Finite Group Databasebeta

← C11×#22056 #14599249

Subgroups — C11×#22056 #14599249

Order 2816.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#447C211yesmaximal, characteristic
2C11×#2324C211yesmaximal, characteristic, complemented
3C11×#2309C211yesmaximal, characteristic, complemented
4C11×#1972C211yesmaximal, characteristic, complemented
5C11×#1970C211yesmaximal, characteristic, complemented
6C11×#1936C211yesmaximal, characteristic, complemented
7C11×#1934C211yesmaximal, characteristic, complemented
8C11×#1926C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1875C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1786C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic, complemented
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C11×#447C418yescomplemented
24C2×C11×#107C2211yescharacteristic, complemented
25C2×C11×#106C2211yescharacteristic, complemented
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic, complemented
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic, complemented
37C2×C4×C8×C11C2211yescharacteristic, complemented
38C11×#390—21no—
39C11×#390—21no—
40C11×#390—21no—
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#390C2211yescharacteristic, complemented
46C11×#389C2211yescharacteristic, complemented
47C11×#388—21no—
48C11×#386—21no—
49C11×#385—21no—
50C11×#380C2211yescharacteristic
51C11×#379—21no—
52C11×#379—21no—
53C4×C11×C4⋊C4C2211yescharacteristic, complemented
54C11×#340C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58C11×#336C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C25×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—22no—
64C22×D4×C11—41no—
65C22×D4×C11—41no—
66C22×D4×C11—41no—
67C22×D4×C11—41no—
68C22×D4×C11C2×C414yescomplemented
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C2×C11×D8—41no—
75C2×C11×D8—41no—
76C2×C11×D8—41no—
77C2×C11×D8—41no—
78C2×C11×D8C2×C414yes—
79C2×C11×D8C2×C414yes—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×#121—22no—
85C11×#121C2×C414yes—
86C4×D4×C11—41no—
87C4×D4×C11—41no—
88C11×#117—41no—
89C11×#117—41no—
90C11×#117—41no—
91C11×#117—41no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
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⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C42×C11—21no—
117C2×C42×C11—21no—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C11×#107—41no—
121C11×#106—41no—
122C11×#102—41no—
123C11×#102—41no—
124C11×#102—41no—
125C11×#102—41no—
126C11×#102—41no—
127C11×#102—41no—
128C11×#102C2×C414yescomplemented
129C11×#102C2×C414yescomplemented
130C11×C22⋊C8—22no—
131C11×C22⋊C8C2×C414yescomplemented
132C11×#97—41no—
133C4×C8×C11—41no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137#22056C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—24no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—81no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11—81no—
148C24×C11C2×D411yescharacteristic
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—44no—
167C2×D4×C11—44no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11—44no—
171C2×D4×C11—44no—
172C2×D4×C11—81no—
173C2×D4×C11—81no—
174C2×D4×C11C22×C412yes—
175C2×D4×C11C22×C412yes—
176C2×D4×C11C22×C412yes—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—42no—
187C22×C4×C11—81no—
188C22×C4×C11—81no—
189C22×C4×C11C22×C412yes—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11#4112yes—
196C22×C4×C11C2411yescharacteristic
197C11×D8—44no—
