Finite Group Databasebeta

← C2×#13080551 #15630232

Subgroups — C2×#13080551 #15630232

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623064C211yesmaximal, characteristic, complemented
2C2×#10623365C211yesmaximal, characteristic
3#13080551C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622616C211yesmaximal, characteristic, complemented
6C2×#10622392C211yesmaximal, characteristic, complemented
7C2×#10622404C211yesmaximal, characteristic, complemented
8C2×#10622727C211yesmaximal, characteristic, complemented
9C2×#10622391C211yesmaximal, characteristic, complemented
10C2×#10622375C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622852C211yesmaximal, characteristic, complemented
13C2×#10622403C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#416C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21#10623365—24no—
22#10623365C2218yes—
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C2×#66993—21no—
26C2×#66993C2211yescharacteristic
27C2×#66991—21no—
28C2×#66991C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C2×#66983—21no—
31C2×#66983C2211yescharacteristic
32C2×C4×C22⋊D11—21no—
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C22×#4314C2211yescharacteristic
36C22×C8×D11C2211yescharacteristic
37#10623064—24no—
38#10623064C2218yescomplemented
39C2×#66950C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66938—21no—
44C2×#66932—21no—
45C2×#66929—21no—
46C2×C4×Dic22—21no—
47C11×#416C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622852C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622727C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C8×C22⋊D11C2218yescomplemented
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64#10622616C2218yescomplemented
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622423C2218yescomplemented
70#10622417C2218yescomplemented
71#10622404C2218yescomplemented
72#10622403C2218yescomplemented
73#10622392C2218yescomplemented
74#10622391C2218yescomplemented
75#10622375C2218yescomplemented
76#10622373C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11D411yescharacteristic
91C2×#4343—22no—
92C2×#4343—24no—
93C2×#4343—42no—
94C2×#4343C2314yes—
95C22×D44—21no—
96C22×D44C2311yescharacteristic
97C22×C4×D11—21no—
98C22×C4×D11C2311yescharacteristic
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C22×C8×C11—42no—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2314yes—
105C11×#117—22no—
106C11×#117C2314yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C42×C11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11D411yescharacteristic
114Q8×Dic11—22no—
115Q8×Dic11C2314yes—
116C2×#4326—24no—
117C2×#4326C2314yes—
118#66993—28no—
119#66993—22no—
120#66993C2314yes—
121#66991—22no—
122#66991—28no—
123#66991C2314yes—
124C2×#4324—42no—
125C2×#4324C2314yes—
126#66983—22no—
127#66983—28no—
128#66983C2314yes—
129C4×C22⋊D11—28no—
130C4×C22⋊D11D414yes—
131C4×C22⋊D11C2314yes—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4D411yescharacteristic
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140#66977—22no—
141#66977C2314yes—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4D411yescharacteristic
146C2×C4×Dic11—21no—
147C2×C4×Dic11—21no—
148C2×C4×Dic11—21no—
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×#4314—42no—
153C2×#4314C2314yes—
154C2×C8×D11—42no—
155C2×C8×D11C2314yes—
156#66950—22no—
157#66950C2314yes—
158#66945—22no—
159#66945C2314yes—
160#66941—22no—
161#66941C2314yes—
162#66940—22no—
163#66940C2314yes—
164#66938—28no—
165#66932—28no—
166#66929—28no—
167C4×Dic22—28no—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172#66899C2314yes—
173#66896C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66881C2314yes—
178#66880C2314yes—
