Finite Group Databasebeta

← #34101354

Subgroups — #34101354

Order 20096.

278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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#23757847C211yesmaximal, characteristic
2#23757315C211yesmaximal, characteristic, complemented
3C2×#19097697C211yesmaximal, characteristic
4#23757275C211yesmaximal, characteristic
5#23757180C211yesmaximal, characteristic, complemented
6#23757034C211yesmaximal, characteristic, complemented
7C2×#101×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9#19097769—21no—
10#19097760—21no—
11#19097754—22no—
12#19097747—21no—
13#19097747—21no—
14#19097730C2211yescharacteristic
15C2×C4⋊Dic157C2211yescharacteristic
16C2×C4×Dic157C2211yescharacteristic
17#19097705—21no—
18#19097703—21no—
19#19097697—22no—
20#19097696—21no—
21#19097693—21no—
22#19097678—22no—
23C22×Q8×C157C2211yescharacteristic
24C2×M16×C157C2211yescharacteristic
25C2×M16×C157C2211yescharacteristic
26#101×C157—22no—
27#14578954—21no—
28#14578954—21no—
29#14578954—21no—
30#14578954—21no—
31C2×Dic314D411yescharacteristic
32C2×D628D411yescharacteristic
33C2×C22⋊D157—21no—
34C22×Dic157—21no—
35C22×Dic157—21no—
36C2×C4×D157—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157—21no—
39C4⋊Dic157D411yescharacteristic
40C4⋊Dic157D411yescharacteristic
41#14578933—22no—
42#14578933—22no—
43C22⋊Dic157—21no—
44#14578931—22no—
45#14578931—22no—
46C4×Dic157—21no—
47C4×Dic157—21no—
48C4×Dic157—21no—
49C2×Q8×C157—21no—
50C2×Q8×C157—21no—
51C2×Q8×C157—21no—
52C2×Q8×C157—21no—
53C2×Q8×C157—21no—
54C2×Q8×C157—21no—
55C22×C4×C157D412yes—
56C22×C4×C157C2311yescharacteristic
57M16×C157—21no—
58M16×C157—21no—
59M16×C157—21no—
60M16×C157D412yes—
61C2×C8×C157—21no—
62C2×C8×C157—21no—
63C22×D157—21no—
64Dic314—21no—
65Dic314—21no—
66D628—21no—
67D628—21no—
68C22⋊D157—41no—
69C22⋊D157—41no—
70C2×Dic157—22no—
71C2×Dic157—21no—
72C2×Dic157—21no—
73C2×Dic157—21no—
74C2×Dic157—41no—
75C2×Dic157—41no—
76C2×Dic157—42no—
77C2×Dic157—41no—
78C4×D157—41no—
79C4×D157—41no—
80C23×C157C2×D411yescharacteristic
81Q8×C157—41no—
82Q8×C157—41no—
83Q8×C157—41no—
84Q8×C157—41no—
85C2×C4×C157—22no—
86C2×C4×C157—22no—
87C2×C4×C157—22no—
88C2×C4×C157C2×D411yescharacteristic
89C2×C4×C157C2×D411yescharacteristic
90C2×C4×C157C2×D411yescharacteristic
91C2×C4×C157#4111yescharacteristic
92C2×C4×C157#4111yescharacteristic
93C2×C4×C157#4111yescharacteristic
94C8×C157—22no—
95C8×C157—41no—
96C22×C157—21no—
97C22×C157—21no—
98C22×C157#12011yescharacteristic
99C22×C157#12111yescharacteristic
100C22×C157#12311yescharacteristic
101C2×D157—41no—
102C2×D157—41no—
103C2×D157—41no—
104C4×C157—42no—
105C4×C157#12111yescharacteristic
106C4×C157#12111yescharacteristic
107C4×C157#12311yescharacteristic
108C4×C157#12411yescharacteristic
109Dic157—42no—
110Dic157—41no—
111Dic157—41no—
112Dic157—41no—
113Dic157—81no—
114C2×C157—21no—
115C2×C157—21no—
116C2×C157#39411yescharacteristic
117C2×C157#45411yescharacteristic
