Finite Group Databasebeta

← C2×#13082398 #15662187

Subgroups — C2×#13082398 #15662187

Order 2816.

11126 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67040C211yesmaximal, characteristic, complemented
2C22×#67043C211yesmaximal, characteristic, complemented
3#13082398C2132yesmaximal, direct product factor
4C2×#10623163C214yesmaximal, complemented
5C2×#10623162C214yesmaximal, complemented
6C2×#10623186C218yesmaximal, complemented
7C2×#10623057C211yesmaximal, characteristic, complemented
8C2×#10623255C212yesmaximal, complemented
9C2×#10623206C212yesmaximal, complemented
10C2×#10623199C212yesmaximal, complemented
11C2×#10623363C211yesmaximal, characteristic, complemented
12C22×#66997C211yesmaximal, characteristic, complemented
13C2×D11×C4⋊Q8C212yesmaximal, complemented
14C2×#10623053C211yesmaximal, characteristic, complemented
15C2×C11×#536C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C2×#67043—216no—
19C2×#67043C22116yescomplemented
20C2×#67040—216no—
21C2×#67040C22116yescomplemented
22C22×#4343C2212yes—
23C22×#4343C2212yes—
24C22×Q8×D11C2212yes—
25C22×Q8×D11C2212yes—
26C22×Q8×D11C2212yes—
27C22×#4341C2212yes—
28C22×#4341C2214yes—
29C22×#4339C2212yes—
30C22×#4339C2211yescharacteristic
31C22×#4339C2214yes—
32C22×#4339C2211yescharacteristic
33C23×Dic22C2211yescharacteristic
34C23×Dic22C2212yes—
35C11×#536C22116yescomplemented
36C2×C11×C4⋊Q8C2212yes—
37C2×C11×#124C2212yes—
38C2×C11×#123C2214yes—
39C2×C11×C22⋊Q8C2214yes—
40C2×C11×#117C2211yescharacteristic
41#10623363C22116yescomplemented
42C2×#67000C2211yescharacteristic
43C2×#66997C2211yescharacteristic
44C2×#66997C2212yes—
45C2×#66997C2212yes—
46C2×#66997C2214yes—
47C2×#66997C22116yescomplemented
48C2×#66993C2211yescharacteristic
49C2×#66992C2214yes—
50C2×#66989C2211yescharacteristic
51C2×C4×C22⋊D11C2214yes—
52C22×Dic11⋊C4C2214yes—
53C22×C4×Dic11C2211yescharacteristic
54#10623255C22132yescomplemented
55D11×C4⋊Q8C22132yescomplemented
56#10623206C22132yescomplemented
57#10623199C22132yescomplemented
58#10623186C221128yescomplemented
59#10623163C22164yescomplemented
60#10623162C22164yescomplemented
61#10623057C22116yescomplemented
62#10623053C22116yescomplemented
63C2×#66950C2214yes—
64C2×#66949C2218yes—
65C2×#66947C2218yes—
66C2×#66946C2212yes—
67C2×C4⋊C4×D11C2218yes—
68C2×#66941C2218yes—
69C2×#66940C2212yes—
70C2×#66939C2214yes—
71C2×#66937C2218yes—
72C2×#66936C2218yes—
73C2×(C22⋊D11)⋊C4C2218yes—
74C2×(C22⋊D11)⋊C4C2214yes—
75C2×#66931C2218yes—
76C2×#66928C2212yes—
77C2×#66925C2212yes—
78C2×C42×D11C2212yes—
79C2×#66922C2212yes—
80C2×C11×#41—28no—
81C2×C11×#41C2318yes—
