Finite Group Databasebeta

← C2×#13082428 #15662098

Subgroups — C2×#13082428 #15662098

Order 2816.

7478 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082428C2132yesmaximal, direct product factor
2C2×Q8×Dic22C212yesmaximal, complemented
3C2×#10623098C212yesmaximal, complemented
4C2×#10623110C212yesmaximal, complemented
5C2×#10623166C214yesmaximal, complemented
6C2×Q8×D44C212yesmaximal, complemented
7C2×#10623163C214yesmaximal, complemented
8C2×#10623220C214yesmaximal, complemented
9C2×#10623050C212yesmaximal, complemented
10C2×#10623259C212yesmaximal, complemented
11C22×#66922C211yesmaximal, characteristic, complemented
12C2×D11×C4⋊Q8C212yesmaximal, complemented
13C2×#10623054C212yesmaximal
14C2×C4×#4339C211yesmaximal, characteristic
15C2×C11×#533C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2214yes—
17C22×#4339C2211yescharacteristic
18C23×Dic22C2212yes—
19C11×#533C22116yescomplemented
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#125C2212yes—
23C2×C11×C22⋊Q8C2212yes—
24C2×C11×C22⋊Q8C2212yes—
25C2×C4×Q8×C11C2212yes—
26C2×C4×Q8×C11C2212yes—
27C2×C11×#117C2212yes—
28C22×C42×C11C2211yescharacteristic
29C2×#66999C2214yes—
30C2×Q8×Dic11C2214yes—
31C2×#66997C2214yes—
32C2×C4×C22⋊D11C2212yes—
33C2×C4×C22⋊D11C2212yes—
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11C2212yes—
36C22×C4⋊Dic11C2212yes—
37#10623259C22132yescomplemented
38D11×C4⋊Q8C22132yescomplemented
39#10623220C22164yescomplemented
40#10623166C22164yescomplemented
41#10623163C22164yescomplemented
42#10623110C22132yescomplemented
43Q8×D44C22132yescomplemented
44#10623098C22132yescomplemented
45Q8×Dic22C22132yescomplemented
46#10623054C22132yes—
47#10623050C22132yescomplemented
48C2×#66950C2218yes—
49C2×#66950C2214yes—
50C2×#66949C2218yes—
51C2×#66945C2214yes—
52C2×C4⋊C4×D11C2214yes—
53C2×C4⋊C4×D11C2214yes—
54C2×#66943C2214yes—
55C2×#66942C2218yes—
56C2×#66941C2214yes—
57C2×#66941C2214yes—
58C2×#66941C2218yes—
59C2×#66940C2214yes—
60C2×(C22⋊D11)⋊C4C2218yes—
61C2×#66931C2218yes—
62C4×#4339C22116yes—
63C2×C4×D44C2211yescharacteristic
64C2×C4×D44C2214yes—
65C2×C4×D44C2211yescharacteristic
66C2×#66925C2212yes—
67C2×C42×D11C2212yes—
68C2×#66923C2214yes—
69C2×#66922C2212yes—
70C2×#66922C2212yes—
71C2×#66922C2212yes—
72C2×#66922C2212yes—
73C2×#66922C2214yes—
74C2×#66922C22116yescomplemented
75C2×C4×Dic22C2211yescharacteristic
76C2×C4×Dic22C2214yes—
77C2×C4×Dic22C2211yescharacteristic
78C22×Q8×C11C2312yes—
79C22×Q8×C11C2312yes—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11C2312yes—
84C23×Dic11C2314yes—
85C2×Q8×D11—416no—
86C2×Q8×D11C23132yes—
87C2×#4339Q8116yescomplemented
88C2×#4339C2318yes—
89C22×D44C2311yescharacteristic
90C22×C4×D11C2312yes—
91C22×C4×D11C2312yes—
92C22×C4×D11C2318yes—
93C22×C4×D11C2312yes—
