Finite Group Databasebeta

← C2×#13082262 #15661935

Subgroups — C2×#13082262 #15661935

Order 2816.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67043C211yesmaximal, characteristic, complemented
2C23×Q8×D11C211yesmaximal, characteristic, complemented
3#13082262C2132yesmaximal, direct product factor
4C2×Q8×D44C211yesmaximal, characteristic, complemented
5C2×D4×Dic22C213yesmaximal, complemented
6C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
7C2×#10623163C213yesmaximal, complemented
8C2×#10623208C213yesmaximal, complemented
9C2×#10623362C211yesmaximal, characteristic, complemented
10C2×#10623129C213yesmaximal, complemented
11C2×#10623159C213yesmaximal, complemented
12C2×#10623206C213yesmaximal, complemented
13C2×#10623137C213yesmaximal, complemented
14C2×#10623078C213yesmaximal, complemented
15C2×#10623103C211yesmaximal, characteristic, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C23×Q8×C11C2211yescharacteristic
19C2×#67043—216no—
20C2×#67043C22116yescomplemented
21C22×Q8×D11—216no—
22C22×Q8×D11C2213yes—
23C22×Q8×D11C2211yescharacteristic
24C22×Q8×D11C2213yes—
25C22×Q8×D11C2211yescharacteristic
26C22×Q8×D11C22116yescomplemented
27C22×Q8×D11C2211yescharacteristic, complemented
28C22×#4341C2213yes—
29C22×#4341C2213yescomplemented
30C22×#4339C2213yes—
31C23×C4×D11C2213yes—
32C23×Dic22C2213yes—
33C23×Dic22C2213yescomplemented
34C11×#548C22116yescomplemented
35C2×C11×#124C2213yescomplemented
36C2×C11×C22⋊Q8C2213yescomplemented
37C2×C11×#121C2213yes—
38C2×C4×Q8×C11C2211yescharacteristic, complemented
39C2×C4×D4×C11C2213yes—
40#10623362C22116yescomplemented
41Q8×C22⋊D11C22116yescomplemented
42C2×#66999C2213yescomplemented
43C2×Q8×Dic11C2211yescharacteristic, complemented
44C2×#66997C2213yescomplemented
45C2×#66992C2213yes—
46C2×#66991C2213yes—
47C2×#66990C2213yes—
48C2×#66989C2213yescomplemented
49C2×D4×Dic11C2216yes—
50C2×C4×C22⋊D11C2213yes—
51C2×C4×C22⋊D11C2213yes—
52C2×#66977C2213yes—
53C2×#66977C2213yescomplemented
54#10623208C22148yescomplemented
55#10623206C22148yescomplemented
56#10623163C22148yescomplemented
57#10623159C22148yescomplemented
58#10623137C22148yescomplemented
59#10623129C22148yescomplemented
60Q8×D44C22116yescomplemented
61#10623103C22116yescomplemented
62#10623078C22148yescomplemented
63D4×Dic22C22148yescomplemented
64C2×#66950C2213yes—
65C2×#66950C2213yescomplemented
66C2×#66949C2213yes—
67C2×#66947C2213yes—
68C2×#66945C2213yes—
69C2×#66941C2216yescomplemented
70C2×#66940C2213yescomplemented
71C2×#66938C2216yescomplemented
72C2×#66937C2213yes—
73C2×#66936C2213yes—
74C2×#66936C2216yes—
75C2×#66935C2211yescharacteristic
