Finite Group Databasebeta

← C2×#13080906 #15630666

Subgroups — C2×#13080906 #15630666

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623063C211yesmaximal, characteristic
2C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
3#13080906C2116yesmaximal, direct product factor
4C2×#10622405C211yesmaximal, characteristic, complemented
5C2×#10622609C211yesmaximal, characteristic, complemented
6C2×#10622427C211yesmaximal, characteristic, complemented
7C2×#10622407C211yesmaximal, characteristic, complemented
8C2×#10622425C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622431C211yesmaximal, characteristic, complemented
11C2×#10622419C211yesmaximal, characteristic, complemented
12C2×#10622840C211yesmaximal, characteristic, complemented
13C2×#10622401C211yesmaximal, characteristic, complemented
14C2×#10622741C211yesmaximal, characteristic, complemented
15C2×#10622415C211yesmaximal, characteristic, complemented
16C2×C11×#419C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21Q8×C22⋊D11—24no—
22Q8×C22⋊D11C2218yescomplemented
23C2×#66999—21no—
24C2×#66999C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×#66997—21no—
27C2×#66997C2211yescharacteristic
28C22×#4325C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×C4×C22⋊D11—21no—
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×#66977—21no—
34C2×#66977C2211yescharacteristic
35C22×#4314C2211yescharacteristic
36C22×#4313C2211yescharacteristic
37#10623063—24no—
38#10623063C2218yes—
39C2×#66948C2211yescharacteristic
40C2×#66946C2211yescharacteristic
41C2×#66945C2211yescharacteristic
42C2×#66941C2211yescharacteristic
43C2×#66938—21no—
44C2×#66937—21no—
45C2×#66928—21no—
46C2×#66925—21no—
47C11×#419C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52#10622840C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622747C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64#10622609C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622431C2218yescomplemented
70#10622427C2218yescomplemented
71#10622425C2218yescomplemented
72#10622419C2218yescomplemented
73#10622415C2218yescomplemented
74#10622407C2218yescomplemented
75#10622405C2218yescomplemented
76#10622401C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11—22no—
79C22×Q8×C11—24no—
80C22×Q8×C11—42no—
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2314yes—
83C22×Q8×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C22×C22⋊D11D411yescharacteristic
88C2×Q8×D11—22no—
89C2×Q8×D11—24no—
90C2×Q8×D11—42no—
91C2×Q8×D11C2314yes—
92C22×D44—21no—
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C22×C4×D11—21no—
96C22×C4×D11C2311yescharacteristic
97C22×Dic22—21no—
98C22×Dic22—21no—
99C22×Dic22C2311yescharacteristic
100C2×C11×M16—42no—
101C2×C11×M16C2314yes—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C11×#117—22no—
105C11×#117C2314yes—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C42×C11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11D411yescharacteristic
112#66999—22no—
113#66999—28no—
114#66999C2314yes—
115Q8×Dic11—22no—
116Q8×Dic11C2314yes—
117#66997—28no—
118#66997—22no—
119#66997C2314yes—
120C2×#4325—24no—
121C2×#4325—42no—
122C2×#4325C2314yes—
123C2×#4325C2314yes—
124#66983—22no—
125#66983C2314yes—
126C4×C22⋊D11—28no—
127C4×C22⋊D11D414yes—
128C4×C22⋊D11C2314yes—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4D411yescharacteristic
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138#66977—22no—
139#66977—28no—
140#66977C2314yes—
141C2×Dic11⋊C4—21no—
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×#4314—42no—
153C2×#4314C2314yes—
154C2×#4313—42no—
155C2×#4313C2314yes—
156#66948—22no—
157#66948C2314yes—
158#66946—22no—
159#66946C2314yes—
160#66945—22no—
161#66945C2314yes—
162#66941—22no—
163#66941C2314yes—
164#66938—28no—
165#66937—28no—
