Finite Group Databasebeta

← #14677011

Subgroups — #14677011

Order 2816.

1946 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×#10622282C211yesmaximal, characteristic, complemented
3C2×#10622278C211yesmaximal, characteristic
4C2×#10622277C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6#13066872C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066856C211yesmaximal, characteristic
10#13066854C211yesmaximal, characteristic, complemented
11#13066854C211yesmaximal, characteristic, complemented
12#13066854C211yesmaximal, characteristic, complemented
13#13066850C211yesmaximal, characteristic, complemented
14#13066849C211yesmaximal, characteristic, complemented
15C4×C11×#95C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
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#10622552—24no—
52C4×(C2×D11)⋊C4—24no—
53#10622282—24no—
54#10622278C418yescomplemented
55#10622277—24no—
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—22no—
81C22×C4×D11—22no—
82C22×C4×D11—41no—
83C22×C4×D11—41no—
84C22×C4×D11C2×C414yes—
85C2×C42×C11—22no—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C42×C11—22no—
90C2×C42×C11—41no—
91C2×C42×C11—41no—
92C2×C42×C11—41no—
93C2×C42×C11—41no—
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—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)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4C2×C414yes—
124C2×(C2×D11)⋊C4C2×C414yes—
125C2×(C2×D11)⋊C4C2×C414yes—
126C2×(C2×D11)⋊C4D414yes—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—41no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—41no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—41no—
136C11×#95—22no—
137C11×#95—22no—
138C11×#95C2×C414yes—
139C11×#95D414yescomplemented
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95C2×C414yes—
152#14007—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×C11C22×C412yes—
221C22×C4×C11C22×C412yes—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×D412yes—
225C22×C4×C11C2×D412yes—
226C22×C4×C11C2×D412yes—
227C22×C4×C11#4112yes—
228C22×C4×C11#4112yes—
229C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
272C22×Dic11C22×C412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11#4112yes—
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—28no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C42×C11—44no—
290C42×C11—44no—
291C42×C11—44no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
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—
302(C2×D11)⋊C4—44no—
303C4⋊Dic11—44no—
304Dic11⋊C4—44no—
305C4×Dic11—44no—
306C2×#390—111no—
307C2×#388—111no—
308C2×#386—111no—
309C2×#381—111no—
310C2×C4×C22⋊C4—111no—
311#1442—111no—
312#1440—111no—
313#1439—111no—
314#1438—111no—
315#1437—111no—
316#1437—111no—
317#1437—111no—
318#1436—111no—
319#1436—111no—
320C4×#95D1111yescharacteristic, complemented
321C23×C11C23×C411yescharacteristic
322C23×C11C22×D411yescharacteristic
323C23×C11C22×D411yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
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—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
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#11714yes—
453C2×C4×C11C4×D414yes—
454C2×C4×C11#12314yes—
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—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
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×C22⋊C4—111no—
504C22×C22⋊C4—111no—
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×C42—111no—
515C22×C42C2×D1111yescharacteristic
516C22×C42C2×D1111yescharacteristic
517C22×C42C2×D1111yescharacteristic
518#390—224no—
519#388—224no—
520#386—118no—
521#381—224no—
522C4×C22⋊C4—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×#95—111no—
535C2×#95C2×D1111yescharacteristic
