D61—416no—
393Dic122—216no—
394Dic122—28no—
395Dic122—48no—
396C2×#3515—611nomaximal, Sylow
397C22×C61—24no—
398C22×C61—24no—
399C22×C61—216no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—44no—
404C22×C61C22×#4118yes—
405C22×C61C22×#4112yes—
406C22×C61C2×2−1+412yes—
407C22×C61#58512yes—
408C22×C61C2611yescharacteristic
409C2×D61—24no—
410C2×D61—24no—
411C2×D61—24no—
412C2×D61—48no—
413C4×C61—22no—
414C4×C61—24no—
415C4×C61—22no—
416C4×C61—24no—
417C4×C61—22no—
418C4×C61—24no—
419C4×C61—22no—
420C4×C61C22×#4114yes—
421C4×C61C2×2−1+414yes—
422Dic61—28no—
423Dic61—24no—
424Dic61—24no—
425Dic61—28no—
426Dic61—24no—
427#3515—6132no—
428C2×#557—611no—
429C2×#554—611no—
430C2×#554—611no—
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—611no—
441C2×#529—612no—
442C22×#125—612no—
443C2×#520—612no—
444C2×C4×#41D6111yescharacteristic, complemented
445C2×C61—28no—
446C2×C61—42no—
447C2×C61#351514yescomplemented
448C2×C61C23×#4111yescharacteristic
449C2×C61C22×2−1+411yescharacteristic
450C2×C61C2×#58511yescharacteristic
451D61—44no—
452C22×#41—612no—
453C22×#41C2×D6111yescharacteristic
454#557—6116no—
455#554—6116no—
456#554—6116no—
457#553—6132no—
458#552—6132no—
459#552—6132no—
460#552—6164no—
461#547—6132no—
462#547—6116no—
463#541—6132no—
464#539—6164no—
465#533—6116no—
466C2×C4⋊Q8—612no—
467C2×C4⋊Q8—611no—
468C2×C4⋊Q8—611no—
469#529—6132no—
470#529—6116no—
471C2×#126—614no—
472C2×#126—614no—
473C2×#126—614no—
474C2×#126—612no—
475C2×#125—614no—
476C2×#125—614no—
477C2×#125—612no—
478C2×#125—611no—
479C2×#125—612no—
480C2×#125—614no—
481C2×#125—614no—
482C2×#125—612no—
483C2×#125—612no—
484C2×#125—6132no—
485C2×#124—611no—
486C2×#123—614no—
487C2×#123—612no—
488C2×#123—614no—
489C2×#123—614no—
490C2×#123—614no—
491C2×C22⋊Q8—612no—
492C2×C22⋊Q8—611no—
493C2×C22⋊Q8—612no—
494C2×C22⋊Q8—612no—
495C2×C22⋊Q8—612no—
496C2×C22⋊Q8—614no—
497C2×C22⋊Q8—612no—
498C2×C22⋊Q8—614no—
499C2×#121—614no—
500C2×#121—612no—
501C2×#121—611no—
502#520—6132no—
503C4×#41C2×D61116yescomplemented
504C2×C4×Q8—612no—
505C2×C4×Q8—612no—
506C2×C4×Q8—612no—
507C2×C4×Q8—611no—
508C2×C4×Q8—612no—
509C2×C4×Q8C2×D6111yescharacteristic
510C2×C4×Q8C2×D6111yescharacteristic
511C2×C4×D4—612no—
512C2×C4×D4—614no—
513C2×C4×D4—612no—
514C2×C4×D4—614no—
515C2×C4×D4—611no—
516C2×C4×D4—612no—
517C2×C4×D4C2×D6111yescharacteristic
518C2×C4×D4C2×D6112yes—
519C2×C4×D4C2×D6111yescharacteristic
520C2×C4×D4C2×D6112yes—
521C2×#117—612no—
522C2×#117—614no—
523C2×#117—612no—
524C2×#117—614no—
525C2×#117C2×D6111yescharacteristic
526C2×#117C2×D6112yes—
527C22×C4⋊C4—614no—
528C22×C4⋊C4—614no—
529C22×C4⋊C4—612no—
530C22×C4⋊C4—612no—
531C22×C4⋊C4—612no—
532C22×C42C2×D6112yes—
