Finite Group Databasebeta

← C11×#34720 #14611913

Subgroups — C11×#34720 #14611913

Order 2816.

2548 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C2×C4×C11×#41C211yesmaximal, characteristic, complemented
3C11×#2477C212yesmaximal, complemented
4C11×#2475C212yesmaximal, complemented
5C11×#2463C212yesmaximal, complemented
6C11×#2460C212yesmaximal, complemented
7C11×#2452C211yesmaximal, characteristic, complemented
8C11×#2446C211yesmaximal, characteristic, complemented
9C11×#2439C211yesmaximal, characteristic, complemented
10C11×#2432C211yesmaximal, characteristic, complemented
11C11×#2427C211yesmaximal, characteristic, complemented
12C11×#2421C211yesmaximal, characteristic, complemented
13C11×#2415C211yesmaximal, characteristic, complemented
14C11×#2407C211yesmaximal, characteristic
15C11×#2398C212yesmaximal, complemented
16C11×#2392C212yesmaximal, complemented
17C4×C11×#124C211yesmaximal, characteristic, complemented
18C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
19C4×C11×C22⋊Q8C212yesmaximal, complemented
20C4×C11×#121C211yesmaximal, characteristic, complemented
21C11×#2295C211yesmaximal, characteristic, complemented
22C11×#2290C212yesmaximal, complemented
23C42×D4×C11C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C11×#533—28no—
26C2×C11×C4⋊Q8C2211yescharacteristic
27C2×C11×C4⋊Q8C2211yescharacteristic
28C2×C11×#125C2212yes—
29C2×C11×#124C2211yescharacteristic
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C11×C22⋊Q8C2212yes—
34C2×C11×C22⋊Q8C2212yes—
35C2×C11×#121C2211yescharacteristic
36C4×C11×#41—28no—
37C2×C4×Q8×C11C2212yes—
38C2×C4×Q8×C11C2211yescharacteristic
39C2×C4×Q8×C11C2211yescharacteristic
40C2×C4×Q8×C11C2211yescharacteristic
41C2×C4×D4×C11C2211yescharacteristic
42C2×C4×D4×C11C2212yes—
43C2×C4×D4×C11C2212yes—
44C2×C4×D4×C11C2211yescharacteristic
45C2×C4×D4×C11C2212yes—
46C2×C4×D4×C11C2211yescharacteristic
47C2×C4×D4×C11C2211yescharacteristic
48C2×C4×D4×C11C2211yescharacteristic
49C2×C11×#117C2212yes—
50C2×C11×#117C2211yescharacteristic
51C2×C11×#117C2212yes—
52C22×C42×C11C2211yescharacteristic
53C22×C42×C11C2212yes—
54C22×C42×C11C2211yescharacteristic
55C11×#400C2212yes—
56C11×#400C2212yes—
57C11×#398C2212yes—
58C11×#397C2212yes—
59C11×#397C2212yes—
60C11×#397C2212yes—
61C11×#396C2212yes—
62C11×#396C2212yes—
63C11×#394C2212yes—
64C11×#394C2212yes—
65C11×#394C2212yes—
66C11×#394C2212yes—
67C11×#394C2212yes—
68C11×#393C2212yes—
69C11×#393C2212yes—
70C11×#392C2212yes—
71C11×#391C2211yescharacteristic
72C11×#391C2211yescharacteristic
73C11×#391C2211yescharacteristic
74C11×#391C2211yescharacteristic
75C11×#391C2212yes—
76C11×#390C2211yescharacteristic
77C11×#390C2211yescharacteristic
78C11×#389C2211yescharacteristic
79C11×#389C2212yes—
80C11×#389C2211yescharacteristic
81C11×#389C2211yescharacteristic
82C11×#389C2211yescharacteristic
83C11×#388C2212yes—
84C11×#388C2212yes—
85C11×#388C2212yes—
86C11×#388C2212yes—
87C11×#388C2212yes—
88C11×#387C2212yes—
89C11×#387C2212yes—
90C11×#387C2212yes—
91C11×#387C2212yes—
92C11×#387C2212yes—
93C11×#387C2212yes—
94C11×#387C2212yes—
95C11×#386C2212yes—
96C11×#386C2212yes—
97C11×#386C2212yes—
98C11×#385C2212yes—
