Finite Group Databasebeta

← #37581000

Subgroups — #37581000

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×#20259370C211yesmaximal, characteristic
2#27133429C212yesmaximal, complemented
3#27132646C214yesmaximal, complemented
4#27132645C212yesmaximal, complemented
5C2×#20259241C211yesmaximal, characteristic, complemented
6#101×D191C214yesmaximal, complemented
7C2×#101×C191C211yesmaximal, characteristic, complemented
8#20259370—24no—
9#20259370—24no—
10C2×#15690288C412yes—
11C2×#15690288C2212yes—
12C2×#15690287C414yes—
13C2×#15690287C2211yescharacteristic
14C2×#15690287C2211yescharacteristic
15C2×Q8×D191C412yes—
16C2×Q8×D191C2212yes—
17#20259330—24no—
18#20259328—24no—
19C2×#15690271C2212yes—
20M16×D191C2218yes—
21#20259241C2214yes—
22#20259240C2214yes—
23#20259238C2214yes—
24C22×Q8×C191C2211yescharacteristic
25C2×M16×C191C2212yes—
26#101×C191C2214yes—
27#15690288—28no—
28#15690288—28no—
29#15690287—28no—
30#15690287—28no—
31#15690287—22no—
32#15690287—22no—
33#15690287D414yes—
34#15690287D414yes—
35C2×Dic382C2×C414yes—
36C2×Dic382C2×C411yescharacteristic
37C2×Dic382C2311yescharacteristic
38Q8×D191—28no—
39Q8×D191—28no—
40C2×D764C2×C414yes—
41C2×D764C2×C411yescharacteristic
42C2×D764C2311yescharacteristic
43C2×C22⋊D191C2×C412yes—
44C2×C22⋊D191C2×C412yes—
45C2×C4×D191C2×C414yes—
46C2×C4×D191C2×C412yes—
47C2×C4×D191C2×C414yes—
48C2×C4×D191C2312yes—
49#15690271—22no—
50#15690271C2314yes—
51#15690270—28no—
52C2×C191⋊C8—22no—
53C8×D191—28no—
54C2×Q8×C191—22no—
55C2×Q8×C191—22no—
56C2×Q8×C191C2×C412yes—
57C2×Q8×C191C2312yes—
58C22×C4×C191C2×C412yes—
59C22×C4×C191C2311yescharacteristic
60M16×C191—22no—
61M16×C191C2314yes—
62C2×C8×C191—22no—
63C22×D191C22×C412yes—
64C22×D191C22×C412yes—
65Dic382—22no—
66Dic382—28no—
67Dic382C22⋊C414yes—
68D764—28no—
69D764—22no—
70D764C22⋊C414yes—
71C22⋊D191—22no—
72C22⋊D191—22no—
73C22⋊D191C22⋊C414yes—
74C22⋊D191C22⋊C414yes—
75C2×Dic191C22×C412yes—
76C2×Dic191C22×C412yes—
77C4×D191—28no—
78C4×D191—24no—
79C4×D191—28no—
80C4×D191C2×D418yes—
81C191⋊C8—24no—
82C23×C191C22×C411yescharacteristic
83Q8×C191—24no—
84Q8×C191—24no—
85C2×C4×C191—22no—
86C2×C4×C191—22no—
87C2×C4×C191C22×C414yes—
88C2×C4×C191C22×C411yescharacteristic
89C2×C4×C191C2×D412yes—
90C2×C4×C191C2×D412yes—
91C2×C4×C191C2411yescharacteristic
92C8×C191—24no—
93C22×C191—41no—
94C22×C191C2×C22⋊C411yescharacteristic
95C22×C191C2×C22⋊C411yescharacteristic
96C22×C191C23×C411yescharacteristic
97C2×D191—22no—
98C2×D191—42no—
99C2×D191—42no—
100C2×D191C2×C22⋊C414yes—
101C4×C191—24no—
102C4×C191C2×C22⋊C412yes—
103C4×C191C22×D412yes—
104Dic191—22no—
105Dic191C2×C22⋊C414yes—
106C2×C191—21no—
107C2×C191—21no—
108C2×C191—21no—
109C2×C191C22×C22⋊C411yescharacteristic
110D191—24no—
111D191—42no—
