Finite Group Databasebeta

← C11×#34919 #14612112

Subgroups — C11×#34919 #14612112

Order 2816.

2392 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C2×C11×#529C211yesmaximal, characteristic, complemented
3C11×#2560C212yesmaximal, complemented
4C11×#2558C212yesmaximal, complemented
5C11×#2550C211yesmaximal, characteristic, complemented
6C11×#2545C211yesmaximal, characteristic, complemented
7C11×#2540C211yesmaximal, characteristic
8C11×#2536C211yesmaximal, characteristic, complemented
9C11×#2519C212yesmaximal, complemented
10C11×#2491C211yesmaximal, characteristic, complemented
11C11×#2489C211yesmaximal, characteristic, complemented
12C11×#2461C212yesmaximal, complemented
13C11×#2429C211yesmaximal, characteristic, complemented
14C11×#2426C211yesmaximal, characteristic, complemented
15C11×#2396C212yesmaximal, complemented
16C11×#2392C212yesmaximal, complemented
17C4×C11×#124C211yesmaximal, characteristic, complemented
18C4×C11×#124C212yesmaximal, complemented
19C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
20C4×C11×#121C211yesmaximal, characteristic, complemented
21C11×#2293C212yesmaximal, complemented
22C42×Q8×C11C211yesmaximal, characteristic, complemented
23C42×D4×C11C211yesmaximal, characteristic, complemented
24C11×#533—28no—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×C4⋊Q8C2211yescharacteristic
27C11×#529—28no—
28C2×C11×#126C2212yes—
29C2×C11×#125C2211yescharacteristic
30C2×C11×#125C2212yes—
31C2×C11×#124C2211yescharacteristic
32C2×C11×#124C2212yes—
33C2×C11×#124C2211yescharacteristic
34C2×C11×#123C2212yes—
35C2×C11×C22⋊Q8C2211yescharacteristic
36C2×C11×C22⋊Q8C2211yescharacteristic
37C2×C11×C22⋊Q8C2212yes—
38C2×C11×C22⋊Q8C2211yescharacteristic
39C2×C11×C22⋊Q8C2211yescharacteristic
40C2×C11×#121C2211yescharacteristic
41C2×C11×#121C2211yescharacteristic
42C2×C4×Q8×C11C2212yes—
43C2×C4×Q8×C11C2211yescharacteristic
44C2×C4×Q8×C11C2211yescharacteristic
45C2×C4×Q8×C11C2211yescharacteristic
46C2×C4×Q8×C11C2211yescharacteristic
47C2×C4×D4×C11C2211yescharacteristic
48C2×C4×D4×C11C2212yes—
49C2×C4×D4×C11C2212yes—
50C2×C4×D4×C11C2211yescharacteristic
51C2×C4×D4×C11C2211yescharacteristic
52C2×C4×D4×C11C2211yescharacteristic
53C2×C11×#117C2212yes—
54C2×C11×#117C2212yes—
55C22×C42×C11C2211yescharacteristic
56C22×C42×C11C2211yescharacteristic
57C11×#400C2212yes—
58C11×#399C2212yes—
59C11×#398C2212yes—
60C11×#398C2212yes—
61C11×#398C2212yes—
62C11×#397C2212yes—
63C11×#396C2212yes—
64C11×#396C2212yes—
65C11×#396C2212yes—
66C11×#396C2212yes—
67C11×#395C2212yes—
68C11×#394C2212yes—
69C11×#394C2212yes—
70C11×#394C2212yes—
71C11×#393C2212yes—
72C11×#392C2212yes—
73C11×#391C2211yescharacteristic
74C11×#391C2211yescharacteristic
75C11×#391C2212yes—
76C11×#390C2212yes—
77C11×#390C2211yescharacteristic
78C11×#390C2211yescharacteristic
79C11×#390C2212yes—
