Finite Group Databasebeta

← C2×#13080949 #15630713

Subgroups — C2×#13080949 #15630713

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic, complemented
2C2×#10623130C211yesmaximal, characteristic
3#13080949C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622495C211yesmaximal, characteristic, complemented
6C2×#10622646C211yesmaximal, characteristic, complemented
7C2×#10622488C211yesmaximal, characteristic, complemented
8C2×#10622425C211yesmaximal, characteristic, complemented
9C2×#10622776C211yesmaximal, characteristic, complemented
10C2×#10622660C211yesmaximal, characteristic, complemented
11C2×#10622786C211yesmaximal, characteristic, complemented
12C2×#10622403C211yesmaximal, characteristic, complemented
13C2×#10622741C211yesmaximal, characteristic, complemented
14C2×#10622746C211yesmaximal, characteristic, complemented
15C2×#10622384C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C22×#4325C2211yescharacteristic
27C2×#66993—21no—
28C2×#66993C2211yescharacteristic
29C2×#66992—21no—
30C2×C4×C22⋊D11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33#10623166—24no—
34#10623166C2218yescomplemented
35#10623130—24no—
36#10623130C2218yes—
37C2×#66950—21no—
38C2×#66948C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66942—21no—
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66937—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×(C22⋊D11)⋊C4—21no—
46C2×#66931—21no—
47C11×#468C2218yescomplemented
48C2×C11×#107C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622786C2218yescomplemented
55#10622776C2218yescomplemented
56#10622746C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622660C2218yescomplemented
66#10622646C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622495C2218yescomplemented
72#10622488C2218yescomplemented
73#10622425C2218yescomplemented
74#10622403C2218yescomplemented
75#10622384C2218yescomplemented
76#10622373C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11D411yescharacteristic
86C23×Dic11—21no—
87C23×Dic11—21no—
88C2×#4341—22no—
89C2×#4341—24no—
90C2×#4341—42no—
91C2×#4341C2314yes—
92C2×#4339—22no—
93C2×#4339—24no—
94C2×#4339—42no—
95C2×#4339C2314yes—
96C22×D44—21no—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11C2311yescharacteristic
101C22×Dic22—21no—
102C22×Dic22C2311yescharacteristic
103C2×C11×SD16—42no—
104C2×C11×SD16C2314yes—
105C2×C11×M16—42no—
106C2×C11×M16C2314yes—
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8C2314yes—
111C11×#121—22no—
112C11×#121C2314yes—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C22⋊Dic11D411yescharacteristic
119#66999—22no—
120#66999C2314yes—
121Q8×Dic11—22no—
122Q8×Dic11C2314yes—
123C2×#4326—24no—
124C2×#4326C2314yes—
125C2×#4325—42no—
126C2×#4325C2314yes—
127#66993—28no—
128#66993—22no—
129#66993C2314yes—
130#66992—28no—
131C4×C22⋊D11D414yes—
132C4×C22⋊D11C2314yes—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4D411yescharacteristic
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—22no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4D411yescharacteristic
147C2×C4×Dic11—21no—
148C2×C4×Dic11—21no—
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×#4313—42no—
153C2×#4313C2314yes—
154#66950—28no—
155#66948—22no—
156#66948C2314yes—
157C4⋊C4×D11—22no—
158C4⋊C4×D11C2314yes—
159#66942—28no—
160#66941—22no—
161#66941C2314yes—
162#66940—22no—
163#66940C2314yes—
164#66937—28no—
165(C22⋊D11)⋊C4—28no—
166(C22⋊D11)⋊C4—28no—
167#66931—28no—
168C11×#107C2314yes—
169C11×#103C2314yes—
170C11×#102C2314yes—
171#66896C2314yes—
172#66896C2314yes—
173C22⋊(C11⋊C8)C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179Dic11⋊C8C2314yes—
180C8×Dic11C2314yes—
181#66874C2314yes—
182#66873C2314yes—
183#66871C2314yes—
184#66871C2314yes—
185C2×#3333—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11C2×D411yescharacteristic
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11C2412yes—
