Finite Group Databasebeta

← C11×#24403 #14601596

Subgroups — C11×#24403 #14601596

Order 2816.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#575C211yesmaximal, characteristic
2C2×C11×#473C211yesmaximal, characteristic, complemented
3C2×C11×#471C211yesmaximal, characteristic, complemented
4C11×#3007C211yesmaximal, characteristic, complemented
5C2×C11×#452C211yesmaximal, characteristic, complemented
6C11×#2880C211yesmaximal, characteristic, complemented
7C11×#2052C211yesmaximal, characteristic, complemented
8C11×#2051C211yesmaximal, characteristic, complemented
9C11×#2020C211yesmaximal, characteristic, complemented
10C11×#2019C211yesmaximal, characteristic, complemented
11C11×#1908C211yesmaximal, characteristic, complemented
12C11×#1907C211yesmaximal, characteristic, complemented
13C11×#1901C211yesmaximal, characteristic, complemented
14C11×#1855C211yesmaximal, characteristic, complemented
15C11×#1785C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#575—24no—
19C11×#575—24no—
20C2×C11×#137—21no—
21C2×C11×#137C2211yescharacteristic
22C2×C11×#137C2211yescharacteristic
23C2×C11×#137C2211yescharacteristic
24C2×C11×#137C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)—21no—
26C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C11×#135—21no—
29C2×C11×#135—21no—
30C22×C11×Q16C2211yescharacteristic, complemented
31C22×C11×SD16C2211yescharacteristic, complemented
32C2×C11×#131C2211yescharacteristic
33C2×C11×#131C2211yescharacteristic
34C22×C11×M16C2211yescharacteristic
35C2×C11×C22⋊Q8C2211yescharacteristic
36C11×#473—24no—
37C11×#471—24no—
38C11×#452—21no—
39C11×#452—21no—
40C11×#452—21no—
41C11×#452—21no—
42C11×#452—21no—
43C11×#452—21no—
44C11×#451—21no—
45C11×#450—21no—
46C2×C11×#108C2211yescharacteristic, complemented
47C2×C11×#108C2211yescharacteristic, complemented
48C11×#417C2211yescharacteristic
49C11×#417C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×C11×#101C2211yescharacteristic, complemented
53C2×C11×#101C2211yescharacteristic, complemented
54C2×C11×#101C2211yescharacteristic, complemented
55C2×C11×#101C2211yescharacteristic, complemented
56C2×C11×#100C2211yescharacteristic, complemented
57C2×C11×#100C2211yescharacteristic, complemented
58C11×#408—21no—
59C11×#408—21no—
60C11×#408C2211yescharacteristic
61C11×#408C2211yescharacteristic
62C11×#407—21no—
63C11×#407C2211yescharacteristic
64C11×#407C2211yescharacteristic
65C2×C11×C22⋊C8—21no—
66C2×C11×C22⋊C8C2211yescharacteristic
67C11×#343C2211yescharacteristic, complemented
68C11×#343C2211yescharacteristic, complemented
69C11×#341C2211yescharacteristic, complemented
70C11×#341C2211yescharacteristic, complemented
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—22no—
74C2×C11×#41—22no—
75C2×C11×#41—22no—
76C2×C11×#41—22no—
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—41no—
82C2×C11×#41—41no—
83C2×C11×#41—41no—
84C2×C11×#41—41no—
85C2×C11×#41D411yescharacteristic
86C2×C11×#41D411yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C22×Q8×C11D411yescharacteristic
90C22×Q8×C11C2311yescharacteristic
91C22×Q8×C11C2311yescharacteristic
92C22×D4×C11—21no—
93C22×D4×C11—21no—
94C22×D4×C11D411yescharacteristic
95C22×D4×C11C2311yescharacteristic
96C23×C4×C11—21no—
97C23×C4×C11—21no—
98C23×C4×C11C2311yescharacteristic
99C11×#137—28no—
100C11×#137—22no—
101C11×#137—22no—
102C11×#137—22no—
103C11×#137—22no—
104C11×#137—22no—
105C11×#137—41no—
