Finite Group Databasebeta

← C11×#24535 #14601728

Subgroups — C11×#24535 #14601728

Order 2816.

1020 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#449C211yesmaximal, characteristic
2C2×C11×#416C211yesmaximal, characteristic, complemented
3C11×#2500C211yesmaximal, characteristic, complemented
4C11×#2341C211yesmaximal, characteristic, complemented
5C11×#2073C211yesmaximal, characteristic, complemented
6C11×#2071C211yesmaximal, characteristic, complemented
7C11×#2054C211yesmaximal, characteristic, complemented
8C11×#2054C211yesmaximal, characteristic, complemented
9C11×#1893C211yesmaximal, characteristic, complemented
10C11×#1880C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic, complemented
12C11×#1850C211yesmaximal, characteristic, complemented
13C11×#1825C211yesmaximal, characteristic, complemented
14C11×#1805C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#449—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#416—24no—
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#394—21no—
38C11×#394—21no—
39C11×#390—21no—
40C11×#390—21no—
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#388—21no—
46C11×#388—21no—
47C11×#384C2211yescharacteristic
48C11×#382C2211yescharacteristic
49C11×#380—21no—
50C11×#380C2211yescharacteristic
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41D414yes—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C2×C11×SD16—22no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×D8—22no—
78C2×C11×D8—41no—
79C2×C11×D8—41no—
80C22×C8×C11—22no—
81C22×C8×C11—41no—
82C22×C8×C11—41no—
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C11×#121—22no—
88C11×#121—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—41no—
92C4×Q8×C11—41no—
93C11×#117—22no—
94C11×#117—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C42×C11—21no—
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C11×C4⋊C8—41no—
123C11×C4⋊C8—41no—
124C11×#103—22no—
125C11×#103—22no—
126C11×#103—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#102—22no—
130C11×#102—41no—
131C11×#102—41no—
132C11×C22⋊C8—22no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#24535C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C11×#41—28no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D412yes—
150C2×Q8×C11#4112yes—
151C2×Q8×C11#4112yes—
152C2×D4×C11—24no—
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—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—81no—
168C2×D4×C11—81no—
169C2×D4×C11C2×D412yes—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—24no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11#4112yes—
190C22×C4×C11C2411yescharacteristic
191C11×SD16—44no—
192C11×D8—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×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—44no—
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—81no—
219C11×C4⋊C4—81no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4—42no—
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—
230C11×C22⋊C4—81no—
231C11×C22⋊C4—81no—
232C11×C22⋊C4—81no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—42no—
238C42×C11—42no—
239C42×C11—42no—
240C2×#449C2×C1111yescharacteristic
241C2×#416C2×C1111yescharacteristic, complemented
242#2500C2×C1111yescharacteristic, complemented
243#2341C2×C1111yescharacteristic, complemented
244#2073C2×C1111yescharacteristic, complemented
245#2071C2×C1111yescharacteristic, complemented
246#2054C2×C1111yescharacteristic, complemented
247#2054C2×C1111yescharacteristic, complemented
248#1893C2×C1111yescharacteristic, complemented
249#1880C2×C1111yescharacteristic, complemented
250#1880C2×C1111yescharacteristic, complemented
251#1850C2×C1111yescharacteristic, complemented
252#1825C2×C1111yescharacteristic, complemented
253#1805C2×C1111yescharacteristic, complemented
254#1803C2×C1111yescharacteristic, complemented
