Finite Group Databasebeta

← C2×#13082282 #15662080

Subgroups — C2×#13082282 #15662080

Order 2816.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67042C211yesmaximal, characteristic, complemented
2C23×#4343C211yesmaximal, characteristic, complemented
3#13082282C2132yesmaximal, direct product factor
4C2×#10623108C211yesmaximal, characteristic, complemented
5C2×#10623365C211yesmaximal, characteristic, complemented
6C2×#10623348C211yesmaximal, characteristic, complemented
7C2×#10623207C213yesmaximal, complemented
8C2×#10623161C213yesmaximal, complemented
9C2×D4×D44C213yesmaximal, complemented
10C2×#10623140C213yesmaximal, complemented
11C2×#10623160C213yesmaximal, complemented
12C2×#10623205C213yesmaximal, complemented
13C2×#10623078C213yesmaximal, complemented
14C2×D11×#121C213yesmaximal, complemented
15C2×#10623105C211yesmaximal, characteristic, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C23×Q8×C11C2211yescharacteristic, complemented
19C2×#67042—216no—
20C2×#67042C22116yescomplemented
21C22×#4343—216no—
22C22×#4343C2211yescharacteristic
23C22×#4343C2213yescomplemented
24C22×#4343C2213yescomplemented
25C22×#4343C2211yescharacteristic, complemented
26C22×#4343C2211yescharacteristic, complemented
27C22×#4343C22116yescomplemented
28C22×D4×D11C2213yescomplemented
29C22×D4×D11C2213yescomplemented
30C22×D4×D11C2216yescomplemented
31C22×#4339C2213yescomplemented
32C23×D44C2213yescomplemented
33C23×D44C2213yescomplemented
34C23×C4×D11C2213yescomplemented
35C11×#548C22116yescomplemented
36C2×C11×#124C2213yescomplemented
37C2×C11×C22⋊Q8C2213yescomplemented
38C2×C11×#121C2213yescomplemented
39C2×C4×Q8×C11C2211yescharacteristic, complemented
40C2×C4×D4×C11C2213yescomplemented
41#10623365C22116yescomplemented
42#10623348C22116yescomplemented
43C2×#67000C2213yescomplemented
44C2×#66999C2213yescomplemented
45C2×Q8×Dic11C2211yescharacteristic, complemented
46C2×#66993C2213yescomplemented
47C2×#66992C2213yescomplemented
48C2×#66991C2213yescomplemented
49C2×#66990C2213yescomplemented
50C2×#66983C2213yescomplemented
51C2×#66983C2213yescomplemented
52C2×C4×C22⋊D11C2213yescomplemented
53C2×C4×C22⋊D11C2213yescomplemented
54#10623207C22148yescomplemented
55#10623205C22148yescomplemented
56#10623161C22148yescomplemented
57#10623160C22148yescomplemented
58#10623140C22148yescomplemented
59D11×#121C22148yescomplemented
60#10623108C22116yescomplemented
61#10623105C22116yescomplemented
62D4×D44C22148yescomplemented
63#10623078C22148yescomplemented
64C2×#66949C2213yescomplemented
65C2×#66948C2213yescomplemented
66C2×#66948C2216yescomplemented
67C2×#66948C2213yescomplemented
68C2×#66947C2213yescomplemented
69C2×#66946C2213yescomplemented
70C2×C4⋊C4×D11C2213yescomplemented
71C2×#66937C2213yescomplemented
72C2×#66937C2216yescomplemented
73C2×#66937C2216yescomplemented
74C2×#66936C2213yescomplemented
75C2×#66935C2213yescomplemented
76C2×#66935C2216yescomplemented
77C2×#66935C2216yescomplemented
78C2×C22⋊C4×D11C2216yescomplemented
79C2×#66931C2211yescharacteristic, complemented
