Finite Group Databasebeta

← #14764872

Subgroups — #14764872

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622342C211yesmaximal, characteristic, complemented
2C2×#10622820C211yesmaximal, characteristic, complemented
3C4×#67006C211yesmaximal, characteristic
4#13069412C211yesmaximal, characteristic, complemented
5#13069408C211yesmaximal, characteristic, complemented
6#13069226C211yesmaximal, characteristic, complemented
7#13069225C211yesmaximal, characteristic, complemented
8#13069225C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic, complemented
10#13068911C211yesmaximal, characteristic, complemented
11#13068910C211yesmaximal, characteristic, complemented
12#13068910C211yesmaximal, characteristic, complemented
13#13068798C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1779C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C2×#67006C411yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4313C2211yescharacteristic, complemented
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30#10622860C411yescharacteristic
31#10622826C411yescharacteristic
32#10622826C411yescharacteristic
33#10622826C411yescharacteristic
34#10622823C411yescharacteristic
35#10622823C411yescharacteristic
36#10622823C411yescharacteristic
37C4×C22⋊Dic11C2211yescharacteristic
38C4×C22⋊Dic11C2211yescharacteristic
39C4×C22⋊Dic11C2211yescharacteristic
40#10622820—24no—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
46C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
47C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
48C2×#66879C2211yescharacteristic, complemented
49C2×Dic11⋊C8C2211yescharacteristic, complemented
50C2×Dic11⋊C8C2211yescharacteristic, complemented
51C2×Dic11⋊C8C2211yescharacteristic, complemented
52C2×C8×Dic11C2211yescharacteristic, complemented
53C2×C8×Dic11C2211yescharacteristic, complemented
54#10622342—24no—
55#10622188C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622188C2211yescharacteristic, complemented
61C25×C11C2×C411yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—41no—
65C23×C4×C11—41no—
66C23×C4×C11—41no—
67C23×C4×C11—41no—
68C23×C4×C11C2×C411yescharacteristic
69C23×C4×C11C2×C411yescharacteristic
70C23×C4×C11C2×C411yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11C2×C411yescharacteristic
75C22×C22⋊D11C2×C411yescharacteristic
76C22×C22⋊D11C2×C411yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82#67006—24no—
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90C2×C22⋊Dic11C2×C411yescharacteristic
91C2×C22⋊Dic11C2×C411yescharacteristic
92C4×C22⋊D11—22no—
93C4×C22⋊D11—22no—
94C4×C22⋊D11—41no—
95C4×C22⋊D11—41no—
96C4×C22⋊D11—41no—
97C4×C22⋊D11—41no—
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×Dic11⋊C4C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×#4318—22no—
108C2×#4318—41no—
109C2×#4318—41no—
110C2×#4318—41no—
111C2×#4318—41no—
112C2×#4318D414yescomplemented
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C2×#4313—22no—
118C2×#4313—41no—
119C2×#4313—41no—
120C11×C22⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—41no—
123C11×C22⋊C8—41no—
124C11×C22⋊C8—41no—
125C11×C22⋊C8—41no—
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C11⋊#95C2×C411yescharacteristic
131C11⋊#95C2×C411yescharacteristic
132C22⋊(C11⋊C8)—22no—
133C22⋊(C11⋊C8)—22no—
134C22⋊(C11⋊C8)—22no—
135C22⋊(C11⋊C8)—22no—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—41no—
138(C2×D11)⋊C8—41no—
139#66879—41no—
140Dic11⋊C8—22no—
141Dic11⋊C8—41no—
142Dic11⋊C8—41no—
143C8×Dic11—22no—
144C8×Dic11—41no—
145#22038—111nomaximal, Sylow
