Finite Group Databasebeta

← C2×#13080895 #15630654

Subgroups — C2×#13080895 #15630654

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623064C211yesmaximal, characteristic
2C2×Q8×C22⋊D11C211yesmaximal, characteristic
3#13080895C2116yesmaximal, direct product factor
4C2×#10622405C211yesmaximal, characteristic, complemented
5C2×#10622609C211yesmaximal, characteristic, complemented
6C2×#10622428C211yesmaximal, characteristic, complemented
7C2×#10622404C211yesmaximal, characteristic, complemented
8C2×#10622750C211yesmaximal, characteristic, complemented
9C2×#10622429C211yesmaximal, characteristic, complemented
10C2×#10622406C211yesmaximal, characteristic, complemented
11C2×#10622421C211yesmaximal, characteristic, complemented
12C2×#10622841C211yesmaximal, characteristic, complemented
13C2×#10622403C211yesmaximal, characteristic, complemented
14C2×#10622741C211yesmaximal, characteristic
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⋊D11C2218yes—
23C2×#66999—21no—
24C2×#66999C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×#66997—21no—
27C2×#66997C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C2×C4×C22⋊D11—21no—
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×#66977—21no—
33C2×#66977C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C22×Dic44C2211yescharacteristic
36C22×#4313C2211yescharacteristic
37#10623064—24no—
38#10623064C2218yes—
39C2×#66950C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66938—21no—
44C2×#66932—21no—
45C2×#66929—21no—
46C2×C4×Dic22—21no—
47C11×#419C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52#10622841C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622750C2218yescomplemented
57#10622741C2218yes—
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64#10622609C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622429C2218yescomplemented
70#10622428C2218yescomplemented
71#10622421C2218yescomplemented
72#10622415C2218yescomplemented
73#10622406C2218yescomplemented
74#10622405C2218yescomplemented
75#10622404C2218yescomplemented
76#10622403C2218yescomplemented
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⋊D11D411yescharacteristic
87C2×Q8×D11—22no—
88C2×Q8×D11—24no—
89C2×Q8×D11—42no—
90C2×Q8×D11C2314yes—
91C22×C4×D11—21no—
92C22×C4×D11C2311yescharacteristic
93C22×Dic22—21no—
94C22×Dic22—21no—
95C22×Dic22C2311yescharacteristic
96C22×Dic22C2311yescharacteristic
97C2×C11×M16—42no—
98C2×C11×M16C2314yes—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×#117—22no—
102C11×#117C2314yes—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C42×C11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11D411yescharacteristic
110#66999—22no—
111#66999—28no—
112#66999C2314yes—
113Q8×Dic11—22no—
114Q8×Dic11C2314yes—
115#66997—28no—
116#66997—22no—
117#66997C2314yes—
118C2×#4326—24no—
119C2×#4326—42no—
120C2×#4326C2314yes—
121C2×#4326C2314yes—
122C4×C22⋊D11—28no—
123C4×C22⋊D11D414yes—
124C4×C22⋊D11C2314yes—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4D411yescharacteristic
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133#66977—22no—
134#66977—22no—
135#66977—28no—
136#66977C2314yes—
137#66977C2314yes—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
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×Dic44—42no—
153C2×Dic44C2314yes—
154C2×#4313—42no—
155C2×#4313C2314yes—
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×#103C2314yes—
171C11×#103C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175(C2×D11)⋊C8C2314yes—
176#66881C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179Dic11⋊C8C2314yes—
180C8×Dic11C2314yes—
