Finite Group Databasebeta

← #14772788

Subgroups — #14772788

Order 2816.

1052 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622298C211yesmaximal, characteristic, complemented
2C22×Dic11⋊C8C211yesmaximal, characteristic, complemented
3C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic
4#13069222C211yesmaximal, characteristic, complemented
5#13069220C211yesmaximal, characteristic, complemented
6#13069173C211yesmaximal, characteristic, complemented
7#13069171C211yesmaximal, characteristic, complemented
8#13068908C211yesmaximal, characteristic
9#13068906C211yesmaximal, characteristic
10#13068731C211yesmaximal, characteristic, complemented
11#13068595C211yesmaximal, characteristic, complemented
12#13068594C211yesmaximal, characteristic, complemented
13C4×Dic11⋊C8C211yesmaximal, characteristic, complemented
14C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
15C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×(C22⋊D11)⋊C4C411yescharacteristic
21C2×(C22⋊D11)⋊C4C411yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×Dic11⋊C8—24no—
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C22⋊C4×Dic11C411yescharacteristic
40C22⋊C4×Dic11C411yescharacteristic
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C42×Dic11C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46#10622298—24no—
47#10622279C411yescharacteristic
48#10622279C411yescharacteristic
49#10622262C411yescharacteristic
50#10622262C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2×C411yescharacteristic
63C23×Dic11C2×C411yescharacteristic
64C23×Dic11C2×C411yescharacteristic
65C22×C4×D11C2×C411yescharacteristic
66C22×C4×D11C2×C411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C8×C11—22no—
69C22×C8×C11—22no—
70C22×C8×C11—41no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C22⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11C2×C411yescharacteristic
80C4×C22⋊D11—22no—
81C4×C22⋊D11—22no—
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×(C2×D11)⋊C4C2×C411yescharacteristic
84C2×(C2×D11)⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11C2×C411yescharacteristic
93C2×C4×Dic11C2×C411yescharacteristic
94C2×C4×Dic11C2×C411yescharacteristic
95C2×C4×Dic11C2×C411yescharacteristic
96C2×C4×Dic11C2×C411yescharacteristic
97C2×C4×Dic11C2×C411yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108(C22⋊D11)⋊C4—24no—
109(C22⋊D11)⋊C4C818yescomplemented
110C42×D11—22no—
111C42×D11—22no—
112C11×C22⋊C8—22no—
113C4×C8×C11—22no—
114C4×C8×C11—41no—
115C11×#95C2×C411yescharacteristic
116C11×#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C22⋊(C11⋊C8)—22no—
122(C2×D11)⋊C8—22no—
123(C2×D11)⋊C8—22no—
124(C2×D11)⋊C8—41no—
125(C2×D11)⋊C8—41no—
126Dic11⋊C8—22no—
127Dic11⋊C8—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—22no—
130Dic11⋊C8—22no—
131Dic11⋊C8D414yescomplemented
132C4×C11⋊C8—22no—
133C4×C11⋊C8—41no—
134#22748—111nomaximal, Sylow
135C24×C11C22×C411yescharacteristic
136C23×D11C22×C411yescharacteristic
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11#4112yes—
147C22×C4×C11#4112yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—22no—
150C2×C22⋊D11—22no—
151C2×C22⋊D11C2×C814yes—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—41no—
157C22×Dic11C2×C814yes—
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
163C22×Dic11C22×C411yescharacteristic
164C22×Dic11C22×C411yescharacteristic
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—41no—
176C2×C4×D11C2×C814yescomplemented
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—44no—
189C2×C8×C11C2×D412yes—
190C11×C22⋊C4C2×C814yes—
191C11×C22⋊C4M1614yes—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C22⋊Dic11—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4C2×C814yescomplemented
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4C2×C814yescomplemented
203C4×Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—41no—
214C4×Dic11C2×C814yescomplemented
215C4×Dic11C2×D412yes—
216C4×Dic11#4112yes—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—44no—
229C2×C11⋊C8C2×D412yes—
230C2×#431—111no—
231C22×C4⋊C8—111no—
232C42×D4—111no—
233#1923—111no—
234#1923—111no—
235#1916—111no—
236#1916—111no—
237#1869—111no—
238#1869—111no—
239#1831—111no—
240#1797—111no—
