Finite Group Databasebeta

← C2×#21460202 #30587711

Subgroups — C2×#21460202 #30587711

Order 15616.

7182 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#21460202C2132yesmaximal, direct product factor
2C2×#16840508C214yesmaximal, complemented
3C2×#16840478C211yesmaximal, characteristic, complemented
4C2×#16840475C212yesmaximal, complemented
5C2×#16840473C211yesmaximal, characteristic, complemented
6C2×#16840456C212yesmaximal, complemented
7C2×#16840453C212yesmaximal, complemented
8C2×#16840427C211yesmaximal, characteristic, complemented
9C2×#16840424C212yesmaximal, complemented
10C2×#16840415C211yesmaximal, characteristic, complemented
11C2×#16840392C212yesmaximal, complemented
12C2×#16840384C214yesmaximal, complemented
13C2×#16840368C212yesmaximal, complemented
14C2×#16840342C212yesmaximal, complemented
15C2×#16840335C212yesmaximal, complemented
16C2×#16840312C211yesmaximal, characteristic, complemented
17C2×#16840296C211yesmaximal, characteristic, complemented
18C2×C61×#533C211yesmaximal, characteristic, complemented
19C22×#11758226C2212yes—
20C22×#11758222C2212yes—
21C22×Q8×D61C2212yes—
22#16840508C22164yescomplemented
23#16840478C22116yescomplemented
24#16840475C22132yescomplemented
25#16840473C22116yescomplemented
26#16840456C22132yescomplemented
27#16840453C22132yescomplemented
28#16840427C22116yescomplemented
29#16840424C22132yescomplemented
30#16840415C22116yescomplemented
31#16840392C22132yescomplemented
32#16840384C22164yescomplemented
33#16840368C22132yescomplemented
34#16840342C22132yescomplemented
35#16840335C22132yescomplemented
36#16840312C22116yescomplemented
37C2×#14519777C2211yescharacteristic
38C2×#14519776C2212yes—
39C2×#14519776C2214yes—
40C2×#14519774C2211yescharacteristic
41#16840296C22116yescomplemented
42C2×#14519771C2214yes—
43C2×#14519771C2212yes—
44C2×#14519769C2211yescharacteristic
45C2×#14519768C2212yes—
46C2×#14519767C2214yes—
47C2×#14519766C2214yes—
48C2×#14519765C2211yescharacteristic
49C2×#14519765C2214yes—
50C2×#14519765C2212yes—
51C2×#14519763C2214yes—
52C2×#14519762C2214yes—
53C2×#14519762C2214yes—
54C2×#14519762C2214yes—
55C2×#14519760C2212yes—
56C2×#14519759C2214yes—
57C2×#14519757C2214yes—
58C2×#14519757C2212yes—
59C2×#14519756C2211yescharacteristic
60C2×#14519755C2214yes—
61C2×#14519755C2214yes—
62C2×#14519753C2212yes—
63C2×#14519753C2212yes—
64C2×#14519753C2214yes—
65C2×#14519752C2212yes—
66C2×#14519752C2212yes—
67C2×#14519752C2214yes—
68C2×#14519752C2212yes—
69C2×#14519752C2214yes—
70C2×#14519751C2211yescharacteristic
71C2×#14519751C2211yescharacteristic
72C2×#14519751C2211yescharacteristic
73C2×#14519751C2212yes—
74C2×#14519750C2214yes—
