Finite Group Databasebeta

← #14764030

Subgroups — #14764030

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622847C212yesmaximal
2#13068801C214yesmaximal, complemented
3#13068796C214yesmaximal, complemented
4#13068600C212yesmaximal, complemented
5#13068596C212yesmaximal, complemented
6C11×#2297C211yesmaximal, characteristic
7C22×C11×#41C2211yescharacteristic
8C2×C11×#117C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C22×#4318C2212yes—
11C23×C11⋊C8C2212yes—
12C11×#391C412yes—
13C11×#390C412yes—
14C11×#386C412yes—
15C11×#386C412yes—
16C4×C11×C22⋊C4C2214yes—
17#10622847—28no—
18C2×C22⋊(C11⋊C8)C2214yes—
19C2×C22⋊(C11⋊C8)C2214yes—
20C2×C4⋊(C11⋊C8)C2214yes—
21C2×C4⋊(C11⋊C8)C2214yes—
22#10622162C2212yes—
23#10622162C2212yes—
24#10622162C2212yes—
25#10622162C2212yes—
26C2×C11×#41—42no—
27C2×C11×#41—42no—
28C2×C11×#41D414yes—
29C2×C11×#41Q814yes—
30C22×Q8×C11C2×C411yescharacteristic
31C22×D4×C11C2×C412yes—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C11×#117—42no—
38C2×C11×C4⋊C4C2×C412yes—
39C2×C11×C22⋊C4C2×C414yes—
40C2×C11×C22⋊C4C2×C412yes—
41C2×C11×C22⋊C4C2×C414yes—
42C2×C42×C11—42no—
43C2×C42×C11C2×C412yes—
44C2×C42×C11C2312yes—
45C2×C42×C11C2312yes—
46C2×#4318—24no—
47C2×#4318—42no—
48C2×#4318—42no—
49C22×C11⋊C8—24no—
50C22×C11⋊C8—42no—
51C22×C11⋊C8—42no—
52C22×C11⋊C8C2314yes—
53C22×C11⋊C8C2314yes—
54C11×#95C2×C414yes—
55C11×#95C2×C414yes—
56C22⋊(C11⋊C8)—28no—
57C22⋊(C11⋊C8)—28no—
58C4⋊(C11⋊C8)—44no—
59C4⋊(C11⋊C8)—44no—
60#21937—111nomaximal, Sylow
61C24×C11C22×C412yes—
62C24×C11C22×C411yescharacteristic
63C11×#41—48no—
64C11×#41—48no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11C4⋊C414yes—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11C4⋊C418yes—
73C2×D4×C11C4⋊C414yes—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—24no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—42no—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C22×C414yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C412yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D414yes—
91C22×C4×C11C2×Q814yes—
92C22×C4×C11C2×Q812yes—
93C22×C4×C11C2411yescharacteristic
94C11×C4⋊C4—42no—
95C11×C22⋊C4—28no—
96C11×C22⋊C4—44no—
97C11×C22⋊C4—42no—
98C42×C11—24no—
99C42×C11—24no—
100C42×C11—42no—
101#4318—48no—
102C2×C11⋊C8—24no—
103C2×C11⋊C8—24no—
104C2×C11⋊C8—24no—
105C2×C11⋊C8—24no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—24no—
108C2×C11⋊C8—48no—
109C2×#408—112no—
110#2297D1111yescharacteristic
111#1851—114no—
112#1850—114no—
113#1798—112no—
114#1797—112no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11—24no—
120C23×C11—22no—
121C23×C11—24no—
122C23×C11—22no—
123C23×C11C2×C4⋊C412yes—
124C23×C11C2×C4⋊C414yes—
125C23×C11C23×C411yescharacteristic
126Q8×C11—44no—
127D4×C11—44no—
128D4×C11—48no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—22no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—22no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11C2×C4⋊C414yes—
150C2×C4×C11C2×C4⋊C412yes—
151C2×C4×C11#13114yes—
152C2×C4×C11C22×D411yescharacteristic
153C2×C4×C11C22×Q811yescharacteristic
154C2×C4×C11H(5,𝔽2)12yes—
155C2×C4×C11H(5,𝔽2)12yes—
156C11⋊C8—44no—
157C11⋊C8—44no—
158C22×#41C2×D1111yescharacteristic
159C22×M16—112no—
160C23×C8—112no—
161C2×#117C2×D1111yescharacteristic
162C22×C42C2×D1111yescharacteristic
163C2×C4⋊C8—114no—
164C2×C4⋊C8—114no—
165#408—228no—
166C2×C22⋊C8—114no—
167C2×C22⋊C8—114no—
168#391Dic1112yes—
169#390Dic1112yes—
170#386Dic1112yes—
171#386Dic1112yes—
172C4×C22⋊C4C2×D1114yes—
173#336—112no—
174#336—112no—
175#336—112no—
176#336—112no—
177C22×C11—24no—
178C22×C11—22no—
179C22×C11—28no—
180C22×C11—24no—
