Finite Group Databasebeta

← #46783112

Subgroups — #46783112

Order 33664.

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

normal subgroups only

This group has 310 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#30682736C211yesmaximal, characteristic
2#30682704C211yesmaximal, characteristic, complemented
3#30681955C211yesmaximal, characteristic, complemented
4#30681935C211yesmaximal, characteristic, complemented
5#30681709C211yesmaximal, characteristic, complemented
6#30681703C211yesmaximal, characteristic, complemented
7#408×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501C412yescomplemented
10#22554500—21no—
11#22554496C412yescomplemented
12#22554495—21no—
13#22554490—22no—
14#22554478—22no—
15#22554476—22no—
16C2×#16862360C2211yescharacteristic
17C2×#16862360C2211yescharacteristic
18M16×D263—22no—
19#22554429C2211yescharacteristic
20#22554397—22no—
21#22554395—21no—
22#22554392—21no—
23C2×#41×C263C2211yescharacteristic
24C2×M16×C263C2211yescharacteristic
25C22×C8×C263C2211yescharacteristic
26C22⋊C8×C263—22no—
27#16862376—21no—
28#16862376—21no—
29#16862376C2×C412yes—
30#16862376D412yes—
31C2×Dic526D411yescharacteristic
32C2×D1052D411yescharacteristic
33C2×C22⋊D263—21no—
34C2×C4×D263—21no—
35#16862366—22no—
36#16862364—22no—
37#16862363—22no—
38#16862361—22no—
39#16862360—21no—
40#16862360—21no—
41#16862360C2×C412yes—
42#16862360D412yes—
43#16862359—24no—
44C2×C263⋊C8—21no—
45C2×C263⋊C8—21no—
46C8×D263—24no—
47C4⋊Dic263—21no—
48C22⋊Dic263—21no—
49C4×Dic263—21no—
50#41×C263—21no—
51#41×C263—21no—
52#41×C263—21no—
53#41×C263—21no—
54C2×Q8×C263C2×C411yescharacteristic
55C2×D4×C263—21no—
56C2×D4×C263C2×C411yescharacteristic
57C22×C4×C263—21no—
58C22×C4×C263C2311yescharacteristic
59M16×C263—21no—
60M16×C263—21no—
61C2×C8×C263—21no—
62C2×C8×C263—21no—
63C2×C8×C263—21no—
64C2×C8×C263D412yes—
65C22×D263—21no—
66Dic526—21no—
67Dic526C22⋊C412yes—
68D1052—21no—
69D1052C22⋊C412yes—
70C22⋊D263—22no—
71C22⋊D263—22no—
72C2×Dic263—21no—
73C2×Dic263—41no—
74C4×D263—22no—
75C4×D263—22no—
76C263⋊C8—22no—
77C263⋊C8—22no—
78C23×C263—21no—
79C23×C263#4111yescharacteristic
80Q8×C263—21no—
81Q8×C263—21no—
82D4×C263—21no—
83D4×C263—21no—
84D4×C263—41no—
85D4×C263—41no—
86C2×C4×C263—21no—
87C2×C4×C263—41no—
88C2×C4×C263—41no—
89C2×C4×C263C22×C411yescharacteristic
90C2×C4×C263C2×D411yescharacteristic
91C2×C4×C263C2×D411yescharacteristic
92C2×C4×C263C2×D411yescharacteristic
93C2×C4×C263C2×D411yescharacteristic
94C2×C4×C263#4111yescharacteristic
95C8×C263—22no—
96C8×C263—41no—
97C22×C263—41no—
98C22×C263—42no—
99C22×C263—41no—
100C22×C263C4×D411yescharacteristic
101C22×C263#12111yescharacteristic
102C22×C263#12311yescharacteristic
103C2×D263—22no—
104C2×D263—81no—
105C4×C263—41no—
106C4×C263C2×C22⋊C411yescharacteristic
107C4×C263C4×D411yescharacteristic
108C4×C263#12011yescharacteristic
109C4×C263#12111yescharacteristic
110Dic263—22no—
111Dic263—81no—
112C2×C263—21no—
113C2×C263—21no—
114C2×C263—21no—
115C2×C263—81no—
116C2×C263#38611yescharacteristic