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11#12112yes—
276C23×C11C22×D411yescharacteristic
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—22no—
280Q8×C11#12314yes—
281D4×C11—22no—
282D4×C11—22no—
283D4×C11—48no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—41no—
287D4×C11—41no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—84no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
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—48no—
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—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11#12112yes—
328C2×C4×C11#13512yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11H(5,𝔽2)11yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C8×C11—41no—
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339C22×#41C22×C1111yescharacteristic
340C22×SD16C22×C1111yescharacteristic
341C22×D8C22×C1111yescharacteristic
342C23×C8C22×C1111yescharacteristic
343C2×#121C22×C1111yescharacteristic
344C2×C4×Q8C22×C1111yescharacteristic
345C2×C4×Q8C22×C1111yescharacteristic
346C2×#117C22×C1111yescharacteristic
347#449—24no—
348C2×C4⋊C8C22×C1111yescharacteristic
349C2×C4⋊C8C22×C1111yescharacteristic
350#416—24no—
351C2×#103C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#103C22×C1111yescharacteristic
354C2×#102C22×C1111yescharacteristic
355C2×#102C22×C1111yescharacteristic
356C2×#102C22×C1111yescharacteristic
357C2×#102C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359C2×C22⋊C8C22×C1111yescharacteristic
360#394—21no—
361#394—21no—
362#390—21no—
363#390—21no—
364#390C22×C1111yescharacteristic
365#390C22×C1111yescharacteristic
366#390C22×C1111yescharacteristic
367#390C22×C1111yescharacteristic
368#388—21no—
369#388—21no—
370#384C22×C1111yescharacteristic
371#382C22×C1111yescharacteristic
372#380—21no—
373#380C22×C1111yescharacteristic
374C4×C22⋊C4—21no—
375C4×C22⋊C4C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377#340C22×C1111yescharacteristic
378#340C22×C1111yescharacteristic
379#340C22×C1111yescharacteristic
380#340C22×C1111yescharacteristic
381#340C22×C1111yescharacteristic
382#336C22×C1111yescharacteristic
383#336C22×C1111yescharacteristic
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11C2×#12111yescharacteristic
406C22×C11#54611yescharacteristic
407C22×C11#54611yescharacteristic
408C22×C11C2×#13511yescharacteristic
409C22×C11#57511yescharacteristic
410C22×C11#57611yescharacteristic
411C22×C11#57711yescharacteristic
412C4×C11—22no—
413C4×C11—24no—
414C4×C11—22no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11—81no—
422C4×C11—81no—
423C4×C11C2×#12311yescharacteristic
424C4×C11#53411yescharacteristic
425C4×C11#55111yescharacteristic
426C4×C11#55111yescharacteristic
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—41no—
431C2×#41—41no—
432C2×#41D4×C1114yes—
433C22×Q8C23×C1111yescharacteristic
434C22×D4—21no—
435C22×D4—21no—
436C22×D4C23×C1111yescharacteristic
437C22×D4C23×C1111yescharacteristic
438C23×C4—21no—
439C23×C4C23×C1111yescharacteristic
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×D8—22no—
444C2×D8—41no—
445C2×D8—41no—
446C22×C8—22no—
447C22×C8—41no—
448C22×C8—41no—
449C22×C8C23×C1111yescharacteristic
450C22×C8C23×C1111yescharacteristic
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453#121—22no—
454#121—22no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—41no—
458C4×Q8—41no—
459#117—22no—
460#117—22no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4C23×C1111yescharacteristic
466C2×C4⋊C4C23×C1111yescharacteristic
467C2×C4⋊C4C23×C1111yescharacteristic
468C2×C4⋊C4C23×C1111yescharacteristic
469C2×C4⋊C4C23×C1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4D4×C1111yescharacteristic
482C2×C22⋊C4D4×C1111yescharacteristic
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42C23×C1111yescharacteristic
487C2×C42C23×C1111yescharacteristic
488C4⋊C8—41no—
489C4⋊C8—41no—
490#103—22no—
