Finite Group Databasebeta

← #14681635

Subgroups — #14681635

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622283C211yesmaximal, characteristic, complemented
3C2×#10622603C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic
5C2×#10622600C211yesmaximal, characteristic, complemented
6#13066881C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066862C211yesmaximal, characteristic, complemented
10#13066862C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic
12#13066850C211yesmaximal, characteristic, complemented
13#13066843C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, 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×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
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#10622603—24no—
52#10622600—24no—
53#10622552—24no—
54#10622283—24no—
55#10622278C418yescomplemented
56C24×D11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—41no—
76C22×D44—41no—
77C22×D44C2×C414yes—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—41no—
81C22×C4×D11—41no—
82C22×C4×D11—41no—
83C22×C4×D11—41no—
84C22×C4×D11C2×C414yes—
85C2×C11×C4⋊C4—41no—
86C2×C11×C4⋊C4—41no—
87C2×C11×C4⋊C4D414yescomplemented
88C2×C42×C11—22no—
89C2×C42×C11—22no—
90C2×C42×C11—41no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
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—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4—41no—
108C2×(C2×D11)⋊C4—41no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4C2×C414yes—
121C2×(C2×D11)⋊C4C2×C414yes—
122C2×(C2×D11)⋊C4C2×C414yes—
123C2×(C2×D11)⋊C4D414yes—
124C2×C4⋊Dic11—22no—
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11—22no—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—41no—
129C2×C4⋊Dic11—41no—
130C2×C4⋊Dic11—41no—
131C2×C4⋊Dic11—41no—
132C2×C4⋊Dic11—41no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—41no—
136C11×#95—22no—
137C11×#95—22no—
138C11×#95—22no—
139C11×#95—41no—
140C11×#95C2×C414yes—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95C2×C414yes—
152#14397—111nomaximal, Sylow
153C24×C11C2411yescharacteristic
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
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×D11C22×C412yes—
181C23×D11C22×C412yes—
182C23×D11C2×D412yes—
183C23×D11#4112yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
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×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11C22×C412yes—
226C22×C4×C11C2×D412yes—
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×D412yes—
230C22×C4×C11#4112yes—
231C22×C4×C11#4112yes—
232C22×C4×C11#4112yes—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
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×Dic11—21no—
272C22×Dic11C22×C412yes—
273C22×Dic11C22×C412yes—
274C22×Dic11C2×D412yes—
275C2×D44—28no—
276C2×D44—28no—
277C2×D44—44no—
278C2×D44—44no—
279C2×D44—44no—
280C2×D44—44no—
281C2×D44—44no—
282C2×C4×D11—28no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C11×C4⋊C4—44no—
290C42×C11—44no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—44no—
294(C2×D11)⋊C4—44no—
295(C2×D11)⋊C4—44no—
296(C2×D11)⋊C4—44no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302C4⋊Dic11—44no—
303C4⋊Dic11—44no—
304C4⋊Dic11—44no—
305C4×Dic11—44no—
306C2×#390—111no—
307C2×#388—111no—
308C2×#388—111no—
309C2×#386—111no—
310C2×#380—111no—
311#1444—111no—
312#1440—111no—
313#1440—111no—
314#1439—111no—
315#1439—111no—
316#1438—111no—
317#1436—111no—
318#1436D1111yescharacteristic, complemented
319#1434—111no—
320C22⋊#95—111no—
321C23×C11C23×C411yescharacteristic
322C23×C11C22×D411yescharacteristic
323C23×C11C22×D411yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11H(5,𝔽2)11yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C112−1+411yescharacteristic
335C23×C112−1+411yescharacteristic
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
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—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
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×D11C4×D414yes—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
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—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
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#11714yes—
454C2×C4×C11C4×D414yes—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
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—
497D44—416no—
498C4×D11—416no—
499C23×D4—111no—
500C24×C4—111no—
501C22×C4⋊C4—111no—
502C22×C4⋊C4—111no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4C2×D1111yescharacteristic
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—111no—
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C42—111no—
517C22×C42C2×D1111yescharacteristic
518#390—224no—
519#388—224no—
520#388—224no—
521#386—118no—
522#380—224no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95C2×D1111yescharacteristic
