Finite Group Databasebeta

← C11×#22057 #14599250

Subgroups — C11×#22057 #14599250

Order 2816.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#452C211yesmaximal, characteristic
2C11×#2323C211yesmaximal, characteristic, complemented
3C11×#2311C211yesmaximal, characteristic
4C11×#1973C211yesmaximal, characteristic, complemented
5C11×#1969C211yesmaximal, characteristic, complemented
6C11×#1935C211yesmaximal, characteristic, complemented
7C11×#1934C211yesmaximal, characteristic, complemented
8C11×#1928C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1880C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1872C211yesmaximal, characteristic, complemented
13C11×#1852C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic
15C11×#1750C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#452C418yescomplemented
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C11×#391C2211yescharacteristic
39C11×#391C2211yescharacteristic
40C11×#391C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#389—21no—
44C11×#389C2211yescharacteristic
45C11×#388—21no—
46C11×#388—21no—
47C11×#387—21no—
48C11×#386—21no—
49C11×#386—21no—
50C11×#380—21no—
51C11×#380—21no—
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C2×C11×#41—22no—
61C2×C11×#41—41no—
62C2×C11×#41—41no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41C2×C414yes—
66C22×Q8×C11C2311yescharacteristic
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C2×C11×Q16—41no—
74C2×C11×Q16—41no—
75C2×C11×Q16C2×C414yescomplemented
76C2×C11×SD16—41no—
77C2×C11×SD16—41no—
78C2×C11×SD16C2×C414yescomplemented
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8C2×C414yes—
85C4×Q8×C11—41no—
86C4×Q8×C11—41no—
87C11×#117—41no—
88C11×#117—41no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#107—41no—
115C11×#107—41no—
116C11×#103—41no—
117C11×#103—41no—
118C11×#103—41no—
119C11×#103—41no—
120C11×#103C2×C414yescomplemented
121C11×#102—41no—
122C11×#102—41no—
123C11×#102C2×C414yescomplemented
124C11×C22⋊C8—22no—
125C11×C22⋊C8C2×C414yes—
126C11×#97—41no—
127C4×C8×C11—41no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137#22057C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C11×#41—44no—
141C11×#41—44no—
142C11×#41—44no—
143C11×#41—44no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11C22×C412yes—
155C2×Q8×C11C22×C412yes—
156C2×D4×C11—24no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11C22×C412yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—24no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—81no—
181C22×C4×C11—81no—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11#4112yes—
189C22×C4×C11C2411yescharacteristic
190C11×Q16—44no—
191C11×SD16—44no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11C22×C412yes—
203C2×C8×C11C22×C412yes—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—41no—
215C11×C4⋊C4—41no—
216C11×C4⋊C4—42no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4—81no—
219C11×C4⋊C4C22×C412yes—
220C11×C22⋊C4—24no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—81no—
224C11×C22⋊C4—81no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C11×C22⋊C4—81no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—42no—
233C42×C11—81no—
234C2×#452C2×C1111yescharacteristic
235#2323C2×C1111yescharacteristic, complemented
236#2311C2×C1111yescharacteristic
237#1973C2×C1111yescharacteristic, complemented
238#1969C2×C1111yescharacteristic, complemented
239#1935C2×C1111yescharacteristic, complemented
240#1934C2×C1111yescharacteristic, complemented
241#1928C2×C1111yescharacteristic, complemented
242#1925C2×C1111yescharacteristic, complemented
243#1880C2×C1111yescharacteristic, complemented
244#1878C2×C1111yescharacteristic, complemented
245#1872C2×C1111yescharacteristic, complemented
246#1852C2×C1111yescharacteristic, complemented
247#1788C2×C1111yescharacteristic
