Finite Group Databasebeta

← #14913834

Subgroups — #14913834

Order 2816.

2806 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
1#13071493C218yesmaximal, complemented
2#13071485C218yesmaximal, complemented
3#13071234C212yesmaximal, complemented
4#13071219C214yesmaximal, complemented
5#13070999C212yesmaximal
6#13070999C214yesmaximal
7#13070973C212yesmaximal, complemented
8C23×C11×C4⋊C4C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C24×C4×C11C2212yes—
11C22×C11×C4⋊C4C4116yescomplemented
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2214yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2214yes—
17C2×#66979C2214yes—
18C2×#66979C2218yes—
19#10622860C2214yes—
20#10622825C2218yes—
21#10622825C2214yes—
22#10622825C2218yes—
23#10622825C2214yes—
24#10622824C2214yes—
25#10622824C2218yes—
26C4×C22⋊Dic11C2218yes—
27C4×C22⋊Dic11C2214yes—
28C4×C22⋊Dic11C2214yes—
29C4×C22⋊Dic11C2218yes—
30#10622598C22116yescomplemented
31#10622594C22132yescomplemented
32C4⋊C4×Dic11C22116yescomplemented
33C25×C11C2311yescharacteristic
34C23×C4×C11—28no—
35C23×C4×C11—48no—
36C23×C4×C11C2×C418yes—
37C23×C4×C11C2×C4116yes—
38C23×C4×C11C2314yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2314yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×C4⋊C4C2×C4132yes—
47C2×C11×C4⋊C4C2×C4116yes—
48C2×C11×C4⋊C4C2×C4132yes—
49C2×C11×C4⋊C4C2×C418yes—
50C2×C11×C4⋊C4C2×C418yes—
51C2×C11×C4⋊C4C2314yes—
52C2×C11×C4⋊C4C2318yes—
53C2×C11×C4⋊C4C2314yes—
54C2×C22⋊Dic11C2318yes—
55C2×C22⋊Dic11C2318yes—
56C2×C22⋊Dic11C2318yes—
57#66979—216no—
58#66979—416no—
59C2×C4⋊Dic11C2318yes—
60C2×C4⋊Dic11C23116yes—
61C2×C4×Dic11C2318yes—
62C2×C4×Dic11C23116yes—
63C11⋊#95C23116yes—
64C11⋊#95C2318yes—
65C11⋊#95C2318yes—
66C11⋊#95C23116yes—
67#34178—111nomaximal, Sylow
68C24×C11—24no—
69C24×C11—24no—
70C24×C11—24no—
71C24×C11C22×C414yes—
72C24×C11C2411yescharacteristic
73C24×C11C2411yescharacteristic
74C24×C11C2411yescharacteristic
75C22×C4×C11—24no—
76C22×C4×C11—216no—
77C22×C4×C11—232no—
78C22×C4×C11—28no—
79C22×C4×C11—28no—
80C22×C4×C11—432no—
81C22×C4×C11—44no—
82C22×C4×C11—48no—
83C22×C4×C11—44no—
84C22×C4×C11C22×C414yes—
85C22×C4×C11C22×C4116yes—
86C22×C4×C11C22×C418yes—
87C22×C4×C11C22×C418yes—
88C22×C4×C11C22×C418yes—
89C22×C4×C11C22×C418yes—
90C22×C4×C11C22×C4116yes—
91C22×C4×C11C22×C414yes—
92C22×C4×C11#4118yes—
93C22×C4×C11C2412yes—
94C22×C4×C11C2414yes—
95C22×C4×C11C2414yes—
96C22×C4×C11C2412yes—
97C22×Dic11C24116yes—
98C11×C4⋊C4C22×C4132yes—
99C11×C4⋊C4C22×C4116yes—
100C11×C4⋊C4C22×C4116yes—
101C22⋊Dic11—216no—
102C22⋊Dic11—216no—
103C22⋊Dic11—216no—
104C4⋊Dic11—216no—
105C4⋊Dic11—416no—
106C4×Dic11—216no—
107C4×Dic11—416no—
108C23×C4⋊C4D1111yescharacteristic