181C22×C11—41no—
182C22×C11—42no—
183C22×C11—41no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—44no—
187C22×C11C22×C4⋊C411yescharacteristic
188C22×C11#51811yescharacteristic
189C22×C11#51811yescharacteristic
190C22×C11C2×#13112yes—
191C22×C11#56812yes—
192C4×C11—22no—
193C4×C11—24no—
194C4×C11—24no—
195C4×C11—42no—
196C4×C11—44no—
197C4×C11#53412yes—
198C4×C11#54312yes—
199C2×#41—42no—
200C2×#41—42no—
201C2×#41Dic2214yes—
202C2×#41D4414yes—
203C22×Q8C2×Dic1111yescharacteristic
204C22×D4C2×Dic1112yes—
205C22×D4C2×Dic1111yescharacteristic
206C23×C4C2×Dic1111yescharacteristic
207C23×C4C2×Dic1111yescharacteristic
208C23×C4C22×D1111yescharacteristic
209C23×C4C22×D1112yes—
210C2×M16—224no—
211C2×M16—442no—
212C2×M16—442no—
213C22×C8—114no—
214C22×C8—114no—
215C22×C8—224no—
216C22×C8—442no—
217C22×C8—442no—
218#117—42no—
219C2×C4⋊C4C2×Dic1112yes—
220C2×C22⋊C4C2×Dic1114yes—
221C2×C22⋊C4C2×Dic1112yes—
222C2×C22⋊C4C2×Dic1114yes—
223C2×C42—42no—
224C2×C42C2×Dic1112yes—
225C2×C42C22×D1112yes—
226C2×C42C22×D1112yes—
227C4⋊C8—444no—
228C4⋊C8—444no—
229C22⋊C8—228no—
230C22⋊C8—228no—
231#95C2×Dic1114yes—
232#95C2×Dic1114yes—
233C2×C11—42no—
234C2×C11—44no—
235C2×C11#231511yescharacteristic
236C2×C11#290612yes—
237C2×C11#297711yescharacteristic
238C2×C11#297811yescharacteristic
239C2×C11#298112yes—
240C24C22×Dic1112yes—
241C24C22×Dic1111yescharacteristic
242#41—48no—
243#41—48no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C4⋊Dic1114yes—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4C4⋊Dic1118yes—
252C2×D4C4⋊Dic1114yes—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4C2×Dic2212yes—
264C22×C4C2×Dic2214yes—
265C22×C4C2×D4412yes—
266C22×C4C2×D4414yes—
267C22×C4C22×Dic1112yes—
268C22×C4C22×Dic1114yes—
269C22×C4C22×Dic1112yes—
270C22×C4C22×Dic1111yescharacteristic
271C22×C4C22×Dic1112yes—
272C22×C4C23×D1111yescharacteristic
273M16—448no—
274C2×C8—224no—
275C2×C8—224no—
276C2×C8—224no—
277C2×C8—224no—
278C2×C8—224no—
279C2×C8—224no—
280C2×C8—448no—
281C4⋊C4—42no—
282C22⋊C4—28no—
283C22⋊C4—42no—
284C22⋊C4—44no—
285C42—24no—
286C42—24no—
287C42—42no—
288C11#2193711yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—24no—
294C23—22no—
295C23—24no—
296C23—22no—
297C23C2×C4⋊Dic1112yes—
298C23C2×C4⋊Dic1114yes—
299C23C23×Dic1111yescharacteristic
300Q8—44no—
301D4—44no—
302D4—48no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4C2×C4⋊Dic1112yes—
324C2×C4C2×C4⋊Dic1114yes—
325C2×C4#6700114yes—
326C2×C4C22×Dic2211yescharacteristic
327C2×C4C22×D4411yescharacteristic
328C2×C4#6703712yes—
329C2×C4#6703712yes—
330C8—444no—
331C8—444no—
332C22—24no—
333C22—22no—
334C22—28no—
335C22—24no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—42no—
340C22—42no—
341C22—44no—
342C22C22×C4⋊Dic1111yescharacteristic
343C22#1062332911yescharacteristic
344C22#1062332911yescharacteristic
345C22C2×#6700112yes—
346C22#1062335012yes—
347C4—22no—
348C4—24no—
349C4—24no—
350C4—42no—
351C4—44no—
352C4#1062301412yes—
353C4#1062302412yes—
354C2—42no—
355C2—44no—
356C2#1307123011yescharacteristic
357C2#1307718412yes—
358C2#1307767211yescharacteristic
359C2#1307767811yescharacteristic
360C2#1307769212yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2297C2
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2297D11
hypocenterC11#21937
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. #13068801C2semidirect
3. #13068796C2semidirect
4. #13068600C2semidirect
5. #13068596C2semidirect
288. C11#21937semidirect

Maximal subgroups

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

subgroupindex
C2×#106228472
#130688012
#130687962
#130686002
#130685962
C11×#22972
#2193711