Finite Group Databasebeta

← C11×#61380 #14638573

Subgroups — C11×#61380 #14638573

Order 2816.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3504C211yesmaximal, characteristic, complemented
2C11×#3503C211yesmaximal, characteristic, complemented
3C11×#3390C212yesmaximal, complemented
4C11×#3389C212yesmaximal, complemented
5C11×#3388C212yesmaximal, complemented
6C11×#3388C212yesmaximal, complemented
7C11×#3387C212yesmaximal, complemented
8C11×#3386C212yesmaximal, complemented
9C11×#3385C212yesmaximal, complemented
10C11×#3384C212yesmaximal, complemented
11C11×#3164C211yesmaximal, characteristic, complemented
12C11×#3163C211yesmaximal, characteristic, complemented
13C2×C11×#501C211yesmaximal, characteristic, complemented
14C11×#3084C211yesmaximal, characteristic, complemented
15C11×#3084C211yesmaximal, characteristic, complemented
16C11×#3083C211yesmaximal, characteristic, complemented
17C11×#3083C211yesmaximal, characteristic, complemented
18C11×#3080C211yesmaximal, characteristic, complemented
19C11×#3079C211yesmaximal, characteristic, complemented
20C11×#2961C211yesmaximal, characteristic, complemented
21C11×#2952C211yesmaximal, characteristic
22C11×#2951C211yesmaximal, characteristic
23C11×#2943C211yesmaximal, characteristic
24C2×C11×#135C2211yescharacteristic
25Q82×C11C2212yes—
26C11×#557C2212yes—
27C11×#557C2212yes—
28C11×#557C2212yes—
29C11×#554—22no—
30C11×#554—22no—
31C11×#554—22no—
32C11×#554C2212yes—
33C11×#554C2212yes—
34C11×#554C2212yes—
35D4×Q8×C11—22no—
36D4×Q8×C11C2212yes—
37C11×#544—21no—
38C11×#544—21no—
39C11×#544—21no—
40C11×#544—21no—
41C11×#544C2211yescharacteristic
42C11×#544C2211yescharacteristic
43C11×#544C2211yescharacteristic
44C11×#544C2211yescharacteristic
45C11×#533—21no—
46C11×#533—21no—
47C11×#533C2211yescharacteristic
48C2×C11×C4⋊Q8—21no—
49C2×C11×C4⋊Q8C2211yescharacteristic
50C2×C11×#125—21no—
51C2×C11×#125C2211yescharacteristic
52C11×#520C2211yescharacteristic
53C11×#520C2211yescharacteristic
54C11×#520C2211yescharacteristic
55C11×#520C2211yescharacteristic
56C4×C11×#41C2211yescharacteristic
57C4×C11×#41C2211yescharacteristic
58C11×#501C2212yes—
59C11×#501C2212yes—
60C11×#501C2212yes—
61C11×#501C2212yes—
62C11×#501C2212yes—
63C11×#501C2212yes—
64C11×#501C2212yes—
65C11×#501C2212yes—
66C11×#500C2212yes—
67C11×#499C2212yes—
68C11×#499C2212yes—
69C11×#498C2212yes—
70C11×#479C2212yes—
71C11×#479C2212yes—
72C11×#479C2212yes—
73C11×#479C2212yes—
74C11×#479C2212yes—
75C11×#479C2212yes—
76C11×#478C2212yes—
77C11×#478C2212yes—
78C11×#478C2212yes—
79C11×#478C2212yes—
80C11×#478C2212yes—
81C11×#478C2212yes—
82C11×#477C2212yes—
83C11×#477C2212yes—
84C11×#477C2212yes—
85C11×#476C2212yes—
86C11×#476C2212yes—
87C11×#476C2212yes—
88C11×#475C2212yes—
89C11×#475C2212yes—
90C11×#475C2212yes—
91C11×#474C2212yes—
92C11×#474C2212yes—
93C11×#474C2212yes—
94C11×#446C2212yes—
95C11×#446C2212yes—
96C11×#446C2212yes—
97C11×#446C2212yes—
98C11×#442C2211yescharacteristic
99C11×#442C2211yescharacteristic
100C11×#442C2212yes—
101C11×#441C2211yescharacteristic
102C11×#441C2211yescharacteristic
103C11×#441C2212yes—
104C11×#440C2211yescharacteristic
105C11×#440C2211yescharacteristic
106C11×#440C2211yescharacteristic
107C11×#440C2211yescharacteristic
108C11×#440C2212yes—
109C11×#440C2212yes—
110C4×C11×Q16C2212yes—
111C4×C11×SD16C2212yes—
112C4×C11×SD16C2212yes—
