Finite Group Databasebeta

← C11×#21874 #14599067

Subgroups — C11×#21874 #14599067

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C11×#2280C211yesmaximal, characteristic, complemented
3C2×C11×#380C211yesmaximal, characteristic, complemented
4C11×#1996C212yesmaximal, complemented
5C11×#1964C212yesmaximal, complemented
6C11×#1898C214yesmaximal, complemented
7C11×#1799C214yesmaximal, complemented
8C22×C11×#41C411yescharacteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C11×#525—21no—
11C11×#525—21no—
12C11×#525—21no—
13C11×#525—21no—
14C11×#525—21no—
15C11×#525—21no—
16C11×#525—21no—
17C11×#525—21no—
18C2×C11×#123C412yescomplemented
19C2×C11×C22⋊Q8C411yescharacteristic, complemented
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C411yescharacteristic, complemented
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120C2212yes—
24C2×C4×D4×C11C412yescomplemented
25C2×C4×D4×C11C2212yes—
26C2×C11×#117—21no—
27C2×C11×#117C411yescharacteristic, complemented
28C22×C11×C4⋊C4—21no—
29C22×C11×C22⋊C4C2212yes—
30C2×C11×#99C2218yes—
31C11×#381—21no—
32C11×#380—21no—
33C11×#380—21no—
34C11×#380—21no—
35C11×#380C2212yes—
36C11×#380C2212yes—
37C11×#380C2212yes—
38C11×#379C2212yes—
39C4×C11×C22⋊C4—21no—
40C4×C11×C22⋊C4C2212yes—
41C2×C11×#95—21no—
42C11×#342C2218yes—
43C25×C11C2311yescharacteristic
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—44no—
49C22×Q8×C11C2×C411yescharacteristic, complemented
50C22×D4×C11C2×C412yes—
51C22×D4×C11C2×C412yes—
52C22×D4×C11C2×C411yescharacteristic, complemented
53C22×D4×C11C2312yes—
54C23×C4×C11—22no—
55C23×C4×C11—44no—
56C23×C4×C11C2×C411yescharacteristic
57C23×C4×C11C2×C411yescharacteristic
58C23×C4×C11C2×C411yescharacteristic
59C23×C4×C11C2×C411yescharacteristic
60C23×C4×C11C2×C412yescomplemented
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11D411yescharacteristic
68C23×C4×C11D411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#120—22no—
92C11×#120—22no—
93C11×#120—22no—
94C11×#120—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C11×#117—21no—
104C11×#117—21no—
105C11×#117—21no—
106C11×#117—21no—
107C11×#117—44no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—44no—
112C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
113C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
114C2×C11×C4⋊C4C2×C412yescomplemented
115C2×C11×C4⋊C4C2×C412yescomplemented
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—44no—
120C2×C11×C22⋊C4C2×C412yes—
121C2×C11×C22⋊C4C2×C412yes—
122C2×C11×C22⋊C4C2×C412yescomplemented
123C2×C11×C22⋊C4C2×C412yescomplemented
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C42×C11—22no—
128C2×C42×C11C2×C412yescomplemented
129C11×#99—48no—
130C11×#95—22no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—22no—
134#21874C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—42no—
138C24×C11—42no—
139C24×C11C22×C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C412yes—
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C24×C11C2×D411yescharacteristic
146C24×C11C2411yescharacteristic
147C11×#41—44no—
148C11×#41—44no—
149C11×#41—44no—
150C11×#41—44no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—42no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—24no—
161C2×D4×C11—24no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—42no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C22×C4×C11—24no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—24no—
173C22×C4×C11—24no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—44no—
186C22×C4×C11—44no—
187C22×C4×C11—44no—
188C22×C4×C11—44no—
189C22×C4×C11C22⋊C411yescharacteristic
190C22×C4×C11C22⋊C411yescharacteristic
191C22×C4×C11C22⋊C411yescharacteristic
192C22×C4×C11C22⋊C411yescharacteristic
