Finite Group Databasebeta

← #37573660

Subgroups — #37573660

Order 24448.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#20259321C211yesmaximal, characteristic
2C2×#20259247C211yesmaximal, characteristic
3C2×#20259245C211yesmaximal, characteristic
4#27132568C211yesmaximal, characteristic
5#27132425C211yesmaximal, characteristic
6#27132417C211yesmaximal, characteristic
7#340×C191C211yesmaximal, characteristic
8C22×Dic382—21no—
9C22×Dic382C2211yescharacteristic
10C22×C191⋊C8C2211yescharacteristic
11#20259321—22no—
12#20259321—22no—
13C2×C4⋊Dic191C2211yescharacteristic
14C2×Dic191⋊C4—21no—
15C2×C4×Dic191C2211yescharacteristic
16#20259247—22no—
17#20259245—22no—
18C191⋊#95—21no—
19C191⋊#95—21no—
20C22×C8×C191C2211yescharacteristic
21C2×C4⋊C4×C191C2211yescharacteristic
22C2×C4⋊C4×C191C2211yescharacteristic
23C2×Dic382—24no—
24C2×Dic382—21no—
25C2×Dic382—21no—
26C2×Dic382—21no—
27C2×Dic382—21no—
28C2×Dic382—21no—
29C2×Dic382—42no—
30C2×Dic382—42no—
31C2×Dic382Q812yescomplemented
32C22×Dic191—21no—
33C22×Dic191—21no—
34C22×Dic191D411yescharacteristic
35C22×Dic191D411yescharacteristic
36C2×C191⋊C8—21no—
37C2×C191⋊C8—21no—
38C2×C191⋊C8—21no—
39C4⋊Dic191—21no—
40C4⋊Dic191D412yes—
41Dic191⋊C4—24no—
42C4×Dic191—21no—
43C4×Dic191—21no—
44C22×C4×C191—21no—
45C22×C4×C191—21no—
46C22×C4×C191C2311yescharacteristic
47C2×C8×C191—21no—
48C2×C8×C191—21no—
49C2×C8×C191—21no—
50C4⋊C4×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191D412yes—
54Dic382—22no—
55Dic382—22no—
56Dic382—48no—
57Dic382—41no—
58Dic382—41no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—21no—
62C2×Dic191—21no—
63C2×Dic191—22no—
64C2×Dic191—22no—
65C2×Dic191—41no—
66C2×Dic191—41no—
67C2×Dic191—41no—
68C2×Dic191—41no—
69C2×Dic191SD1612yes—
70C2×Dic191Q1612yes—
71C191⋊C8—41no—
72C23×C191C2×D411yescharacteristic
73C2×C4×C191—22no—
74C2×C4×C191—41no—
75C2×C4×C191—41no—
76C2×C4×C191—41no—
77C2×C4×C191—41no—
78C2×C4×C191—41no—
79C2×C4×C191C2×D411yescharacteristic
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191C2×Q811yescharacteristic
82C2×C4×C191#4111yescharacteristic
83C2×C4×C191#4111yescharacteristic
84C2×C4×C191#4111yescharacteristic
85C8×C191—41no—
86C22×C191#12011yescharacteristic
87C22×C191C22⋊Q811yescharacteristic
88C22×C191#12411yescharacteristic
89C22×C191C2×SD1611yescharacteristic
90C22×C191C2×Q1611yescharacteristic
91C22×C191AGL(1,ℤ/8)11yescharacteristic
92C22×C191#13711yescharacteristic
93C4×C191—42no—
94C4×C191—81no—
95C4×C191C22⋊Q811yescharacteristic
96C4×C191C22⋊Q811yescharacteristic
97C4×C191#12411yescharacteristic
98C4×C191#12411yescharacteristic
99Dic191—22no—
100Dic191—22no—
101Dic191—42no—
102Dic191—42no—
103C2×C191#39311yescharacteristic
104C2×C191#45011yescharacteristic
105C2×C191#45111yescharacteristic
106C2×C191#47511yescharacteristic
107C2×C191#47711yescharacteristic
108C2×C191#48711yescharacteristic
109C2×C191#48911yescharacteristic
110C191#202411yescharacteristic, complemented, Sylow
111#2024—1911nomaximal, Sylow
112C2×C4⋊Q8—1911no—
113C2×#103—1911no—
114C2×#103—1911no—
115#391—1911no—
116#340—1911no—
117#340D19111yescharacteristic
118#336—1911no—
119C22×Q8—3821no—
120C22×Q8—1911no—
121C22×C8—1911no—
122C22×C8C2×D19111yescharacteristic
123C4⋊Q8—3822no—
124C4⋊Q8—3822no—
125C2×C4⋊C4—3821no—
126C2×C4⋊C4—1911no—
127C2×C4⋊C4C2×D19111yescharacteristic
128C2×C4⋊C4C2×D19111yescharacteristic
129C2×C42—1911no—
130#103—3822no—
131#103—3822no—
132#95—3821no—
133#95—3821no—
134C2×Q8—3824no—
135C2×Q8—3821no—
136C2×Q8—3821no—
137C2×Q8—3821no—
138C2×Q8—3821no—
139C2×Q8—3821no—
140C2×Q8—1912no—
141C2×Q8—7642no—
142C2×Q8—7642no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—3821no—
146C22×C4—3821no—
147C22×C4—1911no—
148C22×C4—1911no—
149C22×C4C22×D19111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—3821no—
154C2×C8—3821no—
155C2×C8—3821no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—3824no—
160C4⋊C4—3821no—
161C4⋊C4—1912no—
162C4⋊C4D76412yes—
163C42—3821no—
164C42—3821no—
165C23D4×D19111yescharacteristic
166Q8—3822no—
167Q8—3822no—
168Q8—7648no—
169Q8—7641no—
170Q8—7641no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—3821no—
178C2×C4—3821no—
179C2×C4—3821no—
180C2×C4—3821no—
181C2×C4—3822no—
182C2×C4—3822no—
183C2×C4—1912no—
184C2×C4—1912no—
185C2×C4—7641no—
186C2×C4—7641no—
187C2×C4—7641no—
188C2×C4—7641no—
189C2×C4D4×D19111yescharacteristic
190C2×C4C2×D76411yescharacteristic
191C2×C4Q8×D19111yescharacteristic
192C2×C4#1569028611yescharacteristic
193C2×C4#1569028711yescharacteristic
194C2×C4#1569028711yescharacteristic
195C8—41no—
196C8—7641no—
197C22#2025929211yescharacteristic
198C22#2025930011yescharacteristic
199C22#2025930811yescharacteristic
200C22SD16×D19111yescharacteristic
201C22Q16×D19111yescharacteristic
202C22#2025934611yescharacteristic
203C22#2025935111yescharacteristic
204C4—42no—
205C4—81no—
206C4—3822no—
207C4—3822no—
208C4—7642no—
209C4—7642no—
210C4#2025930011yescharacteristic
211C4#2025930211yescharacteristic
212C4#2025930811yescharacteristic
213C4#2025931011yescharacteristic
214C2#2713257611yescharacteristic
215C2#2713281511yescharacteristic
216C2#2713282011yescharacteristic
217C2#2713294711yescharacteristic
218C2#2713295711yescharacteristic
219C2#2713301211yescharacteristic
220C2#2713302111yescharacteristic
subgroupG/H
centerC23D4×D191
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#340×C191C2
socle, prime radicalC23×C191C2×D4
hypercenter#340D191
hypocenterC191#2024
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic382Q8semidirect
110. C191#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#202593212
C2×#202592472
C2×#202592452
#271325682
#271324252
#271324172
#340×C1912
#2024191