Finite Group Databasebeta

← C11×#22847 #14600040

Subgroups — C11×#22847 #14600040

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C211yesmaximal, characteristic, complemented
2C2×C8×D4×C11C211yesmaximal, characteristic, complemented
3C2×C11×#408C211yesmaximal, characteristic, complemented
4C2×C11×#408C211yesmaximal, characteristic, complemented
5C11×#2388C211yesmaximal, characteristic
6C11×#1954C211yesmaximal, characteristic, complemented
7C11×#1924C211yesmaximal, characteristic, complemented
8C11×#1923C211yesmaximal, characteristic, complemented
9C11×#1870C211yesmaximal, characteristic, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1753C211yesmaximal, characteristic, complemented
15C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C11×#435—24no—
26C8×D4×C11—24no—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C11×#408—24no—
31C11×#408—24no—
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43C2×C11×#97C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C2×C4×C8×C11C2211yescharacteristic
46C11×#395C411yescharacteristic
47C11×#394C411yescharacteristic
48C11×#394C411yescharacteristic
49C11×#394C411yescharacteristic
50C11×#393C411yescharacteristic
51C11×#392C411yescharacteristic
52C11×#392C411yescharacteristic
53C11×#392C411yescharacteristic
54C4×C11×C22⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11C2×C411yescharacteristic
70C22×D4×C11C2×C411yescharacteristic
71C22×D4×C11C2×C411yescharacteristic
72C22×D4×C11C2×C411yescharacteristic
73C22×D4×C11C2×C411yescharacteristic
74C22×D4×C11C2×C411yescharacteristic
75C22×D4×C11C2×C411yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C2×C11×M16—22no—
81C2×C11×M16—22no—
82C2×C11×M16—22no—
83C2×C11×M16—22no—
84C2×C11×M16—41no—
85C2×C11×M16—41no—
86C22×C8×C11—22no—
87C22×C8×C11—22no—
88C22×C8×C11—22no—
89C22×C8×C11—22no—
90C22×C8×C11—22no—
91C22×C8×C11—22no—
92C22×C8×C11—41no—
93C22×C8×C11—41no—
94C22×C8×C11—41no—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11—41no—
108C4×D4×C11—41no—
109C2×C11×C4⋊C4C2×C411yescharacteristic
110C2×C11×C4⋊C4C2×C411yescharacteristic
111C2×C11×C4⋊C4C2×C411yescharacteristic
112C2×C11×C22⋊C4C2×C411yescharacteristic
113C2×C11×C22⋊C4C2×C411yescharacteristic
114C2×C11×C22⋊C4C2×C411yescharacteristic
115C2×C11×C22⋊C4C2×C411yescharacteristic
116C2×C11×C22⋊C4C2×C411yescharacteristic
117C2×C11×C22⋊C4C2×C411yescharacteristic
118C2×C11×C22⋊C4C2×C411yescharacteristic
119C2×C11×C22⋊C4C2×C411yescharacteristic
120C2×C11×C22⋊C4C2×C411yescharacteristic
121C2×C11×C22⋊C4C2×C411yescharacteristic
122C2×C11×C22⋊C4C2×C411yescharacteristic
123C2×C11×C22⋊C4C2×C411yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C11×C4⋊C8—22no—
128C11×C4⋊C8—22no—
129C11×C4⋊C8—41no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8—22no—
132C11×C22⋊C8—22no—
133C11×C22⋊C8—22no—
134C11×C22⋊C8—22no—
135C11×C22⋊C8—22no—
136C11×C22⋊C8—22no—
137C11×C22⋊C8—22no—
138C11×C22⋊C8—41no—
139C11×C22⋊C8D414yescomplemented
140C11×C22⋊C8D414yescomplemented
141C11×#97—22no—
142C4×C8×C11—22no—
143C4×C8×C11—41no—
144C11×#95C2×C411yescharacteristic
145C11×#95C2×C411yescharacteristic
146C11×#95C2×C411yescharacteristic
147C11×#95C2×C411yescharacteristic
148C11×#95C2×C411yescharacteristic
149C11×#95C2×C411yescharacteristic
150#22847C1111yesmaximal, characteristic, direct product factor, Sylow
151C24×C11C22×C411yescharacteristic
152C24×C11C22×C411yescharacteristic
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C11×#41—44no—
156C11×#41—44no—
157C11×#41—44no—
158C11×#41—44no—
159C2×Q8×C11—22no—
160C2×Q8×C11—22no—
161C2×Q8×C11—41no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—22no—
173C2×D4×C11—22no—
174C2×D4×C11—22no—