535C2×#95C2×D1111yescharacteristic
536C2×#95C2×D1111yescharacteristic
537C2×#95C2×D1111yescharacteristic
538C2×#95C2×D1111yescharacteristic
539C22×C11C2×#11711yescharacteristic
540C22×C11C2×C4×D411yescharacteristic
541C22×C11C2×C4×D411yescharacteristic
542C22×C11#51811yescharacteristic
543C22×C11#51811yescharacteristic
544C22×C11#52011yescharacteristic
545C22×C11#52011yescharacteristic
546C22×C11#53411yescharacteristic
547C22×C11#53411yescharacteristic
548C22×C11#53511yescharacteristic
549C22×C11#53711yescharacteristic
550C22×C11#53811yescharacteristic
551C22×C11#53811yescharacteristic
552C22×C11#53811yescharacteristic
553C22×C11#53911yescharacteristic
554C22×C11#54011yescharacteristic
555C22×C11#54011yescharacteristic
556C22×C11#54211yescharacteristic
557C22×C11#54211yescharacteristic
558C22×C11D4211yescharacteristic
559C22×C11#54611yescharacteristic
560C22×C11#54611yescharacteristic
561C22×C11#54711yescharacteristic
562C22×C11#54711yescharacteristic
563C22×C11#54811yescharacteristic
564C22×C11#55011yescharacteristic
565C22×C11#55111yescharacteristic
566C22×C11#55111yescharacteristic
567C22×C11#55311yescharacteristic
568C22×C11#55511yescharacteristic
569C22×C11#55611yescharacteristic
570C22×C11#56011yescharacteristic
571C22×C11#56211yescharacteristic
572C22×C11#56211yescharacteristic
573C22×C11#56311yescharacteristic
574C2×D11—24no—
575C2×D11—24no—
576C2×D11—24no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—42no—
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—81no—
597C2×D11—81no—
598C2×D11—81no—
599C2×D11—81no—
600C2×D11—81no—
601C2×D11—81no—
602C2×D11—81no—
603C2×D11—81no—
604C4×C11—24no—
605C4×C11—24no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—81no—
611Dic11—42no—
612Dic11—42no—
613Dic11—42no—
614Dic11—81no—
615Dic11—81no—
616Dic11—81no—
617C25—111no—
618C25—111no—
619C22×D4—114no—
620C22×D4—222no—
621C22×D4—222no—
622C22×D4—222no—
623C22×D4—222no—
624C22×D4—441no—
625C22×D4—441no—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—114no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—222no—
634C23×C4—222no—
635C23×C4—441no—
636C23×C4—441no—
637C23×C4—441no—
638C23×C4—441no—
639C23×C4C22×D1111yescharacteristic
640C23×C4C22×D1111yescharacteristic
641C23×C4C22×D1111yescharacteristic
642C23×C4C22×D1111yescharacteristic
643C23×C4C22×D1111yescharacteristic
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1111yescharacteristic
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—222no—
649C2×C4⋊C4—222no—
650C2×C4⋊C4—222no—
651C2×C4⋊C4—222no—
652C2×C4⋊C4—441no—
653C2×C4⋊C4—441no—
654C2×C4⋊C4—441no—
655C2×C4⋊C4—441no—
656C2×C4⋊C4—441no—
657C2×C4⋊C4D4414yescomplemented
658C2×C22⋊C4—114no—
659C2×C22⋊C4—114no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—222no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4—222no—
667C2×C22⋊C4—222no—
668C2×C22⋊C4—222no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—441no—
676C2×C22⋊C4—441no—
677C2×C22⋊C4—441no—
678C2×C22⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4—441no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4—441no—
688C2×C22⋊C4—441no—
689C2×C22⋊C4—441no—
690C2×C22⋊C4—441no—
691C2×C42—22no—
692C2×C42—22no—
693C2×C42—41no—
694C2×C42—222no—
695C2×C42—222no—
696C2×C42—441no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—41no—
701#95—114no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—222no—
708#95—441no—
709#95—441no—
710#95—441no—
711#95—441no—
712#95C4×D1114yes—
713C2×C11#231911yescharacteristic
714C2×C11#232111yescharacteristic
715C2×C11#232511yescharacteristic
716C2×C11#234211yescharacteristic
717C2×C11#235411yescharacteristic
718C2×C11#236111yescharacteristic
719C2×C11#237611yescharacteristic
720C2×C11#267111yescharacteristic
721C2×C11#267311yescharacteristic
722C2×C11#268611yescharacteristic
723C2×C11#271511yescharacteristic
724C2×C11#272311yescharacteristic
725C2×C11#273011yescharacteristic
726C2×C11#275611yescharacteristic
727C2×C11#278611yescharacteristic
728D11—44no—
729D11—82no—
730C24—112no—
731C24—112no—
732C24—112no—
733C24—112no—
734C24—221no—
735C24—221no—
736C24—221no—
737C24—221no—
738C24—221no—
739C24—221no—
740C24—221no—
741C24—221no—
742C24—221no—
743C24—221no—
744C24—221no—
745C24—221no—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24C23×D1111yescharacteristic
761C2×D4—228no—
762C2×D4—228no—
763C2×D4—444no—
764C2×D4—444no—
765C2×D4—444no—
766C2×D4—444no—
767C2×D4—444no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
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—112no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—228no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
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—444no—
851C22×C4—444no—
852C22×C4—444no—
853C22×C4—444no—
854C22×C4—444no—
855C22×C4—444no—
856C22×C4C2×C4×D1112yes—
857C22×C4C2×C4×D1112yes—
858C22×C4C2×C4×D1112yes—
859C22×C4C2×D4412yes—
