Finite Group Databasebeta

← #14726771

Subgroups — #14726771

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C212yesmaximal, complemented
2#13072933C211yesmaximal, characteristic
3#13067658C214yesmaximal, complemented
4#13067641C214yesmaximal, complemented
5#13067188C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic
7C11×#3501C211yesmaximal, characteristic
8C11×#554—24no—
9C11×#554—22no—
10D4×Q8×C11—22no—
11C11×#544C2212yes—
12C11×#543—21no—
13C11×#543C2212yes—
14C11×#533—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C11×C22⋊Q8C2212yes—
17C11×#518—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×#66899—22no—
21#10622833—21no—
22#10622825—21no—
23#10622825C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2212yes—
25#10622657—24no—
26#10622657C2218yes—
27#10622599C2212yes—
28C2×#66871—22no—
29#10622562C2212yes—
30#10622559—21no—
31#10622541—21no—
32#10622176C2218yes—
33#10622166C2212yes—
34#10622163C2212yes—
35C22×Q8×C11—21no—
36C22×Q8×C11D412yes—
37C22×D4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—24no—
44C11×#125—22no—
45C11×#125—24no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8D414yes—
57C11×C22⋊Q8C2314yes—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—24no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C11×#117—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4C2311yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2312yes—
82C2×Dic11⋊C4—22no—
83C22×C11⋊C8—22no—
84#66899—28no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95C2312yes—
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)C2314yes—
90#66871—28no—
91#18205—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C24×C11C2×D411yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—44no—
98C2×Q8×C11—82no—
99C2×Q8×C11C2×D414yes—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11Q1614yes—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—42no—
121C22×Dic11—82no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4C2×D414yes—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—22no—
138C42×C11—24no—
139C42×C11—21no—
140C42×C11—21no—
141C22⋊Dic11—42no—
142C22⋊Dic11—82no—
143C4⋊Dic11—24no—
144C4⋊Dic11—42no—
145C4⋊Dic11—41no—
146C4⋊Dic11—41no—
147Dic11⋊C4—82no—
148C2×C11⋊C8—24no—
149C2×C11⋊C8—44no—
150#3501D1111yescharacteristic
151C2×#484—112no—
152#2487—111no—
153#1617—114no—
154#1614—114no—
155#1520—112no—
156#1459—111no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11#12012yes—
164C23×C11C2×Q1612yes—
165C23×C11C2×Q1612yes—
166C23×C11#13712yes—
167C23×C11C22×D411yescharacteristic
168Q8×C11—44no—
169Q8×C11—44no—
170Q8×C11—82no—
171Q8×C11—82no—
172D4×C11—28no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—21no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—21no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—81no—
187C2×C4×C11—82no—
188C2×C4×C11—82no—
189C2×C4×C11—82no—
190C2×C4×C11—82no—
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11C2×Q1612yes—
194C2×C4×C11C22×D412yes—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—84no—
202C11⋊C8—44no—
203#554—24no—
204#554—22no—
205D4×Q8—22no—
206#544C2×D1112yes—
207#543—21no—
208#543C2×D1112yes—
209#533—21no—
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8C2×D1112yes—
212#518—21no—
213C2×C4×D4C2×D1111yescharacteristic
214C22×C4⋊C4—111no—
215#484—118no—
216#484—224no—
217C2×#107—222no—
218C2×#103—222no—
219C2×C22⋊C8—112no—
220#400—112no—
221#399—112no—
222#389—221no—
223#386—221no—
224#385—221no—
225#380—111no—
226#380—221no—
227#328—118no—
228#324—112no—
229#323—112no—
230C22×C11—21no—
231C22×C11—22no—
232C22×C11—21no—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—81no—
241C22×C11#45114yes—
242C22×C11C2×#12011yescharacteristic
243C22×C11C22×Q1611yescharacteristic
244C22×C11C2×#13711yescharacteristic
245C4×C11—22no—
