Finite Group Databasebeta

← C2×#21459698 #30588449

Subgroups — C2×#21459698 #30588449

Order 15616.

7022 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459698C2132yesmaximal, direct product factor
2C2×#16840489C212yesmaximal, complemented
3C2×#16840488C212yesmaximal, complemented
4C2×#16840483C212yesmaximal, complemented
5C2×#16840480C212yesmaximal, complemented
6C2×#16840453C212yesmaximal, complemented
7C2×#16840451C212yesmaximal, complemented
8C2×#16840450C212yesmaximal, complemented
9C2×#16840446C212yesmaximal, complemented
10C2×#16840372C212yesmaximal, complemented
11C2×#16840370C212yesmaximal, complemented
12C2×#16840335C212yesmaximal
13C2×#16840319C211yesmaximal, characteristic, complemented
14C2×#16840317C211yesmaximal, characteristic, complemented
15C2×#16840317C211yesmaximal, characteristic, complemented
16C2×#16840317C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
18C2×#16840238C212yesmaximal, complemented
19C2×C4×#11758222C211yesmaximal, characteristic
20C2×C61×#533C211yesmaximal, characteristic, complemented
21C22×#11758222C2211yescharacteristic
22C22×Q8×D61C2212yes—
23#16840489C22132yescomplemented
24#16840488C22132yescomplemented
25#16840483C22132yescomplemented
26#16840480C22132yescomplemented
27#16840453C22132yescomplemented
28#16840451C22132yescomplemented
29#16840450C22132yescomplemented
30#16840446C22132yescomplemented
31#16840372C22132yescomplemented
32#16840370C22132yescomplemented
33#16840335C22132yes—
34#16840319C22116yescomplemented
35#16840317C22116yescomplemented
36#16840317C22116yescomplemented
37#16840317C22116yescomplemented
38C2×#14519777C2211yescharacteristic
39C2×#14519777C2211yescharacteristic
40C2×#14519776C2212yes—
41C2×#14519776C2212yes—
42C2×#14519776C2214yes—
43C2×#14519775C2212yes—
44C4⋊Q8×D61C22116yescomplemented
45C2×#14519772C2214yes—
46C2×#14519771C2214yes—
47C2×#14519770C2214yes—
48C2×#14519770C2214yes—
49C2×#14519769C2214yes—
50C2×#14519769C2212yes—
51C2×#14519768C2212yes—
52C2×#14519768C2214yes—
53C2×#14519768C2212yes—
54C2×#14519768C2212yes—
55C2×#14519767C2214yes—
56C2×#14519767C2214yes—
57C2×#14519763C2214yes—
58C2×#14519762C2214yes—
59C2×#14519759C2214yes—
60C2×#14519757C2212yes—
61C2×#14519757C2212yes—
62C2×#14519757C2212yes—
63C2×#14519756C2212yes—
64C2×#14519756C2212yes—
65C2×#14519753C2212yes—
66C2×#14519753C2212yes—
67C2×#14519753C2212yes—
68#16840238C22132yescomplemented
69C4×#11758222C22116yes—
70C2×Q8×Dic61C2212yes—
71C2×Q8×Dic61C2212yes—
72C2×Q8×Dic61C2212yes—
73C2×C4×Dic122C2211yescharacteristic
74C2×C4×Dic122C2211yescharacteristic
75C2×C4×Dic122C2214yes—
76C2×C4×Dic122C2212yes—
77C2×C4×Dic122C2212yes—
78C2×#14519742C2212yes—
79C2×#14519742C2214yes—
80C2×#14519742C2212yes—
81C2×#14519742C2212yes—
82C2×C4×D244C2211yescharacteristic
83C2×C4×D244C2211yescharacteristic