76C2×(C22⋊D11)⋊C4C2216yes—
77C2×#66931C2213yes—
78C2×#66931C2216yescomplemented
79C2×#66931C2216yescomplemented
80C2×C4×D44C2213yes—
81C2×#66925C2213yes—
82C2×#66922C2213yescomplemented
83C2×C4×Dic22C2213yescomplemented
84C24×D11C2311yescharacteristic
85C2×C11×#41—28no—
86C2×C11×#41C2318yescomplemented
87C22×Q8×C11—28no—
88C22×Q8×C11C2313yes—
89C22×Q8×C11C2318yes—
90C22×Q8×C11C2311yescharacteristic
91C22×D4×C11C2313yes—
92C22×D4×C11C2313yes—
93C23×C4×C11C2313yes—
94C23×C4×C11C2313yes—
95C22×C22⋊D11C2313yes—
96C22×C22⋊D11C2311yescharacteristic
97C22×C22⋊D11C2313yes—
98C22×C22⋊D11C2313yes—
99C23×Dic11C2313yes—
100C23×Dic11C2316yes—
101#67043—2128no—
102C2×Q8×D11—28no—
103C2×Q8×D11—28no—
104C2×Q8×D11—2128no—
105C2×Q8×D11—224no—
106C2×Q8×D11—224no—
107C2×Q8×D11D4116yescomplemented
108C2×Q8×D11C2318yes—
109C2×Q8×D11C23124yes—
110C2×Q8×D11C23124yes—
111C2×Q8×D11C2318yes—
112C2×Q8×D11C2318yescomplemented
113C2×#4341—224no—
114C2×#4341—224no—
115C2×#4341C23124yes—
116C2×#4341C23124yescomplemented
117C2×#4339—224no—
118C2×#4339C23124yes—
119C22×D44C2311yescharacteristic
120C22×D44C2311yescharacteristic
121C22×C4×D11—224no—
122C22×C4×D11C2313yes—
123C22×C4×D11C2313yes—
124C22×C4×D11C2313yes—
125C22×C4×D11C2313yes—
126C22×C4×D11C23124yes—
127C22×C4×D11C2313yes—
128C22×Dic22—224no—
129C22×Dic22—224no—
130C22×Dic22C2313yes—
131C22×Dic22C2313yes—
132C22×Dic22C2313yes—
133C22×Dic22C2316yes—
134C22×Dic22C23124yes—
135C22×Dic22C2313yes—
136C22×Dic22C23124yescomplemented
137C11×#124C23124yescomplemented
138C11×C22⋊Q8C23124yescomplemented
139C11×#121C23124yes—
140C4×Q8×C11C2318yescomplemented
141C4×D4×C11C23124yes—
142C2×C11×C4⋊C4C2313yes—
143C2×C11×C4⋊C4C2313yes—
144C2×C11×C22⋊C4C2311yescharacteristic
145C2×C11×C22⋊C4C2313yes—
146C2×C11×C22⋊C4C2316yes—
147C2×C42×C11C2313yes—
148C2×C22⋊Dic11C2313yes—
149C2×C22⋊Dic11C2313yes—
150C2×C22⋊Dic11C2316yes—
151#66999C23124yescomplemented
152Q8×Dic11C2318yescomplemented
153#66997C23124yescomplemented
154#66992C23124yes—
155#66991C23124yes—
156#66990C23124yes—
157#66989C23124yescomplemented
158D4×Dic11C23148yes—
159C4×C22⋊D11C23124yes—
160C4×C22⋊D11C23124yes—
161C2×(C2×D11)⋊C4C2311yescharacteristic
162C2×(C2×D11)⋊C4C2313yes—
163C2×(C2×D11)⋊C4C2313yes—
164C2×(C2×D11)⋊C4C2313yes—
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2313yes—
167C2×C4⋊Dic11C2313yes—
168C2×C4⋊Dic11C2313yes—
169C2×C4⋊Dic11C2316yes—
170#66977C23124yes—
171#66977C23124yescomplemented
172C2×Dic11⋊C4C2313yes—
173C2×Dic11⋊C4C2313yes—
174C2×Dic11⋊C4C2313yes—
175C2×Dic11⋊C4C2313yes—
176C2×Dic11⋊C4C2316yes—
177C2×C4×Dic11C2316yes—
178C2×C4×Dic11C2313yes—
179#66950C23124yes—
