Finite Group Databasebeta

← #46783103

Subgroups — #46783103

Order 33664.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#16862365C211yesmaximal, characteristic
2C2×#22554435C211yesmaximal, characteristic, complemented
3C2×#22554393C211yesmaximal, characteristic, complemented
4C2×#22554390C211yesmaximal, characteristic
5#30681839C211yesmaximal, characteristic
6#30681692C211yesmaximal, characteristic, complemented
7#340×C263C211yesmaximal, characteristic, complemented
8C22×Dic526C2211yescharacteristic
9C22×D1052C2211yescharacteristic
10C2×#16862365—22no—
11C2×#16862365—22no—
12C2×#16862365C414yescomplemented
13C22×C263⋊C8C2211yescharacteristic
14#22554435—22no—
15#22554435—22no—
16C2×Dic263⋊C4—21no—
17C2×(C2×D263)⋊C4—21no—
18C2×(C2×D263)⋊C4—21no—
19C2×C4×Dic263—21no—
20C2×C4×Dic263C2211yescharacteristic
21#22554393—22no—
22#22554390—22no—
23C22×C8×C263C2211yescharacteristic
24C2×C4⋊C4×C263C2211yescharacteristic
25C2×C4⋊C4×C263C2211yescharacteristic
26C23×D263—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526—21no—
30C2×Dic526C2×C412yes—
31C2×Dic526D412yes—
32C2×Dic526D412yes—
33C2×D1052—21no—
34C2×D1052—21no—
35C2×D1052—21no—
36C2×D1052—21no—
37C2×D1052—21no—
38C2×D1052C2×C412yes—
39C22×Dic263—21no—
40C22×Dic263D411yescharacteristic
41C22×Dic263D411yescharacteristic
42#16862365—28no—
43C2×C263⋊C8—21no—
44C2×C263⋊C8—21no—
45C2×C263⋊C8—21no—
46Dic263⋊C4—24no—
47(C2×D263)⋊C4—42no—
48(C2×D263)⋊C4—42no—
49C4×Dic263—24no—
50C4×Dic263—21no—
51C4×Dic263—21no—
52C22×C4×C263—21no—
53C22×C4×C263—21no—
54C22×C4×C263C2311yescharacteristic
55C2×C8×C263—21no—
56C2×C8×C263—21no—
57C2×C8×C263C2×C412yes—
58C4⋊C4×C263—21no—
59C4⋊C4×C263—21no—
60C4⋊C4×C263—21no—
61C4⋊C4×C263D412yes—
62C22×D263—22no—
63C22×D263—41no—
64C22×D263—41no—
65C22×D263—41no—
66C22×D263—41no—
67C22×D263—41no—
68C22×D263—41no—
69Dic526—22no—
70Dic526—22no—
71Dic526—22no—
72Dic526C22⋊C414yescomplemented
73D1052—22no—
74D1052—22no—
75D1052—41no—
76D1052—41no—
77C2×Dic263—22no—
78C2×Dic263—21no—
79C2×Dic263—22no—
80C2×Dic263—22no—
81C2×Dic263—21no—
82C2×Dic263—21no—
83C2×Dic263—21no—
84C2×Dic263—21no—
85C2×Dic263SD1612yescomplemented
86C263⋊C8—41no—
87C23×C263C2×D411yescharacteristic
88C2×C4×C263—22no—
89C2×C4×C263—41no—
90C2×C4×C263—41no—
91C2×C4×C263—41no—
92C2×C4×C263—41no—
93C2×C4×C263—41no—
94C2×C4×C263C22×C411yescharacteristic
95C2×C4×C263C2×D411yescharacteristic
96C2×C4×C263C2×D411yescharacteristic
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263#4111yescharacteristic
99C2×C4×C263#4111yescharacteristic
100C8×C263—22no—
101C22×C263C4×D411yescharacteristic
102C22×C263#12011yescharacteristic
103C22×C263#12111yescharacteristic
104C22×C263C2×SD1611yescharacteristic
105C22×C263#13511yescharacteristic
106C22×C263AGL(1,ℤ/8)11yescharacteristic
107C22×C263#13711yescharacteristic
108C2×D263—42no—
109C2×D263—42no—
110C2×D263—42no—
111C2×D263—81no—
112C2×D263—81no—
113C2×D263—81no—
114C2×D263—81no—
115C4×C263—42no—
116C4×C263—81no—
117C4×C263C2×C22⋊C411yescharacteristic
118C4×C263C4×D411yescharacteristic
119C4×C263#12111yescharacteristic
120C4×C263#12311yescharacteristic
121Dic263—24no—
122Dic263—22no—
123Dic263—41no—
124C2×C263#38611yescharacteristic
125C2×C263C4×SD1611yescharacteristic
126C2×C263#44011yescharacteristic
127C2×C263#44811yescharacteristic
128C2×C263#44911yescharacteristic
129C2×C263#46011yescharacteristic
130C2×C263#46411yescharacteristic
131D263—82no—
