Finite Group Databasebeta

← #14769359

Subgroups — #14769359

Order 2816.

1458 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623348C211yesmaximal, characteristic
2C2×#10622740C211yesmaximal, characteristic, complemented
3C2×#10622417C211yesmaximal, characteristic, complemented
4#13071566C211yesmaximal, characteristic, complemented
5#13069545C211yesmaximal, characteristic, complemented
6#13069429C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069036C211yesmaximal, characteristic, complemented
9#13068938C211yesmaximal, characteristic, complemented
10#13068925C211yesmaximal, characteristic, complemented
11#13068619C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068551C211yesmaximal, characteristic, complemented
14#13068448C211yesmaximal, characteristic, complemented
15C2×C11×#419C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×#4343C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20#10623348—24no—
21#10623348C418yescomplemented
22C2×#67000—21no—
23C2×#67000C2211yescharacteristic
24C2×#66999—21no—
25C2×#66999C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C2×#66983—21no—
28C2×#66983C2211yescharacteristic
29C2×C4×C22⋊D11—21no—
30C2×C4×C22⋊D11C2211yescharacteristic
31C22×C8×D11C2211yescharacteristic
32C2×#66945C2211yescharacteristic
33C11×#419—24no—
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42#10622825C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622740—24no—
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×#66879C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50#10622600C2211yescharacteristic
51#10622589C2211yescharacteristic
52C4⋊C4×Dic11C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55#10622570—21no—
56#10622557—21no—
57#10622553—21no—
58C4×Dic11⋊C4—21no—
59#10622417—24no—
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11—21no—
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2×C414yes—
71C22×Q8×C11C2311yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C22×C22⋊D11D411yescharacteristic
77C2×#4343—22no—
78C2×#4343—22no—
79C2×#4343—22no—
80C2×#4343—41no—
81C2×#4343—41no—
82C2×#4343C2×C414yes—
83C22×D44—21no—
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C2×C11×M16—22no—
88C2×C11×M16—22no—
89C2×C11×M16—41no—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×#117—22no—
93C11×#117—41no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C42×C11—21no—
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11D411yescharacteristic
100#67000—28no—
101#67000—22no—
102#67000C2×C414yes—
103#66999—22no—
104#66999—28no—
105#66999C2×C414yes—
106Q8×Dic11—22no—
107Q8×Dic11C2×C414yes—
108#66983—22no—
109#66983—28no—
110#66983C2×C414yes—
111C4×C22⋊D11—28no—
112C4×C22⋊D11C2×C414yes—
113C4×C22⋊D11D414yes—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4D411yescharacteristic
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4D411yescharacteristic
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×C8×D11—22no—
136C2×C8×D11—22no—
137C2×C8×D11—41no—
138#66945—22no—
139#66945—41no—
140C11×#103—22no—
141C11×#103—22no—
142C11×#103—22no—
143C11×#103D414yescomplemented
144#66899—22no—
145#66899—22no—
146#66899—41no—
147#66899—41no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C22⋊(C11⋊C8)—22no—
152#66885—22no—
153#66885—41no—
154(C2×D11)⋊C8—22no—
155#66879—22no—
156Dic11⋊C8—22no—
157#66873—22no—
158#66873—41no—
159#22426—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C23×D11—21no—
162C23×D11C2×D411yescharacteristic
163C2×Q8×C11—24no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—28no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—42no—
174C2×Q8×C11—42no—
175C2×Q8×C11—44no—
176C2×Q8×C11—44no—
177C2×Q8×C11—44no—
178C2×Q8×C11C22×C412yes—
