Finite Group Databasebeta

← #37581001

Subgroups — #37581001

Order 24448.

704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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×#20259369C211yesmaximal, characteristic
2#27133429C212yesmaximal, complemented
3#27132647C211yesmaximal, characteristic, complemented
4#27132644C214yesmaximal, complemented
5C2×#20259240C212yesmaximal, complemented
6#101×D191C214yesmaximal, complemented
7#413×C191C211yesmaximal, characteristic, complemented
8#20259369—24no—
9#20259369—24no—
10C2×#15690287C412yes—
11C2×#15690287C2211yescharacteristic
12C2×#15690286C414yes—
13C2×#15690286C2212yes—
14C22×Dic382C412yes—
15C22×Dic382C2211yescharacteristic
16C2×Q8×D191C2212yes—
17#20259330—24no—
18#20259328—24no—
19C2×#15690271C2212yes—
20M16×D191C2218yes—
21#20259241C2212yes—
22#20259240C2218yes—
23#20259239C2212yes—
24C2×#41×C191C2211yescharacteristic
25C2×M16×C191C2212yes—
26#101×C191C2212yes—
27#100×C191C2212yes—
28#15690287—24no—
29#15690287—24no—
30#15690287D414yes—
31#15690287D414yes—
32#15690286—216no—
33#15690286—28no—
34C2×Dic382—24no—
35C2×Dic382—24no—
36C2×Dic382—22no—
37C2×Dic382—22no—
38C2×Dic382C2×C414yes—
39C2×Dic382C2×C412yes—
40C2×Dic382C2×C411yescharacteristic
41C2×Dic382C2312yes—
42Q8×D191—28no—
43C2×D764C2×C411yescharacteristic
44C2×C22⋊D191C2×C414yes—
45C2×C22⋊D191C2×C412yes—
46C22×Dic191C2×C414yes—
47C22×Dic191C2×C412yes—
48C2×C4×D191C2×C414yes—
49C2×C4×D191C2312yes—
50#15690271—22no—
51#15690271C2314yes—
52#15690270—28no—
53C2×C191⋊C8—22no—
54C8×D191—28no—
55#41×C191—22no—
56#41×C191—22no—
57C2×Q8×C191C2311yescharacteristic
58C2×D4×C191C2×C412yes—
59C2×D4×C191C2311yescharacteristic
60C22×C4×C191C2×C412yes—
61C22×C4×C191C2311yescharacteristic
62M16×C191—22no—
63M16×C191C2314yes—
64C2×C8×C191—22no—
65C22×D191C22×C412yes—
66Dic382—22no—
67Dic382—22no—
68Dic382—24no—
69Dic382—28no—
70Dic382C22⋊C412yes—
71Dic382C22⋊C412yes—
72D764C22⋊C412yes—
73D764C22⋊C412yes—
74C22⋊D191—28no—
75C22⋊D191C22⋊C418yes—
76C2×Dic191—24no—
77C2×Dic191—28no—
78C2×Dic191C22×C414yes—
79C2×Dic191C22×C412yes—
80C4×D191—28no—
81C4×D191C2×D418yes—
82C191⋊C8—24no—
83C23×C191C22×C412yes—
84C23×C191C22×C411yescharacteristic
85Q8×C191—22no—
86D4×C191—24no—
87D4×C191—22no—
88C2×C4×C191—22no—
89C2×C4×C191—22no—
90C2×C4×C191C22×C412yes—
91C2×C4×C191C22×C411yescharacteristic
92C2×C4×C191C2×D412yes—
93C2×C4×C191C2×D412yes—
94C2×C4×C191C2411yescharacteristic
95C8×C191—24no—
96C22×C191—22no—
97C22×C191—41no—
98C22×C191—42no—
99C22×C191C2×C22⋊C412yes—
100C22×C191C23×C411yescharacteristic
101C2×D191—42no—
102C2×D191C2×C22⋊C414yes—
103C4×C191—22no—
104C4×C191C2×C22⋊C411yescharacteristic
105C4×C191C2×C22⋊C411yescharacteristic
106C4×C191C22×D412yes—
107Dic191—24no—
108Dic191C2×C22⋊C414yes—
109C2×C191—21no—
110C2×C191—22no—
111C2×C191—42no—
112C2×C191C22×C22⋊C411yescharacteristic
