Finite Group Databasebeta

← C2×#13080651 #15630442

Subgroups — C2×#13080651 #15630442

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623207C211yesmaximal, characteristic
3#13080651C2116yesmaximal, direct product factor
4C2×#10622427C211yesmaximal, characteristic, complemented
5C2×#10622397C211yesmaximal, characteristic, complemented
6C2×#10622697C211yesmaximal, characteristic, complemented
7C2×#10622429C211yesmaximal, characteristic, complemented
8C2×#10622391C211yesmaximal, characteristic, complemented
9C2×#10622667C211yesmaximal, characteristic, complemented
10C2×#10622423C211yesmaximal, characteristic, complemented
11C2×#10622389C211yesmaximal, characteristic, complemented
12C2×#10622323C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622383C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#489C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic, complemented
20C2×C11×#124C2211yescharacteristic
21C2×#67000—21no—
22C2×#66999C2211yescharacteristic
23C2×Q8×Dic11—21no—
24C22×#4326C2211yescharacteristic, complemented
25C2×#66991C2211yescharacteristic
26C22×#4324C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic, complemented
30#10623263—24no—
31#10623263C2218yescomplemented
32#10623207—24no—
33#10623207C2218yes—
34C2×#66951—21no—
35C2×#66951—21no—
36C2×#66950C2211yescharacteristic
37C2×#66950C2211yescharacteristic, complemented
38C2×#66945C2211yescharacteristic
39C2×#66945C2211yescharacteristic, complemented
40C2×#66937—21no—
41C2×#66936—21no—
42C2×#66935—21no—
43C2×C22⋊C4×D11—21no—
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic, complemented
47C11×#489C2218yescomplemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#97C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
58C2×#66882C2211yescharacteristic, complemented
59C2×#66880C2211yescharacteristic, complemented
60#10622697C2218yescomplemented
61#10622667C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic, complemented
65C2×#66872C2211yescharacteristic, complemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
67#10622429C2218yescomplemented
68#10622427C2218yescomplemented
69#10622423C2218yescomplemented
70#10622417C2218yescomplemented
71#10622397C2218yescomplemented
72#10622391C2218yescomplemented
73#10622389C2218yescomplemented
74#10622383C2218yescomplemented
75#10622323C2218yescomplemented
76#10622319C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11—21no—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×#4343—22no—
84C2×#4343—24no—
85C2×#4343—42no—
86C2×#4343C2314yes—
87C2×D4×D11—24no—
88C2×D4×D11—22no—
89C2×D4×D11—42no—
90C2×D4×D11C2314yes—
91C22×D44—21no—
92C22×D44D411yescharacteristic
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C22×C4×D11—21no—
96C22×C4×D11C2311yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×Dic22C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8C2314yescomplemented
103C11×#124—22no—
104C11×#124C2314yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C22⋊Dic11—21no—
112#67000—28no—
113#66999—22no—
114#66999C2314yes—
115Q8×Dic11—28no—
116C2×#4326—42no—
117C2×#4326C2314yescomplemented
118#66991—22no—
119#66991C2314yes—
120C2×#4324—42no—
121C2×#4324C2314yes—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4D411yescharacteristic
129C2×(C2×D11)⋊C4D411yescharacteristic
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11D411yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11—21no—
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×#4314—24no—
143C2×#4314C2314yes—
144C2×#4313—42no—
145C2×#4313C2314yes—
146C2×C8×D11—42no—
147C2×C8×D11C2314yescomplemented
148#66951—28no—
149#66951—28no—
150#66950—22no—
151#66950—22no—
152#66950C2314yes—
153#66950C2314yescomplemented
154#66945—22no—
155#66945—22no—
156#66945C2314yes—
157#66945C2314yescomplemented
158#66937—28no—
159#66936—28no—
160#66935—28no—
161C22⋊C4×D11—28no—
162C4×D44—22no—
163C4×D44D414yes—
164C4×D44C2314yes—
165C4×D44C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yescomplemented
168C11×#103C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#102C2314yes—
171C11×#102C2314yes—
