Finite Group Databasebeta

← #15772135

Subgroups — #15772135

Order 3328.

310 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 87 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#13123476C211yesmaximal, characteristic
2#13116636C211yesmaximal, characteristic, complemented
3#13116632C211yesmaximal, characteristic, complemented
4#13112777C211yesmaximal, characteristic, complemented
5#13112777C211yesmaximal, characteristic, complemented
6#13112762C211yesmaximal, characteristic
7C13×#1315C211yesmaximal, characteristic
8#41×Dic13C411yescharacteristic
9C13×#408C2211yescharacteristic
10#11718895C411yescharacteristic
11#11718780C411yescharacteristic
12M16×Dic13C411yescharacteristic
13#11718763C2211yescharacteristic
14C2×C8×Dic13C2211yescharacteristic
15#11718381—21no—
16#11718381—21no—
17#11718379—21no—
18#11718379—21no—
19C13×C22⋊C16C2211yescharacteristic
20C13×C22⋊C16C2211yescharacteristic
21C22⋊#6090C2211yescharacteristic
22C22⋊#6090C2211yescharacteristic
23#11718094—21no—
24#11718093—21no—
25#11718093—21no—
26C16×Dic13—21no—
27C2×C13×#41C2×C411yescharacteristic
28C2×C13×M16C2×C411yescharacteristic
29C22×C8×C13C2311yescharacteristic
30Q8×Dic13C811yescharacteristic
31Q8×Dic13C811yescharacteristic
32D4×Dic13—21no—
33D4×Dic13—21no—
34D4×Dic13C811yescharacteristic
35D4×Dic13C811yescharacteristic
36#88180—21no—
37#88180C2×C411yescharacteristic
38C2×C4×Dic13—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×#6099C2×C411yescharacteristic
41C22×#1055C2×C411yescharacteristic
42C2×C13×C16—21no—
43C2×C13×C16—21no—
44C13×C22⋊C8—21no—
45C13×C22⋊C8—21no—
46C22⋊#1055—21no—
47C22⋊#1055—21no—
48#88055—21no—
49#88054—21no—
50#88054—21no—
51#88054—21no—
52#88054—21no—
53C8×Dic13—21no—
54C8×Dic13D411yescharacteristic
55C8×Dic13D411yescharacteristic
56C8×Dic13D411yescharacteristic
57C8×Dic13D411yescharacteristic
58C2×#6090—21no—
59C2×#6090—21no—
60#11464—131nomaximal, Sylow
61C13×#41—41no—
62C13×#41—41no—
63C2×Q8×C13C2×C811yescharacteristic
64C2×D4×C13—21no—
65C2×D4×C13C2×C811yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13M1611yescharacteristic
71C22×Dic13M1611yescharacteristic
72C13×M16—41no—
73C2×C8×C13—21no—
74C2×C8×C13—41no—
75C2×C8×C13C2×D411yescharacteristic
76C2×C8×C13C2×D411yescharacteristic
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13C2×C811yescharacteristic
83C4⋊Dic13C2×C811yescharacteristic
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—21no—
87C4×Dic13C22⋊C411yescharacteristic
88C4×Dic13C22⋊C411yescharacteristic
89C4×Dic13C2×C811yescharacteristic
90C4×Dic13C2×C811yescharacteristic
91#6099—41no—
92C2×#1055—21no—
93C2×#1055—41no—
94C2×#1055C22⋊C411yescharacteristic
95C2×#1055C22⋊C411yescharacteristic
96C13×C16—41no—
97C13×C16—41no—
98#6090—41no—
99#6090—41no—
100#2922—131no—
101#2163—131no—
102#2162—131no—
103#1323—131no—
104#1323—131no—
105#1315—131no—
106#1315D1311yescharacteristic
107C23×C13—21no—
108C23×C13C2×M1611yescharacteristic
109Q8×C13—41no—
110D4×C13—41no—
111D4×C13—42no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13C2×C22⋊C411yescharacteristic
118C2×C4×C13C22×C811yescharacteristic
119C2×Dic13—22no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—41no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13C22⋊C811yescharacteristic
126C2×Dic13C22⋊C811yescharacteristic
127C2×Dic13C22⋊C811yescharacteristic
128C2×Dic13C22⋊C811yescharacteristic
129C8×C13—21no—
130C8×C13—21no—
131C8×C13—41no—
132#1055—21no—
133#1055—21no—
134#1055—41no—
