Finite Group Databasebeta

← #14764891

Subgroups — #14764891

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622741C211yesmaximal, characteristic, complemented
2#13071829C211yesmaximal, 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#13068910C211yesmaximal, characteristic, complemented
10#13068910C211yesmaximal, characteristic, complemented
11#13068908C211yesmaximal, characteristic, complemented
12#13068794C211yesmaximal, characteristic, complemented
13#13068528C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C2×C11×#408C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23C11×#408—24no—
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28#10622844C411yescharacteristic
29#10622842C411yescharacteristic
30#10622836C411yescharacteristic
31#10622836C411yescharacteristic
32#10622836C411yescharacteristic
33#10622835C411yescharacteristic
34#10622835C411yescharacteristic
35#10622835C411yescharacteristic
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
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49C2×#66879C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×Dic11⋊C8C2211yescharacteristic
52C2×Dic11⋊C8C2211yescharacteristic
53C2×C8×Dic11C2211yescharacteristic
54C2×C8×Dic11C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2×C411yescharacteristic
68C22×D4×C11C2×C411yescharacteristic
69C22×D4×C11C2×C411yescharacteristic
70C22×D4×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—41no—
79C2×C11×M16—41no—
80C2×C11×M16D414yescomplemented
81C22×C8×C11—22no—
82C22×C8×C11—41no—
83C22×C8×C11—41no—
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
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
97C4×C22⋊D11—22no—
98C4×C22⋊D11—22no—
99C4×C22⋊D11—41no—
100C4×C22⋊D11—41no—
101C4×C22⋊D11—41no—
102C4×C22⋊D11—41no—
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×(C2×D11)⋊C4C2×C411yescharacteristic
106C2×Dic11⋊C4C2×C411yescharacteristic
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×Dic11⋊C4C2×C411yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C2×#4313—22no—
117C2×#4313—41no—
118C2×#4313—41no—
119C11×C22⋊C8—22no—
120C11×C22⋊C8—22no—
121C11×C22⋊C8—22no—
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—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—41no—
132C22⋊(C11⋊C8)—41no—
133C22⋊(C11⋊C8)—41no—
134C22⋊(C11⋊C8)—41no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—41no—
137(C2×D11)⋊C8—41no—
138#66879—41no—
139Dic11⋊C8—22no—
140Dic11⋊C8—41no—
141Dic11⋊C8—41no—
142C8×Dic11—22no—
143C8×Dic11—41no—
144#22039—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C11×#41—44no—
150C11×#41—44no—
151C11×#41—44no—
152C11×#41—44no—
153C2×Q8×C11—22no—
154C2×Q8×C11—41no—
155C2×Q8×C11—41no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
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—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11#4112yes—
186C22×C4×C11C2411yescharacteristic
187C2×C22⋊D11—22no—
188C2×C22⋊D11—22no—
189C2×C22⋊D11—22no—
190C2×C22⋊D11—41no—
191C2×C22⋊D11—41no—
192C2×C22⋊D11—41no—
193C2×C22⋊D11—41no—
194C2×C22⋊D11—41no—
195C2×C22⋊D11—41no—
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C411yescharacteristic
198C22×Dic11C22×C411yescharacteristic
199C22×Dic11C22×C411yescharacteristic
200C22×Dic11C22×C411yescharacteristic
201C22×Dic11C22×C411yescharacteristic
202C22×Dic11C22×C411yescharacteristic
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—21no—
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C11×M16—44no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—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—44no—
221C2×C8×C11C2×D412yes—
222C2×C8×C11C2×D412yes—
223C22⋊Dic11—22no—
224C22⋊Dic11—22no—
225C22⋊Dic11—22no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11—41no—
229C22⋊Dic11—41no—
230C22⋊Dic11—41no—
231C22⋊Dic11—41no—
232(C2×D11)⋊C4—22no—
233(C2×D11)⋊C4—41no—
234(C2×D11)⋊C4—41no—
235Dic11⋊C4—22no—
236Dic11⋊C4—41no—
237Dic11⋊C4—41no—
238C4×Dic11—21no—
239C4×Dic11—21no—
240C4×Dic11—21no—
241C4×Dic11—21no—
242C4×Dic11—21no—
243C4×Dic11—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
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—
256#4313—44no—
257C2×#436—111no—
258C2×#408D1111yescharacteristic, complemented
