Finite Group Databasebeta

← #14739324

Subgroups — #14739324

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079538C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3#13077657C211yesmaximal, characteristic, complemented
4#13068165C214yesmaximal, complemented
5#13068079C214yesmaximal, complemented
6#13067392C211yesmaximal, characteristic, complemented
7#13067302C211yesmaximal, characteristic, complemented
8#13067265C211yesmaximal, characteristic, complemented
9C11×#3036C211yesmaximal, characteristic
10C2×C11×AGL(1,ℤ/8)—21no—
11C11×#532C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#463—22no—
15C11×#461C2212yes—
16C11×#459C2212yes—
17C11×#423C2211yescharacteristic
18C11×#417—21no—
19C2×#66896—21no—
20#10622820—22no—
21#10622706C2212yescomplemented
22#10622689C2212yescomplemented
23#10622653—22no—
24#10622632—22no—
25#10622625—22no—
26#10622625C2214yes—
27#10622620—22no—
28#10622620C2214yes—
29C2×#66871—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622185C2212yescomplemented
34#10622182C2212yescomplemented
35#10622124C2214yescomplemented
36#10622117C2214yescomplemented
37C2×C11×#41—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C22×Dic22—21no—
41C11×AGL(1,ℤ/8)—44no—
42C2×C11×SD16—22no—
43C2×C11×D8—22no—
44C2×C11×M16—21no—
45C11×C4⋊Q8C2311yescharacteristic
46C11×#127C2311yescharacteristic
47C11×#124—21no—
48C11×#121—21no—
49C11×#121—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11D412yes—
55C4×D4×C11C2312yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4324—24no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×#4318—24no—
63C22×C11⋊C8—21no—
64#66922—21no—
65#66922—21no—
66#66922—21no—
67#66922C2312yes—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×#103—22no—
71C11×#102—22no—
72#66896—24no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—24no—
75C22⋊(C11⋊C8)D412yes—
76#66874—24no—
77#66871—24no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)D412yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8C2312yes—
84#19421—111nomaximal, Sylow
85C24×C11—21no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C2×D4×C11C2×D412yes—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—41no—
101C22×C4×C11—82no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×Dic11—41no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—82no—
109C11×SD16—44no—
110C11×D8—44no—
111C11×M16—42no—
112C2×C8×C11—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4C2×D412yes—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11C2411yescharacteristic
125#4324—84no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130#4318—84no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—42no—
134C2×C11⋊C8C2×D414yes—
135#3206—111no—
136C2×#474—111no—
137#3036D1111yescharacteristic
138#2975—111no—
139#1699—114no—
140#1685—114no—
141#1571—111no—
142#1549—111no—
143#1540—111no—
144C23×C11—22no—
145C23×C11—42no—
146C23×C11—41no—
147C23×C11—81no—
148C23×C11—81no—
149C23×C11#12111yescharacteristic
150Q8×C11—41no—
151Q8×C11—41no—
152D4×C11—22no—
153D4×C11—22no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—81no—
159D4×C11—82no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—44no—
164C2×C4×C11—41no—
165C2×C4×C11—82no—
166C2×C4×C11—81no—
167C2×C4×C11—82no—
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)12yes—
172C2×C4×C11#13712yes—
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×Dic11—42no—
177C2×Dic11—82no—
178Dic22—44no—
179Dic22—82no—
180C8×C11—42no—
181C11⋊C8—24no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C2×AGL(1,ℤ/8)—21no—
185#532C2×D1111yescharacteristic
186C2×C4⋊Q8—111no—
187C2×C4×D4C2×D1111yescharacteristic
188#492—112no—
189#487—112no—
190#474—114no—
191#474—222no—
192#463—22no—
193#461—222no—
194#461C2×D1112yes—
195#459C2×D1112yes—
196#448—222no—
197#436—114no—
198#436—222no—
199#431—111no—
200#431—111no—
201C2×#107—221no—
202#423C2×D1111yescharacteristic
203C2×C4⋊C8—111no—
204#417—21no—
205C2×#102—221no—
206#407—222no—
207#335—114no—
208#332—112no—
209#332—114no—
