Finite Group Databasebeta

← C2×#13082432 #15662099

Subgroups — C2×#13082432 #15662099

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#13082432C2132yesmaximal, direct product factor
2C2×#10623253C212yesmaximal, complemented
3C2×#10623252C212yesmaximal, complemented
4C2×#10623261C212yesmaximal, complemented
5C2×#10623042C214yesmaximal, complemented
6C2×#10623258C212yesmaximal, complemented
7C2×Q8×C22⋊D11C214yesmaximal, complemented
8C2×#10623031C212yesmaximal, complemented
9C2×#10623260C214yesmaximal, complemented
10C2×#10623001C211yesmaximal, characteristic, complemented
11C2×#10623259C212yesmaximal, complemented
12C2×D11×C4⋊Q8C212yesmaximal, complemented
13C2×#10623035C212yesmaximal
14C2×C4×#4339C211yesmaximal, characteristic
15C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2212yes—
17C22×Q8×D11C2214yes—
18C22×#4339C2211yescharacteristic
19C2×C11×C4⋊Q8C2212yes—
20C2×C11×C4⋊Q8C2212yes—
21C2×C11×C4⋊Q8C2212yes—
22C2×C11×C4⋊Q8C2212yes—
23C2×C11×C4⋊Q8C22116yescomplemented
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C4⋊C4C2212yes—
26C22×C42×C11C2211yescharacteristic
27Q8×C22⋊D11C22164yescomplemented
28C2×#66999C2218yes—
29C2×#66999C2214yes—
30C2×Q8×Dic11C2214yes—
31C2×#66997C2214yes—
32C2×#66997C2218yes—
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2218yes—
35C2×C4×C22⋊D11C2212yes—
36C2×#66979C2212yes—
37C2×#66979C2211yescharacteristic
38C2×#66977C2212yes—
39C2×#66977C2218yes—
40C2×#66977C2212yes—
41#10623261C22132yescomplemented
42#10623260C22164yescomplemented
43#10623259C22132yescomplemented
44#10623258C22132yescomplemented
45D11×C4⋊Q8C22132yescomplemented
46#10623253C22132yescomplemented
47#10623252C22132yescomplemented
48#10623042C22164yescomplemented
49C2×#66950C2214yes—
50C2×#66949C2218yes—
51#10623035C22132yes—
52C2×#66946C2214yes—
53C2×#66945C2214yes—
54C2×C4⋊C4×D11C2214yes—
55C2×C4⋊C4×D11C2214yes—
56#10623031C22132yescomplemented
57C2×#66943C2214yes—
58C2×#66943C2214yes—
59C2×#66942C2218yes—
60C2×#66941C2214yes—
61C2×#66941C2214yes—
62C2×#66941C2214yes—
63C2×#66940C2214yes—
64C2×#66940C2214yes—
65C4×#4339C22116yes—
66C2×C4×D44C2211yescharacteristic
67C2×C4×D44C2211yescharacteristic
68C2×#66925C2212yes—
69C2×C42×D11C2212yes—
70#10623001C22116yescomplemented
71C2×#66923C2212yes—
72C2×#66922C2211yescharacteristic
73C2×#66922C2211yescharacteristic
74C2×C4×Dic22C2212yes—
75C2×C4×Dic22C2212yes—
76C2×C4×Dic22C2211yescharacteristic
77C2×C4×Dic22C2211yescharacteristic
78C22×Q8×C11—48no—
79C22×Q8×C11C2314yes—
80C22×Q8×C11C2314yes—
