Finite Group Databasebeta

← #44508548

Subgroups — #44508548

Order 30848.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#29508515C212yesmaximal, complemented
2#29507685C211yesmaximal, characteristic, complemented
3#29507684C212yesmaximal, complemented
4#29507475C211yesmaximal, characteristic, complemented
5#575×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2211yescharacteristic
7#21440673—22no—
8#21440672—22no—
9#21440668—22no—
10#21440667—22no—
11#21440662—24no—
12C2×#16838754C2212yes—
13C22×#14515349C2211yescharacteristic
14C22⋊#14515349—24no—
15#21440554—22no—
16C2×#41×C241C2212yes—
17#137×C241—22no—
18AGL(1,ℤ/8)×C241—22no—
19#135×C241—22no—
20C2×M16×C241C2211yescharacteristic
21#16838770—22no—
22#16838770—22no—
23C2×Dic482D411yescharacteristic
24C2×D964D411yescharacteristic
25C2×C22⋊D241—21no—
26C2×C4×D241—21no—
27#16838760—24no—
28#16838758—24no—
29#16838757—24no—
30#16838755—24no—
31#16838754—22no—
32#16838754—22no—
33C2×#14515349—21no—
34C2×#14515349—22no—
35C2×#14515349D414yes—
36#41×C241—22no—
37#41×C241—22no—
38#41×C241—22no—
39#41×C241—22no—
40C2×Q8×C241D412yes—
41C2×D4×C241—22no—
42C2×D4×C241D412yes—
43C22×C4×C241—22no—
44C22×C4×C241C2311yescharacteristic
45Q16×C241—22no—
46SD16×C241—24no—
47D8×C241—22no—
48M16×C241—22no—
49C2×C8×C241D412yes—
50C22×D241—21no—
51Dic482—22no—
52D964—22no—
53C22⋊D241—42no—
54C2×Dic241—21no—
55C4×D241—41no—
56C4×D241—41no—
57#14515349—24no—
58#14515349—41no—
59C23×C241—22no—
60C23×C241#4111yescharacteristic
61Q8×C241—22no—
62Q8×C241—22no—
63D4×C241—22no—
64D4×C241—22no—
65D4×C241—42no—
66D4×C241—42no—
67C2×C4×C241—22no—
68C2×C4×C241—42no—
69C2×C4×C241—42no—
70C2×C4×C241C2×D411yescharacteristic
71C2×C4×C241C2×D412yes—
72C2×C4×C241C2×D412yes—
73C2×C4×C241C2×D411yescharacteristic
74C8×C241—22no—
75C22×C241—41no—
76C22×C241—44no—
77C22×C241—42no—
78C22×C241#12111yescharacteristic
79C22×C241#12112yes—
80C2×D241—42no—
81C2×D241—41no—
82C4×C241—42no—
83C4×C241#12012yes—
84C4×C241#12011yescharacteristic
85C4×C241#12711yescharacteristic
86Dic241—41no—
87C2×C241—21no—
88C2×C241—22no—
89C2×C241—82no—
90C2×C241#39211yescharacteristic
91D241—81no—
92C241#201711yescharacteristic, complemented, Sylow
93#2017—2411nomaximal, Sylow
94#575—2412no—
95#575D24111yescharacteristic, complemented
96#408—2412no—
97#408—2411no—
98#338—2411no—
99C2×#41—2411no—
100C2×#41C2×D24112yes—
101#137—22no—
102#137—4822no—
103#137—4822no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—4822no—
106AGL(1,ℤ/8)—4822no—
107#135—22no—
108#135—4824no—
109C2×M16—2412no—
110C2×M16C2×D24111yescharacteristic
111C22×C8—2411no—
112C22⋊C8—4824no—
113C22⋊C8—4822no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—4822no—
119#41—4822no—
120C2×Q8—2411no—
121C2×Q8C22⋊D24112yes—
122C2×D4—22no—
123C2×D4—4821no—
124C2×D4—2411no—
125C2×D4C22⋊D24112yes—
126C22×C4—22no—
127C22×C4—4821no—
128C22×C4C22×D24111yescharacteristic
129Q16—22no—
130Q16—4824no—
131SD16—24no—
132SD16—4824no—
133SD16—4824no—
134D8—22no—
135D8—4824no—
136M16—22no—
137M16—4822no—
138M16—4822no—
139C2×C8—4822no—
140C2×C8—4821no—
141C2×C8—2414no—
142C2×C8C22⋊D24112yes—
143C23—22no—
144C23—4821no—
145C23#1683876911yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—4822no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—9642no—
154D4—4822no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—9641no—
159C2×C4—9641no—
160C2×C4—4821no—
161C2×C4D4×D24111yescharacteristic
162C2×C4D4×D24112yes—
163C2×C4C2×C22⋊D24112yes—
164C2×C4C2×C22⋊D24111yescharacteristic
165C8—22no—
166C8—9641no—
167C8—4824no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—9642no—
172C22—9641no—
173C22#2144061311yescharacteristic
174C22#2144061412yes—
175C4—42no—
176C4—9641no—
177C4#2144061012yes—
178C4#2144061111yescharacteristic
179C4#2144063811yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—19281no—
184C2#2950762511yescharacteristic
subgroupG/H
centerC4#21440638
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#575×C241C2
socleC2×C241#392
hypercenter#575D241
hypocenterC241#2017
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #29508515C2semidirect
2. #29507685C2semidirect
3. #29507684C2semidirect
4. #29507475C2semidirect
5. #575×C241C2semidirect
92. C241#2017semidirect
95. #575D241semidirect

Maximal subgroups

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

subgroupindex
#295085152
#295076852
#295076842
#295074752
#575×C2412
#2017241