Finite Group Databasebeta

← #46783164

Subgroups — #46783164

Order 33664.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#30682704C211yesmaximal, characteristic, complemented
2#30682450C211yesmaximal, characteristic
3#30681920C211yesmaximal, characteristic, complemented
4#30681901C211yesmaximal, characteristic, complemented
5#30681901C211yesmaximal, characteristic, complemented
6#30681708C211yesmaximal, characteristic, complemented
7#344×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×C4×D263C2211yescharacteristic
10#22554478—22no—
11#22554476—22no—
12C2×#16862360C2211yescharacteristic
13C2×#16862360C2211yescharacteristic
14M16×D263—22no—
15#22554454C412yes—
16#22554450—21no—
17#22554445—21no—
18#22554440C412yes—
19C4×D1052—22no—
20#22554388—21no—
21#22554386—21no—
22(C2×D263)⋊C8—22no—
23(C2×D263)⋊C8—22no—
24C2×M16×C263C2211yescharacteristic
25C2×M16×C263C2211yescharacteristic
26#117×C263C2211yescharacteristic
27C23×D263C2×C411yescharacteristic
28#16862376—21no—
29#16862376—21no—
30#16862376—21no—
31#16862376—21no—
32C2×Dic526D411yescharacteristic
33C2×D1052—22no—
34C2×D1052D411yescharacteristic
35C2×C22⋊D263C2×C412yes—
36C22×Dic263C2×C411yescharacteristic
37C2×C4×D263—21no—
38C2×C4×D263—21no—
39C2×C4×D263—21no—
40C2×C4×D263—21no—
41C2×C4×D263—21no—
42C2×C4×D263—21no—
43C2×C4×D263D412yes—
44#16862360—21no—
45#16862360—21no—
46#16862360—21no—
47#16862360—21no—
48#16862359—24no—
49C2×C263⋊C8—21no—
50C2×C263⋊C8D412yescomplemented
51C8×D263—24no—
52C4⋊Dic263—22no—
53(C2×D263)⋊C4—22no—
54(C2×D263)⋊C4—22no—
55C22×C4×C263C2311yescharacteristic
56M16×C263—21no—
57M16×C263—21no—
58M16×C263—21no—
59M16×C263—21no—
60C2×C8×C263—21no—
61C2×C8×C263D412yescomplemented
62C4⋊C4×C263—21no—
63C22⋊C4×C263C2×C412yes—
64C42×C263—21no—
65C22×D263—21no—
66C22×D263—21no—
67C22×D263—21no—
68C22×D263—42no—
69C22×D263C22⋊C412yes—
70Dic526—21no—
71Dic526—21no—
72D1052—21no—
73D1052—21no—
74D1052—44no—
75C22⋊D263—22no—
76C22⋊D263—22no—
77C2×Dic263—21no—
78C2×Dic263—21no—
79C2×Dic263—21no—
80C2×Dic263C22⋊C412yes—
81C4×D263—22no—
82C4×D263—22no—
83C4×D263—41no—
84C4×D263—41no—
85C4×D263—41no—
86C4×D263—41no—
87C263⋊C8—22no—
88C263⋊C8—41no—
89C23×C263C22×C411yescharacteristic
90C2×C4×C263—22no—
91C2×C4×C263C2×D411yescharacteristic
92C2×C4×C263C2×D411yescharacteristic
93C2×C4×C263C2×D411yescharacteristic
94C2×C4×C263C2×D411yescharacteristic
95C2×C4×C263#4111yescharacteristic
96C2×C4×C263#4111yescharacteristic
97C8×C263—22no—
98C8×C263—41no—
99C22×C263—41no—
100C22×C263C2×C22⋊C411yescharacteristic
101C22×C263C4×D411yescharacteristic
102C22×C263C4×D411yescharacteristic
103C2×D263—22no—
104C2×D263—22no—
105C2×D263—22no—
106C2×D263—22no—
107C2×D263—41no—
108C2×D263—41no—
109C2×D263—41no—
110C2×D263—41no—
111C2×D263—42no—
112C4×C263—42no—
113C4×C263#12011yescharacteristic
114C4×C263#12111yescharacteristic
115C4×C263#12111yescharacteristic
116C4×C263#12311yescharacteristic
117Dic263—22no—
118Dic263—41no—
119C2×C263—21no—
120C2×C263—21no—
121C2×C263—21no—
122C2×C263#38611yescharacteristic
123D263—42no—
124D263—42no—
125C263#189111yescharacteristic, complemented, Sylow
