Finite Group Databasebeta

← #16787375

Subgroups — #16787375

Order 3328.

378 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 112 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#13131196C211yesmaximal, characteristic, complemented
2C4×D13⋊C16C211yesmaximal, characteristic, complemented
3#13129803C212yesmaximal, complemented
4D4⋊#6092C212yesmaximal, complemented
5C8×#6129C211yesmaximal, characteristic
6C4×#6129C411yescharacteristic
7C2×D13⋊C16—21no—
8C8×D4×C13C411yescharacteristic
9C8×C22⋊D13—21no—
10C2×C8×Dic13—21no—
11D4×#1055C2211yescharacteristic
12#11718494C411yescharacteristic
13#11718491C2211yescharacteristic
14#11718386—21no—
15#11718379—21no—
16C4×C8×D13C2211yescharacteristic
17C8×Dic26C411yescharacteristic
18#11718259—21no—
19#11718257—21no—
20#11718257—21no—
21C4⋊#6092C2212yes—
22C4×#6092C2212yes—
23C2×#6129C811yescharacteristic
24C22×C8×C13—21no—
25C4×D4×C13C2×C411yescharacteristic
26D4×Dic13C811yescharacteristic
27C4×C22⋊D13—21no—
28C2×C4×Dic13—21no—
29C22×#1055—21no—
30C2×C8×D13D411yescharacteristic
31C2×C8×D13D411yescharacteristic
32#88146C811yescharacteristic
33#88141C811yescharacteristic
34#88135—21no—
35#88131—21no—
36C42×D13C2×C411yescharacteristic
37C4×Dic26C2×C411yescharacteristic
38C2×#6092—22no—
39C2×#6092—22no—
40D13⋊C16—24no—
41C13×C4⋊C8C2×C411yescharacteristic
42C13×C22⋊C8—21no—
43C4×C8×C13C2×C411yescharacteristic
44C22⋊#1055—21no—
45#88060—21no—
46#88054—21no—
47#88054—21no—
48C8×Dic13—21no—
49C8×Dic13—21no—
50C8×Dic13—21no—
51C8×Dic13D411yescharacteristic
52C8×Dic13D411yescharacteristic
53C4⋊#1055C2×C411yescharacteristic
54C4×#1055C2311yescharacteristic
55#11613—131nomaximal, Sylow
56C2×D4×C13C2×C811yescharacteristic
57C22×C4×C13—21no—
58C2×C22⋊D13—21no—
59C22×Dic13—21no—
60C22×Dic13—21no—
61#6129—22no—
62#6129C1614yescomplemented
63C2×C4×D13C22⋊C411yescharacteristic
64C2×C4×D13C2×C811yescharacteristic
65C2×C4×D13M1611yescharacteristic
66C2×Dic26C2×C811yescharacteristic
67C2×C8×C13—21no—
68C2×C8×C13—42no—
69C2×C8×C13C22⋊C411yescharacteristic
70C2×C8×C13C22⋊C411yescharacteristic
71C13×C4⋊C4C2×C811yescharacteristic
72C13×C22⋊C4—21no—
73C42×C13C22×C411yescharacteristic
74C22⋊Dic13—21no—
75#6103—21no—
76C4⋊Dic13C2×C811yescharacteristic
77#6101—21no—
78#6101—21no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13—21no—
82C4×Dic13C22⋊C411yescharacteristic
83C4×Dic13C2×C811yescharacteristic
84C4×Dic13M1611yescharacteristic
85C2×#1055—21no—
86C2×#1055—42no—
87C2×#1055C2×D411yescharacteristic
88C2×#1055C2×D411yescharacteristic
89C8×D13—22no—
90C8×D13—22no—
91#6092—24no—
92#6092—42no—
93C8×#41—131no—
94#2162—131no—
95C2×C4×C16—131no—
96Q8⋊C16—132no—
97D4⋊C16—132no—
98C23×C13—21no—
99C22×D13C22⋊C811yescharacteristic
100D4×C13—21no—
101D4×C13C2×C1612yescomplemented
102C2×C4×C13—21no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13C2×C22⋊C411yescharacteristic
106C2×C4×C13C22×C811yescharacteristic
107C2×C4×C13C2×M1611yescharacteristic
108C22⋊D13—24no—
109C2×Dic13—21no—
110C2×Dic13—24no—
111C2×Dic13—21no—
112C2×Dic13—42no—
113C2×Dic13C22⋊C811yescharacteristic
114C2×Dic13C22⋊C811yescharacteristic
115C2×Dic13C22⋊C811yescharacteristic
116C4×D13—21no—
117C4×D13—21no—
118C4×D13—22no—
119C4×D13C2×C1612yes—
120C4×D13M3212yes—
121Dic26—21no—
122Dic26C2×C1612yescomplemented
123C8×C13—21no—
124C8×C13—41no—
125C8×C13#10412yes—
126#1055—21no—
127#1055—41no—
128#1055#13512yes—
129C4×#41—131no—
130C22×C16—261no—
131C8×Q8—131no—
132C8×Q8—131no—
133C8×D4—131no—
134C8×D4—261no—
135C8×D4—261no—
136C8×D4#26111yescharacteristic
137#431—131no—
138#431—261no—
139C2×C4×C8—131no—
140C2×C4×C8—261no—
