Finite Group Databasebeta

← #14685251

Subgroups — #14685251

Order 2816.

3494 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C211yesmaximal, characteristic
2C2×#10622607C211yesmaximal, characteristic, complemented
3C2×#10622602C211yesmaximal, characteristic, complemented
4C2×#10622602C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×#10622568C211yesmaximal, characteristic
7C2×#10622568C211yesmaximal, characteristic
8#13066861C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066858C211yesmaximal, characteristic, complemented
13#13066858C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#396C211yesmaximal, characteristic, complemented
16C25×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic, complemented
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21C22×C11×C4⋊C4C2211yescharacteristic, complemented
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic, complemented
39C22×Dic11⋊C4C2211yescharacteristic, complemented
40C22×Dic11⋊C4C2211yescharacteristic, complemented
41C2×C22⋊C4×D11—24no—
42C2×C22⋊C4×D11—24no—
43C2×C22⋊C4×D11—24no—
44C11×#396—24no—
45C2×C11×#95C2211yescharacteristic, complemented
46C2×C11⋊#95C2211yescharacteristic, complemented
47C2×C11⋊#95C2211yescharacteristic, complemented
48C2×C11⋊#95C2211yescharacteristic, complemented
49C2×C11⋊#95C2211yescharacteristic, complemented
50C2×C11⋊#95C2211yescharacteristic, complemented
51C2×C11⋊#95C2211yescharacteristic, complemented
52C2×C11⋊#95C2211yescharacteristic, complemented
53C2×C11⋊#95C2211yescharacteristic, complemented
54C2×C11⋊#95C2211yescharacteristic, complemented
55#10622607—24no—
56#10622602—24no—
57#10622602—24no—
58#10622600—24no—
59#10622568—24no—
60#10622568—24no—
61C25×C11C2311yescharacteristic
62C24×D11—22no—
63C24×D11—22no—
64C24×D11—22no—
65C24×D11—22no—
66C24×D11—22no—
67C24×D11—22no—
68C24×D11—22no—
69C24×D11—22no—
70C24×D11—22no—
71C24×D11—22no—
72C24×D11—41no—
73C24×D11—41no—
74C24×D11—41no—
75C24×D11—41no—
76C24×D11Q814yes—
77C24×D11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—22no—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—41no—
101C22×C4×D11—41no—
102C22×C4×D11—41no—
103C22×C4×D11—41no—
104C22×C4×D11D414yes—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—41no—
113C2×C11×C4⋊C4—41no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—41no—
121C2×C11×C22⋊C4—41no—
122C2×C11×C22⋊C4D414yes—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11—22no—
130C2×C22⋊Dic11—41no—
131C2×C22⋊Dic11—41no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—22no—
139C2×(C2×D11)⋊C4—22no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—22no—
142C2×(C2×D11)⋊C4—22no—
143C2×(C2×D11)⋊C4—22no—
144C2×(C2×D11)⋊C4—22no—
145C2×(C2×D11)⋊C4—22no—
146C2×(C2×D11)⋊C4—22no—
147C2×(C2×D11)⋊C4—22no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4—22no—
150C2×(C2×D11)⋊C4—22no—
151C2×(C2×D11)⋊C4—22no—
152C2×(C2×D11)⋊C4—22no—
153C2×(C2×D11)⋊C4—22no—
154C2×(C2×D11)⋊C4—22no—
155C2×(C2×D11)⋊C4—41no—
156C2×(C2×D11)⋊C4—41no—
157C2×(C2×D11)⋊C4—41no—
158C2×(C2×D11)⋊C4—41no—
159C2×(C2×D11)⋊C4D414yes—
160C2×(C2×D11)⋊C4D414yes—
161C2×(C2×D11)⋊C4D414yes—
162C2×C4⋊Dic11—22no—
