Finite Group Databasebeta

← #13113389

Subgroups — #13113389

Order 1664.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#11719311C211yesmaximal, characteristic
2D13×C22⋊C8C211yesmaximal, characteristic, complemented
3#11718325C211yesmaximal, characteristic, complemented
4C13×#327C211yesmaximal, characteristic, complemented
5#11718129C211yesmaximal, characteristic, complemented
6#11718059C211yesmaximal, characteristic, complemented
7#11718044C211yesmaximal, characteristic, complemented
8C2×#6129C411yescharacteristic, complemented
9C22×C4×D13C2211yescharacteristic
10C13×#121C2211yescharacteristic
11#88192C411yescharacteristic, complemented
12#88191—21no—
13D4×Dic13—21no—
14C2×#6103—21no—
15#88178C2211yescharacteristic
16C2×C8×D13—21no—
17#88151C411yescharacteristic, complemented
18#88146C411yescharacteristic, complemented
19#88137—21no—
20#88135—21no—
21C13×C22⋊C8C2211yescharacteristic
22C13×#95C2211yescharacteristic
23#88071—21no—
24#88071C2211yescharacteristic
25C22⋊#1055C2211yescharacteristic
26#88060—21no—
27C23×D13D411yescharacteristic
28C2×D4×C13—21no—
29C2×D4×C13C2×C411yescharacteristic
30C22×C4×C13—21no—
31C22×C4×C13C2311yescharacteristic
32C2×C22⋊D13—21no—
33C2×C22⋊D13—21no—
34C22×Dic13—21no—
35C22×Dic13—21no—
36C22×Dic13D411yescharacteristic
37#6129—42no—
38C2×C4×D13—42no—
39C2×C4×D13C2×C411yescharacteristic
40C2×C4×D13C2×C411yescharacteristic
41C2×C4×D13D411yescharacteristic
42C2×C4×D13D411yescharacteristic
43C2×Dic26C2×C411yescharacteristic
44C2×C8×C13—21no—
45C13×C4⋊C4C2×C411yescharacteristic
46C13×C22⋊C4—21no—
47C22⋊Dic13—21no—
48C22⋊Dic13—21no—
49#6103—21no—
50#6103—21no—
51#6103—42no—
52C4⋊Dic13—21no—
53C4⋊Dic13C2×C411yescharacteristic
54#6101—21no—
55C4×Dic13—21no—
56C2×#1055—21no—
57C8×D13—42no—
58#1516—131nomaximal, Sylow
59C23×C13—21no—
60C23×C13C2×D411yescharacteristic
61C22×D13—21no—
62C22×D13—21no—
63C22×D13—22no—
64C22×D13—41no—
65C22×D13C22⋊C411yescharacteristic
66C22×D13C22⋊C411yescharacteristic
67D4×C13—41no—
68D4×C13—41no—
69D4×C13—41no—
70C2×C4×C13—21no—
71C2×C4×C13—41no—
72C2×C4×C13—41no—
73C2×C4×C13—41no—
74C2×C4×C13—41no—
75C2×C4×C13C22×C411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C22⋊D13—42no—
78C22⋊D13—42no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—41no—
82C2×Dic13—42no—
83C2×Dic13—41no—
84C2×Dic13—41no—
85C2×Dic13—41no—
86C2×Dic13C22⋊C411yescharacteristic
87C2×Dic13C22⋊C411yescharacteristic
88C4×D13—22no—
89C4×D13—22no—
90C4×D13—41no—
91C4×D13—41no—
92Dic26—41no—
93C8×C13—41no—
94#1055—41no—
95#525—131no—
96C2×C22⋊C8—131no—
97#381—131no—
98#328—131no—
99#328—131no—
100#327—131no—
101#327D1311yescharacteristic, complemented
102C22×C13—21no—
103C22×C13—21no—
104C22×C13—41no—
105C22×C13—41no—
106C22×C13—41no—
107C22×C13C2×C22⋊C411yescharacteristic
108C22×C13#13511yescharacteristic
109C22×C13#13511yescharacteristic
110C2×D13—21no—
111C2×D13—21no—
112C2×D13—21no—
113C2×D13—21no—
114C2×D13—21no—
115C2×D13—42no—
116C2×D13—42no—
117C2×D13#9912yes—