84C2×C4×C22⋊D61C2211yescharacteristic
85C2×C4×C22⋊D61C2211yescharacteristic
86C2×C4×C22⋊D61C2211yescharacteristic
87C2×C4×C22⋊D61C2211yescharacteristic
88C2×#14519736C2211yescharacteristic
89C2×#14519736C2212yes—
90C2×#14519735C2214yes—
91C2×#14519735C2212yes—
92C2×#14519735C2212yes—
93C2×#14519735C2212yes—
94C2×#14519734C2211yescharacteristic
95C2×#14519734C2211yescharacteristic
96C2×#14519734C2214yes—
97C2×C4⋊C4×D61C2212yes—
98C2×C4⋊C4×D61C2212yes—
99C2×C42×D61C2211yescharacteristic
100C2×C42×D61C2211yescharacteristic
101C61×#533C22116yescomplemented
102C2×C4⋊Q8×C61C2211yescharacteristic
103C2×C4⋊Q8×C61C2211yescharacteristic
104C2×#125×C61C2212yes—
105C2×C22⋊Q8×C61C2212yes—
106C2×C22⋊Q8×C61C2212yes—
107C2×C4×Q8×C61C2212yes—
108C2×C4×Q8×C61C2212yes—
109C2×#117×C61C2212yes—
110C22×C42×C61C2211yescharacteristic
111C2×#11758222—28no—
112C2×#11758222C2318yes—
113C22×Dic122C2312yes—
114C22×Dic122C2312yes—
115C22×Dic122C2314yes—
116C22×Dic122C2311yescharacteristic
117C2×Q8×D61—216no—
118C2×Q8×D61C23116yes—
119C22×D244C2311yescharacteristic
120C22×C22⋊D61C2311yescharacteristic
121C22×C22⋊D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127C22×C4×D61C2314yes—
128C22×C4×D61C2311yescharacteristic
129#14519777C2318yes—
130#14519777C2318yes—
131#14519776C23116yes—
132#14519776C23116yes—
133#14519776C23132yes—
134#14519775C23116yes—
135#14519772C23132yes—
136#14519771C23132yes—
137#14519770C23132yes—
138#14519770C23132yes—
139#14519769C23132yes—
140#14519769C23116yes—
141#14519768C23132yes—
142#14519768C23116yes—
143#14519768C23116yes—
144#14519768C23116yes—
145#14519767C23132yes—
146#14519767C23132yes—
147#14519763C23132yes—
148#14519762C23132yes—
149#14519759C23132yes—
150#14519757C23116yes—
151#14519757C23116yes—
152#14519757C23116yes—
153#14519756C23116yes—
154#14519756C23116yes—
155#14519753C23116yes—
156#14519753C23116yes—
157#14519753C23116yes—
158Q8×Dic61C23116yes—
159Q8×Dic61C23116yes—
160Q8×Dic61C23116yes—
161C4×Dic122C23116yes—
162C4×Dic122C23132yes—
163C4×Dic122C2318yes—
164C4×Dic122C2318yes—
165C4×Dic122C23116yes—
166#14519742C23116yes—
167#14519742C23116yes—
168#14519742C23132yes—
169#14519742C23116yes—
170C4×D244C2318yes—
171C4×D244C2318yes—
172C4×C22⋊D61C2318yes—
173C4×C22⋊D61C2318yes—
174C4×C22⋊D61C2318yes—
175C4×C22⋊D61C2318yes—
176#14519736C23116yes—
177#14519736C2318yes—
178#14519735C23116yes—
179#14519735C23132yes—
180#14519735C23116yes—
181#14519735C23116yes—
182#14519734C23132yes—
183#14519734C2318yes—
184#14519734C2318yes—
185C2×C4⋊Dic61C2312yes—
186C2×C4⋊Dic61C2312yes—
187C2×C4⋊Dic61C2312yes—
188C2×C4⋊Dic61C2312yes—
189C2×C4⋊Dic61C2314yes—
190C2×C4⋊Dic61C2311yescharacteristic
191C2×C4⋊Dic61C2311yescharacteristic
192C2×C4⋊Dic61C2314yes—
193C2×C4⋊Dic61C2314yes—
194C2×#11758196C2314yes—
195C2×#11758196C2314yes—