80C11×#390C2212yes—
81C11×#389C2211yescharacteristic
82C11×#389C2212yes—
83C11×#389C2211yescharacteristic
84C11×#389C2212yes—
85C11×#388C2212yes—
86C11×#388C2212yes—
87C11×#388C2212yes—
88C11×#388C2212yes—
89C11×#388C2212yes—
90C11×#388C2212yes—
91C11×#388C2212yes—
92C11×#388C2212yes—
93C11×#388C2212yes—
94C11×#388C2212yes—
95C11×#388C2212yes—
96C11×#387C2212yes—
97C11×#386C2212yes—
98C11×#385C2212yes—
99C11×#382C2212yes—
100C11×#382C2211yescharacteristic
101C11×#380C2211yescharacteristic
102C11×#380C2211yescharacteristic
103C4×C11×C4⋊C4C2212yes—
104C4×C11×C4⋊C4C2211yescharacteristic
105C4×C11×C4⋊C4C2212yes—
106C4×C11×C4⋊C4C2212yes—
107C4×C11×C4⋊C4C2211yescharacteristic
108C4×C11×C4⋊C4C2211yescharacteristic
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2211yescharacteristic
112C4×C11×C4⋊C4C2212yes—
113C4×C11×C22⋊C4C2212yes—
114C4×C11×C22⋊C4C2212yes—
115C4×C11×C22⋊C4C2212yes—
116C4×C11×C22⋊C4C2211yescharacteristic
117C4×C11×C22⋊C4C2211yescharacteristic
118C4×C11×C22⋊C4C2211yescharacteristic
119C4×C11×C22⋊C4C2211yescharacteristic
120C4×C11×C22⋊C4C2211yescharacteristic
121C4×C11×C22⋊C4C2211yescharacteristic
122C4×C11×C22⋊C4C2212yes—
123C43×C11C2211yescharacteristic
124C43×C11C2212yes—
125C22×Q8×C11C2311yescharacteristic
126C22×Q8×C11C2312yes—
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C22×D4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C23×C4×C11C2311yescharacteristic
139C11×C4⋊Q8—24no—
140C11×C4⋊Q8—24no—
141C11×#126—28no—
142C11×#125—24no—
143C11×#125—28no—
144C11×#124—24no—
145C11×#124—28no—
146C11×#124—24no—
147C11×#123—28no—
148C11×C22⋊Q8—24no—
149C11×C22⋊Q8—24no—
150C11×C22⋊Q8—24no—
151C11×C22⋊Q8—28no—
152C11×C22⋊Q8—24no—
153C11×#121—24no—
154C11×#121—24no—
155C4×Q8×C11—24no—
156C4×Q8×C11—28no—
157C4×Q8×C11—24no—
158C4×Q8×C11—24no—
159C4×Q8×C11D418yescomplemented
160C4×D4×C11—24no—
161C4×D4×C11—28no—
162C4×D4×C11—24no—
163C4×D4×C11—24no—
164C4×D4×C11—28no—
165C4×D4×C11—24no—
166C11×#117—28no—
167C11×#117—28no—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2311yescharacteristic
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2311yescharacteristic
179C2×C11×C4⋊C4C2312yes—
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C4⋊C4C2312yes—
182C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4C2312yes—
190C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4C2312yes—
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×C11×C22⋊C4C2312yes—
212C2×C11×C22⋊C4C2312yes—
213C2×C11×C22⋊C4C2311yescharacteristic
214C2×C42×C11—24no—
215C2×C42×C11—24no—
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2311yescharacteristic
218C2×C42×C11C2311yescharacteristic
219C2×C42×C11C2311yescharacteristic
220C2×C42×C11C2311yescharacteristic
221C2×C42×C11C2311yescharacteristic
222C2×C42×C11C2312yes—
223C2×C42×C11C2312yes—
224C2×C42×C11C2312yes—
