Finite Group Databasebeta

← C11×#34314 #14611507

Subgroups — C11×#34314 #14611507

Order 2816.

2264 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2C11×#2373C212yesmaximal, complemented
3C11×#2370C211yesmaximal, characteristic, complemented
4C11×#2370C212yesmaximal, complemented
5C11×#2362C211yesmaximal, characteristic, complemented
6C11×#2360C211yesmaximal, characteristic, complemented
7C11×#2359C212yesmaximal
8C11×#2352C211yesmaximal, characteristic
9C11×#2351C211yesmaximal, characteristic, complemented
10C11×#2347C211yesmaximal, characteristic, complemented
11C11×#2344C211yesmaximal, characteristic, complemented
12C11×#2343C212yesmaximal, complemented
13C11×#2336C212yesmaximal, complemented
14C11×#2334C212yesmaximal, complemented
15C11×#2322C212yesmaximal
16C4×C11×#125C211yesmaximal, characteristic, complemented
17C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
18C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
19C11×#2296C211yesmaximal, characteristic, complemented
20C11×#2295C211yesmaximal, characteristic, complemented
21C2×C11×#389C211yesmaximal, characteristic, complemented
22C11×#2274C212yesmaximal, complemented
23C42×D4×C11C211yesmaximal, characteristic
24C11×#552C4116yescomplemented
25C2×C11×#126C2212yes—
26C2×C11×#125C2211yescharacteristic
27C2×C11×#125C2212yes—
28C2×C11×#123C2212yes—
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C4×Q8×C11C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C2×C4×D4×C11C2211yescharacteristic
37C2×C11×#117C2212yes—
38C2×C11×#117C2211yescharacteristic
39C2×C11×#117C2212yes—
40C2×C11×#117C2211yescharacteristic
41C22×C11×C4⋊C4C2212yes—
42C22×C11×C4⋊C4C2211yescharacteristic
43C22×C11×C4⋊C4C2211yescharacteristic
44C22×C42×C11C2211yescharacteristic
45C22×C42×C11C2211yescharacteristic
46C11×#391C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#389C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#389C2212yes—
51C11×#389C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#389C2212yes—
54C11×#389C2211yescharacteristic
55C11×#389C2211yescharacteristic
56C11×#389C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#389C2212yes—
59C11×#389C2212yes—
60C11×#389C2212yes—
61C11×#389C2212yes—
62C11×#388C2212yes—
63C11×#388C2212yes—
64C11×#388C2212yes—
65C11×#388C2212yes—
66C11×#388C2212yes—
67C11×#387C2212yes—
68C11×#387C2212yes—
69C11×#387C2212yes—
70C11×#387C2212yes—
71C11×#387C2212yes—
72C11×#387C2212yes—
73C11×#387C2212yes—
74C11×#387C2212yes—
75C11×#387C2212yes—
76C11×#387C2212yes—
77C11×#387C2212yes—
78C11×#387C2212yes—
79C11×#387C2212yes—
80C11×#386C2212yes—
81C11×#385C2212yes—
82C11×#385C2212yes—
83C11×#385C2212yes—
84C11×#385C2212yes—
85C11×#385C2212yes—
86C11×#383C2212yes—
87C11×#382C2211yescharacteristic
88C11×#382C2212yes—
89C11×#381C2212yes—
90C11×#380C2211yescharacteristic
91C11×#380C2211yescharacteristic
92C4×C11×C4⋊C4C2211yescharacteristic
93C4×C11×C4⋊C4C2211yescharacteristic