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—41no—
121C4×C13—81no—
122Dic13—21no—
123Dic13—21no—
124Dic13—41no—
125Dic13—41no—
126Dic13—81no—
127C2×#41—131no—
128C23×C4—131no—
129C22×C8—261no—
130#123—261no—
131C22⋊Q8—131no—
132C22⋊Q8—131no—
133#121—131no—
134#121C2×D1311yescharacteristic
135#120—261no—
136C4×D4—261no—
137C4×D4—261no—
138#117—131no—
139C2×C22⋊C4—261no—
140C22⋊C8—131no—
141C22⋊C8—261no—
142C22⋊C8C2×D1311yescharacteristic
143#95—131no—
144#95—261no—
145#95C2×D1311yescharacteristic
146C2×C13—21no—
147C2×C13—21no—
148C2×C13—81no—
149C2×C13C2×#9911yescharacteristic
150C2×C13#41611yescharacteristic
151C2×C13#42111yescharacteristic
152D13—22no—
153D13—41no—
154C24—131no—
155#41—522no—
156C2×Q8—131no—
157C2×D4—21no—
158C2×D4—261no—
159C2×D4—261no—
160C2×D4C4×D1311yescharacteristic
161C22×C4—21no—
162C22×C4—131no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—261no—
168C22×C4—261no—
169C22×C4—522no—
170C22×C4C22×D1311yescharacteristic
171C2×C8—21no—
172C2×C8—261no—
173C2×C8—522no—
174C4⋊C4—131no—
175C4⋊C4—261no—
176C4⋊C4—261no—
177C4⋊C4C4×D1311yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—261no—
180C22⋊C4—261no—
181C22⋊C4—261no—
182C22⋊C4—261no—
183C22⋊C4—522no—
184C42—261no—
185C13#151611yescharacteristic, complemented, Sylow
186C23—21no—
187C23—131no—
188C23—131no—
189C23—262no—
190C23—261no—
191C23—261no—
192C23—521no—
193C23D4×D1311yescharacteristic
194Q8—521no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—522no—
199D4—522no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—131no—
206C2×C4—131no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—521no—
212C2×C4—521no—
213C2×C4—521no—
214C2×C4—522no—
215C2×C4—521no—
216C2×C4—521no—
217C2×C4—521no—
218C2×C4C2×C4×D1311yescharacteristic
219C2×C4D4×D1311yescharacteristic
220C8—41no—
221C8—521no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—132no—
228C22—261no—
229C22—261no—
230C22—261no—
231C22—261no—
232C22—261no—
233C22—522no—
234C22—522no—
235C22C22⋊C4×D1311yescharacteristic
236C22#8816611yescharacteristic
237C22#8817011yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—261no—
243C4—261no—
244C4—521no—
245C4—521no—
246C4—1041no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—262no—
251C2—521no—
252C2D13×#9911yescharacteristic
253C2#1171843311yescharacteristic
254C2#1171848211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#327C2
socleC22×C13C2×C22⋊C4
prime radical#11719311C2
cosocleC22×C4×C13C23
hypercenter#327D13
hypocenterC13#1516
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. D13×C22⋊C8C2semidirect
3. #11718325C2semidirect
4. C13×#327C2semidirect
5. #11718129C2semidirect
6. #11718059C2semidirect
7. #11718044C2semidirect
8. C2×#6129C4semidirect
11. #88192C4semidirect
17. #88151C4semidirect
18. #88146C4semidirect
101. #327D13semidirect
185. C13#1516semidirect

Maximal subgroups

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

subgroupindex
#117193112
D13×C22⋊C82
#117183252
C13×#3272
#117181292
#117180592
#117180442
#151613