Finite Group Databasebeta

← C11×#61385 #14638578

Subgroups — C11×#61385 #14638578

Order 2816.

1758 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×#3501C211yesmaximal, characteristic, complemented
3C11×#3389C212yesmaximal, complemented
4C11×#3389C212yesmaximal, complemented
5C11×#3388C212yesmaximal, complemented
6C11×#3388C212yesmaximal, complemented
7C11×#3386C212yesmaximal, complemented
8C11×#3384C212yesmaximal, complemented
9C11×#3381C212yesmaximal, complemented
10C11×#3380C212yesmaximal, complemented
11C11×#3166C211yesmaximal, characteristic, complemented
12C11×#3164C211yesmaximal, characteristic, complemented
13C11×#3163C211yesmaximal, characteristic, complemented
14C11×#3084C211yesmaximal, characteristic, complemented
15C11×#3083C211yesmaximal, characteristic, complemented
16C11×#3081C211yesmaximal, characteristic, complemented
17C11×#3081C211yesmaximal, characteristic, complemented
18C11×#3076C211yesmaximal, characteristic, complemented
19C2×C11×#478C211yesmaximal, characteristic, complemented
20C11×#2962C211yesmaximal, characteristic, complemented
21C11×#2946C211yesmaximal, characteristic
22C11×#2946C211yesmaximal, characteristic
23C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
24C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
25C11×#557C2212yescomplemented
26C11×#557C2212yescomplemented
27C11×#554—21no—
28C11×#554—21no—
29C11×#554—21no—
30C11×#554—22no—
31C11×#554—22no—
32C11×#554C2212yes—
33C11×#554C2212yes—
34C11×#554C2212yes—
35C11×#554C2212yescomplemented
36C11×#554C2212yescomplemented
37D4×Q8×C11—21no—
38D4×Q8×C11C2212yes—
39C11×#544—21no—
40C11×#544—21no—
41C11×#544C2211yescharacteristic
42C11×#544C2211yescharacteristic
43C11×#544C2211yescharacteristic
44C11×#544C2211yescharacteristic
45C11×#543—22no—
46C11×#533—21no—
47C11×#533C2211yescharacteristic
48C11×#533C2211yescharacteristic
49C2×C11×#125—21no—
50C2×C11×#125C2211yescharacteristic
51C2×C11×C22⋊Q8—22no—
52C11×#520C2211yescharacteristic
53C11×#520C2211yescharacteristic
54C11×#518C2211yescharacteristic
55C11×#518C2211yescharacteristic
56C4×C11×#41C2211yescharacteristic
57C2×C4×D4×C11C2211yescharacteristic
58C11×#501C2212yescomplemented
59C11×#501C2212yescomplemented
60C11×#501C2212yescomplemented
61C11×#501C2212yescomplemented
62C11×#501C2212yescomplemented
63C11×#501C2212yescomplemented
64C11×#500C2212yescomplemented
65C11×#499C2212yescomplemented
66C11×#499C2212yescomplemented
67C11×#499C2212yescomplemented
68C11×#499C2212yescomplemented
69C11×#498C2212yescomplemented
70C11×#479C2211yescharacteristic, complemented
71C11×#479C2211yescharacteristic, complemented
72C11×#479C2212yescomplemented
73C11×#479C2212yescomplemented
74C11×#478C2212yes—
75C11×#478C2212yes—
76C11×#478C2212yes—
77C11×#478C2212yes—
78C11×#478C2212yes—
79C11×#478C2212yes—
80C11×#478C2212yes—
81C11×#478C2212yes—
82C11×#478C2211yescharacteristic, complemented
83C11×#478C2211yescharacteristic, complemented
84C11×#478C2212yescomplemented
85C11×#478C2212yescomplemented
86C11×#477C2211yescharacteristic, complemented
87C11×#477C2212yescomplemented
88C11×#476C2212yes—
89C11×#476C2212yes—
90C11×#476C2211yescharacteristic, complemented
91C11×#476C2212yescomplemented
92C11×#475C2211yescharacteristic, complemented
93C11×#475C2212yescomplemented
94C11×#474C2212yes—
95C11×#474C2212yes—
96C11×#474C2211yescharacteristic, complemented
97C11×#474C2212yescomplemented
98C11×#446C2212yescomplemented
99C11×#446C2212yescomplemented
100C11×#446C2212yescomplemented
101C8×Q8×C11C2212yescomplemented
102C11×#442C2212yes—
103C11×#442C2212yes—
