Finite Group Databasebeta

← #14769062

Subgroups — #14769062

Order 2816.

1582 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2C2×#10622451C211yesmaximal, characteristic, complemented
3C2×#10622319C211yesmaximal, characteristic, complemented
4C2×#10622340C211yesmaximal, characteristic, complemented
5C2×#10622339C211yesmaximal, characteristic, complemented
6#13069411C211yesmaximal, characteristic, complemented
7#13068910C211yesmaximal, characteristic, complemented
8#13068910C211yesmaximal, characteristic, complemented
9#13068910C211yesmaximal, characteristic, complemented
10#13068905C211yesmaximal, characteristic, complemented
11#13068597C211yesmaximal, characteristic, complemented
12#13068527C211yesmaximal, characteristic, complemented
13#13068525C211yesmaximal, characteristic, complemented
14#13068385C211yesmaximal, characteristic, complemented
15C11×#1955C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66992C411yescharacteristic
20C2×#66990C411yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C22×#4313C2211yescharacteristic
25C22×#4313C2211yescharacteristic, complemented
26C22×C8×D11C2211yescharacteristic, complemented
27#10623078—24no—
28#10623078—24no—
29C2×#66949C411yescharacteristic
30C2×#66947C411yescharacteristic
31C2×#66937C411yescharacteristic
32C2×#66936C411yescharacteristic
33C2×#66935C411yescharacteristic
34C2×#66931C411yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×#66925C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic, complemented
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic, complemented
41C2×C11×C22⋊C8C2211yescharacteristic, complemented
42C2×C11×#97C2211yescharacteristic, complemented
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
46C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×(C2×D11)⋊C8C2211yescharacteristic
51C2×(C2×D11)⋊C8C2211yescharacteristic
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622451—24no—
58#10622340—24no—
59#10622339—24no—
60#10622319—24no—
61#10622188C2211yescharacteristic, complemented
62#10622188C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, complemented
64#10622188C2211yescharacteristic, complemented
65C24×D11C2×C411yescharacteristic
66C22×D4×C11C2×C411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11C2×C411yescharacteristic
70C22×C22⋊D11C2×C411yescharacteristic
71C22×C22⋊D11C2×C411yescharacteristic
72C22×C22⋊D11C2×C411yescharacteristic
73C23×Dic11C2×C411yescharacteristic
74C2×#4339—22no—
75C2×#4339—22no—
76C2×#4339—22no—
77C2×#4339—22no—
78C2×#4339—41no—
79C2×#4339—41no—
80C22×D44C2×C411yescharacteristic
81C22×D44C2×C411yescharacteristic
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—41no—
87C22×C4×D11—41no—
88C22×C4×D11C2×C411yescharacteristic
89C22×C4×D11C2×C411yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C22×C4×D11C2311yescharacteristic
93C22×Dic22C2×C411yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C2×C11×C4⋊C4C2×C411yescharacteristic
101C2×C11×C22⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C22⋊Dic11C2×C411yescharacteristic
105C2×C22⋊Dic11C2×C411yescharacteristic
106#66992—24no—
107#66990—24no—
108C4×C22⋊D11—22no—
109C4×C22⋊D11—22no—
110C4×C22⋊D11—22no—
111C4×C22⋊D11—22no—