196C2×#11758196C2311yescharacteristic
197C2×#11758196C2311yescharacteristic
198C2×#11758196C2311yescharacteristic
199C2×#11758196C2311yescharacteristic
200C2×#11758196C2314yes—
201C2×#11758196C2314yes—
202C2×#11758196C2314yes—
203C2×#11758196C2314yes—
204C2×#11758196C2314yes—
205C4⋊C4×D61C23116yes—
206C4⋊C4×D61C23116yes—
207C2×C22⋊Dic61C2311yescharacteristic
208C2×C22⋊Dic61C2311yescharacteristic
209C2×C22⋊Dic61C2314yes—
210C2×#11758198C2311yescharacteristic
211C2×#11758198C2311yescharacteristic
212C2×#11758198C2314yes—
213C2×#11758198C2311yescharacteristic
214C2×#11758198C2311yescharacteristic
215C2×#11758198C2314yes—
216C2×#11758198C2314yes—
217C2×C4×Dic61C2311yescharacteristic
218C2×C4×Dic61C2311yescharacteristic
219C2×C4×Dic61C2311yescharacteristic
220C2×C4×Dic61C2311yescharacteristic
221C2×C4×Dic61C2311yescharacteristic
222C2×C4×Dic61C2311yescharacteristic
223C2×C4×Dic61C2314yes—
224C2×C4×Dic61C2314yes—
225C2×C4×Dic61C2314yes—
226C2×C4×Dic61C2314yes—
227C42×D61C2318yes—
228C42×D61C2318yes—
229C22×Q8×C61C2312yes—
230C22×Q8×C61C2312yes—
231C23×C4×C61C2311yescharacteristic
232C23×C4×C61C2311yescharacteristic
233C23×C4×C61C2311yescharacteristic
234C4⋊Q8×C61C2318yes—
235C4⋊Q8×C61C2318yes—
236#125×C61C23116yes—
237C22⋊Q8×C61C23116yes—
238C22⋊Q8×C61C23116yes—
239C4×Q8×C61C23116yes—
240C4×Q8×C61C23116yes—
241#117×C61C23116yes—
242C2×C4⋊C4×C61C2312yes—
243C2×C4⋊C4×C61C2312yes—
244C2×C4⋊C4×C61C2312yes—
245C2×C4⋊C4×C61C2312yes—
246C2×C4⋊C4×C61C2314yes—
247C2×C4⋊C4×C61C2314yes—
248C2×C22⋊C4×C61C2314yes—
249C2×C42×C61C2311yescharacteristic
250C2×C42×C61C2318yes—
251C2×C42×C61C2311yescharacteristic
252C2×C42×C61C2314yes—
253C2×C42×C61C2311yescharacteristic
254C2×C42×C61C2311yescharacteristic
255C24×C61C2411yescharacteristic
256C23×D61C2411yescharacteristic
257C23×D61C2411yescharacteristic
258C2×Q8×C61—28no—
259C2×Q8×C61—28no—
260C2×Q8×C61C2418yes—
261C2×Q8×C61C2418yes—
262C22×C4×C61—24no—
263C22×C4×C61—24no—
264C22×C4×C61—24no—
265C22×C4×C61C2414yes—
266C22×C4×C61C2411yescharacteristic
267C22×C4×C61C2414yes—
268C22×C4×C61C2411yescharacteristic
269C22×C4×C61C2411yescharacteristic
270C22×C4×C61C2414yes—
271C22×C4×C61C2414yes—
272C22×C4×C61C2414yes—
273C22×C4×C61C2411yescharacteristic
274C22×C4×C61C2411yescharacteristic
275C22×C4×C61C2411yescharacteristic
276C2×C22⋊D61—24no—
277C2×C22⋊D61—24no—
278C2×C22⋊D61C2414yes—
279C2×C22⋊D61C2414yes—
280C22×Dic61C2411yescharacteristic
281C22×Dic61C2414yes—
282C22×Dic61C2411yescharacteristic
283C22×Dic61C2411yescharacteristic
284C22×Dic61C2411yescharacteristic
285C22×Dic61C2411yescharacteristic
286C22×Dic61C2414yes—
287C22×Dic61C2411yescharacteristic
288Q8×D61—264no—
289#11758222—232no—
290C2×D244—24no—
291C2×D244C2414yes—
292C2×C4×D61—216no—
293C2×C4×D61—24no—
294C2×C4×D61—24no—
295C2×C4×D61—24no—
