Finite Group Databasebeta

← #37574525

Subgroups — #37574525

Order 24448.

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

normal subgroups only

This group has 260 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#27133402C211yesmaximal, characteristic, complemented
2#27132853C211yesmaximal, characteristic, complemented
3#27132831C211yesmaximal, characteristic, complemented
4#27132455C211yesmaximal, characteristic, complemented
5#27132452C211yesmaximal, characteristic, complemented
6#27132450C211yesmaximal, characteristic, complemented
7B(4,𝔽2)×C191C211yesmaximal, characteristic, complemented
8#20259347—21no—
9#20259318C2211yescharacteristic
10#20259315—21no—
11#20259304—21no—
12#20259303—21no—
13#20259303C2211yescharacteristic
14#20259295—21no—
15#20259294—21no—
16#20259293—21no—
17#20259291—21no—
18#20259249—21no—
19#20259239C2211yescharacteristic
20#20259237—21no—
21#20259237C2211yescharacteristic
22H(5,𝔽2)×C191C2211yescharacteristic
23#120×C191—21no—
24#120×C191C2211yescharacteristic
25#99×C191—21no—
26#99×C191C2211yescharacteristic
27C2×D764D411yescharacteristic, complemented
28C2×C22⋊D191—21no—
29C2×C22⋊D191—21no—
30C2×C22⋊D191—21no—
31C2×C22⋊D191—21no—
32C22×Dic191D411yescharacteristic, complemented
33C2×C4×D191—21no—
34#15690274—41no—
35#15690272—41no—
36#15690271—21no—
37C4⋊Dic191—21no—
38Dic191⋊C4—21no—
39Dic191⋊C4—21no—
40Dic191⋊C4—41no—
41C22⋊Dic191—21no—
42C22⋊Dic191—21no—
43C22⋊Dic191—21no—
44C22⋊Dic191—21no—
45C22⋊Dic191—41no—
46C22⋊Dic191D411yescharacteristic, complemented
47(C2×D191)⋊C4—21no—
48C4×Dic191D411yescharacteristic, complemented
49C24×C191D411yescharacteristic
50#41×C191—21no—
51#41×C191—41no—
52C2×D4×C191—21no—
53C2×D4×C191—21no—
54C2×D4×C191—21no—
55C2×D4×C191—41no—
56C2×D4×C191—41no—
57C2×D4×C191C2311yescharacteristic
58C22⋊C4×C191—21no—
59C22⋊C4×C191—21no—
60C22⋊C4×C191—41no—
61C22⋊C4×C191D411yescharacteristic
62C22×D191—21no—
63D764—41no—
64C22⋊D191—81no—
65C22⋊D191—81no—
66C22⋊D191—81no—
67C22⋊D191—81no—
68C2×Dic191—21no—
69C2×Dic191—21no—
70C2×Dic191—21no—
71C2×Dic191—41no—
72C2×Dic191—41no—
73C4×D191—81no—
74C191⋊C8—41no—
75C23×C191—21no—
76C23×C191—21no—
77C23×C191—21no—
78C23×C191—41no—
79C23×C191—81no—
80C23×C191C2×D411yescharacteristic
81C23×C191C2×D411yescharacteristic
82Q8×C191—21no—
83D4×C191—21no—
84D4×C191—41no—
85D4×C191—41no—
86D4×C191—41no—
87D4×C191—41no—
88D4×C191—81no—
89D4×C191—82no—
90C2×C4×C191—21no—
91C2×C4×C191—21no—
92C2×C4×C191—21no—
93C2×C4×C191—41no—
94C2×C4×C191—41no—
95C2×C4×C191C2×D411yescharacteristic
96C22×C191—21no—
97C22×C191—21no—
98C22×C191—41no—
99C22×C191—41no—
100C22×C191—41no—
101C22×C191—41no—
102C22×C191—42no—
103C22×C191—41no—
104C22×C191—41no—
105C22×C191—81no—
106C22×C191—81no—
107C22×C191—81no—
108C22×C191#12011yescharacteristic
109C2×D191—41no—
110C2×D191—41no—
111C2×D191—41no—
112C4×C191—21no—
113C4×C191—41no—
114C4×C191—41no—
115C4×C191—81no—
116Dic191—41no—
117Dic191—41no—
118Dic191—41no—
