Finite Group Databasebeta

← #14806879

Subgroups — #14806879

Order 2816.

1124 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×#10622584C211yesmaximal, characteristic, complemented
2C2×#10622665C211yesmaximal, characteristic, complemented
3#13072045C211yesmaximal, characteristic
4#13069946C211yesmaximal, characteristic, complemented
5#13069809C211yesmaximal, characteristic, complemented
6#13069754C211yesmaximal, characteristic, complemented
7#13069624C211yesmaximal, characteristic, complemented
8#13068957C211yesmaximal, characteristic, complemented
9#13068929C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic, complemented
13#13068809C211yesmaximal, characteristic, complemented
14#13068335C211yesmaximal, characteristic, complemented
15C2×C11×#554C211yesmaximal, characteristic
16C11×#554—24no—
17C11×#554—24no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#125—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C2×#66977C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37#10622835—21no—
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622665—24no—
43#10622585—21no—
44#10622584—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51#10622565—21no—
52#10622558—21no—
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11D411yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8—22no—
73C11×#125—28no—
74C11×C22⋊Q8—28no—
75C11×C22⋊Q8—28no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8D414yes—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×D4×C11—28no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4D414yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×#4326—22no—
110C2×#4326—22no—
111C2×#4326—41no—
112#66979—22no—
113#66979—41no—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117#66977—22no—
118#66977—22no—
119#66977—22no—
120#66977—41no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C2×#4318—22no—
126C2×#4318—22no—
127C2×#4318—41no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132#66899—22no—
133#66899—22no—
134#66899—41no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—41no—
142#66874—22no—
143#66874—22no—
144#66874—22no—
145#66872—22no—
146#66872—22no—
147#66872—22no—
148#25561—111nomaximal, Sylow
149C24×C11C2×D411yescharacteristic
150C24×C11C2×D411yescharacteristic
151C2×Q8×C11—24no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—81no—
158C2×Q8×C11—81no—
159C2×Q8×C11C2×D412yes—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
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—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—81no—
180C22×C4×C11—81no—
181C22×C4×C11—81no—
182C22×C4×C11—81no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4C2×D412yes—
211C11×C4⋊C4C2×D412yes—
212C11×C4⋊C4C2×D412yes—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C42×C11—24no—
218C42×C11—21no—
219C42×C11—21no—
220C22⋊Dic11—42no—
221C22⋊Dic11—42no—
222C22⋊Dic11—42no—
223C22⋊Dic11—42no—
224#4326—44no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11#4112yes—
231Dic11⋊C4—42no—
232Dic11⋊C4—42no—
233Dic11⋊C4—42no—
234C4×Dic11—42no—
235#4318—44no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8#4112yes—
248C2×#554D1111yescharacteristic
249C2×#483—111no—
250C2×#470—111no—
251#2415—111no—
252#2058—111no—
253#2035—111no—
254#2024—111no—
255#2001—111no—
256#1878—111no—
257#1873—111no—
258#1872—111no—
259#1870—111no—
260#1865—111no—
261#1853—111no—
262#1736—111no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11#12012yes—
276C23×C11#13712yes—
277C23×C11C22×D411yescharacteristic
278Q8×C11—22no—
279Q8×C11—22no—
280Q8×C11—41no—
281Q8×C11—41no—
282Q8×C11—84no—
283D4×C11—28no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—41no—
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—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—84no—
315C2×C4×C11—84no—
316C2×C4×C11#12012yes—
317C2×C4×C11#13712yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C112−1+411yescharacteristic
324C2×Dic11—22no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336Dic22—41no—
337Dic22—41no—
338Dic22—41no—
339Dic22—41no—
340C11⋊C8—22no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C22×Q16—111no—
345C22×M16—111no—
346#554—24no—
347#554—24no—
348C2×C4⋊Q8C2×D1111yescharacteristic
349C2×#125—21no—
350C2×C22⋊Q8—21no—
351C2×C22⋊Q8—21no—
352C2×C22⋊Q8—111no—
353C2×C22⋊Q8—111no—
354C2×C22⋊Q8C2×D1111yescharacteristic
355C2×C22⋊Q8C2×D1111yescharacteristic
356C2×C4×Q8C2×D1111yescharacteristic
357C2×C4×D4—21no—
358C2×C4×D4C2×D1111yescharacteristic
359C2×#117—111no—
360C22×C4⋊C4C2×D1111yescharacteristic
361C22×C4⋊C4C2×D1111yescharacteristic
362#483—224no—
363#470—224no—
364C2×#106—111no—
365C2×#106—111no—
366C2×#106—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#103—111no—
370C2×#103—111no—
371C2×#103—111no—
372C2×#103—111no—
373C2×C22⋊C8—111no—
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376#397—221no—
377#394—221no—
378#391—111no—
379#389—111no—
380#389—221no—
381#388—221no—
382#380—111no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#340—111no—
388#340—111no—
389#336—111no—
390#336—111no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11C2×#12011yescharacteristic
406C22×C11#54611yescharacteristic