296C2×C4×D61—24no—
297C2×C4×D61—24no—
298C2×C4×D61#4118yes—
299C2×C4×D61C24116yes—
300C2×C4×D61C2414yes—
301C2×C4×D61C2414yes—
302C2×C4×D61C2414yes—
303C2×C4×D61C2414yes—
304C2×C4×D61C2414yes—
305C2×C4×D61C2414yes—
306C2×Dic122—28no—
307C2×Dic122—28no—
308C2×Dic122—216no—
309C2×Dic122—24no—
310C2×Dic122C2418yes—
311C2×Dic122C24116yes—
312C2×Dic122C2414yes—
313C2×Dic122C2418yes—
314C4⋊C4×C61C2418yes—
315C4⋊C4×C61C2418yes—
316C4⋊C4×C61C24116yes—
317C4⋊C4×C61C24116yes—
318C4⋊C4×C61C2418yes—
319C4⋊C4×C61C2418yes—
320C22⋊C4×C61C24116yes—
321C42×C61C2414yes—
322C42×C61C2414yes—
323C42×C61C2414yes—
324C42×C61C2414yes—
325C42×C61C24116yes—
326C22⋊Dic61C2414yes—
327C22⋊Dic61C2414yes—
328C22⋊Dic61C24116yes—
329#11758198C2414yes—
330#11758198C2414yes—
331#11758198C24116yes—
332#11758198C2414yes—
333#11758198C2414yes—
334#11758198C24116yes—
335#11758198C24116yes—
336C4⋊Dic61C2418yes—
337C4⋊Dic61C2418yes—
338C4⋊Dic61C2418yes—
339C4⋊Dic61C2418yes—
340C4⋊Dic61C24116yes—
341C4⋊Dic61C2414yes—
342C4⋊Dic61C2414yes—
343C4⋊Dic61C24116yes—
344C4⋊Dic61C24116yes—
345#11758196C24116yes—
346#11758196C24116yes—
347#11758196C2414yes—
348#11758196C2414yes—
349#11758196C2414yes—
350#11758196C2414yes—
351#11758196C24116yes—
352#11758196C24116yes—
353#11758196C24116yes—
354#11758196C24116yes—
355#11758196C24116yes—
356C4×Dic61C2414yes—
357C4×Dic61C2414yes—
358C4×Dic61C2414yes—
359C4×Dic61C2414yes—
360C4×Dic61C2414yes—
361C4×Dic61C2414yes—
362C4×Dic61C24116yes—
363C4×Dic61C24116yes—
364C4×Dic61C24116yes—
365C4×Dic61C24116yes—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61C2512yes—
370C23×C61C2511yescharacteristic
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61C2×#4114yes—
377C22×D61C2512yes—
378C22×D61C2512yes—
379Q8×C61—216no—
380Q8×C61—216no—
381C2×C4×C61—28no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—28no—
386C2×C4×C61—28no—
387C2×C4×C61—28no—
388C2×C4×C61—28no—
389C2×C4×C61C2×#4114yes—
390C2×C4×C612−1+414yes—
391C2×C4×C612−1+414yes—
392C2×C4×C61C2512yes—
393C2×C4×C61C2518yes—
394C2×C4×C61C2518yes—
395C2×C4×C61C2512yes—
396C2×C4×C61C2512yes—
397C2×C4×C61C2512yes—
398C2×C4×C61C2512yes—
399C2×C4×C61C2512yes—
400C22⋊D61—28no—
401C22⋊D61—28no—
402C2×Dic61—28no—
403C2×Dic61—22no—
404C2×Dic61—28no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61C2×#4114yes—
410C2×Dic61C2512yes—
411C2×Dic61C2512yes—
412C2×Dic61C2518yes—
413C2×Dic61C2512yes—
414C2×Dic61C2512yes—
415C2×Dic61C2512yes—
416C2×Dic61C2518yes—
417C2×Dic61C2512yes—
418D244—28no—
419C4×D61—232no—
420C4×D61—28no—
421C4×D61—28no—
422C4×D61—28no—
423C4×D61—28no—
424C4×D61—28no—
425C4×D61C2×#41116yes—
426Dic122—216no—
427Dic122—216no—
428Dic122—28no—
429Dic122—232no—
430C2×#3509—611nomaximal, Sylow
431C22×C61—22no—
432C22×C61—22no—
433C22×C61—22no—
434C22×C61—44no—
435C22×C61C22×#4112yes—