80C2×#66927C2213yescomplemented
81C2×C4×D44C2213yescomplemented
82C2×C4×D44C2213yescomplemented
83C2×#66925C2213yescomplemented
84C24×D11C2313yes—
85C24×D11C2316yes—
86C2×C11×#41—28no—
87C2×C11×#41C2318yescomplemented
88C22×Q8×C11—28no—
89C22×Q8×C11C2313yes—
90C22×Q8×C11C2311yescharacteristic
91C22×Q8×C11C2318yescomplemented
92C22×D4×C11C2313yes—
93C22×D4×C11C2313yes—
94C23×C4×C11C2313yes—
95C23×C4×C11C2313yes—
96C22×C22⋊D11C2313yes—
97C22×C22⋊D11C2313yes—
98C22×C22⋊D11C2313yes—
99C22×C22⋊D11C2313yes—
100C22×C22⋊D11C2316yes—
101C23×Dic11C2311yescharacteristic
102#67042—2128no—
103C2×#4343—28no—
104C2×#4343—28no—
105C2×#4343—2128no—
106C2×#4343—224no—
107C2×#4343—224no—
108C2×#4343D4116yescomplemented
109C2×#4343C2318yes—
110C2×#4343C2318yescomplemented
111C2×#4343C2318yescomplemented
112C2×#4343C23124yescomplemented
113C2×#4343C23124yescomplemented
114C2×D4×D11—224no—
115C2×D4×D11—224no—
116C2×D4×D11—424no—
117C2×D4×D11C23124yescomplemented
118C2×D4×D11C23124yescomplemented
119C2×D4×D11C23148yescomplemented
120C2×#4339—224no—
121C2×#4339C23124yescomplemented
122C22×D44—224no—
123C22×D44—224no—
124C22×D44C2313yes—
125C22×D44C2313yes—
126C22×D44C2316yes—
127C22×D44C2313yes—
128C22×D44C2313yes—
129C22×D44C2316yes—
130C22×D44C2313yes—
131C22×D44C23124yescomplemented
132C22×D44C23124yescomplemented
133C22×C4×D11—224no—
134C22×C4×D11C2313yes—
135C22×C4×D11C2313yes—
136C22×C4×D11C2313yes—
137C22×C4×D11C2313yes—
138C22×C4×D11C2316yes—
139C22×C4×D11C2313yes—
140C22×C4×D11C23124yescomplemented
141C22×Dic22C2311yescharacteristic
142C11×#124C23124yescomplemented
143C11×C22⋊Q8C23124yescomplemented
144C11×#121C23124yescomplemented
145C4×Q8×C11C2318yescomplemented
146C4×D4×C11C23124yescomplemented
147C2×C11×C4⋊C4C2313yes—
148C2×C11×C4⋊C4C2313yes—
149C2×C11×C22⋊C4C2311yescharacteristic
150C2×C11×C22⋊C4C2316yes—
151C2×C11×C22⋊C4C2313yes—
152C2×C42×C11C2313yes—
153C2×C22⋊Dic11C2311yescharacteristic
154C2×C22⋊Dic11C2313yes—
155#67000C23124yescomplemented
156#66999C23124yescomplemented
157Q8×Dic11C2318yescomplemented
158#66993C23124yescomplemented
159#66992C23124yescomplemented
160#66991C23124yescomplemented
161#66990C23124yescomplemented
162#66983C23124yescomplemented
163#66983C23124yescomplemented
164C4×C22⋊D11C23124yescomplemented
165C4×C22⋊D11C23124yescomplemented
166C2×(C2×D11)⋊C4C2313yes—
167C2×(C2×D11)⋊C4C2313yes—
168C2×(C2×D11)⋊C4C2313yes—
169C2×(C2×D11)⋊C4C2313yes—
170C2×(C2×D11)⋊C4C2316yes—
171C2×(C2×D11)⋊C4C2313yes—
172C2×(C2×D11)⋊C4C2313yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2313yes—
175C2×Dic11⋊C4C2311yescharacteristic
176C2×Dic11⋊C4C2313yes—
177C2×Dic11⋊C4C2311yescharacteristic
178C2×Dic11⋊C4C2313yes—
179C2×C4×Dic11C2313yes—
180#66949C23124yescomplemented
181#66948C23148yescomplemented
182#66948C23124yescomplemented
183#66948C23124yescomplemented
184#66947C23124yescomplemented
185#66946C23124yescomplemented
186C4⋊C4×D11C23124yescomplemented
187#66937C23124yescomplemented
188#66937C23148yescomplemented
