Finite Group Databasebeta

← #37574203

Subgroups — #37574203

Order 24448.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#27133209C211yesmaximal, characteristic
2#27132647C211yesmaximal, characteristic, complemented
3#27132461C212yesmaximal, complemented
4#27132459C212yesmaximal, complemented
5#413×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C411yescharacteristic
7C2×#15690271—21no—
8#20259320C2211yescharacteristic
9#20259318C411yescharacteristic
10#20259311C2211yescharacteristic
11#20259309C411yescharacteristic
12#20259294—21no—
13#20259294—21no—
14C4×C22⋊D191—21no—
15C4×C22⋊D191—21no—
16C2×C4×Dic191C411yescharacteristic
17#20259241C2212yes—
18#20259239—21no—
19C2×#41×C191C2211yescharacteristic
20C2×M16×C191—21no—
21#101×C191C2212yes—
22#100×C191—21no—
23#15690287—41no—
24#15690287—41no—
25C2×Dic382C2×C411yescharacteristic
26C2×D764C2×C411yescharacteristic
27C2×C22⋊D191—21no—
28C2×C22⋊D191—21no—
29C2×C22⋊D191—21no—
30C22×Dic191—21no—
31C2×C4×D191—21no—
32#15690271—22no—
33#15690271—41no—
34C2×C191⋊C8—41no—
35Dic191⋊C4—21no—
36Dic191⋊C4—21no—
37C22⋊Dic191—21no—
38C22⋊Dic191—21no—
39(C2×D191)⋊C4—21no—
40(C2×D191)⋊C4—21no—
41C4×Dic191—21no—
42C4×Dic191C2×C411yescharacteristic
43C4×Dic191C2×C411yescharacteristic
44#41×C191—41no—
45#41×C191—41no—
46C2×Q8×C191C2311yescharacteristic
47C2×D4×C191C2×C411yescharacteristic
48C2×D4×C191D411yescharacteristic
49C2×D4×C191D411yescharacteristic
50C22×C4×C191C2×C411yescharacteristic
51C22×C4×C191D411yescharacteristic
52C22×C4×C191D411yescharacteristic
53M16×C191—22no—
54M16×C191—41no—
55C2×C8×C191—41no—
56C22×D191—21no—
57Dic382—41no—
58D764—41no—
59C22⋊D191—42no—
60C22⋊D191—42no—
61C22⋊D191—42no—
62C2×Dic191—21no—
63C2×Dic191—21no—
64C2×Dic191—21no—
65C2×Dic191—42no—
66C4×D191—41no—
67C4×D191—41no—
68C191⋊C8—42no—
69C23×C191C22⋊C411yescharacteristic
70C23×C191C22⋊C411yescharacteristic
71C23×C191C22⋊C411yescharacteristic
72Q8×C191—41no—
73D4×C191—41no—
74D4×C191—41no—
75D4×C191—41no—
76C2×C4×C191—21no—
77C2×C4×C191—21no—
78C2×C4×C191—21no—
79C2×C4×C191—21no—
80C2×C4×C191—21no—
81C2×C4×C191—21no—
82C2×C4×C191C22⋊C411yescharacteristic
83C2×C4×C191C22×C411yescharacteristic
84C2×C4×C191C2×D411yescharacteristic
85C2×C4×C191C2×D411yescharacteristic
86C8×C191—42no—
87C22×C191—21no—
88C22×C191—21no—
89C22×C191—21no—
90C22×C191—41no—
91C22×C191—41no—
92C22×C191—41no—
93C22×C191C2×C22⋊C411yescharacteristic
94C2×D191—41no—
95C2×D191—41no—
96C2×D191—41no—
97C4×C191—21no—
98C4×C191—21no—
99C4×C191—21no—
100C4×C191#9911yescharacteristic
101C4×C191#9911yescharacteristic
102Dic191—22no—
103Dic191—41no—
104Dic191—41no—
105C2×C191—21no—
106C2×C191—41no—
107C2×C191—41no—
108C2×C191—41no—
109C2×C191C2×#9911yescharacteristic
110D191—81no—
111C191#213211yescharacteristic, complemented, Sylow
112#2132—1911nomaximal, Sylow
113#532—1911no—
114#413—1911no—
115#413D19111yescharacteristic, complemented
116#356—1912no—
117#355—1912no—
118C2×#41—1911no—
119C2×#41C2×D19111yescharacteristic
120C2×M16—21no—
121C2×M16—3821no—
122C4⋊Q8—1911no—
123#127—1911no—
124#124—1911no—
125#124—1911no—
126#121—3821no—
127#121—3821no—
128C4×D4—3821no—
129C4×D4—3821no—
130C2×C42—1911no—
131#101—1912no—
132#101C2×D19112yes—
133#100—21no—
134#100—3821no—
135#41—41no—
136#41—41no—
137#41—7641no—
138#41—7641no—
139C2×Q8—1911no—
140C2×Q8C22×D19111yescharacteristic
141C2×D4—3821no—
142C2×D4—3821no—
143C2×D4—3821no—
144C2×D4—1911no—
145C2×D4C4×D19111yescharacteristic
146C2×D4C22⋊D19111yescharacteristic
147C2×D4D76411yescharacteristic
148C22×C4—3821no—
149C22×C4—3821no—
150C22×C4C4×D19111yescharacteristic
151C22×C4C22⋊D19111yescharacteristic
152C22×C4D76411yescharacteristic
153M16—22no—
154M16—41no—
155M16—3822no—
156M16—7641no—
157C2×C8—41no—
158C2×C8—7641no—
159C4⋊C4—3821no—
160C4⋊C4—3821no—
161C22⋊C4—3821no—
162C22⋊C4—3821no—
163C22⋊C4—3821no—
164C22⋊C4—3821no—
165C42—3821no—
166C42—1911no—
167C42—1911no—
168C23—3821no—
169C23(C2×D191)⋊C411yescharacteristic
170C23(C2×D191)⋊C411yescharacteristic
171C23(C2×D191)⋊C411yescharacteristic
172Q8—41no—
173Q8—7641no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—7641no—
178D4—7642no—
179D4—7642no—
180D4—7642no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—3821no—
188C2×C4—3821no—
189C2×C4—3821no—
190C2×C4—7642no—
191C2×C4—7641no—
192C2×C4—7641no—
193C2×C4(C2×D191)⋊C411yescharacteristic
194C2×C4C2×C4×D19111yescharacteristic
195C2×C4C2×C22⋊D19111yescharacteristic
196C2×C4C2×D76411yescharacteristic
197C8—42no—
198C8—7642no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—7641no—
206C22—7641no—
207C22—7641no—
208C22C2×(C2×D191)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—3822no—
213C4—7641no—
214C4—7641no—
215C4#2025923611yescharacteristic
216C4#2025923611yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—15281no—
222C2C2×#2025923611yescharacteristic
subgroupG/H
centerC4#20259236
commutatorC2×C4×C191C22×C4
FrattiniC2×Q8C22×D191
Fitting#413×C191C2
socleC2×C191C2×#99
prime radical#27133209C2
cosocleC2×Q8×C191C23
hypercenter#413D191
hypocenterC191#2132
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #27132647C2semidirect
3. #27132461C2semidirect
4. #27132459C2semidirect
5. #413×C191C2semidirect
111. C191#2132semidirect
115. #413D191semidirect

Maximal subgroups

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

subgroupindex
#271332092
#271326472
#271324612
#271324592
#413×C1912
#2132191