Finite Group Databasebeta

← C2×#21459306 #30586972

Subgroups — C2×#21459306 #30586972

Order 15616.

12314 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D61C212yesmaximal, complemented
2#21459306C2132yesmaximal, direct product factor
3C2×#16840433C211yesmaximal, characteristic, complemented
4C2×#16840427C211yesmaximal, characteristic, complemented
5C2×#16840422C212yesmaximal, complemented
6C2×#16840413C212yesmaximal, complemented
7C2×#16840404C214yesmaximal, complemented
8C2×#16840400C212yesmaximal, complemented
9C2×D4×D244C211yesmaximal, characteristic, complemented
10C2×#16840396C212yesmaximal, complemented
11C2×#16840313C211yesmaximal, characteristic, complemented
12C2×#16840307C212yesmaximal, complemented
13C2×#16840275C212yesmaximal, complemented
14C2×#16840270C214yesmaximal, complemented
15C2×C4×#11758224C211yesmaximal, characteristic, complemented
16C22×#14519739C212yesmaximal, complemented
17C2×C4×D4×D61C211yesmaximal, characteristic, complemented
18C2×C61×#547C211yesmaximal, characteristic, complemented
19C22×#11758226C2212yescomplemented
20C22×#11758222C2214yescomplemented
21C22×#11758222C2212yescomplemented
22C22×#11758224C2211yescharacteristic
23C22×#11758224C2214yescomplemented
24C2×#41×D61—232no—
25C2×#41×D61C22132yescomplemented
26C22×Q8×D61C2212yescomplemented
27C23×D244C2212yes—
28C22×D4×D61C2211yescharacteristic
29C22×D4×D61C2214yescomplemented
30C22×D4×D61C2212yescomplemented
31C23×C4×D61C2212yescomplemented
32C23×C4×D61C2214yescomplemented
33#16840433C22116yescomplemented
34#16840427C22116yescomplemented
35#16840422C22132yescomplemented
36#16840413C22132yescomplemented
37#16840404C22164yescomplemented
38#16840400C22132yescomplemented
39D4×D244C22116yescomplemented
40#16840396C22132yescomplemented
41#16840313C22116yescomplemented
42#16840307C22132yescomplemented
43C2×#14519776C2212yescomplemented
44C2×#14519774C2211yescharacteristic, complemented
45C2×#14519773C2212yescomplemented
46C2×#14519766C2212yescomplemented
47C2×#14519763C2214yescomplemented
48#16840275C22132yescomplemented
49#16840270C22164yescomplemented
50C2×#14519762C2214yescomplemented
51C2×#14519760C2214yescomplemented
52C2×#14519755C2214yescomplemented
53C2×#14519755C2214yescomplemented
54C2×#14519753C2212yescomplemented
55C2×#14519752C2212yescomplemented
56C2×#14519752C2212yescomplemented
57C2×#14519752C2212yescomplemented
58C2×#14519751C2212yescomplemented
59C2×#14519751C2212yescomplemented
60C2×#14519750C2214yescomplemented
61C2×#14519750C2214yescomplemented
62C2×#14519749C2214yescomplemented
63C2×#14519747C2214yescomplemented
64C2×#14519747C2214yescomplemented
65C2×#14519745C2214yescomplemented
66C4×#11758224C22116yescomplemented
67C2×C4×Dic122C2211yescharacteristic, complemented
68C2×#14519742C2211yescharacteristic, complemented
69C2×C4×D244C2211yescharacteristic
70C2×D4×Dic61C2211yescharacteristic, complemented
71C2×D4×Dic61C2211yescharacteristic, complemented
72C2×#14519739C2211yescharacteristic
73C2×#14519739C2212yes—
74C2×#14519739C2214yescomplemented
75C2×#14519739C2212yescomplemented
76C2×#14519739C2214yescomplemented
77C2×#14519739C2212yescomplemented
78C2×#14519739C2212yescomplemented
79C2×#14519739C22132yescomplemented
80C2×C4×C22⋊D61C2212yescomplemented
81C2×C4×C22⋊D61C2212yescomplemented
82C2×#14519737C2212yescomplemented
83C2×#14519737C2212yescomplemented
84C2×#14519737C2214yescomplemented
85C4×D4×D61C22116yescomplemented
86C2×#14519735C2211yescharacteristic, complemented
87C2×#14519733C2212yescomplemented
88C2×C4⋊C4×D61C2211yescharacteristic, complemented
89C22×#11758198C2214yescomplemented
90C2×C22⋊C4×D61C2212yescomplemented
91C22×C4×Dic61C2212yescomplemented
92C2×C42×D61C2211yescharacteristic, complemented
93C22×#41×C61C2212yescomplemented