106C11×#137—41no—
107C11×#137D414yes—
108C11×AGL(1,ℤ/8)—28no—
109C11×AGL(1,ℤ/8)—22no—
110C11×AGL(1,ℤ/8)—22no—
111C11×AGL(1,ℤ/8)—22no—
112C11×AGL(1,ℤ/8)D414yes—
113C11×#135—28no—
114C11×#135—28no—
115C2×C11×Q16—21no—
116C2×C11×Q16—21no—
117C2×C11×Q16—22no—
118C2×C11×Q16—21no—
119C2×C11×Q16—21no—
120C2×C11×Q16—21no—
121C2×C11×Q16—21no—
122C2×C11×Q16—41no—
123C2×C11×SD16—21no—
124C2×C11×SD16—21no—
125C2×C11×SD16—21no—
126C2×C11×SD16—21no—
127C2×C11×SD16—22no—
128C2×C11×SD16—21no—
129C2×C11×SD16—21no—
130C2×C11×SD16—21no—
131C2×C11×SD16—21no—
132C2×C11×SD16—41no—
133C2×C11×D8—21no—
134C2×C11×D8—21no—
135C11×#131—22no—
136C11×#131—22no—
137C11×#131—41no—
138C11×#131—41no—
139C2×C11×M16—21no—
140C2×C11×M16—22no—
141C2×C11×M16—22no—
142C2×C11×M16—21no—
143C2×C11×M16—21no—
144C2×C11×M16C2311yescharacteristic
145C2×C11×M16C2311yescharacteristic
146C2×C11×M16C2311yescharacteristic
147C2×C11×M16C2311yescharacteristic
148C2×C11×M16C2311yescharacteristic
149C2×C11×M16C2311yescharacteristic
150C22×C8×C11—21no—
151C22×C8×C11—21no—
152C22×C8×C11—21no—
153C22×C8×C11C2311yescharacteristic
154C22×C8×C11C2311yescharacteristic
155C11×C22⋊Q8—21no—
156C11×C22⋊Q8—21no—
157C11×C22⋊Q8—21no—
158C11×C22⋊Q8—21no—
159C2×C11×C4⋊C4—21no—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4—21no—
162C11×#108—22no—
163C11×#108—22no—
164C11×#103—21no—
165C11×#103—21no—
166C11×#103—21no—
167C11×#103—21no—
168C11×#102—21no—
169C11×#102—21no—
170C11×#102—21no—
171C11×#102—21no—
172C11×#101—22no—
173C11×#101—22no—
174C11×#101—22no—
175C11×#101—41no—
176C11×#100—22no—
177C11×#100—41no—
178C11×C22⋊C8—21no—
179C11×C22⋊C8—21no—
180C11×C22⋊C8—21no—
181C11×C22⋊C8—21no—
182C11×C22⋊C8—21no—
183C11×C22⋊C8—21no—
184C11×C22⋊C8—21no—
185C11×C22⋊C8—21no—
186C11×C22⋊C8D411yescharacteristic
187C11×C22⋊C8D411yescharacteristic
188C11×C22⋊C8D411yescharacteristic
189C11×C22⋊C8D411yescharacteristic
190#24403C1111yesmaximal, characteristic, direct product factor, Sylow
191C24×C11—21no—
192C24×C11—21no—
193C24×C11#4111yescharacteristic
194C11×#41—21no—
195C11×#41—21no—
196C11×#41—24no—
197C11×#41—24no—
198C11×#41—22no—
199C11×#41—22no—
200C11×#41—21no—
201C11×#41—21no—
202C11×#41—21no—
203C11×#41—21no—
204C11×#41—42no—
205C11×#41—42no—
206C11×#41—41no—
207C11×#41—41no—
208C11×#41—42no—
209C11×#41—42no—
210C11×#41—42no—
211C11×#41—42no—
212C11×#41—42no—
213C11×#41—42no—
214C11×#41—42no—
215C11×#41—42no—
216C11×#41C2×D412yes—
217C11×#41C2×D412yes—
218C2×Q8×C11—21no—
219C2×Q8×C11—21no—
220C2×Q8×C11—22no—
221C2×Q8×C11—21no—
222C2×Q8×C11—21no—
223C2×Q8×C11—21no—
224C2×Q8×C11—21no—
225C2×Q8×C11—21no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11—21no—
229C2×Q8×C11—21no—
230C2×Q8×C11—21no—
231C2×Q8×C11—41no—
232C2×Q8×C11C2×D412yes—
233C2×Q8×C11C2×D411yescharacteristic
234C2×Q8×C11C2×D411yescharacteristic
235C2×D4×C11—21no—
236C2×D4×C11—22no—
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11—21no—
241C2×D4×C11—21no—
242C2×D4×C11—21no—
243C2×D4×C11—21no—
244C2×D4×C11—21no—
245C2×D4×C11—21no—
246C2×D4×C11—41no—
247C2×D4×C11—42no—
248C2×D4×C11—42no—
249C2×D4×C11—42no—
250C2×D4×C11—42no—
251C2×D4×C11—41no—
252C2×D4×C11—41no—
253C2×D4×C11C2×D412yes—
254C2×D4×C11C2×D411yescharacteristic
255C2×D4×C11C2×D411yescharacteristic
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—42no—
269C22×C4×C11—42no—
270C22×C4×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11—41no—
273C22×C4×C11—41no—