113C4×C11×D8C2212yes—
114C11×#428C2211yescharacteristic
115C11×#428C2211yescharacteristic
116C11×#428C2211yescharacteristic
117C11×#428C2211yescharacteristic
118C11×#427C2211yescharacteristic
119C2×C11×#107C2211yescharacteristic
120C2×C11×#107C2211yescharacteristic
121C2×C11×#106C2211yescharacteristic
122C2×C11×#106C2211yescharacteristic
123C11×#424C2211yescharacteristic
124C11×#424C2211yescharacteristic
125C11×#423C2211yescharacteristic
126C11×#417C2211yescharacteristic
127C11×#417C2211yescharacteristic
128C11×#417C2211yescharacteristic
129C11×#417C2211yescharacteristic
130C11×#416C2211yescharacteristic
131C11×#416C2211yescharacteristic
132C11×#405C2211yescharacteristic
133C11×#405C2211yescharacteristic
134C2×C11×#97C2211yescharacteristic
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137C22×Q8×C11—22no—
138C22×Q8×C11—21no—
139C11×#135Q818yescomplemented
140C2×C11×Q16C2311yescharacteristic
141C2×C11×SD16C2311yescharacteristic
142C2×C11×SD16C2311yescharacteristic
143C2×C11×D8C2311yescharacteristic
144C2×C11×M16C2311yescharacteristic
145C2×C11×M16C2311yescharacteristic
146C22×C8×C11C2311yescharacteristic
147C22×C8×C11C2311yescharacteristic
148C11×C4⋊Q8—22no—
149C11×C4⋊Q8—22no—
150C11×C4⋊Q8—22no—
151C11×C4⋊Q8—21no—
152C11×C4⋊Q8—21no—
153C11×C4⋊Q8—22no—
154C11×C4⋊Q8—21no—
155C11×C4⋊Q8—21no—
156C11×C4⋊Q8—22no—
157C11×C4⋊Q8—22no—
158C11×C4⋊Q8—21no—
159C11×C4⋊Q8—21no—
160C11×C4⋊Q8D411yescharacteristic
161C11×C4⋊Q8D411yescharacteristic
162C11×C4⋊Q8C2312yes—
163C11×C4⋊Q8C2312yes—
164C11×C4⋊Q8C2312yes—
165C11×C4⋊Q8C2312yes—
166C11×C4⋊Q8C2312yes—
167C11×C4⋊Q8C2312yes—
168C11×#125—21no—
169C11×#125—21no—
170C11×#125—22no—
171C11×#125—22no—
172C11×#125—21no—
173C11×#125—21no—
174C11×#125—22no—
175C11×#125—22no—
176C11×#125—22no—
177C11×#125—22no—
178C11×#125—21no—
179C11×#125—21no—
180C11×#125D411yescharacteristic
181C11×#125D411yescharacteristic
182C11×#125C2312yes—
183C11×#125C2312yes—
184C11×#125C2312yes—
185C11×#125C2312yes—
186C11×#125C2312yes—
187C11×#125C2312yes—
188C11×C22⋊Q8—22no—
189C11×C22⋊Q8—22no—
190C11×C22⋊Q8—22no—
191C11×C22⋊Q8—22no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8—22no—
195C11×C22⋊Q8—22no—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8—22no—
200C11×C22⋊Q8—22no—
201C11×C22⋊Q8—22no—
202C11×C22⋊Q8—22no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8D412yes—
205C11×C22⋊Q8D412yes—
206C4×Q8×C11—22no—
207C4×Q8×C11—22no—
208C4×Q8×C11—22no—
209C4×Q8×C11—22no—
210C4×Q8×C11C2311yescharacteristic
211C4×Q8×C11C2311yescharacteristic
212C4×Q8×C11C2311yescharacteristic
213C4×Q8×C11C2311yescharacteristic
214C4×Q8×C11C2312yes—
215C4×Q8×C11C2312yes—
216C4×Q8×C11C2312yes—
217C4×Q8×C11C2312yes—
218C4×Q8×C11C2312yes—
219C4×Q8×C11C2312yes—
220C4×D4×C11—21no—
221C4×D4×C11—21no—
222C4×D4×C11—21no—
223C4×D4×C11—21no—
224C4×D4×C11—22no—
225C4×D4×C11—22no—
226C4×D4×C11—22no—
227C4×D4×C11—22no—
228C4×D4×C11C2311yescharacteristic
229C4×D4×C11C2311yescharacteristic
230C4×D4×C11C2311yescharacteristic
231C4×D4×C11C2311yescharacteristic
232C4×D4×C11C2312yes—
233C4×D4×C11C2312yes—
234C4×D4×C11C2312yes—
235C4×D4×C11C2312yes—
236C11×#117—21no—
237C11×#117—21no—
238C11×#117—21no—
239C11×#117—21no—
240C11×#117—21no—
241C11×#117—21no—
242C11×#117C2311yescharacteristic
243C11×#117C2311yescharacteristic
244C11×#117C2311yescharacteristic
245C11×#117C2311yescharacteristic
