Finite Group Databasebeta

← #14759809

Subgroups — #14759809

Order 2816.

1110 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×#10622341C211yesmaximal, characteristic, complemented
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×M16×Dic11C211yesmaximal, characteristic, complemented
5C4×#66992C211yesmaximal, characteristic
6#13069408C211yesmaximal, characteristic, complemented
7#13069333C211yesmaximal, characteristic, complemented
8#13069230C211yesmaximal, characteristic, complemented
9#13069226C211yesmaximal, characteristic, complemented
10#13068913C211yesmaximal, characteristic, complemented
11#13068594C211yesmaximal, characteristic, complemented
12#13068482C211yesmaximal, characteristic, complemented
13#13068395C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66992C411yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28#10622833C411yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32M16×Dic11—24no—
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622624—24no—
45#10622603C411yescharacteristic
46#10622585C411yescharacteristic
47#10622571C411yescharacteristic
48#10622570C411yescharacteristic
49#10622558C411yescharacteristic
50#10622555C411yescharacteristic
51C4×(C2×D11)⋊C4C2211yescharacteristic
52C4×Dic11⋊C4C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55#10622341—24no—
56(C22⋊D11)⋊C8—24no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88#66992—24no—
89C4×C22⋊D11—22no—
90C4×C22⋊D11—22no—
91C4×C22⋊D11—22no—
92C4×C22⋊D11—22no—
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×Dic11⋊C4C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11C2×C411yescharacteristic
104C2×C4×Dic11C2×C411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×#4318—22no—
109C2×#4318—22no—
110C2×#4318D414yescomplemented
111C22×C11⋊C8—22no—
112C22×C11⋊C8—22no—
113C22×C11⋊C8—22no—
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—22no—
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#66879—22no—
136#66879—22no—
137#66879—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142C8×Dic11D414yescomplemented
143C4⋊(C11⋊C8)—22no—
144#66867—22no—
145#21486—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—41no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4112yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—22no—
173C2×C22⋊D11—41no—
174C2×C22⋊D11M1614yescomplemented
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—41no—
180C22×Dic11—41no—
181C22×Dic11C22×C411yescharacteristic
182C22×Dic11C22×C411yescharacteristic
183C22×Dic11C22×C411yescharacteristic
184C22×Dic11C22×C411yescharacteristic
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C411yescharacteristic
187C22×Dic11C22×C411yescharacteristic
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C11×M16—28no—
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—21no—
205C2×C8×C11C2×D412yes—
206C2×C8×C11#4112yes—
207C11×C4⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C42×C11—21no—
211C42×C11—21no—
212C22⋊Dic11—22no—
213C22⋊Dic11—22no—
214C22⋊Dic11—22no—
215C22⋊Dic11—41no—
216(C2×D11)⋊C4—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—22no—
219(C2×D11)⋊C4—41no—
220Dic11⋊C4—22no—
221Dic11⋊C4—22no—
222Dic11⋊C4—22no—
223Dic11⋊C4—22no—
224C4×Dic11—22no—
225C4×Dic11—22no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11C2×D412yes—
231C4×Dic11#4112yes—
232#4318—28no—
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—44no—
242C2×C11⋊C8C2×D412yes—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245C2×C11⋊C8#4112yes—
246C8×D11—44no—
247C2×#435—111no—
248C2×#435—111no—
249C2×C8×D4—111no—
250C2×C4×M16—111no—
251C4×#121—111no—
252#1954—111no—
253#1939—111no—
254#1924—111no—
255#1924—111no—
256#1870—111no—
257#1870D1111yescharacteristic, complemented
258#1797—111no—
259#1770—111no—
260#1752—111no—
261#1752—111no—
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×C11C4×D412yes—
275C23×C11C2×M1612yes—
276C23×C11C23×C411yescharacteristic
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11C2×M1612yes—
284D4×C11—44no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
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—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11C4×D412yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C22⋊D11—28no—
312C22⋊D11—44no—
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—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—44no—
331C2×Dic11—44no—
332C2×Dic11C4×D412yes—
333C2×Dic11C4×D412yes—
334C2×Dic11C2×M1612yes—
335C2×Dic11#13112yes—
336C4×D11—41no—
337C4×D11—41no—
338C4×D11—41no—
339C4×D11—41no—
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—22no—
345C11⋊C8—41no—
346C11⋊C8—41no—
347C11⋊C8#12114yescomplemented
348C22×M16—111no—
349C22×M16C2×D1111yescharacteristic
350C23×C8—111no—
351C23×C8—111no—
352C2×#121—111no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4C2×D1111yescharacteristic
356C22×C42—111no—
357#435—224no—
358#435—224no—
359C8×D4—224no—
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8—111no—
366C2×C22⋊C8—111no—
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8C2×D1111yescharacteristic
370C2×C22⋊C8C2×D1111yescharacteristic
371C2×C22⋊C8C2×D1111yescharacteristic
372C4×M16—224no—
373C2×#97—111no—
374C2×#97—111no—
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⋊C4—111no—
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—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11C2×C4×D411yescharacteristic
410C22×C11C2×C4×D411yescharacteristic
411C22×C11C4×#4111yescharacteristic
412C22×C11C22×M1611yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11#56811yescharacteristic
