Finite Group Databasebeta

← #37571546

Subgroups — #37571546

Order 24448.

236 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 51 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#27133288C211yesmaximal, characteristic
2#27132999C211yesmaximal, characteristic, complemented
3#27132996C211yesmaximal, characteristic, complemented
4#27132600C211yesmaximal, characteristic
5#27132399C211yesmaximal, characteristic, complemented
6#27132386C211yesmaximal, characteristic
7#328×C191C211yesmaximal, characteristic, complemented
8#20259302—21no—
9#20259301C2211yescharacteristic
10#20259300—21no—
11#20259300—21no—
12#20259299—21no—
13#20259298—21no—
14C2×C4⋊Dic191—21no—
15C2×C4⋊Dic191C2211yescharacteristic
16C2×(C2×D191)⋊C4—21no—
17C2×(C2×D191)⋊C4C2211yescharacteristic
18C22⋊C4×D191—21no—
19#20259256—21no—
20#20259255—21no—
21#20259247—21no—
22#20259246—21no—
23C22⋊(C191⋊C8)C2211yescharacteristic
24C22⋊Q8×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26#95×C191C2211yescharacteristic
27C23×D191D411yescharacteristic
28C2×Dic382—21no—
29C2×Dic382D411yescharacteristic
30C22×Dic191—21no—
31C22×Dic191D411yescharacteristic
32C2×C4×D191—21no—
33C2×C4×D191—21no—
34C2×C191⋊C8—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191—21no—
37C4⋊Dic191—21no—
38C4⋊Dic191—42no—
39C4⋊Dic191D411yescharacteristic
40Dic191⋊C4—21no—
41Dic191⋊C4—21no—
42Dic191⋊C4—21no—
43C22⋊Dic191—21no—
44(C2×D191)⋊C4—21no—
45(C2×D191)⋊C4—21no—
46(C2×D191)⋊C4—21no—
47(C2×D191)⋊C4—21no—
48(C2×D191)⋊C4—42no—
49C2×Q8×C191D411yescharacteristic
50C22×C4×C191—21no—
51C22×C4×C191C2311yescharacteristic
52C2×C8×C191—21no—
53C4⋊C4×C191—21no—
54C4⋊C4×C191D411yescharacteristic
55C22⋊C4×C191—21no—
56C22×D191—21no—
57C22×D191—21no—
58C22×D191—41no—
59C22×D191—41no—
60C22×D191Q1612yes—
61Dic382—41no—
62Dic382—81no—
63C2×Dic191—21no—
64C2×Dic191—21no—
65C2×Dic191—21no—
66C2×Dic191—41no—
67C2×Dic191—41no—
68C2×Dic191—41no—
69C2×Dic191—41no—
70C4×D191—81no—
71C4×D191—81no—
72C191⋊C8—41no—
73C23×C191C2×D411yescharacteristic
74Q8×C191—41no—
75C2×C4×C191—22no—
76C2×C4×C191—21no—
77C2×C4×C191—21no—
78C2×C4×C191—41no—
79C2×C4×C191—41no—
80C2×C4×C191—41no—
81C2×C4×C191C2×D411yescharacteristic
82C2×C4×C191C2×D411yescharacteristic
83C8×C191—41no—
84C22×C191—21no—
85C22×C191—21no—
86C22×C191#12011yescharacteristic
87C22×C191C2×Q1611yescharacteristic
88C22×C191#13711yescharacteristic
89C2×D191—22no—
90C2×D191—41no—
91C2×D191—41no—
92C2×D191—42no—
93C2×D191—81no—
94C4×C191—21no—
95C4×C191—21no—
96C4×C191—42no—
97C4×C191—41no—
98C4×C191—41no—
99Dic191—41no—
100Dic191—41no—
101Dic191—41no—
102Dic191—81no—
103C2×C191—21no—
104C2×C191—21no—
105C2×C191#45111yescharacteristic
106C2×C191#45311yescharacteristic
107C2×C191#45811yescharacteristic
108D191—42no—
109C191#161411yescharacteristic, complemented, Sylow
110#1614—1911nomaximal, Sylow
111#543—1911no—
112#484—1911no—
113#484—1911no—
114#399—1911no—
115#328—1911no—
116#328D19111yescharacteristic, complemented
117#323—1911no—
118C22⋊Q8—3821no—
119C22⋊Q8—3821no—
120C22⋊Q8—3821no—
121C22⋊Q8—3821no—
122C22⋊Q8—3821no—
123C22⋊Q8—1911no—
124C22⋊Q8C2×D19111yescharacteristic
125C2×C4⋊C4—3821no—
126C2×C4⋊C4—1911no—
127C2×C22⋊C4—3821no—
128C2×C22⋊C4—3821no—
129C2×C22⋊C4—1911no—
130#107—3821no—
131#107—3821no—
132#103—3821no—
133#103—3821no—
134C22⋊C8—1911no—
135C22⋊C8C2×D19111yescharacteristic
136#95C2×D19111yescharacteristic
137C24—1911no—
138C2×Q8—3821no—
139C2×Q8—1911no—
140C2×Q8D76411yescharacteristic
141C22×C4—21no—
142C22×C4—3821no—
143C22×C4—3821no—
144C22×C4—3821no—
145C22×C4—1911no—
146C22×C4C22×D19111yescharacteristic
147C2×C8—21no—
148C2×C8—3821no—
149C4⋊C4—21no—
150C4⋊C4—3821no—
151C4⋊C4—3821no—
152C4⋊C4—3821no—
153C4⋊C4—3821no—
154C4⋊C4—3821no—
155C4⋊C4—3821no—
156C4⋊C4—1911no—
157C4⋊C4—7642no—
158C4⋊C4D76411yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—3821no—
161C22⋊C4—3821no—
162C22⋊C4—3821no—
163C22⋊C4—3821no—
164C22⋊C4—3821no—
165C22⋊C4—7642no—
166C23—3821no—
167C23—3821no—
168C23—1912no—
169C23—7641no—
170C23—7641no—
171C23D4×D19111yescharacteristic
172Q8—41no—
173Q8—15281no—
174Q8—7641no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—3821no—
182C2×C4—3821no—
183C2×C4—3821no—
184C2×C4—15281no—
185C2×C4—15281no—
186C2×C4—7641no—
187C2×C4—7641no—
188C2×C4—7641no—
189C2×C4—7641no—
190C2×C4D4×D19111yescharacteristic
191C2×C4C2×D76411yescharacteristic
192C8—41no—
193C8—7641no—
194C22—21no—
195C22—21no—
196C22—3822no—
197C22—15281no—
198C22—7642no—
199C22—7641no—
200C22—7641no—
201C22#2025929211yescharacteristic
202C22Q16×D19111yescharacteristic
203C22#2025935111yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—15281no—
210C4—7641no—
211C4—7641no—
212C4—7641no—
213C2—21no—
214C2—21no—
215C2—7642no—
216C2#2713282011yescharacteristic
217C2#2713283211yescharacteristic
218C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#328×C191C2
socleC22×C191#120
prime radicalC23×D191D4
hypercenter#328D191
hypocenterC191#1614
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #27132999C2semidirect
3. #27132996C2semidirect
5. #27132399C2semidirect
7. #328×C191C2semidirect
109. C191#1614semidirect
116. #328D191semidirect

Maximal subgroups

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

subgroupindex
#271332882
#271329992
#271329962
#271326002
#271323992
#271323862
#328×C1912
#1614191