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D411yescharacteristic
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11#4111yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C11×Q16—24no—
281C11×Q16—24no—
282C11×Q16—42no—
283C11×Q16—42no—
284C11×Q16—42no—
285C11×Q16—42no—
286C11×SD16—24no—
287C11×SD16—24no—
288C11×SD16—24no—
289C11×SD16—24no—
290C11×SD16—42no—
291C11×SD16—42no—
292C11×SD16—42no—
293C11×SD16—42no—
294C11×D8—24no—
295C11×D8—24no—
296C11×M16—24no—
297C11×M16—21no—
298C11×M16—21no—
299C11×M16—21no—
300C11×M16—21no—
301C11×M16—21no—
302C11×M16—21no—
303C11×M16—21no—
304C11×M16—21no—
305C11×M16—21no—
306C11×M16—21no—
307C11×M16—42no—
308C11×M16—42no—
309C11×M16C2×D412yes—
310C11×M16C2×D412yes—
311C2×C8×C11—24no—
312C2×C8×C11—21no—
313C2×C8×C11—21no—
314C2×C8×C11—21no—
315C2×C8×C11—21no—
316C2×C8×C11—21no—
317C2×C8×C11—21no—
318C2×C8×C11—21no—
319C2×C8×C11—21no—
320C2×C8×C11—21no—
321C2×C8×C11—21no—
322C2×C8×C11—42no—
323C2×C8×C11—42no—
324C2×C8×C11C2×D411yescharacteristic
325C2×C8×C11C2×D411yescharacteristic
326C2×C8×C11C2×D411yescharacteristic
327C2×C8×C11C2×D411yescharacteristic
328C11×C4⋊C4—21no—
329C11×C4⋊C4—21no—
330C11×C4⋊C4—41no—
331C11×C4⋊C4—41no—
332C11×C22⋊C4—41no—
333C11×C22⋊C4—41no—
334C2×#575C2×C1111yescharacteristic
335C2×#473C2×C1111yescharacteristic, complemented
336C2×#471C2×C1111yescharacteristic, complemented
337#3007C2×C1111yescharacteristic, complemented
338C2×#452C2×C1111yescharacteristic, complemented
339#2880C2×C1111yescharacteristic, complemented
340#2052C2×C1111yescharacteristic, complemented
341#2051C2×C1111yescharacteristic, complemented
342#2020C2×C1111yescharacteristic, complemented
343#2019C2×C1111yescharacteristic, complemented
344#1908C2×C1111yescharacteristic, complemented
345#1907C2×C1111yescharacteristic, complemented
346#1901C2×C1111yescharacteristic, complemented
347#1855C2×C1111yescharacteristic, complemented
348#1785C2×C1111yescharacteristic, complemented
349C23×C11—21no—
350C23×C11—21no—
351C23×C11—21no—
352C23×C11—21no—
353C23×C11—22no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—81no—
361C23×C11—81no—
362C23×C11—81no—
363C23×C11#12111yescharacteristic
364C23×C11#12111yescharacteristic
365C23×C11C2×#4111yescharacteristic
366Q8×C11—21no—
367Q8×C11—21no—
368Q8×C11—22no—
369Q8×C11—21no—
370Q8×C11—22no—
371Q8×C11—42no—
372Q8×C11—41no—
373Q8×C11—41no—
374Q8×C11—41no—
375Q8×C11—41no—
376Q8×C11—41no—
377Q8×C11—41no—
378Q8×C11#12012yes—
379D4×C11—22no—
380D4×C11—22no—
381D4×C11—21no—
382D4×C11—22no—
383D4×C11—21no—
384D4×C11—21no—
385D4×C11—22no—
386D4×C11—42no—
387D4×C11—42no—
388D4×C11—42no—
389D4×C11—44no—
390D4×C11—44no—
391D4×C11—41no—
392D4×C11—41no—
393D4×C11—41no—
394D4×C11—41no—
395D4×C11#12012yes—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—22no—
411C2×C4×C11—42no—
412C2×C4×C11—42no—
413C2×C4×C11—42no—
414C2×C4×C11—44no—
415C2×C4×C11—44no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—81no—
425C2×C4×C11#12111yescharacteristic
426C2×C4×C11#12111yescharacteristic
427C2×C4×C11C22×D411yescharacteristic
428C2×C4×C11C22×D411yescharacteristic
429C2×C4×C11C22×D411yescharacteristic
430C2×C4×C11C22×D411yescharacteristic
431C2×C4×C11H(5,𝔽2)11yescharacteristic
432C2×C4×C11H(5,𝔽2)11yescharacteristic
433C8×C11—22no—
434C8×C11—22no—
435C8×C11—21no—
436C8×C11—21no—
437C8×C11—21no—
438C8×C11—21no—
439C8×C11—41no—
440C8×C11—41no—
441C8×C11—41no—
