Finite Group Databasebeta

← #13127226

Subgroups — #13127226

Order 1664.

356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719216C212yesmaximal
2C2×C13×#107C211yesmaximal, characteristic, complemented
3#11718777C211yesmaximal, characteristic, complemented
4C8×C22⋊D13C211yesmaximal, characteristic
5#11718631C212yesmaximal, complemented
6#11718548C211yesmaximal, characteristic, complemented
7#11718545C212yesmaximal, complemented
8D13×#107C211yesmaximal, characteristic, complemented
9#11718536C212yesmaximal, complemented
10#11718535C211yesmaximal, characteristic, complemented
11#11718534C211yesmaximal, characteristic, complemented
12C22×C8×C13C2211yescharacteristic
13C2×C13×C4⋊C4C2212yes—
14C4×C22⋊D13—22no—
15C4×C22⋊D13C2211yescharacteristic
16#88178—22no—
17#88178C2212yes—
18C2×Dic52C2211yescharacteristic
19C2×C8×D13C2211yescharacteristic
20#88151C2212yes—
21#88150—22no—
22C4⋊C4×D13C2212yes—
23#88143—22no—
24#88142C2212yes—
25#88141C2212yes—
26C13×#107C2211yescharacteristic
27C13×#107C2211yescharacteristic
28C13×#107C2212yes—
29C22⋊#1055C2211yescharacteristic
30#88060C2211yescharacteristic
31#88058C2211yescharacteristic
32#88056C2212yes—
33#88054C2211yescharacteristic
34C8×Dic13C2211yescharacteristic
35#88050C2212yes—
36#88050C2212yes—
37#88047C2212yes—
38#88047C2212yes—
39C22×C4×C13—22no—
40C22×C4×C13C2311yescharacteristic
41C2×C22⋊D13D411yescharacteristic
42C2×C4×D13—22no—
43C2×C4×D13C2311yescharacteristic
44C2×Dic26—22no—
45C2×Dic26C2312yes—
46C2×C8×C13—22no—
47C2×C8×C13C2311yescharacteristic
48C2×C8×C13C2311yescharacteristic
49C13×C4⋊C4—22no—
50C13×C4⋊C4C2312yes—
51C13×C4⋊C4C2312yes—
52C22⋊Dic13—22no—
53C22⋊Dic13D411yescharacteristic
54#6103—22no—
55#6103D411yescharacteristic
56C4⋊Dic13—22no—
57C4⋊Dic13C2312yes—
58#6101—22no—
59#6101—22no—
60#6101—22no—
61#6101—22no—
62#6101D411yescharacteristic
63C4×Dic13—22no—
64C4×Dic13C2311yescharacteristic
65C2×#1055C2311yescharacteristic
66C2×#1055C2311yescharacteristic
67Dic52—22no—
68C8×D13—22no—
69#3338—131nomaximal, Sylow
70C23×C13C2×D411yescharacteristic
71C22×D13C2×D411yescharacteristic
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—82no—
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2411yescharacteristic
79C22⋊D13Q1614yescomplemented
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13C2×D411yescharacteristic
83C2×Dic13C2×D411yescharacteristic
84C2×Dic13C2×D411yescharacteristic
85C4×D13—21no—
86C4×D13—21no—
87C4×D13—82no—
88Dic26—22no—
89Dic26—22no—
90Dic26—82no—
91C8×C13—21no—
92C8×C13#4112yes—
93#1055—21no—
94#1055—21no—
95#554—132no—
96#500—131no—
97#484—132no—
98#484—132no—
99#477—132no—
100#467—131no—
101#467—131no—
102C4×Q16—131no—
103C8×D4—131no—
104C2×#107—131no—
105C2×#107D1311yescharacteristic, complemented
106C22×C13—21no—
107C22×C13—21no—
108C22×C13C2×Q1612yes—
109C22×C13C22×D411yescharacteristic
110C2×D13—21no—
111C2×D13—21no—
112C2×D13C2×Q1612yes—
113C4×C13—21no—
114C4×C13—42no—
115C4×C13—42no—