113D191—24no—
114C191#288911yescharacteristic, complemented, Sylow
115#2889—1911nomaximal, Sylow
116C2×2−1+4—1911no—
117#568—1912no—
118#413—1911no—
119#413—1914no—
120#413D19111yescharacteristic, complemented
121C2×#101—1912no—
122C2×#101—1914no—
1232−1+4—3824no—
1242−1+4—3824no—
125C2×#41—1914no—
126C2×#41—1912no—
127C2×#41—1912no—
128C2×#41—1911no—
129C2×#41C2×D19111yescharacteristic
130C22×Q8—1912no—
131C22×Q8—1912no—
132C22×Q8—1911no—
133#131—3824no—
134#131—3824no—
135C2×M16—1912no—
136C2×M16—1918no—
137C2×M16C2×D19112yes—
138#101—1912no—
139#101—1918no—
140#101C2×D19112yes—
141#100—1912no—
142#100C2×D19112yes—
143#41—22no—
144#41—22no—
145#41—3824no—
146#41—3824no—
147#41—38216no—
148#41—3828no—
149#41—1914no—
150#41—1914no—
151C2×Q8—3824no—
152C2×Q8—3824no—
153C2×Q8—3828no—
154C2×Q8—3822no—
155C2×Q8—3822no—
156C2×Q8—1912no—
157C2×Q8—1914no—
158C2×Q8—1911no—
159C2×Q8—1912no—
160C2×Q8C22×D19111yescharacteristic
161C2×D4—1914no—
162C2×D4—1912no—
163C2×D4—1911no—
164C2×D4C4×D19112yes—
165C2×D4C22×D19111yescharacteristic
166C22×C4—1912no—
167C22×C4—1914no—
168C22×C4—1914no—
169C22×C4—1912no—
170C22×C4C4×D19112yes—
171C22×C4C22×D19111yescharacteristic
172M16—22no—
173M16—3828no—
174M16—3822no—
175M16—1914no—
176M16C22×D19114yes—
177C2×C8—22no—
178C2×C8—3828no—
179C2×C8—3822no—
180C23—1912no—
181C23C2×C4×D19112yes—
182C23C2×C4×D19111yescharacteristic
183Q8—22no—
184Q8—3828no—
185Q8—3824no—
186Q8—3822no—
187Q8—3822no—
188Q8—1912no—
189Q8—1912no—
190D4—24no—
191D4—22no—
192D4—3828no—
193D4—1918no—
194D4—1912no—
195D4—1912no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—3828no—
199C2×C4—3824no—
200C2×C4—3828no—
201C2×C4—1914no—
202C2×C4—1912no—
203C2×C4—1918no—
204C2×C4C2×C4×D19112yes—
205C2×C4C2×C4×D19111yescharacteristic
206C2×C4D4×D19112yes—
207C2×C4D4×D19112yes—
208C2×C4C23×D19111yescharacteristic
209C8—24no—
210C8—3824no—
211C22—22no—
212C22—41no—
213C22—42no—
214C22—1914no—
215C22—7642no—
216C22C22⋊C4×D19112yes—
217C22C22×C4×D19111yescharacteristic
218C4—22no—
219C4—3824no—
220C4—1914no—
221C4C22⋊C4×D19111yescharacteristic
222C4C22⋊C4×D19111yescharacteristic
223C4C2×D4×D19112yes—
224C2—21no—
225C2—22no—
226C2—42no—
227C2—3824no—
228C2C2×C22⋊C4×D19111yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D191
commutatorC22×C191C23×C4
FrattiniC2×C4C23×D191
Fitting#413×C191C2
socleC2×C191C22×C22⋊C4
prime radicalC2×#20259369C2
cosocleC2×C4×C191C24
hypercenter#413D191
hypocenterC191#2889
LCSG ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #27133429C2semidirect
3. #27132647C2semidirect
4. #27132644C2semidirect
5. C2×#20259240C2semidirect
6. #101×D191C2semidirect
7. #413×C191C2semidirect
114. C191#2889semidirect
120. #413D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593692
#271334292
#271326472
#271326442
C2×#202592402
#101×D1912
#413×C1912
#2889191