225C2×C42×C11C2311yescharacteristic
226C2×C42×C11C2311yescharacteristic
227C2×C42×C11C2311yescharacteristic
228C2×C42×C11C2311yescharacteristic
229C2×C42×C11C2312yes—
230C2×C42×C11C2312yes—
231C2×C42×C11C2311yescharacteristic
232C2×C42×C11C2312yes—
233C2×C42×C11C2311yescharacteristic
234C2×C42×C11C2312yes—
235C2×C42×C11C2311yescharacteristic
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#34919C1111yesmaximal, characteristic, direct product factor, Sylow
256C24×C11C2412yes—
257C24×C11C2411yescharacteristic
258C24×C11C2411yescharacteristic
259C2×Q8×C11—24no—
260C2×Q8×C11—22no—
261C2×Q8×C11—22no—
262C2×Q8×C11—22no—
263C2×Q8×C11—22no—
264C2×Q8×C11—24no—
265C2×Q8×C11—22no—
266C2×Q8×C11—42no—
267C2×Q8×C11C2×D414yes—
268C2×D4×C11—22no—
269C2×D4×C11—22no—
270C2×D4×C11—24no—
271C2×D4×C11—24no—
272C2×D4×C11—24no—
273C2×D4×C11—22no—
274C2×D4×C11—22no—
275C2×D4×C11—24no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
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—24no—
294C22×C4×C11—22no—
295C22×C4×C11—22no—
296C22×C4×C11—22no—
297C22×C4×C11—24no—
298C22×C4×C11—41no—
299C22×C4×C11—41no—
300C22×C4×C11#4114yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2412yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C22×C4×C11C2412yes—
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2412yes—
312C22×C4×C11C2412yes—
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—22no—
332C11×C4⋊C4—22no—
333C11×C4⋊C4—24no—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—22no—
336C11×C4⋊C4—24no—
337C11×C4⋊C4—24no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—24no—
340C11×C4⋊C4—42no—
341C11×C4⋊C4C2×D414yes—
342C11×C4⋊C4C2×D418yes—
343C11×C4⋊C4#4114yes—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—24no—
346C11×C22⋊C4—24no—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—24no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—24no—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—22no—
355C11×C22⋊C4—24no—
356C11×C22⋊C4—22no—
357C11×C22⋊C4—22no—
358C11×C22⋊C4—22no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4#4114yes—
367C42×C11—22no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—22no—
372C42×C11—22no—
373C42×C11—24no—
374C42×C11—22no—
375C42×C11—22no—
376C42×C11—24no—
377C42×C11—24no—
378C42×C11—22no—
379C42×C11—24no—
380C42×C11—24no—
381C42×C11—22no—
382C42×C11—42no—
383C42×C11—41no—
384C42×C11C2×D414yes—
385C42×C11C2×D418yes—
386C42×C11#4114yes—
387C2×#533C2×C1111yescharacteristic, complemented
388C2×#529C2×C1111yescharacteristic, complemented
389#2560C2×C1112yescomplemented
390#2558C2×C1112yescomplemented
391#2550C2×C1111yescharacteristic, complemented
392#2545C2×C1111yescharacteristic, complemented
393#2540C2×C1111yescharacteristic
394#2536C2×C1111yescharacteristic, complemented
395#2519C2×C1112yescomplemented
