Finite Group Databasebeta

← #15756961

Subgroups — #15756961

Order 3328.

348 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 107 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#13115777C211yesmaximal, characteristic
2#13113622C212yesmaximal
3#13113160C211yesmaximal, characteristic
4#13112734C212yesmaximal
5C13×#2983C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C13×#446—22no—
8C13×#446—22no—
9C13×#432—21no—
10C13×#432C2212yes—
11C13×#431—21no—
12#11718586C2212yes—
13C2×C4⋊#1055C2211yescharacteristic
14C2×#88043C2211yescharacteristic
15#11718120C412yes—
16#11718120C412yes—
17#11718116—21no—
18#11718116—21no—
19#11718072—22no—
20#11718071—22no—
21C22×Q8×C13Q811yescharacteristic
22C4×Q8×C13—22no—
23C4×Q8×C13—22no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4Q811yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13C2311yescharacteristic
30C22×#1055—21no—
31C22×#1055—21no—
32C13×C4⋊C8—21no—
33C13×C4⋊C8—21no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C4⋊C8D412yes—
37C13×C4⋊C8D412yes—
38C13×C22⋊C8—22no—
39C13×#97—22no—
40C13×#97—22no—
41C4×C8×C13—22no—
42C22⋊#1055C2×C414yes—
43C4⋊#1055—22no—
44C4⋊#1055—22no—
45#88043—22no—
46C4×#1055—22no—
47#8865—131nomaximal, Sylow
48C2×Q8×C13—22no—
49C2×Q8×C13—22no—
50C2×Q8×C13—41no—
51C22×C4×C13C4⋊C411yescharacteristic
52C22×C4×C13C4⋊C411yescharacteristic
53C22×C4×C13C4⋊C411yescharacteristic
54C22×C4×C13C4⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13C2×Q811yescharacteristic
58C2×C8×C13—22no—
59C2×C8×C13—22no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—22no—
63C42×C13—21no—
64C42×C13—21no—
65C42×C13—21no—
66C42×C13—21no—
67C42×C13C2×D412yes—
68C42×C13#4112yes—
69C2×#1055—22no—
70C2×#1055—24no—
71C2×#1055—41no—
72C2×#1055—41no—
73C2×#1055—42no—
74C2×#1055—41no—
75#2983D1311yescharacteristic
76#1985—131no—
77#1573—132no—
78#1461—131no—
79#1302—132no—
80C23×C13C2×C4⋊C411yescharacteristic
81Q8×C13—44no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13#10812yes—
97C2×C4×C13C4×D412yes—
98C2×C4×C13#12011yescharacteristic
99C2×C4×C13C22⋊Q812yes—
100C2×C4×C13#12311yescharacteristic
101C8×C13—42no—
102C8×C13—42no—
103#1055—44no—
104#1055—42no—
105#1055—81no—
106C2×C4×Q8C2×D1311yescharacteristic
107#446—22no—
108#446—22no—
109#432—21no—
110#432C2×D1312yes—
111#431—21no—
112#431—132no—
113C2×C4⋊C8—131no—
114C2×#97—131no—
115#336—261no—
116#336—261no—
117#335—262no—
118#334—262no—
119#324—132no—
120#324—132no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#38511yescharacteristic
124C22×C13C2×#10811yescharacteristic
125C22×C13#43011yescharacteristic
126C4×C13—22no—
127C4×C13—22no—
128C4×C13—21no—
129C4×C13—22no—
130C4×C13—41no—
131C4×C13—41no—
132C4×C13—41no—
133C4×C13#45411yescharacteristic
134C4×C13#45611yescharacteristic
135C22×Q8Dic2611yescharacteristic
136C22×C8—261no—
137C22×C8—261no—
138C4×Q8—22no—
139C4×Q8—22no—
140C2×C4⋊C4Dic2611yescharacteristic
141C2×C4⋊C4C4×D1311yescharacteristic
142C2×C4⋊C4C4×D1311yescharacteristic
143C2×C42C22⋊D1311yescharacteristic
144C2×C42C22⋊D1311yescharacteristic
145C2×C42C22×D1311yescharacteristic
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—262no—
151C4⋊C8—262no—
152C4⋊C8C22⋊D1312yes—
153C4⋊C8C22⋊D1312yes—
154C22⋊C8—22no—
155C22⋊C8—134no—
156#97—22no—
157#97—22no—
158#97—262no—
159C4×C8—22no—
160C4×C8—262no—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13#185511yescharacteristic
164C2×C13#185711yescharacteristic
165C2×C13#186811yescharacteristic
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—41no—
169C22×C4#610111yescharacteristic
170C22×C4#610111yescharacteristic
171C22×C4#610111yescharacteristic
172C22×C4#610111yescharacteristic
173C22×C4C2×Dic2611yescharacteristic
174C22×C4C2×C4×D1311yescharacteristic
175C22×C4C2×C22⋊D1311yescharacteristic
176C2×C8—22no—
177C2×C8—22no—
178C2×C8—262no—
179C2×C8—264no—
180C2×C8—521no—
181C2×C8—521no—
182C2×C8—522no—
183C2×C8—521no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C42—21no—
188C42—21no—
189C42—21no—
190C42—21no—
191C42#612712yes—
192C42C2×C22⋊D1312yes—
193C13#886511yescharacteristic, complemented, Sylow
194C23C2×#610111yescharacteristic
195Q8—44no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4#8806212yes—
211C2×C4#8817812yes—
212C2×C4C4×C22⋊D1312yes—
213C2×C4#8818311yescharacteristic
214C2×C4#8820711yescharacteristic
215C8—42no—
216C8—42no—
217C8—524no—
218C8—522no—
219C8—1041no—
220C22—21no—
221C22—21no—
222C22C2×#8806211yescharacteristic
223C22#1171878511yescharacteristic
224C22#1171887111yescharacteristic
225C4—22no—
226C4—22no—
227C4—21no—
228C4—22no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4#1171890611yescharacteristic
233C4#1171890711yescharacteristic
234C2—21no—
235C2—21no—
236C2#1311504111yescharacteristic
237C2#1311505111yescharacteristic
238C2#1311512211yescharacteristic
subgroupG/H
centerC2×C4#88207
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#385
prime radicalC23×C13C2×C4⋊C4
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#8865
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
193. C13#8865semidirect

Maximal subgroups

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

subgroupindex
#131157772
#131136222
#131131602
#131127342
C13×#29832
#886513