Finite Group Databasebeta

← C11×#24793 #14601986

Subgroups — C11×#24793 #14601986

Order 2816.

956 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#470C211yesmaximal, characteristic, complemented
2C2×C11×#470C211yesmaximal, characteristic, complemented
3C2×C11×#436C211yesmaximal, characteristic
4C2×C11×#428C211yesmaximal, characteristic, complemented
5C11×#2417C211yesmaximal, characteristic
6C11×#2415C211yesmaximal, characteristic
7C11×#2068C211yesmaximal, characteristic, complemented
8C11×#2066C211yesmaximal, characteristic, complemented
9C11×#2036C211yesmaximal, characteristic, complemented
10C11×#2035C211yesmaximal, characteristic, complemented
11C11×#1969C211yesmaximal, characteristic, complemented
12C11×#1941C211yesmaximal, characteristic, complemented
13C11×#1873C211yesmaximal, characteristic, complemented
14C11×#1872C211yesmaximal, characteristic, complemented
15C11×#1809C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C11×#470—24no—
27C11×#470—24no—
28C11×#436—24no—
29C11×#428—24no—
30C2×C11×#107C2211yescharacteristic
31C2×C11×#107C2211yescharacteristic
32C2×C11×#106C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic
34C2×C11×#106C2211yescharacteristic
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C11×#398—21no—
46C11×#397—21no—
47C11×#396—21no—
48C11×#394—21no—
49C11×#391C2211yescharacteristic
50C11×#391C2211yescharacteristic
51C11×#389—21no—
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#388—21no—
55C11×#386—21no—
56C11×#380—21no—
57C11×#380C2211yescharacteristic
58C11×#380C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11D411yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×Q16—22no—
70C2×C11×Q16—22no—
71C2×C11×Q16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C2×C11×M16D414yes—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—41no—
89C11×C22⋊Q8—41no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C11×#117—22no—
93C11×#117—41no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—41no—
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C42×C11—21no—
120C2×C42×C11C2311yescharacteristic
121C11×#107—22no—
122C11×#107—22no—
123C11×#106—22no—
124C11×#106—22no—
125C11×#106D414yescomplemented
126C11×C4⋊C8—22no—
127C11×#103—22no—
128C11×#103—22no—
129C11×#103—22no—
130C11×#103—22no—
131C11×#103—41no—
132C11×#103—41no—
133C11×C22⋊C8—22no—
134C11×C22⋊C8—22no—
135C4×C8×C11—22no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144#24793C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11C2×D411yescharacteristic
146C24×C11C2×D411yescharacteristic
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×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—41no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
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—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—81no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11#4112yes—
189C22×C4×C11C2411yescharacteristic
190C11×Q16—44no—
191C11×M16—28no—
192C11×M16—44no—
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×C11C2×D412yes—
202C2×C8×C11C2×D412yes—
203C2×C8×C11C2×D412yes—
204C2×C8×C11#4112yes—
205C11×C4⋊C4—22no—
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—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—42no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—42no—
222C11×C4⋊C4—81no—
223C11×C4⋊C4C2×D412yes—
224C11×C4⋊C4C2×D412yes—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—81no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—42no—
237C2×#470C2×C1111yescharacteristic, complemented
238C2×#470C2×C1111yescharacteristic, complemented
239C2×#436C2×C1111yescharacteristic
240C2×#428C2×C1111yescharacteristic, complemented
241#2417C2×C1111yescharacteristic
242#2415C2×C1111yescharacteristic
243#2068C2×C1111yescharacteristic, complemented