99C11×#385C2212yes—
100C11×#385C2212yes—
101C11×#385C2212yes—
102C11×#385C2212yes—
103C11×#382C2211yescharacteristic
104C11×#380C2211yescharacteristic
105C11×#380C2211yescharacteristic
106C11×#380C2212yes—
107C4×C11×C4⋊C4C2212yes—
108C4×C11×C4⋊C4C2211yescharacteristic
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2212yes—
112C4×C11×C4⋊C4C2211yescharacteristic
113C4×C11×C22⋊C4C2212yes—
114C4×C11×C22⋊C4C2212yes—
115C4×C11×C22⋊C4C2211yescharacteristic
116C4×C11×C22⋊C4C2212yes—
117C4×C11×C22⋊C4C2212yes—
118C4×C11×C22⋊C4C2211yescharacteristic
119C4×C11×C22⋊C4C2211yescharacteristic
120C4×C11×C22⋊C4C2211yescharacteristic
121C4×C11×C22⋊C4C2211yescharacteristic
122C4×C11×C22⋊C4C2211yescharacteristic
123C11×#376C2212yes—
124C43×C11C2211yescharacteristic
125C2×C11×#41—24no—
126C2×C11×#41—24no—
127C2×C11×#41—24no—
128C22×Q8×C11C2311yescharacteristic
129C22×Q8×C11C2312yes—
130C22×Q8×C11C2311yescharacteristic
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2312yes—
133C22×D4×C11C2312yes—
134C22×D4×C11C2311yescharacteristic
135C23×C4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C23×C4×C11C2312yes—
139C23×C4×C11C2311yescharacteristic
140C23×C4×C11C2311yescharacteristic
141C23×C4×C11C2312yes—
142C23×C4×C11C2311yescharacteristic
143C23×C4×C11C2311yescharacteristic
144C11×C4⋊Q8—24no—
145C11×C4⋊Q8—24no—
146C11×#125—28no—
147C11×#124—24no—
148C11×C22⋊Q8—24no—
149C11×C22⋊Q8—24no—
150C11×C22⋊Q8—24no—
151C11×C22⋊Q8—28no—
152C11×C22⋊Q8—28no—
153C11×#121—24no—
154C4×Q8×C11—24no—
155C4×Q8×C11—28no—
156C4×Q8×C11—24no—
157C4×Q8×C11D418yescomplemented
158C4×D4×C11—24no—
159C4×D4×C11—24no—
160C4×D4×C11—28no—
161C4×D4×C11—28no—
162C4×D4×C11—24no—
163C4×D4×C11—24no—
164C4×D4×C11—24no—
165C4×D4×C11—28no—
166C11×#117—28no—
167C11×#117—24no—
168C11×#117—28no—
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2312yes—
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2311yescharacteristic
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C4⋊C4C2312yes—
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C4⋊C4C2312yes—
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C4⋊C4C2312yes—
187C2×C11×C4⋊C4C2312yes—
188C2×C11×C4⋊C4C2311yescharacteristic
189C2×C11×C4⋊C4C2311yescharacteristic
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C11×C22⋊C4C2312yes—
193C2×C11×C22⋊C4C2312yes—
194C2×C11×C22⋊C4C2312yes—
195C2×C11×C22⋊C4C2311yescharacteristic
196C2×C11×C22⋊C4C2311yescharacteristic
197C2×C11×C22⋊C4C2311yescharacteristic
198C2×C11×C22⋊C4C2311yescharacteristic
199C2×C11×C22⋊C4C2311yescharacteristic
200C2×C11×C22⋊C4C2311yescharacteristic
201C2×C11×C22⋊C4C2312yes—
202C2×C11×C22⋊C4C2312yes—
203C2×C11×C22⋊C4C2312yes—
204C2×C11×C22⋊C4C2312yes—
205C2×C11×C22⋊C4C2312yes—
206C2×C11×C22⋊C4C2312yes—
207C2×C11×C22⋊C4C2312yes—
208C2×C11×C22⋊C4C2312yes—
209C2×C11×C22⋊C4C2312yes—
210C2×C11×C22⋊C4C2312yes—
211C2×C42×C11—24no—
212C2×C42×C11—28no—
213C2×C42×C11—24no—
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2312yes—
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2311yescharacteristic
218C2×C42×C11C2311yescharacteristic
219C2×C42×C11C2312yes—
220C2×C42×C11C2311yescharacteristic