248#1750C2×C1111yescharacteristic, complemented
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—22no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11C4×D412yes—
263C23×C11C22×D411yescharacteristic
264Q8×C11—22no—
265Q8×C11—22no—
266Q8×C11—22no—
267Q8×C11—22no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—41no—
271Q8×C11—41no—
272D4×C11—22no—
273D4×C11—22no—
274D4×C11—48no—
275D4×C11—41no—
276D4×C11—41no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—48no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—84no—
318C2×C4×C11C4×D412yes—
319C2×C4×C11C23×C411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C8×C11—22no—
326C8×C11—22no—
327C8×C11—41no—
328C8×C11—41no—
329C22×#41C22×C1111yescharacteristic
330C22×Q16C22×C1111yescharacteristic
331C22×SD16C22×C1111yescharacteristic
332C2×C22⋊Q8C22×C1111yescharacteristic
333C2×C4×Q8C22×C1111yescharacteristic
334C2×#117C22×C1111yescharacteristic
335C22×C4⋊C4C22×C1111yescharacteristic
336#452C4×C1118yescomplemented
337C2×#107C22×C1111yescharacteristic
338C2×#107C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#102C22×C1111yescharacteristic
345C2×#102C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×C22⋊C8C22×C1111yescharacteristic
348C2×C22⋊C8C22×C1111yescharacteristic
349C2×#97C22×C1111yescharacteristic
350C2×C4×C8C22×C1111yescharacteristic
351#391C22×C1111yescharacteristic
352#391C22×C1111yescharacteristic
353#391C22×C1111yescharacteristic
354#390C22×C1111yescharacteristic
355#390C22×C1111yescharacteristic
356#389—21no—
357#389C22×C1111yescharacteristic
358#388—21no—
359#388—21no—
360#387—21no—
361#386—21no—
362#386—21no—
363#380—21no—
364#380—21no—
365#380C22×C1111yescharacteristic
366C4×C4⋊C4C22×C1111yescharacteristic
367#340C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371#336C22×C1111yescharacteristic
372#336C22×C1111yescharacteristic
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11C2×C4×D411yescharacteristic
388C22×C11#53411yescharacteristic
389C22×C11#53511yescharacteristic
390C22×C11#57611yescharacteristic
391C22×C11#57711yescharacteristic
392C22×C11#57811yescharacteristic
393C22×C11#57811yescharacteristic
394C4×C11—22no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—42no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11#51811yescharacteristic
407C4×C11#51811yescharacteristic
408C4×C11#53811yescharacteristic
409C4×C11#53811yescharacteristic
410C2×#41—22no—
411C2×#41—41no—
412C2×#41—41no—
413C2×#41—41no—
414C2×#41—41no—
415C2×#41C2×C4×C1114yes—
416C22×Q8C23×C1111yescharacteristic
417C22×Q8C23×C1111yescharacteristic
418C22×D4—21no—
419C22×D4C23×C1111yescharacteristic
420C23×C4—21no—
421C23×C4—21no—
422C23×C4C23×C1111yescharacteristic
423C2×Q16—41no—
424C2×Q16—41no—
425C2×Q16C2×C4×C1114yescomplemented
426C2×SD16—41no—
427C2×SD16—41no—
428C2×SD16C2×C4×C1114yescomplemented
429C22×C8C23×C1111yescharacteristic
430C22×C8C23×C1111yescharacteristic
431C22×C8C23×C1111yescharacteristic
432C22×C8C23×C1111yescharacteristic
433C22⋊Q8—22no—
434C22⋊Q8C2×C4×C1114yes—
435C4×Q8—41no—
436C4×Q8—41no—
437#117—41no—
438#117—41no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4D4×C1111yescharacteristic
446C2×C4⋊C4D4×C1111yescharacteristic
447C2×C4⋊C4C23×C1111yescharacteristic
448C2×C4⋊C4C23×C1111yescharacteristic
449C2×C4⋊C4C23×C1111yescharacteristic
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C4⋊C4C23×C1111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C1111yescharacteristic
459C2×C22⋊C4D4×C1111yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C1111yescharacteristic
463C2×C42C23×C1111yescharacteristic
464#107—41no—
465#107—41no—
466#103—41no—
467#103—41no—
468#103—41no—
469#103—41no—
470#103C2×C4×C1114yescomplemented
471#102—41no—
472#102—41no—
473#102C2×C4×C1114yescomplemented
474C22⋊C8—22no—
475C22⋊C8C2×C4×C1114yes—
476#97—41no—
