Finite Group Databasebeta

← #14675690

Subgroups — #14675690

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 1418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3C2×#10622282C211yesmaximal, characteristic, complemented
4C2×#10622280C211yesmaximal, characteristic, complemented
5C2×#10622568C211yesmaximal, characteristic
6C2×#10622568C211yesmaximal, characteristic
7C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066853C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C25×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic, complemented
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic, complemented
37C22×Dic11⋊C4C2211yescharacteristic, complemented
38C22×C4×Dic11C2211yescharacteristic, complemented
39C2×C22⋊C4×D11—24no—
40C2×C22⋊C4×D11—24no—
41C2×C22⋊C4×D11C418yescomplemented
42C2×C11×#95C2211yescharacteristic, complemented
43C2×C11×#95C2211yescharacteristic, complemented
44C2×C11×#95C2211yescharacteristic, complemented
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
54#10622568—24no—
55#10622568—24no—
56#10622553—24no—
57C4×(C2×D11)⋊C4—24no—
58#10622282—24no—
59#10622280—24no—
60C25×C11C2311yescharacteristic
61C24×D11—22no—
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—41no—
72C24×D11—41no—
73C24×D11—41no—
74C24×D11—41no—
75C24×D11C2×C414yes—
76C24×D11C2311yescharacteristic
77C24×D11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×C4×D11—22no—
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—41no—
99C22×C4×D11—41no—
100C22×C4×D11—41no—
101C22×C4×D11—41no—
102C22×C4×D11C2×C414yes—
103C22×C4×D11C2×C414yes—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4C2×C414yes—
113C2×C42×C11—22no—
114C2×C42×C11—22no—
115C2×C42×C11—41no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—41no—
123C2×C22⋊Dic11—41no—
124C2×C22⋊Dic11C2×C414yes—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
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—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4—41no—
148C2×(C2×D11)⋊C4—41no—
149C2×(C2×D11)⋊C4C2×C414yes—
150C2×(C2×D11)⋊C4C2×C414yes—
151C2×(C2×D11)⋊C4D414yes—
152C2×(C2×D11)⋊C4D414yes—
153C2×(C2×D11)⋊C4D414yes—
154C2×(C2×D11)⋊C4D414yes—
155C2×Dic11⋊C4—22no—
156C2×Dic11⋊C4—22no—
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4—22no—
159C2×Dic11⋊C4—41no—
160C2×Dic11⋊C4—41no—
161C2×C4×Dic11—22no—
162C2×C4×Dic11—22no—
163C2×C4×Dic11—41no—
164C22⋊C4×D11—232no—
165C11×#95—22no—
166C11×#95—22no—
167C11×#95—41no—
168C11⋊#95—22no—
169C11⋊#95—22no—
170C11⋊#95—22no—
171C11⋊#95—22no—
172C11⋊#95—22no—
173C11⋊#95—22no—
174C11⋊#95—41no—
175C11⋊#95—41no—
176C11⋊#95—41no—
177#13873—111nomaximal, Sylow
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11C22×C412yes—
191C24×C11#4112yes—
192C24×C11#4112yes—
193C24×C11C2411yescharacteristic
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—28no—
203C23×D11—28no—
204C23×D11—28no—
205C23×D11—28no—
206C23×D11—28no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11—21no—
215C23×D11—21no—
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—28no—
220C23×D11—28no—
221C23×D11—28no—
222C23×D11—28no—
223C23×D11—44no—
224C23×D11—44no—
225C23×D11—44no—
226C23×D11—44no—
227C23×D11—44no—
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×D11C22×C412yes—
250C23×D11C22×C412yes—
251C23×D11C2×D412yes—
252C23×D11C2×D412yes—
253C23×D11C2×D412yes—
254C23×D11C2×D412yes—
255C23×D11#4112yes—
256C23×D11#4112yes—