180#66950C23124yescomplemented
181#66949C23124yes—
182#66947C23124yes—
183#66945C23124yes—
184#66941C23148yescomplemented
185#66940C23124yescomplemented
186#66938C23148yescomplemented
187#66937C23124yes—
188#66936C23124yes—
189#66936C23148yes—
190#66935C2318yes—
191(C22⋊D11)⋊C4C23148yes—
192#66931C23124yes—
193#66931C23148yescomplemented
194#66931C23148yescomplemented
195C4×D44C23124yes—
196#66925C23124yes—
197#66922C23124yescomplemented
198C4×Dic22C23124yescomplemented
199C2×#3486—111nomaximal, Sylow
200C24×C11C2413yes—
201C24×C11C2411yescharacteristic
202C23×D11—24no—
203C23×D11—24no—
204C23×D11—24no—
205C23×D11C2414yes—
206C23×D11C2411yescharacteristic
207C23×D11C2411yescharacteristic
208C23×D11C2411yescharacteristic
209C11×#41—232no—
210C2×Q8×C11—232no—
211C2×Q8×C11—212no—
212C2×Q8×C11C2×D418yes—
213C2×Q8×C11C24112yes—
214C2×Q8×C11C2414yes—
215C2×D4×C11—212no—
216C2×D4×C11—212no—
217C2×D4×C11C24112yes—
218C2×D4×C11C24112yes—
219C22×C4×C11—212no—
220C22×C4×C11—212no—
221C22×C4×C11C2413yes—
222C22×C4×C11C2411yescharacteristic
223C22×C4×C11C2413yes—
224C22×C4×C11C2411yescharacteristic
225C22×C4×C11C24112yes—
226C22×C4×C11C24112yes—
227C22×C4×C11C2413yes—
228C2×C22⋊D11—212no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—212no—
231C2×C22⋊D11—212no—
232C2×C22⋊D11C24112yes—
233C2×C22⋊D11C2414yes—
234C2×C22⋊D11C24112yes—
235C2×C22⋊D11C24112yes—
236C22×Dic11—212no—
237C22×Dic11—224no—
238C22×Dic11C24112yes—
239C22×Dic11C24124yes—
240C22×Dic11C2411yescharacteristic
241C22×Dic11C2413yes—
242C22×Dic11C2413yes—
243C22×Dic11C2413yes—
244C22×Dic11C2413yes—
245Q8×D11—296no—
246Q8×D11—296no—
247Q8×D11—232no—
248Q8×D11—232no—
249Q8×D11C2×D4164yescomplemented
250#4341—296no—
251#4341—296no—
252#4339—296no—
253C2×D44—24no—
254C2×D44—24no—
255C2×D44C2414yes—
256C2×D44C2414yes—
257C2×C4×D11—212no—
258C2×C4×D11—296no—
259C2×C4×D11—212no—
260C2×C4×D11—212no—
261C2×C4×D11—212no—
262C2×C4×D11C2×D4124yes—
263C2×C4×D11C24112yes—
264C2×C4×D11C24112yes—
265C2×C4×D11C24112yes—
266C2×C4×D11C24112yes—
267C2×C4×D11C24112yes—
268C2×Dic22—212no—
269C2×Dic22—224no—
270C2×Dic22—296no—
271C2×Dic22—296no—
272C2×Dic22—212no—
273C2×Dic22—212no—
274C2×Dic22C2×D4124yes—
275C2×Dic22C24112yes—
276C2×Dic22C24112yes—
277C2×Dic22C24112yes—
278C2×Dic22C24124yes—
279C2×Dic22C24112yes—
280C11×C4⋊C4C24112yes—
281C11×C4⋊C4C24112yes—
282C11×C22⋊C4C2414yes—
283C11×C22⋊C4C24112yes—
284C11×C22⋊C4C24124yes—
285C42×C11C24112yes—
286C22⋊Dic11C24112yes—
287C22⋊Dic11C24112yes—
288C22⋊Dic11C24124yes—
289(C2×D11)⋊C4C2414yes—
290(C2×D11)⋊C4C24112yes—
291(C2×D11)⋊C4C24112yes—
292(C2×D11)⋊C4C24112yes—
