Finite Group Databasebeta

← #14764874

Subgroups — #14764874

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×#10622739C211yesmaximal, characteristic, complemented
3C4×#66935C211yesmaximal, characteristic
4#13069413C211yesmaximal, characteristic, complemented
5#13069409C211yesmaximal, characteristic, complemented
6#13069227C211yesmaximal, characteristic, complemented
7#13069221C211yesmaximal, characteristic, complemented
8#13069221C211yesmaximal, characteristic, complemented
9#13069220C211yesmaximal, characteristic, complemented
10#13068913C211yesmaximal, characteristic, complemented
11#13068912C211yesmaximal, characteristic, complemented
12#13068912C211yesmaximal, characteristic, complemented
13#13068525C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#1851C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C22×#4313C2211yescharacteristic, complemented
21C2×#66935C411yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic, complemented
25C2×C11×C4⋊C8C2211yescharacteristic, complemented
26C2×C11×C22⋊C8C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622739—24no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
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×(C2×D11)⋊C8C2211yescharacteristic, complemented
39C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
41C2×Dic11⋊C8C2211yescharacteristic, complemented
42C2×C8×Dic11C2211yescharacteristic, complemented
43#10622571C411yescharacteristic
44#10622568C411yescharacteristic
45#10622563C411yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47C4×(C2×D11)⋊C4C2211yescharacteristic
48C2×#66867C2211yescharacteristic, complemented
49C2×C4×C11⋊C8C2211yescharacteristic, complemented
50#10622342—24no—
51#10622281C411yescharacteristic
52#10622281C411yescharacteristic
53#10622278C411yescharacteristic
54#10622278C411yescharacteristic
55C11×#336C2211yescharacteristic, complemented
56C11×#336C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C24×D11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11C2×C411yescharacteristic
64C23×Dic11C2×C411yescharacteristic
65C22×D44C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11—41no—
70C22×C4×D11—41no—
71C22×C4×D11—41no—
72C22×C4×D11—41no—
73C22×C4×D11C2×C411yescharacteristic
74C22×C4×D11C2×C411yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C2×C11×M16—22no—
79C2×C11×M16—41no—
80C2×C11×M16—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90C4×C22⋊D11—22no—
91C4×C22⋊D11—22no—
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×C4⋊Dic11C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C2×#4318—41no—
106C2×#4318—41no—
107C2×#4318D414yescomplemented
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×#4313—22no—
113C2×#4313—41no—
114C2×#4313—41no—
115#66935—24no—
116C4×D44—41no—
117C4×D44—41no—
118C4×D44—41no—
119C4×D44—41no—
120C11×C4⋊C8—41no—
121C11×C4⋊C8—41no—
122C11×C22⋊C8—22no—
123C11×#95C2×C411yescharacteristic
124C11×#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C22⋊(C11⋊C8)—22no—
130(C2×D11)⋊C8—22no—
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(C2×D11)⋊C8—41no—
138(C2×D11)⋊C8—41no—
139(C2×D11)⋊C8—41no—
140(C2×D11)⋊C8—41no—
141Dic11⋊C8—22no—
142C8×Dic11—22no—
143#66867—41no—
144C4×C11⋊C8—41no—
145#22038—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—41no—
151C23×D11—41no—
152C23×D11—41no—
153C23×D11—41no—
154C23×D11C22×C411yescharacteristic
155C23×D11C22×C411yescharacteristic
156C23×D11C22×C411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C22×C411yescharacteristic
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—41no—
172C22×Dic11—22no—
173C22×Dic11—41no—
174C22×Dic11—41no—
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—22no—
183C2×D44—41no—
184C2×D44—41no—
185C2×D44—41no—
186C2×C4×D11—22no—
187C2×C4×D11—22no—
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×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—21no—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—41no—
207C2×C4×D11—41no—
208C2×C4×D11—41no—
209C2×C4×D11—41no—
210C2×C4×D11—44no—
211C2×C4×D11—44no—
212C2×C4×D11—44no—
213C2×C4×D11—44no—
214C11×M16—44no—
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—
226C2×C8×C11—21no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—41no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C22⋊Dic11—22no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—22no—
