Finite Group Databasebeta

← C11×#23148 #14600341

Subgroups — C11×#23148 #14600341

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3054C211yesmaximal, characteristic
2C11×#2933C211yesmaximal, characteristic, complemented
3C11×#2933C211yesmaximal, characteristic, complemented
4C11×#1938C211yesmaximal, characteristic, complemented
5C11×#1937C211yesmaximal, characteristic, complemented
6C11×#1922C211yesmaximal, characteristic, complemented
7C11×#1922C211yesmaximal, characteristic, complemented
8C11×#1876C211yesmaximal, characteristic, complemented
9C11×#1876C211yesmaximal, characteristic, complemented
10C11×#1871C211yesmaximal, characteristic, complemented
11C11×#1871C211yesmaximal, characteristic, complemented
12C11×#1765C211yesmaximal, characteristic, complemented
13C11×#1764C211yesmaximal, characteristic, complemented
14C11×#1753C211yesmaximal, characteristic, complemented
15C11×#1738C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#525C2211yescharacteristic
23C11×#525C2211yescharacteristic
24C11×#470C411yescharacteristic, complemented
25C11×#470C411yescharacteristic, complemented
26C11×#469C411yescharacteristic, complemented
27C11×#469C411yescharacteristic, complemented
28C11×#468C411yescharacteristic, complemented
29C11×#468C411yescharacteristic, complemented
30C11×#468C411yescharacteristic, complemented
31C11×#468C411yescharacteristic, complemented
32C11×#436—21no—
33C11×#436—21no—
34C11×#435—21no—
35C11×#435—21no—
36C11×#435—21no—
37C11×#435—21no—
38C8×D4×C11—21no—
39C8×D4×C11—21no—
40C11×#427C2211yescharacteristic
41C11×#424C2211yescharacteristic
42C11×#424C2211yescharacteristic
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C2×C11×#104C2211yescharacteristic
47C11×#416C2211yescharacteristic
48C11×#416C2211yescharacteristic
49C11×#408C2211yescharacteristic
50C11×#408C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C11×#405C2211yescharacteristic
53C11×#405C2211yescharacteristic
54C2×C11×#97C2211yescharacteristic
55C2×C4×C8×C11C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#341C2211yescharacteristic
58C11×#341C2211yescharacteristic
59C11×#341C2211yescharacteristic
60C11×#341C2211yescharacteristic
61C11×#339C2211yescharacteristic
62C11×#339C2211yescharacteristic
63C11×#339C2211yescharacteristic
64C11×#339C2211yescharacteristic
65C11×#336C2211yescharacteristic
66C11×#336C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C11×#135—41no—
71C11×#135—41no—
72C2×C11×Q16C2×C411yescharacteristic
73C2×C11×SD16C2×C411yescharacteristic
74C2×C11×SD16C2×C411yescharacteristic
75C2×C11×D8C2×C411yescharacteristic
76C11×#131—22no—
77C11×#131—22no—
78C11×#131—41no—
79C11×#131—41no—
80C2×C11×M16—21no—
81C2×C11×M16—21no—
82C2×C11×M16—21no—
83C2×C11×M16—21no—
84C2×C11×M16—22no—
85C2×C11×M16—22no—
86C2×C11×M16—41no—
87C2×C11×M16—41no—
88C2×C11×M16—41no—
89C2×C11×M16—41no—
90C2×C11×M16C2×C411yescharacteristic
91C2×C11×M16C2×C411yescharacteristic
92C2×C11×M16C2×C411yescharacteristic
93C2×C11×M16C2×C411yescharacteristic
94C2×C11×M16C2311yescharacteristic
95C2×C11×M16C2311yescharacteristic
96C2×C11×M16C2311yescharacteristic
97C2×C11×M16C2311yescharacteristic
98C22×C8×C11—21no—
99C22×C8×C11—21no—
100C22×C8×C11—21no—
101C22×C8×C11—21no—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#123—21no—
107C11×#123—21no—
108C11×C22⋊Q8C2×C411yescharacteristic
109C11×C22⋊Q8C2×C411yescharacteristic
110C11×C22⋊Q8C2×C411yescharacteristic
111C11×C22⋊Q8C2×C411yescharacteristic
