Finite Group Databasebeta

← #14775912

Subgroups — #14775912

Order 2816.

1050 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×#10622342C211yesmaximal, characteristic, complemented
2C2×#10622341C211yesmaximal, characteristic, complemented
3C2×#10622319C211yesmaximal, characteristic, complemented
4C2×#10622537C211yesmaximal, characteristic, complemented
5C4×#66983C211yesmaximal, characteristic
6#13069414C211yesmaximal, characteristic, complemented
7#13069339C211yesmaximal, characteristic, complemented
8#13069230C211yesmaximal, characteristic, complemented
9#13069223C211yesmaximal, characteristic, complemented
10#13068911C211yesmaximal, characteristic, complemented
11#13068911C211yesmaximal, 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
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
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
49#10622537—24no—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54#10622342—24no—
55#10622341—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
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318—22no—
106C2×#4318—22no—
107C2×#4318—41no—
108C2×#4318—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#22988—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—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
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—41no—
172C2×C22⋊D11—41no—
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—41no—
220(C2×D11)⋊C4—41no—
221(C2×D11)⋊C4M1614yescomplemented
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—
231#4318—44no—
232#4318—44no—
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⋊C8—21no—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245#4313—44no—
246C8×D11—44no—
247C2×#436—111no—
248C2×#435—111no—
249C2×#435—111no—
250C2×#423—111no—
251C4×#121—111no—
252#1955—111no—
253#1940—111no—
254#1924—111no—
255#1923—111no—
256#1870—111no—
257#1870—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×C11—21no—
267C23×C11—21no—
268C23×C11C4×D412yes—
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—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—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—44no—
300C2×C4×C11—44no—
301C2×C4×C11C4×D412yes—
302C2×C4×C11C4×D412yes—
303C2×C4×C11C4×D412yes—
304C2×C4×C11C2×M1612yes—
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—44no—
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—
349C22×M16—111no—
350C22×M16—111no—
351C23×C8—111no—
352C2×#121—111no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4—111no—
356C22×C42C2×D1111yescharacteristic
357#436—224no—
358#435—224no—
359#435—224no—
360#423—224no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×C4⋊C8—111no—
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—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×C11#56811yescharacteristic
407C22×C11#56811yescharacteristic
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—222no—
449C2×M16—222no—
450C2×M16—222no—
451C2×M16—222no—
452C2×M16—441no—
453C2×M16—441no—
454C2×M16—441no—
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⋊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—42no—
521C2×C11#236111yescharacteristic
522C2×C11#293011yescharacteristic
523C2×C11#293211yescharacteristic
524C2×C11D4×M1611yescharacteristic
525C2×C11D4×M1611yescharacteristic
526C2×C11#298911yescharacteristic
527C2×C11#299511yescharacteristic
528D11—42no—
529D11—81no—
530C24—111no—
531C24—111no—
532C24C2×C4×D1111yescharacteristic
533C2×D4—222no—
534C2×D4—222no—
535C2×D4—222no—
536C2×D4—222no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—441no—
540C2×D4—441no—
541C2×D4—441no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—41no—
550C22×C4—41no—
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—
579M16—444no—
580M16—444no—
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—21no—
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×C8C2×D4412yes—
605C2×C8C2×D4412yes—
606C4⋊C4—222no—
607C4⋊C4—222no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—441no—
611C22⋊C4—114no—
612C22⋊C4—222no—
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—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—221no—
626C42—221no—
627C42—221no—
628C42—221no—
629C42D4×D1112yes—
630C42#434112yes—
631C11#2298811yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—112no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23—221no—
652C23C4×D4412yes—
653C23C22×C4×D1111yescharacteristic
654D4—444no—
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—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—44no—
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×C4M16×D1112yes—
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—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—222no—
726C22—222no—
727C22—222no—
728C22—441no—
729C22—441no—
730C22—441no—
731C22—441no—
732C22—441no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—441no—
739C22C2×C4×D4411yescharacteristic
740C22C2×(C22⋊D11)⋊C411yescharacteristic
741C22#1062305411yescharacteristic
742C22C2×M16×D1111yescharacteristic
743C22#1062327611yescharacteristic
744C22#1062327611yescharacteristic
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—42no—
762C2—442no—
763C2—881no—
764C2#1307163011yescharacteristic
765C2#1307731511yescharacteristic
766C2#1307733511yescharacteristic
767C2#1307734811yescharacteristic
768C2M16×D4411yescharacteristic
769C2#1307773511yescharacteristic
770C2#1307778811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1749C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1749D11
hypocenterC11#22988
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C2×#10622342C2semidirect
2. C2×#10622341C2semidirect
3. C2×#10622319C2semidirect
4. C2×#10622537C2semidirect
6. #13069414C2semidirect
7. #13069339C2semidirect
8. #13069230C2semidirect
9. #13069223C2semidirect
10. #13068911C2semidirect
11. #13068911C2semidirect
12. #13068800C2semidirect
13. #13068795C2semidirect
14. #13068488C2semidirect
15. C11×#1749C2semidirect
122. C11×C22⋊C8D4semidirect
144. C4⋊(C11⋊C8)D4semidirect
221. (C2×D11)⋊C4M16semidirect
261. #1749D11semidirect
509. C22⋊C8D44semidirect
631. C11#22988semidirect

Maximal subgroups

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

subgroupindex
C2×#106223422
C2×#106223412
C2×#106223192
C2×#106225372
C4×#669832
#130694142
#130693392
#130692302
#130692232
#130689112
#130688002
#130687952
#130684882
C11×#17492
#2298811