536C2×#95C2×D1111yescharacteristic
537C2×#95C2×D1111yescharacteristic
538C2×#95C2×D1111yescharacteristic
539C22×C11C2×#11711yescharacteristic
540C22×C11C2×C4×D411yescharacteristic
541C22×C11C2×C4×D411yescharacteristic
542C22×C11C4×#4111yescharacteristic
543C22×C11C4×#4111yescharacteristic
544C22×C11#51811yescharacteristic
545C22×C11#51811yescharacteristic
546C22×C11C2×#12311yescharacteristic
547C22×C11#52511yescharacteristic
548C22×C11#52911yescharacteristic
549C22×C11#52911yescharacteristic
550C22×C11#52911yescharacteristic
551C22×C11#52911yescharacteristic
552C22×C11#53211yescharacteristic
553C22×C11#53211yescharacteristic
554C22×C11#53811yescharacteristic
555C22×C11#53811yescharacteristic
556C22×C11#54011yescharacteristic
557C22×C11#54011yescharacteristic
558C22×C11D4211yescharacteristic
559C22×C11#54611yescharacteristic
560C22×C11#54611yescharacteristic
561C22×C11#54611yescharacteristic
562C22×C11#54611yescharacteristic
563C22×C11#54611yescharacteristic
564C22×C11#55011yescharacteristic
565C22×C11#55111yescharacteristic
566C22×C11#55111yescharacteristic
567C22×C11#55111yescharacteristic
568C22×C11#55311yescharacteristic
569C22×C11#55311yescharacteristic
570C22×C11#55311yescharacteristic
571C22×C11#55511yescharacteristic
572C22×C11#55911yescharacteristic
573C22×C11#55911yescharacteristic
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—24no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—42no—
611Dic11—42no—
612Dic11—42no—
613Dic11—42no—
614Dic11—42no—
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—111no—
630C23×C4—114no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—222no—
634C23×C4—222no—
635C23×C4—222no—
636C23×C4—222no—
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—222no—
647C2×C4⋊C4—222no—
648C2×C4⋊C4—222no—
649C2×C4⋊C4—222no—
650C2×C4⋊C4—441no—
651C2×C4⋊C4—441no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—222no—
658C2×C22⋊C4—222no—
659C2×C22⋊C4—222no—
660C2×C22⋊C4—222no—
661C2×C22⋊C4—222no—
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×C42—22no—
686C2×C42—22no—
687C2×C42—22no—
688C2×C42—22no—
689C2×C42—22no—
690C2×C42—41no—
691C2×C42—41no—
692C2×C42—41no—
693C2×C42—41no—
694C2×C42—222no—
695C2×C42—222no—
696C2×C42—441no—
697#95—22no—
698#95—22no—
699#95—114no—
700#95—222no—
701#95—222no—
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#95C4×D1114yes—
712#95D4414yescomplemented
713C2×C11#229311yescharacteristic
714C2×C11C4×#12311yescharacteristic
715C2×C11#233311yescharacteristic
716C2×C11#234211yescharacteristic
717C2×C11#235711yescharacteristic
718C2×C11#235811yescharacteristic
719C2×C11#236311yescharacteristic
720C2×C11#244411yescharacteristic
721C2×C11#244511yescharacteristic
722C2×C11#245911yescharacteristic
723C2×C11#246411yescharacteristic
724C2×C11#251611yescharacteristic
725C2×C11#252611yescharacteristic
726C2×C11#255411yescharacteristic
727C2×C11#255711yescharacteristic
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—112no—
805C22×C4—112no—
806C22×C4—112no—
807C22×C4—112no—
808C22×C4—228no—
809C22×C4—221no—
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—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—228no—
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—444no—
849C22×C4—444no—
850C22×C4—444no—
851C22×C4—444no—
852C22×C4—444no—
853C22×C4C2×C4×D1112yes—
854C22×C4C2×C4×D1112yes—
855C22×C4C2×C4×D1112yes—
856C22×C4C2×D4412yes—
857C22×C4C2×D4412yes—
858C22×C4C2×D4412yes—
859C22×C4#433912yes—
860C22×C4#433912yes—
861C22×C4#433912yes—
862C22×C4#433912yes—
863C22×C4#433912yes—
864C22×C4D4×D1112yes—
865C22×C4#434312yes—
866C4⋊C4—444no—
867C4⋊C4—444no—
868C22⋊C4—228no—
869C22⋊C4—228no—
870C22⋊C4—228no—
871C22⋊C4—444no—
872C22⋊C4—444no—
873C22⋊C4—444no—
