Finite Group Databasebeta

← #34102147

Subgroups — #34102147

Order 20096.

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

normal subgroups only

This group has 226 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#23758026C211yesmaximal, characteristic, complemented
2#23757463C211yesmaximal, characteristic
3#23757451C211yesmaximal, characteristic
4#23757067C211yesmaximal, characteristic, complemented
5#23757063C211yesmaximal, characteristic, complemented
6#23757062C211yesmaximal, characteristic, complemented
7#458×C157C211yesmaximal, characteristic
8#19097801—21no—
9#19097770—21no—
10#19097764—21no—
11#19097764—21no—
12#19097761—21no—
13#19097758C2211yescharacteristic
14#19097752—21no—
15#19097752C2211yescharacteristic
16#19097750—21no—
17#19097748—21no—
18#19097698—21no—
19#19097688C2211yescharacteristic
20#19097686—21no—
21#19097686C2211yescharacteristic
22H(5,𝔽2)×C157C2211yescharacteristic
23#123×C157—21no—
24#123×C157C2211yescharacteristic
25#99×C157—21no—
26#99×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314D411yescharacteristic
29C22×Dic157D411yescharacteristic
30#14578944—41no—
31#14578942—41no—
32#14578938—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35#14578933—21no—
36#14578933—21no—
37#14578933—21no—
38#14578933—21no—
39#14578933—21no—
40#14578933—41no—
41C22⋊Dic157—21no—
42C22⋊Dic157—21no—
43C22⋊Dic157—21no—
44C22⋊Dic157—21no—
45C22⋊Dic157—41no—
46C22⋊Dic157D411yescharacteristic
47C4×Dic157—21no—
48C4×Dic157D411yescharacteristic
49#41×C157—21no—
50#41×C157—41no—
51C2×D4×C157—21no—
52C2×D4×C157—21no—
53C2×D4×C157—41no—
54C2×D4×C157C2311yescharacteristic
55C22×C4×C157D411yescharacteristic
56C4⋊C4×C157—21no—
57C4⋊C4×C157—41no—
58C22⋊C4×C157—21no—
59C22⋊C4×C157—21no—
60C22⋊C4×C157—41no—
61C22⋊C4×C157D411yescharacteristic
62Dic314—41no—
63Dic314—81no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—21no—
67C2×Dic157—21no—
68C2×Dic157—41no—
69C2×Dic157—41no—
70#11929434—41no—
71C23×C157—21no—
72C23×C157—21no—
73C23×C157C2×D411yescharacteristic
74C23×C157C2×D411yescharacteristic
75Q8×C157—21no—
76D4×C157—21no—
77D4×C157—41no—
78D4×C157—41no—
79D4×C157—41no—
80D4×C157—41no—
81C2×C4×C157—21no—
82C2×C4×C157—21no—
83C2×C4×C157—21no—
84C2×C4×C157—21no—
85C2×C4×C157—41no—
86C2×C4×C157—41no—
87C2×C4×C157—41no—
88C2×C4×C157C2×D411yescharacteristic
89C22×C157—21no—
90C22×C157—21no—
91C22×C157—41no—
92C22×C157—41no—
93C22×C157—41no—
94C22×C157—81no—
95C22×C157—81no—
96C22×C157#12011yescharacteristic
97C4×C157—21no—
98C4×C157—41no—
99C4×C157—41no—
100C4×C157—41no—
101C4×C157—81no—
102Dic157—41no—
103Dic157—41no—
104Dic157—41no—
105Dic157—41no—
106Dic157—81no—
107C2×C157—21no—
108C2×C157—41no—
109C2×C157—41no—
110C2×C157—81no—
111C2×C157B(4,𝔽2)11yescharacteristic
112C157#220111yescharacteristic, complemented, Sylow
113#2201—1571nomaximal, Sylow
114#563—1571no—
115#458—1571no—
116#458D15711yescharacteristic
117#455—1571no—
118#354—1571no—
119#352—1571no—
120#352—1571no—
121H(5,𝔽2)C2×D15711yescharacteristic
122#137—3141no—
123C4⋊Q8—3141no—
124#126—3141no—
125#126—3141no—
126#125—3141no—
127#124—1571no—
128#123—21no—
129#123—3141no—
130#123—1571no—
131#123C2×D15711yescharacteristic
132C22⋊Q8—3141no—
133C22⋊Q8—3141no—
134#104—3141no—
135#100—1571no—
136#99—21no—
137#99—3141no—
138#99—1571no—
139#99C2×D15711yescharacteristic
140#41—21no—
141#41—41no—
142C2×Q8—3141no—
143C2×Q8—1571no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4C22×D15711yescharacteristic
148C22×C4—1571no—
149C22×C4C22⋊D15711yescharacteristic
150Q16—6281no—
151SD16—6281no—
152M16—3141no—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—3141no—
156C4⋊C4—3141no—
157C4⋊C4—3141no—
158C4⋊C4—3141no—
159C4⋊C4—3141no—
160C4⋊C4—3141no—
161C4⋊C4—3141no—
162C4⋊C4—6281no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—41no—
166C22⋊C4—3141no—
167C22⋊C4—3141no—
168C22⋊C4—3141no—
169C22⋊C4—3141no—
170C22⋊C4—6281no—
171C22⋊C4—1571no—
172C22⋊C4C22⋊D15711yescharacteristic
173C42—3141no—
174C42—1571no—
175C23—21no—
176C23—21no—
177C23D4×D15711yescharacteristic
178C23C2×C22⋊D15711yescharacteristic
179Q8—21no—
180Q8—6281no—
181Q8—12561no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—3141no—
195C2×C4—3141no—
196C2×C4—3141no—
197C2×C4—3141no—
198C2×C4—6281no—
199C2×C4—6281no—
200C2×C4D4×D15711yescharacteristic
201C8—6281no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#1909773911yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—6281no—
216C4—6281no—
217C4—6281no—
218C4—6281no—
219C4—12561no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#2375745911yescharacteristic
subgroupG/H
centerC2#23757459
commutator, cosocleC2×D4×C157C23
FrattiniC2×D4C22×D157
Fitting#458×C157C2
socleC2×C157B(4,𝔽2)
prime radicalH(5,𝔽2)×C157C22
hypercenter#458D157
hypocenterC157#2201
LCSG ▷ C2×D4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #23758026C2semidirect
4. #23757067C2semidirect
5. #23757063C2semidirect
6. #23757062C2semidirect
112. C157#2201semidirect

Maximal subgroups

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

subgroupindex
#237580262
#237574632
#237574512
#237570672
#237570632
#237570622
#458×C1572
#2201157