Finite Group Databasebeta

← #37582053

Subgroups — #37582053

Order 24448.

458 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 133 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×Dic764C211yesmaximal, characteristic, complemented
3#27133234C211yesmaximal, characteristic
4#27133140C211yesmaximal, characteristic, complemented
5#27132884C214yesmaximal, complemented
6#27132872C214yesmaximal, complemented
7#27132689C211yesmaximal, characteristic, complemented
8#27132671C211yesmaximal, characteristic, complemented
9#416×C191C211yesmaximal, characteristic
10C22×Dic382C2211yescharacteristic
11C22×Dic382C2211yescharacteristic
12#20259352—24no—
13C2×Dic764—24no—
14C2×Dic764C2214yes—
15C2×#15690277C2212yes—
16C2×#15690275C2212yes—
17C2×#15690271C2211yescharacteristic
18#20259320C2212yes—
19#20259309C2212yes—
20#20259303—22no—
21#20259301—22no—
22C4×Dic382—22no—
23#20259287C2214yes—
24#20259281C2211yescharacteristic
25#20259278—22no—
26Dic191⋊C8C2214yes—
27#20259245C2214yes—
28C2×#41×C191C2211yescharacteristic
29C22×C8×C191C2211yescharacteristic
30#117×C191C2211yescharacteristic
31#103×C191C2212yes—
32#102×C191C2212yes—
33C2×Dic382—21no—
34C2×Dic382—21no—
35C2×Dic382—22no—
36C2×Dic382—22no—
37C2×Dic382—22no—
38C2×Dic382D414yes—
39C2×Dic382C2312yes—
40C2×Dic382C2312yes—
41C22×Dic191—21no—
42C22×Dic191—21no—
43Dic764—28no—
44#15690277—24no—
45#15690275—24no—
46#15690271—22no—
47C2×C191⋊C8C2312yes—
48C4⋊Dic191D412yes—
49Dic191⋊C4—24no—
50Dic191⋊C4—24no—
51C22⋊Dic191—24no—
52C22⋊Dic191D412yes—
53C4×Dic191—24no—
54C4×Dic191C2312yes—
55#41×C191—22no—
56#41×C191—22no—
57C2×Q8×C191C2311yescharacteristic
58C2×D4×C191—21no—
59C2×D4×C191C2311yescharacteristic
60C22×C4×C191—21no—
61C22×C4×C191C2311yescharacteristic
62C2×C8×C191—22no—
63C2×C8×C191C2312yes—
64C4⋊C4×C191C2312yes—
65C22⋊C4×C191—21no—
66C42×C191—21no—
67Dic382—24no—
68Dic382—22no—
69Dic382—22no—
70Dic382—22no—
71Dic382—42no—
72Dic382C2×D414yes—
73C2×Dic191—24no—
74C2×Dic191—22no—
75C2×Dic191—22no—
76C2×Dic191—42no—
77C2×Dic191C2×D414yes—
78C191⋊C8—22no—
79C23×C191—21no—
80C23×C191C2×D411yescharacteristic
81Q8×C191—21no—
82Q8×C191—21no—
83D4×C191—21no—
84D4×C191—21no—
85D4×C191—42no—
86C2×C4×C191—22no—
87C2×C4×C191—21no—
88C2×C4×C191—42no—
89C2×C4×C191C2×D411yescharacteristic
90C2×C4×C191C2×D412yes—
91C2×C4×C191#4112yes—
92C2×C4×C191C2411yescharacteristic
93C8×C191—22no—
94C22×C191—22no—
95C22×C191—41no—
96C22×C191—42no—
97C22×C191#12112yes—
98C22×C191C22×D411yescharacteristic
99C4×C191—41no—
100C4×C191—42no—
101C4×C191#12112yes—
102C4×C191C22×D411yescharacteristic
103C4×C191C2×#4111yescharacteristic
104Dic191—24no—
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#536—1911no—
116#519—1911no—
117#464—1914no—
118#462—1914no—
119#424—1911no—
120#419—1911no—
121#416D19111yescharacteristic
122C2×#41C2×D19111yescharacteristic
123C22×Q8—1911no—
124C22×Q8—1911no—
125#137—3824no—
126C2×Q16—3824no—
127C2×Q16—1912no—
128C2×Q16—1914no—
129C2×SD16—1912no—
130C2×M16—1911no—
131C22×C8C2×D19111yescharacteristic
132C4⋊Q8—1912no—
133#124—1912no—
134#123—3822no—
135C22⋊Q8—3822no—
136C4×Q8—3822no—
137C4×Q8—1914no—
138#117—3822no—
139#117—1911no—
140#117C2×D19111yescharacteristic
141C4⋊C8—1914no—
142#103—1914no—
143#103C2×D19112yes—
144#102C2×D19112yes—
145#41—22no—
146#41—22no—
147C2×Q8—3821no—
148C2×Q8—3821no—
149C2×Q8—3822no—
150C2×Q8—3822no—
151C2×Q8—3822no—
152C2×Q8—1914no—
153C2×Q8—1912no—
154C2×Q8—1912no—
155C2×Q8C22×D19111yescharacteristic
156C2×D4—21no—
157C2×D4C22×D19111yescharacteristic
158C22×C4—21no—
159C22×C4—3821no—
160C22×C4—3821no—
161C22×C4C22×D19111yescharacteristic
162Q16—3828no—
163Q16—3824no—
164SD16—3824no—
165M16—3822no—
166C2×C8—22no—
167C2×C8—1912no—
168C2×C8C22×D19112yes—
169C4⋊C4—3824no—
170C4⋊C4—3824no—
171C4⋊C4—1912no—
172C4⋊C4C22×D19112yes—
173C22⋊C4—21no—
174C22⋊C4—3824no—
175C22⋊C4—1912no—
176C42—21no—
177C42—3824no—
178C42—1912no—
179C23—21no—
180C23D4×D19111yescharacteristic
181Q8—21no—
182Q8—21no—
183Q8—3822no—
184Q8—3824no—
185Q8—3822no—
186Q8—3822no—
187Q8—1914no—
188Q8—7642no—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—3822no—
196C2×C4—3824no—
197C2×C4—3822no—
198C2×C4—1914no—
199C2×C4—7642no—
200C2×C4D4×D19112yes—
201C2×C4D4×D19111yescharacteristic
202C2×C4#1569028712yes—
203C2×C4C23×D19111yescharacteristic
204C8—22no—
205C8—3822no—
206C22—22no—
207C22—42no—
208C22—41no—
209C22#2025929512yes—
210C22C2×D4×D19111yescharacteristic
211C4—42no—
212C4—41no—
213C4—3824no—
214C4—3824no—
215C4—7642no—
216C4#2025929512yes—
217C4C2×D4×D19111yescharacteristic
218C4C2×#1569028711yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#2025929511yescharacteristic
222C2#2713347712yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#416×C191C2
socleC22×C191C22×D4
prime radicalC2×#41×C191C22
hypercenter#416D191
hypocenterC191#3044
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C22×Dic764C2semidirect
4. #27133140C2semidirect
5. #27132884C2semidirect
6. #27132872C2semidirect
7. #27132689C2semidirect
8. #27132671C2semidirect
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×Dic7642
#271332342
#271331402
#271328842
#271328722
#271326892
#271326712
#416×C1912
#3044191