Finite Group Databasebeta

← C11×#24734 #14601927

Subgroups — C11×#24734 #14601927

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#464C211yesmaximal, characteristic, complemented
2C2×C11×#464C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic
4C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
5C11×#2544C211yesmaximal, characteristic
6C11×#2351C211yesmaximal, characteristic, complemented
7C11×#2066C211yesmaximal, characteristic, complemented
8C11×#2065C211yesmaximal, characteristic, complemented
9C11×#2042C211yesmaximal, characteristic, complemented
10C11×#2041C211yesmaximal, characteristic
11C11×#1958C211yesmaximal, characteristic, complemented
12C11×#1939C211yesmaximal, characteristic, complemented
13C11×#1880C211yesmaximal, characteristic, complemented
14C11×#1878C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#464—24no—
27C11×#464—24no—
28C11×#460—24no—
29C4×C11×SD16—24no—
30C2×C11×#106C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C11×#394—21no—
46C11×#394—21no—
47C11×#391C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#389—21no—
50C11×#389—21no—
51C11×#389C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#386—21no—
54C11×#386—21no—
55C11×#382—21no—
56C11×#382C2211yescharacteristic
57C4×C11×C4⋊C4—21no—
58C4×C11×C4⋊C4C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C2×C11×Q16—22no—
71C2×C11×Q16—22no—
72C2×C11×Q16—22no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—22no—
78C2×C11×SD16D414yes—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×#127—22no—
84C11×#127—41no—
85C11×#124—22no—
86C11×#124—22no—
87C11×#124—22no—
88C11×#124—41no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11—41no—
93C4×Q8×C11—41no—
94C4×Q8×C11D414yescomplemented
95C4×D4×C11—22no—
96C4×D4×C11—22no—
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⋊C4D411yescharacteristic
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
115C2×C42×C11—21no—
116C2×C42×C11—21no—
117C2×C42×C11—21no—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C11×#106—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C4⋊C8—22no—
125C11×#103—22no—
126C11×#103—22no—
127C11×#103—22no—
128C11×#103—41no—
129C11×#102—22no—
130C11×#102—22no—
131C11×#102—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—41no—
135C4×C8×C11—22no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95D411yescharacteristic
143C11×#95D411yescharacteristic
144#24734C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11—21no—
146C24×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×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11C2×D412yes—
157C2×Q8×C11C2×D412yes—
158C2×Q8×C11#4112yes—
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—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—81no—
175C2×D4×C11—81no—
176C2×D4×C11C2×D412yes—
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—42no—
184C22×C4×C11—81no—
185C22×C4×C11—81no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C11×Q16—44no—
194C11×SD16—28no—
195C11×SD16—44no—
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×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11C2×D412yes—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—22no—
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—21no—
217C11×C4⋊C4—41no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—42no—
222C11×C4⋊C4C2×D412yes—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—81no—
229C11×C22⋊C4—81no—
230C42×C11—24no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—42no—
236C42×C11—42no—
237C42×C11C2×D412yes—
238C42×C11#4112yes—
239C2×#464C2×C1111yescharacteristic, complemented
240C2×#464C2×C1111yescharacteristic, complemented
241C2×#460C2×C1111yescharacteristic
242C2×C4×SD16C2×C1111yescharacteristic, complemented
243#2544C2×C1111yescharacteristic
244#2351C2×C1111yescharacteristic, complemented
245#2066C2×C1111yescharacteristic, complemented
246#2065C2×C1111yescharacteristic, complemented
247#2042C2×C1111yescharacteristic, complemented
248#2041C2×C1111yescharacteristic
249#1958C2×C1111yescharacteristic, complemented
250#1939C2×C1111yescharacteristic, complemented
