Finite Group Databasebeta

← #104×#10597845 #34115898

Subgroups — #104×#10597845 #34115898

Order 20096.

360 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 92 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#41×#10597845C211yesmaximal, characteristic
2D157⋊#104C211yesmaximal, characteristic
3M16×#10597845C211yesmaximal, characteristic, complemented
4C42×#10597845C211yesmaximal, characteristic, complemented
5#23758145C211yesmaximal, characteristic, complemented
6#23758144C211yesmaximal, characteristic, complemented
7#104×D157C211yesmaximal, characteristic
8D157⋊M16C2211yescharacteristic
9Q8×#10597845C412yescomplemented
10D4×#10597845—22no—
11D4×#10597845C412yescomplemented
12#19097850—21no—
13#19097850C2211yescharacteristic
14C2×C4×#10597845—22no—
15C2×C4×#10597845—21no—
16C2×C4×#10597845C2211yescharacteristic
17C2×C4×#10597845C2211yescharacteristic
18#19097836C412yescomplemented
19#19097835C412yescomplemented
20#19097825—21no—
21C8×#10597845—21no—
22#41×D157C2211yescharacteristic
23M16×D157C2211yescharacteristic
24C42×D157C2211yescharacteristic
25#19097699C411yescharacteristic, complemented
26#19097698C411yescharacteristic, complemented
27#19097697C411yescharacteristic, complemented
28#104×C157C411yescharacteristic, complemented
29C22×#10597845—22no—
30C22×#10597845—21no—
31C22×#10597845D412yes—
32#14578964C2×C412yescomplemented
33#14578963—21no—
34D157⋊C8—21no—
35C4⋊#10597845—22no—
36C4⋊#10597845C2×C412yes—
37C22⋊#10597845—22no—
38C22⋊#10597845—21no—
39C4×#10597845—28no—
40C4×#10597845—22no—
41C4×#10597845—21no—
42C4×#10597845—21no—
43C4×#10597845C2×C412yes—
44C4×#10597845C2×C412yescomplemented
45C4×#10597845D411yescharacteristic
46C4×#10597845D411yescharacteristic
47#14578955C2×C411yescharacteristic
48#14578954—21no—
49#14578954C2×C411yescharacteristic
50#14578953—21no—
51#14578953C2×C411yescharacteristic
52Q8×D157C2×C411yescharacteristic
53D4×D157—21no—
54D4×D157C2×C411yescharacteristic
55C2×C4×D157—21no—
56C2×C4×D157—21no—
57C2×C4×D157C2311yescharacteristic
58#14578938C2×C411yescharacteristic, complemented
59#14578937—21no—
60C8×D157—21no—
61C4×Dic157—21no—
62C4×Dic157C2×C411yescharacteristic, complemented
63#41×C157C2×C411yescharacteristic
64M16×C157C2×C411yescharacteristic, complemented
65C42×C157C2×C411yescharacteristic, complemented
66C2×#10597845—24no—
67C2×#10597845—22no—
68C2×#10597845—24no—
69C2×#10597845—22no—
70C2×#10597845—44no—
71C2×#10597845C22⋊C412yes—
72C2×#10597845C22⋊C412yes—
73#11929441—22no—
74C22×D157—21no—
75C22×D157C2×D411yescharacteristic
76Dic314—21no—
77Dic314C4211yescharacteristic, complemented
78D628—21no—
79D628C4211yescharacteristic, complemented
80C22⋊D157—21no—
81C22⋊D157—21no—
82C22⋊D157—21no—
83C2×Dic157—21no—
84C2×Dic157—21no—
85C2×Dic157#4111yescharacteristic
86C4×D157—24no—
87C4×D157—21no—
88C4×D157—21no—
89C4×D157—21no—
90C4×D157C22×C411yescharacteristic
91C4×D157C22×C411yescharacteristic
92C4×D157C2×D411yescharacteristic
93C4×D157#4111yescharacteristic
94#11929434—21no—
95Q8×C157C4211yescharacteristic, complemented
96D4×C157—21no—
97D4×C157C4211yescharacteristic, complemented
98C2×C4×C157—21no—
99C2×C4×C157—21no—
100C2×C4×C157C22×C411yescharacteristic
101C8×C157—21no—
102C22×C157—21no—
103C22×C157C4×D411yescharacteristic
104C2×D157—22no—
105C2×D157—21no—
106C2×D157—42no—
107C2×D157C2×C22⋊C411yescharacteristic
108C2×D157C4×D411yescharacteristic
109#10597845—24no—
110#10597845—22no—
111#10597845—42no—
112#10597845#10414yesdirect product factor
113C4×C157—22no—
114C4×C157—21no—
115C4×C157C2×C4211yescharacteristic
116C4×C157C4×D411yescharacteristic
117Dic157—22no—
118Dic157—21no—
119Dic157#11711yescharacteristic
120Dic157C4×D411yescharacteristic
121C2×C157—21no—
122C2×C157—41no—
123C2×C157C4×C22⋊C411yescharacteristic