132C263#188011yescharacteristic, complemented, Sylow
133#1880—2631nomaximal, Sylow
134C22×SD16—2631no—
135C2×C4×Q8—2631no—
136C2×#103—2631no—
137C2×#102—2631no—
138#390—2631no—
139#340D26311yescharacteristic, complemented
140#336—2631no—
141C22×Q8—2631no—
142C22×D4—2631no—
143C2×SD16—2634no—
144C2×SD16—5262no—
145C2×SD16—5262no—
146C22×C8—2631no—
147C22×C8C2×D26311yescharacteristic
148C4×Q8—5262no—
149C4×Q8—5262no—
150C2×C4⋊C4—5261no—
151C2×C4⋊C4C2×D26311yescharacteristic
152C2×C4⋊C4C2×D26311yescharacteristic
153C2×C22⋊C4—5261no—
154C2×C22⋊C4—5261no—
155C2×C42—2631no—
156C2×C42—5261no—
157#103—5262no—
158#102—5262no—
159C24—5261no—
160C2×Q8—2632no—
161C2×Q8—2632no—
162C2×Q8—2632no—
163C2×Q8—5261no—
164C2×Q8—5261no—
165C2×Q8—5261no—
166C2×D4—2632no—
167C2×D4—5261no—
168C2×D4—5261no—
169C2×D4—5261no—
170C2×D4—5261no—
171C2×D4—5261no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—2631no—
175C22×C4—2631no—
176C22×C4—5261no—
177C22×C4C22×D26311yescharacteristic
178SD16—5268no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—5261no—
182C2×C8—5261no—
183C2×C8—5261no—
184C2×C8C4×D26312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—5264no—
189C4⋊C4D105212yes—
190C22⋊C4—10522no—
191C22⋊C4—10522no—
192C42—5264no—
193C42—5261no—
194C42—5261no—
195C23—5262no—
196C23—10521no—
197C23—10521no—
198C23—10521no—
199C23—10521no—
200C23—10521no—
201C23—10521no—
202C23D4×D26311yescharacteristic
203Q8—2634no—
204Q8—5262no—
205Q8—5262no—
206Q8—5262no—
207D4—5262no—
208D4—5262no—
209D4—10521no—
210D4—10521no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—2632no—
218C2×C4—5262no—
219C2×C4—5261no—
220C2×C4—5262no—
221C2×C4—5262no—
222C2×C4—5261no—
223C2×C4—5261no—
224C2×C4—5261no—
225C2×C4—5261no—
226C2×C4C2×C4×D26311yescharacteristic
227C2×C4D4×D26311yescharacteristic
228C2×C4D4×D26311yescharacteristic
229C2×C4C2×D105211yescharacteristic
230C2×C4#1686237611yescharacteristic
231C2×C4#1686237711yescharacteristic
232C8—22no—
233C8—10521no—
234C22—10522no—
235C22—10522no—
236C22—10522no—
237C22—21041no—
238C22—21041no—
239C22—21041no—
240C22—21041no—
241C22#2255443211yescharacteristic
242C22#2255444011yescharacteristic
243C22#2255444311yescharacteristic
244C22SD16×D26311yescharacteristic
245C22#2255449111yescharacteristic
246C22#2255449411yescharacteristic
247C22#2255450211yescharacteristic
248C4—42no—
249C4—81no—
250C4—5264no—
251C4—5262no—
252C4—10521no—
253C4C22⋊C4×D26311yescharacteristic
254C4C4×D105211yescharacteristic
255C4#2255444511yescharacteristic
256C4#2255445511yescharacteristic
257C2—21042no—
258C2#3068181611yescharacteristic
259C2#3068202511yescharacteristic
260C2#3068203711yescharacteristic
261C2#3068207811yescharacteristic
262C2#3068208411yescharacteristic
263C2#3068213711yescharacteristic
264C2#3068216311yescharacteristic
subgroupG/H
centerC23D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#340×C263C2
socleC23×C263C2×D4
prime radicalC22×D1052C22
cosocleC22×C4×C263C23
hypercenter#340D263
hypocenterC263#1880
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#22554435C2semidirect
3. C2×#22554393C2semidirect
6. #30681692C2semidirect
7. #340×C263C2semidirect
12. C2×#16862365C4semidirect
72. Dic526C22⋊C4semidirect
85. C2×Dic263SD16semidirect
132. C263#1880semidirect
139. #340D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623652
C2×#225544352
C2×#225543932
C2×#225543902
#306818392
#306816922
#340×C2632
#1880263