Finite Group Databasebeta

← #16787360

Subgroups — #16787360

Order 3328.

334 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 106 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#13131169C211yesmaximal, characteristic
2C4×D13⋊C16C211yesmaximal, characteristic
3#13129803C212yesmaximal, complemented
4Q8⋊#6092C212yesmaximal, complemented
5#13123767C211yesmaximal, characteristic
6#11719283C411yescharacteristic
7C2×#88098—21no—
8C2×D13⋊C16—21no—
9C13×#446C411yescharacteristic
10Q8×#1055C2211yescharacteristic
11#11718500—21no—
12#11718498C411yescharacteristic
13#11718491—21no—
14#11718491C2211yescharacteristic
15#11718369—21no—
16#11718362—21no—
17C4×C8×D13C2211yescharacteristic
18#11718340C411yescharacteristic
19#11718260—21no—
20#11718257—21no—
21C4⋊#6092C2212yes—
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—
39#88098—42no—
40D13⋊C16—24no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8C2×C411yescharacteristic
43C13×#97—21no—
44C4×C8×C13C2×C411yescharacteristic
45#88055—21no—
46#88054—21no—
47#88054—21no—
48#88054—21no—
49C8×Dic13—21no—
50C8×Dic13D411yescharacteristic
51C8×Dic13D411yescharacteristic
52C4⋊#1055—21no—
53C4⋊#1055C2×C411yescharacteristic
54C4×#1055—21no—
55C4×#1055C2311yescharacteristic
56#11608—131nomaximal, Sylow
57C2×Q8×C13C2×C811yescharacteristic
58C2×C4×D13C22⋊C411yescharacteristic
59C2×C4×D13C2×C811yescharacteristic
60C2×C4×D13M1611yescharacteristic
61C2×Dic26—21no—
62C2×Dic26C2×C811yescharacteristic
63C2×C8×C13—21no—
64C2×C8×C13C22⋊C411yescharacteristic
65C2×C8×C13C22⋊C411yescharacteristic
66C13×C4⋊C4—21no—
67C13×C4⋊C4C2×C811yescharacteristic
68C42×C13—21no—
69C42×C13C22×C411yescharacteristic
70#6103—21no—
71#6103—21no—
72C4⋊Dic13—21no—
73C4⋊Dic13C2×C811yescharacteristic
74#6101—21no—
75#6101—21no—
76#6101—21no—
77#6101—21no—
78#6101—21no—
79C4×Dic13—21no—
80C4×Dic13C22⋊C411yescharacteristic
81C4×Dic13C2×C811yescharacteristic
82C4×Dic13M1611yescharacteristic
83C2×#1055—21no—
84C2×#1055C2×D411yescharacteristic
85C2×#1055C2×D411yescharacteristic
86#6094—42no—
87C8×D13—22no—
88C8×D13SD1612yes—
89C8×D13Q1612yes—
90#6092—24no—
91#6092—42no—
92#2960—131no—
93#2150—131no—
94C2×C4×C16—131no—
95Q8⋊C16—132no—
96Q8⋊C16—132no—
97C22×D13C22⋊C811yescharacteristic
98Q8×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13C2×C22⋊C411yescharacteristic
102C2×C4×C13C22×C811yescharacteristic
103C2×C4×C13C2×M1611yescharacteristic
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13C22⋊C811yescharacteristic
107C2×Dic13C22⋊C811yescharacteristic
108C2×Dic13C22⋊C811yescharacteristic
109C4×D13—22no—
110C4×D13—22no—
111C4×D13#10312yes—
112C4×D13#10412yes—
113Dic26—22no—
114Dic26—42no—
115C8×C13—21no—
116C8×C13—41no—
117C8×C13#10312yes—
118#1055—21no—
119#1055—41no—
120#1055C2×SD1611yescharacteristic
121#1055C2×Q1611yescharacteristic
122#533—131no—
123C2×M32—261no—
124C22×C16—261no—
125#446—131no—
126#446—261no—
127#446#26111yescharacteristic
128C8×Q8—131no—
129C8×Q8—131no—
130C8×Q8—261no—
131#424—261no—
132#423—131no—
133#405—261no—
134C2×C4×C8—131no—
135C4⋊C16—132no—
136C4⋊C16—261no—
137C4×C16—132no—
138C4×C16—261no—