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—41no—
150C24×C11—41no—
151C24×C11—41no—
152C24×C11—41no—
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C24×C11C22×C411yescharacteristic
156C23×D11C22×C411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11—41no—
180C22×C4×C11—41no—
181C22×C4×C11—41no—
182C22×C4×C11—44no—
183C22×C4×C11—44no—
184C22×C4×C11—44no—
185C22×C4×C11—44no—
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—22no—
193C2×C22⋊D11—22no—
194C2×C22⋊D11—22no—
195C2×C22⋊D11—22no—
196C2×C22⋊D11—22no—
197C2×C22⋊D11—41no—
198C2×C22⋊D11—41no—
199C2×C22⋊D11—41no—
200C2×C22⋊D11—41no—
201C22×Dic11C22×C411yescharacteristic
202C22×Dic11C22×C411yescharacteristic
203C22×Dic11C22×C411yescharacteristic
204C22×Dic11C22×C411yescharacteristic
205C22×Dic11C22×C411yescharacteristic
206C22×Dic11C22×C411yescharacteristic
207C22×Dic11C22×C411yescharacteristic
208C2×C4×D11—21no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—21no—
212C2×C4×D11—21no—
213C2×C4×D11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11—22no—
229C22⋊Dic11—22no—
230C22⋊Dic11—41no—
231C22⋊Dic11—41no—
232C22⋊Dic11—41no—
233C22⋊Dic11—41no—
234C22⋊Dic11M1614yescomplemented
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—41no—
237(C2×D11)⋊C4—41no—
238Dic11⋊C4—22no—
239Dic11⋊C4—41no—
240Dic11⋊C4—41no—
241C4×Dic11—21no—
242C4×Dic11—21no—
243C4×Dic11—21no—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C4×Dic11—21no—
247#4318—44no—
248#4318—44no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8C2×D412yes—
260C2×C11⋊C8C2×D412yes—
261#4313—44no—
262C2×#436—111no—
263C2×#407—111no—
264C4×#120—111no—
265#1955—111no—
266#1954—111no—
267#1924—111no—
268#1923—111no—
269#1923—111no—
270#1923—111no—
271#1870—111no—
272#1870—111no—
273#1870—111no—
274#1851—111no—
275#1779D1111yescharacteristic, complemented
276#1753—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11C4×D412yes—
303C23×C11C2×M1612yes—
304C23×C11#13112yes—
305C23×C11C23×C411yescharacteristic
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11—44no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11C4×D412yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C22⋊D11—44no—
344C22⋊D11—44no—
345C22⋊D11—44no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—21no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11C2×M1612yes—
366C2×Dic11C2×M1612yes—
367C4×D11—41no—
368C4×D11—41no—
369C4×D11—41no—
370C4×D11—41no—
371C8×C11—41no—
372C8×C11—41no—
373C8×C11—41no—
374C8×C11—41no—
375C11⋊C8—22no—
376C11⋊C8—22no—
377C11⋊C8—41no—
378C11⋊C8—41no—
379C24×C4C2×D1111yescharacteristic
380C22×M16—111no—
381C22×M16—111no—
382C22×M16—111no—
383C2×#120—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—111no—
387#436—224no—
388C2×C4⋊C8—111no—
389C2×C4⋊C8—111no—
390C2×C4⋊C8—111no—
391#407—224no—
392C2×C22⋊C8—111no—
393C2×C22⋊C8—111no—
394C2×C22⋊C8—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×C22⋊C8—111no—
398C2×C22⋊C8—111no—
399C2×C22⋊C8C2×D1111yescharacteristic
400C2×C22⋊C8C2×D1111yescharacteristic
401C2×C22⋊C8C2×D1111yescharacteristic
402C2×C22⋊C8C2×D1111yescharacteristic
403C2×C22⋊C8C2×D1111yescharacteristic
404C2×C22⋊C8C2×D1111yescharacteristic
405C2×#97—111no—
406C2×C4×C8—111no—
407C2×C4×C8—111no—
408#386—111no—
409#386—111no—
410#386—111no—
411#385—111no—
412#385—111no—
413#385—111no—
414#379—111no—
415C4×C22⋊C4—111no—
416C4×C22⋊C4—111no—
417C4×C22⋊C4—111no—
418#336—111no—
419#336—111no—
420#336—111no—
421#336—111no—
422#336—111no—
423#336—111no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—416no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11C2×C4×D411yescharacteristic