163C2×C4⋊Dic11—22no—
164C2×C4⋊Dic11—41no—
165C2×Dic11⋊C4—22no—
166C2×Dic11⋊C4—22no—
167C2×Dic11⋊C4—22no—
168C2×Dic11⋊C4—41no—
169C2×Dic11⋊C4—41no—
170C2×Dic11⋊C4—41no—
171C22⋊C4×D11—232no—
172C11×#95—22no—
173C11⋊#95—22no—
174C11⋊#95—22no—
175C11⋊#95—22no—
176C11⋊#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—41no—
181C11⋊#95—41no—
182#14726—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11C2×D412yes—
196C24×C11C2×Q812yes—
197C24×C11#4112yes—
198C24×C11C2411yescharacteristic
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—28no—
208C23×D11—28no—
209C23×D11—28no—
210C23×D11—28no—
211C23×D11—28no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11—21no—
215C23×D11—21no—
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—21no—
220C23×D11—21no—
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—28no—
225C23×D11—28no—
226C23×D11—28no—
227C23×D11—28no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—44no—
231C23×D11—44no—
232C23×D11—44no—
233C23×D11—44no—
234C23×D11—44no—
235C23×D11—44no—
236C23×D11—44no—
237C23×D11—44no—
238C23×D11—44no—
239C23×D11—44no—
240C23×D11—44no—
241C23×D11—44no—
242C23×D11—44no—
243C23×D11—44no—
244C23×D11—44no—
245C23×D11—44no—
246C23×D11—44no—
247C23×D11—44no—
248C23×D11—44no—
249C23×D11—44no—
250C23×D11—44no—
251C23×D11—44no—
252C23×D11—44no—
253C23×D11—44no—
254C23×D11C2×D412yes—
255C23×D11C2×D412yes—
256C23×D11C2×D412yes—
257C23×D11C2×D412yes—
258C23×D11C2×Q812yes—
259C23×D11C2×Q812yes—
260C23×D11#4112yes—
261C23×D11#4112yes—
262C23×D11#4112yes—
263C23×D11#4112yes—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—21no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—21no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—21no—
285C22×C4×C11—21no—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—21no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11—21no—
296C22×C4×C11—21no—
297C22×C4×C11—21no—
298C22×C4×C11—21no—
299C22×C4×C11—21no—
300C22×C4×C11C2×D412yes—
301C22×C4×C11C2×D412yes—
302C22×C4×C11C2×D412yes—
303C22×C4×C11C2×D412yes—
304C22×C4×C11C2×D412yes—
305C22×C4×C11C2×D412yes—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
316C22×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—21no—
319C22×Dic11—21no—
320C22×Dic11—21no—
321C22×Dic11—21no—
322C22×Dic11—21no—
323C22×Dic11—21no—
324C22×Dic11—21no—
325C22×Dic11—21no—
326C22×Dic11—21no—
327C22×Dic11—21no—
328C22×Dic11—21no—
329C22×Dic11—21no—
330C22×Dic11—21no—
331C22×Dic11—21no—
332C22×Dic11—21no—
333C22×Dic11—21no—
334C22×Dic11—21no—
335C22×Dic11—21no—
336C22×Dic11—21no—
337C22×Dic11—21no—
338C22×Dic11—21no—
339C22×Dic11—21no—
340C22×Dic11—21no—
341C22×Dic11—21no—
342C22×Dic11—21no—
343C22×Dic11—21no—
344C22×Dic11C2×D412yes—
345C22×Dic11C2×D412yes—
346C22×Dic11C2×D412yes—
347C22×Dic11C2×D412yes—
348C2×C4×D11—28no—
349C2×C4×D11—28no—
350C2×C4×D11—28no—
351C2×C4×D11—44no—
352C2×C4×D11—44no—
353C2×C4×D11—44no—
354C2×C4×D11—44no—
355C2×C4×D11—44no—
356C2×C4×D11—44no—
357C2×C4×D11—44no—
358C2×C4×D11—44no—
359C2×C4×D11—44no—
360C2×C4×D11—44no—
361C2×C4×D11—44no—
362C11×C4⋊C4—44no—
363C11×C4⋊C4—44no—
364C11×C4⋊C4—44no—