82C22×Q8×C11—28no—
83C22×Q8×C11C2312yes—
84C22×Q8×C11C2312yes—
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2318yes—
87C22×D4×C11C2311yescharacteristic
88C22×D4×C11C2312yes—
89C23×C4×C11C2312yes—
90C23×C4×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2314yes—
94C22×C22⋊D11C2312yes—
95C22×C22⋊D11C2312yes—
96C23×Dic11C2314yes—
97C23×Dic11C2312yes—
98C23×Dic11C2312yes—
99#67043—2128no—
100#67040—2128no—
101C2×#4343—216no—
102C2×#4343—216no—
103C2×#4343C23116yes—
104C2×#4343C23116yes—
105C2×Q8×D11—216no—
106C2×Q8×D11—216no—
107C2×Q8×D11—216no—
108C2×Q8×D11C23116yes—
109C2×Q8×D11C23116yes—
110C2×Q8×D11C23116yes—
111C2×#4341—232no—
112C2×#4341—216no—
113C2×#4341C23132yes—
114C2×#4341C23116yes—
115C2×#4339—28no—
116C2×#4339—232no—
117C2×#4339—216no—
118C2×#4339D4116yescomplemented
119C2×#4339C2318yes—
120C2×#4339C23116yes—
121C2×#4339C23132yes—
122C2×#4339C2318yes—
123C22×D44C2311yescharacteristic
124C22×D44C2314yes—
125C22×D44C2311yescharacteristic
126C22×C4×D11C2314yes—
127C22×C4×D11C2314yes—
128C22×C4×D11C2314yes—
129C22×C4×D11C2314yes—
130C22×C4×D11C2312yes—
131C22×C4×D11C2312yes—
132C22×Dic22—28no—
133C22×Dic22—216no—
134C22×Dic22C2311yescharacteristic
135C22×Dic22C2312yes—
136C22×Dic22C2314yes—
137C22×Dic22C2314yes—
138C22×Dic22C2312yes—
139C22×Dic22C2318yes—
140C22×Dic22C23116yes—
141C22×Dic22C2311yescharacteristic
142C11×C4⋊Q8C23116yes—
143C11×#124C23116yes—
144C11×#123C23132yes—
145C11×C22⋊Q8C23132yes—
146C11×#117C2318yes—
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C4⋊C4C2318yes—
149C2×C11×C22⋊C4C2318yes—
150C2×C11×C22⋊C4C2312yes—
151C2×C42×C11C2312yes—
152C2×C22⋊Dic11C2314yes—
153#67000C2318yes—
154#66997C2318yes—
155#66997C23116yes—
156#66997C23116yes—
157#66997C23132yes—
158#66993C2318yes—
159#66992C23132yes—
160#66989C2318yes—
161C4×C22⋊D11C23132yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2318yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×C4⋊Dic11C2318yes—
166C2×Dic11⋊C4C2314yes—
167C2×Dic11⋊C4C2318yes—
168C2×Dic11⋊C4C2318yes—
169C2×Dic11⋊C4C2314yes—
170C2×Dic11⋊C4C23132yes—
171C2×C4×Dic11C2311yescharacteristic
172C2×C4×Dic11C2314yes—
173C2×C4×Dic11C2311yescharacteristic
174C2×C4×Dic11C2312yes—
175C2×C4×Dic11C2318yes—
176#66950C23132yes—
177#66949C23164yes—
178#66947C23164yes—
179#66946C23116yes—
180C4⋊C4×D11C23164yes—
181#66941C23164yes—
182#66940C23116yes—
183#66939C23132yes—
184#66937C23164yes—
185#66936C23164yes—
186(C22⋊D11)⋊C4C23132yes—
187(C22⋊D11)⋊C4C23164yes—
188#66931C23164yes—
189#66928C23116yes—
190#66925C23116yes—
191C42×D11C23116yes—
192#66922C23116yes—
193C2×#3499—111nomaximal, Sylow
