Finite Group Databasebeta

← #14764164

Subgroups — #14764164

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622537C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic
3#13069384C214yesmaximal, complemented
4#13069377C212yesmaximal, complemented
5#13069372C212yesmaximal, complemented
6#13068647C214yesmaximal
7C11×#2285C211yesmaximal, characteristic
8C2×C11×#117—21no—
9C22×C42×C11C2211yescharacteristic
10C22×#4318C2212yes—
11C11×#384C2212yes—
12C11×#382—21no—
13C11×#380—21no—
14C11×#380C2212yes—
15C4×C11×C4⋊C4—21no—
16C4×C11×C4⋊C4C2212yes—
17#10622825C2212yes—
18#10622824—21no—
19C4×C22⋊Dic11—21no—
20C2×#66872C2214yes—
21C2×#66871C2214yes—
22#10622550—21no—
23#10622549C2212yes—
24C4×C4⋊Dic11C2211yescharacteristic
25C4×C4⋊Dic11C2211yescharacteristic
26#10622545—21no—
27#10622537C418yescomplemented
28C2×C4⋊(C11⋊C8)C2212yes—
29C2×C4⋊(C11⋊C8)C2212yes—
30#10622167C2214yes—
31#10622167C2214yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C11×#117—44no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4C2314yes—
39C2×C11×C22⋊C4—22no—
40C2×C42×C11—22no—
41C2×C42×C11C2×C414yes—
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11Q814yes—
45C2×C42×C11C2311yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C22⋊Dic11—22no—
48C2×C4⋊Dic11C2312yes—
49C2×C4⋊Dic11C2312yes—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52C2×#4318—44no—
53C2×#4318C2×C418yes—
54C22×C11⋊C8C2314yes—
55C11×#95—22no—
56C11×#95—22no—
57C11⋊#95—22no—
58C11⋊#95—22no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—22no—
62#66872—44no—
63#66871—44no—
64C4⋊(C11⋊C8)C2×C418yes—
65C4⋊(C11⋊C8)C2×C418yes—
66#21963—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—24no—
73C22×C4×C11—42no—
74C22×C4×C11C4⋊C414yes—
75C22×C4×C11C4⋊C414yes—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×Q812yes—
83C22×C4×C11C2411yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—22no—
86C11×C4⋊C4—24no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—44no—
89C11×C4⋊C4—44no—
90C11×C22⋊C4—44no—
91C42×C11—44no—
92C42×C11C4⋊C414yes—
93C42×C11C4⋊C414yes—
94C42×C11C22×C412yes—
95C42×C11C22×C412yes—
96C42×C11C2×Q812yes—
97C42×C11C2×Q812yes—
98C22⋊Dic11—44no—
99C4⋊Dic11—22no—
100C4⋊Dic11—22no—
101C4⋊Dic11—22no—
102C4⋊Dic11—22no—
103C4×Dic11—42no—
104C4×Dic11—42no—
105#4318—48no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—24no—
108C2×C11⋊C8C22×C418yes—
109C2×#423—111no—
110#2285D1111yescharacteristic
111#2283—111no—
112#1949—114no—
113#1948—112no—
114#1947—112no—
115#1809—114no—
116C23×C11—22no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—22no—
120C23×C11C2×C4⋊C412yes—
121C23×C11C22×D411yescharacteristic
122C2×C4×C11—22no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—24no—
130C2×C4×C11—28no—
131C2×C4×C11—44no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11—44no—
135C2×C4×C11C2×C4⋊C412yes—
136C2×C4×C11C2×C4⋊C412yes—
137C2×C4×C11C2×C4⋊C412yes—
138C2×C4×C11C2×C4⋊C412yes—
139C2×C4×C11C2×C4⋊C412yes—
140C2×C4×C11AGL(1,ℤ/8)12yes—
141C2×C4×C11#13712yes—
142C2×C4×C11C23×C411yescharacteristic
143C2×C4×C11C22×Q811yescharacteristic
144C2×C4×C11H(5,𝔽2)12yes—
145C2×C4×C112−1+412yes—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C11⋊C8—28no—
153C22×M16—112no—
154C2×#117—21no—
155C22×C42C2×D1111yescharacteristic
156C2×#107—114no—
157C2×#106—114no—
158#423—118no—
159C2×C4⋊C8—112no—
160C2×C4⋊C8—112no—
161#384C2×D1112yes—
162#383—221no—
163#382—21no—
164#382—112no—
165#381—221no—
166#380—21no—
167#380—112no—
168#380C2×D1112yes—
169C4×C4⋊C4—21no—
170C4×C4⋊C4—111no—
171C4×C4⋊C4—111no—
172C4×C4⋊C4C2×D1112yes—
173C4×C22⋊C4—221no—
174#376—221no—
175#340—114no—