436C22×C61C2×2−1+412yes—
437C22×C61C2×2−1+412yes—
438C22×C61C2611yescharacteristic
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—28no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—44no—
446C2×D61C22×#4114yes—
447C4×C61—28no—
448C4×C61—22no—
449C4×C61—22no—
450C4×C61—22no—
451C4×C61—28no—
452C4×C61C22×#4114yes—
453C4×C61C2×2−1+414yes—
454C4×C61C2×2−1+414yes—
455Dic61—28no—
456Dic61—22no—
457Dic61—28no—
458Dic61—22no—
459Dic61—22no—
460Dic61—22no—
461Dic61—22no—
462Dic61C22×#4114yes—
463#3509—6132no—
464C2×#557—612no—
465C2×#557—612no—
466C2×#556—612no—
467C2×#556—612no—
468C2×#552—612no—
469C2×#552—612no—
470C2×#552—612no—
471C2×#552—612no—
472C2×#541—612no—
473C2×#541—612no—
474C2×#536—612no—
475C2×#533—611no—
476C2×#533—611no—
477C2×#533—611no—
478C2×#533—611no—
479C2×#533D6111yescharacteristic, complemented
480C22×C4⋊Q8—611no—
481C2×#519—612no—
482C2×C4×#41—611no—
483C2×C61—42no—
484C2×C61#350914yescomplemented
485C2×C61C23×#4111yescharacteristic
486C2×C61C22×2−1+411yescharacteristic
487C2×C61C22×2−1+411yescharacteristic
488D61—24no—
489D61—42no—
490C22×#41—611no—
491C23×Q8—612no—
492#557—6132no—
493#557—6132no—
494#556—6132no—
495#556—6132no—
496#552—6132no—
497#552—6132no—
498#552—6132no—
499#552—6132no—
500#541—6132no—
501#541—6132no—
502#536—6132no—
503#533—6116no—
504#533—6116no—
505#533—6116no—
506#533—6116no—
507#533C2×D61116yescomplemented
508C2×C4⋊Q8—612no—
509C2×C4⋊Q8—6116no—
510C2×C4⋊Q8—612no—
511C2×C4⋊Q8—612no—
512C2×C4⋊Q8—614no—
513C2×C4⋊Q8—611no—
514C2×C4⋊Q8—611no—
515C2×C4⋊Q8C2×D6111yescharacteristic
516C2×C4⋊Q8C2×D6111yescharacteristic
517C2×#126—614no—
518C2×#126—614no—
519C2×#126—614no—
520C2×#126—614no—
521C2×#125—614no—
522C2×#125—614no—
523C2×#125—612no—
524C2×#125—612no—
525C2×#125—612no—
526C2×#125—614no—
527C2×#125—612no—
528C2×#125—614no—
529C2×#125C2×D6112yes—
530C2×#124—614no—
531C2×#123—614no—
532C2×#123—614no—
533C2×C22⋊Q8—612no—
534C2×C22⋊Q8—612no—
535C2×C22⋊Q8—612no—
536C2×C22⋊Q8—612no—
537C2×C22⋊Q8—612no—
538C2×C22⋊Q8—612no—
539C2×C22⋊Q8—612no—
540C2×C22⋊Q8—612no—
541C2×C22⋊Q8C2×D6112yes—
542C2×C22⋊Q8C2×D6112yes—
543#519—6132no—
544C4×#41—6116no—
545C2×C4×Q8—612no—
546C2×C4×Q8—612no—
547C2×C4×Q8—612no—
548C2×C4×Q8—612no—
549C2×C4×Q8—614no—
550C2×C4×Q8—612no—
551C2×C4×Q8—612no—
552C2×C4×Q8—611no—
553C2×C4×Q8—611no—
554C2×C4×Q8—612no—
555C2×C4×Q8—614no—
556C2×C4×Q8—612no—
557C2×C4×Q8C2×D6112yes—
558C2×C4×Q8C2×D6112yes—
559C2×C4×D4—611no—
560C2×C4×D4—611no—
561C2×C4×D4—611no—
562C2×C4×D4—611no—
563C2×C4×D4—611no—
564C2×C4×D4—611no—
565C2×#117—611no—
566C2×#117—612no—
567C2×#117—612no—
568C2×#117—614no—
569C2×#117—612no—
570C2×#117—612no—
571C2×#117—611no—
572C2×#117—611no—
573C2×#117—614no—
574C2×#117C2×D6112yes—
575C22×C4⋊C4—612no—
576C22×C4⋊C4—612no—
577C22×C42—611no—
