Finite Group Databasebeta

← #34116097

Subgroups — #34116097

Order 20096.

262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 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#23758352C211yesmaximal, characteristic
2#23758288C211yesmaximal, characteristic, complemented
3#23758277C211yesmaximal, characteristic, complemented
4#23758270C211yesmaximal, characteristic
5#23758156C211yesmaximal, characteristic, complemented
6#23758144C211yesmaximal, characteristic, complemented
7#104×D157C211yesmaximal, characteristic
8#19097859—21no—
9#19097858—22no—
10#19097858—21no—
11C2×#14578964—21no—
12C2×#14578964C2211yescharacteristic
13C2×#14578964C2211yescharacteristic
14D157⋊M16—21no—
15D157⋊M16C2211yescharacteristic
16#19097850C2211yescharacteristic
17#19097842—21no—
18#19097841—21no—
19C4⋊#11929441—22no—
20#19097836—21no—
21#19097835—21no—
22#41×D157C2211yescharacteristic
23M16×D157C2211yescharacteristic
24C42×D157C2211yescharacteristic
25#19097699C411yescharacteristic, complemented
26#19097698C411yescharacteristic, complemented
27#19097697C411yescharacteristic, complemented
28#104×C157C411yescharacteristic, complemented
29#14578964—22no—
30#14578964—21no—
31#14578964—21no—
32#14578964—21no—
33#14578964—21no—
34#14578964D411yescharacteristic
35#14578964D411yescharacteristic
36#14578963—22no—
37#14578963—21no—
38D157⋊C8—22no—
39D157⋊C8—21no—
40C2×#11929441—22no—
41C2×#11929441—21no—
42C2×#11929441D412yes—
43C4⋊#10597845—21no—
44C22⋊#10597845—21no—
45C4×#10597845—21no—
46#14578955D411yescharacteristic
47#14578954—21no—
48#14578954C2×C411yescharacteristic
49#14578953—21no—
50#14578953D411yescharacteristic
51Q8×D157Q811yescharacteristic
52D4×D157—21no—
53D4×D157Q811yescharacteristic
54C2×C4×D157—21no—
55C2×C4×D157—21no—
56C2×C4×D157C2311yescharacteristic
57#14578938C2×C411yescharacteristic
58#14578937—21no—
59C8×D157—21no—
60C4×Dic157—21no—
61C4×Dic157C2×C411yescharacteristic
62#41×C157C2×C411yescharacteristic
63M16×C157C2×C411yescharacteristic
64C42×C157C2×C411yescharacteristic
65C2×#10597845—41no—
66#11929441—21no—
67#11929441—22no—
68#11929441—21no—
69#11929441—41no—
70C22×D157—21no—
71C22×D157#4111yescharacteristic
72Dic314—21no—
73Dic314C4⋊C411yescharacteristic
74D628—21no—
75D628C4⋊C411yescharacteristic
76C22⋊D157—21no—
77C22⋊D157—21no—
78C22⋊D157—21no—
79C2×Dic157—21no—
80C2×Dic157—21no—
81C2×Dic157C2×D411yescharacteristic
82C4×D157—21no—
83C4×D157—21no—
84C4×D157—21no—
85C4×D157—42no—
86C4×D157C2×D411yescharacteristic
87C4×D157C2×D411yescharacteristic
88C4×D157C2×Q811yescharacteristic
89C4×D157#4111yescharacteristic
90#11929434—21no—
91Q8×C157C4⋊C411yescharacteristic
92D4×C157—21no—
93D4×C157C4⋊C411yescharacteristic
94C2×C4×C157—21no—
95C2×C4×C157—21no—
96C2×C4×C157C22×C411yescharacteristic
97C8×C157—21no—
98C22×C157—21no—
99C22×C157C4×D411yescharacteristic
100C2×D157—21no—
101C2×D157—41no—
102C2×D157—81no—
103C2×D157C22⋊Q811yescharacteristic
104C2×D157#12311yescharacteristic
105#10597845—81no—
106C4×C157—22no—
107C4×C157—21no—
108C4×C157C2×C4⋊C411yescharacteristic
109C4×C157C4×D411yescharacteristic
110Dic157—21no—
