Finite Group Databasebeta

← C11×#34691 #14611884

Subgroups — C11×#34691 #14611884

Order 2816.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
3C11×#2473C212yesmaximal, complemented
4C11×#2465C212yesmaximal, complemented
5C11×#2462C212yesmaximal, complemented
6C11×#2451C211yesmaximal, characteristic, complemented
7C11×#2449C212yesmaximal
8C11×#2446C211yesmaximal, characteristic, complemented
9C11×#2440C211yesmaximal, characteristic, complemented
10C11×#2434C211yesmaximal, characteristic, complemented
11C11×#2429C211yesmaximal, characteristic, complemented
12C11×#2423C211yesmaximal, characteristic, complemented
13C11×#2417C211yesmaximal, characteristic
14C11×#2409C211yesmaximal, characteristic
15C11×#2399C212yesmaximal, complemented
16C11×#2396C212yesmaximal, complemented
17C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
18C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
19C4×C11×C22⋊Q8C212yesmaximal, complemented
20C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
21C11×#2295C211yesmaximal, characteristic, complemented
22C11×#2290C212yesmaximal
23C42×D4×C11C211yesmaximal, characteristic
24C23×Q8×C11C2211yescharacteristic
25C11×#533—28no—
26C2×C11×C4⋊Q8C2211yescharacteristic
27C2×C11×C4⋊Q8C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic
29C2×C11×#125C2212yes—
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C11×C22⋊Q8C2211yescharacteristic
34C2×C11×C22⋊Q8C2212yes—
35C2×C11×C22⋊Q8C2212yes—
36C2×C4×Q8×C11—28no—
37C2×C4×Q8×C11C2212yes—
38C2×C4×Q8×C11C2212yes—
39C2×C4×Q8×C11C2211yescharacteristic
40C2×C4×Q8×C11C2211yescharacteristic
41C2×C4×Q8×C11C2212yes—
42C2×C4×Q8×C11C2211yescharacteristic
43C2×C4×Q8×C11C2211yescharacteristic
44C2×C4×Q8×C11C2211yescharacteristic
45C2×C4×D4×C11C2211yescharacteristic
46C2×C4×D4×C11C2211yescharacteristic
47C2×C4×D4×C11C2211yescharacteristic
48C2×C11×#117C2212yes—
49C22×C11×C4⋊C4C2211yescharacteristic
50C22×C11×C4⋊C4C2212yes—
51C22×C42×C11C2211yescharacteristic
52C22×C42×C11C2212yes—
53C22×C42×C11C2211yescharacteristic
54C11×#400C2212yes—
55C11×#399C2212yes—
56C11×#398C2212yes—
57C11×#398C2212yes—
58C11×#398C2212yes—
59C11×#398C2212yes—
60C11×#398C2212yes—
61C11×#398C2212yes—
62C11×#396C2212yes—
63C11×#396C2212yes—
64C11×#395C2212yes—
65C11×#395C2212yes—
66C11×#395C2212yes—
67C11×#395C2212yes—
68C11×#395C2212yes—
69C11×#393C2212yes—
70C11×#391C2211yescharacteristic
71C11×#391C2211yescharacteristic
72C11×#391C2211yescharacteristic
73C11×#391C2211yescharacteristic
74C11×#391C2211yescharacteristic
75C11×#391C2211yescharacteristic
76C11×#391C2212yes—
77C11×#389C2211yescharacteristic
78C11×#389C2211yescharacteristic
79C11×#389C2211yescharacteristic
80C11×#389C2212yes—
81C11×#389C2211yescharacteristic
82C11×#389C2212yes—
83C11×#389C2212yes—
84C11×#388C2212yes—
85C11×#388C2212yes—
86C11×#387C2212yes—
87C11×#387C2212yes—
88C11×#387C2212yes—
89C11×#387C2212yes—
90C11×#387C2212yes—
91C11×#387C2212yes—
92C11×#387C2212yes—
93C11×#387C2212yes—
94C11×#386C2212yes—
95C11×#386C2212yes—
96C11×#385C2212yes—
97C11×#385C2212yes—
98C11×#385C2212yes—
