Finite Group Databasebeta

← #14772792

Subgroups — #14772792

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×#10622331C211yesmaximal, characteristic, complemented
2C22×Dic11⋊C8C211yesmaximal, characteristic, complemented
3C4×D4×Dic11C211yesmaximal, characteristic
4#13069225C211yesmaximal, characteristic, complemented
5#13069219C211yesmaximal, characteristic, complemented
6#13069174C211yesmaximal, characteristic, complemented
7#13069172C211yesmaximal, characteristic, complemented
8#13068909C211yesmaximal, characteristic
9#13068731C211yesmaximal, characteristic, complemented
10#13068594C211yesmaximal, characteristic, complemented
11#13068594C211yesmaximal, characteristic, complemented
12#13068464C211yesmaximal, characteristic, complemented
13#13068390C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C411yescharacteristic
19C2×D4×Dic11C411yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×Dic11⋊C8—24no—
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C411yescharacteristic
43C4⋊C4×Dic11C411yescharacteristic
44C22⋊C4×Dic11C411yescharacteristic
45C22⋊C4×Dic11C411yescharacteristic
46C22⋊C4×Dic11C411yescharacteristic
47C22⋊C4×Dic11C411yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49C42×Dic11C2211yescharacteristic
50#10622331—24no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2×C411yescharacteristic
65C23×Dic11C2×C411yescharacteristic
66C23×Dic11C2×C411yescharacteristic
67C23×Dic11C2×C411yescharacteristic
68C22×C8×C11—22no—
69C22×C8×C11—22no—
70C22×C8×C11—41no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85D4×Dic11—24no—
86D4×Dic11C818yescomplemented
87C2×C4⋊Dic11C2×C411yescharacteristic
88C2×C4⋊Dic11C2×C411yescharacteristic
89C2×C4×Dic11—22no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11C2×C411yescharacteristic
94C2×C4×Dic11C2×C411yescharacteristic
95C2×C4×Dic11C2×C411yescharacteristic
96C2×C4×Dic11C2×C411yescharacteristic
97C2×C4×Dic11C2×C411yescharacteristic
98C2×C4×Dic11C2×C411yescharacteristic
99C2×C4×Dic11C2×C411yescharacteristic
100C2×C4×Dic11C2×C411yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—41no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×C22⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—41no—
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C22⋊(C11⋊C8)—22no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—41no—
124Dic11⋊C8—22no—
125Dic11⋊C8—22no—
126Dic11⋊C8—22no—
127Dic11⋊C8—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8D414yescomplemented
130C8×Dic11—22no—
131C8×Dic11—22no—
132C8×Dic11—41no—
133C8×Dic11—41no—
134#22748—111nomaximal, Sylow
135C24×C11C22×C411yescharacteristic
136C24×C11C22×C411yescharacteristic
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11C2×C814yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—41no—
166C22×Dic11—41no—
167C22×Dic11C2×C814yes—
168C22×Dic11C2×C814yescomplemented
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C22×Dic11C22×C411yescharacteristic
173C22×Dic11C22×C411yescharacteristic
174C22×Dic11C22×C411yescharacteristic
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
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×C4⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C42×C11—21no—
194C42×C11—21no—
195C22⋊Dic11—22no—
196C22⋊Dic11C2×C814yes—
197C22⋊Dic11C2×C814yescomplemented
198C22⋊Dic11M1614yes—
199C4⋊Dic11—22no—
200C4⋊Dic11C2×C814yescomplemented
201C4×Dic11—22no—
202C4×Dic11—22no—
203C4×Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—21no—
208C4×Dic11—21no—
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#1869D1111yescharacteristic
239#1831—111no—
240#1797—111no—
241#1797—111no—
242C4×C4⋊C8—111no—
243C8×C22⋊C4—111no—
244C8×C22⋊C4—111no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11#11712yes—
256C23×C11C22×C812yes—
257C23×C11C22×C812yes—
258C23×C11C2×M1612yes—
259C23×C11C23×C411yescharacteristic
260D4×C11—28no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11#11712yes—
280C2×C4×C11C22×C812yes—
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×C4×C112−1+411yescharacteristic
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—28no—
300C2×Dic11—28no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—44no—
305C2×Dic11—44no—
306C2×Dic11C4×D412yes—
307C2×Dic11C4×D412yes—
308C2×Dic11C22×C812yes—
309C2×Dic11C22×C812yes—
310C2×Dic11C22×C812yes—
311C2×Dic11C22×C812yes—
312C2×Dic11C2×M1612yes—
313C2×Dic11C2×M1612yes—
314C2×Dic11#13112yes—
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×D4C2×D1111yescharacteristic
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⋊C8C2×D1111yescharacteristic
342C2×C22⋊C8C2×D1111yescharacteristic
343C2×C22⋊C8C2×D1111yescharacteristic
344C2×C4×C8—111no—
345C2×C4×C8—111no—
346C2×C4×C8—111no—
347C2×C4×C8—111no—
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⋊C4—111no—
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—22no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11#43114yescomplemented
382C22×C11C2×#11711yescharacteristic
383C22×C11C2×C4×D411yescharacteristic
384C22×C11#52011yescharacteristic
385C22×C11C23×C811yescharacteristic
