Finite Group Databasebeta

← C11×#34475 #14611668

Subgroups — C11×#34475 #14611668

Order 2816.

2280 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic
2C11×#2381C212yesmaximal, complemented
3C11×#2378C212yesmaximal, complemented
4C11×#2368C212yesmaximal, complemented
5C11×#2365C211yesmaximal, characteristic, complemented
6C11×#2362C211yesmaximal, characteristic, complemented
7C11×#2360C211yesmaximal, characteristic, complemented
8C11×#2356C211yesmaximal, characteristic, complemented
9C11×#2353C212yesmaximal
10C11×#2352C211yesmaximal, characteristic
11Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
13C11×#2332C212yesmaximal, complemented
14C11×#2331C212yesmaximal, complemented
15C11×#2329C212yesmaximal, complemented
16C11×#2327C211yesmaximal, characteristic, complemented
17C11×#2323C211yesmaximal, characteristic, complemented
18C11×#2320C211yesmaximal, characteristic, complemented
19C11×#2318C212yesmaximal
20C11×#2310C211yesmaximal, characteristic, complemented
21C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
22C2×C11×#391C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic
24C23×Q8×C11C2211yescharacteristic
25C23×Q8×C11C2211yescharacteristic
26D4×Q8×C11C4116yescomplemented
27C2×C11×C4⋊Q8C2212yes—
28C2×C11×C4⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×C22⋊Q8C2212yes—
31C2×C11×C22⋊Q8C2212yes—
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35C2×C4×Q8×C11C2211yescharacteristic
36C2×C4×Q8×C11C2211yescharacteristic
37C2×C4×Q8×C11C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic
39C2×C4×D4×C11C2212yes—
40C2×C11×#117C2211yescharacteristic
41C2×C11×#117C2211yescharacteristic
42C22×C11×C4⋊C4C2211yescharacteristic
43C22×C42×C11C2211yescharacteristic
44C11×#391C2212yes—
45C11×#391C2212yes—
46C11×#391C2212yes—
47C11×#391C2212yes—
48C11×#391C2212yes—
49C11×#391C2211yescharacteristic
50C11×#391C2211yescharacteristic
51C11×#391C2212yes—
52C11×#391C2211yescharacteristic
53C11×#391C2211yescharacteristic
54C11×#391C2211yescharacteristic
55C11×#391C2212yes—
56C11×#391C2211yescharacteristic
57C11×#391C2211yescharacteristic
58C11×#391C2211yescharacteristic
59C11×#391C2212yes—
60C11×#389C2212yes—
61C11×#389C2212yes—
62C11×#389C2211yescharacteristic
63C11×#389C2211yescharacteristic
64C11×#389C2212yes—
65C11×#388C2211yescharacteristic
66C11×#388C2212yes—
67C11×#388C2212yes—
68C11×#388C2212yes—
69C11×#388C2211yescharacteristic
70C11×#388C2212yes—
71C11×#388C2212yes—
72C11×#387C2212yes—
73C11×#387C2212yes—
74C11×#387C2212yes—
75C11×#387C2212yes—
76C11×#387C2211yescharacteristic
77C11×#387C2212yes—
78C11×#387C2212yes—
79C11×#387C2212yes—
80C11×#387C2212yes—
81C11×#387C2212yes—
82C11×#387C2212yes—
83C11×#387C2211yescharacteristic
84C11×#387C2212yes—
85C11×#387C2212yes—
86C11×#387C2212yes—
87C11×#387C2212yes—
88C11×#387C2212yes—
89C11×#386C2211yescharacteristic
90C11×#386C2211yescharacteristic