246C2×C11×C4⋊C4—21no—
247C2×C11×C4⋊C4—21no—
248C2×C11×C4⋊C4—21no—
249C2×C11×C4⋊C4—21no—
250C2×C11×C4⋊C4—21no—
251C2×C11×C4⋊C4—21no—
252C2×C11×C4⋊C4—21no—
253C2×C11×C4⋊C4—22no—
254C2×C11×C4⋊C4—22no—
255C2×C11×C4⋊C4—22no—
256C2×C11×C4⋊C4C2311yescharacteristic
257C2×C11×C4⋊C4C2311yescharacteristic
258C2×C11×C4⋊C4C2311yescharacteristic
259C2×C11×C4⋊C4C2311yescharacteristic
260C2×C42×C11—21no—
261C2×C42×C11—21no—
262C2×C42×C11C2311yescharacteristic
263C11×#107C2311yescharacteristic
264C11×#107C2312yes—
265C11×#107C2312yes—
266C11×#107C2312yes—
267C11×#107C2311yescharacteristic
268C11×#107C2312yes—
269C11×#107C2312yes—
270C11×#107C2312yes—
271C11×#107C2312yes—
272C11×#107C2312yes—
273C11×#106C2311yescharacteristic
274C11×#106C2312yes—
275C11×#106C2312yes—
276C11×#106C2312yes—
277C11×#106C2311yescharacteristic
278C11×#106C2312yes—
279C11×#106C2312yes—
280C11×#106C2312yes—
281C11×#106C2312yes—
282C11×#106C2312yes—
283C11×C4⋊C8C2312yes—
284C11×C4⋊C8C2312yes—
285C11×C4⋊C8C2312yes—
286C11×C4⋊C8C2312yes—
287C11×C4⋊C8C2312yes—
288C11×C4⋊C8C2312yes—
289C11×#103C2311yescharacteristic
290C11×#103C2311yescharacteristic
291C11×#103C2311yescharacteristic
292C11×#103C2311yescharacteristic
293C11×#103C2312yes—
294C11×#103C2312yes—
295C11×#103C2312yes—
296C11×#103C2312yes—
297C11×#102C2311yescharacteristic
298C11×#102C2311yescharacteristic
299C11×#102C2311yescharacteristic
300C11×#102C2311yescharacteristic
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2312yes—
304C11×#102C2312yes—
305C11×#97C2311yescharacteristic
306C11×#97C2311yescharacteristic
307C11×#97C2311yescharacteristic
308C11×#97C2311yescharacteristic
309C11×#97C2312yes—
310C11×#97C2312yes—
311C4×C8×C11C2312yes—
312C4×C8×C11C2312yes—
313#61380C1111yesmaximal, characteristic, direct product factor, Sylow
314C11×#41—22no—
315C11×#41—22no—
316C11×#41C2×Q814yes—
317C11×#41C2×Q814yescomplemented
318C2×Q8×C11—22no—
319C2×Q8×C11—22no—
320C2×Q8×C11—22no—
321C2×Q8×C11—22no—
322C2×Q8×C11—22no—
323C2×Q8×C11—22no—
324C2×Q8×C11—82no—
325C2×Q8×C11—84no—
326C2×Q8×C11C2×D412yes—
327C2×Q8×C11C2×D412yes—
328C2×Q8×C11C2411yescharacteristic
329C2×Q8×C11C2411yescharacteristic
330C2×D4×C11—21no—
331C2×D4×C11—21no—
332C2×D4×C11C2411yescharacteristic
333C2×D4×C11C2411yescharacteristic
334C22×C4×C11—21no—
335C22×C4×C11—21no—
336C22×C4×C11—21no—
337C22×C4×C11—21no—
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11—21no—
341C22×C4×C11—21no—
342C22×C4×C11—21no—
343C22×C4×C11—21no—
344C22×C4×C11—22no—
345C22×C4×C11—22no—
346C22×C4×C11—22no—
347C22×C4×C11—22no—
348C22×C4×C11C2×D411yescharacteristic
349C22×C4×C11C2×D411yescharacteristic
350C22×C4×C11C2411yescharacteristic
351C11×Q16C2×Q814yescomplemented
352C11×SD16C2×Q814yescomplemented
353C11×SD16C2×Q814yescomplemented
354C11×D8C2×Q814yescomplemented
355C11×M16—22no—
356C11×M16—22no—
357C2×C8×C11—22no—
358C2×C8×C11C2×Q814yescomplemented
359C2×C8×C11C2412yes—
360C2×C8×C11C2412yes—
361C2×C8×C11C2411yescharacteristic
362C2×C8×C11C2411yescharacteristic
363C2×C8×C11C2411yescharacteristic
364C2×C8×C11C2411yescharacteristic
365C11×C4⋊C4—22no—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—21no—
369C11×C4⋊C4—21no—
370C11×C4⋊C4—21no—
371C11×C4⋊C4—21no—
372C11×C4⋊C4—22no—
373C11×C4⋊C4—22no—
374C11×C4⋊C4—22no—
375C11×C4⋊C4—22no—
376C11×C4⋊C4—22no—
377C11×C4⋊C4—22no—
378C11×C4⋊C4—22no—
