Finite Group Databasebeta

← #14807398

Subgroups — #14807398

Order 2816.

1158 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622672C211yesmaximal, characteristic, complemented
2C2×#10622702C211yesmaximal, characteristic, complemented
3#13074373C211yesmaximal, characteristic, complemented
4#13069624C211yesmaximal, characteristic, complemented
5#13069619C211yesmaximal, characteristic, complemented
6#13069617C211yesmaximal, characteristic, complemented
7#13069612C211yesmaximal, characteristic
8#13069578C211yesmaximal, characteristic, complemented
9#13069433C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068957C211yesmaximal, characteristic, complemented
13#13068950C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C2×C11×#542C211yesmaximal, characteristic, complemented
16C11×#542—24no—
17C11×#542—24no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#126—21no—
20C2×C11×#124—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C22×#4324C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66928C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622702—24no—
43#10622672—24no—
44#10622607—21no—
45#10622607—21no—
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50#10622574—21no—
51#10622574—21no—
52#10622552C2211yescharacteristic
53#10622548C2211yescharacteristic
54#10622542C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×D44C2311yescharacteristic
71C22×Dic22C2311yescharacteristic
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8D414yescomplemented
74C11×#126—28no—
75C11×#124—28no—
76C11×#124—22no—
77C11×#124D414yescomplemented
78C11×#123—28no—
79C11×C22⋊Q8—28no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×#121—22no—
83C11×#121—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C11×#117—22no—
89C11×#117—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×#4326—22no—
109C2×#4326—22no—
110C2×#4326—41no—
111C2×#4325—22no—
112C2×#4325—22no—
113C2×#4325—41no—
114C2×#4324—22no—
115C2×#4324—22no—
116C2×#4324—41no—
117C2×#4323—22no—
118C2×#4323—22no—
119C2×#4323—41no—
120#66983—41no—
121#66983—41no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131#66977—41no—
132#66977—41no—
133C2×Dic11⋊C4—21no—
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138#66928—22no—
139#66928—22no—
140#66899—41no—
141#66899—41no—
142#66896—41no—
143#66896—41no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C22⋊(C11⋊C8)—22no—
147C22⋊(C11⋊C8)—22no—
148#66874—22no—
149#66874—22no—
150#66873—22no—
151#66873—22no—
152#66867—22no—
153C4×C11⋊C8—22no—
154#25610—111nomaximal, Sylow
155C24×C11—21no—
156C24×C11C2×D411yescharacteristic
157C23×D11—21no—
158C2×Q8×C11—24no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—81no—
165C2×Q8×C11—81no—
166C2×Q8×C11C2×D412yes—
167C2×D4×C11—24no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C2×D4×C11C2×D412yes—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—24no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C2×C22⋊D11—42no—
195C2×C22⋊D11—81no—
196C2×C22⋊D11—81no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4C2×D412yes—
220C11×C4⋊C4C2×D412yes—
221C11×C22⋊C4—24no—
222C11×C22⋊C4—24no—
223C11×C22⋊C4—24no—
224C11×C22⋊C4—24no—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—22no—
228C42×C11—24no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11C2×D412yes—
232C42×C11C2×D412yes—
233C22⋊Dic11—42no—
234#4326—44no—
235#4325—44no—
236#4324—44no—
237#4323—44no—
238(C2×D11)⋊C4—42no—
239(C2×D11)⋊C4—42no—
240(C2×D11)⋊C4—42no—
241(C2×D11)⋊C4—81no—
242(C2×D11)⋊C4—81no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—81no—
248C4⋊Dic11—81no—
249Dic11⋊C4—42no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8#4112yes—
261C2×C11⋊C8#4112yes—
262C2×#542D1111yescharacteristic, complemented
263C2×#495—111no—
264C2×#489—111no—
265#2620—111no—
266#2001—111no—
267#2000—111no—
268#2000—111no—
269#1999—111no—
270#1990—111no—
271#1959—111no—
272#1880—111no—
273#1879—111no—
274#1878—111no—
275#1877—111no—
276#1750—111no—
277C23×C11—21no—
278C23×C11—22no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11C22×D411yescharacteristic