91C11×#386C2212yes—
92C11×#385C2211yescharacteristic
93C11×#385C2211yescharacteristic
94C11×#385C2212yes—
95C11×#385C2212yes—
96C11×#383C2212yes—
97C11×#383C2212yes—
98C11×#382C2212yes—
99C11×#382C2211yescharacteristic
100C11×#381C2212yes—
101C11×#381C2212yes—
102C11×#380C2212yes—
103C11×#380C2211yescharacteristic
104C11×#380C2211yescharacteristic
105C11×#380C2212yes—
106C4×C11×C4⋊C4C2211yescharacteristic
107C4×C11×C4⋊C4C2212yes—
108C4×C11×C4⋊C4C2211yescharacteristic
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2212yes—
112C4×C11×C4⋊C4C2212yes—
113C4×C11×C22⋊C4C2211yescharacteristic
114C4×C11×C22⋊C4C2211yescharacteristic
115C4×C11×C22⋊C4C2212yes—
116C4×C11×C22⋊C4C2212yes—
117C4×C11×C22⋊C4C2212yes—
118C4×C11×C22⋊C4C2212yes—
119C4×C11×C22⋊C4C2212yes—
120C11×#376C2211yescharacteristic
121C11×#376C2212yes—
122C2×C11×#95C2212yes—
123C2×C11×#95C2212yes—
124C22×Q8×C11—42no—
125C22×Q8×C11—42no—
126C22×Q8×C11—42no—
127C22×Q8×C11—42no—
128C22×Q8×C11C2×C418yes—
129C22×Q8×C11C2×C418yescomplemented
130C22×Q8×C11C2311yescharacteristic
131C22×Q8×C11C2311yescharacteristic
132C22×Q8×C11C2311yescharacteristic
133C22×Q8×C11C2312yes—
134C22×Q8×C11C2312yes—
135C22×D4×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C23×C4×C11C2311yescharacteristic
139C23×C4×C11C2311yescharacteristic
140C23×C4×C11C2312yes—
141C23×C4×C11C2312yes—
142C23×C4×C11C2312yes—
143C11×C4⋊Q8C2×C418yescomplemented
144C11×C4⋊Q8C2×C4116yescomplemented
145C11×C22⋊Q8C2×C418yes—
146C11×C22⋊Q8C2×C4116yes—
147C11×C22⋊Q8C2×C418yescomplemented
148C11×C22⋊Q8C2×C4116yescomplemented
149C4×Q8×C11—42no—
150C4×Q8×C11—42no—
151C4×Q8×C11—42no—
152C4×Q8×C11—42no—
153C4×Q8×C11C2×C418yescomplemented
154C4×D4×C11C2×C418yes—
155C4×D4×C11C2×C4116yes—
156C11×#117—42no—
157C11×#117—42no—
158C2×C11×C4⋊C4—42no—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
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×C4⋊C4C2312yes—
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2311yescharacteristic
184C2×C11×C22⋊C4C2311yescharacteristic
185C2×C11×C22⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4C2311yescharacteristic
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2311yescharacteristic
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2311yescharacteristic
192C2×C11×C22⋊C4C2311yescharacteristic
193C2×C11×C22⋊C4C2312yes—
194C2×C42×C11—42no—
195C2×C42×C11C2311yescharacteristic
196C2×C42×C11C2311yescharacteristic
197C2×C42×C11C2311yescharacteristic
198C2×C42×C11C2312yes—
199C2×C42×C11C2311yescharacteristic
200C2×C42×C11C2311yescharacteristic
201C2×C42×C11C2311yescharacteristic
202C2×C42×C11C2312yes—
203C2×C42×C11C2312yes—
204C2×C42×C11C2312yes—
205C2×C42×C11C2312yes—
206C2×C42×C11C2312yes—
207C2×C42×C11C2312yes—
208C2×C42×C11C2312yes—
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2312yes—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2311yescharacteristic