94C61×#547C22116yescomplemented
95C2×C4⋊Q8×C61C2211yescharacteristic, complemented
96C2×#123×C61C2214yescomplemented
97C2×C22⋊Q8×C61C2212yescomplemented
98C2×#121×C61C2212yescomplemented
99C2×C4×D4×C61C2211yescharacteristic, complemented
100C2×C4×D4×C61C2211yescharacteristic, complemented
101C22×C4⋊C4×C61C2212yescomplemented
102C24×D61C2312yes—
103C24×D61C2314yes—
104C2×#11758226—216no—
105C2×#11758226C23116yescomplemented
106C2×#11758222—232no—
107C2×#11758222—216no—
108C2×#11758222C23132yescomplemented
109C2×#11758222C23116yescomplemented
110C2×#11758224—232no—
111C2×#11758224D4116yescomplemented
112C2×#11758224C2318yes—
113C2×#11758224C23132yescomplemented
114#41×D61—2256no—
115C22×Dic122C2314yes—
116C22×Dic122C2311yescharacteristic
117C2×Q8×D61—216no—
118C2×Q8×D61C23116yescomplemented
119C22×D244—216no—
120C22×D244C2314yes—
121C22×D244C2312yes—
122C22×D244C23116yes—
123C22×D244C2314yes—
124C22×D244C2312yes—
125C22×D244C2312yes—
126C22×D244C2311yescharacteristic
127C22×C22⋊D61C2312yes—
128C22×C22⋊D61C2314yes—
129C22×C22⋊D61C2314yes—
130C22×C22⋊D61C2314yes—
131C22×C22⋊D61C2312yes—
132C2×D4×D61—216no—
133C2×D4×D61—232no—
134C2×D4×D61—28no—
135C2×D4×D61C2318yes—
136C2×D4×D61C23132yescomplemented
137C2×D4×D61C23116yescomplemented
138C23×Dic61C2312yes—
139C23×Dic61C2312yes—
140C23×Dic61C2312yes—
141C22×C4×D61—232no—
142C22×C4×D61—216no—
143C22×C4×D61C2311yescharacteristic
144C22×C4×D61C2312yes—
145C22×C4×D61C2312yes—
146C22×C4×D61C2314yes—
147C22×C4×D61C2312yes—
148C22×C4×D61C2314yes—
149C22×C4×D61C2314yes—
150C22×C4×D61C2311yescharacteristic
151C22×C4×D61C2311yescharacteristic
152C22×C4×D61C23116yescomplemented
153C22×C4×D61C23132yescomplemented
154#14519776C23116yescomplemented
155#14519774C2318yescomplemented
156#14519773C23116yescomplemented
157#14519766C23116yescomplemented
158#14519763C23132yescomplemented
159#14519762C23132yescomplemented
160#14519760C23132yescomplemented
161#14519755C23132yescomplemented
162#14519755C23132yescomplemented
163#14519753C23116yescomplemented
164#14519752C23116yescomplemented
165#14519752C23116yescomplemented
166#14519752C23116yescomplemented
167#14519751C23116yescomplemented
168#14519751C23116yescomplemented
169#14519750C23132yescomplemented
170#14519750C23132yescomplemented
171#14519749C23132yescomplemented
172#14519747C23132yescomplemented
173#14519747C23132yescomplemented
174#14519745C23132yescomplemented
175C4×Dic122C2318yescomplemented
176#14519742C2318yescomplemented
177C4×D244C2318yes—
178D4×Dic61C2318yescomplemented
179D4×Dic61C2318yescomplemented
180#14519739C2318yes—
181#14519739C23116yes—
182#14519739C23132yescomplemented
183#14519739C23116yescomplemented
184#14519739C23132yescomplemented
185#14519739C23116yescomplemented
186#14519739C23116yescomplemented
187C4×C22⋊D61C23116yescomplemented
188C4×C22⋊D61C23116yescomplemented
189#14519737C23116yescomplemented
190#14519737C23116yescomplemented
191#14519737C23132yescomplemented
192#14519735C2318yescomplemented
193#14519733C23116yescomplemented
194C2×C4⋊Dic61C2311yescharacteristic
195C2×C4⋊Dic61C2311yescharacteristic
196C2×#11758196C2312yes—
197C2×#11758196C2312yes—
198C2×#11758196C2312yes—
199C2×#11758196C2314yes—
200C4⋊C4×D61C2318yescomplemented
201C2×C22⋊Dic61C2312yes—
202C2×C22⋊Dic61C2312yes—
203C2×#11758198C2312yes—
204C2×#11758198C2312yes—
205C2×#11758198C2314yes—
206C2×#11758198C2314yes—
207C2×#11758198C2314yes—
208C2×#11758198C2312yes—
209C2×#11758198C2314yes—
210C2×#11758198C2314yes—
211C2×#11758198C23132yescomplemented
212C22⋊C4×D61C23116yescomplemented
213C2×C4×Dic61C2311yescharacteristic
214C2×C4×Dic61C2311yescharacteristic
215C2×C4×Dic61C2311yescharacteristic
216C2×C4×Dic61C2312yes—
217C2×C4×Dic61C2312yes—
218C2×C4×Dic61C2312yes—