111Dic157—41no—
112Dic157#12011yescharacteristic
113Dic157C22⋊Q811yescharacteristic
114C2×C157—21no—
115C2×C157—41no—
116C2×C157#38511yescharacteristic
117D157—21no—
118D157—21no—
119D157—41no—
120C157#186111yescharacteristic, complemented, Sylow
121#1861—1571nomaximal, Sylow
122#568—1571no—
123#430—1571no—
124#423—1571no—
125#421—1571no—
126C2×#104—1571no—
127#344—1571no—
128#339—1571no—
129C2×#41—1571no—
130#131—3141no—
131#131—3141no—
132#131—3142no—
133C2×M16—3141no—
134C2×M16—3141no—
135C2×M16—1571no—
136C2×M16—1571no—
137C2×M16—1571no—
138C2×M16—1571no—
139#117—1571no—
140C2×C42—1571no—
141#108—3141no—
142#108—3141no—
143C4⋊C8—3142no—
144#104—3141no—
145#104—3141no—
146#104—1571no—
147#104—1571no—
148#104—1571no—
149#104#1059784511yescharacteristic, complemented
150#41—3141no—
151#41—3141no—
152#41—1571no—
153#41—1571no—
154#41—1571no—
155#41C2×#1059784511yescharacteristic
156C2×Q8—1571no—
157C2×D4—3141no—
158C2×D4—1571no—
159C22×C4—3141no—
160C22×C4—3141no—
161C22×C4—1571no—
162M16—3141no—
163M16—3142no—
164M16—3142no—
165M16—3141no—
166M16—3141no—
167M16—3141no—
168M16—3141no—
169M16—3141no—
170M16—1571no—
171M16—1571no—
172M16—1571no—
173M16C2×#1059784511yescharacteristic
174C2×C8—3141no—
175C2×C8—3142no—
176C2×C8—3142no—
177C2×C8—3141no—
178C2×C8—3141no—
179C2×C8—1572no—
180C4⋊C4—3141no—
181C22⋊C4—3141no—
182C42—3141no—
183C42—3141no—
184C42—1571no—
185C42C2×#1059784511yescharacteristic
186C23—3141no—
187C23—1571no—
188Q8—3141no—
189Q8—1571no—
190Q8C4⋊#1059784511yescharacteristic
191D4—21no—
192D4—3141no—
193D4—3141no—
194D4—3141no—
195D4—3141no—
196D4—1571no—
197D4C4⋊#1059784511yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—3141no—
201C2×C4—3141no—
202C2×C4—3141no—
203C2×C4—3141no—
204C2×C4—3141no—
205C2×C4—6282no—
206C2×C4—6281no—
207C2×C4—1571no—
208C2×C4—1571no—
209C2×C4—1571no—
210C2×C4—1571no—
211C2×C4—1571no—
212C2×C4C22×#1059784511yescharacteristic
213C8—21no—
214C8—3141no—
215C8—3141no—
216C8—3142no—
217C8—3141no—
218C8—6281no—
219C22—21no—
220C22—3141no—
221C22—6281no—
222C22—1571no—
223C22—1571no—
224C22—12561no—
225C22D4×#1059784511yescharacteristic
226C4—22no—
227C4—21no—
228C4—3141no—
229C4—6281no—
230C4—1571no—
231C4—1571no—
232C4—12561no—
233C4C2×C4⋊#1059784511yescharacteristic
234C4D4×#1059784511yescharacteristic
235C2—21no—
236C2—41no—
237C2—3141no—
238C2—3141no—
239C2—6281no—
240C2#2375822011yescharacteristic
subgroupG/H
centerC2#23758220
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#104×C157C4
socleC2×C157#385
prime radical#41×D157C22
cosocleC2×C4×D157C23
hypercenter#104#10597845
hypocenterC157#1861
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #23758288C2semidirect
3. #23758277C2semidirect
5. #23758156C2semidirect
6. #23758144C2semidirect
25. #19097699C4semidirect
26. #19097698C4semidirect
27. #19097697C4semidirect
28. #104×C157C4semidirect
120. C157#1861semidirect
149. #104#10597845semidirect

Maximal subgroups

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

subgroupindex
#237583522
#237582882
#237582772
#237582702
#237581562
#237581442
#104×D1572
#1861157