117D263—42no—
118C263#188111yescharacteristic, complemented, Sylow
119#1881—2631nomaximal, Sylow
120#575—2631no—
121#568—2631no—
122#421—2631no—
123#416—2631no—
124#408D26311yescharacteristic, complemented
125#344—2631no—
126#341—2631no—
127C2×#41—2631no—
128C2×#41C2×D26311yescharacteristic
129#137—2632no—
130#137—5261no—
131AGL(1,ℤ/8)—2632no—
132AGL(1,ℤ/8)—5261no—
133#135—5262no—
134#131—5262no—
135#131—5262no—
136C2×M16—2631no—
137C2×M16—2631no—
138C2×M16—5262no—
139C2×M16C2×D26311yescharacteristic
140C22×C8C2×D26311yescharacteristic
141#117—2631no—
142#104—5262no—
143#103—5261no—
144#102—5261no—
145C22⋊C8—22no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—2632no—
151#41—2632no—
152#41—5261no—
153#41—5261no—
154C2×Q8—2631no—
155C2×Q8C4×D26311yescharacteristic
156C2×D4—21no—
157C2×D4—2631no—
158C2×D4—5261no—
159C2×D4C4×D26311yescharacteristic
160C22×C4—21no—
161C22×C4—5261no—
162C22×C4C22×D26311yescharacteristic
163Q16—5262no—
164SD16—5262no—
165SD16—5262no—
166D8—5262no—
167M16—21no—
168M16—21no—
169M16—2632no—
170M16—2632no—
171M16—5264no—
172M16—5261no—
173M16—5261no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—5264no—
178C2×C8—5261no—
179C2×C8—5261no—
180C2×C8C22⋊D26312yes—
181C4⋊C4—5261no—
182C22⋊C4—5261no—
183C42—5261no—
184C23—21no—
185C23—5261no—
186C23#1686237611yescharacteristic
187Q8—21no—
188Q8—21no—
189Q8—2632no—
190Q8—5261no—
191D4—21no—
192D4—21no—
193D4—41no—
194D4—41no—
195D4—2632no—
196D4—5262no—
197D4—5262no—
198D4—5261no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—5261no—
203C2×C4—5262no—
204C2×C4—5262no—
205C2×C4—10521no—
206C2×C4C2×C4×D26311yescharacteristic
207C2×C4D4×D26311yescharacteristic
208C2×C4D4×D26311yescharacteristic
209C2×C4D4×D26311yescharacteristic
210C2×C4C2×C22⋊D26311yescharacteristic
211C2×C4#1686237511yescharacteristic
212C8—22no—
213C8—41no—
214C8—5262no—
215C8—5262no—
216C22—41no—
217C22—42no—
218C22—41no—
219C22—5262no—
220C22—21041no—
221C22C4×C22⋊D26311yescharacteristic
222C22#2255444311yescharacteristic
223C22#2255445211yescharacteristic
224C4—41no—
225C4—5262no—
226C4—21041no—
227C4C22⋊C4×D26311yescharacteristic
228C4(C22⋊D263)⋊C411yescharacteristic
229C4#2255443811yescharacteristic
230C4#2255444111yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—10522no—
236C2#3068181411yescharacteristic
subgroupG/H
centerC4#22554438
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#408×C263C2
socleC2×C263#386
prime radical#30682736C2
cosocleC22×C4×C263C23
hypercenter#408D263
hypocenterC263#1881
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #30682704C2semidirect
3. #30681955C2semidirect
4. #30681935C2semidirect
5. #30681709C2semidirect
6. #30681703C2semidirect
7. #408×C263C2semidirect
9. #22554501C4semidirect
11. #22554496C4semidirect
118. C263#1881semidirect
124. #408D263semidirect

Maximal subgroups

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

subgroupindex
#306827362
#306827042
#306819552
#306819352
#306817092
#306817032
#408×C2632
#1881263