Finite Group Databasebeta

← #14775947

Subgroups — #14775947

Order 2816.

1040 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622724C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#10622452C211yesmaximal, characteristic, complemented
4#13071854C211yesmaximal, characteristic
5#13069415C211yesmaximal, characteristic, complemented
6#13069334C211yesmaximal, characteristic, complemented
7#13069232C211yesmaximal, characteristic, complemented
8#13069225C211yesmaximal, characteristic, complemented
9#13068910C211yesmaximal, characteristic, complemented
10#13068905C211yesmaximal, characteristic, complemented
11#13068794C211yesmaximal, characteristic, complemented
12#13068794C211yesmaximal, characteristic, complemented
13#13068493C211yesmaximal, characteristic, complemented
14#13068383C211yesmaximal, characteristic, complemented
15C2×C8×D4×C11C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×#66925C2211yescharacteristic
24C8×D4×C11—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29#10622836C411yescharacteristic
30#10622835C411yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C4×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622724—24no—
38C8×C22⋊D11—24no—
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×#66879C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×Dic11⋊C8C2211yescharacteristic
46C2×C8×Dic11C2211yescharacteristic
47#10622606C411yescharacteristic
48#10622593C411yescharacteristic
49#10622574C411yescharacteristic
50#10622574C411yescharacteristic
51#10622561C411yescharacteristic
52#10622561C411yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56#10622452—24no—
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—41no—
74C22×C8×C11—41no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90C2×C22⋊Dic11C2×C411yescharacteristic
91C4×C22⋊D11—22no—
92C4×C22⋊D11—22no—
93C4×C22⋊D11—22no—
94C4×C22⋊D11—22no—
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×C4⋊Dic11C2×C411yescharacteristic
100C2×C4⋊Dic11C2×C411yescharacteristic
101C2×Dic11⋊C4C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×#4313—22no—
113C2×#4313—22no—
114C2×#4313—41no—
115C2×C8×D11—22no—
116C2×C8×D11—22no—
117C2×C8×D11—41no—
118#66925—22no—
119#66925—22no—
120C11×C4⋊C8D414yescomplemented
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C4×C8×C11—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—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8D414yescomplemented
136#66879—22no—
137Dic11⋊C8—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142C4⋊(C11⋊C8)—22no—
143#66867—22no—
144#22991—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—22no—
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—22no—
173C2×C22⋊D11—41no—
174C22×Dic11C22×C411yescharacteristic
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C22×Dic11C22×C411yescharacteristic
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11C2×D412yes—
186C2×C4×D11#4112yes—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—44no—
197C2×C8×C11—44no—
198C2×C8×C11C2×D412yes—
199C2×C8×C11C2×D412yes—
200C2×C8×C11C2×D412yes—
201C11×C4⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C42×C11C2×D412yes—
205C42×C11#4112yes—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208C22⋊Dic11—22no—
209C22⋊Dic11—22no—
210C22⋊Dic11—22no—
211C22⋊Dic11—41no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—22no—
214(C2×D11)⋊C4—22no—
215(C2×D11)⋊C4—22no—
216C4⋊Dic11—22no—
217C4⋊Dic11—41no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—22no—
221Dic11⋊C4—22no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8C2×D412yes—
240#4313—44no—
241C8×D11—44no—
242C2×#435—111no—
243C2×C8×D4—111no—
244C2×C8×D4D1111yescharacteristic, complemented
245C2×#424—111no—
246#2392—111no—
247#1955—111no—
248#1939—111no—
249#1924—111no—
250#1923—111no—
251#1870—111no—
252#1869—111no—
253#1850—111no—
254#1850—111no—
255#1771—111no—