257C23×D11#4112yes—
258C23×D11#4112yes—
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—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×C11C22×C412yes—
296C22×C4×C11C22×C412yes—
297C22×C4×C11C2×D412yes—
298C22×C4×C11C2×D412yes—
299C22×C4×C11C2×D412yes—
300C22×C4×C11C2×D412yes—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
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×Dic11C22×C412yes—
338C22×Dic11C22×C412yes—
339C22×Dic11C2×D412yes—
340C22×Dic11C2×D412yes—
341C22×Dic11C2×D412yes—
342C22×Dic11C2×D412yes—
343C2×C4×D11—28no—
344C2×C4×D11—28no—
345C2×C4×D11—28no—
346C2×C4×D11—28no—
347C2×C4×D11—44no—
348C2×C4×D11—44no—
349C2×C4×D11—44no—
350C2×C4×D11—44no—
351C2×C4×D11—44no—
352C2×C4×D11—44no—
353C2×C4×D11—44no—
354C2×C4×D11—44no—
355C2×C4×D11—44no—
356C2×C4×D11—44no—
357C11×C22⋊C4—28no—
358C11×C22⋊C4—44no—
359C11×C22⋊C4—44no—
360C42×C11—44no—
361C22⋊Dic11—28no—
362C22⋊Dic11—44no—
363C22⋊Dic11—44no—
364(C2×D11)⋊C4—28no—
365(C2×D11)⋊C4—28no—
366(C2×D11)⋊C4—28no—
367(C2×D11)⋊C4—44no—
368(C2×D11)⋊C4—44no—
369(C2×D11)⋊C4—44no—
370(C2×D11)⋊C4—44no—
371(C2×D11)⋊C4—44no—
372(C2×D11)⋊C4—44no—
373(C2×D11)⋊C4C22⋊C4116yescomplemented
374Dic11⋊C4—44no—
375Dic11⋊C4—44no—
376C4×Dic11—44no—
377C23×C22⋊C4—111no—
378C2×#388—111no—
379C2×#388—111no—
380C2×#380—111no—
381C2×#379—111no—
382C2×#379—111no—
383C2×C4×C22⋊C4—111no—
384#1440—111no—
385#1440—111no—
386#1439—111no—
387#1439—111no—
388#1437—111no—
389#1437D1111yescharacteristic, complemented
390C22⋊#95—111no—
391C22⋊#95—111no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
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—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
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#11714yes—
427C23×C11C23×C411yescharacteristic
428C23×C11C22×D411yescharacteristic
429C23×C11C22×D411yescharacteristic
430C23×C11C22×D411yescharacteristic
431C23×C11C22×D411yescharacteristic
432C23×C11C2×#4111yescharacteristic
433C23×C11C2×#4111yescharacteristic
434C23×C11C2×#4111yescharacteristic
435C23×C11C2×#4111yescharacteristic
436C23×C11C2×#4111yescharacteristic
437C23×C11C2×#4111yescharacteristic
438C23×C11H(5,𝔽2)11yescharacteristic
439C23×C11H(5,𝔽2)11yescharacteristic
440C23×C11H(5,𝔽2)11yescharacteristic
441C23×C11H(5,𝔽2)11yescharacteristic
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
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—232no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—22no—
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—416no—
490C22×D11—416no—
491C22×D11—416no—
492C22×D11—416no—
493C22×D11—416no—
494C22×D11—416no—
495C22×D11—416no—
496C22×D11—416no—
497C22×D11—416no—
498C22×D11—416no—
499C22×D11—416no—
500C22×D11—416no—
501C22×D11—416no—
502C22×D11—41no—
503C22×D11—41no—
504C22×D11—41no—
505C22×D11—41no—
506C22×D11—41no—
507C22×D11—41no—
508C22×D11—41no—
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—416no—
519C22×D11C2×C22⋊C414yes—
520C22×D11#11714yes—
521C22×D11C4×D414yes—
522C22×D11C4×D414yes—
523C22×D11#12114yes—
524C22×D11#12314yes—
525C22×D11#12414yes—
526C22×D11#12614yes—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
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—41no—
543C2×C4×C11—41no—
544C2×C4×C11—41no—
545C2×C4×C11—41no—
546C2×C4×C11—41no—
547C2×C4×C11—41no—
548C2×C4×C11—41no—
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×C11C2×C22⋊C414yes—
