Finite Group Databasebeta

← #14770788

Subgroups — #14770788

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×#10622453C211yesmaximal, characteristic, complemented
2C2×#10622339C211yesmaximal, characteristic
3#13070997C211yesmaximal, characteristic
4#13069232C211yesmaximal, characteristic, complemented
5#13069224C211yesmaximal, characteristic, complemented
6#13069219C211yesmaximal, characteristic, complemented
7#13068800C211yesmaximal, characteristic, complemented
8#13068797C211yesmaximal, characteristic, complemented
9#13068686C211yesmaximal, characteristic, complemented
10#13068599C211yesmaximal, characteristic, complemented
11#13068525C211yesmaximal, characteristic
12#13068401C211yesmaximal, characteristic, complemented
13#13068396C211yesmaximal, characteristic, complemented
14#13068385C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66925C2211yescharacteristic
20C2×#66925C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic, complemented
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic, complemented
25C4×C11×C22⋊C4C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66879C2211yescharacteristic, complemented
36C2×Dic11⋊C8C2211yescharacteristic, complemented
37C2×Dic11⋊C8C2211yescharacteristic, complemented
38C2×C8×Dic11C2211yescharacteristic, complemented
39#10622568C411yescharacteristic
40#10622568C411yescharacteristic
41#10622555C411yescharacteristic
42#10622555C411yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
46C2×C4×C11⋊C8C2211yescharacteristic, complemented
47#10622453—24no—
48#10622339—24no—
49#10622280C411yescharacteristic
50#10622280C411yescharacteristic
51#10622277C411yescharacteristic
52#10622277C411yescharacteristic
53C11×#336C2211yescharacteristic, complemented
54C11×#336C2211yescharacteristic, complemented
55#10622188C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C24×D11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2×C411yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11—22no—
68C22×C4×D11—41no—
69C22×C4×D11—41no—
70C22×C4×D11C2×C411yescharacteristic
71C22×C4×D11C2×C411yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×(C2×D11)⋊C4C2×C411yescharacteristic
85C2×(C2×D11)⋊C4C2×C411yescharacteristic
86C2×(C2×D11)⋊C4C2×C411yescharacteristic
87C2×(C2×D11)⋊C4C2×C411yescharacteristic
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×Dic11⋊C4C2×C411yescharacteristic
93C2×Dic11⋊C4C2×C411yescharacteristic
94C2×Dic11⋊C4C2×C411yescharacteristic
95C2×Dic11⋊C4C2×C411yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C2×#4313—22no—
103C2×#4313—22no—
104C2×#4313—22no—
105C2×#4313—22no—
106C2×#4313—41no—
107C2×#4313—41no—
108#66925—22no—
109#66925—22no—
110#66925—41no—
111#66925—41no—
112C11×C4⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—41no—
115C11×#97—41no—
116C11×#95C2×C411yescharacteristic
117C11×#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C11⋊#95C2×C411yescharacteristic
122C11⋊#95C2×C411yescharacteristic
123C11⋊#95C2×C411yescharacteristic
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—41no—
126(C2×D11)⋊C8—22no—
127(C2×D11)⋊C8—22no—
128(C2×D11)⋊C8—22no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8D414yes—
132#66879—22no—
133Dic11⋊C8—41no—
134Dic11⋊C8—41no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—22no—
137C4×C11⋊C8—41no—
138#22559—111nomaximal, Sylow
139C24×C11C22×C411yescharacteristic
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—41no—
144C23×D11—41no—
145C23×D11—41no—
146C23×D11—41no—
147C23×D11C22×C411yescharacteristic
148C23×D11C22×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×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—41no—
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—41no—
183C2×C4×D11—41no—
184C2×C4×D11—44no—
185C2×C4×D11—44no—
186C2×C4×D11—44no—
187C2×C4×D11—44no—
188C2×C4×D11C2×D412yes—
189C2×C4×D11#4112yes—
190C2×C4×D11#4112yes—
191C2×C4×D11#4112yes—
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×C11C2×D412yes—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—41no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C22⋊Dic11—22no—