172C11×#97C2314yescomplemented
173#66899C2314yescomplemented
174#66896C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177(C2×D11)⋊C8C2314yescomplemented
178#66882C2314yescomplemented
179#66880C2314yescomplemented
180#66873C2314yes—
181#66873C2314yes—
182#66872C2314yescomplemented
183#66872C2314yescomplemented
184C4⋊(C11⋊C8)C2314yescomplemented
185C2×#3311—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C23×D11—24no—
189C23×D11—44no—
190C23×D11—44no—
191C23×D11—82no—
192C23×D11C2×D411yescharacteristic
193C23×D11C2×D411yescharacteristic
194C2×Q8×C11—24no—
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11—44no—
199C2×Q8×C11C2412yes—
200C2×D4×C11—21no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11C2412yes—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—82no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219#4343—28no—
220#4343—44no—
221#4343—48no—
222D4×D11—28no—
223D4×D11—44no—
224D4×D11—48no—
225C2×D44—24no—
226C2×D44—21no—
227C2×D44—22no—
228C2×D44—42no—
229C2×D44—44no—
230C2×D44C2×D414yes—
231C2×D44#4114yes—
232C2×D44C2412yes—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—44no—
240C2×C4×D11—82no—
241C2×C4×D11C2×D412yes—
242C2×C4×D11C2×D412yes—
243C2×C4×D11C2412yes—
244C2×C4×D11C2412yes—
245C2×Dic22—21no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22C2412yes—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11C2412yes—
252C2×C8×C11C2412yes—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C42×C11C2×D412yes—
261C42×C11C2412yes—
262C22⋊Dic11—24no—
263#4326—44no—
264#4324—44no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4C2×D414yes—
272(C2×D11)⋊C4C2×D414yes—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11C2×D414yes—
278C4⋊Dic11C2412yes—
279C4⋊Dic11C2412yes—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11—24no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289#4314—28no—
290#4313—44no—
291C8×D11—44no—
292C2×#556—111no—
293C2×#546—111no—
294#3311—1116no—
295C2×#489D1111yescharacteristic, complemented
296C2×#485—111no—
297C2×#482—111no—
298C2×#476—111no—
299C2×#470—111no—
300C2×#465—111no—
301C2×#464—111no—
302C2×#452—111no—
303C2×#450—111no—
304C2×#440—111no—
305C2×#435—111no—
306C2×#418—111no—
307C2×#416—111no—
308C23×C11—22no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—24no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—48no—
322C22×D11—48no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—84no—
326C22×D11—816no—
327C22×D11C22×D412yes—
328C22×D11C22×D412yes—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—48no—
332Q8×C11—42no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—42no—
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×D412yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4112yes—
348C2×C4×C11H(5,𝔽2)12yes—
349C2×C4×C11C2511yescharacteristic
350C22⋊D11—48no—
351C22⋊D11—84no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11C22×D412yes—
361C2×Dic11C22×D412yes—
362D44—24no—
363D44—22no—
364D44—44no—
365D44—48no—
366D44C2×#4114yes—
367C4×D11—24no—
368C4×D11—24no—
369C4×D11—22no—
370C4×D11—22no—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—48no—
374C4×D11—84no—
375Dic22—22no—
376Dic22—22no—
377Dic22—42no—
378C8×C11—22no—
379C8×C11—22no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C22×#41—111no—
383C23×D4—111no—
384C22×Q16—111no—
385C22×SD16—111no—
386C22×SD16—111no—
387C22×M16—111no—
388C23×C8—111no—
389#556—118no—
390#556—224no—
391#546—118no—
392#546—224no—
393C2×C4⋊Q8C2×D1111yescharacteristic, complemented
394C2×#126—221no—
395C2×#126—221no—
396C2×#124—221no—
397C2×#124C2×D1111yescharacteristic
398C2×#123—221no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8—111no—
401C2×C22⋊Q8—111no—
402C2×#121—111no—
403C2×#121—221no—
404C2×#120—221no—
405C2×C4×Q8—111no—
406C2×C4×Q8—221no—
407C2×C4×D4—111no—
408C2×C4×D4—111no—
409C2×#117—111no—
410C2×#117—111no—
411C22×C22⋊C4—221no—
412#489C2×D1118yescomplemented
413#485—118no—
414#482—118no—
415#476—118no—
416#470—118no—
417#465—118no—
418#464—118no—
419#452—118no—
420#450—118no—
421#440—118no—
422#435—118no—
