Finite Group Databasebeta

← #14775891

Subgroups — #14775891

Order 2816.

1084 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622724C211yesmaximal, characteristic, complemented
2C2×#10622449C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
4C2×#10622450C211yesmaximal, characteristic, complemented
5C4×#66937C211yesmaximal, characteristic
6#13069408C211yesmaximal, characteristic, complemented
7#13069331C211yesmaximal, characteristic, complemented
8#13069231C211yesmaximal, characteristic, complemented
9#13069228C211yesmaximal, characteristic, complemented
10#13068912C211yesmaximal, characteristic, complemented
11#13068910C211yesmaximal, characteristic, complemented
12#13068795C211yesmaximal, characteristic, complemented
13#13068482C211yesmaximal, characteristic, complemented
14#13068373C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×#66937C411yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622724—24no—
32C8×C22⋊D11—24no—
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622570C411yescharacteristic
45#10622569C411yescharacteristic
46#10622564C411yescharacteristic
47C4×(C2×D11)⋊C4C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622450—24no—
52#10622449—24no—
53#10622282C411yescharacteristic
54#10622280C411yescharacteristic
55#10622278C411yescharacteristic
56#10622260C411yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2×C411yescharacteristic
68C22×C4×D11C2×C411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—41no—
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
84C4×C22⋊D11—22no—
85C4×C22⋊D11—22no—
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×C4⋊Dic11C2×C411yescharacteristic
95C2×Dic11⋊C4C2×C411yescharacteristic
96C2×Dic11⋊C4C2×C411yescharacteristic
97C2×Dic11⋊C4C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×C4×Dic11C2×C411yescharacteristic
100C2×C4×Dic11C2×C411yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C2×#4313—22no—
108C2×#4313—22no—
109C2×#4313—22no—
110C2×#4313—22no—
111C2×#4313—41no—
112C2×#4313—41no—
113C2×C8×D11—22no—
114C2×C8×D11—22no—
115C2×C8×D11—41no—
116#66937—24no—
117C4×D44—22no—
118C4×D44—22no—
119C42×D11—22no—
120C42×D11—22no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C22⋊C8—41no—
124C11×#95C2×C411yescharacteristic
125C11×#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—41no—
136(C2×D11)⋊C8D414yescomplemented
137#66879—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8D414yescomplemented
141C8×Dic11—22no—
142C8×Dic11—22no—
143C4⋊(C11⋊C8)—22no—
144#66867—22no—
145#22986—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
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
161C2×C22⋊D11—22no—
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C2×C22⋊D11—41no—
166C2×C22⋊D11M1614yescomplemented
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C22×Dic11C22×C411yescharacteristic
173C2×D44—22no—
174C2×D44—22no—
175C2×D44—41no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—22no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—41no—
192C2×C4×D11C2×D412yes—
193C2×C4×D11#4112yes—
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—
204C2×C8×C11—44no—
205C2×C8×C11C2×D412yes—
206C2×C8×C11C2×D412yes—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C22⋊Dic11—22no—
214C22⋊Dic11—22no—
215(C2×D11)⋊C4—22no—
216(C2×D11)⋊C4—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—22no—
219(C2×D11)⋊C4—22no—
220(C2×D11)⋊C4—22no—
221C4⋊Dic11—22no—
222Dic11⋊C4—22no—
223Dic11⋊C4—22no—
224Dic11⋊C4—22no—
225Dic11⋊C4—22no—
226C4×Dic11—22no—
227C4×Dic11—22no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11C2×D412yes—
231C4×Dic11#4112yes—
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⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8C2×D412yes—
243C2×C11⋊C8C2×D412yes—
244#4313—44no—
245#4313—44no—
246C8×D11—44no—
247C2×#435—111no—
248C2×#435—111no—
249C2×C8×D4—111no—
250C2×#423—111no—
251C4×#121—111no—
252#1954—111no—
253#1939—111no—
254#1924—111no—
255#1924—111no—
256#1870—111no—
257#1870—111no—
258#1850—111no—
259#1850D1111yescharacteristic, complemented
260#1770—111no—
