Finite Group Databasebeta

← #37573041

Subgroups — #37573041

Order 24448.

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

normal subgroups only

This group has 312 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
1#27133429C211yesmaximal, characteristic
2#27133239C211yesmaximal, characteristic
3#27132673C211yesmaximal, characteristic, complemented
4#27132671C211yesmaximal, characteristic, complemented
5#27132636C211yesmaximal, characteristic
6#27132419C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C191C211yesmaximal, characteristic, complemented
8C2×#15690287C2211yescharacteristic
9C22×Dic382C2211yescharacteristic
10#20259330—22no—
11#20259328—22no—
12C2×#15690271C2211yescharacteristic
13M16×D191—22no—
14#20259322C412yescomplemented
15#20259310C412yescomplemented
16#20259306—22no—
17#20259302—22no—
18#20259281C2211yescharacteristic
19#20259247—22no—
20#20259245—22no—
21#20259236—22no—
22C2×M16×C191C2211yescharacteristic
23#117×C191C2211yescharacteristic
24#117×C191C2211yescharacteristic
25#15690287—21no—
26#15690287—21no—
27#15690287—21no—
28#15690287—21no—
29C2×Dic382—21no—
30C2×Dic382—21no—
31C2×Dic382—21no—
32C2×Dic382—21no—
33C2×Dic382—21no—
34C2×Dic382C2×C412yes—
35C2×Dic382C2×C411yescharacteristic
36C2×D764C2×C411yescharacteristic
37C2×C22⋊D191D412yes—
38C22×Dic191—21no—
39C2×C4×D191D412yes—
40#15690271—21no—
41#15690271—21no—
42#15690270—24no—
43C2×C191⋊C8D412yes—
44C8×D191—24no—
45C4⋊Dic191—24no—
46C4⋊Dic191—21no—
47C22⋊Dic191—21no—
48(C2×D191)⋊C4—24no—
49C4×Dic191—21no—
50C22×C4×C191C2311yescharacteristic
51M16×C191—21no—
52M16×C191—21no—
53C2×C8×C191D412yes—
54C4⋊C4×C191—21no—
55C4⋊C4×C191—21no—
56C22⋊C4×C191—21no—
57C22⋊C4×C191—21no—
58C42×C191—21no—
59C42×C191C2×C412yes—
60C22×D191C22⋊C412yes—
61Dic382—21no—
62Dic382—21no—
63Dic382—22no—
64Dic382—22no—
65Dic382—41no—
66Dic382—41no—
67D764—21no—
68D764—21no—
69C22⋊D191—22no—
70C22⋊D191—22no—
71C2×Dic191—22no—
72C2×Dic191—41no—
73C2×Dic191—41no—
74C2×Dic191—41no—
75C2×Dic191C22⋊C412yes—
76C4×D191—22no—
77C4×D191—22no—
78C191⋊C8—22no—
79C23×C191C2×D411yescharacteristic
80C2×C4×C191—22no—
81C2×C4×C191—41no—
82C2×C4×C191C22×C411yescharacteristic
83C2×C4×C191C2×D411yescharacteristic
84C2×C4×C191C2×D411yescharacteristic
85C2×C4×C191C2×D411yescharacteristic
86C2×C4×C191#4111yescharacteristic
87C2×C4×C191#4111yescharacteristic
88C8×C191—22no—
89C22×C191—41no—
90C22×C191C2×C22⋊C411yescharacteristic
91C22×C191#12111yescharacteristic
92C22×C191#12111yescharacteristic
93C2×D191—22no—
94C2×D191—42no—
95C4×C191—42no—
96C4×C191—81no—
97C4×C191C4×D411yescharacteristic
98C4×C191C4×D411yescharacteristic
99C4×C191#12011yescharacteristic
100C4×C191#12311yescharacteristic
101Dic191—22no—
102Dic191—42no—
103Dic191—81no—
104C2×C191—21no—
105C2×C191—21no—
106C2×C191—21no—
107C2×C191#38611yescharacteristic
108D191—42no—
