Finite Group Databasebeta

← #14769593

Subgroups — #14769593

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D8×D11C211yesmaximal, characteristic
2C2×C4×#4323C211yesmaximal, characteristic, complemented
3C2×#10622369C211yesmaximal, characteristic, complemented
4#13071437C211yesmaximal, characteristic, complemented
5D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6#13069481C211yesmaximal, characteristic, complemented
7#13069479C211yesmaximal, characteristic, complemented
8#13068966C211yesmaximal, characteristic, complemented
9#13068965C211yesmaximal, characteristic, complemented
10#13068963C211yesmaximal, characteristic, complemented
11#13068644C211yesmaximal, characteristic, complemented
12#13068545C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068386C211yesmaximal, characteristic, complemented
15C11×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic, complemented
20C2×D4×Dic11C2211yescharacteristic, complemented
21C22×#4323C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C22×(C2×D11)⋊C4—21no—
24C2×D8×D11—24no—
25C2×D8×D11—24no—
26C2×D8×D11C418yescomplemented
27C22×D88C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29C2×#66946C2211yescharacteristic, complemented
30C2×C22⋊C4×D11—21no—
31C2×C4×D44C2211yescharacteristic, complemented
32C2×C11×#102C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic, complemented
34C11×#390C2211yescharacteristic, complemented
35#10622834C2211yescharacteristic, complemented
36C2×#66896C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic, complemented
38#10622826—21no—
39C2×#66885C2211yescharacteristic, complemented
40C2×#66885C2211yescharacteristic, complemented
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic, complemented
43C4×#4323—24no—
44#10622601C2211yescharacteristic, complemented
45#10622600C2211yescharacteristic
46#10622600C2211yescharacteristic
47C2×#66873C2211yescharacteristic, complemented
48C2×#66873C2211yescharacteristic, complemented
49C2×#66871C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51#10622571—21no—
52#10622569—21no—
53#10622569—21no—
54#10622568—21no—
55#10622568—21no—
56#10622552C2211yescharacteristic, complemented
57C4×(C2×D11)⋊C4C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic, complemented
59#10622369—24no—
60C11×#340C2211yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, complemented
64C24×D11—21no—
65C24×D11—21no—
66C22×D4×C11C2311yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C23×Dic11—21no—
72C2×D4×D11—22no—
73C2×D4×D11—22no—
74C2×D4×D11—22no—
75C2×D4×D11—22no—
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—41no—
79C2×D4×D11—41no—
80C2×D4×D11—41no—
81C2×D4×D11—41no—
82C2×D4×D11C2×C414yescomplemented
83C2×D4×D11C2×C414yescomplemented
84C22×D44C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C2×C11×D8—22no—
90C2×C11×D8—22no—
91C2×C11×D8C2×C414yescomplemented
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C4×D4×C11—22no—
95C4×D4×C11—41no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105D4×Dic11—22no—
106D4×Dic11—41no—
107C2×#4323—22no—
108C2×#4323—22no—
109C2×#4323C2×C414yes—