365C11×C22⋊C4—28no—
366C11×C22⋊C4—44no—
367C11×C22⋊C4—44no—
368C22⋊Dic11—28no—
369C22⋊Dic11—44no—
370C22⋊Dic11—44no—
371(C2×D11)⋊C4—28no—
372(C2×D11)⋊C4—28no—
373(C2×D11)⋊C4—28no—
374(C2×D11)⋊C4—28no—
375(C2×D11)⋊C4—44no—
376(C2×D11)⋊C4—44no—
377(C2×D11)⋊C4—44no—
378(C2×D11)⋊C4—44no—
379(C2×D11)⋊C4—44no—
380(C2×D11)⋊C4—44no—
381C4⋊Dic11—44no—
382Dic11⋊C4—44no—
383Dic11⋊C4—44no—
384C23×C22⋊C4—111no—
385C2×#396—111no—
386C2×#396D1111yescharacteristic, complemented
387C2×#385—111no—
388C2×#385—111no—
389C2×#380—111no—
390C2×#379—111no—
391C2×#379—111no—
392#1439—111no—
393#1439—111no—
394#1439—111no—
395#1439—111no—
396#1439—111no—
397#1439—111no—
398C22⋊#95—111no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11C22⋊Q814yes—
434C23×C11C22×D411yescharacteristic
435C23×C11C22×D411yescharacteristic
436C23×C11C22×D411yescharacteristic
437C23×C11C22×D411yescharacteristic
438C23×C11C22×D411yescharacteristic
439C23×C11C22×Q811yescharacteristic
440C23×C11C2×#4111yescharacteristic
441C23×C11C2×#4111yescharacteristic
442C23×C11C2×#4111yescharacteristic
443C23×C11C2×#4111yescharacteristic
444C23×C11C2×#4111yescharacteristic
445C23×C11H(5,𝔽2)11yescharacteristic
446C23×C11H(5,𝔽2)11yescharacteristic
447C23×C11H(5,𝔽2)11yescharacteristic
448C23×C11H(5,𝔽2)11yescharacteristic
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—232no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—22no—
487C22×D11—22no—
488C22×D11—22no—
489C22×D11—22no—
490C22×D11—22no—
491C22×D11—22no—
492C22×D11—22no—
493C22×D11—22no—
494C22×D11—22no—
495C22×D11—22no—
496C22×D11—416no—
497C22×D11—416no—
498C22×D11—416no—
499C22×D11—416no—
500C22×D11—416no—
501C22×D11—416no—
502C22×D11—416no—
503C22×D11—416no—
504C22×D11—416no—
505C22×D11—416no—
506C22×D11—416no—
507C22×D11—416no—
508C22×D11—416no—
509C22×D11—41no—
510C22×D11—41no—
511C22×D11—41no—
512C22×D11—41no—
513C22×D11—41no—
514C22×D11—41no—
515C22×D11—41no—
516C22×D11—41no—
517C22×D11—41no—
518C22×D11—41no—
519C22×D11—41no—
520C22×D11—41no—
521C22×D11—41no—
522C22×D11—41no—
523C22×D11—41no—
524C22×D11—41no—
525C22×D11—416no—
526C22×D11#12114yes—
527C22×D11#12114yes—
528C22×D11#12114yes—
529C22×D11C22⋊Q814yes—
530C22×D11C22⋊Q814yes—
531C22×D11C22⋊Q814yes—
532C22×D11C22⋊Q814yes—
533C22×D11#12614yes—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—22no—
543C2×C4×C11—22no—
544C2×C4×C11—22no—
545C2×C4×C11—22no—
546C2×C4×C11—22no—
547C2×C4×C11—22no—
548C2×C4×C11—22no—
549C2×C4×C11—41no—
550C2×C4×C11—41no—
551C2×C4×C11—41no—
552C2×C4×C11—41no—
553C2×C4×C11—41no—
554C2×C4×C11—41no—
555C2×C4×C11—41no—
556C2×C4×C11—41no—
557C2×C4×C11—41no—
558C2×C4×C11—41no—
559C2×C4×C11—41no—
560C2×C4×C11—41no—
561C2×C4×C11—41no—
562C2×C4×C11—41no—
563C2×C4×C11—41no—
564C2×C4×C11—41no—
565C2×C4×C11—41no—
566C2×C4×C11—41no—
567C2×C4×C11—41no—
568C2×C4×C11—41no—
569C2×C4×C11—41no—
570C2×C4×C11—41no—
571C2×C4×C11—41no—
572C2×C4×C11—41no—
573C2×C4×C11—41no—
574C2×C4×C11—41no—
575C2×C4×C11#12014yes—
576C2×Dic11—22no—
577C2×Dic11—22no—
578C2×Dic11—22no—
579C2×Dic11—22no—
580C2×Dic11—22no—
581C2×Dic11—22no—
582C2×Dic11—22no—
583C2×Dic11—22no—
584C2×Dic11—22no—
585C2×Dic11—22no—