94C22×Dic22—48no—
95C22×Dic22C2314yes—
96C22×Dic22C2314yes—
97C22×Dic22C2318yes—
98C22×Dic22C23116yes—
99C22×Dic22C2311yescharacteristic
100C11×C4⋊Q8C2318yes—
101C11×C4⋊Q8C2318yes—
102C11×#125C23116yes—
103C11×C22⋊Q8C23116yes—
104C11×C22⋊Q8C23116yes—
105C4×Q8×C11C23116yes—
106C4×Q8×C11C23116yes—
107C11×#117C23116yes—
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2314yes—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2318yes—
121C2×C22⋊Dic11C2312yes—
122#66999C23132yes—
123Q8×Dic11C23132yes—
124#66997C23132yes—
125C4×C22⋊D11C23116yes—
126C4×C22⋊D11C23116yes—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2318yes—
130#66979C2318yes—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2314yes—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2314yes—
135C2×C4⋊Dic11C2314yes—
136C2×C4⋊Dic11C2314yes—
137C2×C4⋊Dic11C2318yes—
138C2×C4⋊Dic11C23116yes—
139C2×C4⋊Dic11C23116yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2318yes—
143C2×Dic11⋊C4C2318yes—
144C2×Dic11⋊C4C2318yes—
145C2×C4×Dic11C2312yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2318yes—
148C2×C4×Dic11C2312yes—
149#66950C23132yes—
150#66950C23164yes—
151#66949C23164yes—
152#66945C23132yes—
153C4⋊C4×D11C23132yes—
154C4⋊C4×D11C23132yes—
155#66943C23132yes—
156#66942C23164yes—
157#66941C23132yes—
158#66941C23132yes—
159#66941C23164yes—
160#66940C23132yes—
161(C22⋊D11)⋊C4C23164yes—
162#66931C23164yes—
163C4×D44C2318yes—
164C4×D44C2318yes—
165C4×D44C23132yes—
166#66925C23116yes—
167C42×D11C23116yes—
168#66923C23132yes—
169#66922C23116yes—
170#66922C23116yes—
171#66922C23116yes—
172#66922C23116yes—
173#66922C23132yes—
174C4×Dic22C2318yes—
175C4×Dic22C2318yes—
176C4×Dic22C23132yes—
177C2×#3503—111nomaximal, Sylow
178C24×C11C2411yescharacteristic
179C23×D11C2412yes—
180C2×Q8×C11—28no—
181C2×Q8×C11—28no—
182C2×Q8×C11C2418yes—
183C2×Q8×C11C2418yes—
184C22×C4×C11—24no—
185C22×C4×C11—24no—
186C22×C4×C11C2×Q818yescomplemented
187C22×C4×C11C2414yes—
188C22×C4×C11C2414yes—
189C22×C4×C11C2411yescharacteristic
190C22×C4×C11C2411yescharacteristic
191C22×C4×C11C2414yes—
192C22×C4×C11C2414yes—
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C22×C4×C11C2414yes—
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11C2×Q8116yescomplemented
199C2×C22⋊D11C2418yes—
200C22×Dic11—48no—
201C22×Dic11C2412yes—
202C22×Dic11C2412yes—
203C22×Dic11C2418yes—
204C22×Dic11C24116yes—
205C22×Dic11C2412yes—
206Q8×D11—464no—
207#4339C2×Q8164yescomplemented
208C2×D44C2×Q818yescomplemented
209C2×D44C2414yes—
210C2×C4×D11—28no—
211C2×C4×D11—28no—
212C2×C4×D11—416no—
213C2×C4×D11C2×Q8116yescomplemented
214C2×C4×D11C2418yes—
215C2×C4×D11C2418yes—
216C2×C4×D11C24132yes—
217C2×C4×D11C2418yes—
218C2×Dic22—216no—
219C2×Dic22—432no—
220C2×Dic22—48no—