181#66874C2314yes—
182#66874C2314yes—
183#66872C2314yes—
184#66871C2314yes—
185C2×#3328—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C23×D11C2×D411yescharacteristic
188C2×Q8×C11—21no—
189C2×Q8×C11—24no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—28no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—44no—
196C2×Q8×C11—44no—
197C2×Q8×C11—48no—
198C2×Q8×C11#4114yes—
199C2×Q8×C11C2412yes—
200C2×Q8×C11C2412yes—
201C22×C4×C11—21no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—24no—
208C22×C4×C11—44no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2411yescharacteristic
213C2×C22⋊D11—24no—
214C2×C22⋊D11C2×D414yes—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222Q8×D11—28no—
223Q8×D11—44no—
224Q8×D11—48no—
225C2×C4×D11—24no—
226C2×C4×D11—22no—
227C2×C4×D11—22no—
228C2×C4×D11—44no—
229C2×C4×D11C2×D412yes—
230C2×C4×D11C2412yes—
231C2×Dic22—24no—
232C2×Dic22—24no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—22no—
236C2×Dic22—22no—
237C2×Dic22—22no—
238C2×Dic22—22no—
239C2×Dic22—44no—
240C2×Dic22—44no—
241C2×Dic22C2412yes—
242C2×Dic22C2412yes—
243C11×M16—44no—
244C2×C8×C11—22no—
245C2×C8×C11—22no—
246C2×C8×C11C2412yes—
247C2×C8×C11C2412yes—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C2412yes—
251C11×C4⋊C4C2412yes—
252C11×C22⋊C4—24no—
253C42×C11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11C2×D414yes—
257#4326—28no—
258#4326—44no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4C2×D414yes—
263C4⋊Dic11—24no—
264C4⋊Dic11—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11C2412yes—
268C4⋊Dic11C2412yes—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4C2×D414yes—
277C4×Dic11—24no—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C4×Dic11C2×D412yes—
281C4×Dic11C2412yes—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8C2412yes—
285C2×C11⋊C8C2412yes—
286Dic44—44no—
287#4313—44no—
288C2×#556—111no—
289C2×D4×Q8—111no—
290#3328—1116no—
291C2×#487—111no—
292C2×#485—111no—
293C2×#485—111no—
294C2×#475—111no—
295C2×#470—111no—
296C2×#470—111no—
297C2×#462—111no—
298C2×#451—111no—
299C2×#451—111no—
300C2×C4×Q16—111no—
301C2×#436—111no—
302C2×#419—111no—
303C2×#419D1111yescharacteristic, complemented
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11C22×D412yes—
308C23×C11C22×D411yescharacteristic
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11C22×D412yes—
313Q8×C11—24no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—48no—
318Q8×C11—42no—
319Q8×C11C2×#4114yes—
320C2×C4×C11—24no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—48no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4112yes—
336C2×C4×C11H(5,𝔽2)12yes—
337C2×C4×C11C2511yescharacteristic
338C22⋊D11—28no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11#13714yes—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352C2×Dic11C22×D412yes—
353C4×D11—24no—
354C4×D11—22no—
355C4×D11—22no—
356C4×D11—48no—
357Dic22—22no—
358Dic22—22no—
359Dic22—22no—
360Dic22—22no—
361Dic22—48no—
362Dic22—42no—
363Dic22—42no—
364Dic22—48no—
365C8×C11—22no—
366C8×C11—22no—
367C11⋊C8—22no—
368C11⋊C8—22no—
369C23×Q8—111no—
370C23×Q8C2×D1111yescharacteristic
371C22×Q16—111no—
372C22×Q16—111no—
373C22×Q16—111no—
374C22×M16—111no—
375C22×M16C2×D1111yescharacteristic
376#556—118no—
377#556—224no—
378D4×Q8—118no—
379D4×Q8—224no—
380C2×C4⋊Q8—111no—
381C2×C4⋊Q8—111no—
382C2×C4⋊Q8—221no—
383C2×#126—221no—
384C2×#126—221no—
385C2×#124—221no—
386C2×C22⋊Q8—111no—
387C2×C22⋊Q8—111no—
388C2×C22⋊Q8—111no—
389C2×C22⋊Q8—111no—
390C2×C22⋊Q8—221no—
391C2×C22⋊Q8—221no—
392C2×C4×Q8—111no—
393C2×C4×Q8—111no—