194C2×D4×C11—24no—
195C2×D4×C11—21no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—82no—
199C2×D4×C11C2412yes—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—82no—
218C2×C22⋊D11C2×D414yes—
219C22×Dic11—24no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—24no—
224C22×Dic11—44no—
225C22×Dic11—82no—
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229#4341—28no—
230#4341—44no—
231#4341—48no—
232#4339—28no—
233#4339—44no—
234#4339—48no—
235C2×D44—24no—
236C2×D44—21no—
237C2×D44—22no—
238C2×D44—22no—
239C2×D44—82no—
240C2×D44C2412yes—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—44no—
246C2×C4×D11—82no—
247C2×C4×D11C2×D412yes—
248C2×C4×D11C2412yes—
249C2×Dic22—24no—
250C2×Dic22—21no—
251C2×Dic22—22no—
252C2×Dic22—82no—
253C2×Dic22#4114yes—
254C2×Dic22C2412yes—
255C11×SD16—44no—
256C11×M16—44no—
257C2×C8×C11—22no—
258C2×C8×C11—22no—
259C2×C8×C11C2412yes—
260C2×C8×C11C2412yes—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—24no—
264C11×C4⋊C4C2412yes—
265C11×C4⋊C4C2412yes—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C22⋊Dic11C2×D414yes—
269#4326—28no—
270#4325—44no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4C2×D414yes—
274C4⋊Dic11—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—24no—
277C4⋊Dic11—21no—
278C4⋊Dic11C2412yes—
279C4⋊Dic11C2412yes—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4C2×D414yes—
285C4×Dic11—24no—
286C4×Dic11—24no—
287C4×Dic11C2×D412yes—
288C4×Dic11C2412yes—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293#4313—44no—
294C2×#554—111no—
295C2×#550—111no—
296#3333—1116no—
297C2×#486—111no—
298C2×#480—111no—
299C2×#480—111no—
300C2×#477—111no—
301C2×#468—111no—
302C2×#468D1111yescharacteristic, complemented
303C2×#460—111no—
304C2×#452—111no—
305C2×#452—111no—
306C2×C4×Q16—111no—
307C2×#436—111no—
308C2×#417—111no—
309C2×#417—111no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11C22×D412yes—
318C23×C11C22×D411yescharacteristic
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11C22×D412yes—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—42no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—42no—
333D4×C11—84no—
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—22no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4112yes—
347C2×C4×C11H(5,𝔽2)12yes—
348C2×C4×C11C2511yescharacteristic
349C22⋊D11—28no—
350C22⋊D11—48no—
351C22⋊D11—48no—
352C22⋊D11—48no—
353C22⋊D11—84no—
354C2×Dic11—24no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—48no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—84no—
364C2×Dic11#13714yes—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368D44—22no—
369D44—22no—
370D44—42no—
371D44—84no—
372C4×D11—24no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—48no—
376C4×D11—84no—
377Dic22—24no—
378Dic22—22no—
379Dic22—84no—
380Dic22C2×#4114yes—
381C8×C11—22no—
382C8×C11—22no—
383C11⋊C8—22no—
384C11⋊C8—22no—
385C22×#41—111no—
386C22×#41—111no—
387C22×Q16—111no—
388C22×SD16—111no—
389C22×SD16C2×D1111yescharacteristic
390C22×M16—111no—
391C22×M16C2×D1111yescharacteristic
392#554—118no—
393#554—224no—
394#550—118no—
395#550—224no—
396C2×C4⋊Q8—111no—
397C2×#127—111no—
398C2×#127—221no—
399C2×#125—221no—
400C2×C22⋊Q8—111no—
401C2×C22⋊Q8—221no—
402C2×C22⋊Q8—221no—
403C2×C22⋊Q8C2×D1111yescharacteristic
404C2×#121—111no—
405C2×#121—221no—
406C2×#121—221no—
407C2×#121C2×D1111yescharacteristic
408C2×C4×Q8—111no—
409C2×C4×Q8—111no—
410C2×C4×D4—111no—
411C2×C4×D4—221no—
412C2×C4×D4—221no—
413C22×C4⋊C4—111no—
414C22×C4⋊C4—111no—
415#486—118no—
416#480—118no—
417#480—118no—
418#477—118no—
419#468—118no—
420#468C2×D1118yescomplemented
421#460—118no—
422#452—118no—
423#452—118no—
424C4×Q16—118no—
425#436—118no—
426C2×#107—111no—
427C2×#107—111no—
428C2×#107C2×D1111yescharacteristic
429C2×C4⋊C8—111no—
430#417—118no—
431#417—118no—
