Finite Group Databasebeta

← #14677098

Subgroups — #14677098

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622601C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3C2×#10622282C211yesmaximal, characteristic, complemented
4C2×#10622282C211yesmaximal, characteristic, complemented
5C2×#10622278C211yesmaximal, characteristic
6C2×#10622280C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
8#13066879C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic
12#13066852C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622601—24no—
52#10622553—24no—
53C4×(C2×D11)⋊C4—24no—
54#10622282—24no—
55#10622282—24no—
56#10622280—24no—
57#10622278C418yescomplemented
58C24×D11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44C2×C414yes—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—41no—
85C22×C4×D11—41no—
86C22×C4×D11C2×C414yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—41no—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—41no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4C2×C414yes—
123C2×(C2×D11)⋊C4C2×C414yes—
124C2×(C2×D11)⋊C4C2×C414yes—
125C2×(C2×D11)⋊C4D414yes—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—41no—
133C2×Dic11⋊C4—41no—
134C2×Dic11⋊C4—41no—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—41no—
143C2×C4×Dic11—41no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95—22no—
148C11×#95C2×C414yes—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—41no—
155C11⋊#95C2×C414yes—
156C11⋊#95D414yescomplemented
157C11⋊#95D414yescomplemented
158#14012—111nomaximal, Sylow
159C24×C11C2411yescharacteristic
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11C22×C412yes—
187C23×D11C22×C412yes—
188C23×D11C2×D412yes—
189C23×D11#4112yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11#4112yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11C22×C412yes—
272C22×Dic11C22×C412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11C2×D412yes—
276C22×Dic11C2×D412yes—
277C22×Dic11C2×D412yes—
278C22×Dic11#4112yes—
279C22×Dic11#4112yes—
280C22×Dic11#4112yes—
281C2×D44—28no—
282C2×D44—28no—
283C2×D44—44no—
284C2×D44—44no—
285C2×D44—44no—
286C2×D44—44no—
287C2×D44—44no—
288C2×C4×D11—28no—
289C2×C4×D11—28no—
290C2×C4×D11—44no—
291C2×C4×D11—44no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C11×C4⋊C4—44no—
296C42×C11—44no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—28no—
301(C2×D11)⋊C4—28no—
302(C2×D11)⋊C4—44no—
303(C2×D11)⋊C4—44no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4—44no—
308Dic11⋊C4—44no—
309Dic11⋊C4—44no—
310Dic11⋊C4—44no—
311C4×Dic11—44no—
312C4×Dic11—44no—
313C4×Dic11—44no—
314C2×#390—111no—
315C2×#388—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#386—111no—
319C2×#380—111no—
320C2×C4×C22⋊C4—111no—
321#1444—111no—
322#1440—111no—
323#1439—111no—
324#1438—111no—
325#1437—111no—
326#1436—111no—
327#1436D1111yescharacteristic, complemented
328C4×#95—111no—
329C23×C11C23×C411yescharacteristic
330C23×C11C22×D411yescharacteristic
331C23×C11C22×D411yescharacteristic
332C23×C11C22×D411yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11C2×#4111yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11H(5,𝔽2)11yescharacteristic
341C23×C11H(5,𝔽2)11yescharacteristic
342C23×C11H(5,𝔽2)11yescharacteristic
343C23×C112−1+411yescharacteristic
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11C4×D414yes—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11#11714yes—
462C2×C4×C11C4×D414yes—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11C4×D414yes—
504C2×Dic11#12114yes—
505D44—416no—
506C4×D11—416no—
507C23×D4—111no—
508C24×C4—111no—
509C22×C4⋊C4—111no—
510C22×C4⋊C4—111no—
511C22×C4⋊C4—111no—
512C22×C4⋊C4C2×D1111yescharacteristic
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4—111no—
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C42—111no—
525C22×C42—111no—
526C22×C42—111no—
527C22×C42C2×D1111yescharacteristic
528#390—224no—
529#388—224no—
530#388—224no—
531#388—224no—
532#386—118no—
533#380—224no—
534C4×C22⋊C4—224no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95C2×D1111yescharacteristic
545C2×#95C2×D1111yescharacteristic
546C2×#95C2×D1111yescharacteristic
547C2×#95C2×D1111yescharacteristic
548C2×#95C2×D1111yescharacteristic
549C22×C11C2×#11711yescharacteristic
550C22×C11C2×C4×D411yescharacteristic
551C22×C11C2×C4×D411yescharacteristic
