Finite Group Databasebeta

← #14770166

Subgroups — #14770166

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2#13071565C211yesmaximal, characteristic, complemented
3#13069586C211yesmaximal, characteristic, complemented
4#13069574C211yesmaximal, characteristic, complemented
5#13069055C211yesmaximal, characteristic, complemented
6#13069045C211yesmaximal, characteristic, complemented
7#13068939C211yesmaximal, characteristic, complemented
8#13068939C211yesmaximal, characteristic, complemented
9#13068711C211yesmaximal, characteristic, complemented
10#13068702C211yesmaximal, characteristic, complemented
11#13068616C211yesmaximal, characteristic, complemented
12#13068441C211yesmaximal, characteristic, complemented
13#13068335C211yesmaximal, characteristic, complemented
14#13068332C211yesmaximal, characteristic, complemented
15C2×C11×#553C211yesmaximal, characteristic
16C11×#553—24no—
17C11×#553C418yescomplemented
18C2×C11×#126—21no—
19C2×C11×#125C2211yescharacteristic
20C2×C11×#123—21no—
21C2×C11×#121—21no—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C23×C11⋊C8C2211yescharacteristic
33#10622834—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622624—24no—
43C4⋊C4×Dic11—21no—
44#10622564—21no—
45#10622564—21no—
46#10622548C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C11×#126—28no—
71C11×#125—22no—
72C11×#125C2×C414yes—
73C11×#123—28no—
74C11×#121—28no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121C2×C414yes—
78C11×#121C2×C414yes—
79C4×D4×C11—28no—
80C4×D4×C11—22no—
81C4×D4×C11C2×C414yes—
82C4×D4×C11C2×C414yes—
83C4×D4×C11D414yes—
84C11×#117—22no—
85C11×#117C2×C414yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4C2×C414yes—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4D411yescharacteristic
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107#66979—22no—
108#66979—22no—
109#66979—41no—
110#66979—41no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4×Dic11—21no—
118C2×C4×Dic11—21no—
119C2×C4×Dic11—21no—
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—41no—
123C22×C11⋊C8—22no—
124C22×C11⋊C8—22no—
125C22×C11⋊C8—41no—
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130#66896—22no—
131#66896—22no—
132#66896—41no—
133#66896—41no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C22⋊(C11⋊C8)—22no—
138C22⋊(C11⋊C8)—22no—
139C4⋊(C11⋊C8)—22no—
140#66867—22no—
141#22498—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—81no—
157C2×D4×C11—81no—
158C2×D4×C11C22⋊C414yes—
159C2×D4×C11C22×C412yes—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
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—24no—
172C22×C4×C11—24no—
173C22×C4×C11—81no—
174C22×C4×C11—81no—
175C22×C4×C11—81no—
176C22×C4×C11—81no—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C22×C412yes—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D412yes—
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2411yescharacteristic
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4C22⋊C414yes—
197C11×C4⋊C4C22×C412yes—
198C11×C4⋊C4C22×C412yes—
199C11×C4⋊C4C22×C412yes—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C11×C22⋊C4C22⋊C414yes—
205C11×C22⋊C4C22⋊C414yes—
206C42×C11—24no—
207C42×C11C22×C412yes—
208C42×C11C2×D412yes—
209C22⋊Dic11—42no—
210C22⋊Dic11—42no—
211C22⋊Dic11—81no—
212C22⋊Dic11—81no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—42no—
221C4⋊Dic11—81no—
222C4⋊Dic11#4112yes—
223C4×Dic11—42no—
224C4×Dic11—42no—
225C4×Dic11—42no—
226#4318—44no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—44no—
239C2×C11⋊C8#4112yes—
240C2×#553D1111yescharacteristic
241C2×#435—111no—
242#2354—111no—
243#1992—111no—
244#1989—111no—