379C11×C4⋊C4—22no—
380C11×C4⋊C4—22no—
381C11×C4⋊C4—22no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4—21no—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4C2×D411yescharacteristic
396C11×C4⋊C4C2×D411yescharacteristic
397C11×C4⋊C4C2×D411yescharacteristic
398C11×C4⋊C4C2×D412yes—
399C11×C4⋊C4C2×D412yes—
400C11×C4⋊C4C2×D412yes—
401C11×C4⋊C4C2×D411yescharacteristic
402C11×C4⋊C4C2×D412yes—
403C11×C4⋊C4C2×D412yes—
404C11×C4⋊C4C2×D412yes—
405C11×C4⋊C4C2412yes—
406C11×C4⋊C4C2411yescharacteristic
407C11×C4⋊C4C2412yes—
408C11×C4⋊C4C2412yes—
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2411yescharacteristic
411C11×C4⋊C4C2412yes—
412C11×C4⋊C4C2411yescharacteristic
413C11×C22⋊C4—21no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—21no—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—21no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4C2×D412yes—
424C11×C22⋊C4C2×D412yes—
425C42×C11—21no—
426C42×C11—21no—
427C42×C11—21no—
428C42×C11—21no—
429C42×C11—21no—
430C42×C11—21no—
431C42×C11—22no—
432C42×C11—22no—
433C42×C11—22no—
434C42×C11—22no—
435C42×C11C2×D411yescharacteristic
436C42×C11C2×D411yescharacteristic
437C42×C11C2412yes—
438C42×C11C2412yes—
439C42×C11C2411yescharacteristic
440C42×C11C2411yescharacteristic
441#3504C2×C1111yescharacteristic, complemented
442#3503C2×C1111yescharacteristic, complemented
443#3390C2×C1112yescomplemented
444#3389C2×C1112yescomplemented
445#3388C2×C1112yescomplemented
446#3388C2×C1112yescomplemented
447#3387C2×C1112yescomplemented
448#3386C2×C1112yescomplemented
449#3385C2×C1112yescomplemented
450#3384C2×C1112yescomplemented
451#3164C2×C1111yescharacteristic, complemented
452#3163C2×C1111yescharacteristic, complemented
453C2×#501C2×C1111yescharacteristic, complemented
454#3084C2×C1111yescharacteristic, complemented
455#3084C2×C1111yescharacteristic, complemented
456#3083C2×C1111yescharacteristic, complemented
457#3083C2×C1111yescharacteristic, complemented
458#3080C2×C1111yescharacteristic, complemented
459#3079C2×C1111yescharacteristic, complemented
460#2961C2×C1111yescharacteristic, complemented
461#2952C2×C1111yescharacteristic
462#2951C2×C1111yescharacteristic
463#2943C2×C1111yescharacteristic
464C23×C11—21no—
465C23×C11—21no—
466C23×C11C22×D411yescharacteristic
467Q8×C11—21no—
468Q8×C11—21no—
469Q8×C11—42no—
470Q8×C11—42no—
471Q8×C11—44no—
472Q8×C11—82no—
473Q8×C11—82no—
474Q8×C11—82no—
475Q8×C11—82no—
476Q8×C11—82no—
477Q8×C11C22×Q812yes—
478Q8×C11C22×Q812yes—
479D4×C11—24no—
480D4×C11—24no—
481D4×C11—21no—
482D4×C11—21no—
483D4×C11C22×Q812yes—
484D4×C11C22×Q812yes—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—24no—
488C2×C4×C11—24no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—42no—
500C2×C4×C11—42no—
501C2×C4×C11—81no—
502C2×C4×C11—82no—
503C2×C4×C11—81no—
504C2×C4×C11—82no—
505C2×C4×C11—82no—
506C2×C4×C11—82no—
507C2×C4×C11—81no—
508C2×C4×C11—81no—
509C2×C4×C11—81no—
510C2×C4×C11—81no—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C22×D411yescharacteristic
513C2×C4×C11C22×D411yescharacteristic
514C2×C4×C11C22×D411yescharacteristic
515C2×C4×C11C22×D411yescharacteristic
516C2×C4×C11C22×D412yes—
517C2×C4×C11C22×D412yes—
518C2×C4×C11C22×D412yes—
519C2×C4×C11C22×D411yescharacteristic
520C2×C4×C11C22×Q812yes—
521C2×C4×C112−1+412yes—
522C2×C4×C11C2511yescharacteristic
523C8×C11—21no—
