Finite Group Databasebeta

← #46783298

Subgroups — #46783298

Order 33664.

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

normal subgroups only

This group has 308 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
2#30682514C211yesmaximal, characteristic
3#30681920C211yesmaximal, characteristic
4C2×#22554388C211yesmaximal, characteristic, complemented
5C2×#22554388C211yesmaximal, characteristic, complemented
6#30681708C211yesmaximal, characteristic, complemented
7#344×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×Dic526C2211yescharacteristic
10#22554478—22no—
11#22554476—22no—
12C2×#16862360C2211yescharacteristic
13C2×#16862360C2211yescharacteristic
14M16×D263—22no—
15#22554470—21no—
16#22554458—21no—
17#22554454C414yes—
18#22554450—22no—
19#22554388—21no—
20#22554388—22no—
21#22554388—22no—
22#22554386—21no—
23C2×M16×C263C2211yescharacteristic
24C2×M16×C263C2211yescharacteristic
25#117×C263C2211yescharacteristic
26#16862376—21no—
27#16862376—21no—
28#16862376—21no—
29#16862376—21no—
30C2×Dic526—21no—
31C2×Dic526—21no—
32C2×Dic526—21no—
33C2×Dic526—21no—
34C2×Dic526—21no—
35C2×Dic526—21no—
36C2×Dic526D411yescharacteristic
37C2×D1052D411yescharacteristic
38C2×C22⋊D263C2×C412yes—
39C22×Dic263C2×C412yes—
40C2×C4×D263D412yes—
41#16862360—21no—
42#16862360—21no—
43#16862360—21no—
44#16862360D412yes—
45#16862359—24no—
46C2×C263⋊C8—21no—
47C2×C263⋊C8—21no—
48C8×D263—24no—
49C4⋊Dic263—24no—
50(C2×D263)⋊C4—24no—
51C22×C4×C263C2311yescharacteristic
52M16×C263—21no—
53M16×C263—21no—
54M16×C263—21no—
55M16×C263D412yes—
56C2×C8×C263—21no—
57C2×C8×C263—21no—
58C4⋊C4×C263—21no—
59C22⋊C4×C263C2×C412yes—
60C42×C263—21no—
61C22×D263C22⋊C412yes—
62Dic526—21no—
63Dic526—21no—
64Dic526—41no—
65Dic526—41no—
66Dic526—41no—
67Dic526—41no—
68D1052—21no—
69D1052—21no—
70C22⋊D263—22no—
71C22⋊D263—22no—
72C2×Dic263—22no—
73C2×Dic263—22no—
74C2×Dic263—22no—
75C2×Dic263C22⋊C412yes—
76C4×D263—22no—
77C4×D263—22no—
78C263⋊C8—22no—
79C263⋊C8—41no—
80C23×C263C22×C411yescharacteristic
81C2×C4×C263—22no—
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C8×C263—22no—
89C8×C263—41no—
90C22×C263—41no—
91C22×C263C2×C22⋊C411yescharacteristic
92C22×C263C4×D411yescharacteristic
93C22×C263C4×D411yescharacteristic
94C2×D263—22no—
95C2×D263—42no—
96C4×C263—42no—
97C4×C263#12011yescharacteristic
98C4×C263#12111yescharacteristic
99C4×C263#12111yescharacteristic
100C4×C263#12311yescharacteristic
101Dic263—22no—
102Dic263—42no—
103C2×C263—21no—
104C2×C263—21no—
105C2×C263—21no—
106C2×C263#38611yescharacteristic
107D263—42no—
108C263#191511yescharacteristic, complemented, Sylow
109#1915—2631nomaximal, Sylow
110#568—2631no—
111#536—2631no—
112#413—2631no—
113C2×#101—2631no—
114C2×#101—2631no—
115#344—2631no—
116#344D26311yescharacteristic, complemented
117C2×#41—2631no—
118C22×Q8—2631no—
119#131—5262no—
120#131—5262no—
121C2×M16—2631no—
122C2×M16—2631no—
123C2×M16—5262no—
124C2×M16C2×D26311yescharacteristic
125C2×M16C2×D26311yescharacteristic
126C4⋊Q8—5261no—
127#124—5261no—
128#123—2634no—
129C22⋊Q8—5262no—
130#117C2×D26311yescharacteristic
131#101—5262no—
132#101—5261no—
133#101—5262no—
134#100—5261no—
135#41—5261no—
136#41—5261no—
137#41—5261no—
138#41—5261no—
139C2×Q8—2631no—
140C2×Q8—5261no—
141C2×Q8—5261no—
142C2×Q8—5261no—
143C2×Q8—5261no—
144C2×Q8—5261no—
145C2×Q8—5261no—
146C2×D4—2632no—
147C2×D4—2631no—
148C22×C4—2632no—
149C22×C4—2632no—
150C22×C4C22×D26311yescharacteristic
151M16—21no—
152M16—21no—
153M16—21no—
154M16—2632no—
155M16—5264no—
156M16—5261no—
157M16—5261no—
158M16—5261no—
159M16D105212yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—5264no—
163C2×C8—5261no—
164C2×C8—5261no—
165C4⋊C4—21no—
166C4⋊C4—5264no—
167C22⋊C4—5264no—
168C22⋊C4C4×D26312yes—
169C42—21no—
170C23—2632no—
171C23C2×C4×D26311yescharacteristic
172Q8—5261no—
173Q8—5261no—
174Q8—10521no—
175Q8—10521no—
176Q8—10521no—
177Q8—10521no—
178D4—5262no—
179D4—5262no—
180D4—5261no—
181D4—5261no—
182C2×C4—22no—
183C2×C4—2632no—
184C2×C4—5262no—
185C2×C4—5262no—
186C2×C4—5262no—
187C2×C4—5262no—
188C2×C4—5262no—
189C2×C4D4×D26311yescharacteristic
190C2×C4D4×D26311yescharacteristic
191C2×C4D4×D26311yescharacteristic
192C2×C4C2×D105211yescharacteristic
193C2×C4#1686237611yescharacteristic
194C2×C4#1686237711yescharacteristic
195C8—22no—
196C8—41no—
197C8—5262no—
198C8—10521no—
199C22—41no—
200C22—5262no—
201C22—10522no—
202C22C22⋊C4×D26311yescharacteristic
203C22#2255443211yescharacteristic
204C22C4×D105211yescharacteristic
205C4—42no—
206C4—5262no—
207C4—10522no—
208C4#2255444011yescharacteristic
209C4#2255444311yescharacteristic
210C4#2255444511yescharacteristic
211C4#2255445511yescharacteristic
212C2—21no—
213C2—21no—
214C2—21no—
215C2—10522no—
216C2#3068181611yescharacteristic
subgroupG/H
centerC2#30681816
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#344×C263C2
socleC2×C263#386
prime radicalC2×#16862376C22
cosocleC22×C4×C263C23
hypercenter#344D263
hypocenterC263#1915
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
4. C2×#22554388C2semidirect
5. C2×#22554388C2semidirect
6. #30681708C2semidirect
7. #344×C263C2semidirect
108. C263#1915semidirect
116. #344D263semidirect

Maximal subgroups

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

subgroupindex
#306827042
#306825142
#306819202
C2×#225543882
#306817082
#344×C2632
#1915263