Finite Group Databasebeta

← #14770785

Subgroups — #14770785

Order 2816.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622333C211yesmaximal, characteristic, complemented
2C2×#10622820C211yesmaximal, characteristic
3#13070999C211yesmaximal, characteristic
4#13069232C211yesmaximal, characteristic, complemented
5#13069226C211yesmaximal, characteristic, complemented
6#13069225C211yesmaximal, characteristic, complemented
7#13069219C211yesmaximal, characteristic, complemented
8#13068798C211yesmaximal, characteristic, complemented
9#13068798C211yesmaximal, characteristic, complemented
10#13068685C211yesmaximal, characteristic, complemented
11#13068598C211yesmaximal, characteristic, complemented
12#13068402C211yesmaximal, characteristic, complemented
13#13068402C211yesmaximal, characteristic, complemented
14#13068384C211yesmaximal, characteristic, complemented
15C11×#1779C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622860C411yescharacteristic
28#10622860C411yescharacteristic
29#10622825C411yescharacteristic
30#10622825C411yescharacteristic
31#10622825C411yescharacteristic
32#10622825C411yescharacteristic
33#10622824C411yescharacteristic
34#10622824C411yescharacteristic
35C4×C22⋊Dic11C2211yescharacteristic
36C4×C22⋊Dic11C2211yescharacteristic
37C4×C22⋊Dic11C2211yescharacteristic
38C4×C22⋊Dic11C2211yescharacteristic
39#10622820—24no—
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×#66879C2211yescharacteristic, complemented
45C2×#66879C2211yescharacteristic, complemented
46C2×Dic11⋊C8C2211yescharacteristic, complemented
47C2×Dic11⋊C8C2211yescharacteristic, complemented
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49C2×Dic11⋊C8C2211yescharacteristic, complemented
50C2×C8×Dic11C2211yescharacteristic, complemented
51C2×C8×Dic11C2211yescharacteristic, complemented
52#10622333—24no—
53#10622188C2211yescharacteristic, complemented
54#10622188C2211yescharacteristic, complemented
55#10622188C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622188C2211yescharacteristic, complemented
61C25×C11C2×C411yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—41no—
67C23×C4×C11—41no—
68C23×C4×C11C2×C411yescharacteristic
69C23×C4×C11C2×C411yescharacteristic
70C23×C4×C11C2×C411yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C2×C22⋊Dic11C2×C411yescharacteristic
79C2×C22⋊Dic11C2×C411yescharacteristic
80C2×C22⋊Dic11C2×C411yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90#66979—22no—
91#66979—22no—
92#66979—41no—
93#66979—41no—
94C2×C4⋊Dic11C2×C411yescharacteristic
95C2×C4⋊Dic11C2×C411yescharacteristic
96C2×C4⋊Dic11C2×C411yescharacteristic
97C2×C4⋊Dic11C2×C411yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×#4318—22no—
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318—22no—
106C2×#4318—41no—
107C2×#4318—41no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×C22⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11×C22⋊C8—22no—
116C11×C22⋊C8—41no—
117C11×C22⋊C8—41no—
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C11⋊#95C2×C411yescharacteristic
122C11⋊#95C2×C411yescharacteristic
123C11⋊#95C2×C411yescharacteristic
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)—22no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)D414yes—
130#66879—22no—
131#66879—41no—
132Dic11⋊C8—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—41no—
135Dic11⋊C8—41no—
136C8×Dic11—22no—
137C8×Dic11—41no—
138#22559—111nomaximal, Sylow
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11—41no—
143C24×C11—41no—
144C24×C11—41no—
145C24×C11—41no—
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C24×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×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—41no—
170C22×C4×C11—41no—
171C22×C4×C11—41no—
172C22×C4×C11—44no—
173C22×C4×C11—44no—
174C22×C4×C11—44no—
175C22×C4×C11—44no—
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11#4112yes—
181C22×C4×C11#4112yes—
182C22×C4×C11#4112yes—
183C22×C4×C11C2411yescharacteristic
184C22×Dic11C22×C411yescharacteristic
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C411yescharacteristic
187C22×Dic11C22×C411yescharacteristic
188C22×Dic11C22×C411yescharacteristic
