Finite Group Databasebeta

← #16786906

Subgroups — #16786906

Order 3328.

428 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 90 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#13130078C212yesmaximal
2#13129779C212yesmaximal
3#13129766C212yesmaximal
4C4×#88198C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic
6C2×#88198C411yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8#11719125—22no—
9#11718891C2211yescharacteristic
10#11718637C2211yescharacteristic
11#11718635C411yescharacteristic
12#11718633—22no—
13C4×#6101—22no—
14C42×Dic13C411yescharacteristic
15#11718286—22no—
16#11718285C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×Dic26C2×C411yescharacteristic
19C4×Q8×C13—41no—
20C4×Q8×C13—41no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C42×C13—21no—
24C2×C42×C13C2×C411yescharacteristic
25#88198—22no—
26#88198C814yescomplemented
27C2×C4⋊Dic13C2311yescharacteristic
28C2×#6101—22no—
29C2×#6101—22no—
30C2×#6101D412yes—
31C2×C4×Dic13—21no—
32C2×C4×Dic13—21no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13D412yes—
36C4×Dic26—41no—
37C4×Dic26—41no—
38C22⋊#1057—24no—
39#88112—42no—
40C4×#1057—42no—
41#88071—22no—
42#88071—22no—
43#11478—131nomaximal, Sylow
44C2×Q8×C13—21no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13C2×C812yes—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13C22⋊C411yescharacteristic
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22×C411yescharacteristic
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13C22⋊C412yes—
56C22×Dic13C2×D412yes—
57C2×Dic26—41no—
58C2×Dic26—41no—
59C2×Dic26C2×C812yes—
60C2×Dic26M1612yes—
61C2×#1057—44no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—42no—
64C42×C13—21no—
65C42×C13—21no—
66C42×C13—41no—
67C42×C13—41no—
68C4⋊Dic13—41no—
69#6101—28no—
70#6101—42no—
71#6101—44no—
72C4×Dic13—24no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75C4×Dic13—21no—
76C4×Dic13—42no—
77C4×Dic13—41no—
78C4×Dic13C2×C812yes—
79C4×C4⋊Q8—131no—
80#1461—132no—
81#1325—132no—
82#1319—132no—
83C23×C13C2×C22⋊C411yescharacteristic
84Q8×C13—42no—
85Q8×C13—42no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13#9911yescharacteristic
97C2×C4×C13#9911yescharacteristic
98C2×C4×C13C22×C811yescharacteristic
99C2×C4×C13C2×M1611yescharacteristic
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—42no—
110C2×Dic13C22⋊C814yes—
111Dic26—42no—
112Dic26—42no—
113#1057—84no—
114C2×C4⋊Q8—131no—
115C2×C4×Q8—131no—
116C2×C4×Q8#26111yescharacteristic
117#431—262no—
118#391—131no—
119#391—131no—
120#389—262no—
121#384—131no—
122C4×C4⋊C4—262no—
123C43—131no—
124#324—134no—
125#324—262no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13C2×C22⋊C811yescharacteristic
129C22×C13C2×#9911yescharacteristic
130C22×C13#41311yescharacteristic
131C4×C13—21no—
132C4×C13—21no—
133C4×C13—21no—
134C4×C13—41no—
135C4×C13—42no—
136C4×C13—81no—
137C4×C13#35612yes—
138Dic13—24no—
139Dic13—24no—
140Dic13—42no—
141Dic13—42no—
142C22×Q8—131no—
143C22×Q8C2×#26111yescharacteristic
144C4⋊Q8—134no—
145C4⋊Q8—262no—
146C4×Q8—41no—
147C4×Q8—41no—
148C4×Q8—521no—
149C4×Q8—521no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—132no—
152C2×C4⋊C4—131no—
153C2×C4⋊C4—262no—
154C2×C4⋊C4—262no—
155C2×C4⋊C4C2×#26111yescharacteristic
156C2×C42—21no—
157C2×C42—131no—
158C2×C42—132no—
159C2×C42—131no—
160C2×C42—261no—
161C2×C42—261no—
162C2×C42C2×#26111yescharacteristic
163C4⋊C8—522no—
164C22⋊C8—264no—
165C4×C8—522no—
166#95—262no—
167#95—262no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#145911yescharacteristic
171C2×C13#212611yescharacteristic
172C2×C13C2×#35611yescharacteristic
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—132no—
177C2×Q8—132no—
178C2×Q8—521no—
179C2×Q8—521no—
180C2×Q8D13⋊C812yes—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—132no—
184C22×C4—132no—
185C22×C4—261no—
186C22×C4—261no—
187C22×C4C22⋊#26111yescharacteristic
188C22×C4C22⋊#26111yescharacteristic
189C22×C4C22×#26111yescharacteristic
190C2×C8—524no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—268no—
194C4⋊C4—522no—
195C4⋊C4—521no—
196C4⋊C4—524no—
197C42—21no—
198C42—21no—
199C42—41no—
200C42—41no—
201C42—132no—
202C42—264no—
203C42—262no—
204C42—262no—
205C42—261no—
206C42—521no—
207C42—522no—
208C13#1147811yescharacteristic, complemented, Sylow
209C23C2×C22⋊#26111yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—522no—
213Q8—522no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—134no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—521no—
233C2×C4—521no—
234C2×C4—522no—
235C2×C4#8811911yescharacteristic
236C2×C4#8811911yescharacteristic
237C2×C4C2×D13⋊C811yescharacteristic
238C2×C4D13⋊M1611yescharacteristic
239C8—1044no—
240C22—21no—
241C22—21no—
242C22D13⋊(C22⋊C8)11yescharacteristic
243C22#1171913211yescharacteristic
244C22C2×#8811911yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—41no—
250C4—81no—
251C4—264no—
252C4—264no—
253C4—522no—
254C4—522no—
255C4#1171830112yes—
256C2—21no—
257C2—21no—
258C2#1313007111yescharacteristic
259C2#1313110711yescharacteristic
260C2C2×#1171830111yescharacteristic
subgroupG/H
centerC2×C4#88119
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#11478
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
26. #88198C8semidirect
208. C13#11478semidirect

Maximal subgroups

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

subgroupindex
#131300782
#131297792
#131297662
C4×#881982
#1147813