Finite Group Databasebeta

← #46783656

Subgroups — #46783656

Order 33664.

316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16862361C211yesmaximal, characteristic
2C2×#22554405C211yesmaximal, characteristic, complemented
3#30681942C211yesmaximal, characteristic, complemented
4C2×#22554387C211yesmaximal, characteristic, complemented
5C2×#22554386C211yesmaximal, characteristic, complemented
6#30681894C211yesmaximal, characteristic, complemented
7#418×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9C2×#16862361—21no—
10C2×#16862361—21no—
11C2×#16862361—22no—
12C2×#16862361C414yescomplemented
13C2×#16862360C2211yescharacteristic
14C2×#16862360C2211yescharacteristic
15C22×C263⋊C8C2211yescharacteristic
16#22554405—22no—
17#22554390—22no—
18#22554387—22no—
19#22554386—22no—
20#22554381—21no—
21C4×C263⋊C8—21no—
22C22×D4×C263C2211yescharacteristic
23C2×M16×C263C2211yescharacteristic
24#117×C263C2211yescharacteristic
25#102×C263—22no—
26C23×D263—21no—
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052—21no—
32C2×D1052C2×C412yes—
33#16862361—24no—
34#16862361—24no—
35#16862360—21no—
36#16862360—21no—
37#16862360—21no—
38#16862360D412yes—
39C2×C263⋊C8—21no—
40C2×C263⋊C8—21no—
41C2×C263⋊C8C2×C412yes—
42C2×C263⋊C8D411yescharacteristic
43C2×C263⋊C8D411yescharacteristic
44C2×C263⋊C8D412yes—
45C24×C263—21no—
46C2×D4×C263—21no—
47C2×D4×C263—21no—
48C2×D4×C263—21no—
49C2×D4×C263—21no—
50C2×D4×C263—21no—
51C2×D4×C263C2×C412yes—
52C22×C4×C263C2311yescharacteristic
53M16×C263—21no—
54M16×C263—21no—
55C2×C8×C263—21no—
56C4⋊C4×C263D412yes—
57C22⋊C4×C263—21no—
58C42×C263—21no—
59C22×D263—22no—
60C22×D263—41no—
61C22×D263—41no—
62C22×D263—82no—
63D1052—22no—
64D1052—22no—
65D1052—41no—
66D1052—41no—
67C263⋊C8—22no—
68C263⋊C8—41no—
69C263⋊C8C22⋊C412yes—
70C263⋊C8C22⋊C412yes—
71C23×C263—22no—
72C23×C263—41no—
73C23×C263—41no—
74C23×C263—82no—
75C23×C263#4111yescharacteristic
76D4×C263—22no—
77D4×C263—22no—
78D4×C263—41no—
79D4×C263—41no—
80C2×C4×C263—22no—
81C2×C4×C263C22×C411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C8×C263—41no—
88C22×C263—22no—
89C22×C263—42no—
90C22×C263—82no—
91C22×C263—82no—
92C22×C263—82no—
93C22×C263C4×D411yescharacteristic
94C22×C263#12111yescharacteristic
95C22×C263#12411yescharacteristic
96C2×D263—42no—
97C2×D263—82no—
98C2×D263—82no—
99C2×D263—82no—
100C4×C263—42no—
101C4×C263C2×C22⋊C411yescharacteristic
102C4×C263C4×D411yescharacteristic
103C4×C263#12111yescharacteristic
104C4×C263#12711yescharacteristic
105C2×C263—21no—
106C2×C263—21no—
107C2×C263—82no—
108C2×C263#39011yescharacteristic
109C2×C263#47212yes—
110D263—82no—
111C263#197811yescharacteristic, complemented, Sylow
112#1978—2631nomaximal, Sylow
113C22×D8—2631no—
114C2×#108—2631no—
115#418—2631no—
116#418D26311yescharacteristic, complemented
117C2×#100—2631no—
118C2×#100—2631no—
119#405—2631no—
120C22×D4—2631no—
121C22×D4C2×D26311yescharacteristic
122C2×D8—2634no—
123C2×D8—5261no—
124C2×D8—5261no—
125C2×D8—5262no—
126C2×M16—2631no—
127C2×M16—2631no—
128C2×M16C2×D26311yescharacteristic
129C22×C8—2631no—
130#117C2×D26311yescharacteristic
131#108—5262no—
132#102—22no—
133#102—5262no—
134#100—5262no—
135#100—5262no—
136#97—5261no—
137C4×C8—5261no—
138C24—21no—
139C24—5261no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—2632no—
146C2×D4—5261no—
147C2×D4—5261no—
148C2×D4—5261no—
149C2×D4—5261no—
150C2×D4—5261no—
151C2×D4C4×D26312yes—
152C22×C4C22×D26311yescharacteristic
153D8—5264no—
154D8—5264no—
155M16—21no—
156M16—21no—
157M16—2632no—
158M16—5261no—
159M16—5261no—
160M16—5261no—
161C2×C8—21no—
162C2×C8—2632no—
163C2×C8—2631no—
164C2×C8—2631no—
165C2×C8—2632no—
166C2×C8—5261no—
167C2×C8—5261no—
168C4⋊C4C22⋊D26312yes—
169C22⋊C4—21no—
170C42—21no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—82no—
175C23—5262no—
176C23—10521no—
177C23—10521no—
178C23—21042no—
179C23#1686237511yescharacteristic
180D4—22no—
181D4—22no—
182D4—41no—
183D4—41no—
184D4—5262no—
185D4—5262no—
186D4—10521no—
187D4—10521no—
188C2×C4—22no—
189C2×C4C2×C4×D26311yescharacteristic
190C2×C4D4×D26311yescharacteristic
191C2×C4D4×D26311yescharacteristic
192C2×C4D4×D26311yescharacteristic
193C2×C4C2×C22⋊D26311yescharacteristic
194C2×C4#1686237611yescharacteristic
195C8—41no—
196C8—2632no—
197C8—2632no—
198C8—5262no—
199C8—10521no—
200C22—22no—
201C22—42no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22—10522no—
206C22—21042no—
207C22—21042no—
208C22—21042no—
209C22(C22⋊D263)⋊C411yescharacteristic
210C22#2255444211yescharacteristic
211C22#2255445611yescharacteristic
212C4—42no—
213C4C22⋊C4×D26311yescharacteristic
214C4C4×C22⋊D26311yescharacteristic
215C4#2255444311yescharacteristic
216C4#2255446611yescharacteristic
217C2—21no—
218C2—21no—
219C2—82no—
220C2—21042no—
221C2#3068183811yescharacteristic
222C2#3068220612yes—
subgroupG/H
centerC22#22554442
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#418×C263C2
socleC22×C263#121
prime radicalC22×#16862361C2
cosocleC22×C4×C263C23
hypercenter#418D263
hypocenterC263#1978
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. C2×#22554405C2semidirect
3. #30681942C2semidirect
4. C2×#22554387C2semidirect
5. C2×#22554386C2semidirect
6. #30681894C2semidirect
7. #418×C263C2semidirect
12. C2×#16862361C4semidirect
111. C263#1978semidirect
116. #418D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623612
C2×#225544052
#306819422
C2×#225543872
C2×#225543862
#306818942
#418×C2632
#1978263