118C2×C157#45611yescharacteristic
119D157—81no—
120C157#203811yescharacteristic, complemented, Sylow
121#2038—1571nomaximal, Sylow
122#536—1571no—
123#428—1571no—
124C2×#104—1571no—
125#417—1571no—
126C2×#101D15711yescharacteristic, complemented
127#391—1571no—
128#339—1571no—
129C2×#41—1571no—
130C22×Q8C2×D15711yescharacteristic
131C2×M16C2×D15711yescharacteristic
132C2×M16C2×D15711yescharacteristic
133C4⋊Q8—3141no—
134#124—3141no—
135#123—3142no—
136C22⋊Q8—3141no—
137C22⋊Q8—3141no—
138#117—1571no—
139C2×C4⋊C4—1571no—
140C2×C42—1571no—
141#107—3141no—
142#106—3141no—
143#104—3142no—
144#103—3141no—
145#102—3141no—
146#101—22no—
147#95—3142no—
148#41—3141no—
149#41—3141no—
150#41—3141no—
151#41—3141no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—1571no—
159C2×D4—3141no—
160C2×D4—1571no—
161C22×C4—3141no—
162C22×C4—3141no—
163C22×C4—3141no—
164C22×C4D62812yes—
165C22×C4C22×D15711yescharacteristic
166M16—21no—
167M16—21no—
168M16—21no—
169M16C22⋊D15712yes—
170C2×C8—21no—
171C2×C8—21no—
172C4⋊C4—3142no—
173C4⋊C4—3142no—
174C4⋊C4—3141no—
175C4⋊C4—3141no—
176C4⋊C4—1571no—
177C4⋊C4—1571no—
178C22⋊C4—3142no—
179C22⋊C4—3142no—
180C22⋊C4—3141no—
181C42—3141no—
182C42—3141no—
183C42—3141no—
184C23—3141no—
185C23C2×D62811yescharacteristic
186Q8—41no—
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—3141no—
191Q8—3141no—
192D4—3141no—
193D4—3141no—
194D4—6281no—
195D4—6281no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—3142no—
200C2×C4—3141no—
201C2×C4—3141no—
202C2×C4—3141no—
203C2×C4—6281no—
204C2×C4—6281no—
205C2×C4—6281no—
206C2×C4—6281no—
207C2×C4—6282no—
208C2×C4—6281no—
209C2×C4D4×D15711yescharacteristic
210C2×C4D4×D15711yescharacteristic
211C2×C4C2×C22⋊D15711yescharacteristic
212C2×C4#1457895311yescharacteristic
213C2×C4#1457895311yescharacteristic
214C2×C4#1457895411yescharacteristic
215C8—22no—
216C8—41no—
217C22—21no—
218C22—21no—
219C22—6281no—
220C22—6281no—
221C22—6281no—
222C22#1909774111yescharacteristic
223C22#1909774511yescharacteristic
224C22#1909775511yescharacteristic
225C4—42no—
226C4—6282no—
227C4—6281no—
228C4—6281no—
229C4—6281no—
230C4—12561no—
231C4#1909774211yescharacteristic
232C4#1909774311yescharacteristic
233C4#1909775311yescharacteristic
234C4#1909775711yescharacteristic
235C2—21no—
236C2—21no—
237C2—12561no—
238C2#2375718911yescharacteristic
239C2#2375744811yescharacteristic
240C2#2375745811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#101×C157C2
socleC22×C157#120
prime radicalC2×#14578954C22
hypercenterC2×#101D157
hypocenterC157#2038
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #23757315C2semidirect
5. #23757180C2semidirect
6. #23757034C2semidirect
7. C2×#101×C157C2semidirect
120. C157#2038semidirect
126. C2×#101D157semidirect

Maximal subgroups

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

subgroupindex
#237578472
#237573152
C2×#190976972
#237572752
#237571802
#237570342
C2×#101×C1572
#2038157