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—41no—
302Q8×C11—41no—
303Q8×C11—84no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—84no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—21no—
316C2×C4×C11—22no—
317C2×C4×C11—21no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
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—84no—
336C2×C4×C11#12012yes—
337C2×C4×C11#12012yes—
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C2×C4×C11C2×#4111yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C22⋊D11—84no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354D44—41no—
355D44—41no—
356D44—41no—
357D44—41no—
358Dic22—41no—
359Dic22—41no—
360Dic22—41no—
361Dic22—41no—
362C11⋊C8—22no—
363C11⋊C8—22no—
364C11⋊C8—41no—
365C11⋊C8—41no—
366C22×Q16—111no—
367C22×SD16—111no—
368C22×SD16—111no—
369C22×D8—111no—
370#542—24no—
371#542—24no—
372C2×C4⋊Q8C2×D1111yescharacteristic
373C2×#126—21no—
374C2×#124—21no—
375C2×#124—111no—
376C2×#124C2×D1111yescharacteristic
377C2×#123—21no—
378C2×C22⋊Q8—21no—
379C2×C22⋊Q8—111no—
380C2×C22⋊Q8C2×D1111yescharacteristic
381C2×#121—111no—
382C2×#121C2×D1111yescharacteristic
383C2×C4×Q8C2×D1111yescharacteristic
384C2×C4×D4C2×D1111yescharacteristic
385C2×#117C2×D1111yescharacteristic
386#495—224no—
387#489—224no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×C22⋊C8—111no—
397C2×C22⋊C8—111no—
398C2×#97—111no—
399C2×C4×C8—111no—
400#396—221no—
401#396—221no—
402#394—221no—
403#394—221no—
404#391—111no—
405#390—111no—
406#384—111no—
407#340—111no—
408#340—111no—
409#340—111no—
410#340—111no—
411#336—111no—
412#336—111no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—42no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—42no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—42no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11C2×#12011yescharacteristic
428C22×C11#53211yescharacteristic
429C22×C11#53511yescharacteristic
430C22×C11#57611yescharacteristic
431C22×C11#57711yescharacteristic
432C22×C11#57711yescharacteristic
433C22×C11#57811yescharacteristic
434C2×D11—81no—
435C2×D11—81no—
436C2×D11—81no—
437C2×D11—81no—
438C2×D11—81no—
439C2×D11—81no—
440C2×D11—81no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—41no—
444C4×C11—42no—
445C4×C11—41no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11—41no—
449C4×C11#54611yescharacteristic
450C4×C11#54611yescharacteristic
451C4×C11#55011yescharacteristic
452C4×C11#55011yescharacteristic
453Dic11—81no—
454Dic11—81no—
455Dic11—81no—
456C22×Q8—21no—
457C22×Q8—111no—
458C22×Q8C22×D1111yescharacteristic
459C22×D4—21no—
460C22×D4—111no—
461C22×D4—221no—
462C22×D4C22×D1111yescharacteristic
463C23×C4—21no—
464C23×C4C22×D1111yescharacteristic
465C2×Q16—222no—
466C2×Q16—222no—
467C2×Q16—441no—
468C2×SD16—222no—
469C2×SD16—222no—
470C2×SD16—222no—
471C2×SD16—222no—
472C2×SD16—441no—
473C2×SD16—441no—
474C2×D8—222no—
475C2×D8—222no—
476C2×D8—441no—
477C22×C8—111no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8—111no—
481C4⋊Q8—22no—
482C4⋊Q8C22⋊D1114yescomplemented
483#126—28no—
484#124—28no—
485#124—22no—
486#124—222no—
487#124—222no—
488#124C22⋊D1114yescomplemented
489#123—28no—
490C22⋊Q8—28no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—441no—
494C22⋊Q8—441no—
495#121—22no—
496#121—22no—
497#121—441no—
498#121—441no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×D4—22no—
502C4×D4—22no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4C22⋊D1111yescharacteristic
514C2×C4⋊C4C22⋊D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4C22⋊D1111yescharacteristic
529C2×C22⋊C4C22⋊D1111yescharacteristic
530C2×C42—21no—
531C2×C42C22×D1111yescharacteristic
532C2×C42C22×D1111yescharacteristic
533#103—222no—
534#103—222no—
535#103—441no—
536#103—441no—
537#102—222no—
538#102—222no—
539#102—441no—
540#102—441no—
541C22⋊C8—222no—
542C22⋊C8—222no—
543#97—222no—
544C4×C8—222no—
545#95—221no—
546#95—221no—
547C2×C11—81no—
548C2×C11—82no—
549C2×C11#243111yescharacteristic
550C2×C11#301211yescharacteristic
551C2×C11#301311yescharacteristic
552C2×C11#317311yescharacteristic
553C2×C11#317511yescharacteristic
554C2×C11#322411yescharacteristic
