Finite Group Databasebeta

← #16787481

Subgroups — #16787481

Order 3328.

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

normal subgroups only

This group has 288 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#13131200C211yesmaximal, characteristic
2#13131199C211yesmaximal, characteristic
3#13129805C212yesmaximal, complemented
4#13129804C212yesmaximal, complemented
5#13123765C211yesmaximal, characteristic
6#11719283C411yescharacteristic
7C8×Q8×C13C411yescharacteristic
8#11718685C2211yescharacteristic
9#11718500—21no—
10#11718498C411yescharacteristic
11#11718492C2211yescharacteristic
12#11718489—21no—
13#11718350—21no—
14C4×C8×D13C2211yescharacteristic
15C8×Dic26—21no—
16C8×Dic26C411yescharacteristic
17#11718260—21no—
18#11718259—21no—
19#11718259—21no—
20#11718258—21no—
21#11718231C2212yes—
22C4⋊#6092C2212yes—
23C4×Q8×C13C2×C411yescharacteristic
24#88200C811yescharacteristic
25#88198C811yescharacteristic
26C2×#6094—21no—
27C2×C8×D13D411yescharacteristic
28C2×C8×D13D411yescharacteristic
29#88151C811yescharacteristic
30#88150—21no—
31#88143—21no—
32#88142C811yescharacteristic
33#88126—21no—
34C42×D13C2×C411yescharacteristic
35C4×Dic26—21no—
36C4×Dic26C2×C411yescharacteristic
37C2×#6092—22no—
38C2×#6092—22no—
39C13×C4⋊C8—21no—
40C13×C4⋊C8C2×C411yescharacteristic
41C4×C8×C13—21no—
42C4×C8×C13C2×C411yescharacteristic
43#88055—21no—
44#88054—21no—
45#88054—21no—
46#88054—21no—
47C8×Dic13—21no—
48C8×Dic13D411yescharacteristic
49C8×Dic13D411yescharacteristic
50C4⋊#1055—21no—
51C4⋊#1055C2×C411yescharacteristic
52#88043—21no—
53C4×#1055C2311yescharacteristic
54#11643—131nomaximal, Sylow
55C2×Q8×C13C2×C811yescharacteristic
56C2×C4×D13C22⋊C411yescharacteristic
57C2×C4×D13C2×C811yescharacteristic
58C2×C4×D13M1611yescharacteristic
59C2×Dic26—21no—
60C2×Dic26C2×C811yescharacteristic
61C2×C8×C13—21no—
62C2×C8×C13C22⋊C411yescharacteristic
63C2×C8×C13C22⋊C411yescharacteristic
64C13×C4⋊C4—21no—
65C13×C4⋊C4C2×C811yescharacteristic
66C42×C13—21no—
67C42×C13C22×C411yescharacteristic
68#6103—21no—
69#6103—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13C2×C811yescharacteristic
72#6101—21no—
73#6101—21no—
74#6101—21no—
75#6101—21no—
76#6101—21no—
77C4×Dic13—21no—
78C4×Dic13C22⋊C411yescharacteristic
79C4×Dic13C2×C811yescharacteristic
80C4×Dic13M1611yescharacteristic
81C2×#1055—21no—
82C2×#1055C2×D411yescharacteristic
83C2×#1055C2×D411yescharacteristic
84#6094—42no—
85C8×D13—22no—
86C8×D13—41no—
87#6092—42no—
88#6092—42no—
89#2960—131no—
90#2163—131no—
91#2163—131no—
92#1338—132no—
93#1338—132no—
94C22×D13C22⋊C811yescharacteristic
95Q8×C13—41no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13C22×C811yescharacteristic
100C2×C4×C13C2×M1611yescharacteristic
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13C22⋊C811yescharacteristic
104C2×Dic13C22⋊C811yescharacteristic
105C2×Dic13C22⋊C811yescharacteristic
106C4×D13—21no—
107C4×D13—21no—
108C4×D13—41no—
109C4×D13—41no—
110Dic26—42no—
111Dic26—41no—
112C8×C13—21no—
113C8×C13—21no—
114C8×C13—41no—
115#1055—21no—
116#1055—41no—
117#1055#13712yes—
118#533—131no—
119#446—131no—
120#446—131no—
121#446—261no—