124D157—21no—
125D157—41no—
126D157C2×#10412yes—
127C157C4×#10411yescharacteristic, complemented, Sylow
128C4×#104—1571nomaximal, Sylow
129C4×#41—1571no—
130C2×#104—1571no—
131C2×#104—1571no—
132C4×M16—1571no—
133C43—1571no—
134#339—1571no—
135#339—1571no—
136C2×#41—1571no—
137C2×M16—1571no—
138C2×M16—1571no—
139C4×Q8—1572no—
140C4×D4—3142no—
141C4×D4—1572no—
142#117—3141no—
143#117—1571no—
144C2×C42—3142no—
145C2×C42—3141no—
146C2×C42—1571no—
147C2×C42—1571no—
148C2×C42—1571no—
149#104—1572no—
150#104—1572no—
151#104—1571no—
152#104—1571no—
153#104—1571no—
154#104#1059784511yescharacteristic, direct product factor
155#97—3141no—
156C4×C8—3141no—
157#41—3141no—
158#41—3141no—
159#41—1571no—
160#41—1571no—
161#41—1571no—
162#41C2×#1059784511yescharacteristic
163C2×Q8—1571no—
164C2×D4—3141no—
165C2×D4—1571no—
166C22×C4—3141no—
167C22×C4—3141no—
168C22×C4—3141no—
169C22×C4—3142no—
170C22×C4—1572no—
171C22×C4—1571no—
172M16—3141no—
173M16—3141no—
174M16—1572no—
175M16—1571no—
176M16C2×#1059784511yescharacteristic, complemented
177C2×C8—3141no—
178C2×C8—3141no—
179C4⋊C4—3142no—
180C4⋊C4—1572no—
181C22⋊C4—3141no—
182C22⋊C4—3142no—
183C42—3141no—
184C42—3148no—
185C42—3141no—
186C42—3142no—
187C42—3141no—
188C42—1572no—
189C42—1571no—
190C42—1572no—
191C42—1571no—
192C42—1571no—
193C42C2×#1059784511yescharacteristic, complemented
194C23—3141no—
195C23—1571no—
196Q8—3141no—
197Q8—1571no—
198Q8C4×#1059784511yescharacteristic, complemented
199D4—21no—
200D4—3141no—
201D4—3141no—
202D4—3141no—
203D4—3141no—
204D4—1571no—
205D4C4×#1059784511yescharacteristic, complemented
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—3144no—
209C2×C4—3141no—
210C2×C4—3141no—
211C2×C4—3144no—
212C2×C4—3142no—
213C2×C4—3141no—
214C2×C4—3141no—
215C2×C4—3144no—
216C2×C4—3141no—
217C2×C4—3142no—
218C2×C4—6284no—
219C2×C4—1572no—
220C2×C4—1572no—
221C2×C4—1571no—
222C2×C4—1571no—
223C2×C4—1571no—
224C2×C4—1571no—
225C2×C4—1571no—
226C2×C4C22×#1059784511yescharacteristic
227C8—21no—
228C8—3142no—
229C8—3141no—
230C22—21no—
231C22—3142no—
232C22—3141no—
233C22—6282no—
234C22—1571no—
235C22—1571no—
236C22D4×#1059784511yescharacteristic
237C4—22no—
238C4—21no—
239C4—3142no—
240C4—3144no—
241C4—3142no—
242C4—3141no—
243C4—6282no—
244C4—1574no—
245C4—1571no—
246C4—1571no—
247C4C2×C4×#1059784511yescharacteristic
248C4D4×#1059784511yescharacteristic
249C2—21no—
250C2—41no—
251C2—3141no—
252C2—6281no—
253C2—1572no—
254C2C22⋊C4×#1059784511yescharacteristic
subgroupG/H
centerC4D4×#10597845
commutatorC4×C157C2×C42
FrattiniC2×C4C22×#10597845
Fitting#104×C157C4
socleC2×C157C4×C22⋊C4
prime radical#41×D157C22
cosocleC2×C4×D157C23
hypercenter#104#10597845
hypocenterC157C4×#104
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
3. M16×#10597845C2semidirect
4. C42×#10597845C2semidirect
5. #23758145C2semidirect
6. #23758144C2semidirect
9. Q8×#10597845C4semidirect
11. D4×#10597845C4semidirect
18. #19097836C4semidirect
19. #19097835C4semidirect
25. #19097699C4semidirect
26. #19097698C4semidirect
27. #19097697C4semidirect
28. #104×C157C4semidirect
32. #14578964C2×C4semidirect
44. C4×#10597845C2×C4semidirect
58. #14578938C2×C4semidirect
62. C4×Dic157C2×C4semidirect
64. M16×C157C2×C4semidirect
65. C42×C157C2×C4semidirect
77. Dic314C42semidirect
79. D628C42semidirect
95. Q8×C157C42semidirect
97. D4×C157C42semidirect
112. #10597845#104direct (N × H)
127. C157C4×#104semidirect
154. #104#10597845direct (N × H)
176. M16C2×#10597845semidirect
193. C42C2×#10597845semidirect
198. Q8C4×#10597845semidirect
205. D4C4×#10597845semidirect

Maximal subgroups

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

subgroupindex
#41×#105978452
D157⋊#1042
M16×#105978452
C42×#105978452
#237581452
#237581442
#104×D1572
C4×#104157