Finite Group Databasebeta

← C11×#24109 #14601302

Subgroups — C11×#24109 #14601302

Order 2816.

1084 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic
2C2×C11×#485C211yesmaximal, characteristic, complemented
3C2×C11×#428C211yesmaximal, characteristic, complemented
4C11×#2485C211yesmaximal, characteristic
5C11×#2058C211yesmaximal, characteristic, complemented
6C11×#2057C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#1894C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic
11C11×#1865C211yesmaximal, characteristic, complemented
12C11×#1863C211yesmaximal, characteristic, complemented
13C11×#1853C211yesmaximal, characteristic, complemented
14C11×#1852C211yesmaximal, characteristic, complemented
15C11×#1823C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C11×#554—24no—
18C11×#554—24no—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#125—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C11×#485—24no—
32C11×#428—24no—
33C2×C11×#107C2211yescharacteristic
34C2×C11×#107C2211yescharacteristic
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×#106C2211yescharacteristic
38C2×C11×#106C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C11×#397—21no—
47C11×#394—21no—
48C11×#389C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#388—21no—
51C11×#387—21no—
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C11×#380C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11D411yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8—22no—
79C11×#125—28no—
80C11×C22⋊Q8—28no—
81C11×C22⋊Q8—28no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8D414yes—
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C4×D4×C11—28no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C11×#117—22no—
92C11×#117—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C4⋊C4D414yes—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C11×C22⋊C4D411yescharacteristic
121C2×C42×C11—21no—
122C2×C42×C11—21no—
123C2×C42×C11C2311yescharacteristic
124C11×#107—22no—
125C11×#107—22no—
126C11×#107—22no—
127C11×#106—22no—
128C11×#106—22no—
129C11×#106—22no—
130C11×#103—22no—
131C11×#103—22no—
132C11×#103—22no—
133C11×#103—22no—
134C11×C22⋊C8—22no—
135C11×C22⋊C8—22no—
136C11×C22⋊C8—22no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142#24109C1111yesmaximal, characteristic, direct product factor, Sylow
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C2×Q8×C11—24no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—81no—
152C2×Q8×C11—81no—
153C2×Q8×C11C2×D412yes—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
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—81no—
178C22×C4×C11—81no—
179C22×C4×C11—81no—
180C22×C4×C11—81no—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C11×M16—28no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
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#4112yes—
200C2×C8×C11#4112yes—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—22no—
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—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—81no—
221C11×C4⋊C4C2×D412yes—
222C11×C4⋊C4C2×D412yes—
223C11×C4⋊C4C2×D412yes—
224C11×C22⋊C4—24no—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—81no—
231C11×C22⋊C4—81no—
232C42×C11—24no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—42no—
236C2×#554C2×C1111yescharacteristic
237C2×#485C2×C1111yescharacteristic, complemented
238C2×#428C2×C1111yescharacteristic, complemented
239#2485C2×C1111yescharacteristic
240#2058C2×C1111yescharacteristic, complemented
241#2057C2×C1111yescharacteristic, complemented
242#2036C2×C1111yescharacteristic, complemented
243#2035C2×C1111yescharacteristic, complemented
244#1894C2×C1111yescharacteristic, complemented
245#1870C2×C1111yescharacteristic