442C8×C11—41no—
443C22×#41C22×C1111yescharacteristic
444C22×#41C22×C1111yescharacteristic
445#575—24no—
446#575—24no—
447C2×#137—21no—
448C2×#137C22×C1111yescharacteristic
449C2×#137C22×C1111yescharacteristic
450C2×#137C22×C1111yescharacteristic
451C2×#137C22×C1111yescharacteristic
452C2×AGL(1,ℤ/8)—21no—
453C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
454C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
455C2×#135—21no—
456C2×#135—21no—
457C22×Q16C22×C1111yescharacteristic, complemented
458C22×SD16C22×C1111yescharacteristic, complemented
459C2×#131C22×C1111yescharacteristic
460C2×#131C22×C1111yescharacteristic
461C22×M16C22×C1111yescharacteristic
462C2×C22⋊Q8C22×C1111yescharacteristic
463#473—24no—
464#471—24no—
465#452—21no—
466#452—21no—
467#452—21no—
468#452—21no—
469#452—21no—
470#452—21no—
471#451—21no—
472#450—21no—
473C2×#108C22×C1111yescharacteristic, complemented
474C2×#108C22×C1111yescharacteristic, complemented
475#417C22×C1111yescharacteristic
476#417C22×C1111yescharacteristic
477C2×#103C22×C1111yescharacteristic, complemented
478C2×#102C22×C1111yescharacteristic, complemented
479C2×#101C22×C1111yescharacteristic, complemented
480C2×#101C22×C1111yescharacteristic, complemented
481C2×#101C22×C1111yescharacteristic, complemented
482C2×#101C22×C1111yescharacteristic, complemented
483C2×#100C22×C1111yescharacteristic, complemented
484C2×#100C22×C1111yescharacteristic, complemented
485#408—21no—
486#408—21no—
487#408C22×C1111yescharacteristic
488#408C22×C1111yescharacteristic
489#407—21no—
490#407C22×C1111yescharacteristic
491#407C22×C1111yescharacteristic
492C2×C22⋊C8—21no—
493C2×C22⋊C8C22×C1111yescharacteristic
494#343C22×C1111yescharacteristic, complemented
495#343C22×C1111yescharacteristic, complemented
496#341C22×C1111yescharacteristic, complemented
497#341C22×C1111yescharacteristic, complemented
498C22×C11—21no—
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—22no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—41no—
508C22×C11—41no—
509C22×C11—41no—
510C22×C11—42no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11—81no—
514C22×C11—81no—
515C22×C11—82no—
516C22×C11—82no—
517C22×C11—84no—
518C22×C11—81no—
519C22×C11—81no—
520C22×C11C2×#12111yescharacteristic
521C22×C11#54611yescharacteristic
522C22×C11#54611yescharacteristic
523C4×C11—21no—
524C4×C11—21no—
525C4×C11—22no—
526C4×C11—41no—
527C4×C11—42no—
528C4×C11—81no—
529C4×C11—81no—
530C4×C11C2×#12011yescharacteristic
531C4×C11#53411yescharacteristic
532C4×C11D4211yescharacteristic
533C4×C11D4211yescharacteristic
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—22no—
537C2×#41—22no—
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—41no—
545C2×#41—41no—
546C2×#41—41no—
547C2×#41—41no—
548C2×#41D4×C1111yescharacteristic
549C2×#41D4×C1111yescharacteristic
550C2×#41C23×C1111yescharacteristic
551C2×#41C23×C1111yescharacteristic
552C22×Q8D4×C1111yescharacteristic
553C22×Q8C23×C1111yescharacteristic
554C22×Q8C23×C1111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4D4×C1111yescharacteristic
558C22×D4C23×C1111yescharacteristic
559C23×C4—21no—
560C23×C4—21no—
561C23×C4C23×C1111yescharacteristic
562#137—28no—
563#137—22no—
564#137—22no—
565#137—22no—
566#137—22no—
567#137—22no—
568#137—41no—
569#137—41no—
570#137D4×C1114yes—
571AGL(1,ℤ/8)—28no—
572AGL(1,ℤ/8)—22no—
573AGL(1,ℤ/8)—22no—
574AGL(1,ℤ/8)—22no—
575AGL(1,ℤ/8)D4×C1114yes—