524C8×C11—21no—
525C8×C11—22no—
526C8×C11—22no—
527C8×C11C22×Q812yes—
528C8×C11C22×Q812yes—
529C2×#135C22×C1111yescharacteristic
530Q82C22×C1112yes—
531#557C22×C1112yes—
532#557C22×C1112yes—
533#557C22×C1112yes—
534#554—22no—
535#554—22no—
536#554—22no—
537#554C22×C1112yes—
538#554C22×C1112yes—
539#554C22×C1112yes—
540D4×Q8—22no—
541D4×Q8C22×C1112yes—
542#544—21no—
543#544—21no—
544#544—21no—
545#544—21no—
546#544C22×C1111yescharacteristic
547#544C22×C1111yescharacteristic
548#544C22×C1111yescharacteristic
549#544C22×C1111yescharacteristic
550#533—21no—
551#533—21no—
552#533C22×C1111yescharacteristic
553C2×C4⋊Q8—21no—
554C2×C4⋊Q8C22×C1111yescharacteristic
555C2×#125—21no—
556C2×#125C22×C1111yescharacteristic
557#520C22×C1111yescharacteristic
558#520C22×C1111yescharacteristic
559#520C22×C1111yescharacteristic
560#520C22×C1111yescharacteristic
561C4×#41C22×C1111yescharacteristic
562C4×#41C22×C1111yescharacteristic
563#501C22×C1112yes—
564#501C22×C1112yes—
565#501C22×C1112yes—
566#501C22×C1112yes—
567#501C22×C1112yes—
568#501C22×C1112yes—
569#501C22×C1112yes—
570#501C22×C1112yes—
571#500C22×C1112yes—
572#499C22×C1112yes—
573#499C22×C1112yes—
574#498C22×C1112yes—
575#479C22×C1112yes—
576#479C22×C1112yes—
577#479C22×C1112yes—
578#479C22×C1112yes—
579#479C22×C1112yes—
580#479C22×C1112yes—
581#478C22×C1112yes—
582#478C22×C1112yes—
583#478C22×C1112yes—
584#478C22×C1112yes—
585#478C22×C1112yes—
586#478C22×C1112yes—
587#477C22×C1112yes—
588#477C22×C1112yes—
589#477C22×C1112yes—
590#476C22×C1112yes—
591#476C22×C1112yes—
592#476C22×C1112yes—
593#475C22×C1112yes—
594#475C22×C1112yes—
595#475C22×C1112yes—
596#474C22×C1112yes—
597#474C22×C1112yes—
598#474C22×C1112yes—
599#446C22×C1112yes—
600#446C22×C1112yes—
601#446C22×C1112yes—
602#446C22×C1112yes—
603#442C22×C1111yescharacteristic
604#442C22×C1112yes—
605#442C22×C1111yescharacteristic
606#441C22×C1111yescharacteristic
607#441C22×C1112yes—
608#441C22×C1111yescharacteristic
609#440C22×C1111yescharacteristic
610#440C22×C1112yes—
611#440C22×C1111yescharacteristic
612#440C22×C1112yes—
613#440C22×C1111yescharacteristic
614#440C22×C1111yescharacteristic
615C4×Q16C22×C1112yes—
616C4×SD16C22×C1112yes—
617C4×SD16C22×C1112yes—
618C4×D8C22×C1112yes—
619#428C22×C1111yescharacteristic
620#428C22×C1111yescharacteristic
621#428C22×C1111yescharacteristic
622#428C22×C1111yescharacteristic
623#427C22×C1111yescharacteristic
624C2×#107C22×C1111yescharacteristic
625C2×#107C22×C1111yescharacteristic
626C2×#106C22×C1111yescharacteristic
627C2×#106C22×C1111yescharacteristic
628#424C22×C1111yescharacteristic
629#424C22×C1111yescharacteristic
630#423C22×C1111yescharacteristic
631#417C22×C1111yescharacteristic
632#417C22×C1111yescharacteristic
633#417C22×C1111yescharacteristic
634#417C22×C1111yescharacteristic
635#416C22×C1111yescharacteristic
636#416C22×C1111yescharacteristic
637#405C22×C1111yescharacteristic
638#405C22×C1111yescharacteristic
639C2×#97C22×C1111yescharacteristic
640C22×C11—21no—
641C22×C11—21no—
642C22×C11—22no—
643C22×C11—22no—
644C22×C11—41no—
645C22×C11—41no—
646C22×C11—41no—
647C22×C11—41no—
648C22×C11D4×Q812yes—
649C22×C11C23×D411yescharacteristic
650C4×C11—21no—
651C4×C11—21no—
652C4×C11—22no—
653C4×C11—22no—
654C4×C11—21no—
655C4×C11—21no—
656C4×C11—22no—
657C4×C11—22no—
658C4×C11—22no—
659C4×C11—22no—
660C4×C11—41no—