293(C2×D11)⋊C4C2414yes—
294(C2×D11)⋊C4C24112yes—
295C4⋊Dic11C24112yes—
296C4⋊Dic11C24112yes—
297C4⋊Dic11C24124yes—
298Dic11⋊C4C24112yes—
299Dic11⋊C4C24112yes—
300Dic11⋊C4C24112yes—
301Dic11⋊C4C24112yes—
302Dic11⋊C4C24124yes—
303C4×Dic11C24124yes—
304C4×Dic11C24112yes—
305C22×2−1+4—111no—
306C24×Q8—111no—
307#3486—1132no—
308C2×D4×Q8—111no—
309C2×D4×Q8—113no—
310C2×D4×Q8—111no—
311C2×D4×Q8—113no—
312C2×#548—111no—
313C2×#548—113no—
314C2×#548—113no—
315C2×#548D1111yescharacteristic, complemented
316C2×#536—113no—
317C2×#536—113no—
318C2×#525—113no—
319C2×#525—113no—
320C2×#519—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—26no—
324C23×C11—26no—
325C23×C11—26no—
326C23×C112−1+414yescomplemented
327C23×C11C2516yes—
328C23×C11C2512yes—
329C23×C11C2511yescharacteristic
330C22×D11—232no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—28no—
336C22×D11—28no—
337C22×D11—28no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11C22×D414yes—
342C22×D112−1+414yescomplemented
343C22×D11C2512yes—
344C22×D11C2512yes—
345C22×D11C2512yes—
346Q8×C11—224no—
347Q8×C11C22×D4116yes—
348D4×C11—224no—
349D4×C11—224no—
350C2×C4×C11—22no—
351C2×C4×C11—26no—
352C2×C4×C11—22no—
353C2×C4×C11—26no—
354C2×C4×C11—224no—
355C2×C4×C11—224no—
356C2×C4×C11C22×D4112yes—
357C2×C4×C11C2516yes—
358C2×C4×C11C2512yes—
359C2×C4×C11C2516yes—
360C2×C4×C11C2512yes—
361C2×C4×C11C2516yes—
362C22⋊D11—28no—
363C22⋊D11—224no—
364C22⋊D11—224no—
365C22⋊D11—224no—
366C2×Dic11—26no—
367C2×Dic11—26no—
368C2×Dic11—22no—
369C2×Dic11—26no—
370C2×Dic11—224no—
371C2×Dic11—248no—
372C2×Dic11C22×D4112yes—
373C2×Dic11C2512yes—
374C2×Dic11C2516yes—
375C2×Dic11C2516yes—
376C2×Dic11C2516yes—
377C2×Dic11C2516yes—
378D44—28no—
379D44—28no—
380C4×D11—224no—
381C4×D11—224no—
382C4×D11—224no—
383C4×D11—224no—
384C4×D11C22×D4148yes—
385Dic22—224no—
386Dic22—224no—
387Dic22—224no—
388Dic22—248no—
389Dic22C22×D4148yes—
390C2×2−1+4—1116no—
391C2×2−1+4—2216no—
392C22×#41—113no—
393C22×#41—113no—
394C22×#41—113no—
395C22×#41C2×D1111yescharacteristic, complemented
396C23×Q8—111no—
397C23×Q8—113no—
398C23×Q8—113no—
399C23×Q8—111no—
400C23×Q8—1116no—
401C23×Q8—111no—
402C23×Q8—113no—
403C23×Q8—113no—
404C23×Q8—2216no—
405C23×Q8C2×D1111yescharacteristic
406C24×C4—113no—
407D4×Q8—1116no—
408D4×Q8—1148no—
409D4×Q8—1116no—
410D4×Q8—1148no—
411#548—1116no—
412#548—1148no—
413#548—1148no—
414#548C2×D11116yescomplemented
415#536—1148no—
416#536—1148no—
417C2×C4⋊Q8—113no—
418C2×C4⋊Q8—116no—
419C2×C4⋊Q8—113no—
420C2×#124—113no—
421C2×#124—116no—
422C2×#124C2×D1113yescomplemented
423#525—1148no—
424#525—1148no—
425C2×#123—113no—