104C11×#442C2212yes—
105C11×#440C2212yes—
106C11×#440C2212yes—
107C11×#440C2212yes—
108C4×C11×SD16C2212yes—
109C4×C11×SD16C2212yes—
110C4×C11×SD16C2212yes—
111C4×C11×D8C2212yes—
112C4×C11×D8C2212yes—
113C4×C11×D8C2212yes—
114C11×#428C2211yescharacteristic
115C11×#428C2211yescharacteristic
116C11×#428C2211yescharacteristic
117C11×#428C2211yescharacteristic
118C11×#428C2211yescharacteristic
119C11×#427C2211yescharacteristic
120C11×#427C2211yescharacteristic
121C2×C11×#107C2211yescharacteristic
122C2×C11×#106C2211yescharacteristic
123C11×#424C2211yescharacteristic
124C11×#424C2211yescharacteristic
125C2×C11×C4⋊C8C2211yescharacteristic
126C11×#418C2211yescharacteristic
127C11×#417C2211yescharacteristic
128C11×#416C2211yescharacteristic
129C11×#416C2211yescharacteristic
130C2×C11×#102C2211yescharacteristic
131C2×C11×#102C2211yescharacteristic
132C11×#405C2211yescharacteristic
133C11×#405C2211yescharacteristic
134C4×C11×M16C2211yescharacteristic
135C2×C11×#41C2311yescharacteristic
136C22×Q8×C11—22no—
137C22×D4×C11C2311yescharacteristic
138C23×C4×C11—21no—
139C11×AGL(1,ℤ/8)Q818yescomplemented
140C2×C11×SD16C2312yes—
141C2×C11×D8C2312yes—
142C2×C11×M16C2311yescharacteristic
143C2×C11×M16C2311yescharacteristic
144C22×C8×C11C2311yescharacteristic
145C22×C8×C11C2311yescharacteristic
146C11×C4⋊Q8—22no—
147C11×C4⋊Q8—22no—
148C11×C4⋊Q8—21no—
149C11×C4⋊Q8—21no—
150C11×C4⋊Q8—21no—
151C11×C4⋊Q8—21no—
152C11×C4⋊Q8D411yescharacteristic
153C11×C4⋊Q8D411yescharacteristic
154C11×C4⋊Q8C2312yes—
155C11×C4⋊Q8C2312yes—
156C11×C4⋊Q8C2312yes—
157C11×C4⋊Q8C2312yes—
158C11×C4⋊Q8C2311yescharacteristic
159C11×C4⋊Q8C2311yescharacteristic
160C11×#125—21no—
161C11×#125—21no—
162C11×#125—22no—
163C11×#125—22no—
164C11×#125—22no—
165C11×#125—22no—
166C11×#125—21no—
167C11×#125—21no—
168C11×#125—21no—
169C11×#125—21no—
170C11×#125D411yescharacteristic
171C11×#125D411yescharacteristic
172C11×#125C2312yes—
173C11×#125C2311yescharacteristic
174C11×#125C2311yescharacteristic
175C11×#125C2312yes—
176C11×#125C2312yes—
177C11×#125C2312yes—
178C11×#125C2312yes—
179C11×#125C2312yes—
180C11×C22⋊Q8—22no—
181C11×C22⋊Q8—22no—
182C11×C22⋊Q8—22no—
183C11×C22⋊Q8—22no—
184C11×C22⋊Q8—22no—
185C11×C22⋊Q8—21no—
186C11×C22⋊Q8—21no—
187C11×C22⋊Q8—22no—
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—21no—
209C4×Q8×C11—21no—
210C4×Q8×C11C2311yescharacteristic
211C4×Q8×C11C2311yescharacteristic
212C4×Q8×C11C2312yes—
213C4×Q8×C11C2312yes—
214C4×Q8×C11C2312yes—
215C4×Q8×C11C2312yes—
216C4×D4×C11—21no—
217C4×D4×C11—21no—
218C4×D4×C11—21no—
219C4×D4×C11—21no—
220C4×D4×C11—21no—
221C4×D4×C11—21no—
222C4×D4×C11—22no—
223C4×D4×C11—22no—
224C4×D4×C11—21no—
225C4×D4×C11—21no—
226C4×D4×C11C2312yes—
227C4×D4×C11C2312yes—
228C4×D4×C11C2311yescharacteristic
229C4×D4×C11C2311yescharacteristic
230C4×D4×C11C2312yes—
231C4×D4×C11C2312yes—
232C4×D4×C11C2312yes—
233C4×D4×C11C2312yes—
234C4×D4×C11C2312yes—
235C4×D4×C11C2312yes—
236C11×#117—21no—
237C11×#117—21no—
238C11×#117—21no—
239C11×#117C2311yescharacteristic
240C11×#117C2311yescharacteristic
241C11×#117C2311yescharacteristic
242C11×#117C2311yescharacteristic
243C11×#117C2311yescharacteristic
244C2×C11×C4⋊C4—21no—
245C2×C11×C4⋊C4—21no—
246C2×C11×C4⋊C4—21no—
247C2×C11×C4⋊C4—21no—
248C2×C11×C4⋊C4—22no—
249C2×C11×C4⋊C4—22no—
250C2×C11×C4⋊C4—22no—
251C2×C11×C4⋊C4—22no—
252C2×C11×C4⋊C4—22no—
253C2×C11×C4⋊C4C2311yescharacteristic
254C2×C11×C4⋊C4C2311yescharacteristic
255C2×C11×C4⋊C4C2311yescharacteristic
256C2×C11×C22⋊C4—21no—
257C2×C11×C22⋊C4—22no—
258C2×C11×C22⋊C4—22no—
259C2×C42×C11—21no—