189#66937C23148yescomplemented
190#66936C23124yescomplemented
191#66935C23124yescomplemented
192#66935C23148yescomplemented
193#66935C23148yescomplemented
194C22⋊C4×D11C23148yescomplemented
195#66931C2318yescomplemented
196#66927C23124yescomplemented
197C4×D44C23124yescomplemented
198C4×D44C23124yescomplemented
199#66925C23124yescomplemented
200C2×#3488—111nomaximal, Sylow
201C24×C11C2413yes—
202C24×C11C2411yescharacteristic
203C23×D11—212no—
204C23×D11—212no—
205C23×D11—224no—
206C23×D11—46no—
207C23×D11—412no—
208C23×D11—412no—
209C23×D11C2413yes—
210C23×D11C2413yes—
211C23×D11C24112yes—
212C23×D11C2413yes—
213C23×D11C24124yes—
214C11×#41—232no—
215C2×Q8×C11—232no—
216C2×Q8×C11—212no—
217C2×Q8×C11C2×D418yescomplemented
218C2×Q8×C11C24112yes—
219C2×Q8×C11C2414yes—
220C2×D4×C11—212no—
221C2×D4×C11—212no—
222C2×D4×C11C24112yes—
223C2×D4×C11C24112yes—
224C22×C4×C11—212no—
225C22×C4×C11—212no—
226C22×C4×C11C2411yescharacteristic
227C22×C4×C11C2413yes—
228C22×C4×C11C2413yes—
229C22×C4×C11C2411yescharacteristic
230C22×C4×C11C24112yes—
231C22×C4×C11C24112yes—
232C22×C4×C11C2413yes—
233C2×C22⋊D11—212no—
234C2×C22⋊D11—212no—
235C2×C22⋊D11—212no—
236C2×C22⋊D11—412no—
237C2×C22⋊D11—46no—
238C2×C22⋊D11C24112yes—
239C2×C22⋊D11C24112yes—
240C2×C22⋊D11C24112yes—
241C2×C22⋊D11C24112yes—
242C2×C22⋊D11C24124yes—
243C22×Dic11—24no—
244C22×Dic11C2414yes—
245C22×Dic11C2411yescharacteristic
246C22×Dic11C2413yes—
247C22×Dic11C2411yescharacteristic
248C22×Dic11C2411yescharacteristic
249C22×Dic11C2411yescharacteristic
250#4343—296no—
251#4343—296no—
252#4343—232no—
253#4343—232no—
254#4343C2×D4164yescomplemented
255D4×D11—296no—
256D4×D11—296no—
257D4×D11—496no—
258#4339—296no—
259C2×D44—296no—
260C2×D44—296no—
261C2×D44—212no—
262C2×D44—224no—
263C2×D44—212no—
264C2×D44—212no—
265C2×D44—46no—
266C2×D44—412no—
267C2×D44C2×D4124yescomplemented
268C2×D44C24112yes—
269C2×D44C24112yes—
270C2×D44C24124yes—
271C2×D44C24112yes—
272C2×D44C24112yes—
273C2×D44C24124yes—
274C2×D44C24112yes—
275C2×C4×D11—212no—
276C2×C4×D11—296no—
277C2×C4×D11—212no—
278C2×C4×D11—212no—
279C2×C4×D11—212no—
280C2×C4×D11—412no—
281C2×C4×D11C2×D4124yescomplemented
282C2×C4×D11C24112yes—
283C2×C4×D11C24112yes—
284C2×C4×D11C24112yes—
285C2×C4×D11C24112yes—
286C2×C4×D11C24124yes—
287C2×C4×D11C24112yes—
288C2×Dic22—24no—
289C2×Dic22C2414yes—
290C11×C4⋊C4C24112yes—
291C11×C4⋊C4C24112yes—
292C11×C22⋊C4C2414yes—
293C11×C22⋊C4C24124yes—
294C11×C22⋊C4C24112yes—
295C42×C11C24112yes—
296C22⋊Dic11C2414yes—
297C22⋊Dic11C24112yes—
298(C2×D11)⋊C4C24112yes—
299(C2×D11)⋊C4C24112yes—
300(C2×D11)⋊C4C24112yes—
301(C2×D11)⋊C4C24112yes—
302(C2×D11)⋊C4C24124yes—
303(C2×D11)⋊C4C24112yes—
304(C2×D11)⋊C4C24112yes—
305C4⋊Dic11C2414yes—
306C4⋊Dic11C24112yes—
307Dic11⋊C4C2414yes—
308Dic11⋊C4C24112yes—
309Dic11⋊C4C2414yes—
310Dic11⋊C4C24112yes—
311C4×Dic11C24112yes—
312C22×H(5,𝔽2)—111no—
313C23×#41—111no—
314#3488—1132no—
315C2×#550—111no—
316C2×#550—111no—
317C2×#548—111no—
318C2×#548D1111yescharacteristic, complemented