533C22×C42C2×D6111yescharacteristic
534C61C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—28no—
536C2×#41—6116no—
537C2×#41—12216no—
538C2×#41C22×D6118yes—
539C22×Q8—611no—
540C22×Q8—612no—
541C22×Q8—612no—
542C22×Q8C22×D6111yescharacteristic
543C22×D4—614no—
544C22×D4—612no—
545C22×D4—611no—
546C22×D4C22×D6112yes—
547C22×D4C22×D6111yescharacteristic
548C23×C4—614no—
549C23×C4—614no—
550C23×C4—612no—
551C23×C4—614no—
552C23×C4C22×D6112yes—
553C23×C4C22×D6112yes—
554C23×C4C22×D6111yescharacteristic
555C23×C4C22×D6111yescharacteristic
556C23×C4C22×D6112yes—
557C23×C4C22×D6111yescharacteristic
558C4⋊Q8—6116no—
559C4⋊Q8—618no—
560C4⋊Q8—618no—
561#126—6132no—
562#126—6132no—
563#126—6132no—
564#126—6116no—
565#125—6132no—
566#125—6132no—
567#125—6116no—
568#125—618no—
569#125—6116no—
570#125—6132no—
571#125—6132no—
572#125—6116no—
573#125—6116no—
574#124—618no—
575#123—6132no—
576#123—6116no—
577#123—6132no—
578#123—6132no—
579#123—6132no—
580C22⋊Q8—6116no—
581C22⋊Q8—618no—
582C22⋊Q8—6116no—
583C22⋊Q8—6116no—
584C22⋊Q8—6116no—
585C22⋊Q8—6132no—
586C22⋊Q8—6116no—
587C22⋊Q8—6132no—
588#121—6132no—
589#121—6116no—
590#121—618no—
591C4×Q8—6116no—
592C4×Q8—6116no—
593C4×Q8—6116no—
594C4×Q8—618no—
595C4×Q8—6116no—
596C4×Q8C22×D6118yes—
597C4×Q8C22×D6118yes—
598C4×D4—6116no—
599C4×D4—6132no—
600C4×D4—6116no—
601C4×D4—6132no—
602C4×D4—618no—
603C4×D4—6116no—
604C4×D4C22×D6118yes—
605C4×D4C22×D61116yes—
606C4×D4C22×D6118yes—
607C4×D4C22×D61116yes—
608#117—6116no—
609#117—6132no—
610#117—6116no—
611#117—6132no—
612#117C22×D6118yes—
613#117C22×D61116yes—
614C2×C4⋊C4—614no—
615C2×C4⋊C4—612no—
616C2×C4⋊C4—611no—
617C2×C4⋊C4—612no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—612no—
620C2×C4⋊C4—612no—
621C2×C4⋊C4—614no—
622C2×C4⋊C4—612no—
623C2×C4⋊C4—614no—
624C2×C4⋊C4—614no—
625C2×C4⋊C4—6132no—
626C2×C4⋊C4—614no—
627C2×C4⋊C4—614no—
628C2×C4⋊C4—614no—
629C2×C4⋊C4—614no—
630C2×C4⋊C4—6132no—
631C2×C4⋊C4—6116no—
632C2×C4⋊C4—6116no—
633C2×C4⋊C4—612no—
634C2×C4⋊C4—614no—
635C2×C4⋊C4—612no—
636C2×C4⋊C4—612no—
637C2×C4⋊C4—614no—
638C2×C4⋊C4—6116no—
639C2×C4⋊C4C22×D6111yescharacteristic
640C2×C4⋊C4C22×D6112yes—
641C2×C4⋊C4C22×D6111yescharacteristic
642C2×C4⋊C4C22×D6112yes—
643C2×C22⋊C4—614no—
644C2×C22⋊C4—614no—
645C2×C22⋊C4—612no—
646C2×C22⋊C4—612no—
647C2×C22⋊C4—612no—
648C2×C22⋊C4—612no—
649C2×C22⋊C4—614no—
650C2×C22⋊C4—614no—
651C2×C22⋊C4—612no—
652C2×C22⋊C4C22×D6112yes—
653C2×C22⋊C4C22×D6112yes—
654C2×C22⋊C4C22×D6112yes—
655C2×C42—614no—
656C2×C42—614no—
657C2×C42—612no—
658C2×C42C22×D6112yes—
659C2×C42C22×D6111yescharacteristic
660C2×C42C22×D6111yescharacteristic
661C2×C42C22×D6112yes—
662C2×C42C22×D6111yescharacteristic