175C2×D4×C11—41no—
176C2×D4×C11—41no—
177C2×D4×C11—41no—
178C2×D4×C11—41no—
179C2×D4×C11—41no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11#4112yes—
213C22×C4×C11#4112yes—
214C22×C4×C11C2411yescharacteristic
215C11×M16—44no—
216C11×M16—44no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—44no—
238C2×C8×C11—44no—
239C2×C8×C11—44no—
240C2×C8×C11C2×D412yes—
241C2×C8×C11C2×D412yes—
242C2×C8×C11C2×D412yes—
243C2×C8×C11C2×D412yes—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—22no—
246C11×C4⋊C4—41no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—22no—
250C11×C22⋊C4—22no—
251C11×C22⋊C4—22no—
252C11×C22⋊C4—22no—
253C11×C22⋊C4—22no—
254C11×C22⋊C4—22no—
255C11×C22⋊C4—41no—
256C11×C22⋊C4—41no—
257C11×C22⋊C4—41no—
258C11×C22⋊C4—41no—
259C42×C11—21no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—21no—
263C42×C11—21no—
264C42×C11—21no—
265C2×#435C2×C1111yescharacteristic, complemented
266C2×C8×D4C2×C1111yescharacteristic, complemented
267C2×#408C2×C1111yescharacteristic, complemented
268C2×#408C2×C1111yescharacteristic, complemented
269#2388C2×C1111yescharacteristic
270#1954C2×C1111yescharacteristic, complemented
271#1924C2×C1111yescharacteristic, complemented
272#1923C2×C1111yescharacteristic, complemented
273#1870C2×C1111yescharacteristic, complemented
274#1869C2×C1111yescharacteristic, complemented
275#1869C2×C1111yescharacteristic, complemented
276#1851C2×C1111yescharacteristic, complemented
277#1850C2×C1111yescharacteristic, complemented
278#1753C2×C1111yescharacteristic, complemented
279C8×C22⋊C4C2×C1111yescharacteristic, complemented
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×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11C4×D412yes—
306C23×C11C4×D412yes—
307C23×C11#13112yes—
308C23×C11C23×C411yescharacteristic
309Q8×C11—44no—
310D4×C11—28no—
311D4×C11—44no—
312D4×C11—44no—
313D4×C11—44no—
314D4×C11—44no—
315D4×C11—44no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11C4×D412yes—
359C2×C4×C11C4×D412yes—
360C2×C4×C11#13112yes—
361C2×C4×C11#13112yes—
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11C2×#4111yescharacteristic
365C2×C4×C11C2×#4111yescharacteristic
366C2×C4×C11H(5,𝔽2)11yescharacteristic
367C2×C4×C11H(5,𝔽2)11yescharacteristic
368C8×C11—22no—
369C8×C11—22no—
370C8×C11—22no—
371C8×C11—22no—
372C8×C11—41no—
373C8×C11—41no—
374C8×C11—41no—
375C8×C11—41no—
376C22×#41C22×C1111yescharacteristic
377C22×M16C22×C1111yescharacteristic
378C22×M16C22×C1111yescharacteristic
379C23×C8C22×C1111yescharacteristic
380C23×C8C22×C1111yescharacteristic
381C23×C8C22×C1111yescharacteristic
382C2×C4×D4C22×C1111yescharacteristic
383C2×C4×D4C22×C1111yescharacteristic
384C2×C4×D4C22×C1111yescharacteristic
385#435—24no—
386C8×D4—24no—
387C2×C4⋊C8C22×C1111yescharacteristic
388C2×C4⋊C8C22×C1111yescharacteristic
389C2×C4⋊C8C22×C1111yescharacteristic
390#408—24no—
391#408—24no—
392C2×C22⋊C8C22×C1111yescharacteristic
393C2×C22⋊C8C22×C1111yescharacteristic
394C2×C22⋊C8C22×C1111yescharacteristic
395C2×C22⋊C8C22×C1111yescharacteristic
396C2×C22⋊C8C22×C1111yescharacteristic
397C2×C22⋊C8C22×C1111yescharacteristic
398C2×C22⋊C8C22×C1111yescharacteristic
399C2×C22⋊C8C22×C1111yescharacteristic
400C2×C22⋊C8C22×C1111yescharacteristic
401C2×C22⋊C8C22×C1111yescharacteristic
402C2×C22⋊C8C22×C1111yescharacteristic
403C2×#97C22×C1111yescharacteristic
404C2×C4×C8C22×C1111yescharacteristic
405C2×C4×C8C22×C1111yescharacteristic
406#395C4×C1111yescharacteristic
407#394C4×C1111yescharacteristic
408#394C4×C1111yescharacteristic
409#394C4×C1111yescharacteristic
410#393C4×C1111yescharacteristic
411#392C4×C1111yescharacteristic
412#392C4×C1111yescharacteristic