221C2×Dic22—416no—
222C2×Dic22C2×Q818yescomplemented
223C2×Dic22C24116yes—
224C2×Dic22C24116yes—
225C2×Dic22C24132yes—
226C2×Dic22C2414yes—
227C11×C4⋊C4C2418yes—
228C11×C4⋊C4C2418yes—
229C11×C4⋊C4C2418yes—
230C11×C4⋊C4C24116yes—
231C11×C4⋊C4C24116yes—
232C11×C4⋊C4C2418yes—
233C11×C22⋊C4C24116yes—
234C42×C11C2414yes—
235C42×C11C2414yes—
236C42×C11C24116yes—
237C42×C11C2414yes—
238C42×C11C2414yes—
239C22⋊Dic11C2418yes—
240(C2×D11)⋊C4C2418yes—
241(C2×D11)⋊C4C2418yes—
242(C2×D11)⋊C4C24132yes—
243C4⋊Dic11C2414yes—
244C4⋊Dic11C24116yes—
245C4⋊Dic11C2414yes—
246C4⋊Dic11C24116yes—
247C4⋊Dic11C24116yes—
248C4⋊Dic11C24116yes—
249C4⋊Dic11C24132yes—
250Dic11⋊C4C2418yes—
251Dic11⋊C4C2418yes—
252Dic11⋊C4C24132yes—
253Dic11⋊C4C24132yes—
254Dic11⋊C4C24132yes—
255C4×Dic11C2418yes—
256C4×Dic11C2418yes—
257C4×Dic11C24132yes—
258C4×Dic11C2418yes—
259#3503—1132no—
260C2×Q82—112no—
261C2×#557—112no—
262C2×#554—114no—
263C2×#554—112no—
264C2×D4×Q8—114no—
265C2×D4×Q8—112no—
266C2×#544—114no—
267C2×#544—112no—
268C2×#533—112no—
269C2×#533D1111yescharacteristic, complemented
270C22×C4⋊Q8—111no—
271C22×C4⋊Q8—112no—
272C2×#520—112no—
273C2×C4×#41—111no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11C22×Q814yes—
277C23×C11C2512yes—
278C23×C11C2511yescharacteristic
279C22×D11—24no—
280C22×D11—24no—
281C22×D11C22×Q818yes—
282C22×D11C2514yes—
283Q8×C11—216no—
284Q8×C11—216no—
285C2×C4×C11—22no—
286C2×C4×C11—28no—
287C2×C4×C11—22no—
288C2×C4×C11—28no—
289C2×C4×C11—28no—
290C2×C4×C11—28no—
291C2×C4×C11C22×Q814yes—
292C2×C4×C11C22×Q814yes—
293C2×C4×C11C22×Q8116yescomplemented
294C2×C4×C11H(5,𝔽2)14yes—
295C2×C4×C112−1+414yes—
296C2×C4×C11C2518yes—
297C2×C4×C11C2518yes—
298C2×C4×C11C2512yes—
299C2×C4×C11C2512yes—
300C2×C4×C11C2512yes—
301C2×C4×C11C2512yes—
302C2×C4×C11C2512yes—
303C2×C4×C11C2512yes—
304C22⋊D11C22×Q8132yescomplemented
305C2×Dic11—216no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—416no—
309C2×Dic11C22×Q818yes—
310C2×Dic11C2514yes—
311C2×Dic11C2514yes—
312C2×Dic11C25116yes—
313C2×Dic11C2514yes—
314D44C22×Q8116yescomplemented
315C4×D11—216no—
316C4×D11—216no—
317C4×D11—432no—
318C4×D11C22×Q8132yescomplemented
319Dic22—232no—
320Dic22—416no—
321Dic22—432no—
322Dic22C22×Q8116yescomplemented
323C22×#41—111no—
324C23×Q8—114no—
325C23×Q8—112no—
326Q82—1132no—
327#557—1132no—
328#554—1164no—
329#554—1132no—
330D4×Q8—1164no—
331D4×Q8—1132no—
332#544—1164no—
333#544—1132no—
334#533—1132no—
335#533C2×D11116yescomplemented
336C2×C4⋊Q8—114no—
337C2×C4⋊Q8—1132no—
338C2×C4⋊Q8—114no—
339C2×C4⋊Q8—114no—
340C2×C4⋊Q8—118no—
341C2×C4⋊Q8—112no—
342C2×C4⋊Q8—112no—
343C2×C4⋊Q8—112no—
344C2×C4⋊Q8—112no—
345C2×C4⋊Q8—114no—
346C2×C4⋊Q8—1116no—
347C2×C4⋊Q8C2×D1111yescharacteristic
348C2×C4⋊Q8C2×D1111yescharacteristic