396#2491C2×C1111yescharacteristic, complemented
397#2489C2×C1111yescharacteristic, complemented
398#2461C2×C1112yescomplemented
399#2429C2×C1111yescharacteristic, complemented
400#2426C2×C1111yescharacteristic, complemented
401#2396C2×C1112yescomplemented
402#2392C2×C1112yescomplemented
403C4×#124C2×C1112yescomplemented
404C4×#124C2×C1111yescharacteristic, complemented
405C4×C22⋊Q8C2×C1111yescharacteristic, complemented
406C4×#121C2×C1111yescharacteristic, complemented
407#2293C2×C1112yescomplemented
408C42×Q8C2×C1111yescharacteristic, complemented
409C42×D4C2×C1111yescharacteristic, complemented
410C23×C11—21no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11—21no—
414C23×C11—21no—
415C23×C11—21no—
416C23×C11—21no—
417C23×C11—21no—
418C23×C11—21no—
419C23×C11—21no—
420C23×C11—21no—
421C23×C11—21no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—22no—
428C23×C11—22no—
429C23×C11C2×#4112yes—
430C23×C11C2×#4112yes—
431C23×C11C2511yescharacteristic
432Q8×C11—28no—
433Q8×C11—48no—
434Q8×C11—44no—
435D4×C11—28no—
436D4×C11—48no—
437D4×C11—48no—
438D4×C11—44no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—21no—
448C2×C4×C11—22no—
449C2×C4×C11—21no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—21no—
455C2×C4×C11—22no—
456C2×C4×C11—21no—
457C2×C4×C11—28no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—22no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—44no—
486C2×C4×C11—44no—
487C2×C4×C11—44no—
488C2×C4×C11—44no—
489C2×C4×C11—44no—
490C2×C4×C11—48no—
491C2×C4×C11C22×D412yes—
492C2×C4×C11C22×D414yes—
493C2×C4×C11C22×D414yes—
494C2×C4×C11C22×D412yes—
495C2×C4×C11C22×D412yes—
496C2×C4×C11C2×#4112yes—
497C2×C4×C11C2×#4112yes—
498C2×C4×C11C2×#4114yes—
499C2×C4×C11C2×#4112yes—
500C2×C4×C11C2×#4112yes—
501C2×C4×C11C2×#4112yes—
502C2×C4×C11C2×#4112yes—
503C2×C4×C11C2×#4112yes—
504C2×C4×C11C2×#4112yes—
505C2×C4×C112−1+412yes—
506#533—28no—
507C2×C4⋊Q8C22×C1111yescharacteristic
508C2×C4⋊Q8C22×C1111yescharacteristic
509#529—28no—
510C2×#126C22×C1112yes—
511C2×#125C22×C1111yescharacteristic
512C2×#125C22×C1112yes—
513C2×#124C22×C1111yescharacteristic
514C2×#124C22×C1112yes—
515C2×#124C22×C1111yescharacteristic
516C2×#123C22×C1112yes—
517C2×C22⋊Q8C22×C1112yes—
518C2×C22⋊Q8C22×C1111yescharacteristic
519C2×C22⋊Q8C22×C1111yescharacteristic
520C2×C22⋊Q8C22×C1111yescharacteristic
521C2×C22⋊Q8C22×C1111yescharacteristic
522C2×#121C22×C1111yescharacteristic
523C2×#121C22×C1111yescharacteristic
524C2×C4×Q8C22×C1112yes—
525C2×C4×Q8C22×C1111yescharacteristic
526C2×C4×Q8C22×C1111yescharacteristic
527C2×C4×Q8C22×C1111yescharacteristic
528C2×C4×Q8C22×C1111yescharacteristic
529C2×C4×D4C22×C1111yescharacteristic
530C2×C4×D4C22×C1112yes—
531C2×C4×D4C22×C1112yes—
532C2×C4×D4C22×C1111yescharacteristic
533C2×C4×D4C22×C1111yescharacteristic
534C2×C4×D4C22×C1111yescharacteristic
