Finite Group Databasebeta

← #37582046

Subgroups — #37582046

Order 24448.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20259352C211yesmaximal, characteristic
2C22×#15690277C211yesmaximal, characteristic, complemented
3#27133140C211yesmaximal, characteristic, complemented
4#27132882C214yesmaximal, complemented
5#27132870C214yesmaximal, complemented
6#27132690C211yesmaximal, characteristic, complemented
7#27132672C211yesmaximal, characteristic, complemented
8#27132659C211yesmaximal, characteristic
9#536×C191C211yesmaximal, characteristic
10C22×Dic382C2211yescharacteristic
11#20259352—24no—
12C2×#15690277—24no—
13C2×#15690277C2212yes—
14C2×#15690277C2214yes—
15C2×#15690275C2212yes—
16C2×#15690271C2211yescharacteristic
17C22×C191⋊C8C2211yescharacteristic
18C4×Dic382C2214yes—
19#20259287—22no—
20#20259281C2211yescharacteristic
21#20259278—22no—
22C4⋊(C191⋊C8)C2214yes—
23#20259246C2214yes—
24#20259246C2212yes—
25#20259243C2212yes—
26C2×#41×C191C2211yescharacteristic
27C22×Q8×C191C2211yescharacteristic
28C4⋊Q8×C191C2212yes—
29#124×C191C2212yes—
30#123×C191—22no—
31C22⋊Q8×C191—22no—
32#117×C191C2211yescharacteristic
33C2×Dic382—21no—
34C2×Dic382—22no—
35C2×Dic382D414yes—
36C2×Dic382C2312yes—
37C22×Dic191—21no—
38#15690277—28no—
39#15690277—24no—
40#15690275—24no—
41#15690271—22no—
42C2×C191⋊C8—22no—
43C2×C191⋊C8C2312yes—
44C2×C191⋊C8C2312yes—
45C4⋊Dic191C2312yes—
46Dic191⋊C4—24no—
47C22⋊Dic191—21no—
48C4×Dic191—24no—
49C4×Dic191—21no—
50#41×C191—22no—
51#41×C191—22no—
52C2×Q8×C191—21no—
53C2×Q8×C191—22no—
54C2×Q8×C191—22no—
55C2×Q8×C191C2312yes—
56C2×Q8×C191C2311yescharacteristic
57C2×D4×C191—21no—
58C2×D4×C191C2311yescharacteristic
59C22×C4×C191—21no—
60C22×C4×C191—21no—
61C22×C4×C191C2311yescharacteristic
62C4⋊C4×C191—24no—
63C4⋊C4×C191D412yes—
64C22⋊C4×C191—24no—
65C22⋊C4×C191D412yes—
66C42×C191C2312yes—
67Dic382—24no—
68Dic382—22no—
69Dic382C2×D414yes—
70C2×Dic191—24no—
71C2×Dic191—22no—
72C2×Dic191—22no—
73C191⋊C8—22no—
74C191⋊C8—22no—
75C23×C191—21no—
76C23×C191C2×D411yescharacteristic
77Q8×C191—22no—
78Q8×C191—21no—
79Q8×C191—22no—
80Q8×C191—21no—
81Q8×C191—42no—
82D4×C191—21no—
83D4×C191—21no—
84D4×C191—42no—
85C2×C4×C191—22no—
86C2×C4×C191—21no—
87C2×C4×C191—42no—
88C2×C4×C191—42no—
89C2×C4×C191C2×D412yes—
90C2×C4×C191C2×D414yes—
91C2×C4×C191C2×D411yescharacteristic
92C2×C4×C191#4112yes—
93C2×C4×C191C2411yescharacteristic
94C22×C191—22no—
95C22×C191—41no—
96C22×C191—42no—
97C22×C191#12112yes—
98C22×C191C22×D411yescharacteristic
99C4×C191—24no—
100C4×C191—41no—
101C4×C191—42no—
102C4×C191#12112yes—
103C4×C191C22×D411yescharacteristic
104C4×C191C2×#4111yescharacteristic
105Dic191—24no—
106Dic191—42no—
107C2×C191—22no—
108C2×C191—81no—