349C2×#125—118no—
350C2×#125—114no—
351C2×#125—114no—
352C2×#125C2×D1112yes—
353C2×C22⋊Q8—114no—
354C2×C22⋊Q8—118no—
355C2×C22⋊Q8—114no—
356C2×C22⋊Q8—118no—
357C2×C22⋊Q8—118no—
358C2×C22⋊Q8C2×D1112yes—
359C2×C22⋊Q8C2×D1112yes—
360#520—1132no—
361C4×#41—1116no—
362C2×C4×Q8—114no—
363C2×C4×Q8—114no—
364C2×C4×Q8—111no—
365C2×C4×Q8—111no—
366C2×C4×Q8—114no—
367C2×C4×Q8C2×D1112yes—
368C2×C4×Q8C2×D1112yes—
369C2×C4×D4—112no—
370C2×C4×D4—112no—
371C2×C4×D4—118no—
372C2×C4×D4—111no—
373C2×C4×D4—111no—
374C2×C4×D4—114no—
375C2×#117—111no—
376C2×#117—114no—
377C2×#117—112no—
378C2×#117C2×D1112yes—
379C22×C4⋊C4—112no—
380C22×C4⋊C4—112no—
381C22×C4⋊C4—114no—
382C22×C4⋊C4—114no—
383C22×C42—112no—
384C22×C42C2×D1111yescharacteristic
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—28no—
388C22×C11C23×Q814yes—
389C22×C11C23×Q812yes—
390C22×C11C2×H(5,𝔽2)12yes—
391C22×C11C2×2−1+412yes—
392C22×C11C2611yescharacteristic
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—216no—
396C2×D11C23×Q818yes—
397C4×C11—22no—
398C4×C11—28no—
399C4×C11—22no—
400C4×C11—28no—
401C4×C11C23×Q814yes—
402C4×C11C23×Q814yes—
403C4×C11C2×H(5,𝔽2)14yes—
404C4×C11C2×2−1+414yes—
405Dic11—216no—
406Dic11—24no—
407Dic11—24no—
408Dic11C23×Q818yes—
409C2×#41—1116no—
410C2×#41—118no—
411C22×Q8—1132no—
412C22×Q8—111no—
413C22×Q8—114no—
414C22×Q8—118no—
415C22×Q8—114no—
416C22×Q8—1116no—
417C22×Q8—448no—
418C22×Q8—4416no—
419C22×Q8C22×D1112yes—
420C22×Q8C22×D1112yes—
421C22×D4—112no—
422C22×D4—111no—
423C23×C4—112no—
424C23×C4—114no—
425C23×C4—112no—
426C23×C4—112no—
427C23×C4—118no—
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1111yescharacteristic
431C4⋊Q8—1132no—
432C4⋊Q8—1132no—
433C4⋊Q8—1132no—
434C4⋊Q8—1164no—
435C4⋊Q8—1116no—
436C4⋊Q8—1116no—
437C4⋊Q8—1116no—
438C4⋊Q8—1116no—
439C4⋊Q8—1132no—
440C4⋊Q8C22×D1118yes—
441C4⋊Q8C22×D1118yes—
442#125—1132no—
443#125—1164no—
444#125—1132no—
445#125C22×D11116yes—
446C22⋊Q8—1132no—
447C22⋊Q8—1132no—
448C22⋊Q8—1164no—
449C22⋊Q8—1164no—
450C22⋊Q8—1164no—
451C22⋊Q8C22×D11116yes—
452C22⋊Q8C22×D11116yes—
453C4×Q8—1132no—
454C4×Q8—1132no—
455C4×Q8—118no—
456C4×Q8—118no—
457C4×Q8—1132no—
458C4×Q8C22×D11116yes—
459C4×Q8C22×D11116yes—
460C4×D4—1116no—
461C4×D4—1116no—
462C4×D4—1164no—
463C4×D4—118no—
464C4×D4—118no—
465C4×D4—1132no—
466#117—118no—
467#117—1132no—
468#117—1116no—
469#117C22×D11116yes—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—118no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—1116no—
475C2×C4⋊C4—118no—
476C2×C4⋊C4—114no—
477C2×C4⋊C4—1116no—
478C2×C4⋊C4—112no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—112no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—118no—
483C2×C4⋊C4—118no—
484C2×C4⋊C4—1132no—
485C2×C4⋊C4—1132no—
486C2×C4⋊C4C22×D1112yes—