109#2345—118no—
110#2344—118no—
111#2316—112no—
112#2313—114no—
113#2280—112no—
114#2280—114no—
115#2274—112no—
116C23×C11—232no—
117C23×C11—28no—
118C23×C11—28no—
119C23×C11—28no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11C23×C412yes—
127C23×C11C23×C412yes—
128C23×C11C23×C412yes—
129C23×C11C2×#4114yes—
130C23×C11H(5,𝔽2)14yes—
131C23×C112−1+414yes—
132C23×C11C2511yescharacteristic
133C2×C4×C11—28no—
134C2×C4×C11—232no—
135C2×C4×C11—24no—
136C2×C4×C11—28no—
137C2×C4×C11—28no—
138C2×C4×C11—216no—
139C2×C4×C11—216no—
140C2×C4×C11—48no—
141C2×C4×C11—416no—
142C2×C4×C11—48no—
143C2×C4×C11#117116yescomplemented
144C2×C4×C11C23×C414yes—
145C2×C4×C11C23×C418yes—
146C2×C4×C11C23×C418yes—
147C2×C4×C11C23×C414yes—
148C2×C4×C11C2×#4118yes—
149C2×Dic11—216no—
150C2×Dic11—216no—
151C2×Dic11—216no—
152C24×C4C2×D1111yescharacteristic
153C24×C4C2×D1112yes—
154C2×#117—114no—
155C2×#117—118no—
156C22×C4⋊C4Dic11116yescomplemented
157C22×C4⋊C4C2×D1112yes—
158C22×C4⋊C4C2×D1111yescharacteristic
159C22×C4⋊C4C2×D1114yes—
160C22×C4⋊C4C2×D1114yes—
161C22×C4⋊C4C2×D1111yescharacteristic
162#389—1116no—
163#387—1132no—
164#381—114no—
165#381—118no—
166#380—118no—
167#380—114no—
168#380—118no—
169#380—114no—
170#379—114no—
171C4×C4⋊C4—1116no—
172C4×C22⋊C4—118no—
173C4×C22⋊C4—114no—
174C4×C22⋊C4—114no—
175C4×C22⋊C4—118no—
176C22×C11—232no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—28no—
184C22×C11—28no—
185C22×C11—28no—
186C22×C11C2×#11714yes—
187C22×C11#51814yes—
188C22×C11#51914yes—
189C22×C11C24×C411yescharacteristic
190C22×C11C22×#4112yes—
191C22×C11C2×H(5,𝔽2)12yes—
192C22×C11C2×2−1+412yes—
193C4×C11—24no—
194C4×C11—28no—
195C4×C11—28no—
196C4×C11C2×#11718yes—
197Dic11—416no—
198C25C22×D1111yescharacteristic
199C23×C4—28no—
200C23×C4—48no—
201C23×C4C2×Dic1118yes—
202C23×C4C2×Dic11116yes—
203C23×C4C22×D1114yes—
204C23×C4C22×D1112yes—
205C23×C4C22×D1112yes—
206C23×C4C22×D1111yescharacteristic
207C23×C4C22×D1112yes—
208C23×C4C22×D1114yes—
209C23×C4C22×D1112yes—
210C23×C4C22×D1111yescharacteristic
211#117—2216no—
212#117—4416no—
213C2×C4⋊C4—118no—
214C2×C4⋊C4—1116no—
215C2×C4⋊C4C2×Dic11132yes—
216C2×C4⋊C4C2×Dic11116yes—
217C2×C4⋊C4C2×Dic11132yes—
218C2×C4⋊C4C2×Dic1118yes—
219C2×C4⋊C4C2×Dic1118yes—
220C2×C4⋊C4C22×D1114yes—
221C2×C4⋊C4C22×D1118yes—
222C2×C4⋊C4C22×D1114yes—
223C2×C22⋊C4—118no—
224C2×C22⋊C4—118no—
225C2×C22⋊C4—118no—
226C2×C42—118no—
227C2×C42—1116no—
228#95—1116no—
229#95—118no—
230#95—118no—
231#95—1116no—
232C2×C11—24no—
233C2×C11—24no—
234C2×C11—24no—
235C2×C11C22×#11711yescharacteristic
236C2×C11C2×#51811yescharacteristic
237C2×C11C2×#51911yescharacteristic
238C2×C11#349214yes—
239C24—24no—
240C24—24no—
241C24—24no—
242C24C22×Dic1114yes—