94C4×C11×C4⋊C4C2211yescharacteristic
95C4×C11×C4⋊C4C2212yes—
96C4×C11×C4⋊C4C2212yes—
97C4×C11×C4⋊C4C2212yes—
98C4×C11×C4⋊C4C2212yes—
99C4×C11×C4⋊C4C2212yes—
100C4×C11×C4⋊C4C2212yes—
101C4×C11×C4⋊C4C2212yes—
102C4×C11×C4⋊C4C2212yes—
103C4×C11×C4⋊C4C2211yescharacteristic
104C4×C11×C4⋊C4C2212yes—
105C4×C11×C4⋊C4C2211yescharacteristic
106C4×C11×C4⋊C4C2211yescharacteristic
107C4×C11×C4⋊C4C2212yes—
108C4×C11×C4⋊C4C2211yescharacteristic
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C4⋊C4C2212yes—
111C4×C11×C22⋊C4C2211yescharacteristic
112C4×C11×C22⋊C4C2211yescharacteristic
113C4×C11×C22⋊C4C2211yescharacteristic
114C4×C11×C22⋊C4C2211yescharacteristic
115C4×C11×C22⋊C4C2211yescharacteristic
116C4×C11×C22⋊C4C2211yescharacteristic
117C4×C11×C22⋊C4C2212yes—
118C4×C11×C22⋊C4C2212yes—
119C4×C11×C22⋊C4C2212yes—
120C4×C11×C22⋊C4C2212yes—
121C11×#376C2212yes—
122C2×C11×#95C2212yes—
123C43×C11C2211yescharacteristic
124C22×Q8×C11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2311yescharacteristic
134C11×#126C2×C4116yescomplemented
135C11×#125C2×C4116yescomplemented
136C11×#125C2×C418yescomplemented
137C11×#123C2×C4116yes—
138C11×C22⋊Q8C2×C418yescomplemented
139C11×C22⋊Q8C2×C418yescomplemented
140C4×Q8×C11—42no—
141C4×Q8×C11—42no—
142C4×Q8×C11C2×C418yescomplemented
143C4×D4×C11—24no—
144C4×D4×C11—24no—
145C4×D4×C11C2×C418yes—
146C11×#117—28no—
147C11×#117—42no—
148C11×#117C2×C418yescomplemented
149C11×#117C2×C4116yescomplemented
150C2×C11×C4⋊C4—28no—
151C2×C11×C4⋊C4—42no—
152C2×C11×C4⋊C4C2×C418yescomplemented
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2311yescharacteristic
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2312yes—
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2312yes—
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C4⋊C4C2312yes—
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2311yescharacteristic
183C2×C11×C22⋊C4C2311yescharacteristic
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2311yescharacteristic
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2311yescharacteristic
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2311yescharacteristic
192C2×C42×C11—42no—
193C2×C42×C11—42no—
194C2×C42×C11C2311yescharacteristic
195C2×C42×C11C2311yescharacteristic
196C2×C42×C11C2311yescharacteristic
197C2×C42×C11C2311yescharacteristic
198C2×C42×C11C2311yescharacteristic
199C2×C42×C11C2311yescharacteristic
200C2×C42×C11C2311yescharacteristic
201C2×C42×C11C2312yes—
202C2×C42×C11C2312yes—
203C2×C42×C11C2311yescharacteristic
204C2×C42×C11C2311yescharacteristic
205C2×C42×C11C2311yescharacteristic
206C2×C42×C11C2311yescharacteristic
207C2×C42×C11C2311yescharacteristic
208C2×C42×C11C2312yes—
209C2×C42×C11C2312yes—
210C2×C42×C11C2312yes—
211C2×C42×C11C2312yes—
212C2×C42×C11C2312yes—
213C2×C42×C11C2312yes—
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2312yes—