578C22×C42—611no—
579C22×C42C2×D6111yescharacteristic
580C61C2×#350911yescharacteristic, complemented, Sylow
581C2×#41—618no—
582C2×#41—1228no—
583C22×Q8—6116no—
584C22×Q8—612no—
585C22×Q8—612no—
586C22×Q8—614no—
587C22×Q8—611no—
588C22×Q8—12216no—
589C22×Q8C22×D6112yes—
590C22×Q8C22×D6112yes—
591C22×D4—611no—
592C22×D4—611no—
593C22×D4—611no—
594C23×C4—611no—
595C23×C4—614no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4C22×D6111yescharacteristic
602C23×C4C22×D6111yescharacteristic
603C23×C4C22×D6111yescharacteristic
604C4⋊Q8—6116no—
605C4⋊Q8—6116no—
606C4⋊Q8—6116no—
607C4⋊Q8—6132no—
608C4⋊Q8—618no—
609C4⋊Q8—618no—
610C4⋊Q8C22×D6118yes—
611C4⋊Q8C22×D6118yes—
612#126—6132no—
613#126—6132no—
614#126—6132no—
615#126—6132no—
616#125—6116no—
617#125—6116no—
618#125—6116no—
619#125—6132no—
620#125—6132no—
621#125—6132no—
622#125—6116no—
623#125—6132no—
624#125C22×D61116yes—
625#124—6132no—
626#123—6132no—
627#123—6132no—
628C22⋊Q8—6116no—
629C22⋊Q8—6116no—
630C22⋊Q8—6116no—
631C22⋊Q8—6116no—
632C22⋊Q8—6116no—
633C22⋊Q8—6116no—
634C22⋊Q8—6116no—
635C22⋊Q8—6116no—
636C22⋊Q8C22×D61116yes—
637C22⋊Q8C22×D61116yes—
638C4×Q8—6116no—
639C4×Q8—6116no—
640C4×Q8—6116no—
641C4×Q8—6116no—
642C4×Q8—6132no—
643C4×Q8—6116no—
644C4×Q8—6116no—
645C4×Q8—618no—
646C4×Q8—618no—
647C4×Q8—6116no—
648C4×Q8—6132no—
649C4×Q8—6116no—
650C4×Q8C22×D61116yes—
651C4×Q8C22×D61116yes—
652C4×D4—618no—
653C4×D4—618no—
654C4×D4—618no—
655C4×D4—618no—
656C4×D4—618no—
657C4×D4—618no—
658#117—618no—
659#117—6116no—
660#117—6116no—
661#117—6132no—
662#117—6116no—
663#117—6116no—
664#117—618no—
665#117—618no—
666#117—6132no—
667#117C22×D61116yes—
668C2×C4⋊C4—612no—
669C2×C4⋊C4—612no—
670C2×C4⋊C4—614no—
671C2×C4⋊C4—614no—
672C2×C4⋊C4—612no—
673C2×C4⋊C4—611no—
674C2×C4⋊C4—611no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—611no—
679C2×C4⋊C4—612no—
680C2×C4⋊C4—614no—
681C2×C4⋊C4—614no—
682C2×C4⋊C4—614no—
683C2×C4⋊C4—614no—
684C2×C4⋊C4—614no—
685C2×C4⋊C4—614no—
686C2×C4⋊C4—614no—
687C2×C4⋊C4—614no—
688C2×C4⋊C4—6116no—
689C2×C4⋊C4—6116no—
690C2×C4⋊C4C22×D6112yes—
691C2×C4⋊C4C22×D6112yes—
692C2×C4⋊C4C22×D6112yes—
693C2×C4⋊C4C22×D6112yes—
694C2×C4⋊C4C22×D6114yes—
695C2×C4⋊C4C22×D6114yes—
696C2×C22⋊C4—611no—
697C2×C22⋊C4—611no—
698C2×C22⋊C4—614no—
699C2×C22⋊C4—611no—
700C2×C22⋊C4—611no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—611no—
703C2×C22⋊C4—611no—
704C2×C22⋊C4—614no—
705C2×C22⋊C4—614no—
706C2×C22⋊C4C22×D6114yes—
707C2×C42—611no—
708C2×C42—614no—
709C2×C42—614no—
710C2×C42—614no—
711C2×C42—611no—
712C2×C42—614no—
713C2×C42—611no—
714C2×C42—611no—
715C2×C42—611no—
716C2×C42—611no—
717C2×C42—618no—
718C2×C42—618no—
719C2×C42C22×D6111yescharacteristic
720C2×C42C22×D6114yes—
721C2×C42C22×D6111yescharacteristic
722C2×C42C22×D6111yescharacteristic
723C2×C42C22×D6118yes—