75C2×#14519750C2214yes—
76C2×C4×Dic122C2211yescharacteristic
77C2×C4×D244C2211yescharacteristic
78C2×C4×D244C2211yescharacteristic
79C2×C4×D244C2212yes—
80C2×C4×D244C2214yes—
81C2×C4×D244C2211yescharacteristic
82C2×#14519739C2212yes—
83C2×#14519739C2212yes—
84C2×C4×C22⋊D61C2212yes—
85C2×#14519735C2212yes—
86C2×#14519735C2212yes—
87C2×#14519734C2212yes—
88C2×#14519734C2214yes—
89C2×C4⋊C4×D61C2212yes—
90C2×C4⋊C4×D61C2212yes—
91C61×#533C22116yescomplemented
92C2×C4⋊Q8×C61C2211yescharacteristic
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×#125×C61C2212yes—
95C2×C22⋊Q8×C61C2212yes—
96C2×C22⋊Q8×C61C2212yes—
97C2×C4×Q8×C61C2212yes—
98C2×C4×Q8×C61C2212yes—
99C2×#117×C61C2212yes—
100C22×C42×C61C2211yescharacteristic
101C2×#11758226—48no—
102C2×#11758226C23116yes—
103C2×#11758222—48no—
104C2×#11758222C23116yes—
105C22×Dic122C2311yescharacteristic
106C22×Dic122C2312yes—
107C22×Dic122C2314yes—
108C2×Q8×D61—48no—
109C2×Q8×D61C23116yes—
110C22×D244C2311yescharacteristic
111C22×D244C2311yescharacteristic
112C22×D244C2311yescharacteristic
113C22×D244C2314yes—
114C22×D244C2312yes—
115C22×D244C2314yes—
116C22×D244C2312yes—
117C22×C22⋊D61C2312yes—
118C22×C22⋊D61C2312yes—
119C22×C22⋊D61C2312yes—
120C22×C4×D61C2312yes—
121C22×C4×D61C2312yes—
122C22×C4×D61C2312yes—
123C22×C4×D61C2314yes—
124C22×C4×D61C2314yes—
125C22×C4×D61C2314yes—
126#14519777C2318yes—
127#14519776C23116yes—
128#14519776C23132yes—
129#14519774C2318yes—
130#14519771C23132yes—
131#14519771C23116yes—
132#14519769C2318yes—
133#14519768C23116yes—
134#14519767C23132yes—
135#14519766C23132yes—
136#14519765C23132yes—
137#14519765C2318yes—
138#14519765C23116yes—
139#14519763C23132yes—
140#14519762C23132yes—
141#14519762C23132yes—
142#14519762C23132yes—
143#14519760C23116yes—
144#14519759C23132yes—
145#14519757C23116yes—
146#14519757C23132yes—
147#14519756C2318yes—
148#14519755C23132yes—
149#14519755C23132yes—
150#14519753C23116yes—
151#14519753C23116yes—
152#14519753C23132yes—
153#14519752C23116yes—
154#14519752C23116yes—
155#14519752C23116yes—
156#14519752C23132yes—
157#14519752C23132yes—
158#14519751C2318yes—
159#14519751C2318yes—
160#14519751C23116yes—
161#14519751C2318yes—
162#14519750C23132yes—
163#14519750C23132yes—
164C4×Dic122C2318yes—
165C4×D244C23116yes—
166C4×D244C23132yes—
167C4×D244C2318yes—
168C4×D244C2318yes—
169C4×D244C2318yes—
170#14519739C23116yes—
171#14519739C23116yes—
172C4×C22⋊D61C23116yes—
173#14519735C23116yes—
174#14519735C23116yes—
175#14519734C23132yes—
176#14519734C23116yes—
177C2×C4⋊Dic61C2311yescharacteristic
178C2×C4⋊Dic61C2311yescharacteristic
179C2×C4⋊Dic61C2311yescharacteristic
180C2×C4⋊Dic61C2311yescharacteristic
