Finite Group Databasebeta

← #14804542

Subgroups — #14804542

Order 2816.

1116 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622651C211yesmaximal, characteristic, complemented
2C2×#10622654C211yesmaximal, characteristic, complemented
3C2×#10622629C211yesmaximal, characteristic, complemented
4C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
5#13073555C211yesmaximal, characteristic, complemented
6#13069819C211yesmaximal, characteristic, complemented
7#13069805C211yesmaximal, characteristic, complemented
8#13069619C211yesmaximal, characteristic, complemented
9#13069612C211yesmaximal, characteristic, complemented
10#13069425C211yesmaximal, characteristic, complemented
11#13069382C211yesmaximal, characteristic, complemented
12#13069042C211yesmaximal, characteristic, complemented
13#13069037C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2535C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic
28C2×#66928C2211yescharacteristic
29C11×#397—21no—
30C11×#392—21no—
31C11×#386—21no—
32C11×#386—21no—
33C11×#382C2211yescharacteristic
34C11×#380C2211yescharacteristic
35C11×#380C2211yescharacteristic
36#10622836—21no—
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622654—24no—
42#10622651—24no—
43#10622629—24no—
44D4×C11⋊C8—24no—
45#10622605—21no—
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622570—21no—
55#10622570—21no—
56C4×C4⋊Dic11C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—21no—
71C22×C22⋊D11—21no—
72C22×D44C2311yescharacteristic
73C22×Dic22C2311yescharacteristic
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—41no—
77C11×#121—41no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×#4324—22no—
97C2×#4324—22no—
98C2×#4324—41no—
99C2×#4323—22no—
100C2×#4323—22no—
101C2×#4323—41no—
102#66983—22no—
103#66983—22no—
104#66983—41no—
105#66983—41no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112#66977—22no—
113#66977—22no—
114#66977—41no—
115#66977—41no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×C4×Dic11—21no—
119C22×C11⋊C8—22no—
120C22×C11⋊C8—22no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—22no—
123C22×C11⋊C8—41no—
124C22×C11⋊C8—41no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129#66928—22no—
130#66928—22no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135#66896—22no—
136#66896D414yescomplemented
137C11⋊#95—21no—
138C22⋊(C11⋊C8)—22no—
139C22⋊(C11⋊C8)—22no—
140#66874—22no—
141#66874—22no—
142#66874—41no—
143#66873—22no—
144#66873—22no—
145#66873—41no—
146#66872—22no—
147#66871—22no—
148C4⋊(C11⋊C8)D414yescomplemented
149C4×C11⋊C8—22no—
150#25388—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C23×D11—21no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—81no—
168C2×D4×C11—81no—
169C2×D4×C11C2×D412yes—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—42no—
186C22×C4×C11—81no—
187C22×C4×C11—81no—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C2×C22⋊D11—42no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—42no—
196C2×C22⋊D11—42no—
197C2×C22⋊D11—81no—
198C2×C22⋊D11—81no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22—21no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—81no—
227C11×C22⋊C4—81no—
228C42×C11C2×D412yes—
229C42×C11#4112yes—
230C22⋊Dic11—42no—
231C22⋊Dic11—42no—
232#4324—44no—
233#4323—44no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—42no—
236(C2×D11)⋊C4—42no—
237(C2×D11)⋊C4—42no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11C2×D412yes—
241C4⋊Dic11#4112yes—
242Dic11⋊C4—42no—
243Dic11⋊C4—42no—
244C4×Dic11—81no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—44no—
255C2×C11⋊C8—44no—
256C2×C11⋊C8C2×D412yes—
257C2×C11⋊C8C2×D412yes—
258C2×C11⋊C8C2×D412yes—
259C2×#466—111no—
260C2×#465—111no—
261C2×#463—111no—
262C2×C8×D4—111no—
263#2540—111no—
264#2535D1111yescharacteristic, complemented
265#2036—111no—
266#2034—111no—