219C2×C4×Dic61C23116yescomplemented
220C42×D61C2318yescomplemented
221C2×#41×C61—216no—
222C2×#41×C61C23116yescomplemented
223C22×Q8×C61C2312yes—
224C22×D4×C61C2311yescharacteristic
225C22×D4×C61C2314yes—
226C22×D4×C61C2311yescharacteristic
227C23×C4×C61C2312yes—
228C23×C4×C61C2314yes—
229C23×C4×C61C2312yes—
230C4⋊Q8×C61C2318yescomplemented
231#123×C61C23132yescomplemented
232C22⋊Q8×C61C23116yescomplemented
233#121×C61C23116yescomplemented
234C4×D4×C61C2318yescomplemented
235C4×D4×C61C2318yescomplemented
236C2×C4⋊C4×C61C2312yes—
237C2×C4⋊C4×C61C2312yes—
238C2×C4⋊C4×C61C2311yescharacteristic
239C2×C4⋊C4×C61C2311yescharacteristic
240C2×C4⋊C4×C61C2314yes—
241C2×C4⋊C4×C61C23116yescomplemented
242C2×C22⋊C4×C61C2312yes—
243C2×C22⋊C4×C61C2312yes—
244C2×C22⋊C4×C61C2314yes—
245C2×C42×C61C2311yescharacteristic
246C24×C61C2412yes—
247C24×C61C2412yes—
248C23×D61—216no—
249C23×D61—28no—
250C23×D61—28no—
251C23×D61—216no—
252C23×D61—44no—
253C23×D61—48no—
254C23×D61C2414yes—
255C23×D61C2418yes—
256C23×D61C24116yes—
257C23×D61C2411yescharacteristic
258C23×D61C2412yes—
259#41×C61—264no—
260C2×Q8×C61—28no—
261C2×Q8×C61C2418yes—
262C2×D4×C61—216no—
263C2×D4×C61—24no—
264C2×D4×C61C2×D418yescomplemented
265C2×D4×C61C2414yes—
266C2×D4×C61C24116yes—
267C2×D4×C61C2414yes—
268C22×C4×C61—216no—
269C22×C4×C61—28no—
270C22×C4×C61—28no—
271C22×C4×C61C2412yes—
272C22×C4×C61C2414yes—
273C22×C4×C61C2411yescharacteristic
274C22×C4×C61C24116yes—
275C22×C4×C61C2418yes—
276C22×C4×C61C2412yes—
277C22×C4×C61C2418yes—
278C22×C4×C61C2411yescharacteristic
279C22×C4×C61C2411yescharacteristic
280C2×C22⋊D61—216no—
281C2×C22⋊D61—28no—
282C2×C22⋊D61—216no—
283C2×C22⋊D61—48no—
284C2×C22⋊D61C2×D4116yescomplemented
285C2×C22⋊D61C2418yes—
286C2×C22⋊D61C24116yes—
287C2×C22⋊D61C24116yes—
288C2×C22⋊D61C24116yes—
289C2×C22⋊D61C2418yes—
290C22×Dic61—28no—
291C22×Dic61—44no—
292C22×Dic61C2×D4116yescomplemented
293C22×Dic61C2412yes—
294C22×Dic61C2411yescharacteristic
295C22×Dic61C2411yescharacteristic
296C22×Dic61C2418yes—
297C22×Dic61C2412yes—
298C22×Dic61C2418yes—
299C22×Dic61C2411yescharacteristic
300C22×Dic61C2412yes—
301C22×Dic61C2418yes—
302#11758226—264no—
303Q8×D61—264no—
304#11758224—2128no—
305#11758224C2×D4164yescomplemented
306D4×D61—264no—
307D4×D61—2128no—
308D4×D61—232no—
309#11758222—2128no—
310#11758222—264no—
311C2×D244—216no—
312C2×D244—216no—
313C2×D244—28no—
314C2×D244—28no—
315C2×D244—264no—
316C2×D244—44no—
317C2×D244#4118yescomplemented
318C2×D244C24116yes—
319C2×D244C2418yes—
320C2×D244C24116yes—
321C2×D244C2418yes—
322C2×D244C2418yes—
323C2×D244C2414yes—
324C2×C4×D61—28no—
325C2×C4×D61—28no—
326C2×C4×D61—24no—
327C2×C4×D61—28no—
328C2×C4×D61—216no—
329C2×C4×D61—216no—
330C2×C4×D61—216no—
331C2×C4×D61—2128no—
332C2×C4×D61—264no—
333C2×C4×D61—42no—
334C2×C4×D61C2×D418yescomplemented
335C2×C4×D61C2418yes—
336C2×C4×D61C2418yes—
337C2×C4×D61C24116yes—
338C2×C4×D61C24116yes—
339C2×C4×D61C2418yes—
340C2×C4×D61C24116yes—
341C2×C4×D61C2414yes—
342C2×C4×D61C2414yes—
343C2×C4×D61C2414yes—
344C2×Dic122—216no—
345C2×Dic122C2×D418yescomplemented
346C2×Dic122C24116yes—
347C2×Dic122C2414yes—
348C4⋊C4×C61C2414yes—
349C4⋊C4×C61C2418yes—
350C4⋊C4×C61C24116yes—
351C4⋊C4×C61C2414yes—
352C4⋊C4×C61C2418yes—
353C22⋊C4×C61C2418yes—
354C22⋊C4×C61C2418yes—
355C22⋊C4×C61C24116yes—
356C42×C61C2414yes—
357C22⋊Dic61C2418yes—
358C22⋊Dic61C2418yes—
359#11758198C2418yes—
360#11758198C2418yes—
361#11758198C24116yes—
362#11758198C24116yes—
363#11758198C24116yes—
364#11758198C2418yes—
365#11758198C24116yes—
366#11758198C24116yes—
367C4⋊Dic61C2414yes—
368C4⋊Dic61C2414yes—
369#11758196C2418yes—
370#11758196C2418yes—
371#11758196C2418yes—
372#11758196C24116yes—
373C4×Dic61C2414yes—
374C4×Dic61C2414yes—