181C2×C4⋊Dic61C2312yes—
182C2×C4⋊Dic61C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C2314yes—
185C2×#11758196C2312yes—
186C2×#11758196C2314yes—
187C2×#11758196C2312yes—
188C2×#11758196C2312yes—
189C2×#11758196C2312yes—
190C4⋊C4×D61C23116yes—
191C4⋊C4×D61C23116yes—
192C2×C22⋊Dic61C2312yes—
193C2×#11758198C2312yes—
194C2×#11758198C2312yes—
195C2×#11758198C2312yes—
196C2×#11758198C2314yes—
197C2×#11758198C2314yes—
198C2×#11758198C2314yes—
199C2×#11758198C2312yes—
200C2×#11758198C2314yes—
201C2×#11758198C2314yes—
202C2×#11758198C2312yes—
203C2×#11758198C2312yes—
204C2×#11758198C2312yes—
205C2×#11758198C2312yes—
206C2×C4×Dic61C2314yes—
207C2×C4×Dic61C2312yes—
208C22×Q8×C61C2312yes—
209C22×Q8×C61C2312yes—
210C23×C4×C61C2311yescharacteristic
211C23×C4×C61C2311yescharacteristic
212C23×C4×C61C2311yescharacteristic
213C4⋊Q8×C61C2318yes—
214C4⋊Q8×C61C2318yes—
215#125×C61C23116yes—
216C22⋊Q8×C61C23116yes—
217C22⋊Q8×C61C23116yes—
218C4×Q8×C61C23116yes—
219C4×Q8×C61C23116yes—
220#117×C61C23116yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2312yes—
224C2×C4⋊C4×C61C2312yes—
225C2×C4⋊C4×C61C2314yes—
226C2×C4⋊C4×C61C2314yes—
227C2×C22⋊C4×C61C2314yes—
228C2×C42×C61C2311yescharacteristic
229C2×C42×C61C2318yes—
230C2×C42×C61C2311yescharacteristic
231C2×C42×C61C2314yes—
232C2×C42×C61C2311yescharacteristic
233C2×C42×C61C2311yescharacteristic
234C24×C61C2411yescharacteristic
235C23×D61C2412yes—
236C23×D61C2412yes—
237C23×D61C2412yes—
238C2×Q8×C61—28no—
239C2×Q8×C61—44no—
240C2×Q8×C61C2418yes—
241C2×Q8×C61C2418yes—
242C22×C4×C61—24no—
243C22×C4×C61—24no—
244C22×C4×C61—42no—
245C22×C4×C61C2414yes—
246C22×C4×C61C2414yes—
247C22×C4×C61C2411yescharacteristic
248C22×C4×C61C2411yescharacteristic
249C22×C4×C61C2414yes—
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2411yescharacteristic
252C22×C4×C61C2414yes—
253C22×C4×C61C2414yes—
254C22×C4×C61C2411yescharacteristic
255C22×C4×C61C2411yescharacteristic
256C2×C22⋊D61—44no—
257C2×C22⋊D61—44no—
258C2×C22⋊D61—44no—
259C2×C22⋊D61C2418yes—
260C2×C22⋊D61C2418yes—
261C2×C22⋊D61C2418yes—
262C22×Dic61C2412yes—
263C22×Dic61C2412yes—
264C22×Dic61C2412yes—
265C22×Dic61C2412yes—
266C22×Dic61C2412yes—
267#11758226—432no—
268Q8×D61—432no—
269#11758222—432no—
270C2×D244—24no—
271C2×D244—24no—
272C2×D244—24no—
273C2×D244—48no—
274C2×D244—44no—
275C2×D244—44no—
276C2×D244—48no—
277C2×D244C2414yes—
278C2×D244C2414yes—
279C2×D244C2414yes—
280C2×D244C2418yes—
281C2×D244C24116yes—
282C2×D244C24116yes—
283C2×D244C2418yes—
284C2×C4×D61—28no—
285C2×C4×D61—28no—
286C2×C4×D61—28no—
287C2×C4×D61—48no—
288C2×C4×D61—48no—
289C2×C4×D61—48no—
290C2×C4×D61C2418yes—
291C2×C4×D61C2418yes—
292C2×C4×D61C2418yes—