267#2000—111no—
268#1999—111no—
269#1958—111no—
270#1949—111no—
271#1893—111no—
272#1892—111no—
273C4×#102—111no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—22no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11#13512yes—
294C23×C11#13512yes—
295C23×C11C22×D411yescharacteristic
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—41no—
303D4×C11—28no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—84no—
309D4×C11—84no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—84no—
338C2×C4×C11#12112yes—
339C2×C4×C11#12112yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C11H(5,𝔽2)11yescharacteristic
346C22⋊D11—84no—
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357D44—41no—
358D44—41no—
359D44—41no—
360D44—41no—
361Dic22—41no—
362Dic22—41no—
363Dic22—41no—
364Dic22—41no—
365C11⋊C8—22no—
366C11⋊C8—22no—
367C11⋊C8—22no—
368C11⋊C8—41no—
369C22×SD16—111no—
370C22×D8—111no—
371C23×C8—111no—
372C23×C8—111no—
373C2×#124—111no—
374C2×C22⋊Q8—111no—
375C2×C22⋊Q8—111no—
376C2×#121—111no—
377C2×#121—111no—
378C2×#121C2×D1111yescharacteristic
379C2×#121C2×D1111yescharacteristic
380C2×C4×D4C2×D1111yescharacteristic
381C2×C4×D4C2×D1111yescharacteristic
382#466—224no—
383#465—224no—
384#463—224no—
385C8×D4—224no—
386C2×#107—111no—
387C2×#106—111no—
388C2×C4⋊C8—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×#102—111no—
397C2×C22⋊C8—111no—
398C2×C22⋊C8—111no—
399C2×C4×C8—111no—
400#399—221no—
401#397—21no—
402#392—21no—
403#392—221no—
404#390—221no—
405#390—221no—
406#386—21no—
407#386—21no—
408#382C2×D1111yescharacteristic
409#380C2×D1111yescharacteristic
410#380C2×D1111yescharacteristic
411C4×C4⋊C4—111no—
412#340—111no—
413#340—111no—
414#340—111no—
415#340—111no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11C2×#12111yescharacteristic
438C22×C11D4211yescharacteristic
439C22×C11#54611yescharacteristic
440C22×C11C2×#13511yescharacteristic
441C22×C11C2×#13511yescharacteristic
442C22×C11#57611yescharacteristic
443C22×C11#57711yescharacteristic
444C2×D11—81no—
445C2×D11—81no—
446C2×D11—81no—
447C2×D11—81no—
448C2×D11—81no—
449C2×D11—81no—
450C2×D11—81no—
451C4×C11—22no—
452C4×C11—22no—
453C4×C11—41no—
454C4×C11—41no—
455C4×C11—81no—
456C4×C11—81no—
457C4×C11—81no—
458C4×C11#53211yescharacteristic
459C4×C11#54011yescharacteristic
460C4×C11D4211yescharacteristic
461C4×C11#55011yescharacteristic
462Dic11—42no—
463Dic11—42no—
464Dic11—81no—
465C22×Q8—111no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—111no—
469C22×D4—221no—
470C22×D4—221no—
471C22×D4C22⋊D1111yescharacteristic
472C22×D4C22×D1111yescharacteristic
473C23×C4—21no—
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C2×SD16—222no—
477C2×SD16—222no—
478C2×SD16—441no—
479C2×D8—222no—
480C2×D8—222no—
481C2×D8—441no—
482C22×C8—111no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—111no—
486C22×C8—222no—
487C22×C8—222no—
488C22×C8—222no—
489C22×C8—222no—
490C22×C8—441no—
491C22×C8—441no—
492#124—222no—
493#124—222no—
494C22⋊Q8—222no—
495C22⋊Q8—222no—
496C22⋊Q8—441no—
497C22⋊Q8—441no—
498#121—22no—
499#121—22no—
500#121—41no—
501#121—41no—
502#121—222no—
503#121—222no—
504#121—441no—
505#121—441no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4C22⋊D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C4⋊C4C22×D1111yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4C22⋊D1111yescharacteristic
530C2×C22⋊C4C22⋊D1111yescharacteristic
531C2×C42—221no—
532C2×C42C22×D1111yescharacteristic
533#107—222no—
534#106—222no—
535C4⋊C8—114no—
536#103—222no—
537#103—222no—
538#103—441no—
539#102—114no—
540#102—222no—
541#102—222no—
542#102—222no—
543#102—441no—
544C22⋊C8—222no—
545C22⋊C8—222no—
546C4×C8—222no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—221no—
552C2×C11—42no—
553C2×C11—42no—
554C2×C11—82no—
555C2×C11#242811yescharacteristic
556C2×C11#305011yescharacteristic