221C2×C42×C11C2311yescharacteristic
222C2×C42×C11C2311yescharacteristic
223C2×C42×C11C2311yescharacteristic
224C2×C42×C11C2311yescharacteristic
225C2×C42×C11C2311yescharacteristic
226C2×C42×C11C2311yescharacteristic
227C2×C42×C11C2312yes—
228C2×C42×C11C2312yes—
229C2×C42×C11C2311yescharacteristic
230C2×C42×C11C2311yescharacteristic
231C2×C42×C11C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11×#95C2311yescharacteristic
239C11×#95C2311yescharacteristic
240C11×#95C2311yescharacteristic
241C11×#95C2311yescharacteristic
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11×#95C2312yes—
254C11×#95C2312yes—
255#34720C1111yesmaximal, characteristic, direct product factor, Sylow
256C24×C11C2411yescharacteristic
257C24×C11C2412yes—
258C24×C11C2411yescharacteristic
259C11×#41—232no—
260C2×Q8×C11—24no—
261C2×Q8×C11—22no—
262C2×Q8×C11—22no—
263C2×Q8×C11—22no—
264C2×Q8×C11—24no—
265C2×Q8×C11—22no—
266C2×Q8×C11—22no—
267C2×Q8×C11—42no—
268C2×Q8×C11C2×D414yes—
269C2×D4×C11—22no—
270C2×D4×C11—22no—
271C2×D4×C11—24no—
272C2×D4×C11—24no—
273C2×D4×C11—24no—
274C2×D4×C11—24no—
275C2×D4×C11—24no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—42no—
280C2×D4×C11#4114yes—
281C22×C4×C11—24no—
282C22×C4×C11—22no—
283C22×C4×C11—24no—
284C22×C4×C11—22no—
285C22×C4×C11—24no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—24no—
290C22×C4×C11—22no—
291C22×C4×C11—24no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—22no—
296C22×C4×C11—22no—
297C22×C4×C11—22no—
298C22×C4×C11—24no—
299C22×C4×C11—22no—
300C22×C4×C11—24no—
301C22×C4×C11—22no—
302C22×C4×C11—24no—
303C22×C4×C11—41no—
304C22×C4×C11—41no—
305C22×C4×C11—42no—
306C22×C4×C11#4114yes—
307C22×C4×C11#4114yescomplemented
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2412yes—
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2412yes—
314C22×C4×C11C2412yes—
315C22×C4×C11C2411yescharacteristic
316C22×C4×C11C2412yes—
317C22×C4×C11C2412yes—
318C22×C4×C11C2412yes—
319C22×C4×C11C2411yescharacteristic
320C22×C4×C11C2412yes—
321C22×C4×C11C2411yescharacteristic
322C22×C4×C11C2411yescharacteristic
323C22×C4×C11C2411yescharacteristic
324C22×C4×C11C2411yescharacteristic
325C22×C4×C11C2411yescharacteristic
326C22×C4×C11C2411yescharacteristic
327C22×C4×C11C2411yescharacteristic
328C11×C4⋊C4—24no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—24no—
331C11×C4⋊C4—24no—
332C11×C4⋊C4—24no—
333C11×C4⋊C4—24no—
334C11×C4⋊C4—24no—
335C11×C4⋊C4—24no—
336C11×C4⋊C4—22no—
337C11×C4⋊C4—22no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—24no—
340C11×C4⋊C4—22no—
341C11×C4⋊C4—24no—
342C11×C4⋊C4—22no—
343C11×C4⋊C4—24no—
344C11×C4⋊C4—24no—
345C11×C4⋊C4—42no—
346C11×C4⋊C4C2×D418yes—
347C11×C4⋊C4C2×D414yes—
348C11×C4⋊C4#4114yescomplemented
349C11×C22⋊C4—22no—
350C11×C22⋊C4—22no—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—24no—
355C11×C22⋊C4—24no—
356C11×C22⋊C4—24no—
357C11×C22⋊C4—24no—
358C11×C22⋊C4—24no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—22no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4—42no—
370C42×C11—22no—
371C42×C11—22no—
372C42×C11—24no—
373C42×C11—24no—
374C42×C11—22no—
375C42×C11—22no—
376C42×C11—22no—
377C42×C11—22no—
