Finite Group Databasebeta

← C11×#24537 #14601730

Subgroups — C11×#24537 #14601730

Order 2816.

1048 conjugacy classes of subgroups.

The subgroup lattice has 758 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×#2339C211yesmaximal, characteristic, complemented
5C11×#2074C211yesmaximal, characteristic, complemented
6C11×#2072C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#1893C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1850C211yesmaximal, characteristic, complemented
13C11×#1825C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×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×#391C2211yescharacteristic
40C11×#391C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#388—21no—
44C11×#388—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#384C2211yescharacteristic
48C11×#382C2211yescharacteristic
49C11×#381—21no—
50C11×#380C2211yescharacteristic
51C4×C11×C22⋊C4C2211yescharacteristic
52C2×C11×#95—21no—
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×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C2×C11×SD16—22no—
77C2×C11×SD16—41no—
78C2×C11×SD16—41no—
79C2×C11×D8—22no—
80C2×C11×D8—22no—
81C2×C11×D8—22no—
82C22×C8×C11—22no—
83C22×C8×C11—41no—
84C22×C8×C11—41no—
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×#121—22no—
90C11×#121—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—41no—
94C4×D4×C11—41no—
95C11×#117—22no—
96C11×#117—22no—
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⋊C4D411yescharacteristic
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C11×C4⋊C8—41no—
119C11×C4⋊C8—41no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—41no—
127C11×#102—41no—
128C11×C22⋊C8—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#24537C1111yesmaximal, 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×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D412yes—
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—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—81no—
166C2×D4×C11—81no—
167C2×D4×C11C2×D412yes—
168C2×D4×C11#4112yes—
169C2×D4×C11#4112yes—
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×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—81no—
188C22×C4×C11—81no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11#4112yes—
196C22×C4×C11C2411yescharacteristic
197C11×SD16—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×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—44no—
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—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—81no—
223C11×C4⋊C4—81no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—41no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—81no—
233C11×C22⋊C4—81no—
234C11×C22⋊C4—81no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—42no—
240C2×#449C2×C1111yescharacteristic
241C2×#416C2×C1111yescharacteristic, complemented
242#2500C2×C1111yescharacteristic, complemented
243#2339C2×C1111yescharacteristic, complemented
244#2074C2×C1111yescharacteristic, complemented
245#2072C2×C1111yescharacteristic, complemented
246#2055C2×C1111yescharacteristic, complemented
247#2055C2×C1111yescharacteristic, complemented
248#1893C2×C1111yescharacteristic, complemented
249#1879C2×C1111yescharacteristic, complemented
250#1879C2×C1111yescharacteristic, complemented
251#1850C2×C1111yescharacteristic, complemented
252#1825C2×C1111yescharacteristic, complemented
253#1804C2×C1111yescharacteristic, complemented
254#1802C2×C1111yescharacteristic, complemented
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
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—41no—
280Q8×C11—41no—
281D4×C11—22no—
282D4×C11—22no—
283D4×C11—22no—
284D4×C11—48no—
285D4×C11—41no—
286D4×C11—41no—
287D4×C11—41no—
288D4×C11—41no—
289D4×C11—84no—
290D4×C11#12314yes—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
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—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—48no—
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—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—84no—
328C2×C4×C11—84no—
329C2×C4×C11#12112yes—
330C2×C4×C11#13512yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C8×C11—41no—
338C8×C11—41no—
339C8×C11—41no—
340C8×C11—41no—
341C22×#41C22×C1111yescharacteristic
342C22×SD16C22×C1111yescharacteristic
343C22×D8C22×C1111yescharacteristic
344C23×C8C22×C1111yescharacteristic
345C2×#121C22×C1111yescharacteristic
346C2×C4×D4C22×C1111yescharacteristic
347C2×C4×D4C22×C1111yescharacteristic
348C2×#117C22×C1111yescharacteristic
349#449—24no—
350C2×C4⋊C8C22×C1111yescharacteristic
351C2×C4⋊C8C22×C1111yescharacteristic
352#416—24no—
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×C22⋊C8C22×C1111yescharacteristic
362#394—21no—
363#394—21no—
364#391C22×C1111yescharacteristic
365#391C22×C1111yescharacteristic
366#390C22×C1111yescharacteristic
367#390C22×C1111yescharacteristic
368#388—21no—
369#388—21no—
370#386—21no—
371#386—21no—
372#384C22×C1111yescharacteristic
373#382C22×C1111yescharacteristic
374#381—21no—
375#380C22×C1111yescharacteristic
376C4×C22⋊C4C22×C1111yescharacteristic
377C2×#95—21no—
378#340C22×C1111yescharacteristic
379#340C22×C1111yescharacteristic
380#340C22×C1111yescharacteristic
381#340C22×C1111yescharacteristic
382#340C22×C1111yescharacteristic
383#340C22×C1111yescharacteristic
384#336C22×C1111yescharacteristic
385#336C22×C1111yescharacteristic
386C22×C11—22no—
387C22×C11—24no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—41no—
393C22×C11—42no—
394C22×C11—41no—
395C22×C11—42no—
396C22×C11—41no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—41no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11C2×#12111yescharacteristic