477C4×C8—41no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487C2×C11—42no—
488C2×C11—82no—
489C2×C11#232111yescharacteristic
490C2×C11#294711yescharacteristic
491C2×C11#295111yescharacteristic
492C2×C11#320111yescharacteristic
493C2×C11#320311yescharacteristic
494C2×C11#322311yescharacteristic
495C2×C11#322411yescharacteristic
496C24—21no—
497C24C2×D4×C1111yescharacteristic
498#41—44no—
499#41—44no—
500#41—44no—
501#41—44no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8C22×C4×C1112yes—
513C2×Q8C22×C4×C1112yes—
514C2×D4—24no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4C22×C4×C1112yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4C22×C4×C1112yes—
541C22×C4C2×D4×C1111yescharacteristic
542C22×C4C2×D4×C1111yescharacteristic
543C22×C4C2×D4×C1111yescharacteristic
544C22×C4C2×D4×C1111yescharacteristic
545C22×C4C2×D4×C1111yescharacteristic
546C22×C4C11×#4112yes—
547C22×C4C24×C1111yescharacteristic
548Q16—44no—
549SD16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8C22×C4×C1112yes—
561C2×C8C22×C4×C1112yes—
562C4⋊C4—24no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—81no—
577C4⋊C4C22×C4×C1112yes—
578C22⋊C4—24no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—42no—
591C42—81no—
592C11#2205711yescharacteristic, direct product factor, Sylow
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C4×D4×C1112yes—
607C23C22×D4×C1111yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616D4—22no—
617D4—22no—
618D4—48no—
619D4—41no—
620D4—41no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—48no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4C4×D4×C1112yes—
663C2×C4C23×C4×C1111yescharacteristic
664C2×C4C2×C11×#4111yescharacteristic
665C2×C4C11×H(5,𝔽2)11yescharacteristic
666C2×C4C11×H(5,𝔽2)11yescharacteristic
667C2×C4C11×H(5,𝔽2)11yescharacteristic
668C2×C4C11×H(5,𝔽2)11yescharacteristic
669C8—22no—
670C8—22no—
671C8—41no—
672C8—41no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22C2×C4×D4×C1111yescharacteristic
688C22C11×#53411yescharacteristic
689C22C11×#53511yescharacteristic
690C22C11×#57611yescharacteristic
691C22C11×#57711yescharacteristic
692C22C11×#57811yescharacteristic
693C22C11×#57811yescharacteristic
694C4—22no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4C11×#51811yescharacteristic
707C4C11×#51811yescharacteristic
708C4C11×#53811yescharacteristic
709C4C11×#53811yescharacteristic
710C2—42no—
711C2—82no—
712C2C11×#232111yescharacteristic
713C2C11×#294711yescharacteristic
714C2C11×#295111yescharacteristic
715C2C11×#320111yescharacteristic
716C2C11×#320311yescharacteristic
717C2C11×#322311yescharacteristic
718C2C11×#322411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2323C2semidirect
4. C11×#1973C2semidirect
5. C11×#1969C2semidirect
6. C11×#1935C2semidirect
7. C11×#1934C2semidirect
8. C11×#1928C2semidirect
9. C11×#1925C2semidirect
10. C11×#1880C2semidirect
11. C11×#1878C2semidirect
12. C11×#1872C2semidirect
13. C11×#1852C2semidirect
15. C11×#1750C2semidirect
23. C11×#452C4semidirect
75. C2×C11×Q16C2×C4semidirect
78. C2×C11×SD16C2×C4semidirect
120. C11×#103C2×C4semidirect
123. C11×#102C2×C4semidirect
137. #22057C11direct (N × H)
235. #2323C2×C11semidirect
237. #1973C2×C11semidirect
238. #1969C2×C11semidirect
239. #1935C2×C11semidirect
240. #1934C2×C11semidirect
241. #1928C2×C11semidirect
242. #1925C2×C11semidirect
243. #1880C2×C11semidirect
244. #1878C2×C11semidirect
245. #1872C2×C11semidirect
246. #1852C2×C11semidirect
248. #1750C2×C11semidirect
336. #452C4×C11semidirect
425. C2×Q16C2×C4×C11semidirect
428. C2×SD16C2×C4×C11semidirect
470. #103C2×C4×C11semidirect
473. #102C2×C4×C11semidirect
592. C11#22057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4522
C11×#23232
C11×#23112
C11×#19732
C11×#19692
C11×#19352
C11×#19342
C11×#19282
C11×#19252
C11×#18802
C11×#18782
C11×#18722
C11×#18522
C11×#17882
C11×#17502
#2205711