378C42×C11—24no—
379C42×C11—22no—
380C42×C11—22no—
381C42×C11—22no—
382C42×C11—24no—
383C42×C11—22no—
384C42×C11—22no—
385C42×C11—41no—
386C42×C11C2×D414yes—
387C42×C11C2×D418yes—
388C2×#533C2×C1111yescharacteristic, complemented
389C2×C4×#41C2×C1111yescharacteristic, complemented
390#2477C2×C1112yescomplemented
391#2475C2×C1112yescomplemented
392#2463C2×C1112yescomplemented
393#2460C2×C1112yescomplemented
394#2452C2×C1111yescharacteristic, complemented
395#2446C2×C1111yescharacteristic, complemented
396#2439C2×C1111yescharacteristic, complemented
397#2432C2×C1111yescharacteristic, complemented
398#2427C2×C1111yescharacteristic, complemented
399#2421C2×C1111yescharacteristic, complemented
400#2415C2×C1111yescharacteristic, complemented
401#2407C2×C1111yescharacteristic
402#2398C2×C1112yescomplemented
403#2392C2×C1112yescomplemented
404C4×#124C2×C1111yescharacteristic, complemented
405C4×C22⋊Q8C2×C1112yescomplemented
406C4×C22⋊Q8C2×C1111yescharacteristic, complemented
407C4×#121C2×C1111yescharacteristic, complemented
408#2295C2×C1111yescharacteristic, complemented
409#2290C2×C1112yescomplemented
410C42×D4C2×C1111yescharacteristic, complemented
411C23×C11—21no—
412C23×C11—22no—
413C23×C11—21no—
414C23×C11—22no—
415C23×C11—21no—
416C23×C11—21no—
417C23×C11—21no—
418C23×C11—21no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—21no—
422C23×C11—21no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11—22no—
426C23×C11—21no—
427C23×C11—22no—
428C23×C11—21no—
429C23×C11C2×#4114yes—
430C23×C11C2×#4112yes—
431C23×C11C2×#4112yes—
432C23×C11C2511yescharacteristic
433Q8×C11—28no—
434Q8×C11—48no—
435Q8×C11—44no—
436D4×C11—28no—
437D4×C11—216no—
438D4×C11—28no—
439D4×C11—48no—
440C2×C4×C11—216no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—22no—
449C2×C4×C11—21no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—21no—
453C2×C4×C11—21no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—28no—
458C2×C4×C11—28no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—44no—
490C2×C4×C11—48no—
491C2×C4×C11—44no—
492C2×C4×C11—44no—
493C2×C4×C11—44no—
494C2×C4×C11—48no—
495C2×C4×C11C22×D412yes—
496C2×C4×C11C22×D414yes—
497C2×C4×C11C22×D414yes—
498C2×C4×C11C22×D412yes—
499C2×C4×C11C22×D412yes—
500C2×C4×C11C2×#4112yes—
501C2×C4×C11C2×#4112yes—
502C2×C4×C11C2×#4112yes—
503C2×C4×C11C2×#4112yes—
504C2×C4×C11C2×#4112yes—
505C2×C4×C11C2×#4112yes—
506C2×C4×C11C2×#4112yes—
507C2×C4×C11C2×#4112yes—
508C2×C4×C112−1+412yes—
509C22×#41C22×C1111yescharacteristic
510#533—28no—
511C2×C4⋊Q8C22×C1111yescharacteristic
512C2×C4⋊Q8C22×C1111yescharacteristic
513C2×#125C22×C1112yes—
514C2×#124C22×C1111yescharacteristic
515C2×C22⋊Q8C22×C1111yescharacteristic
516C2×C22⋊Q8C22×C1111yescharacteristic
517C2×C22⋊Q8C22×C1111yescharacteristic
518C2×C22⋊Q8C22×C1112yes—
519C2×C22⋊Q8C22×C1112yes—
520C2×#121C22×C1111yescharacteristic
521C4×#41—28no—
522C2×C4×Q8C22×C1112yes—
523C2×C4×Q8C22×C1111yescharacteristic
524C2×C4×Q8C22×C1111yescharacteristic
525C2×C4×Q8C22×C1111yescharacteristic
526C2×C4×D4C22×C1111yescharacteristic
527C2×C4×D4C22×C1112yes—
528C2×C4×D4C22×C1112yes—
529C2×C4×D4C22×C1111yescharacteristic