193C22×C4×C11C22⋊C411yescharacteristic
194C22×C4×C11C22⋊C411yescharacteristic
195C22×C4×C11C22⋊C411yescharacteristic
196C22×C4×C11C22⋊C411yescharacteristic
197C22×C4×C11C22⋊C411yescharacteristic
198C22×C4×C11C22⋊C411yescharacteristic
199C22×C4×C11C22⋊C411yescharacteristic
200C22×C4×C11C22⋊C411yescharacteristic
201C22×C4×C11C22⋊C411yescharacteristic
202C22×C4×C11C22⋊C411yescharacteristic
203C22×C4×C11C22⋊C411yescharacteristic
204C22×C4×C11C22⋊C411yescharacteristic
205C22×C4×C11C22×C412yes—
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C412yes—
209C22×C4×C11C22×C412yes—
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C22×C411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—22no—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—44no—
229C11×C4⋊C4—44no—
230C11×C4⋊C4—44no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—22no—
237C11×C22⋊C4—22no—
238C11×C22⋊C4—22no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—28no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4—44no—
245C11×C22⋊C4—44no—
246C11×C22⋊C4—44no—
247C42×C11—22no—
248C42×C11—22no—
249C42×C11—44no—
250C2×#525C2×C1111yescharacteristic
251#2280C2×C1111yescharacteristic, complemented
252C2×#380C2×C1111yescharacteristic, complemented
253#1996C2×C1112yescomplemented
254#1964C2×C1112yescomplemented
255#1898C2×C1114yescomplemented
256#1799C2×C1114yescomplemented
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—24no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—48no—
282C23×C11—48no—
283C23×C11—42no—
284C23×C11—42no—
285C23×C11C2×C22⋊C411yescharacteristic
286C23×C11C2×C22⋊C411yescharacteristic
287C23×C11C2×C22⋊C411yescharacteristic
288C23×C11C2×C22⋊C411yescharacteristic
289C23×C11C23×C411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×D411yescharacteristic
292C23×C11H(5,𝔽2)12yes—
293C23×C112−1+412yes—
294Q8×C11—42no—
295Q8×C11—42no—
296D4×C11—42no—
297D4×C11—44no—
298D4×C11—44no—
299D4×C11—42no—
300D4×C11—42no—
301D4×C11—44no—
302D4×C11—44no—
303D4×C11—44no—
304D4×C11—42no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—44no—
337C2×C4×C11—44no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—44no—
341C2×C4×C11—44no—
342C2×C4×C11—44no—
343C2×C4×C11—44no—
344C2×C4×C11—44no—
345C2×C4×C11—44no—
346C2×C4×C11—88no—
347C2×C4×C11#9914yescomplemented
348C2×C4×C11C2×C22⋊C411yescharacteristic
349C2×C4×C11C2×C22⋊C411yescharacteristic
350C2×C4×C11C2×C22⋊C411yescharacteristic
351C2×C4×C11C2×C22⋊C411yescharacteristic
352C2×C4×C11C2×C22⋊C411yescharacteristic
353C2×C4×C11C2×C22⋊C411yescharacteristic
354C2×C4×C11C2×C22⋊C411yescharacteristic
355C2×C4×C11C2×C22⋊C411yescharacteristic
356C22×#41C4×C1111yescharacteristic, complemented
357C24×C4C22×C1111yescharacteristic
358#525—21no—
359#525—21no—
360#525—21no—
361#525—21no—
362#525—21no—
363#525—21no—
364#525—21no—
365#525—21no—
366C2×#123C4×C1112yescomplemented
367C2×C22⋊Q8C4×C1111yescharacteristic, complemented
368C2×C22⋊Q8C22×C1111yescharacteristic
369C2×#121C4×C1111yescharacteristic, complemented
370C2×#121C22×C1111yescharacteristic
371C2×#120C22×C1112yes—
372C2×C4×D4C4×C1112yescomplemented
373C2×C4×D4C22×C1112yes—
374C2×#117—21no—
375C2×#117C4×C1111yescharacteristic, complemented
376C22×C4⋊C4—21no—
377C22×C22⋊C4C22×C1112yes—
378C2×#99C22×C1118yes—
379#381—21no—
380#380—21no—
381#380—21no—
382#380—21no—
383#380C22×C1112yes—
384#380C22×C1112yes—
385#380C22×C1112yes—
386#379C22×C1112yes—
387C4×C22⋊C4—21no—
388C4×C22⋊C4C22×C1112yes—
389C2×#95—21no—
390#342C22×C1118yes—
391C22×C11—24no—
392C22×C11—24no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—21no—
396C22×C11—21no—
397C22×C11—21no—
398C22×C11—21no—
399C22×C11—21no—
400C22×C11—21no—
401C22×C11—21no—
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—44no—