661C4×C11—42no—
662C4×C11—42no—
663C4×C11—42no—
664C4×C11—41no—
665C4×C11—41no—
666C4×C11—42no—
667C4×C11—41no—
668C4×C11D4×Q812yes—
669C4×C11C23×Q811yescharacteristic
670C4×C11C2×2−1+411yescharacteristic
671C2×#41C23×C1111yescharacteristic
672C2×#41C23×C1111yescharacteristic
673C22×Q8—22no—
674C22×Q8—21no—
675#135Q8×C1118yescomplemented
676C2×Q16C23×C1111yescharacteristic
677C2×SD16C23×C1111yescharacteristic
678C2×SD16C23×C1111yescharacteristic
679C2×D8C23×C1111yescharacteristic
680C2×M16C23×C1111yescharacteristic
681C2×M16C23×C1111yescharacteristic
682C22×C8C23×C1111yescharacteristic
683C22×C8C23×C1111yescharacteristic
684C4⋊Q8—22no—
685C4⋊Q8—22no—
686C4⋊Q8—22no—
687C4⋊Q8—21no—
688C4⋊Q8—21no—
689C4⋊Q8—22no—
690C4⋊Q8—21no—
691C4⋊Q8—21no—
692C4⋊Q8—22no—
693C4⋊Q8—22no—
694C4⋊Q8—21no—
695C4⋊Q8—21no—
696C4⋊Q8D4×C1111yescharacteristic
697C4⋊Q8D4×C1111yescharacteristic
698C4⋊Q8C23×C1112yes—
699C4⋊Q8C23×C1112yes—
700C4⋊Q8C23×C1112yes—
701C4⋊Q8C23×C1112yes—
702C4⋊Q8C23×C1112yes—
703C4⋊Q8C23×C1112yes—
704#125—21no—
705#125—21no—
706#125—22no—
707#125—22no—
708#125—21no—
709#125—21no—
710#125—22no—
711#125—22no—
712#125—22no—
713#125—22no—
714#125—21no—
715#125—21no—
716#125D4×C1111yescharacteristic
717#125D4×C1111yescharacteristic
718#125C23×C1112yes—
719#125C23×C1112yes—
720#125C23×C1112yes—
721#125C23×C1112yes—
722#125C23×C1112yes—
723#125C23×C1112yes—
724C22⋊Q8—22no—
725C22⋊Q8—22no—
726C22⋊Q8—22no—
727C22⋊Q8—22no—
728C22⋊Q8—22no—
729C22⋊Q8—22no—
730C22⋊Q8—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—22no—
735C22⋊Q8—22no—
736C22⋊Q8—22no—
737C22⋊Q8—22no—
738C22⋊Q8—22no—
739C22⋊Q8—22no—
740C22⋊Q8D4×C1112yes—
741C22⋊Q8D4×C1112yes—
742C4×Q8—22no—
743C4×Q8—22no—
744C4×Q8—22no—
745C4×Q8—22no—
746C4×Q8C23×C1111yescharacteristic
747C4×Q8C23×C1111yescharacteristic
748C4×Q8C23×C1111yescharacteristic
749C4×Q8C23×C1111yescharacteristic
750C4×Q8C23×C1112yes—
751C4×Q8C23×C1112yes—
752C4×Q8C23×C1112yes—
753C4×Q8C23×C1112yes—
754C4×Q8C23×C1112yes—
755C4×Q8C23×C1112yes—
756C4×D4—21no—
757C4×D4—21no—
758C4×D4—21no—
759C4×D4—21no—
760C4×D4—22no—
761C4×D4—22no—
762C4×D4—22no—
763C4×D4—22no—
764C4×D4C23×C1111yescharacteristic
765C4×D4C23×C1111yescharacteristic
766C4×D4C23×C1111yescharacteristic
767C4×D4C23×C1111yescharacteristic
768C4×D4C23×C1112yes—
769C4×D4C23×C1112yes—
770C4×D4C23×C1112yes—
771C4×D4C23×C1112yes—
772#117—21no—
773#117—21no—
774#117—21no—
775#117—21no—
776#117—21no—
777#117—21no—
778#117C23×C1111yescharacteristic
779#117C23×C1111yescharacteristic
780#117C23×C1111yescharacteristic
781#117C23×C1111yescharacteristic
782C2×C4⋊C4—21no—
783C2×C4⋊C4—21no—
784C2×C4⋊C4—21no—
785C2×C4⋊C4—21no—
786C2×C4⋊C4—21no—
787C2×C4⋊C4—21no—
788C2×C4⋊C4—21no—
789C2×C4⋊C4—22no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4C23×C1111yescharacteristic
793C2×C4⋊C4C23×C1111yescharacteristic
794C2×C4⋊C4C23×C1111yescharacteristic
795C2×C4⋊C4C23×C1111yescharacteristic
796C2×C42—21no—
797C2×C42—21no—
798C2×C42C23×C1111yescharacteristic
799#107C23×C1112yes—
800#107C23×C1112yes—
801#107C23×C1112yes—
802#107C23×C1112yes—
803#107C23×C1111yescharacteristic
804#107C23×C1111yescharacteristic
805#107C23×C1112yes—
806#107C23×C1112yes—
807#107C23×C1112yes—
808#107C23×C1112yes—
809#106C23×C1112yes—
810#106C23×C1112yes—
811#106C23×C1112yes—
812#106C23×C1112yes—
813#106C23×C1111yescharacteristic