530C2×C4×D4C22×C1112yes—
531C2×C4×D4C22×C1111yescharacteristic
532C2×C4×D4C22×C1111yescharacteristic
533C2×C4×D4C22×C1111yescharacteristic
534C2×#117C22×C1112yes—
535C2×#117C22×C1111yescharacteristic
536C2×#117C22×C1112yes—
537C22×C42C22×C1111yescharacteristic
538C22×C42C22×C1112yes—
539C22×C42C22×C1111yescharacteristic
540#400C22×C1112yes—
541#400C22×C1112yes—
542#398C22×C1112yes—
543#397C22×C1112yes—
544#397C22×C1112yes—
545#397C22×C1112yes—
546#396C22×C1112yes—
547#396C22×C1112yes—
548#394C22×C1112yes—
549#394C22×C1112yes—
550#394C22×C1112yes—
551#394C22×C1112yes—
552#394C22×C1112yes—
553#393C22×C1112yes—
554#393C22×C1112yes—
555#392C22×C1112yes—
556#391C22×C1111yescharacteristic
557#391C22×C1111yescharacteristic
558#391C22×C1111yescharacteristic
559#391C22×C1111yescharacteristic
560#391C22×C1112yes—
561#390C22×C1111yescharacteristic
562#390C22×C1111yescharacteristic
563#389C22×C1111yescharacteristic
564#389C22×C1112yes—
565#389C22×C1111yescharacteristic
566#389C22×C1111yescharacteristic
567#389C22×C1111yescharacteristic
568#388C22×C1112yes—
569#388C22×C1112yes—
570#388C22×C1112yes—
571#388C22×C1112yes—
572#388C22×C1112yes—
573#387C22×C1112yes—
574#387C22×C1112yes—
575#387C22×C1112yes—
576#387C22×C1112yes—
577#387C22×C1112yes—
578#387C22×C1112yes—
579#387C22×C1112yes—
580#386C22×C1112yes—
581#386C22×C1112yes—
582#386C22×C1112yes—
583#385C22×C1112yes—
584#385C22×C1112yes—
585#385C22×C1112yes—
586#385C22×C1112yes—
587#385C22×C1112yes—
588#382C22×C1111yescharacteristic
589#380C22×C1111yescharacteristic
590#380C22×C1111yescharacteristic
591#380C22×C1112yes—
592C4×C4⋊C4C22×C1112yes—
593C4×C4⋊C4C22×C1111yescharacteristic
594C4×C4⋊C4C22×C1111yescharacteristic
595C4×C4⋊C4C22×C1111yescharacteristic
596C4×C4⋊C4C22×C1112yes—
597C4×C4⋊C4C22×C1111yescharacteristic
598C4×C22⋊C4C22×C1112yes—
599C4×C22⋊C4C22×C1112yes—
600C4×C22⋊C4C22×C1111yescharacteristic
601C4×C22⋊C4C22×C1112yes—
602C4×C22⋊C4C22×C1112yes—
603C4×C22⋊C4C22×C1111yescharacteristic
604C4×C22⋊C4C22×C1111yescharacteristic
605C4×C22⋊C4C22×C1111yescharacteristic
606C4×C22⋊C4C22×C1111yescharacteristic
607C4×C22⋊C4C22×C1111yescharacteristic
608#376C22×C1112yes—
609C43C22×C1111yescharacteristic
610C22×C11—24no—
611C22×C11—22no—
612C22×C11—22no—
613C22×C11—22no—
614C22×C11—22no—
615C22×C11—22no—
616C22×C11—22no—
617C22×C11—24no—
618C22×C11—24no—
619C22×C11—41no—
620C22×C11—42no—
621C22×C11—41no—
622C22×C11—42no—
623C22×C11—41no—
624C22×C11—42no—
625C22×C11—41no—
626C22×C11—42no—
627C22×C11—41no—
628C22×C11—41no—
629C22×C11—41no—
630C22×C11—41no—
631C22×C11C23×D411yescharacteristic
632C22×C11C22×#4111yescharacteristic
633C22×C11C22×#4111yescharacteristic
634C22×C11C22×#4111yescharacteristic
635C22×C11C22×#4111yescharacteristic
636C22×C11C2×2−1+411yescharacteristic
637C22×C11#58511yescharacteristic
638C4×C11—22no—
639C4×C11—24no—
640C4×C11—22no—
641C4×C11—22no—
642C4×C11—22no—
643C4×C11—22no—
644C4×C11—24no—
645C4×C11—22no—
646C4×C11—41no—
647C4×C11—42no—
648C4×C11—42no—
649C4×C11—41no—
650C4×C11—41no—
651C4×C11—42no—
652C4×C11—42no—
653C4×C11—41no—
654C4×C11—42no—
655C4×C11—41no—
656C4×C11#52514yes—
657C4×C11#54814yes—
658C2×#41—24no—
659C2×#41—24no—