576#135—28no—
577#135—28no—
578C2×Q16—21no—
579C2×Q16—21no—
580C2×Q16—22no—
581C2×Q16—21no—
582C2×Q16—21no—
583C2×Q16—21no—
584C2×Q16—21no—
585C2×Q16—41no—
586C2×SD16—21no—
587C2×SD16—21no—
588C2×SD16—21no—
589C2×SD16—21no—
590C2×SD16—22no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—41no—
596C2×D8—21no—
597C2×D8—21no—
598#131—22no—
599#131—22no—
600#131—41no—
601#131—41no—
602C2×M16—21no—
603C2×M16—22no—
604C2×M16—22no—
605C2×M16—21no—
606C2×M16—21no—
607C2×M16C23×C1111yescharacteristic
608C2×M16C23×C1111yescharacteristic
609C2×M16C23×C1111yescharacteristic
610C2×M16C23×C1111yescharacteristic
611C2×M16C23×C1111yescharacteristic
612C2×M16C23×C1111yescharacteristic
613C22×C8—21no—
614C22×C8—21no—
615C22×C8—21no—
616C22×C8C23×C1111yescharacteristic
617C22×C8C23×C1111yescharacteristic
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—21no—
621C22⋊Q8—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4C23×C1111yescharacteristic
624C2×C22⋊C4—21no—
625#108—22no—
626#108—22no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103—21no—
631#102—21no—
632#102—21no—
633#102—21no—
634#102—21no—
635#101—22no—
636#101—22no—
637#101—22no—
638#101—41no—
639#100—22no—
640#100—41no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C22⋊C8—21no—
648C22⋊C8—21no—
649C22⋊C8D4×C1111yescharacteristic
650C22⋊C8D4×C1111yescharacteristic
651C22⋊C8D4×C1111yescharacteristic
652C22⋊C8D4×C1111yescharacteristic
653C2×C11—21no—
654C2×C11—21no—
655C2×C11—41no—
656C2×C11—41no—
657C2×C11—42no—
658C2×C11—81no—
659C2×C11—82no—
660C2×C11#241011yescharacteristic
661C2×C11#306711yescharacteristic
662C2×C11#306911yescharacteristic
663C24—21no—
664C24—21no—
665C24C11×#4111yescharacteristic
666#41—21no—
667#41—21no—
668#41—24no—
669#41—24no—
670#41—22no—
671#41—22no—
672#41—21no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—42no—
677#41—42no—
678#41—41no—
679#41—41no—
680#41—42no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41C2×D4×C1112yes—
689#41C2×D4×C1112yes—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—22no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—41no—
704C2×Q8C2×D4×C1112yes—
705C2×Q8C2×D4×C1111yescharacteristic
706C2×Q8C2×D4×C1111yescharacteristic
707C2×D4—21no—
708C2×D4—22no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—41no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—41no—
724C2×D4—41no—
725C2×D4C2×D4×C1112yes—
726C2×D4C2×D4×C1111yescharacteristic
727C2×D4C2×D4×C1111yescharacteristic
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4C2×D4×C1111yescharacteristic
747C22×C4C2×D4×C1111yescharacteristic
748C22×C4C2×D4×C1111yescharacteristic
749C22×C4C2×D4×C1111yescharacteristic
750C22×C4C11×#4111yescharacteristic
751C22×C4C24×C1111yescharacteristic
752Q16—24no—
753Q16—24no—
754Q16—42no—
755Q16—42no—
756Q16—42no—
757Q16—42no—
758SD16—24no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—42no—
763SD16—42no—
764SD16—42no—
765SD16—42no—
766D8—24no—
767D8—24no—
768M16—24no—
769M16—21no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—21no—
779M16—42no—
780M16—42no—
781M16C2×D4×C1112yes—
782M16C2×D4×C1112yes—
783C2×C8—24no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—42no—
795C2×C8—42no—
796C2×C8C2×D4×C1111yescharacteristic
797C2×C8C2×D4×C1111yescharacteristic
798C2×C8C2×D4×C1111yescharacteristic
799C2×C8C2×D4×C1111yescharacteristic
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—41no—
