Finite Group Databasebeta

← #15750652

Subgroups — #15750652

Order 3328.

262 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C2×#11718140C211yesmaximal, characteristic
2#13113562C211yesmaximal, characteristic
3C13×#1886C211yesmaximal, characteristic
4C2×C13×C4⋊Q8C2211yescharacteristic
5C13×#519C411yescharacteristic
6C13×#419—21no—
7C2×C13×#101C411yescharacteristic
8C2×#88076—21no—
9#11718587—21no—
10C13×#339—21no—
11#11718140—21no—
12#11718140C412yescomplemented
13#11718138—21no—
14#11718138C412yescomplemented
15C22×Q8×C13C2×C411yescharacteristic
16C22×Q8×C13D411yescharacteristic
17C2×C13×M16—21no—
18C13×C4⋊Q8—41no—
19C13×C4⋊Q8C2×C411yescharacteristic
20C13×C4⋊Q8C2×C411yescharacteristic
21C13×C4⋊Q8D411yescharacteristic
22C13×C4⋊Q8Q811yescharacteristic
23C4×Q8×C13—42no—
24C13×#117—21no—
25C13×#117—41no—
26C2×C13×C4⋊C4—41no—
27C2×C42×C13D411yescharacteristic
28C2×#6099—41no—
29C13×#103—42no—
30C13×#101—41no—
31#88076—22no—
32#88076—41no—
33C22⋊#1055—41no—
34C4⋊#1055—22no—
35#88043—41no—
36#7483—131nomaximal, Sylow
37C2×Q8×C13—21no—
38C2×Q8×C13—21no—
39C2×Q8×C13—41no—
40C2×Q8×C13—41no—
41C2×Q8×C13—41no—
42C2×Q8×C13—41no—
43C2×Q8×C13C4211yescharacteristic
44C2×Q8×C13C22⋊C411yescharacteristic
45C2×Q8×C13C4⋊C411yescharacteristic
46C2×Q8×C13C4⋊C411yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13C22⋊C411yescharacteristic
51C13×M16—41no—
52C13×M16—41no—
53C2×C8×C13—41no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C13×C4⋊C4—41no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—42no—
60C13×C22⋊C4—41no—
61C42×C13—21no—
62C42×C13—41no—
63C42×C13—42no—
64C42×C13C22⋊C411yescharacteristic
65C42×C13C4⋊C411yescharacteristic
66#6099—42no—
67#6099—81no—
68C2×#1055—42no—
69C2×#1055—81no—
70C2×#356—131no—
71#1886D1311yescharacteristic
72#1558—131no—
73C23×C13#9911yescharacteristic
74Q8×C13—42no—
75Q8×C13—41no—
76Q8×C13—41no—
77Q8×C13—41no—
78Q8×C13—41no—
79Q8×C13—81no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
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—42no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13#9511yescharacteristic
95C2×C4×C13#9911yescharacteristic
96C8×C13—81no—
97#1055—82no—
98#1055—82no—
99C2×C4⋊Q8C2×D1311yescharacteristic
100#519Dic1311yescharacteristic
101#432—261no—
102#419—21no—
103C2×#101—261no—
104C2×#101Dic1311yescharacteristic
105#356—132no—
106#356—261no—
107#339—21no—
108#333—132no—
109#333—261no—
110C22×C13—41no—
111C22×C13#34211yescharacteristic
112C22×C13AΣL(1,𝔽16)11yescharacteristic
113C22×C13#35211yescharacteristic
114C4×C13—22no—
115C4×C13—21no—
116C4×C13—21no—
117C4×C13—41no—
118C4×C13—41no—
119C4×C13—41no—
120C4×C13—41no—
121C4×C13—41no—
122C4×C13—82no—
123C22×Q8C2×Dic1311yescharacteristic
124C22×Q8C22⋊D1311yescharacteristic
125C2×M16—21no—
126C2×M16—521no—
127C4⋊Q8—41no—
128C4⋊Q8Dic2611yescharacteristic
129C4⋊Q8C4×D1311yescharacteristic
130C4⋊Q8C4×D1311yescharacteristic
131C4⋊Q8D5211yescharacteristic
132C4×Q8—42no—
133#117—21no—
134#117—41no—
135C2×C4⋊C4—41no—
136C2×C42C22⋊D1311yescharacteristic
137C4⋊C8—262no—
138#103—42no—
139#101—41no—
140#101—262no—
141#101—521no—
142C22⋊C8—521no—
143#97—521no—
144C2×C13—21no—
145C2×C13—21no—
146C2×C13—21no—
147C2×C13#139011yescharacteristic
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8C4×Dic1311yescharacteristic
155C2×Q8#610111yescharacteristic
156C2×Q8C4⋊Dic1311yescharacteristic
157C2×Q8#610311yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4C22⋊Dic1311yescharacteristic
162M16—41no—
163M16—41no—
164M16—522no—
165M16—1041no—
166C2×C8—41no—
167C2×C8—522no—
168C2×C8—1041no—
169C4⋊C4—22no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C22⋊C4—41no—
176C42—21no—
177C42—41no—
178C42—42no—
179C42#610111yescharacteristic
180C42#610311yescharacteristic
181C13#748311yescharacteristic, complemented, Sylow
182C23#8807411yescharacteristic
183Q8—41no—
184Q8—41no—
185Q8—41no—
186Q8—41no—
187Q8—42no—
188Q8—81no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4#8807111yescharacteristic
204C2×C4#8807411yescharacteristic
205C8—81no—
206C8—1042no—
207C8—1042no—
208C22—41no—
209C22#1171811811yescharacteristic
210C22#1171812811yescharacteristic
211C22#1171813111yescharacteristic
212C4—22no—
213C4—21no—
214C4—21no—
215C4—41no—
216C4—41no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—82no—
221C2—21no—
222C2—21no—
223C2—21no—
224C2#1311295411yescharacteristic
subgroupG/H
centerC2#13112954
commutatorC2×Q8×C13C42
FrattiniC2×C4⋊Q8C2×D13
FittingC13×#1886C2
socleC2×C13#1390
prime radicalC23×C13#99
cosocleC2×C13×C4⋊Q8C22
hypercenter#1886D13
hypocenterC13#7483
LCSG ▷ C2×Q8×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ #1886

Complements

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

NH ≅ G/Ntype
12. #11718140C4semidirect
14. #11718138C4semidirect
181. C13#7483semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
#131135622
C13×#18862
#748313