660C2×#41—24no—
661C22×Q8C23×C1111yescharacteristic
662C22×Q8C23×C1112yes—
663C22×Q8C23×C1111yescharacteristic
664C22×D4C23×C1111yescharacteristic
665C22×D4C23×C1112yes—
666C22×D4C23×C1112yes—
667C22×D4C23×C1111yescharacteristic
668C23×C4C23×C1112yes—
669C23×C4C23×C1111yescharacteristic
670C23×C4C23×C1112yes—
671C23×C4C23×C1111yescharacteristic
672C23×C4C23×C1111yescharacteristic
673C23×C4C23×C1112yes—
674C23×C4C23×C1111yescharacteristic
675C23×C4C23×C1111yescharacteristic
676C23×C4C23×C1111yescharacteristic
677C4⋊Q8—24no—
678C4⋊Q8—24no—
679#125—28no—
680#124—24no—
681C22⋊Q8—24no—
682C22⋊Q8—24no—
683C22⋊Q8—24no—
684C22⋊Q8—28no—
685C22⋊Q8—28no—
686#121—24no—
687C4×Q8—24no—
688C4×Q8—28no—
689C4×Q8—24no—
690C4×Q8D4×C1118yescomplemented
691C4×D4—24no—
692C4×D4—24no—
693C4×D4—28no—
694C4×D4—28no—
695C4×D4—24no—
696C4×D4—24no—
697C4×D4—24no—
698C4×D4—28no—
699#117—28no—
700#117—24no—
701#117—28no—
702C2×C4⋊C4C23×C1111yescharacteristic
703C2×C4⋊C4C23×C1112yes—
704C2×C4⋊C4C23×C1112yes—
705C2×C4⋊C4C23×C1112yes—
706C2×C4⋊C4C23×C1111yescharacteristic
707C2×C4⋊C4C23×C1111yescharacteristic
708C2×C4⋊C4C23×C1112yes—
709C2×C4⋊C4C23×C1112yes—
710C2×C4⋊C4C23×C1112yes—
711C2×C4⋊C4C23×C1112yes—
712C2×C4⋊C4C23×C1111yescharacteristic
713C2×C4⋊C4C23×C1112yes—
714C2×C4⋊C4C23×C1111yescharacteristic
715C2×C4⋊C4C23×C1111yescharacteristic
716C2×C4⋊C4C23×C1112yes—
717C2×C4⋊C4C23×C1112yes—
718C2×C4⋊C4C23×C1112yes—
719C2×C4⋊C4C23×C1112yes—
720C2×C4⋊C4C23×C1112yes—
721C2×C4⋊C4C23×C1111yescharacteristic
722C2×C4⋊C4C23×C1111yescharacteristic
723C2×C22⋊C4C23×C1112yes—
724C2×C22⋊C4C23×C1112yes—
725C2×C22⋊C4C23×C1112yes—
726C2×C22⋊C4C23×C1112yes—
727C2×C22⋊C4C23×C1112yes—
728C2×C22⋊C4C23×C1111yescharacteristic
729C2×C22⋊C4C23×C1111yescharacteristic
730C2×C22⋊C4C23×C1111yescharacteristic
731C2×C22⋊C4C23×C1111yescharacteristic
732C2×C22⋊C4C23×C1111yescharacteristic
733C2×C22⋊C4C23×C1111yescharacteristic
734C2×C22⋊C4C23×C1112yes—
735C2×C22⋊C4C23×C1112yes—
736C2×C22⋊C4C23×C1112yes—
737C2×C22⋊C4C23×C1112yes—
738C2×C22⋊C4C23×C1112yes—
739C2×C22⋊C4C23×C1112yes—
740C2×C22⋊C4C23×C1112yes—
741C2×C22⋊C4C23×C1112yes—
742C2×C22⋊C4C23×C1112yes—
743C2×C22⋊C4C23×C1112yes—
744C2×C42—24no—
745C2×C42—28no—
746C2×C42—24no—
747C2×C42C23×C1111yescharacteristic
748C2×C42C23×C1112yes—
749C2×C42C23×C1112yes—
750C2×C42C23×C1111yescharacteristic
751C2×C42C23×C1112yes—
752C2×C42C23×C1111yescharacteristic
753C2×C42C23×C1111yescharacteristic
754C2×C42C23×C1111yescharacteristic
755C2×C42C23×C1112yes—
756C2×C42C23×C1111yescharacteristic
757C2×C42C23×C1111yescharacteristic
758C2×C42C23×C1111yescharacteristic
759C2×C42C23×C1111yescharacteristic
760C2×C42C23×C1111yescharacteristic
761C2×C42C23×C1111yescharacteristic
762C2×C42C23×C1111yescharacteristic
763C2×C42C23×C1112yes—
764C2×C42C23×C1111yescharacteristic
765#95C23×C1112yes—
766#95C23×C1112yes—
767#95C23×C1112yes—
768#95C23×C1112yes—
769#95C23×C1111yescharacteristic
770#95C23×C1111yescharacteristic
771#95C23×C1111yescharacteristic
772#95C23×C1111yescharacteristic
773#95C23×C1111yescharacteristic
774#95C23×C1111yescharacteristic
775#95C23×C1112yes—
776#95C23×C1112yes—
777#95C23×C1112yes—
778#95C23×C1112yes—