194C24×C11C2412yes—
195C24×C11C2411yescharacteristic
196C23×D11C2412yes—
197C23×D11C2412yes—
198C11×#41—232no—
199C2×Q8×C11—24no—
200C2×Q8×C11—28no—
201C2×Q8×C11—28no—
202C2×Q8×C11—232no—
203C2×Q8×C11C2418yes—
204C2×Q8×C11C2418yes—
205C2×Q8×C11C2414yes—
206C2×D4×C11—28no—
207C2×D4×C11—24no—
208C2×D4×C11C2414yes—
209C2×D4×C11C2418yes—
210C22×C4×C11—28no—
211C22×C4×C11—28no—
212C22×C4×C11C2×D418yes—
213C22×C4×C11C2414yes—
214C22×C4×C11C2414yes—
215C22×C4×C11C2418yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2418yes—
218C22×C4×C11C2411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C22×C4×C11C2414yes—
221C2×C22⋊D11—216no—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—216no—
224C2×C22⋊D11C2×D4116yes—
225C2×C22⋊D11C24116yes—
226C2×C22⋊D11C24116yes—
227C2×C22⋊D11C2418yes—
228C2×C22⋊D11C2418yes—
229C22×Dic11—216no—
230C22×Dic11—28no—
231C22×Dic11—28no—
232C22×Dic11C24116yes—
233C22×Dic11C2418yes—
234C22×Dic11C2418yes—
235C22×Dic11C2412yes—
236C22×Dic11C2414yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240#4343—264no—
241#4343—264no—
242Q8×D11—264no—
243Q8×D11—264no—
244Q8×D11—264no—
245#4341—2128no—
246#4341—264no—
247#4339—2128no—
248#4339—264no—
249#4339—232no—
250#4339C2×D4164yescomplemented
251C2×D44—216no—
252C2×D44—24no—
253C2×D44C2×D418yes—
254C2×D44C2414yes—
255C2×D44C24116yes—
256C2×D44C2414yes—
257C2×C4×D11—216no—
258C2×C4×D11—216no—
259C2×C4×D11—216no—
260C2×C4×D11—216no—
261C2×C4×D11—28no—
262C2×C4×D11C2×D4116yes—
263C2×C4×D11C24116yes—
264C2×C4×D11C24116yes—
265C2×C4×D11C24116yes—
266C2×C4×D11C24116yes—
267C2×C4×D11C2418yes—
268C2×C4×D11C2418yes—
269C2×Dic22—216no—
270C2×Dic22—216no—
271C2×Dic22—264no—
272C2×Dic22—28no—
273C2×Dic22—28no—
274C2×Dic22—232no—
275C2×Dic22—24no—
276C2×Dic22C2×D418yes—
277C2×Dic22C2414yes—
278C2×Dic22C2418yes—
279C2×Dic22C24116yes—
280C2×Dic22C24116yes—
281C2×Dic22C2418yes—
282C2×Dic22C2414yes—
283C11×C4⋊C4C2418yes—
284C11×C4⋊C4C24132yes—
285C11×C22⋊C4C24132yes—
286C11×C22⋊C4C2418yes—
287C42×C11C2418yes—
288C22⋊Dic11C24116yes—
289(C2×D11)⋊C4C24116yes—
290(C2×D11)⋊C4C24132yes—
291(C2×D11)⋊C4C24116yes—
292C4⋊Dic11C24132yes—
293Dic11⋊C4C24116yes—
294Dic11⋊C4C24132yes—
295Dic11⋊C4C24132yes—
296Dic11⋊C4C24116yes—
297C4×Dic11C2414yes—
298C4×Dic11C24116yes—
299C4×Dic11C2414yes—
300C4×Dic11C2418yes—
301C22×2−1+4—111no—
302C22×2−1+4—111no—
303#3499—1132no—
304C2×D4×Q8—114no—
305C2×#547—118no—
306C2×#547—114no—
307C2×#536—112no—
308C2×#536—112no—
309C2×#536—111no—
310C2×#536D1111yescharacteristic, complemented
311C2×#532—111no—
312C2×#532—112no—
313C22×C4⋊Q8—111no—
