Finite Group Databasebeta

← #14764879

Subgroups — #14764879

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×#10622339C211yesmaximal, characteristic, complemented
3C4×#66990C211yesmaximal, characteristic
4#13069412C211yesmaximal, characteristic, complemented
5#13069232C211yesmaximal, characteristic, complemented
6#13069225C211yesmaximal, characteristic, complemented
7#13069222C211yesmaximal, characteristic, complemented
8#13069221C211yesmaximal, characteristic, complemented
9#13068914C211yesmaximal, characteristic, complemented
10#13068911C211yesmaximal, characteristic, complemented
11#13068910C211yesmaximal, characteristic, complemented
12#13068797C211yesmaximal, characteristic, complemented
13#13068525C211yesmaximal, characteristic, complemented
14#13068399C211yesmaximal, characteristic, complemented
15C11×#1954C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66990C411yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×#4318C2211yescharacteristic, complemented
22C22×#4313C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic, complemented
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic, complemented
28C2×C11×C22⋊C8C2211yescharacteristic, complemented
29C2×C4×C8×C11C2211yescharacteristic, complemented
30#10622833C411yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×#66879C2211yescharacteristic, complemented
42C2×Dic11⋊C8C2211yescharacteristic, complemented
43C2×Dic11⋊C8C2211yescharacteristic, complemented
44C2×C8×Dic11C2211yescharacteristic, complemented
45#10622602C411yescharacteristic
46#10622602C411yescharacteristic
47#10622569C411yescharacteristic
48#10622569C411yescharacteristic
49#10622568C411yescharacteristic
50#10622559C411yescharacteristic
51C4×(C2×D11)⋊C4C2211yescharacteristic
52C4×(C2×D11)⋊C4C2211yescharacteristic
53#10622342—24no—
54#10622339—24no—
55#10622188C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C24×D11C2×C411yescharacteristic
62C22×D4×C11C2×C411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C23×Dic11C2×C411yescharacteristic
68C22×C4×D11—22no—
69C22×C4×D11—22no—
70C22×C4×D11—41no—
71C22×C4×D11—41no—
72C22×C4×D11—41no—
73C22×C4×D11—41no—
74C22×C4×D11C2×C411yescharacteristic
75C22×C4×D11C2×C411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C4×D4×C11—41no—
83C4×D4×C11—41no—
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90C2×C22⋊Dic11C2×C411yescharacteristic
91C2×C22⋊Dic11C2×C411yescharacteristic
92#66990—24no—
93C4×C22⋊D11—22no—
94C4×C22⋊D11—22no—
95C4×C22⋊D11—41no—
96C4×C22⋊D11—41no—
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102C2×(C2×D11)⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×#4318—22no—
108C2×#4318—41no—
109C2×#4318—41no—
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C2×#4313—22no—
115C2×#4313—41no—
116C2×#4313—41no—
117C2×#4313—41no—
118C2×#4313—41no—
119C2×#4313D414yescomplemented
120C11×C4⋊C8—41no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—41no—
124C11×C22⋊C8—41no—
125C4×C8×C11—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)—41no—
134C22⋊(C11⋊C8)—41no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—22no—
138(C2×D11)⋊C8—22no—
139(C2×D11)⋊C8—41no—
140(C2×D11)⋊C8—41no—
141#66879—41no—
142Dic11⋊C8—22no—
143Dic11⋊C8—41no—
144C8×Dic11—22no—
145#22038—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—41no—
152C23×D11—41no—
153C23×D11—41no—
154C23×D11—41no—
155C23×D11C22×C411yescharacteristic
156C23×D11C22×C411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—41no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
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×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C2×C22⋊D11—22no—
178C2×C22⋊D11—22no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11—41no—
181C2×C22⋊D11—41no—
182C2×C22⋊D11—41no—
183C22×Dic11—22no—
184C22×Dic11—41no—
185C22×Dic11—41no—
186C22×Dic11C22×C411yescharacteristic
187C22×Dic11C22×C411yescharacteristic
188C22×Dic11C22×C411yescharacteristic
189C22×Dic11C22×C411yescharacteristic
190C22×Dic11C22×C411yescharacteristic
191C22×Dic11C22×C411yescharacteristic
192C2×C4×D11—22no—
193C2×C4×D11—22no—
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—41no—
205C2×C4×D11—41no—
206C2×C4×D11—41no—
207C2×C4×D11—41no—
208C2×C4×D11—44no—
209C2×C4×D11—44no—
210C2×C4×D11—44no—
211C2×C4×D11—44no—