81C22×Q8×C11C23116yes—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11C2312yes—
87C2×Q8×D11—416no—
88C2×Q8×D11C23132yes—
89C2×#4339Q8116yescomplemented
90C2×#4339C2318yes—
91C22×D44C2311yescharacteristic
92C22×C4×D11C2312yes—
93C22×C4×D11C2312yes—
94C22×C4×D11C2318yes—
95C22×C4×D11C2312yes—
96C22×Dic22C2312yes—
97C22×Dic22C2312yes—
98C22×Dic22C2318yes—
99C22×Dic22C2311yescharacteristic
100C11×C4⋊Q8C23116yes—
101C11×C4⋊Q8C23116yes—
102C11×C4⋊Q8C23116yes—
103C11×C4⋊Q8C23116yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C23116yes—
109C2×C11×C4⋊C4C23116yes—
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2318yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2312yes—
117#66999C23132yes—
118#66999C23164yes—
119Q8×Dic11C23132yes—
120#66997C23132yes—
121#66997C23164yes—
122C4×C22⋊D11C23116yes—
123C4×C22⋊D11C23116yes—
124C4×C22⋊D11C23164yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2312yes—
127C2×(C2×D11)⋊C4C2318yes—
128#66979C23116yes—
129#66979C2318yes—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2312yes—
136C2×C4⋊Dic11C2318yes—
137#66977C23116yes—
138#66977C23116yes—
139#66977C23164yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2318yes—
145C2×Dic11⋊C4C2318yes—
146C2×Dic11⋊C4C2318yes—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2312yes—
151C2×C4×Dic11C2318yes—
152#66950C23132yes—
153#66949C23164yes—
154#66946C23132yes—
155#66945C23132yes—
156C4⋊C4×D11C23132yes—
157C4⋊C4×D11C23132yes—
158#66943C23132yes—
159#66943C23132yes—
160#66942C23164yes—
161#66941C23132yes—
162#66941C23132yes—
163#66941C23132yes—
164#66940C23132yes—
165#66940C23132yes—
166C4×D44C2318yes—
167C4×D44C2318yes—
168#66925C23116yes—
169C42×D11C23116yes—
170#66923C23116yes—
171#66922C2318yes—
172#66922C2318yes—
173C4×Dic22C2318yes—
174C4×Dic22C23116yes—
175C4×Dic22C2318yes—
176C4×Dic22C23116yes—
177C2×#3503—111nomaximal, Sylow
178C24×C11C2411yescharacteristic
179C23×D11C2412yes—
180C2×Q8×C11—216no—
181C2×Q8×C11—48no—
182C2×Q8×C11—432no—
183C2×Q8×C11C24116yes—
184C2×Q8×C11C24116yes—
185C22×C4×C11—24no—
186C22×C4×C11—24no—
187C22×C4×C11—48no—
188C22×C4×C11C2×Q818yescomplemented
189C22×C4×C11C2418yes—
190C22×C4×C11C2411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C22×C4×C11C2414yes—
193C22×C4×C11C2414yes—
194C22×C4×C11C24116yes—
195C22×C4×C11C2411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2414yes—
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11C2×Q8116yescomplemented
201C2×C22⋊D11C2418yes—
202C22×Dic11C2414yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C22×Dic11C2414yes—
206C22×Dic11C2412yes—