220C11×#95C2312yes—
221C11×#95C2311yescharacteristic
222C11×#95C2312yes—
223C11×#95C2311yescharacteristic
224C11×#95C2311yescharacteristic
225C11×#95C2311yescharacteristic
226C11×#95C2311yescharacteristic
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11×#95C2311yescharacteristic
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2311yescharacteristic
244C11×#95C2312yes—
245C11×#95C2312yes—
246#34475C1111yesmaximal, characteristic, direct product factor, Sylow
247C24×C11C2411yescharacteristic
248C24×C11C2411yescharacteristic
249C2×Q8×C11—22no—
250C2×Q8×C11—22no—
251C2×Q8×C11—22no—
252C2×Q8×C11—22no—
253C2×Q8×C11—22no—
254C2×Q8×C11—22no—
255C2×Q8×C11—42no—
256C2×Q8×C11—42no—
257C2×Q8×C11—42no—
258C2×Q8×C11—42no—
259C2×Q8×C11—416no—
260C2×Q8×C11—416no—
261C2×Q8×C11C22×C414yes—
262C2×Q8×C11C22×C414yes—
263C2×Q8×C11C22×C414yes—
264C2×Q8×C11C22×C418yes—
265C2×Q8×C11C22×C418yes—
266C2×D4×C11—22no—
267C2×D4×C11—22no—
268C2×D4×C11C22×C414yes—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11—22no—
275C22×C4×C11—24no—
276C22×C4×C11—22no—
277C22×C4×C11—41no—
278C22×C4×C11—41no—
279C22×C4×C11—41no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11C22×C414yes—
287C22×C4×C11C22×C414yes—
288C22×C4×C11C22×C418yes—
289C22×C4×C11C22×C418yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2412yes—
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2412yes—
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2412yes—
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C11×C4⋊C4—22no—
312C11×C4⋊C4—22no—
313C11×C4⋊C4—22no—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—42no—
317C11×C4⋊C4—41no—
318C11×C4⋊C4—42no—
319C11×C4⋊C4—42no—
320C11×C4⋊C4—41no—
321C11×C4⋊C4—41no—
322C11×C4⋊C4—42no—
323C11×C4⋊C4—42no—
324C11×C4⋊C4—42no—
325C11×C4⋊C4—42no—
326C11×C4⋊C4C22×C414yes—
327C11×C4⋊C4C22×C418yes—
328C11×C4⋊C4C22×C418yes—
329C11×C4⋊C4C22×C414yes—
330C11×C4⋊C4C22×C418yes—
331C11×C4⋊C4C22×C418yes—
332C11×C4⋊C4C22×C418yes—
333C11×C22⋊C4—22no—
334C11×C22⋊C4—24no—
335C11×C22⋊C4—22no—
336C11×C22⋊C4—22no—
337C11×C22⋊C4—42no—
338C11×C22⋊C4—41no—
339C11×C22⋊C4—41no—
340C11×C22⋊C4—41no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4C22×C414yes—
343C11×C22⋊C4C22×C418yes—
344C11×C22⋊C4C22×C414yes—
345C11×C22⋊C4C22×C418yes—
346C42×C11—22no—
347C42×C11—22no—
348C42×C11—22no—
349C42×C11—22no—
350C42×C11—24no—
351C42×C11—41no—
352C42×C11—41no—
353C42×C11—42no—
354C42×C11—42no—
355C42×C11—42no—
356C42×C11—42no—
357C42×C11—42no—
358C42×C11—42no—
359C42×C11—42no—
360C42×C11C22×C418yes—
361C42×C11C22×C414yes—
362C2×D4×Q8C2×C1111yescharacteristic
363#2381C2×C1112yescomplemented
364#2378C2×C1112yescomplemented
365#2368C2×C1112yescomplemented
366#2365C2×C1111yescharacteristic, complemented
367#2362C2×C1111yescharacteristic, complemented
368#2360C2×C1111yescharacteristic, complemented
