Finite Group Databasebeta

← #49120327

Subgroups — #49120327

Order 36224.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#31827135C211yesmaximal, characteristic, complemented
2#31826841C211yesmaximal, characteristic, complemented
3#31826666C211yesmaximal, characteristic, complemented
4#31826661C211yesmaximal, characteristic, complemented
5#31826195C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#331×C283C211yesmaximal, characteristic, complemented
8C2×#17985391—21no—
9C2×#17985381—21no—
10C2×D2264—21no—
11C2×#17985377—22no—
12#22583607C2211yescharacteristic
13#22583606—21no—
14#22583582—22no—
15#22583581—21no—
16C4×Dic566C2211yescharacteristic
17C4×D1132C2211yescharacteristic
18D4×Dic283—21no—
19#22583532—21no—
20#22583532—21no—
21C4×C283⋊C8C2211yescharacteristic
22#127×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25#17985391—42no—
26#17985391—42no—
27C2×Dic566D411yescharacteristic
28C2×D1132—21no—
29C2×D1132—21no—
30C2×D1132—21no—
31C2×D1132D411yescharacteristic
32C2×C22⋊D283—22no—
33C2×C22⋊D283—22no—
34C22×Dic283—22no—
35C2×C4×D283—21no—
36#17985381—42no—
37D2264—42no—
38#17985377—44no—
39C2×C283⋊C8—21no—
40C4⋊Dic283D411yescharacteristic
41C4⋊Dic283D411yescharacteristic
42Dic283⋊C4—21no—
43C22⋊Dic283—22no—
44(C2×D283)⋊C4—21no—
45C4×Dic283—21no—
46C2×D4×C283—21no—
47C2×D4×C283—21no—
48C2×D4×C283D412yes—
49C2×C8×C283—21no—
50C2×C8×C283—21no—
51C42×C283C2311yescharacteristic
52C22×D283—21no—
53C22×D283—41no—
54Dic566—21no—
55Dic566D812yescomplemented
56D1132—21no—
57D1132—21no—
58D1132—42no—
59D1132—41no—
60D1132—41no—
61D1132—41no—
62D1132—41no—
63C22⋊D283—44no—
64C22⋊D283—82no—
65C2×Dic283—21no—
66C2×Dic283—21no—
67C2×Dic283—21no—
68C2×Dic283—44no—
69C4×D283—41no—
70C4×D283—41no—
71C283⋊C8—22no—
72C23×C283—22no—
73D4×C283—42no—
74D4×C283—41no—
75D4×C283—41no—
76D4×C283—41no—
77D4×C283—41no—
78C2×C4×C283C2×D411yescharacteristic
79C2×C4×C283C2×D411yescharacteristic
80C2×C4×C283C2×D411yescharacteristic
81C8×C283—41no—
82C8×C283—41no—
83C22×C283—42no—
84C22×C283—42no—
85C22×C283—42no—
86C22×C283#12011yescharacteristic
87C2×D283—41no—
88C2×D283—41no—
89C2×D283—41no—
90C2×D283—81no—
91C2×D283—81no—
92C2×D283—81no—
93C4×C283—21no—
94C4×C283C2×D811yescharacteristic
95C4×C283#13511yescharacteristic
96C4×C283AGL(1,ℤ/8)11yescharacteristic
97C4×C283AGL(1,ℤ/8)11yescharacteristic
98Dic283—22no—
99Dic283—41no—
100Dic283—41no—
101C2×C283—82no—
102C2×C283#44711yescharacteristic
103C2×C283#44911yescharacteristic
104C2×C283#45311yescharacteristic
105D283—81no—
106D283—161no—
107C283#162111yescharacteristic, complemented, Sylow
108#1621—2831nomaximal, Sylow
109#550—2831no—
110#493—2831no—
111#460—2831no—
112#459—2831no—
113#331D28311yescharacteristic, complemented
114Q8⋊C8—2831no—
115D4⋊C8—2831no—
116C2×#41—5661no—
117C2×SD16—5661no—
118C2×D8—5661no—
119C2×D8—5662no—
120#127—2831no—
121#127—5661no—
122#127C2×D28311yescharacteristic
123#121—5661no—
124#121—5662no—
125C4×Q8—2831no—
126C4×D4—2831no—
127C4×D4—5661no—
128C4⋊C8C2×D28311yescharacteristic
129C4⋊C8C2×D28311yescharacteristic
130#102—5661no—
131#102—5661no—
132C4×C8—2831no—
133#41—11322no—
134#41—11322no—
135C2×Q8—2831no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—2831no—
139C2×D4—5662no—
140C2×D4—5662no—
141C2×D4—5661no—
142C2×D4—5661no—
143C2×D4—5661no—
144C2×D4D113212yes—
145C22×C4—5662no—
146C22×C4—5661no—
147SD16—11322no—
148D8—11322no—
149D8—11324no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—5661no—
153C4⋊C4—2831no—
154C4⋊C4—2831no—
155C4⋊C4—5661no—
156C22⋊C4—5662no—
157C22⋊C4—5661no—
158C42—5661no—
159C42C22×D28311yescharacteristic
160C23—22no—
161C23—5661no—
162C23—11321no—
163Q8—2832no—
164Q8—5661no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—5661no—
171D4—5661no—
172D4—11322no—
173D4—11324no—
174D4—11321no—
175D4—11321no—
176D4—11321no—
177D4—11321no—
178D4—22642no—
179C2×C4—5661no—
180C2×C4—5661no—
181C2×C4—5661no—
182C2×C4—11324no—
183C2×C4—11321no—
184C2×C4—11321no—
185C2×C4D4×D28311yescharacteristic
186C2×C4D4×D28311yescharacteristic
187C2×C4C2×D113211yescharacteristic
188C8—41no—
189C8—41no—
190C8—5662no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—11321no—
195C22—11321no—
196C22—11321no—
197C22—22641no—
198C22—22641no—
199C22—22641no—
200C22#2258358011yescharacteristic
201C4—21no—
202C4—5662no—
203C4—11321no—
204C4—11321no—
205C4D8×D28311yescharacteristic
206C4#2258363111yescharacteristic
207C4#2258363411yescharacteristic
208C4#2258363711yescharacteristic
209C2—82no—
210C2—45281no—
211C2—22641no—
212C2#3182660011yescharacteristic
213C2#3182661111yescharacteristic
214C2#3182663511yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#331×C283C2
socleC22×C283#120
hypercenter#331D283
hypocenterC283#1621
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #31827135C2semidirect
2. #31826841C2semidirect
3. #31826666C2semidirect
4. #31826661C2semidirect
5. #31826195C2semidirect
6. #31826192C2semidirect
7. #331×C283C2semidirect
55. Dic566D8semidirect
107. C283#1621semidirect
113. #331D283semidirect

Maximal subgroups

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

subgroupindex
#318271352
#318268412
#318266662
#318266612
#318261952
#318261922
#331×C2832
#1621283