663C2×C42C22×D6112yes—
664C2×C42C22×D61116yes—
665C2×C42C22×D6118yes—
666C2×C42C22×D6111yescharacteristic
667C24—612no—
668C24C23×D6111yescharacteristic
669C24C23×D6112yes—
670#41—232no—
671#41—12264no—
672C2×Q8—24no—
673C2×Q8—614no—
674C2×Q8—618no—
675C2×Q8—618no—
676C2×Q8—1228no—
677C2×Q8—1224no—
678C2×Q8—2444no—
679C2×Q8C23×D6114yes—
680C2×D4—28no—
681C2×D4—6116no—
682C2×D4—618no—
683C2×D4—614no—
684C2×D4—12216no—
685C2×D4—1224no—
686C2×D4—2444no—
687C2×D4#1175822218yes—
688C2×D4C23×D6118yes—
689C2×D4C23×D6114yes—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—28no—
693C22×C4—24no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—6116no—
697C22×C4—612no—
698C22×C4—614no—
699C22×C4—614no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—6116no—
703C22×C4—618no—
704C22×C4—6116no—
705C22×C4—12216no—
706C22×C4—1228no—
707C22×C4—2448no—
708C22×C4—2448no—
709C22×C4C23×D6118yes—
710C22×C4C23×D6118yes—
711C22×C4C23×D6114yes—
712C22×C4C23×D6114yes—
713C22×C4C23×D6111yescharacteristic
714C22×C4C23×D6112yes—
715C22×C4C23×D6111yescharacteristic
716C22×C4C23×D6111yescharacteristic
717C22×C4C23×D6112yes—
718C22×C4C23×D6111yescharacteristic
719C22×C4C23×D6112yes—
720C22×C4C23×D6118yes—
721C22×C4C23×D6114yes—
722C22×C4C23×D6111yescharacteristic
723C22×C4C23×D6111yescharacteristic
724C4⋊C4—6116no—
725C4⋊C4—618no—
726C4⋊C4—618no—
727C4⋊C4—614no—
728C4⋊C4—614no—
729C4⋊C4—6116no—
730C4⋊C4—6116no—
731C4⋊C4—6116no—
732C4⋊C4—6116no—
733C4⋊C4—6116no—
734C4⋊C4—618no—
735C4⋊C4—618no—
736C4⋊C4—618no—
737C4⋊C4—6116no—
738C4⋊C4—6116no—
739C4⋊C4—618no—
740C4⋊C4—6116no—
741C4⋊C4—618no—
742C4⋊C4—6116no—
743C4⋊C4—618no—
744C4⋊C4C23×D6114yes—
745C4⋊C4C23×D6118yes—
746C4⋊C4C23×D6114yes—
747C4⋊C4C23×D6118yes—
748C22⋊C4—6116no—
749C22⋊C4—6116no—
750C22⋊C4—618no—
751C22⋊C4—618no—
752C22⋊C4—618no—
753C22⋊C4—618no—
754C22⋊C4—6116no—
755C22⋊C4—6116no—
756C22⋊C4—618no—
757C22⋊C4C23×D6118yes—
758C22⋊C4C23×D6118yes—
759C22⋊C4C23×D6118yes—
760C42—6116no—
761C42—6116no—
762C42—618no—
763C42C23×D6114yes—
764C42C23×D6118yes—
765C42C23×D6114yes—
766C42C23×D6114yes—
767C42C23×D6118yes—
768C42C23×D6114yes—
769C42C23×D6118yes—
770C23—24no—
771C23—24no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—614no—
776C23—1224no—
777C23—1224no—
778C23—1224no—
779C23C2×#1175822218yes—
780C23C24×D6112yes—
781C23C24×D6114yes—
782C23C24×D6111yescharacteristic
783Q8—28no—
784Q8—12216no—
785Q8—1228no—
786Q8—2448no—
787D4—216no—
788D4—12232no—
789D4—1228no—
790D4—2448no—
791D4C2×#11758222116yes—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—216no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—216no—
802C2×C4—28no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—614no—
