Finite Group Databasebeta

← #14674136

Subgroups — #14674136

Order 2816.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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×#10622186C212yesmaximal
2#13066789C214yesmaximal, complemented
3C11×#3139C211yesmaximal, characteristic
4C11×#533C411yescharacteristic
5C2×C11×C4⋊Q8C2211yescharacteristic
6C11×#491C412yes—
7C11×#491C2212yes—
8C11×#487—22no—
9C11×#419—22no—
10C4×C11×M16C411yescharacteristic
11C2×#66900—22no—
12#10622186—22no—
13#10622186C2214yes—
14C22×Q8×C11D412yes—
15C2×C11×M16—21no—
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8—41no—
18C11×C4⋊Q8C2×C411yescharacteristic
19C11×C4⋊Q8D412yes—
20C11×C4⋊Q8C2311yescharacteristic
21C11×#125C2×C412yes—
22C11×C22⋊Q8—41no—
23C4×Q8×C11—41no—
24C11×#117—21no—
25C2×C11×C4⋊C4—41no—
26C2×C42×C11C2×C411yescharacteristic
27C2×#4318—42no—
28C11×#103—24no—
29C11×#103—24no—
30C11×#97C2×C412yes—
31C4×C8×C11—21no—
32#66900—24no—
33#66900—42no—
34#13599—111nomaximal, Sylow
35C2×Q8×C11—22no—
36C2×Q8×C11—41no—
37C2×Q8×C11—42no—
38C2×Q8×C11—42no—
39C2×Q8×C11C22⋊C412yes—
40C2×Q8×C11C2×D412yes—
41C22×C4×C11—22no—
42C22×C4×C11—21no—
43C22×C4×C11C22⋊C411yescharacteristic
44C11×M16—42no—
45C2×C8×C11—22no—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—41no—
48C11×C4⋊C4—42no—
49C11×C4⋊C4—41no—
50C11×C4⋊C4—41no—
51C11×C4⋊C4—42no—
52C11×C22⋊C4—41no—
53C42×C11—21no—
54C42×C11—41no—
55C42×C11C22⋊C411yescharacteristic
56C42×C11C22×C411yescharacteristic
57#4318—44no—
58#4318—82no—
59C2×C11⋊C8—82no—
60#3139D1111yescharacteristic
61C2×#356—112no—
62#1413—114no—
63C23×C11#9911yescharacteristic
64Q8×C11—42no—
65Q8×C11—42no—
66Q8×C11—82no—
67Q8×C11—82no—
68C2×C4×C11—22no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—42no—
74C2×C4×C11—42no—
75C2×C4×C11—42no—
76C2×C4×C11—42no—
77C2×C4×C11#9911yescharacteristic
78C2×C4×C11C2×C22⋊C411yescharacteristic
79C8×C11—42no—
80C11⋊C8—84no—
81#533Dic1111yescharacteristic
82C2×C4⋊Q8C2×D1111yescharacteristic
83#491Dic1112yes—
84#491C2×D1112yes—
85#487—22no—
86#419—22no—
87C2×#101—222no—
88C4×M16Dic1111yescharacteristic
89#356—114no—
90#356—222no—
91C22×C11—41no—
92C22×C11#35412yes—
93C22×C11C2×#9911yescharacteristic
94C4×C11—22no—
95C4×C11—21no—
96C4×C11—21no—
97C4×C11—41no—
98C4×C11—42no—
99C4×C11—42no—
100C4×C11—82no—
101C22×Q8C22⋊D1112yes—
102C2×M16—21no—
103C2×M16—442no—
104C4⋊Q8—21no—
105C4⋊Q8—41no—
106C4⋊Q8C2×Dic1111yescharacteristic
107C4⋊Q8C22⋊D1112yes—
108C4⋊Q8C22×D1111yescharacteristic
109#125C2×Dic1112yes—
110C22⋊Q8—41no—
111C4×Q8—41no—
112#117—21no—
113C2×C4⋊C4—41no—
114C2×C42C2×Dic1111yescharacteristic
115#103—24no—
116#103—24no—
117#101—224no—
118#101—442no—
119#97C2×Dic1112yes—
120C4×C8—21no—
121C2×C11—21no—
122C2×C11—22no—
123C2×C11C2×#35411yescharacteristic
124C2×Q8—22no—
125C2×Q8—41no—
126C2×Q8—42no—
127C2×Q8—42no—
128C2×Q8C22⋊Dic1112yes—
129C2×Q8C2×C22⋊D1112yes—
130C22×C4—21no—
131C22×C4—22no—
132C22×C4C22⋊Dic1111yescharacteristic
133M16—42no—
134M16—444no—
135M16—882no—
136C2×C8—22no—
137C2×C8—882no—
138C4⋊C4—22no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—42no—
143C4⋊C4—41no—
144C22⋊C4—41no—
145C42—21no—
146C42—41no—
147C42C22⋊Dic1111yescharacteristic
148C42C22×Dic1111yescharacteristic
149C11#1359911yescharacteristic, complemented, Sylow
150C23#6689811yescharacteristic
151Q8—42no—
152Q8—42no—
153Q8—82no—
154Q8—82no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4#6689811yescharacteristic
165C2×C4C2×C22⋊Dic1111yescharacteristic
166C8—42no—
167C8—884no—
168C22—41no—
169C22#1062217912yes—
170C22C2×#6689811yescharacteristic
171C4—22no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—42no—
176C4—42no—
177C4—82no—
178C2—21no—
179C2—22no—
180C2C2×#1062217911yescharacteristic
subgroupG/H
centerC2C2×#10622179
commutatorC42×C11C22×C4
FrattiniC4⋊Q8C22×D11
FittingC11×#3139C2
socleC2×C11C2×#354
prime radicalC23×C11#99
cosocleC11×C4⋊Q8C23
hypercenter#3139D11
hypocenterC11#13599
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ #3139

Complements

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

NH ≅ G/Ntype
2. #13066789C2semidirect
149. C11#13599semidirect

Maximal subgroups

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

subgroupindex
C2×#106221862
#130667892
C11×#31392
#1359911