413#392C4×C1111yescharacteristic
414C4×C22⋊C4C22×C1111yescharacteristic
415C4×C22⋊C4C22×C1111yescharacteristic
416C4×C22⋊C4C22×C1111yescharacteristic
417#336C22×C1111yescharacteristic
418#336C22×C1111yescharacteristic
419#336C22×C1111yescharacteristic
420#336C22×C1111yescharacteristic
421#336C22×C1111yescharacteristic
422#336C22×C1111yescharacteristic
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11C2×C4×D411yescharacteristic
452C22×C11C2×C4×D411yescharacteristic
453C22×C11#51811yescharacteristic
454C22×C11C2×#13111yescharacteristic
455C22×C11C2×#13111yescharacteristic
456C22×C11C2×#13111yescharacteristic
457C22×C11#56811yescharacteristic
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—41no—
463C4×C11—41no—
464C4×C11—41no—
465C4×C11—41no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11D4211yescharacteristic
469C4×C11#54611yescharacteristic
470C4×C11#54611yescharacteristic
471C4×C11#55111yescharacteristic
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C22×Q8C2×C4×C1111yescharacteristic
479C22×D4C2×C4×C1111yescharacteristic
480C22×D4C2×C4×C1111yescharacteristic
481C22×D4C2×C4×C1111yescharacteristic
482C22×D4C2×C4×C1111yescharacteristic
483C22×D4C2×C4×C1111yescharacteristic
484C22×D4C2×C4×C1111yescharacteristic
485C23×C4C23×C1111yescharacteristic
486C23×C4C23×C1111yescharacteristic
487C23×C4C23×C1111yescharacteristic
488C23×C4C23×C1111yescharacteristic
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—22no—
493C2×M16—41no—
494C2×M16—41no—
495C22×C8—22no—
496C22×C8—22no—
497C22×C8—22no—
498C22×C8—22no—
499C22×C8—22no—
500C22×C8—22no—
501C22×C8—41no—
502C22×C8—41no—
503C22×C8—41no—
504C22×C8C23×C1111yescharacteristic
505C22×C8C23×C1111yescharacteristic
506C22×C8C23×C1111yescharacteristic
507C22×C8C23×C1111yescharacteristic
508C22×C8C23×C1111yescharacteristic
509C22×C8C23×C1111yescharacteristic
510C22×C8C23×C1111yescharacteristic
511C22×C8C23×C1111yescharacteristic
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—41no—
517C4×D4—41no—
518C2×C4⋊C4C2×C4×C1111yescharacteristic
519C2×C4⋊C4C2×C4×C1111yescharacteristic
520C2×C4⋊C4C2×C4×C1111yescharacteristic
521C2×C22⋊C4C2×C4×C1111yescharacteristic
522C2×C22⋊C4C2×C4×C1111yescharacteristic
523C2×C22⋊C4C2×C4×C1111yescharacteristic
524C2×C22⋊C4C2×C4×C1111yescharacteristic
525C2×C22⋊C4C2×C4×C1111yescharacteristic
526C2×C22⋊C4C2×C4×C1111yescharacteristic
527C2×C22⋊C4C2×C4×C1111yescharacteristic
528C2×C22⋊C4C2×C4×C1111yescharacteristic
529C2×C22⋊C4C2×C4×C1111yescharacteristic
530C2×C22⋊C4C2×C4×C1111yescharacteristic
531C2×C22⋊C4C2×C4×C1111yescharacteristic
532C2×C22⋊C4C2×C4×C1111yescharacteristic
533C2×C42C23×C1111yescharacteristic
534C2×C42C23×C1111yescharacteristic
535C2×C42C23×C1111yescharacteristic
536C4⋊C8—22no—
537C4⋊C8—22no—
538C4⋊C8—41no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—41no—
548C22⋊C8D4×C1114yescomplemented
549C22⋊C8D4×C1114yescomplemented
550#97—22no—
551C4×C8—22no—
552C4×C8—41no—
553#95C2×C4×C1111yescharacteristic
554#95C2×C4×C1111yescharacteristic
555#95C2×C4×C1111yescharacteristic
556#95C2×C4×C1111yescharacteristic
557#95C2×C4×C1111yescharacteristic
558#95C2×C4×C1111yescharacteristic
559C2×C11—42no—
560C2×C11—42no—
561C2×C11—42no—
562C2×C11—81no—
563C2×C11#235811yescharacteristic
564C2×C11#292911yescharacteristic
565C2×C11#293111yescharacteristic
566C2×C11#293311yescharacteristic
567C2×C11#293511yescharacteristic
568C2×C11#297711yescharacteristic
569C2×C11#298111yescharacteristic
570C24C22×C4×C1111yescharacteristic
571C24C22×C4×C1111yescharacteristic
572C24C22×C4×C1111yescharacteristic
573C24C22×C4×C1111yescharacteristic
574#41—44no—
575#41—44no—
576#41—44no—