207Q8×D11—464no—
208#4339C2×Q8164yescomplemented
209C2×D44C2×Q818yescomplemented
210C2×D44C2414yes—
211C2×C4×D11—28no—
212C2×C4×D11—28no—
213C2×C4×D11—416no—
214C2×C4×D11C2×Q8116yescomplemented
215C2×C4×D11C2418yes—
216C2×C4×D11C2418yes—
217C2×C4×D11C24132yes—
218C2×C4×D11C2418yes—
219C2×Dic22—28no—
220C2×Dic22—28no—
221C2×Dic22—416no—
222C2×Dic22C2×Q818yescomplemented
223C2×Dic22C2418yes—
224C2×Dic22C2418yes—
225C2×Dic22C24132yes—
226C2×Dic22C2414yes—
227C11×C4⋊C4C24116yes—
228C11×C4⋊C4C24116yes—
229C11×C4⋊C4C24116yes—
230C11×C4⋊C4C24116yes—
231C42×C11C2414yes—
232C42×C11C2414yes—
233C42×C11C2414yes—
234C42×C11C2414yes—
235C22⋊Dic11C24116yes—
236C22⋊Dic11C2418yes—
237(C2×D11)⋊C4C2418yes—
238(C2×D11)⋊C4C2418yes—
239(C2×D11)⋊C4C24132yes—
240C4⋊Dic11C2418yes—
241C4⋊Dic11C2418yes—
242C4⋊Dic11C2414yes—
243C4⋊Dic11C2414yes—
244C4⋊Dic11C2418yes—
245C4⋊Dic11C2418yes—
246C4⋊Dic11C24132yes—
247Dic11⋊C4C24116yes—
248Dic11⋊C4C24116yes—
249Dic11⋊C4C2418yes—
250Dic11⋊C4C2418yes—
251Dic11⋊C4C24132yes—
252Dic11⋊C4C24132yes—
253Dic11⋊C4C24132yes—
254C4×Dic11C24116yes—
255C4×Dic11C2418yes—
256C4×Dic11C2418yes—
257C4×Dic11C2418yes—
258C4×Dic11C24132yes—
259#3503—1132no—
260C2×Q82—112no—
261C2×#557—112no—
262C2×#554—112no—
263C2×#554—114no—
264C2×D4×Q8—114no—
265C2×D4×Q8—112no—
266C2×#544—114no—
267C2×#544—112no—
268C2×#533—111no—
269C2×#533—112no—
270C22×C4⋊Q8—112no—
271C22×C4⋊Q8D1111yescharacteristic, complemented
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—232no—
284Q8×C11—416no—
285C2×C4×C11—216no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—28no—
289C2×C4×C11—28no—
290C2×C4×C11—416no—
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×C11C25116yes—
297C2×C4×C11C2512yes—
298C2×C4×C11C2512yes—
299C2×C4×C11C2512yes—
300C2×C4×C11C2512yes—
301C2×C4×C11C2512yes—
302C2×C4×C11C2512yes—
303C22⋊D11C22×Q8132yescomplemented
304C2×Dic11—28no—
305C2×Dic11—24no—
306C2×Dic11—28no—
307C2×Dic11—24no—
308C2×Dic11C22×Q818yes—
309C2×Dic11C2518yes—
310C2×Dic11C2514yes—
311C2×Dic11C2514yes—
312C2×Dic11C2518yes—
313C2×Dic11C2514yes—
314D44C22×Q8116yescomplemented
315C4×D11—216no—
316C4×D11—216no—
317C4×D11—432no—
318C4×D11C22×Q8132yescomplemented
319Dic22—216no—
320Dic22—216no—
321Dic22—432no—
322Dic22C22×Q8116yescomplemented
323C22×#41—111no—
324C23×Q8—114no—
325C23×Q8C2×D1112yes—
326Q82—1132no—
327#557—1132no—
328#554—1132no—
329#554—1164no—
330D4×Q8—1164no—
331D4×Q8—1132no—
332#544—1164no—
333#544—1132no—
334#533—1132no—
335#533—1116no—
336C2×C4⋊Q8—114no—
337C2×C4⋊Q8—118no—
338C2×C4⋊Q8—1132no—
339C2×C4⋊Q8—114no—