166#66928—28no—
167#66925—28no—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171C11×#103C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66882C2314yes—
178#66880C2314yes—
179Dic11⋊C8C2314yes—
180C8×Dic11C2314yes—
181#66874C2314yes—
182#66874C2314yes—
183#66872C2314yes—
184#66871C2314yes—
185C2×#3329—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C23×D11—21no—
188C23×D11C2×D411yescharacteristic
189C2×Q8×C11—21no—
190C2×Q8×C11—24no—
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11—28no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11—44no—
197C2×Q8×C11—44no—
198C2×Q8×C11—48no—
199C2×Q8×C11#4114yes—
200C2×Q8×C11C2412yes—
201C2×Q8×C11C2412yes—
202C22×C4×C11—21no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—21no—
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—82no—
217C2×C22⋊D11C2×D414yes—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224Q8×D11—28no—
225Q8×D11—44no—
226Q8×D11—48no—
227C2×D44—24no—
228C2×D44—21no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—82no—
232C2×D44C2412yes—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—44no—
238C2×C4×D11—44no—
239C2×C4×D11C2×D412yes—
240C2×C4×D11C2412yes—
241C2×Dic22—24no—
242C2×Dic22—24no—
243C2×Dic22—21no—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22—44no—
247C2×Dic22—82no—
248C2×Dic22C2412yes—
249C11×M16—44no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11C2412yes—
253C2×C8×C11C2412yes—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—24no—
259C42×C11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11C2×D414yes—
262#4325—28no—
263#4325—44no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4C2×D414yes—
270C4⋊Dic11—24no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11C2412yes—
274C4⋊Dic11C2412yes—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4C2×D414yes—
281C4×Dic11—24no—
282C4×Dic11—24no—
283C4×Dic11C2×D412yes—
284C4×Dic11C2412yes—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289#4314—44no—
290#4313—44no—
291C2×#555—111no—
292C2×D4×Q8—111no—
293#3329—1116no—
294C2×#487—111no—
295C2×#485—111no—
296C2×#485—111no—
297C2×#477—111no—
298C2×#468—111no—
299C2×#468—111no—
300C2×#461—111no—
301C2×#448—111no—
302C2×#448—111no—
303C2×C4×SD16—111no—
304C2×#436—111no—
305C2×#419—111no—
306C2×#419D1111yescharacteristic, complemented
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11C22×D412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—42no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11C22×D412yes—
320Q8×C11—24no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—22no—
324Q8×C11—48no—
325Q8×C11—42no—
326Q8×C11C2×#4114yes—
327C2×C4×C11—24no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—48no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4112yes—
343C2×C4×C11H(5,𝔽2)12yes—
344C2×C4×C11C2511yescharacteristic
345C22⋊D11—28no—
346C22⋊D11—84no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11#13714yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359D44—22no—
360D44—22no—
361D44—42no—
362D44—84no—
363C4×D11—24no—
364C4×D11—22no—
365C4×D11—22no—
366C4×D11—48no—
367C4×D11—48no—
368Dic22—22no—
369Dic22—22no—
370Dic22—48no—
371Dic22—42no—
372Dic22—84no—
373C8×C11—22no—
374C8×C11—22no—
375C11⋊C8—22no—
376C11⋊C8—22no—
377C23×Q8—111no—
378C23×Q8C2×D1111yescharacteristic
379C22×SD16—111no—
380C22×SD16—111no—
381C22×SD16—111no—
382C22×M16—111no—
383C22×M16C2×D1111yescharacteristic
384#555—118no—
385#555—224no—
386D4×Q8—118no—
387D4×Q8—224no—
388C2×C4⋊Q8—111no—
389C2×C4⋊Q8—111no—
390C2×C4⋊Q8—221no—
391C2×#124—221no—
392C2×#124—221no—
393C2×C22⋊Q8—111no—
394C2×C22⋊Q8—111no—
395C2×C22⋊Q8—221no—
396C2×C22⋊Q8—221no—
397C2×#121—111no—
398C2×#121—111no—
399C2×#121—221no—
400C2×C4×Q8—111no—
401C2×C4×D4—111no—
402C2×C4×D4—111no—
403C2×C4×D4—221no—
404C2×#117—111no—