293C2×C4×D61C24116yes—
294C2×C4×D61C24116yes—
295C2×C4×D61C24116yes—
296C2×Dic122—24no—
297C2×Dic122—48no—
298C2×Dic122—44no—
299C2×Dic122C2414yes—
300C2×Dic122C24116yes—
301C2×Dic122C2418yes—
302C4⋊C4×C61C2418yes—
303C4⋊C4×C61C2418yes—
304C4⋊C4×C61C24116yes—
305C4⋊C4×C61C24116yes—
306C4⋊C4×C61C2418yes—
307C4⋊C4×C61C2418yes—
308C22⋊C4×C61C24116yes—
309C42×C61C2414yes—
310C42×C61C2414yes—
311C42×C61C2414yes—
312C42×C61C2414yes—
313C42×C61C24116yes—
314C22⋊Dic61C2418yes—
315#11758198C2418yes—
316#11758198C2418yes—
317#11758198C2418yes—
318#11758198C24116yes—
319#11758198C24116yes—
320#11758198C24116yes—
321#11758198C2418yes—
322#11758198C24116yes—
323#11758198C24116yes—
324#11758198C2418yes—
325#11758198C2418yes—
326#11758198C2418yes—
327#11758198C2418yes—
328C4⋊Dic61C2414yes—
329C4⋊Dic61C2414yes—
330C4⋊Dic61C2414yes—
331C4⋊Dic61C2414yes—
332C4⋊Dic61C2418yes—
333C4⋊Dic61C24116yes—
334#11758196C24116yes—
335#11758196C24116yes—
336#11758196C2418yes—
337#11758196C24116yes—
338#11758196C2418yes—
339#11758196C2418yes—
340#11758196C2418yes—
341C4×Dic61C24116yes—
342C4×Dic61C2418yes—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61C2512yes—
347C23×C61C2511yescharacteristic
348C22×D61—24no—
349C22×D61—24no—
350C22×D61—24no—
351C22×D61—24no—
352C22×D61—24no—
353C22×D61—24no—
354C22×D61—24no—
355C22×D61—24no—
356C22×D61—24no—
357C22×D61C2514yes—
358C22×D61C2514yes—
359C22×D61C2514yes—
360Q8×C61—216no—
361Q8×C61—48no—
362C2×C4×C61—22no—
363C2×C4×C61—28no—
364C2×C4×C61—22no—
365C2×C4×C61—28no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—28no—
369C2×C4×C61—28no—
370C2×C4×C61—44no—
371C2×C4×C61H(5,𝔽2)14yes—
372C2×C4×C612−1+414yes—
373C2×C4×C61C2518yes—
374C2×C4×C61C2512yes—
375C2×C4×C61C2512yes—
376C2×C4×C61C2512yes—
377C2×C4×C61C2512yes—
378C2×C4×C61C2518yes—
379C2×C4×C61C2512yes—
380C2×C4×C61C2512yes—
381C22⋊D61—48no—
382C22⋊D61—48no—
383C22⋊D61—48no—
384C2×Dic61—24no—
385C2×Dic61—24no—
386C2×Dic61—24no—
387C2×Dic61—24no—
388C2×Dic61—24no—
389C2×Dic61C2514yes—
390C2×Dic61C2514yes—
391C2×Dic61C2514yes—
392C2×Dic61C2514yes—
393C2×Dic61C2514yes—
394D244—28no—
395D244—28no—
396D244—28no—
397D244—416no—
398D244—48no—
399D244—48no—
400D244—416no—
401C4×D61—216no—
402C4×D61—216no—
403C4×D61—216no—
404C4×D61—416no—
405C4×D61—416no—
406C4×D61—416no—
407Dic122—28no—
408Dic122—48no—
409Dic122—416no—
410C2×#3547—611nomaximal, Sylow
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—44no—
415C22×C61C2×H(5,𝔽2)12yes—
416C22×C61C2×2−1+412yes—
417C22×C61#58512yes—
418C22×C61C2611yescharacteristic
419C2×D61—24no—
420C2×D61—24no—
421C2×D61—24no—
422C2×D61—24no—
423C2×D61—24no—
424C2×D61—24no—
425C2×D61—24no—
