Finite Group Databasebeta

← C11×#22647 #14599840

Subgroups — C11×#22647 #14599840

Order 2816.

1028 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×C11×#435C211yesmaximal, characteristic
2C2×C8×D4×C11C211yesmaximal, characteristic
3C2×C11×#424C211yesmaximal, characteristic, complemented
4C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
5C11×#2290C211yesmaximal, characteristic
6C11×#1940C211yesmaximal, characteristic, complemented
7C11×#1939C211yesmaximal, characteristic, complemented
8C11×#1851C211yesmaximal, characteristic, complemented
9C11×#1850C211yesmaximal, characteristic, complemented
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1850C211yesmaximal, characteristic, complemented
12C11×#1843C211yesmaximal, characteristic, complemented
13C11×#1798C211yesmaximal, characteristic, complemented
14C11×#1797C211yesmaximal, characteristic, complemented
15C11×#1768C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C11×#435—24no—
24C8×D4×C11—24no—
25C11×#424—24no—
26C2×C11×C4⋊C8—24no—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43C2×C11×#97C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C11×#388C411yescharacteristic
46C11×#388C411yescharacteristic
47C11×#387C411yescharacteristic
48C11×#387C411yescharacteristic
49C11×#386C411yescharacteristic
50C11×#386C411yescharacteristic
51C11×#385C411yescharacteristic
52C11×#385C411yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4C2211yescharacteristic
56C11×#376C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2×C411yescharacteristic
65C23×C4×C11C2×C411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—41no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—41no—
78C22×C8×C11—41no—
79C22×C8×C11—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C4×D4×C11D414yes—
89C4×D4×C11Q814yes—
90C11×#117—22no—
91C11×#117—22no—
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C4⋊C4C2×C411yescharacteristic
94C2×C11×C4⋊C4C2×C411yescharacteristic
95C2×C11×C4⋊C4C2×C411yescharacteristic
96C2×C11×C4⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C11×C22⋊C4C2×C411yescharacteristic
100C2×C11×C22⋊C4C2×C411yescharacteristic
101C2×C11×C22⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C42×C11—22no—
106C2×C42×C11—22no—
107C2×C42×C11C2×C411yescharacteristic
108C2×C42×C11C2×C411yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×C4⋊C8—22no—
115C11×C4⋊C8—22no—
116C11×C4⋊C8—22no—
117C11×C4⋊C8—22no—
118C11×C4⋊C8—22no—
119C11×C4⋊C8—22no—
120C11×C4⋊C8—22no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—41no—
124C11×C4⋊C8—41no—
125C11×C4⋊C8D414yescomplemented
126C11×C22⋊C8—22no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×#97—22no—
131C4×C8×C11—22no—
132C11×#95C2×C411yescharacteristic
133C11×#95C2×C411yescharacteristic
134C11×#95C2×C411yescharacteristic
135C11×#95C2×C411yescharacteristic
136C11×#95C2×C411yescharacteristic
137C11×#95C2×C411yescharacteristic
138C11×#95C2×C411yescharacteristic
139C11×#95C2×C411yescharacteristic
140C11×#95C2×C411yescharacteristic
141C11×#95C2×C411yescharacteristic
142#22647C1111yesmaximal, characteristic, direct product factor, Sylow
143C24×C11C22×C411yescharacteristic
144C24×C11C22×C411yescharacteristic
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11C4⋊C414yes—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×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—22no—
160C22×C4×C11—22no—
161C22×C4×C11—41no—
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C22×C411yescharacteristic
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×Q812yes—
177C22×C4×C11C2×Q812yes—