110C2×#4323C2×C414yescomplemented
111C2×#4323D414yes—
112C2×#4323D414yes—
113C2×(C2×D11)⋊C4—21no—
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)⋊C4—21no—
121C2×(C2×D11)⋊C4—44no—
122C2×(C2×D11)⋊C4D411yescharacteristic
123C2×(C2×D11)⋊C4D411yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4×Dic11C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129D8×D11—232no—
130C2×D88—22no—
131C2×D88—22no—
132C2×D88C2×C414yescomplemented
133C2×C8×D11—22no—
134C2×C8×D11—22no—
135C2×C8×D11C2×C414yescomplemented
136#66946—22no—
137#66946—41no—
138C22⋊C4×D11—44no—
139C4×D44—22no—
140C4×D44—41no—
141C11×#102—22no—
142C11×#102—41no—
143#66896—22no—
144#66896—41no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95D411yescharacteristic
148C11⋊#95D411yescharacteristic
149#66885—22no—
150#66885—41no—
151(C2×D11)⋊C8—22no—
152C8×Dic11—22no—
153#66873—22no—
154#66873—41no—
155#66871—22no—
156#66871—22no—
157C4×C11⋊C8—22no—
158C22⋊C4×D8—111nomaximal, Sylow
159C24×C11—21no—
160C24×C11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—24no—
164C23×D11—24no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11—81no—
174C23×D11—81no—
175C23×D11—81no—
176C23×D11—81no—
177C23×D11C2×D411yescharacteristic
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11C22×C412yes—
187C2×D4×C11C22×C412yes—
188C2×D4×C11C2×D412yes—
189C2×D4×C11C2×D412yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—81no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—42no—
201C2×C22⋊D11—42no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11—42no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—42no—
207C22×Dic11—42no—
208C22×Dic11—81no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212D4×D11—28no—
213D4×D11—28no—
214D4×D11—44no—
215D4×D11—44no—
216D4×D11—44no—
217D4×D11—44no—
218D4×D11—44no—
219D4×D11—44no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—21no—
226C2×D44—21no—
227C2×D44—21no—
228C2×D44C22×C412yes—
229C2×D44C22×C412yes—
230C2×D44C2×D412yes—
231C2×D44C2×D412yes—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×C4×D11—21no—
236C2×C4×D11—42no—
237C2×C4×D11—42no—
238C2×C4×D11—42no—
239C2×C4×D11—42no—
240C2×C4×D11—81no—
241C2×C4×D11—81no—
242C2×C4×D11C22×C412yes—
243C2×C4×D11#4112yes—
244C11×D8—28no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11C22×C412yes—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C22⋊C4—42no—
256C11×C22⋊C4—42no—
257C11×C22⋊C4—81no—
258C42×C11—21no—
259C42×C11—21no—
260C22⋊Dic11—42no—
261C22⋊Dic11—42no—
262C22⋊Dic11—81no—
263#4323—28no—
264#4323C22⋊C4116yescomplemented
265(C2×D11)⋊C4—22no—
266(C2×D11)⋊C4—42no—
267(C2×D11)⋊C4—42no—
268(C2×D11)⋊C4—42no—
269(C2×D11)⋊C4—42no—
270(C2×D11)⋊C4—42no—
271(C2×D11)⋊C4—42no—
272(C2×D11)⋊C4—81no—
273(C2×D11)⋊C4—81no—
274(C2×D11)⋊C4D814yescomplemented
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4×Dic11—21no—
280C4×Dic11—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8C22×C412yes—
285C2×C11⋊C8C2×D412yes—
286C2×C11⋊C8C2×D412yes—
287D88—28no—
288C8×D11—28no—
289C23×D8—111no—
290C2×C4×D8—111no—
291C2×C4×D8—111no—
292D4×C22⋊C4—111no—
293D4×C22⋊C4—111no—