139C22×C13C2×C22⋊C811yescharacteristic
140C2×D13—21no—
141C2×D13—21no—
142C2×D13Q8⋊C812yes—
143C4×C13—21no—
144C4×C13—41no—
145C4×C13—41no—
146C4×C13C2×#10311yescharacteristic
147C4×C13C2×#10411yescharacteristic
148C4×C13#50412yes—
149Dic13—21no—
150Dic13—41no—
151Dic13—41no—
152Dic13Q8⋊C812yes—
153Dic13#35012yes—
154C2×M16—261no—
155C22×C8—131no—
156C22×C8—131no—
157C4⋊Q8—131no—
158C4⋊Q8—131no—
159#125—261no—
160C22⋊Q8—131no—
161C22⋊Q8—131no—
162C22⋊Q8—261no—
163C4×Q8—131no—
164C4×Q8—261no—
165C4×Q8C2×#26111yescharacteristic
166#117—261no—
167C2×C42—131no—
168M32—522no—
169C2×C16—262no—
170C2×C16—264no—
171C2×C16—262no—
172C4⋊C8—21no—
173C4⋊C8—131no—
174C4⋊C8—261no—
175C4⋊C8—261no—
176C4⋊C8—261no—
177C4⋊C8—261no—
178C4⋊C8C2×#26111yescharacteristic
179#97—21no—
180#97—261no—
181C4×C8—131no—
182C4×C8—131no—
183C4×C8—131no—
184C4×C8—261no—
185C4×C8—261no—
186C4×C8C2×#26111yescharacteristic
187C2×C13C2×Q8⋊C811yescharacteristic
188C2×C13#211311yescharacteristic
189C2×C13C2×#35011yescharacteristic
190D13—22no—
191C2×Q8—131no—
192C2×Q8—261no—
193C2×Q8D13⋊C811yescharacteristic
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—131no—
197M16—522no—
198C2×C8—21no—
199C2×C8—131no—
200C2×C8—132no—
201C2×C8—132no—
202C2×C8—131no—
203C2×C8—262no—
204C2×C8—261no—
205C2×C8C22⋊#26111yescharacteristic
206C2×C8C22⋊#26111yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—131no—
209C4⋊C4—261no—
210C4⋊C4—261no—
211C4⋊C4—261no—
212C4⋊C4—261no—
213C4⋊C4—261no—
214C4⋊C4—261no—
215C4⋊C4D13⋊C811yescharacteristic
216C22⋊C4—261no—
217C22⋊C4—261no—
218C42—21no—
219C42—131no—
220C42—131no—
221C42—131no—
222C42—261no—
223C42C22×#26111yescharacteristic
224C16—264no—
225C16—522no—
226C13#1160811yescharacteristic, complemented, Sylow
227C23—131no—
228Q8—22no—
229Q8—262no—
230Q8—522no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—131no—
234C2×C4—131no—
235C2×C4—132no—
236C2×C4—132no—
237C2×C4—131no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—261no—
241C2×C4—261no—
242C2×C4C2×D13⋊C811yescharacteristic
243C2×C4D13⋊M1611yescharacteristic
244C2×C4C2×C22⋊#26111yescharacteristic
245C8—21no—
246C8—41no—
247C8—131no—
248C8—131no—
249C8—261no—
250C8—521no—
251C8#8811712yes—
252C22—132no—
253C22—261no—
254C22—261no—
255C22D13⋊(C22⋊C8)11yescharacteristic
256C4—21no—
257C4—41no—
258C4—41no—
259C4—132no—
260C4—132no—
261C4—261no—
262C4—521no—
263C4—521no—
264C4#1171909612yes—
265C4C2×#8811711yescharacteristic
266C4D13⋊#10411yescharacteristic
267C2—262no—
268C2D13⋊(Q8⋊C8)11yescharacteristic
269C2#1313106711yescharacteristic
270C2D13⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC42C22×#261
FittingC13×#446C4
socleC22×C13C2×C22⋊C8
prime radicalC22×D13C22⋊C8
cosocleC4×#1055C23
hypercenter#446#261
hypocenterC13#11608
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #446

Complements

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

NH ≅ G/Ntype
3. #13129803C2semidirect
4. Q8⋊#6092C2semidirect
226. C13#11608semidirect

Maximal subgroups

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

subgroupindex
#131311692
C4×D13⋊C162
#131298032
Q8⋊#60922
#131237672
#1160813