Finite Group Databasebeta

← #16786851

Subgroups — #16786851

Order 3328.

310 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131198C211yesmaximal, characteristic, complemented
2#13131194C211yesmaximal, characteristic, complemented
3#13129775C212yesmaximal, complemented
4#13129758C212yesmaximal
5#13123476C211yesmaximal, characteristic
6#41×Dic13C411yescharacteristic
7C13×#408C411yescharacteristic
8#11718895C2211yescharacteristic
9#11718780C2211yescharacteristic
10M16×Dic13C411yescharacteristic
11#11718763C411yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13#11718381—21no—
14#11718381—21no—
15#11718379—21no—
16#11718379—21no—
17C22⋊#6092C2212yes—
18C22⋊#6092C2212yes—
19#11718260—21no—
20#11718260—21no—
21#11718258—21no—
22#11718257—21no—
23C2×C13×#41C2×C411yescharacteristic
24C2×C13×M16C2×C411yescharacteristic
25C22×C8×C13C2×C411yescharacteristic
26Q8×Dic13C811yescharacteristic
27Q8×Dic13C811yescharacteristic
28D4×Dic13—21no—
29D4×Dic13—21no—
30D4×Dic13C811yescharacteristic
31D4×Dic13C811yescharacteristic
32#88180—21no—
33#88180C2×C411yescharacteristic
34C2×C4×Dic13—21no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×#6099C2×C411yescharacteristic
37C22×#1055C2311yescharacteristic
38C2×#6092—22no—
39C2×#6092—22no—
40C13×C22⋊C8—21no—
41C13×C22⋊C8—21no—
42C22⋊#1055—21no—
43C22⋊#1055—21no—
44#88055—21no—
45#88054—21no—
46#88054—21no—
47#88054—21no—
48#88054—21no—
49C8×Dic13—21no—
50C8×Dic13D411yescharacteristic
51C8×Dic13D411yescharacteristic
52C8×Dic13D411yescharacteristic
53C8×Dic13D411yescharacteristic
54#11464—131nomaximal, Sylow
55C13×#41—41no—
56C13×#41—41no—
57C2×Q8×C13C2×C811yescharacteristic
58C2×D4×C13—21no—
59C2×D4×C13C2×C811yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13M1611yescharacteristic
65C22×Dic13M1611yescharacteristic
66C13×M16—41no—
67C2×C8×C13—21no—
68C2×C8×C13—41no—
69C2×C8×C13C22⋊C411yescharacteristic
70C2×C8×C13C22⋊C411yescharacteristic
71C22⋊Dic13—21no—
72C22⋊Dic13—21no—
73C22⋊Dic13—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13C2×C811yescharacteristic
77C4⋊Dic13C2×C811yescharacteristic
78C4×Dic13—21no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13C22⋊C411yescharacteristic
82C4×Dic13C22⋊C411yescharacteristic
83C4×Dic13C2×C811yescharacteristic
84C4×Dic13C2×C811yescharacteristic
85#6099—41no—
86C2×#1055—21no—
87C2×#1055—41no—
88C2×#1055C2×D411yescharacteristic
89C2×#1055C2×D411yescharacteristic
90#6092—42no—
91#6092—42no—
92#2922—131no—
93#2163—131no—
94#2162—131no—
95#1323—132no—
96#1315—132no—
97C23×C13—21no—
98C23×C13C2×M1611yescharacteristic
99Q8×C13—41no—
100D4×C13—41no—
101D4×C13—42no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13C2×C22⋊C411yescharacteristic
108C2×C4×C13C22×C811yescharacteristic
109C2×Dic13—22no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—41no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13C22⋊C811yescharacteristic
116C2×Dic13C22⋊C811yescharacteristic
117C2×Dic13C22⋊C811yescharacteristic
118C2×Dic13C22⋊C811yescharacteristic
119C8×C13—21no—
120C8×C13—21no—
121C8×C13—41no—
122#1055—21no—
123#1055—21no—
124#1055—41no—
125C4×#41—131no—
126#433—261no—
127#433—261no—
128#431—261no—
129#431—261no—
130#424—131no—