99C11×#385C2212yes—
100C11×#385C2212yes—
101C11×#385C2212yes—
102C11×#384C2211yescharacteristic
103C11×#380C2211yescharacteristic
104C11×#380C2211yescharacteristic
105C11×#380C2212yes—
106C4×C11×C4⋊C4C2212yes—
107C4×C11×C4⋊C4C2212yes—
108C4×C11×C4⋊C4C2212yes—
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C4⋊C4C2212yes—
111C4×C11×C4⋊C4C2212yes—
112C4×C11×C4⋊C4C2211yescharacteristic
113C4×C11×C4⋊C4C2211yescharacteristic
114C4×C11×C4⋊C4C2211yescharacteristic
115C4×C11×C22⋊C4C2211yescharacteristic
116C4×C11×C22⋊C4C2212yes—
117C4×C11×C22⋊C4C2211yescharacteristic
118C4×C11×C22⋊C4C2211yescharacteristic
119C4×C11×C22⋊C4C2211yescharacteristic
120C4×C11×C22⋊C4C2211yescharacteristic
121C4×C11×C22⋊C4C2211yescharacteristic
122C4×C11×C22⋊C4C2212yes—
123C11×#376C2212yes—
124C43×C11C2211yescharacteristic
125C22×Q8×C11—24no—
126C22×Q8×C11—24no—
127C22×Q8×C11—24no—
128C22×Q8×C11C2312yes—
129C22×Q8×C11C2311yescharacteristic
130C22×Q8×C11C2312yes—
131C22×Q8×C11C2311yescharacteristic
132C22×Q8×C11C2311yescharacteristic
133C22×D4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C23×C4×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2312yes—
138C23×C4×C11C2311yescharacteristic
139C23×C4×C11C2311yescharacteristic
140C23×C4×C11C2311yescharacteristic
141C23×C4×C11C2311yescharacteristic
142C11×C4⋊Q8—24no—
143C11×C4⋊Q8—24no—
144C11×C4⋊Q8—24no—
145C11×#125—28no—
146C11×C22⋊Q8—24no—
147C11×C22⋊Q8—24no—
148C11×C22⋊Q8—24no—
149C11×C22⋊Q8—24no—
150C11×C22⋊Q8—28no—
151C11×C22⋊Q8—28no—
152C4×Q8×C11—24no—
153C4×Q8×C11—28no—
154C4×Q8×C11—24no—
155C4×Q8×C11—24no—
156C4×Q8×C11—28no—
157C4×Q8×C11—28no—
158C4×Q8×C11—24no—
159C4×Q8×C11D418yescomplemented
160C4×D4×C11—24no—
161C4×D4×C11—24no—
162C4×D4×C11Q818yescomplemented
163C11×#117—28no—
164C2×C11×C4⋊C4—28no—
165C2×C11×C4⋊C4—24no—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C4⋊C4C2312yes—
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C4⋊C4C2312yes—
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C4⋊C4C2311yescharacteristic
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C4⋊C4C2312yes—
187C2×C11×C4⋊C4C2312yes—
188C2×C11×C4⋊C4C2312yes—
189C2×C11×C4⋊C4C2312yes—
190C2×C11×C4⋊C4C2312yes—
191C2×C11×C4⋊C4C2312yes—
192C2×C11×C4⋊C4C2312yes—
193C2×C11×C4⋊C4C2311yescharacteristic
194C2×C11×C4⋊C4C2311yescharacteristic
195C2×C11×C22⋊C4C2312yes—
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2311yescharacteristic
198C2×C11×C22⋊C4C2311yescharacteristic
199C2×C11×C22⋊C4C2311yescharacteristic
200C2×C11×C22⋊C4C2312yes—
201C2×C11×C22⋊C4C2312yes—
202C2×C11×C22⋊C4C2312yes—
203C2×C11×C22⋊C4C2312yes—
204C2×C11×C22⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4C2311yescharacteristic
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C42×C11—24no—
208C2×C42×C11—28no—
209C2×C42×C11—24no—
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2312yes—
215C2×C42×C11C2312yes—
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2311yescharacteristic
218C2×C42×C11C2311yescharacteristic
219C2×C42×C11C2311yescharacteristic
220C2×C42×C11C2312yes—