237(C2×D11)⋊C4—41no—
238(C2×D11)⋊C4—41no—
239(C2×D11)⋊C4—41no—
240(C2×D11)⋊C4—41no—
241(C2×D11)⋊C4—41no—
242(C2×D11)⋊C4M1614yescomplemented
243C4⋊Dic11—41no—
244C4⋊Dic11—41no—
245Dic11⋊C4—22no—
246C4×Dic11—21no—
247C4×Dic11—21no—
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#1851D1111yescharacteristic, complemented
275#1779—111no—
276#1753—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11C4×D412yes—
284C23×C11C23×C411yescharacteristic
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11—44no—
308C22×D11—44no—
309C22×D11—44no—
310C22×D11—44no—
311C22×D11C2×M1612yes—
312C22×D11#13112yes—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11C4×D412yes—
331C2×C4×C11C2×M1612yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C22⋊D11—44no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—44no—
354C2×Dic11C2×M1612yes—
355D44—44no—
356D44—44no—
357C4×D11—44no—
358C4×D11—44no—
359C4×D11—41no—
360C4×D11—41no—
361C4×D11—41no—
362C4×D11—41no—
363C4×D11—41no—
364C4×D11—41no—
365C4×D11—41no—
366C4×D11—41no—
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×C4—111no—
380C22×M16—111no—
381C22×M16—111no—
382C22×M16C2×D1111yescharacteristic
383C2×#120—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—111no—
387#436—224no—
388C2×C4⋊C8—111no—
389C2×C4⋊C8C2×D1111yescharacteristic, complemented
390C2×C4⋊C8C2×D1111yescharacteristic, complemented
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⋊C8—111no—
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×C22⋊C8—111no—
403C2×C22⋊C8—111no—
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⋊C4C2×D1111yescharacteristic
418#336—111no—
419#336—111no—
420#336—111no—
421#336—111no—
422#336C2×D1111yescharacteristic, complemented
423#336C2×D1111yescharacteristic, complemented
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11C2×C4×D411yescharacteristic
432C22×C11#51811yescharacteristic
433C22×C11#51811yescharacteristic
434C22×C11C22×M1611yescharacteristic
435C22×C11C2×#13111yescharacteristic
436C22×C11#56811yescharacteristic
437C22×C11#56811yescharacteristic
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—22no—
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—416no—
445C2×D11—41no—
446C2×D11—41no—
447C2×D11—41no—
448C2×D11—41no—
449C2×D11—41no—
450C2×D11—41no—
451C2×D11—41no—
452C2×D11—41no—
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—22no—
462C4×C11—41no—
463C4×C11—41no—
464C4×C11—41no—
465C4×C11#53411yescharacteristic
466C4×C11#53511yescharacteristic
467C4×C11#53811yescharacteristic
468C4×C11#53811yescharacteristic
469Dic11—22no—
470Dic11—41no—
471Dic11—41no—
472Dic11—41no—
473Dic11—41no—
474C25—111no—
475C22×D4—111no—
476C22×D4—111no—
477C22×D4—111no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—222no—
485C23×C4—222no—
486C23×C4—441no—
487C23×C4—441no—
488C23×C4—441no—
489C23×C4—441no—
490C23×C4C22×D1111yescharacteristic
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—114no—
495C2×M16—222no—
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⋊C4C4×D1111yescharacteristic
529C2×C22⋊C4C4×D1111yescharacteristic
530C2×C42—111no—
531C2×C42C22×D1111yescharacteristic
532C2×C42C22×D1111yescharacteristic
533C4⋊C8—41no—
534C4⋊C8—41no—
535C4⋊C8—222no—
536C22⋊C8—22no—
537C22⋊C8—222no—
538C22⋊C8—222no—
539C22⋊C8—222no—
540C22⋊C8—222no—
541C22⋊C8—222no—
542C22⋊C8—222no—
543C22⋊C8—441no—
544C22⋊C8—441no—
545C22⋊C8—441no—
546C22⋊C8—441no—
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#95C4×D1111yescharacteristic
557#95C4×D1111yescharacteristic
558C2×C11—42no—
559C2×C11#232111yescharacteristic
560C2×C11#293311yescharacteristic
561C2×C11D4×M1611yescharacteristic
562C2×C11#297411yescharacteristic
563C2×C11#297511yescharacteristic
564C2×C11#297611yescharacteristic
565C2×C11#297811yescharacteristic
566D11—42no—
567D11—42no—
568D11—81no—
569C24—111no—
570C24—111no—
571C24—111no—
572C24—222no—
573C24—222no—
574C24—222no—
575C24—441no—
576C24—441no—
577C24—441no—
578C24—441no—
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—111no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—441no—
620C22×C4—441no—
621C22×C4—441no—
622C22×C4—441no—
623C22×C4—444no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4—444no—
627C22×C4—441no—
