Finite Group Databasebeta

← #14775897

Subgroups — #14775897

Order 2816.

1098 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×#10622319C211yesmaximal, characteristic, complemented
2C2×#10622343C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C4×#66983C211yesmaximal, characteristic
6#13069414C211yesmaximal, characteristic, complemented
7#13069339C211yesmaximal, characteristic, complemented
8#13069230C211yesmaximal, characteristic, complemented
9#13069223C211yesmaximal, characteristic, complemented
10#13068906C211yesmaximal, characteristic, complemented
11#13068906C211yesmaximal, characteristic, complemented
12#13068800C211yesmaximal, characteristic, complemented
13#13068795C211yesmaximal, characteristic, complemented
14#13068488C211yesmaximal, characteristic, complemented
15C11×#1749C211yesmaximal, characteristic, complemented
16C22×C42×C11C2211yescharacteristic
17C2×#66983C411yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29#10622826C411yescharacteristic
30#10622826C411yescharacteristic
31#10622825C411yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
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×C8×Dic11C2211yescharacteristic
42#10622553C411yescharacteristic
43#10622553C411yescharacteristic
44#10622552C411yescharacteristic
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622541C411yescharacteristic
49C2×C4⋊(C11⋊C8)—24no—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54#10622343—24no—
55(C22⋊D11)⋊C8—24no—
56#10622319—24no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63C23×C4×C11C2×C411yescharacteristic
64C23×C4×C11C2×C411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C22×D44C2×C411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C42×C11—22no—
76C2×C42×C11—22no—
77C2×C42×C11C2×C411yescharacteristic
78C2×C42×C11C2×C411yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83#66983—24no—
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×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×C4⋊Dic11C2×C411yescharacteristic
97C2×C4⋊Dic11C2×C411yescharacteristic
98C2×C4⋊Dic11C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—41no—
108C22×C11⋊C8—41no—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C2×#4313—22no—
114C2×#4313—22no—
115C2×#4313—41no—
116C2×C8×D11—22no—
117C2×C8×D11—22no—
118C2×C8×D11—41no—
119C4×D44—22no—
120C4×D44—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8D414yescomplemented
123C11×#97—22no—
124C11×#97—22no—
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C11⋊#95C2×C411yescharacteristic
131(C2×D11)⋊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)⋊C8—41no—
137#66879—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140C8×Dic11—22no—
141C4⋊(C11⋊C8)—22no—
142C4⋊(C11⋊C8)—22no—
143C4⋊(C11⋊C8)—22no—
144C4⋊(C11⋊C8)D414yescomplemented
145#22987—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—41no—
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C2×C22⋊D11—22no—
168C2×C22⋊D11—22no—
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11M1614yescomplemented
173C22×Dic11C22×C411yescharacteristic
174C22×Dic11C22×C411yescharacteristic
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—41no—
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—21no—
192C2×C4×D11—21no—
193C2×C4×D11—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—
204C2×C8×C11C2×D412yes—
205C2×C8×C11C2×D412yes—
206C42×C11—22no—
207C42×C11—22no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11C2×D412yes—
211C42×C11#4112yes—
212C22⋊Dic11—22no—
213C22⋊Dic11—22no—
214(C2×D11)⋊C4—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—
221(C2×D11)⋊C4—22no—
222C4⋊Dic11—22no—
223C4⋊Dic11—22no—
224C4⋊Dic11—41no—
225Dic11⋊C4—22no—
226Dic11⋊C4—22no—
227C4×Dic11—21no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11—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⋊C8—21no—
241C2×C11⋊C8—44no—
242C2×C11⋊C8—44no—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245#4313—44no—
246C8×D11—44no—
247C2×#435—111no—
248C2×#435—111no—
249C2×C8×D4—111no—
250C22×C4⋊C8—111no—
251C4×#121—111no—
252#1955—111no—
253#1940—111no—
254#1924—111no—
255#1923—111no—
256#1869—111no—
257#1869—111no—
258#1851—111no—
259#1850—111no—
260#1771—111no—
261#1749D1111yescharacteristic, complemented
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11C4×D412yes—
267C23×C11C2×M1612yes—
268C23×C11#13112yes—
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×D11—21no—
283C22×D11C2×M1612yes—
284C2×C4×C11—28no—
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—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—44no—
301C2×C4×C11C4×D412yes—
302C2×C4×C11C4×D412yes—
303C2×C4×C11C4×D412yes—
304C2×C4×C11#13112yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
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×Dic11C2×M1612yes—
331D44—44no—
332C4×D11—41no—
333C4×D11—41no—
334C4×D11—41no—
335C4×D11—41no—
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—22no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C22×M16—111no—
349C23×C8—111no—
350C23×C8—111no—
351C23×C8—111no—
352C2×#121—111no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4—111no—
356C22×C42C2×D1111yescharacteristic
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×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×C4⋊C8—224no—
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⋊C8C2×D1111yescharacteristic
374C2×C22⋊C8C2×D1111yescharacteristic
375C2×#97—111no—
376C2×#97C2×D1111yescharacteristic
377C2×#97C2×D1111yescharacteristic
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#43514yescomplemented
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—41no—
413C2×D11—41no—