432C2×#103—111no—
433C2×#103—111no—
434C2×#103—111no—
435C2×#103C2×D1111yescharacteristic
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—111no—
440C2×#102—111no—
441C2×#102C2×D1111yescharacteristic
442C2×C22⋊C8—111no—
443C2×C22⋊C8—111no—
444C2×C4×C8—111no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—44no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—84no—
453C22×C11#54612yes—
454C22×C11C2×#13712yes—
455C22×C11#57612yes—
456C22×C11C23×D411yescharacteristic
457C2×D11—22no—
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—44no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—84no—
465C4×C11—22no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11#54612yes—
470C4×C11C22×#4111yescharacteristic
471C4×C11C2×H(5,𝔽2)11yescharacteristic
472Dic11—24no—
473Dic11—22no—
474Dic11—22no—
475Dic11—42no—
476Dic11—42no—
477Dic11C2×#13714yes—
478C2×#41—114no—
479C2×#41—114no—
480C2×#41—224no—
481C2×#41—222no—
482C2×#41—222no—
483C2×#41—224no—
484C2×#41—442no—
485C2×#41—442no—
486C22×Q8—111no—
487C22×Q8—221no—
488C22×Q8C22×D1111yescharacteristic
489C22×D4—21no—
490C22×D4—111no—
491C22×D4—111no—
492C22×D4—221no—
493C22×D4—221no—
494C22×D4—221no—
495C22×D4—221no—
496C22×D4—221no—
497C22×D4C22×D1111yescharacteristic
498C23×C4—111no—
499C23×C4—221no—
500C23×C4—221no—
501C23×C4—221no—
502C23×C4—221no—
503C23×C4C22×D1111yescharacteristic
504C2×Q16—114no—
505C2×Q16—224no—
506C2×SD16—42no—
507C2×SD16—114no—
508C2×SD16—442no—
509C2×SD16C22×D1114yes—
510C2×M16—42no—
511C2×M16—114no—
512C2×M16—442no—
513C2×M16C22×D1114yes—
514C22×C8—111no—
515C22×C8—111no—
516C22×C8C22×D1111yescharacteristic
517C22×C8C22×D1111yescharacteristic
518C4⋊Q8—114no—
519C4⋊Q8—222no—
520#127—114no—
521#127—222no—
522#127—228no—
523#125—228no—
524C22⋊Q8—22no—
525C22⋊Q8—114no—
526C22⋊Q8—228no—
527C22⋊Q8—228no—
528C22⋊Q8—222no—
529C22⋊Q8C22×D1114yes—
530#121—22no—
531#121—114no—
532#121—228no—
533#121—228no—
534#121—222no—
535#121C22×D1114yes—
536C4×Q8—114no—
537C4×Q8—114no—
538C4×Q8—222no—
539C4×Q8—222no—
540C4×D4—114no—
541C4×D4—114no—
542C4×D4—228no—
543C4×D4—228no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4—114no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4—222no—
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C4⋊C4C22×D1111yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—111no—
563C2×C22⋊C4—111no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C42—111no—
567C2×C42—221no—
568C2×C42—221no—
569#107—114no—
570#107—114no—
571#107C22×D1114yes—
572C4⋊C8—114no—
573#103—114no—
574#103—114no—
575#103—114no—
576#103C22×D1114yes—
577#102—114no—
578#102—114no—
579#102—114no—
580#102—114no—
581#102—114no—
582#102C22×D1114yes—
583C22⋊C8—114no—
584C22⋊C8—114no—
585C4×C8—114no—
586C2×C11—42no—
587C2×C11—82no—
588C2×C11#333314yescomplemented
589C2×C11C2×#54611yescharacteristic
590C2×C11C22×#13711yescharacteristic
591C2×C11C2×#57611yescharacteristic
592D11—42no—
593D11—82no—
594C24—21no—
595C24—111no—
596C24—221no—
597C24D4×D1111yescharacteristic
598#41—228no—
599#41—228no—
600#41—444no—
601#41—448no—
602#41—444no—
603#41—448no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—114no—
608C2×Q8—112no—
609C2×Q8—224no—
610C2×Q8—221no—
611C2×Q8—222no—
612C2×Q8—882no—
613C2×Q8C23×D1112yes—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—82no—
619C2×D4—114no—
620C2×D4—112no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—221no—
628C2×D4—222no—
629C2×D4—222no—
630C2×D4—444no—
631C2×D4—444no—
632C2×D4—444no—
633C2×D4—882no—
634C2×D4—882no—
635C2×D4C23×D1112yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—111no—
642C22×C4—111no—
643C22×C4—111no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—224no—
647C22×C4—224no—
648C22×C4—221no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—221no—
652C22×C4—221no—
653C22×C4—224no—
654C22×C4—224no—
655C22×C4—444no—
656C22×C4—444no—