112C11×#121C2×C411yescharacteristic
113C11×#121C2×C411yescharacteristic
114C11×#121C2×C411yescharacteristic
115C11×#121C2×C411yescharacteristic
116C11×#120—21no—
117C11×#120—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C11×#117C2311yescharacteristic
123C11×#117C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C11×#107C2×C411yescharacteristic
128C11×#107C2×C411yescharacteristic
129C11×#106C2×C411yescharacteristic
130C11×#106C2×C411yescharacteristic
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8—21no—
134C11×C4⋊C8—21no—
135C11×#104—22no—
136C11×#104—22no—
137C11×#104—41no—
138C11×#104—41no—
139C11×#103C2×C411yescharacteristic
140C11×#103C2×C411yescharacteristic
141C11×#103C2×C411yescharacteristic
142C11×#103C2×C411yescharacteristic
143C11×#102C2×C411yescharacteristic
144C11×#102C2×C411yescharacteristic
145C11×#102C2×C411yescharacteristic
146C11×#102C2×C411yescharacteristic
147C11×C22⋊C8—21no—
148C11×C22⋊C8—21no—
149C11×C22⋊C8—21no—
150C11×C22⋊C8—21no—
151C11×C22⋊C8D411yescharacteristic
152C11×C22⋊C8D411yescharacteristic
153C11×C22⋊C8D411yescharacteristic
154C11×C22⋊C8D411yescharacteristic
155C11×#97—21no—
156C11×#97—21no—
157C11×#97—41no—
158C4×C8×C11—21no—
159C4×C8×C11—21no—
160C4×C8×C11—41no—
161C11×#95—21no—
162#23148C1111yesmaximal, characteristic, direct product factor, Sylow
163C24×C11#4111yescharacteristic
164C11×#41—21no—
165C11×#41—21no—
166C11×#41—21no—
167C11×#41—21no—
168C11×#41—21no—
169C11×#41—21no—
170C11×#41—21no—
171C11×#41—21no—
172C2×Q8×C11C22×C411yescharacteristic
173C2×Q8×C11C22×C411yescharacteristic
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11C22×C411yescharacteristic
181C2×D4×C11C22×C411yescharacteristic
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11#4111yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C11×Q16—41no—
197C11×SD16—41no—
198C11×SD16—41no—
199C11×D8—41no—
200C11×M16—21no—
201C11×M16—21no—
202C11×M16—21no—
203C11×M16—21no—
204C11×M16—21no—
205C11×M16—21no—
206C11×M16—41no—
207C11×M16—41no—
208C11×M16—41no—
209C11×M16—41no—
210C11×M16—42no—
211C11×M16—42no—
212C11×M16—42no—
213C11×M16—42no—
214C11×M16#4112yes—
215C11×M16#4112yes—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—42no—
229C2×C8×C11—42no—
230C2×C8×C11—42no—
231C2×C8×C11—42no—
232C2×C8×C11C22×C411yescharacteristic
233C2×C8×C11C22×C411yescharacteristic
234C2×C8×C11C22×C411yescharacteristic
235C2×C8×C11C22×C411yescharacteristic
236C2×C8×C11C2×D411yescharacteristic
237C2×C8×C11C2×D411yescharacteristic
238C2×C8×C11C2×D411yescharacteristic
239C2×C8×C11C2×D411yescharacteristic
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4C22×C411yescharacteristic
245C11×C4⋊C4C22×C411yescharacteristic
246C11×C4⋊C4C22×C411yescharacteristic
247C11×C4⋊C4C22×C411yescharacteristic
248C11×C22⋊C4—21no—
249C11×C22⋊C4—21no—
250C11×C22⋊C4—21no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—21no—
253C11×C22⋊C4—21no—
254C11×C22⋊C4—21no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—21no—
257C11×C22⋊C4—21no—
258C11×C22⋊C4—42no—
259C42×C11—21no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—21no—
263C42×C11—21no—
264C42×C11—21no—
265#3054C2×C1111yescharacteristic
266#2933C2×C1111yescharacteristic, complemented
267#2933C2×C1111yescharacteristic, complemented
268#1938C2×C1111yescharacteristic, complemented
269#1937C2×C1111yescharacteristic, complemented
270#1922C2×C1111yescharacteristic, complemented