119Dic191—81no—
120C2×C191—21no—
121C2×C191—41no—
122C2×C191—41no—
123C2×C191—81no—
124C2×C191—81no—
125C2×C191B(4,𝔽2)11yescharacteristic
126D191—81no—
127C191#220011yescharacteristic, complemented, Sylow
128#2200—1911nomaximal, Sylow
129#560—1911no—
130#458—1911no—
131B(4,𝔽2)D19111yescharacteristic, complemented
132#453—1911no—
133#353—1911no—
134#352—1911no—
135AΣL(1,𝔽16)—1911no—
136H(5,𝔽2)C2×D19111yescharacteristic
137AGL(1,ℤ/8)—3821no—
138#127—1911no—
139#126—3821no—
140#123—3821no—
141#123—3821no—
142#123—1911no—
143#121—3821no—
144#121—3821no—
145#121—3821no—
146#120—21no—
147#120—3821no—
148#120C2×D19111yescharacteristic
149#104—3821no—
150#100—1911no—
151#99—21no—
152#99—3821no—
153#99—1911no—
154#99C2×D19111yescharacteristic
155C24C22⋊D19111yescharacteristic
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—3821no—
164C2×D4—3821no—
165C2×D4—3821no—
166C2×D4—3821no—
167C2×D4—1911no—
168C2×D4C22×D19111yescharacteristic
169C22×C4—3821no—
170C22×C4—1911no—
171SD16—7641no—
172D8—7641no—
173M16—3821no—
174C4⋊C4—3821no—
175C4⋊C4—3821no—
176C4⋊C4—3821no—
177C4⋊C4—7641no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—41no—
181C22⋊C4—3821no—
182C22⋊C4—3821no—
183C22⋊C4—3821no—
184C22⋊C4—3821no—
185C22⋊C4—3821no—
186C22⋊C4—1911no—
187C22⋊C4—7641no—
188C22⋊C4C22⋊D19111yescharacteristic
189C42—1911no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—3821no—
196C23D4×D19111yescharacteristic
197C23C2×C22⋊D19111yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—81no—
205D4—82no—
206D4—15281no—
207D4—15281no—
208D4—15281no—
209D4—15281no—
210D4—7641no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—3821no—
217C2×C4—3821no—
218C2×C4—3821no—
219C2×C4—15281no—
220C2×C4—7641no—
221C2×C4—7641no—
222C2×C4D4×D19111yescharacteristic
223C8—7641no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—81no—
234C22—81no—
235C22—81no—
236C22—7641no—
237C22—7641no—
238C22—7641no—
239C22#2025929011yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—81no—
244C4—15281no—
245C4—7641no—
246C4—7641no—
247C4—7641no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—15281no—
254C2#2713284911yescharacteristic
subgroupG/H
centerC2#27132849
commutator, cosocleC2×D4×C191C23
FrattiniC2×D4C22×D191
FittingB(4,𝔽2)×C191C2
socleC2×C191B(4,𝔽2)
hypercenterB(4,𝔽2)D191
hypocenterC191#2200
LCSG ▷ C2×D4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ B(4,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #27133402C2semidirect
2. #27132853C2semidirect
3. #27132831C2semidirect
4. #27132455C2semidirect
5. #27132452C2semidirect
6. #27132450C2semidirect
7. B(4,𝔽2)×C191C2semidirect
27. C2×D764D4semidirect
32. C22×Dic191D4semidirect
46. C22⋊Dic191D4semidirect
48. C4×Dic191D4semidirect
127. C191#2200semidirect
131. B(4,𝔽2)D191semidirect

Maximal subgroups

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

subgroupindex
#271334022
#271328532
#271328312
#271324552
#271324522
#271324502
B(4,𝔽2)×C1912
#2200191