179C2×Q8×C11C22×C412yes—
180C2×Q8×C11C2×D412yes—
181C2×Q8×C11#4112yes—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—24no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—41no—
199C2×C22⋊D11—41no—
200C2×C22⋊D11—42no—
201C2×C22⋊D11—42no—
202C2×C22⋊D11C22⋊C414yes—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209#4343—28no—
210#4343—44no—
211#4343—44no—
212#4343—44no—
213C2×D44—24no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—42no—
220C2×D44—42no—
221C2×D44C22×C412yes—
222C2×C4×D11—24no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—21no—
226C2×C4×D11—21no—
227C2×C4×D11—42no—
228C2×C4×D11—42no—
229C2×C4×D11C22×C412yes—
230C2×C4×D11C2×D412yes—
231C11×M16—44no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11C2×D412yes—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4C2×D412yes—
242C11×C22⋊C4—42no—
243C42×C11—42no—
244C22⋊Dic11—81no—
245C22⋊Dic11C22⋊C414yes—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—42no—
251(C2×D11)⋊C4—81no—
252(C2×D11)⋊C4C22⋊C414yes—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11C22×C412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—42no—
262Dic11⋊C4—81no—
263Dic11⋊C4C22⋊C414yes—
264C4×Dic11—24no—
265C4×Dic11—42no—
266C4×Dic11—42no—
267C4×Dic11C22×C412yes—
268C4×Dic11C2×D412yes—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C8×D11—44no—
276C2×#548—111no—
277C2×#435—111no—
278C2×#419D1111yescharacteristic, complemented
279C2×#416—111no—
280#2354—111no—
281#1983—111no—
282#1959—111no—
283#1895—111no—
284#1892—111no—
285#1875—111no—
286#1873—111no—
287#1803—111no—
288#1788—111no—
289#1787—111no—
290#1763—111no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11C2×C22⋊C412yes—
298C23×C11C22×D411yescharacteristic
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—22no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11C2×C22⋊C412yes—
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—22no—
318Q8×C11—48no—
319Q8×C11—41no—
320Q8×C11—41no—
321Q8×C11C4×D414yes—
322C2×C4×C11—22no—
323C2×C4×C11—21no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—21no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—48no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11C2×C22⋊C412yes—
342C2×C4×C11C23×C411yescharacteristic
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C2×#4111yescharacteristic
346C2×C4×C11H(5,𝔽2)11yescharacteristic
347C2×C4×C11H(5,𝔽2)11yescharacteristic
348C22⋊D11—44no—
349C22⋊D11—48no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—22no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11C2×C22⋊C412yes—
366C2×Dic11C2×C22⋊C412yes—
367C2×Dic11C2×C22⋊C412yes—
368D44—22no—
369D44—22no—
370D44—48no—
371D44—41no—
372D44—41no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—48no—
378C8×C11—22no—
379C8×C11—41no—
380C11⋊C8—41no—
381C11⋊C8—41no—
382C22×#41—111no—
383C23×Q8C2×D1111yescharacteristic
384C22×M16C2×D1111yescharacteristic
385C23×C8—111no—
386#548—118no—
387#548—224no—
388C2×#124—111no—
389C2×#124—221no—
390C2×C22⋊Q8—111no—
391C2×C22⋊Q8—221no—
392C2×#121—111no—
393C2×#121—221no—
394C2×C4×Q8—111no—
395C2×C4×D4—111no—
396C2×C4×D4—221no—
397C2×#117—111no—
398C2×#117C2×D1111yescharacteristic
399#435—224no—
400C2×C4⋊C8—111no—
401#419—24no—
402#416—224no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103C2×D1111yescharacteristic
408C2×#103C2×D1111yescharacteristic
409C2×#103C2×D1111yescharacteristic
410C2×#103C2×D1111yescharacteristic
411C2×#102—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×C22⋊C8—111no—
416C2×C22⋊C8—111no—
417C2×#97—111no—
418#390—221no—
419#388—221no—
420#388—221no—
421#384—111no—
422#380—111no—
423#380—111no—
424C4×C4⋊C4—111no—
425C4×C4⋊C4—221no—
426#340—111no—
427#340—111no—