141C4⋊C16—132no—
142C22⋊C16—261no—
143C4×C16—132no—
144C4×C16—261no—
145C4×C16—261no—
146C22×C13—22no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13C2×C22⋊C811yescharacteristic
150C2×D13—21no—
151C2×D13—21no—
152C2×D13C22⋊C1612yes—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13#41611yescharacteristic
156C4×C13C2×#10411yescharacteristic
157C4×C13C22×C1611yescharacteristic
158C4×C13C2×M3211yescharacteristic
159Dic13—22no—
160Dic13—21no—
161Dic13—41no—
162Dic13C22⋊C1612yes—
163Dic13#35012yes—
164C2×#41—131no—
165C22×C8—21no—
166C22×C8—131no—
167C22×C8—131no—
168C22×C8—261no—
169C4×Q8—131no—
170C4×Q8—131no—
171C4×D4—131no—
172C4×D4—261no—
173C4×D4—261no—
174C4×D4C2×#26111yescharacteristic
175#117—131no—
176#117—261no—
177C2×C42—131no—
178C2×C42—261no—
179C2×C16—262no—
180C2×C16—264no—
181C2×C16—262no—
182C4⋊C8—131no—
183C4⋊C8—261no—
184C4⋊C8—261no—
185C4⋊C8C2×#26111yescharacteristic
186C22⋊C8—21no—
187C22⋊C8—261no—
188C22⋊C8—261no—
189C4×C8—131no—
190C4×C8—131no—
191C4×C8—131no—
192C4×C8—261no—
193C4×C8—261no—
194C4×C8—261no—
195C4×C8C2×#26111yescharacteristic
196C2×C13—42no—
197C2×C13#147611yescharacteristic
198C2×C13C2×C22⋊C1611yescharacteristic
199C2×C13C2×#35011yescharacteristic
200D13—22no—
201#41—134no—
202#41—262no—
203C2×Q8—131no—
204C2×D4—261no—
205C2×D4D13⋊C811yescharacteristic
206C22×C4—21no—
207C22×C4—131no—
208C22×C4—131no—
209C22×C4—131no—
210C22×C4—261no—
211C22×C4—261no—
212C2×C8—21no—
213C2×C8—42no—
214C2×C8—131no—
215C2×C8—131no—
216C2×C8—262no—
217C2×C8—262no—
218C2×C8—261no—
219C2×C8—522no—
220C2×C8C22⋊#26111yescharacteristic
221C2×C8C22⋊#26111yescharacteristic
222C4⋊C4—131no—
223C4⋊C4—261no—
224C4⋊C4—261no—
225C4⋊C4D13⋊C811yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—261no—
228C22⋊C4—261no—
229C42—131no—
230C42—131no—
231C42—131no—
232C42—261no—
233C42—261no—
234C42—261no—
235C42C22×#26111yescharacteristic
236C16—264no—
237C16—522no—
238C13#1161311yescharacteristic, complemented, Sylow
239C23—21no—
240C23—131no—
241Q8—132no—
242Q8—261no—
243D4—21no—
244D4—264no—
245D4D13⋊C1612yescomplemented
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—131no—
250C2×C4—131no—
251C2×C4—132no—
252C2×C4—132no—
253C2×C4—131no—
254C2×C4—262no—
255C2×C4—264no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—522no—
261C2×C4C2×D13⋊C811yescharacteristic
262C2×C4D13⋊M1611yescharacteristic
263C2×C4C2×C22⋊#26111yescharacteristic
264C8—21no—
265C8—41no—
266C8—132no—
267C8—261no—
268C8—521no—
269C8#8811612yes—
270C22—22no—
271C22—41no—
272C22—41no—
273C22—132no—
274C22—261no—
275C22—261no—
276C22D13⋊(C22⋊C8)11yescharacteristic
277C4—21no—
278C4—41no—
279C4—132no—
280C4—132no—
281C4—262no—
282C4—261no—
283C4—521no—
284C4C2×D13⋊C1611yescharacteristic
285C4D13⋊M3211yescharacteristic
286C4C2×#8811611yescharacteristic
287C4#1171916511yescharacteristic
288C2—42no—
289C2—262no—
290C2#1313012811yescharacteristic
291C2D13⋊(C22⋊C16)11yescharacteristic
292C2D13⋊#35011yescharacteristic
subgroupG/H
centerC2×C8C22⋊#261
commutatorC4×C13C22×C16
FrattiniC42C22×#261
FittingC8×D4×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC2×#6129C8
cosocleC4×#1055C23
hypercenterC8×D4#261
hypocenterC13#11613
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #13131196C2semidirect
2. C4×D13⋊C16C2semidirect
3. #13129803C2semidirect
4. D4⋊#6092C2semidirect
62. #6129C16semidirect
101. D4×C13C2×C16semidirect
122. Dic26C2×C16semidirect
238. C13#11613semidirect
245. D4D13⋊C16semidirect

Maximal subgroups

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

subgroupindex
#131311962
C4×D13⋊C162
#131298032
D4⋊#60922
C8×#61292
#1161313