Finite Group Databasebeta

← #32996833

Subgroups — #32996833

Order 18688.

324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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#22620669C211yesmaximal, characteristic
2#22610080C211yesmaximal, characteristic, complemented
3#22607923C212yesmaximal, complemented
4#22607917C212yesmaximal, complemented
5C73×#2165C211yesmaximal, characteristic, complemented
6#17989137—21no—
7#17988985C411yescharacteristic, complemented
8#17988964C411yescharacteristic, complemented
9#17988934—21no—
10#17988840—21no—
11#17988840C2212yes—
12#17988700—21no—
13#17988700C412yescomplemented
14#17988358—21no—
15#17988347—21no—
16#17988345C2211yescharacteristic
17#17988344C2211yescharacteristic
18C4×M16×C73C2211yescharacteristic
19#364×C73—21no—
20#349×C73C2212yes—
21#347×C73—21no—
22C2×#11924028—41no—
23C2×D584—21no—
24C2×D584C2×C412yes—
25C2×#11924012—21no—
26#14556591—21no—
27#14556588—21no—
28#14556579—41no—
29#14556565—22no—
30#14556565—41no—
31C4×D292—22no—
32C4×D292—41no—
33#14556550—21no—
34#14556523—21no—
35#14556523C2×C412yes—
36#14556513—22no—
37#14556513—22no—
38C2×M16×C73D411yescharacteristic
39C2×M16×C73C2311yescharacteristic
40C2×C42×C73D411yescharacteristic
41M32×C73—22no—
42#97×C73C2×C411yescharacteristic
43#97×C73D411yescharacteristic
44C4×C8×C73C2×C411yescharacteristic
45C4×C8×C73D411yescharacteristic
46#11924028—84no—
47C2×Dic146—41no—
48C2×D292—22no—
49C2×D292—41no—
50C2×D292—41no—
51C2×C22⋊D73—42no—
52C2×C4×D73—42no—
53D584—42no—
54D584—42no—
55#11924012—41no—
56#11924012—41no—
57C2×#10596831—41no—
58C4⋊Dic73—22no—
59C4⋊Dic73—41no—
60C4⋊Dic73—41no—
61C22⋊Dic73—41no—
62#11924005—42no—
63#11924005—42no—
64C4×Dic73—41no—
65C22×C4×C73—21no—
66C22×C4×C73C2×D411yescharacteristic
67M16×C73—41no—
68M16×C73—41no—
69C2×C8×C73C22⋊C411yescharacteristic
70C2×C8×C73C22⋊C411yescharacteristic
71C2×C8×C73C22×C411yescharacteristic
72C2×C8×C73C2×D411yescharacteristic
73C42×C73—21no—
74C42×C73C22⋊C411yescharacteristic
75C42×C73C22⋊C411yescharacteristic
76C16×C73—42no—
77C23×C73AGL(1,ℤ/8)11yescharacteristic
78C22×D73—42no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—42no—
84C2×C4×C73C2×C22⋊C411yescharacteristic
85C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
86C22⋊D73—84no—
87C2×Dic73—42no—
88C2×Dic73—81no—
89D292—42no—
90D292—42no—
91D292—82no—
92D292—82no—
93C4×D73—84no—
94Dic146—82no—
95C8×C73—21no—
96C8×C73—21no—
97C8×C73—21no—
98C8×C73—21no—
99#10596831—81no—
100C22×C73—21no—
101C22×C73—41no—
102C22×C73#41811yescharacteristic
103C2×D73—82no—
104C2×D73—82no—
105C2×D73—82no—
106C4×C73—22no—
107C4×C73—21no—
108C4×C73—41no—
109C4×C73#41011yescharacteristic
110C4×C73#42111yescharacteristic
111Dic73—82no—
112Dic73—161no—
113#11837—731nomaximal, Sylow
114C2×C73—21no—
115C2×C73—41no—
116C2×C73#151411yescharacteristic
117D73—162no—
118#3184—731no—