569C2×Dic11—22no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—22no—
574C2×Dic11—22no—
575C2×Dic11—22no—
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—41no—
585C2×Dic11—41no—
586C2×Dic11—41no—
587C2×Dic11—41no—
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×Dic11C2×C22⋊C414yes—
611C4×D11—416no—
612C4×D11—416no—
613C26—111no—
614C24×C4—111no—
615C24×C4—111no—
616C22×C4⋊C4—111no—
617C22×C4⋊C4—111no—
618C22×C22⋊C4—111no—
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4—118no—
624C22×C22⋊C4—111no—
625C22×C22⋊C4—111no—
626C22×C22⋊C4—111no—
627C22×C22⋊C4—111no—
628C22×C22⋊C4—111no—
629C22×C22⋊C4—111no—
630C22×C22⋊C4—111no—
631C22×C22⋊C4—111no—
632C22×C22⋊C4—224no—
633C22×C22⋊C4—224no—
634C22×C22⋊C4C2×D1111yescharacteristic
635C22×C22⋊C4C2×D1111yescharacteristic
636C22×C22⋊C4C2×D1111yescharacteristic
637C22×C42—111no—
638C22×C42C2×D1111yescharacteristic, complemented
639#388—224no—
640#388—224no—
641#380—224no—
642#379—224no—
643#379—224no—
644C4×C22⋊C4—224no—
645C2×#95—111no—
646C2×#95—111no—
647C2×#95—111no—
648C2×#95—111no—
649C2×#95—111no—
650C2×#95—111no—
651C2×#95—111no—
652C2×#95—111no—
653C2×#95—111no—
654C2×#95C2×D1111yescharacteristic, complemented
655C2×#95C2×D1111yescharacteristic, complemented
656C2×#95C2×D1111yescharacteristic, complemented
657C22×C11—24no—
658C22×C11—24no—
659C22×C11—24no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11C22×C22⋊C411yescharacteristic
673C22×C11C2×#11711yescharacteristic
674C22×C11C2×#11711yescharacteristic
675C22×C11C2×C4×D411yescharacteristic
676C22×C11C2×C4×D411yescharacteristic
677C22×C11#51811yescharacteristic
678C22×C11#51811yescharacteristic
679C22×C11C2×#12111yescharacteristic
680C22×C11C2×#12311yescharacteristic
681C22×C11#52511yescharacteristic
682C22×C11#52511yescharacteristic
683C22×C11#52511yescharacteristic
684C22×C11#52511yescharacteristic
685C22×C11C2×#12411yescharacteristic
686C22×C11C2×#12611yescharacteristic
687C22×C11#53811yescharacteristic
688C22×C11#53811yescharacteristic
689C22×C11#53811yescharacteristic
690C22×C11#53811yescharacteristic
691C22×C11D4211yescharacteristic
692C22×C11D4211yescharacteristic
693C22×C11D4211yescharacteristic
694C22×C11D4211yescharacteristic
695C22×C11#54611yescharacteristic
696C22×C11#54611yescharacteristic
697C22×C11#54611yescharacteristic
698C22×C11#54611yescharacteristic
699C22×C11#54611yescharacteristic
700C22×C11#54611yescharacteristic
701C22×C11#54611yescharacteristic
702C22×C11#54611yescharacteristic
703C22×C11#55111yescharacteristic
704C22×C11#55111yescharacteristic
705C22×C11#55111yescharacteristic
706C22×C11#55111yescharacteristic
707C2×D11—24no—
708C2×D11—24no—
709C2×D11—24no—
710C2×D11—24no—
711C2×D11—24no—
712C2×D11—24no—
713C2×D11—24no—
714C2×D11—24no—
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—464no—
725C2×D11—42no—
726C2×D11—42no—
727C2×D11—42no—
728C2×D11—42no—
729C2×D11—42no—
730C2×D11—42no—
731C2×D11—42no—
732C2×D11—42no—
733C2×D11—42no—
734C2×D11—42no—
735C2×D11—42no—
736C2×D11—42no—
737C2×D11#38818yescomplemented
738C4×C11—24no—
739C4×C11—42no—
740C4×C11—42no—
741C4×C11—42no—
742C4×C11—81no—
743C4×C11—81no—
744Dic11—24no—
745Dic11—42no—
746Dic11—42no—
747Dic11—42no—
748Dic11—81no—
749Dic11—81no—
750C25—111no—
751C25—111no—
752C25—114no—
753C25—222no—
754C25—222no—
755C25—222no—
756C25—222no—
757C25—222no—
758C25—222no—
759C25—222no—
760C25—222no—
761C25—222no—
762C25—222no—
763C25—441no—
764C25—441no—
765C25—441no—