577#41—44no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—41no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4C22×C4×C1111yescharacteristic
620C22×C4C22×C4×C1111yescharacteristic
621C22×C4C22×C4×C1111yescharacteristic
622C22×C4C22×C4×C1111yescharacteristic
623C22×C4C22×C4×C1111yescharacteristic
624C22×C4C22×C4×C1111yescharacteristic
625C22×C4C22×C4×C1111yescharacteristic
626C22×C4C22×C4×C1111yescharacteristic
627C22×C4C22×C4×C1111yescharacteristic
628C22×C4C22×C4×C1111yescharacteristic
629C22×C4C2×D4×C1112yes—
630C22×C4C2×D4×C1112yes—
631C22×C4C11×#4112yes—
632C22×C4C11×#4112yes—
633C22×C4C24×C1111yescharacteristic
634M16—44no—
635M16—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—44no—
657C2×C8—44no—
658C2×C8—44no—
659C2×C8C2×D4×C1112yes—
660C2×C8C2×D4×C1112yes—
661C2×C8C2×D4×C1112yes—
662C2×C8C2×D4×C1112yes—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—41no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C11#2284711yescharacteristic, direct product factor, Sylow
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23C4×D4×C1112yes—
711C23C4×D4×C1112yes—
712C23C11×#13112yes—
713C23C23×C4×C1111yescharacteristic
714Q8—44no—
715D4—28no—
716D4—44no—
717D4—44no—
718D4—44no—
719D4—44no—
720D4—44no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4C4×D4×C1112yes—
764C2×C4C4×D4×C1112yes—
765C2×C4C11×#13112yes—
766C2×C4C11×#13112yes—
767C2×C4C22×D4×C1111yescharacteristic
768C2×C4C22×D4×C1111yescharacteristic
769C2×C4C2×C11×#4111yescharacteristic
770C2×C4C2×C11×#4111yescharacteristic
771C2×C4C11×H(5,𝔽2)11yescharacteristic
772C2×C4C11×H(5,𝔽2)11yescharacteristic
773C8—22no—
774C8—22no—
775C8—22no—
776C8—22no—
777C8—41no—
778C8—41no—
779C8—41no—
780C8—41no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22C2×C4×D4×C1111yescharacteristic
810C22C2×C4×D4×C1111yescharacteristic
811C22C11×#51811yescharacteristic
812C22C2×C11×#13111yescharacteristic
813C22C2×C11×#13111yescharacteristic
814C22C2×C11×#13111yescharacteristic
815C22C11×#56811yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4D42×C1111yescharacteristic
827C4C11×#54611yescharacteristic
828C4C11×#54611yescharacteristic
829C4C11×#55111yescharacteristic
830C2—42no—
831C2—42no—
832C2—42no—
833C2—81no—
834C2C11×#235811yescharacteristic
835C2C11×#292911yescharacteristic
836C2C11×#293111yescharacteristic
837C2C11×#293311yescharacteristic
838C2C11×#293511yescharacteristic
839C2C11×#297711yescharacteristic
840C2C11×#298111yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC11×#2388C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#435C2semidirect
2. C2×C8×D4×C11C2semidirect
3. C2×C11×#408C2semidirect
4. C2×C11×#408C2semidirect
6. C11×#1954C2semidirect
7. C11×#1924C2semidirect
8. C11×#1923C2semidirect
9. C11×#1870C2semidirect
10. C11×#1869C2semidirect
11. C11×#1869C2semidirect
12. C11×#1851C2semidirect
13. C11×#1850C2semidirect
14. C11×#1753C2semidirect
15. C8×C11×C22⋊C4C2semidirect
139. C11×C22⋊C8D4semidirect
140. C11×C22⋊C8D4semidirect
150. #22847C11direct (N × H)
265. C2×#435C2×C11semidirect
266. C2×C8×D4C2×C11semidirect
267. C2×#408C2×C11semidirect
268. C2×#408C2×C11semidirect
270. #1954C2×C11semidirect
271. #1924C2×C11semidirect
272. #1923C2×C11semidirect
273. #1870C2×C11semidirect
274. #1869C2×C11semidirect
275. #1869C2×C11semidirect
276. #1851C2×C11semidirect
277. #1850C2×C11semidirect
278. #1753C2×C11semidirect
279. C8×C22⋊C4C2×C11semidirect
548. C22⋊C8D4×C11semidirect
549. C22⋊C8D4×C11semidirect
684. C11#22847direct (N × H)

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×#4082
C11×#23882
C11×#19542
C11×#19242
C11×#19232
C11×#18702
C11×#18692
C11×#18512
C11×#18502
C11×#17532
C8×C11×C22⋊C42
#2284711