426C2×#123—116no—
427C2×#123—113no—
428C2×C22⋊Q8—113no—
429C2×C22⋊Q8—113no—
430C2×C22⋊Q8—113no—
431C2×C22⋊Q8—113no—
432C2×C22⋊Q8—113no—
433C2×C22⋊Q8—113no—
434C2×C22⋊Q8—113no—
435C2×C22⋊Q8—116no—
436C2×C22⋊Q8—116no—
437C2×C22⋊Q8C2×D1113yescomplemented
438C2×#121—113no—
439C2×#121—113no—
440C2×#121—113no—
441C2×#121C2×D1113yes—
442C2×#120—113no—
443C2×#120—111no—
444#519—1116no—
445C2×C4×Q8—111no—
446C2×C4×Q8—113no—
447C2×C4×Q8—113no—
448C2×C4×Q8C2×D1111yescharacteristic, complemented
449C2×C4×D4—116no—
450C2×C4×D4—113no—
451C2×C4×D4—113no—
452C2×C4×D4—116no—
453C2×C4×D4—113no—
454C2×C4×D4C2×D1113yes—
455C2×#117—113no—
456C2×#117—113no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—28no—
460C22×C11—26no—
461C22×C11—26no—
462C22×C11—26no—
463C22×C11—412no—
464C22×C11C23×D412yes—
465C22×C11C2×2−1+412yes—
466C22×C11C2×2−1+412yes—
467C22×C11C2×2−1+414yescomplemented
468C22×C11C2611yescharacteristic
469C2×D11—232no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—28no—
475C2×D11—28no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—44no—
480C2×D11C23×D414yes—
481C2×D11C2×2−1+414yescomplemented
482C4×C11—22no—
483C4×C11—26no—
484C4×C11—26no—
485C4×C11—22no—
486C4×C11C23×D4112yes—
487Dic11—26no—
488Dic11—26no—
489Dic11—26no—
490Dic11—22no—
491Dic11C23×D4112yes—
492C25—111no—
4932−1+4—22128no—
494C2×#41—28no—
495C2×#41—1124no—
496C2×#41—1124no—
497C2×#41—1124no—
498C2×#41—2224no—
499C2×#41—2224no—
500C2×#41—2224no—
501C2×#41C22×D1118yescomplemented
502C22×Q8—28no—
503C22×Q8—1116no—
504C22×Q8—118no—
505C22×Q8—1124no—
506C22×Q8—1124no—
507C22×Q8—118no—
508C22×Q8—118no—
509C22×Q8—113no—
510C22×Q8—116no—
511C22×Q8—113no—
512C22×Q8—113no—
513C22×Q8—113no—
514C22×Q8—1124no—
515C22×Q8—1124no—
516C22×Q8—2224no—
517C22×Q8—2224no—
518C22×Q8—2224no—
519C22×Q8—22128no—
520C22×Q8—2224no—
521C22×Q8—228no—
522C22×Q8—228no—
523C22×Q8C22×D1113yes—
524C22×Q8C22×D1118yes—
525C22×Q8C22×D1111yescharacteristic
526C22×D4—113no—
527C22×D4—111no—
528C22×D4—113no—
529C22×D4—113no—
530C22×D4—111no—
531C22×D4—111no—
532C22×D4C22×D1113yes—
533C22×D4C22×D1113yes—
534C23×C4—113no—
535C23×C4—113no—
536C23×C4—116no—
537C23×C4—113no—
538C23×C4—113no—
539C23×C4—113no—
540C23×C4—113no—
541C23×C4—1124no—
542C23×C4—2224no—
543C23×C4C22×D1113yes—
544C23×C4C22×D1113yes—
545C4⋊Q8—1124no—
546C4⋊Q8—1148no—
547C4⋊Q8—1124no—
548#124—1124no—
549#124—1148no—
550#124C22×D11124yescomplemented
551#123—1124no—
552#123—1148no—
553#123—1124no—
554C22⋊Q8—1124no—
555C22⋊Q8—1124no—
556C22⋊Q8—1124no—
557C22⋊Q8—1124no—
558C22⋊Q8—1124no—
559C22⋊Q8—1124no—
560C22⋊Q8—1124no—
561C22⋊Q8—1148no—
562C22⋊Q8—1148no—