221C2×C42×C11C2311yescharacteristic
222C2×C42×C11C2311yescharacteristic
223C2×C42×C11C2312yes—
224C2×C42×C11C2312yes—
225C2×C42×C11C2311yescharacteristic
226C2×C42×C11C2311yescharacteristic
227C2×C42×C11C2312yes—
228C2×C42×C11C2311yescharacteristic
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2311yescharacteristic
234C11×#95C2311yescharacteristic
235C11×#95C2311yescharacteristic
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11×#95C2311yescharacteristic
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11×#95C2312yes—
254#34691C1111yesmaximal, characteristic, direct product factor, Sylow
255C24×C11C2411yescharacteristic
256C24×C11C2411yescharacteristic
257C2×Q8×C11—232no—
258C2×Q8×C11—24no—
259C2×Q8×C11—22no—
260C2×Q8×C11—24no—
261C2×Q8×C11—22no—
262C2×Q8×C11—24no—
263C2×Q8×C11—24no—
264C2×Q8×C11—22no—
265C2×Q8×C11—22no—
266C2×Q8×C11—22no—
267C2×Q8×C11—24no—
268C2×Q8×C11—22no—
269C2×Q8×C11—22no—
270C2×Q8×C11—42no—
271C2×Q8×C11C2×D414yes—
272C2×Q8×C11#4114yes—
273C2×D4×C11—22no—
274C2×D4×C11—22no—
275C2×D4×C11C2×Q814yes—
276C22×C4×C11—24no—
277C22×C4×C11—22no—
278C22×C4×C11—24no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—24no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—22no—
288C22×C4×C11—24no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—41no—
295C22×C4×C11—41no—
296C22×C4×C11—42no—
297C22×C4×C11C2×Q814yes—
298C22×C4×C11C2×Q814yescomplemented
299C22×C4×C11#4114yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2412yes—
306C22×C4×C11C2412yes—
307C22×C4×C11C2412yes—
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2412yes—
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2411yescharacteristic
315C22×C4×C11C2411yescharacteristic
316C22×C4×C11C2412yes—
317C22×C4×C11C2411yescharacteristic
318C22×C4×C11C2411yescharacteristic
319C22×C4×C11C2411yescharacteristic
320C22×C4×C11C2411yescharacteristic
321C11×C4⋊C4—24no—
322C11×C4⋊C4—24no—
323C11×C4⋊C4—24no—
324C11×C4⋊C4—24no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—24no—
327C11×C4⋊C4—24no—
328C11×C4⋊C4—24no—
329C11×C4⋊C4—24no—
330C11×C4⋊C4—24no—
331C11×C4⋊C4—24no—
332C11×C4⋊C4—22no—
333C11×C4⋊C4—22no—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—24no—
336C11×C4⋊C4—22no—
337C11×C4⋊C4—22no—
338C11×C4⋊C4—24no—
339C11×C4⋊C4—24no—
340C11×C4⋊C4—24no—
341C11×C4⋊C4—24no—
342C11×C4⋊C4—24no—
343C11×C4⋊C4—24no—
344C11×C4⋊C4—42no—
345C11×C4⋊C4—42no—
346C11×C4⋊C4—42no—
347C11×C4⋊C4C2×D418yes—
348C11×C4⋊C4C2×D414yes—
349C11×C4⋊C4C2×Q814yescomplemented
350C11×C22⋊C4—22no—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—24no—
355C11×C22⋊C4—22no—
356C11×C22⋊C4—22no—
357C11×C22⋊C4—24no—
358C11×C22⋊C4—42no—
359C11×C22⋊C4C2×Q814yes—
360C11×C22⋊C4C2×Q814yescomplemented
361C11×C22⋊C4#4114yes—
362C42×C11—22no—
363C42×C11—24no—
364C42×C11—24no—
365C42×C11—22no—
366C42×C11—22no—
367C42×C11—24no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—24no—
372C42×C11—22no—
373C42×C11—22no—
374C42×C11—22no—
375C42×C11—22no—
376C42×C11—24no—
377C42×C11—41no—
378C42×C11C2×D414yes—
379C42×C11C2×D418yes—
380C42×C11C2×Q814yescomplemented