369#2356C2×C1111yescharacteristic, complemented
370#2353C2×C1112yes—
371#2352C2×C1111yescharacteristic
372Q8×C22⋊C4C2×C1111yescharacteristic, complemented
373Q8×C22⋊C4C2×C1111yescharacteristic, complemented
374#2332C2×C1112yescomplemented
375#2331C2×C1112yescomplemented
376#2329C2×C1112yescomplemented
377#2327C2×C1111yescharacteristic, complemented
378#2323C2×C1111yescharacteristic, complemented
379#2320C2×C1111yescharacteristic, complemented
380#2318C2×C1112yes—
381#2310C2×C1111yescharacteristic, complemented
382C4×C22⋊Q8C2×C1111yescharacteristic, complemented
383C2×#391C2×C1111yescharacteristic, complemented
384#2290C2×C1111yescharacteristic
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×C11—21no—
394C23×C11—21no—
395C23×C11C23×C412yes—
396C23×C11C23×C412yes—
397C23×C112−1+412yes—
398C23×C112−1+412yes—
399C23×C11C2511yescharacteristic
400Q8×C11—28no—
401Q8×C11—28no—
402Q8×C11—28no—
403Q8×C11—48no—
404Q8×C11—48no—
405D4×C11—28no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—22no—
424C2×C4×C11—28no—
425C2×C4×C11—28no—
426C2×C4×C11—21no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—22no—
441C2×C4×C11—21no—
442C2×C4×C11—22no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—21no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—48no—
460C2×C4×C11—48no—
461C2×C4×C11—44no—
462C2×C4×C11—44no—
463C2×C4×C11—84no—
464C2×C4×C11C23×C412yes—
465C2×C4×C11C23×C414yes—
466C2×C4×C11C23×C412yes—
467C2×C4×C11C23×C414yes—
468C2×C4×C11C23×C412yes—
469C2×C4×C11C23×C412yes—
470C2×C4×C11C23×C414yes—
471C2×C4×C11C23×C414yes—
472C2×C4×C11C23×C412yes—
473C2×C4×C11H(5,𝔽2)12yes—
474C2×C4×C11H(5,𝔽2)12yes—
475C2×C4×C112−1+412yes—
476C23×Q8C22×C1111yescharacteristic
477C23×Q8C22×C1111yescharacteristic
478D4×Q8C4×C11116yescomplemented
479C2×C4⋊Q8C22×C1111yescharacteristic
480C2×C4⋊Q8C22×C1112yes—
481C2×C22⋊Q8C22×C1112yes—
482C2×C22⋊Q8C22×C1111yescharacteristic
483C2×C22⋊Q8C22×C1111yescharacteristic
484C2×C22⋊Q8C22×C1112yes—
485C2×C4×Q8C22×C1111yescharacteristic
486C2×C4×Q8C22×C1111yescharacteristic
487C2×C4×Q8C22×C1111yescharacteristic
488C2×C4×Q8C22×C1111yescharacteristic
489C2×C4×Q8C22×C1111yescharacteristic
490C2×C4×D4C22×C1112yes—
491C2×C4×D4C22×C1111yescharacteristic
492C2×#117C22×C1111yescharacteristic
493C2×#117C22×C1111yescharacteristic
494C22×C4⋊C4C22×C1111yescharacteristic
495C22×C42C22×C1111yescharacteristic
496#391C22×C1111yescharacteristic
497#391C22×C1111yescharacteristic
498#391C22×C1112yes—
499#391C22×C1111yescharacteristic
500#391C22×C1111yescharacteristic
501#391C22×C1112yes—
502#391C22×C1111yescharacteristic
503#391C22×C1111yescharacteristic
504#391C22×C1112yes—
505#391C22×C1112yes—
506#391C22×C1112yes—
507#391C22×C1112yes—
508#391C22×C1112yes—
509#391C22×C1111yescharacteristic
510#391C22×C1111yescharacteristic
511#391C22×C1112yes—
512#389C22×C1111yescharacteristic
513#389C22×C1111yescharacteristic
514#389C22×C1112yes—