535C2×#117C22×C1112yes—
536C2×#117C22×C1112yes—
537C22×C42C22×C1111yescharacteristic
538C22×C42C22×C1111yescharacteristic
539#400C22×C1112yes—
540#399C22×C1112yes—
541#398C22×C1112yes—
542#398C22×C1112yes—
543#398C22×C1112yes—
544#397C22×C1112yes—
545#396C22×C1112yes—
546#396C22×C1112yes—
547#396C22×C1112yes—
548#396C22×C1112yes—
549#395C22×C1112yes—
550#394C22×C1112yes—
551#394C22×C1112yes—
552#394C22×C1112yes—
553#393C22×C1112yes—
554#392C22×C1112yes—
555#391C22×C1112yes—
556#391C22×C1111yescharacteristic
557#391C22×C1111yescharacteristic
558#390C22×C1112yes—
559#390C22×C1112yes—
560#390C22×C1111yescharacteristic
561#390C22×C1111yescharacteristic
562#390C22×C1112yes—
563#389C22×C1111yescharacteristic
564#389C22×C1112yes—
565#389C22×C1111yescharacteristic
566#389C22×C1112yes—
567#388C22×C1112yes—
568#388C22×C1112yes—
569#388C22×C1112yes—
570#388C22×C1112yes—
571#388C22×C1112yes—
572#388C22×C1112yes—
573#388C22×C1112yes—
574#388C22×C1112yes—
575#388C22×C1112yes—
576#388C22×C1112yes—
577#388C22×C1112yes—
578#387C22×C1112yes—
579#386C22×C1112yes—
580#385C22×C1112yes—
581#382C22×C1112yes—
582#382C22×C1111yescharacteristic
583#380C22×C1111yescharacteristic
584#380C22×C1111yescharacteristic
585C4×C4⋊C4C22×C1112yes—
586C4×C4⋊C4C22×C1112yes—
587C4×C4⋊C4C22×C1111yescharacteristic
588C4×C4⋊C4C22×C1112yes—
589C4×C4⋊C4C22×C1112yes—
590C4×C4⋊C4C22×C1111yescharacteristic
591C4×C4⋊C4C22×C1111yescharacteristic
592C4×C4⋊C4C22×C1111yescharacteristic
593C4×C4⋊C4C22×C1111yescharacteristic
594C4×C4⋊C4C22×C1111yescharacteristic
595C4×C22⋊C4C22×C1111yescharacteristic
596C4×C22⋊C4C22×C1112yes—
597C4×C22⋊C4C22×C1112yes—
598C4×C22⋊C4C22×C1112yes—
599C4×C22⋊C4C22×C1111yescharacteristic
600C4×C22⋊C4C22×C1111yescharacteristic
601C4×C22⋊C4C22×C1111yescharacteristic
602C4×C22⋊C4C22×C1111yescharacteristic
603C4×C22⋊C4C22×C1111yescharacteristic
604C4×C22⋊C4C22×C1112yes—
605C43C22×C1111yescharacteristic
606C43C22×C1112yes—
607C22×C11—22no—
608C22×C11—22no—
609C22×C11—22no—
610C22×C11—22no—
611C22×C11—22no—
612C22×C11—22no—
613C22×C11—41no—
614C22×C11—41no—
615C22×C11—41no—
616C22×C11—41no—
617C22×C11—41no—
618C22×C11—41no—
619C22×C11—41no—
620C22×C11—41no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—42no—
627C22×C11—42no—
628C22×C11C23×D411yescharacteristic
629C22×C11C22×#4111yescharacteristic
630C22×C11C22×#4111yescharacteristic
631C22×C11C22×#4111yescharacteristic
632C22×C11C22×#4111yescharacteristic
633C22×C11C2×2−1+411yescharacteristic
634C22×C11#58511yescharacteristic
635C4×C11—24no—
636C4×C11—22no—
637C4×C11—22no—
638C4×C11—22no—
639C4×C11—22no—
640C4×C11—22no—
641C4×C11—24no—
642C4×C11—24no—
643C4×C11—22no—
644C4×C11—41no—
645C4×C11—41no—
646C4×C11—42no—
647C4×C11—42no—
648C4×C11—41no—
649C4×C11—42no—
650C4×C11—41no—
651C4×C11—42no—
652C4×C11—41no—
653C4×C11#53214yes—