179Dic11⋊C8C2314yes—
180C8×Dic11C2314yes—
181#66873C2314yes—
182#66873C2314yes—
183#66872C2314yes—
184#66871C2314yes—
185C2×#3304—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11C2×D411yescharacteristic
190C11×#41—28no—
191C11×#41—44no—
192C11×#41—48no—
193C2×Q8×C11—21no—
194C2×Q8×C11—22no—
195C2×Q8×C11#4114yes—
196C2×Q8×C11C2412yes—
197C2×D4×C11—24no—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—44no—
202C2×D4×C11C2412yes—
203C22×C4×C11—21no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—24no—
209C22×C4×C11—44no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—82no—
221C2×C22⋊D11—82no—
222C2×C22⋊D11—82no—
223C2×C22⋊D11C2×D414yes—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230#4343—28no—
231#4343—44no—
232#4343—48no—
233C2×D44—24no—
234C2×D44—21no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44—44no—
238C2×D44C2412yes—
239C2×C4×D11—24no—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—44no—
243C2×C4×D11C2×D412yes—
244C2×C4×D11C2412yes—
245C2×Dic22—24no—
246C2×Dic22—21no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22—44no—
250C2×Dic22C2412yes—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11—44no—
254C2×C8×C11C2412yes—
255C2×C8×C11C2412yes—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4C2412yes—
259C11×C4⋊C4C2412yes—
260C11×C22⋊C4—24no—
261C42×C11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11C2×D414yes—
265#4326—28no—
266#4324—44no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4C2×D414yes—
271C4⋊Dic11—24no—
272C4⋊Dic11—24no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11C2412yes—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4C2×D414yes—
281C4×Dic11—24no—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2412yes—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290#4314—44no—
291C8×D11—44no—
292C2×#556—111no—
293C2×#550—111no—
294#3304—1116no—
295C2×#486—111no—
296C2×#482—111no—
297C2×#482—111no—
298C2×#475—111no—
299C2×#465—111no—
300C2×#465—111no—
301C2×#460—111no—
302C2×#452—111no—
303C2×#452—111no—
304C2×C4×Q16—111no—
305C2×C8×D4—111no—
306C2×#416—111no—
307C2×#416D1111yescharacteristic, complemented
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11C22×D412yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11C22×D412yes—
325Q8×C11—24no—
326Q8×C11—22no—
327Q8×C11C2×#4114yes—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—48no—
331D4×C11—42no—
332C2×C4×C11—24no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—48no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C2×#4112yes—
346C2×C4×C11H(5,𝔽2)12yes—
347C2×C4×C11C2511yescharacteristic
348C22⋊D11—28no—
349C22⋊D11—48no—
350C22⋊D11—84no—
351C22⋊D11—84no—
352C22⋊D11—84no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11#13514yes—
362C2×Dic11C22×D412yes—
363C2×Dic11C22×D412yes—
364C2×Dic11C22×D412yes—
365D44—22no—
366D44—22no—
367D44—48no—
368D44—42no—
369C4×D11—24no—
370C4×D11—22no—
371C4×D11—22no—
372C4×D11—48no—
373Dic22—22no—
374Dic22—22no—
375Dic22—42no—
376Dic22—48no—
377C8×C11—22no—
378C8×C11—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41—111no—
382C22×#41C2×D1111yescharacteristic
383C22×Q16—111no—
384C22×SD16—111no—
385C22×SD16—111no—
386C23×C8—111no—
387C23×C8C2×D1111yescharacteristic
388#556—118no—
389#556—224no—
390#550—118no—
391#550—224no—
392C2×C4⋊Q8—111no—
393C2×#127—111no—
394C2×#127—221no—
395C2×#126—221no—
396C2×#126—221no—
397C2×#124—221no—
398C2×C22⋊Q8—111no—
399C2×C22⋊Q8—111no—
400C2×#121—111no—
401C2×#121—111no—
402C2×#121—221no—
403C2×#121—221no—
404C2×C4×Q8—111no—
405C2×C4×Q8—111no—
406C2×C4×Q8—221no—
407C2×C4×D4—111no—
408C2×C4×D4—221no—
409C2×#117—111no—
410C2×#117C2×D1111yescharacteristic
411#486—118no—
412#482—118no—
413#482—118no—