112C2×(C2×D11)⋊C4C2×C411yescharacteristic
113C2×(C2×D11)⋊C4C2×C411yescharacteristic
114C2×(C2×D11)⋊C4C2×C411yescharacteristic
115C2×(C2×D11)⋊C4C2×C411yescharacteristic
116C2×(C2×D11)⋊C4C2×C411yescharacteristic
117C2×(C2×D11)⋊C4C2×C411yescharacteristic
118C2×C4⋊Dic11C2×C411yescharacteristic
119C2×Dic11⋊C4C2×C411yescharacteristic
120C2×Dic11⋊C4C2×C411yescharacteristic
121C2×Dic11⋊C4C2×C411yescharacteristic
122C2×Dic11⋊C4C2×C411yescharacteristic
123C2×C4×Dic11C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C2×#4313—22no—
129C2×#4313—22no—
130C2×#4313—22no—
131C2×#4313—22no—
132C2×#4313—22no—
133C2×#4313—22no—
134C2×#4313—41no—
135C2×#4313—41no—
136C2×#4313—41no—
137C2×C8×D11—22no—
138C2×C8×D11—22no—
139C2×C8×D11—41no—
140#66949—24no—
141#66947—24no—
142#66937—24no—
143#66936—24no—
144#66935—24no—
145#66931—24no—
146C4×D44D414yes—
147C4×D44D414yes—
148#66925—22no—
149#66925—22no—
150C11×C4⋊C8—22no—
151C11×C22⋊C8—22no—
152C11×C22⋊C8—22no—
153C11×C22⋊C8—41no—
154C11×C22⋊C8—41no—
155C11×#97—22no—
156C22⋊(C11⋊C8)—22no—
157C22⋊(C11⋊C8)—22no—
158C22⋊(C11⋊C8)—41no—
159C22⋊(C11⋊C8)—41no—
160(C2×D11)⋊C8—22no—
161(C2×D11)⋊C8—22no—
162(C2×D11)⋊C8—22no—
163(C2×D11)⋊C8—22no—
164(C2×D11)⋊C8—22no—
165(C2×D11)⋊C8—22no—
166(C2×D11)⋊C8—22no—
167(C2×D11)⋊C8D414yescomplemented
168C4⋊(C11⋊C8)—22no—
169C4×C11⋊C8—22no—
170#22400—111nomaximal, Sylow
171C24×C11C22×C411yescharacteristic
172C24×C11C22×C411yescharacteristic
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—41no—
177C23×D11—41no—
178C23×D11—41no—
179C23×D11—41no—
180C23×D11C22×C411yescharacteristic
181C23×D11C22×C411yescharacteristic
182C23×D11C22×C411yescharacteristic
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—41no—
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×C11C22×C411yescharacteristic
199C22×C4×C11C22×C411yescharacteristic
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—22no—
204C2×C22⋊D11—22no—
205C2×C22⋊D11—22no—
206C2×C22⋊D11—22no—
207C2×C22⋊D11—22no—
208C2×C22⋊D11—22no—
209C2×C22⋊D11—22no—
210C2×C22⋊D11—41no—
211C2×C22⋊D11—41no—
212C2×C22⋊D11—41no—
213C2×C22⋊D11—41no—
214C2×C22⋊D11—41no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—41no—
218C22×Dic11C22×C411yescharacteristic
219C22×Dic11C22×C411yescharacteristic
220C22×Dic11C22×C411yescharacteristic
221C22×Dic11C22×C411yescharacteristic
222C22×Dic11C22×C411yescharacteristic
223#4339—44no—
224#4339—44no—
225#4339—44no—
226#4339—44no—
227C2×D44—22no—
228C2×D44—22no—
229C2×D44—41no—
230C2×D44—41no—
231C2×D44—41no—
232C2×D44C22⋊C414yes—
233C2×C4×D11—22no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11—21no—
240C2×C4×D11—21no—
241C2×C4×D11—21no—
242C2×C4×D11—21no—
243C2×C4×D11—21no—
244C2×C4×D11—21no—
245C2×C4×D11—21no—
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—41no—
250C2×C4×D11—41no—
251C2×C4×D11—44no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11C2×D412yes—
256C2×C4×D11C2×D412yes—
257C2×C4×D11C2×D412yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2×D412yes—
260C2×C4×D11#4112yes—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—41no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11C2×D412yes—
276C11×C4⋊C4—22no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—22no—