803C4⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C11#2440311yescharacteristic, direct product factor, Sylow
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23C11×#12111yescharacteristic
822C23C11×#12111yescharacteristic
823C23C2×C11×#4111yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—41no—
833Q8—41no—
834Q8—41no—
835Q8—41no—
836Q8C11×#12012yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4C11×#12012yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—81no—
883C2×C4C11×#12111yescharacteristic
884C2×C4C11×#12111yescharacteristic
885C2×C4C22×D4×C1111yescharacteristic
886C2×C4C22×D4×C1111yescharacteristic
887C2×C4C22×D4×C1111yescharacteristic
888C2×C4C22×D4×C1111yescharacteristic
889C2×C4C11×H(5,𝔽2)11yescharacteristic
890C2×C4C11×H(5,𝔽2)11yescharacteristic
891C8—22no—
892C8—22no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—41no—
898C8—41no—
899C8—41no—
900C8—41no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—22no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×C11×#12111yescharacteristic
924C22C11×#54611yescharacteristic
925C22C11×#54611yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×C11×#12011yescharacteristic
934C4C11×#53411yescharacteristic
935C4D42×C1111yescharacteristic
936C4D42×C1111yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C11×#241011yescharacteristic
945C2C11×#306711yescharacteristic
946C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#473C2semidirect
3. C2×C11×#471C2semidirect
4. C11×#3007C2semidirect
5. C2×C11×#452C2semidirect
6. C11×#2880C2semidirect
7. C11×#2052C2semidirect
8. C11×#2051C2semidirect
9. C11×#2020C2semidirect
10. C11×#2019C2semidirect
11. C11×#1908C2semidirect
12. C11×#1907C2semidirect
13. C11×#1901C2semidirect
14. C11×#1855C2semidirect
15. C11×#1785C2semidirect
30. C22×C11×Q16C22semidirect
31. C22×C11×SD16C22semidirect
46. C2×C11×#108C22semidirect
47. C2×C11×#108C22semidirect
50. C2×C11×#103C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×#101C22semidirect
53. C2×C11×#101C22semidirect
54. C2×C11×#101C22semidirect
55. C2×C11×#101C22semidirect
56. C2×C11×#100C22semidirect
57. C2×C11×#100C22semidirect
67. C11×#343C22semidirect
68. C11×#343C22semidirect
69. C11×#341C22semidirect
70. C11×#341C22semidirect
190. #24403C11direct (N × H)
335. C2×#473C2×C11semidirect
336. C2×#471C2×C11semidirect
337. #3007C2×C11semidirect
338. C2×#452C2×C11semidirect
339. #2880C2×C11semidirect
340. #2052C2×C11semidirect
341. #2051C2×C11semidirect
342. #2020C2×C11semidirect
343. #2019C2×C11semidirect
344. #1908C2×C11semidirect
345. #1907C2×C11semidirect
346. #1901C2×C11semidirect
347. #1855C2×C11semidirect
348. #1785C2×C11semidirect
457. C22×Q16C22×C11semidirect
458. C22×SD16C22×C11semidirect
473. C2×#108C22×C11semidirect
474. C2×#108C22×C11semidirect
477. C2×#103C22×C11semidirect
478. C2×#102C22×C11semidirect
479. C2×#101C22×C11semidirect
480. C2×#101C22×C11semidirect
481. C2×#101C22×C11semidirect
482. C2×#101C22×C11semidirect
483. C2×#100C22×C11semidirect
484. C2×#100C22×C11semidirect
494. #343C22×C11semidirect
495. #343C22×C11semidirect
496. #341C22×C11semidirect
497. #341C22×C11semidirect
806. C11#24403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5752
C2×C11×#4732
C2×C11×#4712
C11×#30072
C2×C11×#4522
C11×#28802
C11×#20522
C11×#20512
C11×#20202
C11×#20192
C11×#19082
C11×#19072
C11×#19012
C11×#18552
C11×#17852
#2440311