Finite Group Databasebeta

← #14652796

Subgroups — #14652796

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068469C211yesmaximal, characteristic, complemented
2#13068365C211yesmaximal, characteristic, complemented
3C2×#10622178C214yesmaximal, complemented
4C11×#2858C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C11×#127C411yescharacteristic
7C2×C11×#124C412yes—
8C2×C11×#124C2212yes—
9C11×#390—21no—
10C11×#390—21no—
11C11×#390—21no—
12C11×#390—21no—
13C43×C11C2211yescharacteristic
14C2×C4⋊(C11⋊C8)—21no—
15C2×#66867C2212yes—
16C2×#66867C2212yes—
17#10622178—28no—
18#10622162—21no—
19#10622162—21no—
20#10622162—21no—
21C22×Q8×C11C2×C412yes—
22C22×D4×C11—21no—
23C22×D4×C11—21no—
24C22×D4×C11C2×C412yes—
25C11×C4⋊Q8—42no—
26C11×#127—42no—
27C11×#124—24no—
28C11×#124—24no—
29C11×#124—44no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C22×C11⋊C8—22no—
44C22×C11⋊C8—22no—
45C4⋊(C11⋊C8)—24no—
46#66867—22no—
47#66867—24no—
48#66867D414yescomplemented
49#9689—111nomaximal, Sylow
50C24×C11—22no—
51C2×Q8×C11—24no—
52C2×Q8×C11—42no—
53C2×Q8×C11—42no—
54C2×D4×C11—24no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C22×C4×C11—22no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C11×C22⋊C4—44no—
74C11×C22⋊C4—44no—
75C11×C22⋊C4—44no—
76C11×C22⋊C4—42no—
77C11×C22⋊C4—42no—
78C42×C11—22no—
79C42×C11—22no—
80C42×C11—22no—
81C42×C11—41no—
82C42×C11—41no—
83C42×C11—41no—
84C42×C11C2×D412yes—
85C42×C11#4112yes—
86C2×C11⋊C8—24no—
87C2×C11⋊C8—24no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92#2858D1111yescharacteristic
93#1767—111no—
94#1745—111no—
95C2×#329—114no—
96C23×C11—42no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11C2×C22⋊C411yescharacteristic
104Q8×C11—84no—
105D4×C11—84no—
106D4×C11—84no—
107D4×C11—84no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11#10012yes—
127C2×C4×C11#10012yes—
128C2×C4×C11#10412yes—
129C2×C4×C11C4×D412yes—
130C2×C4×C11#12112yes—
131C2×C4×C11#12411yescharacteristic
132C2×C4×C11#12711yescharacteristic
133C11⋊C8—44no—
134C11⋊C8—44no—
135C2×C4⋊Q8Dic1111yescharacteristic
136C2×#127Dic1111yescharacteristic
137C2×#124Dic1112yes—
138C2×#124C2×D1112yes—
139C2×C4⋊C8—221no—
140C2×#97—112no—
141C2×#97—112no—
142#390—21no—
143#390—21no—
144#390—21no—
145#390—21no—
146C43C2×D1111yescharacteristic
147#336—221no—
148#336—221no—
149#336—221no—
150#329—228no—
151C22×C11—82no—
152C22×C11—82no—
153C22×C11—82no—
154C22×C11—82no—
155C22×C11—82no—
156C22×C11—82no—
157C22×C11—82no—
158C22×C11#39011yescharacteristic
159C22×C11C2×#10011yescharacteristic
160C22×C11C2×#10011yescharacteristic
161C22×C11C2×#10411yescharacteristic
162C22×C11#42111yescharacteristic
163C22×C11#42111yescharacteristic
164C22×C11#42111yescharacteristic
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—41no—
173C4×C11—82no—
174C22×Q8C2×Dic1112yes—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4C2×Dic1112yes—
178C22×C8—222no—
179C22×C8—222no—
180C4⋊Q8—42no—
181#127—42no—
182#124—24no—
183#124—24no—
184#124—44no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C42C2×Dic1111yescharacteristic
192C2×C42C2×Dic1111yescharacteristic
193C2×C42C22⋊D1111yescharacteristic
194C2×C42C22⋊D1111yescharacteristic
195C2×C42C22⋊D1111yescharacteristic
196C2×C42C22⋊D1111yescharacteristic
197C2×C42C22×D1111yescharacteristic
198C4⋊C8—224no—
199#97—114no—
200#97—224no—
201#97—222no—
202C2×C11—162no—
203C2×C11#152711yescharacteristic
204C2×C11#153011yescharacteristic
205C2×C11#153311yescharacteristic
206C2×C11#153611yescharacteristic
207C2×C11#196311yescharacteristic
208C2×C11#196511yescharacteristic
209C2×C11#198011yescharacteristic
210C24—22no—
211C2×Q8—24no—
212C2×Q8—42no—
213C2×Q8—42no—
214C2×D4—24no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4—42no—
222C2×D4—42no—
223C22×C4—22no—
224C22×C4C22⋊Dic1111yescharacteristic
225C22×C4C22⋊Dic1111yescharacteristic
226C22×C4C22⋊Dic1111yescharacteristic
227C22×C4C22⋊Dic1111yescharacteristic
228C22×C4C22×Dic1111yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231C2×C8—224no—
232C2×C8—224no—
233C2×C8—442no—
234C2×C8—442no—
235C2×C8—442no—
236C2×C8—442no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C22⋊C4—44no—
240C22⋊C4—44no—
241C22⋊C4—42no—
242C22⋊C4—44no—
243C22⋊C4—42no—
244C42—22no—
245C42—22no—
246C42—22no—
247C42—41no—
248C42—41no—
249C42—41no—
250C42D4×D1112yes—
251C42#434112yes—
252C11#968911yescharacteristic, complemented, Sylow
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23C2×C22⋊Dic1111yescharacteristic
261Q8—84no—
262D4—84no—
263D4—84no—
264D4—84no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4#6689712yes—
284C2×C4#6689712yes—
285C2×C4#6690112yes—
286C2×C4D4×Dic1112yes—
287C2×C4#6698911yescharacteristic
288C2×C4#6699112yes—
289C2×C4#6699311yescharacteristic
290C8—444no—
291C8—444no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22C2×#6689711yescharacteristic
300C22C2×#6689711yescharacteristic
301C22#1062283411yescharacteristic
302C22C2×#6690111yescharacteristic
303C22#1062284911yescharacteristic
304C22#1062284911yescharacteristic
305C22#1062284911yescharacteristic
306C4—22no—
307C4—22no—
308C4—22no—
309C4—22no—
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—82no—
315C2—162no—
316C2#1306721411yescharacteristic
317C2#1306722711yescharacteristic
318C2#1306724011yescharacteristic
319C2#1306725111yescharacteristic
320C2#1306944911yescharacteristic
321C2#1306945711yescharacteristic
322C2#1306953611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2858C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#127C4
cosocleC2×C42×C11C23
hypercenter#2858D11
hypocenterC11#9689
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2858

Complements

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

NH ≅ G/Ntype
1. #13068469C2semidirect
2. #13068365C2semidirect
3. C2×#10622178C2semidirect
48. #66867D4semidirect
252. C11#9689semidirect

Maximal subgroups

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

subgroupindex
#130684692
#130683652
C2×#106221782
C11×#28582
#968911