412C22×C11—44no—
413C22×C11—44no—
414C22×C11—44no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—84no—
421C22×C11C2×#9912yes—
422C22×C11#41012yes—
423C22×C11C22×C22⋊C411yescharacteristic
424C22×C11#52012yes—
425C22×C11#53511yescharacteristic
426C22×C11#53611yescharacteristic
427C22×C11#53712yes—
428C4×C11—21no—
429C4×C11—21no—
430C4×C11—21no—
431C4×C11—21no—
432C4×C11—21no—
433C4×C11—21no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—84no—
438C4×C11—84no—
439C4×C11C2×#9912yes—
440C4×C11C2×#9912yes—
441C25C23×C1111yescharacteristic
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—44no—
447C22×Q8C2×C4×C1111yescharacteristic, complemented
448C22×D4C2×C4×C1112yes—
449C22×D4C2×C4×C1112yes—
450C22×D4C2×C4×C1111yescharacteristic, complemented
451C22×D4C23×C1112yes—
452C23×C4—22no—
453C23×C4—44no—
454C23×C4C2×C4×C1111yescharacteristic
455C23×C4C2×C4×C1111yescharacteristic
456C23×C4C2×C4×C1111yescharacteristic
457C23×C4C2×C4×C1111yescharacteristic
458C23×C4C2×C4×C1112yescomplemented
459C23×C4D4×C1111yescharacteristic
460C23×C4D4×C1111yescharacteristic
461C23×C4D4×C1111yescharacteristic
462C23×C4D4×C1111yescharacteristic
463C23×C4D4×C1111yescharacteristic
464C23×C4D4×C1111yescharacteristic
465C23×C4D4×C1111yescharacteristic
466C23×C4D4×C1111yescharacteristic
467C23×C4C23×C1111yescharacteristic
468C23×C4C23×C1111yescharacteristic
469#123—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481#121—21no—
482#121—21no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—44no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—44no—
510C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
511C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
512C2×C4⋊C4C2×C4×C1112yescomplemented
513C2×C4⋊C4C2×C4×C1112yescomplemented
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—44no—
518C2×C22⋊C4C2×C4×C1112yes—
519C2×C22⋊C4C2×C4×C1112yes—
520C2×C22⋊C4C2×C4×C1112yescomplemented
521C2×C22⋊C4C2×C4×C1112yescomplemented
522C2×C22⋊C4C23×C1114yes—
523C2×C22⋊C4C23×C1114yes—
524C2×C22⋊C4C23×C1112yes—
525C2×C42—22no—
526C2×C42C2×C4×C1112yescomplemented
527#99—48no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532C2×C11—21no—
533C2×C11—22no—
534C2×C11—21no—
535C2×C11—22no—
536C2×C11—22no—
537C2×C11—22no—
538C2×C11—41no—
539C2×C11—41no—
540C2×C11—82no—
541C2×C11#231111yescharacteristic
542C2×C11C22×#9911yescharacteristic
543C2×C11C2×#41011yescharacteristic
544C24—22no—
545C24—22no—
546C24—42no—
547C24—42no—
548C24C22×C4×C1111yescharacteristic
549C24C22×C4×C1111yescharacteristic
550C24C22×C4×C1112yes—
551C24C2×D4×C1111yescharacteristic
552C24C2×D4×C1111yescharacteristic
553C24C2×D4×C1111yescharacteristic
554C24C2×D4×C1111yescharacteristic
555C24C24×C1111yescharacteristic
556#41—44no—
557#41—44no—
558#41—44no—
559#41—44no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—42no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—44no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4C11×C22⋊C411yescharacteristic
599C22×C4C11×C22⋊C411yescharacteristic
600C22×C4C11×C22⋊C411yescharacteristic
601C22×C4C11×C22⋊C411yescharacteristic
602C22×C4C11×C22⋊C411yescharacteristic
603C22×C4C11×C22⋊C411yescharacteristic
604C22×C4C11×C22⋊C411yescharacteristic
605C22×C4C11×C22⋊C411yescharacteristic
606C22×C4C11×C22⋊C411yescharacteristic
607C22×C4C11×C22⋊C411yescharacteristic
608C22×C4C11×C22⋊C411yescharacteristic
609C22×C4C11×C22⋊C411yescharacteristic
610C22×C4C11×C22⋊C411yescharacteristic
611C22×C4C11×C22⋊C411yescharacteristic
612C22×C4C11×C22⋊C411yescharacteristic
613C22×C4C11×C22⋊C411yescharacteristic
614C22×C4C22×C4×C1112yes—
615C22×C4C22×C4×C1111yescharacteristic
616C22×C4C22×C4×C1111yescharacteristic
617C22×C4C22×C4×C1112yes—