340C2×C4⋊Q8—114no—
341C2×C4⋊Q8—114no—
342C2×C4⋊Q8—111no—
343C2×C4⋊Q8—111no—
344C2×C4⋊Q8C2×D1112yes—
345C2×C4⋊Q8C2×D1112yes—
346C2×C4⋊Q8C2×D1112yes—
347C2×C4⋊Q8C2×D1112yes—
348C2×C4⋊Q8C2×D11116yescomplemented
349C2×#125—118no—
350C2×#125—114no—
351C2×#125—114no—
352C2×#125—112no—
353C2×C22⋊Q8—114no—
354C2×C22⋊Q8—118no—
355C2×C22⋊Q8—112no—
356C2×C22⋊Q8—112no—
357C2×C22⋊Q8—118no—
358C2×C22⋊Q8—118no—
359C2×C22⋊Q8—114no—
360#520—1132no—
361C4×#41—1116no—
362C2×C4×Q8—114no—
363C2×C4×Q8—114no—
364C2×C4×Q8—114no—
365C2×C4×Q8—111no—
366C2×C4×Q8—111no—
367C2×C4×Q8—112no—
368C2×C4×Q8—112no—
369C2×C4×D4—112no—
370C2×C4×D4—112no—
371C2×C4×D4—118no—
372C2×C4×D4—114no—
373C2×C4×D4—111no—
374C2×C4×D4—111no—
375C2×#117—111no—
376C2×#117—112no—
377C2×#117—114no—
378C2×#117—112no—
379C22×C4⋊C4—114no—
380C22×C4⋊C4—114no—
381C22×C4⋊C4C2×D1112yes—
382C22×C4⋊C4C2×D1112yes—
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—216no—
399C4×C11—22no—
400C4×C11C23×Q814yes—
401C4×C11C23×Q814yes—
402C4×C11C2×H(5,𝔽2)14yes—
403C4×C11C2×2−1+414yes—
404Dic11—28no—
405Dic11—24no—
406Dic11—28no—
407Dic11—24no—
408Dic11C23×Q818yes—
409C2×#41—1116no—
410C2×#41—118no—
411C22×Q8—48no—
412C22×Q8—1132no—
413C22×Q8—111no—
414C22×Q8—112no—
415C22×Q8—112no—
416C22×Q8—118no—
417C22×Q8—4416no—
418C22×Q8C22×D1114yes—
419C22×Q8C22×D1114yes—
420C22×Q8C22×D11116yes—
421C22×D4—112no—
422C22×D4—111no—
423C23×C4—112no—
424C23×C4—112no—
425C23×C4—112no—
426C23×C4—118no—
427C23×C4C22×D1111yescharacteristic
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1114yes—
430C23×C4C22×D1111yescharacteristic
431C4⋊Q8—1132no—
432C4⋊Q8—1164no—
433C4⋊Q8—1132no—
434C4⋊Q8—1132no—
435C4⋊Q8—1132no—
436C4⋊Q8—118no—
437C4⋊Q8—118no—
438C4⋊Q8C22×D11116yes—
439C4⋊Q8C22×D11116yes—
440C4⋊Q8C22×D11116yes—
441C4⋊Q8C22×D11116yes—
442#125—1132no—
443#125—1164no—
444#125—1132no—
445#125—1116no—
446C22⋊Q8—1132no—
447C22⋊Q8—1164no—
448C22⋊Q8—1116no—
449C22⋊Q8—1116no—
450C22⋊Q8—1164no—
451C22⋊Q8—1132no—
452C22⋊Q8—1164no—
453C4×Q8—1132no—
454C4×Q8—1132no—
455C4×Q8—1132no—
456C4×Q8—118no—
457C4×Q8—118no—
458C4×Q8—1116no—
459C4×Q8—1116no—
460C4×D4—1116no—
461C4×D4—1116no—
462C4×D4—1164no—
463C4×D4—1132no—
464C4×D4—118no—
465C4×D4—118no—
466#117—118no—
467#117—1116no—
468#117—1132no—
469#117—1116no—
470C2×C4⋊C4—112no—
471C2×C4⋊C4—112no—
472C2×C4⋊C4—118no—
473C2×C4⋊C4—118no—
474C2×C4⋊C4—112no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—112no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—112no—
480C2×C4⋊C4—114no—
481C2×C4⋊C4—118no—