245#1895—111no—
246#1893—111no—
247#1875—111no—
248#1875—111no—
249#1825—111no—
250#1823—111no—
251#1802—111no—
252#1762—111no—
253#1736—111no—
254#1735—111no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—22no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11C2×C22⋊C412yes—
275C23×C11C2×C22⋊C412yes—
276C23×C11C22×D411yescharacteristic
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—44no—
280D4×C11—48no—
281D4×C11—41no—
282D4×C11—41no—
283D4×C11—84no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—84no—
310C2×C4×C11—84no—
311C2×C4×C11C2×C22⋊C412yes—
312C2×C4×C11C2×C22⋊C412yes—
313C2×C4×C11C2×C22⋊C412yes—
314C2×C4×C11C2×C22⋊C412yes—
315C2×C4×C11C23×C411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C112−1+411yescharacteristic
321C2×Dic11—22no—
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—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C11⋊C8—22no—
334C11⋊C8—41no—
335C11⋊C8—41no—
336C11⋊C8—41no—
337C22×M16—111no—
338C23×C8—111no—
339#553—24no—
340#553Dic1118yescomplemented
341C2×#126—21no—
342C2×#125C2×D1111yescharacteristic
343C2×#123—21no—
344C2×#121—21no—
345C2×#121C2×D1111yescharacteristic
346C2×#121C2×D1111yescharacteristic
347C2×C4×D4—21no—
348C2×C4×D4C2×D1111yescharacteristic
349C2×C4×D4C2×D1111yescharacteristic
350C2×#117—111no—
351C2×#117—111no—
352C2×#117C2×D1111yescharacteristic
353C22×C4⋊C4C2×D1111yescharacteristic
354#435—224no—
355C2×C4⋊C8—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×#97—111no—
363#390—221no—
364#388—221no—
365#388—221no—
366#384—111no—
367#380—111no—
368#380—111no—
369C4×C4⋊C4—111no—
370C4×C4⋊C4—221no—
371#340—111no—
372#340—111no—
373#340—111no—
374#340—111no—
375#340—111no—
376#340—111no—
377#340—111no—
378#340—111no—
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11C22×C22⋊C411yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11#54711yescharacteristic
407C22×C11#57511yescharacteristic
408C22×C11#57511yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57711yescharacteristic
411C4×C11—22no—
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—42no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11C4×#4111yescharacteristic
419C4×C11#52011yescharacteristic
420C4×C11#54611yescharacteristic
421C4×C11#54711yescharacteristic
422Dic11—42no—
423Dic11—81no—
424Dic11—81no—
425Dic11—81no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4C22⋊D1111yescharacteristic
429C22×D4C22×D1111yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434C2×M16—222no—
435C2×M16—222no—
436C2×M16—441no—
437C22×C8—111no—
438C22×C8—111no—
439C22×C8—111no—
440C22×C8—111no—
441C22×C8—222no—
442C22×C8—222no—
443C22×C8—441no—
444#126—28no—
445#125—22no—
446#125C2×Dic1114yes—
447#123—28no—
448#121—28no—
449#121—22no—
450#121—22no—
451#121C2×Dic1114yes—
452#121C2×Dic1114yes—
453C4×D4—28no—
454C4×D4—22no—
455C4×D4C2×Dic1114yes—
456C4×D4C2×Dic1114yes—
457C4×D4C22⋊D1114yes—
458#117—22no—
459#117—222no—
460#117—222no—
461#117—441no—
462#117—441no—
463#117C2×Dic1114yes—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4C2×Dic1114yes—
475C2×C4⋊C4C22⋊D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4C22⋊D1111yescharacteristic
488C2×C22⋊C4C22⋊D1111yescharacteristic
489C2×C42—21no—
490C2×C42—221no—
491C2×C42—221no—
492C2×C42—221no—
493C2×C42C22×D1111yescharacteristic
494C4⋊C8—222no—
495#102—222no—
496#102—222no—
497#102—441no—
498#102—441no—
499C22⋊C8—222no—
500C22⋊C8—222no—
501#97—222no—
502#95—221no—
503#95—221no—
504#95—221no—
505C2×C11—42no—
506C2×C11—42no—
507C2×C11—82no—
508C2×C11#233911yescharacteristic
509C2×C11#289611yescharacteristic
510C2×C11#289711yescharacteristic
511C2×C11#330711yescharacteristic