243C24C23×D1111yescharacteristic
244C24C23×D1111yescharacteristic
245C24C23×D1111yescharacteristic
246C22×C4—24no—
247C22×C4—216no—
248C22×C4—232no—
249C22×C4—28no—
250C22×C4—28no—
251C22×C4—44no—
252C22×C4—48no—
253C22×C4—44no—
254C22×C4—432no—
255C22×C4—1116no—
256C22×C4#433918yes—
257C22×C4C22×Dic1114yes—
258C22×C4C22×Dic11116yes—
259C22×C4C22×Dic1118yes—
260C22×C4C22×Dic1118yes—
261C22×C4C22×Dic1118yes—
262C22×C4C22×Dic1118yes—
263C22×C4C22×Dic11116yes—
264C22×C4C22×Dic1114yes—
265C22×C4C23×D1112yes—
266C22×C4C23×D1114yes—
267C22×C4C23×D1114yes—
268C22×C4C23×D1112yes—
269C4⋊C4—2216no—
270C4⋊C4—4416no—
271C4⋊C4C22×Dic11132yes—
272C4⋊C4C22×Dic11116yes—
273C4⋊C4C22×Dic11116yes—
274C22⋊C4—2216no—
275C22⋊C4—2216no—
276C22⋊C4—2216no—
277C42—2216no—
278C42—4416no—
279C11#3417811yescharacteristic, complemented, Sylow
280C23—232no—
281C23—28no—
282C23—28no—
283C23—28no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23C2×#433914yes—
291C23#6703714yes—
292C23#6704014yes—
293C23C23×Dic1112yes—
294C23C23×Dic1112yes—
295C23C23×Dic1112yes—
296C23C24×D1111yescharacteristic
297C2×C4—28no—
298C2×C4—232no—
299C2×C4—24no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—216no—
303C2×C4—216no—
304C2×C4—48no—
305C2×C4—416no—
306C2×C4—48no—
307C2×C4—2216no—
308C2×C4—2216no—
309C2×C4—2216no—
310C2×C4#66979116yescomplemented
311C2×C4C2×#433918yes—
312C2×C4C23×Dic1114yes—
313C2×C4C23×Dic1118yes—
314C2×C4C23×Dic1118yes—
315C2×C4C23×Dic1114yes—
316C22—232no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—28no—
324C22—28no—
325C22—28no—
326C22C2×#6697914yes—
327C22#1062332914yes—
328C22#1062334314yes—
329C22C22×#433912yes—
330C22C2×#6703712yes—
331C22C2×#6704012yes—
332C22C24×Dic1111yescharacteristic
333C4—24no—
334C4—28no—
335C4—28no—
336C4—4416no—
337C4C2×#6697918yes—
338C2—24no—
339C2—24no—
340C2—24no—
341C2C22×#6697911yescharacteristic
342C2C2×#1062332911yescharacteristic
343C2C2×#1062334311yescharacteristic
344C2#1308232514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC23×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC25×C11C23
hypercenterC23×C4⋊C4D11
hypocenterC11#34178
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13071493C2semidirect
2. #13071485C2semidirect
3. #13071234C2semidirect
4. #13071219C2semidirect
7. #13070973C2semidirect
11. C22×C11×C4⋊C4C4semidirect
30. #10622598C22semidirect
31. #10622594C22semidirect
32. C4⋊C4×Dic11C22semidirect
143. C2×C4×C11#117semidirect
156. C22×C4⋊C4Dic11semidirect
279. C11#34178semidirect
310. C2×C4#66979semidirect

Maximal subgroups

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

subgroupindex
#130714932
#130714852
#130712342
#130712192
#130709992
#130709732
C23×C11×C4⋊C42
#3417811