Finite Group Databasebeta

← #14787725

Subgroups — #14787725

Order 2816.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic
2C2×#10622407C211yesmaximal, characteristic, complemented
3C2×Q16×Dic11C211yesmaximal, characteristic, complemented
4#13073535C211yesmaximal, characteristic
5#13069818C211yesmaximal, characteristic, complemented
6#13069816C211yesmaximal, characteristic, complemented
7#13069623C211yesmaximal, characteristic, complemented
8#13069575C211yesmaximal, characteristic, complemented
9#13069408C211yesmaximal, characteristic
10#13068924C211yesmaximal, characteristic, complemented
11#13068920C211yesmaximal, characteristic, complemented
12#13068806C211yesmaximal, characteristic, complemented
13#13068805C211yesmaximal, characteristic, complemented
14#13068619C211yesmaximal, characteristic, complemented
15C11×#2001C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25#10623166—24no—
26#10623166—24no—
27C2×#66950—21no—
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×#66942—21no—
30C2×#66941C2211yescharacteristic
31C2×(C22⋊D11)⋊C4—21no—
32C2×#66931—21no—
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40#10622825C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42Q16×Dic11—24no—
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×#66882C2211yescharacteristic
46C2×#66882C2211yescharacteristic
47C2×Dic11⋊C8C2211yescharacteristic
48C2×C8×Dic11C2211yescharacteristic
49#10622607—21no—
50#10622600C2211yescharacteristic
51#10622589C2211yescharacteristic
52#10622585—21no—
53C2×#66871C2211yescharacteristic
54#10622570—21no—
55#10622561—21no—
56#10622407—24no—
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11D411yescharacteristic
67C23×Dic11—21no—
68C22×C4×D11—21no—
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—21no—
71C2×C11×Q16—22no—
72C2×C11×Q16—22no—
73C2×C11×Q16—22no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—41no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11D411yescharacteristic
88#66999—22no—
89#66999—22no—
90#66999—22no—
91#66999—41no—
92Q8×Dic11—22no—
93Q8×Dic11—22no—
94Q8×Dic11—22no—
95Q8×Dic11D414yes—
96C4×C22⋊D11—22no—
97C4×C22⋊D11—22no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4D411yescharacteristic
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4D411yescharacteristic
118C2×C4×Dic11—21no—
119C2×C4×Dic11—21no—
120C2×C4×Dic11C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123#66950—28no—
124C4⋊C4×D11—22no—
125C4⋊C4×D11—22no—
126#66942—28no—
127#66941—22no—
128#66941D414yes—
129(C22⋊D11)⋊C4—28no—
130#66931—28no—
131C11×#103—22no—
132C11×#103—41no—
133C11×C22⋊C8—22no—
134#66899—22no—
135#66899—22no—
136#66899—22no—
137#66899—41no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—41no—
141(C2×D11)⋊C8—22no—
142(C2×D11)⋊C8—41no—
143#66882—22no—
144#66882—22no—
145Dic11⋊C8—22no—
146C8×Dic11—22no—
147#66871—22no—
148#24122—111nomaximal, Sylow
149C24×C11C2×D411yescharacteristic
150C23×D11C2×D411yescharacteristic
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11C2×D412yes—
162C2×Q8×C11#4112yes—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C2×C22⋊D11—22no—
176C2×C22⋊D11—22no—
177C2×C22⋊D11Q1614yescomplemented
178C22×Dic11—24no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—81no—
184C22×Dic11—81no—
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C2×C4×D11—24no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—81no—
196C2×C4×D11—81no—
197C2×Dic22—24no—
198C2×Dic22—81no—
199C2×Dic22—81no—
200C11×Q16—28no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11#4112yes—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4C2×D412yes—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—42no—
215C22⋊Dic11—22no—
216C22⋊Dic11—81no—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—22no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—81no—
221C4⋊Dic11—24no—
222C4⋊Dic11—24no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—42no—
230C4⋊Dic11C2×D412yes—
231C4⋊Dic11C2×D412yes—
232Dic11⋊C4—24no—
233Dic11⋊C4—24no—
234Dic11⋊C4—24no—
235Dic11⋊C4—22no—
236Dic11⋊C4—42no—