394C2×C4×Q8—221no—
395C2×C4×D4—111no—
396C2×C4×D4—221no—
397C2×#117—111no—
398C2×#117C2×D1111yescharacteristic
399#487—118no—
400#485—118no—
401#485—118no—
402#475—118no—
403#470—118no—
404#470—118no—
405#462—118no—
406#451—118no—
407#451—118no—
408C4×Q16—118no—
409#436—118no—
410C2×#107—111no—
411C2×#106—111no—
412C2×#106—111no—
413C2×C4⋊C8—111no—
414#419—118no—
415#419C2×D1118yescomplemented
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103C2×D1111yescharacteristic
423C2×#103C2×D1111yescharacteristic
424C2×#103C2×D1111yescharacteristic
425C2×#103C2×D1111yescharacteristic
426C2×C22⋊C8—111no—
427C2×C22⋊C8—111no—
428C2×C4×C8—111no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—44no—
433C22×C11#54612yes—
434C22×C11C2×#13712yes—
435C22×C11#57812yes—
436C22×C11C23×D411yescharacteristic
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—44no—
441C4×C11—22no—
442C4×C11—24no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11#54612yes—
447C4×C11C22×#4111yescharacteristic
448C4×C11C2×H(5,𝔽2)11yescharacteristic
449Dic11—22no—
450Dic11—22no—
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454Dic11—42no—
455Dic11C2×#13714yes—
456C22×Q8—21no—
457C22×Q8—22no—
458C22×Q8—24no—
459C22×Q8—42no—
460C22×Q8—114no—
461C22×Q8—111no—
462C22×Q8—111no—
463C22×Q8—221no—
464C22×Q8—221no—
465C22×Q8—222no—
466C22×Q8—224no—
467C22×Q8—442no—
468C22×Q8C22×D1111yescharacteristic
469C22×Q8C22×D1114yes—
470C22×Q8C22×D1111yescharacteristic
471C22×D4—111no—
472C23×C4—21no—
473C23×C4—111no—
474C23×C4—221no—
475C23×C4C22×D1111yescharacteristic
476C2×Q16—114no—
477C2×Q16—114no—
478C2×Q16—114no—
479C2×Q16—224no—
480C2×Q16—442no—
481C2×Q16—442no—
482C2×M16—42no—
483C2×M16—114no—
484C2×M16—442no—
485C2×M16C22×D1114yes—
486C22×C8—111no—
487C22×C8—111no—
488C22×C8C22×D1111yescharacteristic
489C22×C8C22×D1111yescharacteristic
490C4⋊Q8—114no—
491C4⋊Q8—114no—
492C4⋊Q8—222no—
493C4⋊Q8—222no—
494C4⋊Q8—228no—
495#126—228no—
496#126—228no—
497#124—228no—
498C22⋊Q8—114no—
499C22⋊Q8—114no—
500C22⋊Q8—114no—
501C22⋊Q8—114no—
502C22⋊Q8—228no—
503C22⋊Q8—228no—
504C22⋊Q8—222no—
505C22⋊Q8—222no—
506C22⋊Q8—222no—
507C22⋊Q8—222no—
508C4×Q8—114no—
509C4×Q8—114no—
510C4×Q8—228no—
511C4×Q8—222no—
512C4×Q8—222no—
513C4×D4—114no—
514C4×D4—114no—
515C4×D4—228no—
516#117—22no—
517#117—114no—
518#117—222no—
519#117C22×D1114yes—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4—221no—
526C2×C4⋊C4—221no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—111no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C42—21no—
543C2×C42—111no—
544C2×C42—221no—
545C2×C42—221no—
546C2×C42—221no—
547#107—114no—
548#106—114no—
549#106—114no—
550C4⋊C8—114no—
551#103—114no—
552#103—114no—
553#103—114no—
554#103—114no—
555#103—114no—
556#103—114no—
557#103C22×D1114yes—
558#103C22×D1114yes—
559#103C22×D1114yes—
560#103C22×D1114yes—
561C22⋊C8—114no—
562C22⋊C8—114no—
563C4×C8—114no—
564C2×C11—42no—
565C2×C11#332814yescomplemented
566C2×C11C2×#54611yescharacteristic
567C2×C11C22×#13711yescharacteristic
568C2×C11C2×#57811yescharacteristic
569D11—42no—
570C24—111no—
571C24D4×D1111yescharacteristic
572C2×Q8—21no—
573C2×Q8—24no—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—28no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—48no—
582C2×Q8—112no—
583C2×Q8—112no—
584C2×Q8—224no—
585C2×Q8—224no—
586C2×Q8—221no—
587C2×Q8—221no—
588C2×Q8—228no—
589C2×Q8—222no—
590C2×Q8—222no—
591C2×Q8—222no—
592C2×Q8—222no—
593C2×Q8—444no—
594C2×Q8—444no—
595C2×Q8—444no—
596C2×Q8—448no—
597C2×Q8#433914yes—
598C2×Q8C23×D1112yes—
599C2×Q8C23×D1112yes—
600C2×D4—114no—