414C2×D11—41no—
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—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—41no—
428C4×C11D4211yescharacteristic
429C4×C11#54711yescharacteristic
430C4×C11#54811yescharacteristic
431C4×C11#55311yescharacteristic
432Dic11—22no—
433Dic11—41no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437Dic11—41no—
438C22×D4—111no—
439C22×D4—111no—
440C22×D4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4C4×D1111yescharacteristic
444C23×C4C4×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C2×M16—222no—
447C2×M16—222no—
448C2×M16—441no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—222no—
454C22×C8—222no—
455C22×C8—222no—
456C22×C8—222no—
457C22×C8—222no—
458C22×C8—222no—
459C22×C8—441no—
460C22×C8—441no—
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⋊C4—111no—
487C2×C22⋊C4—111no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—111no—
491C2×C42—111no—
492C2×C42C4×D1111yescharacteristic
493C2×C42C4×D1111yescharacteristic
494C2×C42C22×D1111yescharacteristic
495C2×C42C22×D1111yescharacteristic
496C4⋊C8—114no—
497C4⋊C8—222no—
498C4⋊C8—222no—
499C4⋊C8—222no—
500C4⋊C8—222no—
501C4⋊C8—222no—
502C22⋊C8—22no—
503C22⋊C8—222no—
504C22⋊C8—222no—
505C22⋊C8—222no—
506C22⋊C8—222no—
507C22⋊C8—441no—
508C22⋊C8—441no—
509C22⋊C8D4414yescomplemented
510#97—22no—
511#97—22no—
512#97—222no—
513C4×C8—222no—
514#95—111no—
515#95—111no—
516#95—111no—
517#95—111no—
518#95—111no—
519#95—111no—
520C2×C11—24no—
521C2×C11#236111yescharacteristic
522C2×C11C2×#43511yescharacteristic
523C2×C11#292911yescharacteristic
524C2×C11D4×M1611yescharacteristic
525C2×C11#293511yescharacteristic
526C2×C11#299011yescharacteristic
527C2×C11#299211yescharacteristic
528D11—42no—
529D11—81no—
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—222no—
541C2×D4—441no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—41no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4C2×C4×D1111yescharacteristic
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4C2×D4412yes—
576C22×C4#433912yes—
577C22×C4C23×D1111yescharacteristic
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—112no—
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—444no—
602C2×C8—444no—
603C2×C8—444no—
604C2×C8C2×D4412yes—
605C2×C8C2×D4412yes—
606C4⋊C4—222no—
607C4⋊C4—222no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—441no—
611C22⋊C4—222no—
612C22⋊C4—222no—
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—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—221no—
626C42—221no—
627C42—221no—
628C42—221no—
629C42D4×D1112yes—
630C42#434112yes—
631C11#2298711yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—112no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23C4×D4412yes—
651C23M16×D1112yes—
652C23#6696012yes—
653C23C22×C4×D1111yescharacteristic
654D4—228no—
655D4—444no—
656D4—444no—
657C2×C4—28no—
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—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—44no—
674C2×C4—112no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
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—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4C4×D4412yes—
701C2×C4(C22⋊D11)⋊C412yes—
702C2×C4(C22⋊D11)⋊C412yes—
703C2×C4#6696012yes—
704C2×C4C22×D4411yescharacteristic
705C2×C4C2×#433911yescharacteristic
706C2×C4C2×D4×D1111yescharacteristic
707C2×C4C2×#434111yescharacteristic
708C2×C4#6704211yescharacteristic
709C2×C4#6704311yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—222no—
715C8—222no—
716C8—441no—
717C8—441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—222no—
725C22—222no—
726C22—222no—
727C22—441no—
728C22—441no—
729C22—441no—
730C22—441no—
731C22—441no—
732C22—441no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22#1062231914yescomplemented
739C22C2×C4×D4411yescharacteristic
740C22C2×(C22⋊D11)⋊C411yescharacteristic
741C22#1062305411yescharacteristic
742C22C2×M16×D1111yescharacteristic
743C22C2×#6696011yescharacteristic
744C22C2×#6696011yescharacteristic
745C22#1062327611yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—222no—
752C4—441no—
753C4—441no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4D4×D4411yescharacteristic
758C4#1062308311yescharacteristic
759C4#1062308611yescharacteristic
760C4#1062309611yescharacteristic
761C2—24no—
762C2—442no—
763C2—881no—
764C2#1307163011yescharacteristic
765C2C2×#1062231911yescharacteristic
766C2#1307730611yescharacteristic
767C2#1307734811yescharacteristic
768C2#1307736211yescharacteristic
769C2#1307774311yescharacteristic
770C2#1307775711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1749C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1749D11
hypocenterC11#22987
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C2×#10622319C2semidirect
2. C2×#10622343C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
4. C22×C4⋊(C11⋊C8)C2semidirect
6. #13069414C2semidirect
7. #13069339C2semidirect
8. #13069230C2semidirect
9. #13069223C2semidirect
10. #13068906C2semidirect
11. #13068906C2semidirect
12. #13068800C2semidirect
13. #13068795C2semidirect
14. #13068488C2semidirect
15. C11×#1749C2semidirect
122. C11×C22⋊C8D4semidirect
144. C4⋊(C11⋊C8)D4semidirect
172. C2×C22⋊D11M16semidirect
261. #1749D11semidirect
401. C22×C11#435semidirect
509. C22⋊C8D44semidirect
631. C11#22987semidirect
738. C22#10622319semidirect

Maximal subgroups

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

subgroupindex
C2×#106223192
C2×#106223432
C2×(C22⋊D11)⋊C82
C22×C4⋊(C11⋊C8)2
C4×#669832
#130694142
#130693392
#130692302
#130692232
#130689062
#130688002
#130687952
#130684882
C11×#17492
#2298711