386C22×C11C22×M1611yescharacteristic
387C22×C11C2×#13111yescharacteristic
388C22×C11#56811yescharacteristic
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—41no—
392C4×C11—41no—
393C4×C11#54611yescharacteristic
394C4×C11#54811yescharacteristic
395C4×C11#55211yescharacteristic
396C4×C11#55311yescharacteristic
397Dic11—22no—
398Dic11—22no—
399Dic11—22no—
400Dic11—22no—
401Dic11—22no—
402Dic11—22no—
403Dic11—41no—
404Dic11C8×D414yes—
405C22×D4C4×D1111yescharacteristic
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—111no—
409C23×C4—111no—
410C23×C4C22×D1111yescharacteristic
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—22no—
427C4×D4—22no—
428C4×D4—118no—
429C4×D4—224no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4C4×D1111yescharacteristic
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—111no—
451C2×C42—222no—
452C2×C42—222no—
453C2×C42—222no—
454C2×C42—222no—
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—22no—
464C22⋊C8—41no—
465C22⋊C8—222no—
466C22⋊C8—222no—
467C22⋊C8—441no—
468C4×C8—222no—
469C4×C8—222no—
470C4×C8—441no—
471C4×C8—441no—
472#95—111no—
473#95—111no—
474#95—111no—
475#95—111no—
476#95—111no—
477#95—111no—
478C2×C11—24no—
479C2×C11—42no—
480C2×C11#235211yescharacteristic
481C2×C11C2×#43111yescharacteristic
482C2×C11#292511yescharacteristic
483C2×C11C2×C8×D411yescharacteristic
484C2×C11D4×M1611yescharacteristic
485C2×C11#298811yescharacteristic
486C2×C11#299011yescharacteristic
487C24C2×C4×D1111yescharacteristic
488C24C2×C4×D1111yescharacteristic
489C2×D4—22no—
490C2×D4—22no—
491C2×D4C8×D1114yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—111no—
503C22×C4—114no—
504C22×C4—114no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—441no—
521C22×C4—441no—
522C22×C4C2×C4×D1111yescharacteristic
523C22×C4C2×C4×D1111yescharacteristic
524C22×C4C2×C4×D1111yescharacteristic
525C22×C4C2×C4×D1111yescharacteristic
526C22×C4#434112yes—
527C22×C4#434112yes—
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—22no—
556C4⋊C4—114no—
557C4⋊C4—222no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—114no—
561C22⋊C4—114no—
562C22⋊C4—114no—
563C22⋊C4—222no—
564C42—21no—
565C42—21no—
566C42—114no—
567C42—112no—
568C42—112no—
569C42—222no—
570C42—222no—
571C42—222no—
572C42—222no—
573C42—222no—
574C42—222no—
575C42—221no—
576C42—221no—
577C42—221no—
578C42—221no—
579C42—221no—
580C42—221no—
581C42—441no—
582C11#2274811yescharacteristic, complemented, Sylow
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23#6693012yes—
594C23C2×C8×D1112yes—
595C23C2×C8×D1112yes—
596C23M16×D1112yes—
597C23C22×C4×D1111yescharacteristic
598D4—28no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—112no—
618C2×C4—112no—
619C2×C4—112no—
620C2×C4—112no—
621C2×C4—112no—
622C2×C4—112no—
623C2×C4—112no—
624C2×C4—112no—
625C2×C4—112no—
626C2×C4—228no—
627C2×C4—228no—
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—221no—
637C2×C4—221no—
638C2×C4—221no—
639C2×C4—221no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—221no—
643C2×C4—444no—
644C2×C4—444no—
645C2×C4#6693012yes—
646C2×C4C2×C8×D1112yes—
647C2×C4C2×D4×D1111yescharacteristic
648C2×C4C2×#434111yescharacteristic
649C2×C4C2×#434111yescharacteristic
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—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22#1062233114yescomplemented
675C22C2×#6693011yescharacteristic
676C22C4×D4×D1111yescharacteristic
677C22#1062307711yescharacteristic
678C22C22×C8×D1111yescharacteristic
679C22C2×M16×D1111yescharacteristic
680C22D11×#13111yescharacteristic
681C22#1062328111yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—114no—
687C4—222no—
688C4—222no—
689C4—222no—
690C4—222no—
691C4—222no—
692C4—222no—
693C4—441no—
694C4#1062312211yescharacteristic
695C4#1062312911yescharacteristic
696C4#1062313211yescharacteristic
697C4#1062318111yescharacteristic
698C2—24no—
699C2—42no—
700C2#1307154311yescharacteristic
701C2C2×#1062233111yescharacteristic
702C2#1307727811yescharacteristic
703C2C8×D4×D1111yescharacteristic
704C2#1307734911yescharacteristic
705C2#1307772311yescharacteristic
706C2#1307773611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1869C2
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#22748
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#10622331C2semidirect
2. C22×Dic11⋊C8C2semidirect
4. #13069225C2semidirect
5. #13069219C2semidirect
6. #13069174C2semidirect
7. #13069172C2semidirect
9. #13068731C2semidirect
10. #13068594C2semidirect
11. #13068594C2semidirect
12. #13068464C2semidirect
13. #13068390C2semidirect
14. C8×C22⋊Dic11C2semidirect
86. D4×Dic11C8semidirect
129. Dic11⋊C8D4semidirect
168. C22×Dic11C2×C8semidirect
197. C22⋊Dic11C2×C8semidirect
200. C4⋊Dic11C2×C8semidirect
214. C4×Dic11C2×C8semidirect
381. C22×C11#431semidirect
582. C11#22748semidirect
674. C22#10622331semidirect

Maximal subgroups

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

subgroupindex
C2×#106223312
C22×Dic11⋊C82
C4×D4×Dic112
#130692252
#130692192
#130691742
#130691722
#130689092
#130687312
#130685942
#130684642
#130683902
C8×C22⋊Dic112
C11×#18692
#2274811