552C22×C11C2×C4×D411yescharacteristic
553C22×C11C4×#4111yescharacteristic
554C22×C11#51811yescharacteristic
555C22×C11#52011yescharacteristic
556C22×C11C2×#12111yescharacteristic
557C22×C11#52511yescharacteristic
558C22×C11#52911yescharacteristic
559C22×C11#52911yescharacteristic
560C22×C11#52911yescharacteristic
561C22×C11#53211yescharacteristic
562C22×C11#53211yescharacteristic
563C22×C11#53211yescharacteristic
564C22×C11#53811yescharacteristic
565C22×C11#53911yescharacteristic
566C22×C11#54011yescharacteristic
567C22×C11#54211yescharacteristic
568C22×C11D4211yescharacteristic
569C22×C11D4211yescharacteristic
570C22×C11#54611yescharacteristic
571C22×C11#54611yescharacteristic
572C22×C11#54611yescharacteristic
573C22×C11#54611yescharacteristic
574C22×C11#54711yescharacteristic
575C22×C11#54711yescharacteristic
576C22×C11#54811yescharacteristic
577C22×C11#55011yescharacteristic
578C22×C11#55111yescharacteristic
579C22×C11#55111yescharacteristic
580C22×C11#55111yescharacteristic
581C22×C11#55311yescharacteristic
582C22×C11#55511yescharacteristic
583C22×C11#55611yescharacteristic
584C2×D11—24no—
585C2×D11—24no—
586C2×D11—24no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—81no—
607C2×D11—81no—
608C2×D11—81no—
609C2×D11—81no—
610C2×D11—81no—
611C2×D11—81no—
612C2×D11—81no—
613C2×D11—81no—
614C4×C11—24no—
615C4×C11—24no—
616C4×C11—42no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—81no—
620C4×C11—81no—
621Dic11—24no—
622Dic11—24no—
623Dic11—42no—
624Dic11—42no—
625Dic11—42no—
626Dic11—42no—
627C25—111no—
628C25—111no—
629C22×D4—114no—
630C22×D4—222no—
631C22×D4—222no—
632C22×D4—222no—
633C22×D4—222no—
634C22×D4—441no—
635C22×D4—441no—
636C23×C4—111no—
637C23×C4—111no—
638C23×C4—111no—
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—111no—
642C23×C4—114no—
643C23×C4—222no—
644C23×C4—222no—
645C23×C4—222no—
646C23×C4—222no—
647C23×C4—441no—
648C23×C4—441no—
649C23×C4C22×D1111yescharacteristic
650C23×C4C22×D1111yescharacteristic
651C23×C4C22×D1111yescharacteristic
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—222no—
660C2×C4⋊C4—222no—
661C2×C4⋊C4—222no—
662C2×C4⋊C4—222no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4—222no—
665C2×C4⋊C4—441no—
666C2×C4⋊C4—441no—
667C2×C4⋊C4—441no—
668C2×C22⋊C4—114no—
669C2×C22⋊C4—114no—
670C2×C22⋊C4—114no—
671C2×C22⋊C4—114no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—441no—
696C2×C22⋊C4—441no—
697C2×C22⋊C4—441no—
698C2×C22⋊C4—441no—
699C2×C22⋊C4—441no—
700C2×C22⋊C4—441no—
701C2×C42—22no—
702C2×C42—22no—
703C2×C42—41no—
704C2×C42—222no—
705C2×C42—222no—
706C2×C42—222no—
707C2×C42—222no—
708C2×C42—222no—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—441no—
712C2×C42—441no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—114no—
718#95—114no—
719#95—114no—
720#95—222no—
721#95—222no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—441no—
726#95C4×D1114yes—
727C2×C11#229311yescharacteristic
728C2×C11C4×#12111yescharacteristic
729C2×C11#233511yescharacteristic
730C2×C11#234211yescharacteristic
731C2×C11#235411yescharacteristic
732C2×C11#235811yescharacteristic
733C2×C11#236111yescharacteristic
734C2×C11#242511yescharacteristic
735C2×C11#242811yescharacteristic
736C2×C11#246111yescharacteristic
737C2×C11#246711yescharacteristic
738C2×C11#252111yescharacteristic
739C2×C11#253111yescharacteristic
740C2×C11#255511yescharacteristic
741C2×C11#256011yescharacteristic
742D11—44no—
743D11—82no—
744C24—112no—
745C24—112no—
746C24—112no—
747C24—112no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24—221no—
763C24—221no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24C23×D1111yescharacteristic
775C2×D4—228no—
776C2×D4—228no—
777C2×D4—444no—
778C2×D4—444no—
779C2×D4—444no—
780C2×D4—444no—
781C2×D4—444no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—112no—
823C22×C4—112no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—228no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—228no—
866C22×C4—444no—
867C22×C4—444no—
868C22×C4—444no—
869C22×C4—444no—
870C22×C4—444no—
871C22×C4C2×C4×D1112yes—
872C22×C4C2×C4×D1112yes—
873C22×C4C2×C4×D1112yes—
874C22×C4#433912yes—
875C22×C4#433912yes—
876C22×C4D4×D1112yes—
877C22×C4D4×D1112yes—
878C22×C4D4×D1112yes—
879C22×C4#434312yes—
880C4⋊C4—44no—
881C4⋊C4—444no—
882C4⋊C4—444no—
883C4⋊C4—444no—
884C22⋊C4—228no—
885C22⋊C4—228no—
886C22⋊C4—228no—