109C191#190911yescharacteristic, complemented, Sylow
110#1909—1911nomaximal, Sylow
111#568—1911no—
112#536—1911no—
113#419—1911no—
114#419—1911no—
115#410—1911no—
116H(3,ℤ/4)—1911no—
117H(3,ℤ/4)D19111yescharacteristic, complemented
118C2×#41—1911no—
119C22×Q8—1911no—
120#131—3822no—
121#131—3822no—
122C2×M16—3822no—
123C2×M16—1911no—
124C2×M16C2×D19111yescharacteristic
125C4⋊Q8—1912no—
126#124—1912no—
127#123—3822no—
128C22⋊Q8—3822no—
129#117—1911no—
130#117C2×D19111yescharacteristic
131#117C2×D19111yescharacteristic
132#103—3822no—
133#103—3822no—
134#99—3822no—
135#41—3821no—
136#41—3821no—
137#41—3821no—
138#41—3821no—
139C2×Q8—3821no—
140C2×Q8—3821no—
141C2×Q8—3821no—
142C2×Q8—3821no—
143C2×Q8—3821no—
144C2×Q8—1912no—
145C2×Q8—1911no—
146C2×D4—1912no—
147C2×D4—1911no—
148C22×C4—3821no—
149C22×C4—1912no—
150C22×C4C22×D19111yescharacteristic
151M16—21no—
152M16—21no—
153M16—3824no—
154M16—3821no—
155M16—3821no—
156C2×C8—3824no—
157C2×C8—1912no—
158C2×C8D76412yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—3824no—
162C4⋊C4—3821no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—3824no—
166C22⋊C4—3821no—
167C42—21no—
168C42—3821no—
169C42C4×D19112yes—
170C23—1912no—
171C23D4×D19111yescharacteristic
172Q8—3821no—
173Q8—3821no—
174Q8—3822no—
175Q8—3822no—
176Q8—7641no—
177Q8—7641no—
178D4—3822no—
179D4—3822no—
180D4—3821no—
181D4—3821no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—3822no—
185C2×C4—3822no—
186C2×C4—3822no—
187C2×C4—1912no—
188C2×C4—7641no—
189C2×C4—7641no—
190C2×C4—7641no—
191C2×C4C2×C4×D19111yescharacteristic
192C2×C4D4×D19111yescharacteristic
193C2×C4D4×D19111yescharacteristic
194C2×C4C2×D76411yescharacteristic
195C2×C4#1569028711yescharacteristic
196C2×C4#1569028811yescharacteristic
197C8—22no—
198C8—3822no—
199C22—41no—
200C22—3822no—
201C22—7642no—
202C22C22⋊C4×D19111yescharacteristic
203C22#2025929511yescharacteristic
204C22#2025929711yescharacteristic
205C4—42no—
206C4—81no—
207C4—3822no—
208C4—15281no—
209C4—7642no—
210C4#2025928411yescharacteristic
211C4C4×D76411yescharacteristic
212C4#2025929211yescharacteristic
213C4#2025930711yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—7642no—
218C2#2713254111yescharacteristic
subgroupG/H
centerC2#27132541
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
FittingH(3,ℤ/4)×C191C2
socleC2×C191#386
prime radicalC2×#15690287C22
cosocleC22×C4×C191C23
hypercenterH(3,ℤ/4)D191
hypocenterC191#1909
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
3. #27132673C2semidirect
4. #27132671C2semidirect
6. #27132419C2semidirect
7. H(3,ℤ/4)×C191C2semidirect
14. #20259322C4semidirect
15. #20259310C4semidirect
109. C191#1909semidirect
117. H(3,ℤ/4)D191semidirect

Maximal subgroups

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

subgroupindex
#271334292
#271332392
#271326732
#271326712
#271326362
#271324192
H(3,ℤ/4)×C1912
#1909191