279C42×C11C2×D412yes—
280C42×C11C2×D412yes—
281C22⋊Dic11—22no—
282C22⋊Dic11—22no—
283(C2×D11)⋊C4—22no—
284(C2×D11)⋊C4—22no—
285(C2×D11)⋊C4—22no—
286(C2×D11)⋊C4—22no—
287(C2×D11)⋊C4C22⋊C414yes—
288(C2×D11)⋊C4C22⋊C414yes—
289C4⋊Dic11C22⋊C414yes—
290Dic11⋊C4—22no—
291Dic11⋊C4—22no—
292Dic11⋊C4—22no—
293Dic11⋊C4—22no—
294C4×Dic11—21no—
295C4×Dic11—21no—
296C2×C11⋊C8—21no—
297C2×C11⋊C8—21no—
298C2×C11⋊C8—21no—
299C2×C11⋊C8—21no—
300C2×C11⋊C8—21no—
301C2×C11⋊C8—21no—
302C2×C11⋊C8—21no—
303C2×C11⋊C8—21no—
304C2×C11⋊C8—21no—
305C2×C11⋊C8—21no—
306C2×C11⋊C8—21no—
307C2×C11⋊C8C2×D412yes—
308#4313—44no—
309#4313—44no—
310#4313—44no—
311C8×D11—44no—
312C2×#525—111no—
313C2×#436—111no—
314C2×#435—111no—
315C2×#408—111no—
316C2×#407—111no—
317#1955D1111yescharacteristic, complemented
318#1954—111no—
319#1870—111no—
320#1870—111no—
321#1870—111no—
322#1869—111no—
323#1798—111no—
324#1780—111no—
325#1779—111no—
326#1750—111no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—21no—
336C23×C11—21no—
337C23×C11—21no—
338C23×C11—21no—
339C23×C11—21no—
340C23×C11#13112yes—
341C23×C11C23×C411yescharacteristic
342C22×D11—21no—
343C22×D11—21no—
344C22×D11—21no—
345C22×D11—21no—
346C22×D11—21no—
347C22×D11—21no—
348C22×D11—21no—
349C22×D11—21no—
350C22×D11—21no—
351C22×D11—21no—
352C22×D11—21no—
353C22×D11—21no—
354C22×D11—21no—
355C22×D11—21no—
356C22×D11—21no—
357C22×D11—21no—
358C22×D11—21no—
359C22×D11—21no—
360C22×D11—44no—
361C22×D11—44no—
362C22×D11—44no—
363C22×D11—44no—
364C22×D11—44no—
365C22×D11—44no—
366C22×D11—44no—
367C22×D11C2×C22⋊C412yes—
368C22×D11C2×C22⋊C412yes—
369C22×D11C4×D412yes—
370D4×C11—44no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11C2×C22⋊C412yes—
390C2×C4×C11C2×C22⋊C412yes—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C2×#4111yescharacteristic
395C2×C4×C11H(5,𝔽2)11yescharacteristic
396C2×C4×C11H(5,𝔽2)11yescharacteristic
397C22⋊D11—44no—
398C22⋊D11—44no—
399C22⋊D11—44no—
400C22⋊D11—44no—
401C2×Dic11—21no—
402C2×Dic11—21no—
403C2×Dic11—21no—
404C2×Dic11—21no—
405C2×Dic11—21no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—21no—
409C2×Dic11—21no—
410C2×Dic11—21no—
411C2×Dic11—21no—
412C2×Dic11—21no—
413C2×Dic11—44no—
414C2×Dic11C2×C22⋊C412yes—
415C2×Dic11C2×C22⋊C412yes—
416C2×Dic11C4×D412yes—
417D44—44no—
418D44—44no—
419C4×D11—22no—
420C4×D11—22no—
421C4×D11—22no—
422C4×D11—22no—
423C4×D11—22no—
424C4×D11—22no—
425C4×D11—22no—
426C4×D11—22no—
427C4×D11—22no—
428C4×D11—22no—
429C4×D11—22no—
430C4×D11—22no—
431C4×D11—44no—
432C4×D11—44no—
433Dic22—44no—
434C8×C11—22no—
435C8×C11—41no—
436C8×C11—41no—
437C8×C11—41no—
438C11⋊C8—22no—
439C11⋊C8—41no—
440C11⋊C8—41no—
441C11⋊C8—41no—
442C22×#41—111no—
443C24×C4—111no—
444C22×M16—111no—
445C22×M16—111no—
446C22×M16—111no—
447C23×C8—111no—
448#525—224no—
449#525—224no—
450C2×#123—111no—
451C2×#123—111no—
452C2×C22⋊Q8—111no—
453C2×C22⋊Q8—111no—
454C2×#121—111no—
455C2×#121—111no—
456C2×#120—111no—
457C2×#120—111no—
458C2×C4×D4—111no—
459C2×C4×D4—111no—
460C2×C4×D4—111no—
461C2×C4×D4C2×D1111yescharacteristic
462C2×#117—111no—
463#436—224no—
464#435—224no—
465C2×C4⋊C8—111no—
466C2×C4⋊C8C2×D1111yescharacteristic, complemented
467#408—224no—
468#407—224no—