109C2×C191C2×#12111yescharacteristic
110C2×C191#57812yes—
111C191#304411yescharacteristic, complemented, Sylow
112#3044—1911nomaximal, Sylow
113C2×#137—1911no—
114C22×Q16—1911no—
115#536D19111yescharacteristic
116#519—1911no—
117#464—1914no—
118#462—1914no—
119#424—1911no—
120#419—1911no—
121#416—1911no—
122C2×#41C2×D19111yescharacteristic
123C22×Q8—1911no—
124C22×Q8C2×D19111yescharacteristic
125#137—3824no—
126C2×Q16—3824no—
127C2×Q16—1914no—
128C2×Q16—1912no—
129C2×SD16—1912no—
130C2×M16—1911no—
131C22×C8—1911no—
132C4⋊Q8C2×D19112yes—
133#124C2×D19112yes—
134#123—22no—
135C22⋊Q8—22no—
136C4×Q8—3822no—
137C4×Q8—1914no—
138#117—3822no—
139#117—1911no—
140#117C2×D19111yescharacteristic
141C4⋊C8—1914no—
142#103—1912no—
143#103—1914no—
144#102—1912no—
145#41—22no—
146#41—22no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—3821no—
151C2×Q8—3822no—
152C2×Q8—1914no—
153C2×Q8—1912no—
154C2×Q8C22×D19112yes—
155C2×Q8C22×D19111yescharacteristic
156C2×D4—21no—
157C2×D4C22×D19111yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—3821no—
161C22×C4C22×D19111yescharacteristic
162Q16—3828no—
163Q16—3824no—
164SD16—3824no—
165M16—3822no—
166C2×C8—3822no—
167C2×C8—1912no—
168C2×C8—1912no—
169C4⋊C4—24no—
170C4⋊C4—3824no—
171C4⋊C4—1912no—
172C4⋊C4C22⋊D19112yes—
173C22⋊C4—24no—
174C22⋊C4—3821no—
175C22⋊C4C22⋊D19112yes—
176C42—3824no—
177C42—3821no—
178C42C22×D19112yes—
179C23—21no—
180C23C2×C22⋊D19111yescharacteristic
181Q8—22no—
182Q8—21no—
183Q8—22no—
184Q8—21no—
185Q8—42no—
186Q8—3822no—
187Q8—3824no—
188Q8—1914no—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—3822no—
197C2×C4—3824no—
198C2×C4—3822no—
199C2×C4D4×D19112yes—
200C2×C4C2×C22⋊D19114yes—
201C2×C4C2×C22⋊D19111yescharacteristic
202C2×C4#1569028612yes—
203C2×C4C23×D19111yescharacteristic
204C8—3822no—
205C8—3822no—
206C22—22no—
207C22—42no—
208C22—41no—
209C22#2025929312yes—
210C22C22×C22⋊D19111yescharacteristic
211C4—24no—
212C4—41no—
213C4—42no—
214C4—3824no—
215C4—7642no—
216C4#2025929312yes—
217C4C2×D4×D19111yescharacteristic
218C4C2×#1569028611yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#2025929311yescharacteristic
222C2#2713347812yes—
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#536×C191C2
socleC22×C191C22×D4
prime radicalC2×#41×C191C22
hypercenter#536D191
hypocenterC191#3044
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C22×#15690277C2semidirect
3. #27133140C2semidirect
4. #27132882C2semidirect
5. #27132870C2semidirect
6. #27132690C2semidirect
7. #27132672C2semidirect
111. C191#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#202593522
C22×#156902772
#271331402
#271328822
#271328702
#271326902
#271326722
#271326592
#536×C1912
#3044191