314C22×C4⋊Q8—112no—
315C2×C4×#41—111no—
316C23×C11—24no—
317C23×C11—24no—
318C23×C11—28no—
319C23×C11C22×D414yes—
320C23×C11C2514yes—
321C23×C11C2512yes—
322C23×C11C2511yescharacteristic
323C22×D11—28no—
324C22×D11—24no—
325C22×D11—28no—
326C22×D11C22×D418yes—
327C22×D11C2514yes—
328C22×D11C2514yes—
329Q8×C11—28no—
330Q8×C11—216no—
331Q8×C11—216no—
332D4×C11—216no—
333D4×C11—28no—
334C2×C4×C11—24no—
335C2×C4×C11—28no—
336C2×C4×C11—216no—
337C2×C4×C11—28no—
338C2×C4×C11—216no—
339C2×C4×C11C22×D414yes—
340C2×C4×C11C22×D414yes—
341C2×C4×C11C22×D4116yes—
342C2×C4×C11C2518yes—
343C2×C4×C11C2518yes—
344C2×C4×C11C2514yes—
345C2×C4×C11C2512yes—
346C2×C4×C11C2512yes—
347C22⋊D11—216no—
348C22⋊D11—232no—
349C22⋊D11—232no—
350C22⋊D11C22×D4132yes—
351C2×Dic11—24no—
352C2×Dic11—28no—
353C2×Dic11—216no—
354C2×Dic11—24no—
355C2×Dic11—232no—
356C2×Dic11—216no—
357C2×Dic11C22×D418yes—
358C2×Dic112−1+418yescomplemented
359C2×Dic11C2514yes—
360C2×Dic11C2518yes—
361C2×Dic11C2514yes—
362C2×Dic11C2514yes—
363C2×Dic11C2514yes—
364D44—232no—
365D44—28no—
366D44C22×D4116yes—
367C4×D11—232no—
368C4×D11—232no—
369C4×D11—216no—
370C4×D11—232no—
371C4×D11—232no—
372C4×D11C22×D4132yes—
373Dic22—216no—
374Dic22—216no—
375Dic22—28no—
376Dic22—232no—
377Dic22—232no—
378Dic22C22×D4116yes—
379C2×2−1+4—1116no—
380C2×2−1+4—1116no—
381C2×2−1+4—2216no—
382C2×2−1+4—2216no—
383C22×#41—112no—
384C22×#41—112no—
385C22×#41—112no—
386C22×#41—114no—
387C22×#41—111no—
388C22×#41—111no—
389C22×#41—112no—
390C22×#41—114no—
391C22×#41C2×D1111yescharacteristic
392C23×Q8—112no—
393C23×Q8—112no—
394C23×Q8—112no—
395C23×Q8—111no—
396C23×Q8—112no—
397C23×Q8C2×D1111yescharacteristic
398D4×Q8—1164no—
399#547—11128no—
400#547—1164no—
401#536—1132no—
402#536—1132no—
403#536—1116no—
404#536C2×D11116yescomplemented
405#532—1116no—
406#532—1132no—
407C2×C4⋊Q8—111no—
408C2×C4⋊Q8—112no—
409C2×C4⋊Q8—112no—
410C2×C4⋊Q8—114no—
411C2×C4⋊Q8—1116no—
412C2×C4⋊Q8—1132no—
413C2×C4⋊Q8—118no—
414C2×C4⋊Q8—112no—
415C2×C4⋊Q8C2×D1112yes—
416C2×#127—111no—
417C2×#124—111no—
418C2×#124—111no—
419C2×#124—112no—
420C2×#124C2×D1112yes—
421C2×#123—118no—
422C2×#123—118no—
423C2×#123—114no—
424C2×#123C2×D1114yes—
425C2×C22⋊Q8—118no—
426C2×C22⋊Q8—114no—
427C2×C22⋊Q8—118no—
428C2×C22⋊Q8C2×D1114yes—
429C2×#121—114no—
430C2×#121—118no—
431C4×#41—1116no—
432C2×C4×Q8—112no—
433C2×C4×D4—114no—
434C2×C4×D4—112no—
435C2×C4×D4—114no—
436C2×C4×D4—118no—
437C2×#117—112no—
438C2×#117C2×D1111yescharacteristic
439C22×C4⋊C4—114no—
440C22×C4⋊C4—118no—
441C22×C42—111no—
442C22×C42—112no—
443C22×C11—24no—
444C22×C11—28no—
445C22×C11—24no—