211C22⋊Dic11—41no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—22no—
214(C2×D11)⋊C4—41no—
215(C2×D11)⋊C4—41no—
216(C2×D11)⋊C4—41no—
217(C2×D11)⋊C4—41no—
218(C2×D11)⋊C4—41no—
219(C2×D11)⋊C4—41no—
220Dic11⋊C4—22no—
221Dic11⋊C4—22no—
222Dic11⋊C4—41no—
223Dic11⋊C4—41no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—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—21no—
239C2×C11⋊C8C2×D412yes—
240#4313—44no—
241#4313—44no—
242C2×#433—111no—
243C2×#407—111no—
244#2280—111no—
245#1924—111no—
246#1924D1111yescharacteristic, complemented
247#1923—111no—
248#1923—111no—
249#1851—111no—
250#1851—111no—
251#1818—111no—
252#1798—111no—
253#1779—111no—
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#13112yes—
264C23×C11C23×C411yescharacteristic
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—44no—
278C22×D11—44no—
279C22×D11—44no—
280C22×D11—44no—
281C22×D11—44no—
282C22×D11—44no—
283C22×D11—44no—
284C22×D11#11712yes—
285C22×D11C4×D412yes—
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—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
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—44no—
328C2×Dic11#11712yes—
329C2×Dic11C4×D412yes—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—22no—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—22no—
338C4×D11—44no—
339C4×D11—44no—
340C8×C11—22no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—22no—
345C11⋊C8—41no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C24×C4—111no—
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⋊C8C2×D1111yescharacteristic, complemented
358#407—224no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8—111no—
366C2×C22⋊C8—111no—
367C2×C22⋊C8C2×D1111yescharacteristic
368C2×C22⋊C8C2×D1111yescharacteristic
369C2×#97—111no—
370C2×#97C2×D1111yescharacteristic, complemented
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⋊C4C2×D1111yescharacteristic
385#336—111no—
386#336—111no—
387#336—111no—
388#336—111no—
389#336—111no—
390#336—111no—
391#336C2×D1111yescharacteristic, complemented
392#336C2×D1111yescharacteristic, complemented
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11C2×#11711yescharacteristic
401C22×C11C2×C4×D411yescharacteristic
402C22×C11#51811yescharacteristic
403C22×C11C2×#13111yescharacteristic
404C22×C11#56811yescharacteristic
405C22×C11#56811yescharacteristic
406C22×C11#56811yescharacteristic
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—416no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11—41no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C4×C11—41no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11#54611yescharacteristic
428C4×C11#54611yescharacteristic
429C4×C11#55111yescharacteristic
430C4×C11#55111yescharacteristic
431Dic11—22no—
432Dic11—22no—
433Dic11—41no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437C25—111no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—222no—
444C23×C4—222no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—441no—
448C23×C4—441no—
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⋊C4C4×D1111yescharacteristic
483C2×C22⋊C4C4×D1111yescharacteristic
484C2×C42—111no—
485C2×C42—111no—
486C2×C42C22×D1111yescharacteristic
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—222no—
490C4⋊C8—441no—
491C4⋊C8—441no—
492C22⋊C8—22no—
493C22⋊C8—41no—
494C22⋊C8—114no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500C22⋊C8—222no—
501C22⋊C8—441no—
502#97—41no—
503#97—222no—
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#95C4×D1111yescharacteristic
513#95C4×D1111yescharacteristic
514C2×C11—42no—
515C2×C11#234211yescharacteristic
516C2×C11#292111yescharacteristic
517C2×C11#292411yescharacteristic
518C2×C11#293011yescharacteristic
519C2×C11#293311yescharacteristic
520C2×C11#297611yescharacteristic
521C2×C11#297811yescharacteristic
522D11—42no—
523D11—42no—
524C24—111no—