260C2×C42×C11C2311yescharacteristic
261C11×#107C2312yes—
262C11×#107C2311yescharacteristic
263C11×#107C2312yes—
264C11×#107C2312yes—
265C11×#107C2312yes—
266C11×#107C2312yes—
267C11×#107C2312yes—
268C11×#107C2311yescharacteristic
269C11×#107C2312yes—
270C11×#107C2311yescharacteristic
271C11×#107C2311yescharacteristic
272C11×#106C2311yescharacteristic
273C11×#106C2312yes—
274C11×#106C2312yes—
275C11×#106C2312yes—
276C11×#106C2312yes—
277C11×#106C2311yescharacteristic
278C11×#106C2312yes—
279C11×#106C2312yes—
280C11×#106C2312yes—
281C11×#106C2311yescharacteristic
282C11×#106C2311yescharacteristic
283C11×C4⋊C8C2311yescharacteristic
284C11×C4⋊C8C2311yescharacteristic
285C11×C4⋊C8C2311yescharacteristic
286C11×C4⋊C8C2311yescharacteristic
287C11×C4⋊C8C2312yes—
288C11×C4⋊C8C2312yes—
289C11×C4⋊C8C2312yes—
290C11×C4⋊C8C2312yes—
291C11×#103C2311yescharacteristic
292C11×#103C2311yescharacteristic
293C11×#103C2311yescharacteristic
294C11×#103C2311yescharacteristic
295C11×#103C2312yes—
296C11×#102C2312yes—
297C11×#102C2312yes—
298C11×#102C2312yes—
299C11×#102C2312yes—
300C11×#102C2311yescharacteristic
301C11×#102C2311yescharacteristic
302C11×#102C2311yescharacteristic
303C11×#102C2311yescharacteristic
304C11×#102C2312yes—
305C11×#102C2312yes—
306C11×#102C2312yes—
307C11×#97C2312yes—
308C11×#97C2312yes—
309C11×#97C2312yes—
310C4×C8×C11C2312yes—
311C4×C8×C11C2312yes—
312C4×C8×C11C2312yes—
313#61385C1111yesmaximal, characteristic, direct product factor, Sylow
314C24×C11—21no—
315C11×#41—22no—
316C11×#41C2×Q814yescomplemented
317C2×Q8×C11—21no—
318C2×Q8×C11—21no—
319C2×Q8×C11—22no—
320C2×Q8×C11—22no—
321C2×Q8×C11—22no—
322C2×Q8×C11—22no—
323C2×Q8×C11—84no—
324C2×Q8×C11C2×D412yes—
325C2×Q8×C11C2×D412yes—
326C2×Q8×C11C2411yescharacteristic
327C2×D4×C11—21no—
328C2×D4×C11—21no—
329C2×D4×C11—22no—
330C2×D4×C11C2×Q814yes—
331C2×D4×C11C2411yescharacteristic
332C2×D4×C11C2412yes—
333C22×C4×C11—21no—
334C22×C4×C11—21no—
335C22×C4×C11—21no—
336C22×C4×C11—21no—
337C22×C4×C11—22no—
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11—22no—
341C22×C4×C11—22no—
342C22×C4×C11—22no—
343C22×C4×C11—22no—
344C22×C4×C11—22no—
345C22×C4×C11—22no—
346C22×C4×C11—22no—
347C22×C4×C11—82no—
348C22×C4×C11C2×D411yescharacteristic
349C22×C4×C11C2×D411yescharacteristic
350C22×C4×C11C2411yescharacteristic
351C11×SD16C2×Q818yescomplemented
352C11×D8C2×Q818yescomplemented
353C11×M16—22no—
354C11×M16C2×Q814yescomplemented
355C2×C8×C11—22no—
356C2×C8×C11—22no—
357C2×C8×C11C2411yescharacteristic
358C2×C8×C11C2411yescharacteristic
359C2×C8×C11C2412yes—
360C2×C8×C11C2411yescharacteristic
361C2×C8×C11C2411yescharacteristic
362C2×C8×C11C2412yes—
363C11×C4⋊C4—21no—
364C11×C4⋊C4—21no—
365C11×C4⋊C4—21no—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—21no—
369C11×C4⋊C4—21no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—22no—
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—21no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4—21no—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4C2×D412yes—
393C11×C4⋊C4C2×D411yescharacteristic
394C11×C4⋊C4C2×D411yescharacteristic
395C11×C4⋊C4C2×D412yes—
396C11×C4⋊C4C2×D412yes—
397C11×C4⋊C4C2×D412yes—
398C11×C4⋊C4C2×D411yescharacteristic
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D412yes—
401C11×C4⋊C4C2×D412yes—
402C11×C4⋊C4C2412yes—
403C11×C4⋊C4C2411yescharacteristic
404C11×C4⋊C4C2412yes—
405C11×C4⋊C4C2411yescharacteristic
406C11×C4⋊C4C2412yes—
407C11×C4⋊C4C2411yescharacteristic
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2411yescharacteristic