446C22×C11—28no—
447C22×C11—48no—
448C22×C11C23×D414yes—
449C22×C11C23×D412yes—
450C22×C11C2×2−1+414yes—
451C22×C11C2611yescharacteristic
452C2×D11—28no—
453C2×D11—216no—
454C2×D11—24no—
455C2×D11—28no—
456C2×D11—48no—
457C2×D11C23×D418yes—
458C4×C11—24no—
459C4×C11—28no—
460C4×C11—28no—
461C4×C11C23×D414yes—
462C4×C11C23×D414yes—
463Dic11—24no—
464Dic11—28no—
465Dic11—24no—
466Dic11C23×D418yes—
467Dic11C2×2−1+418yescomplemented
4682−1+4—22128no—
4692−1+4—22128no—
470C2×#41—28no—
471C2×#41—1116no—
472C2×#41—1116no—
473C2×#41—1116no—
474C2×#41—1132no—
475C2×#41—1116no—
476C2×#41—118no—
477C2×#41—118no—
478C2×#41—1116no—
479C2×#41—1132no—
480C2×#41—2232no—
481C2×#41—2216no—
482C2×#41—2216no—
483C2×#41—2216no—
484C2×#41—2232no—
485C2×#41—2216no—
486C2×#41—228no—
487C2×#41C22×D1118yes—
488C22×Q8—28no—
489C22×Q8—1116no—
490C22×Q8—1116no—
491C22×Q8—1116no—
492C22×Q8—111no—
493C22×Q8—114no—
494C22×Q8—114no—
495C22×Q8—112no—
496C22×Q8—111no—
497C22×Q8—112no—
498C22×Q8—118no—
499C22×Q8—1116no—
500C22×Q8—2216no—
501C22×Q8—2216no—
502C22×Q8—2216no—
503C22×Q8—2216no—
504C22×Q8—228no—
505C22×Q8C22×D1112yes—
506C22×Q8C22×D1111yescharacteristic
507C22×Q8C22×D1112yes—
508C22×Q8C22×D1118yes—
509C22×D4—112no—
510C22×D4—114no—
511C22×D4—114no—
512C22×D4—112no—
513C22×D4—111no—
514C22×D4—114no—
515C22×D4—111no—
516C22×D4C22×D1112yes—
517C22×D4C22×D1111yescharacteristic
518C23×C4—112no—
519C23×C4—112no—
520C23×C4—112no—
521C23×C4—114no—
522C23×C4—114no—
523C23×C4—114no—
524C23×C4—114no—
525C23×C4—114no—
526C23×C4—112no—
527C23×C4C22×D1112yes—
528C23×C4C22×D1112yes—
529C23×C4C22×D1111yescharacteristic
530C4⋊Q8—118no—
531C4⋊Q8—1116no—
532C4⋊Q8—1116no—
533C4⋊Q8—1132no—
534C4⋊Q8—1164no—
535C4⋊Q8—1116no—
536C4⋊Q8C22×D11116yes—
537#127—118no—
538#124—118no—
539#124—118no—
540#124—1116no—
541#124C22×D11116yes—
542#123—1164no—
543#123—1164no—
544#123—1132no—
545#123C22×D11132yes—
546C22⋊Q8—1164no—
547C22⋊Q8—1132no—
548C22⋊Q8—1164no—
549C22⋊Q8C22×D11132yes—
550#121—1132no—
551#121—1164no—
552C4×Q8—1116no—
553C4×D4—1132no—
554C4×D4—1116no—
555C4×D4—1132no—
556C4×D4—1164no—
557#117—1116no—
558#117C22×D1118yes—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—118no—
561C2×C4⋊C4—118no—
562C2×C4⋊C4—118no—
563C2×C4⋊C4—1132no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—1164no—
566C2×C4⋊C4C22×D1118yes—
567C2×C4⋊C4C22×D1112yes—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—118no—
572C2×C22⋊C4C22×D1112yes—
573C2×C22⋊C4C22×D1118yes—
574C2×C42—111no—
575C2×C42—114no—
576C2×C42—112no—
577C2×C42—118no—
578C2×C42—111no—
579C2×C42—1116no—
580C2×C42C22×D1112yes—