319C2×#546—113no—
320C2×#546—113no—
321C2×D42—113no—
322C2×D42—113no—
323C2×#537—113no—
324C2×#535—113no—
325C2×#525—113no—
326C22×#121—113no—
327C2×#520—111no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—26no—
331C23×C11—26no—
332C23×C11—26no—
333C23×C11H(5,𝔽2)14yescomplemented
334C23×C11C2516yes—
335C23×C11C2512yes—
336C23×C11C2511yescharacteristic
337C22×D11—26no—
338C22×D11—26no—
339C22×D11—26no—
340C22×D11—26no—
341C22×D11—26no—
342C22×D11—26no—
343C22×D11—224no—
344C22×D11—26no—
345C22×D11—26no—
346C22×D11—224no—
347C22×D11—248no—
348C22×D11—412no—
349C22×D11—424no—
350C22×D11—424no—
351C22×D11—448no—
352C22×D11—848no—
353C22×D11C22×D4112yes—
354C22×D11C2516yes—
355C22×D11C2516yes—
356C22×D11C2516yes—
357Q8×C11—224no—
358Q8×C11C22×D4116yescomplemented
359D4×C11—224no—
360D4×C11—224no—
361C2×C4×C11—22no—
362C2×C4×C11—26no—
363C2×C4×C11—26no—
364C2×C4×C11—22no—
365C2×C4×C11—224no—
366C2×C4×C11—224no—
367C2×C4×C11C22×D4112yes—
368C2×C4×C11C2512yes—
369C2×C4×C11C2516yes—
370C2×C4×C11C2516yes—
371C2×C4×C11C2512yes—
372C2×C4×C11C2516yes—
373C22⋊D11—224no—
374C22⋊D11—224no—
375C22⋊D11—224no—
376C22⋊D11—424no—
377C22⋊D11—412no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—26no—
381C2×Dic11—22no—
382C2×Dic11—28no—
383C2×Dic11C22×D414yes—
384C2×Dic11C2512yes—
385C2×Dic11C2516yes—
386C2×Dic11C2512yes—
387C2×Dic11C2512yes—
388C2×Dic11C2512yes—
389D44—224no—
390D44—248no—
391D44—224no—
392D44—224no—
393D44—412no—
394D44—424no—
395D44C22×D4148yescomplemented
396C4×D11—224no—
397C4×D11—224no—
398C4×D11—224no—
399C4×D11—224no—
400C4×D11—424no—
401C4×D11C22×D4148yescomplemented
402Dic22—28no—
403C2×H(5,𝔽2)—1116no—
404C2×H(5,𝔽2)—2216no—
405C22×#41—111no—
406C22×#41—113no—
407C22×#41—113no—
408C22×#41—111no—
409C22×#41—111no—
410C22×#41—1116no—
411C22×#41—113no—
412C22×#41—2216no—
413C22×#41C2×D1111yescharacteristic, complemented
414C23×Q8C2×D1111yescharacteristic, complemented
415C23×D4—113no—
416C23×D4—113no—
417C23×D4—116no—
418C23×D4—113no—
419C23×D4—113no—
420C24×C4—113no—
421#550—1116no—
422#550—1116no—
423#548—1116no—
424#548C2×D11116yescomplemented
425#546—1148no—
426#546—1148no—
427D42—1148no—
428D42—1148no—
429#537—1148no—
430#535—1148no—
431C2×#127—113no—
432C2×#127—113no—
433C2×#124—113no—
434C2×#124C2×D1113yescomplemented
435#525—1148no—
436C2×#123—113no—
437C2×#123—113no—
438C2×C22⋊Q8—113no—
439C2×C22⋊Q8—113no—
440C2×C22⋊Q8—111no—
441C2×C22⋊Q8C2×D1113yescomplemented
442C2×#121—113no—
443C2×#121—113no—
444C2×#121—113no—
445C2×#121—113no—
446C2×#121—1148no—
447C2×#121—113no—
448C2×#121—116no—
449C2×#121—113no—
450C2×#121—116no—
451C2×#121—113no—
452C2×#121—116no—
453C2×#121C2×D1113yescomplemented
454C2×#120—113no—
455C2×#120—113no—
456C2×#120—116no—
457C2×#120—116no—
458#520—1116no—
459C2×C4×Q8—111no—
460C2×C4×Q8C2×D1111yescharacteristic, complemented
461C2×C4×D4—113no—
462C2×C4×D4—113no—
463C2×C4×D4—113no—
464C2×C4×D4—113no—
465C2×C4×D4—113no—
466C2×C4×D4C2×D1113yescomplemented
467C2×#117—113no—
468C22×C4⋊C4—113no—