375C4×Dic61C2414yes—
376C4×Dic61C2418yes—
377C4×Dic61C2418yes—
378C4×Dic61C2418yes—
379C23×C61—24no—
380C23×C61—24no—
381C23×C61—24no—
382C23×C61—24no—
383C23×C61—24no—
384C23×C61C22×D418yes—
385C23×C61C2514yes—
386C23×C61C2514yes—
387C23×C61C2511yescharacteristic
388C22×D61—24no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—24no—
392C22×D61—28no—
393C22×D61—232no—
394C22×D61—28no—
395C22×D61—28no—
396C22×D61—216no—
397C22×D61—232no—
398C22×D61—216no—
399C22×D61—48no—
400C22×D61—416no—
401C22×D61—432no—
402C22×D61—464no—
403C22×D61C22×D414yes—
404C22×D61C2×#4118yescomplemented
405C22×D61C2518yes—
406C22×D61C2512yes—
407C22×D61C2514yes—
408Q8×C61—216no—
409D4×C61—232no—
410D4×C61—28no—
411D4×C61C22×D4116yescomplemented
412C2×C4×C61—28no—
413C2×C4×C61—24no—
414C2×C4×C61—232no—
415C2×C4×C61—24no—
416C2×C4×C61—22no—
417C2×C4×C61—216no—
418C2×C4×C61—216no—
419C2×C4×C61C22×D414yes—
420C2×C4×C61C2×#4114yescomplemented
421C2×C4×C61C2514yes—
422C2×C4×C61C2512yes—
423C2×C4×C61C2518yes—
424C2×C4×C61C2514yes—
425C2×C4×C61C2512yes—
426C2×C4×C61C2512yes—
427C22⋊D61—232no—
428C22⋊D61—216no—
429C22⋊D61—232no—
430C22⋊D61—416no—
431C22⋊D61C22×D4132yescomplemented
432C2×Dic61—24no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—24no—
436C2×Dic61—216no—
437C2×Dic61—48no—
438C2×Dic61C22×D418yes—
439C2×Dic61C22×D414yes—
440C2×Dic61C22×D4132yescomplemented
441C2×Dic61C2512yes—
442C2×Dic61C2512yes—
443C2×Dic61C2514yes—
444C2×Dic61C2514yes—
445C2×Dic61C2512yes—
446C2×Dic61C2514yes—
447D244—232no—
448D244—232no—
449D244—216no—
450D244—216no—
451D244—48no—
452D244C2×#41116yescomplemented
453C4×D61—216no—
454C4×D61—216no—
455C4×D61—28no—
456C4×D61—216no—
457C4×D61—232no—
458C4×D61—232no—
459C4×D61—232no—
460C4×D61—44no—
461C4×D61C22×D4116yescomplemented
462Dic122—232no—
463Dic122C22×D4116yescomplemented
464C2×D4×#41—611nomaximal, Sylow
465C22×C61—24no—
466C22×C61—24no—
467C22×C61—216no—
468C22×C61—24no—
469C22×C61—24no—
470C22×C61—24no—
471C22×C61—48no—
472C22×C61C23×D418yes—
473C22×C61C23×D412yes—
474C22×C61C22×#4112yes—
475C22×C61#58512yes—
476C22×C61C2611yescharacteristic
477C2×D61—24no—
478C2×D61—22no—
479C2×D61—22no—
480C2×D61—24no—
481C2×D61—216no—
482C2×D61—28no—
483C2×D61—28no—
484C2×D61—28no—
485C2×D61—28no—
486C2×D61—432no—
487C2×D61—464no—
488C2×D61—416no—
489C2×D61C23×D414yes—
490C2×D61C22×#4118yescomplemented
491C4×C61—28no—
492C4×C61—24no—
493C4×C61—24no—
494C4×C61—22no—
495C4×C61C23×D414yes—
496C4×C61C22×#4114yescomplemented
497Dic61—24no—
498Dic61—22no—
499Dic61—22no—
500Dic61—24no—
501Dic61C23×D418yes—
502Dic61C23×D414yes—
503C23×#41—612no—
504D4×#41—6132no—
505C2×#550—611no—
506C2×D4×Q8—611no—
507C2×#548—612no—
508C2×#547—612no—
509C2×#547D6111yescharacteristic, complemented
510C2×#546—612no—
511C2×#546—614no—
512C2×D42—612no—
513C2×D42—611no—
514C2×#532—611no—
515C2×#532—612no—
516C2×#525—614no—
517C2×#525—612no—
518C2×C4×#41—611no—
519C22×C4×D4—611no—
520C22×C4×D4—612no—
521C2×C61—28no—
522C2×C61—44no—
523C2×C61D4×#4114yescomplemented
524C2×C61C24×D411yescharacteristic
525C2×C61C23×#4111yescharacteristic
526C2×C61C2×#58511yescharacteristic
527D61—28no—
528D61—24no—
529D61—48no—
530C22×#41—6132no—
531C22×#41—612no—
532C22×#41—611no—
533C22×#41—614no—
534C22×#41—614no—
535C22×#41—612no—
536C22×#41—12232no—
537C22×#41C2×D6112yescomplemented
538C23×Q8—612no—
539C23×D4—614no—
540C23×D4—612no—
541C23×D4—611no—
542C23×D4—612no—
543C24×C4—614no—
544C24×C4—612no—
545#550—6116no—
546D4×Q8—6116no—
547#548—6132no—
548#547—6132no—
549#547C2×D61116yescomplemented
550#546—6132no—
551#546—6164no—
552D42—6132no—
553D42—6116no—
554#532—6116no—
555#532—6132no—
556C2×C4⋊Q8—612no—
557C2×C4⋊Q8C2×D6111yescharacteristic, complemented
558C2×#127—612no—