563C22⋊Q8C22×D11124yescomplemented
564#121—1124no—
565#121—1124no—
566#121—1124no—
567#121C22×D11124yes—
568#120—1124no—
569#120—118no—
570C4×Q8—118no—
571C4×Q8—1124no—
572C4×Q8—1124no—
573C4×Q8C22×D1118yescomplemented
574C4×D4—1148no—
575C4×D4—1124no—
576C4×D4—1124no—
577C4×D4—1148no—
578C4×D4—1124no—
579C4×D4C22×D11124yes—
580#117—1124no—
581#117—1124no—
582C2×C4⋊C4—113no—
583C2×C4⋊C4—113no—
584C2×C4⋊C4—113no—
585C2×C4⋊C4—113no—
586C2×C4⋊C4—113no—
587C2×C4⋊C4—116no—
588C2×C4⋊C4—116no—
589C2×C4⋊C4—113no—
590C2×C4⋊C4C22×D1113yes—
591C2×C4⋊C4C22×D1113yes—
592C2×C22⋊C4—113no—
593C2×C22⋊C4—116no—
594C2×C22⋊C4—113no—
595C2×C22⋊C4—113no—
596C2×C22⋊C4—111no—
597C2×C22⋊C4—111no—
598C2×C22⋊C4—113no—
599C2×C22⋊C4—113no—
600C2×C22⋊C4—113no—
601C2×C22⋊C4C22×D1116yes—
602C2×C22⋊C4C22×D1111yescharacteristic
603C2×C22⋊C4C22×D1113yes—
604C2×C42—116no—
605C2×C42—113no—
606C2×C42C22×D1113yes—
607C2×C11—24no—
608C2×C11—46no—
609C2×C11#348614yescomplemented
610C2×C11C24×D411yescharacteristic
611C2×C11C22×2−1+411yescharacteristic
612C2×C11C22×2−1+411yescharacteristic
613D11—24no—
614D11—24no—
615D11—42no—
616C24—111no—
617C24—111no—
618C24—114no—
619C24—111no—
620C24—224no—
621C24—224no—
622C24—224no—
623C24C23×D1113yes—
624C24C23×D1111yescharacteristic
625#41—232no—
626#41—2296no—
627#41—2296no—
628#41—2296no—
629C2×Q8—232no—
630C2×Q8—212no—
631C2×Q8—1164no—
632C2×Q8—1124no—
633C2×Q8—1112no—
634C2×Q8—1124no—
635C2×Q8—1112no—
636C2×Q8—1112no—
637C2×Q8—1112no—
638C2×Q8—2224no—
639C2×Q8—2212no—
640C2×Q8—2296no—
641C2×Q8—2296no—
642C2×Q8—2296no—
643C2×Q8—2296no—
644C2×Q8—2232no—
645C2×Q8—2232no—
646C2×Q8—2212no—
647C2×Q8—2212no—
648C2×Q8D4×D1118yes—
649C2×Q8C23×D11112yes—
650C2×Q8C23×D1114yes—
651C2×D4—212no—
652C2×D4—212no—
653C2×D4—1112no—
654C2×D4—114no—
655C2×D4—1112no—
656C2×D4—1112no—
657C2×D4—114no—
658C2×D4—114no—
659C2×D4—224no—
660C2×D4—224no—
661C2×D4—2212no—
662C2×D4—2212no—
663C2×D4—2212no—
664C2×D4—224no—
665C2×D4C23×D11112yes—
666C2×D4C23×D11112yes—
667C22×C4—212no—
668C22×C4—212no—
669C22×C4—113no—
670C22×C4—1124no—
671C22×C4—1112no—
672C22×C4—1112no—
673C22×C4—1124no—
674C22×C4—111no—
675C22×C4—113no—
676C22×C4—113no—
677C22×C4—113no—
678C22×C4—1112no—
679C22×C4—1112no—
680C22×C4—1112no—
681C22×C4—1112no—
682C22×C4—2212no—
683C22×C4—2296no—
684C22×C4—2212no—
685C22×C4—2212no—
686C22×C4—2224no—
687C22×C4—2212no—
688C22×C4—2212no—
689C22×C4C23×D11112yes—
690C22×C4C23×D11112yes—
691C22×C4C23×D1113yes—
692C22×C4C23×D1111yescharacteristic
693C22×C4C23×D1113yes—
694C22×C4C23×D1111yescharacteristic
695C22×C4C23×D1113yes—
696C4⋊C4—1112no—
697C4⋊C4—1112no—
698C4⋊C4—1112no—