654C4×C11#54814yes—
655C22×Q8C23×C1111yescharacteristic
656C22×Q8C23×C1112yes—
657C22×Q8C23×C1111yescharacteristic
658C22×D4C23×C1111yescharacteristic
659C22×D4C23×C1111yescharacteristic
660C22×D4C23×C1112yes—
661C22×D4C23×C1112yes—
662C23×C4C23×C1112yes—
663C23×C4C23×C1111yescharacteristic
664C23×C4C23×C1111yescharacteristic
665C23×C4C23×C1111yescharacteristic
666C23×C4C23×C1111yescharacteristic
667C23×C4C23×C1111yescharacteristic
668C23×C4C23×C1111yescharacteristic
669C4⋊Q8—24no—
670C4⋊Q8—24no—
671#126—28no—
672#125—24no—
673#125—28no—
674#124—24no—
675#124—28no—
676#124—24no—
677#123—28no—
678C22⋊Q8—24no—
679C22⋊Q8—24no—
680C22⋊Q8—24no—
681C22⋊Q8—28no—
682C22⋊Q8—24no—
683#121—24no—
684#121—24no—
685C4×Q8—24no—
686C4×Q8—28no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8D4×C1118yescomplemented
690C4×D4—24no—
691C4×D4—28no—
692C4×D4—24no—
693C4×D4—24no—
694C4×D4—28no—
695C4×D4—24no—
696#117—28no—
697#117—28no—
698C2×C4⋊C4C23×C1112yes—
699C2×C4⋊C4C23×C1112yes—
700C2×C4⋊C4C23×C1112yes—
701C2×C4⋊C4C23×C1112yes—
702C2×C4⋊C4C23×C1111yescharacteristic
703C2×C4⋊C4C23×C1112yes—
704C2×C4⋊C4C23×C1111yescharacteristic
705C2×C4⋊C4C23×C1111yescharacteristic
706C2×C4⋊C4C23×C1111yescharacteristic
707C2×C4⋊C4C23×C1112yes—
708C2×C4⋊C4C23×C1112yes—
709C2×C4⋊C4C23×C1112yes—
710C2×C4⋊C4C23×C1112yes—
711C2×C4⋊C4C23×C1111yescharacteristic
712C2×C4⋊C4C23×C1112yes—
713C2×C4⋊C4C23×C1111yescharacteristic
714C2×C4⋊C4C23×C1112yes—
715C2×C4⋊C4C23×C1112yes—
716C2×C4⋊C4C23×C1112yes—
717C2×C4⋊C4C23×C1112yes—
718C2×C4⋊C4C23×C1111yescharacteristic
719C2×C4⋊C4C23×C1112yes—
720C2×C4⋊C4C23×C1111yescharacteristic
721C2×C22⋊C4C23×C1112yes—
722C2×C22⋊C4C23×C1112yes—
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×C1112yes—
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×C1111yescharacteristic
744C2×C42—24no—
745C2×C42—24no—
746C2×C42C23×C1111yescharacteristic
747C2×C42C23×C1112yes—
748C2×C42C23×C1111yescharacteristic
749C2×C42C23×C1112yes—
750C2×C42C23×C1111yescharacteristic
751C2×C42C23×C1111yescharacteristic
752C2×C42C23×C1111yescharacteristic
753C2×C42C23×C1112yes—
754C2×C42C23×C1112yes—
755C2×C42C23×C1111yescharacteristic
756C2×C42C23×C1112yes—
757C2×C42C23×C1111yescharacteristic
758C2×C42C23×C1111yescharacteristic
759C2×C42C23×C1111yescharacteristic
760C2×C42C23×C1111yescharacteristic
761C2×C42C23×C1111yescharacteristic
762C2×C42C23×C1112yes—
763C2×C42C23×C1112yes—
764C2×C42C23×C1111yescharacteristic
765C2×C42C23×C1111yescharacteristic
766#95C23×C1111yescharacteristic
767#95C23×C1111yescharacteristic
768#95C23×C1111yescharacteristic
769#95C23×C1111yescharacteristic
770#95C23×C1111yescharacteristic
771#95C23×C1111yescharacteristic
772#95C23×C1112yes—
773#95C23×C1112yes—
774#95C23×C1112yes—
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—
785C2×C11—42no—
786C2×C11—42no—