525C24—111no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24—441no—
530C24—441no—
531C24—441no—
532C24—441no—
533C24C2×C4×D1111yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—111no—
541C22×C4—111no—
542C22×C4—112no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—112no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—111no—
549C22×C4—111no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—441no—
565C22×C4—441no—
566C22×C4—444no—
567C22×C4—444no—
568C22×C4—444no—
569C22×C4—444no—
570C22×C4—441no—
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4C2×C4×D1111yescharacteristic
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—112no—
591C2×C8—221no—
592C2×C8—221no—
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×C8D4×D1112yes—
603C4⋊C4—222no—
604C4⋊C4—222no—
605C4⋊C4—441no—
606C4⋊C4—441no—
607C22⋊C4—22no—
608C22⋊C4—41no—
609C22⋊C4—222no—
610C22⋊C4—222no—
611C22⋊C4—222no—
612C22⋊C4—441no—
613C22⋊C4—441no—
614C22⋊C4—441no—
615C22⋊C4—441no—
616C22⋊C4—441no—
617C22⋊C4—441no—
618C22⋊C4—441no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
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—112no—
635C23—112no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—444no—
649C23—444no—
650C23—444no—
651C23—444no—
652C23—444no—
653C23—444no—
654C23—444no—
655C23#6696012yes—
656C23C22×C4×D1111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
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—444no—
703C2×C4—444no—
704C2×C4—444no—
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4#6703711yescharacteristic
707C2×C4#41×D1111yescharacteristic
708C2×C4#41×D1111yescharacteristic
709C2×C4#41×D1111yescharacteristic
710C2×C4#6704211yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—222no—
716C8—441no—
717C8—441no—
718C8—441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—222no—
727C22—222no—
728C22—222no—
729C22—222no—
730C22—222no—
731C22—222no—
732C22—4416no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—441no—
739C22—441no—
740C22—441no—
741C22D11×#11711yescharacteristic
742C22C4×D4×D1111yescharacteristic
743C22#1062307611yescharacteristic
744C22C2×#6696011yescharacteristic
745C22#1062327611yescharacteristic
746C22#1062328111yescharacteristic
747C22#1062328111yescharacteristic
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—222no—
754C4—222no—
755C4—441no—
756C4—441no—
757C4—441no—
758C4—441no—
759C4#1062314111yescharacteristic
760C4#1062319011yescharacteristic
761C4#1062320711yescharacteristic
762C4#1062323611yescharacteristic
763C2—42no—
764C2—442no—
765C2—442no—
766C2#1307146411yescharacteristic
767C2#1307725011yescharacteristic
768C2#1307727511yescharacteristic
769C2#1307731411yescharacteristic
770C2#1307734211yescharacteristic
771C2#1307766511yescharacteristic
772C2#1307767311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1924C2
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1924D11
hypocenterC11#22559
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#10622453C2semidirect
4. #13069232C2semidirect
5. #13069224C2semidirect
6. #13069219C2semidirect
7. #13068800C2semidirect
8. #13068797C2semidirect
9. #13068686C2semidirect
10. #13068599C2semidirect
12. #13068401C2semidirect
13. #13068396C2semidirect
14. #13068385C2semidirect
15. C11×#1924C2semidirect
21. C2×C11×C4⋊C8C22semidirect
24. C2×C11×#97C22semidirect
35. C2×#66879C22semidirect
36. C2×Dic11⋊C8C22semidirect
37. C2×Dic11⋊C8C22semidirect
38. C2×C8×Dic11C22semidirect
45. C2×C4⋊(C11⋊C8)C22semidirect
46. C2×C4×C11⋊C8C22semidirect
53. C11×#336C22semidirect
54. C11×#336C22semidirect
55. #10622188C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
246. #1924D11semidirect
357. C2×C4⋊C8C2×D11semidirect
370. C2×#97C2×D11semidirect
391. #336C2×D11semidirect
392. #336C2×D11semidirect
627. C11#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#106224532
C2×#106223392
#130709972
#130692322
#130692242
#130692192
#130688002
#130687972
#130686862
#130685992
#130685252
#130684012
#130683962
#130683852
C11×#19242
#2255911