482C2×C4⋊C4—118no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—1132no—
485C2×C4⋊C4—1132no—
486C2×C4⋊C4C22×D1114yes—
487C2×C4⋊C4C22×D1114yes—
488C2×C4⋊C4C22×D1114yes—
489C2×C4⋊C4C22×D11116yes—
490C2×C4⋊C4C22×D1114yes—
491C2×C4⋊C4C22×D11116yes—
492C2×C22⋊C4—114no—
493C2×C22⋊C4—112no—
494C2×C22⋊C4—118no—
495C2×C22⋊C4—112no—
496C2×C22⋊C4—112no—
497C2×C42—112no—
498C2×C42—118no—
499C2×C42—114no—
500C2×C42—112no—
501C2×C42—112no—
502C2×C42—1116no—
503C2×C42C22×D1111yescharacteristic
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—216no—
518C2×Q8—48no—
519C2×Q8—432no—
520C2×Q8—118no—
521C2×Q8—114no—
522C2×Q8—118no—
523C2×Q8—118no—
524C2×Q8—1132no—
525C2×Q8—228no—
526C2×Q8—228no—
527C2×Q8—4416no—
528C2×Q8—4464no—
529C2×Q8C23×D11116yes—
530C2×Q8C23×D11116yes—
531C2×D4—1116no—
532C2×D4—118no—
533C2×D4—118no—
534C2×D4—114no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—48no—
538C22×C4—112no—
539C22×C4—1116no—
540C22×C4—118no—
541C22×C4—114no—
542C22×C4—112no—
543C22×C4—112no—
544C22×C4—114no—
545C22×C4—118no—
546C22×C4—118no—
547C22×C4—1132no—
548C22×C4—228no—
549C22×C4—228no—
550C22×C4—4416no—
551C22×C4Q8×D1118yescomplemented
552C22×C4C23×D1114yes—
553C22×C4C23×D1114yes—
554C22×C4C23×D1118yes—
555C22×C4C23×D1111yescharacteristic
556C22×C4C23×D1111yescharacteristic
557C22×C4C23×D11116yes—
558C22×C4C23×D1111yescharacteristic
559C22×C4C23×D1111yescharacteristic
560C22×C4C23×D1111yescharacteristic
561C22×C4C23×D1114yes—
562C22×C4C23×D1111yescharacteristic
563C4⋊C4—118no—
564C4⋊C4—118no—
565C4⋊C4—1132no—
566C4⋊C4—1132no—
567C4⋊C4—118no—
568C4⋊C4—118no—
569C4⋊C4—114no—
570C4⋊C4—118no—
571C4⋊C4—114no—
572C4⋊C4—118no—
573C4⋊C4—1116no—
574C4⋊C4—1132no—
575C4⋊C4—1132no—
576C4⋊C4—1116no—
577C4⋊C4C23×D11116yes—
578C4⋊C4C23×D11116yes—
579C4⋊C4C23×D11116yes—
580C4⋊C4C23×D11116yes—
581C22⋊C4—1116no—
582C22⋊C4—118no—
583C22⋊C4—1132no—
584C22⋊C4—118no—
585C22⋊C4—118no—
586C42—118no—
587C42—118no—
588C42—118no—
589C42—1132no—
590C42—1116no—
591C42C23×D1114yes—
592C42C23×D1114yes—
593C42C23×D1114yes—
594C42C23×D1114yes—
595C11C2×#350311yescharacteristic, complemented, Sylow
596C23—22no—
597C23—22no—
598C23—118no—
599C23—114no—
600C23—224no—
601C23—224no—
602C23C2×Q8×D1114yes—
603C23C24×D1112yes—
604C23C24×D1111yescharacteristic
605Q8—232no—
606Q8—416no—
607Q8—1116no—
608Q8—2216no—
609Q8—2216no—
610Q8—4432no—
611D4—1132no—
612D4—1116no—
613C2×C4—22no—
614C2×C4—216no—
615C2×C4—22no—
616C2×C4—28no—
617C2×C4—28no—
618C2×C4—416no—
619C2×C4—118no—
620C2×C4—114no—
621C2×C4—1132no—
622C2×C4—118no—
623C2×C4—114no—
624C2×C4—114no—
625C2×C4—118no—