294#1970—111no—
295#1970—111no—
296#1879—111no—
297#1879—111no—
298#1879—111no—
299#1879D1111yescharacteristic, complemented
300#1808—111no—
301#1786—111no—
302#1786—111no—
303C8×C22⋊C4—111no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11C22×D411yescharacteristic
319C22×D11—21no—
320C22×D11—21no—
321C22×D11—21no—
322C22×D11—21no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—48no—
328C22×D11—48no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—48no—
340C22×D11—48no—
341C22×D11—84no—
342C22×D11—84no—
343C22×D11—84no—
344C22×D11—84no—
345C22×D11—84no—
346C22×D11—84no—
347C22×D11—84no—
348C22×D11—84no—
349C22×D11—84no—
350C22×D11—84no—
351C22×D11C4×D412yes—
352C22×D11C2×D812yes—
353C22×D11#13512yes—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—41no—
360D4×C11—41no—
361D4×C11C2×C22⋊C414yescomplemented
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—84no—
374C2×C4×C11C2×D812yescomplemented
375C2×C4×C11C23×C411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C2×#4111yescharacteristic
379C2×C4×C11H(5,𝔽2)11yescharacteristic
380C2×C4×C11H(5,𝔽2)11yescharacteristic
381C22⋊D11—48no—
382C22⋊D11—48no—
383C2×Dic11—21no—
384C2×Dic11—21no—
385C2×Dic11—21no—
386C2×Dic11—21no—
387C2×Dic11—21no—
388C2×Dic11—21no—
389C2×Dic11—21no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—84no—
397C2×Dic11C4×D412yes—
398C2×Dic11C2×D812yescomplemented
399D44—22no—
400D44—22no—
401D44—22no—
402D44—22no—
403D44—22no—
404D44—41no—
405D44—41no—
406D44C2×C22⋊C414yescomplemented
407C4×D11—22no—
408C4×D11—22no—
409C4×D11—22no—
410C4×D11—22no—
411C4×D11—84no—
412C4×D11—84no—
413C8×C11—22no—
414C8×C11—41no—
415C11⋊C8—41no—
416C11⋊C8C2×C22⋊C414yescomplemented
417C23×D4—111no—
418C23×D4—111no—
419C22×D8—111no—
420C22×D8—111no—
421C22×D8—118no—
422C22×D8—111no—
423C22×D8—224no—
424C22×D8—224no—
425C22×D8C2×D1111yescharacteristic
426C23×C8—111no—
427C2×C4×D4—111no—
428C2×C4×D4—111no—
429C2×C4×D4—111no—
430C2×C4×D4C2×D1111yescharacteristic, complemented
431C22×C22⋊C4—221no—
432C22×C22⋊C4—221no—
433C4×D8—224no—
434C4×D8—224no—
435C2×#107—111no—
436C2×#107—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102C2×D1111yescharacteristic, complemented
444C2×#102C2×D1111yescharacteristic, complemented
445C2×C22⋊C8—111no—
446C2×C4×C8—111no—
447C2×C4×C8—111no—
448#390—111no—
449#390—111no—
450#390—111no—
451#390C2×D1111yescharacteristic, complemented
452#386—221no—
453#386—221no—
454#386—221no—
455#386—221no—
456#380—111no—
457#380—111no—
458#379—221no—
459#379—221no—
460C4×C22⋊C4—111no—
461#340—111no—
462#340C2×D1111yescharacteristic, complemented
463#336—111no—
464#336C2×D1111yescharacteristic, complemented
465C22×C11—24no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—81no—
476C22×C11—81no—
477C22×C11—81no—
478C22×C11—81no—
479C22×C11C2×C4×D411yescharacteristic
480C22×C11D4211yescharacteristic
481C22×C11D4211yescharacteristic
482C22×C11C22×D811yescharacteristic
483C22×C11C2×#13511yescharacteristic
484C22×C11#57611yescharacteristic
485C22×C11#57611yescharacteristic
486C2×D11—22no—
487C2×D11—22no—
488C2×D11—22no—
