Finite Group Databasebeta

← #44507940

Subgroups — #44507940

Order 30848.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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×#21440675C211yesmaximal, characteristic
2#29508194C211yesmaximal, characteristic, complemented
3#29507735C211yesmaximal, characteristic
4#29507725C211yesmaximal, characteristic, complemented
5#29507690C211yesmaximal, characteristic
6#29507488C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9C22×Dic482C2211yescharacteristic
10#21440675—22no—
11#21440675—22no—
12C2×Dic964C412yescomplemented
13C2×#16838759C412yescomplemented
14C2×#16838754C2211yescharacteristic
15C4×Dic482—22no—
16#21440607—22no—
17#21440601C2211yescharacteristic
18#21440598—22no—
19#21440570—22no—
20#21440565—22no—
21#21440556—22no—
22C2×M16×C241C2211yescharacteristic
23#117×C241C2211yescharacteristic
24#117×C241C2211yescharacteristic
25#16838770—21no—
26#16838770—21no—
27#16838770—21no—
28#16838770—21no—
29C2×Dic482—21no—
30C2×Dic482—21no—
31C2×Dic482—21no—
32C2×Dic482C2×C411yescharacteristic
33C2×Dic482C2×C412yes—
34C2×Dic482D412yes—
35C2×Dic482D412yes—
36C2×D964C2×C411yescharacteristic
37C2×C22⋊D241—21no—
38C22×Dic241—21no—
39C2×C4×D241—21no—
40Dic964—24no—
41#16838759—24no—
42#16838754—21no—
43#16838754—21no—
44C2×#14515349—21no—
45C4⋊Dic241—21no—
46#16838749—24no—
47C22⋊Dic241D412yes—
48C4×Dic241—24no—
49C4×Dic241—21no—
50C22×C4×C241C2311yescharacteristic
51M16×C241—21no—
52M16×C241—21no—
53C2×C8×C241C2×C412yes—
54C4⋊C4×C241—21no—
55C4⋊C4×C241—21no—
56C22⋊C4×C241—21no—
57C22⋊C4×C241—21no—
58C42×C241—21no—
59C42×C241D412yes—
60C22×D241—21no—
61Dic482—22no—
62Dic482—22no—
63Dic482—22no—
64Dic482—21no—
65Dic482—21no—
66Dic482C22⋊C414yes—
67D964—21no—
68D964—21no—
69C22⋊D241—41no—
70C22⋊D241—41no—
71C2×Dic241—22no—
72C2×Dic241—22no—
73C2×Dic241—22no—
74C2×Dic241—21no—
75C2×Dic241—22no—
76C4×D241—41no—
77C4×D241—41no—
78#14515349—41no—
79C23×C241C2×D411yescharacteristic
80C2×C4×C241—22no—
81C2×C4×C241—41no—
82C2×C4×C241C22×C411yescharacteristic
83C2×C4×C241C2×D411yescharacteristic
84C2×C4×C241C2×D411yescharacteristic
85C2×C4×C241C2×D411yescharacteristic
86C2×C4×C241#4111yescharacteristic
87C2×C4×C241#4111yescharacteristic
88C8×C241—22no—
89C22×C241—41no—
90C22×C241C4×D411yescharacteristic
91C22×C241#12011yescharacteristic
92C22×C241#12111yescharacteristic
93C2×D241—41no—
94C2×D241—81no—
95C4×C241—42no—
96C4×C241—81no—
97C4×C241C2×C22⋊C411yescharacteristic
98C4×C241C4×D411yescharacteristic
99C4×C241#12111yescharacteristic
100C4×C241#12311yescharacteristic
101Dic241—24no—
102Dic241—42no—
103Dic241—41no—
104C2×C241—21no—
105C2×C241—21no—
106C2×C241—21no—
107C2×C241#38611yescharacteristic
108D241—81no—
109C241#190511yescharacteristic, complemented, Sylow
110#1905—2411nomaximal, Sylow
111C2×#137—2411no—
112#519—2411no—
113#421—2411no—
114#419—2411no—
115#410—2411no—
116#344—2411no—
117H(3,ℤ/4)D24111yescharacteristic, complemented
118C2×#41—2411no—
119C22×Q8—2411no—
120#137—4822no—
121#137—4822no—
122C2×Q16—2412no—
123C2×SD16—2412no—
124C2×M16—2411no—
125C2×M16C2×D24111yescharacteristic
126C4×Q8—4822no—
127C4×Q8—4822no—
128#117—4822no—
129#117—2411no—
130#117C2×D24111yescharacteristic
131#117C2×D24111yescharacteristic
132#104—4822no—
133#103—4822no—
134#99—4822no—
135#41—4821no—
136#41—4821no—
137#41—4821no—
138#41—4821no—
139C2×Q8—4821no—
140C2×Q8—4821no—
141C2×Q8—4821no—
142C2×Q8—2411no—
143C2×Q8—2412no—
144C2×Q8—2412no—
145C2×Q8—2412no—
146C2×D4—4821no—
147C2×D4—2411no—
148C22×C4—4821no—
149C22×C4—4821no—
150C22×C4C22×D24111yescharacteristic
151Q16—4824no—
152SD16—4824no—
153M16—21no—
154M16—21no—
155M16—4821no—
156M16—4821no—
157C2×C8—4821no—
158C2×C8C4×D24112yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—4824no—
162C4⋊C4—4821no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—2412no—
166C42—21no—
167C42—4824no—
168C42—4821no—
169C42D96412yes—
170C23—4821no—
171C23D4×D24111yescharacteristic
172Q8—4821no—
173Q8—4821no—
174Q8—4822no—
175Q8—4822no—
176Q8—4822no—
177Q8—2414no—
178D4—9641no—
179D4—9641no—
180D4—4821no—
181D4—4821no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—9641no—
185C2×C4—9641no—
186C2×C4—4821no—
187C2×C4—4822no—
188C2×C4—4822no—
189C2×C4—4822no—
190C2×C4—4822no—
191C2×C4C2×C4×D24111yescharacteristic
192C2×C4D4×D24111yescharacteristic
193C2×C4D4×D24111yescharacteristic
194C2×C4C2×D96411yescharacteristic
195C2×C4#1683877011yescharacteristic
196C2×C4#1683877111yescharacteristic
197C8—22no—
198C8—9641no—
199C22—41no—
200C22—19281no—
201C22—9641no—
202C22#2144060411yescharacteristic
203C22#2144061211yescharacteristic
204C22#2144061511yescharacteristic
205C4—42no—
206C4—81no—
207C4—9642no—
208C4—9641no—
209C4—4824no—
210C4C22⋊C4×D24111yescharacteristic
211C4C4×D96411yescharacteristic
212C4#2144061711yescharacteristic
213C4#2144062711yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—19281no—
218C2#2950759511yescharacteristic
subgroupG/H
centerC2#29507595
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
FittingH(3,ℤ/4)×C241C2
socleC2×C241#386
prime radicalC2×#16838770C22
cosocleC22×C4×C241C23
hypercenterH(3,ℤ/4)D241
hypocenterC241#1905
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #29508194C2semidirect
4. #29507725C2semidirect
6. #29507488C2semidirect
7. H(3,ℤ/4)×C241C2semidirect
12. C2×Dic964C4semidirect
13. C2×#16838759C4semidirect
109. C241#1905semidirect
117. H(3,ℤ/4)D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406752
#295081942
#295077352
#295077252
#295076902
#295074882
H(3,ℤ/4)×C2412
#1905241