Finite Group Databasebeta

← #34098671

Subgroups — #34098671

Order 20096.

222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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#23757804C211yesmaximal, characteristic
2#23757327C211yesmaximal, characteristic, complemented
3#23757137C211yesmaximal, characteristic, complemented
4#23757011C211yesmaximal, characteristic, complemented
5#23757009C211yesmaximal, characteristic, complemented
6#23757007C211yesmaximal, characteristic
7#327×C157C211yesmaximal, characteristic
8#19097764—21no—
9#19097762C411yescharacteristic, complemented
10#19097758C411yescharacteristic, complemented
11#19097752—21no—
12#19097750C2211yescharacteristic
13#19097736C411yescharacteristic, complemented
14D4×Dic157—21no—
15D4×Dic157C411yescharacteristic, complemented
16#19097727—21no—
17C2×#14578933—21no—
18C2×C4×Dic157C2211yescharacteristic
19#19097700—21no—
20C22⋊#11929434C2211yescharacteristic
21#19097681—21no—
22#19097678—21no—
23#19097678C2211yescharacteristic
24#121×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C2×Dic314C2×C411yescharacteristic
28C22×Dic157—21no—
29C22×Dic157—21no—
30C22×Dic157D411yescharacteristic
31C22×Dic157D411yescharacteristic
32C2×#11929434—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157C2×C411yescharacteristic
35#14578933—21no—
36#14578933—21no—
37#14578933—21no—
38#14578933—42no—
39C22⋊Dic157—21no—
40C22⋊Dic157—21no—
41C22⋊Dic157—21no—
42C22⋊Dic157—21no—
43C4×Dic157—21no—
44C4×Dic157C2×C411yescharacteristic
45C4×Dic157C2×C411yescharacteristic
46C4×Dic157D411yescharacteristic
47C4×Dic157D411yescharacteristic
48C2×D4×C157—21no—
49C2×D4×C157C2×C411yescharacteristic
50C22×C4×C157—21no—
51C22×C4×C157C2311yescharacteristic
52C2×C8×C157—21no—
53C4⋊C4×C157C2×C411yescharacteristic
54C22⋊C4×C157—21no—
55Dic314—41no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—21no—
60C2×Dic157—41no—
61C2×Dic157—42no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157—41no—
65C2×Dic157C22⋊C411yescharacteristic
66C2×Dic157C22⋊C411yescharacteristic
67C2×Dic157C22⋊C411yescharacteristic
68C2×Dic157C22⋊C411yescharacteristic
69#11929434—41no—
70C23×C157—21no—
71C23×C157C2×D411yescharacteristic
72D4×C157—41no—
73D4×C157—41no—
74D4×C157—41no—
75C2×C4×C157—21no—
76C2×C4×C157—41no—
77C2×C4×C157—41no—
78C2×C4×C157—41no—
79C2×C4×C157—41no—
80C2×C4×C157C22×C411yescharacteristic
81C2×C4×C157C2×D411yescharacteristic
82C8×C157—41no—
83C22×C157—21no—
84C22×C157—21no—
85C22×C157—41no—
86C22×C157—41no—
87C22×C157—41no—
88C22×C157C2×C22⋊C411yescharacteristic
89C22×C157AGL(1,ℤ/8)11yescharacteristic
90C22×C157#13711yescharacteristic
91C4×C157—21no—
92C4×C157—21no—
93C4×C157—41no—
94C4×C157—81no—
95Dic157—21no—
96Dic157—21no—
97Dic157—21no—
98Dic157—21no—
99Dic157—41no—
100Dic157—41no—
101Dic157—81no—
102C2×C157—21no—
103C2×C157—21no—
104C2×C157—81no—
105C2×C157#41011yescharacteristic
106C2×C157#41711yescharacteristic
107C2×C157#42111yescharacteristic
108C157#151211yescharacteristic, complemented, Sylow
109#1512—1571nomaximal, Sylow
110#529—1571no—
111#432—1571no—
112#382—1571no—
113#328—1571no—
114#328—1571no—
115#327—1571no—
116#327D15711yescharacteristic
117#126—3141no—
118#125—1571no—
119#124—1571no—
120#123—3141no—
121C22⋊Q8—1571no—
122#121C2×D15711yescharacteristic
123C4×Q8—1571no—
124C4×D4—3141no—
125C4×D4—1571no—
126#117—3141no—
127C2×C4⋊C4—3141no—
128C2×C42—1571no—
129C4⋊C8—3141no—
130C22⋊C8—1571no—
131C22⋊C8C2×D15711yescharacteristic
132#97—3141no—
133#95—3141no—
134#95—1571no—
135#95C2×D15711yescharacteristic
136C2×Q8—1571no—
137C2×D4—21no—
138C2×D4C4×D15711yescharacteristic
139C22×C4—21no—
140C22×C4—3141no—
141C22×C4—3141no—
142C22×C4—1571no—
143C22×C4—1571no—
144C22×C4C22×D15711yescharacteristic
145C2×C8—21no—
146C2×C8—3141no—
147C4⋊C4—3141no—
148C4⋊C4—3141no—
149C4⋊C4—3141no—
150C4⋊C4—3141no—
151C4⋊C4—6282no—
152C4⋊C4—1571no—
153C4⋊C4C4×D15711yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—3141no—
156C22⋊C4—3141no—
157C22⋊C4—3141no—
158C22⋊C4—3141no—
159C42—3141no—
160C42—1571no—
161C42—1571no—
162C42—1571no—
163C42—1571no—
164C23—21no—
165C23D4×D15711yescharacteristic
166Q8—6281no—
167D4—41no—
168D4—41no—
169D4—41no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—3141no—
176C2×C4—3141no—
177C2×C4—3141no—
178C2×C4—3141no—
179C2×C4—6281no—
180C2×C4—6282no—
181C2×C4—6281no—
182C2×C4—6281no—
183C2×C4—6281no—
184C2×C4—1571no—
185C2×C4—1571no—
186C2×C4—1571no—
187C2×C4—1571no—
188C2×C4C2×C4×D15711yescharacteristic
189C2×C4D4×D15711yescharacteristic
190C8—41no—
191C8—6281no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22C22⋊C4×D15711yescharacteristic
198C22#1909779511yescharacteristic
199C22#1909780011yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—81no—
204C4—3141no—
205C4—3141no—
206C4—3141no—
207C4—3141no—
208C4—6281no—
209C4—6281no—
210C4—12561no—
211C2—21no—
212C2—21no—
213C2—81no—
214C2#2375724511yescharacteristic
215C2#2375727111yescharacteristic
216C2#2375728811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#327×C157C2
socleC22×C157C2×C22⋊C4
prime radical#121×C157C22
cosocleC22×C4×C157C23
hypercenter#327D157
hypocenterC157#1512
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #23757327C2semidirect
3. #23757137C2semidirect
4. #23757011C2semidirect
5. #23757009C2semidirect
9. #19097762C4semidirect
10. #19097758C4semidirect
13. #19097736C4semidirect
15. D4×Dic157C4semidirect
108. C157#1512semidirect

Maximal subgroups

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

subgroupindex
#237578042
#237573272
#237571372
#237570112
#237570092
#237570072
#327×C1572
#1512157