Finite Group Databasebeta

← #49094375

Subgroups — #49094375

Order 35968.

236 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 61 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#31823837C211yesmaximal, characteristic, complemented
2#31823663C211yesmaximal, characteristic, complemented
3#31823658C211yesmaximal, characteristic
4#31823212C211yesmaximal, characteristic, complemented
5Q8⋊#14555886C211yesmaximal, characteristic, complemented
6D4⋊#14555886C211yesmaximal, characteristic, complemented
7#554×C281C211yesmaximal, characteristic, complemented
8C2×#17985125—21no—
9C2×#17985125—22no—
10C2×#17985123—21no—
11#22582876C2211yescharacteristic
12C4⋊#14555886C2211yescharacteristic
13C4⋊#14555886C2211yescharacteristic
14#22582799—21no—
15#22582799—21no—
16C4×#14555886C2211yescharacteristic
17C4⋊Q8×C281C2211yescharacteristic
18#125×C281—21no—
19C22⋊Q8×C281—21no—
20C22⋊Q8×C281—22no—
21C4×Q8×C281C2211yescharacteristic
22C4×D4×C281—21no—
23C4×D4×C281C2211yescharacteristic
24C2×C4⋊C4×C281—21no—
25C2×D1124—21no—
26C2×D1124—21no—
27C2×D1124—21no—
28#17985125—42no—
29#17985125—44no—
30#17985123—42no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C2×#14555886—21no—
34C2×Q8×C281D411yescharacteristic
35C2×Q8×C281D412yes—
36C2×D4×C281D411yescharacteristic
37C22×C4×C281—22no—
38C22×C4×C281—21no—
39C4⋊C4×C281—22no—
40C4⋊C4×C281—22no—
41C4⋊C4×C281—21no—
42C4⋊C4×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281D411yescharacteristic
45C4⋊C4×C281D411yescharacteristic
46C22⋊C4×C281—22no—
47C22⋊C4×C281—21no—
48C42×C281—21no—
49C42×C281C2311yescharacteristic
50C22×D281—41no—
51D1124—42no—
52D1124—41no—
53D1124—41no—
54D1124—41no—
55D1124—41no—
56#14555886—22no—
57#14555886—41no—
58#14555886—41no—
59C23×C281—21no—
60Q8×C281—21no—
61Q8×C281—21no—
62Q8×C281—42no—
63D4×C281—21no—
64D4×C281SD1612yescomplemented
65C2×C4×C281—21no—
66C2×C4×C281—21no—
67C2×C4×C281—21no—
68C2×C4×C281—22no—
69C2×C4×C281—41no—
70C2×C4×C281—41no—
71C2×C4×C281—82no—
72C2×C4×C281C2×D411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C2×C4×C281C2×D411yescharacteristic
75C22×C281—22no—
76C22×C281—41no—
77C22×C281—41no—
78C22×C281#12011yescharacteristic
79C2×D281—81no—
80C2×D281—81no—
81C2×D281—81no—
82C4×C281—21no—
83C4×C281—41no—
84C4×C281—41no—
85C4×C281—41no—
86C4×C281—42no—
87C4×C281C2×SD1611yescharacteristic
88C4×C281#13511yescharacteristic
89C4×C281AGL(1,ℤ/8)11yescharacteristic
90C4×C281#13711yescharacteristic
91C2×C281—42no—
92C2×C281#44811yescharacteristic
93C2×C281#44911yescharacteristic
94C2×C281#45311yescharacteristic
95D281—161no—
96C281#162211yescharacteristic, complemented, Sylow
97#1622—2811nomaximal, Sylow
98#554D28111yescharacteristic, complemented
99#492—2811no—
100#460—2811no—
101#459—2811no—
102#333—2811no—
103Q8⋊C8—2811no—
104D4⋊C8—2811no—
105C2×SD16—5621no—
106C2×SD16—5622no—
107C2×D8—5621no—
108C4⋊Q8C2×D28111yescharacteristic
109#127—2811no—
110#125—21no—
111C22⋊Q8—21no—
112C22⋊Q8—22no—
113C4×Q8C2×D28111yescharacteristic
114C4×D4—21no—
115C4×D4C2×D28111yescharacteristic
116C2×C4⋊C4—21no—
117C4⋊C8—2811no—
118C4⋊C8—2811no—
119#102—5621no—
120#102—5621no—
121C4×C8—2811no—
122C2×Q8C22⋊D28111yescharacteristic
123C2×Q8C22⋊D28112yes—
124C2×D4—5621no—
125C2×D4—5621no—
126C2×D4—5621no—
127C2×D4C22⋊D28111yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130SD16—11244no—
131SD16—11242no—
132D8—11242no—
133C2×C8—5621no—
134C2×C8—5621no—
135C2×C8—5621no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4C22⋊D28111yescharacteristic
142C4⋊C4C22⋊D28111yescharacteristic
143C22⋊C4—22no—
144C22⋊C4—21no—
145C42—21no—
146C42C22×D28111yescharacteristic
147C23—21no—
148C23—11241no—
149Q8—21no—
150Q8—21no—
151Q8—42no—
152D4—21no—
153D4—11242no—
154D4—11241no—
155D4—11241no—
156D4—11241no—
157D4—11241no—
158D4#1798512512yescomplemented
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—82no—
166C2×C4C2×C22⋊D28111yescharacteristic
167C2×C4C2×C22⋊D28111yescharacteristic
168C2×C4C2×C22⋊D28111yescharacteristic
169C8—5622no—
170C8—11241no—
171C8—11241no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—22481no—
176C22—22481no—
177C22—22481no—
178C22#2258284811yescharacteristic
179C4—21no—
180C4—41no—
181C4—42no—
182C4—41no—
183C4—41no—
184C4C2×#1798512511yescharacteristic
185C4#2258289911yescharacteristic
186C4#2258290411yescharacteristic
187C4#2258291011yescharacteristic
188C2—42no—
189C2—44961no—
190C2#3182360211yescharacteristic
191C2#3182360811yescharacteristic
192C2#3182363111yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#554×C281C2
socleC22×C281#120
prime radical#31823658C2
hypercenter#554D281
hypocenterC281#1622
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #31823837C2semidirect
2. #31823663C2semidirect
4. #31823212C2semidirect
5. Q8⋊#14555886C2semidirect
6. D4⋊#14555886C2semidirect
7. #554×C281C2semidirect
64. D4×C281SD16semidirect
96. C281#1622semidirect
98. #554D281semidirect
158. D4#17985125semidirect

Maximal subgroups

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

subgroupindex
#318238372
#318236632
#318236582
#318232122
Q8⋊#145558862
D4⋊#145558862
#554×C2812
#1622281