423C2×#107—111no—
424C2×#106—111no—
425C2×#106—111no—
426C2×C4⋊C8—111no—
427#418—118no—
428#416—118no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103C2×D1111yescharacteristic, complemented
432C2×#103C2×D1111yescharacteristic, complemented
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102C2×D1111yescharacteristic
438C2×#102C2×D1111yescharacteristic
439C2×C22⋊C8—111no—
440C2×C22⋊C8—111no—
441C2×#97C2×D1111yescharacteristic, complemented
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—84no—
446C22×C11#54612yes—
447C22×C11#57512yes—
448C22×C11#57712yes—
449C22×C11C23×D411yescharacteristic
450C2×D11—24no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—22no—
457C2×D11—44no—
458C2×D11—44no—
459C2×D11—48no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—816no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11#54612yes—
469C4×C11C22×#4111yescharacteristic
470C4×C11C2×H(5,𝔽2)11yescharacteristic
471Dic11—22no—
472Dic11—22no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476C25—221no—
477C2×#41—114no—
478C2×#41—222no—
479C2×#41—224no—
480C2×#41—442no—
481C22×Q8—21no—
482C22×Q8—111no—
483C22×Q8C22×D1111yescharacteristic
484C22×D4—114no—
485C22×D4—111no—
486C22×D4—111no—
487C22×D4—221no—
488C22×D4—222no—
489C22×D4—221no—
490C22×D4—224no—
491C22×D4—221no—
492C22×D4—442no—
493C22×D4C22×D1111yescharacteristic
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—221no—
497C23×C4—221no—
498C2×Q16—114no—
499C2×Q16—442no—
500C2×SD16—114no—
501C2×SD16—114no—
502C2×SD16—224no—
503C2×SD16—442no—
504C2×M16—114no—
505C2×M16—442no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—114no—
509C22×C8—442no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8C22×D1114yescomplemented
514#126—228no—
515#126—228no—
516#124—22no—
517#124—228no—
518#124C22×D1114yes—
519#123—228no—
520C22⋊Q8—114no—
521C22⋊Q8—114no—
522C22⋊Q8—114no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8—222no—
526#121—114no—
527#121—228no—
528#121—222no—
529#120—228no—
530C4×Q8—114no—
531C4×Q8—228no—
532C4×Q8—222no—
533C4×D4—114no—
534C4×D4—114no—
535C4×D4—114no—
536C4×D4—222no—
537#117—114no—
538#117—114no—
539#117—222no—
540#117—222no—
541C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—111no—
555C2×C22⋊C4—228no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C42—221no—
564C2×C42—221no—
565C2×C42—221no—
566C2×C42C22×D1111yescharacteristic
567#107—114no—
568#106—114no—
569#106—114no—
570C4⋊C8—114no—
571#103—114no—
572#103—114no—
573#103C22×D1114yescomplemented
574#103C22×D1114yescomplemented
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579#102C22×D1114yes—
580#102C22×D1114yes—
581C22⋊C8—114no—
582C22⋊C8—114no—
583#97C22×D1114yescomplemented
584C2×C11—82no—
585C2×C11#331114yescomplemented
586C2×C11C2×#54611yescharacteristic
587C2×C11C2×#57511yescharacteristic
588C2×C11C2×#57711yescharacteristic
589D11—42no—
590D11—42no—
591D11—44no—
592C24—21no—
593C24—111no—
594C24—111no—
595C24—224no—
596C24—221no—
597C24—444no—
598C24—444no—
599C24—882no—
600#41—228no—
601#41—444no—
602#41—448no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—44no—
608C2×Q8—112no—
609C2×Q8—221no—
610C2×Q8—222no—
611C2×Q8—222no—
612C2×Q8C23×D1112yes—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—114no—
617C2×D4—114no—
618C2×D4—112no—
619C2×D4—224no—
620C2×D4—224no—
621C2×D4—228no—
622C2×D4—224no—
623C2×D4—221no—
624C2×D4—222no—
625C2×D4—442no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—448no—
629C2×D4—444no—
630C2×D4—882no—
631C2×D4C23×D1112yes—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—224no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—224no—
650C22×C4—444no—
651C22×C4—882no—
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655Q16—444no—
656SD16—228no—
657SD16—444no—
658M16—444no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—444no—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—114no—
672C4⋊C4—112no—
673C4⋊C4—112no—
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—24no—
684C22⋊C4—114no—
685C22⋊C4—114no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C42—224no—