261C4×C22⋊C8—111no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11C2×M1612yes—
269C23×C11C23×C411yescharacteristic
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11C4×D412yes—
283C22×D11C2×M1612yes—
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—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11#13112yes—
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11H(5,𝔽2)11yescharacteristic
308C2×C4×C112−1+411yescharacteristic
309C22⋊D11—28no—
310C22⋊D11—44no—
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×Dic11C4×D412yes—
325C2×Dic11C4×D412yes—
326C2×Dic11C4×D412yes—
327C2×Dic11C2×M1612yes—
328C2×Dic11#13112yes—
329D44—44no—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—44no—
335C4×D11—41no—
336C4×D11—41no—
337C4×D11—41no—
338C4×D11—41no—
339C4×D11—44no—
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C22×M16—111no—
349C22×M16—111no—
350C23×C8—111no—
351C23×C8C2×D1111yescharacteristic
352C2×#121—111no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4—111no—
356C22×C42—111no—
357#435—224no—
358#435—224no—
359C8×D4—224no—
360#423—224no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8C2×D1111yescharacteristic
366C2×C4⋊C8C2×D1111yescharacteristic
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373C2×C22⋊C8—111no—
374C2×C22⋊C8C2×D1111yescharacteristic
375C2×#97—111no—
376C2×#97—111no—
377C2×C4×C8—111no—
378C2×C4×C8—111no—
379#390—111no—
380#389—111no—
381#388—111no—
382#388—111no—
383#386—111no—
384#386—111no—
385#380—111no—
386C4×C4⋊C4—111no—
387C4×C22⋊C4—111no—
388C4×C22⋊C4C2×D1111yescharacteristic
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
393#336C2×D1111yescharacteristic
394#336C2×D1111yescharacteristic
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11C2×C4×D411yescharacteristic
403C22×C11C2×C4×D411yescharacteristic
404C22×C11#52011yescharacteristic
405C22×C11C22×M1611yescharacteristic
406C22×C11C2×#13111yescharacteristic
407C22×C11C2×#13111yescharacteristic
408C22×C11#56811yescharacteristic
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—22no—
415C2×D11—41no—
416C2×D11—41no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C2×D11—41no—
423C4×C11—22no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11D4211yescharacteristic
429C4×C11#54711yescharacteristic
430C4×C11#54811yescharacteristic
431C4×C11#55311yescharacteristic
432Dic11—22no—
433Dic11—22no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437Dic11#43514yescomplemented
438C22×D4—111no—
439C22×D4—111no—
440C22×D4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4C22×D1111yescharacteristic
446C2×M16—222no—
447C2×M16—222no—
448C2×M16—222no—
449C2×M16—222no—
450C2×M16—441no—
451C2×M16—441no—
452C22×C8—22no—
453C22×C8—22no—
454C22×C8—41no—
455C22×C8—111no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—222no—
460C22×C8—222no—
461C22×C8—441no—
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1111yescharacteristic
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466#121—224no—
467C4×D4—222no—
468C4×D4—222no—
469C4×D4—222no—
470C4×D4—222no—
471C4×D4—222no—
472C4×D4—222no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊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×C22⋊C4—111no—
485C2×C22⋊C4—111no—
486C2×C22⋊C4C4×D1111yescharacteristic
487C2×C22⋊C4C4×D1111yescharacteristic
488C2×C42—111no—
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—111no—
492C2×C42—222no—
493C2×C42—222no—
494C2×C42C22×D1111yescharacteristic
495C2×C42C22×D1111yescharacteristic
496C4⋊C8—22no—
497C4⋊C8—22no—
498C4⋊C8—114no—
499C4⋊C8—222no—
500C4⋊C8—222no—
501C4⋊C8—222no—
502C22⋊C8—41no—
503C22⋊C8—114no—
504C22⋊C8—222no—
505C22⋊C8—222no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508C22⋊C8—222no—
509C22⋊C8—441no—
510#97—222no—
511#97—222no—
512C4×C8—222no—
513C4×C8—222no—
514#95—111no—
515#95—111no—
516#95—111no—
517#95—111no—
518#95C4×D1111yescharacteristic
519#95C4×D1111yescharacteristic
520C2×C11—42no—
521C2×C11#236111yescharacteristic
522C2×C11C2×#43511yescharacteristic
523C2×C11#293111yescharacteristic
524C2×C11#293311yescharacteristic
525C2×C11D4×M1611yescharacteristic
