Finite Group Databasebeta

← #15750676

Subgroups — #15750676

Order 3328.

276 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 63 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
2C2×#11718138C211yesmaximal, characteristic
3C13×#1886C211yesmaximal, characteristic
4C2×C13×C4⋊Q8C2211yescharacteristic
5C13×#519C411yescharacteristic
6C13×#419—21no—
7C2×C13×#101C411yescharacteristic
8C2×#88076—21no—
9C2×C4⋊#1055—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—
29C22×#1055—41no—
30C13×#103—42no—
31C13×#101—41no—
32#88076—22no—
33#88076—41no—
34C4⋊#1055—22no—
35C4⋊#1055—41no—
36#7491—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—82no—
70C2×#1055—81no—
71C2×#356—131no—
72#1886D1311yescharacteristic
73C2×#333—131no—
74C23×C13#9911yescharacteristic
75Q8×C13—42no—
76Q8×C13—41no—
77Q8×C13—41no—
78Q8×C13—41no—
79Q8×C13—41no—
80Q8×C13—81no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—42no—
96C2×C4×C13#9511yescharacteristic
97C2×C4×C13#9911yescharacteristic
98C8×C13—81no—
99#1055—82no—
100#1055—82no—
101C2×C4⋊Q8C2×D1311yescharacteristic
102#519Dic1311yescharacteristic
103C2×C4⋊C8—261no—
104#419—21no—
105C2×#101—261no—
106C2×#101Dic1311yescharacteristic
107#356—132no—
108#356—261no—
109#339—21no—
110#333—132no—
111#333—261no—
112C22×C13—22no—
113C22×C13#34211yescharacteristic
114C22×C13AΣL(1,𝔽16)11yescharacteristic
115C22×C13#35211yescharacteristic
116C4×C13—21no—
117C4×C13—22no—
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—21no—
121C4×C13—41no—
122C4×C13—41no—
123C4×C13—41no—
124C4×C13—41no—
125C4×C13—82no—
126C22×Q8C2×Dic1311yescharacteristic
127C22×Q8C22⋊D1311yescharacteristic
128C2×M16—21no—
129C2×M16—521no—
130C22×C8—521no—
131C4⋊Q8—41no—
132C4⋊Q8Dic2611yescharacteristic
133C4⋊Q8C4×D1311yescharacteristic
134C4⋊Q8C4×D1311yescharacteristic
135C4⋊Q8D5211yescharacteristic
136C4×Q8—42no—
137#117—21no—
138#117—41no—
139C2×C4⋊C4—41no—
140C2×C42C22⋊D1311yescharacteristic
141C4⋊C8—262no—
142C4⋊C8—521no—
143#103—42no—
144#101—41no—
145#101—262no—
146#101—521no—
147C2×C13—21no—
148C2×C13—21no—
149C2×C13#139011yescharacteristic
150C2×C13#140512yes—
151C2×Q8—21no—
152C2×Q8—21no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8C4×Dic1311yescharacteristic
158C2×Q8#610111yescharacteristic
159C2×Q8C4⋊Dic1311yescharacteristic
160C2×Q8#610311yescharacteristic
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4C22⋊Dic1311yescharacteristic
165M16—41no—
166M16—41no—
167M16—522no—
168M16—1041no—
169C2×C8—41no—
170C2×C8—522no—
171C2×C8—1042no—
172C2×C8—1041no—
173C4⋊C4—22no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C22⋊C4—41no—
180C42—21no—
181C42—41no—
182C42—42no—
183C42#610111yescharacteristic
184C42#610311yescharacteristic
185C13#749111yescharacteristic, complemented, Sylow
186C23#8807411yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—42no—
192Q8—81no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4#8807111yescharacteristic
209C2×C4#8807411yescharacteristic
210C8—81no—
211C8—1042no—
212C8—1042no—
213C22—22no—
214C22#1171811811yescharacteristic
215C22#1171812811yescharacteristic
216C22#1171813111yescharacteristic
217C4—21no—
218C4—22no—
219C4—21no—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—82no—
227C2—21no—
228C2—21no—
229C2#1311295411yescharacteristic
230C2#1311299012yes—
subgroupG/H
centerC22#11718128
commutatorC2×Q8×C13C42
FrattiniC2×C4⋊Q8C2×D13
FittingC13×#1886C2
socleC22×C13AΣL(1,𝔽16)
prime radicalC23×C13#99
cosocleC2×C13×C4⋊Q8C22
hypercenter#1886D13
hypocenterC13#7491
LCSG ▷ C2×Q8×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ 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
185. C13#7491semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
C2×#117181382
C13×#18862
#749113