189C22×Dic11C22×C411yescharacteristic
190C22×Dic11C22×C411yescharacteristic
191C22×Dic11C22×C411yescharacteristic
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C22⋊Dic11—22no—
205C22⋊Dic11—22no—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208C22⋊Dic11—41no—
209C22⋊Dic11—41no—
210C22⋊Dic11—41no—
211C22⋊Dic11—41no—
212C22⋊Dic11—41no—
213C22⋊Dic11—41no—
214C22⋊Dic11—41no—
215C22⋊Dic11—41no—
216C4⋊Dic11—22no—
217C4⋊Dic11—22no—
218C4⋊Dic11—41no—
219C4⋊Dic11—41no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228#4318—44no—
229#4318—44no—
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—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8C2×D412yes—
241C2×C11⋊C8C2×D412yes—
242C2×#433—111no—
243C2×#407—111no—
244#2280—111no—
245#1924—111no—
246#1924—111no—
247#1923—111no—
248#1923—111no—
249#1851—111no—
250#1851—111no—
251#1818—111no—
252#1798—111no—
253#1779D1111yescharacteristic
254#1753—111no—
255#1753—111no—
256#1750—111no—
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—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11#11712yes—
283C23×C11C4×D412yes—
284C23×C11#13112yes—
285C23×C11C23×C411yescharacteristic
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
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—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—44no—
302C2×C4×C11—44no—
303C2×C4×C11—44no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11#11712yes—
309C2×C4×C11C4×D412yes—
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C8×C11—41no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C24×C4C2×D1111yescharacteristic
349C22×M16—111no—
350C22×M16—111no—
351C2×#117—111no—
352C2×#117—111no—
353#433—224no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8—111no—
356C2×C4⋊C8—111no—
357C2×C4⋊C8—111no—
358#407—224no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C22⋊C8C2×D1111yescharacteristic
364C2×C22⋊C8C2×D1111yescharacteristic
365C2×C22⋊C8C2×D1111yescharacteristic
366C2×C22⋊C8C2×D1111yescharacteristic
367C2×C22⋊C8C2×D1111yescharacteristic
368C2×C22⋊C8C2×D1111yescharacteristic
369C2×#97—111no—
370C2×#97—111no—
371C2×C4×C8—111no—
372C2×C4×C8—111no—
373#381—111no—
374#381—111no—
375#380—111no—
376#380—111no—
377#380—111no—
378#380—111no—
379#379—111no—
380#379—111no—
381C4×C22⋊C4—111no—
382C4×C22⋊C4—111no—
383C4×C22⋊C4—111no—
384C4×C22⋊C4—111no—
385#336—111no—
386#336—111no—
387#336—111no—
388#336—111no—
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—416no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11C2×#11711yescharacteristic
416C22×C11C2×C4×D411yescharacteristic
417C22×C11#51811yescharacteristic
418C22×C11C2×#13111yescharacteristic
419C22×C11#56811yescharacteristic
420C22×C11#56811yescharacteristic
421C22×C11#56811yescharacteristic
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—41no—
425C4×C11#54611yescharacteristic
426C4×C11#54611yescharacteristic
427C4×C11#55111yescharacteristic
428C4×C11#55111yescharacteristic
429Dic11—41no—
430Dic11—41no—
431Dic11—41no—
432Dic11—41no—
433Dic11—41no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437C25C4×D1111yescharacteristic
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—41no—
443C23×C4—41no—
444C23×C4C4×D1111yescharacteristic
445C23×C4C4×D1111yescharacteristic
446C23×C4C4×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C2×M16—222no—
451C2×M16—222no—
452C2×M16—222no—
453C2×M16—222no—
454C2×M16—441no—
455C2×M16—441no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1111yescharacteristic
464#117—222no—
465#117—222no—
466#117—441no—
467#117—441no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C22⋊C4—111no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—111no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
484C2×C42—111no—
485C2×C42—111no—
486C2×C42—111no—
487C2×C42—111no—
488C4⋊C8—222no—
489C4⋊C8—222no—
490C4⋊C8—441no—
491C4⋊C8—441no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8—41no—
497C22⋊C8—41no—
498C22⋊C8—114no—
499C22⋊C8—222no—
500C22⋊C8—222no—
501C22⋊C8—222no—
502#97—222no—
503#97—441no—
504C4×C8—222no—
505C4×C8—441no—
506#95—111no—
507#95—111no—
508#95—111no—
509#95—111no—
510#95—111no—
511#95—111no—