581C2×C11—24no—
582C2×C11—44no—
583C2×C11#349914yescomplemented
584C2×C11C24×D411yescharacteristic
585C2×C11C22×2−1+412yes—
586D11—28no—
587D11—44no—
588C24—112no—
589C24—112no—
590C24C23×D1112yes—
591C24C23×D1111yescharacteristic
592#41—232no—
593#41—1164no—
594#41—22128no—
595#41—2264no—
596#41—2264no—
597#41—2264no—
598#41—22128no—
599#41—2264no—
600#41—2232no—
601C2×Q8—28no—
602C2×Q8—28no—
603C2×Q8—232no—
604C2×Q8—24no—
605C2×Q8—118no—
606C2×Q8—114no—
607C2×Q8—1116no—
608C2×Q8—1116no—
609C2×Q8—118no—
610C2×Q8—114no—
611C2×Q8—118no—
612C2×Q8—2216no—
613C2×Q8—2216no—
614C2×Q8—2264no—
615C2×Q8—2264no—
616C2×Q8—2264no—
617C2×Q8—2264no—
618C2×Q8—228no—
619C2×Q8—224no—
620C2×Q8—228no—
621C2×Q8—2232no—
622C2×Q8C23×D1118yes—
623C2×Q8C23×D1114yes—
624C2×Q8C23×D1118yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—1116no—
628C2×D4—118no—
629C2×D4—1116no—
630C2×D4—1116no—
631C2×D4—118no—
632C2×D4—118no—
633C2×D4—114no—
634C2×D4—1116no—
635C2×D4—114no—
636C2×D4—2216no—
637C2×D4—2216no—
638C2×D4—2216no—
639C2×D4—228no—
640C2×D4—224no—
641C2×D4C23×D1118yes—
642C2×D4C23×D1114yes—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—1116no—
648C22×C4—118no—
649C22×C4—118no—
650C22×C4—118no—
651C22×C4—1116no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—114no—
655C22×C4—1116no—
656C22×C4—1116no—
657C22×C4—1116no—
658C22×C4—1116no—
659C22×C4—118no—
660C22×C4—2216no—
661C22×C4—2216no—
662C22×C4—2216no—
663C22×C4—2216no—
664C22×C4—2216no—
665C22×C4—228no—
666C22×C4—228no—
667C22×C4—228no—
668C22×C4D4×D1118yes—
669C22×C4C23×D1118yes—
670C22×C4C23×D1118yes—
671C22×C4C23×D1114yes—
672C22×C4C23×D1112yes—
673C22×C4C23×D1114yes—
674C22×C4C23×D1114yes—
675C22×C4C23×D1111yescharacteristic
676C22×C4C23×D1111yescharacteristic
677C4⋊C4—1116no—
678C4⋊C4—1132no—
679C4⋊C4—1132no—
680C4⋊C4—1132no—
681C4⋊C4—1116no—
682C4⋊C4C23×D11132yes—
683C4⋊C4C23×D1118yes—
684C22⋊C4—1116no—
685C22⋊C4—1116no—
686C22⋊C4—1116no—
687C22⋊C4—1132no—
688C22⋊C4C23×D1118yes—
689C22⋊C4C23×D11132yes—
690C42—114no—
691C42—114no—
692C42—1116no—
693C42—118no—
694C42C23×D1118yes—
695C11C2×#349911yescharacteristic, complemented, Sylow
696C23—24no—
697C23—24no—
698C23—28no—
699C23—118no—
700C23—114no—
701C23—114no—
702C23—228no—
703C23—224no—
704C23—228no—
705C23C2×D4×D1114yes—
706C23C24×D1114yes—
707C23C24×D1112yes—
708C23C24×D1111yescharacteristic
709Q8—216no—
710Q8—216no—
711Q8—28no—
712Q8—1116no—
713Q8—2232no—
714Q8—2232no—
715Q8—2216no—
716Q8—228no—
717Q8—2216no—
718D4—216no—
719D4—28no—
720D4—1132no—
721D4—1116no—
722D4—2232no—
723D4—2232no—
724D4—2232no—
725D4—2216no—