469C22×C22⋊C4—116no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—28no—
473C22×C11—26no—
474C22×C11—26no—
475C22×C11—26no—
476C22×C11—412no—
477C22×C11C23×D412yes—
478C22×C11C2×H(5,𝔽2)12yes—
479C22×C11C2×H(5,𝔽2)14yescomplemented
480C22×C11#58512yes—
481C22×C11C2611yescharacteristic
482C2×D11—26no—
483C2×D11—26no—
484C2×D11—224no—
485C2×D11—26no—
486C2×D11—26no—
487C2×D11—26no—
488C2×D11—26no—
489C2×D11—26no—
490C2×D11—26no—
491C2×D11—448no—
492C2×D11—412no—
493C2×D11—412no—
494C2×D11—848no—
495C2×D11C23×D4112yes—
496C4×C11—22no—
497C4×C11—26no—
498C4×C11—26no—
499C4×C11—22no—
500C4×C11C23×D4112yes—
501Dic11—22no—
502Dic11—22no—
503Dic11—26no—
504Dic11—22no—
505Dic11C23×D414yes—
506C25—113no—
507C25—116no—
508H(5,𝔽2)—22128no—
509C2×#41—28no—
510C2×#41—1116no—
511C2×#41—118no—
512C2×#41—1124no—
513C2×#41—1124no—
514C2×#41—118no—
515C2×#41—118no—
516C2×#41—1124no—
517C2×#41—2224no—
518C2×#41—2224no—
519C2×#41—2224no—
520C2×#41—22128no—
521C2×#41—228no—
522C2×#41—228no—
523C2×#41C22×D1118yescomplemented
524C22×Q8—28no—
525C22×Q8—111no—
526C22×Q8C22×D1113yes—
527C22×Q8C22×D1111yescharacteristic
528C22×Q8C22×D1118yescomplemented
529C22×D4—113no—
530C22×D4—113no—
531C22×D4—113no—
532C22×D4—113no—
533C22×D4—116no—
534C22×D4—1124no—
535C22×D4—1124no—
536C22×D4—1148no—
537C22×D4—113no—
538C22×D4—116no—
539C22×D4—113no—
540C22×D4—113no—
541C22×D4—113no—
542C22×D4—1124no—
543C22×D4—1124no—
544C22×D4—113no—
545C22×D4—116no—
546C22×D4—2224no—
547C22×D4—2224no—
548C22×D4—2224no—
549C22×D4—2224no—
550C22×D4—4424no—
551C22×D4C22×D1113yes—
552C22×D4C22×D1113yes—
553C23×C4—113no—
554C23×C4—111no—
555C23×C4—113no—
556C23×C4—113no—
557C23×C4—113no—
558C23×C4—113no—
559C23×C4—1124no—
560C23×C4—116no—
561C23×C4—2224no—
562C23×C4C22×D1113yes—
563C23×C4C22×D1113yes—
564#127—1124no—
565#127—1124no—
566#124—1124no—
567#124C22×D11124yescomplemented
568#123—1124no—
569#123—1124no—
570C22⋊Q8—1124no—
571C22⋊Q8—1124no—
572C22⋊Q8—118no—
573C22⋊Q8C22×D11124yescomplemented
574#121—1124no—
575#121—1124no—
576#121—1124no—
577#121—1124no—
578#121—1124no—
579#121—1148no—
580#121—1124no—
581#121—1148no—
582#121—1124no—
583#121—1148no—
584#121C22×D11124yescomplemented
585#120—1124no—
586#120—1124no—
587#120—1148no—
588#120—1148no—
589C4×Q8—118no—
590C4×Q8C22×D1118yescomplemented
591C4×D4—1124no—
592C4×D4—1124no—
593C4×D4—1124no—
594C4×D4—1124no—
595C4×D4—1124no—
596C4×D4C22×D11124yescomplemented
597#117—1124no—
598C2×C4⋊C4—113no—
599C2×C4⋊C4—113no—
600C2×C4⋊C4—111no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—113no—
604C2×C4⋊C4—1124no—
605C2×C4⋊C4C22×D1113yes—
606C2×C4⋊C4C22×D1113yes—
607C2×C22⋊C4—113no—
608C2×C22⋊C4—111no—
609C2×C22⋊C4—113no—
610C2×C22⋊C4—116no—
611C2×C22⋊C4—113no—
612C2×C22⋊C4—113no—
613C2×C22⋊C4—113no—
614C2×C22⋊C4—113no—
615C2×C22⋊C4—113no—
616C2×C22⋊C4—1148no—
617C2×C22⋊C4C22×D1116yes—
618C2×C22⋊C4C22×D1111yescharacteristic
619C2×C22⋊C4C22×D1113yes—
620C2×C42—113no—
621C2×C42C22×D1113yes—
622C2×C11—24no—
623C2×C11—46no—
624C2×C11#348814yescomplemented