237Dic11⋊C4—42no—
238Dic11⋊C4—81no—
239C4×Dic11—24no—
240C4×Dic11—42no—
241C4×Dic11C2×D412yes—
242C4×Dic11C2×D412yes—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×#554—111no—
250C2×#477—111no—
251C2×C4×Q16—111no—
252#2538—111no—
253#2036—111no—
254#2036—111no—
255#2001—111no—
256#2001D1111yescharacteristic, complemented
257#1990—111no—
258#1954—111no—
259#1872—111no—
260#1872—111no—
261#1852—111no—
262#1852—111no—
263#1803—111no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11C2×Q1612yes—
271C23×C11C22×D411yescharacteristic
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11C2×Q1612yes—
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—22no—
282Q8×C11—22no—
283Q8×C11—41no—
284Q8×C11—41no—
285Q8×C11—41no—
286Q8×C11—41no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C112−1+411yescharacteristic
312C22⋊D11—28no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—22no—
316C2×Dic11—21no—
317C2×Dic11—22no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—84no—
331C2×Dic11#12012yes—
332C2×Dic11#12012yes—
333C2×Dic11C2×Q1612yes—
334C2×Dic11#13712yes—
335C4×D11—41no—
336C4×D11—41no—
337C4×D11—41no—
338C4×D11—41no—
339C4×D11—84no—
340Dic22—84no—
341C8×C11—22no—
342C8×C11—41no—
343C11⋊C8—41no—
344C11⋊C8—41no—
345C22×Q16C2×D1111yescharacteristic
346#554—224no—
347#554—224no—
348C2×C4⋊Q8—111no—
349C2×#125—221no—
350C2×C22⋊Q8—111no—
351C2×C22⋊Q8—111no—
352C2×C22⋊Q8—221no—
353C2×C22⋊Q8—221no—
354C2×C22⋊Q8C2×D1111yescharacteristic
355C2×C22⋊Q8C2×D1111yescharacteristic
356C2×C4×Q8—111no—
357C2×C4×Q8—111no—
358C2×C4×D4—111no—
359C2×C4×D4—221no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4—111no—
362#477—224no—
363C4×Q16—224no—
364C2×#107—111no—
365C2×#107—111no—
366C2×#107—111no—
367C2×C4⋊C8—111no—
368C2×#103—111no—
369C2×#103—111no—
370C2×#103—111no—
371C2×#103—111no—
372C2×#103C2×D1111yescharacteristic
373C2×#103C2×D1111yescharacteristic
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376C2×C22⋊C8—111no—
377C2×C22⋊C8C2×D1111yescharacteristic
378C2×C4×C8—111no—
379#396—221no—
380#396—221no—
381#390—221no—
382#389—221no—
383#384—111no—
384#380—111no—
385#380—111no—
386#340—111no—
387#340—111no—
388#340—111no—
389#340—111no—
390#340—111no—
391#340C2×D1111yescharacteristic
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11C2×#12011yescharacteristic
400C22×C11#54611yescharacteristic
401C22×C11#54711yescharacteristic
402C22×C11C22×Q1611yescharacteristic
403C22×C11C2×#13711yescharacteristic
404C22×C11#57611yescharacteristic
405C22×C11#57711yescharacteristic
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—41no—
412C2×D11—41no—
413C4×C11—41no—
414C4×C11—42no—
415C4×C11—42no—
416C4×C11—42no—
417C4×C11—81no—
418C4×C11#52511yescharacteristic
419C4×C11#53711yescharacteristic
420C4×C11#54811yescharacteristic
421C4×C11#55011yescharacteristic
422Dic11—22no—
423Dic11—41no—
424Dic11—42no—
425Dic11—42no—
426Dic11—81no—
427Dic11—81no—
428Dic11#45114yes—
429C22×Q8—221no—
430C22×Q8C22×D1111yescharacteristic
431C22×Q8C22×D1111yescharacteristic
432C22×D4—111no—
433C23×C4—111no—
434C23×C4—221no—
435C23×C4—221no—
436C23×C4C22×D1111yescharacteristic
437C2×Q16—22no—
438C2×Q16—22no—
439C2×Q16—22no—
440C22×C8—111no—
441C22×C8—111no—
442C22×C8C22×D1111yescharacteristic
443C22×C8C22×D1111yescharacteristic
444C4⋊Q8—114no—
445C4⋊Q8—222no—
446#125—228no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—41no—
451C22⋊Q8—228no—
452C22⋊Q8—228no—
453C22⋊Q8—222no—
454C22⋊Q8—222no—
455C22⋊Q8—222no—
456C22⋊Q8—441no—
457C4×Q8—114no—
458C4×Q8—222no—
459C4×Q8—222no—
460C4×Q8—222no—
461C4×D4—222no—
462C4×D4—222no—
463C4×D4—228no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—222no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4—222no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—222no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—111no—
489C2×C22⋊C4—111no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C42—111no—
495C2×C42—221no—
496C2×C42—221no—
497#107—222no—
498#107—222no—
499#107—222no—
500C4⋊C8—222no—
501#103—22no—
502#103—41no—