699C4⋊C4—1112no—
700C4⋊C4—1112no—
701C4⋊C4—1124no—
702C4⋊C4—1124no—
703C4⋊C4—1112no—
704C4⋊C4C23×D11112yes—
705C4⋊C4C23×D11112yes—
706C22⋊C4—1112no—
707C22⋊C4—1124no—
708C22⋊C4—1112no—
709C22⋊C4—1112no—
710C22⋊C4—114no—
711C22⋊C4—114no—
712C22⋊C4—1112no—
713C22⋊C4—1112no—
714C22⋊C4—1112no—
715C22⋊C4C23×D11124yes—
716C22⋊C4C23×D1114yes—
717C22⋊C4C23×D11112yes—
718C42—1124no—
719C42—1112no—
720C42C23×D11112yes—
721C11C2×#348611yescharacteristic, complemented, Sylow
722C23—22no—
723C23—22no—
724C23—26no—
725C23—26no—
726C23—26no—
727C23—114no—
728C23—114no—
729C23—112no—
730C23—112no—
731C23—112no—
732C23—228no—
733C23—228no—
734C23—2232no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—228no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23#6704314yescomplemented
744C23C24×D1116yes—
745C23C24×D1112yes—
746C23C24×D1111yescharacteristic
747Q8—224no—
748Q8—1148no—
749Q8—2248no—
750Q8—2224no—
751Q8—2224no—
752Q8—2224no—
753Q8C2×D4×D11116yes—
754D4—224no—
755D4—224no—
756D4—228no—
757D4—228no—
758D4—2224no—
759D4—2224no—
760D4—2224no—
761D4—228no—
762C2×C4—22no—
763C2×C4—26no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—1112no—
769C2×C4—116no—
770C2×C4—1148no—
771C2×C4—116no—
772C2×C4—112no—
773C2×C4—116no—
774C2×C4—116no—
775C2×C4—2224no—
776C2×C4—2224no—
777C2×C4—2224no—
778C2×C4—2248no—
779C2×C4—226no—
780C2×C4—226no—
781C2×C4—222no—
782C2×C4—226no—
783C2×C4—2224no—
784C2×C4—2224no—
785C2×C4C2×D4×D11112yes—
786C2×C4C24×D1116yes—
787C2×C4C24×D1112yes—
788C2×C4C24×D1116yes—
789C2×C4C24×D1112yes—
790C2×C4C24×D1116yes—
791C22—22no—
792C22—22no—
793C22—28no—
794C22—26no—
795C22—26no—
796C22—26no—
797C22—412no—
798C22—114no—
799C22—114no—
800C22—2232no—
801C22—222no—
802C22—222no—
803C22—222no—
804C22—222no—
805C22—228no—
806C22—228no—
807C22—222no—
808C22—222no—
809C22—222no—
810C22—444no—
811C22C22×D4×D1112yes—
812C22C2×#6704312yes—
813C22C2×#6704314yescomplemented
814C22D11×2−1+412yes—
815C22C25×D1111yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—1112no—
821C4—226no—
822C4—226no—
823C4—226no—
824C4—222no—
825C4C22×D4×D11112yes—
826C2—24no—
827C2—46no—
828C2—224no—
829C2—224no—
830C2—442no—
831C2#1308226214yesdirect product factor
832C2C23×D4×D1111yescharacteristic
833C2C2×D11×2−1+411yescharacteristic
834C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#548C2
socleC23×C11C25
hypercenterC2×#548D11
hypocenterC11C2×#3486
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#67043C2semidirect
2. C23×Q8×D11C2semidirect
3. #13082262C2direct (N × H)
4. C2×Q8×D44C2semidirect
5. C2×D4×Dic22C2semidirect
6. C2×Q8×C22⋊D11C2semidirect
7. C2×#10623163C2semidirect