241#1797—111no—
242C4×C4⋊C8—111no—
243C8×C22⋊C4—111no—
244C8×C22⋊C4D1111yescharacteristic, complemented
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11#11712yes—
250C23×C11C22×C812yes—
251C23×C11C2×M1612yes—
252C23×C11C23×C411yescharacteristic
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—21no—
258C22×D11—21no—
259C22×D11C22×C812yes—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11#11712yes—
275C2×C4×C11C22×C812yes—
276C2×C4×C11C22×C812yes—
277C2×C4×C11C2×M1612yes—
278C2×C4×C11C2×M1612yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C22⋊D11—28no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—28no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—44no—
303C2×Dic11C4×D412yes—
304C2×Dic11C4×D412yes—
305C2×Dic11C22×C812yes—
306C2×Dic11C22×C812yes—
307C2×Dic11C22×C812yes—
308C2×Dic11#13112yes—
309C4×D11—28no—
310C4×D11—44no—
311C4×D11—41no—
312C4×D11—41no—
313C4×D11—41no—
314C4×D11—41no—
315C8×C11—22no—
316C8×C11—41no—
317C8×C11—41no—
318C8×C11—41no—
319C11⋊C8—22no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C11⋊C8—41no—
323C23×C8—111no—
324C23×C8C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×C4×D4—111no—
327C2×C4×D4—111no—
328C22×C42—111no—
329C22×C42—111no—
330#431—224no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—111no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335C2×C4⋊C8—111no—
336C2×C4⋊C8—111no—
337C2×C4⋊C8—224no—
338C2×C22⋊C8—111no—
339C2×C22⋊C8—111no—
340C2×C22⋊C8—111no—
341C2×C22⋊C8—111no—
342C2×C22⋊C8—111no—
343C2×C22⋊C8C2×D1111yescharacteristic
344C2×C4×C8—111no—
345C2×C4×C8—111no—
346C2×C4×C8C2×D1111yescharacteristic
347C2×C4×C8C2×D1111yescharacteristic
348C4×C4⋊C4—111no—
349C4×C4⋊C4—111no—
350C4×C4⋊C4—111no—
351C4×C22⋊C4—111no—
352C4×C22⋊C4—111no—
353C4×C22⋊C4—111no—
354C4×C22⋊C4—111no—
355C4×C22⋊C4—111no—
356C4×C22⋊C4C2×D1111yescharacteristic
357C43—111no—
358#336—111no—
359#336—111no—
360#336—111no—
361#336—111no—
362#336—111no—
363#336—111no—
364#336—111no—
365#336—111no—
366#336C2×D1111yescharacteristic
367#336C2×D1111yescharacteristic
368C22×C11—22no—
369C22×C11—22no—
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11#43114yescomplemented
375C22×C11C2×#11711yescharacteristic
376C22×C11C2×C4×D411yescharacteristic
377C22×C11#52011yescharacteristic
378C22×C11C23×C811yescharacteristic
379C22×C11C22×M1611yescharacteristic
380C22×C11C2×#13111yescharacteristic
381C22×C11#56811yescharacteristic
382C2×D11—22no—
383C2×D11—22no—
384C2×D11—22no—
385C2×D11—41no—
386C2×D11—41no—
387C2×D11—41no—
388C2×D11—41no—
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—22no—
394C4×C11#54611yescharacteristic
395C4×C11#54811yescharacteristic
396C4×C11#55211yescharacteristic
397C4×C11#55311yescharacteristic
398Dic11—22no—
399Dic11—22no—
400Dic11—22no—
401Dic11—41no—
402Dic11—41no—
403Dic11—41no—
404Dic11C8×D414yes—
405C22×D4—111no—
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—111no—
409C23×C4—111no—
410C23×C4—111no—
411C23×C4C22×D1111yescharacteristic
412C22×C8—22no—
413C22×C8—22no—
414C22×C8—41no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8—222no—
420C22×C8—222no—
421C22×C8—441no—
422C22×C8C22×D1111yescharacteristic
423C22×C8C22×D1111yescharacteristic
424C22×C8C22×D1111yescharacteristic
425C22×C8C22×D1111yescharacteristic
426C4×D4—118no—
427C4×D4—222no—
428C4×D4—222no—
429C4×D4—224no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4C4×D1111yescharacteristic
438C2×C22⋊C4C4×D1111yescharacteristic
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—222no—
451C2×C42—222no—
452C2×C42—222no—
453C2×C42—222no—
454C2×C42C22×D1111yescharacteristic
455C2×C42C22×D1111yescharacteristic
456C4⋊C8—114no—
457C4⋊C8—222no—
458C4⋊C8—222no—
459C4⋊C8—222no—
460C4⋊C8—222no—
461C4⋊C8—222no—
462C22⋊C8—22no—
463C22⋊C8—222no—
464C22⋊C8—222no—
465C22⋊C8—222no—
466C22⋊C8—441no—
467C22⋊C8—441no—
468C4×C8—22no—
469C4×C8—41no—
470C4×C8—222no—
471C4×C8—441no—
472#95—111no—
473#95—111no—
474#95—111no—
475#95—111no—
476#95C4×D1111yescharacteristic
477#95C4×D1111yescharacteristic
478C2×C11—24no—
479C2×C11#235211yescharacteristic
480C2×C11C2×#43111yescharacteristic
481C2×C11#292511yescharacteristic
482C2×C11C2×C8×D411yescharacteristic
483C2×C11D4×M1611yescharacteristic