216C2×C42×C11C2312yes—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2312yes—
221C11×#95C2312yes—
222C11×#95C2312yes—
223C11×#95C2312yes—
224C11×#95C2311yescharacteristic
225C11×#95C2311yescharacteristic
226C11×#95C2311yescharacteristic
227C11×#95C2311yescharacteristic
228C11×#95C2311yescharacteristic
229C11×#95C2311yescharacteristic
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244#34314C1111yesmaximal, characteristic, direct product factor, Sylow
245C24×C11C2411yescharacteristic
246C24×C11C2411yescharacteristic
247C2×Q8×C11—22no—
248C2×Q8×C11—22no—
249C2×Q8×C11C22×C414yes—
250C2×D4×C11—22no—
251C2×D4×C11—22no—
252C2×D4×C11C22×C414yes—
253C22×C4×C11—24no—
254C22×C4×C11—24no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—22no—
260C22×C4×C11—24no—
261C22×C4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—41no—
266C22×C4×C11—41no—
267C22×C4×C11—41no—
268C22×C4×C11—41no—
269C22×C4×C11—41no—
270C22×C4×C11—41no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
273C22×C4×C11C22×C418yes—
274C22×C4×C11C22×C414yes—
275C22×C4×C11C22×C414yes—
276C22×C4×C11#4114yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C11×C4⋊C4—24no—
299C11×C4⋊C4—24no—
300C11×C4⋊C4—24no—
301C11×C4⋊C4—24no—
302C11×C4⋊C4—24no—
303C11×C4⋊C4—24no—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—22no—
307C11×C4⋊C4—22no—
308C11×C4⋊C4—22no—
309C11×C4⋊C4—24no—
310C11×C4⋊C4—22no—
311C11×C4⋊C4—42no—
312C11×C4⋊C4—42no—
313C11×C4⋊C4—42no—
314C11×C4⋊C4—42no—
315C11×C4⋊C4C22×C414yes—
316C11×C4⋊C4C22×C414yes—
317C11×C4⋊C4C22×C418yes—
318C11×C4⋊C4C22×C418yes—
319C11×C4⋊C4C22×C414yes—
320C11×C4⋊C4C22×C418yes—
321C11×C4⋊C4C22×C414yes—
322C11×C4⋊C4C22×C418yes—
323C11×C4⋊C4C22×C418yes—
324C11×C4⋊C4C22×C418yes—
325C11×C22⋊C4—24no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—22no—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—42no—
330C11×C22⋊C4—42no—
331C11×C22⋊C4C22×C414yes—
332C11×C22⋊C4C22×C418yes—
333C11×C22⋊C4C22×C418yes—
334C11×C22⋊C4C22×C414yes—
335C11×C22⋊C4C22×C418yes—
336C11×C22⋊C4#4114yes—
337C42×C11—24no—
338C42×C11—24no—
339C42×C11—22no—
340C42×C11—22no—
341C42×C11—22no—
342C42×C11—22no—
343C42×C11—22no—
344C42×C11—22no—
345C42×C11—22no—
346C42×C11—41no—
347C42×C11—41no—
348C42×C11—41no—
349C42×C11—41no—
350C42×C11—41no—
351C42×C11—42no—
352C42×C11—42no—
353C42×C11—42no—
354C42×C11—42no—
355C42×C11—42no—
356C42×C11—42no—
357C42×C11C22×C418yes—
358C42×C11C22×C418yes—
359C42×C11C22×C414yes—
360C2×#552C2×C1111yescharacteristic
361#2373C2×C1112yescomplemented
362#2370C2×C1111yescharacteristic, complemented
363#2370C2×C1112yescomplemented
364#2362C2×C1111yescharacteristic, complemented
365#2360C2×C1111yescharacteristic, complemented
366#2359C2×C1112yes—
367#2352C2×C1111yescharacteristic
368#2351C2×C1111yescharacteristic, complemented
369#2347C2×C1111yescharacteristic, complemented
370#2344C2×C1111yescharacteristic, complemented
371#2343C2×C1112yescomplemented
372#2336C2×C1112yescomplemented