515#389C22×C1112yes—
516#389C22×C1112yes—
517#388C22×C1112yes—
518#388C22×C1112yes—
519#388C22×C1112yes—
520#388C22×C1111yescharacteristic
521#388C22×C1112yes—
522#388C22×C1112yes—
523#388C22×C1111yescharacteristic
524#387C22×C1112yes—
525#387C22×C1112yes—
526#387C22×C1112yes—
527#387C22×C1112yes—
528#387C22×C1112yes—
529#387C22×C1112yes—
530#387C22×C1112yes—
531#387C22×C1112yes—
532#387C22×C1112yes—
533#387C22×C1112yes—
534#387C22×C1111yescharacteristic
535#387C22×C1112yes—
536#387C22×C1112yes—
537#387C22×C1112yes—
538#387C22×C1112yes—
539#387C22×C1112yes—
540#387C22×C1111yescharacteristic
541#386C22×C1111yescharacteristic
542#386C22×C1112yes—
543#386C22×C1111yescharacteristic
544#385C22×C1112yes—
545#385C22×C1112yes—
546#385C22×C1111yescharacteristic
547#385C22×C1111yescharacteristic
548#383C22×C1112yes—
549#383C22×C1112yes—
550#382C22×C1112yes—
551#382C22×C1111yescharacteristic
552#381C22×C1112yes—
553#381C22×C1112yes—
554#380C22×C1112yes—
555#380C22×C1111yescharacteristic
556#380C22×C1112yes—
557#380C22×C1111yescharacteristic
558C4×C4⋊C4C22×C1111yescharacteristic
559C4×C4⋊C4C22×C1111yescharacteristic
560C4×C4⋊C4C22×C1112yes—
561C4×C4⋊C4C22×C1112yes—
562C4×C4⋊C4C22×C1112yes—
563C4×C4⋊C4C22×C1111yescharacteristic
564C4×C4⋊C4C22×C1111yescharacteristic
565C4×C22⋊C4C22×C1112yes—
566C4×C22⋊C4C22×C1112yes—
567C4×C22⋊C4C22×C1112yes—
568C4×C22⋊C4C22×C1112yes—
569C4×C22⋊C4C22×C1111yescharacteristic
570C4×C22⋊C4C22×C1111yescharacteristic
571C4×C22⋊C4C22×C1112yes—
572#376C22×C1111yescharacteristic
573#376C22×C1112yes—
574C2×#95C22×C1112yes—
575C2×#95C22×C1112yes—
576C22×C11—22no—
577C22×C11—22no—
578C22×C11—22no—
579C22×C11—22no—
580C22×C11—22no—
581C22×C11—22no—
582C22×C11—22no—
583C22×C11—22no—
584C22×C11—22no—
585C22×C11—41no—
586C22×C11—41no—
587C22×C11—41no—
588C22×C11—41no—
589C22×C11#51914yes—
590C22×C11C24×C411yescharacteristic
591C22×C11C2×H(5,𝔽2)11yescharacteristic
592C22×C11C2×H(5,𝔽2)11yescharacteristic
593C22×C11C2×2−1+411yescharacteristic
594C22×C11C2×2−1+411yescharacteristic
595C22×C11C2×2−1+411yescharacteristic
596C22×C11#58511yescharacteristic
597C4×C11—22no—
598C4×C11—22no—
599C4×C11—24no—
600C4×C11—24no—
601C4×C11—24no—
602C4×C11—22no—
603C4×C11—24no—
604C4×C11—22no—
605C4×C11—22no—
606C4×C11—41no—
607C4×C11—41no—
608C4×C11—41no—
609C4×C11—42no—
610C4×C11—41no—
611C4×C11—41no—
612C4×C11—41no—
613C4×C11—42no—
614C4×C11—41no—
615C4×C11—42no—
616C4×C11—42no—
617C4×C11#51814yes—
618C22×Q8—42no—
619C22×Q8—42no—
620C22×Q8—42no—
621C22×Q8—42no—
622C22×Q8C2×C4×C1118yes—
623C22×Q8C2×C4×C1118yescomplemented
624C22×Q8C23×C1111yescharacteristic
625C22×Q8C23×C1111yescharacteristic
626C22×Q8C23×C1111yescharacteristic
627C22×Q8C23×C1112yes—
628C22×Q8C23×C1112yes—
629C22×D4C23×C1111yescharacteristic
630C23×C4C23×C1111yescharacteristic
631C23×C4C23×C1111yescharacteristic
632C23×C4C23×C1111yescharacteristic