411C11×C22⋊C4—21no—
412C11×C22⋊C4—21no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—21no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4C2×D412yes—
425C11×C22⋊C4C2×D412yes—
426C42×C11—21no—
427C42×C11—21no—
428C42×C11—21no—
429C42×C11—22no—
430C42×C11—22no—
431C42×C11—21no—
432C42×C11—21no—
433C42×C11C2×D411yescharacteristic
434C42×C11C2×D411yescharacteristic
435C42×C11C2411yescharacteristic
436C42×C11C2412yes—
437C42×C11C2412yes—
438C42×C11C2411yescharacteristic
439#3504C2×C1111yescharacteristic, complemented
440#3501C2×C1111yescharacteristic, complemented
441#3389C2×C1112yescomplemented
442#3389C2×C1112yescomplemented
443#3388C2×C1112yescomplemented
444#3388C2×C1112yescomplemented
445#3386C2×C1112yescomplemented
446#3384C2×C1112yescomplemented
447#3381C2×C1112yescomplemented
448#3380C2×C1112yescomplemented
449#3166C2×C1111yescharacteristic, complemented
450#3164C2×C1111yescharacteristic, complemented
451#3163C2×C1111yescharacteristic, complemented
452#3084C2×C1111yescharacteristic, complemented
453#3083C2×C1111yescharacteristic, complemented
454#3081C2×C1111yescharacteristic, complemented
455#3081C2×C1111yescharacteristic, complemented
456#3076C2×C1111yescharacteristic, complemented
457C2×#478C2×C1111yescharacteristic, complemented
458#2962C2×C1111yescharacteristic, complemented
459#2946C2×C1111yescharacteristic
460#2946C2×C1111yescharacteristic
461C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
462C23×C11—21no—
463C23×C11—22no—
464C23×C11—24no—
465C23×C11—81no—
466C23×C11—81no—
467C23×C11C22×D411yescharacteristic
468Q8×C11—21no—
469Q8×C11—42no—
470Q8×C11—42no—
471Q8×C11—42no—
472Q8×C11—81no—
473Q8×C11—82no—
474Q8×C11—82no—
475Q8×C11—82no—
476Q8×C11—82no—
477Q8×C11C22×Q812yes—
478D4×C11—24no—
479D4×C11—24no—
480D4×C11—22no—
481D4×C11—21no—
482D4×C11C22×Q812yes—
483D4×C11C22×Q814yes—
484C2×C4×C11—21no—
485C2×C4×C11—24no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—44no—
498C2×C4×C11—81no—
499C2×C4×C11—82no—
500C2×C4×C11—82no—
501C2×C4×C11—82no—
502C2×C4×C11—81no—
503C2×C4×C11—82no—
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×C11C22×D411yescharacteristic
511C2×C4×C11C22×D411yescharacteristic
512C2×C4×C11C22×D412yes—
513C2×C4×C11C22×D412yes—
514C2×C4×C11C22×D411yescharacteristic
515C2×C4×C11C22×D411yescharacteristic
516C2×C4×C11C22×D412yes—
517C2×C4×C11C22×D412yes—
518C2×C4×C11C22×D411yescharacteristic
519C2×C4×C11C22×Q812yes—
520C2×C4×C112−1+412yes—
521C2×C4×C11C2511yescharacteristic
522C8×C11—21no—
523C8×C11—21no—
524C8×C11—21no—
525C8×C11—21no—
526C8×C11—22no—
527C8×C11C22×Q814yes—
528C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
529#557C22×C1112yescomplemented
530#557C22×C1112yescomplemented
531#554—21no—
532#554—21no—
533#554—21no—
534#554—22no—
535#554—22no—
536#554C22×C1112yes—
537#554C22×C1112yes—
538#554C22×C1112yes—
539#554C22×C1112yescomplemented
540#554C22×C1112yescomplemented
541D4×Q8—21no—
542D4×Q8C22×C1112yes—
543#544—21no—
544#544—21no—
545#544C22×C1111yescharacteristic
546#544C22×C1111yescharacteristic
547#544C22×C1111yescharacteristic
548#544C22×C1111yescharacteristic
549#543—22no—
550#533—21no—
551#533C22×C1111yescharacteristic
552#533C22×C1111yescharacteristic
553C2×#125—21no—
554C2×#125C22×C1111yescharacteristic
555C2×C22⋊Q8—22no—
556#520C22×C1111yescharacteristic
557#520C22×C1111yescharacteristic
558#518C22×C1111yescharacteristic
559#518C22×C1111yescharacteristic
560C4×#41C22×C1111yescharacteristic
561C2×C4×D4C22×C1111yescharacteristic
562#501C22×C1112yescomplemented
563#501C22×C1112yescomplemented