428#340—111no—
429#340—111no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11C22×C22⋊C411yescharacteristic
438C22×C11D4211yescharacteristic
439C22×C11#54611yescharacteristic
440C22×C11#57511yescharacteristic
441C22×C11#57511yescharacteristic
442C22×C11#57711yescharacteristic
443C22×C11#57811yescharacteristic
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—41no—
448C2×D11—41no—
449C2×D11—41no—
450C2×D11—41no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—81no—
455C2×D11—81no—
456C2×D11—81no—
457C2×D11—81no—
458C4×C11—22no—
459C4×C11—24no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11—81no—
463C4×C11C2×C4×D411yescharacteristic
464C4×C11#51811yescharacteristic
465C4×C11D4211yescharacteristic
466C4×C11#54611yescharacteristic
467Dic11—22no—
468Dic11—22no—
469Dic11—22no—
470Dic11—42no—
471Dic11—81no—
472Dic11—81no—
473C2×#41—114no—
474C2×#41—222no—
475C2×#41—222no—
476C2×#41—222no—
477C2×#41—441no—
478C2×#41—441no—
479C22×Q8—21no—
480C22×Q8—22no—
481C22×Q8—22no—
482C22×Q8—22no—
483C22×Q8—41no—
484C22×Q8—41no—
485C22×Q8C4×D1114yes—
486C22×Q8C22×D1111yescharacteristic
487C22×Q8C22×D1111yescharacteristic
488C22×D4—111no—
489C22×D4—111no—
490C22×D4—221no—
491C22×D4—221no—
492C23×C4—21no—
493C23×C4—111no—
494C23×C4—221no—
495C23×C4C22×D1111yescharacteristic
496C2×M16—22no—
497C2×M16—22no—
498C2×M16—41no—
499C22×C8—111no—
500C22×C8—111no—
501C22×C8—222no—
502C22×C8—222no—
503C22×C8—441no—
504C22×C8C22×D1111yescharacteristic
505C22×C8C22×D1111yescharacteristic
506#124—114no—
507#124—222no—
508#124—228no—
509C22⋊Q8—114no—
510C22⋊Q8—228no—
511C22⋊Q8—222no—
512#121—114no—
513#121—228no—
514#121—222no—
515C4×Q8—114no—
516C4×Q8—222no—
517C4×D4—114no—
518C4×D4—114no—
519C4×D4—228no—
520#117—22no—
521#117—41no—
522#117—222no—
523#117—441no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
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×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C42—21no—
545C2×C42—111no—
546C2×C42—221no—
547C2×C42—221no—
548C2×C42—221no—
549C4⋊C8—222no—
550#103—22no—
551#103—22no—
552#103—22no—
553#103—222no—
554#103—222no—
555#103—441no—
556#103—441no—
557#103C22⋊D1114yescomplemented
558#102—222no—
559#102—222no—
560#102—441no—
561#102—441no—
562C22⋊C8—222no—
563C22⋊C8—222no—
564#97—222no—
565#95—221no—
566#95—221no—
567#95—221no—
568C2×C11—42no—
569C2×C11D4×C22⋊C411yescharacteristic
570C2×C11#289611yescharacteristic
571C2×C11#289811yescharacteristic
572C2×C11#326911yescharacteristic
573C2×C11#327111yescharacteristic
574C2×C11#331311yescharacteristic
575C2×C11#332111yescharacteristic
576D11—42no—
577D11—82no—
578C24—111no—
579C24—221no—
580C24D4×D1111yescharacteristic
581#41—228no—
582#41—444no—
583#41—444no—
584#41—444no—
585C2×Q8—24no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—28no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—42no—
596C2×Q8—42no—
597C2×Q8—44no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8C2×C4×D1112yes—
601C2×Q8C2×C4×D1112yes—
602C2×Q8#433912yes—
603C2×Q8C2×C22⋊D1112yes—
604C2×D4—114no—
605C2×D4—112no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—221no—
609C2×D4—221no—
610C2×D4—221no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—442no—
614C2×D4—442no—
615C2×D4—441no—
616C2×D4—441no—
617C2×D4—442no—
618C2×D4—442no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—24no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—111no—
631C22×C4—111no—
632C22×C4—111no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—224no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—442no—
644C22×C4—442no—
645C22×C4C2×C4×D1112yes—
646C22×C4D4×D1111yescharacteristic
647C22×C4D4×D1112yes—
648C22×C4C23×D1111yescharacteristic
