Finite Group Databasebeta

← #34109788

Subgroups — #34109788

Order 20096.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#14578944C211yesmaximal, characteristic, complemented
2C2×#19097778C211yesmaximal, characteristic
3#23757844C211yesmaximal, characteristic
4#23757529C214yesmaximal, complemented
5#23757512C214yesmaximal, complemented
6#23757309C211yesmaximal, characteristic, complemented
7#23757282C211yesmaximal, characteristic, complemented
8#23757281C211yesmaximal, characteristic, complemented
9#536×C157C211yesmaximal, characteristic
10C22×Dic314C2211yescharacteristic
11C2×#14578944—24no—
12C2×#14578944C2212yes—
13C2×#14578944C2212yes—
14#19097778—24no—
15C2×#14578938C2212yes—
16C2×#14578938C2211yescharacteristic
17C22×#11929434C2212yes—
18C22×#11929434C2211yescharacteristic
19#19097769—21no—
20#19097758—21no—
21#19097752—22no—
22#19097750C2214yes—
23#19097730C2211yescharacteristic
24#19097704C2212yes—
25#19097702C2212yes—
26#19097695C2214yes—
27#19097694C2214yes—
28C2×#41×C157C2211yescharacteristic
29C22×Q8×C157C2211yescharacteristic
30C4⋊Q8×C157—21no—
31#124×C157—21no—
32#123×C157—22no—
33C22⋊Q8×C157C2214yes—
34#117×C157C2211yescharacteristic
35C2×Dic314—21no—
36C2×Dic314—22no—
37C2×Dic314—22no—
38C2×Dic314C2312yes—
39C22×Dic157—21no—
40#14578944—24no—
41#14578944—24no—
42#14578938—24no—
43#14578938—22no—
44C2×#11929434—24no—
45C2×#11929434D414yes—
46C2×#11929434C2312yes—
47C2×#11929434C2311yescharacteristic
48C2×#11929434C2311yescharacteristic
49C4⋊Dic157C2312yes—
50#14578933—24no—
51C22⋊Dic157—21no—
52C22⋊Dic157—24no—
53C4×Dic157—21no—
54#41×C157—22no—
55#41×C157—22no—
56C2×Q8×C157—21no—
57C2×Q8×C157—22no—
58C2×Q8×C157—22no—
59C2×Q8×C157D411yescharacteristic
60C2×Q8×C157C2312yes—
61C2×D4×C157D412yes—
62C2×D4×C157D411yescharacteristic
63C22×C4×C157—21no—
64C22×C4×C157C2312yes—
65C22×C4×C157C2311yescharacteristic
66C4⋊C4×C157—24no—
67C4⋊C4×C157C2312yes—
68C22⋊C4×C157—21no—
69C22⋊C4×C157—24no—
70C42×C157—21no—
71Dic314—22no—
72Dic314—22no—
73Dic314—42no—
74C2×Dic157—22no—
75C2×Dic157—22no—
76C2×Dic157—42no—
77#11929434—22no—
78#11929434C2×D412yes—
79#11929434C2×D412yes—
80C23×C157C2×D412yes—
81C23×C157C2×D411yescharacteristic
82Q8×C157—22no—
83Q8×C157—22no—
84Q8×C157—22no—
85Q8×C157—42no—
86D4×C157—24no—
87D4×C157—22no—
88C2×C4×C157—22no—
89C2×C4×C157—22no—
90C2×C4×C157—22no—
91C2×C4×C157—22no—
92C2×C4×C157—42no—
93C2×C4×C157C2×D412yes—
94C2×C4×C157C2×D412yes—
95C2×C4×C157C2×D411yescharacteristic
96C2×C4×C157#4112yes—
97C2×C4×C157C2411yescharacteristic
98C22×C157—22no—
99C22×C157—22no—
100C22×C157—24no—
101C22×C157#12112yes—
102C22×C157C22×D411yescharacteristic
103C4×C157—22no—
104C4×C157—42no—
105C4×C157—42no—
106C4×C157#12112yes—
107C4×C157C22×D411yescharacteristic
108C4×C157C2×#4111yescharacteristic
109Dic157—42no—
110Dic157—42no—