564#501C22×C1112yescomplemented
565#501C22×C1112yescomplemented
566#501C22×C1112yescomplemented
567#501C22×C1112yescomplemented
568#500C22×C1112yescomplemented
569#499C22×C1112yescomplemented
570#499C22×C1112yescomplemented
571#499C22×C1112yescomplemented
572#499C22×C1112yescomplemented
573#498C22×C1112yescomplemented
574#479C22×C1111yescharacteristic, complemented
575#479C22×C1111yescharacteristic, complemented
576#479C22×C1112yescomplemented
577#479C22×C1112yescomplemented
578#478C22×C1112yes—
579#478C22×C1112yes—
580#478C22×C1112yes—
581#478C22×C1112yes—
582#478C22×C1112yes—
583#478C22×C1112yes—
584#478C22×C1112yes—
585#478C22×C1112yes—
586#478C22×C1111yescharacteristic, complemented
587#478C22×C1111yescharacteristic, complemented
588#478C22×C1112yescomplemented
589#478C22×C1112yescomplemented
590#477C22×C1111yescharacteristic, complemented
591#477C22×C1112yescomplemented
592#476C22×C1112yes—
593#476C22×C1112yes—
594#476C22×C1111yescharacteristic, complemented
595#476C22×C1112yescomplemented
596#475C22×C1111yescharacteristic, complemented
597#475C22×C1112yescomplemented
598#474C22×C1112yes—
599#474C22×C1112yes—
600#474C22×C1111yescharacteristic, complemented
601#474C22×C1112yescomplemented
602#446C22×C1112yescomplemented
603#446C22×C1112yescomplemented
604#446C22×C1112yescomplemented
605C8×Q8C22×C1112yescomplemented
606#442C22×C1112yes—
607#442C22×C1112yes—
608#442C22×C1112yes—
609#440C22×C1112yes—
610#440C22×C1112yes—
611#440C22×C1112yes—
612C4×SD16C22×C1112yes—
613C4×SD16C22×C1112yes—
614C4×SD16C22×C1112yes—
615C4×D8C22×C1112yes—
616C4×D8C22×C1112yes—
617C4×D8C22×C1112yes—
618#428C22×C1111yescharacteristic
619#428C22×C1111yescharacteristic
620#428C22×C1111yescharacteristic
621#428C22×C1111yescharacteristic
622#428C22×C1111yescharacteristic
623#427C22×C1111yescharacteristic
624#427C22×C1111yescharacteristic
625C2×#107C22×C1111yescharacteristic
626C2×#106C22×C1111yescharacteristic
627#424C22×C1111yescharacteristic
628#424C22×C1111yescharacteristic
629C2×C4⋊C8C22×C1111yescharacteristic
630#418C22×C1111yescharacteristic
631#417C22×C1111yescharacteristic
632#416C22×C1111yescharacteristic
633#416C22×C1111yescharacteristic
634C2×#102C22×C1111yescharacteristic
635C2×#102C22×C1111yescharacteristic
636#405C22×C1111yescharacteristic
637#405C22×C1111yescharacteristic
638C4×M16C22×C1111yescharacteristic
639C22×C11—21no—
640C22×C11—21no—
641C22×C11—22no—
642C22×C11—24no—
643C22×C11—41no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—41no—
647C22×C11—84no—
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—41no—
660C4×C11—41no—
661C4×C11—42no—
662C4×C11—41no—
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
672C22×Q8—22no—
673C22×D4C23×C1111yescharacteristic
674C23×C4—21no—
675AGL(1,ℤ/8)Q8×C1118yescomplemented
676C2×SD16C23×C1112yes—
677C2×D8C23×C1112yes—
678C2×M16C23×C1111yescharacteristic
679C2×M16C23×C1111yescharacteristic
680C22×C8C23×C1111yescharacteristic
681C22×C8C23×C1111yescharacteristic
682C4⋊Q8—22no—
683C4⋊Q8—22no—
684C4⋊Q8—21no—
685C4⋊Q8—21no—
686C4⋊Q8—21no—
687C4⋊Q8—21no—
688C4⋊Q8D4×C1111yescharacteristic
689C4⋊Q8D4×C1111yescharacteristic
690C4⋊Q8C23×C1111yescharacteristic
691C4⋊Q8C23×C1111yescharacteristic
692C4⋊Q8C23×C1112yes—
693C4⋊Q8C23×C1112yes—
694C4⋊Q8C23×C1112yes—
695C4⋊Q8C23×C1112yes—
696#125—21no—
697#125—21no—
698#125—22no—
699#125—22no—
700#125—22no—
701#125—22no—
702#125—21no—
703#125—21no—
704#125—21no—
705#125—21no—
706#125D4×C1111yescharacteristic
707#125D4×C1111yescharacteristic
708#125C23×C1112yes—
709#125C23×C1112yes—