414#475—118no—
415#465—118no—
416#465—118no—
417#460—118no—
418#452—118no—
419#452—118no—
420C4×Q16—118no—
421C8×D4—118no—
422C2×#107—111no—
423C2×#106—111no—
424C2×#106—111no—
425C2×C4⋊C8—111no—
426#416—118no—
427#416C2×D1118yescomplemented
428C2×#103—111no—
429C2×#103—111no—
430C2×#103C2×D1111yescharacteristic
431C2×#103C2×D1111yescharacteristic
432C2×#102—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102C2×D1111yescharacteristic
437C2×#102C2×D1111yescharacteristic
438C2×C22⋊C8—111no—
439C2×C22⋊C8—111no—
440C2×C4×C8—111no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—44no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—84no—
449C22×C11#54612yes—
450C22×C11C2×#13512yes—
451C22×C11#57712yes—
452C22×C11C23×D411yescharacteristic
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—44no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—84no—
461C4×C11—22no—
462C4×C11—24no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11#54612yes—
466C4×C11C22×#4111yescharacteristic
467C4×C11C2×H(5,𝔽2)11yescharacteristic
468Dic11—22no—
469Dic11—22no—
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11C2×#13514yes—
474C2×#41—22no—
475C2×#41—24no—
476C2×#41—42no—
477C2×#41—114no—
478C2×#41—222no—
479C2×#41—224no—
480C2×#41—442no—
481C2×#41C22×D1114yes—
482C22×Q8—111no—
483C22×Q8—221no—
484C22×Q8C22×D1111yescharacteristic
485C22×D4—21no—
486C22×D4—111no—
487C22×D4—111no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4—221no—
492C22×D4—221no—
493C22×D4C22×D1111yescharacteristic
494C23×C4—21no—
495C23×C4—111no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×Q16—114no—
499C2×Q16—224no—
500C2×SD16—114no—
501C2×SD16—114no—
502C2×SD16—442no—
503C2×SD16—442no—
504C22×C8—42no—
505C22×C8—111no—
506C22×C8—111no—
507C22×C8—114no—
508C22×C8—442no—
509C22×C8C22×D1111yescharacteristic
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1114yes—
512C4⋊Q8—114no—
513C4⋊Q8—222no—
514#127—114no—
515#127—222no—
516#127—228no—
517#126—228no—
518#126—228no—
519#124—228no—
520C22⋊Q8—114no—
521C22⋊Q8—114no—
522C22⋊Q8—222no—
523C22⋊Q8—222no—
524#121—114no—
525#121—114no—
526#121—228no—
527#121—228no—
528#121—222no—
529#121—222no—
530C4×Q8—114no—
531C4×Q8—114no—
532C4×Q8—228no—
533C4×Q8—222no—
534C4×Q8—222no—
535C4×D4—114no—
536C4×D4—114no—
537C4×D4—228no—
538#117—22no—
539#117—114no—
540#117—222no—
541#117C22×D1114yes—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—111no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C42—21no—
561C2×C42—111no—
562C2×C42—221no—
563C2×C42—221no—
564C2×C42—221no—
565#107—114no—
566#106—114no—
567#106—114no—
568C4⋊C8—114no—
569#103—114no—
570#103—114no—
571#103C22×D1114yes—
572#103C22×D1114yes—
573#102—114no—
574#102—114no—
575#102—114no—
576#102—114no—
577#102C22×D1114yes—
578#102C22×D1114yes—
579C22⋊C8—114no—
580C22⋊C8—114no—
581C4×C8—114no—
582C2×C11—42no—
583C2×C11—82no—
584C2×C11#330414yescomplemented
585C2×C11C2×#54611yescharacteristic
586C2×C11C22×#13511yescharacteristic
587C2×C11C2×#57711yescharacteristic
588D11—42no—
589D11—82no—
590C24—21no—
591C24—111no—
592C24—221no—
593C24D4×D1111yescharacteristic
594#41—28no—
595#41—44no—
596#41—48no—
597#41—228no—
598#41—444no—
599#41—448no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—112no—
603C2×Q8—224no—
604C2×Q8—221no—
605C2×Q8—222no—
606C2×Q8—222no—
607C2×Q8—444no—
608C2×Q8#433914yes—
609C2×Q8C23×D1112yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4—114no—
616C2×D4—112no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—224no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—222no—
624C2×D4—221no—
625C2×D4—222no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—882no—
629C2×D4—882no—
630C2×D4—882no—