119#2165D7311yescharacteristic, complemented
120#1841—731no—
121#1341—732no—
122#1339—732no—
123C73#1183711yescharacteristic, complemented, Sylow
124#532—1461no—
125#498—731no—
126#493—731no—
127#486—1461no—
128#469—732no—
129#469—1461no—
130#442—732no—
131#442—1461no—
132C4×M16C2×D7311yescharacteristic
133#364—21no—
134#349C2×D7312yes—
135#347—21no—
136#344—1461no—
137#339—1461no—
138#338—731no—
139H(3,ℤ/4)—731no—
140C2×#41—2921no—
141C2×D8—732no—
142C2×D8—1461no—
143C2×M16—1461no—
144C2×M16D29211yescharacteristic
145C2×M16C22×D7311yescharacteristic
146C4⋊Q8—1461no—
147#127—1461no—
148#124—2921no—
149#121—2921no—
150#121—1462no—
151C4×D4—2921no—
152C4×D4—1462no—
153#117—1461no—
154C2×C42D29211yescharacteristic
155M32—22no—
156#106—732no—
157#106—1461no—
158#102—1462no—
159#102—1462no—
160#97C4×D7311yescharacteristic
161#97C22⋊D7311yescharacteristic
162C4×C8C4×D7311yescharacteristic
163C4×C8C22⋊D7311yescharacteristic
164#41—5844no—
165C2×Q8—2921no—
166C2×D4—2921no—
167C2×D4—2921no—
168C2×D4—2922no—
169C2×D4—1462no—
170C22×C4—21no—
171C22×C4—2922no—
172C22×C4C2×D29211yescharacteristic
173D8—2922no—
174D8—2922no—
175M16—41no—
176M16—41no—
177M16—2921no—
178M16—2921no—
179C2×C8—2921no—
180C2×C8#1192400511yescharacteristic
181C2×C8#1192400511yescharacteristic
182C2×C8C2×C4×D7311yescharacteristic
183C2×C8C2×C22⋊D7311yescharacteristic
184C4⋊C4—2921no—
185C4⋊C4—2921no—
186C4⋊C4—1462no—
187C22⋊C4—2922no—
188C22⋊C4—2922no—
189C22⋊C4—2921no—
190C42—21no—
191C42—2921no—
192C42#1192400511yescharacteristic
193C42#1192400511yescharacteristic
194C16—42no—
195C23—2922no—
196C23#1455661911yescharacteristic
197Q8—5842no—
198D4—2922no—
199D4—2922no—
200D4—5842no—
201D4—5842no—
202D4—5844no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—2922no—
209C2×C4—5844no—
210C2×C4—5841no—
211C2×C4C2×#1192400511yescharacteristic
212C2×C4#1455661911yescharacteristic
213C8—21no—
214C8—21no—
215C8—21no—
216C8—21no—
217C8—5841no—
218C22—21no—
219C22—41no—
220C22—5842no—
221C22—5842no—
222C22—5842no—
223C22#1798859311yescharacteristic
224C4—22no—
225C4—21no—
226C4—41no—
227C4—5842no—
228C4—11681no—
229C4#1798856011yescharacteristic
230C4#1798860311yescharacteristic
231C2—21no—
232C2—41no—
233C2—11682no—
234C2#2260847911yescharacteristic
subgroupG/H
centerC2#22608479
commutatorC2×C8×C73C22×C4
FrattiniC2×M16C22×D73
FittingC73×#2165C2
socleC2×C73#1514
prime radical#22620669C2
cosocleC2×M16×C73C23
hypercenter#2165D73
hypocenterC73#11837
LCSG ▷ C2×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #22610080C2semidirect
3. #22607923C2semidirect
4. #22607917C2semidirect
5. C73×#2165C2semidirect
7. #17988985C4semidirect
8. #17988964C4semidirect
13. #17988700C4semidirect
119. #2165D73semidirect
123. C73#11837semidirect

Maximal subgroups

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

subgroupindex
#226206692
#226100802
#226079232
#226079172
C73×#21652
#1183773