246C4×C11—21no—
247C4×C11—22no—
248C4×C11—41no—
249C4×C11—44no—
250C4×C11—41no—
251C4×C11—44no—
252C4×C11#45812yes—
253Dic11—82no—
254Dic11—82no—
255C22×Q8—21no—
256C22×Q8C22⋊D1112yes—
257C22×D4C22⋊D1111yescharacteristic
258C23×C4—221no—
259C23×C4C22⋊D1111yescharacteristic
260C23×C4C22×D1111yescharacteristic
261C22×C8—222no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—24no—
265#125—22no—
266#125—24no—
267C22⋊Q8—22no—
268C22⋊Q8—22no—
269C22⋊Q8—24no—
270C22⋊Q8—24no—
271C22⋊Q8—24no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C22⋊Q8—22no—
275C22⋊Q8—22no—
276C22⋊Q8—24no—
277C22⋊Q8C22⋊D1114yes—
278C22⋊Q8C22×D1114yes—
279C4×Q8—22no—
280C4×Q8—22no—
281C4×D4—24no—
282C4×D4—24no—
283C4×D4—22no—
284C4×D4—22no—
285#117—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4C22⋊D1112yes—
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—222no—
301C2×C22⋊C4C22⋊D1111yescharacteristic
302C2×C22⋊C4C22×D1111yescharacteristic
303C2×C42C22⋊D1111yescharacteristic
304#107—228no—
305#103—228no—
306C22⋊C8—114no—
307C22⋊C8—222no—
308#95—112no—
309#95—222no—
310#95—222no—
311C2×C11—21no—
312C2×C11—21no—
313C2×C11—24no—
314C2×C11—42no—
315C2×C11C2×#45111yescharacteristic
316C2×C11#302111yescharacteristic
317C2×C11C2×#45811yescharacteristic
318C24C2×C22⋊D1111yescharacteristic
319C24C2×C22⋊D1111yescharacteristic
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—44no—
324C2×Q8—82no—
325C2×Q8C2×C22⋊D1114yes—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4#432614yes—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—442no—
340C22×C4—882no—
341C22×C4C2×C22⋊D1111yescharacteristic
342C22×C4C2×C22⋊D1111yescharacteristic
343C22×C4C2×C22⋊D1112yes—
344C22×C4C2×C22⋊D1111yescharacteristic
345C22×C4C2×C22⋊D1111yescharacteristic
346C22×C4C2×C22⋊D1112yes—
347C22×C4C23×D1111yescharacteristic
348C2×C8—224no—
349C2×C8—444no—
350C4⋊C4—22no—
351C4⋊C4—24no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—24no—
355C4⋊C4—22no—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—224no—
361C4⋊C4—442no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—882no—
365C4⋊C4C2×C22⋊D1114yes—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—22no—
369C22⋊C4—24no—
370C22⋊C4—22no—
371C22⋊C4—442no—
372C22⋊C4—882no—
373C42—24no—
374C42—21no—
375C42—21no—
376C11#1820511yescharacteristic, complemented, Sylow
377C23—21no—
378C23—21no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23#6699512yes—
384C23C2×#432612yes—
385C23C2×#432612yes—
386C23#6700612yes—
387C23C22×C22⋊D1111yescharacteristic
388Q8—44no—
389Q8—44no—
390Q8—82no—
391Q8—82no—
392D4—28no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—21no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—81no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—884no—
418C2×C4C2×#432612yes—
419C2×C4#6700611yescharacteristic
420C2×C4#6700611yescharacteristic
421C2×C4C22×C22⋊D1112yes—
422C8—444no—
423C22—21no—
424C22—22no—
425C22—21no—
426C22—22no—
427C22—22no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—41no—
432C22—41no—
433C22—81no—
434C22#1062284114yes—
435C22C2×#6699511yescharacteristic
436C22C22×#432611yescharacteristic
437C22C2×#6700611yescharacteristic
438C4—22no—
439C4—22no—
440C4—21no—
441C4—41no—
442C4—44no—
443C4—41no—
444C4—44no—
445C4—882no—
446C4—882no—
447C4#1062285612yes—
448C2—21no—
449C2—21no—
450C2—24no—
451C2—42no—
452C2C2×#1062284111yescharacteristic
453C2#1307798811yescharacteristic
454C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenter#3501D11
hypocenterC11#18205
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. C2×#10622657C2semidirect
3. #13067658C2semidirect
4. #13067641C2semidirect
5. #13067188C2semidirect
376. C11#18205semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
#130729332
#130676582
#130676412
#130671882
#130669342
C11×#35012
#1820511