503#103—222no—
504#103—222no—
505#103—222no—
506#103—441no—
507C22⋊C8—22no—
508C22⋊C8—222no—
509C22⋊C8—441no—
510C22⋊C8—441no—
511C4×C8—222no—
512#95—221no—
513#95—221no—
514C2×C11—42no—
515C2×C11#240711yescharacteristic
516C2×C11C2×#45111yescharacteristic
517C2×C11#301211yescharacteristic
518C2×C11#329911yescharacteristic
519C2×C11#333311yescharacteristic
520C2×C11#333811yescharacteristic
521C2×C11#335611yescharacteristic
522D11—42no—
523C24—111no—
524C24D4×D1111yescharacteristic
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—224no—
536C2×Q8—881no—
537C2×Q8—881no—
538C2×Q8D4×D1112yes—
539C2×Q8#434112yes—
540C2×D4—114no—
541C2×D4—222no—
542C2×D4—222no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—224no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—224no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—881no—
569C22×C4—881no—
570C22×C4—881no—
571C22×C4—881no—
572C22×C4D4×D1111yescharacteristic
573C22×C4C23×D1111yescharacteristic
574Q16—28no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8#434112yes—
587C4⋊C4—24no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—112no—
593C4⋊C4—112no—
594C4⋊C4—222no—
595C4⋊C4—224no—
596C4⋊C4—224no—
597C4⋊C4—224no—
598C4⋊C4—224no—
599C4⋊C4—224no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—442no—
607C4⋊C4—442no—
608C4⋊C4—442no—
609C4⋊C4—881no—
610C4⋊C4D4×D1112yes—
611C22⋊C4—24no—
612C22⋊C4—42no—
613C22⋊C4—222no—
614C22⋊C4—224no—
615C22⋊C4—222no—
616C22⋊C4—442no—
617C22⋊C4—881no—
618C22⋊C4—881no—
619C42—112no—
620C42—112no—
621C42—224no—
622C42—442no—
623C11#2412211yescharacteristic, complemented, Sylow
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—112no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23Q16×D1112yes—
638C23C2×D4×D1111yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—884no—
648D4—228no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—112no—
669C2×C4—112no—
670C2×C4—112no—
671C2×C4—112no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—884no—
694C2×C4—884no—
695C2×C4C2×D4×D1111yescharacteristic
696C2×C4C2×D4×D1111yescharacteristic
697C2×C4C2×#434111yescharacteristic
698C2×C4C2×#434111yescharacteristic
699C2×C4#6703711yescharacteristic
700C2×C4#6704311yescharacteristic
701C8—22no—
702C8—41no—
703C8—441no—
704C8—441no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—222no—
713C22—222no—
714C22—222no—
715C22—441no—
716C22—441no—
717C22—441no—
718C22—441no—
719C22D11×#12011yescharacteristic
720C22#1062312211yescharacteristic
721C22#1062314211yescharacteristic
722C22C2×Q16×D1111yescharacteristic
723C22#1062330011yescharacteristic
724C22D11×#13711yescharacteristic
725C22#1062330911yescharacteristic
726C4—41no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—81no—
731C4—114no—
732C4—222no—
733C4—441no—
734C4—442no—
735C4—442no—
736C4—881no—
737C4—881no—
738C4#1062311711yescharacteristic
739C4#1062312811yescharacteristic
740C4#1062312911yescharacteristic
741C4#1062324911yescharacteristic
742C2—42no—
743C2—442no—
744C2#1307195411yescharacteristic
745C2D11×#45111yescharacteristic
746C2#1307792411yescharacteristic
747C2#1308048511yescharacteristic
748C2#1308094711yescharacteristic
749C2#1308100511yescharacteristic
750C2#1308122611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2001C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#2001D11
hypocenterC11#24122
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#10622407C2semidirect
3. C2×Q16×Dic11C2semidirect
5. #13069818C2semidirect
6. #13069816C2semidirect
7. #13069623C2semidirect
8. #13069575C2semidirect
10. #13068924C2semidirect
11. #13068920C2semidirect
12. #13068806C2semidirect
13. #13068805C2semidirect
14. #13068619C2semidirect
15. C11×#2001C2semidirect
177. C2×C22⋊D11Q16semidirect
256. #2001D11semidirect
623. C11#24122semidirect

Maximal subgroups

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

subgroupindex
C2×#106231662
C2×#106224072
C2×Q16×Dic112
#130735352
#130698182
#130698162
#130696232
#130695752
#130694082
#130689242
#130689202
#130688062
#130688052
#130686192
C11×#20012
#2412211