447C22×C11#51811yescharacteristic
448C22×C11#51811yescharacteristic
449C22×C11C22×M1611yescharacteristic
450C22×C11C2×#13111yescharacteristic
451C22×C11#56811yescharacteristic
452C22×C11#56811yescharacteristic
453C2×D11—41no—
454C2×D11—41no—
455C2×D11—41no—
456C2×D11—41no—
457C2×D11—41no—
458C2×D11—41no—
459C2×D11—41no—
460C4×C11—22no—
461C4×C11—41no—
462C4×C11—41no—
463C4×C11#53411yescharacteristic
464C4×C11#53511yescharacteristic
465C4×C11#53811yescharacteristic
466C4×C11#53811yescharacteristic
467Dic11—22no—
468Dic11—22no—
469Dic11—41no—
470Dic11—41no—
471Dic11—41no—
472Dic11—41no—
473Dic11—41no—
474C25C4×D1111yescharacteristic
475C22×D4—111no—
476C22×D4—111no—
477C22×D4—111no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—41no—
481C23×C4—41no—
482C23×C4—41no—
483C23×C4—41no—
484C23×C4—111no—
485C23×C4C4×D1111yescharacteristic
486C23×C4C4×D1111yescharacteristic
487C23×C4C4×D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C2×M16—114no—
492C2×M16—222no—
493C2×M16—222no—
494C2×M16—441no—
495C2×M16—441no—
496C2×M16—441no—
497C2×M16—441no—
498C2×M16—441no—
499C2×M16—441no—
500C22×C8—111no—
501C22×C8—111no—
502C22×C8—111no—
503C22×C8—111no—
504C22×C8C22×D1111yescharacteristic
505C22×C8C22×D1111yescharacteristic
506C22×C8C22×D1111yescharacteristic
507C22×C8C22×D1111yescharacteristic
508#120—224no—
509C4×D4—222no—
510C4×D4—222no—
511C4×D4—441no—
512C4×D4—441no—
513C4×D4—441no—
514C4×D4—441no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—111no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4—111no—
522C2×C22⋊C4—111no—
523C2×C22⋊C4—111no—
524C2×C22⋊C4—111no—
525C2×C22⋊C4—111no—
526C2×C22⋊C4—111no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—111no—
530C2×C42—111no—
531C2×C42—111no—
532C2×C42—111no—
533C4⋊C8—222no—
534C4⋊C8—441no—
535C4⋊C8—441no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—41no—
539C22⋊C8—41no—
540C22⋊C8—41no—
541C22⋊C8—41no—
542C22⋊C8—222no—
543C22⋊C8—222no—
544C22⋊C8—222no—
545C22⋊C8—222no—
546C22⋊C8—222no—
547C22⋊C8—441no—
548C22⋊C8—441no—
549#97—441no—
550C4×C8—222no—
551C4×C8—441no—
552#95—111no—
553#95—111no—
554#95—111no—
555#95—111no—
556#95—111no—
557#95—111no—
558C2×C11—42no—
559C2×C11—42no—
560C2×C11—42no—
561C2×C11#232111yescharacteristic
562C2×C11#293311yescharacteristic
563C2×C11D4×M1611yescharacteristic
564C2×C11#297411yescharacteristic
565C2×C11#297511yescharacteristic
566C2×C11#297611yescharacteristic
567C2×C11#297811yescharacteristic
568D11—81no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—41no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24—111no—
577C24C2×C4×D1111yescharacteristic
578C24C2×C4×D1111yescharacteristic
579C24C2×C4×D1111yescharacteristic
580C2×D4—222no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—441no—
586C2×D4—441no—
587C2×D4—441no—
588C2×D4—441no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—111no—
619C22×C4—111no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—111no—
623C22×C4—111no—
624C22×C4—111no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4C2×C4×D1111yescharacteristic
632C22×C4C2×C4×D1111yescharacteristic
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4D4×D1112yes—
635C22×C4#434112yes—
636C22×C4C23×D1111yescharacteristic
637M16—444no—
638M16—444no—
639M16—444no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—112no—
653C2×C8—112no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C4⋊C4—222no—
665C4⋊C4—441no—
666C4⋊C4—441no—
667C22⋊C4—114no—
668C22⋊C4—222no—