198C11×D8—44no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11C22×C412yes—
210C2×C8×C11C22×C412yes—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—41no—
221C11×C4⋊C4—41no—
222C11×C4⋊C4—81no—
223C11×C4⋊C4C22×C412yes—
224C11×C22⋊C4—24no—
225C11×C22⋊C4—41no—
226C11×C22⋊C4—41no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—81no—
230C11×C22⋊C4—81no—
231C11×C22⋊C4—81no—
232C11×C22⋊C4—81no—
233C11×C22⋊C4—81no—
234C11×C22⋊C4—81no—
235C11×C22⋊C4—81no—
236C11×C22⋊C4—81no—
237C11×C22⋊C4—81no—
238C11×C22⋊C4—81no—
239C11×C22⋊C4—81no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—42no—
245C42×C11—81no—
246C2×#447C2×C1111yescharacteristic
247#2324C2×C1111yescharacteristic, complemented
248#2309C2×C1111yescharacteristic, complemented
249#1972C2×C1111yescharacteristic, complemented
250#1970C2×C1111yescharacteristic, complemented
251#1936C2×C1111yescharacteristic, complemented
252#1934C2×C1111yescharacteristic, complemented
253#1926C2×C1111yescharacteristic, complemented
254#1925C2×C1111yescharacteristic, complemented
255#1879C2×C1111yescharacteristic, complemented
256#1879C2×C1111yescharacteristic, complemented
257#1875C2×C1111yescharacteristic, complemented
258#1854C2×C1111yescharacteristic, complemented
259#1786C2×C1111yescharacteristic, complemented
260#1750C2×C1111yescharacteristic, complemented
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—48no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—84no—
290C23×C11—84no—
291C23×C11—84no—
292C23×C11—84no—
293C23×C11—84no—
294C23×C11—84no—
295C23×C11C4×D412yes—
296C23×C11C22×D411yescharacteristic
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—48no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—84no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—84no—
345C2×C4×C11C4×D412yes—
346C2×C4×C11C23×C411yescharacteristic
347C2×C4×C11C2×#4111yescharacteristic
348C2×C4×C11H(5,𝔽2)11yescharacteristic
349C2×C4×C11H(5,𝔽2)11yescharacteristic
350C2×C4×C11H(5,𝔽2)11yescharacteristic
351C2×C4×C11H(5,𝔽2)11yescharacteristic
352C8×C11—22no—
353C8×C11—22no—
354C8×C11—41no—
355C8×C11—41no—
356C23×D4C22×C1111yescharacteristic
357C22×D8C22×C1111yescharacteristic
358C22×D8C22×C1111yescharacteristic
359C2×#121C22×C1111yescharacteristic
360C2×C4×D4C22×C1111yescharacteristic, complemented
361C2×#117C22×C1111yescharacteristic
362C2×#117C22×C1111yescharacteristic
363#447C4×C1118yescomplemented
364C2×#107C22×C1111yescharacteristic, complemented
365C2×#106C22×C1111yescharacteristic, complemented
366C2×#102C22×C1111yescharacteristic
367C2×#102C22×C1111yescharacteristic
368C2×#102C22×C1111yescharacteristic
369C2×#102C22×C1111yescharacteristic
370C2×#102C22×C1111yescharacteristic
371C2×#102C22×C1111yescharacteristic
372C2×#102C22×C1111yescharacteristic, complemented
373C2×#102C22×C1111yescharacteristic, complemented
374C2×C22⋊C8C22×C1111yescharacteristic
375C2×C22⋊C8C22×C1111yescharacteristic
376C2×#97C22×C1111yescharacteristic, complemented
377C2×C4×C8C22×C1111yescharacteristic, complemented
378#390—21no—
379#390—21no—
380#390—21no—
381#390C22×C1111yescharacteristic
382#390C22×C1111yescharacteristic
383#390C22×C1111yescharacteristic
384#390C22×C1111yescharacteristic
385#390C22×C1111yescharacteristic, complemented
386#389C22×C1111yescharacteristic, complemented
387#388—21no—
388#386—21no—
389#385—21no—
390#380C22×C1111yescharacteristic
391#379—21no—
392#379—21no—
393C4×C4⋊C4C22×C1111yescharacteristic, complemented
394#340C22×C1111yescharacteristic, complemented
