Finite Group Databasebeta

← #14764876

Subgroups — #14764876

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×#10622741C211yesmaximal, characteristic, complemented
2C4×#67006C211yesmaximal, characteristic
3#13069412C211yesmaximal, characteristic, complemented
4#13069408C211yesmaximal, characteristic, complemented
5#13069232C211yesmaximal, characteristic, complemented
6#13069225C211yesmaximal, characteristic, complemented
7#13069219C211yesmaximal, characteristic, complemented
8#13069219C211yesmaximal, characteristic, complemented
9#13068913C211yesmaximal, characteristic, complemented
10#13068910C211yesmaximal, characteristic, complemented
11#13068910C211yesmaximal, characteristic, complemented
12#13068799C211yesmaximal, characteristic, complemented
13#13068526C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C2×C11×#407C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×#67006C411yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C22×#4313C2211yescharacteristic, complemented
24C11×#407—24no—
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29#10622860C411yescharacteristic
30#10622826C411yescharacteristic
31#10622826C411yescharacteristic
32#10622826C411yescharacteristic
33#10622823C411yescharacteristic
34#10622823C411yescharacteristic
35#10622823C411yescharacteristic
36C4×C22⋊Dic11C2211yescharacteristic
37C4×C22⋊Dic11C2211yescharacteristic
38C4×C22⋊Dic11C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622741—24no—
46C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
47C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
48C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
49C2×#66879C2211yescharacteristic, complemented
50C2×Dic11⋊C8C2211yescharacteristic, complemented
51C2×Dic11⋊C8C2211yescharacteristic, complemented
52C2×Dic11⋊C8C2211yescharacteristic, complemented
53C2×C8×Dic11C2211yescharacteristic, complemented
54C2×C8×Dic11C2211yescharacteristic, complemented
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
78C2×C11×M16—22no—
79C2×C11×M16—41no—
80C2×C11×M16—41no—
81C2×C11×M16—41no—
82C2×C11×M16—41no—
83C2×C11×M16D414yescomplemented
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88#67006—24no—
89C2×C22⋊Dic11C2×C411yescharacteristic
90C2×C22⋊Dic11C2×C411yescharacteristic
91C2×C22⋊Dic11C2×C411yescharacteristic
92C2×C22⋊Dic11C2×C411yescharacteristic
93C2×C22⋊Dic11C2×C411yescharacteristic
94C2×C22⋊Dic11C2×C411yescharacteristic
95C2×C22⋊Dic11C2×C411yescharacteristic
96C2×C22⋊Dic11C2×C411yescharacteristic
97C2×C22⋊Dic11C2×C411yescharacteristic
98C4×C22⋊D11—22no—
99C4×C22⋊D11—22no—
100C4×C22⋊D11—41no—
101C4×C22⋊D11—41no—
102C4×C22⋊D11—41no—
103C4×C22⋊D11—41no—
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×(C2×D11)⋊C4C2×C411yescharacteristic
106C2×(C2×D11)⋊C4C2×C411yescharacteristic
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×Dic11⋊C4C2×C411yescharacteristic
109C2×Dic11⋊C4C2×C411yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
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—22no—
123C11×C22⋊C8—22no—
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—41no—
133C22⋊(C11⋊C8)—41no—
134C22⋊(C11⋊C8)—41no—
135C22⋊(C11⋊C8)—41no—
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—
214C11×M16—44no—
215C11×M16—44no—
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×C11C2×D412yes—
227C2×C8×C11C2×D412yes—
228C22⋊Dic11—22no—
229C22⋊Dic11—22no—
230C22⋊Dic11—22no—
231C22⋊Dic11—22no—
232C22⋊Dic11—41no—
233C22⋊Dic11—41no—
234C22⋊Dic11—41no—
235C22⋊Dic11—41no—
236C22⋊Dic11M1614yescomplemented
237(C2×D11)⋊C4—22no—
238(C2×D11)⋊C4—41no—
239(C2×D11)⋊C4—41no—
240Dic11⋊C4—22no—
241Dic11⋊C4—41no—
242Dic11⋊C4—41no—
243C4×Dic11—21no—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C4×Dic11—21no—
247C4×Dic11—21no—
248C4×Dic11—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⋊C8—21no—
260C2×C11⋊C8—21no—