487C2×C4⋊C4C22×D1112yes—
488C2×C4⋊C4C22×D1112yes—
489C2×C4⋊C4C22×D1112yes—
490C2×C4⋊C4C22×D1114yes—
491C2×C4⋊C4C22×D1114yes—
492C2×C22⋊C4—112no—
493C2×C22⋊C4—112no—
494C2×C22⋊C4—112no—
495C2×C22⋊C4—118no—
496C2×C22⋊C4C22×D1114yes—
497C2×C42—112no—
498C2×C42—118no—
499C2×C42—112no—
500C2×C42—112no—
501C2×C42—1116no—
502C2×C42C22×D1111yescharacteristic
503C2×C42C22×D1114yes—
504C2×C42C22×D1111yescharacteristic
505C2×C42C22×D1111yescharacteristic
506C2×C42C22×D1118yes—
507C2×C42C22×D1111yescharacteristic
508C2×C11—24no—
509C2×C11#350314yescomplemented
510C2×C11C24×Q811yescharacteristic
511C2×C11C22×H(5,𝔽2)11yescharacteristic
512C2×C11C22×2−1+411yescharacteristic
513D11—28no—
514C24—112no—
515C24C23×D1111yescharacteristic
516#41—1164no—
517C2×Q8—28no—
518C2×Q8—28no—
519C2×Q8—118no—
520C2×Q8—114no—
521C2×Q8—1116no—
522C2×Q8—1132no—
523C2×Q8—1116no—
524C2×Q8—2216no—
525C2×Q8—448no—
526C2×Q8—4416no—
527C2×Q8—4432no—
528C2×Q8—4464no—
529C2×Q8C23×D1118yes—
530C2×Q8C23×D1118yes—
531C2×D4—1116no—
532C2×D4—118no—
533C2×D4—118no—
534C2×D4—114no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—112no—
538C22×C4—1116no—
539C22×C4—118no—
540C22×C4—112no—
541C22×C4—112no—
542C22×C4—118no—
543C22×C4—1116no—
544C22×C4—118no—
545C22×C4—118no—
546C22×C4—1132no—
547C22×C4—228no—
548C22×C4—228no—
549C22×C4—4416no—
550C22×C4—448no—
551C22×C4Q8×D1118yescomplemented
552C22×C4C23×D1114yes—
553C22×C4C23×D1114yes—
554C22×C4C23×D1114yes—
555C22×C4C23×D1111yescharacteristic
556C22×C4C23×D1111yescharacteristic
557C22×C4C23×D1114yes—
558C22×C4C23×D1111yescharacteristic
559C22×C4C23×D1111yescharacteristic
560C22×C4C23×D1114yes—
561C22×C4C23×D1111yescharacteristic
562C22×C4C23×D1111yescharacteristic
563C4⋊C4—1116no—
564C4⋊C4—1116no—
565C4⋊C4—1132no—
566C4⋊C4—1116no—
567C4⋊C4—1132no—
568C4⋊C4—1116no—
569C4⋊C4—118no—
570C4⋊C4—114no—
571C4⋊C4—118no—
572C4⋊C4—114no—
573C4⋊C4—1132no—
574C4⋊C4—1132no—
575C4⋊C4C23×D1118yes—
576C4⋊C4C23×D1118yes—
577C4⋊C4C23×D1118yes—
578C4⋊C4C23×D1118yes—
579C4⋊C4C23×D11116yes—
580C4⋊C4C23×D11116yes—
581C22⋊C4—118no—
582C22⋊C4—118no—
583C22⋊C4—118no—
584C22⋊C4—1132no—
585C22⋊C4C23×D11116yes—
586C42—118no—
587C42—118no—
588C42—118no—
589C42—1132no—
590C42C23×D1114yes—
591C42C23×D1114yes—
592C42C23×D1114yes—
593C42C23×D1114yes—
594C42C23×D11116yes—
595C11C2×#350311yescharacteristic, complemented, Sylow
596C23—22no—
597C23—22no—
598C23—118no—
599C23—114no—
600C23—224no—
601C23—224no—
602C23C2×Q8×D1114yes—
603C23C24×D1112yes—
604C23C24×D1111yescharacteristic
605Q8—216no—
606Q8—216no—
607Q8—1116no—
608Q8—2232no—
609Q8—4416no—
610Q8—4432no—
611D4—1132no—
612D4—1116no—
613C2×C4—22no—
614C2×C4—28no—
615C2×C4—22no—
616C2×C4—28no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—118no—
620C2×C4—114no—