625C2×C11C24×D411yescharacteristic
626C2×C11C22×H(5,𝔽2)11yescharacteristic
627C2×C11C2×#58511yescharacteristic
628D11—212no—
629D11—46no—
630D11—46no—
631C24—113no—
632C24—113no—
633C24—113no—
634C24—1112no—
635C24—1124no—
636C24—2212no—
637C24—2224no—
638C24—2212no—
639C24—446no—
640C24—4412no—
641C24—4412no—
642C24C23×D1113yes—
643C24C23×D1111yescharacteristic
644#41—232no—
645#41—1164no—
646#41—2296no—
647#41—2296no—
648#41—2296no—
649#41—2232no—
650#41—2232no—
651C2×Q8—232no—
652C2×Q8—212no—
653C2×Q8—114no—
654C2×Q8—224no—
655C2×Q8D4×D1118yescomplemented
656C2×Q8C23×D11112yes—
657C2×Q8C23×D1114yes—
658C2×D4—212no—
659C2×D4—212no—
660C2×D4—1112no—
661C2×D4—1112no—
662C2×D4—1112no—
663C2×D4—1112no—
664C2×D4—1124no—
665C2×D4—1124no—
666C2×D4—1112no—
667C2×D4—1124no—
668C2×D4—1112no—
669C2×D4—1112no—
670C2×D4—1112no—
671C2×D4—1112no—
672C2×D4—1124no—
673C2×D4—2296no—
674C2×D4—2296no—
675C2×D4—2212no—
676C2×D4—2224no—
677C2×D4—2296no—
678C2×D4—2212no—
679C2×D4—2296no—
680C2×D4—2212no—
681C2×D4—2212no—
682C2×D4—2212no—
683C2×D4—2212no—
684C2×D4—4412no—
685C2×D4—446no—
686C2×D4—4412no—
687C2×D4—446no—
688C2×D4—4496no—
689C2×D4C23×D11112yes—
690C2×D4C23×D11112yes—
691C22×C4—212no—
692C22×C4—212no—
693C22×C4—111no—
694C22×C4—1124no—
695C22×C4—1112no—
696C22×C4—114no—
697C22×C4—111no—
698C22×C4—113no—
699C22×C4—111no—
700C22×C4—111no—
701C22×C4—1112no—
702C22×C4—1112no—
703C22×C4—1112no—
704C22×C4—1112no—
705C22×C4—1124no—
706C22×C4—2212no—
707C22×C4—2296no—
708C22×C4—2212no—
709C22×C4—224no—
710C22×C4—2212no—
711C22×C4—2212no—
712C22×C4—4412no—
713C22×C4C23×D11112yes—
714C22×C4C23×D11112yes—
715C22×C4C23×D1111yescharacteristic
716C22×C4C23×D1113yes—
717C22×C4C23×D1113yes—
718C22×C4C23×D1111yescharacteristic
719C22×C4C23×D1113yes—
720C4⋊C4—1112no—
721C4⋊C4—1112no—
722C4⋊C4—114no—
723C4⋊C4—114no—
724C4⋊C4—114no—
725C4⋊C4—1112no—
726C4⋊C4C23×D11112yes—
727C4⋊C4C23×D11112yes—
728C22⋊C4—1112no—
729C22⋊C4—114no—
730C22⋊C4—1112no—
731C22⋊C4—1124no—
732C22⋊C4—1112no—
733C22⋊C4—1112no—
734C22⋊C4—1112no—
735C22⋊C4—1112no—
736C22⋊C4—1112no—
737C22⋊C4C23×D11124yes—
738C22⋊C4C23×D1114yes—
739C22⋊C4C23×D11112yes—
740C42—1112no—
741C42C23×D11112yes—
742C11C2×#348811yescharacteristic, complemented, Sylow
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—1112no—
749C23—116no—
750C23—116no—
751C23—116no—
752C23—2224no—
753C23—2248no—
754C23—226no—
755C23—226no—
756C23—226no—
757C23—226no—
758C23—226no—
759C23—226no—
760C23—2224no—
761C23—226no—
762C23—226no—
763C23—4412no—
764C23—4424no—
765C23—4424no—
766C23—4448no—
767C23—8848no—
768C23#6704214yescomplemented
769C23C24×D1116yes—
770C23C24×D1112yes—
771C23C24×D1111yescharacteristic
772Q8—224no—
773Q8—228no—
774Q8C2×D4×D11116yescomplemented
775D4—224no—
776D4—224no—
777D4—1148no—
778D4—2224no—
779D4—2248no—
780D4—2224no—
781D4—2224no—
782D4—2224no—
783D4—2224no—
784D4—2224no—
785D4—4424no—
786D4—4412no—
787D4—4424no—
788D4—4412no—
789C2×C4—22no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—114no—