256#1750—111no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11#13112yes—
270C23×C11#13112yes—
271C23×C11C23×C411yescharacteristic
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11C4×D412yes—
279D4×C11—28no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11C4×D412yes—
299C2×C4×C11C4×D412yes—
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C2×C4×C112−1+411yescharacteristic
306C22⋊D11—28no—
307C22⋊D11—44no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11C4×D412yes—
328C2×Dic11#13112yes—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—22no—
333C8×C11—22no—
334C8×C11—22no—
335C8×C11—22no—
336C8×C11—41no—
337C11⋊C8—22no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C22×M16—111no—
342C23×C8—111no—
343C23×C8C2×D1111yescharacteristic
344C23×C8C2×D1111yescharacteristic
345C2×C4×D4—111no—
346C2×C4×D4—111no—
347C2×C4×D4C2×D1111yescharacteristic
348C2×#117—111no—
349#435—224no—
350C8×D4—24no—
351C8×D4—224no—
352#424—224no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8—111no—
356C2×C4⋊C8—111no—
357C2×C4⋊C8—111no—
358C2×C4⋊C8C2×D1111yescharacteristic
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8C2×D1111yescharacteristic
366C2×C22⋊C8C2×D1111yescharacteristic
367C2×#97—111no—
368C2×#97—111no—
369C2×C4×C8—111no—
370C2×C4×C8C2×D1111yescharacteristic
371#398—111no—
372#397—111no—
373#396—111no—
374#396—111no—
375#394—111no—
376#394—111no—
377#394—111no—
378#392—111no—
379C4×C4⋊C4—111no—
380C4×C22⋊C4—111no—
381C4×C22⋊C4—111no—
382#336—111no—
383#336—111no—
384#336—111no—
385#336—111no—
386#336—111no—
387#336—111no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11C2×C4×D411yescharacteristic
403C22×C11C2×C4×D411yescharacteristic
404C22×C11#52011yescharacteristic
405C22×C11C2×#13111yescharacteristic
406C22×C11C2×#13111yescharacteristic
407C22×C11C2×#13111yescharacteristic
408C22×C11#56811yescharacteristic
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11D4211yescharacteristic
421C4×C11#54711yescharacteristic
422C4×C11#54811yescharacteristic
423C4×C11#55311yescharacteristic
424Dic11—22no—
425Dic11—22no—
426Dic11—41no—
427Dic11—41no—
428Dic11—41no—
429Dic11—41no—
430Dic11—41no—
431C22×D4—111no—
432C22×D4—111no—
433C22×D4C4×D1111yescharacteristic
434C23×C4—111no—
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437C2×M16—222no—
438C2×M16—222no—
439C2×M16—441no—
440C22×C8—22no—
441C22×C8—22no—
442C22×C8—22no—
443C22×C8—22no—
444C22×C8—41no—
445C22×C8—41no—
446C22×C8—111no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—111no—
450C22×C8—222no—
451C22×C8—222no—
452C22×C8—441no—
453C22×C8C22×D1111yescharacteristic
454C22×C8C22×D1111yescharacteristic
455C22×C8C22×D1111yescharacteristic
456C22×C8C22×D1111yescharacteristic
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—222no—
460C4×D4—222no—
461C4×D4—222no—
462C4×D4—222no—
463#117—222no—
464#117—222no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4C4×D1111yescharacteristic
472C2×C22⋊C4—111no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—111no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4C4×D1111yescharacteristic
483C2×C22⋊C4C4×D1111yescharacteristic
484C2×C42—111no—
485C2×C42—111no—
486C2×C42—111no—
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—222no—
489C4⋊C8—222no—
490C4⋊C8—222no—
491C4⋊C8—222no—
492C4⋊C8—222no—
493C4⋊C8C22⋊D1114yescomplemented
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8—114no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500C22⋊C8—441no—
501C22⋊C8—441no—
502#97—222no—
503#97—222no—
504C4×C8—22no—
505C4×C8—222no—
506#95—111no—
507#95—111no—
508#95—111no—
509#95—111no—
510#95—111no—
511#95—111no—
512C2×C11—42no—
513C2×C11—42no—
514C2×C11#236111yescharacteristic
515C2×C11#292911yescharacteristic
516C2×C11#292911yescharacteristic
517C2×C11#293311yescharacteristic
518C2×C11#293511yescharacteristic
519C2×C11#299211yescharacteristic