586C2×Dic11—22no—
587C2×Dic11—22no—
588C2×Dic11—41no—
589C2×Dic11—41no—
590C2×Dic11—41no—
591C2×Dic11—41no—
592C2×Dic11—41no—
593C2×Dic11—41no—
594C2×Dic11—41no—
595C2×Dic11—41no—
596C2×Dic11—41no—
597C2×Dic11—41no—
598C2×Dic11—41no—
599C2×Dic11—41no—
600C2×Dic11—41no—
601C2×Dic11—41no—
602C2×Dic11—41no—
603C2×Dic11—41no—
604C2×Dic11—41no—
605C2×Dic11—41no—
606C2×Dic11—41no—
607C2×Dic11—41no—
608C2×Dic11—41no—
609C2×Dic11—41no—
610C2×Dic11—41no—
611C2×Dic11—41no—
612C2×Dic11—41no—
613C2×Dic11—41no—
614C2×Dic11—41no—
615C2×Dic11—41no—
616C2×Dic11—41no—
617C2×Dic11—41no—
618C4×D11—416no—
619C4×D11—416no—
620C26—111no—
621C24×C4—111no—
622C24×C4—111no—
623C22×C4⋊C4—111no—
624C22×C4⋊C4—111no—
625C22×C4⋊C4—111no—
626C22×C4⋊C4C2×D1111yescharacteristic, complemented
627C22×C4⋊C4C2×D1111yescharacteristic, complemented
628C22×C4⋊C4C2×D1111yescharacteristic, complemented
629C22×C22⋊C4—111no—
630C22×C22⋊C4—111no—
631C22×C22⋊C4—111no—
632C22×C22⋊C4—111no—
633C22×C22⋊C4—111no—
634C22×C22⋊C4—111no—
635C22×C22⋊C4—111no—
636C22×C22⋊C4—111no—
637C22×C22⋊C4—111no—
638C22×C22⋊C4—111no—
639C22×C22⋊C4—111no—
640C22×C22⋊C4—111no—
641C22×C22⋊C4—111no—
642C22×C22⋊C4—224no—
643C22×C22⋊C4—224no—
644C22×C22⋊C4—224no—
645C22×C22⋊C4C2×D1111yescharacteristic
646C22×C22⋊C4C2×D1111yescharacteristic
647C22×C22⋊C4C2×D1111yescharacteristic
648#396—24no—
649#396—224no—
650#385—224no—
651#385—224no—
652#380—224no—
653#379—224no—
654#379—224no—
655C2×#95—111no—
656C2×#95—111no—
657C2×#95—111no—
658C2×#95—111no—
659C2×#95—111no—
660C2×#95—111no—
661C2×#95—111no—
662C2×#95—111no—
663C2×#95—111no—
664C2×#95C2×D1111yescharacteristic, complemented
665C22×C11—24no—
666C22×C11—24no—
667C22×C11—24no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11C2×#12011yescharacteristic
681C22×C11C2×#12111yescharacteristic
682C22×C11C2×#12111yescharacteristic
683C22×C11C2×#12111yescharacteristic
684C22×C11C2×C22⋊Q811yescharacteristic
685C22×C11C2×C22⋊Q811yescharacteristic
686C22×C11C2×C22⋊Q811yescharacteristic
687C22×C11C2×C22⋊Q811yescharacteristic
688C22×C11C2×C22⋊Q811yescharacteristic
689C22×C11#52511yescharacteristic
690C22×C11#52511yescharacteristic
691C22×C11#52511yescharacteristic
692C22×C11C2×#12611yescharacteristic
693C22×C11#53411yescharacteristic
694C22×C11#53511yescharacteristic
695C22×C11#53811yescharacteristic
696C22×C11#53811yescharacteristic
697C22×C11#54311yescharacteristic
698C22×C11#54311yescharacteristic
699C22×C11D4211yescharacteristic
700C22×C11D4211yescharacteristic
701C22×C11D4211yescharacteristic
702C22×C11D4211yescharacteristic
703C22×C11#54611yescharacteristic
704C22×C11#54611yescharacteristic
705C22×C11#54611yescharacteristic
706C22×C11#54611yescharacteristic
707C22×C11#54611yescharacteristic
708C22×C11#54611yescharacteristic
709C22×C11#54611yescharacteristic
710C22×C11#54611yescharacteristic
711C22×C11#55111yescharacteristic
712C22×C11#55111yescharacteristic
713C22×C11#55111yescharacteristic
714C22×C11#55111yescharacteristic
715C2×D11—24no—
716C2×D11—24no—
717C2×D11—24no—
718C2×D11—24no—
719C2×D11—24no—
720C2×D11—24no—
721C2×D11—24no—
722C2×D11—24no—
723C2×D11—24no—
724C2×D11—24no—