178C22×C4×C11C2411yescharacteristic
179C11×M16—44no—
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—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—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—44no—
203C2×C8×C11—44no—
204C2×C8×C11—44no—
205C2×C8×C11C2×D412yes—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—41no—
211C11×C4⋊C4C4⋊C414yes—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—41no—
218C11×C22⋊C4C4⋊C414yes—
219C11×C22⋊C4C4⋊C414yes—
220C42×C11—22no—
221C42×C11—22no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11C2×D412yes—
229C42×C11C2×D412yes—
230C42×C11C2×Q812yes—
231C42×C11#4112yes—
232C2×#435C2×C1111yescharacteristic
233C2×C8×D4C2×C1111yescharacteristic
234C2×#424C2×C1111yescharacteristic, complemented
235C22×C4⋊C8C2×C1111yescharacteristic, complemented
236#2290C2×C1111yescharacteristic
237#1940C2×C1111yescharacteristic, complemented
238#1939C2×C1111yescharacteristic, complemented
239#1851C2×C1111yescharacteristic, complemented
240#1850C2×C1111yescharacteristic, complemented
241#1850C2×C1111yescharacteristic, complemented
242#1850C2×C1111yescharacteristic, complemented
243#1843C2×C1111yescharacteristic, complemented
244#1798C2×C1111yescharacteristic, complemented
245#1797C2×C1111yescharacteristic, complemented
246#1768C2×C1111yescharacteristic, complemented
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—21no—
256C23×C11—21no—
257C23×C11C2×C4⋊C412yes—
258C23×C11C2×C4⋊C412yes—
259C23×C11#13112yes—
260C23×C11#13112yes—
261C23×C11C23×C411yescharacteristic
262D4×C11—28no—
263C2×C4×C11—28no—
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—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—44no—
302C2×C4×C11C2×C4⋊C412yes—
303C2×C4×C11C2×C4⋊C412yes—
304C2×C4×C11C2×C4⋊C412yes—
305C2×C4×C11C2×C4⋊C412yes—
306C2×C4×C11C4×D412yes—
307C2×C4×C11C4×D412yes—
308C2×C4×C11#13112yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C22×Q811yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C112−1+411yescharacteristic
315C8×C11—22no—
316C8×C11—22no—
317C8×C11—41no—
318C8×C11—41no—
319C8×C11—41no—
320C8×C11—41no—
321C8×C11—41no—
322C8×C11—41no—
323C22×M16C22×C1111yescharacteristic
324C23×C8C22×C1111yescharacteristic
325C23×C8C22×C1111yescharacteristic
326C23×C8C22×C1111yescharacteristic
327C2×C4×D4C22×C1111yescharacteristic
328C2×#117C22×C1111yescharacteristic
329C22×C42C22×C1111yescharacteristic
330#435—24no—
331C8×D4—24no—
332#424—24no—
333C2×C4⋊C8—24no—
334C2×C4⋊C8C22×C1111yescharacteristic
335C2×C4⋊C8C22×C1111yescharacteristic
336C2×C4⋊C8C22×C1111yescharacteristic
337C2×C4⋊C8C22×C1111yescharacteristic
338C2×C4⋊C8C22×C1111yescharacteristic
339C2×C4⋊C8C22×C1111yescharacteristic
340C2×C4⋊C8C22×C1111yescharacteristic
341C2×C4⋊C8C22×C1111yescharacteristic
342C2×C4⋊C8C22×C1111yescharacteristic
343C2×C4⋊C8C22×C1111yescharacteristic
344C2×C4⋊C8C22×C1111yescharacteristic
345C2×C4⋊C8C22×C1111yescharacteristic
346C2×C22⋊C8C22×C1111yescharacteristic
347C2×C22⋊C8C22×C1111yescharacteristic
348C2×C22⋊C8C22×C1111yescharacteristic
349C2×C22⋊C8C22×C1111yescharacteristic
350C2×#97C22×C1111yescharacteristic
351C2×C4×C8C22×C1111yescharacteristic
352#388C4×C1111yescharacteristic
353#388C4×C1111yescharacteristic
354#387C4×C1111yescharacteristic
355#387C4×C1111yescharacteristic
356#386C4×C1111yescharacteristic
357#386C4×C1111yescharacteristic
358#385C4×C1111yescharacteristic
359#385C4×C1111yescharacteristic
360C4×C4⋊C4C22×C1111yescharacteristic
361C4×C22⋊C4C22×C1111yescharacteristic
362C4×C22⋊C4C22×C1111yescharacteristic
363#376C22×C1111yescharacteristic