112C191#288911yescharacteristic, complemented, Sylow
113#2889—1911nomaximal, Sylow
114C2×2−1+4—1911no—
115#568—1912no—
116#413—1912no—
117#413—1914no—
118C2×#101—1911no—
119C2×#101—1914no—
120C2×#101D19111yescharacteristic, complemented
1212−1+4—3824no—
1222−1+4—3824no—
123C2×#41—1912no—
124C2×#41—1912no—
125C2×#41—1914no—
126C2×#41—1911no—
127C2×#41—1911no—
128C22×Q8—1912no—
129C22×Q8—1912no—
130C22×Q8C2×D19111yescharacteristic
131#131—3824no—
132#131—3824no—
133C2×M16—1912no—
134C2×M16—1918no—
135C2×M16C2×D19112yes—
136#101—1914no—
137#101—1914no—
138#101C2×D19114yes—
139#100—1914no—
140#41—3828no—
141#41—3828no—
142#41—3828no—
143#41—3828no—
144#41—3822no—
145#41—3822no—
146#41—1914no—
147#41—1914no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—3828no—
151C2×Q8—3828no—
152C2×Q8—1914no—
153C2×Q8—1911no—
154C2×Q8—1911no—
155C2×Q8C4×D19112yes—
156C2×Q8C22×D19112yes—
157C2×D4—1912no—
158C2×D4—1912no—
159C2×D4—1914no—
160C2×D4—1911no—
161C2×D4—1911no—
162C22×C4—1914no—
163C22×C4—1914no—
164C22×C4—1912no—
165C22×C4—1912no—
166C22×C4C4×D19112yes—
167C22×C4C22×D19111yescharacteristic
168M16—22no—
169M16—3828no—
170M16—3822no—
171M16—1914no—
172M16C22×D19114yes—
173C2×C8—22no—
174C2×C8—3828no—
175C2×C8—3822no—
176C23—1912no—
177C23—1912no—
178C23C2×C4×D19111yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—3828no—
182Q8—3822no—
183Q8—1914no—
184D4—3828no—
185D4—3822no—
186D4—3822no—
187D4—3822no—
188D4—1914no—
189D4—1914no—
190D4—1914no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—3828no—
194C2×C4—3828no—
195C2×C4—3824no—
196C2×C4—1912no—
197C2×C4—1912no—
198C2×C4—1918no—
199C2×C4C2×C4×D19114yes—
200C2×C4C2×C4×D19111yescharacteristic
201C2×C4D4×D19112yes—
202C2×C4D4×D19112yes—
203C2×C4C23×D19111yescharacteristic
204C8—24no—
205C8—3824no—
206C22—41no—
207C22—3822no—
208C22—1914no—
209C22—7642no—
210C22—7642no—
211C22C22⋊C4×D19111yescharacteristic
212C22C22⋊C4×D19111yescharacteristic
213C22C22×C4×D19111yescharacteristic
214C4—24no—
215C4—3822no—
216C4—1914no—
217C4C22⋊C4×D19112yes—
218C4C2×D4×D19112yes—
219C2—21no—
220C2—21no—
221C2—21no—
222C2—3824no—
223C2—7642no—
224C2C2×C22⋊C4×D19111yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D191
commutatorC22×C191C23×C4
FrattiniC2×C4C23×D191
FittingC2×#101×C191C2
socleC2×C191C22×C22⋊C4
prime radicalC2×#20259370C2
cosocleC2×C4×C191C24
hypercenterC2×#101D191
hypocenterC191#2889
LCSG ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #27133429C2semidirect
3. #27132646C2semidirect
4. #27132645C2semidirect
5. C2×#20259241C2semidirect
6. #101×D191C2semidirect
7. C2×#101×C191C2semidirect
112. C191#2889semidirect
120. C2×#101D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593702
#271334292
#271326462
#271326452
C2×#202592412
#101×D1912
C2×#101×C1912
#2889191