271#1922C2×C1111yescharacteristic, complemented
272#1876C2×C1111yescharacteristic, complemented
273#1876C2×C1111yescharacteristic, complemented
274#1871C2×C1111yescharacteristic, complemented
275#1871C2×C1111yescharacteristic, complemented
276#1765C2×C1111yescharacteristic, complemented
277#1764C2×C1111yescharacteristic, complemented
278#1753C2×C1111yescharacteristic, complemented
279#1738C2×C1111yescharacteristic, complemented
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11C4×D411yescharacteristic
287C23×C11C4×D411yescharacteristic
288C23×C11C2×#4111yescharacteristic
289Q8×C11—21no—
290Q8×C11—21no—
291Q8×C11—21no—
292Q8×C11—21no—
293D4×C11—21no—
294D4×C11—21no—
295D4×C11—21no—
296D4×C11—21no—
297D4×C11—42no—
298D4×C11—42no—
299D4×C11—41no—
300D4×C11—41no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—81no—
304D4×C11—81no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11C4×D411yescharacteristic
333C2×C4×C11C23×C411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C8×C11—21no—
340C8×C11—21no—
341C8×C11—21no—
342C8×C11—21no—
343C8×C11—21no—
344C8×C11—21no—
345C8×C11—21no—
346C8×C11—21no—
347C8×C11—22no—
348C8×C11—22no—
349C8×C11—41no—
350C8×C11—41no—
351C2×#135C22×C1111yescharacteristic
352C2×#131C22×C1111yescharacteristic
353C2×#131C22×C1111yescharacteristic
354C22×M16C22×C1111yescharacteristic
355C22×M16C22×C1111yescharacteristic
356C22×M16C22×C1111yescharacteristic
357#525C22×C1111yescharacteristic
358#525C22×C1111yescharacteristic
359#470C4×C1111yescharacteristic, complemented
360#470C4×C1111yescharacteristic, complemented
361#469C4×C1111yescharacteristic, complemented
362#469C4×C1111yescharacteristic, complemented
363#468C4×C1111yescharacteristic, complemented
364#468C4×C1111yescharacteristic, complemented
365#468C4×C1111yescharacteristic, complemented
366#468C4×C1111yescharacteristic, complemented
367#436—21no—
368#436—21no—
369#435—21no—
370#435—21no—
371#435—21no—
372#435—21no—
373C8×D4—21no—
374C8×D4—21no—
375#427C22×C1111yescharacteristic
376#424C22×C1111yescharacteristic
377#424C22×C1111yescharacteristic
378C2×#104C22×C1111yescharacteristic
379C2×#104C22×C1111yescharacteristic
380C2×#104C22×C1111yescharacteristic
381C2×#104C22×C1111yescharacteristic
382#416C22×C1111yescharacteristic
383#416C22×C1111yescharacteristic
384#408C22×C1111yescharacteristic
385#408C22×C1111yescharacteristic
386C2×C22⋊C8C22×C1111yescharacteristic
387#405C22×C1111yescharacteristic
388#405C22×C1111yescharacteristic
389C2×#97C22×C1111yescharacteristic
390C2×C4×C8C22×C1111yescharacteristic
391C4×C22⋊C4C22×C1111yescharacteristic
392#341C22×C1111yescharacteristic
393#341C22×C1111yescharacteristic
394#341C22×C1111yescharacteristic
395#341C22×C1111yescharacteristic
396#339C22×C1111yescharacteristic
397#339C22×C1111yescharacteristic
398#339C22×C1111yescharacteristic
399#339C22×C1111yescharacteristic
400#336C22×C1111yescharacteristic
401#336C22×C1111yescharacteristic
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11C2×C4×D411yescharacteristic
419C22×C11#55311yescharacteristic
420C22×C11#55311yescharacteristic
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—42no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—81no—
431C4×C11C4×#4111yescharacteristic
432C4×C11#51811yescharacteristic
433C4×C11#54611yescharacteristic
434C4×C11#54611yescharacteristic
435C2×#41C23×C1111yescharacteristic
436C2×#41C23×C1111yescharacteristic
437C23×C4C23×C1111yescharacteristic
438#135—41no—