559C2×#127—611no—
560C2×#124—612no—
561C2×#124—614no—
562#525—6164no—
563#525—6132no—
564C2×#123—614no—
565C2×#123—614no—
566C2×#123C2×D6114yescomplemented
567C2×C22⋊Q8—612no—
568C2×C22⋊Q8—614no—
569C2×C22⋊Q8—614no—
570C2×C22⋊Q8C2×D6112yescomplemented
571C2×#121—614no—
572C2×#121—612no—
573C2×#121—612no—
574C2×#121—612no—
575C2×#121—612no—
576C2×#121—612no—
577C2×#121—614no—
578C2×#121—614no—
579C2×#121C2×D6112yescomplemented
580C2×#120—614no—
581C2×#120—614no—
582C2×#120—614no—
583C4×#41—6116no—
584C2×C4×Q8—611no—
585C2×C4×Q8—611no—
586C2×C4×D4—611no—
587C2×C4×D4—611no—
588C2×C4×D4—612no—
589C2×C4×D4—612no—
590C2×C4×D4—6116no—
591C2×C4×D4—611no—
592C2×C4×D4—612no—
593C2×C4×D4—614no—
594C2×C4×D4—612no—
595C2×C4×D4—614no—
596C2×C4×D4—612no—
597C2×C4×D4—612no—
598C2×C4×D4—6132no—
599C2×C4×D4—612no—
600C2×C4×D4—612no—
601C2×C4×D4—614no—
602C2×C4×D4—611no—
603C2×C4×D4C2×D6111yescharacteristic, complemented
604C2×C4×D4C2×D6111yescharacteristic, complemented
605C2×#117—611no—
606C2×#117—612no—
607C22×C4⋊C4—611no—
608C22×C4⋊C4C2×D6112yescomplemented
609C22×C22⋊C4—614no—
610C22×C22⋊C4—612no—
611C22×C42—612no—
612C22×C42—611no—
613C61C2×D4×#4111yescharacteristic, complemented, Sylow
614C25—612no—
615C25—614no—
616C2×#41—216no—
617C2×#41—6116no—
618C2×#41—6116no—
619C2×#41—618no—
620C2×#41—6132no—
621C2×#41—6132no—
622C2×#41—6116no—
623C2×#41—12232no—
624C2×#41—12216no—
625C2×#41—12232no—
626C2×#41—12216no—
627C2×#41—122256no—
628C2×#41C22×D61116yescomplemented
629C22×Q8—6116no—
630C22×Q8—611no—
631C22×Q8—614no—
632C22×Q8—12216no—
633C22×Q8C22×D6112yes—
634C22×D4—612no—
635C22×D4—612no—
636C22×D4—614no—
637C22×D4—614no—
638C22×D4—614no—
639C22×D4—618no—
640C22×D4—6132no—
641C22×D4—6116no—
642C22×D4—611no—
643C22×D4—614no—
644C22×D4—612no—
645C22×D4—6116no—
646C22×D4—614no—
647C22×D4—612no—
648C22×D4—612no—
649C22×D4—12216no—
650C22×D4—1228no—
651C22×D4—12232no—
652C22×D4—12216no—
653C22×D4C22×D6111yescharacteristic
654C22×D4C22×D6114yes—
655C22×D4C22×D6111yescharacteristic
656C23×C4—612no—
657C23×C4—611no—
658C23×C4—612no—
659C23×C4—612no—
660C23×C4—612no—
661C23×C4—611no—
662C23×C4—612no—
663C23×C4—614no—
664C23×C4—614no—
665C23×C4—612no—
666C23×C4—614no—
667C23×C4—6132no—
668C23×C4—6116no—
669C23×C4—611no—
670C23×C4—12232no—
671C23×C4—12216no—
672C23×C4C22×D6114yes—
673C23×C4C22×D6112yes—
674C23×C4C22×D6112yes—
675C4⋊Q8—6116no—
676C4⋊Q8C22×D6118yescomplemented
677#127—6116no—
678#127—618no—
679#124—6116no—
680#124—6132no—
681#123—6132no—
682#123—6132no—
683#123C22×D61132yescomplemented
684C22⋊Q8—6116no—
685C22⋊Q8—6132no—
686C22⋊Q8—6132no—
687C22⋊Q8C22×D61116yescomplemented
688#121—6132no—
689#121—6116no—
690#121—6116no—
691#121—6116no—
692#121—6116no—
693#121—6116no—
694#121—6132no—
695#121—6132no—
696#121C22×D61116yescomplemented
697#120—6132no—
698#120—6132no—
699#120—6132no—
700C4×Q8—618no—
701C4×Q8—618no—
702C4×D4—618no—
703C4×D4—618no—
704C4×D4—6116no—
705C4×D4—6116no—
706C4×D4—618no—
707C4×D4—6132no—
708C4×D4—6116no—
709C4×D4—6116no—
710C4×D4—6132no—
711C4×D4—6116no—
712C4×D4—6116no—
713C4×D4—6116no—
714C4×D4—6116no—
715C4×D4—6132no—
716C4×D4—618no—
717C4×D4C22×D6118yescomplemented
718C4×D4C22×D6118yescomplemented
719#117—618no—
720#117—6116no—
721C2×C4⋊C4—611no—
722C2×C4⋊C4—612no—
723C2×C4⋊C4—612no—
724C2×C4⋊C4—612no—
725C2×C4⋊C4—611no—
726C2×C4⋊C4—614no—
727C2×C4⋊C4—618no—
728C2×C4⋊C4C22×D6111yescharacteristic
729C2×C4⋊C4C22×D6112yes—
730C2×C4⋊C4C22×D6114yes—
731C2×C4⋊C4C22×D6111yescharacteristic
732C2×C4⋊C4C22×D6112yes—
733C2×C4⋊C4C22×D61116yescomplemented
734C2×C22⋊C4—612no—
735C2×C22⋊C4—612no—
736C2×C22⋊C4—612no—
737C2×C22⋊C4—614no—
738C2×C22⋊C4—612no—
739C2×C22⋊C4—614no—
740C2×C22⋊C4—614no—
741C2×C22⋊C4—6132no—
742C2×C22⋊C4—612no—