724C2×C42C22×D6111yescharacteristic
725C24—611no—
726C24—611no—
727C24C23×D6111yescharacteristic
728#41—12232no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—618no—
732C2×Q8—618no—
733C2×Q8—6116no—
734C2×Q8—614no—
735C2×Q8—12216no—
736C2×Q8—1224no—
737C2×Q8—12264no—
738C2×Q8—1228no—
739C2×Q8—1228no—
740C2×Q8C23×D6118yes—
741C2×Q8C23×D6118yes—
742C2×D4—614no—
743C2×D4—614no—
744C2×D4—614no—
745C2×D4—1224no—
746C2×D4—1224no—
747C2×D4—1224no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—611no—
752C22×C4—618no—
753C22×C4—614no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—614no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—614no—
760C22×C4—611no—
761C22×C4—614no—
762C22×C4—614no—
763C22×C4—614no—
764C22×C4—614no—
765C22×C4—614no—
766C22×C4—6116no—
767C22×C4—12216no—
768C22×C4—1224no—
769C22×C4—1224no—
770C22×C4—1224no—
771C22×C4—1224no—
772C22×C4—1224no—
773C22×C4C23×D6114yes—
774C22×C4C23×D6114yes—
775C22×C4C23×D6114yes—
776C22×C4C23×D6111yescharacteristic
777C22×C4C23×D6114yes—
778C22×C4C23×D6114yes—
779C22×C4C23×D6111yescharacteristic
780C22×C4C23×D6111yescharacteristic
781C22×C4C23×D6111yescharacteristic
782C22×C4C23×D6111yescharacteristic
783C22×C4C23×D6111yescharacteristic
784C4⋊C4—6116no—
785C4⋊C4—6116no—
786C4⋊C4—618no—
787C4⋊C4—618no—
788C4⋊C4—614no—
789C4⋊C4—614no—
790C4⋊C4—614no—
791C4⋊C4—614no—
792C4⋊C4—6116no—
793C4⋊C4—6116no—
794C4⋊C4—6116no—
795C4⋊C4—6116no—
796C4⋊C4—6116no—
797C4⋊C4—618no—
798C4⋊C4—614no—
799C4⋊C4—614no—
800C4⋊C4—618no—
801C4⋊C4—6116no—
802C4⋊C4—6116no—
803C4⋊C4—6116no—
804C4⋊C4C23×D6118yes—
805C4⋊C4C23×D6118yes—
806C4⋊C4C23×D6118yes—
807C4⋊C4C23×D6118yes—
808C4⋊C4C23×D61116yes—
809C4⋊C4C23×D61116yes—
810C22⋊C4—614no—
811C22⋊C4—614no—
812C22⋊C4—6116no—
813C22⋊C4—614no—
814C22⋊C4—614no—
815C22⋊C4—6116no—
816C22⋊C4—614no—
817C22⋊C4—614no—
818C22⋊C4—6116no—
819C22⋊C4—6116no—
820C22⋊C4C23×D61116yes—
821C42—614no—
822C42—614no—
823C42—614no—
824C42—614no—
825C42—614no—
826C42—614no—
827C42—6116no—
828C42—6116no—
829C42—6116no—
830C42—6116no—
831C42C23×D6114yes—
832C42C23×D6114yes—
833C42C23×D6114yes—
834C42C23×D6114yes—
835C42C23×D61116yes—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—614no—
840C23—612no—
841C23—612no—
842C23—1222no—
843C23—1222no—
844C23—1222no—
845C23—1222no—
846C23—1222no—
847C23C24×D6112yes—
848C23C24×D6111yescharacteristic
849Q8—216no—
850Q8—216no—
851Q8—12232no—
852Q8—1228no—
853Q8—12216no—
854Q8—12216no—
855D4—1228no—
856D4—1228no—
857D4—1228no—
858C2×C4—22no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—22no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—614no—
867C2×C4—612no—
868C2×C4—6116no—
869C2×C4—612no—
870C2×C4—612no—
871C2×C4—618no—
872C2×C4—612no—
873C2×C4—612no—
874C2×C4—618no—
875C2×C4—612no—
876C2×C4—12232no—