8. C2×#10623208C2semidirect
9. C2×#10623362C2semidirect
10. C2×#10623129C2semidirect
11. C2×#10623159C2semidirect
12. C2×#10623206C2semidirect
13. C2×#10623137C2semidirect
14. C2×#10623078C2semidirect
15. C2×#10623103C2semidirect
16. C2×C11×#548C2semidirect
17. C22×C11×#41C22semidirect
20. C2×#67043C22semidirect
26. C22×Q8×D11C22semidirect
27. C22×Q8×D11C22semidirect
29. C22×#4341C22semidirect
33. C23×Dic22C22semidirect
34. C11×#548C22semidirect
35. C2×C11×#124C22semidirect
36. C2×C11×C22⋊Q8C22semidirect
38. C2×C4×Q8×C11C22semidirect
40. #10623362C22semidirect
41. Q8×C22⋊D11C22semidirect
42. C2×#66999C22semidirect
43. C2×Q8×Dic11C22semidirect
44. C2×#66997C22semidirect
48. C2×#66989C22semidirect
53. C2×#66977C22semidirect
54. #10623208C22semidirect
55. #10623206C22semidirect
56. #10623163C22semidirect
57. #10623159C22semidirect
58. #10623137C22semidirect
59. #10623129C22semidirect
60. Q8×D44C22semidirect
61. #10623103C22semidirect
62. #10623078C22semidirect
63. D4×Dic22C22semidirect
65. C2×#66950C22semidirect
69. C2×#66941C22semidirect
70. C2×#66940C22semidirect
71. C2×#66938C22semidirect
78. C2×#66931C22semidirect
79. C2×#66931C22semidirect
82. C2×#66922C22semidirect
83. C2×C4×Dic22C22semidirect
86. C2×C11×#41C23semidirect
107. C2×Q8×D11D4semidirect
112. C2×Q8×D11C23semidirect
116. C2×#4341C23semidirect
136. C22×Dic22C23semidirect
137. C11×#124C23semidirect
138. C11×C22⋊Q8C23semidirect
140. C4×Q8×C11C23semidirect
151. #66999C23semidirect
152. Q8×Dic11C23semidirect
153. #66997C23semidirect
157. #66989C23semidirect
171. #66977C23semidirect
180. #66950C23semidirect
184. #66941C23semidirect
185. #66940C23semidirect
186. #66938C23semidirect
193. #66931C23semidirect
194. #66931C23semidirect
197. #66922C23semidirect
198. C4×Dic22C23semidirect
249. Q8×D11C2×D4semidirect
315. C2×#548D11semidirect
326. C23×C112−1+4semidirect
342. C22×D112−1+4semidirect
395. C22×#41C2×D11semidirect
414. #548C2×D11semidirect
422. C2×#124C2×D11semidirect
437. C2×C22⋊Q8C2×D11semidirect
448. C2×C4×Q8C2×D11semidirect
467. C22×C11C2×2−1+4semidirect
481. C2×D11C2×2−1+4semidirect
501. C2×#41C22×D11semidirect
550. #124C22×D11semidirect
563. C22⋊Q8C22×D11semidirect
573. C4×Q8C22×D11semidirect
609. C2×C11#3486semidirect
721. C11C2×#3486semidirect
743. C23#67043semidirect
813. C22C2×#67043semidirect
831. C2#13082262direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670432
C23×Q8×D112
#130822622
C2×Q8×D442
C2×D4×Dic222
C2×Q8×C22⋊D112
C2×#106231632
C2×#106232082
C2×#106233622
C2×#106231292
C2×#106231592
C2×#106232062
C2×#106231372
C2×#106230782
C2×#106231032
C2×C11×#5482
C2×#348611