743C2×C22⋊C4—614no—
744C2×C22⋊C4—614no—
745C2×C22⋊C4—6116no—
746C2×C22⋊C4C22×D6112yes—
747C2×C22⋊C4C22×D6112yes—
748C2×C22⋊C4C22×D6114yes—
749C2×C42—612no—
750C2×C42—611no—
751C2×C42—611no—
752C2×C42—612no—
753C2×C42—611no—
754C2×C42—612no—
755C2×C42—6116no—
756C2×C42—618no—
757C2×C42C22×D6111yescharacteristic
758C24—612no—
759C24—611no—
760C24—614no—
761C24—618no—
762C24—6116no—
763C24—1228no—
764C24—12216no—
765C24—1228no—
766C24—12216no—
767C24—2448no—
768C24—2444no—
769C24C23×D6112yes—
770C24C23×D6112yes—
771#41—264no—
772#41—6164no—
773#41—122128no—
774#41—12264no—
775#41—122128no—
776#41—12264no—
777C2×Q8—28no—
778C2×Q8—618no—
779C2×Q8—614no—
780C2×Q8—6116no—
781C2×Q8—12216no—
782C2×Q8—12264no—
783C2×Q8C23×D6118yes—
784C2×D4—216no—
785C2×D4—24no—
786C2×D4—6116no—
787C2×D4—618no—
788C2×D4—618no—
789C2×D4—6116no—
790C2×D4—6116no—
791C2×D4—6116no—
792C2×D4—618no—
793C2×D4—614no—
794C2×D4—6116no—
795C2×D4—618no—
796C2×D4—6116no—
797C2×D4—618no—
798C2×D4—618no—
799C2×D4—12264no—
800C2×D4—12216no—
801C2×D4—12216no—
802C2×D4—12216no—
803C2×D4—122128no—
804C2×D4—12232no—
805C2×D4—1228no—
806C2×D4—12216no—
807C2×D4—12264no—
808C2×D4—1228no—
809C2×D4—1228no—
810C2×D4—2444no—
811C2×D4—2448no—
812C2×D4D4×D6118yescomplemented
813C2×D4C23×D6114yes—
814C2×D4C23×D61116yes—
815C2×D4C23×D6114yes—
816C22×C4—216no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—6116no—
820C22×C4—618no—
821C22×C4—611no—
822C22×C4—612no—
823C22×C4—618no—
824C22×C4—614no—
825C22×C4—618no—
826C22×C4—611no—
827C22×C4—611no—
828C22×C4—612no—
829C22×C4—612no—
830C22×C4—618no—
831C22×C4—614no—
832C22×C4—618no—
833C22×C4—618no—
834C22×C4—6116no—
835C22×C4—6116no—
836C22×C4—618no—
837C22×C4—6116no—
838C22×C4—614no—
839C22×C4—1228no—
840C22×C4—12216no—
841C22×C4—12216no—
842C22×C4—12216no—
843C22×C4—122128no—
844C22×C4—12264no—
845C22×C4—1228no—
846C22×C4—1228no—
847C22×C4—1228no—
848C22×C4—1224no—
849C22×C4—2442no—
850C22×C4—2444no—
851C22×C4C23×D6118yes—
852C22×C4C23×D61116yes—
853C22×C4C23×D6118yes—
854C22×C4C23×D6112yes—
855C22×C4C23×D6111yescharacteristic
856C22×C4C23×D6112yes—
857C22×C4C23×D6114yes—
858C22×C4C23×D6111yescharacteristic
859C22×C4C23×D6111yescharacteristic
860C4⋊C4—618no—
861C4⋊C4—614no—
862C4⋊C4—618no—
863C4⋊C4—618no—
864C4⋊C4—6116no—
865C4⋊C4—614no—
866C4⋊C4C23×D6114yes—
867C4⋊C4C23×D6118yes—
868C4⋊C4C23×D61116yes—
869C4⋊C4C23×D6114yes—
870C4⋊C4C23×D6118yes—
871C22⋊C4—618no—
872C22⋊C4—618no—
873C22⋊C4—618no—
874C22⋊C4—6116no—
875C22⋊C4—618no—
876C22⋊C4—6116no—
877C22⋊C4—6116no—
878C22⋊C4—618no—
879C22⋊C4—6116no—
880C22⋊C4—6116no—
881C22⋊C4C23×D6118yes—
882C22⋊C4C23×D6118yes—
883C22⋊C4C23×D61116yes—
884C42—614no—
885C42—618no—
886C42—614no—
887C42—618no—
888C42—614no—
889C42—618no—
890C42C23×D6114yes—
891C23—24no—
892C23—24no—
893C23—24no—
894C23—24no—
895C23—24no—
896C23—614no—
897C23—618no—
898C23—614no—
899C23—612no—
900C23—618no—
901C23—12216no—
902C23—12232no—
903C23—12216no—
904C23—1224no—
905C23—1222no—
906C23—1222no—
907C23—1224no—
908C23—12232no—
909C23—1228no—
910C23—1228no—
911C23—1228no—
912C23—24416no—
913C23—2448no—
914C23—24464no—
915C23—24432no—
916C23C2×D4×D6118yes—
917C23C24×D6114yes—
918C23C24×D6114yes—
919C23C24×D6111yescharacteristic
920Q8—216no—
921Q8—6116no—
922Q8—12232no—
923D4—232no—
924D4—28no—
925D4—6132no—
926D4—6116no—
927D4—12232no—
928D4—12232no—
929D4—12232no—
930D4—12216no—
931D4—12232no—
932D4—12216no—
933D4—12216no—
934D4—2448no—
935D4—24416no—
936D4C2×D4×D61116yescomplemented
937C2×C4—24no—
938C2×C4—28no—
939C2×C4—232no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—216no—
943C2×C4—216no—
944C2×C4—614no—
945C2×C4—618no—
946C2×C4—6132no—
947C2×C4—612no—
948C2×C4—614no—
949C2×C4—6116no—
950C2×C4—612no—
951C2×C4—612no—