259#2388—111no—
260#1955—111no—
261#1954—111no—
262#1924—111no—
263#1923—111no—
264#1923—111no—
265#1923—111no—
266#1870—111no—
267#1870—111no—
268#1869—111no—
269#1850—111no—
270#1780—111no—
271#1753—111no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
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×C11C4×D412yes—
293C23×C11C23×C411yescharacteristic
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301Q8×C11—44no—
302D4×C11—44no—
303D4×C11—44no—
304D4×C11—44no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11C4×D412yes—
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C22⋊D11—44no—
333C22⋊D11—44no—
334C22⋊D11—44no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
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—21no—
354C2×Dic11#13112yes—
355C2×Dic11#13112yes—
356C4×D11—41no—
357C4×D11—41no—
358C4×D11—41no—
359C4×D11—41no—
360C8×C11—22no—
361C8×C11—22no—
362C8×C11—41no—
363C8×C11—41no—
364C11⋊C8—41no—
365C11⋊C8—41no—
366C11⋊C8—41no—
367C11⋊C8—41no—
368C22×#41C2×D1111yescharacteristic
369C22×M16—111no—
370C22×M16C2×D1111yescharacteristic
371C23×C8C2×D1111yescharacteristic
372C2×C4×D4—111no—
373C2×C4×D4—111no—
374C2×C4×D4—111no—
375#436—224no—
376C2×C4⋊C8—111no—
377C2×C4⋊C8—111no—
378C2×C4⋊C8—111no—
379#408—24no—
380C2×C22⋊C8—111no—
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×C22⋊C8—111no—
384C2×C22⋊C8—111no—
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C22⋊C8—111no—
388C2×C22⋊C8—111no—
389C2×C22⋊C8C2×D1111yescharacteristic
390C2×C22⋊C8C2×D1111yescharacteristic
391C2×C22⋊C8C2×D1111yescharacteristic
392C2×C22⋊C8C2×D1111yescharacteristic
393C2×#97—111no—
394C2×C4×C8—111no—
395C2×C4×C8—111no—
396#395—111no—
397#394—111no—
398#394—111no—
399#394—111no—
400#393—111no—
401#392—111no—
402#392—111no—
403#392—111no—
404C4×C22⋊C4—111no—
405C4×C22⋊C4—111no—
406C4×C22⋊C4—111no—
407#336—111no—
408#336—111no—
409#336—111no—
410#336—111no—
411#336—111no—
412#336—111no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11C2×C4×D411yescharacteristic
435C22×C11#51811yescharacteristic
436C22×C11#51811yescharacteristic
437C22×C11C2×#13111yescharacteristic
438C22×C11C2×#13111yescharacteristic
439C22×C11#56811yescharacteristic
440C22×C11#56811yescharacteristic
441C2×D11—41no—
442C2×D11—41no—
443C2×D11—41no—
444C2×D11—41no—
445C2×D11—41no—
446C2×D11—41no—
447C2×D11—41no—
448C4×C11—22no—
449C4×C11—41no—
450C4×C11—41no—
451C4×C11#53411yescharacteristic
452C4×C11#53511yescharacteristic
453C4×C11#53811yescharacteristic
454C4×C11#53811yescharacteristic
455Dic11—22no—
456Dic11—22no—
457Dic11—41no—
458Dic11—41no—
459Dic11—41no—
460Dic11—41no—
461Dic11—41no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41—41no—
467C2×#41—41no—
468C22×Q8C4×D1111yescharacteristic
469C22×D4—111no—
470C22×D4—111no—
471C22×D4—111no—
472C22×D4C4×D1111yescharacteristic
473C22×D4C4×D1111yescharacteristic
474C22×D4C4×D1111yescharacteristic
475C23×C4—111no—
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C2×M16—41no—
480C2×M16—41no—
481C2×M16—222no—
482C2×M16—441no—
483C2×M16—441no—
484C2×M16C22⋊D1114yescomplemented
485C22×C8—22no—
486C22×C8—41no—
487C22×C8—41no—
488C22×C8—111no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8—111no—
492C22×C8C22×D1111yescharacteristic
493C22×C8C22×D1111yescharacteristic
494C22×C8C22×D1111yescharacteristic
495C22×C8C22×D1111yescharacteristic
496C4×D4—222no—
497C4×D4—222no—
498C4×D4—441no—
499C4×D4—441no—
500C4×D4—441no—
501C4×D4—441no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C22⋊C4—111no—
506C2×C22⋊C4—111no—
507C2×C22⋊C4—111no—
508C2×C22⋊C4—111no—
509C2×C22⋊C4—111no—
510C2×C22⋊C4—111no—
511C2×C22⋊C4—111no—
512C2×C22⋊C4—111no—
513C2×C22⋊C4—111no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—111no—
517C2×C42—111no—
518C2×C42—111no—
519C2×C42—111no—
520C4⋊C8—222no—
521C4⋊C8—441no—
522C4⋊C8—441no—
523C22⋊C8—22no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—22no—
527C22⋊C8—222no—
528C22⋊C8—222no—
529C22⋊C8—222no—
530C22⋊C8—441no—
531C22⋊C8—441no—
532C22⋊C8—441no—
533C22⋊C8—441no—
534C22⋊C8—441no—
535C22⋊C8—441no—
536#97—441no—
537C4×C8—222no—
538C4×C8—441no—
539#95—111no—
540#95—111no—
541#95—111no—
542#95—111no—
543#95—111no—