710#125C23×C1111yescharacteristic
711#125C23×C1111yescharacteristic
712#125C23×C1112yes—
713#125C23×C1112yes—
714#125C23×C1112yes—
715#125C23×C1112yes—
716C22⋊Q8—22no—
717C22⋊Q8—22no—
718C22⋊Q8—22no—
719C22⋊Q8—22no—
720C22⋊Q8—22no—
721C22⋊Q8—21no—
722C22⋊Q8—21no—
723C22⋊Q8—22no—
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—21no—
745C4×Q8—21no—
746C4×Q8C23×C1111yescharacteristic
747C4×Q8C23×C1111yescharacteristic
748C4×Q8C23×C1112yes—
749C4×Q8C23×C1112yes—
750C4×Q8C23×C1112yes—
751C4×Q8C23×C1112yes—
752C4×D4—21no—
753C4×D4—21no—
754C4×D4—21no—
755C4×D4—21no—
756C4×D4—21no—
757C4×D4—21no—
758C4×D4—22no—
759C4×D4—22no—
760C4×D4—21no—
761C4×D4—21no—
762C4×D4C23×C1112yes—
763C4×D4C23×C1112yes—
764C4×D4C23×C1111yescharacteristic
765C4×D4C23×C1111yescharacteristic
766C4×D4C23×C1112yes—
767C4×D4C23×C1112yes—
768C4×D4C23×C1112yes—
769C4×D4C23×C1112yes—
770C4×D4C23×C1112yes—
771C4×D4C23×C1112yes—
772#117—21no—
773#117—21no—
774#117—21no—
775#117C23×C1111yescharacteristic
776#117C23×C1111yescharacteristic
777#117C23×C1111yescharacteristic
778#117C23×C1111yescharacteristic
779#117C23×C1111yescharacteristic
780C2×C4⋊C4—21no—
781C2×C4⋊C4—21no—
782C2×C4⋊C4—21no—
783C2×C4⋊C4—21no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—22no—
789C2×C4⋊C4C23×C1111yescharacteristic
790C2×C4⋊C4C23×C1111yescharacteristic
791C2×C4⋊C4C23×C1111yescharacteristic
792C2×C22⋊C4—21no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C42—21no—
796C2×C42C23×C1111yescharacteristic
797#107C23×C1112yes—
798#107C23×C1112yes—
799#107C23×C1111yescharacteristic
800#107C23×C1111yescharacteristic
801#107C23×C1111yescharacteristic
802#107C23×C1111yescharacteristic
803#107C23×C1112yes—
804#107C23×C1112yes—
805#107C23×C1112yes—
806#107C23×C1112yes—
807#107C23×C1112yes—
808#106C23×C1112yes—
809#106C23×C1112yes—
810#106C23×C1111yescharacteristic
811#106C23×C1111yescharacteristic
812#106C23×C1111yescharacteristic
813#106C23×C1111yescharacteristic
814#106C23×C1112yes—
815#106C23×C1112yes—
816#106C23×C1112yes—
817#106C23×C1112yes—
818#106C23×C1112yes—
819C4⋊C8C23×C1111yescharacteristic
820C4⋊C8C23×C1111yescharacteristic
821C4⋊C8C23×C1111yescharacteristic
822C4⋊C8C23×C1111yescharacteristic
823C4⋊C8C23×C1112yes—
824C4⋊C8C23×C1112yes—
825C4⋊C8C23×C1112yes—
826C4⋊C8C23×C1112yes—
827#103C23×C1111yescharacteristic
828#103C23×C1111yescharacteristic
829#103C23×C1111yescharacteristic
830#103C23×C1111yescharacteristic
831#103C23×C1112yes—
832#102C23×C1112yes—
833#102C23×C1112yes—
834#102C23×C1112yes—
835#102C23×C1112yes—
836#102C23×C1111yescharacteristic
837#102C23×C1111yescharacteristic
838#102C23×C1111yescharacteristic
839#102C23×C1111yescharacteristic
840#102C23×C1112yes—
841#102C23×C1112yes—
842#102C23×C1112yes—
843#97C23×C1112yes—
844#97C23×C1112yes—
845#97C23×C1112yes—
846C4×C8C23×C1112yes—
847C4×C8C23×C1112yes—
848C4×C8C23×C1112yes—
849C2×C11—22no—
850C2×C11—42no—
851C2×C11—44no—
852C2×C11C2×D4×Q811yescharacteristic
853C2×C11#358411yescharacteristic
854C2×C11#358511yescharacteristic
855C24—21no—
856#41—22no—
857#41C2×Q8×C1114yescomplemented
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—22no—
861C2×Q8—22no—
862C2×Q8—22no—
863C2×Q8—22no—
864C2×Q8—84no—
865C2×Q8C2×D4×C1112yes—
866C2×Q8C2×D4×C1112yes—
867C2×Q8C24×C1111yescharacteristic
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—22no—
871C2×D4C2×Q8×C1114yes—
872C2×D4C24×C1111yescharacteristic
873C2×D4C24×C1112yes—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—22no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—82no—
889C22×C4C2×D4×C1111yescharacteristic