246#1865C2×C1111yescharacteristic, complemented
247#1863C2×C1111yescharacteristic, complemented
248#1853C2×C1111yescharacteristic, complemented
249#1852C2×C1111yescharacteristic, complemented
250#1823C2×C1111yescharacteristic, complemented
251C23×C11—21no—
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#12012yes—
264C23×C11#13712yes—
265C23×C11C22×D411yescharacteristic
266Q8×C11—22no—
267Q8×C11—22no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—84no—
271D4×C11—28no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
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—84no—
315C2×C4×C11—84no—
316C2×C4×C11#12012yes—
317C2×C4×C11#13712yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C112−1+411yescharacteristic
323C2×C4×C112−1+411yescharacteristic
324C8×C11—22no—
325C8×C11—22no—
326C8×C11—41no—
327C8×C11—41no—
328C22×M16C22×C1111yescharacteristic
329#554—24no—
330#554—24no—
331C2×C4⋊Q8C22×C1111yescharacteristic
332C2×#125—21no—
333C2×C22⋊Q8—21no—
334C2×C22⋊Q8—21no—
335C2×C22⋊Q8C22×C1111yescharacteristic
336C2×C22⋊Q8C22×C1111yescharacteristic
337C2×C4×Q8C22×C1111yescharacteristic
338C2×C4×D4—21no—
339C2×C4×D4C22×C1111yescharacteristic
340C2×#117C22×C1111yescharacteristic
341C22×C4⋊C4C22×C1111yescharacteristic
342C22×C4⋊C4C22×C1111yescharacteristic
343#485—24no—
344#428—24no—
345C2×#107C22×C1111yescharacteristic
346C2×#107C22×C1111yescharacteristic
347C2×#107C22×C1111yescharacteristic
348C2×#106C22×C1111yescharacteristic
349C2×#106C22×C1111yescharacteristic
350C2×#106C22×C1111yescharacteristic
351C2×#103C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#103C22×C1111yescharacteristic
354C2×#103C22×C1111yescharacteristic
355C2×C22⋊C8C22×C1111yescharacteristic
356C2×C22⋊C8C22×C1111yescharacteristic
357C2×C22⋊C8C22×C1111yescharacteristic
358#397—21no—
359#394—21no—
360#389C22×C1111yescharacteristic
361#389C22×C1111yescharacteristic
362#388—21no—
363#387—21no—
364#380C22×C1111yescharacteristic
365#380C22×C1111yescharacteristic
366#380C22×C1111yescharacteristic
367#340C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373#336C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—22no—
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×C11C2×#12011yescharacteristic
390C22×C11#54711yescharacteristic
391C22×C11#54711yescharacteristic
392C22×C11C2×#13711yescharacteristic
393C22×C11C2×#13711yescharacteristic
394C22×C11#57611yescharacteristic
395C22×C11#57711yescharacteristic
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—41no—
399C4×C11—42no—
400C4×C11—41no—
401C4×C11—42no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11#52511yescharacteristic
409C4×C11#53611yescharacteristic
410C4×C11#54711yescharacteristic
411C4×C11#54711yescharacteristic
412C22×Q8—21no—
413C22×Q8C23×C1111yescharacteristic
414C22×D4D4×C1111yescharacteristic
415C23×C4—21no—
416C23×C4—21no—
417C23×C4C23×C1111yescharacteristic
418C23×C4C23×C1111yescharacteristic
419C2×M16—22no—
420C2×M16—22no—
421C2×M16—22no—
422C22×C8C23×C1111yescharacteristic
423C22×C8C23×C1111yescharacteristic
424C22×C8C23×C1111yescharacteristic
425C22×C8C23×C1111yescharacteristic
426C4⋊Q8—22no—
427C4⋊Q8—22no—
428#125—28no—
429C22⋊Q8—28no—
430C22⋊Q8—28no—
431C22⋊Q8—22no—
432C22⋊Q8—22no—
433C22⋊Q8—22no—
434C22⋊Q8D4×C1114yes—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×D4—28no—
438C4×D4—22no—
439C4×D4—22no—
440#117—22no—
441#117—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4D4×C1111yescharacteristic
454C2×C4⋊C4D4×C1114yes—
455C2×C4⋊C4C23×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⋊C4D4×C1111yescharacteristic
469C2×C22⋊C4D4×C1111yescharacteristic
470C2×C42—21no—
471C2×C42—21no—
472C2×C42C23×C1111yescharacteristic
473#107—22no—
474#107—22no—
475#107—22no—
476#106—22no—
477#106—22no—