407C22×C11#54711yescharacteristic
408C22×C11C2×#13711yescharacteristic
409C22×C11C2×#13711yescharacteristic
410C22×C11#57711yescharacteristic
411C22×C11#57711yescharacteristic
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—41no—
415C4×C11—42no—
416C4×C11—41no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11#53211yescharacteristic
421C4×C11#53711yescharacteristic
422C4×C11#54611yescharacteristic
423C4×C11#54711yescharacteristic
424Dic11—42no—
425Dic11—81no—
426Dic11—81no—
427Dic11—81no—
428C22×Q8—21no—
429C22×Q8—111no—
430C22×Q8C22×D1111yescharacteristic
431C22×D4C22⋊D1111yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4C22×D1111yescharacteristic
435C23×C4C22×D1111yescharacteristic
436C2×Q16—222no—
437C2×Q16—222no—
438C2×Q16—441no—
439C2×M16—222no—
440C2×M16—222no—
441C2×M16—441no—
442C22×C8—111no—
443C22×C8—111no—
444C22×C8—111no—
445C22×C8—111no—
446C4⋊Q8—22no—
447C4⋊Q8—22no—
448#125—28no—
449C22⋊Q8—28no—
450C22⋊Q8—28no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—222no—
455C22⋊Q8—222no—
456C22⋊Q8—222no—
457C22⋊Q8—441no—
458C22⋊Q8C22⋊D1114yes—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×D4—28no—
462C4×D4—22no—
463C4×D4—22no—
464#117—222no—
465#117—441no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4C22⋊D1111yescharacteristic
482C2×C4⋊C4C22⋊D1114yes—
483C2×C4⋊C4C22×D1111yescharacteristic
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4C22⋊D1111yescharacteristic
493C2×C22⋊C4C22⋊D1111yescharacteristic
494C2×C42—21no—
495C2×C42—221no—
496C2×C42C22×D1111yescharacteristic
497#106—222no—
498#106—222no—
499#106—222no—
500#103—222no—
501#103—222no—
502#103—222no—
503#103—222no—
504#103—222no—
505#103—441no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508C22⋊C8—441no—
509#95—221no—
510#95—221no—
511#95—221no—
512#95—221no—
513C2×C11—42no—
514C2×C11—42no—
515C2×C11#243011yescharacteristic
516C2×C11#300411yescharacteristic
517C2×C11#300911yescharacteristic
518C2×C11#331611yescharacteristic
519C2×C11#333111yescharacteristic
520C2×C11#334411yescharacteristic
521C2×C11#335611yescharacteristic
522C24C2×C22⋊D1111yescharacteristic
523C24C2×C22⋊D1111yescharacteristic
524C2×Q8—24no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—81no—
531C2×Q8—81no—
532C2×Q8—221no—
533C2×Q8—221no—
534C2×Q8—221no—
535C2×Q8—221no—
536C2×Q8—221no—
537C2×Q8—221no—
538C2×Q8C2×C22⋊D1112yes—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—81no—
561C22×C4—81no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1112yes—
571C22×C4C2×C22⋊D1112yes—
572C22×C4C23×D1111yescharacteristic
573Q16—444no—
574M16—444no—
575C2×C8—112no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—112no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—442no—
604C4⋊C4—442no—
605C4⋊C4—442no—
606C4⋊C4C2×C22⋊D1112yes—
607C4⋊C4C2×C22⋊D1112yes—
608C4⋊C4C2×C22⋊D1112yes—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C42—24no—
618C42—21no—
619C42—21no—
620C42—442no—
621C11#2556111yescharacteristic, complemented, Sylow
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23#6699512yes—
635C23#6700612yes—
636C23C22×C22⋊D1111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641Q8—84no—
642Q8—441no—
643Q8—441no—
644Q8—441no—
645Q8—441no—
646D4—28no—
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—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4—222no—
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#6699512yes—
692C2×C4#6700612yes—
693C2×C4#41×D1111yescharacteristic
694C2×C4#41×D1111yescharacteristic
695C2×C4#6704211yescharacteristic
696C2×C4#6704311yescharacteristic
697C2×C4C22×C22⋊D1111yescharacteristic
698C2×C4C22×C22⋊D1111yescharacteristic
699C8—222no—
700C8—441no—
701C8—441no—
702C8—441no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C2×#6699511yescharacteristic
718C22C2×#6699511yescharacteristic
719C22#1062335511yescharacteristic
720C22#1062336011yescharacteristic
721C22#1062336711yescharacteristic
722C22#1062336711yescharacteristic
723C22C2×#6700611yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—442no—
733C4—881no—
734C4—881no—
735C4—881no—
736C4#1062335511yescharacteristic
737C4#1062336011yescharacteristic
738C4#1062336311yescharacteristic
739C4#1062336411yescharacteristic
740C2—42no—
741C2—42no—
742C2#1307222011yescharacteristic
743C2#1307785011yescharacteristic
744C2#1307789311yescharacteristic
745C2#1308072111yescharacteristic
746C2#1308092611yescharacteristic
747C2#1308106511yescharacteristic
748C2#1308123111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#554D11
hypocenterC11#25561
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622584C2semidirect
2. C2×#10622665C2semidirect
4. #13069946C2semidirect
5. #13069809C2semidirect
6. #13069754C2semidirect
7. #13069624C2semidirect
8. #13068957C2semidirect
9. #13068929C2semidirect
10. #13068923C2semidirect
12. #13068884C2semidirect
13. #13068809C2semidirect
14. #13068335C2semidirect
621. C11#25561semidirect

Maximal subgroups

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

subgroupindex
C2×#106225842
C2×#106226652
#130720452
#130699462
#130698092
#130697542
#130696242
#130689572
#130689292
#130689232
#130689142
#130688842
#130688092
#130683352
C2×C11×#5542
#2556111