122C8×Q8—131no—
123C8×Q8—261no—
124C8×Q8#26111yescharacteristic
125#424—261no—
126#423—131no—
127#405—261no—
128C2×C4×C8—131no—
129C4⋊C16—132no—
130C4⋊C16—261no—
131C22⋊C16—261no—
132C22⋊C16—261no—
133#346—132no—
134#346—261no—
135C22×C13C2×C22⋊C811yescharacteristic
136C2×D13—21no—
137C2×D13—21no—
138C2×D13—21no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13#41911yescharacteristic
144C4×C13#42111yescharacteristic
145Dic13—21no—
146Dic13—21no—
147Dic13—21no—
148Dic13—41no—
149Dic13—41no—
150C2×M16—261no—
151C22×C8—131no—
152C22×C8—131no—
153C4⋊Q8—131no—
154C4⋊Q8—131no—
155#125—261no—
156C22⋊Q8—131no—
157C22⋊Q8—131no—
158C22⋊Q8—261no—
159C4×Q8—131no—
160C4×Q8—261no—
161C4×Q8C2×#26111yescharacteristic
162#117—261no—
163C2×C42—131no—
164C2×C16—262no—
165C2×C16—262no—
166C4⋊C8—21no—
167C4⋊C8—131no—
168C4⋊C8—261no—
169C4⋊C8—261no—
170C4⋊C8—261no—
171C4⋊C8—261no—
172C4⋊C8C2×#26111yescharacteristic
173#97—261no—
174#97—261no—
175C4×C8—21no—
176C4×C8—131no—
177C4×C8—131no—
178C4×C8—131no—
179C4×C8—261no—
180C4×C8C2×#26111yescharacteristic
181C2×C13#147911yescharacteristic
182C2×C13#211511yescharacteristic
183C2×C13#211711yescharacteristic
184D13—41no—
185C2×Q8—131no—
186C2×Q8—261no—
187C2×Q8D13⋊C811yescharacteristic
188C22×C4—131no—
189C22×C4—131no—
190C22×C4—131no—
191M16—522no—
192C2×C8—21no—
193C2×C8—131no—
194C2×C8—131no—
195C2×C8—262no—
196C2×C8—261no—
197C2×C8—521no—
198C2×C8C22⋊#26111yescharacteristic
199C2×C8C22⋊#26111yescharacteristic
200C4⋊C4—21no—
201C4⋊C4—131no—
202C4⋊C4—261no—
203C4⋊C4—261no—
204C4⋊C4—261no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4—261no—
208C4⋊C4D13⋊C811yescharacteristic
209C22⋊C4—261no—
210C22⋊C4—261no—
211C42—21no—
212C42—131no—
213C42—131no—
214C42—131no—
215C42—261no—
216C42C22×#26111yescharacteristic
217C16—522no—
218C16—522no—
219C13#1164311yescharacteristic, complemented, Sylow
220C23—131no—
221Q8—41no—
222Q8—521no—
223Q8—522no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—131no—
227C2×C4—131no—
228C2×C4—131no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—521no—
234C2×C4—521no—
235C2×C4C2×D13⋊C811yescharacteristic
236C2×C4D13⋊M1611yescharacteristic
237C2×C4C2×C22⋊#26111yescharacteristic
238C8—21no—
239C8—21no—
240C8—41no—
241C8—132no—
242C8—261no—
243C8—521no—
244C22—261no—
245C22—261no—
246C22—261no—
247C22D13⋊(C22⋊C8)11yescharacteristic
248C4—21no—
249C4—21no—
250C4—41no—
251C4—41no—
252C4—261no—
253C4—261no—
254C4—261no—
255C4—521no—
256C4—521no—
257C4#1171915311yescharacteristic
258C4#1171916611yescharacteristic
259C2—521no—
260C2#1313013911yescharacteristic
261C2#1313107311yescharacteristic
262C2#1313107911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC42C22×#261
FittingC8×Q8×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC22×D13C22⋊C8
cosocleC4×#1055C23
hypercenterC8×Q8#261
hypocenterC13#11643
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
3. #13129805C2semidirect
4. #13129804C2semidirect
219. C13#11643semidirect

Maximal subgroups

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

subgroupindex
#131312002
#131311992
#131298052
#131298042
#131237652
#1164313