426C2×D61—24no—
427C2×D61—24no—
428C2×D61—48no—
429C2×D61—48no—
430C2×D61—48no—
431C4×C61—22no—
432C4×C61—28no—
433C4×C61—22no—
434C4×C61—28no—
435C4×C61—22no—
436C4×C61—22no—
437C4×C61C2×H(5,𝔽2)14yes—
438C4×C61C2×2−1+414yes—
439Dic61—24no—
440Dic61—24no—
441Dic61—24no—
442Dic61—24no—
443Dic61—24no—
444#3547—6132no—
445C2×#562—614no—
446C2×#555—611no—
447C2×#555—612no—
448C2×#554—611no—
449C2×#553—612no—
450C2×#552—612no—
451C2×D4×Q8—611no—
452C2×#548—612no—
453C2×#547—611no—
454C2×#544—612no—
455C2×#542—614no—
456C2×#540—612no—
457C2×#537—612no—
458C2×#536—612no—
459C2×#533D6111yescharacteristic, complemented
460C2×#532—611no—
461C2×#529—611no—
462C2×C61—42no—
463C2×C61#354714yescomplemented
464C2×C61C22×H(5,𝔽2)11yescharacteristic
465C2×C61C22×2−1+411yescharacteristic
466C2×C61C2×#58511yescharacteristic
467D61—44no—
468D61—44no—
469D61—44no—
470C22×#41—612no—
471C22×#41—612no—
472C23×Q8—612no—
473#562—6164no—
474#555—6116no—
475#555—6132no—
476#554—6116no—
477#553—6132no—
478#552—6132no—
479D4×Q8—6116no—
480#548—6132no—
481#547—6116no—
482#544—6132no—
483#542—6164no—
484#540—6132no—
485#537—6132no—
486#536—6132no—
487#533C2×D61116yescomplemented
488#532—6116no—
489C2×C4⋊Q8—614no—
490C2×C4⋊Q8—612no—
491C2×C4⋊Q8—611no—
492C2×C4⋊Q8C2×D6111yescharacteristic
493C2×C4⋊Q8C2×D6111yescharacteristic
494C2×#127—611no—
495#529—6116no—
496C2×#126—612no—
497C2×#126—614no—
498C2×#125—614no—
499C2×#125—612no—
500C2×#125—611no—
501C2×#125C2×D6112yes—
502C2×#124—614no—
503C2×#124—614no—
504C2×#124—611no—
505C2×#124—612no—
506C2×#124—614no—
507C2×#123—612no—
508C2×#123—614no—
509C2×#123—614no—
510C2×#123—614no—
511C2×#123—614no—
512C2×C22⋊Q8—612no—
513C2×C22⋊Q8—612no—
514C2×C22⋊Q8—614no—
515C2×C22⋊Q8—611no—
516C2×C22⋊Q8—614no—
517C2×C22⋊Q8—614no—
518C2×C22⋊Q8—612no—
519C2×C22⋊Q8—614no—
520C2×C22⋊Q8C2×D6112yes—
521C2×C22⋊Q8C2×D6112yes—
522C2×#121—611no—
523C2×#121—611no—
524C2×#121—611no—
525C2×#121—612no—
526C2×#121—614no—
527C2×#121—612no—
528C2×#121—612no—
529C2×#121—614no—
530C2×#121—612no—
531C2×#121—614no—
532C2×#121—614no—
533C2×C4×Q8—611no—
534C2×C4×Q8C2×D6112yes—
535C2×C4×Q8C2×D6112yes—
536C2×C4×D4—612no—
537C2×C4×D4—612no—
538C2×C4×D4—612no—
539C2×C4×D4—611no—
540C2×C4×D4—611no—
541C2×C4×D4—612no—
542C2×C4×D4—611no—
543C2×C4×D4—614no—
544C2×#117—612no—
545C2×#117—612no—
546C2×#117—612no—
547C2×#117—614no—
548C2×#117C2×D6112yes—
549C22×C4⋊C4—612no—
550C22×C4⋊C4—612no—
551C22×C42C2×D6111yescharacteristic
552C61C2×#354711yescharacteristic, complemented, Sylow
553C2×#41—6116no—
554C2×#41—6116no—
555C2×#41—2448no—
556C2×#41—2448no—
557C22×Q8—6116no—
558C22×Q8—611no—
559C22×Q8—614no—
560C22×Q8—612no—