814#106C23×C1111yescharacteristic
815#106C23×C1112yes—
816#106C23×C1112yes—
817#106C23×C1112yes—
818#106C23×C1112yes—
819C4⋊C8C23×C1112yes—
820C4⋊C8C23×C1112yes—
821C4⋊C8C23×C1112yes—
822C4⋊C8C23×C1112yes—
823C4⋊C8C23×C1112yes—
824C4⋊C8C23×C1112yes—
825#103C23×C1111yescharacteristic
826#103C23×C1111yescharacteristic
827#103C23×C1111yescharacteristic
828#103C23×C1111yescharacteristic
829#103C23×C1112yes—
830#103C23×C1112yes—
831#103C23×C1112yes—
832#103C23×C1112yes—
833#102C23×C1111yescharacteristic
834#102C23×C1111yescharacteristic
835#102C23×C1111yescharacteristic
836#102C23×C1111yescharacteristic
837#102C23×C1112yes—
838#102C23×C1112yes—
839#102C23×C1112yes—
840#102C23×C1112yes—
841#97C23×C1111yescharacteristic
842#97C23×C1111yescharacteristic
843#97C23×C1111yescharacteristic
844#97C23×C1111yescharacteristic
845#97C23×C1112yes—
846#97C23×C1112yes—
847C4×C8C23×C1112yes—
848C4×C8C23×C1112yes—
849C2×C11—22no—
850C2×C11—42no—
851C2×C11—42no—
852C2×C11C2×D4×Q811yescharacteristic
853C2×C11#358511yescharacteristic
854C2×C11#358611yescharacteristic
855#41—22no—
856#41—22no—
857#41C2×Q8×C1114yes—
858#41C2×Q8×C1114yescomplemented
859C2×Q8—22no—
860C2×Q8—22no—
861C2×Q8—22no—
862C2×Q8—22no—
863C2×Q8—22no—
864C2×Q8—22no—
865C2×Q8—82no—
866C2×Q8—84no—
867C2×Q8C2×D4×C1112yes—
868C2×Q8C2×D4×C1112yes—
869C2×Q8C24×C1111yescharacteristic
870C2×Q8C24×C1111yescharacteristic
871C2×D4—21no—
872C2×D4—21no—
873C2×D4C24×C1111yescharacteristic
874C2×D4C24×C1111yescharacteristic
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4C2×D4×C1111yescharacteristic
890C22×C4C2×D4×C1111yescharacteristic
891C22×C4C24×C1111yescharacteristic
892Q16C2×Q8×C1114yescomplemented
893SD16C2×Q8×C1114yescomplemented
894SD16C2×Q8×C1114yescomplemented
895D8C2×Q8×C1114yescomplemented
896M16—22no—
897M16—22no—
898C2×C8—22no—
899C2×C8C2×Q8×C1114yescomplemented
900C2×C8C24×C1112yes—
901C2×C8C24×C1112yes—
902C2×C8C24×C1111yescharacteristic
903C2×C8C24×C1111yescharacteristic
904C2×C8C24×C1111yescharacteristic
905C2×C8C24×C1111yescharacteristic
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—22no—
914C4⋊C4—22no—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4C2×D4×C1111yescharacteristic
937C4⋊C4C2×D4×C1111yescharacteristic
938C4⋊C4C2×D4×C1111yescharacteristic
939C4⋊C4C2×D4×C1112yes—
940C4⋊C4C2×D4×C1112yes—
941C4⋊C4C2×D4×C1112yes—
942C4⋊C4C2×D4×C1111yescharacteristic
943C4⋊C4C2×D4×C1112yes—
944C4⋊C4C2×D4×C1112yes—
945C4⋊C4C2×D4×C1112yes—
946C4⋊C4C24×C1112yes—
947C4⋊C4C24×C1111yescharacteristic
948C4⋊C4C24×C1112yes—
949C4⋊C4C24×C1112yes—
950C4⋊C4C24×C1111yescharacteristic
951C4⋊C4C24×C1111yescharacteristic
952C4⋊C4C24×C1112yes—
953C4⋊C4C24×C1111yescharacteristic
954C22⋊C4—21no—
955C22⋊C4—21no—
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—21no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4C2×D4×C1112yes—
965C22⋊C4C2×D4×C1112yes—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—22no—
976C42C2×D4×C1111yescharacteristic
977C42C2×D4×C1111yescharacteristic
978C42C24×C1112yes—
979C42C24×C1112yes—
980C42C24×C1111yescharacteristic
981C42C24×C1111yescharacteristic
982C11#6138011yescharacteristic, direct product factor, Sylow
983C23—21no—
984C23—21no—
985C23C22×D4×C1111yescharacteristic
986Q8—21no—
987Q8—21no—
988Q8—42no—
989Q8—42no—
990Q8—44no—
991Q8—82no—
992Q8—82no—
993Q8—82no—
994Q8—82no—
995Q8—82no—
