Finite Group Databasebeta

← #49096997

Subgroups — #49096997

Order 35968.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#31824034C211yesmaximal, characteristic
2#31823447C211yesmaximal, characteristic
3#31823261C214yesmaximal, complemented
4#413×C281C211yesmaximal, characteristic
5C22×Dic562C411yescharacteristic
6C2×#17985122—21no—
7#22582877C2212yes—
8#22582866C412yes—
9#22582860—21no—
10#22582860—21no—
11#22582858—21no—
12#22582858—21no—
13#22582838C411yescharacteristic
14#22582798C2212yes—
15#22582796—21no—
16C2×#41×C281C2211yescharacteristic
17C2×M16×C281—21no—
18#101×C281C2212yes—
19#100×C281—21no—
20C2×Dic562—21no—
21C2×Dic562—41no—
22C2×Dic562—41no—
23C2×Dic562C2×C412yes—
24C22×Dic281—21no—
25#17985122—22no—
26#17985122—41no—
27C2×#14555886—41no—
28C4⋊Dic281—21no—
29#17985117—22no—
30#17985117—22no—
31C22⋊Dic281—21no—
32C22⋊Dic281—22no—
33C22⋊Dic281—22no—
34C4×Dic281C2×C412yes—
35#41×C281—41no—
36#41×C281—41no—
37C2×Q8×C281C2311yescharacteristic
38C2×D4×C281C2×C411yescharacteristic
39C2×D4×C281D411yescharacteristic
40C2×D4×C281D411yescharacteristic
41C22×C4×C281C2×C411yescharacteristic
42C22×C4×C281D411yescharacteristic
43C22×C4×C281D411yescharacteristic
44M16×C281—22no—
45M16×C281—41no—
46C2×C8×C281—41no—
47Dic562—41no—
48Dic562—41no—
49Dic562—42no—
50C2×Dic281—22no—
51C2×Dic281—22no—
52C2×Dic281—42no—
53#14555886—42no—
54C23×C281C22⋊C411yescharacteristic
55C23×C281C22⋊C411yescharacteristic
56C23×C281C22⋊C411yescharacteristic
57Q8×C281—41no—
58D4×C281—41no—
59D4×C281—41no—
60D4×C281—41no—
61C2×C4×C281—21no—
62C2×C4×C281—21no—
63C2×C4×C281—21no—
64C2×C4×C281—21no—
65C2×C4×C281—21no—
66C2×C4×C281—21no—
67C2×C4×C281C22⋊C411yescharacteristic
68C2×C4×C281C22×C411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
71C8×C281—42no—
72C22×C281—21no—
73C22×C281—21no—
74C22×C281—21no—
75C22×C281—41no—
76C22×C281—41no—
77C22×C281—41no—
78C22×C281C2×C22⋊C411yescharacteristic
79C4×C281—21no—
80C4×C281—21no—
81C4×C281—21no—
82C4×C281#9911yescharacteristic
83C4×C281#9911yescharacteristic
84Dic281—42no—
85Dic281—42no—
86C2×C281—21no—
87C2×C281—41no—
88C2×C281—41no—
89C2×C281—41no—
90C2×C281C2×#9911yescharacteristic
91C281#213511yescharacteristic, complemented, Sylow
92#2135—2811nomaximal, Sylow
93#536—2811no—
94#413—2811no—
95#413D28111yescharacteristic
96#356—2814no—
97C2×#41C2×D28111yescharacteristic
98C22×Q8—2811no—
99C2×M16—21no—
100C2×M16—5621no—
101C4⋊Q8—2812no—
102#124—2812no—
103#123—5621no—
104#123—5621no—
105C22⋊Q8—5621no—
106C22⋊Q8—5621no—
107#117—2811no—
108#101—2812no—
109#101C2×D28112yes—
110#100—21no—
111#100—5621no—
112#41—41no—
113#41—41no—
114C2×Q8—2812no—
115C2×Q8—5621no—
116C2×Q8—11241no—
117C2×Q8—11241no—
118C2×Q8C22×D28111yescharacteristic
119C2×D4C4×D28111yescharacteristic
120C2×D4C22⋊D28111yescharacteristic
121C2×D4D112411yescharacteristic
122C22×C4—5621no—
123C22×C4C4×D28111yescharacteristic
124C22×C4C22⋊D28111yescharacteristic
125C22×C4D112411yescharacteristic
126M16—22no—
127M16—41no—
128M16—5622no—
129M16—11241no—
130C2×C8—41no—
131C2×C8—11241no—
132C4⋊C4—5621no—
133C4⋊C4—5622no—
134C4⋊C4—5622no—
135C22⋊C4—5621no—
136C22⋊C4—5622no—
137C22⋊C4—5622no—
138C42—2812no—
139C23#1798511511yescharacteristic
140C23#1798511511yescharacteristic
141C23#1798511511yescharacteristic
142Q8—41no—
143Q8—11242no—
144Q8—11241no—
145Q8—11241no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—5622no—
156C2×C4—5622no—
157C2×C4—11242no—
158C2×C4#1798511511yescharacteristic
159C2×C4C2×C4×D28111yescharacteristic
160C2×C4C2×C22⋊D28111yescharacteristic
161C2×C4C2×D112411yescharacteristic
162C8—42no—
163C8—11242no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×#1798511511yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—11242no—
175C4—11242no—
176C4#2258279311yescharacteristic
177C4#2258279311yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#2258279311yescharacteristic
subgroupG/H
centerC2C2×#22582793
commutatorC2×C4×C281C22×C4
FrattiniC2×Q8C22×D281
Fitting#413×C281C2
socleC2×C281C2×#99
prime radicalC2×#41×C281C22
cosocleC2×Q8×C281C23
hypercenter#413D281
hypocenterC281#2135
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #31823261C2semidirect
91. C281#2135semidirect

Maximal subgroups

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

subgroupindex
#318240342
#318234472
#318232612
#413×C2812
#2135281