626C2×C4—224no—
627C2×C4—228no—
628C2×C4—224no—
629C2×C4—228no—
630C2×C4—2216no—
631C2×C4—2216no—
632C2×C4—4432no—
633C2×C4#6703714yes—
634C2×C4C2×Q8×D1114yes—
635C2×C4C2×Q8×D1114yes—
636C2×C4C2×Q8×D11116yescomplemented
637C2×C4#6704014yes—
638C2×C4C24×D11116yes—
639C2×C4C24×D1112yes—
640C2×C4C24×D1112yes—
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—
652C22C2×#6703712yes—
653C22C22×Q8×D1114yes—
654C22C22×Q8×D1112yes—
655C22C2×#6704012yes—
656C22C25×D1111yescharacteristic
657C4—22no—
658C4—216no—
659C4—22no—
660C4—118no—
661C4—224no—
662C4—228no—
663C4—224no—
664C4—228no—
665C4C2×#6703714yes—
666C4C22×Q8×D1114yes—
667C4C22×Q8×D1114yes—
668C4C2×#6704014yes—
669C2—24no—
670C2—228no—
671C2#1308243214yesdirect product factor
672C2C23×Q8×D1111yescharacteristic
673C2C22×#6703711yescharacteristic
674C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11C25
prime radicalC22×#4339C22
hypercenterC22×C4⋊Q8D11
hypocenterC11C2×#3503
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13082432C2direct (N × H)
2. C2×#10623253C2semidirect
3. C2×#10623252C2semidirect
4. C2×#10623261C2semidirect
5. C2×#10623042C2semidirect
6. C2×#10623258C2semidirect
7. C2×Q8×C22⋊D11C2semidirect
8. C2×#10623031C2semidirect
9. C2×#10623260C2semidirect
10. C2×#10623001C2semidirect
11. C2×#10623259C2semidirect
12. C2×D11×C4⋊Q8C2semidirect
15. C22×C11×C4⋊Q8C2semidirect
23. C2×C11×C4⋊Q8C22semidirect
27. Q8×C22⋊D11C22semidirect
41. #10623261C22semidirect
42. #10623260C22semidirect
43. #10623259C22semidirect
44. #10623258C22semidirect
45. D11×C4⋊Q8C22semidirect
46. #10623253C22semidirect
47. #10623252C22semidirect
48. #10623042C22semidirect
56. #10623031C22semidirect
70. #10623001C22semidirect
89. C2×#4339Q8semidirect
188. C22×C4×C11C2×Q8semidirect
200. C2×C22⋊D11C2×Q8semidirect
208. #4339C2×Q8semidirect
209. C2×D44C2×Q8semidirect
214. C2×C4×D11C2×Q8semidirect
222. C2×Dic22C2×Q8semidirect
271. C22×C4⋊Q8D11semidirect
293. C2×C4×C11C22×Q8semidirect
303. C22⋊D11C22×Q8semidirect
314. D44C22×Q8semidirect
318. C4×D11C22×Q8semidirect
322. Dic22C22×Q8semidirect
348. C2×C4⋊Q8C2×D11semidirect
509. C2×C11#3503semidirect
551. C22×C4Q8×D11semidirect
595. C11C2×#3503semidirect
636. C2×C4C2×Q8×D11semidirect
671. C2#13082432direct (N × H)

Maximal subgroups

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

subgroupindex
#130824322
C2×#106232532
C2×#106232522
C2×#106232612
C2×#106230422
C2×#106232582
C2×Q8×C22⋊D112
C2×#106230312
C2×#106232602
C2×#106230012
C2×#106232592
C2×D11×C4⋊Q82
C2×#106230352
C2×C4×#43392
C22×C11×C4⋊Q82
C2×#350311