890C22×C4C2×D4×C1111yescharacteristic
891C22×C4C24×C1111yescharacteristic
892SD16C2×Q8×C1118yescomplemented
893D8C2×Q8×C1118yescomplemented
894M16—22no—
895M16C2×Q8×C1114yescomplemented
896C2×C8—22no—
897C2×C8—22no—
898C2×C8C24×C1111yescharacteristic
899C2×C8C24×C1111yescharacteristic
900C2×C8C24×C1112yes—
901C2×C8C24×C1111yescharacteristic
902C2×C8C24×C1111yescharacteristic
903C2×C8C24×C1112yes—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—22no—
912C4⋊C4—22no—
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—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4C2×D4×C1112yes—
934C4⋊C4C2×D4×C1111yescharacteristic
935C4⋊C4C2×D4×C1111yescharacteristic
936C4⋊C4C2×D4×C1112yes—
937C4⋊C4C2×D4×C1112yes—
938C4⋊C4C2×D4×C1112yes—
939C4⋊C4C2×D4×C1111yescharacteristic
940C4⋊C4C2×D4×C1111yescharacteristic
941C4⋊C4C2×D4×C1112yes—
942C4⋊C4C2×D4×C1112yes—
943C4⋊C4C24×C1112yes—
944C4⋊C4C24×C1111yescharacteristic
945C4⋊C4C24×C1112yes—
946C4⋊C4C24×C1111yescharacteristic
947C4⋊C4C24×C1112yes—
948C4⋊C4C24×C1111yescharacteristic
949C4⋊C4C24×C1111yescharacteristic
950C4⋊C4C24×C1111yescharacteristic
951C4⋊C4C24×C1111yescharacteristic
952C22⋊C4—21no—
953C22⋊C4—21no—
954C22⋊C4—21no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—21no—
962C22⋊C4—21no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4C2×D4×C1112yes—
966C22⋊C4C2×D4×C1112yes—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—22no—
971C42—22no—
972C42—21no—
973C42—21no—
974C42C2×D4×C1111yescharacteristic
975C42C2×D4×C1111yescharacteristic
976C42C24×C1111yescharacteristic
977C42C24×C1112yes—
978C42C24×C1112yes—
979C42C24×C1111yescharacteristic
980C11#6138511yescharacteristic, direct product factor, Sylow
981C23—21no—
982C23—22no—
983C23—24no—
984C23—81no—
985C23—81no—
986C23C22×D4×C1111yescharacteristic
987Q8—21no—
988Q8—42no—
989Q8—42no—
990Q8—42no—
991Q8—81no—
992Q8—82no—
993Q8—82no—
994Q8—82no—
995Q8—82no—
996Q8C22×Q8×C1112yes—
997D4—24no—
998D4—24no—
999D4—22no—
1000D4—21no—
1001D4C22×Q8×C1112yes—
1002D4C22×Q8×C1114yes—
1003C2×C4—21no—
1004C2×C4—24no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—44no—
1017C2×C4—81no—
1018C2×C4—82no—
1019C2×C4—82no—
1020C2×C4—82no—
1021C2×C4—81no—
1022C2×C4—82no—
1023C2×C4—82no—
1024C2×C4—82no—
1025C2×C4—82no—
1026C2×C4—81no—
1027C2×C4—81no—
1028C2×C4—81no—
1029C2×C4C22×D4×C1111yescharacteristic
1030C2×C4C22×D4×C1111yescharacteristic
1031C2×C4C22×D4×C1112yes—
1032C2×C4C22×D4×C1112yes—
1033C2×C4C22×D4×C1111yescharacteristic
1034C2×C4C22×D4×C1111yescharacteristic
1035C2×C4C22×D4×C1112yes—
1036C2×C4C22×D4×C1112yes—
1037C2×C4C22×D4×C1111yescharacteristic
1038C2×C4C22×Q8×C1112yes—
1039C2×C4C11×2−1+412yes—
1040C2×C4C25×C1111yescharacteristic
1041C8—21no—
1042C8—21no—
1043C8—21no—
1044C8—21no—
1045C8—22no—
1046C8C22×Q8×C1114yes—
1047C22—21no—
1048C22—21no—
1049C22—22no—
1050C22—24no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—84no—
1056C22D4×Q8×C1112yes—
1057C22C23×D4×C1111yescharacteristic
1058C4—22no—
1059C4—21no—
1060C4—21no—
1061C4—22no—
1062C4—22no—
1063C4—21no—
1064C4—21no—
1065C4—22no—
1066C4—22no—
1067C4—41no—
1068C4—41no—
1069C4—42no—
1070C4—41no—
1071C4—42no—
1072C4—41no—
1073C4—41no—
1074C4—42no—
1075C4—41no—
1076C4D4×Q8×C1112yes—
1077C4C23×Q8×C1111yescharacteristic
1078C4C2×C11×2−1+411yescharacteristic
1079C2—22no—
1080C2—44no—
1081C2—42no—
1082C2C2×D4×Q8×C1111yescharacteristic
1083C2C11×#358411yescharacteristic
1084C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×AGL(1,ℤ/8)C22
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×#3501C2semidirect