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—444no—
662C2×C8C2×C22⋊D1112yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—114no—
667C4⋊C4—112no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—221no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—442no—
676C4⋊C4—881no—
677C4⋊C4C2×C22⋊D1112yes—
678C22⋊C4—42no—
679C22⋊C4—114no—
680C22⋊C4—114no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—442no—
686C22⋊C4—881no—
687C22⋊C4—881no—
688C42—42no—
689C42—112no—
690C42—112no—
691C42—224no—
692C42—442no—
693C42—442no—
694C11#2242611yescharacteristic, complemented, Sylow
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—112no—
702C23—221no—
703C23—221no—
704C23—221no—
705C23—221no—
706C23—221no—
707C23—221no—
708C23—222no—
709C23—441no—
710C23—441no—
711C23—441no—
712C23—441no—
713C23—441no—
714C23—441no—
715C23C22⋊C4×D1112yes—
716C23C2×D4×D1111yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—48no—
723Q8—41no—
724Q8—41no—
725Q8C4×C22⋊D1114yes—
726D4—222no—
727D4—222no—
728D4—448no—
729D4—444no—
730D4—448no—
731D4—441no—
732D4—441no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—48no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—112no—
753C2×C4—112no—
754C2×C4—112no—
755C2×C4—221no—
756C2×C4—221no—
757C2×C4—221no—
758C2×C4—221no—
759C2×C4—221no—
760C2×C4—221no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—448no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4C22⋊C4×D1112yes—
776C2×C4C22×C4×D1111yescharacteristic
777C2×C4C2×#433911yescharacteristic
778C2×C4C2×D4×D1111yescharacteristic
779C2×C4#6703711yescharacteristic
780C2×C4#6703711yescharacteristic
781C2×C4C22×C22⋊D1111yescharacteristic
782C8—22no—
783C8—41no—
784C8—441no—
785C8—441no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—222no—
794C22—222no—
795C22—222no—
796C22—441no—
797C22—441no—
798C22—441no—
799C22—441no—
800C22—442no—
801C22—442no—
802C22—442no—
803C22—881no—
804C22—881no—
805C22—881no—
806C22—881no—
807C22C2×C22⋊C4×D1111yescharacteristic
808C22#1062302111yescharacteristic
809C22#1062330811yescharacteristic
810C22#1062330811yescharacteristic
811C22#1062330911yescharacteristic
812C22#1062331011yescharacteristic
813C22D4×C22⋊D1111yescharacteristic
814C4—22no—
815C4—24no—
816C4—42no—
817C4—42no—
818C4—81no—
819C4—222no—
820C4—222no—
821C4—222no—
822C4—442no—
823C4—881no—
824C4—881no—
825C4#1062301711yescharacteristic
826C4#1062302111yescharacteristic
827C4C2×C4×C22⋊D1111yescharacteristic
828C4D4×C22⋊D1111yescharacteristic
829C2—42no—
830C2—442no—
831C2—882no—
832C2C22⋊C4×C22⋊D1111yescharacteristic
833C2#1307713411yescharacteristic
834C2#1307714811yescharacteristic
835C2#1308016511yescharacteristic
836C2#1308019511yescharacteristic
837C2#1308068311yescharacteristic
838C2#1308080311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC2×#10623348C2
cosocleC22×C4×C11C24
hypercenterC2×#419D11
hypocenterC11#22426
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×#10622740C2semidirect
3. C2×#10622417C2semidirect
4. #13071566C2semidirect
5. #13069545C2semidirect
6. #13069429C2semidirect
7. #13069054C2semidirect
8. #13069036C2semidirect
9. #13068938C2semidirect
10. #13068925C2semidirect
11. #13068619C2semidirect
12. #13068555C2semidirect
13. #13068551C2semidirect
14. #13068448C2semidirect
15. C2×C11×#419C2semidirect
21. #10623348C4semidirect
143. C11×#103D4semidirect
278. C2×#419D11semidirect
557. #103C22⋊D11semidirect
694. C11#22426semidirect

Maximal subgroups

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

subgroupindex
C2×#106233482
C2×#106227402
C2×#106224172
#130715662
#130695452
#130694292
#130690542
#130690362
#130689382
#130689252
#130686192
#130685552
#130685512
#130684482
C2×C11×#4192
#2242611