Finite Group Databasebeta

← #37574514

Subgroups — #37574514

Order 24448.

246 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 41 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
1#27133397C211yesmaximal, characteristic, complemented
2#27132853C211yesmaximal, characteristic, complemented
3#27132831C211yesmaximal, characteristic
4#27132455C211yesmaximal, characteristic, complemented
5#27132453C211yesmaximal, characteristic, complemented
6#27132452C211yesmaximal, characteristic, complemented
7#458×C191C211yesmaximal, characteristic, complemented
8#20259347—21no—
9#20259318C2211yescharacteristic
10#20259308—21no—
11#20259308—21no—
12#20259307—21no—
13#20259303—21no—
14#20259303C2211yescharacteristic
15#20259287—21no—
16C4×C22⋊D191—21no—
17(C22⋊D191)⋊C4—21no—
18#20259249—21no—
19#20259239C2211yescharacteristic
20#20259237—21no—
21#20259237C2211yescharacteristic
22H(5,𝔽2)×C191C2211yescharacteristic
23#123×C191—21no—
24#123×C191C2211yescharacteristic
25#99×C191—21no—
26#99×C191C2211yescharacteristic
27C2×Dic382—21no—
28C2×D764D411yescharacteristic
29C2×C22⋊D191—21no—
30C2×C22⋊D191—21no—
31C22×Dic191D411yescharacteristic
32C2×C4×D191—21no—
33#15690274—41no—
34#15690272—41no—
35#15690271—21no—
36Dic191⋊C4—21no—
37Dic191⋊C4—21no—
38Dic191⋊C4—41no—
39C22⋊Dic191—21no—
40C22⋊Dic191—21no—
41C22⋊Dic191—41no—
42C22⋊Dic191D411yescharacteristic
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—21no—
45(C2×D191)⋊C4—21no—
46C4×Dic191—21no—
47C4×Dic191—21no—
48C4×Dic191D411yescharacteristic
49#41×C191—21no—
50#41×C191—41no—
51C2×D4×C191—21no—
52C2×D4×C191—21no—
53C2×D4×C191—41no—
54C2×D4×C191C2311yescharacteristic
55C22×C4×C191D411yescharacteristic
56C4⋊C4×C191—21no—
57C4⋊C4×C191—41no—
58C22⋊C4×C191—21no—
59C22⋊C4×C191—21no—
60C22⋊C4×C191—41no—
61C22⋊C4×C191D411yescharacteristic
62C22×D191—21no—
63Dic382—42no—
64D764—41no—
65C22⋊D191—42no—
66C22⋊D191—42no—
67C2×Dic191—21no—
68C2×Dic191—21no—
69C2×Dic191—21no—
70C2×Dic191—41no—
71C2×Dic191—41no—
72C4×D191—81no—
73C191⋊C8—41no—
74C23×C191—21no—
75C23×C191—21no—
76C23×C191C2×D411yescharacteristic
77C23×C191C2×D411yescharacteristic
78Q8×C191—21no—
79D4×C191—21no—
80D4×C191—41no—
81D4×C191—41no—
82D4×C191—41no—
83D4×C191—41no—
84C2×C4×C191—21no—
85C2×C4×C191—21no—
86C2×C4×C191—21no—
87C2×C4×C191—21no—
88C2×C4×C191—41no—
89C2×C4×C191—41no—
90C2×C4×C191—41no—
91C2×C4×C191C2×D411yescharacteristic
92C22×C191—21no—
93C22×C191—21no—
94C22×C191—41no—
95C22×C191—41no—
96C22×C191—41no—
97C22×C191—81no—
98C22×C191—81no—
99C22×C191#12011yescharacteristic
100C2×D191—41no—
101C2×D191—41no—
102C2×D191—41no—
103C4×C191—21no—
104C4×C191—41no—
105C4×C191—41no—
106C4×C191—41no—
107C4×C191—81no—
108Dic191—22no—
109Dic191—41no—
110Dic191—41no—
111Dic191—81no—
112C2×C191—21no—
113C2×C191—41no—
114C2×C191—41no—
115C2×C191—81no—
116C2×C191B(4,𝔽2)11yescharacteristic
117D191—81no—
118C191#219811yescharacteristic, complemented, Sylow
119#2198—1911nomaximal, Sylow
120#559—1911no—
121#458—1911no—
122#458D19111yescharacteristic, complemented
123#453—1911no—
124#353—1911no—
125#352—1911no—
126#352—1911no—
127H(5,𝔽2)C2×D19111yescharacteristic
128AGL(1,ℤ/8)—3821no—
129#127—1911no—
130#124—3821no—
131#124—3821no—
132#123—21no—
133#123—3821no—
134#123—3821no—
135#123—1911no—
136#123C2×D19111yescharacteristic
137C4×Q8—3821no—
138C4×D4—3821no—
139C4×D4—3821no—
140#104—3821no—
141#100—1911no—
142#99—21no—
143#99—3821no—
144#99—1911no—
145#99C2×D19111yescharacteristic
146#41—21no—
147#41—41no—
148C2×Q8—3821no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—3821no—
153C2×D4—3821no—
154C2×D4—1911no—
155C2×D4C22×D19111yescharacteristic
156C22×C4—3821no—
157C22×C4—1911no—
158C22×C4C22⋊D19111yescharacteristic
159SD16—7641no—
160D8—7641no—
161M16—3821no—
162C4⋊C4—21no—
163C4⋊C4—41no—
164C4⋊C4—3821no—
165C4⋊C4—3821no—
166C4⋊C4—7641no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—41no—
170C22⋊C4—3821no—
171C22⋊C4—3821no—
172C22⋊C4—3821no—
173C22⋊C4—3821no—
174C22⋊C4—3821no—
175C22⋊C4—1911no—
176C22⋊C4—7641no—
177C22⋊C4C22⋊D19111yescharacteristic
178C42—3821no—
179C42—3821no—
180C42—1911no—
181C23—21no—
182C23—21no—
183C23—3821no—
184C23D4×D19111yescharacteristic
185C23C2×C22⋊D19111yescharacteristic
186Q8—21no—
187Q8—7642no—
188D4—21no—
189D4—41no—
190D4—41no—
191D4—41no—
192D4—41no—
193D4—7641no—
194D4—7642no—
195D4—7642no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—3821no—
204C2×C4—3821no—
205C2×C4—3821no—
206C2×C4—15281no—
207C2×C4—7641no—
208C2×C4—7641no—
209C2×C4D4×D19111yescharacteristic
210C8—7641no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—81no—
218C22—7641no—
219C22—7641no—
220C22—7641no—
221C22#2025929011yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—3822no—
228C4—15281no—
229C4—7641no—
230C4—7641no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—81no—
235C2—15281no—
236C2#2713284911yescharacteristic
subgroupG/H
centerC2#27132849
commutator, cosocleC2×D4×C191C23
FrattiniC2×D4C22×D191
Fitting#458×C191C2
socleC2×C191B(4,𝔽2)
prime radical#27132831C2
hypercenter#458D191
hypocenterC191#2198
LCSG ▷ C2×D4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #27133397C2semidirect
2. #27132853C2semidirect
4. #27132455C2semidirect
5. #27132453C2semidirect
6. #27132452C2semidirect
7. #458×C191C2semidirect
118. C191#2198semidirect
122. #458D191semidirect

Maximal subgroups

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

subgroupindex
#271333972
#271328532
#271328312
#271324552
#271324532
#271324522
#458×C1912
#2198191