364#336C22×C1111yescharacteristic
365#336C22×C1111yescharacteristic
366#336C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369#336C22×C1111yescharacteristic
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11#42414yescomplemented
384C22×C11C22×C4⋊C411yescharacteristic
385C22×C11C2×C4×D411yescharacteristic
386C22×C11#52011yescharacteristic
387C22×C11C2×#13111yescharacteristic
388C22×C11C2×#13111yescharacteristic
389C22×C11C2×#13111yescharacteristic
390C22×C11#56811yescharacteristic
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11D4211yescharacteristic
404C4×C11#54711yescharacteristic
405C4×C11D4×Q811yescharacteristic
406C4×C11#55411yescharacteristic
407C22×D4C2×C4×C1111yescharacteristic
408C23×C4C2×C4×C1111yescharacteristic
409C23×C4C2×C4×C1111yescharacteristic
410C23×C4C23×C1111yescharacteristic
411C23×C4C23×C1111yescharacteristic
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—41no—
415C22×C8—22no—
416C22×C8—22no—
417C22×C8—22no—
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—22no—
421C22×C8—41no—
422C22×C8—41no—
423C22×C8—41no—
424C22×C8C23×C1111yescharacteristic
425C22×C8C23×C1111yescharacteristic
426C22×C8C23×C1111yescharacteristic
427C22×C8C23×C1111yescharacteristic
428C22×C8C23×C1111yescharacteristic
429C22×C8C23×C1111yescharacteristic
430C22×C8C23×C1111yescharacteristic
431C22×C8C23×C1111yescharacteristic
432C4×D4D4×C1114yes—
433C4×D4Q8×C1114yes—
434#117—22no—
435#117—22no—
436C2×C4⋊C4C2×C4×C1111yescharacteristic
437C2×C4⋊C4C2×C4×C1111yescharacteristic
438C2×C4⋊C4C2×C4×C1111yescharacteristic
439C2×C4⋊C4C2×C4×C1111yescharacteristic
440C2×C4⋊C4C2×C4×C1111yescharacteristic
441C2×C22⋊C4C2×C4×C1111yescharacteristic
442C2×C22⋊C4C2×C4×C1111yescharacteristic
443C2×C22⋊C4C2×C4×C1111yescharacteristic
444C2×C22⋊C4C2×C4×C1111yescharacteristic
445C2×C22⋊C4C2×C4×C1111yescharacteristic
446C2×C22⋊C4C2×C4×C1111yescharacteristic
447C2×C22⋊C4C2×C4×C1111yescharacteristic
448C2×C22⋊C4C2×C4×C1111yescharacteristic
449C2×C42—22no—
450C2×C42—22no—
451C2×C42C2×C4×C1111yescharacteristic
452C2×C42C2×C4×C1111yescharacteristic
453C2×C42C23×C1111yescharacteristic
454C2×C42C23×C1111yescharacteristic
455C2×C42C23×C1111yescharacteristic
456C2×C42C23×C1111yescharacteristic
457C2×C42C23×C1111yescharacteristic
458C4⋊C8—22no—
459C4⋊C8—22no—
460C4⋊C8—22no—
461C4⋊C8—22no—
462C4⋊C8—22no—
463C4⋊C8—22no—
464C4⋊C8—22no—
465C4⋊C8—22no—
466C4⋊C8—22no—
467C4⋊C8—41no—
468C4⋊C8—41no—
469C4⋊C8D4×C1114yescomplemented
470C22⋊C8—22no—
471C22⋊C8—22no—
472C22⋊C8—22no—
473C22⋊C8—22no—
474#97—22no—
475C4×C8—22no—
476#95C2×C4×C1111yescharacteristic
477#95C2×C4×C1111yescharacteristic
478#95C2×C4×C1111yescharacteristic
479#95C2×C4×C1111yescharacteristic
480#95C2×C4×C1111yescharacteristic
481#95C2×C4×C1111yescharacteristic
482#95C2×C4×C1111yescharacteristic
483#95C2×C4×C1111yescharacteristic
484#95C2×C4×C1111yescharacteristic
485#95C2×C4×C1111yescharacteristic
486C2×C11—24no—
487C2×C11—42no—
488C2×C11D4×C4⋊C411yescharacteristic
489C2×C11C2×#42411yescharacteristic
490C2×C11#290611yescharacteristic
491C2×C11#292911yescharacteristic
492C2×C11#293311yescharacteristic
493C2×C11#299211yescharacteristic
494C2×C11#299411yescharacteristic
495C24C22×C4×C1111yescharacteristic
496C24C22×C4×C1111yescharacteristic
497C2×D4—22no—
498C2×D4—22no—
499C2×D4C11×C4⋊C414yes—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—41no—
514C22×C4C22×C4×C1111yescharacteristic
515C22×C4C22×C4×C1111yescharacteristic
516C22×C4C22×C4×C1111yescharacteristic
517C22×C4C22×C4×C1111yescharacteristic
518C22×C4C22×C4×C1111yescharacteristic
519C22×C4C22×C4×C1111yescharacteristic