381C2×#533C2×C1111yescharacteristic, complemented
382C22×C4×Q8C2×C1111yescharacteristic, complemented
383#2473C2×C1112yescomplemented
384#2465C2×C1112yescomplemented
385#2462C2×C1112yescomplemented
386#2451C2×C1111yescharacteristic, complemented
387#2449C2×C1112yes—
388#2446C2×C1111yescharacteristic, complemented
389#2440C2×C1111yescharacteristic, complemented
390#2434C2×C1111yescharacteristic, complemented
391#2429C2×C1111yescharacteristic, complemented
392#2423C2×C1111yescharacteristic, complemented
393#2417C2×C1111yescharacteristic
394#2409C2×C1111yescharacteristic
395#2399C2×C1112yescomplemented
396#2396C2×C1112yescomplemented
397C4×C4⋊Q8C2×C1111yescharacteristic, complemented
398C4×C22⋊Q8C2×C1111yescharacteristic, complemented
399C4×C22⋊Q8C2×C1111yescharacteristic, complemented
400C4×C22⋊Q8C2×C1112yescomplemented
401#2295C2×C1111yescharacteristic, complemented
402#2290C2×C1112yes—
403C42×D4C2×C1111yescharacteristic
404C23×C11—21no—
405C23×C11—21no—
406C23×C11—21no—
407C23×C11—21no—
408C23×C11—21no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11—21no—
414C23×C11C22×Q812yes—
415C23×C11C22×Q812yes—
416C23×C11C2×#4112yes—
417C23×C11C2×#4112yes—
418C23×C11C2511yescharacteristic
419Q8×C11—216no—
420Q8×C11—28no—
421Q8×C11—28no—
422Q8×C11—48no—
423Q8×C11—44no—
424D4×C11—28no—
425C2×C4×C11—216no—
426C2×C4×C11—21no—
427C2×C4×C11—21no—
428C2×C4×C11—22no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—22no—
447C2×C4×C11—21no—
448C2×C4×C11—28no—
449C2×C4×C11—28no—
450C2×C4×C11—28no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—21no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—21no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—44no—
476C2×C4×C11—44no—
477C2×C4×C11—48no—
478C2×C4×C11—44no—
479C2×C4×C11C22×D412yes—
480C2×C4×C11C22×D414yes—
481C2×C4×C11C22×D414yes—
482C2×C4×C11C22×D412yes—
483C2×C4×C11C22×D412yes—
484C2×C4×C11C22×Q812yes—
485C2×C4×C11C22×Q812yes—
486C2×C4×C11C22×Q812yes—
487C2×C4×C11C22×Q812yes—
488C2×C4×C11C22×Q812yes—
489C2×C4×C11C2×#4112yes—
490C2×C4×C11C2×#4114yes—
491C2×C4×C11C2×#4112yes—
492C2×C4×C11C2×#4112yes—
493C2×C4×C11C2×#4112yes—
494C2×C4×C11C2×#4112yes—
495C2×C4×C112−1+412yes—
496C23×Q8C22×C1111yescharacteristic
497#533—28no—
498C2×C4⋊Q8C22×C1111yescharacteristic
499C2×C4⋊Q8C22×C1111yescharacteristic
500C2×C4⋊Q8C22×C1111yescharacteristic
501C2×#125C22×C1112yes—
502C2×C22⋊Q8C22×C1111yescharacteristic
503C2×C22⋊Q8C22×C1111yescharacteristic
504C2×C22⋊Q8C22×C1111yescharacteristic
505C2×C22⋊Q8C22×C1111yescharacteristic
506C2×C22⋊Q8C22×C1112yes—
507C2×C22⋊Q8C22×C1112yes—
508C2×C4×Q8—28no—
509C2×C4×Q8C22×C1111yescharacteristic
510C2×C4×Q8C22×C1111yescharacteristic
511C2×C4×Q8C22×C1112yes—
512C2×C4×Q8C22×C1112yes—
513C2×C4×Q8C22×C1111yescharacteristic
514C2×C4×Q8C22×C1111yescharacteristic
515C2×C4×Q8C22×C1112yes—
516C2×C4×Q8C22×C1111yescharacteristic
517C2×C4×D4C22×C1111yescharacteristic
518C2×C4×D4C22×C1111yescharacteristic
519C2×C4×D4C22×C1111yescharacteristic
520C2×#117C22×C1112yes—
521C22×C4⋊C4C22×C1111yescharacteristic