726D4—228no—
727C2×C4—24no—
728C2×C4—28no—
729C2×C4—216no—
730C2×C4—28no—
731C2×C4—216no—
732C2×C4—118no—
733C2×C4—118no—
734C2×C4—114no—
735C2×C4—114no—
736C2×C4—1132no—
737C2×C4—114no—
738C2×C4—114no—
739C2×C4—118no—
740C2×C4—2232no—
741C2×C4—2232no—
742C2×C4—2232no—
743C2×C4—2232no—
744C2×C4—2232no—
745C2×C4—2216no—
746C2×C4—224no—
747C2×C4—228no—
748C2×C4—2216no—
749C2×C4—224no—
750C2×C4—2216no—
751C2×C4C2×D4×D1114yes—
752C2×C4C2×D4×D1114yes—
753C2×C4C2×D4×D11116yes—
754C2×C4C24×D1118yes—
755C2×C4C24×D1114yes—
756C2×C4C24×D1118yes—
757C2×C4C24×D1112yes—
758C2×C4C24×D1112yes—
759C22—24no—
760C22—28no—
761C22—24no—
762C22—28no—
763C22—48no—
764C22—118no—
765C22—228no—
766C22—2216no—
767C22—224no—
768C22—228no—
769C22—448no—
770C22C22×D4×D1114yes—
771C22C22×D4×D1112yes—
772C22D11×2−1+414yes—
773C22C25×D1111yescharacteristic
774C4—24no—
775C4—28no—
776C4—28no—
777C4—118no—
778C4—118no—
779C4—224no—
780C4—228no—
781C4—224no—
782C4C22×D4×D1114yes—
783C4C22×D4×D1114yes—
784C2—24no—
785C2—44no—
786C2—228no—
787C2—444no—
788C2#1308239814yesdirect product factor
789C2C23×D4×D1111yescharacteristic
790C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#536C2
socleC23×C11C25
hypercenterC2×#536D11
hypocenterC11C2×#3499
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C22×#67040C2semidirect
2. C22×#67043C2semidirect
3. #13082398C2direct (N × H)
4. C2×#10623163C2semidirect
5. C2×#10623162C2semidirect
6. C2×#10623186C2semidirect
7. C2×#10623057C2semidirect
8. C2×#10623255C2semidirect
9. C2×#10623206C2semidirect
10. C2×#10623199C2semidirect
11. C2×#10623363C2semidirect
12. C22×#66997C2semidirect
13. C2×D11×C4⋊Q8C2semidirect
14. C2×#10623053C2semidirect
15. C2×C11×#536C2semidirect
19. C2×#67043C22semidirect
21. C2×#67040C22semidirect
35. C11×#536C22semidirect
41. #10623363C22semidirect
47. C2×#66997C22semidirect
54. #10623255C22semidirect
55. D11×C4⋊Q8C22semidirect
56. #10623206C22semidirect
57. #10623199C22semidirect
58. #10623186C22semidirect
59. #10623163C22semidirect
60. #10623162C22semidirect
61. #10623057C22semidirect
62. #10623053C22semidirect
118. C2×#4339D4semidirect
250. #4339C2×D4semidirect
310. C2×#536D11semidirect
358. C2×Dic112−1+4semidirect
404. #536C2×D11semidirect
467. Dic11C2×2−1+4semidirect
583. C2×C11#3499semidirect
695. C11C2×#3499semidirect
788. C2#13082398direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670402
C22×#670432
#130823982
C2×#106231632
C2×#106231622
C2×#106231862
C2×#106230572
C2×#106232552
C2×#106232062
C2×#106231992
C2×#106233632
C22×#669972
C2×D11×C4⋊Q82
C2×#106230532
C2×C11×#5362
C2×#349911