887C22⋊C4—228no—
888C22⋊C4—228no—
889C22⋊C4—444no—
890C22⋊C4—444no—
891C22⋊C4—444no—
892C22⋊C4—444no—
893C22⋊C4—444no—
894C22⋊C4—444no—
895C42—44no—
896C42—444no—
897C42—444no—
898C42—444no—
899C11#1401211yescharacteristic, complemented, Sylow
900C23—114no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23—222no—
908C23—222no—
909C23—222no—
910C23—222no—
911C23—222no—
912C23—222no—
913C23—222no—
914C23—222no—
915C23—222no—
916C23—222no—
917C23—222no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23C22×C4×D1111yescharacteristic
971C23C2×#433911yescharacteristic
972C23C2×#433911yescharacteristic
973C23C2×D4×D1111yescharacteristic
974C23C2×D4×D1111yescharacteristic
975C23C2×D4×D1111yescharacteristic
976C23#6703711yescharacteristic
977C23C2×#434311yescharacteristic
978C23#6704011yescharacteristic
979C23#41×D1111yescharacteristic
980C23#41×D1111yescharacteristic
981C23#41×D1111yescharacteristic
982C23#41×D1111yescharacteristic
983C23#6704211yescharacteristic
984C23#6704211yescharacteristic
985D4—4416no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—114no—
1034C2×C4—114no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—4416no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4#6692514yes—
1077C2×C4#6694614yes—
1078C22—224no—
1079C22—224no—
1080C22—224no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—442no—
1085C22—442no—
1086C22—442no—
1087C22—442no—
1088C22—442no—
1089C22—442no—
1090C22—442no—
1091C22—442no—
1092C22—442no—
1093C22—442no—
1094C22—442no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—881no—
1101C22—881no—
1102C22—881no—
1103C22—881no—
1104C22—881no—
1105C22—881no—
1106C22—881no—
1107C22—881no—
1108C22C2×#6692511yescharacteristic
1109C22#1062302111yescharacteristic
1110C22C2×#6694611yescharacteristic
1111C22#1062303811yescharacteristic
1112C22#1062305311yescharacteristic
1113C22#1062305811yescharacteristic
1114C22#1062306311yescharacteristic
1115C22C4×D4×D1111yescharacteristic
1116C22C4×D4×D1111yescharacteristic
1117C22#1062307611yescharacteristic
1118C22#1062307911yescharacteristic
1119C22#1062307911yescharacteristic
1120C22#1062308111yescharacteristic
1121C22#1062308411yescharacteristic
1122C22#1062308711yescharacteristic
1123C22#1062309911yescharacteristic
1124C22#1062310511yescharacteristic
1125C22#1062311111yescharacteristic
1126C22#1062311111yescharacteristic
1127C22#1062312111yescharacteristic
1128C22D11×#12111yescharacteristic
1129C22#1062314011yescharacteristic
1130C22#1062316111yescharacteristic
1131C22#1062316411yescharacteristic
1132C22#1062316811yescharacteristic
1133C22#1062317111yescharacteristic
1134C22#1062318511yescharacteristic
1135C22#1062318711yescharacteristic
1136C22#1062319411yescharacteristic
1137C22#1062319911yescharacteristic
1138C22#1062322311yescharacteristic
1139C22#1062322611yescharacteristic
1140C22#1062323511yescharacteristic
1141C22#1062323711yescharacteristic
1142C22#1062325711yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C4—224no—
1151C4—224no—
1152C4—442no—
1153C4—442no—
1154C4—442no—
1155C4—442no—
1156C2—444no—
1157C2—882no—
1158C2#1307107711yescharacteristic
1159C2#1307112811yescharacteristic
1160C2#1307141211yescharacteristic
1161C2#1307145911yescharacteristic
1162C2#1307156111yescharacteristic
1163C2#1307159211yescharacteristic
1164C2#1307163111yescharacteristic
1165C2#1307217411yescharacteristic
1166C2#1307220311yescharacteristic
1167C2#1307258011yescharacteristic
1168C2#1307266411yescharacteristic
1169C2#1307332511yescharacteristic
1170C2#1307346911yescharacteristic
1171C2#1307369211yescharacteristic
1172C2#1307376611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14012
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. C2×#10622282C2semidirect
4. C2×#10622282C2semidirect
6. C2×#10622280C2semidirect
7. C2×C4×(C2×D11)⋊C4C2semidirect
8. #13066879C2semidirect
9. #13066864C2semidirect
10. #13066860C2semidirect
12. #13066852C2semidirect
13. #13066847C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1436C2semidirect
57. #10622278C4semidirect
156. C11⋊#95D4semidirect
157. C11⋊#95D4semidirect
327. #1436D11semidirect
899. C11#14012semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106225532
C2×#106222822
C2×#106222782
C2×#106222802
C2×C4×(C2×D11)⋊C42
#130668792
#130668642
#130668602
#130668562
#130668522
#130668472
#95×Dic112
C11×#14362
#1401211