561C22×Q8—2448no—
562C22×Q8C22×D6112yes—
563C22×Q8C22×D6112yes—
564C22×D4—612no—
565C22×D4—612no—
566C22×D4—612no—
567C22×D4—611no—
568C22×D4—611no—
569C22×D4—611no—
570C22×D4—614no—
571C22×D4—612no—
572C22×D4—614no—
573C22×D4—612no—
574C23×C4—612no—
575C23×C4—612no—
576C23×C4—612no—
577C23×C4—614no—
578C23×C4—614no—
579C23×C4—614no—
580C23×C4C22×D6111yescharacteristic
581C23×C4C22×D6111yescharacteristic
582C23×C4C22×D6111yescharacteristic
583C4⋊Q8—6132no—
584C4⋊Q8—6116no—
585C4⋊Q8—618no—
586C4⋊Q8C22×D6118yes—
587C4⋊Q8C22×D6118yes—
588#127—618no—
589#126—6116no—
590#126—6132no—
591#125—6132no—
592#125—6116no—
593#125—618no—
594#125C22×D61116yes—
595#124—6132no—
596#124—6132no—
597#124—618no—
598#124—6116no—
599#124—6132no—
600#123—6116no—
601#123—6132no—
602#123—6132no—
603#123—6132no—
604#123—6132no—
605C22⋊Q8—6116no—
606C22⋊Q8—6116no—
607C22⋊Q8—6132no—
608C22⋊Q8—618no—
609C22⋊Q8—6116no—
610C22⋊Q8—6132no—
611C22⋊Q8—6132no—
612C22⋊Q8—6132no—
613C22⋊Q8C22×D61116yes—
614C22⋊Q8C22×D61116yes—
615#121—618no—
616#121—618no—
617#121—618no—
618#121—6116no—
619#121—6132no—
620#121—6116no—
621#121—6116no—
622#121—6132no—
623#121—6116no—
624#121—6132no—
625#121—6132no—
626C4×Q8—618no—
627C4×Q8C22×D61116yes—
628C4×Q8C22×D61116yes—
629C4×D4—6116no—
630C4×D4—6116no—
631C4×D4—6116no—
632C4×D4—618no—
633C4×D4—618no—
634C4×D4—6116no—
635C4×D4—618no—
636C4×D4—6132no—
637#117—6116no—
638#117—6116no—
639#117—6116no—
640#117—6132no—
641#117C22×D61116yes—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—614no—
645C2×C4⋊C4—614no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—611no—
648C2×C4⋊C4—612no—
649C2×C4⋊C4—614no—
650C2×C4⋊C4—612no—
651C2×C4⋊C4—612no—
652C2×C4⋊C4—612no—
653C2×C4⋊C4—614no—
654C2×C4⋊C4—612no—
655C2×C4⋊C4—6116no—
656C2×C4⋊C4—6116no—
657C2×C4⋊C4C22×D6112yes—
658C2×C4⋊C4C22×D6112yes—
659C2×C4⋊C4C22×D6112yes—
660C2×C4⋊C4C22×D6114yes—
661C2×C4⋊C4C22×D6114yes—
662C2×C4⋊C4C22×D6112yes—
663C2×C22⋊C4—612no—
664C2×C22⋊C4—612no—
665C2×C22⋊C4—612no—
666C2×C22⋊C4—612no—
667C2×C22⋊C4—614no—
668C2×C22⋊C4—614no—
669C2×C22⋊C4—614no—
670C2×C22⋊C4—612no—
671C2×C22⋊C4—612no—
672C2×C22⋊C4—614no—
673C2×C22⋊C4—612no—
674C2×C22⋊C4—614no—
675C2×C22⋊C4—612no—
676C2×C22⋊C4—612no—
677C2×C22⋊C4C22×D6114yes—
678C2×C42—614no—
679C2×C42—612no—
680C2×C42C22×D6111yescharacteristic
681C2×C42C22×D6114yes—
682C2×C42C22×D6111yescharacteristic
683C2×C42C22×D6111yescharacteristic
684C2×C42C22×D6111yescharacteristic
685C2×C42C22×D6118yes—
686C24—612no—
687C24—612no—
688C24—612no—
689C24C23×D6111yescharacteristic
690#41—24432no—
691#41—24432no—
692C2×Q8—28no—
693C2×Q8—44no—
694C2×Q8—614no—
695C2×Q8—6116no—
696C2×Q8—618no—
697C2×Q8—1224no—