212C2×C4×D11C2×D412yes—
213C2×C4×D11#4112yes—
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×C11C2×D412yes—
226C11×C4⋊C4—41no—
227C11×C22⋊C4—41no—
228C11×C22⋊C4—41no—
229C42×C11—21no—
230C42×C11—21no—
231C22⋊Dic11—22no—
232C22⋊Dic11—22no—
233C22⋊Dic11—22no—
234C22⋊Dic11—41no—
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)⋊C4M1614yescomplemented
241Dic11⋊C4—22no—
242Dic11⋊C4—41no—
243C4×Dic11—21no—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C4×Dic11—21no—
247#4318—44no—
248C2×C11⋊C8—21no—
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—
260#4313—44no—
261#4313—44no—
262C2×#436—111no—
263C2×#407—111no—
264C4×#120—111no—
265#1955—111no—
266#1954D1111yescharacteristic, complemented
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#1779—111no—
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#13112yes—
291C23×C11C23×C411yescharacteristic
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×D11C4×D412yes—
312C22×D11C2×M1612yes—
313D4×C11—44no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
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—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11C2×M1612yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C22⋊D11—44no—
341C22⋊D11—44no—
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—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—44no—
359C2×Dic11C4×D412yes—
360C2×Dic11C2×M1612yes—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—22no—
365C4×D11—44no—
366C4×D11—44no—
367C4×D11—41no—
368C4×D11—41no—
369C4×D11—41no—
370C4×D11—41no—
371C8×C11—22no—
372C8×C11—41no—
373C8×C11—41no—
374C8×C11—41no—
375C11⋊C8—22no—
376C11⋊C8—41no—
377C11⋊C8—41no—
378C11⋊C8—41no—
379C24×C4—111no—
380C22×M16—111no—
381C22×M16—111no—
382C22×M16—111no—
383C2×#120—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4C2×D1111yescharacteristic
387#436—224no—
388C2×C4⋊C8—111no—
389C2×C4⋊C8—111no—
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⋊C8C2×D1111yescharacteristic
402C2×C22⋊C8C2×D1111yescharacteristic
403C2×C22⋊C8C2×D1111yescharacteristic, complemented
404C2×C22⋊C8C2×D1111yescharacteristic, complemented
405C2×#97—111no—
406C2×C4×C8—111no—
407C2×C4×C8C2×D1111yescharacteristic, complemented
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—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11C2×C4×D411yescharacteristic
439C22×C11#51811yescharacteristic
440C22×C11#51811yescharacteristic
441C22×C11C22×M1611yescharacteristic
442C22×C11C2×#13111yescharacteristic
443C22×C11#56811yescharacteristic
444C22×C11#56811yescharacteristic
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—416no—
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—41no—
462C4×C11—41no—
463C4×C11—41no—
464C4×C11#53411yescharacteristic
465C4×C11#53511yescharacteristic
466C4×C11#53811yescharacteristic
467C4×C11#53811yescharacteristic
468Dic11—22no—
469Dic11—22no—
470Dic11—41no—
471Dic11—41no—
472Dic11—41no—
473Dic11—41no—
474C25—111no—
475C22×D4—111no—
476C22×D4—111no—
477C22×D4C4×D1111yescharacteristic
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—441no—
486C23×C4—441no—
487C23×C4—441no—
488C23×C4—441no—
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—41no—
510C4×D4—41no—
511C4×D4—222no—
512C4×D4—222no—
513C4×D4—441no—
514C4×D4—441no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4C4×D1111yescharacteristic
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×C42—111no—
532C2×C42C22×D1111yescharacteristic
533C4⋊C8—41no—
534C4⋊C8—222no—
535C4⋊C8—441no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—41no—
539C22⋊C8—41no—
540C22⋊C8—222no—
541C22⋊C8—222no—
542C22⋊C8—222no—
543C22⋊C8—222no—
544C22⋊C8—222no—
545C22⋊C8—441no—
546C22⋊C8—441no—
547C22⋊C8—441no—
548C22⋊C8—441no—
549#97—441no—
550C4×C8—41no—
551C4×C8—222no—
552#95—111no—
553#95—111no—
554#95—111no—
555#95—111no—
556#95—111no—
557#95—111no—
558C2×C11—42no—
559C2×C11—81no—
560C2×C11#232111yescharacteristic
561C2×C11#293311yescharacteristic
562C2×C11D4×M1611yescharacteristic
563C2×C11#297411yescharacteristic
564C2×C11#297511yescharacteristic
565C2×C11#297611yescharacteristic
566C2×C11#297811yescharacteristic
567D11—42no—
568D11—42no—
569C24—111no—
570C24—111no—
571C24—222no—
572C24—222no—
573C24—222no—
574C24—441no—
575C24—441no—
576C24—441no—
577C24—441no—
578C24C2×C4×D1111yescharacteristic
