Finite Group Databasebeta

← #49096349

Subgroups — #49096349

Order 35968.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22582910C212yesmaximal, complemented
2#31824044C211yesmaximal, characteristic
3C2×#22582807C212yesmaximal, complemented
4#31823232C211yesmaximal, characteristic, complemented
5#391×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2212yes—
7#22582910—24no—
8#22582910—24no—
9C2×#17985128—22no—
10C2×#17985125—22no—
11C2×#17985122C2212yes—
12#22582859—22no—
13#22582854—22no—
14#22582853—22no—
15#22582807—24no—
16C22×Q8×C281C2211yescharacteristic
17C2×C4⋊C4×C281C2211yescharacteristic
18C2×C42×C281C2211yescharacteristic
19#95×C281—22no—
20#17985138—22no—
21#17985138—22no—
22#17985138—22no—
23#17985138—22no—
24C2×Dic562D412yes—
25C2×D1124—22no—
26C2×D1124D412yes—
27C2×C22⋊D281—22no—
28C2×C4×D281—22no—
29#17985128—28no—
30#17985125—28no—
31#17985122—22no—
32#17985122D414yescomplemented
33C2×#14555886—22no—
34C4⋊Dic281—22no—
35#17985115—24no—
36C2×Q8×C281—21no—
37C2×Q8×C281—22no—
38C2×Q8×C281—22no—
39C2×Q8×C281D412yescomplemented
40C22×C4×C281—21no—
41C22×C4×C281—21no—
42C22×C4×C281D412yes—
43C22×C4×C281C2311yescharacteristic
44C4⋊C4×C281—22no—
45C42×C281—22no—
46C22×D281—22no—
47Dic562—22no—
48Dic562—22no—
49D1124—22no—
50D1124—22no—
51D1124—82no—
52C22⋊D281—42no—
53C22⋊D281—42no—
54C2×Dic281—22no—
55C4×D281—42no—
56C4×D281—42no—
57#14555886—24no—
58C23×C281C2×D411yescharacteristic
59Q8×C281—24no—
60Q8×C281—42no—
61C2×C4×C281—22no—
62C2×C4×C281—22no—
63C2×C4×C281—22no—
64C2×C4×C281—41no—
65C2×C4×C281—41no—
66C2×C4×C281—41no—
67C2×C4×C281—41no—
68C2×C4×C281—42no—
69C2×C4×C281C2×D412yes—
70C2×C4×C281C2×D412yes—
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281#4111yescharacteristic
73C22×C281—21no—
74C22×C281—21no—
75C22×C281#12011yescharacteristic
76C22×C281#12111yescharacteristic
77C22×C281#12711yescharacteristic
78C2×D281—42no—
79C2×D281—42no—
80C2×D281—42no—
81C4×C281—42no—
82C4×C281—42no—
83C4×C281—42no—
84C4×C281#12012yes—
85C4×C281#12112yes—
86Dic281—42no—
87C2×C281—21no—
88C2×C281—21no—
89C2×C281#39211yescharacteristic
90C2×C281#45511yescharacteristic
91C2×C281#45611yescharacteristic
92D281—82no—
93C281#200711yescharacteristic, complemented, Sylow
94#2007—2811nomaximal, Sylow
95C2×#137—2812no—
96#537—2811no—
97C2×#104—2812no—
98#391D28111yescharacteristic, complemented
99#343—2811no—
100C2×#41—2812no—
101C22×Q8C2×D28111yescharacteristic
102#137—5624no—
103#137—5624no—
104C2×Q16—5622no—
105C2×SD16—5622no—
106C2×M16—2812no—
107C22⋊Q8—5622no—
108#121—5622no—
109#121—5622no—
110C2×C4⋊C4C2×D28111yescharacteristic
111C2×C42C2×D28111yescharacteristic
112#104—5624no—
113#95—22no—
114#41—5622no—
115#41—5622no—
116#41—5622no—
117#41—5622no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—2812no—
122C2×Q8D112412yescomplemented
123C2×D4—2812no—
124C2×D4—5622no—
125C2×D4—5622no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—5622no—
129C22×C4C22⋊D28112yes—
130C22×C4C22×D28111yescharacteristic
131Q16—5628no—
132SD16—5628no—
133M16—2814no—
134M16—5622no—
135C2×C8—5622no—
136C4⋊C4—22no—
137C4⋊C4—5622no—
138C22⋊C4—5624no—
139C42—22no—
140C23—5622no—
141C23C2×C22⋊D28111yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—5622no—
145Q8—5622no—
146D4—5622no—
147D4—5622no—
148D4—11242no—
149D4—11242no—
150D4—22482no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—5622no—
160C2×C4—11242no—
161C2×C4—11242no—
162C2×C4D4×D28112yes—
163C2×C4D4×D28112yes—
164C2×C4C2×D112411yescharacteristic
165C2×C4#1798513811yescharacteristic
166C8—5624no—
167C22—21no—
168C22—21no—
169C22—11242no—
170C22—11242no—
171C22—11242no—
172C22#2258284711yescharacteristic
173C22#2258285311yescharacteristic
174C22#2258287511yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—11242no—
179C4#2258284912yes—
180C4#2258285212yes—
181C2—21no—
182C2—21no—
183C2—22482no—
184C2#3182337211yescharacteristic
185C2#3182364011yescharacteristic
186C2#3182364511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#391×C281C2
socleC22×C281#120
prime radical#31824044C2
hypercenter#391D281
hypocenterC281#2007
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#22582910C2semidirect
3. C2×#22582807C2semidirect
4. #31823232C2semidirect
5. #391×C281C2semidirect
32. #17985122D4semidirect
39. C2×Q8×C281D4semidirect
93. C281#2007semidirect
98. #391D281semidirect
122. C2×Q8D1124semidirect

Maximal subgroups

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

subgroupindex
C2×#225829102
#318240442
C2×#225828072
#318232322
#391×C2812
#2007281