373#2334C2×C1112yescomplemented
374#2322C2×C1112yes—
375C4×#125C2×C1111yescharacteristic, complemented
376C4×C22⋊Q8C2×C1111yescharacteristic, complemented
377C4×C22⋊Q8C2×C1111yescharacteristic, complemented
378#2296C2×C1111yescharacteristic, complemented
379#2295C2×C1111yescharacteristic, complemented
380C2×#389C2×C1111yescharacteristic, complemented
381#2274C2×C1112yescomplemented
382C42×D4C2×C1111yescharacteristic
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—21no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—21no—
391C23×C11—21no—
392C23×C11—21no—
393C23×C11C23×C412yes—
394C23×C11C23×C412yes—
395C23×C11C2×#4112yes—
396C23×C11C2×#4112yes—
397C23×C11C2511yescharacteristic
398Q8×C11—28no—
399D4×C11—28no—
400C2×C4×C11—216no—
401C2×C4×C11—22no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—22no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—22no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—22no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—28no—
428C2×C4×C11—28no—
429C2×C4×C11—21no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—21no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—21no—
450C2×C4×C11—44no—
451C2×C4×C11—44no—
452C2×C4×C11—44no—
453C2×C4×C11—44no—
454C2×C4×C11—84no—
455C2×C4×C11C23×C412yes—
456C2×C4×C11C23×C414yes—
457C2×C4×C11C23×C412yes—
458C2×C4×C11C23×C414yes—
459C2×C4×C11C23×C414yes—
460C2×C4×C11C23×C412yes—
461C2×C4×C11C23×C414yes—
462C2×C4×C11C23×C412yes—
463C2×C4×C11C23×C412yes—
464C2×C4×C11C2×#4112yes—
465C2×C4×C11C2×#4112yes—
466C2×C4×C11C2×#4112yes—
467C2×C4×C11C2×#4112yes—
468C2×C4×C11H(5,𝔽2)12yes—
469C2×C4×C112−1+412yes—
470C2×C4×C112−1+412yes—
471#552C4×C11116yescomplemented
472C2×#126C22×C1112yes—
473C2×#125C22×C1111yescharacteristic
474C2×#125C22×C1112yes—
475C2×#123C22×C1112yes—
476C2×C22⋊Q8C22×C1111yescharacteristic
477C2×C22⋊Q8C22×C1111yescharacteristic
478C2×C4×Q8C22×C1111yescharacteristic
479C2×C4×Q8C22×C1111yescharacteristic
480C2×C4×Q8C22×C1111yescharacteristic
481C2×C4×D4C22×C1111yescharacteristic
482C2×C4×D4C22×C1111yescharacteristic
483C2×C4×D4C22×C1111yescharacteristic
484C2×#117C22×C1112yes—
485C2×#117C22×C1111yescharacteristic
486C2×#117C22×C1112yes—
487C2×#117C22×C1111yescharacteristic
488C22×C4⋊C4C22×C1112yes—
489C22×C4⋊C4C22×C1111yescharacteristic
490C22×C4⋊C4C22×C1111yescharacteristic
491C22×C42C22×C1111yescharacteristic
492C22×C42C22×C1111yescharacteristic
493#391C22×C1111yescharacteristic
494#391C22×C1111yescharacteristic
495#389C22×C1111yescharacteristic
496#389C22×C1111yescharacteristic
497#389C22×C1112yes—
498#389C22×C1112yes—
499#389C22×C1112yes—
500#389C22×C1112yes—
501#389C22×C1112yes—
502#389C22×C1111yescharacteristic
503#389C22×C1111yescharacteristic
504#389C22×C1111yescharacteristic
505#389C22×C1111yescharacteristic
506#389C22×C1111yescharacteristic
507#389C22×C1112yes—
508#389C22×C1111yescharacteristic
509#388C22×C1112yes—