952C2×C4—614no—
953C2×C4—614no—
954C2×C4—12216no—
955C2×C4—12232no—
956C2×C4—12232no—
957C2×C4—12232no—
958C2×C4—12216no—
959C2×C4—12216no—
960C2×C4—1224no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1224no—
964C2×C4—12216no—
965C2×C4—1228no—
966C2×C4—2444no—
967C2×C4—2448no—
968C2×C4C2×D4×D6114yes—
969C2×C4#41×D6114yescomplemented
970C2×C4C24×D6114yes—
971C2×C4C24×D6112yes—
972C2×C4C24×D6114yes—
973C2×C4C24×D6118yes—
974C2×C4C24×D6112yes—
975C2×C4C24×D6112yes—
976C22—216no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—48no—
983C22—614no—
984C22—618no—
985C22—1228no—
986C22—12216no—
987C22—1224no—
988C22—1222no—
989C22—1222no—
990C22—1224no—
991C22—1228no—
992C22—1228no—
993C22—1228no—
994C22—24464no—
995C22—24432no—
996C22—24416no—
997C22C22×D4×D6118yes—
998C22C22×D4×D6112yes—
999C22C2×#41×D6112yes—
1000C22#1684059912yes—
1001C22C25×D6111yescharacteristic
1002C4—24no—
1003C4—28no—
1004C4—24no—
1005C4—22no—
1006C4—614no—
1007C4—618no—
1008C4—1224no—
1009C4—1222no—
1010C4—1222no—
1011C4—1224no—
1012C4C22×D4×D6114yes—
1013C4C2×#41×D6114yescomplemented
1014C2—28no—
1015C2—44no—
1016C2—1228no—
1017C2—1224no—
1018C2—2448no—
1019C2#2145930614yesdirect product factor
1020C2C23×D4×D6111yescharacteristic
1021C2C22×#41×D6111yescharacteristic
1022C2C2×#1684059911yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#547C2
socleC23×C61C25
hypercenterC2×#547D61
hypocenterC61C2×D4×#41
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#41×D61C2semidirect
2. #21459306C2direct (N × H)
3. C2×#16840433C2semidirect
4. C2×#16840427C2semidirect
5. C2×#16840422C2semidirect
6. C2×#16840413C2semidirect
7. C2×#16840404C2semidirect
8. C2×#16840400C2semidirect
9. C2×D4×D244C2semidirect
10. C2×#16840396C2semidirect
11. C2×#16840313C2semidirect
12. C2×#16840307C2semidirect
13. C2×#16840275C2semidirect
14. C2×#16840270C2semidirect
15. C2×C4×#11758224C2semidirect
16. C22×#14519739C2semidirect
17. C2×C4×D4×D61C2semidirect
18. C2×C61×#547C2semidirect
19. C22×#11758226C22semidirect
20. C22×#11758222C22semidirect
21. C22×#11758222C22semidirect
23. C22×#11758224C22semidirect
25. C2×#41×D61C22semidirect
26. C22×Q8×D61C22semidirect
29. C22×D4×D61C22semidirect
30. C22×D4×D61C22semidirect
31. C23×C4×D61C22semidirect
32. C23×C4×D61C22semidirect
33. #16840433C22semidirect
34. #16840427C22semidirect
35. #16840422C22semidirect
36. #16840413C22semidirect
37. #16840404C22semidirect
38. #16840400C22semidirect
39. D4×D244C22semidirect
40. #16840396C22semidirect
41. #16840313C22semidirect
42. #16840307C22semidirect
43. C2×#14519776C22semidirect
44. C2×#14519774C22semidirect
45. C2×#14519773C22semidirect
46. C2×#14519766C22semidirect
47. C2×#14519763C22semidirect
48. #16840275C22semidirect
49. #16840270C22semidirect
50. C2×#14519762C22semidirect
51. C2×#14519760C22semidirect
52. C2×#14519755C22semidirect
53. C2×#14519755C22semidirect
54. C2×#14519753C22semidirect
55. C2×#14519752C22semidirect
56. C2×#14519752C22semidirect
57. C2×#14519752C22semidirect
58. C2×#14519751C22semidirect
59. C2×#14519751C22semidirect
60. C2×#14519750C22semidirect
61. C2×#14519750C22semidirect
62. C2×#14519749C22semidirect
63. C2×#14519747C22semidirect
64. C2×#14519747C22semidirect
65. C2×#14519745C22semidirect
66. C4×#11758224C22semidirect
67. C2×C4×Dic122C22semidirect
68. C2×#14519742C22semidirect
70. C2×D4×Dic61C22semidirect
71. C2×D4×Dic61C22semidirect
74. C2×#14519739C22semidirect
75. C2×#14519739C22semidirect
76. C2×#14519739C22semidirect
77. C2×#14519739C22semidirect
78. C2×#14519739C22semidirect
79. C2×#14519739C22semidirect
80. C2×C4×C22⋊D61C22semidirect
81. C2×C4×C22⋊D61C22semidirect
82. C2×#14519737C22semidirect
83. C2×#14519737C22semidirect
84. C2×#14519737C22semidirect