555C2×C11#322511yescharacteristic
556D11—161no—
557C24—21no—
558C24—221no—
559C24C2×C22⋊D1111yescharacteristic
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×Q8—221no—
569C2×Q8—221no—
570C2×Q8—221no—
571C2×Q8—221no—
572C2×Q8—221no—
573C2×Q8—221no—
574C2×Q8C2×C22⋊D1112yes—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—221no—
584C2×D4—221no—
585C2×D4—221no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—442no—
590C2×D4—881no—
591C2×D4—881no—
592C2×D4C2×C22⋊D1112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4C2×C22⋊D1111yescharacteristic
609C22×C4C2×C22⋊D1111yescharacteristic
610C22×C4C2×C22⋊D1111yescharacteristic
611C22×C4C2×C22⋊D1111yescharacteristic
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C23×D1111yescharacteristic
614Q16—444no—
615SD16—444no—
616SD16—444no—
617D8—444no—
618C2×C8—112no—
619C2×C8—112no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—221no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—442no—
642C4⋊C4—881no—
643C4⋊C4—881no—
644C4⋊C4C2×C22⋊D1112yes—
645C4⋊C4C2×C22⋊D1112yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—442no—
654C22⋊C4—442no—
655C22⋊C4—442no—
656C22⋊C4—442no—
657C22⋊C4—881no—
658C22⋊C4—881no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42C2×C22⋊D1112yes—
663C42C2×C22⋊D1112yes—
664C11#2561011yescharacteristic, complemented, Sylow
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—441no—
680C23—441no—
681C23—441no—
682C23—441no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23C22×C22⋊D1111yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—41no—
690Q8—41no—
691Q8—84no—
692Q8—441no—
693Q8—441no—
694Q8—441no—
695Q8—441no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—84no—
701D4—441no—
702D4—441no—
703D4—441no—
704D4—441no—
705D4—884no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4#6700612yes—
743C2×C4#6700612yes—
744C2×C4#41×D1111yescharacteristic
745C2×C4#41×D1111yescharacteristic
746C2×C4#6704211yescharacteristic
747C2×C4#6704211yescharacteristic
748C2×C4C22×C22⋊D1111yescharacteristic
749C2×C4C22×C22⋊D1111yescharacteristic
750C8—222no—
751C8—222no—
752C8—441no—
753C8—441no—
754C22—41no—
755C22—42no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—41no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—881no—
769C22—881no—
770C22—881no—
771C22—881no—
772C22—881no—
773C22—881no—
774C22—881no—
775C22#1062336111yescharacteristic
776C22#1062336311yescharacteristic
777C22#1062336611yescharacteristic
778C22#1062336711yescharacteristic
779C22#1062336811yescharacteristic
780C22#1062336911yescharacteristic
781C22C2×#6700611yescharacteristic
782C4—22no—
783C4—22no—
784C4—41no—
785C4—42no—
786C4—41no—
787C4—42no—
788C4—42no—
789C4—41no—
790C4—881no—
791C4—881no—
792C4—881no—
793C4#1062336011yescharacteristic
794C4#1062336011yescharacteristic
795C4#1062336511yescharacteristic
796C4#1062336511yescharacteristic
797C2—81no—
798C2—82no—
799C2—1761no—
800C2#1307223111yescharacteristic
801C2#1307792011yescharacteristic
802C2#1307793111yescharacteristic
803C2#1307922711yescharacteristic
804C2#1307924911yescharacteristic
805C2#1307970411yescharacteristic
806C2#1307971911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
prime radical#13069612C2
hypercenterC2×#542D11
hypocenterC11#25610
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10622672C2semidirect
2. C2×#10622702C2semidirect
3. #13074373C2semidirect
4. #13069624C2semidirect
5. #13069619C2semidirect
6. #13069617C2semidirect
8. #13069578C2semidirect
9. #13069433C2semidirect
10. #13068971C2semidirect
11. #13068964C2semidirect
12. #13068957C2semidirect
13. #13068950C2semidirect
14. #13068382C2semidirect
15. C2×C11×#542C2semidirect
73. C11×C4⋊Q8D4semidirect
77. C11×#124D4semidirect
262. C2×#542D11semidirect
482. C4⋊Q8C22⋊D11semidirect
488. #124C22⋊D11semidirect
664. C11#25610semidirect

Maximal subgroups

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

subgroupindex
C2×#106226722
C2×#106227022
#130743732
#130696242
#130696192
#130696172
#130696122
#130695782
#130694332
#130689712
#130689642
#130689572
#130689502
#130683822
C2×C11×#5422
#2561011