244#2066C2×C1111yescharacteristic, complemented
245#2036C2×C1111yescharacteristic, complemented
246#2035C2×C1111yescharacteristic, complemented
247#1969C2×C1111yescharacteristic, complemented
248#1941C2×C1111yescharacteristic, complemented
249#1873C2×C1111yescharacteristic, complemented
250#1872C2×C1111yescharacteristic, complemented
251#1809C2×C1111yescharacteristic, complemented
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11#12112yes—
266C23×C11C22×D411yescharacteristic
267Q8×C11—41no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—41no—
273Q8×C11—41no—
274Q8×C11—41no—
275D4×C11—44no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
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—41no—
318C2×C4×C11—84no—
319C2×C4×C11#12112yes—
320C2×C4×C11#13712yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C112−1+411yescharacteristic
327C8×C11—22no—
328C8×C11—41no—
329C8×C11—41no—
330C8×C11#12114yes—
331C22×Q16C22×C1111yescharacteristic
332C22×M16C22×C1111yescharacteristic
333C22×M16C22×C1111yescharacteristic
334C2×C22⋊Q8C22×C1111yescharacteristic
335C2×C22⋊Q8C22×C1111yescharacteristic
336C2×C22⋊Q8C22×C1111yescharacteristic
337C2×C22⋊Q8C22×C1111yescharacteristic
338C2×C4×D4C22×C1111yescharacteristic
339C2×#117C22×C1111yescharacteristic
340C22×C4⋊C4C22×C1111yescharacteristic
341#470—24no—
342#470—24no—
343#436—24no—
344#428—24no—
345C2×#107C22×C1111yescharacteristic
346C2×#107C22×C1111yescharacteristic
347C2×#106C22×C1111yescharacteristic
348C2×#106C22×C1111yescharacteristic
349C2×#106C22×C1111yescharacteristic
350C2×C4⋊C8C22×C1111yescharacteristic
351C2×#103C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#103C22×C1111yescharacteristic
354C2×#103C22×C1111yescharacteristic
355C2×#103C22×C1111yescharacteristic
356C2×#103C22×C1111yescharacteristic
357C2×C22⋊C8C22×C1111yescharacteristic
358C2×C22⋊C8C22×C1111yescharacteristic
359C2×C4×C8C22×C1111yescharacteristic
360#398—21no—
361#397—21no—
362#396—21no—
363#394—21no—
364#391C22×C1111yescharacteristic
365#391C22×C1111yescharacteristic
366#389—21no—
367#389C22×C1111yescharacteristic
368#389C22×C1111yescharacteristic
369#388—21no—
370#386—21no—
371#380—21no—
372#380C22×C1111yescharacteristic
373#380C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377#340C22×C1111yescharacteristic
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11C2×#12111yescharacteristic
393C22×C11D4211yescharacteristic
394C22×C11#54711yescharacteristic
395C22×C11C2×#13711yescharacteristic
396C22×C11#57511yescharacteristic
397C22×C11#57711yescharacteristic
398C22×C11#57811yescharacteristic
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—41no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—41no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11—81no—
410C4×C11—81no—
411C4×C11C2×#12111yescharacteristic
412C4×C11#53711yescharacteristic
413C4×C11#54811yescharacteristic
414C4×C11#55311yescharacteristic
415C22×Q8C23×C1111yescharacteristic
416C22×Q8C23×C1111yescharacteristic
417C22×D4D4×C1111yescharacteristic
418C23×C4—21no—
419C23×C4C23×C1111yescharacteristic
420C23×C4C23×C1111yescharacteristic
421C2×Q16—22no—
422C2×Q16—22no—
423C2×Q16—22no—
424C2×M16—22no—
425C2×M16—22no—
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—22no—
429C2×M16D4×C1114yes—
430C22×C8C23×C1111yescharacteristic
431C22×C8C23×C1111yescharacteristic
432C22×C8C23×C1111yescharacteristic
433C22×C8C23×C1111yescharacteristic
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8—41no—
441C22⋊Q8—41no—
442C4×D4—22no—
443C4×D4—22no—
444#117—22no—
445#117—41no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4D4×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C4⋊C4C23×C1111yescharacteristic
461C2×C4⋊C4C23×C1111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4D4×C1111yescharacteristic
470C2×C22⋊C4D4×C1111yescharacteristic