510#388C22×C1112yes—
511#388C22×C1112yes—
512#388C22×C1112yes—
513#388C22×C1112yes—
514#387C22×C1112yes—
515#387C22×C1112yes—
516#387C22×C1112yes—
517#387C22×C1112yes—
518#387C22×C1112yes—
519#387C22×C1112yes—
520#387C22×C1112yes—
521#387C22×C1112yes—
522#387C22×C1112yes—
523#387C22×C1112yes—
524#387C22×C1112yes—
525#387C22×C1112yes—
526#387C22×C1112yes—
527#386C22×C1112yes—
528#385C22×C1112yes—
529#385C22×C1112yes—
530#385C22×C1112yes—
531#385C22×C1112yes—
532#385C22×C1112yes—
533#383C22×C1112yes—
534#382C22×C1111yescharacteristic
535#382C22×C1112yes—
536#381C22×C1112yes—
537#380C22×C1111yescharacteristic
538#380C22×C1111yescharacteristic
539C4×C4⋊C4C22×C1112yes—
540C4×C4⋊C4C22×C1111yescharacteristic
541C4×C4⋊C4C22×C1111yescharacteristic
542C4×C4⋊C4C22×C1112yes—
543C4×C4⋊C4C22×C1112yes—
544C4×C4⋊C4C22×C1111yescharacteristic
545C4×C4⋊C4C22×C1112yes—
546C4×C4⋊C4C22×C1112yes—
547C4×C4⋊C4C22×C1112yes—
548C4×C4⋊C4C22×C1111yescharacteristic
549C4×C4⋊C4C22×C1112yes—
550C4×C4⋊C4C22×C1111yescharacteristic
551C4×C4⋊C4C22×C1111yescharacteristic
552C4×C4⋊C4C22×C1112yes—
553C4×C4⋊C4C22×C1111yescharacteristic
554C4×C4⋊C4C22×C1112yes—
555C4×C4⋊C4C22×C1111yescharacteristic
556C4×C4⋊C4C22×C1112yes—
557C4×C4⋊C4C22×C1112yes—
558C4×C22⋊C4C22×C1112yes—
559C4×C22⋊C4C22×C1111yescharacteristic
560C4×C22⋊C4C22×C1111yescharacteristic
561C4×C22⋊C4C22×C1112yes—
562C4×C22⋊C4C22×C1111yescharacteristic
563C4×C22⋊C4C22×C1111yescharacteristic
564C4×C22⋊C4C22×C1112yes—
565C4×C22⋊C4C22×C1112yes—
566C4×C22⋊C4C22×C1111yescharacteristic
567C4×C22⋊C4C22×C1111yescharacteristic
568#376C22×C1112yes—
569C2×#95C22×C1112yes—
570C43C22×C1111yescharacteristic
571C22×C11—22no—
572C22×C11—22no—
573C22×C11—22no—
574C22×C11—22no—
575C22×C11—22no—
576C22×C11—22no—
577C22×C11—22no—
578C22×C11—22no—
579C22×C11—22no—
580C22×C11—41no—
581C22×C11—41no—
582C22×C11—41no—
583C22×C11—41no—
584C22×C11C4×#4114yes—
585C22×C11C24×C411yescharacteristic
586C22×C11C22×#4111yescharacteristic
587C22×C11C22×#4111yescharacteristic
588C22×C11C2×H(5,𝔽2)11yescharacteristic
589C22×C11C2×2−1+411yescharacteristic
590C22×C11C2×2−1+411yescharacteristic
591C22×C11#58511yescharacteristic
592C4×C11—24no—
593C4×C11—24no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—22no—
597C4×C11—24no—
598C4×C11—22no—
599C4×C11—24no—
600C4×C11—22no—
601C4×C11—22no—
602C4×C11—22no—
603C4×C11—22no—
604C4×C11—22no—
605C4×C11—41no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—41no—
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—41no—
612C4×C11#52014yes—
613C22×Q8C23×C1111yescharacteristic
614C22×D4C23×C1111yescharacteristic
615C23×C4C23×C1111yescharacteristic
616C23×C4C23×C1111yescharacteristic
617C23×C4C23×C1112yes—
618C23×C4C23×C1111yescharacteristic
619C23×C4C23×C1111yescharacteristic
620C23×C4C23×C1112yes—
621C23×C4C23×C1111yescharacteristic
622C23×C4C23×C1111yescharacteristic
623#126C2×C4×C11116yescomplemented
624#125C2×C4×C11116yescomplemented