491#103—22no—
492#103—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#102—41no—
497#102—41no—
498C22⋊C8—22no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95D4×C1111yescharacteristic
503#95D4×C1111yescharacteristic
504C2×C11—42no—
505C2×C11—82no—
506C2×C11—161no—
507C2×C11#241211yescharacteristic
508C2×C11#303511yescharacteristic
509C2×C11#304511yescharacteristic
510C2×C11#330111yescharacteristic
511C2×C11#330511yescharacteristic
512C2×C11#330911yescharacteristic
513C2×C11#332111yescharacteristic
514C24—21no—
515C24—21no—
516C24C2×D4×C1111yescharacteristic
517#41—28no—
518#41—44no—
519#41—44no—
520#41—44no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8C2×D4×C1112yes—
525C2×Q8C11×#4112yes—
526C2×Q8C11×#4112yes—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4C2×D4×C1112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4C2×D4×C1111yescharacteristic
559C22×C4C2×D4×C1111yescharacteristic
560C22×C4C2×D4×C1111yescharacteristic
561C22×C4C2×D4×C1111yescharacteristic
562C22×C4C2×D4×C1112yes—
563C22×C4C2×D4×C1111yescharacteristic
564C22×C4C11×#4112yes—
565C22×C4C24×C1111yescharacteristic
566SD16—44no—
567D8—44no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—44no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—81no—
594C4⋊C4—81no—
595C22⋊C4—22no—
596C22⋊C4—41no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—42no—
613C42—42no—
614C42—42no—
615C11#2453511yescharacteristic, direct product factor, Sylow
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23C11×#12112yes—
637C23C22×D4×C1111yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8C11×#12314yes—
642D4—22no—
643D4—22no—
644D4—48no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—84no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—48no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4C11×#12112yes—
689C2×C4C11×#13512yes—
690C2×C4C22×D4×C1111yescharacteristic
691C2×C4C2×C11×#4111yescharacteristic
692C2×C4C2×C11×#4111yescharacteristic
693C2×C4C2×C11×#4111yescharacteristic
694C2×C4C11×H(5,𝔽2)11yescharacteristic
695C2×C4C11×H(5,𝔽2)11yescharacteristic
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C2×C11×#12111yescharacteristic
722C22C11×#54611yescharacteristic
723C22C11×#54611yescharacteristic
724C22C2×C11×#13511yescharacteristic
725C22C11×#57511yescharacteristic
726C22C11×#57611yescharacteristic
727C22C11×#57711yescharacteristic
728C4—22no—
729C4—24no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4C2×C11×#12311yescharacteristic
740C4C11×#53411yescharacteristic
741C4C11×#55111yescharacteristic
742C4C11×#55111yescharacteristic
743C2—42no—
744C2—82no—
745C2—161no—
746C2C11×#241211yescharacteristic
747C2C11×#303511yescharacteristic
748C2C11×#304511yescharacteristic
749C2C11×#330111yescharacteristic
750C2C11×#330511yescharacteristic
751C2C11×#330911yescharacteristic
752C2C11×#332111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#416C2semidirect
3. C11×#2500C2semidirect
4. C11×#2341C2semidirect
5. C11×#2073C2semidirect
6. C11×#2071C2semidirect
7. C11×#2054C2semidirect
8. C11×#2054C2semidirect
9. C11×#1893C2semidirect
10. C11×#1880C2semidirect
11. C11×#1880C2semidirect
12. C11×#1850C2semidirect
13. C11×#1825C2semidirect
14. C11×#1805C2semidirect
15. C11×#1803C2semidirect
138. #24535C11direct (N × H)
241. C2×#416C2×C11semidirect
242. #2500C2×C11semidirect
243. #2341C2×C11semidirect
244. #2073C2×C11semidirect
245. #2071C2×C11semidirect
246. #2054C2×C11semidirect
247. #2054C2×C11semidirect
248. #1893C2×C11semidirect
249. #1880C2×C11semidirect
250. #1880C2×C11semidirect
251. #1850C2×C11semidirect
252. #1825C2×C11semidirect
253. #1805C2×C11semidirect
254. #1803C2×C11semidirect
615. C11#24535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4492
C2×C11×#4162
C11×#25002
C11×#23412
C11×#20732
C11×#20712
C11×#20542
C11×#18932
C11×#18802
C11×#18502
C11×#18252
C11×#18052
C11×#18032
#2453511