633C23×C4C23×C1112yes—
634C23×C4C23×C1111yescharacteristic
635C23×C4C23×C1112yes—
636C23×C4C23×C1112yes—
637C4⋊Q8C2×C4×C1118yescomplemented
638C4⋊Q8C2×C4×C11116yescomplemented
639C22⋊Q8C2×C4×C1118yes—
640C22⋊Q8C2×C4×C11116yes—
641C22⋊Q8C2×C4×C1118yescomplemented
642C22⋊Q8C2×C4×C11116yescomplemented
643C4×Q8—42no—
644C4×Q8—42no—
645C4×Q8—42no—
646C4×Q8—42no—
647C4×Q8C2×C4×C1118yescomplemented
648C4×D4C2×C4×C1118yes—
649C4×D4C2×C4×C11116yes—
650#117—42no—
651#117—42no—
652C2×C4⋊C4—42no—
653C2×C4⋊C4C23×C1111yescharacteristic
654C2×C4⋊C4C23×C1111yescharacteristic
655C2×C4⋊C4C23×C1111yescharacteristic
656C2×C4⋊C4C23×C1111yescharacteristic
657C2×C4⋊C4C23×C1111yescharacteristic
658C2×C4⋊C4C23×C1112yes—
659C2×C4⋊C4C23×C1111yescharacteristic
660C2×C4⋊C4C23×C1111yescharacteristic
661C2×C4⋊C4C23×C1112yes—
662C2×C4⋊C4C23×C1112yes—
663C2×C4⋊C4C23×C1112yes—
664C2×C4⋊C4C23×C1112yes—
665C2×C4⋊C4C23×C1112yes—
666C2×C4⋊C4C23×C1112yes—
667C2×C4⋊C4C23×C1111yescharacteristic
668C2×C4⋊C4C23×C1112yes—
669C2×C4⋊C4C23×C1111yescharacteristic
670C2×C4⋊C4C23×C1111yescharacteristic
671C2×C4⋊C4C23×C1112yes—
672C2×C4⋊C4C23×C1112yes—
673C2×C4⋊C4C23×C1112yes—
674C2×C4⋊C4C23×C1112yes—
675C2×C22⋊C4C23×C1112yes—
676C2×C22⋊C4C23×C1111yescharacteristic
677C2×C22⋊C4C23×C1111yescharacteristic
678C2×C22⋊C4C23×C1111yescharacteristic
679C2×C22⋊C4C23×C1111yescharacteristic
680C2×C22⋊C4C23×C1111yescharacteristic
681C2×C22⋊C4C23×C1112yes—
682C2×C22⋊C4C23×C1112yes—
683C2×C22⋊C4C23×C1111yescharacteristic
684C2×C22⋊C4C23×C1112yes—
685C2×C22⋊C4C23×C1111yescharacteristic
686C2×C22⋊C4C23×C1112yes—
687C2×C22⋊C4C23×C1111yescharacteristic
688C2×C42—42no—
689C2×C42C23×C1111yescharacteristic
690C2×C42C23×C1111yescharacteristic
691C2×C42C23×C1111yescharacteristic
692C2×C42C23×C1111yescharacteristic
693C2×C42C23×C1112yes—
694C2×C42C23×C1112yes—
695C2×C42C23×C1112yes—
696C2×C42C23×C1112yes—
697C2×C42C23×C1112yes—
698C2×C42C23×C1112yes—
699C2×C42C23×C1112yes—
700C2×C42C23×C1112yes—
701C2×C42C23×C1111yescharacteristic
702C2×C42C23×C1111yescharacteristic
703C2×C42C23×C1111yescharacteristic
704C2×C42C23×C1112yes—
705#95C23×C1112yes—
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×C1112yes—
715#95C23×C1111yescharacteristic
716#95C23×C1112yes—
717#95C23×C1111yescharacteristic
718#95C23×C1111yescharacteristic
719#95C23×C1111yescharacteristic
720#95C23×C1111yescharacteristic
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×C1111yescharacteristic
731#95C23×C1111yescharacteristic
732#95C23×C1111yescharacteristic
733#95C23×C1112yes—
734#95C23×C1112yes—
735#95C23×C1112yes—
736#95C23×C1112yes—
737#95C23×C1111yescharacteristic
738#95C23×C1112yes—
739#95C23×C1112yes—
740C2×C11—24no—
741C2×C11—42no—
742C2×C11C2×#51811yescharacteristic
743C2×C11C2×#51911yescharacteristic
744C2×C11C4×2−1+411yescharacteristic
745C2×C11#353811yescharacteristic
746C2×C11#354111yescharacteristic