395#340C22×C1111yescharacteristic, complemented
396#340C22×C1111yescharacteristic, complemented
397#340C22×C1111yescharacteristic, complemented
398#336C22×C1111yescharacteristic, complemented
399#336C22×C1111yescharacteristic, complemented
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—816no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11C2×C4×D411yescharacteristic
430C22×C11#53411yescharacteristic
431C22×C11#53511yescharacteristic
432C22×C11#57611yescharacteristic
433C22×C11#57611yescharacteristic
434C22×C11#57611yescharacteristic
435C22×C11#57711yescharacteristic
436C4×C11—22no—
437C4×C11—41no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11—42no—
442C4×C11—81no—
443C4×C11—81no—
444C4×C11—81no—
445C4×C11—81no—
446C4×C11#51811yescharacteristic
447C4×C11#51811yescharacteristic
448C4×C11#53811yescharacteristic
449C4×C11#53811yescharacteristic
450C25—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—41no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4—41no—
458C22×D4C2×C4×C1114yescomplemented
459C22×D4C23×C1111yescharacteristic
460C22×D4C23×C1111yescharacteristic
461C22×D4C23×C1111yescharacteristic
462C23×C4—21no—
463C23×C4C23×C1111yescharacteristic
464C2×D8—41no—
465C2×D8—41no—
466C2×D8—41no—
467C2×D8—41no—
468C2×D8C2×C4×C1114yes—
469C2×D8C2×C4×C1114yes—
470C22×C8C23×C1111yescharacteristic
471C22×C8C23×C1111yescharacteristic
472C22×C8C23×C1111yescharacteristic
473C22×C8C23×C1111yescharacteristic
474#121—22no—
475#121C2×C4×C1114yes—
476C4×D4—41no—
477C4×D4—41no—
478#117—41no—
479#117—41no—
480#117—41no—
481#117—41no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4D4×C1111yescharacteristic
484C2×C4⋊C4D4×C1111yescharacteristic
485C2×C4⋊C4C23×C1111yescharacteristic
486C2×C4⋊C4C23×C1111yescharacteristic
487C2×C4⋊C4C23×C1111yescharacteristic
488C2×C4⋊C4C23×C1111yescharacteristic
489C2×C4⋊C4C23×C1111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C1111yescharacteristic
505C2×C22⋊C4D4×C1111yescharacteristic
506C2×C42—21no—
507C2×C42—21no—
508C2×C42C23×C1111yescharacteristic
509C2×C42C23×C1111yescharacteristic
510#107—41no—
511#106—41no—
512#102—41no—
513#102—41no—
514#102—41no—
515#102—41no—
516#102—41no—
517#102—41no—
518#102C2×C4×C1114yescomplemented
519#102C2×C4×C1114yescomplemented
520C22⋊C8—22no—
521C22⋊C8C2×C4×C1114yescomplemented
522#97—41no—
523C4×C8—41no—
524#95—21no—
525#95—21no—
526#95—21no—
527C2×C11—42no—
528C2×C11—82no—
529C2×C11—82no—
530C2×C11—82no—
531C2×C11#232111yescharacteristic
532C2×C11#294611yescharacteristic
533C2×C11#294811yescharacteristic
534C2×C11#319811yescharacteristic
535C2×C11#319911yescharacteristic
536C2×C11#322011yescharacteristic
537C2×C11#322411yescharacteristic
538C24—21no—
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24C2×D4×C1111yescharacteristic
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4C22×C4×C1112yes—
575C2×D4C22×C4×C1112yes—
576C2×D4C22×C4×C1112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4C22×C4×C1112yes—
590C22×C4C2×D4×C1111yescharacteristic
591C22×C4C2×D4×C1111yescharacteristic
592C22×C4C2×D4×C1111yescharacteristic
593C22×C4C2×D4×C1111yescharacteristic
594C22×C4C2×D4×C1111yescharacteristic
595C22×C4C11×#4112yes—
596C22×C4C24×C1111yescharacteristic
597D8—44no—
598D8—44no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8C22×C4×C1112yes—
610C2×C8C22×C4×C1112yes—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—81no—
623C4⋊C4C22×C4×C1112yes—