512#95—111no—
513#95—111no—
514C2×C11—42no—
515C2×C11—42no—
516C2×C11—42no—
517C2×C11#234211yescharacteristic
518C2×C11#292111yescharacteristic
519C2×C11#292411yescharacteristic
520C2×C11#293011yescharacteristic
521C2×C11#293311yescharacteristic
522C2×C11#297611yescharacteristic
523C2×C11#297811yescharacteristic
524C24—22no—
525C24—22no—
526C24—22no—
527C24—41no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24C2×C4×D1111yescharacteristic
532C24C2×C4×D1111yescharacteristic
533C24C2×C4×D1111yescharacteristic
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—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—111no—
565C22×C4—111no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—111no—
569C22×C4C2×C4×D1111yescharacteristic
570C22×C4C2×C4×D1111yescharacteristic
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4D4×D1112yes—
573C22×C4#434112yes—
574C22×C4#434112yes—
575C22×C4#434112yes—
576C22×C4C23×D1111yescharacteristic
577M16—444no—
578M16—444no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—112no—
592C2×C8—112no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C4⋊C4—222no—
604C4⋊C4—222no—
605C4⋊C4—441no—
606C4⋊C4—441no—
607C22⋊C4—222no—
608C22⋊C4—222no—
609C22⋊C4—222no—
610C22⋊C4—222no—
611C22⋊C4—441no—
612C22⋊C4—441no—
613C22⋊C4—441no—
614C22⋊C4—441no—
615C22⋊C4—441no—
616C22⋊C4—441no—
617C22⋊C4—441no—
618C22⋊C4—441no—
619C42—221no—
620C42—221no—
621C42—221no—
622C42—221no—
623C42—221no—
624C42—221no—
625C42—221no—
626C42—221no—
627C11#2255911yescharacteristic, complemented, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#6693012yes—
654C23(C22⋊D11)⋊C412yes—
655C23#6695412yes—
656C23C22×C4×D1111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—221no—
698C2×C4—221no—
699C2×C4—221no—
700C2×C4—221no—
701C2×C4—221no—
702C2×C4—221no—
703C2×C4#6693012yes—
704C2×C4(C22⋊D11)⋊C412yes—
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4C2×#434111yescharacteristic
707C2×C4C2×#434111yescharacteristic
708C2×C4C2×#434111yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4#6703711yescharacteristic
711C8—41no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—222no—
716C8—222no—
717C8—441no—
718C8—441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—416no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22C2×#6693011yescharacteristic
742C22C2×(C22⋊D11)⋊C411yescharacteristic
743C22#1062301711yescharacteristic
744C22C2×#6695411yescharacteristic
745C22#1062327611yescharacteristic
746C22#1062327611yescharacteristic
747C22#1062327611yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—441no—
752C4—441no—
753C4—441no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4—441no—
758C4—441no—
759C4#1062311811yescharacteristic
760C4#1062311811yescharacteristic
761C4#1062312211yescharacteristic
762C4#1062312211yescharacteristic
763C2—42no—
764C2—42no—
765C2—42no—
766C2#1307146711yescharacteristic
767C2#1307725111yescharacteristic
768C2#1307727011yescharacteristic
769C2#1307731511yescharacteristic
770C2#1307733711yescharacteristic
771C2#1307766111yescharacteristic
772C2#1307767611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1779C2
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1779D11
hypocenterC11#22559
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
1. C2×#10622333C2semidirect
4. #13069232C2semidirect
5. #13069226C2semidirect
6. #13069225C2semidirect
7. #13069219C2semidirect
8. #13068798C2semidirect
9. #13068798C2semidirect
10. #13068685C2semidirect
11. #13068598C2semidirect
12. #13068402C2semidirect
13. #13068402C2semidirect
14. #13068384C2semidirect
44. C2×#66879C22semidirect
45. C2×#66879C22semidirect
46. C2×Dic11⋊C8C22semidirect
47. C2×Dic11⋊C8C22semidirect
48. C2×Dic11⋊C8C22semidirect
49. C2×Dic11⋊C8C22semidirect
50. C2×C8×Dic11C22semidirect
51. C2×C8×Dic11C22semidirect
53. #10622188C22semidirect
54. #10622188C22semidirect
55. #10622188C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622188C22semidirect
627. C11#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#106223332
C2×#106228202
#130709992
#130692322
#130692262
#130692252
#130692192
#130687982
#130686852
#130685982
#130684022
#130683842
C11×#17792
#2255911