Finite Group Databasebeta

← #14775907

Subgroups — #14775907

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×#10622341C211yesmaximal, characteristic, complemented
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
5C4×#66991C211yesmaximal, characteristic
6#13069337C211yesmaximal, characteristic, complemented
7#13069226C211yesmaximal, characteristic, complemented
8#13069219C211yesmaximal, characteristic, complemented
9#13068905C211yesmaximal, characteristic, complemented
10#13068905C211yesmaximal, characteristic, complemented
11#13068798C211yesmaximal, characteristic, complemented
12#13068793C211yesmaximal, characteristic, complemented
13#13068488C211yesmaximal, characteristic, complemented
14#13068379C211yesmaximal, characteristic, complemented
15C11×#1955C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C411yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×#97C2211yescharacteristic
31#10622834C411yescharacteristic
32C4×C22⋊Dic11C2211yescharacteristic
33C4×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622624—24no—
45#10622600C411yescharacteristic
46#10622586C411yescharacteristic
47#10622569C411yescharacteristic
48#10622569C411yescharacteristic
49#10622557C411yescharacteristic
50#10622557C411yescharacteristic
51C4×C4⋊Dic11C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×#66867C2211yescharacteristic
54D11×C4⋊C8—24no—
55#10622341—24no—
56(C22⋊D11)⋊C8—24no—
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
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
68C22×C4×D11C2×C411yescharacteristic
69C22×C4×D11C2×C411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87#66991—24no—
88C4×C22⋊D11—22no—
89C4×C22⋊D11—22no—
90C4×C22⋊D11—22no—
91C4×C22⋊D11—22no—
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×C4⋊Dic11C2×C411yescharacteristic
95C2×C4⋊Dic11C2×C411yescharacteristic
96C2×Dic11⋊C4C2×C411yescharacteristic
97C2×Dic11⋊C4C2×C411yescharacteristic
98C2×C4×Dic11C2×C411yescharacteristic
99C2×C4×Dic11C2×C411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318—41no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—22no—
108C22×C11⋊C8—41no—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C2×C8×D11—22no—
114C2×C8×D11—22no—
115C2×C8×D11—22no—
116C2×C8×D11—22no—
117C2×C8×D11—41no—
118C2×C8×D11—41no—
119C42×D11—22no—
120C42×D11—22no—
121C11×C4⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—22no—
124C11×C22⋊C8—41no—
125C11×C22⋊C8—41no—
126C11×#97—22no—
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C11⋊#95C2×C411yescharacteristic
131C11⋊#95C2×C411yescharacteristic
132C11⋊#95C2×C411yescharacteristic
133C22⋊(C11⋊C8)—22no—
134C22⋊(C11⋊C8)—22no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8D414yescomplemented
137#66879—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141Dic11⋊C8—22no—
142C8×Dic11—22no—
143C4⋊(C11⋊C8)D414yescomplemented
144#66867—22no—
145#22987—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×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—22no—
173C2×C22⋊D11—22no—
174C2×C22⋊D11M1614yescomplemented
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C22×Dic11C22×C411yescharacteristic
181C22×Dic11C22×C411yescharacteristic
182C2×C4×D11—22no—
183C2×C4×D11—22no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
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—21no—
205C2×C8×C11C2×D412yes—
206C11×C4⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C42×C11C2×D412yes—
210C42×C11#4112yes—
211C22⋊Dic11—22no—
212C22⋊Dic11—22no—
213C22⋊Dic11—22no—
214C22⋊Dic11—22no—
215C22⋊Dic11—22no—
216C22⋊Dic11—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—22no—
219C4⋊Dic11—22no—
220C4⋊Dic11—41no—
221Dic11⋊C4—22no—
222Dic11⋊C4—22no—
223C4×Dic11—22no—
224C4×Dic11—22no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231#4318—44no—
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⋊C8C2×D412yes—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245C8×D11—44no—
246C8×D11—44no—
247C2×#435—111no—
248C2×#435—111no—
249C2×C8×D4—111no—
250C22×C4⋊C8—111no—
251C4×#121—111no—
252#1955D1111yescharacteristic, complemented
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#1749—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×C11—21no—
275C23×C11C2×M1612yes—
276C23×C11C23×C411yescharacteristic
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11C4×D412yes—
282C22×D11C2×M1612yes—
283C22×D11#13112yes—
284D4×C11—44no—
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—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11C4×D412yes—
304C2×C4×C11C4×D412yes—
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×Dic11—21no—
331C2×Dic11C4×D412yes—
332C2×Dic11C2×M1612yes—
333C2×Dic11#13112yes—
334C4×D11—28no—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—44no—
340C8×C11—22no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8—22no—
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×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×C4⋊C8—111no—
365C2×C4⋊C8—224no—
366C2×C4⋊C8C2×D1111yescharacteristic
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8C2×D1111yescharacteristic