628C22×C4—441no—
629C22×C4C2×C4×D1111yescharacteristic
630C22×C4C2×C4×D1111yescharacteristic
631C22×C4C2×C4×D1111yescharacteristic
632C22×C4C2×C4×D1111yescharacteristic
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4D4×D1112yes—
635C22×C4#434312yes—
636C22×C4C23×D1111yescharacteristic
637M16—44no—
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—22no—
668C22⋊C4—41no—
669C22⋊C4—114no—
670C22⋊C4—222no—
671C22⋊C4—222no—
672C22⋊C4—222no—
673C22⋊C4—222no—
674C22⋊C4—441no—
675C22⋊C4—441no—
676C22⋊C4—441no—
677C22⋊C4—441no—
678C22⋊C4—441no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—221no—
684C42—221no—
685C11#2203811yescharacteristic, complemented, Sylow
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—112no—
693C23—112no—
694C23—221no—
695C23—221no—
696C23—221no—
697C23—221no—
698C23—221no—
699C23—221no—
700C23—221no—
701C23—221no—
702C23—221no—
703C23—221no—
704C23—221no—
705C23—221no—
706C23—221no—
707C23—221no—
708C23—221no—
709C23—221no—
710C23—221no—
711C23—221no—
712C23—221no—
713C23—444no—
714C23—444no—
715C23—444no—
716C23—444no—
717C23—444no—
718C23—444no—
719C23—444no—
720C23#6694612yes—
721C23C22×C4×D1111yescharacteristic
722D4—444no—
723D4—444no—
724D4—444no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—112no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—221no—
753C2×C4—221no—
754C2×C4—221no—
755C2×C4—221no—
756C2×C4—221no—
757C2×C4—444no—
758C2×C4—444no—
759C2×C4—444no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4#6694612yes—
773C2×C4M16×D1112yes—
774C2×C4C2×D4×D1111yescharacteristic
775C2×C4#6703711yescharacteristic
776C2×C4#6703711yescharacteristic
777C2×C4C2×#434311yescharacteristic
778C2×C4#6704211yescharacteristic
779C2×C4#6704211yescharacteristic
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—222no—
785C8—222no—
786C8—441no—
787C8—441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—222no—
796C22—222no—
797C22—222no—
798C22—222no—
799C22—222no—
800C22—222no—
801C22—4416no—
802C22—441no—
803C22—441no—
804C22—441no—
805C22—441no—
806C22—441no—
807C22—441no—
808C22—441no—
809C22—441no—
810C22—441no—
811C22—441no—
812C22—441no—
813C22—441no—
814C22—441no—
815C22—441no—
816C22—441no—
817C22C2×#6694611yescharacteristic
818C22#1062307611yescharacteristic
819C22#1062307611yescharacteristic
820C22C2×M16×D1111yescharacteristic
821C22#1062327611yescharacteristic
822C22D11×#13111yescharacteristic
823C22#1062328111yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—222no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4—441no—
834C4#1062312311yescharacteristic
835C4#1062317511yescharacteristic
836C4#1062317511yescharacteristic
837C4#1062318411yescharacteristic
838C2—42no—
839C2—442no—
840C2—442no—
841C2—881no—
842C2#1307127311yescharacteristic
843C2#1307734011yescharacteristic
844C2#1307735111yescharacteristic
845C2#1307764611yescharacteristic
846C2#1307765411yescharacteristic
847C2#1307766311yescharacteristic
848C2#1307767311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1851C2
prime radicalC2×#66935C4
cosocleC22×C4×C11C24
hypercenter#1851D11
hypocenterC11#22038
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#10622342C2semidirect
2. C2×#10622739C2semidirect
4. #13069413C2semidirect
5. #13069409C2semidirect
6. #13069227C2semidirect
7. #13069221C2semidirect
8. #13069221C2semidirect
9. #13069220C2semidirect
10. #13068913C2semidirect
11. #13068912C2semidirect
12. #13068912C2semidirect
13. #13068525C2semidirect
14. #13068400C2semidirect
15. C11×#1851C2semidirect
20. C22×#4313C22semidirect
24. C2×C11×C4⋊C8C22semidirect
25. C2×C11×C4⋊C8C22semidirect
38. C2×(C2×D11)⋊C8C22semidirect
39. C2×(C2×D11)⋊C8C22semidirect
40. C2×(C2×D11)⋊C8C22semidirect
41. C2×Dic11⋊C8C22semidirect
42. C2×C8×Dic11C22semidirect
48. C2×#66867C22semidirect
49. C2×C4×C11⋊C8C22semidirect
55. C11×#336C22semidirect
56. C11×#336C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
107. C2×#4318D4semidirect
242. (C2×D11)⋊C4M16semidirect
274. #1851D11semidirect
389. C2×C4⋊C8C2×D11semidirect
390. C2×C4⋊C8C2×D11semidirect
422. #336C2×D11semidirect
423. #336C2×D11semidirect
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×#106227392
C4×#669352
#130694132
#130694092
#130692272
#130692212
#130692202
#130689132
#130689122
#130685252
#130684002
C11×#18512
#2203811