669C22⋊C4—222no—
670C22⋊C4—222no—
671C22⋊C4—222no—
672C22⋊C4—222no—
673C22⋊C4—441no—
674C22⋊C4—441no—
675C22⋊C4—441no—
676C22⋊C4—441no—
677C22⋊C4—441no—
678C22⋊C4—441no—
679C42—221no—
680C42—221no—
681C42—221no—
682C42—221no—
683C42—221no—
684C42—221no—
685C11#2203811yescharacteristic, complemented, Sylow
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—221no—
712C23—221no—
713C23—221no—
714C23—221no—
715C23—221no—
716C23—221no—
717C23—221no—
718C23(C22⋊D11)⋊C412yes—
719C23#6695412yes—
720C23M16×D1112yes—
721C23C22×C4×D1111yescharacteristic
722D4—444no—
723D4—444no—
724D4—444no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—112no—
749C2×C4—112no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—221no—
753C2×C4—221no—
754C2×C4—221no—
755C2×C4—221no—
756C2×C4—221no—
757C2×C4—221no—
758C2×C4—221no—
759C2×C4—221no—
760C2×C4—221no—
761C2×C4—221no—
762C2×C4—221no—
763C2×C4—221no—
764C2×C4—221no—
765C2×C4—221no—
766C2×C4—221no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4(C22⋊D11)⋊C412yes—
774C2×C4C2×D4×D1111yescharacteristic
775C2×C4C2×#434111yescharacteristic
776C2×C4#6703711yescharacteristic
777C2×C4#6703711yescharacteristic
778C2×C4#6703711yescharacteristic
779C2×C4#6703711yescharacteristic
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—222no—
785C8—222no—
786C8—441no—
787C8—441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—441no—
811C22—441no—
812C22—441no—
813C22—441no—
814C22—441no—
815C22—441no—
816C22—441no—
817C22C2×(C22⋊D11)⋊C411yescharacteristic
818C22#1062301711yescharacteristic
819C22#1062301711yescharacteristic
820C22C2×#6695411yescharacteristic
821C22C2×M16×D1111yescharacteristic
822C22#1062327611yescharacteristic
823C22#1062327611yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—222no—
828C4—222no—
829C4—441no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4—441no—
834C4#1062312011yescharacteristic
835C4#1062312311yescharacteristic
836C4#1062312411yescharacteristic
837C4#1062312411yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—881no—
842C2#1307127111yescharacteristic
843C2#1307733711yescharacteristic
844C2#1307734811yescharacteristic
845C2#1307764711yescharacteristic
846C2#1307765511yescharacteristic
847C2#1307766111yescharacteristic
848C2#1307767611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1779C2
prime radicalC2×#67006C4
cosocleC22×C4×C11C24
hypercenter#1779D11
hypocenterC11#22038
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
1. C2×#10622342C2semidirect
2. C2×#10622820C2semidirect
4. #13069412C2semidirect
5. #13069408C2semidirect
6. #13069226C2semidirect
7. #13069225C2semidirect
8. #13069225C2semidirect
9. #13069219C2semidirect
10. #13068911C2semidirect
11. #13068910C2semidirect
12. #13068910C2semidirect
13. #13068798C2semidirect
14. #13068402C2semidirect
15. C11×#1779C2semidirect
23. C22×#4313C22semidirect
45. C2×(C2×D11)⋊C8C22semidirect
46. C2×(C2×D11)⋊C8C22semidirect
47. C2×(C2×D11)⋊C8C22semidirect
48. C2×#66879C22semidirect
49. C2×Dic11⋊C8C22semidirect
50. C2×Dic11⋊C8C22semidirect
51. C2×Dic11⋊C8C22semidirect
52. C2×C8×Dic11C22semidirect
53. C2×C8×Dic11C22semidirect
55. #10622188C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622188C22semidirect
112. C2×#4318D4semidirect
234. C22⋊Dic11M16semidirect
275. #1779D11semidirect
685. C11#22038semidirect

Maximal subgroups

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

subgroupindex
C2×#106223422
C2×#106228202
C4×#670062
#130694122
#130694082
#130692262
#130692252
#130692192
#130689112
#130689102
#130687982
#130684022
C11×#17792
#2203811