624C22⋊C4—24no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—42no—
645C42—81no—
646C11#2205611yescharacteristic, direct product factor, Sylow
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23C4×D4×C1112yes—
682C23C22×D4×C1111yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4C4×D4×C1112yes—
732C2×C4C23×C4×C1111yescharacteristic
733C2×C4C2×C11×#4111yescharacteristic
734C2×C4C11×H(5,𝔽2)11yescharacteristic
735C2×C4C11×H(5,𝔽2)11yescharacteristic
736C2×C4C11×H(5,𝔽2)11yescharacteristic
737C2×C4C11×H(5,𝔽2)11yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×C4×D4×C1111yescharacteristic
772C22C11×#53411yescharacteristic
773C22C11×#53511yescharacteristic
774C22C11×#57611yescharacteristic
775C22C11×#57611yescharacteristic
776C22C11×#57611yescharacteristic
777C22C11×#57711yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4C11×#51811yescharacteristic
789C4C11×#51811yescharacteristic
790C4C11×#53811yescharacteristic
791C4C11×#53811yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2C11×#232111yescharacteristic
797C2C11×#294611yescharacteristic
798C2C11×#294811yescharacteristic
799C2C11×#319811yescharacteristic
800C2C11×#319911yescharacteristic
801C2C11×#322011yescharacteristic
802C2C11×#322411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
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×#2324C2semidirect
3. C11×#2309C2semidirect
4. C11×#1972C2semidirect
5. C11×#1970C2semidirect
6. C11×#1936C2semidirect
7. C11×#1934C2semidirect
8. C11×#1926C2semidirect
9. C11×#1925C2semidirect
10. C11×#1879C2semidirect
11. C11×#1879C2semidirect
12. C11×#1875C2semidirect
13. C11×#1854C2semidirect
14. C11×#1786C2semidirect
15. C11×#1750C2semidirect
20. C2×C4×D4×C11C22semidirect
23. C11×#447C4semidirect
24. C2×C11×#107C22semidirect
25. C2×C11×#106C22semidirect
32. C2×C11×#102C22semidirect
33. C2×C11×#102C22semidirect
36. C2×C11×#97C22semidirect
37. C2×C4×C8×C11C22semidirect
45. C11×#390C22semidirect
46. C11×#389C22semidirect
53. C4×C11×C4⋊C4C22semidirect
54. C11×#340C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#336C22semidirect
59. C11×#336C22semidirect
68. C22×D4×C11C2×C4semidirect
128. C11×#102C2×C4semidirect
129. C11×#102C2×C4semidirect
131. C11×C22⋊C8C2×C4semidirect
137. #22056C11direct (N × H)
247. #2324C2×C11semidirect
248. #2309C2×C11semidirect
249. #1972C2×C11semidirect
250. #1970C2×C11semidirect
251. #1936C2×C11semidirect
252. #1934C2×C11semidirect
253. #1926C2×C11semidirect
254. #1925C2×C11semidirect
255. #1879C2×C11semidirect
256. #1879C2×C11semidirect
257. #1875C2×C11semidirect
258. #1854C2×C11semidirect
259. #1786C2×C11semidirect
260. #1750C2×C11semidirect
360. C2×C4×D4C22×C11semidirect
363. #447C4×C11semidirect
364. C2×#107C22×C11semidirect
365. C2×#106C22×C11semidirect
372. C2×#102C22×C11semidirect
373. C2×#102C22×C11semidirect
376. C2×#97C22×C11semidirect
377. C2×C4×C8C22×C11semidirect
385. #390C22×C11semidirect
386. #389C22×C11semidirect
393. C4×C4⋊C4C22×C11semidirect
394. #340C22×C11semidirect
395. #340C22×C11semidirect
396. #340C22×C11semidirect
397. #340C22×C11semidirect
398. #336C22×C11semidirect
399. #336C22×C11semidirect
458. C22×D4C2×C4×C11semidirect
518. #102C2×C4×C11semidirect
519. #102C2×C4×C11semidirect
521. C22⋊C8C2×C4×C11semidirect
646. C11#22056direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4472
C11×#23242
C11×#23092
C11×#19722
C11×#19702
C11×#19362
C11×#19342
C11×#19262
C11×#19252
C11×#18792
C11×#18752
C11×#18542
C11×#17862
C11×#17502
#2205611