Finite Group Databasebeta

← #13127746

Subgroups — #13127746

Order 1664.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C13×#554C211yesmaximal, characteristic
2Q8×Dic26C211yesmaximal, characteristic, complemented
3#11718752C211yesmaximal, characteristic, complemented
4#11718739C211yesmaximal, characteristic, complemented
5#11718726C212yesmaximal, complemented
6#11718724C212yesmaximal, complemented
7#11718685C211yesmaximal, characteristic, complemented
8#11718679C212yesmaximal
9C4×#6105C211yesmaximal, characteristic
10#11718669C211yesmaximal, characteristic
11#11718668C212yesmaximal
12C13×C4⋊Q8C2211yescharacteristic
13C13×#125C2212yes—
14C13×C22⋊Q8—21no—
15C13×C22⋊Q8—22no—
16C4×Q8×C13C2211yescharacteristic
17C4×D4×C13C2212yes—
18C4×D4×C13C2211yescharacteristic
19C2×C13×C4⋊C4—21no—
20Q8×Dic13—21no—
21C2×#6105C2211yescharacteristic
22#88142—21no—
23#88142—22no—
24#88123C2212yes—
25#88123C2211yescharacteristic
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2212yes—
28#88072C2211yescharacteristic
29#88072C2212yes—
30#88050C2211yescharacteristic
31#88050C2212yes—
32#88048C2212yes—
33#88048C2211yescharacteristic
34#88047C2212yes—
35#88047C2212yes—
36#88047C2212yes—
37C4⋊#1055C2212yes—
38C4⋊#1055C2211yescharacteristic
39#88043C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13D411yescharacteristic
43C2×D4×C13C2311yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13—22no—
46C2×Dic26—21no—
47C2×Dic26—22no—
48C2×Dic26C2311yescharacteristic
49C13×C4⋊C4—22no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4D411yescharacteristic
53C13×C4⋊C4D412yes—
54C13×C4⋊C4C2311yescharacteristic
55C13×C4⋊C4C2312yes—
56C13×C22⋊C4—21no—
57C13×C22⋊C4—22no—
58C42×C13C2312yes—
59C42×C13C2311yescharacteristic
60#6105Q814yescomplemented
61C4⋊Dic13—22no—
62C4⋊Dic13—21no—
63C4⋊Dic13C2311yescharacteristic
64C4⋊Dic13C2312yes—
65#6101—21no—
66#6101—22no—
67C4×Dic13—22no—
68C4×Dic13—21no—
69C2×#1055C2311yescharacteristic
70C2×#1055C2312yes—
71C2×#1055C2311yescharacteristic
72#3385—131nomaximal, Sylow
73C23×C13—21no—
74Q8×C13—22no—
75Q8×C13—81no—
76D4×C13—21no—
77D4×C13C2×Q812yes—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—42no—
81C2×C4×C13—82no—
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D412yes—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—21no—
90Dic26—21no—
91Dic26—82no—
92Dic26—81no—
93Dic26C2×Q812yes—
94#1055—21no—
95#1055—22no—
96#1055C2×Q812yes—
97Q82—131no—
98#554D1311yescharacteristic
99#501—132no—
100#500—131no—
101#479—132no—
102#477—131no—
103#476—131no—
104#474—132no—
105#446—131no—
106#440—132no—
107C4×SD16—131no—
108C22×C13—22no—
109C22×C13—41no—
110C22×C13—41no—
111C22×C13C22×D411yescharacteristic
112C4×C13—22no—
113C4×C13—22no—
114C4×C13—21no—
115C4×C13—41no—
116C4×C13—42no—
117C4×C13#13712yes—
118C4×C13C22×Q811yescharacteristic
119C4×C132−1+411yescharacteristic
120Dic13—22no—
121Dic13—41no—
122Dic13—42no—
123C2×SD16—131no—
124C4⋊Q8—132no—
125C4⋊Q8—131no—
126C4⋊Q8—261no—
127C4⋊Q8—262no—
128C4⋊Q8C2×D1311yescharacteristic
129#125C2×D1312yes—
130C22⋊Q8—21no—
131C22⋊Q8—22no—
132C4×Q8—131no—
133C4×Q8—132no—
134C4×Q8—261no—
135C4×Q8C2×D1311yescharacteristic
136C4×D4C2×D1311yescharacteristic
137C4×D4C2×D1312yes—
138C2×C4⋊C4—21no—
139#107—132no—
140#107—132no—
141#107—132no—
142#106—131no—
143#106—132no—
144C4⋊C8—132no—
145C4⋊C8—131no—
146#103—131no—
147#103—132no—
148#102—131no—
149#102—132no—
150#97—132no—
151C4×C8—131no—
152C2×C13—42no—
153C2×C13D4×Q811yescharacteristic
154C2×C13C2×#13711yescharacteristic
155C2×C13#57611yescharacteristic
156C2×Q8—21no—
157C2×Q8—131no—
158C2×Q8—261no—
159C2×Q8—262no—
160C2×Q8C22⋊D1311yescharacteristic
161C2×D4C22×D1311yescharacteristic
162C22×C4—21no—
163C22×C4—22no—
164SD16—134no—
165C2×C8—131no—
166C2×C8—131no—
167C2×C8—132no—
168C4⋊C4—22no—
169C4⋊C4—21no—
170C4⋊C4—22no—
171C4⋊C4—131no—
172C4⋊C4—132no—
173C4⋊C4—261no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—261no—
177C4⋊C4C22⋊D1311yescharacteristic
178C4⋊C4C22⋊D1312yes—
179C4⋊C4C22×D1311yescharacteristic
180C4⋊C4C22×D1312yes—
181C22⋊C4—21no—
182C22⋊C4—22no—
183C42—262no—
184C42—261no—
185C42C22×D1311yescharacteristic
186C42C22×D1312yes—
187C13#338511yescharacteristic, complemented, Sylow
188C23—21no—
189Q8—22no—
190Q8—81no—
191Q8—132no—
192Q8—261no—
193Q8—1042no—
194Q8—1041no—
195D4—21no—
196D4Q8×D1312yes—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—82no—
201C2×C4—261no—
202C2×C4—262no—
203C2×C4—261no—
204C2×C4C2×C22⋊D1312yes—
205C2×C4C2×C22⋊D1311yescharacteristic
206C2×C4C2×C22⋊D1312yes—
207C2×C4C2×C22⋊D1311yescharacteristic
208C2×C4C23×D1311yescharacteristic
209C8—132no—
210C8—261no—
211C8—262no—
212C22—22no—
213C22—41no—
214C22—41no—
215C22C22×C22⋊D1311yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—41no—
220C4—42no—
221C4—262no—
222C4—521no—
223C4—522no—
224C4#8820512yes—
225C4C2×Q8×D1311yescharacteristic
226C4#8825411yescharacteristic
227C2—42no—
228C2Q8×C22⋊D1311yescharacteristic
229C2C2×#8820511yescharacteristic
230C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#554C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#554D13
hypocenterC13#3385
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
2. Q8×Dic26C2semidirect
3. #11718752C2semidirect
4. #11718739C2semidirect
5. #11718726C2semidirect
6. #11718724C2semidirect
7. #11718685C2semidirect
60. #6105Q8semidirect
187. C13#3385semidirect

Maximal subgroups

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

subgroupindex
C13×#5542
Q8×Dic262
#117187522
#117187392
#117187262
#117187242
#117186852
#117186792
C4×#61052
#117186692
#117186682
#338513