725C2×D11—24no—
726C2×D11—24no—
727C2×D11—24no—
728C2×D11—24no—
729C2×D11—24no—
730C2×D11—24no—
731C2×D11—24no—
732C2×D11—464no—
733C2×D11—42no—
734C2×D11—42no—
735C2×D11—42no—
736C2×D11—42no—
737C2×D11—42no—
738C2×D11—42no—
739C2×D11—42no—
740C2×D11—42no—
741C2×D11—42no—
742C2×D11—42no—
743C2×D11—42no—
744C2×D11—42no—
745C2×D11#39618yescomplemented
746C4×C11—24no—
747C4×C11—42no—
748C4×C11—42no—
749C4×C11—42no—
750C4×C11—81no—
751C4×C11—81no—
752Dic11—42no—
753Dic11—42no—
754Dic11—42no—
755Dic11—42no—
756Dic11—81no—
757Dic11—81no—
758C25—111no—
759C25—111no—
760C25—114no—
761C25—222no—
762C25—222no—
763C25—222no—
764C25—222no—
765C25—222no—
766C25—222no—
767C25—222no—
768C25—222no—
769C25—222no—
770C25—222no—
771C25—441no—
772C25—441no—
773C25—441no—
774C25—441no—
775C25C22×D1111yescharacteristic
776C23×C4—111no—
777C23×C4—111no—
778C23×C4—111no—
779C23×C4—111no—
780C23×C4—114no—
781C23×C4—111no—
782C23×C4—111no—
783C23×C4—222no—
784C23×C4—222no—
785C23×C4—222no—
786C23×C4—222no—
787C23×C4—222no—
788C23×C4—222no—
789C23×C4—222no—
790C23×C4—222no—
791C23×C4—222no—
792C23×C4—441no—
793C23×C4—441no—
794C23×C4—441no—
795C23×C4—441no—
796C23×C4C22×D1111yescharacteristic
797C23×C4C22×D1111yescharacteristic
798C23×C4C22×D1111yescharacteristic
799C23×C4C22×D1111yescharacteristic
800C23×C4C22×D1111yescharacteristic
801C23×C4C22×D1111yescharacteristic
802C2×C4⋊C4—22no—
803C2×C4⋊C4—22no—
804C2×C4⋊C4—22no—
805C2×C4⋊C4—22no—
806C2×C4⋊C4—22no—
807C2×C4⋊C4—22no—
808C2×C4⋊C4—22no—
809C2×C4⋊C4—41no—
810C2×C4⋊C4—41no—
811C2×C4⋊C4—222no—
812C2×C4⋊C4—222no—
813C2×C4⋊C4—222no—
814C2×C4⋊C4—222no—
815C2×C4⋊C4—222no—
816C2×C4⋊C4—441no—
817C2×C4⋊C4—441no—
818C2×C4⋊C4—441no—
819C2×C4⋊C4—441no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4—114no—
829C2×C22⋊C4—114no—
830C2×C22⋊C4—114no—
831C2×C22⋊C4—2232no—
832C2×C22⋊C4—222no—
833C2×C22⋊C4—222no—
834C2×C22⋊C4—222no—
835C2×C22⋊C4—222no—
836C2×C22⋊C4—222no—
837C2×C22⋊C4—222no—
838C2×C22⋊C4—222no—
839C2×C22⋊C4—222no—
840C2×C22⋊C4—222no—
841C2×C22⋊C4—222no—
842C2×C22⋊C4—222no—
843C2×C22⋊C4—222no—
844C2×C22⋊C4—222no—
845C2×C22⋊C4—222no—
846C2×C22⋊C4—222no—
847C2×C22⋊C4—222no—
848C2×C22⋊C4—222no—
849C2×C22⋊C4—222no—
850C2×C22⋊C4—222no—
851C2×C22⋊C4—222no—
852C2×C22⋊C4—222no—
853C2×C22⋊C4—222no—
854C2×C22⋊C4—222no—
855C2×C22⋊C4—222no—
856C2×C22⋊C4—222no—
857C2×C22⋊C4—222no—
858C2×C22⋊C4—222no—
859C2×C22⋊C4—222no—
860C2×C22⋊C4—222no—
861C2×C22⋊C4—222no—
862C2×C22⋊C4—441no—
863C2×C22⋊C4—441no—
864C2×C22⋊C4—441no—
865C2×C22⋊C4—441no—
866C2×C22⋊C4—441no—
867C2×C22⋊C4—441no—
868C2×C22⋊C4C22⋊D1114yes—
869#95—22no—
870#95—222no—
871#95—222no—
872#95—222no—
873#95—222no—
874#95—222no—
875#95—222no—
876#95—222no—
877#95—441no—
878#95—441no—
879C2×C11—44no—
880C2×C11C2×#39611yescharacteristic
881C2×C11#240811yescharacteristic
882C2×C11#241011yescharacteristic
883C2×C11#241111yescharacteristic
884C2×C11#242411yescharacteristic
885C2×C11#242411yescharacteristic
886C2×C11#243711yescharacteristic
887C2×C11#243711yescharacteristic
888C2×C11#243711yescharacteristic
889C2×C11#243711yescharacteristic
890C2×C11#248011yescharacteristic
891C2×C11#248011yescharacteristic