126#1891—2631nomaximal, Sylow
127#568—2631no—
128#525—2631no—
129#413—2631no—
130#407—2631no—
131#407—2631no—
132#344—2631no—
133#344D26311yescharacteristic, complemented
134C2×#41—2631no—
135C23×C4—2631no—
136#131—5262no—
137#131—5262no—
138C2×M16—2631no—
139C2×M16—2631no—
140C2×M16—5262no—
141C2×M16C2×D26311yescharacteristic
142C2×M16C2×D26311yescharacteristic
143#123—2632no—
144C22⋊Q8—5261no—
145#121—5261no—
146#120—2632no—
147C4×D4—5262no—
148#117C2×D26311yescharacteristic
149#101—5261no—
150#100—5261no—
151C22⋊C8—5262no—
152C22⋊C8—5262no—
153C24—2631no—
154#41—5261no—
155#41—5261no—
156#41—5261no—
157#41—5261no—
158C2×Q8—2631no—
159C2×D4—2632no—
160C2×D4—2631no—
161C2×D4—5262no—
162C22×C4—2632no—
163C22×C4—2631no—
164C22×C4—5261no—
165C22×C4—5261no—
166C22×C4—5261no—
167C22×C4—5261no—
168C22×C4—5261no—
169C22×C4—5261no—
170C22×C4C22×D26311yescharacteristic
171M16—21no—
172M16—21no—
173M16—21no—
174M16—21no—
175M16—5264no—
176M16—5261no—
177M16—5261no—
178M16—5261no—
179M16—5261no—
180C2×C8—21no—
181C2×C8—2632no—
182C2×C8—5264no—
183C2×C8—5261no—
184C2×C8D105212yescomplemented
185C4⋊C4—21no—
186C4⋊C4—5262no—
187C22⋊C4—5262no—
188C22⋊C4—5262no—
189C22⋊C4C4×D26312yes—
190C42—21no—
191C23—2632no—
192C23—5261no—
193C23—5261no—
194C23—5261no—
195C23—10522no—
196C23C2×C4×D26311yescharacteristic
197Q8—5261no—
198Q8—5261no—
199D4—5262no—
200D4—5262no—
201D4—5261no—
202D4—5261no—
203D4—10524no—
204C2×C4—22no—
205C2×C4—2632no—
206C2×C4—5262no—
207C2×C4—5262no—
208C2×C4—5261no—
209C2×C4—5261no—
210C2×C4—5261no—
211C2×C4—10521no—
212C2×C4—10521no—
213C2×C4—10521no—
214C2×C4—10521no—
215C2×C4D4×D26311yescharacteristic
216C2×C4D4×D26311yescharacteristic
217C2×C4D4×D26311yescharacteristic
218C2×C4C2×D105211yescharacteristic
219C2×C4#1686237611yescharacteristic
220C2×C4#1686237711yescharacteristic
221C8—22no—
222C8—41no—
223C8—5262no—
224C8—10521no—
225C22—41no—
226C22—5262no—
227C22—5262no—
228C22—5262no—
229C22—5262no—
230C22—10522no—
231C22—10521no—
232C22—10521no—
233C22—10521no—
234C22—10521no—
235C22C22⋊C4×D26311yescharacteristic
236C22#2255443211yescharacteristic
237C22C4×D105211yescharacteristic
238C4—42no—
239C4—5262no—
240C4—10521no—
241C4#2255444011yescharacteristic
242C4#2255444311yescharacteristic
243C4#2255444511yescharacteristic
244C4#2255445511yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—10522no—
249C2—10522no—
250C2#3068181611yescharacteristic
subgroupG/H
centerC4#22554440
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#344×C263C2
socleC2×C263#386
prime radical#30682450C2
cosocleC22×C4×C263C23
hypercenter#344D263
hypocenterC263#1891
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #30682704C2semidirect
3. #30681920C2semidirect
4. #30681901C2semidirect
5. #30681901C2semidirect
6. #30681708C2semidirect
7. #344×C263C2semidirect
50. C2×C263⋊C8D4semidirect
61. C2×C8×C263D4semidirect
125. C263#1891semidirect
133. #344D263semidirect
184. C2×C8D1052semidirect

Maximal subgroups

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

subgroupindex
#306827042
#306824502
#306819202
#306819012
#306817082
#344×C2632
#1891263