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—24no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—816no—
503C2×D11—816no—
504C2×D11—81no—
505C2×D11—81no—
506C2×D11—81no—
507C2×D11—81no—
508C2×D11C4×D814yescomplemented
509C4×C11—22no—
510C4×C11—41no—
511C4×C11—81no—
512C4×C11—81no—
513C4×C11C22×C22⋊C411yescharacteristic
514C4×C11#51811yescharacteristic
515C4×C11#54611yescharacteristic
516C4×C11#54611yescharacteristic
517Dic11—22no—
518Dic11—22no—
519Dic11—41no—
520Dic11—81no—
521Dic11—81no—
522C25—221no—
523C25—221no—
524C22×D4—114no—
525C22×D4—114no—
526C22×D4—111no—
527C22×D4—111no—
528C22×D4—222no—
529C22×D4—222no—
530C22×D4—221no—
531C22×D4—221no—
532C22×D4—222no—
533C22×D4—222no—
534C22×D4—222no—
535C22×D4—222no—
536C22×D4—441no—
537C22×D4—441no—
538C22×D4—441no—
539C22×D4—441no—
540C22×D4C22×D1111yescharacteristic
541C22×D4C22×D1111yescharacteristic
542C23×C4—21no—
543C23×C4—111no—
544C23×C4—221no—
545C23×C4—221no—
546C23×C4—221no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—114no—
550C2×D8—114no—
551C2×D8—114no—
552C2×D8—114no—
553C2×D8—114no—
554C2×D8—222no—
555C2×D8—222no—
556C2×D8—222no—
557C2×D8—222no—
558C2×D8—2232no—
559C2×D8C4×D1114yescomplemented
560C22×C8—111no—
561C22×C8—114no—
562C22×C8—111no—
563C22×C8—222no—
564C22×C8—222no—
565C22×C8C22×D1111yescharacteristic
566C22×C8C22×D1111yescharacteristic
567C4×D4—22no—
568C4×D4—41no—
569C4×D4—222no—
570C4×D4—222no—
571C4×D4—222no—
572C4×D4—441no—
573C4×D4—441no—
574C4×D4—441no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—111no—
577C2×C4⋊C4C22×D1111yescharacteristic
578C2×C4⋊C4C22×D1111yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—111no—
583C2×C22⋊C4—111no—
584C2×C22⋊C4—221no—
585C2×C22⋊C4—221no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C22⋊C4—221no—
595C2×C22⋊C4—444no—
596C2×C22⋊C4—444no—
597C2×C42—111no—
598C2×C42C22×D1111yescharacteristic
599#107—222no—
600#107—222no—
601#102—22no—
602#102—41no—
603#102—222no—
604#102—222no—
605#102—222no—
606#102—441no—
607#102—441no—
608#102—441no—
609C22⋊C8—222no—
610C4×C8—222no—
611C4×C8—222no—
612#95—111no—
613#95—111no—
614#95—221no—
615#95—221no—
616C2×C11—44no—
617C2×C11—82no—
618C2×C11D4×C22⋊C411yescharacteristic
619C2×C11C2×C4×D811yescharacteristic
620C2×C11#294811yescharacteristic
621C2×C11D4×D811yescharacteristic
622C2×C11D4×D811yescharacteristic
623C2×C11#328011yescharacteristic
624C2×C11#328011yescharacteristic
625D11—24no—
626D11—44no—
627D11—82no—
628C24—21no—
629C24—21no—
630C24—111no—
631C24—224no—
632C24—224no—
633C24—221no—
634C24—221no—
635C24—442no—
636C24—442no—
637C24—442no—
638C24—442no—
639C24—442no—
640C24—442no—
641C24—442no—
642C24—442no—
643C24—881no—
644C24—881no—
645C24—881no—
646C24—881no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—112no—
656C2×D4—112no—
657C2×D4—112no—
658C2×D4—112no—
659C2×D4—224no—
660C2×D4—224no—
661C2×D4—228no—
662C2×D4—228no—
663C2×D4—221no—
664C2×D4—221no—
665C2×D4—221no—
666C2×D4—221no—
667C2×D4—221no—
668C2×D4—221no—
669C2×D4—221no—
670C2×D4—221no—
671C2×D4—444no—
672C2×D4—444no—
673C2×D4—444no—
674C2×D4—444no—
675C2×D4—444no—
676C2×D4—444no—
677C2×D4—442no—