806C2×C4—618no—
807C2×C4—618no—
808C2×C4—614no—
809C2×C4—614no—
810C2×C4—1224no—
811C2×C4—1228no—
812C2×C4—12232no—
813C2×C4—1224no—
814C2×C4—1224no—
815C2×C4—1228no—
816C2×C4—12216no—
817C2×C4—24416no—
818C2×C4—24416no—
819C2×C4C2×#1175822214yes—
820C2×C4#1451982414yes—
821C2×C4C24×D6112yes—
822C2×C4C24×D6114yes—
823C2×C4C24×D6112yes—
824C2×C4C24×D6112yes—
825C2×C4C24×D6114yes—
826C2×C4C24×D6112yes—
827C2×C4C24×D6114yes—
828C2×C4C24×D6112yes—
829C2×C4C24×D6112yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—1224no—
838C22—1224no—
839C22—1224no—
840C22—2448no—
841C22C22×#1175822218yes—
842C22C22×#1175822212yes—
843C22C2×#1451982412yes—
844C22#1684059812yes—
845C22C25×D6111yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—1224no—
854C4—1228no—
855C4—1224no—
856C4—1224no—
857C4—1228no—
858C4C22×#1175822214yes—
859C4C2×#1451982414yes—
860C2—28no—
861C2—42no—
862C2—2444no—
863C2#2145979714yesdirect product factor
864C2C23×#1175822211yescharacteristic
865C2C22×#1451982411yescharacteristic
866C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C4×#41×C61C2
socleC23×C61C25
hypercenterC2×C4×#41D61
hypocenterC61C2×#3515
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #21459797C2direct (N × H)
2. C2×#16840490C2semidirect
3. C2×#16840472C2semidirect
4. C2×#16840469C2semidirect
5. C2×#16840458C2semidirect
6. C2×#16840452C2semidirect
7. C2×#16840451C2semidirect
8. C2×#16840445C2semidirect
9. C2×#16840416C2semidirect
10. C2×#16840411C2semidirect
11. C2×#16840370C2semidirect
12. C2×#16840354C2semidirect
13. C2×#16840319C2semidirect
14. C2×#16840296C2semidirect
15. C2×#16840296C2semidirect
16. C22×#14519769C2semidirect
17. C2×#16840241C2semidirect
18. C2×C4×#41×C61C2semidirect
20. #16840490C22semidirect
21. #16840472C22semidirect
22. #16840469C22semidirect
23. #16840458C22semidirect
24. #16840452C22semidirect
25. #16840451C22semidirect
26. #16840445C22semidirect
27. #16840416C22semidirect
28. #16840411C22semidirect
29. #16840370C22semidirect
30. #16840354C22semidirect
31. #16840319C22semidirect
35. #16840296C22semidirect
36. #16840296C22semidirect
47. C2×#14519769C22semidirect
68. #16840241C22semidirect
90. C4×#41×C61C22semidirect
444. C2×C4×#41D61semidirect
447. C2×C61#3515semidirect
503. C4×#41C2×D61semidirect
534. C61C2×#3515semidirect
863. C2#21459797direct (N × H)

Maximal subgroups

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

subgroupindex
#214597972
C2×#168404902
C2×#168404722
C2×#168404692
C2×#168404582
C2×#168404522
C2×#168404512
C2×#168404452
C2×#168404162
C2×#168404112
C2×#168403702
C2×#168403542
C2×#168403192
C2×#168402962
C22×#145197692
C2×#168402412
C2×C4×#41×C612
C2×#351561