601C2×D4—224no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—44no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—112no—
614C22×C4—112no—
615C22×C4—224no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—444no—
623C22×C4D4×D1112yes—
624C22×C4D4×D1111yescharacteristic
625C22×C4C23×D1112yes—
626C22×C4C23×D1111yescharacteristic
627Q16—228no—
628Q16—444no—
629Q16—444no—
630M16—44no—
631M16—444no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—112no—
635C2×C8—112no—
636C2×C8—222no—
637C2×C8—222no—
638C2×C8C23×D1112yes—
639C2×C8C23×D1112yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—114no—
643C4⋊C4—112no—
644C4⋊C4—112no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—224no—
655C4⋊C4—224no—
656C4⋊C4C23×D1112yes—
657C4⋊C4C23×D1112yes—
658C22⋊C4—24no—
659C22⋊C4—114no—
660C22⋊C4—114no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C22⋊C4—224no—
666C42—24no—
667C42—112no—
668C42—112no—
669C42—224no—
670C42—224no—
671C42—224no—
672C11C2×#332811yescharacteristic, complemented, Sylow
673C23—22no—
674C23—22no—
675C23—22no—
676C23—112no—
677C23—222no—
678C23—222no—
679C23—222no—
680C23C2×D4×D1112yes—
681C23C2×D4×D1111yescharacteristic
682Q8—24no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—42no—
688Q8—222no—
689Q8—222no—
690Q8—222no—
691Q8—222no—
692Q8—448no—
693Q8—448no—
694Q8—442no—
695Q8—442no—
696Q8C2×#433914yes—
697D4—228no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—114no—
712C2×C4—112no—
713C2×C4—112no—
714C2×C4—112no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—224no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—448no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4C2×#433912yes—
730C2×C4C2×D4×D1112yes—
731C2×C4C2×D4×D1111yescharacteristic
732C2×C4#6703712yes—
733C2×C4C24×D1111yescharacteristic
734C8—22no—
735C8—22no—
736C8—222no—
737C8—222no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—222no—
743C22—222no—
744C22—222no—
745C22—444no—
746C22#1062302112yes—
747C22D11×#13712yes—
748C22#1062331012yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—114no—
756C4—222no—
757C4—222no—
758C4—442no—
759C4—442no—
760C4—442no—
761C4—442no—
762C4#1062302112yes—
763C4C22×#433911yescharacteristic
764C4C2×#6703711yescharacteristic
765C2—42no—
766C2—442no—
767C2#1308089514yesdirect product factor
768C2C2×#1062302111yescharacteristic
769C2C2×D11×#13711yescharacteristic
770C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC2×#419D11
hypocenterC11C2×#3328
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
3. #13080895C2direct (N × H)
4. C2×#10622405C2semidirect
5. C2×#10622609C2semidirect
6. C2×#10622428C2semidirect
7. C2×#10622404C2semidirect
8. C2×#10622750C2semidirect
9. C2×#10622429C2semidirect
10. C2×#10622406C2semidirect
11. C2×#10622421C2semidirect
12. C2×#10622841C2semidirect
13. C2×#10622403C2semidirect
15. C2×#10622415C2semidirect
16. C2×C11×#419C2semidirect
47. C11×#419C22semidirect
52. #10622841C22semidirect
56. #10622750C22semidirect
64. #10622609C22semidirect
69. #10622429C22semidirect
70. #10622428C22semidirect
71. #10622421C22semidirect
72. #10622415C22semidirect
73. #10622406C22semidirect
74. #10622405C22semidirect
75. #10622404C22semidirect
76. #10622403C22semidirect
303. C2×#419D11semidirect
415. #419C2×D11semidirect
565. C2×C11#3328semidirect
672. C11C2×#3328semidirect
767. C2#13080895direct (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×Q8×C22⋊D112
#130808952
C2×#106224052
C2×#106226092
C2×#106224282
C2×#106224042
C2×#106227502
C2×#106224292
C2×#106224062
C2×#106224212
C2×#106228412
C2×#106224032
C2×#106227412
C2×#106224152
C2×C11×#4192
C2×#332811