625#125C2×C4×C1118yescomplemented
626#123C2×C4×C11116yes—
627C22⋊Q8C2×C4×C1118yescomplemented
628C22⋊Q8C2×C4×C1118yescomplemented
629C4×Q8—42no—
630C4×Q8—42no—
631C4×Q8C2×C4×C1118yescomplemented
632C4×D4—24no—
633C4×D4—24no—
634C4×D4C2×C4×C1118yes—
635#117—28no—
636#117—42no—
637#117C2×C4×C1118yescomplemented
638#117C2×C4×C11116yescomplemented
639C2×C4⋊C4—28no—
640C2×C4⋊C4—42no—
641C2×C4⋊C4C2×C4×C1118yescomplemented
642C2×C4⋊C4C23×C1111yescharacteristic
643C2×C4⋊C4C23×C1111yescharacteristic
644C2×C4⋊C4C23×C1112yes—
645C2×C4⋊C4C23×C1112yes—
646C2×C4⋊C4C23×C1112yes—
647C2×C4⋊C4C23×C1112yes—
648C2×C4⋊C4C23×C1111yescharacteristic
649C2×C4⋊C4C23×C1112yes—
650C2×C4⋊C4C23×C1112yes—
651C2×C4⋊C4C23×C1111yescharacteristic
652C2×C4⋊C4C23×C1111yescharacteristic
653C2×C4⋊C4C23×C1111yescharacteristic
654C2×C4⋊C4C23×C1112yes—
655C2×C4⋊C4C23×C1112yes—
656C2×C4⋊C4C23×C1112yes—
657C2×C4⋊C4C23×C1112yes—
658C2×C4⋊C4C23×C1112yes—
659C2×C4⋊C4C23×C1111yescharacteristic
660C2×C4⋊C4C23×C1111yescharacteristic
661C2×C4⋊C4C23×C1112yes—
662C2×C4⋊C4C23×C1112yes—
663C2×C4⋊C4C23×C1111yescharacteristic
664C2×C4⋊C4C23×C1112yes—
665C2×C4⋊C4C23×C1111yescharacteristic
666C2×C4⋊C4C23×C1112yes—
667C2×C4⋊C4C23×C1112yes—
668C2×C4⋊C4C23×C1112yes—
669C2×C22⋊C4C23×C1112yes—
670C2×C22⋊C4C23×C1111yescharacteristic
671C2×C22⋊C4C23×C1111yescharacteristic
672C2×C22⋊C4C23×C1111yescharacteristic
673C2×C22⋊C4C23×C1112yes—
674C2×C22⋊C4C23×C1112yes—
675C2×C22⋊C4C23×C1111yescharacteristic
676C2×C22⋊C4C23×C1112yes—
677C2×C22⋊C4C23×C1112yes—
678C2×C22⋊C4C23×C1111yescharacteristic
679C2×C22⋊C4C23×C1112yes—
680C2×C22⋊C4C23×C1111yescharacteristic
681C2×C42—42no—
682C2×C42—42no—
683C2×C42C23×C1112yes—
684C2×C42C23×C1112yes—
685C2×C42C23×C1111yescharacteristic
686C2×C42C23×C1111yescharacteristic
687C2×C42C23×C1111yescharacteristic
688C2×C42C23×C1111yescharacteristic
689C2×C42C23×C1111yescharacteristic
690C2×C42C23×C1111yescharacteristic
691C2×C42C23×C1111yescharacteristic
692C2×C42C23×C1112yes—
693C2×C42C23×C1112yes—
694C2×C42C23×C1112yes—
695C2×C42C23×C1111yescharacteristic
696C2×C42C23×C1112yes—
697C2×C42C23×C1111yescharacteristic
698C2×C42C23×C1112yes—
699C2×C42C23×C1112yes—
700C2×C42C23×C1111yescharacteristic
701C2×C42C23×C1111yescharacteristic
702C2×C42C23×C1111yescharacteristic
703C2×C42C23×C1112yes—
704C2×C42C23×C1112yes—
705C2×C42C23×C1111yescharacteristic
706#95C23×C1112yes—
707#95C23×C1112yes—
708#95C23×C1112yes—
709#95C23×C1112yes—
710#95C23×C1112yes—
711#95C23×C1112yes—
712#95C23×C1112yes—
713#95C23×C1111yescharacteristic
714#95C23×C1111yescharacteristic
715#95C23×C1111yescharacteristic
716#95C23×C1111yescharacteristic
717#95C23×C1111yescharacteristic
718#95C23×C1111yescharacteristic
719#95C23×C1112yes—
720#95C23×C1112yes—
721#95C23×C1112yes—
722#95C23×C1112yes—
723#95C23×C1112yes—
724#95C23×C1112yes—
725#95C23×C1112yes—
726#95C23×C1112yes—
727#95C23×C1112yes—
728#95C23×C1112yes—