698C2×Q8—2448no—
699C2×Q8—2444no—
700C2×Q8—24432no—
701C2×Q8C23×D6118yes—
702C2×Q8C23×D6118yes—
703C2×D4—618no—
704C2×D4—618no—
705C2×D4—618no—
706C2×D4—614no—
707C2×D4—614no—
708C2×D4—614no—
709C2×D4—6116no—
710C2×D4—618no—
711C2×D4—6116no—
712C2×D4—618no—
713C2×D4—1224no—
714C2×D4—1224no—
715C2×D4—1224no—
716C2×D4—2444no—
717C2×D4—2448no—
718C2×D4—2444no—
719C2×D4—2448no—
720C2×D4—2444no—
721C2×D4—2444no—
722C2×D4—2444no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—42no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—612no—
729C22×C4—612no—
730C22×C4—612no—
731C22×C4—618no—
732C22×C4—618no—
733C22×C4—618no—
734C22×C4—6116no—
735C22×C4—6116no—
736C22×C4—6116no—
737C22×C4—1228no—
738C22×C4—1228no—
739C22×C4—1228no—
740C22×C4—2448no—
741C22×C4—2448no—
742C22×C4—2448no—
743C22×C4C23×D6114yes—
744C22×C4C23×D6114yes—
745C22×C4C23×D6114yes—
746C22×C4C23×D6111yescharacteristic
747C22×C4C23×D6111yescharacteristic
748C22×C4C23×D6111yescharacteristic
749C22×C4C23×D6111yescharacteristic
750C22×C4C23×D6114yes—
751C22×C4C23×D6114yes—
752C22×C4C23×D6111yescharacteristic
753C22×C4C23×D6111yescharacteristic
754C4⋊C4—614no—
755C4⋊C4—614no—
756C4⋊C4—6116no—
757C4⋊C4—6116no—
758C4⋊C4—618no—
759C4⋊C4—6116no—
760C4⋊C4—618no—
761C4⋊C4—618no—
762C4⋊C4—618no—
763C4⋊C4—614no—
764C4⋊C4—614no—
765C4⋊C4—618no—
766C4⋊C4—6116no—
767C4⋊C4C23×D6118yes—
768C4⋊C4C23×D6118yes—
769C4⋊C4C23×D6118yes—
770C4⋊C4C23×D61116yes—
771C4⋊C4C23×D61116yes—
772C4⋊C4C23×D6118yes—
773C22⋊C4—618no—
774C22⋊C4—618no—
775C22⋊C4—618no—
776C22⋊C4—618no—
777C22⋊C4—6116no—
778C22⋊C4—6116no—
779C22⋊C4—6116no—
780C22⋊C4—618no—
781C22⋊C4—618no—
782C22⋊C4—6116no—
783C22⋊C4—618no—
784C22⋊C4—6116no—
785C22⋊C4—618no—
786C22⋊C4—618no—
787C22⋊C4C23×D61116yes—
788C42—6116no—
789C42—618no—
790C42C23×D6114yes—
791C42C23×D6114yes—
792C42C23×D6114yes—
793C42C23×D6114yes—
794C42C23×D61116yes—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—614no—
799C23—614no—
800C23—614no—
801C23—1224no—
802C23—1224no—
803C23—1224no—
804C23—1224no—
805C23—1224no—
806C23—1224no—
807C23—1224no—
808C23—1224no—
809C23—1224no—
810C23C24×D6112yes—
811C23C24×D6111yescharacteristic
812Q8—216no—
813Q8—48no—
814Q8—1228no—
815Q8—24416no—
816Q8—2448no—
817D4—1228no—
818D4—1228no—
819D4—1228no—
820D4—2448no—
821D4—24416no—
822D4—2448no—
823D4—24416no—
824D4—2448no—
825D4—2448no—
826D4—2448no—
827C2×C4—22no—
828C2×C4—28no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—44no—
836C2×C4—614no—
837C2×C4—614no—
838C2×C4—614no—
839C2×C4—614no—
840C2×C4—614no—
841C2×C4—1224no—
842C2×C4—1224no—
843C2×C4—1224no—
844C2×C4—1224no—
845C2×C4—1224no—
846C2×C4—12216no—
847C2×C4—12216no—
