Finite Group Databasebeta

← #16787407

Subgroups — #16787407

Order 3328.

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

normal subgroups only

This group has 362 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#13131195C211yesmaximal, characteristic, complemented
2D13⋊(C4⋊C16)C211yesmaximal, 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#11718260—21no—
19#11718260—21no—
20#11718259—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—42no—
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#11621—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—41no—
87C2×#1055—41no—
88C2×#1055C2×D411yescharacteristic
89C2×#1055C2×D411yescharacteristic
90C8×D13—21no—
91C8×D13—21no—
92C8×D13—41no—
93#6092—42no—
94#6092—42no—
95C8×#41—131no—
96#2162—131no—
97C2×C4⋊C16—131no—
98Q8⋊C16—132no—
99D4⋊C16—132no—
100C23×C13—21no—
101C22×D13C22⋊C811yescharacteristic
102D4×C13—21no—
103D4×C13C2×C1612yescomplemented
104C2×C4×C13—21no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13C2×C22⋊C411yescharacteristic
108C2×C4×C13C22×C811yescharacteristic
109C2×C4×C13C2×M1611yescharacteristic
110C22⋊D13—24no—
111C2×Dic13—21no—
112C2×Dic13—24no—
113C2×Dic13—21no—
114C2×Dic13—42no—
115C2×Dic13C22⋊C811yescharacteristic
116C2×Dic13C22⋊C811yescharacteristic
117C2×Dic13C22⋊C811yescharacteristic
118C4×D13—21no—
119C4×D13—21no—
120C4×D13—41no—
121C4×D13C2×C1612yes—
122C4×D13M3212yes—
123Dic26—21no—
124Dic26C2×C1612yescomplemented
125C8×C13—21no—
126C8×C13—21no—
127C8×C13—41no—
128#1055—21no—
129#1055—41no—
130#1055AGL(1,ℤ/8)11yescharacteristic
131#1055#13711yescharacteristic
132C4×#41—131no—
133C22×C16—261no—
134C8×Q8—131no—
135C8×Q8—131no—
136C8×D4—131no—
137C8×D4—261no—
138C8×D4—261no—
139C8×D4#26111yescharacteristic
140#431—131no—
141#431—261no—
142C2×C4×C8—131no—
143C2×C4×C8—261no—
144C4⋊C16—132no—
145C4⋊C16—261no—
146C4⋊C16—261no—
147C22⋊C16—261no—
148C4×C16—132no—
149C22×C13—22no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13C2×C22⋊C811yescharacteristic
153C2×D13—21no—
154C2×D13—21no—
155C2×D13C22⋊C1612yes—
156C4×C13—21no—
157C4×C13—41no—
158C4×C13#41711yescharacteristic
159C4×C13#42111yescharacteristic
160C4×C13C22×C1611yescharacteristic
161C4×C13C2×M3211yescharacteristic
162Dic13—22no—
163Dic13—21no—
164Dic13—21no—
165Dic13—41no—
166Dic13C22⋊C1612yes—
167C2×#41—131no—
168C22×C8—21no—
169C22×C8—131no—
170C22×C8—131no—
171C22×C8—261no—
172C4×Q8—131no—
173C4×Q8—131no—
174C4×D4—131no—
175C4×D4—261no—
176C4×D4—261no—
177C4×D4C2×#26111yescharacteristic
178#117—131no—
179#117—261no—
180C2×C42—131no—
181C2×C42—261no—
182C2×C16—262no—
183C2×C16—262no—
184C2×C16—522no—
185C4⋊C8—131no—
186C4⋊C8—261no—
187C4⋊C8—261no—
188C4⋊C8C2×#26111yescharacteristic
189C22⋊C8—21no—
190C22⋊C8—261no—
191C22⋊C8—261no—
192C4×C8—131no—
193C4×C8—131no—
194C4×C8—131no—
195C4×C8—261no—
196C4×C8—261no—
197C4×C8—261no—
198C4×C8C2×#26111yescharacteristic
199C2×C13—42no—
200C2×C13#147711yescharacteristic
201C2×C13C2×C22⋊C1611yescharacteristic
202C2×C13#211711yescharacteristic
203D13—22no—
204#41—134no—
205#41—262no—
206C2×Q8—131no—
207C2×D4—261no—
208C2×D4D13⋊C811yescharacteristic
209C22×C4—21no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—261no—
214C22×C4—261no—
215C2×C8—21no—
216C2×C8—42no—
217C2×C8—131no—
218C2×C8—131no—
219C2×C8—261no—
220C2×C8—261no—
221C2×C8—261no—
222C2×C8—521no—
223C2×C8—521no—
224C2×C8—521no—
225C2×C8C22⋊#26111yescharacteristic
226C2×C8C22⋊#26111yescharacteristic
227C4⋊C4—131no—
228C4⋊C4—261no—
229C4⋊C4—261no—
230C4⋊C4D13⋊C811yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—261no—
233C22⋊C4—261no—
234C42—131no—
235C42—131no—
236C42—131no—
237C42—261no—
238C42—261no—
239C42—261no—
240C42C22×#26111yescharacteristic
241C16—522no—
242C16—522no—
243C13#1162111yescharacteristic, complemented, Sylow
244C23—21no—
245C23—131no—
246Q8—132no—
247Q8—261no—
248D4—21no—
249D4—264no—
250D4D13⋊C1612yescomplemented
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—131no—
255C2×C4—132no—
256C2×C4—132no—
257C2×C4—131no—
258C2×C4—131no—
259C2×C4—264no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—521no—
265C2×C4—522no—
266C2×C4C2×D13⋊C811yescharacteristic
267C2×C4D13⋊M1611yescharacteristic
268C2×C4C2×C22⋊#26111yescharacteristic
269C8—21no—
270C8—21no—
271C8—41no—
272C8—131no—
273C8—131no—
274C8—261no—
275C8—521no—
276C22—22no—
277C22—41no—
278C22—41no—
279C22—132no—
280C22—261no—
281C22—261no—
282C22D13⋊(C22⋊C8)11yescharacteristic
283C4—21no—
284C4—41no—
285C4—132no—
286C4—262no—
287C4—261no—
288C4—261no—
289C4—521no—
290C4C2×D13⋊C1611yescharacteristic
291C4D13⋊M3211yescharacteristic
292C4#1171914011yescharacteristic
293C4#1171916411yescharacteristic
294C2—42no—
295C2—262no—
296C2#1313013211yescharacteristic
297C2D13⋊(C22⋊C16)11yescharacteristic
298C2#1313107911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC4×C13C22×C16
FrattiniC42C22×#261
FittingC8×D4×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC2×#6129C8
cosocleC4×#1055C23
hypercenterC8×D4#261
hypocenterC13#11621
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #13131195C2semidirect
2. D13⋊(C4⋊C16)C2semidirect
3. #13129803C2semidirect
4. D4⋊#6092C2semidirect
62. #6129C16semidirect
103. D4×C13C2×C16semidirect
124. Dic26C2×C16semidirect
243. C13#11621semidirect
250. D4D13⋊C16semidirect

Maximal subgroups

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

subgroupindex
#131311952
D13⋊(C4⋊C16)2
#131298032
D4⋊#60922
C8×#61292
#1162113