251#1880C2×C1111yescharacteristic, complemented
252#1878C2×C1111yescharacteristic, complemented
253#1804C2×C1111yescharacteristic, complemented
254C23×C11—22no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11C22×D411yescharacteristic
269Q8×C11—22no—
270Q8×C11—22no—
271Q8×C11—22no—
272Q8×C11—41no—
273Q8×C11—41no—
274Q8×C11—41no—
275Q8×C11—41no—
276Q8×C11#12114yes—
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—41no—
280D4×C11—41no—
281D4×C11—41no—
282D4×C11—41no—
283D4×C11—41no—
284D4×C11—41no—
285D4×C11—84no—
286D4×C11—84no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
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—41no—
319C2×C4×C11—41no—
320C2×C4×C11—84no—
321C2×C4×C11#12112yes—
322C2×C4×C11#12112yes—
323C2×C4×C11#13512yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×C4×C112−1+411yescharacteristic
330C8×C11—22no—
331C8×C11—41no—
332C8×C11—41no—
333C8×C11—41no—
334C22×Q16C22×C1111yescharacteristic
335C22×SD16C22×C1111yescharacteristic
336C22×SD16C22×C1111yescharacteristic
337C2×#127C22×C1111yescharacteristic
338C2×#124C22×C1111yescharacteristic
339C2×#124C22×C1111yescharacteristic
340C2×C4×Q8C22×C1111yescharacteristic
341C2×C4×Q8C22×C1111yescharacteristic
342C2×C4×Q8C22×C1111yescharacteristic
343C2×C4×D4C22×C1111yescharacteristic
344#464—24no—
345#464—24no—
346#460—24no—
347C4×SD16—24no—
348C2×#106C22×C1111yescharacteristic
349C2×C4⋊C8C22×C1111yescharacteristic
350C2×C4⋊C8C22×C1111yescharacteristic
351C2×C4⋊C8C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#103C22×C1111yescharacteristic
354C2×#103C22×C1111yescharacteristic
355C2×#103C22×C1111yescharacteristic
356C2×#102C22×C1111yescharacteristic
357C2×#102C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359C2×#102C22×C1111yescharacteristic
360C2×#102C22×C1111yescharacteristic
361C2×#102C22×C1111yescharacteristic
362C2×C4×C8C22×C1111yescharacteristic
363#394—21no—
364#394—21no—
365#391C22×C1111yescharacteristic
366#390C22×C1111yescharacteristic
367#389—21no—
368#389—21no—
369#389C22×C1111yescharacteristic
370#389C22×C1111yescharacteristic
371#386—21no—
372#386—21no—
373#382—21no—
374#382C22×C1111yescharacteristic
375C4×C4⋊C4—21no—
376C4×C4⋊C4C22×C1111yescharacteristic
377#340C22×C1111yescharacteristic
378#340C22×C1111yescharacteristic
379#336C22×C1111yescharacteristic
380#336C22×C1111yescharacteristic
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11—81no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11C2×#12111yescharacteristic
396C22×C11D4211yescharacteristic
397C22×C11#54811yescharacteristic
398C22×C11C2×#13511yescharacteristic
399C22×C11#57511yescharacteristic
400C22×C11#57711yescharacteristic
401C22×C11#57711yescharacteristic
402C4×C11—24no—
403C4×C11—22no—
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—41no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—42no—
410C4×C11—81no—
411C4×C11—81no—
412C4×C11—81no—
413C4×C11—81no—
414C4×C11C2×#12111yescharacteristic
415C4×C11#53711yescharacteristic
416C4×C11#54711yescharacteristic
417C4×C11#55311yescharacteristic
418C22×Q8C23×C1111yescharacteristic
419C22×Q8C23×C1111yescharacteristic
420C22×D4—21no—
421C22×D4—21no—
422C22×D4C23×C1111yescharacteristic
423C22×D4C23×C1111yescharacteristic
424C23×C4—21no—
425C2×Q16—22no—
426C2×Q16—22no—
427C2×Q16—22no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—22no—
433C2×SD16D4×C1114yes—
434C22×C8C23×C1111yescharacteristic
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438#127—22no—
439#127—41no—
440#124—22no—
441#124—22no—
442#124—22no—
443#124—41no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×Q8—41no—
448C4×Q8—41no—
449C4×Q8D4×C1114yescomplemented
450C4×D4—22no—
451C4×D4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4D4×C1111yescharacteristic
458C2×C4⋊C4D4×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C4⋊C4C23×C1111yescharacteristic
461C2×C4⋊C4C23×C1111yescharacteristic
462C2×C4⋊C4C23×C1111yescharacteristic
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⋊C4—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42C23×C1111yescharacteristic
474C2×C42C23×C1111yescharacteristic
475C2×C42C23×C1111yescharacteristic
476#106—22no—