408C22×C11#54611yescharacteristic
409C22×C11#54611yescharacteristic
410C22×C11C2×#13511yescharacteristic
411C22×C11#57511yescharacteristic
412C22×C11#57611yescharacteristic
413C22×C11#57711yescharacteristic
414C4×C11—22no—
415C4×C11—22no—
416C4×C11—42no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—81no—
421C4×C11—81no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11C2×#12311yescharacteristic
426C4×C11#53411yescharacteristic
427C4×C11#55111yescharacteristic
428C4×C11#55111yescharacteristic
429C2×#41—22no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—41no—
433C2×#41—41no—
434C2×#41D4×C1114yes—
435C22×Q8C23×C1111yescharacteristic
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C23×C1111yescharacteristic
439C22×D4C23×C1111yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C23×C1111yescharacteristic
444C2×SD16—22no—
445C2×SD16—41no—
446C2×SD16—41no—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—22no—
450C22×C8—22no—
451C22×C8—41no—
452C22×C8—41no—
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457#121—22no—
458#121—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—41no—
462C4×D4—41no—
463#117—22no—
464#117—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4C23×C1111yescharacteristic
468C2×C4⋊C4C23×C1111yescharacteristic
469C2×C4⋊C4C23×C1111yescharacteristic
470C2×C4⋊C4C23×C1111yescharacteristic
471C2×C4⋊C4C23×C1111yescharacteristic
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×C42C23×C1111yescharacteristic
485C2×C42C23×C1111yescharacteristic
486C4⋊C8—41no—
487C4⋊C8—41no—
488#103—22no—
489#103—22no—
490#103—22no—
491#102—22no—
492#102—22no—
493#102—22no—
494#102—41no—
495#102—41no—
496C22⋊C8—22no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95D4×C1111yescharacteristic
505#95D4×C1111yescharacteristic
506C2×C11—42no—
507C2×C11—44no—
508C2×C11—161no—
509C2×C11#241211yescharacteristic
510C2×C11#303511yescharacteristic
511C2×C11#304511yescharacteristic
512C2×C11#329711yescharacteristic
513C2×C11#330311yescharacteristic
514C2×C11#330711yescharacteristic
515C2×C11#331911yescharacteristic
516C24—21no—
517C24—21no—
518C24C2×D4×C1111yescharacteristic
519#41—28no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×D4×C1112yes—
529C2×D4—24no—
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—
545C2×D4C11×#4112yes—
546C2×D4C11×#4112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4C2×D4×C1111yescharacteristic
567C22×C4C2×D4×C1111yescharacteristic
568C22×C4C2×D4×C1111yescharacteristic
569C22×C4C2×D4×C1111yescharacteristic
570C22×C4C2×D4×C1112yes—
571C22×C4C2×D4×C1111yescharacteristic
572C22×C4C11×#4112yes—
573C22×C4C24×C1111yescharacteristic
574SD16—44no—
575D8—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—44no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—81no—
600C4⋊C4—81no—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—42no—
617C11#2453711yescharacteristic, direct product factor, Sylow
618C23—22no—
619C23—22no—
620C23—22no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23C11×#12112yes—
639C23C22×D4×C1111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—48no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—84no—
653D4C11×#12314yes—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
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×C4—41no—
689C2×C4—41no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4C11×#12112yes—
693C2×C4C11×#13512yes—
694C2×C4C22×D4×C1111yescharacteristic
695C2×C4C2×C11×#4111yescharacteristic
696C2×C4C2×C11×#4111yescharacteristic
697C2×C4C2×C11×#4111yescharacteristic
698C2×C4C11×H(5,𝔽2)11yescharacteristic
699C2×C4C11×H(5,𝔽2)11yescharacteristic
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C22—22no—
705C22—24no—
706C22—22no—
707C22—22no—
708C22—42no—
709C22—42no—
710C22—41no—
711C22—42no—
712C22—41no—
713C22—42no—
714C22—41no—
715C22—42no—
716C22—42no—
717C22—41no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22C2×C11×#12111yescharacteristic
726C22C11×#54611yescharacteristic
727C22C11×#54611yescharacteristic
728C22C2×C11×#13511yescharacteristic
729C22C11×#57511yescharacteristic
730C22C11×#57611yescharacteristic
731C22C11×#57711yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4C2×C11×#12311yescharacteristic
744C4C11×#53411yescharacteristic
745C4C11×#55111yescharacteristic
746C4C11×#55111yescharacteristic
747C2—42no—
748C2—44no—
749C2—161no—
750C2C11×#241211yescharacteristic
751C2C11×#303511yescharacteristic
752C2C11×#304511yescharacteristic
753C2C11×#329711yescharacteristic
754C2C11×#330311yescharacteristic
755C2C11×#330711yescharacteristic
756C2C11×#331911yescharacteristic
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×#2339C2semidirect
5. C11×#2074C2semidirect
6. C11×#2072C2semidirect
7. C11×#2055C2semidirect
8. C11×#2055C2semidirect
9. C11×#1893C2semidirect
10. C11×#1879C2semidirect
11. C11×#1879C2semidirect
12. C11×#1850C2semidirect
13. C11×#1825C2semidirect
14. C11×#1804C2semidirect
15. C11×#1802C2semidirect
138. #24537C11direct (N × H)
241. C2×#416C2×C11semidirect
242. #2500C2×C11semidirect
243. #2339C2×C11semidirect
244. #2074C2×C11semidirect
245. #2072C2×C11semidirect
246. #2055C2×C11semidirect
247. #2055C2×C11semidirect
248. #1893C2×C11semidirect
249. #1879C2×C11semidirect
250. #1879C2×C11semidirect
251. #1850C2×C11semidirect
252. #1825C2×C11semidirect
253. #1804C2×C11semidirect
254. #1802C2×C11semidirect
617. C11#24537direct (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×#23392
C11×#20742
C11×#20722
C11×#20552
C11×#18932
C11×#18792
C11×#18502
C11×#18252
C11×#18042
C11×#18022
#2453711