469C2×C22⋊C8—111no—
470C2×C22⋊C8—111no—
471C2×C22⋊C8—111no—
472C2×C22⋊C8—111no—
473C2×C22⋊C8—111no—
474C2×C22⋊C8—111no—
475C2×C22⋊C8—111no—
476C2×C22⋊C8—111no—
477C2×C22⋊C8—111no—
478C2×C22⋊C8—111no—
479C2×C22⋊C8—111no—
480C2×C22⋊C8—111no—
481C2×C22⋊C8C2×D1111yescharacteristic
482C2×C22⋊C8C2×D1111yescharacteristic
483C2×C22⋊C8C2×D1111yescharacteristic, complemented
484C2×C22⋊C8C2×D1111yescharacteristic, complemented
485C2×#97C2×D1111yescharacteristic, complemented
486C2×C4×C8—111no—
487#336—111no—
488#336—111no—
489#336—111no—
490#336—111no—
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—41no—
499C22×C11—41no—
500C22×C11—41no—
501C22×C11—41no—
502C22×C11—41no—
503C22×C11—41no—
504C22×C11—41no—
505C22×C11C22×C22⋊C411yescharacteristic
506C22×C11C2×C4×D411yescharacteristic
507C22×C11#51811yescharacteristic
508C22×C11C2×#13111yescharacteristic
509C22×C11#56811yescharacteristic
510C22×C11#56811yescharacteristic
511C22×C11#56811yescharacteristic
512C2×D11—22no—
513C2×D11—22no—
514C2×D11—22no—
515C2×D11—22no—
516C2×D11—22no—
517C2×D11—22no—
518C2×D11—22no—
519C2×D11—22no—
520C2×D11—22no—
521C2×D11—416no—
522C2×D11—41no—
523C2×D11—41no—
524C2×D11—41no—
525C2×D11—41no—
526C2×D11—41no—
527C2×D11—41no—
528C2×D11—41no—
529C2×D11—41no—
530C2×D11—41no—
531C2×D11—41no—
532C2×D11—41no—
533C2×D11—41no—
534C4×C11—22no—
535C4×C11—22no—
536C4×C11—41no—
537C4×C11—41no—
538C4×C11D4211yescharacteristic
539C4×C11D4211yescharacteristic
540C4×C11#54611yescharacteristic
541C4×C11#54611yescharacteristic
542Dic11—22no—
543Dic11—22no—
544Dic11—22no—
545Dic11—41no—
546Dic11—41no—
547C25—111no—
548C2×#41—222no—
549C2×#41—222no—
550C2×#41—222no—
551C2×#41—222no—
552C2×#41—441no—
553C2×#41—441no—
554C22×Q8—111no—
555C22×D4—111no—
556C22×D4—111no—
557C22×D4—111no—
558C22×D4—111no—
559C22×D4—111no—
560C22×D4—111no—
561C22×D4C4×D1111yescharacteristic
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—222no—
569C23×C4—222no—
570C23×C4—222no—
571C23×C4—222no—
572C23×C4—441no—
573C23×C4—441no—
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1111yescharacteristic
576C2×M16—222no—
577C2×M16—222no—
578C2×M16—222no—
579C2×M16—222no—
580C2×M16—222no—
581C2×M16—222no—
582C2×M16—441no—
583C2×M16—441no—
584C2×M16—441no—
585C22×C8—111no—
586C22×C8—111no—
587C22×C8—111no—
588C22×C8—111no—
589C22×C8—222no—
590C22×C8—222no—
591C22×C8—441no—
592C22×C8C22×D1111yescharacteristic
593C22×C8C22×D1111yescharacteristic
594C22×C8C22×D1111yescharacteristic
595C22×C8C22×D1111yescharacteristic
596#123—224no—
597#123—224no—
598C22⋊Q8—224no—
599C22⋊Q8—224no—
600#121—224no—
601#121—224no—
602#120—224no—
603#120—224no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—114no—
607C4×D4—114no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4—222no—
611C4×D4—222no—
612#117—222no—
613#117—222no—
614C2×C4⋊C4—111no—
615C2×C4⋊C4—111no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4C4×D1111yescharacteristic
620C2×C22⋊C4—111no—
621C2×C22⋊C4—111no—
622C2×C22⋊C4—111no—
623C2×C22⋊C4—111no—
624C2×C22⋊C4—111no—
625C2×C22⋊C4—111no—
626C2×C22⋊C4—111no—
627C2×C22⋊C4—111no—
628C2×C22⋊C4C4×D1111yescharacteristic
629C2×C22⋊C4C4×D1111yescharacteristic
630C2×C42—111no—
631C2×C42C22×D1111yescharacteristic