522C22×C4⋊C4C22×C1112yes—
523C22×C42C22×C1111yescharacteristic
524C22×C42C22×C1112yes—
525C22×C42C22×C1111yescharacteristic
526#400C22×C1112yes—
527#399C22×C1112yes—
528#398C22×C1112yes—
529#398C22×C1112yes—
530#398C22×C1112yes—
531#398C22×C1112yes—
532#398C22×C1112yes—
533#398C22×C1112yes—
534#396C22×C1112yes—
535#396C22×C1112yes—
536#395C22×C1112yes—
537#395C22×C1112yes—
538#395C22×C1112yes—
539#395C22×C1112yes—
540#395C22×C1112yes—
541#393C22×C1112yes—
542#391C22×C1111yescharacteristic
543#391C22×C1111yescharacteristic
544#391C22×C1111yescharacteristic
545#391C22×C1111yescharacteristic
546#391C22×C1111yescharacteristic
547#391C22×C1111yescharacteristic
548#391C22×C1112yes—
549#389C22×C1112yes—
550#389C22×C1112yes—
551#389C22×C1111yescharacteristic
552#389C22×C1111yescharacteristic
553#389C22×C1111yescharacteristic
554#389C22×C1112yes—
555#389C22×C1111yescharacteristic
556#388C22×C1112yes—
557#388C22×C1112yes—
558#387C22×C1112yes—
559#387C22×C1112yes—
560#387C22×C1112yes—
561#387C22×C1112yes—
562#387C22×C1112yes—
563#387C22×C1112yes—
564#387C22×C1112yes—
565#387C22×C1112yes—
566#386C22×C1112yes—
567#386C22×C1112yes—
568#385C22×C1112yes—
569#385C22×C1112yes—
570#385C22×C1112yes—
571#385C22×C1112yes—
572#385C22×C1112yes—
573#385C22×C1112yes—
574#384C22×C1111yescharacteristic
575#380C22×C1111yescharacteristic
576#380C22×C1111yescharacteristic
577#380C22×C1112yes—
578C4×C4⋊C4C22×C1112yes—
579C4×C4⋊C4C22×C1112yes—
580C4×C4⋊C4C22×C1112yes—
581C4×C4⋊C4C22×C1112yes—
582C4×C4⋊C4C22×C1111yescharacteristic
583C4×C4⋊C4C22×C1112yes—
584C4×C4⋊C4C22×C1111yescharacteristic
585C4×C4⋊C4C22×C1111yescharacteristic
586C4×C4⋊C4C22×C1111yescharacteristic
587C4×C22⋊C4C22×C1111yescharacteristic
588C4×C22⋊C4C22×C1112yes—
589C4×C22⋊C4C22×C1111yescharacteristic
590C4×C22⋊C4C22×C1111yescharacteristic
591C4×C22⋊C4C22×C1111yescharacteristic
592C4×C22⋊C4C22×C1111yescharacteristic
593C4×C22⋊C4C22×C1111yescharacteristic
594C4×C22⋊C4C22×C1112yes—
595#376C22×C1112yes—
596C43C22×C1111yescharacteristic
597C22×C11—22no—
598C22×C11—22no—
599C22×C11—22no—
600C22×C11—22no—
601C22×C11—22no—
602C22×C11—22no—
603C22×C11—22no—
604C22×C11—22no—
605C22×C11—22no—
606C22×C11—41no—
607C22×C11—41no—
608C22×C11—41no—
609C22×C11—41no—
610C22×C11#53314yescomplemented
611C22×C11C23×D411yescharacteristic
612C22×C11C23×Q811yescharacteristic
613C22×C11C22×#4111yescharacteristic
614C22×C11C22×#4111yescharacteristic
615C22×C11C22×#4111yescharacteristic
616C22×C11C2×2−1+411yescharacteristic
617C22×C11#58511yescharacteristic
618C4×C11—24no—
619C4×C11—24no—
620C4×C11—22no—
621C4×C11—22no—
622C4×C11—22no—
623C4×C11—22no—
624C4×C11—22no—
625C4×C11—24no—
626C4×C11—22no—
627C4×C11—22no—
628C4×C11—22no—
629C4×C11—41no—
630C4×C11—42no—
631C4×C11—41no—
632C4×C11—42no—
633C4×C11—41no—
634C4×C11—42no—
635C4×C11—42no—
636C4×C11—42no—
637C4×C11#52514yes—
638C4×C11D4×Q814yes—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C23×C1112yes—
643C22×Q8C23×C1111yescharacteristic
644C22×Q8C23×C1112yes—
645C22×Q8C23×C1111yescharacteristic
646C22×Q8C23×C1111yescharacteristic