631C2×D4C23×D1112yes—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—224no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—444no—
651C22×C4D4×D1112yes—
652C22×C4D4×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—228no—
656SD16—444no—
657SD16—444no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—44no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—444no—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—114no—
671C4⋊C4—112no—
672C4⋊C4—112no—
673C4⋊C4—224no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—224no—
680C4⋊C4C23×D1112yes—
681C4⋊C4C23×D1112yes—
682C22⋊C4—24no—
683C22⋊C4—114no—
684C22⋊C4—114no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C42—24no—
691C42—112no—
692C42—112no—
693C42—224no—
694C42—224no—
695C42—224no—
696C11C2×#330411yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—112no—
705C23—222no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—442no—
710C23—442no—
711C23—442no—
712C23C2×D4×D1112yes—
713C23C2×D4×D1111yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—222no—
717Q8—222no—
718Q8—448no—
719Q8—442no—
720Q8C2×#433914yes—
721D4—22no—
722D4—22no—
723D4—48no—
724D4—42no—
725D4—228no—
726D4—222no—
727D4—222no—
728D4—448no—
729D4—448no—
730D4—442no—
731D4—884no—
732D4—884no—
733D4—884no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—48no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—114no—
746C2×C4—112no—
747C2×C4—112no—
748C2×C4—112no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—224no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—448no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4C2×#433912yes—
762C2×C4C2×D4×D1112yes—
763C2×C4C2×D4×D1111yescharacteristic
764C2×C4#6703712yes—
765C2×C4C24×D1111yescharacteristic
766C8—22no—
767C8—22no—
768C8—222no—
769C8—222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—222no—
779C22—222no—
780C22—222no—
781C22—444no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—884no—
786C22#1062302112yes—
787C22D11×#13512yes—
788C22#1062330112yes—
789C22C22×D4×D1111yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—114no—
795C4—222no—
796C4—222no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4#1062302112yes—
801C4C22×#433911yescharacteristic
802C4C2×#6703711yescharacteristic
803C2—42no—
804C2—82no—
805C2—442no—
806C2—882no—
807C2#1308055114yesdirect product factor
808C2C2×#1062302111yescharacteristic
809C2C2×D11×#13511yescharacteristic
810C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623365C2
hypercenterC2×#416D11
hypocenterC11C2×#3304
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#10623064C2semidirect
3. #13080551C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622404C2semidirect
8. C2×#10622727C2semidirect
9. C2×#10622391C2semidirect
10. C2×#10622375C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622852C2semidirect
13. C2×#10622403C2semidirect
14. C2×C8×C22⋊D11C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#416C2semidirect
38. #10623064C22semidirect
47. C11×#416C22semidirect
52. #10622852C22semidirect
56. #10622727C22semidirect
58. C8×C22⋊D11C22semidirect
64. #10622616C22semidirect
69. #10622423C22semidirect
70. #10622417C22semidirect
71. #10622404C22semidirect
72. #10622403C22semidirect
73. #10622392C22semidirect
74. #10622391C22semidirect
75. #10622375C22semidirect
76. #10622373C22semidirect
307. C2×#416D11semidirect
427. #416C2×D11semidirect
584. C2×C11#3304semidirect
696. C11C2×#3304semidirect
807. C2#13080551direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230642
C2×#106233652
#130805512
C2×#106223732
C2×#106226162
C2×#106223922
C2×#106224042
C2×#106227272
C2×#106223912
C2×#106223752
C2×#106224232
C2×#106228522
C2×#106224032
C2×C8×C22⋊D112
C2×#106224172
C2×C11×#4162
C2×#330411