405C2×#117—221no—
406C2×#117C2×D1111yescharacteristic
407#487—118no—
408#485—118no—
409#485—118no—
410#477—118no—
411#468—118no—
412#468—118no—
413#461—118no—
414#448—118no—
415#448—118no—
416C4×SD16—118no—
417#436—118no—
418C2×#107—111no—
419C2×#107—111no—
420C2×#106—111no—
421C2×C4⋊C8—111no—
422#419—118no—
423#419C2×D1118yescomplemented
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103C2×D1111yescharacteristic
430C2×#103C2×D1111yescharacteristic
431C2×#103C2×D1111yescharacteristic
432C2×#103C2×D1111yescharacteristic
433C2×#102—111no—
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436C2×C4×C8—111no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—44no—
441C22×C11#54612yes—
442C22×C11C2×#13712yes—
443C22×C11#57712yes—
444C22×C11C23×D411yescharacteristic
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—44no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—84no—
453C4×C11—22no—
454C4×C11—24no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11#54612yes—
459C4×C11C22×#4111yescharacteristic
460C4×C11C2×H(5,𝔽2)11yescharacteristic
461Dic11—22no—
462Dic11—22no—
463Dic11—42no—
464Dic11—42no—
465Dic11—42no—
466Dic11C2×#13714yes—
467C22×Q8—21no—
468C22×Q8—22no—
469C22×Q8—24no—
470C22×Q8—42no—
471C22×Q8—114no—
472C22×Q8—111no—
473C22×Q8—221no—
474C22×Q8—221no—
475C22×Q8—222no—
476C22×Q8—224no—
477C22×Q8—442no—
478C22×Q8C22×D1111yescharacteristic
479C22×Q8C22×D1114yes—
480C22×Q8C22×D1111yescharacteristic
481C22×D4—111no—
482C22×D4—111no—
483C22×D4—221no—
484C22×D4—221no—
485C23×C4—21no—
486C23×C4—111no—
487C23×C4—221no—
488C23×C4—221no—
489C23×C4C22×D1111yescharacteristic
490C2×SD16—114no—
491C2×SD16—114no—
492C2×SD16—114no—
493C2×SD16—224no—
494C2×SD16—442no—
495C2×SD16—442no—
496C2×M16—42no—
497C2×M16—114no—
498C2×M16—442no—
499C2×M16C22×D1114yes—
500C22×C8—111no—
501C22×C8—111no—
502C22×C8C22×D1111yescharacteristic
503C22×C8C22×D1111yescharacteristic
504C4⋊Q8—114no—
505C4⋊Q8—114no—
506C4⋊Q8—222no—
507C4⋊Q8—222no—
508C4⋊Q8—228no—
509#124—228no—
510#124—228no—
511C22⋊Q8—114no—
512C22⋊Q8—114no—
513C22⋊Q8—228no—
514C22⋊Q8—228no—
515C22⋊Q8—222no—
516C22⋊Q8—222no—
517#121—114no—
518#121—114no—
519#121—228no—
520#121—222no—
521#121—222no—
522C4×Q8—114no—
523C4×Q8—222no—
524C4×D4—114no—
525C4×D4—114no—
526C4×D4—114no—
527C4×D4—222no—
528C4×D4—228no—
529#117—22no—
530#117—114no—
531#117—228no—
532#117—222no—
533#117C22×D1114yes—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4C22×D1111yescharacteristic
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—111no—
547C2×C22⋊C4—111no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C42—21no—
555C2×C42—111no—
556C2×C42—221no—
557C2×C42—221no—
558#107—114no—
559#107—114no—
560#106—114no—
561C4⋊C8—114no—
562#103—114no—
563#103—114no—
564#103—114no—
565#103—114no—
566#103—114no—
567#103C22×D1114yes—
568#103C22×D1114yes—
569#103C22×D1114yes—
570#103C22×D1114yes—
571#102—114no—
572C22⋊C8—114no—
573C22⋊C8—114no—
574C4×C8—114no—
575C2×C11—42no—
576C2×C11#332914yescomplemented
577C2×C11C2×#54611yescharacteristic
578C2×C11C22×#13711yescharacteristic
579C2×C11C2×#57711yescharacteristic
580D11—42no—
581D11—82no—
582C24—111no—
583C24—221no—
584C24D4×D1111yescharacteristic
585C2×Q8—21no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—28no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—48no—
595C2×Q8—112no—
596C2×Q8—224no—
597C2×Q8—224no—
598C2×Q8—221no—
599C2×Q8—228no—
600C2×Q8—222no—
601C2×Q8—222no—
602C2×Q8—444no—
603C2×Q8—444no—
604C2×Q8—448no—
605C2×Q8—882no—
606C2×Q8#433914yes—
607C2×Q8C23×D1112yes—
608C2×Q8C23×D1112yes—
609C2×D4—114no—
610C2×D4—112no—
611C2×D4—224no—
612C2×D4—224no—
613C2×D4—224no—
614C2×D4—222no—
615C2×D4—221no—
616C2×D4—222no—
617C2×D4—882no—
618C2×D4—882no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—44no—