779#95C23×C1112yes—
780#95C23×C1112yes—
781#95C23×C1112yes—
782#95C23×C1112yes—
783#95C23×C1112yes—
784#95C23×C1112yes—
785#95C23×C1112yes—
786#95C23×C1112yes—
787#95C23×C1112yes—
788C2×C11—42no—
789C2×C11—44no—
790C2×C11—42no—
791C2×C11C2×#52511yescharacteristic
792C2×C11#344411yescharacteristic
793C2×C11#346111yescharacteristic
794C2×C11C2×#54811yescharacteristic
795C2×C11D4×#4111yescharacteristic
796C2×C11#347511yescharacteristic
797C2×C11#348211yescharacteristic
798C24C24×C1111yescharacteristic
799C24C24×C1112yes—
800C24C24×C1111yescharacteristic
801#41—232no—
802C2×Q8—24no—
803C2×Q8—22no—
804C2×Q8—22no—
805C2×Q8—22no—
806C2×Q8—24no—
807C2×Q8—22no—
808C2×Q8—22no—
809C2×Q8—42no—
810C2×Q8C2×D4×C1114yes—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—42no—
822C2×D4C11×#4114yes—
823C22×C4—24no—
824C22×C4—22no—
825C22×C4—24no—
826C22×C4—22no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—24no—
832C22×C4—22no—
833C22×C4—24no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—24no—
841C22×C4—22no—
842C22×C4—24no—
843C22×C4—22no—
844C22×C4—24no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—42no—
848C22×C4C11×#4114yes—
849C22×C4C11×#4114yescomplemented
850C22×C4C24×C1111yescharacteristic
851C22×C4C24×C1111yescharacteristic
852C22×C4C24×C1112yes—
853C22×C4C24×C1111yescharacteristic
854C22×C4C24×C1111yescharacteristic
855C22×C4C24×C1112yes—
856C22×C4C24×C1112yes—
857C22×C4C24×C1111yescharacteristic
858C22×C4C24×C1112yes—
859C22×C4C24×C1112yes—
860C22×C4C24×C1112yes—
861C22×C4C24×C1111yescharacteristic
862C22×C4C24×C1112yes—
863C22×C4C24×C1111yescharacteristic
864C22×C4C24×C1111yescharacteristic
865C22×C4C24×C1111yescharacteristic
866C22×C4C24×C1111yescharacteristic
867C22×C4C24×C1111yescharacteristic
868C22×C4C24×C1111yescharacteristic
869C22×C4C24×C1111yescharacteristic
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—42no—
888C4⋊C4C2×D4×C1118yes—
889C4⋊C4C2×D4×C1114yes—
890C4⋊C4C11×#4114yescomplemented
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—22no—
904C22⋊C4—24no—
905C22⋊C4—22no—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C42—22no—
913C42—22no—
914C42—24no—
915C42—24no—
916C42—22no—
917C42—22no—
918C42—22no—
919C42—22no—
920C42—24no—
921C42—22no—
922C42—22no—
923C42—22no—
924C42—24no—
925C42—22no—
926C42—22no—
927C42—41no—
928C42C2×D4×C1114yes—
929C42C2×D4×C1118yes—
930C11#3472011yescharacteristic, direct product factor, Sylow
931C23—21no—
932C23—22no—
933C23—21no—
934C23—22no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—22no—
940C23—22no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—22no—
946C23—21no—
947C23—22no—
948C23—21no—
949C23C2×C11×#4114yes—
950C23C2×C11×#4112yes—
951C23C2×C11×#4112yes—
952C23C25×C1111yescharacteristic
953Q8—28no—
954Q8—48no—
955Q8—44no—
956D4—28no—
957D4—216no—
958D4—28no—
959D4—48no—
960C2×C4—216no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—21no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—44no—
1010C2×C4—48no—
1011C2×C4—44no—
1012C2×C4—44no—
1013C2×C4—44no—
1014C2×C4—48no—
1015C2×C4C22×D4×C1112yes—
1016C2×C4C22×D4×C1114yes—
1017C2×C4C22×D4×C1114yes—
1018C2×C4C22×D4×C1112yes—