176#340—114no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11C22×C4⋊C411yescharacteristic
183C22×C11#53712yes—
184C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
185C22×C11C2×#13711yescharacteristic
186C22×C11#57512yes—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—84no—
192C4×C11#42814yes—
193C4×C11#51811yescharacteristic
194C4×C11#51911yescharacteristic
195C4×C11#54412yes—
196Dic11—82no—
197Dic11—82no—
198C23×C4C22⋊D1111yescharacteristic
199C23×C4C22⋊D1111yescharacteristic
200C23×C4C22×D1111yescharacteristic
201C2×M16—118no—
202C2×M16—444no—
203C22×C8—114no—
204#117—44no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—112no—
208C2×C4⋊C4—112no—
209C2×C4⋊C4C22×D1114yes—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—222no—
212C2×C42—22no—
213C2×C42—221no—
214C2×C42—221no—
215C2×C42Dic2214yes—
216C2×C42C4×D1114yes—
217C2×C42C22⋊D1111yescharacteristic
218C2×C42C22⋊D1111yescharacteristic
219C2×C42C22×D1111yescharacteristic
220C2×C42C22×D1111yescharacteristic
221#107—444no—
222#106—444no—
223C4⋊C8—118no—
224C4⋊C8—118no—
225#95—22no—
226#95—22no—
227#95—222no—
228#95—222no—
229#95—222no—
230#95—221no—
231#95—221no—
232C2×C11—42no—
233C2×C11#231611yescharacteristic
234C2×C11C2×#42811yescharacteristic
235C2×C11#291111yescharacteristic
236C2×C11#325112yes—
237C2×C11#325212yes—
238C24C2×C22⋊D1111yescharacteristic
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—42no—
245C22×C4—222no—
246C22×C4—222no—
247C22×C4Dic11⋊C414yes—
248C22×C4Dic11⋊C414yes—
249C22×C4C2×Dic2212yes—
250C22×C4C2×C4×D1112yes—
251C22×C4C2×C22⋊D1111yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256C22×C4C23×D1111yescharacteristic
257M16—448no—
258C2×C8—118no—
259C2×C8—224no—
260C2×C8—224no—
261C4⋊C4—24no—
262C4⋊C4—24no—
263C4⋊C4—44no—
264C4⋊C4—44no—
265C4⋊C4—222no—
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—222no—
269C22⋊C4—44no—
270C22⋊C4—444no—
271C42—44no—
272C42—442no—
273C42—442no—
274C42Dic11⋊C414yes—
275C42Dic11⋊C414yes—
276C42C2×Dic2212yes—
277C42C2×Dic2212yes—
278C42C2×C4×D1112yes—
279C42C2×C4×D1112yes—
280C11#2196311yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—22no—
284C23—22no—
285C23C2×Dic11⋊C412yes—
286C23C22×C22⋊D1111yescharacteristic
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—28no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4C2×Dic11⋊C412yes—
307C2×C4C2×Dic11⋊C412yes—
308C2×C4C2×Dic11⋊C412yes—
309C2×C4C2×Dic11⋊C412yes—
310C2×C4C2×Dic11⋊C412yes—
311C2×C4#6698512yes—
312C2×C4#6699512yes—
313C2×C4C22×Dic2211yescharacteristic
314C2×C4C22×C4×D1111yescharacteristic
315C2×C4#6704212yes—
316C2×C4#6704312yes—
317C8—228no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—42no—
322C22—42no—
323C22C22×Dic11⋊C411yescharacteristic
324C22C2×#6698511yescharacteristic
325C22C2×#6699511yescharacteristic
326C22#1062335312yes—
327C22#1062336412yes—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—22no—
332C4—84no—
333C4—882no—
334C4—882no—
335C4#1062257714yes—
336C4#1062304711yescharacteristic
337C4#1062305012yes—
338C4#1062305211yescharacteristic
339C2—42no—
340C2#1307123211yescharacteristic
341C2C2×#1062257711yescharacteristic
342C2#1307720511yescharacteristic
343C2#1307997212yes—
344C2#1307998312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2285C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2285D11
hypocenterC11#21963
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
3. #13069384C2semidirect
4. #13069377C2semidirect
5. #13069372C2semidirect
27. #10622537C4semidirect
280. C11#21963semidirect

Maximal subgroups

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

subgroupindex
C2×#106225372
#130710142
#130693842
#130693772
#130693722
#130686472
C11×#22852
#2196311