796C2×C4—112no—
797C2×C4—1148no—
798C2×C4—112no—
799C2×C4—116no—
800C2×C4—112no—
801C2×C4—112no—
802C2×C4—2224no—
803C2×C4—2224no—
804C2×C4—228no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—226no—
808C2×C4—222no—
809C2×C4—2224no—
810C2×C4—2224no—
811C2×C4—4424no—
812C2×C4C2×D4×D11112yes—
813C2×C4C24×D1112yes—
814C2×C4C24×D1116yes—
815C2×C4C24×D1116yes—
816C2×C4C24×D1112yes—
817C2×C4C24×D1116yes—
818C22—22no—
819C22—22no—
820C22—28no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—1112no—
826C22—226no—
827C22—226no—
828C22—2224no—
829C22—226no—
830C22—226no—
831C22—226no—
832C22—226no—
833C22—226no—
834C22—226no—
835C22—4448no—
836C22—4412no—
837C22—4412no—
838C22—8848no—
839C22C22×D4×D1112yes—
840C22C2×#6704212yes—
841C22C2×#6704214yescomplemented
842C22#1062345712yes—
843C22C25×D1111yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—114no—
849C4—222no—
850C4—222no—
851C4—226no—
852C4—222no—
853C4C22×D4×D11112yes—
854C2—24no—
855C2—46no—
856C2—2212no—
857C2—446no—
858C2—446no—
859C2#1308228214yesdirect product factor
860C2C23×D4×D1111yescharacteristic
861C2C22×#6704211yescharacteristic
862C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#548C2
socleC23×C11C25
hypercenterC2×#548D11
hypocenterC11C2×#3488
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#67042C2semidirect
2. C23×#4343C2semidirect
3. #13082282C2direct (N × H)
4. C2×#10623108C2semidirect
5. C2×#10623365C2semidirect
6. C2×#10623348C2semidirect
7. C2×#10623207C2semidirect
8. C2×#10623161C2semidirect
9. C2×D4×D44C2semidirect
10. C2×#10623140C2semidirect
11. C2×#10623160C2semidirect
12. C2×#10623205C2semidirect
13. C2×#10623078C2semidirect
14. C2×D11×#121C2semidirect
15. C2×#10623105C2semidirect
16. C2×C11×#548C2semidirect
17. C22×C11×#41C22semidirect
18. C23×Q8×C11C22semidirect
20. C2×#67042C22semidirect
23. C22×#4343C22semidirect
24. C22×#4343C22semidirect
25. C22×#4343C22semidirect
26. C22×#4343C22semidirect
27. C22×#4343C22semidirect
28. C22×D4×D11C22semidirect
29. C22×D4×D11C22semidirect
30. C22×D4×D11C22semidirect
31. C22×#4339C22semidirect
32. C23×D44C22semidirect
33. C23×D44C22semidirect
34. C23×C4×D11C22semidirect
35. C11×#548C22semidirect
36. C2×C11×#124C22semidirect
37. C2×C11×C22⋊Q8C22semidirect
38. C2×C11×#121C22semidirect
39. C2×C4×Q8×C11C22semidirect
40. C2×C4×D4×C11C22semidirect
41. #10623365C22semidirect
42. #10623348C22semidirect
43. C2×#67000C22semidirect
44. C2×#66999C22semidirect
45. C2×Q8×Dic11C22semidirect
46. C2×#66993C22semidirect
47. C2×#66992C22semidirect
48. C2×#66991C22semidirect
49. C2×#66990C22semidirect
50. C2×#66983C22semidirect
51. C2×#66983C22semidirect
52. C2×C4×C22⋊D11C22semidirect
53. C2×C4×C22⋊D11C22semidirect
54. #10623207C22semidirect
55. #10623205C22semidirect
56. #10623161C22semidirect
57. #10623160C22semidirect
58. #10623140C22semidirect
59. D11×#121C22semidirect
60. #10623108C22semidirect
61. #10623105C22semidirect
62. D4×D44C22semidirect
63. #10623078C22semidirect
64. C2×#66949C22semidirect