694C42—224no—
695C42—224no—
696C42D4×D1112yes—
697C42C23×D1112yes—
698C11C2×#331111yescharacteristic, complemented, Sylow
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—112no—
704C23—112no—
705C23—222no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—222no—
712C23—224no—
713C23—448no—
714C23—448no—
715C23—442no—
716C23—442no—
717C23—884no—
718C23—8816no—
719C23C2×D4×D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—48no—
723Q8—42no—
724Q8—222no—
725Q8—222no—
726Q8—442no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—114no—
731D4—222no—
732D4—224no—
733D4—444no—
734D4—448no—
735D4—448no—
736D4—884no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—448no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—884no—
763C2×C4C2×D4×D1112yes—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4#41×D1112yes—
767C2×C4#6704212yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—222no—
772C8—222no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—222no—
778C22—222no—
779C22—224no—
780C22—222no—
781C22—222no—
782C22—222no—
783C22—222no—
784C22—444no—
785C22—444no—
786C22—448no—
787C22—442no—
788C22—442no—
789C22—8816no—
790C22#1062320712yes—
791C22#1062330412yes—
792C22#1062330912yes—
793C22C22×D4×D1111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—222no—
800C4—222no—
801C4—442no—
802C4—442no—
803C4—442no—
804C4#1062320712yes—
805C4C2×#41×D1111yescharacteristic
806C4C2×#6704211yescharacteristic
807C2—82no—
808C2—442no—
809C2—442no—
810C2—444no—
811C2#1308065114yesdirect product factor
812C2C2×#1062320711yescharacteristic
813C2C2×#1062330411yescharacteristic
814C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC2×#10623207C2
hypercenterC2×#489D11
hypocenterC11C2×#3311
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623263C2semidirect
3. #13080651C2direct (N × H)
4. C2×#10622427C2semidirect
5. C2×#10622397C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622429C2semidirect
8. C2×#10622391C2semidirect
9. C2×#10622667C2semidirect
10. C2×#10622423C2semidirect
11. C2×#10622389C2semidirect
12. C2×#10622323C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622383C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#489C2semidirect
19. C2×C11×C4⋊Q8C22semidirect
24. C22×#4326C22semidirect
29. C22×C8×D11C22semidirect
31. #10623263C22semidirect
37. C2×#66950C22semidirect
39. C2×#66945C22semidirect
46. C2×C4×Dic22C22semidirect
47. C11×#489C22semidirect
48. C2×C11×#103C22semidirect
49. C2×C11×#103C22semidirect
52. C2×C11×#97C22semidirect
53. C2×#66899C22semidirect
57. C2×(C2×D11)⋊C8C22semidirect
58. C2×#66882C22semidirect
59. C2×#66880C22semidirect
60. #10622697C22semidirect
61. #10622667C22semidirect
64. C2×#66872C22semidirect
65. C2×#66872C22semidirect
66. C2×C4⋊(C11⋊C8)C22semidirect
67. #10622429C22semidirect
68. #10622427C22semidirect
69. #10622423C22semidirect
70. #10622417C22semidirect
71. #10622397C22semidirect
72. #10622391C22semidirect
73. #10622389C22semidirect
74. #10622383C22semidirect
75. #10622323C22semidirect
76. #10622319C22semidirect
102. C11×C4⋊Q8C23semidirect
117. C2×#4326C23semidirect
147. C2×C8×D11C23semidirect
153. #66950C23semidirect
157. #66945C23semidirect
167. C4×Dic22C23semidirect
168. C11×#103C23semidirect
169. C11×#103C23semidirect
172. C11×#97C23semidirect
173. #66899C23semidirect
177. (C2×D11)⋊C8C23semidirect
178. #66882C23semidirect
179. #66880C23semidirect
182. #66872C23semidirect
183. #66872C23semidirect
184. C4⋊(C11⋊C8)C23semidirect
295. C2×#489D11semidirect
393. C2×C4⋊Q8C2×D11semidirect
412. #489C2×D11semidirect
431. C2×#103C2×D11semidirect
432. C2×#103C2×D11semidirect
441. C2×#97C2×D11semidirect
513. C4⋊Q8C22×D11semidirect
573. #103C22×D11semidirect
574. #103C22×D11semidirect
583. #97C22×D11semidirect
585. C2×C11#3311semidirect
698. C11C2×#3311semidirect
811. C2#13080651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106232072
#130806512
C2×#106224272
C2×#106223972
C2×#106226972
C2×#106224292
C2×#106223912
C2×#106226672
C2×#106224232
C2×#106223892
C2×#106223232
C2×#106223192
C2×#106223832
C2×#106224172
C2×C11×#4892
C2×#331111