657C22×C4—882no—
658C22×C4—882no—
659C22×C4D4×D1112yes—
660C22×C4D4×D1111yescharacteristic
661C22×C4C23×D1112yes—
662C22×C4C23×D1111yescharacteristic
663Q16—228no—
664SD16—44no—
665SD16—444no—
666M16—44no—
667M16—444no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—112no—
671C2×C8—112no—
672C2×C8—222no—
673C2×C8—222no—
674C2×C8C23×D1112yes—
675C2×C8C23×D1112yes—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—114no—
680C4⋊C4—112no—
681C4⋊C4—112no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—221no—
688C4⋊C4—224no—
689C4⋊C4—221no—
690C4⋊C4C23×D1112yes—
691C4⋊C4C23×D1112yes—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—114no—
695C22⋊C4—114no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C42—112no—
699C42—112no—
700C42—224no—
701C42—224no—
702C11C2×#333311yescharacteristic, complemented, Sylow
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—112no—
711C23—222no—
712C23—222no—
713C23—222no—
714C23—222no—
715C23—442no—
716C23—442no—
717C23—442no—
718C23C2×D4×D1112yes—
719C23C2×D4×D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—114no—
724Q8—224no—
725Q8—222no—
726Q8—884no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—228no—
732D4—222no—
733D4—222no—
734D4—448no—
735D4—448no—
736D4—448no—
737D4—442no—
738D4—884no—
739D4—884no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—114no—
751C2×C4—112no—
752C2×C4—112no—
753C2×C4—112no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—224no—
757C2×C4—222no—
758C2×C4—224no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—448no—
764C2×C4—448no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—884no—
768C2×C4—884no—
769C2×C4C2×D4×D1112yes—
770C2×C4C2×D4×D1111yescharacteristic
771C2×C4#6703712yes—
772C2×C4#41×D1112yes—
773C2×C4C24×D1111yescharacteristic
774C8—22no—
775C8—22no—
776C8—222no—
777C8—222no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—222no—
787C22—222no—
788C22—222no—
789C22—444no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—884no—
794C22#1062314112yes—
795C22#1062330512yes—
796C22D11×#13712yes—
797C22C22×D4×D1111yescharacteristic
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—114no—
803C4—222no—
804C4—224no—
805C4—222no—
806C4—442no—
807C4—442no—
808C4#1062314112yes—
809C4C2×#6703711yescharacteristic
810C4C2×#41×D1111yescharacteristic
811C2—42no—
812C2—82no—
813C2—442no—
814C2—882no—
815C2#1308094914yesdirect product factor
816C2C2×#1062314111yescharacteristic
817C2C2×D11×#13711yescharacteristic
818C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
prime radicalC2×#10623130C2
hypercenterC2×#468D11
hypocenterC11C2×#3333
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623166C2semidirect
3. #13080949C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622495C2semidirect
6. C2×#10622646C2semidirect
7. C2×#10622488C2semidirect
8. C2×#10622425C2semidirect
9. C2×#10622776C2semidirect
10. C2×#10622660C2semidirect
11. C2×#10622786C2semidirect
12. C2×#10622403C2semidirect
13. C2×#10622741C2semidirect
14. C2×#10622746C2semidirect
15. C2×#10622384C2semidirect
16. C2×C11×#468C2semidirect
34. #10623166C22semidirect
47. C11×#468C22semidirect
54. #10622786C22semidirect
55. #10622776C22semidirect
56. #10622746C22semidirect
57. #10622741C22semidirect
65. #10622660C22semidirect
66. #10622646C22semidirect
71. #10622495C22semidirect
72. #10622488C22semidirect
73. #10622425C22semidirect
74. #10622403C22semidirect
75. #10622384C22semidirect
76. #10622373C22semidirect
302. C2×#468D11semidirect
420. #468C2×D11semidirect
588. C2×C11#3333semidirect
702. C11C2×#3333semidirect
815. C2#13080949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231662
C2×#106231302
#130809492
C2×#106223732
C2×#106224952
C2×#106226462
C2×#106224882
C2×#106224252
C2×#106227762
C2×#106226602
C2×#106227862
C2×#106224032
C2×#106227412
C2×#106227462
C2×#106223842
C2×C11×#4682
C2×#333311