85. C4×D4×D61C22semidirect
86. C2×#14519735C22semidirect
87. C2×#14519733C22semidirect
88. C2×C4⋊C4×D61C22semidirect
89. C22×#11758198C22semidirect
90. C2×C22⋊C4×D61C22semidirect
91. C22×C4×Dic61C22semidirect
92. C2×C42×D61C22semidirect
93. C22×#41×C61C22semidirect
94. C61×#547C22semidirect
95. C2×C4⋊Q8×C61C22semidirect
96. C2×#123×C61C22semidirect
97. C2×C22⋊Q8×C61C22semidirect
98. C2×#121×C61C22semidirect
99. C2×C4×D4×C61C22semidirect
100. C2×C4×D4×C61C22semidirect
101. C22×C4⋊C4×C61C22semidirect
105. C2×#11758226C23semidirect
108. C2×#11758222C23semidirect
109. C2×#11758222C23semidirect
111. C2×#11758224D4semidirect
113. C2×#11758224C23semidirect
118. C2×Q8×D61C23semidirect
136. C2×D4×D61C23semidirect
137. C2×D4×D61C23semidirect
152. C22×C4×D61C23semidirect
153. C22×C4×D61C23semidirect
154. #14519776C23semidirect
155. #14519774C23semidirect
156. #14519773C23semidirect
157. #14519766C23semidirect
158. #14519763C23semidirect
159. #14519762C23semidirect
160. #14519760C23semidirect
161. #14519755C23semidirect
162. #14519755C23semidirect
163. #14519753C23semidirect
164. #14519752C23semidirect
165. #14519752C23semidirect
166. #14519752C23semidirect
167. #14519751C23semidirect
168. #14519751C23semidirect
169. #14519750C23semidirect
170. #14519750C23semidirect
171. #14519749C23semidirect
172. #14519747C23semidirect
173. #14519747C23semidirect
174. #14519745C23semidirect
175. C4×Dic122C23semidirect
176. #14519742C23semidirect
178. D4×Dic61C23semidirect
179. D4×Dic61C23semidirect
182. #14519739C23semidirect
183. #14519739C23semidirect
184. #14519739C23semidirect
185. #14519739C23semidirect
186. #14519739C23semidirect
187. C4×C22⋊D61C23semidirect
188. C4×C22⋊D61C23semidirect
189. #14519737C23semidirect
190. #14519737C23semidirect
191. #14519737C23semidirect
192. #14519735C23semidirect
193. #14519733C23semidirect
200. C4⋊C4×D61C23semidirect
211. C2×#11758198C23semidirect
212. C22⋊C4×D61C23semidirect
219. C2×C4×Dic61C23semidirect
220. C42×D61C23semidirect
222. C2×#41×C61C23semidirect
230. C4⋊Q8×C61C23semidirect
231. #123×C61C23semidirect
232. C22⋊Q8×C61C23semidirect
233. #121×C61C23semidirect
234. C4×D4×C61C23semidirect
235. C4×D4×C61C23semidirect
241. C2×C4⋊C4×C61C23semidirect
264. C2×D4×C61C2×D4semidirect
284. C2×C22⋊D61C2×D4semidirect
292. C22×Dic61C2×D4semidirect
305. #11758224C2×D4semidirect
317. C2×D244#41semidirect
334. C2×C4×D61C2×D4semidirect
345. C2×Dic122C2×D4semidirect
404. C22×D61C2×#41semidirect
411. D4×C61C22×D4semidirect
420. C2×C4×C61C2×#41semidirect
431. C22⋊D61C22×D4semidirect
440. C2×Dic61C22×D4semidirect
452. D244C2×#41semidirect
461. C4×D61C22×D4semidirect
463. Dic122C22×D4semidirect
490. C2×D61C22×#41semidirect
496. C4×C61C22×#41semidirect
509. C2×#547D61semidirect
523. C2×C61D4×#41semidirect
537. C22×#41C2×D61semidirect
549. #547C2×D61semidirect
557. C2×C4⋊Q8C2×D61semidirect
566. C2×#123C2×D61semidirect
570. C2×C22⋊Q8C2×D61semidirect
579. C2×#121C2×D61semidirect
603. C2×C4×D4C2×D61semidirect
604. C2×C4×D4C2×D61semidirect
608. C22×C4⋊C4C2×D61semidirect
613. C61C2×D4×#41semidirect
628. C2×#41C22×D61semidirect
676. C4⋊Q8C22×D61semidirect
683. #123C22×D61semidirect
687. C22⋊Q8C22×D61semidirect
696. #121C22×D61semidirect
717. C4×D4C22×D61semidirect
718. C4×D4C22×D61semidirect
733. C2×C4⋊C4C22×D61semidirect
812. C2×D4D4×D61semidirect
936. D4C2×D4×D61semidirect
969. C2×C4#41×D61semidirect
1013. C4C2×#41×D61semidirect
1019. C2#21459306direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D612
#214593062
C2×#168404332
C2×#168404272
C2×#168404222
C2×#168404132
C2×#168404042
C2×#168404002
C2×D4×D2442
C2×#168403962
C2×#168403132
C2×#168403072
C2×#168402752
C2×#168402702
C2×C4×#117582242
C22×#145197392
C2×C4×D4×D612
C2×C61×#5472
C2×D4×#4161