892C2×C11#253411yescharacteristic
893C2×C11#262611yescharacteristic
894C2×C11#284811yescharacteristic
895D11—28no—
896D11—44no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—21no—
904C24—21no—
905C24—21no—
906C24—21no—
907C24—21no—
908C24—21no—
909C24—112no—
910C24—112no—
911C24—112no—
912C24—112no—
913C24—112no—
914C24—112no—
915C24—112no—
916C24—112no—
917C24—112no—
918C24—112no—
919C24—228no—
920C24—228no—
921C24—228no—
922C24—228no—
923C24—228no—
924C24—228no—
925C24—228no—
926C24—228no—
927C24—221no—
928C24—221no—
929C24—221no—
930C24—221no—
931C24—221no—
932C24—221no—
933C24—221no—
934C24—221no—
935C24—228no—
936C24—221no—
937C24—221no—
938C24—221no—
939C24—221no—
940C24—221no—
941C24—221no—
942C24—221no—
943C24—221no—
944C24—221no—
945C24—221no—
946C24—221no—
947C24—221no—
948C24—444no—
949C24—444no—
950C24—444no—
951C24—444no—
952C24—444no—
953C24—444no—
954C24—444no—
955C24—444no—
956C24—444no—
957C24—444no—
958C24—444no—
959C24—444no—
960C24—444no—
961C24—444no—
962C24—444no—
963C24—444no—
964C24—444no—
965C24—444no—
966C24—444no—
967C24—444no—
968C24—444no—
969C24—444no—
970C24—444no—
971C24—444no—
972C24—444no—
973C24—444no—
974C24Q8×D1112yes—
975C24#434312yes—
976C24C2×C22⋊D1112yes—
977C24C23×D1111yescharacteristic
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—21no—
1013C22×C4—21no—
1014C22×C4—112no—
1015C22×C4—112no—
1016C22×C4—112no—
1017C22×C4—112no—
1018C22×C4—228no—
1019C22×C4—228no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—221no—
1031C22×C4—221no—
1032C22×C4—221no—
1033C22×C4—221no—
1034C22×C4—221no—
1035C22×C4—221no—
1036C22×C4—221no—
1037C22×C4—221no—
1038C22×C4—221no—
1039C22×C4—221no—
1040C22×C4—221no—
1041C22×C4—221no—
1042C22×C4—221no—
1043C22×C4—221no—
1044C22×C4—228no—
1045C22×C4—221no—
1046C22×C4—221no—
1047C22×C4—221no—
1048C22×C4—221no—
1049C22×C4—221no—
1050C22×C4—221no—
1051C22×C4—221no—
1052C22×C4—221no—
1053C22×C4—221no—
1054C22×C4—221no—
1055C22×C4—221no—
1056C22×C4—221no—
1057C22×C4—221no—
1058C22×C4—221no—
1059C22×C4—444no—
1060C22×C4—444no—
1061C22×C4—444no—
1062C22×C4—444no—
1063C22×C4—444no—
1064C22×C4—444no—
1065C22×C4—444no—
1066C22×C4—444no—
1067C22×C4—444no—
1068C22×C4—444no—
1069C22×C4—444no—
1070C22×C4D4×D1112yes—
1071C22×C4D4×D1112yes—
1072C22×C4D4×D1112yes—
1073C22×C4D4×D1112yes—
1074C22×C4C2×C22⋊D1112yes—
1075C22×C4C2×C22⋊D1112yes—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—444no—
1080C4⋊C4—444no—
1081C4⋊C4—444no—
1082C22⋊C4—28no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—228no—
1086C22⋊C4—228no—
1087C22⋊C4—228no—
1088C22⋊C4—228no—
1089C22⋊C4—228no—
1090C22⋊C4—444no—
1091C22⋊C4—444no—
1092C22⋊C4—444no—
1093C22⋊C4—444no—
1094C22⋊C4—444no—
1095C22⋊C4—444no—
1096C22⋊C4—444no—
1097C22⋊C4—444no—
1098C11#1472611yescharacteristic, complemented, Sylow
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—114no—
1134C23—114no—
1135C23—114no—
1136C23—114no—
1137C23—114no—
1138C23—114no—
1139C23—114no—
1140C23—114no—
1141C23—2232no—
1142C23—222no—
1143C23—222no—
1144C23—222no—
1145C23—222no—
1146C23—222no—
1147C23—222no—
1148C23—222no—
1149C23—222no—
1150C23—222no—
1151C23—222no—