766C25—441no—
767C25C22×D1111yescharacteristic
768C23×C4—111no—
769C23×C4—111no—
770C23×C4—111no—
771C23×C4—111no—
772C23×C4—114no—
773C23×C4—114no—
774C23×C4—111no—
775C23×C4—111no—
776C23×C4—222no—
777C23×C4—222no—
778C23×C4—222no—
779C23×C4—222no—
780C23×C4—222no—
781C23×C4—222no—
782C23×C4—222no—
783C23×C4—222no—
784C23×C4—441no—
785C23×C4—441no—
786C23×C4—441no—
787C23×C4—441no—
788C23×C4C22×D1111yescharacteristic
789C23×C4C22×D1111yescharacteristic
790C23×C4C22×D1111yescharacteristic
791C23×C4C22×D1111yescharacteristic
792C23×C4C22×D1111yescharacteristic
793C23×C4C22×D1111yescharacteristic
794C2×C4⋊C4—222no—
795C2×C4⋊C4—222no—
796C2×C4⋊C4—222no—
797C2×C4⋊C4—222no—
798C2×C4⋊C4—441no—
799C2×C4⋊C4—441no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—114no—
809C2×C22⋊C4—114no—
810C2×C22⋊C4—114no—
811C2×C22⋊C4—114no—
812C2×C22⋊C4—114no—
813C2×C22⋊C4—114no—
814C2×C22⋊C4—114no—
815C2×C22⋊C4—2232no—
816C2×C22⋊C4—222no—
817C2×C22⋊C4—222no—
818C2×C22⋊C4—222no—
819C2×C22⋊C4—222no—
820C2×C22⋊C4—222no—
821C2×C22⋊C4—222no—
822C2×C22⋊C4—222no—
823C2×C22⋊C4—222no—
824C2×C22⋊C4—222no—
825C2×C22⋊C4—222no—
826C2×C22⋊C4—222no—
827C2×C22⋊C4—222no—
828C2×C22⋊C4—222no—
829C2×C22⋊C4—222no—
830C2×C22⋊C4—222no—
831C2×C22⋊C4—222no—
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—441no—
843C2×C22⋊C4—441no—
844C2×C22⋊C4—441no—
845C2×C22⋊C4—441no—
846C2×C22⋊C4—441no—
847C2×C22⋊C4—441no—
848C2×C22⋊C4C4×D1114yes—
849C2×C42—22no—
850C2×C42—22no—
851C2×C42—41no—
852C2×C42—222no—
853C2×C42—222no—
854C2×C42—441no—
855#95—22no—
856#95—22no—
857#95—41no—
858#95—222no—
859#95—222no—
860#95—222no—
861#95—222no—
862#95—222no—
863#95—222no—
864#95—441no—
865#95—441no—
866#95—441no—
867C2×C11—44no—
868C2×C11#228011yescharacteristic
869C2×C11C2×#38811yescharacteristic
870C2×C11#231211yescharacteristic
871C2×C11D4×C22⋊C411yescharacteristic
872C2×C11D4×C22⋊C411yescharacteristic
873C2×C11#234211yescharacteristic
874C2×C11#234211yescharacteristic
875C2×C11#241811yescharacteristic
876C2×C11#241811yescharacteristic
877C2×C11#242411yescharacteristic
878C2×C11#242411yescharacteristic
879C2×C11#247211yescharacteristic
880C2×C11#247211yescharacteristic
881C2×C11#248011yescharacteristic
882C2×C11#248011yescharacteristic
883D11—28no—
884D11—44no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—112no—
898C24—112no—
899C24—112no—
900C24—112no—
901C24—112no—
902C24—112no—
903C24—112no—
904C24—112no—
905C24—112no—
906C24—112no—
907C24—228no—
908C24—228no—
909C24—228no—
910C24—228no—
911C24—228no—
912C24—228no—
913C24—228no—
914C24—228no—
915C24—221no—
916C24—221no—
917C24—221no—
918C24—221no—
919C24—221no—
920C24—221no—
921C24—221no—
922C24—221no—
923C24—228no—
924C24—221no—
925C24—221no—
926C24—221no—
927C24—221no—
928C24—221no—
929C24—221no—
930C24—221no—
931C24—221no—
932C24—221no—
933C24—221no—
934C24—221no—
935C24—221no—
936C24—444no—
937C24—444no—
938C24—444no—
939C24—444no—
940C24—444no—
941C24—444no—
942C24—444no—
943C24—444no—
944C24—444no—
945C24—444no—
946C24—444no—
947C24—444no—
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—
962C24C2×C4×D1112yes—
963C24#433912yes—
964C24#433912yes—
965C24C23×D1111yescharacteristic
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
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—112no—
1003C22×C4—112no—
1004C22×C4—112no—
1005C22×C4—112no—
1006C22×C4—112no—
1007C22×C4—112no—
1008C22×C4—228no—
1009C22×C4—228no—
1010C22×C4—228no—