647C22×D4C23×C1111yescharacteristic
648C23×C4C23×C1112yes—
649C23×C4C23×C1111yescharacteristic
650C23×C4C23×C1111yescharacteristic
651C23×C4C23×C1112yes—
652C23×C4C23×C1111yescharacteristic
653C23×C4C23×C1111yescharacteristic
654C23×C4C23×C1111yescharacteristic
655C23×C4C23×C1111yescharacteristic
656C4⋊Q8—24no—
657C4⋊Q8—24no—
658C4⋊Q8—24no—
659#125—28no—
660C22⋊Q8—24no—
661C22⋊Q8—24no—
662C22⋊Q8—24no—
663C22⋊Q8—24no—
664C22⋊Q8—28no—
665C22⋊Q8—28no—
666C4×Q8—24no—
667C4×Q8—28no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—28no—
671C4×Q8—28no—
672C4×Q8—24no—
673C4×Q8D4×C1118yescomplemented
674C4×D4—24no—
675C4×D4—24no—
676C4×D4Q8×C1118yescomplemented
677#117—28no—
678C2×C4⋊C4—28no—
679C2×C4⋊C4—24no—
680C2×C4⋊C4C23×C1111yescharacteristic
681C2×C4⋊C4C23×C1112yes—
682C2×C4⋊C4C23×C1112yes—
683C2×C4⋊C4C23×C1112yes—
684C2×C4⋊C4C23×C1112yes—
685C2×C4⋊C4C23×C1112yes—
686C2×C4⋊C4C23×C1112yes—
687C2×C4⋊C4C23×C1111yescharacteristic
688C2×C4⋊C4C23×C1111yescharacteristic
689C2×C4⋊C4C23×C1112yes—
690C2×C4⋊C4C23×C1112yes—
691C2×C4⋊C4C23×C1112yes—
692C2×C4⋊C4C23×C1111yescharacteristic
693C2×C4⋊C4C23×C1112yes—
694C2×C4⋊C4C23×C1111yescharacteristic
695C2×C4⋊C4C23×C1111yescharacteristic
696C2×C4⋊C4C23×C1112yes—
697C2×C4⋊C4C23×C1112yes—
698C2×C4⋊C4C23×C1112yes—
699C2×C4⋊C4C23×C1112yes—
700C2×C4⋊C4C23×C1112yes—
701C2×C4⋊C4C23×C1112yes—
702C2×C4⋊C4C23×C1112yes—
703C2×C4⋊C4C23×C1112yes—
704C2×C4⋊C4C23×C1112yes—
705C2×C4⋊C4C23×C1112yes—
706C2×C4⋊C4C23×C1112yes—
707C2×C4⋊C4C23×C1111yescharacteristic
708C2×C4⋊C4C23×C1111yescharacteristic
709C2×C22⋊C4C23×C1112yes—
710C2×C22⋊C4C23×C1112yes—
711C2×C22⋊C4C23×C1111yescharacteristic
712C2×C22⋊C4C23×C1111yescharacteristic
713C2×C22⋊C4C23×C1111yescharacteristic
714C2×C22⋊C4C23×C1112yes—
715C2×C22⋊C4C23×C1112yes—
716C2×C22⋊C4C23×C1112yes—
717C2×C22⋊C4C23×C1112yes—
718C2×C22⋊C4C23×C1111yescharacteristic
719C2×C22⋊C4C23×C1111yescharacteristic
720C2×C22⋊C4C23×C1111yescharacteristic
721C2×C42—24no—
722C2×C42—28no—
723C2×C42—24no—
724C2×C42C23×C1112yes—
725C2×C42C23×C1111yescharacteristic
726C2×C42C23×C1111yescharacteristic
727C2×C42C23×C1112yes—
728C2×C42C23×C1111yescharacteristic
729C2×C42C23×C1111yescharacteristic
730C2×C42C23×C1111yescharacteristic
731C2×C42C23×C1111yescharacteristic
732C2×C42C23×C1112yes—
733C2×C42C23×C1112yes—
734C2×C42C23×C1111yescharacteristic
735C2×C42C23×C1111yescharacteristic
736C2×C42C23×C1111yescharacteristic
737C2×C42C23×C1111yescharacteristic
738C2×C42C23×C1112yes—
739C2×C42C23×C1111yescharacteristic
740C2×C42C23×C1112yes—
741C2×C42C23×C1111yescharacteristic
742C2×C42C23×C1111yescharacteristic
743#95C23×C1112yes—
744#95C23×C1112yes—
745#95C23×C1112yes—
746#95C23×C1112yes—
747#95C23×C1111yescharacteristic
748#95C23×C1111yescharacteristic
749#95C23×C1111yescharacteristic
750#95C23×C1111yescharacteristic
751#95C23×C1111yescharacteristic
752#95C23×C1111yescharacteristic
753#95C23×C1112yes—
754#95C23×C1112yes—
755#95C23×C1112yes—
756#95C23×C1112yes—
757#95C23×C1112yes—
758#95C23×C1112yes—
759#95C23×C1112yes—
760#95C23×C1112yes—
761#95C23×C1112yes—
762#95C23×C1112yes—