544#95—111no—
545C2×C11—42no—
546C2×C11—81no—
547C2×C11—81no—
548C2×C11#232111yescharacteristic
549C2×C11#293311yescharacteristic
550C2×C11#293511yescharacteristic
551C2×C11#297611yescharacteristic
552C2×C11#297811yescharacteristic
553C2×C11#297911yescharacteristic
554C2×C11#298111yescharacteristic
555D11—81no—
556C24—111no—
557C24C2×C4×D1111yescharacteristic
558C24C2×C4×D1111yescharacteristic
559C24C2×C4×D1111yescharacteristic
560#41—44no—
561#41—44no—
562#41—44no—
563#41—44no—
564C2×Q8—22no—
565C2×Q8—41no—
566C2×Q8—41no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—222no—
577C2×D4—222no—
578C2×D4—222no—
579C2×D4—441no—
580C2×D4—441no—
581C2×D4—441no—
582C2×D4—441no—
583C2×D4—441no—
584C2×D4—441no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
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—111no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4C2×C4×D1111yescharacteristic
615C22×C4C2×C4×D1111yescharacteristic
616C22×C4C2×C4×D1111yescharacteristic
617C22×C4#433912yes—
618C22×C4C2×C22⋊D1112yes—
619C22×C4C23×D1111yescharacteristic
620M16—44no—
621M16—444no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—44no—
633C2×C8—221no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8C2×C22⋊D1112yes—
646C2×C8C2×C22⋊D1112yes—
647C4⋊C4—222no—
648C4⋊C4—441no—
649C4⋊C4—441no—
650C22⋊C4—222no—
651C22⋊C4—222no—
652C22⋊C4—222no—
653C22⋊C4—222no—
654C22⋊C4—222no—
655C22⋊C4—222no—
656C22⋊C4—441no—
657C22⋊C4—441no—
658C22⋊C4—441no—
659C22⋊C4—441no—
660C22⋊C4—441no—
661C22⋊C4—441no—
662C42—221no—
663C42—221no—
664C42—221no—
665C42—221no—
666C42—221no—
667C42—221no—
668C11#2203911yescharacteristic, complemented, Sylow
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—221no—
690C23—221no—
691C23—221no—
692C23—221no—
693C23—221no—
694C23—221no—
695C23—221no—
696C23C4×C22⋊D1112yes—
697C23C22×C4×D1111yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—444no—
703D4—444no—
704D4—444no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—112no—
726C2×C4—112no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—221no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—221no—
738C2×C4—221no—
739C2×C4—221no—
740C2×C4—221no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4C4×C22⋊D1112yes—
751C2×C4C2×#433911yescharacteristic
752C2×C4#6703711yescharacteristic
753C2×C4#6703711yescharacteristic
754C2×C4#6703711yescharacteristic
755C2×C4#6703711yescharacteristic
756C2×C4C22×C22⋊D1111yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—441no—
762C8—441no—
763C8—441no—
764C8—441no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—441no—
787C22—441no—
788C22—441no—
789C22—441no—
790C22—441no—
791C22—441no—
792C22—441no—
793C22#1062301711yescharacteristic
794C22#1062301711yescharacteristic
795C22D11×#13111yescharacteristic
796C22D11×#13111yescharacteristic
797C22#1062328111yescharacteristic
798C22#1062328111yescharacteristic
799C22C2×C4×C22⋊D1111yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—222no—
804C4—222no—
805C4—441no—
806C4—441no—
807C4—441no—
808C4—441no—
809C4—441no—
810C4#1062302511yescharacteristic
811C4#1062302511yescharacteristic
812C4#1062333511yescharacteristic
813C4#1062333611yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—881no—
818C2#1307127411yescharacteristic
819C2#1307733811yescharacteristic
820C2#1307735811yescharacteristic
821C2#1307765911yescharacteristic
822C2#1307767411yescharacteristic
823C2#1307768011yescharacteristic
824C2#1307768911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#408C2
prime radical#13071829C2
cosocleC22×C4×C11C24
hypercenterC2×#408D11
hypocenterC11#22039
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#408

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. #13068910C2semidirect
10. #13068910C2semidirect
11. #13068908C2semidirect
12. #13068794C2semidirect
13. #13068528C2semidirect
14. #13068397C2semidirect
15. C2×C11×#408C2semidirect
80. C2×C11×M16D4semidirect
258. C2×#408D11semidirect
484. C2×M16C22⋊D11semidirect
668. C11#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#106227412
#130718292
#130694122
#130694082
#130692322
#130692252
#130692192
#130689102
#130689082
#130687942
#130685282
#130683972
C2×C11×#4082
#2203911