1011C22×C4—221no—
1012C22×C4—221no—
1013C22×C4—221no—
1014C22×C4—221no—
1015C22×C4—221no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—221no—
1019C22×C4—221no—
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—228no—
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—221no—
1045C22×C4—221no—
1046C22×C4—221no—
1047C22×C4—221no—
1048C22×C4—444no—
1049C22×C4—444no—
1050C22×C4—444no—
1051C22×C4—444no—
1052C22×C4—444no—
1053C22×C4—444no—
1054C22×C4—444no—
1055C22×C4—444no—
1056C22×C4—444no—
1057C22×C4—444no—
1058C22×C4C2×C4×D1112yes—
1059C22×C4C2×C4×D1112yes—
1060C22×C4D4×D1112yes—
1061C22×C4D4×D1112yes—
1062C22×C4D4×D1112yes—
1063C22×C4D4×D1112yes—
1064C4⋊C4—444no—
1065C4⋊C4—444no—
1066C22⋊C4—28no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—1116no—
1070C22⋊C4—228no—
1071C22⋊C4—228no—
1072C22⋊C4—228no—
1073C22⋊C4—228no—
1074C22⋊C4—444no—
1075C22⋊C4—444no—
1076C22⋊C4—444no—
1077C22⋊C4—444no—
1078C22⋊C4—444no—
1079C22⋊C4—444no—
1080C22⋊C4—444no—
1081C22⋊C4—444no—
1082C42—44no—
1083C42—444no—
1084C11#1387311yescharacteristic, complemented, Sylow
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—114no—
1120C23—114no—
1121C23—114no—
1122C23—114no—
1123C23—114no—
1124C23—114no—
1125C23—114no—
1126C23—114no—
1127C23—2232no—
1128C23—222no—
1129C23—222no—
1130C23—222no—
1131C23—222no—
1132C23—222no—
1133C23—222no—
1134C23—222no—
1135C23—222no—
1136C23—222no—
1137C23—222no—
1138C23—222no—
1139C23—222no—
1140C23—222no—
1141C23—222no—
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—4416no—
1175C23—4416no—
1176C23—4416no—
1177C23—4416no—
1178C23—4416no—
1179C23—4416no—
1180C23—4416no—
1181C23—4416no—
1182C23—4416no—
1183C23—4416no—
1184C23—4416no—
1185C23—4416no—
1186C23—4416no—
1187C23—4416no—
1188C23—441no—
1189C23—441no—
1190C23—441no—
1191C23—441no—
1192C23—441no—
1193C23—441no—
1194C23—441no—
1195C23—441no—
1196C23—441no—
1197C23—441no—
1198C23—441no—
1199C23—441no—
1200C23—441no—
1201C23—441no—
1202C23—441no—
1203C23—441no—
1204C23#6692514yes—
1205C23C22×C4×D1111yescharacteristic
1206C23C2×#433911yescharacteristic
1207C23C2×#433911yescharacteristic
1208C23C2×D4×D1111yescharacteristic
1209C23C2×D4×D1111yescharacteristic
1210C23C2×D4×D1111yescharacteristic
1211C23C2×D4×D1111yescharacteristic
1212C23#6703711yescharacteristic
1213C23#6703711yescharacteristic
1214C23#41×D1111yescharacteristic
1215C23#41×D1111yescharacteristic
1216C23#41×D1111yescharacteristic
1217C23#41×D1111yescharacteristic
1218C23#6704211yescharacteristic
1219C23#6704211yescharacteristic
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
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—114no—
1262C2×C4—222no—
1263C2×C4—222no—
1264C2×C4—222no—
1265C2×C4—222no—
1266C2×C4—222no—
1267C2×C4—222no—
1268C2×C4—222no—
1269C2×C4—222no—
1270C2×C4—222no—
1271C2×C4—222no—
1272C2×C4—222no—
1273C2×C4—222no—
1274C2×C4—222no—
1275C2×C4—222no—
1276C2×C4—222no—
1277C2×C4—4416no—
1278C2×C4—4416no—
1279C2×C4—441no—
1280C2×C4—441no—
1281C2×C4—441no—
1282C2×C4—441no—
1283C2×C4—441no—
1284C2×C4—441no—
1285C2×C4—441no—
1286C2×C4—441no—
1287C2×C4—441no—
1288C2×C4—441no—
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×C4C22⋊C4×D1114yes—
1306C22—24no—
1307C22—24no—
1308C22—24no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—118no—
1322C22—224no—
1323C22—224no—
1324C22—224no—
1325C22—224no—
1326C22—224no—
1327C22—224no—
1328C22—224no—
1329C22—224no—
1330C22—224no—