874C22⋊C4—444no—
875C22⋊C4—444no—
876C22⋊C4—444no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C42—44no—
880C42—44no—
881C42—44no—
882C42—444no—
883C11#1400711yescharacteristic, 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×#433911yescharacteristic
958C23C2×#433911yescharacteristic
959C23C2×#433911yescharacteristic
960C23C2×#433911yescharacteristic
961C23C2×D4×D1111yescharacteristic
962C23#6703711yescharacteristic
963C23#6703711yescharacteristic
964C23C2×#434311yescharacteristic
965C23#41×D1111yescharacteristic
966C23#41×D1111yescharacteristic
967C23#6704211yescharacteristic
968C23#6704211yescharacteristic
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—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
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—222no—
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—222no—
1027C2×C4—222no—
1028C2×C4—4416no—
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#6692514yes—
1060C2×C4C4×D4414yes—
1061C2×C4#6694714yes—
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×#6692511yescharacteristic
1093C22C2×C4×D4411yescharacteristic
1094C22C4×#433911yescharacteristic
1095C22#1062300811yescharacteristic
1096C22#1062300811yescharacteristic
1097C22#1062301011yescharacteristic
1098C22#1062301011yescharacteristic
1099C22#1062302111yescharacteristic
1100C22#1062302111yescharacteristic
1101C22#1062302511yescharacteristic
1102C22C2×#6694711yescharacteristic
1103C22#1062304511yescharacteristic
1104C22#1062304511yescharacteristic
1105C22#1062305811yescharacteristic
1106C22#1062305811yescharacteristic
1107C22#1062305911yescharacteristic
1108C22#1062306111yescharacteristic
1109C22#1062306311yescharacteristic
1110C22#1062306611yescharacteristic
1111C22C4×D4×D1111yescharacteristic
1112C22#1062307611yescharacteristic
1113C22#1062307611yescharacteristic
1114C22#1062307811yescharacteristic
1115C22D4×D4411yescharacteristic
1116C22#1062308111yescharacteristic
1117C22#1062308511yescharacteristic
1118C22#1062308511yescharacteristic
1119C22#1062308711yescharacteristic
1120C22#1062309011yescharacteristic
1121C22#1062309111yescharacteristic
1122C22#1062309311yescharacteristic
1123C22C4×#434311yescharacteristic
1124C22#1062310811yescharacteristic
1125C22#1062311111yescharacteristic
1126C22#1062311611yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—442no—
1135C4—442no—
1136C4—442no—
1137C4—442no—
1138C4—881no—
1139C4—881no—
1140C2—444no—
1141C2—882no—
1142C2#1307108011yescharacteristic
1143C2C4×#6694711yescharacteristic
1144C2#1307137611yescharacteristic
1145C2#1307145911yescharacteristic
1146C2#1307158511yescharacteristic
1147C2#1307159811yescharacteristic
1148C2#1307165611yescharacteristic
1149C2#1307236611yescharacteristic
1150C2#1307238111yescharacteristic
1151C2#1307255311yescharacteristic
1152C2#1307262211yescharacteristic
1153C2#1307324411yescharacteristic
1154C2#1307338211yescharacteristic
1155C2#1307367011yescharacteristic
1156C2#1307370911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4×#95D11
hypocenterC11#14007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622282C2semidirect
4. C2×#10622277C2semidirect
5. C2×C4×(C2×D11)⋊C4C2semidirect
6. #13066872C2semidirect
7. #13066864C2semidirect
8. #13066860C2semidirect
10. #13066854C2semidirect
11. #13066854C2semidirect
12. #13066854C2semidirect
13. #13066850C2semidirect
14. #13066849C2semidirect
15. C4×C11×#95C2semidirect
54. #10622278C4semidirect
139. C11×#95D4semidirect
320. C4×#95D11semidirect
712. #95D44semidirect
883. C11#14007semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222822
C2×#106222782
C2×#106222772
C2×C4×(C2×D11)⋊C42
#130668722
#130668642
#130668602
#130668562
#130668542
#130668502
#130668492
C4×C11×#952
#1400711