678C2×D4—442no—
679C2×D4—442no—
680C2×D4—442no—
681C2×D4C2×C4×D1112yes—
682C2×D4C2×C4×D1112yes—
683C2×D4D4×D1112yes—
684C2×D4D4×D1112yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—81no—
690C22×C4—111no—
691C22×C4—111no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—111no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—442no—
702C22×C4—442no—
703C22×C4—442no—
704C22×C4—442no—
705C22×C4—442no—
706C22×C4—442no—
707C22×C4—881no—
708C22×C4—881no—
709C22×C4—881no—
710C22×C4D4×D1111yescharacteristic
711C22×C4D4×D1111yescharacteristic
712C22×C4C23×D1111yescharacteristic
713D8—28no—
714D8—1116no—
715D8—228no—
716D8—228no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—112no—
723C2×C8—112no—
724C2×C8—112no—
725C2×C8—228no—
726C2×C8—221no—
727C2×C8—221no—
728C2×C8—221no—
729C2×C8C2×C4×D1112yes—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—221no—
735C4⋊C4—221no—
736C4⋊C4—221no—
737C4⋊C4—221no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—81no—
741C22⋊C4—114no—
742C22⋊C4—222no—
743C22⋊C4—442no—
744C22⋊C4—442no—
745C22⋊C4—442no—
746C22⋊C4—442no—
747C22⋊C4—442no—
748C22⋊C4—442no—
749C22⋊C4—442no—
750C22⋊C4—442no—
751C22⋊C4—881no—
752C22⋊C4—881no—
753C22⋊C4—881no—
754C42—21no—
755C42—21no—
756C42—221no—
757C42—221no—
758C11C22⋊C4×D811yescharacteristic, complemented, Sylow
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—112no—
774C23—112no—
775C23—112no—
776C23—221no—
777C23—221no—
778C23—221no—
779C23—221no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—448no—
785C23—448no—
786C23—448no—
787C23—448no—
788C23—441no—
789C23—441no—
790C23—441no—
791C23—441no—
792C23—441no—
793C23—441no—
794C23—441no—
795C23—441no—
796C23—441no—
797C23—441no—
798C23—884no—
799C23—884no—
800C23—884no—
801C23—884no—
802C23—884no—
803C23—884no—
804C23—884no—
805C23—884no—
806C23—884no—
807C23—884no—
808C23C2×D4×D1111yescharacteristic
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—41no—
815D4—41no—
816D4—114no—
817D4—222no—
818D4—222no—
819D4—222no—
820D4—222no—
821D4—222no—
822D4—448no—
823D4—448no—
824D4—441no—
825D4—441no—
826D4C22⋊C4×D1114yescomplemented
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—84no—
839C2×C4—112no—
840C2×C4—112no—
841C2×C4—221no—
842C2×C4—221no—
843C2×C4—221no—
844C2×C4—221no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—221no—
850C2×C4—221no—
851C2×C4—221no—
852C2×C4—441no—
853C2×C4—441no—
854C2×C4—441no—
855C2×C4—441no—
856C2×C4—441no—
857C2×C4—441no—
858C2×C4—884no—
859C2×C4—884no—
860C2×C4—884no—
861C2×C4D8×D1112yescomplemented
862C2×C4C22×C4×D1111yescharacteristic
863C2×C4C2×D4×D1111yescharacteristic
864C2×C4C2×D4×D1111yescharacteristic
865C2×C4#6703711yescharacteristic
866C2×C4#41×D1111yescharacteristic
867C2×C4#6704211yescharacteristic
868C8—22no—
869C8—41no—
870C8—114no—
871C8—441no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—114no—
887C22—222no—
888C22—222no—
889C22—222no—
890C22—222no—
891C22—222no—
892C22—222no—
893C22—224no—
894C22—442no—
895C22—442no—
896C22—442no—
897C22—442no—
898C22—442no—
899C22—442no—
900C22—442no—
901C22—442no—
902C22—442no—