1331C22—224no—
1332C22—224no—
1333C22—224no—
1334C22—224no—
1335C22—224no—
1336C22—224no—
1337C22—224no—
1338C22—224no—
1339C22—4464no—
1340C22—442no—
1341C22—442no—
1342C22—442no—
1343C22—442no—
1344C22—442no—
1345C22—442no—
1346C22—442no—
1347C22—442no—
1348C22—442no—
1349C22—442no—
1350C22—442no—
1351C22—442no—
1352C22C2×#6692511yescharacteristic
1353C22C2×C22⋊C4×D1111yescharacteristic
1354C22#1062302111yescharacteristic
1355C22#1062302111yescharacteristic
1356C22D11×#11711yescharacteristic
1357C22#1062305811yescharacteristic
1358C22#1062305811yescharacteristic
1359C22C4×D4×D1111yescharacteristic
1360C22C4×D4×D1111yescharacteristic
1361C22#1062307611yescharacteristic
1362C22#1062307611yescharacteristic
1363C22#1062307811yescharacteristic
1364C22#1062307811yescharacteristic
1365C22#1062307811yescharacteristic
1366C22#1062307811yescharacteristic
1367C22#1062308111yescharacteristic
1368C22#1062308111yescharacteristic
1369C22#1062308711yescharacteristic
1370C22#1062308711yescharacteristic
1371C22#1062312111yescharacteristic
1372C22D11×#12111yescharacteristic
1373C22#1062314011yescharacteristic
1374C22#1062314011yescharacteristic
1375C22#1062314111yescharacteristic
1376C22#1062314311yescharacteristic
1377C22#1062314411yescharacteristic
1378C22D11×#12311yescharacteristic
1379C22#1062318511yescharacteristic
1380C22#1062318811yescharacteristic
1381C22D11×#12411yescharacteristic
1382C22#1062320711yescharacteristic
1383C22#1062320911yescharacteristic
1384C22D11×#12611yescharacteristic
1385C22#1062323511yescharacteristic
1386C22#1062324811yescharacteristic
1387C4—24no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—81no—
1392C4—81no—
1393C4—224no—
1394C4—442no—
1395C4—442no—
1396C4—442no—
1397C4—881no—
1398C4—881no—
1399C2—44no—
1400C2—228no—
1401C2—444no—
1402C2#1307099711yescharacteristic
1403C2D11×#38811yescharacteristic
1404C2#1307121011yescharacteristic
1405C2#1307143411yescharacteristic
1406C2#1307143711yescharacteristic
1407C2#1307145911yescharacteristic
1408C2#1307145911yescharacteristic
1409C2#1307207711yescharacteristic
1410C2#1307208511yescharacteristic
1411C2#1307215111yescharacteristic
1412C2#1307215911yescharacteristic
1413C2#1307274611yescharacteristic
1414C2#1307274811yescharacteristic
1415C2#1307286611yescharacteristic
1416C2#1307286811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenter#1437D11
hypocenterC11#13873
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. C2×#10622282C2semidirect
4. C2×#10622280C2semidirect
7. C2×C4×(C2×D11)⋊C4C2semidirect
8. #13066864C2semidirect
9. #13066864C2semidirect
10. #13066859C2semidirect
11. #13066859C2semidirect
12. #13066853C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1437C2semidirect
22. C22×C42×C11C22semidirect
36. C22×Dic11⋊C4C22semidirect
37. C22×Dic11⋊C4C22semidirect
38. C22×C4×Dic11C22semidirect
41. C2×C22⋊C4×D11C4semidirect
42. C2×C11×#95C22semidirect
43. C2×C11×#95C22semidirect
44. C2×C11×#95C22semidirect
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
373. (C2×D11)⋊C4C22⋊C4semidirect
389. #1437D11semidirect
638. C22×C42C2×D11semidirect
654. C2×#95C2×D11semidirect
655. C2×#95C2×D11semidirect
656. C2×#95C2×D11semidirect
737. C2×D11#388semidirect
1084. C11#13873semidirect

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×#106225532
C2×#106222822
C2×#106222802
C2×#106225682
C2×C4×(C2×D11)⋊C42
#130668642
#130668592
#130668532
(C2×D11)⋊#952
C11×#14372
#1387311