1019C2×C4C22×D4×C1112yes—
1020C2×C4C2×C11×#4112yes—
1021C2×C4C2×C11×#4112yes—
1022C2×C4C2×C11×#4112yes—
1023C2×C4C2×C11×#4112yes—
1024C2×C4C2×C11×#4112yes—
1025C2×C4C2×C11×#4112yes—
1026C2×C4C2×C11×#4112yes—
1027C2×C4C2×C11×#4112yes—
1028C2×C4C11×2−1+412yes—
1029C22—24no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—24no—
1037C22—24no—
1038C22—41no—
1039C22—42no—
1040C22—41no—
1041C22—42no—
1042C22—41no—
1043C22—42no—
1044C22—41no—
1045C22—42no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22C23×D4×C1111yescharacteristic
1051C22C22×C11×#4111yescharacteristic
1052C22C22×C11×#4111yescharacteristic
1053C22C22×C11×#4111yescharacteristic
1054C22C22×C11×#4111yescharacteristic
1055C22C2×C11×2−1+411yescharacteristic
1056C22C11×#58511yescharacteristic
1057C4—22no—
1058C4—24no—
1059C4—22no—
1060C4—22no—
1061C4—22no—
1062C4—22no—
1063C4—24no—
1064C4—22no—
1065C4—41no—
1066C4—42no—
1067C4—42no—
1068C4—41no—
1069C4—41no—
1070C4—42no—
1071C4—42no—
1072C4—42no—
1073C4—41no—
1074C4—41no—
1075C4C11×#52514yes—
1076C4C11×#54814yes—
1077C2—42no—
1078C2—44no—
1079C2—42no—
1080C2C2×C11×#52511yescharacteristic
1081C2C11×#344411yescharacteristic
1082C2C11×#346111yescharacteristic
1083C2C2×C11×#54811yescharacteristic
1084C2D4×C11×#4111yescharacteristic
1085C2C11×#347511yescharacteristic
1086C2C11×#348211yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC11×#2407C2
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×#533C2semidirect
2. C2×C4×C11×#41C2semidirect
3. C11×#2477C2semidirect
4. C11×#2475C2semidirect
5. C11×#2463C2semidirect
6. C11×#2460C2semidirect
7. C11×#2452C2semidirect
8. C11×#2446C2semidirect
9. C11×#2439C2semidirect
10. C11×#2432C2semidirect
11. C11×#2427C2semidirect
12. C11×#2421C2semidirect
13. C11×#2415C2semidirect
15. C11×#2398C2semidirect
16. C11×#2392C2semidirect
17. C4×C11×#124C2semidirect
18. C4×C11×C22⋊Q8C2semidirect
19. C4×C11×C22⋊Q8C2semidirect
20. C4×C11×#121C2semidirect
21. C11×#2295C2semidirect
22. C11×#2290C2semidirect
23. C42×D4×C11C2semidirect
157. C4×Q8×C11D4semidirect
255. #34720C11direct (N × H)
307. C22×C4×C11#41semidirect
348. C11×C4⋊C4#41semidirect
388. C2×#533C2×C11semidirect
389. C2×C4×#41C2×C11semidirect
390. #2477C2×C11semidirect
391. #2475C2×C11semidirect
392. #2463C2×C11semidirect
393. #2460C2×C11semidirect
394. #2452C2×C11semidirect
395. #2446C2×C11semidirect
396. #2439C2×C11semidirect
397. #2432C2×C11semidirect
398. #2427C2×C11semidirect
399. #2421C2×C11semidirect
400. #2415C2×C11semidirect
402. #2398C2×C11semidirect
403. #2392C2×C11semidirect
404. C4×#124C2×C11semidirect
405. C4×C22⋊Q8C2×C11semidirect
406. C4×C22⋊Q8C2×C11semidirect
407. C4×#121C2×C11semidirect
408. #2295C2×C11semidirect
409. #2290C2×C11semidirect
410. C42×D4C2×C11semidirect
690. C4×Q8D4×C11semidirect
849. C22×C4C11×#41semidirect
890. C4⋊C4C11×#41semidirect
930. C11#34720direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C4×C11×#412
C11×#24772
C11×#24752
C11×#24632
C11×#24602
C11×#24522
C11×#24462
C11×#24392
C11×#24322
C11×#24272
C11×#24212
C11×#24152
C11×#24072
C11×#23982
C11×#23922
C4×C11×#1242
C4×C11×C22⋊Q82
C4×C11×#1212
C11×#22952
C11×#22902
C42×D4×C112
#3472011