65. C2×#66948C22semidirect
66. C2×#66948C22semidirect
67. C2×#66948C22semidirect
68. C2×#66947C22semidirect
69. C2×#66946C22semidirect
70. C2×C4⋊C4×D11C22semidirect
71. C2×#66937C22semidirect
72. C2×#66937C22semidirect
73. C2×#66937C22semidirect
74. C2×#66936C22semidirect
75. C2×#66935C22semidirect
76. C2×#66935C22semidirect
77. C2×#66935C22semidirect
78. C2×C22⋊C4×D11C22semidirect
79. C2×#66931C22semidirect
80. C2×#66927C22semidirect
81. C2×C4×D44C22semidirect
82. C2×C4×D44C22semidirect
83. C2×#66925C22semidirect
87. C2×C11×#41C23semidirect
91. C22×Q8×C11C23semidirect
108. C2×#4343D4semidirect
110. C2×#4343C23semidirect
111. C2×#4343C23semidirect
112. C2×#4343C23semidirect
113. C2×#4343C23semidirect
117. C2×D4×D11C23semidirect
118. C2×D4×D11C23semidirect
119. C2×D4×D11C23semidirect
121. C2×#4339C23semidirect
131. C22×D44C23semidirect
132. C22×D44C23semidirect
140. C22×C4×D11C23semidirect
142. C11×#124C23semidirect
143. C11×C22⋊Q8C23semidirect
144. C11×#121C23semidirect
145. C4×Q8×C11C23semidirect
146. C4×D4×C11C23semidirect
155. #67000C23semidirect
156. #66999C23semidirect
157. Q8×Dic11C23semidirect
158. #66993C23semidirect
159. #66992C23semidirect
160. #66991C23semidirect
161. #66990C23semidirect
162. #66983C23semidirect
163. #66983C23semidirect
164. C4×C22⋊D11C23semidirect
165. C4×C22⋊D11C23semidirect
180. #66949C23semidirect
181. #66948C23semidirect
182. #66948C23semidirect
183. #66948C23semidirect
184. #66947C23semidirect
185. #66946C23semidirect
186. C4⋊C4×D11C23semidirect
187. #66937C23semidirect
188. #66937C23semidirect
189. #66937C23semidirect
190. #66936C23semidirect
191. #66935C23semidirect
192. #66935C23semidirect
193. #66935C23semidirect
194. C22⋊C4×D11C23semidirect
195. #66931C23semidirect
196. #66927C23semidirect
197. C4×D44C23semidirect
198. C4×D44C23semidirect
199. #66925C23semidirect
217. C2×Q8×C11C2×D4semidirect
254. #4343C2×D4semidirect
267. C2×D44C2×D4semidirect
281. C2×C4×D11C2×D4semidirect
318. C2×#548D11semidirect
333. C23×C11H(5,𝔽2)semidirect
358. Q8×C11C22×D4semidirect
395. D44C22×D4semidirect
401. C4×D11C22×D4semidirect
413. C22×#41C2×D11semidirect
414. C23×Q8C2×D11semidirect
424. #548C2×D11semidirect
434. C2×#124C2×D11semidirect
441. C2×C22⋊Q8C2×D11semidirect
453. C2×#121C2×D11semidirect
460. C2×C4×Q8C2×D11semidirect
466. C2×C4×D4C2×D11semidirect
479. C22×C11C2×H(5,𝔽2)semidirect
523. C2×#41C22×D11semidirect
528. C22×Q8C22×D11semidirect
567. #124C22×D11semidirect
573. C22⋊Q8C22×D11semidirect
584. #121C22×D11semidirect
590. C4×Q8C22×D11semidirect
596. C4×D4C22×D11semidirect
624. C2×C11#3488semidirect
655. C2×Q8D4×D11semidirect
742. C11C2×#3488semidirect
768. C23#67042semidirect
774. Q8C2×D4×D11semidirect
841. C22C2×#67042semidirect
859. C2#13082282direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670422
C23×#43432
#130822822
C2×#106231082
C2×#106233652
C2×#106233482
C2×#106232072
C2×#106231612
C2×D4×D442
C2×#106231402
C2×#106231602
C2×#106232052
C2×#106230782
C2×D11×#1212
C2×#106231052
C2×C11×#5482
C2×#348811