131#424—131no—
132#408—131no—
133#408#26111yescharacteristic
134C4×M16—131no—
135C2×C4×C8—131no—
136C4⋊C16—261no—
137C4⋊C16—261no—
138C22⋊C16—132no—
139C22⋊C16—132no—
140#346—261no—
141C4×C16—261no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—41no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13C2×C22⋊C811yescharacteristic
149C4×C13—21no—
150C4×C13—41no—
151C4×C13#41011yescharacteristic
152C4×C13#41311yescharacteristic
153Dic13—21no—
154Dic13—21no—
155Dic13—21no—
156Dic13—41no—
157Dic13—41no—
158Dic13#35012yes—
159C2×#41C2×#26111yescharacteristic
160C2×M16—131no—
161C2×M16C2×#26111yescharacteristic
162C22×C8—131no—
163C22×C8C2×#26111yescharacteristic
164C4×Q8—131no—
165C4×Q8—131no—
166C4×D4—131no—
167C4×D4—131no—
168C4×D4—261no—
169C4×D4—261no—
170#117—131no—
171#117—261no—
172C2×C42—131no—
173C2×C42—261no—
174C2×C16—262no—
175C2×C16—262no—
176C4⋊C8—261no—
177C4⋊C8—261no—
178C4⋊C8—261no—
179C4⋊C8—261no—
180C22⋊C8—21no—
181C22⋊C8—21no—
182C22⋊C8—261no—
183C22⋊C8—261no—
184#97—261no—
185C4×C8—131no—
186C4×C8—131no—
187C4×C8—131no—
188C4×C8—131no—
189C4×C8—261no—
190C2×C13—41no—
191C2×C13—81no—
192C2×C13#145811yescharacteristic
193C2×C13C2×#35011yescharacteristic
194C2×C13#211711yescharacteristic
195#41—41no—
196#41—41no—
197C2×Q8D13⋊C811yescharacteristic
198C2×D4—21no—
199C2×D4D13⋊C811yescharacteristic
200C22×C4—21no—
201C22×C4—131no—
202C22×C4—131no—
203C22×C4—261no—
204C22×C4—261no—
205C22×C4C22×#26111yescharacteristic
206M16—41no—
207M16—521no—
208C2×C8—21no—
209C2×C8—41no—
210C2×C8—131no—
211C2×C8—131no—
212C2×C8—261no—
213C2×C8—521no—
214C2×C8C22⋊#26111yescharacteristic
215C2×C8C22⋊#26111yescharacteristic
216C4⋊C4—131no—
217C4⋊C4—131no—
218C4⋊C4—261no—
219C4⋊C4—261no—
220C22⋊C4—261no—
221C22⋊C4—261no—
222C22⋊C4—261no—
223C42—131no—
224C42—131no—
225C42—131no—
226C42—131no—
227C42—261no—
228C42—261no—
229C42—261no—
230C16—522no—
231C16—522no—
232C13#1146411yescharacteristic, complemented, Sylow
233C23—21no—
234C23D13⋊M1611yescharacteristic
235Q8—41no—
236D4—41no—
237D4—42no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—131no—
244C2×C4—131no—
245C2×C4—131no—
246C2×C4—131no—
247C2×C4—262no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—522no—
251C2×C4—521no—
252C2×C4—522no—
253C2×C4C2×D13⋊C811yescharacteristic
254C2×C4C2×C22⋊#26111yescharacteristic
255C8—21no—
256C8—21no—
257C8—41no—
258C8—261no—
259C8—261no—
260C8—521no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22D13⋊(C22⋊C8)11yescharacteristic
268C4—21no—
269C4—41no—
270C4—132no—
271C4—261no—
272C4—261no—
273C4—261no—
274C4—521no—
275C4—521no—
276C4#1171914211yescharacteristic
277C4#1171914811yescharacteristic
278C2—41no—
279C2—81no—
280C2#1313006811yescharacteristic
281C2D13⋊#35011yescharacteristic
282C2#1313107911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#408C4
socleC22×C13C2×C22⋊C8
prime radicalC2×C13×#41C2×C4
cosocleC22×#1055C23
hypercenter#408#261
hypocenterC13#11464
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #13131198C2semidirect
2. #13131194C2semidirect
3. #13129775C2semidirect
232. C13#11464semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131311942
#131297752
#131297582
#131234762
#1146413