111C2×C157—22no—
112C2×C157—42no—
113C2×C157C2×#12111yescharacteristic
114C2×C157#57812yes—
115C157#305911yescharacteristic, complemented, Sylow
116#3059—1571nomaximal, Sylow
117C22×Q16—1571no—
118C2×#131—1571no—
119#536—1571no—
120#536D15711yescharacteristic
121#470—1574no—
122#467—1574no—
123#427—1571no—
124#419—1571no—
125#419—1571no—
126C2×#41C2×D15711yescharacteristic
127C22×Q8—1571no—
128C22×Q8C2×D15711yescharacteristic
129C2×Q16—3144no—
130C2×Q16—1572no—
131C2×Q16—1572no—
132#131—3144no—
133C2×M16—1571no—
134C2×M16—1572no—
135C22×C8—1572no—
136C22×C8—1571no—
137C4⋊Q8—21no—
138C4⋊Q8—3141no—
139#124—21no—
140#124—3141no—
141#123—22no—
142#123—3142no—
143C22⋊Q8—1574no—
144C22⋊Q8C2×D15714yes—
145#117—1571no—
146#117C2×D15711yescharacteristic
147#107—1572no—
148#106—1572no—
149#103—1574no—
150#103—1574no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—3141no—
157C2×Q8—3142no—
158C2×Q8—3142no—
159C2×Q8—1572no—
160C2×Q8C22⋊D15711yescharacteristic
161C2×Q8C22×D15712yes—
162C2×D4C22⋊D15712yes—
163C2×D4C22⋊D15711yescharacteristic
164C22×C4—21no—
165C22×C4—3141no—
166C22×C4C22×D15712yes—
167C22×C4C22×D15711yescharacteristic
168Q16—3144no—
169Q16—3144no—
170M16—3142no—
171M16—3144no—
172C2×C8—3144no—
173C2×C8—1572no—
174C2×C8—1574no—
175C2×C8—1571no—
176C2×C8—1571no—
177C4⋊C4—24no—
178C4⋊C4—3144no—
179C4⋊C4—1572no—
180C4⋊C4C22×D15712yes—
181C22⋊C4—21no—
182C22⋊C4—24no—
183C22⋊C4—3141no—
184C22⋊C4—3144no—
185C42—21no—
186C42—3141no—
187C23C2×C22⋊D15712yes—
188C23C2×C22⋊D15711yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—3142no—
194Q8—3142no—
195Q8—6282no—
196D4—24no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—3142no—
204C2×C4—3142no—
205C2×C4—6282no—
206C2×C4D4×D15712yes—
207C2×C4C2×C22⋊D15712yes—
208C2×C4C2×C22⋊D15711yescharacteristic
209C2×C4#1457895312yes—
210C2×C4C23×D15711yescharacteristic
211C8—3142no—
212C8—1572no—
213C8—1572no—
214C22—22no—
215C22—24no—
216C22—22no—
217C22#1909774312yes—
218C22C22×C22⋊D15711yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—6282no—
223C4—6282no—
224C4#1909774312yes—
225C4C2×D4×D15711yescharacteristic
226C4C2×#1457895311yescharacteristic
227C2—22no—
228C2—42no—
229C2C2×#1909774311yescharacteristic
230C2#2375808812yes—
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#536×C157C2
socleC22×C157C22×D4
prime radicalC2×#41×C157C22
hypercenter#536D157
hypocenterC157#3059
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C22×#14578944C2semidirect
4. #23757529C2semidirect
5. #23757512C2semidirect
6. #23757309C2semidirect
7. #23757282C2semidirect
8. #23757281C2semidirect
115. C157#3059semidirect

Maximal subgroups

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

subgroupindex
C22×#145789442
C2×#190977782
#237578442
#237575292
#237575122
#237573092
#237572822
#237572812
#536×C1572
#3059157