860C22×C4C2×D4412yes—
861C22×C4C2×D4412yes—
862C22×C4#433912yes—
863C22×C4D4×D1112yes—
864C22×C4#434112yes—
865C22×C4#434312yes—
866C4⋊C4—44no—
867C4⋊C4—444no—
868C4⋊C4—444no—
869C4⋊C4—444no—
870C22⋊C4—228no—
871C22⋊C4—228no—
872C22⋊C4—444no—
873C22⋊C4—444no—
874C22⋊C4—444no—
875C22⋊C4—444no—
876C22⋊C4—444no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C22⋊C4—444no—
880C22⋊C4—444no—
881C42—44no—
882C42—444no—
883C11#1439711yescharacteristic, complemented, Sylow
884C23—114no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23—222no—
893C23—222no—
894C23—222no—
895C23—222no—
896C23—222no—
897C23—222no—
898C23—222no—
899C23—222no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23—222no—
908C23—222no—
909C23—222no—
910C23—441no—
911C23—441no—
912C23—441no—
913C23—441no—
914C23—441no—
915C23—441no—
916C23—441no—
917C23—441no—
918C23—441no—
919C23—441no—
920C23—441no—
921C23—441no—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
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—
954C23C22×C4×D1111yescharacteristic
955C23C22×D4411yescharacteristic
956C23C2×#433911yescharacteristic
957C23C2×D4×D1111yescharacteristic
958C23C2×#434111yescharacteristic
959C23#6703711yescharacteristic
960C23#6703711yescharacteristic
961C23C2×#434311yescharacteristic
962C23#6704011yescharacteristic
963C23#41×D1111yescharacteristic
964C23#6704211yescharacteristic
965C23#6704211yescharacteristic
966C23#6704211yescharacteristic
967C23#6704211yescharacteristic
968C23#6704311yescharacteristic
969D4—4416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
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—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
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—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—4416no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4C4×D4414yes—
1061C2×C4#6694514yes—
1062C22—224no—
1063C22—224no—
1064C22—224no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22—442no—
1074C22—442no—
1075C22—442no—
1076C22—442no—
1077C22—442no—
1078C22—442no—
1079C22—442no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—881no—
1085C22—881no—
1086C22—881no—
1087C22—881no—
1088C22—881no—
1089C22—881no—
1090C22—881no—
1091C22—881no—
1092C22C2×C4×D4411yescharacteristic
1093C22#1062302411yescharacteristic
1094C22C2×#6694511yescharacteristic
1095C22#1062303811yescharacteristic
1096C22#1062305411yescharacteristic
1097C22#1062305611yescharacteristic
1098C22#1062306111yescharacteristic
1099C22C4×D4×D1111yescharacteristic
1100C22#1062307611yescharacteristic
1101C22#1062307611yescharacteristic
1102C22D4×D4411yescharacteristic
1103C22#1062308611yescharacteristic
1104C22#1062309111yescharacteristic
1105C22#1062309111yescharacteristic
1106C22#1062309411yescharacteristic
1107C22#1062310511yescharacteristic
1108C22#1062310711yescharacteristic
1109C22#1062310811yescharacteristic
1110C22#1062311511yescharacteristic
1111C22#1062312211yescharacteristic
1112C22#1062313911yescharacteristic
1113C22#1062315011yescharacteristic
1114C22#1062316111yescharacteristic
1115C22#1062316811yescharacteristic
1116C22#1062317411yescharacteristic
1117C22#1062317811yescharacteristic
1118C22#1062318411yescharacteristic
1119C22#1062318911yescharacteristic
1120C22#1062319811yescharacteristic
1121C22#1062320911yescharacteristic
1122C22#1062322911yescharacteristic
1123C22#1062323011yescharacteristic
1124C22#1062323811yescharacteristic
1125C22#1062324211yescharacteristic
1126C22#1062326411yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—442no—
1135C4—442no—
1136C4—442no—
1137C4—881no—
1138C4—881no—
1139C4—881no—
1140C2—444no—
1141C2—882no—
1142C2#1307125511yescharacteristic
1143C2#1307127611yescharacteristic
1144C2#1307132011yescharacteristic
1145C2#1307146311yescharacteristic
1146C2#1307156311yescharacteristic
1147C2#1307163411yescharacteristic
1148C2#1307176311yescharacteristic
1149C2#1307485011yescharacteristic
1150C2#1307488511yescharacteristic
1151C2#1307502611yescharacteristic
1152C2#1307542811yescharacteristic
1153C2#1307553311yescharacteristic
1154C2#1307561111yescharacteristic
1155C2#1307594211yescharacteristic
1156C2#1307633011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14397
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622283C2semidirect
3. C2×#10622603C2semidirect
5. C2×#10622600C2semidirect
6. #13066881C2semidirect
7. #13066864C2semidirect
8. #13066864C2semidirect
9. #13066862C2semidirect
10. #13066862C2semidirect
12. #13066850C2semidirect
13. #13066843C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1436C2semidirect
55. #10622278C4semidirect
87. C2×C11×C4⋊C4D4semidirect
318. #1436D11semidirect
657. C2×C4⋊C4D44semidirect
883. C11#14397semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222832
C2×#106226032
C2×#106222782
C2×#106226002
#130668812
#130668642
#130668622
#130668562
#130668502
#130668432
(C2×D11)⋊#952
C11×#14362
#1439711