210#331—112no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—84no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#46812yes—
221C22×C11C2×#12111yescharacteristic
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—42no—
226C4×C11—81no—
227C4×C11#46812yes—
228C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C4×C11C2×#13711yescharacteristic
230C4×C11#57612yes—
231Dic11—82no—
232C2×#41—21no—
233C22×Q8—221no—
234C22×D4C22⋊D1111yescharacteristic
235C23×C4—21no—
236AGL(1,ℤ/8)—44no—
237C2×SD16—22no—
238C2×SD16—224no—
239C2×D8—22no—
240C2×M16—21no—
241C2×M16—224no—
242C22×C8—221no—
243C4⋊Q8—112no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8C22×D1111yescharacteristic
248#127C22×D1111yescharacteristic
249#124—21no—
250#121—21no—
251#121—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4C22⋊D1112yes—
257C4×D4C22×D1112yes—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4C22⋊D1111yescharacteristic
261C2×C22⋊C4—21no—
262C2×C42C22×D1111yescharacteristic
263#107—224no—
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8C22×D1112yes—
270#103—22no—
271#103—224no—
272#102—22no—
273#102—224no—
274C22⋊C8—112no—
275C22⋊C8—224no—
276C22⋊C8—221no—
277C4×C8—112no—
278C4×C8—221no—
279C2×C11—22no—
280C2×C11—82no—
281C2×C11—161no—
282C2×C11#304111yescharacteristic
283C2×C11C2×#46811yescharacteristic
284C2×C11#306911yescharacteristic
285C24—21no—
286#41—42no—
287#41—42no—
288C2×Q8—21no—
289C2×Q8—222no—
290C2×Q8—441no—
291C2×Q8—882no—
292C2×D4—22no—
293C2×D4—21no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4C2×C22⋊D1112yes—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—82no—
305C22×C4—441no—
306C22×C4D4×D1111yescharacteristic
307C22×C4#434111yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309SD16—44no—
310SD16—884no—
311D8—44no—
312M16—42no—
313M16—884no—
314C2×C8—22no—
315C2×C8—114no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—442no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—222no—
323C4⋊C4—222no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4C2×C22⋊D1112yes—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C42D4×D1111yescharacteristic
332C42#434111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C42C23×D1111yescharacteristic
335C11#1942111yescharacteristic, complemented, Sylow
336C23—22no—
337C23—42no—
338C23—41no—
339C23—81no—
340C23—81no—
341C23#6699211yescharacteristic
342Q8—41no—
343Q8—41no—
344Q8—444no—
345Q8—882no—
346D4—22no—
347D4—22no—
348D4—42no—
349D4—41no—
350D4—41no—
351D4—42no—
352D4—81no—
353D4—82no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—44no—
358C2×C4—41no—
359C2×C4—82no—
360C2×C4—81no—
361C2×C4—82no—
362C2×C4—442no—
363C2×C4—882no—
364C2×C4#6698512yes—
365C2×C4#6699211yescharacteristic
366C2×C4#6699211yescharacteristic
367C2×C4#6699211yescharacteristic
368C2×C4#6700412yes—
369C2×C4C2×D4×D1111yescharacteristic
370C2×C4C2×#434111yescharacteristic
371C2×C4C22×C22⋊D1111yescharacteristic
372C8—42no—
373C8—224no—
374C8—442no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—84no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#1062265512yes—
386C22C2×#6699211yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—81no—
392C4—882no—
393C4#1062265512yes—
394C4#1062330512yes—
395C4C2×#6698511yescharacteristic
396C4C2×#6700411yescharacteristic
397C2—22no—
398C2—82no—
399C2—161no—
400C2#1307812111yescharacteristic
401C2C2×#1062265511yescharacteristic
402C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11C2×#121
hypercenter#3036D11
hypocenterC11#19421
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. C2×#10622620C2semidirect
3. #13077657C2semidirect
4. #13068165C2semidirect
5. #13068079C2semidirect
6. #13067392C2semidirect
7. #13067302C2semidirect
8. #13067265C2semidirect
21. #10622706C22semidirect
22. #10622689C22semidirect
33. #10622185C22semidirect
34. #10622182C22semidirect
35. #10622124C22semidirect
36. #10622117C22semidirect
335. C11#19421semidirect

Maximal subgroups

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

subgroupindex
#130795382
C2×#106226202
#130776572
#130681652
#130680792
#130673922
#130673022
#130672652
C11×#30362
#1942111