747C2×C11#355211yescharacteristic
748C2×C11#356111yescharacteristic
749C24C24×C1111yescharacteristic
750C24C24×C1111yescharacteristic
751C2×Q8—22no—
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—22no—
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8—416no—
762C2×Q8—416no—
763C2×Q8C22×C4×C1114yes—
764C2×Q8C22×C4×C1114yes—
765C2×Q8C22×C4×C1114yes—
766C2×Q8C22×C4×C1118yes—
767C2×Q8C22×C4×C1118yes—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4C22×C4×C1114yes—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—24no—
778C22×C4—22no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—41no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4C22×C4×C1114yes—
789C22×C4C22×C4×C1114yes—
790C22×C4C22×C4×C1118yes—
791C22×C4C22×C4×C1118yes—
792C22×C4C24×C1111yescharacteristic
793C22×C4C24×C1111yescharacteristic
794C22×C4C24×C1111yescharacteristic
795C22×C4C24×C1112yes—
796C22×C4C24×C1111yescharacteristic
797C22×C4C24×C1111yescharacteristic
798C22×C4C24×C1112yes—
799C22×C4C24×C1112yes—
800C22×C4C24×C1111yescharacteristic
801C22×C4C24×C1111yescharacteristic
802C22×C4C24×C1112yes—
803C22×C4C24×C1111yescharacteristic
804C22×C4C24×C1112yes—
805C22×C4C24×C1112yes—
806C22×C4C24×C1111yescharacteristic
807C22×C4C24×C1111yescharacteristic
808C22×C4C24×C1111yescharacteristic
809C22×C4C24×C1112yes—
810C22×C4C24×C1112yes—
811C22×C4C24×C1111yescharacteristic
812C22×C4C24×C1111yescharacteristic
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—42no—
819C4⋊C4—41no—
820C4⋊C4—41no—
821C4⋊C4—42no—
822C4⋊C4—42no—
823C4⋊C4—42no—
824C4⋊C4—42no—
825C4⋊C4—41no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C4⋊C4C22×C4×C1114yes—
829C4⋊C4C22×C4×C1118yes—
830C4⋊C4C22×C4×C1118yes—
831C4⋊C4C22×C4×C1114yes—
832C4⋊C4C22×C4×C1118yes—
833C4⋊C4C22×C4×C1118yes—
834C4⋊C4C22×C4×C1118yes—
835C22⋊C4—24no—
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—41no—
840C22⋊C4—41no—
841C22⋊C4—42no—
842C22⋊C4—42no—
843C22⋊C4—41no—
844C22⋊C4C22×C4×C1114yes—
845C22⋊C4C22×C4×C1118yes—
846C22⋊C4C22×C4×C1114yes—
847C22⋊C4C22×C4×C1118yes—
848C42—22no—
849C42—22no—
850C42—22no—
851C42—22no—
852C42—24no—
853C42—41no—
854C42—41no—
855C42—42no—
856C42—42no—
857C42—42no—
858C42—42no—
859C42—42no—
860C42—42no—
861C42—42no—
862C42C22×C4×C1118yes—
863C42C22×C4×C1114yes—
864C11#3447511yescharacteristic, direct product factor, Sylow
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23C23×C4×C1112yes—
876C23C23×C4×C1112yes—
877C23C11×2−1+412yes—
878C23C11×2−1+412yes—
879C23C25×C1111yescharacteristic
880Q8—28no—
881Q8—28no—
882Q8—28no—
883Q8—48no—
884Q8—48no—
885D4—28no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—22no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—48no—
940C2×C4—48no—
941C2×C4—44no—
942C2×C4—44no—
943C2×C4—84no—
944C2×C4C23×C4×C1112yes—
945C2×C4C23×C4×C1114yes—
946C2×C4C23×C4×C1112yes—
947C2×C4C23×C4×C1114yes—