439#135—41no—
440C2×Q16C2×C4×C1111yescharacteristic
441C2×SD16C2×C4×C1111yescharacteristic
442C2×SD16C2×C4×C1111yescharacteristic
443C2×D8C2×C4×C1111yescharacteristic
444#131—22no—
445#131—22no—
446#131—41no—
447#131—41no—
448C2×M16—21no—
449C2×M16—21no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—41no—
455C2×M16—41no—
456C2×M16—41no—
457C2×M16—41no—
458C2×M16C2×C4×C1111yescharacteristic
459C2×M16C2×C4×C1111yescharacteristic
460C2×M16C2×C4×C1111yescharacteristic
461C2×M16C2×C4×C1111yescharacteristic
462C2×M16C23×C1111yescharacteristic
463C2×M16C23×C1111yescharacteristic
464C2×M16C23×C1111yescharacteristic
465C2×M16C23×C1111yescharacteristic
466C22×C8—21no—
467C22×C8—21no—
468C22×C8—21no—
469C22×C8—21no—
470C22×C8C23×C1111yescharacteristic
471C22×C8C23×C1111yescharacteristic
472C22×C8C23×C1111yescharacteristic
473C22×C8C23×C1111yescharacteristic
474#123—21no—
475#123—21no—
476C22⋊Q8C2×C4×C1111yescharacteristic
477C22⋊Q8C2×C4×C1111yescharacteristic
478C22⋊Q8C2×C4×C1111yescharacteristic
479C22⋊Q8C2×C4×C1111yescharacteristic
480#121C2×C4×C1111yescharacteristic
481#121C2×C4×C1111yescharacteristic
482#121C2×C4×C1111yescharacteristic
483#121C2×C4×C1111yescharacteristic
484#120—21no—
485#120—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490#117C23×C1111yescharacteristic
491#117C23×C1111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C42C23×C1111yescharacteristic
494C2×C42C23×C1111yescharacteristic
495#107C2×C4×C1111yescharacteristic
496#107C2×C4×C1111yescharacteristic
497#106C2×C4×C1111yescharacteristic
498#106C2×C4×C1111yescharacteristic
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503#104—22no—
504#104—22no—
505#104—41no—
506#104—41no—
507#103C2×C4×C1111yescharacteristic
508#103C2×C4×C1111yescharacteristic
509#103C2×C4×C1111yescharacteristic
510#103C2×C4×C1111yescharacteristic
511#102C2×C4×C1111yescharacteristic
512#102C2×C4×C1111yescharacteristic
513#102C2×C4×C1111yescharacteristic
514#102C2×C4×C1111yescharacteristic
515C22⋊C8—21no—
516C22⋊C8—21no—
517C22⋊C8—21no—
518C22⋊C8—21no—
519C22⋊C8D4×C1111yescharacteristic
520C22⋊C8D4×C1111yescharacteristic
521C22⋊C8D4×C1111yescharacteristic
522C22⋊C8D4×C1111yescharacteristic
523#97—21no—
524#97—21no—
525#97—41no—
526C4×C8—21no—
527C4×C8—21no—
528C4×C8—41no—
529#95—21no—
530C2×C11—21no—
531C2×C11—21no—
532C2×C11—41no—
533C2×C11—41no—
534C2×C11—81no—
535C2×C11—81no—
536C2×C11#236411yescharacteristic
537C2×C11#295511yescharacteristic
538C2×C11#295611yescharacteristic
539C24C11×#4111yescharacteristic
540#41—21no—
541#41—21no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548C2×Q8C22×C4×C1111yescharacteristic
549C2×Q8C22×C4×C1111yescharacteristic
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4C22×C4×C1111yescharacteristic
557C2×D4C22×C4×C1111yescharacteristic
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4C22×C4×C1111yescharacteristic
567C22×C4C22×C4×C1111yescharacteristic
568C22×C4C2×D4×C1111yescharacteristic
569C22×C4C2×D4×C1111yescharacteristic
570C22×C4C11×#4111yescharacteristic
571C22×C4C24×C1111yescharacteristic
572Q16—41no—
573SD16—41no—
574SD16—41no—
575D8—41no—
576M16—21no—
577M16—21no—
578M16—21no—
579M16—21no—
580M16—21no—
581M16—21no—
582M16—41no—
583M16—41no—
584M16—41no—
585M16—41no—
586M16—42no—
587M16—42no—
588M16—42no—
589M16—42no—
590M16C11×#4112yes—
591M16C11×#4112yes—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C2×C8—42no—
606C2×C8—42no—
607C2×C8—42no—