3. C11×#3389C2semidirect
4. C11×#3389C2semidirect
5. C11×#3388C2semidirect
6. C11×#3388C2semidirect
7. C11×#3386C2semidirect
8. C11×#3384C2semidirect
9. C11×#3381C2semidirect
10. C11×#3380C2semidirect
11. C11×#3166C2semidirect
12. C11×#3164C2semidirect
13. C11×#3163C2semidirect
14. C11×#3084C2semidirect
15. C11×#3083C2semidirect
16. C11×#3081C2semidirect
17. C11×#3081C2semidirect
18. C11×#3076C2semidirect
19. C2×C11×#478C2semidirect
20. C11×#2962C2semidirect
25. C11×#557C22semidirect
26. C11×#557C22semidirect
35. C11×#554C22semidirect
36. C11×#554C22semidirect
58. C11×#501C22semidirect
59. C11×#501C22semidirect
60. C11×#501C22semidirect
61. C11×#501C22semidirect
62. C11×#501C22semidirect
63. C11×#501C22semidirect
64. C11×#500C22semidirect
65. C11×#499C22semidirect
66. C11×#499C22semidirect
67. C11×#499C22semidirect
68. C11×#499C22semidirect
69. C11×#498C22semidirect
70. C11×#479C22semidirect
71. C11×#479C22semidirect
72. C11×#479C22semidirect
73. C11×#479C22semidirect
82. C11×#478C22semidirect
83. C11×#478C22semidirect
84. C11×#478C22semidirect
85. C11×#478C22semidirect
86. C11×#477C22semidirect
87. C11×#477C22semidirect
90. C11×#476C22semidirect
91. C11×#476C22semidirect
92. C11×#475C22semidirect
93. C11×#475C22semidirect
96. C11×#474C22semidirect
97. C11×#474C22semidirect
98. C11×#446C22semidirect
99. C11×#446C22semidirect
100. C11×#446C22semidirect
101. C8×Q8×C11C22semidirect
139. C11×AGL(1,ℤ/8)Q8semidirect
313. #61385C11direct (N × H)
316. C11×#41C2×Q8semidirect
351. C11×SD16C2×Q8semidirect
352. C11×D8C2×Q8semidirect
354. C11×M16C2×Q8semidirect
439. #3504C2×C11semidirect
440. #3501C2×C11semidirect
441. #3389C2×C11semidirect
442. #3389C2×C11semidirect
443. #3388C2×C11semidirect
444. #3388C2×C11semidirect
445. #3386C2×C11semidirect
446. #3384C2×C11semidirect
447. #3381C2×C11semidirect
448. #3380C2×C11semidirect
449. #3166C2×C11semidirect
450. #3164C2×C11semidirect
451. #3163C2×C11semidirect
452. #3084C2×C11semidirect
453. #3083C2×C11semidirect
454. #3081C2×C11semidirect
455. #3081C2×C11semidirect
456. #3076C2×C11semidirect
457. C2×#478C2×C11semidirect
458. #2962C2×C11semidirect
529. #557C22×C11semidirect
530. #557C22×C11semidirect
539. #554C22×C11semidirect
540. #554C22×C11semidirect
562. #501C22×C11semidirect
563. #501C22×C11semidirect
564. #501C22×C11semidirect
565. #501C22×C11semidirect
566. #501C22×C11semidirect
567. #501C22×C11semidirect
568. #500C22×C11semidirect
569. #499C22×C11semidirect
570. #499C22×C11semidirect
571. #499C22×C11semidirect
572. #499C22×C11semidirect
573. #498C22×C11semidirect
574. #479C22×C11semidirect
575. #479C22×C11semidirect
576. #479C22×C11semidirect
577. #479C22×C11semidirect
586. #478C22×C11semidirect
587. #478C22×C11semidirect
588. #478C22×C11semidirect
589. #478C22×C11semidirect
590. #477C22×C11semidirect
591. #477C22×C11semidirect
594. #476C22×C11semidirect
595. #476C22×C11semidirect
596. #475C22×C11semidirect
597. #475C22×C11semidirect
600. #474C22×C11semidirect
601. #474C22×C11semidirect
602. #446C22×C11semidirect
603. #446C22×C11semidirect
604. #446C22×C11semidirect
605. C8×Q8C22×C11semidirect
675. AGL(1,ℤ/8)Q8×C11semidirect
857. #41C2×Q8×C11semidirect
892. SD16C2×Q8×C11semidirect
893. D8C2×Q8×C11semidirect
895. M16C2×Q8×C11semidirect
980. C11#61385direct (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×#35012
C11×#33892
C11×#33882
C11×#33862
C11×#33842
C11×#33812
C11×#33802
C11×#31662
C11×#31642
C11×#31632
C11×#30842
C11×#30832
C11×#30812
C11×#30762
C2×C11×#4782
C11×#29622
C11×#29462
C4×C11×AGL(1,ℤ/8)2
#6138511