632C4⋊C8—22no—
633C4⋊C8—222no—
634C22⋊C8—22no—
635C22⋊C8—22no—
636C22⋊C8—41no—
637C22⋊C8—41no—
638C22⋊C8—114no—
639C22⋊C8—222no—
640C22⋊C8—222no—
641C22⋊C8—222no—
642C22⋊C8—222no—
643C22⋊C8—222no—
644C22⋊C8—222no—
645C22⋊C8—222no—
646C22⋊C8—222no—
647C22⋊C8—222no—
648C22⋊C8—441no—
649C22⋊C8—441no—
650#97—22no—
651C4×C8—222no—
652C2×C11—42no—
653C2×C11—81no—
654C2×C11D4×C22⋊C411yescharacteristic
655C2×C11#287911yescharacteristic
656C2×C11#288011yescharacteristic
657C2×C11#293011yescharacteristic
658C2×C11#293311yescharacteristic
659C2×C11#297611yescharacteristic
660C2×C11#297811yescharacteristic
661D11—42no—
662D11—42no—
663D11—42no—
664C24—111no—
665C24—111no—
666C24—111no—
667C24—222no—
668C24—222no—
669C24—222no—
670C24—441no—
671C24—441no—
672C24—441no—
673C24—441no—
674C24C2×C4×D1111yescharacteristic
675C24C2×C4×D1111yescharacteristic
676#41—444no—
677#41—444no—
678#41—444no—
679#41—444no—
680C2×Q8—222no—
681C2×Q8—222no—
682C2×Q8—441no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—41no—
686C2×D4—114no—
687C2×D4—222no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4—222no—
692C2×D4—222no—
693C2×D4—222no—
694C2×D4—222no—
695C2×D4—222no—
696C2×D4—441no—
697C2×D4—441no—
698C2×D4—441no—
699C2×D4—441no—
700C2×D4—441no—
701C2×D4—441no—
702C2×D4—441no—
703C2×D4—441no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—111no—
717C22×C4—111no—
718C22×C4—111no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—111no—
726C22×C4—111no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—441no—
746C22×C4—441no—
747C22×C4—444no—
748C22×C4—444no—
749C22×C4—444no—
750C22×C4—444no—
751C22×C4—441no—
752C22×C4C2×C4×D1111yescharacteristic
753C22×C4C2×C4×D1111yescharacteristic
754C22×C4C2×C4×D1111yescharacteristic
755C22×C4C2×C4×D1111yescharacteristic
756C22×C4C23×D1111yescharacteristic
757M16—444no—
758M16—444no—
759M16—444no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—112no—
772C2×C8—221no—
773C2×C8—221no—
774C2×C8—221no—
775C2×C8—221no—
776C2×C8—221no—
777C2×C8—221no—
778C2×C8—221no—
779C2×C8—221no—
780C2×C8—221no—
781C2×C8—221no—
782C2×C8—221no—
783C2×C8—444no—
784C2×C8D4×D1112yes—
785C4⋊C4—22no—
786C4⋊C4—114no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C22⋊C4—22no—
792C22⋊C4—22no—
793C22⋊C4—114no—
794C22⋊C4—114no—
795C22⋊C4—222no—
796C22⋊C4—222no—
797C22⋊C4—222no—
798C22⋊C4—222no—
799C22⋊C4—222no—
800C22⋊C4—222no—
801C42—221no—
802C42—221no—
803C42D4×D1112yes—
804C42D4×D1112yes—
805C11#2240011yescharacteristic, complemented, Sylow
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—112no—
820C23—112no—
821C23—112no—
822C23—221no—
823C23—221no—
824C23—221no—
825C23—221no—
826C23—221no—
827C23—221no—
828C23—221no—
829C23—221no—
830C23—221no—
831C23—221no—
832C23—221no—
833C23—221no—
834C23—221no—
835C23—221no—
836C23—221no—
837C23—221no—
838C23—221no—
839C23—221no—
840C23—444no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23#6696012yes—
848C23C22×C4×D1111yescharacteristic
849Q8—444no—
850D4—44no—
851D4—444no—
852D4—444no—
853D4—444no—
854D4—444no—
855D4—444no—
856D4—444no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—112no—
876C2×C4—112no—
877C2×C4—112no—
878C2×C4—221no—
879C2×C4—221no—
880C2×C4—221no—