948C2×C4C23×C4×C1112yes—
949C2×C4C23×C4×C1112yes—
950C2×C4C23×C4×C1114yes—
951C2×C4C23×C4×C1114yes—
952C2×C4C23×C4×C1112yes—
953C2×C4C11×H(5,𝔽2)12yes—
954C2×C4C11×H(5,𝔽2)12yes—
955C2×C4C11×2−1+412yes—
956C22—22no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22C11×#51914yes—
970C22C24×C4×C1111yescharacteristic
971C22C2×C11×H(5,𝔽2)11yescharacteristic
972C22C2×C11×H(5,𝔽2)11yescharacteristic
973C22C2×C11×2−1+411yescharacteristic
974C22C2×C11×2−1+411yescharacteristic
975C22C2×C11×2−1+411yescharacteristic
976C22C11×#58511yescharacteristic
977C4—22no—
978C4—22no—
979C4—24no—
980C4—24no—
981C4—24no—
982C4—22no—
983C4—24no—
984C4—22no—
985C4—22no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—42no—
992C4—41no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—41no—
997C4C11×#51814yes—
998C2—24no—
999C2—42no—
1000C2C2×C11×#51811yescharacteristic
1001C2C2×C11×#51911yescharacteristic
1002C2C4×C11×2−1+411yescharacteristic
1003C2C11×#353811yescharacteristic
1004C2C11×#354111yescharacteristic
1005C2C11×#355211yescharacteristic
1006C2C11×#356111yescharacteristic
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×#2381C2semidirect
3. C11×#2378C2semidirect
4. C11×#2368C2semidirect
5. C11×#2365C2semidirect
6. C11×#2362C2semidirect
7. C11×#2360C2semidirect
8. C11×#2356C2semidirect
11. Q8×C11×C22⋊C4C2semidirect
12. Q8×C11×C22⋊C4C2semidirect
13. C11×#2332C2semidirect
14. C11×#2331C2semidirect
15. C11×#2329C2semidirect
16. C11×#2327C2semidirect
17. C11×#2323C2semidirect
18. C11×#2320C2semidirect
20. C11×#2310C2semidirect
21. C4×C11×C22⋊Q8C2semidirect
22. C2×C11×#391C2semidirect
26. D4×Q8×C11C4semidirect
129. C22×Q8×C11C2×C4semidirect
143. C11×C4⋊Q8C2×C4semidirect
144. C11×C4⋊Q8C2×C4semidirect
147. C11×C22⋊Q8C2×C4semidirect
148. C11×C22⋊Q8C2×C4semidirect
153. C4×Q8×C11C2×C4semidirect
246. #34475C11direct (N × H)
363. #2381C2×C11semidirect
364. #2378C2×C11semidirect
365. #2368C2×C11semidirect
366. #2365C2×C11semidirect
367. #2362C2×C11semidirect
368. #2360C2×C11semidirect
369. #2356C2×C11semidirect
372. Q8×C22⋊C4C2×C11semidirect
373. Q8×C22⋊C4C2×C11semidirect
374. #2332C2×C11semidirect
375. #2331C2×C11semidirect
376. #2329C2×C11semidirect
377. #2327C2×C11semidirect
378. #2323C2×C11semidirect
379. #2320C2×C11semidirect
381. #2310C2×C11semidirect
382. C4×C22⋊Q8C2×C11semidirect
383. C2×#391C2×C11semidirect
478. D4×Q8C4×C11semidirect
623. C22×Q8C2×C4×C11semidirect
637. C4⋊Q8C2×C4×C11semidirect
638. C4⋊Q8C2×C4×C11semidirect
641. C22⋊Q8C2×C4×C11semidirect
642. C22⋊Q8C2×C4×C11semidirect
647. C4×Q8C2×C4×C11semidirect
864. C11#34475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C11×#23812
C11×#23782
C11×#23682
C11×#23652
C11×#23622
C11×#23602
C11×#23562
C11×#23532
C11×#23522
Q8×C11×C22⋊C42
C11×#23322
C11×#23312
C11×#23292
C11×#23272
C11×#23232
C11×#23202
C11×#23182
C11×#23102
C4×C11×C22⋊Q82
C2×C11×#3912
C11×#22902
#3447511