Finite Group Databasebeta

← #46783661

Subgroups — #46783661

Order 33664.

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

normal subgroups only

This group has 276 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×#16862366C211yesmaximal, characteristic
2C2×#22554405C211yesmaximal, characteristic
3#30681946C211yesmaximal, characteristic
4C2×#22554389C211yesmaximal, characteristic
5C2×#22554388C211yesmaximal, characteristic
6#30681894C211yesmaximal, characteristic
7#419×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862366—21no—
10C2×#16862366—21no—
11C2×#16862366—22no—
12C2×#16862366C414yescomplemented
13C2×#16862360C2211yescharacteristic
14C2×#16862360C2211yescharacteristic
15C22×C263⋊C8C2211yescharacteristic
16#22554405—22no—
17#22554393—22no—
18#22554389—22no—
19#22554388—22no—
20#22554381—21no—
21C4×C263⋊C8—21no—
22C22×Q8×C263C2211yescharacteristic
23C2×M16×C263C2211yescharacteristic
24#117×C263C2211yescharacteristic
25#103×C263—22no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526—21no—
30C2×Dic526—21no—
31C2×Dic526C2×C412yes—
32C22×Dic263—21no—
33#16862366—24no—
34#16862366—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—
45C2×Q8×C263—21no—
46C2×Q8×C263—21no—
47C2×Q8×C263—21no—
48C2×Q8×C263—21no—
49C2×Q8×C263—21no—
50C2×Q8×C263C2×C412yes—
51C22×C4×C263—21no—
52C22×C4×C263C2311yescharacteristic
53M16×C263—21no—
54M16×C263—21no—
55C2×C8×C263—21no—
56C4⋊C4×C263D412yes—
57C22⋊C4×C263—21no—
58C42×C263—21no—
59Dic526—22no—
60Dic526—22no—
61Dic526—41no—
62Dic526—41no—
63C2×Dic263—22no—
64C2×Dic263—41no—
65C2×Dic263—41no—
66C263⋊C8—22no—
67C263⋊C8—41no—
68C263⋊C8C22⋊C412yes—
69C263⋊C8C22⋊C412yes—
70C23×C263#4111yescharacteristic
71Q8×C263—22no—
72Q8×C263—22no—
73Q8×C263—41no—
74Q8×C263—41no—
75C2×C4×C263—22no—
76C2×C4×C263—22no—
77C2×C4×C263—41no—
78C2×C4×C263—41no—
79C2×C4×C263C22×C411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263#4111yescharacteristic
85C8×C263—41no—
86C22×C263—22no—
87C22×C263C4×D411yescharacteristic
88C22×C263#12111yescharacteristic
89C22×C263#12411yescharacteristic
90C4×C263—42no—
91C4×C263—42no—
92C4×C263C2×C22⋊C411yescharacteristic
93C4×C263C4×D411yescharacteristic
94C4×C263#12111yescharacteristic
95C4×C263#12711yescharacteristic
96Dic263—42no—
97C2×C263—21no—
98C2×C263—21no—
99C2×C263#39011yescharacteristic
100C2×C263#47312yes—
101C263#197911yescharacteristic, complemented, Sylow
102#1979—2631nomaximal, Sylow
103C22×Q16—2631no—
104C2×#108—2631no—
105#419—2631no—
106#419D26311yescharacteristic
107C2×#101—2631no—
108C2×#101—2631no—
109#405—2631no—
110C22×Q8—2631no—
111C22×Q8C2×D26311yescharacteristic
112C2×Q16—2634no—
113C2×Q16—5261no—
114C2×Q16—5261no—
115C2×Q16—5262no—
116C2×M16—2631no—
117C2×M16—2631no—
118C2×M16C2×D26311yescharacteristic
119C22×C8—2631no—
120#117C2×D26311yescharacteristic
121#108—5262no—
122#103—22no—
123#103—5262no—
124#101—5262no—
125#101—5262no—
126#97—5261no—
127C4×C8—5261no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—2632no—
134C2×Q8—5261no—
135C2×Q8—5261no—
136C2×Q8—5261no—
137C2×Q8—5261no—
138C2×Q8—5261no—
139C2×Q8C4×D26312yes—
140C22×C4—21no—
141C22×C4—5261no—
142C22×C4C22×D26311yescharacteristic
143Q16—5264no—
144Q16—5264no—
145M16—21no—
146M16—21no—
147M16—2632no—
148M16—5261no—
149M16—5261no—
150M16—5261no—
151C2×C8—21no—
152C2×C8—2632no—
153C2×C8—2631no—
154C2×C8—2631no—
155C2×C8—2632no—
156C2×C8—5261no—
157C2×C8—5261no—
158C4⋊C4C22⋊D26312yes—
159C22⋊C4—21no—
160C42—21no—
161C23#1686237511yescharacteristic
162Q8—22no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—5262no—
167Q8—5262no—
168Q8—10521no—
169Q8—10521no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5262no—
175C2×C4—10521no—
176C2×C4—10521no—
177C2×C4C2×C4×D26311yescharacteristic
178C2×C4D4×D26311yescharacteristic
179C2×C4D4×D26311yescharacteristic
180C2×C4D4×D26311yescharacteristic
181C2×C4C2×C22⋊D26311yescharacteristic
182C2×C4#1686237611yescharacteristic
183C8—41no—
184C8—2632no—
185C8—2632no—
186C8—5262no—
187C8—10521no—
188C22—22no—
189C22(C22⋊D263)⋊C411yescharacteristic
190C22#2255444211yescharacteristic
191C22#2255445611yescharacteristic
192C4—42no—
193C4—42no—
194C4—10522no—
195C4C22⋊C4×D26311yescharacteristic
196C4C4×C22⋊D26311yescharacteristic
197C4#2255444311yescharacteristic
198C4#2255446611yescharacteristic
199C2—21no—
200C2—21no—
201C2#3068183811yescharacteristic
202C2#3068221112yes—
subgroupG/H
centerC22#22554442
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#419×C263C2
socleC22×C263#121
prime radicalC23×C263#41
cosocleC22×C4×C263C23
hypercenter#419D263
hypocenterC263#1979
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
12. C2×#16862366C4semidirect
101. C263#1979semidirect

Maximal subgroups

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

subgroupindex
C22×#168623662
C2×#225544052
#306819462
C2×#225543892
C2×#225543882
#306818942
#419×C2632
#1979263