579C24C2×C4×D1111yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—41no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—441no—
587C2×D4—441no—
588C2×D4—441no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—111no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—111no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—441no—
623C22×C4—441no—
624C22×C4—441no—
625C22×C4—441no—
626C22×C4—444no—
627C22×C4—444no—
628C22×C4—444no—
629C22×C4—444no—
630C22×C4—441no—
631C22×C4—441no—
632C22×C4C2×C4×D1111yescharacteristic
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4C2×C4×D1111yescharacteristic
635C22×C4C2×C4×D1111yescharacteristic
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—112no—
652C2×C8—221no—
653C2×C8—221no—
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×C8D4×D1112yes—
664C4⋊C4—41no—
665C4⋊C4—222no—
666C4⋊C4—441no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—114no—
670C22⋊C4—222no—
671C22⋊C4—222no—
672C22⋊C4—222no—
673C22⋊C4—222no—
674C22⋊C4—222no—
675C22⋊C4—441no—
676C22⋊C4—441no—
677C22⋊C4—441no—
678C22⋊C4—441no—
679C42—21no—
680C42—21no—
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—112no—
700C23—112no—
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#6695412yes—
721C23C22×C4×D1111yescharacteristic
722D4—44no—
723D4—444no—
724D4—444no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—112no—
745C2×C4—112no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
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—444no—
767C2×C4—444no—
768C2×C4—444no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4M16×D1112yes—
774C2×C4C2×D4×D1111yescharacteristic
775C2×C4#6703711yescharacteristic
776C2×C4#6703711yescharacteristic
777C2×C4#6703711yescharacteristic
778C2×C4#41×D1111yescharacteristic
779C2×C4#6704211yescharacteristic
780C8—22no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—222no—
785C8—441no—
786C8—441no—
787C8—441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—222no—
803C22—222no—
804C22—222no—
805C22—222no—
806C22—222no—
807C22—222no—
808C22—4416no—
809C22—441no—
810C22—441no—
811C22—441no—
812C22—441no—
813C22—441no—
814C22—441no—
815C22—441no—
816C22—441no—
817C22#1062301711yescharacteristic
818C22C4×D4×D1111yescharacteristic
819C22#1062307611yescharacteristic
820C22C2×#6695411yescharacteristic
821C22C2×M16×D1111yescharacteristic
822C22#1062328111yescharacteristic
823C22#1062328111yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—222no—
829C4—222no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4—441no—
834C4#1062313611yescharacteristic
835C4#1062314411yescharacteristic
836C4#1062320911yescharacteristic
837C4#1062324611yescharacteristic
838C2—42no—
839C2—81no—
840C2—442no—
841C2—442no—
842C2#1307127511yescharacteristic
843C2#1307733611yescharacteristic
844C2#1307735211yescharacteristic
845C2#1307764711yescharacteristic
846C2#1307765411yescharacteristic
847C2#1307765811yescharacteristic
848C2#1307767411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1954C2
prime radicalC2×#66990C4
cosocleC22×C4×C11C24
hypercenter#1954D11
hypocenterC11#22038
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10622342C2semidirect
2. C2×#10622339C2semidirect
4. #13069412C2semidirect
5. #13069232C2semidirect
6. #13069225C2semidirect
7. #13069222C2semidirect
8. #13069221C2semidirect
9. #13068914C2semidirect
10. #13068911C2semidirect
11. #13068910C2semidirect
12. #13068797C2semidirect
13. #13068525C2semidirect
14. #13068399C2semidirect
15. C11×#1954C2semidirect
21. C22×#4318C22semidirect
24. C2×C11×C4⋊C8C22semidirect
27. C2×C11×C22⋊C8C22semidirect
28. C2×C11×C22⋊C8C22semidirect
29. C2×C4×C8×C11C22semidirect
34. C2×C22⋊(C11⋊C8)C22semidirect
41. C2×#66879C22semidirect
42. C2×Dic11⋊C8C22semidirect
43. C2×Dic11⋊C8C22semidirect
44. C2×C8×Dic11C22semidirect
55. #10622188C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
119. C2×#4313D4semidirect
240. (C2×D11)⋊C4M16semidirect
266. #1954D11semidirect
390. C2×C4⋊C8C2×D11semidirect
403. C2×C22⋊C8C2×D11semidirect
404. C2×C22⋊C8C2×D11semidirect
407. C2×C4×C8C2×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×#106223392
C4×#669902
#130694122
#130692322
#130692252
#130692222
#130692212
#130689142
#130689112
#130689102
#130687972
#130685252
#130683992
C11×#19542
#2203811