787C2×C11—82no—
788C2×C11C2×#53211yescharacteristic
789C2×C11#344411yescharacteristic
790C2×C11#346111yescharacteristic
791C2×C11C2×#54811yescharacteristic
792C2×C11D4×#4111yescharacteristic
793C2×C11#347511yescharacteristic
794C2×C11#348211yescharacteristic
795C24C24×C1112yes—
796C24C24×C1111yescharacteristic
797C24C24×C1111yescharacteristic
798C2×Q8—24no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—22no—
802C2×Q8—22no—
803C2×Q8—24no—
804C2×Q8—22no—
805C2×Q8—42no—
806C2×Q8C2×D4×C1114yes—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—24no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—42no—
818C2×D4—42no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—24no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—24no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4C11×#4114yes—
840C22×C4C24×C1112yes—
841C22×C4C24×C1111yescharacteristic
842C22×C4C24×C1111yescharacteristic
843C22×C4C24×C1112yes—
844C22×C4C24×C1111yescharacteristic
845C22×C4C24×C1111yescharacteristic
846C22×C4C24×C1111yescharacteristic
847C22×C4C24×C1112yes—
848C22×C4C24×C1112yes—
849C22×C4C24×C1111yescharacteristic
850C22×C4C24×C1112yes—
851C22×C4C24×C1112yes—
852C22×C4C24×C1111yescharacteristic
853C22×C4C24×C1111yescharacteristic
854C22×C4C24×C1111yescharacteristic
855C22×C4C24×C1112yes—
856C22×C4C24×C1111yescharacteristic
857C22×C4C24×C1111yescharacteristic
858C22×C4C24×C1111yescharacteristic
859C22×C4C24×C1111yescharacteristic
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—42no—
880C4⋊C4C2×D4×C1114yes—
881C4⋊C4C2×D4×C1118yes—
882C4⋊C4C11×#4114yes—
883C22⋊C4—22no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—22no—
894C22⋊C4—24no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—42no—
905C22⋊C4C11×#4114yes—
906C42—22no—
907C42—22no—
908C42—22no—
909C42—22no—
910C42—22no—
911C42—22no—
912C42—24no—
913C42—22no—
914C42—22no—
915C42—24no—
916C42—24no—
917C42—22no—
918C42—24no—
919C42—24no—
920C42—22no—
921C42—42no—
922C42—41no—
923C42C2×D4×C1114yes—
924C42C2×D4×C1118yes—
925C42C11×#4114yes—
926C11#3491911yescharacteristic, direct product factor, Sylow
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23C2×C11×#4112yes—
947C23C2×C11×#4112yes—
948C23C25×C1111yescharacteristic
949Q8—28no—
950Q8—48no—
951Q8—44no—
952D4—28no—
953D4—48no—
954D4—48no—
955D4—44no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—28no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—44no—
1003C2×C4—44no—
1004C2×C4—44no—
1005C2×C4—44no—
1006C2×C4—44no—
1007C2×C4—48no—
1008C2×C4C22×D4×C1112yes—
1009C2×C4C22×D4×C1114yes—
1010C2×C4C22×D4×C1114yes—
1011C2×C4C22×D4×C1112yes—
1012C2×C4C22×D4×C1112yes—
1013C2×C4C2×C11×#4112yes—
1014C2×C4C2×C11×#4112yes—
1015C2×C4C2×C11×#4114yes—
1016C2×C4C2×C11×#4112yes—
1017C2×C4C2×C11×#4112yes—
1018C2×C4C2×C11×#4112yes—
1019C2×C4C2×C11×#4112yes—