415C22×C11#56811yescharacteristic
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
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×C11C2×#12111yescharacteristic
428C4×C11#52511yescharacteristic
429C4×C11#52911yescharacteristic
430C4×C11#53211yescharacteristic
431Dic11—22no—
432Dic11—41no—
433Dic11—41no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437Dic11#43514yescomplemented
438C22×D4—111no—
439C22×D4—111no—
440C22×D4C4×D1111yescharacteristic
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—114no—
450C2×M16—222no—
451C2×M16—222no—
452C22×C8—111no—
453C22×C8—111no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8—222no—
457C22×C8—222no—
458C22×C8—222no—
459C22×C8—222no—
460C22×C8—222no—
461C22×C8—222no—
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1111yescharacteristic
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466#121—224no—
467C4×D4—22no—
468C4×D4—22no—
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⋊C4C4×D1111yescharacteristic
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—111no—
493C2×C42—222no—
494C2×C42—222no—
495C2×C42C22×D1111yescharacteristic
496C4⋊C8—222no—
497C4⋊C8—222no—
498C4⋊C8—222no—
499C4⋊C8—222no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503C22⋊C8—222no—
504C22⋊C8—222no—
505C22⋊C8—222no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508#97—222no—
509#97—222no—
510#97—222no—
511#97—222no—
512C4×C8—114no—
513C4×C8—222no—
514#95—111no—
515#95—111no—
516#95—111no—
517#95—111no—
518#95—111no—
519#95—111no—
520C2×C11—42no—
521C2×C11—42no—
522C2×C11C4×#12111yescharacteristic
523C2×C11C2×#43511yescharacteristic
524C2×C11#293011yescharacteristic
525C2×C11D4×M1611yescharacteristic
526C2×C11#293511yescharacteristic
527C2×C11#296911yescharacteristic
528C2×C11#297011yescharacteristic
529D11—42no—
530C24—111no—
531C24C2×C4×D1111yescharacteristic
532C24C2×C4×D1111yescharacteristic
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C2×D4—114no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—222no—
540C2×D4—222no—
541C2×D4—441no—
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—21no—
551C22×C4—21no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—441no—
570C22×C4—441no—
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4D4×D1112yes—
576C22×C4#434112yes—
577C22×C4C23×D1111yescharacteristic
578M16—28no—
579M16—228no—
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—112no—
592C2×C8—112no—
593C2×C8—112no—
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—444no—
603C2×C8—444no—
604C2×C8D4×D1112yes—
605C2×C8#434112yes—
606C4⋊C4—22no—
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—441no—
620C22⋊C4—441no—
621C42—21no—
622C42—21no—
623C42—112no—
624C42—112no—
625C42—222no—
626C42—222no—
627C42—221no—
628C42—221no—
629C42—221no—
630C42—221no—
631C11#2148611yescharacteristic, complemented, Sylow
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—112no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23(C22⋊D11)⋊C412yes—
652C23M16×D1112yes—
653C23C22×C4×D1111yescharacteristic
654D4—44no—
655D4—228no—
656D4—444no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
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—112no—
679C2×C4—112no—
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—444no—
698C2×C4—444no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4(C22⋊D11)⋊C412yes—
704C2×C4C2×D4×D1111yescharacteristic
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4C2×#434111yescharacteristic
707C2×C4C2×#434111yescharacteristic
708C2×C4#41×D1111yescharacteristic
709C2×C4#41×D1111yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—114no—
715C8—222no—
716C8—441no—
717C8—441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—222no—
733C22—222no—
734C22—222no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—441no—
739C22C2×(C22⋊D11)⋊C411yescharacteristic
740C22C4×#434111yescharacteristic
741C22C4×D4×D1111yescharacteristic
742C22C2×M16×D1111yescharacteristic
743C22#1062327611yescharacteristic
744C22D11×#13111yescharacteristic
745C22#1062328111yescharacteristic
746C4—22no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—114no—
751C4—222no—
752C4—441no—
753C4—441no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4#1062311711yescharacteristic
758C4#1062312711yescharacteristic
759C4D11×#12111yescharacteristic
760C4#1062318011yescharacteristic
761C2—42no—
762C2—42no—
763C2—442no—
764C2#1307112611yescharacteristic
765C2D11×#43511yescharacteristic
766C2#1307731611yescharacteristic
767C2#1307734811yescharacteristic
768C2#1307735611yescharacteristic
769C2#1307761511yescharacteristic
770C2#1307762611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC2×#66992C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#21486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#10622341C2semidirect
2. C2×#10622624C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
4. C2×M16×Dic11C2semidirect
6. #13069408C2semidirect
7. #13069333C2semidirect
8. #13069230C2semidirect
9. #13069226C2semidirect
10. #13068913C2semidirect
11. #13068594C2semidirect
12. #13068482C2semidirect
13. #13068395C2semidirect
14. #13068391C2semidirect
15. C11×#1870C2semidirect
110. C2×#4318D4semidirect
142. C8×Dic11D4semidirect
174. C2×C22⋊D11M16semidirect
257. #1870D11semidirect
347. C11⋊C8#121semidirect
437. Dic11#435semidirect
631. C11#21486semidirect

Maximal subgroups

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

subgroupindex
C2×#106223412
C2×#106226242
C2×(C22⋊D11)⋊C82
C2×M16×Dic112
C4×#669922
#130694082
#130693332
#130692302
#130692262
#130689132
#130685942
#130684822
#130683952
#130683912
C11×#18702
#2148611