763#95C23×C1112yes—
764#95C23×C1112yes—
765#95C23×C1112yes—
766#95C23×C1112yes—
767#95C23×C1112yes—
768C2×C11—24no—
769C2×C11—42no—
770C2×C11C2×#52511yescharacteristic
771C2×C11C2×#53311yescharacteristic
772C2×C11#346111yescharacteristic
773C2×C11C2×D4×Q811yescharacteristic
774C2×C11D4×#4111yescharacteristic
775C2×C11Q8×#4111yescharacteristic
776C2×C11#348211yescharacteristic
777C24C24×C1111yescharacteristic
778C24C24×C1111yescharacteristic
779C2×Q8—232no—
780C2×Q8—24no—
781C2×Q8—22no—
782C2×Q8—24no—
783C2×Q8—22no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—24no—
790C2×Q8—22no—
791C2×Q8—22no—
792C2×Q8—42no—
793C2×Q8C2×D4×C1114yes—
794C2×Q8C11×#4114yes—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4C2×Q8×C1114yes—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—24no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—24no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—24no—
809C22×C4—22no—
810C22×C4—24no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—41no—
817C22×C4—41no—
818C22×C4—42no—
819C22×C4C2×Q8×C1114yes—
820C22×C4C2×Q8×C1114yescomplemented
821C22×C4C11×#4114yes—
822C22×C4C24×C1111yescharacteristic
823C22×C4C24×C1112yes—
824C22×C4C24×C1112yes—
825C22×C4C24×C1111yescharacteristic
826C22×C4C24×C1111yescharacteristic
827C22×C4C24×C1112yes—
828C22×C4C24×C1112yes—
829C22×C4C24×C1112yes—
830C22×C4C24×C1112yes—
831C22×C4C24×C1111yescharacteristic
832C22×C4C24×C1112yes—
833C22×C4C24×C1111yescharacteristic
834C22×C4C24×C1111yescharacteristic
835C22×C4C24×C1111yescharacteristic
836C22×C4C24×C1111yescharacteristic
837C22×C4C24×C1111yescharacteristic
838C22×C4C24×C1112yes—
839C22×C4C24×C1111yescharacteristic
840C22×C4C24×C1111yescharacteristic
841C22×C4C24×C1111yescharacteristic
842C22×C4C24×C1111yescharacteristic
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4C2×D4×C1118yes—
870C4⋊C4C2×D4×C1114yes—
871C4⋊C4C2×Q8×C1114yescomplemented
872C22⋊C4—22no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—24no—
880C22⋊C4—42no—
881C22⋊C4C2×Q8×C1114yes—
882C22⋊C4C2×Q8×C1114yescomplemented
883C22⋊C4C11×#4114yes—
884C42—22no—
885C42—24no—
886C42—24no—
887C42—22no—
888C42—22no—
889C42—24no—
890C42—22no—
891C42—22no—
892C42—22no—
893C42—24no—
894C42—22no—
895C42—22no—
896C42—22no—
897C42—22no—
898C42—24no—
899C42—41no—
900C42C2×D4×C1114yes—
901C42C2×D4×C1118yes—
902C42C2×Q8×C1114yescomplemented
903C11#3469111yescharacteristic, direct product factor, Sylow
904C23—21no—
905C23—21no—
906C23—21no—
907C23—21no—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23C22×Q8×C1112yes—
915C23C22×Q8×C1112yes—
916C23C2×C11×#4112yes—
917C23C2×C11×#4112yes—
918C23C25×C1111yescharacteristic
919Q8—216no—
920Q8—28no—
921Q8—28no—
922Q8—48no—
923Q8—44no—
924D4—28no—
925C2×C4—216no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—28no—
949C2×C4—28no—
950C2×C4—28no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—48no—
978C2×C4—44no—
979C2×C4C22×D4×C1112yes—
980C2×C4C22×D4×C1114yes—
981C2×C4C22×D4×C1114yes—
982C2×C4C22×D4×C1112yes—
983C2×C4C22×D4×C1112yes—
984C2×C4C22×Q8×C1112yes—