477C4⋊C8—22no—
478C4⋊C8—22no—
479C4⋊C8—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—41no—
490C4×C8—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95D4×C1111yescharacteristic
498#95D4×C1111yescharacteristic
499C2×C11—82no—
500C2×C11—161no—
501C2×C11#241611yescharacteristic
502C2×C11#303511yescharacteristic
503C2×C11#304311yescharacteristic
504C2×C11#327511yescharacteristic
505C2×C11#328211yescharacteristic
506C2×C11#336511yescharacteristic
507C2×C11#337111yescharacteristic
508C24—21no—
509C24—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×Q8C2×D4×C1112yes—
520C2×Q8C2×D4×C1112yes—
521C2×Q8C11×#4112yes—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—81no—
538C2×D4—81no—
539C2×D4C2×D4×C1112yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4C2×D4×C1111yescharacteristic
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C2×D4×C1111yescharacteristic
552C22×C4C2×D4×C1111yescharacteristic
553C22×C4C2×D4×C1111yescharacteristic
554C22×C4C2×D4×C1111yescharacteristic
555C22×C4C24×C1111yescharacteristic
556Q16—44no—
557SD16—28no—
558SD16—44no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8C2×D4×C1112yes—
571C4⋊C4—24no—
572C4⋊C4—22no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—41no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4C2×D4×C1112yes—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C42—24no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—42no—
599C42—42no—
600C42C2×D4×C1112yes—
601C42C11×#4112yes—
602C11#2473411yescharacteristic, direct product factor, Sylow
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×D4×C1111yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—41no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8C11×#12114yes—
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—84no—
635D4—84no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
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—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—84no—
670C2×C4C11×#12112yes—
671C2×C4C11×#12112yes—
672C2×C4C11×#13512yes—
673C2×C4C22×D4×C1111yescharacteristic
674C2×C4C22×D4×C1111yescharacteristic
675C2×C4C2×C11×#4111yescharacteristic
676C2×C4C2×C11×#4111yescharacteristic
677C2×C4C11×H(5,𝔽2)11yescharacteristic
678C2×C4C11×2−1+411yescharacteristic
679C8—22no—
680C8—41no—
681C8—41no—
682C8—41no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C2×C11×#12111yescharacteristic
698C22D42×C1111yescharacteristic
699C22C11×#54811yescharacteristic
700C22C2×C11×#13511yescharacteristic
701C22C11×#57511yescharacteristic
702C22C11×#57711yescharacteristic
703C22C11×#57711yescharacteristic
704C4—24no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—42no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4C2×C11×#12111yescharacteristic
717C4C11×#53711yescharacteristic
718C4C11×#54711yescharacteristic
719C4C11×#55311yescharacteristic
720C2—82no—
721C2—161no—
722C2C11×#241611yescharacteristic
723C2C11×#303511yescharacteristic
724C2C11×#304311yescharacteristic
725C2C11×#327511yescharacteristic
726C2C11×#328211yescharacteristic
727C2C11×#336511yescharacteristic
728C2C11×#337111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#464C2semidirect
2. C2×C11×#464C2semidirect
4. C2×C4×C11×SD16C2semidirect
6. C11×#2351C2semidirect
7. C11×#2066C2semidirect
8. C11×#2065C2semidirect
9. C11×#2042C2semidirect
11. C11×#1958C2semidirect
12. C11×#1939C2semidirect
13. C11×#1880C2semidirect
14. C11×#1878C2semidirect
15. C11×#1804C2semidirect
94. C4×Q8×C11D4semidirect
144. #24734C11direct (N × H)
239. C2×#464C2×C11semidirect
240. C2×#464C2×C11semidirect
242. C2×C4×SD16C2×C11semidirect
244. #2351C2×C11semidirect
245. #2066C2×C11semidirect
246. #2065C2×C11semidirect
247. #2042C2×C11semidirect
249. #1958C2×C11semidirect
250. #1939C2×C11semidirect
251. #1880C2×C11semidirect
252. #1878C2×C11semidirect
253. #1804C2×C11semidirect
449. C4×Q8D4×C11semidirect
602. C11#24734direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4642
C2×C11×#4602
C2×C4×C11×SD162
C11×#25442
C11×#23512
C11×#20662
C11×#20652
C11×#20422
C11×#20412
C11×#19582
C11×#19392
C11×#18802
C11×#18782
C11×#18042
#2473411