135C4×#41—131no—
136#433—261no—
137#433—261no—
138#431—261no—
139#431—261no—
140#424—131no—
141#424—131no—
142#408—131no—
143#408C2×D1311yescharacteristic
144C4×M16—131no—
145C2×C4×C8—131no—
146C4⋊C16—261no—
147C4⋊C16—261no—
148C22⋊C16—131no—
149C22⋊C16—131no—
150C22⋊C16C2×D1311yescharacteristic
151C22⋊C16C2×D1311yescharacteristic
152#346—261no—
153C4×C16—261no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13C2×C22⋊C811yescharacteristic
161C4×C13—21no—
162C4×C13—41no—
163C4×C13#41011yescharacteristic
164C4×C13#41311yescharacteristic
165Dic13—21no—
166Dic13—21no—
167Dic13—21no—
168Dic13—41no—
169Dic13—41no—
170Dic13#35012yes—
171C2×#41C4×D1311yescharacteristic
172C2×M16—131no—
173C2×M16C4×D1311yescharacteristic
174C22×C8—131no—
175C22×C8C22×D1311yescharacteristic
176C4×Q8—131no—
177C4×Q8—131no—
178C4×D4—131no—
179C4×D4—131no—
180C4×D4—261no—
181C4×D4—261no—
182#117—131no—
183#117—261no—
184C2×C42—131no—
185C2×C42—261no—
186C2×C16—21no—
187C2×C16—21no—
188C2×C16—261no—
189C2×C16—261no—
190C4⋊C8—261no—
191C4⋊C8—261no—
192C4⋊C8—261no—
193C4⋊C8—261no—
194C22⋊C8—21no—
195C22⋊C8—21no—
196C22⋊C8—261no—
197C22⋊C8—261no—
198#97—261no—
199C4×C8—131no—
200C4×C8—131no—
201C4×C8—131no—
202C4×C8—131no—
203C4×C8—261no—
204C2×C13—41no—
205C2×C13—81no—
206C2×C13#145811yescharacteristic
207C2×C13C2×#35011yescharacteristic
208C2×C13#211711yescharacteristic
209#41—41no—
210#41—41no—
211C2×Q8C8×D1311yescharacteristic
212C2×D4—21no—
213C2×D4C8×D1311yescharacteristic
214C22×C4—21no—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—261no—
218C22×C4—261no—
219C22×C4C2×C4×D1311yescharacteristic
220M16—41no—
221M16—521no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8—131no—
225C2×C8—131no—
226C2×C8—261no—
227C2×C8—521no—
228C2×C8D4×D1311yescharacteristic
229C2×C8D4×D1311yescharacteristic
230C4⋊C4—131no—
231C4⋊C4—131no—
232C4⋊C4—261no—
233C4⋊C4—261no—
234C22⋊C4—261no—
235C22⋊C4—261no—
236C22⋊C4—261no—
237C42—131no—
238C42—131no—
239C42—131no—
240C42—131no—
241C42—261no—
242C42—261no—
243C42—261no—
244C16—41no—
245C16—41no—
246C16—521no—
247C16—521no—
248C13#1146411yescharacteristic, complemented, Sylow
249C23—21no—
250C23M16×D1311yescharacteristic
251Q8—41no—
252D4—41no—
253D4—42no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—131no—
260C2×C4—131no—
261C2×C4—131no—
262C2×C4—131no—
263C2×C4—262no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—522no—
267C2×C4—521no—
268C2×C4—522no—
269C2×C4C22⋊C4×D1311yescharacteristic
270C2×C4C2×C8×D1311yescharacteristic
271C8—21no—
272C8—21no—
273C8—41no—
274C8—261no—
275C8—261no—
276C8—521no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22D13×C22⋊C811yescharacteristic
284C4—21no—
285C4—41no—
286C4—132no—
287C4—261no—
288C4—261no—
289C4—261no—
290C4—521no—
291C4—521no—
292C4#1171840111yescharacteristic
293C4#1171840611yescharacteristic
294C2—41no—
295C2—81no—
296C2#1311314711yescharacteristic
297C2D13×#35011yescharacteristic
298C2#1311646211yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#1315C2
socleC22×C13C2×C22⋊C8
prime radicalC2×C13×#41C2×C4
cosocleC22×C8×C13C23
hypercenter#1315D13
hypocenterC13#11464
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #13116636C2semidirect
3. #13116632C2semidirect
4. #13112777C2semidirect
5. #13112777C2semidirect
248. C13#11464semidirect

Maximal subgroups

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

subgroupindex
#131234762
#131166362
#131166322
#131127772
#131127622
C13×#13152
#1146413