1152C23—222no—
1153C23—222no—
1154C23—222no—
1155C23—222no—
1156C23—222no—
1157C23—222no—
1158C23—222no—
1159C23—222no—
1160C23—222no—
1161C23—222no—
1162C23—222no—
1163C23—222no—
1164C23—222no—
1165C23—222no—
1166C23—222no—
1167C23—222no—
1168C23—222no—
1169C23—222no—
1170C23—222no—
1171C23—222no—
1172C23—222no—
1173C23—222no—
1174C23—222no—
1175C23—222no—
1176C23—222no—
1177C23—222no—
1178C23—222no—
1179C23—222no—
1180C23—222no—
1181C23—222no—
1182C23—222no—
1183C23—222no—
1184C23—222no—
1185C23—222no—
1186C23—222no—
1187C23—222no—
1188C23—4416no—
1189C23—4416no—
1190C23—4416no—
1191C23—4416no—
1192C23—4416no—
1193C23—4416no—
1194C23—4416no—
1195C23—4416no—
1196C23—4416no—
1197C23—4416no—
1198C23—4416no—
1199C23—4416no—
1200C23—4416no—
1201C23—4416no—
1202C23—441no—
1203C23—441no—
1204C23—441no—
1205C23—441no—
1206C23—441no—
1207C23—441no—
1208C23—441no—
1209C23—441no—
1210C23—441no—
1211C23—441no—
1212C23—441no—
1213C23—441no—
1214C23—441no—
1215C23—441no—
1216C23—441no—
1217C23—441no—
1218C23#6699914yes—
1219C23C2×D4×D1111yescharacteristic
1220C23C2×D4×D1111yescharacteristic
1221C23C2×D4×D1111yescharacteristic
1222C23C2×D4×D1111yescharacteristic
1223C23#6703711yescharacteristic
1224C23#6703711yescharacteristic
1225C23C2×Q8×D1111yescharacteristic
1226C23C2×#434311yescharacteristic
1227C23#41×D1111yescharacteristic
1228C23#41×D1111yescharacteristic
1229C23#41×D1111yescharacteristic
1230C23#41×D1111yescharacteristic
1231C23#6704211yescharacteristic
1232C23#6704211yescharacteristic
1233C23C22×C22⋊D1111yescharacteristic
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—222no—
1276C2×C4—222no—
1277C2×C4—222no—
1278C2×C4—222no—
1279C2×C4—222no—
1280C2×C4—222no—
1281C2×C4—222no—
1282C2×C4—222no—
1283C2×C4—222no—
1284C2×C4—222no—
1285C2×C4—222no—
1286C2×C4—222no—
1287C2×C4—4416no—
1288C2×C4—4416no—
1289C2×C4—441no—
1290C2×C4—441no—
1291C2×C4—441no—
1292C2×C4—441no—
1293C2×C4—441no—
1294C2×C4—441no—
1295C2×C4—441no—
1296C2×C4—441no—
1297C2×C4—441no—
1298C2×C4—441no—
1299C2×C4—441no—
1300C2×C4—441no—
1301C2×C4—441no—
1302C2×C4—441no—
1303C2×C4—441no—
1304C2×C4—441no—
1305C2×C4—441no—
1306C2×C4—441no—
1307C2×C4—441no—
1308C2×C4—441no—
1309C2×C4—441no—
1310C2×C4—441no—
1311C2×C4—441no—
1312C2×C4—441no—
1313C2×C4—441no—
1314C2×C4—441no—
1315C2×C4—441no—
1316C2×C4—441no—
1317C2×C4—441no—
1318C2×C4—441no—
1319C2×C4#6699014yes—
1320C22—24no—
1321C22—24no—
1322C22—24no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—118no—
1336C22—224no—
1337C22—224no—
1338C22—224no—
1339C22—224no—
1340C22—224no—
1341C22—224no—
1342C22—224no—
1343C22—224no—
1344C22—224no—
1345C22—224no—
1346C22—224no—
1347C22—224no—
1348C22—224no—
1349C22—224no—
1350C22—224no—
1351C22—224no—
1352C22—224no—
1353C22—4464no—
1354C22—442no—
1355C22—442no—
1356C22—442no—
1357C22—442no—
1358C22—442no—
1359C22—442no—
1360C22—442no—
1361C22—442no—
1362C22—442no—
1363C22—442no—
1364C22—442no—
1365C22—442no—
1366C22D11×#12111yescharacteristic
1367C22D11×#12111yescharacteristic
1368C22D11×#12111yescharacteristic
1369C22#1062313611yescharacteristic
1370C22#1062313811yescharacteristic
1371C22#1062314011yescharacteristic