261#4313—44no—
262C2×#436—111no—
263C2×#407D1111yescharacteristic, complemented
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#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—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—22no—
372C8×C11—22no—
373C8×C11—41no—
374C8×C11—41no—
375C11⋊C8—41no—
376C11⋊C8—41no—
377C11⋊C8—41no—
378C11⋊C8—41no—
379C24×C4C2×D1111yescharacteristic
380C22×M16—111no—
381C22×M16C2×D1111yescharacteristic
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⋊C8—111no—
390C2×C4⋊C8—111no—
391#407—24no—
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
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—22no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—41no—
495C2×M16—41no—
496C2×M16—222no—
497C2×M16—441no—
498C2×M16—441no—
499C2×M16C22⋊D1114yescomplemented
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—22no—
539C22⋊C8—22no—
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#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×C4#433912yes—
635C22×C4C2×C22⋊D1112yes—
636C22×C4C23×D1111yescharacteristic
637M16—44no—
638M16—44no—
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—221no—
651C2×C8—221no—
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×C8C2×C22⋊D1112yes—
663C2×C8C2×C22⋊D1112yes—
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—
718C23M16×D1112yes—
719C23#6696012yes—
720C23C4×C22⋊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×C4C4×C22⋊D1112yes—
774C2×C4C2×#433911yescharacteristic
775C2×C4#6703711yescharacteristic
776C2×C4#6703711yescharacteristic
777C2×C4#6703711yescharacteristic
778C2×C4#6703711yescharacteristic
779C2×C4C22×C22⋊D1111yescharacteristic
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C8—441no—
785C8—441no—
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—
817C22#1062301711yescharacteristic
818C22#1062301711yescharacteristic
819C22C2×M16×D1111yescharacteristic
820C22C2×#6696011yescharacteristic
821C22#1062327611yescharacteristic
822C22#1062327611yescharacteristic
823C22C2×C4×C22⋊D1111yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—222no—
828C4—222no—
829C4—441no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4—441no—
834C4#1062302511yescharacteristic
835C4#1062302511yescharacteristic
836C4#1062333511yescharacteristic
837C4#1062333611yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—881no—
842C2#1307127411yescharacteristic
843C2#1307734111yescharacteristic
844C2M16×C22⋊D1111yescharacteristic
845C2#1307765211yescharacteristic
846C2#1307765511yescharacteristic
847C2#1307766611yescharacteristic
848C2#1307767611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#407C2
prime radicalC2×#67006C4
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#22038
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#10622741C2semidirect
3. #13069412C2semidirect
4. #13069408C2semidirect
5. #13069232C2semidirect
6. #13069225C2semidirect
7. #13069219C2semidirect
8. #13069219C2semidirect
9. #13068913C2semidirect
10. #13068910C2semidirect
11. #13068910C2semidirect
12. #13068799C2semidirect
13. #13068526C2semidirect
14. #13068397C2semidirect
15. C2×C11×#407C2semidirect
23. C22×#4313C22semidirect
46. C2×(C2×D11)⋊C8C22semidirect
47. C2×(C2×D11)⋊C8C22semidirect
48. C2×(C2×D11)⋊C8C22semidirect
49. C2×#66879C22semidirect
50. C2×Dic11⋊C8C22semidirect
51. C2×Dic11⋊C8C22semidirect
52. C2×Dic11⋊C8C22semidirect
53. C2×C8×Dic11C22semidirect
54. C2×C8×Dic11C22semidirect
55. #10622188C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622188C22semidirect
83. C2×C11×M16D4semidirect
236. C22⋊Dic11M16semidirect
263. C2×#407D11semidirect
499. C2×M16C22⋊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×#106227412
C4×#670062
#130694122
#130694082
#130692322
#130692252
#130692192
#130689132
#130689102
#130687992
#130685262
#130683972
C2×C11×#4072
#2203811