Finite Group Databasebeta

← #44508486

Subgroups — #44508486

Order 30848.

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

normal subgroups only

This group has 406 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×#21440668C212yesmaximal, complemented
2#29508298C211yesmaximal, characteristic, complemented
3C2×#21440570C212yesmaximal, complemented
4#29507486C211yesmaximal, characteristic, complemented
5#390×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2212yes—
7#21440668—24no—
8#21440668—24no—
9C2×#16838758—22no—
10C2×#16838755—22no—
11C2×#16838754C2212yes—
12#21440622—22no—
13#21440617—22no—
14#21440616—22no—
15#21440570—24no—
16C22×D4×C241C2211yescharacteristic
17C2×C4⋊C4×C241C2211yescharacteristic
18C2×C22⋊C4×C241—22no—
19C2×C42×C241C2211yescharacteristic
20#16838770—22no—
21#16838770—22no—
22#16838770—22no—
23#16838770—22no—
24C2×Dic482D412yes—
25C2×D964—22no—
26C2×D964D412yes—
27C2×C22⋊D241—22no—
28C2×C4×D241—22no—
29#16838758—28no—
30#16838755—28no—
31#16838754—22no—
32#16838754D414yescomplemented
33C2×#14515349—22no—
34C4⋊Dic241—22no—
35#16838747—24no—
36C24×C241—21no—
37C2×D4×C241—22no—
38C2×D4×C241—22no—
39C2×D4×C241—21no—
40C2×D4×C241D412yescomplemented
41C22×C4×C241—21no—
42C22×C4×C241D412yes—
43C22×C4×C241C2311yescharacteristic
44C4⋊C4×C241—22no—
45C22⋊C4×C241—44no—
46C42×C241—22no—
47C22×D241—22no—
48Dic482—22no—
49Dic482—22no—
50D964—22no—
51D964—22no—
52D964—82no—
53C22⋊D241—42no—
54C22⋊D241—42no—
55C2×Dic241—22no—
56C4×D241—42no—
57C4×D241—42no—
58#14515349—24no—
59C23×C241—22no—
60C23×C241—42no—
61C23×C241—42no—
62C23×C241—41no—
63C23×C241—41no—
64C23×C241C2×D411yescharacteristic
65D4×C241—24no—
66D4×C241—42no—
67C2×C4×C241—22no—
68C2×C4×C241—22no—
69C2×C4×C241—41no—
70C2×C4×C241—41no—
71C2×C4×C241—42no—
72C2×C4×C241C2×D412yes—
73C2×C4×C241C2×D412yes—
74C2×C4×C241C2×D411yescharacteristic
75C2×C4×C241#4111yescharacteristic
76C22×C241—21no—
77C22×C241—21no—
78C22×C241—44no—
79C22×C241—42no—
80C22×C241—82no—
81C22×C241—81no—
82C22×C241—81no—
83C22×C241#12011yescharacteristic
84C22×C241#12111yescharacteristic
85C22×C241#12711yescharacteristic
86C2×D241—42no—
87C2×D241—42no—
88C2×D241—42no—
89C4×C241—42no—
90C4×C241—42no—
91C4×C241#12012yes—
92C4×C241#12112yes—
93Dic241—42no—
94C2×C241—21no—
95C2×C241—21no—
96C2×C241—82no—
97C2×C241#39211yescharacteristic
98C2×C241#45311yescharacteristic
99C2×C241#45411yescharacteristic
100D241—82no—
101C241#200611yescharacteristic, complemented, Sylow
102#2006—2411nomaximal, Sylow
103C2×AGL(1,ℤ/8)—2412no—
104#537—2411no—
105C2×#104—2412no—
106#390D24111yescharacteristic, complemented
107#343—2411no—
108C2×#41—2412no—
109C22×D4C2×D24111yescharacteristic
110AGL(1,ℤ/8)—4824no—
111AGL(1,ℤ/8)—4824no—
112C2×SD16—4822no—
113C2×D8—4822no—
114C2×M16—2412no—
115C22⋊Q8—4822no—
116#121—4822no—
117#121—4822no—
118C2×C4⋊C4C2×D24111yescharacteristic
119C2×C22⋊C4—22no—
120C2×C42C2×D24111yescharacteristic
121#104—4824no—
122C24—21no—
123#41—4822no—
124#41—4822no—
125#41—4822no—
126#41—4822no—
127C2×Q8—2412no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—21no—
131C2×D4—4822no—
132C2×D4—4822no—
133C2×D4—2412no—
134C2×D4D96412yescomplemented
135C22×C4—21no—
136C22×C4—4822no—
137C22×C4C22⋊D24112yes—
138C22×C4C22×D24111yescharacteristic
139SD16—4828no—
140D8—4828no—
141M16—4822no—
142M16—2414no—
143C2×C8—4822no—
144C4⋊C4—22no—
145C4⋊C4—4822no—
146C22⋊C4—44no—
147C22⋊C4—4824no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—4822no—
155C23C2×C22⋊D24111yescharacteristic
156Q8—4822no—
157Q8—4822no—
158D4—24no—
159D4—42no—
160D4—19282no—
161D4—9642no—
162D4—9642no—
163D4—4822no—
164D4—4822no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—9642no—
171C2×C4—9642no—
172C2×C4—4822no—
173C2×C4D4×D24112yes—
174C2×C4D4×D24112yes—
175C2×C4C2×D96411yescharacteristic
176C2×C4#1683877011yescharacteristic
177C8—4824no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—9642no—
186C22—9642no—
187C22—9642no—
188C22#2144061011yescharacteristic
189C22#2144061611yescharacteristic
190C22#2144063811yescharacteristic
191C4—42no—
192C4—42no—
193C4—9642no—
194C4#2144061212yes—
195C4#2144061512yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—19282no—
200C2#2950762611yescharacteristic
201C2#2950788411yescharacteristic
202C2#2950788911yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#390×C241C2
socleC22×C241#120
hypercenter#390D241
hypocenterC241#2006
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#21440668C2semidirect
2. #29508298C2semidirect
3. C2×#21440570C2semidirect
4. #29507486C2semidirect
5. #390×C241C2semidirect
32. #16838754D4semidirect
40. C2×D4×C241D4semidirect
101. C241#2006semidirect
106. #390D241semidirect
134. C2×D4D964semidirect

Maximal subgroups

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

subgroupindex
C2×#214406682
#295082982
C2×#214405702
#295074862
#390×C2412
#2006241