618C22×C4C22×C4×C1112yes—
619C22×C4C22×C4×C1111yescharacteristic
620C22×C4C22×C4×C1111yescharacteristic
621C22×C4C2×D4×C1111yescharacteristic
622C22×C4C2×D4×C1111yescharacteristic
623C22×C4C2×D4×C1111yescharacteristic
624C22×C4C2×D4×C1111yescharacteristic
625C22×C4C2×D4×C1111yescharacteristic
626C22×C4C2×D4×C1111yescharacteristic
627C22×C4C2×D4×C1111yescharacteristic
628C22×C4C2×D4×C1111yescharacteristic
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—24no—
651C22⋊C4—28no—
652C22⋊C4—24no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C42—22no—
657C42—22no—
658C42—44no—
659C11#2187411yescharacteristic, direct product factor, Sylow
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—48no—
685C23—48no—
686C23—42no—
687C23—42no—
688C23C2×C11×C22⋊C411yescharacteristic
689C23C2×C11×C22⋊C411yescharacteristic
690C23C2×C11×C22⋊C411yescharacteristic
691C23C2×C11×C22⋊C411yescharacteristic
692C23C23×C4×C1111yescharacteristic
693C23C22×D4×C1111yescharacteristic
694C23C22×D4×C1111yescharacteristic
695C23C11×H(5,𝔽2)12yes—
696C23C11×2−1+412yes—
697Q8—42no—
698Q8—42no—
699D4—42no—
700D4—44no—
701D4—44no—
702D4—42no—
703D4—42no—
704D4—44no—
705D4—44no—
706D4—44no—
707D4—42no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—88no—
750C2×C4C11×#9914yescomplemented
751C2×C4C2×C11×C22⋊C411yescharacteristic
752C2×C4C2×C11×C22⋊C411yescharacteristic
753C2×C4C2×C11×C22⋊C411yescharacteristic
754C2×C4C2×C11×C22⋊C411yescharacteristic
755C2×C4C2×C11×C22⋊C411yescharacteristic
756C2×C4C2×C11×C22⋊C411yescharacteristic
757C2×C4C2×C11×C22⋊C411yescharacteristic
758C2×C4C2×C11×C22⋊C411yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22C2×C11×#9912yes—
790C22C11×#41012yes—
791C22C22×C11×C22⋊C411yescharacteristic
792C22C11×#52012yes—
793C22C11×#53511yescharacteristic
794C22C11×#53611yescharacteristic
795C22C11×#53712yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—84no—
806C4—84no—
807C4C2×C11×#9912yes—
808C4C2×C11×#9912yes—
809C2—21no—
810C2—22no—
811C2—21no—
812C2—22no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2C11×#231111yescharacteristic
819C2C22×C11×#9911yescharacteristic
820C2C2×C11×#41011yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2280C2semidirect
3. C2×C11×#380C2semidirect
4. C11×#1996C2semidirect
5. C11×#1964C2semidirect
6. C11×#1898C2semidirect
7. C11×#1799C2semidirect
8. C22×C11×#41C4semidirect
18. C2×C11×#123C4semidirect
19. C2×C11×C22⋊Q8C4semidirect
21. C2×C11×#121C4semidirect
24. C2×C4×D4×C11C4semidirect
27. C2×C11×#117C4semidirect
49. C22×Q8×C11C2×C4semidirect
52. C22×D4×C11C2×C4semidirect
60. C23×C4×C11C2×C4semidirect
112. C2×C11×C4⋊C4C2×C4semidirect
113. C2×C11×C4⋊C4C2×C4semidirect
114. C2×C11×C4⋊C4C2×C4semidirect
115. C2×C11×C4⋊C4C2×C4semidirect
122. C2×C11×C22⋊C4C2×C4semidirect
123. C2×C11×C22⋊C4C2×C4semidirect
128. C2×C42×C11C2×C4semidirect
134. #21874C11direct (N × H)
251. #2280C2×C11semidirect
252. C2×#380C2×C11semidirect
253. #1996C2×C11semidirect
254. #1964C2×C11semidirect
255. #1898C2×C11semidirect
256. #1799C2×C11semidirect
347. C2×C4×C11#99semidirect
356. C22×#41C4×C11semidirect
366. C2×#123C4×C11semidirect
367. C2×C22⋊Q8C4×C11semidirect
369. C2×#121C4×C11semidirect
372. C2×C4×D4C4×C11semidirect
375. C2×#117C4×C11semidirect
447. C22×Q8C2×C4×C11semidirect
450. C22×D4C2×C4×C11semidirect
458. C23×C4C2×C4×C11semidirect
510. C2×C4⋊C4C2×C4×C11semidirect
511. C2×C4⋊C4C2×C4×C11semidirect
512. C2×C4⋊C4C2×C4×C11semidirect
513. C2×C4⋊C4C2×C4×C11semidirect
520. C2×C22⋊C4C2×C4×C11semidirect
521. C2×C22⋊C4C2×C4×C11semidirect
526. C2×C42C2×C4×C11semidirect
659. C11#21874direct (N × H)
750. C2×C4C11×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C11×#22802
C2×C11×#3802
C11×#19962
C11×#19642
C11×#18982
C11×#17992
#2187411