484C2×C11#298811yescharacteristic
485C2×C11#299011yescharacteristic
486D11—42no—
487C24—111no—
488C24C2×C4×D1111yescharacteristic
489C2×D4—114no—
490C2×D4—222no—
491C2×D4—222no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—111no—
497C22×C4—114no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—114no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—441no—
520C22×C4—441no—
521C22×C4C2×C4×D1111yescharacteristic
522C22×C4C2×C4×D1111yescharacteristic
523C22×C4C2×C4×D1111yescharacteristic
524C22×C4C2×C4×D1111yescharacteristic
525C22×C4C2×C4×D1111yescharacteristic
526C22×C4#433912yes—
527C22×C4#433912yes—
528C22×C4C23×D1111yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—44no—
541C2×C8—112no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—444no—
554C2×C8D4×D1112yes—
555C4⋊C4—114no—
556C4⋊C4—222no—
557C4⋊C4—222no—
558C22⋊C4—114no—
559C22⋊C4—222no—
560C22⋊C4—222no—
561C22⋊C4—222no—
562C22⋊C4C8×D1114yes—
563C22⋊C4#431314yes—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—114no—
569C42—112no—
570C42—112no—
571C42—222no—
572C42—222no—
573C42—222no—
574C42—222no—
575C42—222no—
576C42—222no—
577C42—221no—
578C42—221no—
579C42—221no—
580C42—221no—
581C42—441no—
582C11#2274811yescharacteristic, complemented, Sylow
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—112no—
588C23—221no—
589C23—221no—
590C23—221no—
591C23—221no—
592C23—221no—
593C23—221no—
594C23#6692512yes—
595C23C2×C8×D1112yes—
596C23C2×#431312yes—
597C23C22×C4×D1111yescharacteristic
598D4—228no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—112no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—112no—
618C2×C4—112no—
619C2×C4—228no—
620C2×C4—228no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—444no—
637C2×C4—444no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4#6692512yes—
643C2×C4C2×C8×D1112yes—
644C2×C4C2×C8×D1112yes—
645C2×C4C2×#431312yes—
646C2×C4C2×#431312yes—
647C2×C4C2×#433911yescharacteristic
648C2×C4C2×#433911yescharacteristic
649C2×C4C2×D4×D1111yescharacteristic
650C2×C4#6703711yescharacteristic
651C2×C4#41×D1111yescharacteristic
652C2×C4#6704311yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—222no—
658C8—441no—
659C8—441no—
660C8—441no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—222no—
668C22—222no—
669C22—222no—
670C22—441no—
671C22—441no—
672C22—441no—
673C22—441no—
674C22#1062229814yescomplemented
675C22C2×#6692511yescharacteristic
676C22C4×D4×D1111yescharacteristic
677C22#1062307711yescharacteristic
678C22C22×C8×D1111yescharacteristic
679C22C22×#431311yescharacteristic
680C22D11×#13111yescharacteristic
681C22#1062328111yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—22no—
687C4—114no—
688C4—222no—
689C4—222no—
690C4—222no—
691C4—441no—
692C4—441no—
693C4—441no—
694C4#1062302111yescharacteristic
695C4#1062306211yescharacteristic
696C4#1062307111yescharacteristic
697C4#1062308311yescharacteristic
698C2—24no—
699C2—442no—
700C2#1307153911yescharacteristic
701C2C2×#1062229811yescharacteristic
702C2#1307728011yescharacteristic
703C2C8×D4×D1111yescharacteristic
704C2D4×#431311yescharacteristic
705C2#1307772311yescharacteristic
706C2#1307773911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC8×C11×C22⋊C4C2
socleC23×C11C23×C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11#22748
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622298C2semidirect
2. C22×Dic11⋊C8C2semidirect
4. #13069222C2semidirect
5. #13069220C2semidirect
6. #13069173C2semidirect
7. #13069171C2semidirect
10. #13068731C2semidirect
11. #13068595C2semidirect
12. #13068594C2semidirect
13. C4×Dic11⋊C8C2semidirect
14. C22⋊C4×C11⋊C8C2semidirect
15. C8×C11×C22⋊C4C2semidirect
109. (C22⋊D11)⋊C4C8semidirect
131. Dic11⋊C8D4semidirect
176. C2×C4×D11C2×C8semidirect
199. (C2×D11)⋊C4C2×C8semidirect
202. Dic11⋊C4C2×C8semidirect
214. C4×Dic11C2×C8semidirect
244. C8×C22⋊C4D11semidirect
374. C22×C11#431semidirect
582. C11#22748semidirect
674. C22#10622298semidirect

Maximal subgroups

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

subgroupindex
C2×#106222982
C22×Dic11⋊C82
C4×(C22⋊D11)⋊C42
#130692222
#130692202
#130691732
#130691712
#130689082
#130689062
#130687312
#130685952
#130685942
C4×Dic11⋊C82
C22⋊C4×C11⋊C82
C8×C11×C22⋊C42
#2274811