116C4×C13C2×#4111yescharacteristic
117C4×C132−1+411yescharacteristic
118Dic13—21no—
119Dic13—21no—
120Dic13—42no—
121Dic13—42no—
122Dic13C2×Q1612yes—
123C2×Q16—131no—
124C22×C8—131no—
125C22×C8C2×D1311yescharacteristic
126C4⋊Q8—132no—
127#125—262no—
128C22⋊Q8—132no—
129C22⋊Q8—132no—
130C22⋊Q8—262no—
131C22⋊Q8—262no—
132C4×Q8—132no—
133C4×D4—131no—
134C4×D4—262no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4C2×D1312yes—
137#107—131no—
138#107—132no—
139#107—132no—
140#107C2×D1311yescharacteristic
141#107C2×D1311yescharacteristic
142#107C2×D1312yes—
143C4⋊C8—131no—
144#103—132no—
145#103—132no—
146#103—132no—
147C22⋊C8—131no—
148C22⋊C8—131no—
149C4×C8—131no—
150C2×C13—22no—
151C2×C13#54711yescharacteristic
152C2×C13C22×Q1611yescharacteristic
153C2×C13#57611yescharacteristic
154D13—22no—
155C2×Q8—132no—
156C2×Q8—262no—
157C2×D4—131no—
158C22×C4—22no—
159C22×C4—131no—
160C22×C4—262no—
161C22×C4C22×D1311yescharacteristic
162Q16—262no—
163C2×C8—22no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8—262no—
167C2×C8C22×D1311yescharacteristic
168C2×C8C22×D1311yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—131no—
171C4⋊C4—132no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4C22×D1312yes—
178C4⋊C4C22×D1312yes—
179C22⋊C4—131no—
180C22⋊C4—131no—
181C22⋊C4—262no—
182C22⋊C4—262no—
183C42—131no—
184C42—262no—
185C13#333811yescharacteristic, complemented, Sylow
186C23—131no—
187C23D4×D1311yescharacteristic
188Q8—262no—
189Q8—262no—
190Q8—1042no—
191D4—134no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—82no—
197C2×C4—131no—
198C2×C4—131no—
199C2×C4—131no—
200C2×C4—261no—
201C2×C4—261no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—1042no—
205C2×C4D4×D1311yescharacteristic
206C2×C4C23×D1311yescharacteristic
207C8—21no—
208C8—261no—
209C8—261no—
210C8#612712yes—
211C22—21no—
212C22—21no—
213C22—132no—
214C22—261no—
215C22—261no—
216C22Q16×D1312yes—
217C22C2×D4×D1311yescharacteristic
218C4—21no—
219C4—42no—
220C4—42no—
221C4—132no—
222C4—261no—
223C4—261no—
224C4—522no—
225C4—522no—
226C4C2×#612711yescharacteristic
227C4#8825411yescharacteristic
228C2—22no—
229C2—262no—
230C2#1171921211yescharacteristic
231C2#1171946211yescharacteristic
232C2C2×Q16×D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#107C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenterC2×#107D13
hypocenterC13#3338
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C13×#107C2semidirect
3. #11718777C2semidirect
5. #11718631C2semidirect
6. #11718548C2semidirect
7. #11718545C2semidirect
8. D13×#107C2semidirect
9. #11718536C2semidirect
10. #11718535C2semidirect
11. #11718534C2semidirect
79. C22⋊D13Q16semidirect
105. C2×#107D13semidirect
185. C13#3338semidirect

Maximal subgroups

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

subgroupindex
#117192162
C2×C13×#1072
#117187772
C8×C22⋊D132
#117186312
#117185482
#117185452
D13×#1072
#117185362
#117185352
#117185342
#333813