903C22—8816no—
904C22—8816no—
905C22—881no—
906C22—881no—
907C22—881no—
908C22—881no—
909C22C4×D4×D1111yescharacteristic
910C22#1062312111yescharacteristic
911C22#1062314011yescharacteristic
912C22C2×D8×D1111yescharacteristic
913C22D11×#13511yescharacteristic
914C22#1062330511yescharacteristic
915C22#1062330511yescharacteristic
916C4—22no—
917C4—41no—
918C4—81no—
919C4—81no—
920C4—222no—
921C4—222no—
922C4—441no—
923C4—881no—
924C4—881no—
925C4C2×C22⋊C4×D1111yescharacteristic
926C4#1062307611yescharacteristic
927C4#1062314111yescharacteristic
928C4#1062318511yescharacteristic
929C2—44no—
930C2—82no—
931C2—224no—
932C2—444no—
933C2—882no—
934C2#1307143411yescharacteristic
935C2C4×D8×D1111yescharacteristic
936C2#1307746511yescharacteristic
937C2#1308028611yescharacteristic
938C2#1308028811yescharacteristic
939C2#1308029611yescharacteristic
940C2#1308029911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1879C2
socleC23×C11C22×D4
prime radicalC22×D8×D11C2
cosocleC22×C4×C11C24
hypercenter#1879D11
hypocenterC11C22⋊C4×D8
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4323C2semidirect
3. C2×#10622369C2semidirect
4. #13071437C2semidirect
5. D4×(C2×D11)⋊C4C2semidirect
6. #13069481C2semidirect
7. #13069479C2semidirect
8. #13068966C2semidirect
9. #13068965C2semidirect
10. #13068963C2semidirect
11. #13068644C2semidirect
12. #13068545C2semidirect
13. #13068545C2semidirect
14. #13068386C2semidirect
15. C11×#1879C2semidirect
19. C2×C4×D4×C11C22semidirect
20. C2×D4×Dic11C22semidirect
26. C2×D8×D11C4semidirect
29. C2×#66946C22semidirect
31. C2×C4×D44C22semidirect
32. C2×C11×#102C22semidirect
33. C2×C11×#102C22semidirect
34. C11×#390C22semidirect
35. #10622834C22semidirect
36. C2×#66896C22semidirect
37. C2×#66896C22semidirect
39. C2×#66885C22semidirect
40. C2×#66885C22semidirect
42. C2×C8×Dic11C22semidirect
44. #10622601C22semidirect
47. C2×#66873C22semidirect
48. C2×#66873C22semidirect
49. C2×#66871C22semidirect
50. C2×#66871C22semidirect
56. #10622552C22semidirect
58. C2×C4×C11⋊C8C22semidirect
60. C11×#340C22semidirect
61. C11×#336C22semidirect
62. #10622189C22semidirect
63. #10622188C22semidirect
82. C2×D4×D11C2×C4semidirect
83. C2×D4×D11C2×C4semidirect
91. C2×C11×D8C2×C4semidirect
110. C2×#4323C2×C4semidirect
132. C2×D88C2×C4semidirect
135. C2×C8×D11C2×C4semidirect
264. #4323C22⋊C4semidirect
274. (C2×D11)⋊C4D8semidirect
299. #1879D11semidirect
361. D4×C11C2×C22⋊C4semidirect
374. C2×C4×C11C2×D8semidirect
398. C2×Dic11C2×D8semidirect
406. D44C2×C22⋊C4semidirect
416. C11⋊C8C2×C22⋊C4semidirect
430. C2×C4×D4C2×D11semidirect
443. C2×#102C2×D11semidirect
444. C2×#102C2×D11semidirect
451. #390C2×D11semidirect
462. #340C2×D11semidirect
464. #336C2×D11semidirect
508. C2×D11C4×D8semidirect
559. C2×D8C4×D11semidirect
758. C11C22⋊C4×D8semidirect
826. D4C22⋊C4×D11semidirect
861. C2×C4D8×D11semidirect

Maximal subgroups

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

subgroupindex
C22×D8×D112
C2×C4×#43232
C2×#106223692
#130714372
D4×(C2×D11)⋊C42
#130694812
#130694792
#130689662
#130689652
#130689632
#130686442
#130685452
#130683862
C11×#18792
C22⋊C4×D811