877C2×C4—1222no—
878C2×C4—1228no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1228no—
884C2×C4—1228no—
885C2×C4—1228no—
886C2×C4—1228no—
887C2×C4—1228no—
888C2×C4—1228no—
889C2×C4#41×D6114yes—
890C2×C4#1451982414yes—
891C2×C4#1451982514yes—
892C2×C4C24×D6112yes—
893C2×C4C24×D6118yes—
894C2×C4C24×D6118yes—
895C2×C4C24×D6112yes—
896C2×C4C24×D6112yes—
897C2×C4C24×D6112yes—
898C2×C4C24×D6112yes—
899C2×C4C24×D6112yes—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—44no—
904C22—614no—
905C22—1222no—
906C22—1222no—
907C22—1228no—
908C22—1222no—
909C22—1222no—
910C22—1222no—
911C22—2444no—
912C22C2×#41×D6112yes—
913C22C2×#1451982412yes—
914C22C2×#1451982512yes—
915C22C25×D6111yescharacteristic
916C4—22no—
917C4—28no—
918C4—22no—
919C4—28no—
920C4—22no—
921C4—614no—
922C4—1222no—
923C4—1228no—
924C4—1222no—
925C4—1222no—
926C4—1222no—
927C4—1222no—
928C4—1228no—
929C4C2×#41×D6114yes—
930C4C2×#1451982414yes—
931C4C2×#1451982514yes—
932C2—42no—
933C2—1224no—
934C2—2442no—
935C2#2145969814yesdirect product factor
936C2C22×#41×D6111yescharacteristic
937C2C22×#1451982411yescharacteristic
938C2C22×#1451982511yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#533C2
socleC23×C61C25
prime radicalC22×#11758222C22
hypercenterC2×#533D61
hypocenterC61C2×#3509
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #21459698C2direct (N × H)
2. C2×#16840489C2semidirect
3. C2×#16840488C2semidirect
4. C2×#16840483C2semidirect
5. C2×#16840480C2semidirect
6. C2×#16840453C2semidirect
7. C2×#16840451C2semidirect
8. C2×#16840450C2semidirect
9. C2×#16840446C2semidirect
10. C2×#16840372C2semidirect
11. C2×#16840370C2semidirect
13. C2×#16840319C2semidirect
14. C2×#16840317C2semidirect
15. C2×#16840317C2semidirect
16. C2×#16840317C2semidirect
17. C2×C4⋊Q8×D61C2semidirect
18. C2×#16840238C2semidirect
20. C2×C61×#533C2semidirect
23. #16840489C22semidirect
24. #16840488C22semidirect
25. #16840483C22semidirect
26. #16840480C22semidirect
27. #16840453C22semidirect
28. #16840451C22semidirect
29. #16840450C22semidirect
30. #16840446C22semidirect
31. #16840372C22semidirect
32. #16840370C22semidirect
34. #16840319C22semidirect
35. #16840317C22semidirect
36. #16840317C22semidirect
37. #16840317C22semidirect
44. C4⋊Q8×D61C22semidirect
68. #16840238C22semidirect
101. C61×#533C22semidirect
479. C2×#533D61semidirect
484. C2×C61#3509semidirect
507. #533C2×D61semidirect
580. C61C2×#3509semidirect
935. C2#21459698direct (N × H)

Maximal subgroups

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

subgroupindex
#214596982
C2×#168404892
C2×#168404882
C2×#168404832
C2×#168404802
C2×#168404532
C2×#168404512
C2×#168404502
C2×#168404462
C2×#168403722
C2×#168403702
C2×#168403352
C2×#168403192
C2×#168403172
C2×C4⋊Q8×D612
C2×#168402382
C2×C4×#117582222
C2×C61×#5332
C2×#350961