608C2×C8C22×C4×C1111yescharacteristic
609C2×C8C22×C4×C1111yescharacteristic
610C2×C8C22×C4×C1111yescharacteristic
611C2×C8C22×C4×C1111yescharacteristic
612C2×C8C2×D4×C1111yescharacteristic
613C2×C8C2×D4×C1111yescharacteristic
614C2×C8C2×D4×C1111yescharacteristic
615C2×C8C2×D4×C1111yescharacteristic
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4C22×C4×C1111yescharacteristic
621C4⋊C4C22×C4×C1111yescharacteristic
622C4⋊C4C22×C4×C1111yescharacteristic
623C4⋊C4C22×C4×C1111yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—42no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C11#2314811yescharacteristic, direct product factor, Sylow
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—41no—
647C23—41no—
648C23C4×D4×C1111yescharacteristic
649C23C4×D4×C1111yescharacteristic
650C23C2×C11×#4111yescharacteristic
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—42no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4C4×D4×C1111yescharacteristic
694C2×C4C4×D4×C1111yescharacteristic
695C2×C4C23×C4×C1111yescharacteristic
696C2×C4C22×D4×C1111yescharacteristic
697C2×C4C2×C11×#4111yescharacteristic
698C2×C4C2×C11×#4111yescharacteristic
699C2×C4C11×H(5,𝔽2)11yescharacteristic
700C2×C4C11×H(5,𝔽2)11yescharacteristic
701C8—21no—
702C8—21no—
703C8—21no—
704C8—21no—
705C8—21no—
706C8—21no—
707C8—21no—
708C8—21no—
709C8—22no—
710C8—22no—
711C8—41no—
712C8—41no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22C2×C4×D4×C1111yescharacteristic
730C22C11×#55311yescharacteristic
731C22C11×#55311yescharacteristic
732C4—21no—
733C4—21no—
734C4—42no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—81no—
742C4C4×C11×#4111yescharacteristic
743C4C11×#51811yescharacteristic
744C4C11×#54611yescharacteristic
745C4C11×#54611yescharacteristic
746C2—21no—
747C2—21no—
748C2—41no—
749C2—41no—
750C2—81no—
751C2—81no—
752C2C11×#236411yescharacteristic
753C2C11×#295511yescharacteristic
754C2C11×#295611yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×C4×D4
prime radicalC11×#3054C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2933C2semidirect
3. C11×#2933C2semidirect
4. C11×#1938C2semidirect
5. C11×#1937C2semidirect
6. C11×#1922C2semidirect
7. C11×#1922C2semidirect
8. C11×#1876C2semidirect
9. C11×#1876C2semidirect
10. C11×#1871C2semidirect
11. C11×#1871C2semidirect
12. C11×#1765C2semidirect
13. C11×#1764C2semidirect
14. C11×#1753C2semidirect
15. C11×#1738C2semidirect
24. C11×#470C4semidirect
25. C11×#470C4semidirect
26. C11×#469C4semidirect
27. C11×#469C4semidirect
28. C11×#468C4semidirect
29. C11×#468C4semidirect
30. C11×#468C4semidirect
31. C11×#468C4semidirect
162. #23148C11direct (N × H)
266. #2933C2×C11semidirect
267. #2933C2×C11semidirect
268. #1938C2×C11semidirect
269. #1937C2×C11semidirect
270. #1922C2×C11semidirect
271. #1922C2×C11semidirect
272. #1876C2×C11semidirect
273. #1876C2×C11semidirect
274. #1871C2×C11semidirect
275. #1871C2×C11semidirect
276. #1765C2×C11semidirect
277. #1764C2×C11semidirect
278. #1753C2×C11semidirect
279. #1738C2×C11semidirect
359. #470C4×C11semidirect
360. #470C4×C11semidirect
361. #469C4×C11semidirect
362. #469C4×C11semidirect
363. #468C4×C11semidirect
364. #468C4×C11semidirect
365. #468C4×C11semidirect
366. #468C4×C11semidirect
641. C11#23148direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30542
C11×#29332
C11×#19382
C11×#19372
C11×#19222
C11×#18762
C11×#18712
C11×#17652
C11×#17642
C11×#17532
C11×#17382
#2314811