1020C2×C4C2×C11×#4112yes—
1021C2×C4C2×C11×#4112yes—
1022C2×C4C11×2−1+412yes—
1023C22—22no—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—22no—
1028C22—22no—
1029C22—41no—
1030C22—41no—
1031C22—41no—
1032C22—41no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—41no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22C23×D4×C1111yescharacteristic
1045C22C22×C11×#4111yescharacteristic
1046C22C22×C11×#4111yescharacteristic
1047C22C22×C11×#4111yescharacteristic
1048C22C22×C11×#4111yescharacteristic
1049C22C2×C11×2−1+411yescharacteristic
1050C22C11×#58511yescharacteristic
1051C4—24no—
1052C4—22no—
1053C4—22no—
1054C4—22no—
1055C4—22no—
1056C4—22no—
1057C4—24no—
1058C4—24no—
1059C4—22no—
1060C4—41no—
1061C4—41no—
1062C4—42no—
1063C4—42no—
1064C4—41no—
1065C4—42no—
1066C4—41no—
1067C4—42no—
1068C4—41no—
1069C4C11×#53214yes—
1070C4C11×#54814yes—
1071C2—42no—
1072C2—42no—
1073C2—82no—
1074C2C2×C11×#53211yescharacteristic
1075C2C11×#344411yescharacteristic
1076C2C11×#346111yescharacteristic
1077C2C2×C11×#54811yescharacteristic
1078C2D4×C11×#4111yescharacteristic
1079C2C11×#347511yescharacteristic
1080C2C11×#348211yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC11×#2540C2
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×C11×#529C2semidirect
3. C11×#2560C2semidirect
4. C11×#2558C2semidirect
5. C11×#2550C2semidirect
6. C11×#2545C2semidirect
8. C11×#2536C2semidirect
9. C11×#2519C2semidirect
10. C11×#2491C2semidirect
11. C11×#2489C2semidirect
12. C11×#2461C2semidirect
13. C11×#2429C2semidirect
14. C11×#2426C2semidirect
15. C11×#2396C2semidirect
16. C11×#2392C2semidirect
17. C4×C11×#124C2semidirect
18. C4×C11×#124C2semidirect
19. C4×C11×C22⋊Q8C2semidirect
20. C4×C11×#121C2semidirect
21. C11×#2293C2semidirect
22. C42×Q8×C11C2semidirect
23. C42×D4×C11C2semidirect
159. C4×Q8×C11D4semidirect
255. #34919C11direct (N × H)
387. C2×#533C2×C11semidirect
388. C2×#529C2×C11semidirect
389. #2560C2×C11semidirect
390. #2558C2×C11semidirect
391. #2550C2×C11semidirect
392. #2545C2×C11semidirect
394. #2536C2×C11semidirect
395. #2519C2×C11semidirect
396. #2491C2×C11semidirect
397. #2489C2×C11semidirect
398. #2461C2×C11semidirect
399. #2429C2×C11semidirect
400. #2426C2×C11semidirect
401. #2396C2×C11semidirect
402. #2392C2×C11semidirect
403. C4×#124C2×C11semidirect
404. C4×#124C2×C11semidirect
405. C4×C22⋊Q8C2×C11semidirect
406. C4×#121C2×C11semidirect
407. #2293C2×C11semidirect
408. C42×Q8C2×C11semidirect
409. C42×D4C2×C11semidirect
689. C4×Q8D4×C11semidirect
926. C11#34919direct (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×C11×#5292
C11×#25602
C11×#25582
C11×#25502
C11×#25452
C11×#25402
C11×#25362
C11×#25192
C11×#24912
C11×#24892
C11×#24612
C11×#24292
C11×#24262
C11×#23962
C11×#23922
C4×C11×#1242
C4×C11×C22⋊Q82
C4×C11×#1212
C11×#22932
C42×Q8×C112
C42×D4×C112
#3491911