526C2×C11#299011yescharacteristic
527C2×C11#299311yescharacteristic
528D11—42no—
529D11—42no—
530C24—111no—
531C24—111no—
532C24C2×C4×D1111yescharacteristic
533C2×D4—114no—
534C2×D4—222no—
535C2×D4—222no—
536C2×D4—222no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—222no—
540C2×D4—441no—
541C2×D4—441no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—111no—
549C22×C4—111no—
550C22×C4—111no—
551C22×C4—112no—
552C22×C4—112no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—222no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—441no—
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4C2×C4×D1111yescharacteristic
576C22×C4C2×C4×D1111yescharacteristic
577C22×C4C23×D1111yescharacteristic
578M16—444no—
579M16—444no—
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—44no—
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—
603C2×C8—444no—
604C2×C8D4×D1112yes—
605C2×C8D4×D1112yes—
606C4⋊C4—222no—
607C4⋊C4—222no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—222no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—222no—
616C22⋊C4—222no—
617C22⋊C4—222no—
618C22⋊C4—222no—
619C22⋊C4—222no—
620C22⋊C4—222no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—112no—
626C42—112no—
627C42—222no—
628C42—222no—
629C42—221no—
630C42—221no—
631C11#2298611yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—112no—
639C23—112no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23—221no—
652C23M16×D1112yes—
653C23C22×C4×D1111yescharacteristic
654D4—228no—
655D4—444no—
656D4—444no—
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—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
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—444no—
698C2×C4—444no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4#6695412yes—
704C2×C4C2×D4×D1111yescharacteristic
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4#6703711yescharacteristic
707C2×C4#6704011yescharacteristic
708C2×C4#41×D1111yescharacteristic
709C2×C4#41×D1111yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—222no—
715C8—222no—
716C8—441no—
717C8—441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—222no—
726C22—222no—
727C22—222no—
728C22—222no—
729C22—222no—
730C22—222no—
731C22—441no—
732C22—441no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—441no—
739C22#1062303511yescharacteristic
740C22C4×D4×D1111yescharacteristic
741C22C4×D4×D1111yescharacteristic
742C22C2×#6695411yescharacteristic
743C22C2×M16×D1111yescharacteristic
744C22D11×#13111yescharacteristic
745C22#1062328111yescharacteristic
746C4—22no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—114no—
752C4—222no—
753C4—222no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4#1062312111yescharacteristic
758C4#1062316211yescharacteristic
759C4#1062316411yescharacteristic
760C4#1062319211yescharacteristic
761C2—42no—
762C2—442no—
763C2—442no—
764C2#1307163511yescharacteristic
765C2D11×#43511yescharacteristic
766C2#1307732311yescharacteristic
767C2#1307733611yescharacteristic
768C2#1307734911yescharacteristic
769C2#1307773811yescharacteristic
770C2#1307776311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1850C2
prime radicalC2×#66937C4
cosocleC22×C4×C11C24
hypercenter#1850D11
hypocenterC11#22986
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#10622724C2semidirect
2. C2×#10622449C2semidirect
3. C2×C8×C22⋊D11C2semidirect
4. C2×#10622450C2semidirect
6. #13069408C2semidirect
7. #13069331C2semidirect
8. #13069231C2semidirect
9. #13069228C2semidirect
10. #13068912C2semidirect
11. #13068910C2semidirect
12. #13068795C2semidirect
13. #13068482C2semidirect
14. #13068373C2semidirect
15. C11×#1850C2semidirect
136. (C2×D11)⋊C8D4semidirect
140. Dic11⋊C8D4semidirect
166. C2×C22⋊D11M16semidirect
259. #1850D11semidirect
437. Dic11#435semidirect
631. C11#22986semidirect

Maximal subgroups

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

subgroupindex
C2×#106227242
C2×#106224492
C2×C8×C22⋊D112
C2×#106224502
C4×#669372
#130694082
#130693312
#130692312
#130692282
#130689122
#130689102
#130687952
#130684822
#130683732
C11×#18502
#2298611