881C2×C4—221no—
882C2×C4—221no—
883C2×C4—221no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—221no—
897C2×C4—221no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—221no—
901C2×C4—221no—
902C2×C4—444no—
903C2×C4—444no—
904C2×C4—444no—
905C2×C4C22⋊C4×D1112yes—
906C2×C4C22⋊C4×D1112yes—
907C2×C4C2×D4×D1111yescharacteristic
908C2×C4C2×D4×D1111yescharacteristic
909C2×C4C2×D4×D1111yescharacteristic
910C2×C4#6703711yescharacteristic
911C2×C4#41×D1111yescharacteristic
912C2×C4#6704211yescharacteristic
913C8—22no—
914C8—41no—
915C8—41no—
916C8—41no—
917C8—222no—
918C8—441no—
919C8—441no—
920C8—441no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—222no—
936C22—222no—
937C22—222no—
938C22—222no—
939C22—222no—
940C22—222no—
941C22—222no—
942C22—222no—
943C22—222no—
944C22—4416no—
945C22—441no—
946C22—441no—
947C22—441no—
948C22—441no—
949C22—441no—
950C22—441no—
951C22—441no—
952C22—441no—
953C22—441no—
954C22—441no—
955C22—441no—
956C22—441no—
957C22C2×C22⋊C4×D1111yescharacteristic
958C22C4×D4×D1111yescharacteristic
959C22#1062307611yescharacteristic
960C22C2×#6696011yescharacteristic
961C22#1062327611yescharacteristic
962C22#1062328111yescharacteristic
963C22#1062328111yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—41no—
968C4—222no—
969C4—222no—
970C4—222no—
971C4—441no—
972C4—441no—
973C4#1062314011yescharacteristic
974C4#1062314311yescharacteristic
975C4#1062320711yescharacteristic
976C4#1062324811yescharacteristic
977C2—42no—
978C2—81no—
979C2—442no—
980C2—442no—
981C2—442no—
982C2#1307143711yescharacteristic
983C2#1307705811yescharacteristic
984C2#1307706611yescharacteristic
985C2#1307731411yescharacteristic
986C2#1307734211yescharacteristic
987C2#1307766511yescharacteristic
988C2#1307767511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1955C2
prime radicalC2×#10623078C2
cosocleC22×C4×C11C24
hypercenter#1955D11
hypocenterC11#22400
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#10622451C2semidirect
3. C2×#10622319C2semidirect
4. C2×#10622340C2semidirect
5. C2×#10622339C2semidirect
6. #13069411C2semidirect
7. #13068910C2semidirect
8. #13068910C2semidirect
9. #13068910C2semidirect
10. #13068905C2semidirect
11. #13068597C2semidirect
12. #13068527C2semidirect
13. #13068525C2semidirect
14. #13068385C2semidirect
15. C11×#1955C2semidirect
25. C22×#4313C22semidirect
26. C22×C8×D11C22semidirect
37. C2×C11×C4⋊C8C22semidirect
40. C2×C11×C22⋊C8C22semidirect
41. C2×C11×C22⋊C8C22semidirect
42. C2×C11×#97C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
46. C2×C22⋊(C11⋊C8)C22semidirect
53. C2×(C2×D11)⋊C8C22semidirect
54. C2×(C2×D11)⋊C8C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×C4×C11⋊C8C22semidirect
61. #10622188C22semidirect
62. #10622188C22semidirect
63. #10622188C22semidirect
64. #10622188C22semidirect
167. (C2×D11)⋊C8D4semidirect
317. #1955D11semidirect
466. C2×C4⋊C8C2×D11semidirect
483. C2×C22⋊C8C2×D11semidirect
484. C2×C22⋊C8C2×D11semidirect
485. C2×#97C2×D11semidirect
805. C11#22400semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C2×#106224512
C2×#106223192
C2×#106223402
C2×#106223392
#130694112
#130689102
#130689052
#130685972
#130685272
#130685252
#130683852
C11×#19552
#2240011