512C2×C11#330911yescharacteristic
513C2×C11#334711yescharacteristic
514C2×C11#335011yescharacteristic
515C24—21no—
516C24C2×C22⋊D1111yescharacteristic
517C24C2×C22⋊D1111yescharacteristic
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4C22⋊Dic1114yes—
532C2×D4C22×Dic1112yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4C22×Dic1112yes—
555C22×C4C22×Dic1112yes—
556C22×C4C2×C22⋊D1111yescharacteristic
557C22×C4C2×C22⋊D1111yescharacteristic
558C22×C4C2×C22⋊D1111yescharacteristic
559C22×C4C2×C22⋊D1111yescharacteristic
560C22×C4C2×C22⋊D1112yes—
561C22×C4C2×C22⋊D1112yes—
562C22×C4C23×D1111yescharacteristic
563M16—444no—
564C2×C8—112no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—444no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—112no—
584C4⋊C4—221no—
585C4⋊C4—221no—
586C4⋊C4—221no—
587C4⋊C4—221no—
588C4⋊C4—221no—
589C4⋊C4—221no—
590C4⋊C4—221no—
591C4⋊C4—442no—
592C4⋊C4—881no—
593C4⋊C4C22⋊Dic1114yes—
594C4⋊C4C22×Dic1112yes—
595C4⋊C4C22×Dic1112yes—
596C4⋊C4C22×Dic1112yes—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—442no—
602C22⋊C4—442no—
603C22⋊C4—881no—
604C22⋊C4—881no—
605C22⋊C4C22⋊Dic1114yes—
606C22⋊C4C22⋊Dic1114yes—
607C42—24no—
608C42—442no—
609C42—442no—
610C42—442no—
611C42C22×Dic1112yes—
612C42C2×C22⋊D1112yes—
613C11#2249811yescharacteristic, complemented, Sylow
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C2×C22⋊Dic1112yes—
634C23C2×C22⋊Dic1112yes—
635C23C22×C22⋊D1111yescharacteristic
636D4—22no—
637D4—22no—
638D4—44no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—84no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—84no—
670C2×C4—222no—
671C2×C4—441no—
672C2×C4—441no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4C2×C22⋊Dic1112yes—
683C2×C4C2×C22⋊Dic1112yes—
684C2×C4C2×C22⋊Dic1112yes—
685C2×C4C2×C22⋊Dic1112yes—
686C2×C4#41×D1111yescharacteristic
687C2×C4#41×D1111yescharacteristic
688C2×C4#6704211yescharacteristic
689C2×C4#6704311yescharacteristic
690C2×C4C23×Dic1111yescharacteristic
691C2×C4C22×C22⋊D1111yescharacteristic
692C8—222no—
693C8—441no—
694C8—441no—
695C8—441no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22#1062335311yescharacteristic
718C22#1062335311yescharacteristic
719C22#1062335511yescharacteristic
720C22#1062336011yescharacteristic
721C22#1062336611yescharacteristic
722C22#1062336711yescharacteristic
723C22C22×C22⋊Dic1111yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—442no—
732C4—881no—
733C4—881no—
734C4—881no—
735C4#1062335511yescharacteristic
736C4#41×Dic1111yescharacteristic
737C4#1062335811yescharacteristic
738C4#1062336011yescharacteristic
739C2—42no—
740C2—42no—
741C2—82no—
742C2#1307144611yescharacteristic
743C2#1307713511yescharacteristic
744C2#1307714211yescharacteristic
745C2#1308058611yescharacteristic
746C2#1308061611yescharacteristic
747C2#1308111011yescharacteristic
748C2#1308115511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#553C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#553D11
hypocenterC11#22498
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. #13071565C2semidirect
3. #13069586C2semidirect
4. #13069574C2semidirect
5. #13069055C2semidirect
6. #13069045C2semidirect
7. #13068939C2semidirect
8. #13068939C2semidirect
9. #13068711C2semidirect
10. #13068702C2semidirect
11. #13068616C2semidirect
12. #13068441C2semidirect
13. #13068335C2semidirect
14. #13068332C2semidirect
17. C11×#553C4semidirect
340. #553Dic11semidirect
613. C11#22498semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
#130715652
#130695862
#130695742
#130690552
#130690452
#130689392
#130687112
#130687022
#130686162
#130684412
#130683352
#130683322
C2×C11×#5532
#2249811