627C22×C4—111no—
628C22×C4—111no—
629C22×C4—111no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—224no—
633C22×C4—224no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—444no—
640C22×C4—444no—
641C22×C4D4×D1112yes—
642C22×C4D4×D1111yescharacteristic
643C22×C4C23×D1112yes—
644C22×C4C23×D1111yescharacteristic
645SD16—228no—
646SD16—444no—
647SD16—444no—
648M16—44no—
649M16—444no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—112no—
653C2×C8—112no—
654C2×C8—222no—
655C2×C8—222no—
656C2×C8C23×D1112yes—
657C2×C8C23×D1112yes—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—114no—
661C4⋊C4—112no—
662C4⋊C4—112no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—221no—
669C4⋊C4—221no—
670C4⋊C4—224no—
671C4⋊C4C23×D1112yes—
672C4⋊C4C23×D1112yes—
673C22⋊C4—24no—
674C22⋊C4—114no—
675C22⋊C4—114no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C42—24no—
683C42—112no—
684C42—112no—
685C42—224no—
686C42—224no—
687C11C2×#332911yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—112no—
692C23—222no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—442no—
697C23—442no—
698C23—442no—
699C23C2×D4×D1112yes—
700C23C2×D4×D1111yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—222no—
708Q8—222no—
709Q8—448no—
710Q8—442no—
711Q8—884no—
712Q8C2×#433914yes—
713D4—228no—
714D4—222no—
715D4—222no—
716D4—442no—
717D4—884no—
718D4—884no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—48no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—114no—
733C2×C4—112no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—448no—
745C2×C4—448no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4C2×#433912yes—
750C2×C4C2×D4×D1112yes—
751C2×C4C2×D4×D1111yescharacteristic
752C2×C4#6703712yes—
753C2×C4C24×D1111yescharacteristic
754C8—22no—
755C8—22no—
756C8—222no—
757C8—222no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—222no—
763C22—222no—
764C22—222no—
765C22—444no—
766C22—442no—
767C22—442no—
768C22—442no—
769C22—884no—
770C22#1062302112yes—
771C22D11×#13712yes—
772C22#1062330912yes—
773C22C22×D4×D1111yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—114no—
780C4—222no—
781C4—222no—
782C4—442no—
783C4—442no—
784C4—442no—
785C4#1062302112yes—
786C4C22×#433911yescharacteristic
787C4C2×#6703711yescharacteristic
788C2—42no—
789C2—442no—
790C2—882no—
791C2#1308090614yesdirect product factor
792C2C2×#1062302111yescharacteristic
793C2C2×D11×#13711yescharacteristic
794C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC2×#10623063C2
hypercenterC2×#419D11
hypocenterC11C2×#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C22⋊D11C2semidirect
3. #13080906C2direct (N × H)
4. C2×#10622405C2semidirect
5. C2×#10622609C2semidirect
6. C2×#10622427C2semidirect
7. C2×#10622407C2semidirect
8. C2×#10622425C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622431C2semidirect
11. C2×#10622419C2semidirect
12. C2×#10622840C2semidirect
13. C2×#10622401C2semidirect
14. C2×#10622741C2semidirect
15. C2×#10622415C2semidirect
16. C2×C11×#419C2semidirect
22. Q8×C22⋊D11C22semidirect
47. C11×#419C22semidirect
52. #10622840C22semidirect
56. #10622747C22semidirect
57. #10622741C22semidirect
64. #10622609C22semidirect
69. #10622431C22semidirect
70. #10622427C22semidirect
71. #10622425C22semidirect
72. #10622419C22semidirect
73. #10622415C22semidirect
74. #10622407C22semidirect
75. #10622405C22semidirect
76. #10622401C22semidirect
306. C2×#419D11semidirect
423. #419C2×D11semidirect
576. C2×C11#3329semidirect
687. C11C2×#3329semidirect
791. C2#13080906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230632
C2×Q8×C22⋊D112
#130809062
C2×#106224052
C2×#106226092
C2×#106224272
C2×#106224072
C2×#106224252
C2×#106227472
C2×#106224312
C2×#106224192
C2×#106228402
C2×#106224012
C2×#106227412
C2×#106224152
C2×C11×#4192
C2×#332911