Finite Group Databasebeta

← #44508549

Subgroups — #44508549

Order 30848.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#29508517C211yesmaximal, characteristic, complemented
2#29508515C212yesmaximal, complemented
3#29507683C212yesmaximal, complemented
4#29507475C211yesmaximal, characteristic, complemented
5#408×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2212yes—
7#21440675—22no—
8#21440673—22no—
9#21440672—22no—
10#21440670—22no—
11#21440668—22no—
12#21440667—22no—
13#21440664—22no—
14#21440662—24no—
15C2×#16838754C2212yes—
16#21440554—24no—
17C2×#41×C241C2211yescharacteristic
18C2×M16×C241C2211yescharacteristic
19C22×C8×C241C2211yescharacteristic
20C22⋊C8×C241—22no—
21#16838770—22no—
22#16838770—22no—
23#16838770—22no—
24#16838770—22no—
25C2×Dic482D412yes—
26C2×D964D412yes—
27C2×C22⋊D241—22no—
28C2×C4×D241—22no—
29Dic964—22no—
30#16838760—24no—
31#16838759—24no—
32#16838758—24no—
33#16838757—24no—
34D1928—22no—
35#16838755—24no—
36#16838754—22no—
37#16838754—22no—
38C2×#14515349D414yes—
39#41×C241—22no—
40#41×C241—22no—
41C2×Q8×C241D411yescharacteristic
42C2×D4×C241—21no—
43C2×D4×C241D411yescharacteristic
44C22×C4×C241—21no—
45C22×C4×C241C2311yescharacteristic
46M16×C241—22no—
47C2×C8×C241—22no—
48C2×C8×C241—21no—
49C2×C8×C241D412yes—
50C22×D241—22no—
51Dic482—22no—
52Dic482—22no—
53D964—22no—
54D964—22no—
55C22⋊D241—42no—
56C22⋊D241—42no—
57C2×Dic241—22no—
58C4×D241—42no—
59C4×D241—42no—
60#14515349—24no—
61C23×C241—21no—
62C23×C241#4111yescharacteristic
63Q8×C241—22no—
64D4×C241—22no—
65D4×C241—42no—
66C2×C4×C241—21no—
67C2×C4×C241—41no—
68C2×C4×C241—41no—
69C2×C4×C241C2×D412yes—
70C2×C4×C241C2×D412yes—
71C2×C4×C241C2×D411yescharacteristic
72C2×C4×C241C2×D411yescharacteristic
73C8×C241—22no—
74C8×C241—41no—
75C22×C241—41no—
76C22×C241—42no—
77C22×C241—41no—
78C22×C241#12112yes—
79C22×C241#12111yescharacteristic
80C2×D241—44no—
81C2×D241—42no—
82C4×C241—41no—
83C4×C241#12011yescharacteristic
84C4×C241#12012yes—
85C4×C241#12711yescharacteristic
86Dic241—42no—
87C2×C241—22no—
88C2×C241—21no—
89C2×C241—81no—
90C2×C241#39211yescharacteristic
91D241—82no—
92C241#201711yescharacteristic, complemented, Sylow
93#2017—2411nomaximal, Sylow
94#575—2412no—
95#575—2411no—
96#408—2412no—
97#408D24111yescharacteristic, complemented
98#338—2411no—
99C2×#41—2412no—
100C2×#41C2×D24111yescharacteristic
101#137—4822no—
102#137—4822no—
103#137—4822no—
104AGL(1,ℤ/8)—4822no—
105AGL(1,ℤ/8)—4822no—
106AGL(1,ℤ/8)—4822no—
107#135—4824no—
108#135—4822no—
109C2×M16—2412no—
110C2×M16C2×D24111yescharacteristic
111C22×C8C2×D24111yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—4824no—
114#41—22no—
115#41—22no—
116#41—4822no—
117#41—4822no—
118#41—4822no—
119#41—4822no—
120C2×Q8—2412no—
121C2×Q8D96411yescharacteristic
122C2×D4—21no—
123C2×D4—4822no—
124C2×D4—2412no—
125C2×D4D96411yescharacteristic
126C22×C4—21no—
127C22×C4—4822no—
128C22×C4C22×D24111yescharacteristic
129Q16—4822no—
130Q16—4824no—
131SD16—4824no—
132SD16—4824no—
133SD16—4824no—
134D8—4822no—
135D8—4824no—
136M16—22no—
137M16—4822no—
138M16—4822no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—2414no—
142C2×C8C22⋊D24112yes—
143C23—21no—
144C23—4822no—
145C23#1683877011yescharacteristic
146Q8—22no—
147Q8—4822no—
148Q8—4822no—
149D4—22no—
150D4—42no—
151D4—9642no—
152D4—9642no—
153D4—4822no—
154D4—4822no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—9642no—
159C2×C4—9642no—
160C2×C4—4822no—
161C2×C4D4×D24112yes—
162C2×C4D4×D24112yes—
163C2×C4C2×C22⋊D24111yescharacteristic
164C2×C4C2×D96411yescharacteristic
165C8—22no—
166C8—41no—
167C8—4824no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—9644no—
172C22—9642no—
173C22#2144061512yes—
174C22#2144061611yescharacteristic
175C4—41no—
176C4—9642no—
177C4#2144061011yescharacteristic
178C4#2144061212yes—
179C4#2144063811yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—19282no—
184C2#2950762611yescharacteristic
subgroupG/H
centerC4#21440638
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#408×C241C2
socleC2×C241#392
hypercenter#408D241
hypocenterC241#2017
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #29508517C2semidirect
2. #29508515C2semidirect
3. #29507683C2semidirect
4. #29507475C2semidirect
5. #408×C241C2semidirect
92. C241#2017semidirect
97. #408D241semidirect

Maximal subgroups

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

subgroupindex
#295085172
#295085152
#295076832
#295074752
#408×C2412
#2017241