848C2×C4—12216no—
849C2×C4—24416no—
850C2×C4—24416no—
851C2×C4—24416no—
852C2×C4#1451982314yes—
853C2×C4#1451982514yes—
854C2×C4C24×D6118yes—
855C2×C4C24×D6112yes—
856C2×C4C24×D6112yes—
857C2×C4C24×D6112yes—
858C2×C4C24×D6112yes—
859C2×C4C24×D6118yes—
860C2×C4C24×D6112yes—
861C2×C4C24×D6112yes—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—44no—
866C22—1224no—
867C22—1224no—
868C22—1224no—
869C22—1224no—
870C22—1224no—
871C22—1224no—
872C22—1224no—
873C22—1224no—
874C22—1224no—
875C22—2448no—
876C22—2448no—
877C22—2448no—
878C22C2×#1451982312yes—
879C22C2×#1451982512yes—
880C22#1684059812yes—
881C22C25×D6111yescharacteristic
882C4—22no—
883C4—28no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—28no—
888C4—1224no—
889C4—1224no—
890C4—1224no—
891C4—1224no—
892C4—1224no—
893C4C2×#1451982314yes—
894C4C2×#1451982514yes—
895C2—42no—
896C2—2444no—
897C2—2444no—
898C2—2444no—
899C2#2146020214yesdirect product factor
900C2C22×#1451982311yescharacteristic
901C2C22×#1451982511yescharacteristic
902C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#533C2
socleC23×C61C25
hypercenterC2×#533D61
hypocenterC61C2×#3547
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #21460202C2direct (N × H)
2. C2×#16840508C2semidirect
3. C2×#16840478C2semidirect
4. C2×#16840475C2semidirect
5. C2×#16840473C2semidirect
6. C2×#16840456C2semidirect
7. C2×#16840453C2semidirect
8. C2×#16840427C2semidirect
9. C2×#16840424C2semidirect
10. C2×#16840415C2semidirect
11. C2×#16840392C2semidirect
12. C2×#16840384C2semidirect
13. C2×#16840368C2semidirect
14. C2×#16840342C2semidirect
15. C2×#16840335C2semidirect
16. C2×#16840312C2semidirect
17. C2×#16840296C2semidirect
18. C2×C61×#533C2semidirect
22. #16840508C22semidirect
23. #16840478C22semidirect
24. #16840475C22semidirect
25. #16840473C22semidirect
26. #16840456C22semidirect
27. #16840453C22semidirect
28. #16840427C22semidirect
29. #16840424C22semidirect
30. #16840415C22semidirect
31. #16840392C22semidirect
32. #16840384C22semidirect
33. #16840368C22semidirect
34. #16840342C22semidirect
35. #16840335C22semidirect
36. #16840312C22semidirect
41. #16840296C22semidirect
91. C61×#533C22semidirect
459. C2×#533D61semidirect
463. C2×C61#3547semidirect
487. #533C2×D61semidirect
552. C61C2×#3547semidirect
899. C2#21460202direct (N × H)

Maximal subgroups

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

subgroupindex
#214602022
C2×#168405082
C2×#168404782
C2×#168404752
C2×#168404732
C2×#168404562
C2×#168404532
C2×#168404272
C2×#168404242
C2×#168404152
C2×#168403922
C2×#168403842
C2×#168403682
C2×#168403422
C2×#168403352
C2×#168403122
C2×#168402962
C2×C61×#5332
C2×#354761