996Q8C22×Q8×C1112yes—
997Q8C22×Q8×C1112yes—
998D4—24no—
999D4—24no—
1000D4—21no—
1001D4—21no—
1002D4C22×Q8×C1112yes—
1003D4C22×Q8×C1112yes—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—81no—
1021C2×C4—82no—
1022C2×C4—81no—
1023C2×C4—82no—
1024C2×C4—82no—
1025C2×C4—82no—
1026C2×C4—81no—
1027C2×C4—81no—
1028C2×C4—81no—
1029C2×C4—81no—
1030C2×C4C22×D4×C1112yes—
1031C2×C4C22×D4×C1111yescharacteristic
1032C2×C4C22×D4×C1111yescharacteristic
1033C2×C4C22×D4×C1111yescharacteristic
1034C2×C4C22×D4×C1111yescharacteristic
1035C2×C4C22×D4×C1112yes—
1036C2×C4C22×D4×C1112yes—
1037C2×C4C22×D4×C1112yes—
1038C2×C4C22×D4×C1111yescharacteristic
1039C2×C4C22×Q8×C1112yes—
1040C2×C4C11×2−1+412yes—
1041C2×C4C25×C1111yescharacteristic
1042C8—21no—
1043C8—21no—
1044C8—22no—
1045C8—22no—
1046C8C22×Q8×C1112yes—
1047C8C22×Q8×C1112yes—
1048C22—21no—
1049C22—21no—
1050C22—22no—
1051C22—22no—
1052C22—41no—
1053C22—41no—
1054C22—41no—
1055C22—41no—
1056C22D4×Q8×C1112yes—
1057C22C23×D4×C1111yescharacteristic
1058C4—22no—
1059C4—22no—
1060C4—21no—
1061C4—21no—
1062C4—22no—
1063C4—22no—
1064C4—21no—
1065C4—21no—
1066C4—22no—
1067C4—22no—
1068C4—41no—
1069C4—42no—
1070C4—42no—
1071C4—42no—
1072C4—41no—
1073C4—41no—
1074C4—42no—
1075C4—41no—
1076C4D4×Q8×C1112yes—
1077C4C23×Q8×C1111yescharacteristic
1078C4C2×C11×2−1+411yescharacteristic
1079C2—22no—
1080C2—42no—
1081C2—42no—
1082C2C2×D4×Q8×C1111yescharacteristic
1083C2C11×#358511yescharacteristic
1084C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#135C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3504C2semidirect
2. C11×#3503C2semidirect
3. C11×#3390C2semidirect
4. C11×#3389C2semidirect
5. C11×#3388C2semidirect
6. C11×#3388C2semidirect
7. C11×#3387C2semidirect
8. C11×#3386C2semidirect
9. C11×#3385C2semidirect
10. C11×#3384C2semidirect
11. C11×#3164C2semidirect
12. C11×#3163C2semidirect
13. C2×C11×#501C2semidirect
14. C11×#3084C2semidirect
15. C11×#3084C2semidirect
16. C11×#3083C2semidirect
17. C11×#3083C2semidirect
18. C11×#3080C2semidirect
19. C11×#3079C2semidirect
20. C11×#2961C2semidirect
139. C11×#135Q8semidirect
313. #61380C11direct (N × H)
317. C11×#41C2×Q8semidirect
351. C11×Q16C2×Q8semidirect
352. C11×SD16C2×Q8semidirect
353. C11×SD16C2×Q8semidirect
354. C11×D8C2×Q8semidirect
358. C2×C8×C11C2×Q8semidirect
441. #3504C2×C11semidirect
442. #3503C2×C11semidirect
443. #3390C2×C11semidirect
444. #3389C2×C11semidirect
445. #3388C2×C11semidirect
446. #3388C2×C11semidirect
447. #3387C2×C11semidirect
448. #3386C2×C11semidirect
449. #3385C2×C11semidirect
450. #3384C2×C11semidirect
451. #3164C2×C11semidirect
452. #3163C2×C11semidirect
453. C2×#501C2×C11semidirect
454. #3084C2×C11semidirect
455. #3084C2×C11semidirect
456. #3083C2×C11semidirect
457. #3083C2×C11semidirect
458. #3080C2×C11semidirect
459. #3079C2×C11semidirect
460. #2961C2×C11semidirect
675. #135Q8×C11semidirect
858. #41C2×Q8×C11semidirect
892. Q16C2×Q8×C11semidirect
893. SD16C2×Q8×C11semidirect
894. SD16C2×Q8×C11semidirect
895. D8C2×Q8×C11semidirect
899. C2×C8C2×Q8×C11semidirect
982. C11#61380direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35042
C11×#35032
C11×#33902
C11×#33892
C11×#33882
C11×#33872
C11×#33862
C11×#33852
C11×#33842
C11×#31642
C11×#31632
C2×C11×#5012
C11×#30842
C11×#30832
C11×#30802
C11×#30792
C11×#29612
C11×#29522
C11×#29512
C11×#29432
#6138011