557C2×C11#306211yescharacteristic
558C2×C11#328011yescharacteristic
559C2×C11#328211yescharacteristic
560C2×C11#329711yescharacteristic
561C2×C11#330111yescharacteristic
562D11—161no—
563C24—21no—
564C24—221no—
565C24C2×C22⋊D1111yescharacteristic
566C24C2×C22⋊D1111yescharacteristic
567C2×Q8—221no—
568C2×Q8—221no—
569C2×Q8—221no—
570C2×Q8—221no—
571C2×Q8—221no—
572C2×Q8—221no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—221no—
592C2×D4—221no—
593C2×D4—442no—
594C2×D4—442no—
595C2×D4—442no—
596C2×D4—442no—
597C2×D4—881no—
598C2×D4—881no—
599C2×D4D4×D1112yes—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C23×D1111yescharacteristic
626SD16—444no—
627D8—444no—
628C2×C8—112no—
629C2×C8—112no—
630C2×C8—112no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—444no—
641C2×C8—444no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—112no—
650C4⋊C4—112no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—442no—
654C4⋊C4—442no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—442no—
663C22⋊C4—442no—
664C22⋊C4—442no—
665C22⋊C4—442no—
666C22⋊C4—442no—
667C22⋊C4—442no—
668C42—881no—
669C42D4×D1112yes—
670C42#434112yes—
671C11#2538811yescharacteristic, complemented, Sylow
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—441no—
692C23—441no—
693C23—441no—
694C23—441no—
695C23—441no—
696C23—441no—
697C23—441no—
698C23#6700312yes—
699C23#6700312yes—
700C23C22×C22⋊D1111yescharacteristic
701Q8—441no—
702Q8—441no—
703Q8—441no—
704Q8—441no—
705D4—28no—
706D4—22no—
707D4—22no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712D4—441no—
713D4—441no—
714D4—441no—
715D4—441no—
716D4—884no—
717D4—884no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—84no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4#6699212yes—
756C2×C4#6699212yes—
757C2×C4C2×D4×D1111yescharacteristic
758C2×C4C2×D4×D1111yescharacteristic
759C2×C4C2×#434111yescharacteristic
760C2×C4#6703711yescharacteristic
761C2×C4#41×D1111yescharacteristic
762C2×C4#6704211yescharacteristic
763C8—222no—
764C8—222no—
765C8—222no—
766C8—441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—881no—
789C22—881no—
790C22—881no—
791C22—881no—
792C22—881no—
793C22—881no—
794C22—881no—
795C22D4×C22⋊D1111yescharacteristic
796C22C2×#6699211yescharacteristic
797C22C2×#6700311yescharacteristic
798C22C2×#6700311yescharacteristic
799C22#1062336011yescharacteristic
800C22#1062336611yescharacteristic
801C22#1062336711yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—442no—
810C4—442no—
811C4—881no—
812C4#1062312711yescharacteristic
813C4#1062313011yescharacteristic
814C4#1062314011yescharacteristic
815C4#1062315011yescharacteristic
816C2—42no—
817C2—42no—
818C2—82no—
819C2—1761no—
820C2#1307220611yescharacteristic
821C2#1307819411yescharacteristic
822C2#1307829211yescharacteristic
823C2#1308029711yescharacteristic
824C2#1308031911yescharacteristic
825C2#1308046011yescharacteristic
826C2#1308051211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2535C2
socleC23×C11C22×D4
hypercenter#2535D11
hypocenterC11#25388
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#10622651C2semidirect
2. C2×#10622654C2semidirect
3. C2×#10622629C2semidirect
4. C2×D4×C11⋊C8C2semidirect
5. #13073555C2semidirect
6. #13069819C2semidirect
7. #13069805C2semidirect
8. #13069619C2semidirect
9. #13069612C2semidirect
10. #13069425C2semidirect
11. #13069382C2semidirect
12. #13069042C2semidirect
13. #13069037C2semidirect
14. C4×#66896C2semidirect
15. C11×#2535C2semidirect
136. #66896D4semidirect
148. C4⋊(C11⋊C8)D4semidirect
264. #2535D11semidirect
671. C11#25388semidirect

Maximal subgroups

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

subgroupindex
C2×#106226512
C2×#106226542
C2×#106226292
C2×D4×C11⋊C82
#130735552
#130698192
#130698052
#130696192
#130696122
#130694252
#130693822
#130690422
#130690372
C4×#668962
C11×#25352
#2538811