621C2×C4—1132no—
622C2×C4—114no—
623C2×C4—114no—
624C2×C4—1116no—
625C2×C4—224no—
626C2×C4—2216no—
627C2×C4—224no—
628C2×C4—2216no—
629C2×C4—2216no—
630C2×C4—4432no—
631C2×C4—4416no—
632C2×C4C2×Q8×D1114yes—
633C2×C4C2×Q8×D1114yes—
634C2×C4C2×Q8×D11116yescomplemented
635C2×C4#6704214yes—
636C2×C4#6704314yes—
637C2×C4C24×D1118yes—
638C2×C4C24×D1112yes—
639C2×C4C24×D1112yes—
640C2×C4C24×D1118yes—
641C2×C4C24×D1112yes—
642C2×C4C24×D1112yes—
643C2×C4C24×D1112yes—
644C2×C4C24×D1112yes—
645C22—22no—
646C22—22no—
647C22—28no—
648C22—118no—
649C22—224no—
650C22—224no—
651C22—2216no—
652C22C22×Q8×D1114yes—
653C22C22×Q8×D1112yes—
654C22C2×#6704212yes—
655C22C2×#6704312yes—
656C22C25×D1111yescharacteristic
657C4—22no—
658C4—28no—
659C4—22no—
660C4—28no—
661C4—118no—
662C4—224no—
663C4—2216no—
664C4—224no—
665C4C22×Q8×D1114yes—
666C4C22×Q8×D1114yes—
667C4C2×#6704214yes—
668C4C2×#6704314yes—
669C2—24no—
670C2—228no—
671C2#1308242814yesdirect product factor
672C2C23×Q8×D1111yescharacteristic
673C2C22×#6704211yescharacteristic
674C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#533C2
socleC23×C11C25
prime radicalC22×#4339C22
hypercenterC2×#533D11
hypocenterC11C2×#3503
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13082428C2direct (N × H)
2. C2×Q8×Dic22C2semidirect
3. C2×#10623098C2semidirect
4. C2×#10623110C2semidirect
5. C2×#10623166C2semidirect
6. C2×Q8×D44C2semidirect
7. C2×#10623163C2semidirect
8. C2×#10623220C2semidirect
9. C2×#10623050C2semidirect
10. C2×#10623259C2semidirect
11. C22×#66922C2semidirect
12. C2×D11×C4⋊Q8C2semidirect
15. C2×C11×#533C2semidirect
19. C11×#533C22semidirect
37. #10623259C22semidirect
38. D11×C4⋊Q8C22semidirect
39. #10623220C22semidirect
40. #10623166C22semidirect
41. #10623163C22semidirect
42. #10623110C22semidirect
43. Q8×D44C22semidirect
44. #10623098C22semidirect
45. Q8×Dic22C22semidirect
47. #10623050C22semidirect
74. C2×#66922C22semidirect
87. C2×#4339Q8semidirect
186. C22×C4×C11C2×Q8semidirect
198. C2×C22⋊D11C2×Q8semidirect
207. #4339C2×Q8semidirect
208. C2×D44C2×Q8semidirect
213. C2×C4×D11C2×Q8semidirect
222. C2×Dic22C2×Q8semidirect
269. C2×#533D11semidirect
293. C2×C4×C11C22×Q8semidirect
304. C22⋊D11C22×Q8semidirect
314. D44C22×Q8semidirect
318. C4×D11C22×Q8semidirect
322. Dic22C22×Q8semidirect
335. #533C2×D11semidirect
509. C2×C11#3503semidirect
551. C22×C4Q8×D11semidirect
595. C11C2×#3503semidirect
634. C2×C4C2×Q8×D11semidirect
671. C2#13082428direct (N × H)

Maximal subgroups

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

subgroupindex
#130824282
C2×Q8×Dic222
C2×#106230982
C2×#106231102
C2×#106231662
C2×Q8×D442
C2×#106231632
C2×#106232202
C2×#106230502
C2×#106232592
C22×#669222
C2×D11×C4⋊Q82
C2×#106230542
C2×C4×#43392
C2×C11×#5332
C2×#350311