729#95C23×C1112yes—
730#95C23×C1112yes—
731#95C23×C1112yes—
732#95C23×C1112yes—
733C2×C11—24no—
734C2×C11—42no—
735C2×C11C2×C4×#4111yescharacteristic
736C2×C11C2×#52011yescharacteristic
737C2×C11C4×2−1+411yescharacteristic
738C2×C11#350511yescharacteristic
739C2×C11#350911yescharacteristic
740C2×C11#351511yescharacteristic
741C2×C11#352011yescharacteristic
742C24C24×C1111yescharacteristic
743C24C24×C1111yescharacteristic
744C2×Q8—22no—
745C2×Q8—22no—
746C2×Q8C22×C4×C1114yes—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4C22×C4×C1114yes—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—24no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4C22×C4×C1118yes—
771C22×C4C22×C4×C1114yes—
772C22×C4C22×C4×C1114yes—
773C22×C4C11×#4114yes—
774C22×C4C24×C1111yescharacteristic
775C22×C4C24×C1112yes—
776C22×C4C24×C1111yescharacteristic
777C22×C4C24×C1112yes—
778C22×C4C24×C1111yescharacteristic
779C22×C4C24×C1112yes—
780C22×C4C24×C1112yes—
781C22×C4C24×C1111yescharacteristic
782C22×C4C24×C1111yescharacteristic
783C22×C4C24×C1112yes—
784C22×C4C24×C1112yes—
785C22×C4C24×C1111yescharacteristic
786C22×C4C24×C1112yes—
787C22×C4C24×C1112yes—
788C22×C4C24×C1111yescharacteristic
789C22×C4C24×C1111yescharacteristic
790C22×C4C24×C1111yescharacteristic
791C22×C4C24×C1111yescharacteristic
792C22×C4C24×C1111yescharacteristic
793C22×C4C24×C1111yescharacteristic
794C22×C4C24×C1111yescharacteristic
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—24no—
807C4⋊C4—22no—
808C4⋊C4—42no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4C22×C4×C1114yes—
813C4⋊C4C22×C4×C1114yes—
814C4⋊C4C22×C4×C1118yes—
815C4⋊C4C22×C4×C1118yes—
816C4⋊C4C22×C4×C1114yes—
817C4⋊C4C22×C4×C1118yes—
818C4⋊C4C22×C4×C1114yes—
819C4⋊C4C22×C4×C1118yes—
820C4⋊C4C22×C4×C1118yes—
821C4⋊C4C22×C4×C1118yes—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4C22×C4×C1114yes—
829C22⋊C4C22×C4×C1118yes—
830C22⋊C4C22×C4×C1118yes—
831C22⋊C4C22×C4×C1114yes—
832C22⋊C4C22×C4×C1118yes—
833C22⋊C4C11×#4114yes—
834C42—24no—
835C42—24no—
836C42—22no—
837C42—22no—
838C42—22no—
839C42—22no—
840C42—22no—
841C42—22no—
842C42—22no—
843C42—41no—
844C42—41no—
845C42—41no—
846C42—41no—
847C42—42no—
848C42—42no—
849C42—42no—
850C42—41no—
851C42—42no—
852C42—42no—
853C42—42no—
854C42C22×C4×C1118yes—
855C42C22×C4×C1118yes—
856C42C22×C4×C1114yes—
857C11#3431411yescharacteristic, direct product factor, Sylow
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23C23×C4×C1112yes—
869C23C23×C4×C1112yes—
870C23C2×C11×#4112yes—
871C23C2×C11×#4112yes—
872C23C25×C1111yescharacteristic
873Q8—28no—
874D4—28no—
875C2×C4—216no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—84no—
930C2×C4C23×C4×C1112yes—
931C2×C4C23×C4×C1114yes—
932C2×C4C23×C4×C1112yes—
933C2×C4C23×C4×C1114yes—
934C2×C4C23×C4×C1114yes—
935C2×C4C23×C4×C1112yes—
936C2×C4C23×C4×C1114yes—
937C2×C4C23×C4×C1112yes—
938C2×C4C23×C4×C1112yes—
939C2×C4C2×C11×#4112yes—
