Finite Group Databasebeta

← #15767916

Subgroups — #15767916

Order 3328.

304 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115776C211yesmaximal, characteristic
2#13114977C211yesmaximal, characteristic
3#13113611C211yesmaximal, characteristic
4#13113607C211yesmaximal, characteristic
5#13113266C211yesmaximal, characteristic
6#13113266C211yesmaximal, characteristic
7C13×#1275C211yesmaximal, characteristic
8C2×C4×Dic26C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C2×C13×#97C2211yescharacteristic
12#11718585C2211yescharacteristic
13#11718585C2211yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15#11718144—22no—
16#11718142—22no—
17#11718050—22no—
18#11718049—22no—
19#11718048—22no—
20#11718048—22no—
21C22×Dic26Q811yescharacteristic
22C22×C8×C13D412yes—
23C2×C42×C13C2311yescharacteristic
24C2×C4⋊Dic13Q811yescharacteristic
25C2×#6101—21no—
26C2×C4×Dic13—21no—
27C2×#6099—21no—
28C2×#6099—21no—
29C22×#1055—21no—
30C4×Dic26—21no—
31C4×Dic26—21no—
32C4×Dic26—21no—
33C4×Dic26—21no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C22⋊C8—21no—
37C13×C22⋊C8—21no—
38C13×#97—21no—
39C13×#97—21no—
40C4×C8×C13D412yes—
41C4×C8×C13D412yes—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48#10664—131nomaximal, Sylow
49C22×C4×C13C2×D411yescharacteristic
50C22×C4×C13C2×Q811yescharacteristic
51C22×C4×C13#4111yescharacteristic
52C22×Dic13—21no—
53C22×Dic13—21no—
54C2×Dic26—21no—
55C2×Dic26—21no—
56C2×Dic26—42no—
57C2×C8×C13—22no—
58C2×C8×C13—22no—
59C2×C8×C13—22no—
60C2×C8×C13—22no—
61C2×C8×C13—22no—
62C42×C13C2×D411yescharacteristic
63C42×C13C2×D411yescharacteristic
64C42×C13#4111yescharacteristic
65C42×C13#4111yescharacteristic
66C4⋊Dic13—21no—
67C4⋊Dic13—21no—
68#6101—41no—
69#6101—41no—
70C4×Dic13—41no—
71C4×Dic13—41no—
72#6099—42no—
73#6099—42no—
74C2×#1055—41no—
75C2×#1055—41no—
76C2×#1055—41no—
77C2×#1055—42no—
78#1985—131no—
79#1838—131no—
80#1571—131no—
81#1570—131no—
82#1487—131no—
83#1487—131no—
84#1275D1311yescharacteristic
85C23×C13C22⋊Q811yescharacteristic
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13C22⋊Q811yescharacteristic
89C2×C4×C13C22⋊Q811yescharacteristic
90C2×C4×C13#12311yescharacteristic
91C2×C4×C13#12311yescharacteristic
92C2×C4×C13#12311yescharacteristic
93C2×C4×C13#12711yescharacteristic
94C2×C4×C13#13512yes—
95C2×C4×C13#13712yes—
96C2×Dic13—22no—
97C2×Dic13—41no—
98C2×Dic13—41no—
99C2×Dic13—42no—
100C2×Dic13—41no—
101Dic26—22no—
102Dic26—22no—
103Dic26—41no—
104Dic26—41no—
105C8×C13—42no—
106C8×C13—42no—
107C8×C13—42no—
108#1055—81no—
109#1055—81no—
110#1055—81no—
111C2×C4×Q8—131no—
112#431C2×D1311yescharacteristic
113#431C2×D1311yescharacteristic
114#423—131no—
115#423—131no—
116C2×C4⋊C8—131no—
117C2×#97C2×D1311yescharacteristic
118#341—262no—
119#336—262no—
120#335—262no—
121#334—262no—
122Q8⋊C8—262no—
123Q8⋊C8—262no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13#39911yescharacteristic
127C22×C13#47912yes—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13#48512yes—
133C4×C13#49511yescharacteristic
134C4×C13#49711yescharacteristic
135Dic13—42no—
136Dic13—81no—
137C22×Q8—131no—
138C2×M16—261no—
139C2×M16—261no—
140C22×C8—261no—
141C22×C8D5212yes—
142C4×Q8—261no—
143C4×Q8—261no—
144C4×Q8—261no—
145C4×Q8—261no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4—261no—
148C2×C42—261no—
149C2×C42C22×D1311yescharacteristic
150C4⋊C8—21no—
151C4⋊C8—21no—
152C4⋊C8—261no—
153C4⋊C8—261no—
154C4⋊C8—261no—
155C4⋊C8—261no—
156C4⋊C8—261no—
157C4⋊C8—261no—
158C22⋊C8—21no—
159C22⋊C8—21no—
160#97—21no—
161#97—21no—
162C4×C8D5212yes—
163C4×C8D5212yes—
164C2×C13—22no—
165C2×C13#209111yescharacteristic
166C2×C13#209711yescharacteristic
167C2×C13#209811yescharacteristic
168C2×Q8—261no—
169C2×Q8—261no—
170C2×Q8—522no—
171C22×C4—261no—
172C22×C4—261no—
173C22×C4C2×D5211yescharacteristic
174C22×C4#612911yescharacteristic
175C22×C4Q8×D1311yescharacteristic
176M16—522no—
177M16—522no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—22no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—521no—
184C2×C8—521no—
185C2×C8—521no—
186C2×C8—522no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4—521no—
190C4⋊C4—521no—
191C42—521no—
192C42—521no—
193C42C2×D5211yescharacteristic
194C42C2×D5211yescharacteristic
195C42#612911yescharacteristic
196C42#612911yescharacteristic
197C13#1066411yescharacteristic, complemented, Sylow
198C23#8815111yescharacteristic
199Q8—262no—
200Q8—262no—
201Q8—521no—
202Q8—521no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—262no—
206C2×C4—521no—
207C2×C4—521no—
208C2×C4—522no—
209C2×C4—521no—
210C2×C4#8812811yescharacteristic
211C2×C4#8814011yescharacteristic
212C2×C4#8814011yescharacteristic
213C2×C4#8814011yescharacteristic
214C2×C4#8815111yescharacteristic
215C2×C4#8815111yescharacteristic
216C2×C4#8815812yes—
217C2×C4#8816312yes—
218C8—42no—
219C8—42no—
220C8—42no—
221C8—1041no—
222C8—1041no—
223C8—1041no—
224C22—21no—
225C22—21no—
226C22#1171833811yescharacteristic
227C22#1171849012yes—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—522no—
233C4—1041no—
234C4#1171835711yescharacteristic
235C4#1171837611yescharacteristic
236C4#1171838412yes—
237C2—22no—
238C2#1311635311yescharacteristic
239C2#1311638311yescharacteristic
240C2#1311639011yescharacteristic
subgroupG/H
centerC2×C4#88128
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1275C2
socleC22×C13#399
prime radicalC23×C13C22⋊Q8
hypercenter#1275D13
hypocenterC13#10664
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
197. C13#10664semidirect

Maximal subgroups

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

subgroupindex
#131157762
#131149772
#131136112
#131136072
#131132662
C13×#12752
#1066413