520C2×C11#299411yescharacteristic
521D11—42no—
522C24—111no—
523C24C2×C4×D1111yescharacteristic
524C24C2×C4×D1111yescharacteristic
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—222no—
529C2×D4—222no—
530C2×D4—222no—
531C2×D4—222no—
532C2×D4—222no—
533C2×D4—441no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—111no—
551C22×C4—111no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4C2×C4×D1111yescharacteristic
560C22×C4C2×C4×D1111yescharacteristic
561C22×C4C2×C4×D1111yescharacteristic
562C22×C4C2×C4×D1111yescharacteristic
563C22×C4C23×D1111yescharacteristic
564M16—444no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—44no—
575C2×C8—44no—
576C2×C8—112no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—444no—
589C2×C8D4×D1112yes—
590C2×C8C2×C22⋊D1112yes—
591C2×C8C2×C22⋊D1112yes—
592C4⋊C4—22no—
593C4⋊C4—222no—
594C4⋊C4—222no—
595C4⋊C4—222no—
596C4⋊C4—222no—
597C4⋊C4—222no—
598C4⋊C4—441no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—222no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—222no—
607C22⋊C4—222no—
608C22⋊C4—222no—
609C22⋊C4—222no—
610C22⋊C4—441no—
611C42—221no—
612C42—221no—
613C42—221no—
614C42—221no—
615C42—221no—
616C42—221no—
617C42#433912yes—
618C42C2×C22⋊D1112yes—
619C11#2299111yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—112no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23#6695412yes—
640C23#6695412yes—
641C23C22×C4×D1111yescharacteristic
642D4—28no—
643D4—228no—
644D4—444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—112no—
664C2×C4—112no—
665C2×C4—221no—
666C2×C4—221no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4C4×C22⋊D1112yes—
689C2×C4C4×C22⋊D1112yes—
690C2×C4C2×#433911yescharacteristic
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4#6703711yescharacteristic
693C2×C4#41×D1111yescharacteristic
694C2×C4#6704311yescharacteristic
695C2×C4C22×C22⋊D1111yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—41no—
700C8—222no—
701C8—441no—
702C8—441no—
703C8—441no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—222no—
719C22—222no—
720C22—222no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—441no—
725C22C4×D4×D1111yescharacteristic
726C22#1062307711yescharacteristic
727C22C2×#6695411yescharacteristic
728C22C2×#6695411yescharacteristic
729C22D11×#13111yescharacteristic
730C22#1062328111yescharacteristic
731C22C2×C4×C22⋊D1111yescharacteristic
732C4—22no—
733C4—22no—
734C4—41no—
735C4—41no—
736C4—222no—
737C4—222no—
738C4—441no—
739C4—441no—
740C4—441no—
741C4—441no—
742C4—441no—
743C4#1062308211yescharacteristic
744C4#1062308911yescharacteristic
745C4D4×C22⋊D1111yescharacteristic
746C4#1062336211yescharacteristic
747C2—42no—
748C2—42no—
749C2—442no—
750C2#1307162811yescharacteristic
751C2#1307730511yescharacteristic
752C2#1307731011yescharacteristic
753C2#1307733611yescharacteristic
754C2#1307735811yescharacteristic
755C2#1307774911yescharacteristic
756C2#1307777311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C8×D4×C11C2
prime radical#10622836C4
cosocleC22×C4×C11C24
hypercenterC2×C8×D4D11
hypocenterC11#22991
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622724C2semidirect
2. C2×C8×C22⋊D11C2semidirect
3. C2×#10622452C2semidirect
5. #13069415C2semidirect
6. #13069334C2semidirect
7. #13069232C2semidirect
8. #13069225C2semidirect
9. #13068910C2semidirect
10. #13068905C2semidirect
11. #13068794C2semidirect
12. #13068794C2semidirect
13. #13068493C2semidirect
14. #13068383C2semidirect
15. C2×C8×D4×C11C2semidirect
120. C11×C4⋊C8D4semidirect
135. (C2×D11)⋊C8D4semidirect
244. C2×C8×D4D11semidirect
493. C4⋊C8C22⋊D11semidirect
619. C11#22991semidirect

Maximal subgroups

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

subgroupindex
C2×#106227242
C2×C8×C22⋊D112
C2×#106224522
#130718542
#130694152
#130693342
#130692322
#130692252
#130689102
#130689052
#130687942
#130684932
#130683832
C2×C8×D4×C112
#2299111