1372C22#1062314011yescharacteristic
1373C22#1062314111yescharacteristic
1374C22#1062314111yescharacteristic
1375C22#1062314311yescharacteristic
1376C22#1062314311yescharacteristic
1377C22#1062314411yescharacteristic
1378C22D11×C22⋊Q811yescharacteristic
1379C22D11×C22⋊Q811yescharacteristic
1380C22D11×C22⋊Q811yescharacteristic
1381C22D11×C22⋊Q811yescharacteristic
1382C22#1062315811yescharacteristic
1383C22#1062315811yescharacteristic
1384C22#1062316111yescharacteristic
1385C22#1062316111yescharacteristic
1386C22#1062316511yescharacteristic
1387C22#1062316511yescharacteristic
1388C22#1062316811yescharacteristic
1389C22#1062316811yescharacteristic
1390C22D11×#12611yescharacteristic
1391C22#1062323511yescharacteristic
1392C22#1062323611yescharacteristic
1393C22#1062323611yescharacteristic
1394C22C2×#6699011yescharacteristic
1395C22D4×C22⋊D1111yescharacteristic
1396C22D4×C22⋊D1111yescharacteristic
1397C22C2×#6699911yescharacteristic
1398C22#1062335911yescharacteristic
1399C22#1062336011yescharacteristic
1400C22#1062336011yescharacteristic
1401C4—24no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—81no—
1406C4—81no—
1407C4—442no—
1408C4—442no—
1409C4—442no—
1410C4—442no—
1411C4—881no—
1412C4—881no—
1413C2—44no—
1414C2—228no—
1415C2—444no—
1416C2D11×#39611yescharacteristic
1417C2#1307196811yescharacteristic
1418C2#1307198711yescharacteristic
1419C2#1307199611yescharacteristic
1420C2#1307214711yescharacteristic
1421C2#1307214911yescharacteristic
1422C2#1307227811yescharacteristic
1423C2#1307227811yescharacteristic
1424C2#1307227911yescharacteristic
1425C2#1307227911yescharacteristic
1426C2#1307285811yescharacteristic
1427C2#1307286511yescharacteristic
1428C2#1307350711yescharacteristic
1429C2#1307442611yescharacteristic
1430C2#1307690011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#396C2
prime radicalC25×D11C22
hypercenterC2×#396D11
hypocenterC11#14726
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C2×#10622607C2semidirect
3. C2×#10622602C2semidirect
4. C2×#10622602C2semidirect
5. C2×#10622600C2semidirect
8. #13066861C2semidirect
9. #13066860C2semidirect
10. #13066859C2semidirect
11. #13066859C2semidirect
12. #13066858C2semidirect
13. #13066858C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#396C2semidirect
19. C22×C11×C4⋊C4C22semidirect
20. C22×C11×C4⋊C4C22semidirect
21. C22×C11×C4⋊C4C22semidirect
38. C22×C4⋊Dic11C22semidirect
39. C22×Dic11⋊C4C22semidirect
40. C22×Dic11⋊C4C22semidirect
45. C2×C11×#95C22semidirect
46. C2×C11⋊#95C22semidirect
47. C2×C11⋊#95C22semidirect
48. C2×C11⋊#95C22semidirect
49. C2×C11⋊#95C22semidirect
50. C2×C11⋊#95C22semidirect
51. C2×C11⋊#95C22semidirect
52. C2×C11⋊#95C22semidirect
53. C2×C11⋊#95C22semidirect
54. C2×C11⋊#95C22semidirect
386. C2×#396D11semidirect
626. C22×C4⋊C4C2×D11semidirect
627. C22×C4⋊C4C2×D11semidirect
628. C22×C4⋊C4C2×D11semidirect
664. C2×#95C2×D11semidirect
745. C2×D11#396semidirect
1098. C11#14726semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D112
C2×#106226072
C2×#106226022
C2×#106226002
C2×#106225682
#130668612
#130668602
#130668592
#130668582
(C2×D11)⋊#952
C2×C11×#3962
#1472611