Finite Group Databasebeta

← #37574544

Subgroups — #37574544

Order 24448.

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

normal subgroups only

This group has 236 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#27133375C211yesmaximal, characteristic, complemented
2#27132846C211yesmaximal, characteristic, complemented
3#27132836C211yesmaximal, characteristic, complemented
4#27132461C211yesmaximal, characteristic, complemented
5#27132460C211yesmaximal, characteristic, complemented
6#27132459C211yesmaximal, characteristic, complemented
7#454×C191C211yesmaximal, characteristic, complemented
8#20259352—21no—
9#20259347—21no—
10#20259320C2211yescharacteristic
11#20259311C2211yescharacteristic
12#20259308—21no—
13#20259295—21no—
14#20259294—21no—
15(C22⋊D191)⋊C4—21no—
16#20259279—21no—
17#20259278—21no—
18#20259249—21no—
19#20259249—21no—
20#20259241C2211yescharacteristic
21#20259241C2211yescharacteristic
222−1+4×C191C2211yescharacteristic
23AGL(1,ℤ/8)×C191—21no—
24#124×C191C2211yescharacteristic
25#104×C191—21no—
26#101×C191C2211yescharacteristic
27C2×Dic382D411yescharacteristic
28C2×D764D411yescharacteristic
29C2×C22⋊D191—21no—
30C2×C22⋊D191—21no—
31C22×Dic191—21no—
32C2×C4×D191—21no—
33#15690277—41no—
34#15690275—41no—
35#15690274—41no—
36#15690272—41no—
37#15690271—21no—
38#15690271—21no—
39Dic191⋊C4—21no—
40Dic191⋊C4—21no—
41Dic191⋊C4—21no—
42C22⋊Dic191—21no—
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—21no—
45(C2×D191)⋊C4—21no—
46C4×Dic191—21no—
47C4×Dic191D411yescharacteristic
48C4×Dic191D411yescharacteristic
49#41×C191—21no—
50#41×C191—21no—
51#41×C191—21no—
52#41×C191—41no—
53C2×Q8×C191—41no—
54C2×Q8×C191C2311yescharacteristic
55C2×D4×C191D411yescharacteristic
56SD16×C191—41no—
57D8×C191—41no—
58M16×C191—21no—
59C22⋊C4×C191—21no—
60C22⋊C4×C191—21no—
61C42×C191D411yescharacteristic
62C22×D191—21no—
63Dic382—41no—
64D764—41no—
65C22⋊D191—42no—
66C22⋊D191—81no—
67C2×Dic191—21no—
68C2×Dic191—21no—
69C2×Dic191—21no—
70C2×Dic191—42no—
71C4×D191—42no—
72C191⋊C8—41no—
73C191⋊C8—41no—
74C23×C191—21no—
75Q8×C191—21no—
76Q8×C191—21no—
77Q8×C191—21no—
78Q8×C191—41no—
79D4×C191—21no—
80D4×C191—21no—
81D4×C191—21no—
82D4×C191—41no—
83D4×C191—41no—
84C2×C4×C191—21no—
85C2×C4×C191—41no—
86C2×C4×C191—41no—
87C2×C4×C191—41no—
88C2×C4×C191C2×D411yescharacteristic
89C2×C4×C191C2×D411yescharacteristic
90C2×C4×C191C2×D411yescharacteristic
91C8×C191—41no—
92C22×C191—41no—
93C22×C191—41no—
94C22×C191—41no—
95C22×C191—41no—
96C22×C191#12011yescharacteristic
97C2×D191—41no—
98C2×D191—41no—
99C2×D191—41no—
100C4×C191—21no—
101C4×C191—21no—
102C4×C191—21no—
103C4×C191—41no—
104C4×C191—41no—
105Dic191—22no—
106Dic191—41no—
107Dic191—41no—
108C2×C191—21no—
109C2×C191—81no—
110C2×C191—81no—
111C2×C191B(4,𝔽2)11yescharacteristic
112D191—81no—
113C191#220411yescharacteristic, complemented, Sylow
114#2204—1911nomaximal, Sylow
115#555—1911no—
116#456—1911no—
117#454—1911no—
118#454D19111yescharacteristic, complemented
119#356—1911no—
120#355—1911no—
121#355—1911no—
1222−1+4C2×D19111yescharacteristic
123#137—3821no—
124AGL(1,ℤ/8)—21no—
125AGL(1,ℤ/8)—3821no—
126C4⋊Q8—1911no—
127#124—3821no—
128#124—1911no—
129#124C2×D19111yescharacteristic
130#121—3821no—
131#121—3821no—
132C4×D4—3821no—
133#117—3821no—
134#117—3821no—
135#104—21no—
136#104—3821no—
137#104—3821no—
138#101—1911no—
139#101—1911no—
140#101C2×D19111yescharacteristic
141#41—21no—
142#41—21no—
143#41—21no—
144#41—41no—
145C2×Q8—41no—
146C2×Q8—1911no—
147C2×Q8C22×D19111yescharacteristic
148C2×D4—3821no—
149C2×D4—3821no—
150C2×D4—1911no—
151C2×D4C22⋊D19111yescharacteristic
152C22×C4—3821no—
153C22×C4—3821no—
154Q16—7641no—
155SD16—41no—
156SD16—7641no—
157SD16—7641no—
158D8—41no—
159D8—7641no—
160M16—21no—
161M16—3821no—
162M16—3821no—
163C4⋊C4—3821no—
164C4⋊C4—3821no—
165C4⋊C4—3821no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—3821no—
169C22⋊C4—3821no—
170C22⋊C4—3821no—
171C22⋊C4—3821no—
172C42—3821no—
173C42—1911no—
174C42—1911no—
175C42C22⋊D19111yescharacteristic
176C23—21no—
177C23—3821no—
178Q8—21no—
179Q8—21no—
180Q8—21no—
181Q8—41no—
182Q8—7641no—
183D4—21no—
184D4—21no—
185D4—21no—
186D4—41no—
187D4—41no—
188D4—15281no—
189D4—7641no—
190D4—7642no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—3821no—
196C2×C4—3821no—
197C2×C4—3821no—
198C2×C4—7642no—
199C2×C4—7642no—
200C2×C4D4×D19111yescharacteristic
201C2×C4D4×D19111yescharacteristic
202C2×C4C2×C22⋊D19111yescharacteristic
203C8—41no—
204C8—7641no—
205C8—7641no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—7641no—
211C22—7641no—
212C22—7641no—
213C22#2025929011yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—41no—
218C4—41no—
219C4—3822no—
220C4—7641no—
221C4—7641no—
222C2—21no—
223C2—81no—
224C2—81no—
225C2—15281no—
226C2#2713284911yescharacteristic
subgroupG/H
centerC2#27132849
commutator, cosocleC2×Q8×C191C23
FrattiniC2×Q8C22×D191
Fitting#454×C191C2
socleC2×C191B(4,𝔽2)
hypercenter#454D191
hypocenterC191#2204
LCSG ▷ C2×Q8×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #27133375C2semidirect
2. #27132846C2semidirect
3. #27132836C2semidirect
4. #27132461C2semidirect
5. #27132460C2semidirect
6. #27132459C2semidirect
7. #454×C191C2semidirect
113. C191#2204semidirect
118. #454D191semidirect

Maximal subgroups

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

subgroupindex
#271333752
#271328462
#271328362
#271324612
#271324602
#271324592
#454×C1912
#2204191