471C2×C42—21no—
472C2×C42C23×C1111yescharacteristic
473#107—22no—
474#107—22no—
475#106—22no—
476#106—22no—
477#106D4×C1114yescomplemented
478C4⋊C8—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C4×C8—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C2×C11—42no—
497C2×C11—81no—
498C2×C11#241611yescharacteristic
499C2×C11#305611yescharacteristic
500C2×C11#306311yescharacteristic
501C2×C11#327511yescharacteristic
502C2×C11#327611yescharacteristic
503C2×C11#335211yescharacteristic
504C2×C11#335611yescharacteristic
505C24C2×D4×C1111yescharacteristic
506C24C2×D4×C1111yescharacteristic
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—41no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—81no—
543C22×C4C2×D4×C1111yescharacteristic
544C22×C4C2×D4×C1111yescharacteristic
545C22×C4C2×D4×C1111yescharacteristic
546C22×C4C2×D4×C1112yes—
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C11×#4112yes—
549C22×C4C24×C1111yescharacteristic
550Q16—44no—
551M16—28no—
552M16—44no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8C2×D4×C1112yes—
562C2×C8C2×D4×C1112yes—
563C2×C8C2×D4×C1112yes—
564C2×C8C11×#4112yes—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—81no—
583C4⋊C4C2×D4×C1112yes—
584C4⋊C4C2×D4×C1112yes—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—81no—
594C42—21no—
595C42—21no—
596C42—42no—
597C11#2479311yescharacteristic, direct product factor, Sylow
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23C11×#12112yes—
612C23C22×D4×C1111yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621D4—44no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
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—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4C11×#12112yes—
666C2×C4C11×#13712yes—
667C2×C4C22×D4×C1111yescharacteristic
668C2×C4C22×D4×C1111yescharacteristic
669C2×C4C2×C11×#4111yescharacteristic
670C2×C4C2×C11×#4111yescharacteristic
671C2×C4C11×H(5,𝔽2)11yescharacteristic
672C2×C4C11×2−1+411yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8C11×#12114yes—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22C2×C11×#12111yescharacteristic
692C22D42×C1111yescharacteristic
693C22C11×#54711yescharacteristic
694C22C2×C11×#13711yescharacteristic
695C22C11×#57511yescharacteristic
696C22C11×#57711yescharacteristic
697C22C11×#57811yescharacteristic
698C4—22no—
699C4—22no—
700C4—41no—
701C4—42no—
702C4—42no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C2×C11×#12111yescharacteristic
711C4C11×#53711yescharacteristic
712C4C11×#54811yescharacteristic
713C4C11×#55311yescharacteristic
714C2—42no—
715C2—81no—
716C2C11×#241611yescharacteristic
717C2C11×#305611yescharacteristic
718C2C11×#306311yescharacteristic
719C2C11×#327511yescharacteristic
720C2C11×#327611yescharacteristic
721C2C11×#335211yescharacteristic
722C2C11×#335611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#470C2semidirect
2. C2×C11×#470C2semidirect
4. C2×C11×#428C2semidirect
7. C11×#2068C2semidirect
8. C11×#2066C2semidirect
9. C11×#2036C2semidirect
10. C11×#2035C2semidirect
11. C11×#1969C2semidirect
12. C11×#1941C2semidirect
13. C11×#1873C2semidirect
14. C11×#1872C2semidirect
15. C11×#1809C2semidirect
125. C11×#106D4semidirect
144. #24793C11direct (N × H)
237. C2×#470C2×C11semidirect
238. C2×#470C2×C11semidirect
240. C2×#428C2×C11semidirect
243. #2068C2×C11semidirect
244. #2066C2×C11semidirect
245. #2036C2×C11semidirect
246. #2035C2×C11semidirect
247. #1969C2×C11semidirect
248. #1941C2×C11semidirect
249. #1873C2×C11semidirect
250. #1872C2×C11semidirect
251. #1809C2×C11semidirect
477. #106D4×C11semidirect
597. C11#24793direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4702
C2×C11×#4362
C2×C11×#4282
C11×#24172
C11×#24152
C11×#20682
C11×#20662
C11×#20362
C11×#20352
C11×#19692
C11×#19412
C11×#18732
C11×#18722
C11×#18092
#2479311