985C2×C4C22×Q8×C1112yes—
986C2×C4C22×Q8×C1112yes—
987C2×C4C22×Q8×C1112yes—
988C2×C4C22×Q8×C1112yes—
989C2×C4C2×C11×#4112yes—
990C2×C4C2×C11×#4114yes—
991C2×C4C2×C11×#4112yes—
992C2×C4C2×C11×#4112yes—
993C2×C4C2×C11×#4112yes—
994C2×C4C2×C11×#4112yes—
995C2×C4C11×2−1+412yes—
996C22—22no—
997C22—22no—
998C22—22no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22C11×#53314yescomplemented
1010C22C23×D4×C1111yescharacteristic
1011C22C23×Q8×C1111yescharacteristic
1012C22C22×C11×#4111yescharacteristic
1013C22C22×C11×#4111yescharacteristic
1014C22C22×C11×#4111yescharacteristic
1015C22C2×C11×2−1+411yescharacteristic
1016C22C11×#58511yescharacteristic
1017C4—24no—
1018C4—24no—
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—22no—
1023C4—22no—
1024C4—24no—
1025C4—22no—
1026C4—22no—
1027C4—22no—
1028C4—41no—
1029C4—42no—
1030C4—41no—
1031C4—42no—
1032C4—41no—
1033C4—42no—
1034C4—42no—
1035C4—42no—
1036C4C11×#52514yes—
1037C4D4×Q8×C1114yes—
1038C2—24no—
1039C2—42no—
1040C2C2×C11×#52511yescharacteristic
1041C2C2×C11×#53311yescharacteristic
1042C2C11×#346111yescharacteristic
1043C2C2×D4×Q8×C1111yescharacteristic
1044C2D4×C11×#4111yescharacteristic
1045C2Q8×C11×#4111yescharacteristic
1046C2C11×#348211yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC22×D4×C11C23
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. C22×C4×Q8×C11C2semidirect
3. C11×#2473C2semidirect
4. C11×#2465C2semidirect
5. C11×#2462C2semidirect
6. C11×#2451C2semidirect
8. C11×#2446C2semidirect
9. C11×#2440C2semidirect
10. C11×#2434C2semidirect
11. C11×#2429C2semidirect
12. C11×#2423C2semidirect
15. C11×#2399C2semidirect
16. C11×#2396C2semidirect
17. C4×C11×C4⋊Q8C2semidirect
18. C4×C11×C22⋊Q8C2semidirect
19. C4×C11×C22⋊Q8C2semidirect
20. C4×C11×C22⋊Q8C2semidirect
21. C11×#2295C2semidirect
159. C4×Q8×C11D4semidirect
162. C4×D4×C11Q8semidirect
254. #34691C11direct (N × H)
298. C22×C4×C11C2×Q8semidirect
349. C11×C4⋊C4C2×Q8semidirect
360. C11×C22⋊C4C2×Q8semidirect
380. C42×C11C2×Q8semidirect
381. C2×#533C2×C11semidirect
382. C22×C4×Q8C2×C11semidirect
383. #2473C2×C11semidirect
384. #2465C2×C11semidirect
385. #2462C2×C11semidirect
386. #2451C2×C11semidirect
388. #2446C2×C11semidirect
389. #2440C2×C11semidirect
390. #2434C2×C11semidirect
391. #2429C2×C11semidirect
392. #2423C2×C11semidirect
395. #2399C2×C11semidirect
396. #2396C2×C11semidirect
397. C4×C4⋊Q8C2×C11semidirect
398. C4×C22⋊Q8C2×C11semidirect
399. C4×C22⋊Q8C2×C11semidirect
400. C4×C22⋊Q8C2×C11semidirect
401. #2295C2×C11semidirect
610. C22×C11#533semidirect
673. C4×Q8D4×C11semidirect
676. C4×D4Q8×C11semidirect
820. C22×C4C2×Q8×C11semidirect
871. C4⋊C4C2×Q8×C11semidirect
882. C22⋊C4C2×Q8×C11semidirect
902. C42C2×Q8×C11semidirect
903. C11#34691direct (N × H)
1009. C22C11×#533semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C22×C4×Q8×C112
C11×#24732
C11×#24652
C11×#24622
C11×#24512
C11×#24492
C11×#24462
C11×#24402
C11×#24342
C11×#24292
C11×#24232
C11×#24172
C11×#24092
C11×#23992
C11×#23962
C4×C11×C4⋊Q82
C4×C11×C22⋊Q82
C11×#22952
C11×#22902
C42×D4×C112
#3469111