372C2×C22⋊C8C2×D1111yescharacteristic
373C2×C22⋊C8C2×D1111yescharacteristic
374C2×C22⋊C8C2×D1111yescharacteristic
375C2×#97—111no—
376C2×#97—111no—
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#336—111no—
394#336—111no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
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×C11#52011yescharacteristic
412C22×C11C22×M1611yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11C2×#13111yescharacteristic
415C22×C11#56811yescharacteristic
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—22no—
422C2×D11#43514yescomplemented
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11D4211yescharacteristic
428C4×C11#54711yescharacteristic
429C4×C11#54811yescharacteristic
430C4×C11#55311yescharacteristic
431Dic11—22no—
432Dic11—22no—
433Dic11—22no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437Dic11—41no—
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—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—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—22no—
497C4⋊C8—114no—
498C4⋊C8—222no—
499C4⋊C8—222no—
500C4⋊C8—222no—
501C4⋊C8—222no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—41no—
505C22⋊C8—41no—
506C22⋊C8—114no—
507C22⋊C8—222no—
508C22⋊C8—222no—
509C22⋊C8—222no—
510#97—22no—
511#97—222no—
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—42no—
521C2×C11—81no—
522C2×C11#236111yescharacteristic
523C2×C11C2×#43511yescharacteristic
524C2×C11#292911yescharacteristic
525C2×C11D4×M1611yescharacteristic
526C2×C11#293511yescharacteristic
527C2×C11#299011yescharacteristic
528C2×C11#299211yescharacteristic
529D11—24no—
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—222no—
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—21no—
553C22×C4—21no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—111no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—441no—
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4C2×C4×D1111yescharacteristic
576C22×C4C2×C4×D1111yescharacteristic
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—21no—
590C2×C8—112no—
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—444no—
603C2×C8—444no—
604C2×C8—444no—
605C2×C8D4×D1112yes—
606C4⋊C4—22no—
607C4⋊C4—222no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—441no—
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—222no—
622C42—222no—
623C42—221no—
624C42—221no—
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—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—112no—
646C23—112no—
647C23—112no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23—221no—
652C23M16×D1112yes—
653C23C22×C4×D1111yescharacteristic
654D4—44no—
655D4—228no—
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—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—228no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
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—444no—
702C2×C4(C22⋊D11)⋊C412yes—
703C2×C4(C22⋊D11)⋊C412yes—
704C2×C4C2×D4×D1111yescharacteristic
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4C2×#434111yescharacteristic
707C2×C4#6703711yescharacteristic
708C2×C4#41×D1111yescharacteristic
709C2×C4#6704311yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—222no—
715C8—222no—
716C8—222no—
717C8—441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—114no—
733C22—222no—
734C22—222no—
735C22—222no—
736C22—222no—
737C22—222no—
738C22—222no—
739C22C2×(C22⋊D11)⋊C411yescharacteristic
740C22C4×D4×D1111yescharacteristic
741C22#1062307711yescharacteristic
742C22C2×M16×D1111yescharacteristic
743C22#1062327611yescharacteristic
744C22D11×#13111yescharacteristic
745C22D11×#13111yescharacteristic
746C4—22no—
747C4—22no—
748C4—41no—
749C4—41no—
750C4—222no—
751C4—222no—
752C4—222no—
753C4—441no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4#1062314211yescharacteristic
758C4#1062314511yescharacteristic
759C4#1062320811yescharacteristic
760C4#1062324811yescharacteristic
761C2—42no—
762C2—81no—
763C2—224no—
764C2#1307163711yescharacteristic
765C2D11×#43511yescharacteristic
766C2#1307731311yescharacteristic
767C2#1307734811yescharacteristic
768C2#1307735711yescharacteristic
769C2#1307773611yescharacteristic
770C2#1307775111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1955C2
prime radicalC2×#66991C4
cosocleC22×C4×C11C24
hypercenter#1955D11
hypocenterC11#22987
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1955

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×D11×C4⋊C8C2semidirect
6. #13069337C2semidirect
7. #13069226C2semidirect
8. #13069219C2semidirect
9. #13068905C2semidirect
10. #13068905C2semidirect
11. #13068798C2semidirect
12. #13068793C2semidirect
13. #13068488C2semidirect
14. #13068379C2semidirect
15. C11×#1955C2semidirect
136. (C2×D11)⋊C8D4semidirect
143. C4⋊(C11⋊C8)D4semidirect
174. C2×C22⋊D11M16semidirect
252. #1955D11semidirect
422. C2×D11#435semidirect
631. C11#22987semidirect

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×D11×C4⋊C82
C4×#669912
#130693372
#130692262
#130692192
#130689052
#130687982
#130687932
#130684882
#130683792
C11×#19552
#2298711