520C22×C4C22×C4×C1111yescharacteristic
521C22×C4C22×C4×C1111yescharacteristic
522C22×C4C22×C4×C1111yescharacteristic
523C22×C4C22×C4×C1111yescharacteristic
524C22×C4C22×C4×C1111yescharacteristic
525C22×C4C22×C4×C1111yescharacteristic
526C22×C4C2×D4×C1112yes—
527C22×C4C2×D4×C1112yes—
528C22×C4C2×Q8×C1112yes—
529C22×C4C2×Q8×C1112yes—
530C22×C4C24×C1111yescharacteristic
531M16—44no—
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—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—44no—
555C2×C8—44no—
556C2×C8—44no—
557C2×C8C2×D4×C1112yes—
558C2×C8C2×D4×C1112yes—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—41no—
563C4⋊C4C11×C4⋊C414yes—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—41no—
570C22⋊C4C11×C4⋊C414yes—
571C22⋊C4C11×C4⋊C414yes—
572C42—22no—
573C42—22no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42C2×D4×C1112yes—
581C42C2×D4×C1112yes—
582C42C2×Q8×C1112yes—
583C42C11×#4112yes—
584C11#2264711yescharacteristic, direct product factor, Sylow
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23C2×C11×C4⋊C412yes—
596C23C2×C11×C4⋊C412yes—
597C23C11×#13112yes—
598C23C11×#13112yes—
599C23C23×C4×C1111yescharacteristic
600D4—28no—
601C2×C4—28no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—44no—
640C2×C4C2×C11×C4⋊C412yes—
641C2×C4C2×C11×C4⋊C412yes—
642C2×C4C2×C11×C4⋊C412yes—
643C2×C4C2×C11×C4⋊C412yes—
644C2×C4C4×D4×C1112yes—
645C2×C4C4×D4×C1112yes—
646C2×C4C11×#13112yes—
647C2×C4C22×D4×C1111yescharacteristic
648C2×C4C22×D4×C1111yescharacteristic
649C2×C4C22×Q8×C1111yescharacteristic
650C2×C4C2×C11×#4111yescharacteristic
651C2×C4C11×H(5,𝔽2)11yescharacteristic
652C2×C4C11×2−1+411yescharacteristic
653C8—22no—
654C8—22no—
655C8—41no—
656C8—41no—
657C8—41no—
658C8—41no—
659C8—41no—
660C8—41no—
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—
674C22C11×#42414yescomplemented
675C22C22×C11×C4⋊C411yescharacteristic
676C22C2×C4×D4×C1111yescharacteristic
677C22C11×#52011yescharacteristic
678C22C2×C11×#13111yescharacteristic
679C22C2×C11×#13111yescharacteristic
680C22C2×C11×#13111yescharacteristic
681C22C11×#56811yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4D42×C1111yescharacteristic
695C4C11×#54711yescharacteristic
696C4D4×Q8×C1111yescharacteristic
697C4C11×#55411yescharacteristic
698C2—24no—
699C2—42no—
700C2D4×C11×C4⋊C411yescharacteristic
701C2C2×C11×#42411yescharacteristic
702C2C11×#290611yescharacteristic
703C2C11×#292911yescharacteristic
704C2C11×#293311yescharacteristic
705C2C11×#299211yescharacteristic
706C2C11×#299411yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#424C2semidirect
4. C22×C11×C4⋊C8C2semidirect
6. C11×#1940C2semidirect
7. C11×#1939C2semidirect
8. C11×#1851C2semidirect
9. C11×#1850C2semidirect
10. C11×#1850C2semidirect
11. C11×#1850C2semidirect
12. C11×#1843C2semidirect
13. C11×#1798C2semidirect
14. C11×#1797C2semidirect
15. C11×#1768C2semidirect
125. C11×C4⋊C8D4semidirect
142. #22647C11direct (N × H)
234. C2×#424C2×C11semidirect
235. C22×C4⋊C8C2×C11semidirect
237. #1940C2×C11semidirect
238. #1939C2×C11semidirect
239. #1851C2×C11semidirect
240. #1850C2×C11semidirect
241. #1850C2×C11semidirect
242. #1850C2×C11semidirect
243. #1843C2×C11semidirect
244. #1798C2×C11semidirect
245. #1797C2×C11semidirect
246. #1768C2×C11semidirect
383. C22×C11#424semidirect
469. C4⋊C8D4×C11semidirect
584. C11#22647direct (N × H)
674. C22C11×#424semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C2×C8×D4×C112
C2×C11×#4242
C22×C11×C4⋊C82
C11×#22902
C11×#19402
C11×#19392
C11×#18512
C11×#18502
C11×#18432
C11×#17982
C11×#17972
C11×#17682
#2264711