940C2×C4C2×C11×#4112yes—
941C2×C4C2×C11×#4112yes—
942C2×C4C2×C11×#4112yes—
943C2×C4C11×H(5,𝔽2)12yes—
944C2×C4C11×2−1+412yes—
945C2×C4C11×2−1+412yes—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22C4×C11×#4114yes—
960C22C24×C4×C1111yescharacteristic
961C22C22×C11×#4111yescharacteristic
962C22C22×C11×#4111yescharacteristic
963C22C2×C11×H(5,𝔽2)11yescharacteristic
964C22C2×C11×2−1+411yescharacteristic
965C22C2×C11×2−1+411yescharacteristic
966C22C11×#58511yescharacteristic
967C4—24no—
968C4—24no—
969C4—22no—
970C4—22no—
971C4—22no—
972C4—24no—
973C4—22no—
974C4—24no—
975C4—22no—
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—41no—
984C4—42no—
985C4—41no—
986C4—42no—
987C4C11×#52014yes—
988C2—24no—
989C2—42no—
990C2C2×C4×C11×#4111yescharacteristic
991C2C2×C11×#52011yescharacteristic
992C2C4×C11×2−1+411yescharacteristic
993C2C11×#350511yescharacteristic
994C2C11×#350911yescharacteristic
995C2C11×#351511yescharacteristic
996C2C11×#352011yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2373C2semidirect
3. C11×#2370C2semidirect
4. C11×#2370C2semidirect
5. C11×#2362C2semidirect
6. C11×#2360C2semidirect
9. C11×#2351C2semidirect
10. C11×#2347C2semidirect
11. C11×#2344C2semidirect
12. C11×#2343C2semidirect
13. C11×#2336C2semidirect
14. C11×#2334C2semidirect
16. C4×C11×#125C2semidirect
17. C4×C11×C22⋊Q8C2semidirect
18. C4×C11×C22⋊Q8C2semidirect
19. C11×#2296C2semidirect
20. C11×#2295C2semidirect
21. C2×C11×#389C2semidirect
22. C11×#2274C2semidirect
24. C11×#552C4semidirect
134. C11×#126C2×C4semidirect
135. C11×#125C2×C4semidirect
136. C11×#125C2×C4semidirect
138. C11×C22⋊Q8C2×C4semidirect
139. C11×C22⋊Q8C2×C4semidirect
142. C4×Q8×C11C2×C4semidirect
148. C11×#117C2×C4semidirect
149. C11×#117C2×C4semidirect
152. C2×C11×C4⋊C4C2×C4semidirect
244. #34314C11direct (N × H)
361. #2373C2×C11semidirect
362. #2370C2×C11semidirect
363. #2370C2×C11semidirect
364. #2362C2×C11semidirect
365. #2360C2×C11semidirect
368. #2351C2×C11semidirect
369. #2347C2×C11semidirect
370. #2344C2×C11semidirect
371. #2343C2×C11semidirect
372. #2336C2×C11semidirect
373. #2334C2×C11semidirect
375. C4×#125C2×C11semidirect
376. C4×C22⋊Q8C2×C11semidirect
377. C4×C22⋊Q8C2×C11semidirect
378. #2296C2×C11semidirect
379. #2295C2×C11semidirect
380. C2×#389C2×C11semidirect
381. #2274C2×C11semidirect
471. #552C4×C11semidirect
623. #126C2×C4×C11semidirect
624. #125C2×C4×C11semidirect
625. #125C2×C4×C11semidirect
627. C22⋊Q8C2×C4×C11semidirect
628. C22⋊Q8C2×C4×C11semidirect
631. C4×Q8C2×C4×C11semidirect
637. #117C2×C4×C11semidirect
638. #117C2×C4×C11semidirect
641. C2×C4⋊C4C2×C4×C11semidirect
857. C11#34314direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C11×#23732
C11×#23702
C11×#23622
C11×#23602
C11×#23592
C11×#23522
C11×#23512
C11×#23472
C11×#23442
C11×#23432
C11×#23362
C11×#23342
C11×#23222
C4×C11×#1252
C4×C11×C22⋊Q82
C11×#22962
C11×#22952
C2×C11×#3892
C11×#22742
C42×D4×C112
#3431411