Finite Group Databasebeta

← #49096352

Subgroups — #49096352

Order 35968.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22582912C212yesmaximal, complemented
2#31824044C211yesmaximal, characteristic
3C2×#22582805C212yesmaximal, complemented
4#31823368C211yesmaximal, characteristic, complemented
5#343×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2212yes—
7C22×Dic562C2211yescharacteristic
8#22582912—24no—
9#22582912—24no—
10C2×Dic1124—22no—
11C2×#17985127—22no—
12#22582859—22no—
13#22582854—22no—
14#22582853—22no—
15C2×C4×Dic281C2211yescharacteristic
16#22582805—24no—
17#22582786—22no—
18C2×M16×C281C2212yes—
19C2×C4⋊C4×C281C2211yescharacteristic
20#17985138—22no—
21#17985138—22no—
22#17985138—22no—
23#17985138—22no—
24C2×Dic562—22no—
25C2×Dic562—22no—
26C2×Dic562—21no—
27C2×Dic562D412yes—
28C2×Dic562D412yescomplemented
29C2×D1124—22no—
30C2×D1124D412yes—
31C2×C22⋊D281—22no—
32C22×Dic281—21no—
33C22×Dic281—21no—
34C2×C4×D281—22no—
35Dic1124—28no—
36#17985127—28no—
37C4⋊Dic281—22no—
38#17985115—24no—
39C4×Dic281—22no—
40C22×C4×C281D412yes—
41C22×C4×C281C2311yescharacteristic
42M16×C281—22no—
43M16×C281D414yescomplemented
44C2×C8×C281—22no—
45C4⋊C4×C281—22no—
46C22×D281—22no—
47Dic562—24no—
48Dic562—22no—
49Dic562—22no—
50Dic562—42no—
51D1124—22no—
52D1124—22no—
53D1124—82no—
54C22⋊D281—42no—
55C22⋊D281—42no—
56C2×Dic281—22no—
57C2×Dic281—22no—
58C2×Dic281—22no—
59C2×Dic281—41no—
60C2×Dic281—41no—
61C2×Dic281—41no—
62C2×Dic281—41no—
63C4×D281—42no—
64C4×D281—42no—
65C23×C281C2×D411yescharacteristic
66C2×C4×C281—22no—
67C2×C4×C281—42no—
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D412yes—
70C2×C4×C281C2×D412yes—
71C2×C4×C281#4111yescharacteristic
72C8×C281—24no—
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#12012yes—
83C4×C281#12112yes—
84Dic281—42no—
85Dic281—42no—
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#391—2811no—
99#343D28111yescharacteristic, complemented
100C2×#41—2812no—
101C22×Q8—2811no—
102#137—5624no—
103#137—5624no—
104C2×Q16—5622no—
105C2×SD16—5622no—
106C2×M16C2×D28112yes—
107C22⋊Q8—5622no—
108#121—5622no—
109#121—5622no—
110C2×C4⋊C4C2×D28111yescharacteristic
111C2×C42—2811no—
112#104—5624no—
113#95—5622no—
114#41—5622no—
115#41—5622no—
116#41—5622no—
117#41—5622no—
118C2×Q8—2812no—
119C2×Q8—2812no—
120C2×Q8—5621no—
121C2×Q8—5622no—
122C2×Q8—5622no—
123C2×D4—2812no—
124C2×D4—5622no—
125C2×D4—5622no—
126C22×C4—5621no—
127C22×C4—5621no—
128C22×C4—5622no—
129C22×C4D112412yes—
130C22×C4C22×D28111yescharacteristic
131Q16—5628no—
132SD16—5628no—
133M16—22no—
134M16D112414yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—5622no—
138C22⋊C4—5624no—
139C42—5622no—
140C23—5622no—
141C23C2×D112411yescharacteristic
142Q8—5624no—
143Q8—5622no—
144Q8—5622no—
145Q8—11242no—
146D4—5622no—
147D4—5622no—
148D4—11242no—
149D4—11242no—
150D4—22482no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—5622no—
154C2×C4—5622no—
155C2×C4—5622no—
156C2×C4—11241no—
157C2×C4—11241no—
158C2×C4—11241no—
159C2×C4—11241no—
160C2×C4—11242no—
161C2×C4—11242no—
162C2×C4D4×D28111yescharacteristic
163C2×C4D4×D28112yes—
164C2×C4C2×D112412yes—
165C2×C4#1798513911yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—11242no—
170C22—11242no—
171C22—11242no—
172C22#2258284911yescharacteristic
173C22#2258285411yescharacteristic
174C22#2258287611yescharacteristic
175C4—42no—
176C4—11242no—
177C4—11242no—
178C4—11242no—
179C4#2258284912yes—
180C4#2258285412yes—
181C2—21no—
182C2—21no—
183C2—22482no—
184C2#3182337311yescharacteristic
185C2#3182364311yescharacteristic
186C2#3182364811yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#343×C281C2
socleC22×C281#120
prime radical#31824044C2
hypercenter#343D281
hypocenterC281#2007
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#22582912C2semidirect
3. C2×#22582805C2semidirect
4. #31823368C2semidirect
5. #343×C281C2semidirect
28. C2×Dic562D4semidirect
43. M16×C281D4semidirect
93. C281#2007semidirect
99. #343D281semidirect
134. M16D1124semidirect

Maximal subgroups

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

subgroupindex
C2×#225829122
#318240442
C2×#225828052
#318233682
#343×C2812
#2007281