478#106—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483C22⋊C8—22no—
484C22⋊C8—22no—
485C22⋊C8—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491C2×C11—42no—
492C2×C11—42no—
493C2×C11#240611yescharacteristic
494C2×C11#300411yescharacteristic
495C2×C11#301211yescharacteristic
496C2×C11#334411yescharacteristic
497C2×C11#334611yescharacteristic
498C2×C11#335611yescharacteristic
499C2×C11#335711yescharacteristic
500C24C2×D4×C1111yescharacteristic
501C24C2×D4×C1111yescharacteristic
502C2×Q8—24no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—81no—
509C2×Q8—81no—
510C2×Q8C2×D4×C1112yes—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—24no—
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—81no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4C2×D4×C1111yescharacteristic
539C22×C4C2×D4×C1111yescharacteristic
540C22×C4C2×D4×C1111yescharacteristic
541C22×C4C2×D4×C1112yes—
542C22×C4C2×D4×C1112yes—
543C22×C4C2×D4×C1111yescharacteristic
544C22×C4C24×C1111yescharacteristic
545M16—28no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8C11×#4112yes—
557C2×C8C11×#4112yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—21no—
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—81no—
578C4⋊C4C2×D4×C1112yes—
579C4⋊C4C2×D4×C1112yes—
580C4⋊C4C2×D4×C1112yes—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C42—24no—
590C42—21no—
591C42—21no—
592C42—42no—
593C11#2410911yescharacteristic, direct product factor, Sylow
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23C11×#12012yes—
607C23C11×#13712yes—
608C23C22×D4×C1111yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—41no—
612Q8—41no—
613Q8—84no—
614D4—28no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
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—84no—
658C2×C4—84no—
659C2×C4C11×#12012yes—
660C2×C4C11×#13712yes—
661C2×C4C22×D4×C1111yescharacteristic
662C2×C4C22×D4×C1111yescharacteristic
663C2×C4C2×C11×#4111yescharacteristic
664C2×C4C2×C11×#4111yescharacteristic
665C2×C4C11×2−1+411yescharacteristic
666C2×C4C11×2−1+411yescharacteristic
667C8—22no—
668C8—22no—
669C8—41no—
670C8—41no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22C2×C11×#12011yescharacteristic
686C22C11×#54711yescharacteristic
687C22C11×#54711yescharacteristic
688C22C2×C11×#13711yescharacteristic
689C22C2×C11×#13711yescharacteristic
690C22C11×#57611yescharacteristic
691C22C11×#57711yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C11×#52511yescharacteristic
705C4C11×#53611yescharacteristic
706C4C11×#54711yescharacteristic
707C4C11×#54711yescharacteristic
708C2—42no—
709C2—42no—
710C2C11×#240611yescharacteristic
711C2C11×#300411yescharacteristic
712C2C11×#301211yescharacteristic
713C2C11×#334411yescharacteristic
714C2C11×#334611yescharacteristic
715C2C11×#335611yescharacteristic
716C2C11×#335711yescharacteristic
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
2. C2×C11×#485C2semidirect
3. C2×C11×#428C2semidirect
5. C11×#2058C2semidirect
6. C11×#2057C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#1894C2semidirect
11. C11×#1865C2semidirect
12. C11×#1863C2semidirect
13. C11×#1853C2semidirect
14. C11×#1852C2semidirect
15. C11×#1823C2semidirect
142. #24109C11direct (N × H)
237. C2×#485C2×C11semidirect
238. C2×#428C2×C11semidirect
240. #2058C2×C11semidirect
241. #2057C2×C11semidirect
242. #2036C2×C11semidirect
243. #2035C2×C11semidirect
244. #1894C2×C11semidirect
246. #1865C2×C11semidirect
247. #1863C2×C11semidirect
248. #1853C2×C11semidirect
249. #1852C2×C11semidirect
250. #1823C2×C11semidirect
593. C11#24109direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4852
C2×C11×#4282
C11×#24852
C11×#20582
C11×#20572
C11×#20362
C11×#20352
C11×#18942
C11×#18702
C11×#18652
C11×#18632
C11×#18532
C11×#18522
C11×#18232
#2410911