Finite Group Databasebeta

← #49119796

Subgroups — #49119796

Order 36224.

222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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#31826996C211yesmaximal, characteristic
2#31826519C211yesmaximal, characteristic, complemented
3#31826329C211yesmaximal, characteristic, complemented
4#31826203C211yesmaximal, characteristic, complemented
5#31826201C211yesmaximal, characteristic, complemented
6#31826199C211yesmaximal, characteristic
7#327×C283C211yesmaximal, characteristic
8#22583603—21no—
9#22583601C411yescharacteristic, complemented
10#22583597C411yescharacteristic, complemented
11#22583591—21no—
12#22583589C2211yescharacteristic
13#22583575C411yescharacteristic, complemented
14D4×Dic283—21no—
15D4×Dic283C411yescharacteristic, complemented
16#22583566—21no—
17C2×Dic283⋊C4—21no—
18C2×C4×Dic283C2211yescharacteristic
19Dic283⋊C8—21no—
20C22⋊(C283⋊C8)C2211yescharacteristic
21#22583520—21no—
22C283⋊#95—21no—
23C283⋊#95C2211yescharacteristic
24#121×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26#95×C283C2211yescharacteristic
27C2×Dic566C2×C411yescharacteristic
28C22×Dic283—21no—
29C22×Dic283—21no—
30C22×Dic283D411yescharacteristic
31C22×Dic283D411yescharacteristic
32C2×C283⋊C8—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283C2×C411yescharacteristic
35Dic283⋊C4—21no—
36Dic283⋊C4—21no—
37Dic283⋊C4—21no—
38Dic283⋊C4—42no—
39C22⋊Dic283—21no—
40C22⋊Dic283—21no—
41C22⋊Dic283—21no—
42C22⋊Dic283—21no—
43C4×Dic283—21no—
44C4×Dic283C2×C411yescharacteristic
45C4×Dic283C2×C411yescharacteristic
46C4×Dic283D411yescharacteristic
47C4×Dic283D411yescharacteristic
48C2×D4×C283—21no—
49C2×D4×C283C2×C411yescharacteristic
50C22×C4×C283—21no—
51C22×C4×C283C2311yescharacteristic
52C2×C8×C283—21no—
53C4⋊C4×C283C2×C411yescharacteristic
54C22⋊C4×C283—21no—
55Dic566—41no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—41no—
61C2×Dic283—42no—
62C2×Dic283—41no—
63C2×Dic283—41no—
64C2×Dic283—41no—
65C2×Dic283C22⋊C411yescharacteristic
66C2×Dic283C22⋊C411yescharacteristic
67C2×Dic283C22⋊C411yescharacteristic
68C2×Dic283C22⋊C411yescharacteristic
69C283⋊C8—41no—
70C23×C283—21no—
71C23×C283C2×D411yescharacteristic
72D4×C283—41no—
73D4×C283—41no—
74D4×C283—41no—
75C2×C4×C283—21no—
76C2×C4×C283—41no—
77C2×C4×C283—41no—
78C2×C4×C283—41no—
79C2×C4×C283—41no—
80C2×C4×C283C22×C411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C8×C283—41no—
83C22×C283—21no—
84C22×C283—21no—
85C22×C283—41no—
86C22×C283—41no—
87C22×C283—41no—
88C22×C283C2×C22⋊C411yescharacteristic
89C22×C283AGL(1,ℤ/8)11yescharacteristic
90C22×C283#13711yescharacteristic
91C4×C283—21no—
92C4×C283—21no—
93C4×C283—41no—
94C4×C283—81no—
95Dic283—21no—
96Dic283—21no—
97Dic283—21no—
98Dic283—21no—
99Dic283—41no—
100Dic283—41no—
101Dic283—81no—
102C2×C283—21no—
103C2×C283—21no—
104C2×C283—81no—
105C2×C283#41011yescharacteristic
106C2×C283#41711yescharacteristic
107C2×C283#42111yescharacteristic
108C283#151211yescharacteristic, complemented, Sylow
109#1512—2831nomaximal, Sylow
110#529—2831no—
111#432—2831no—
112#382—2831no—
113#328—2831no—
114#328—2831no—
115#327—2831no—
116#327D28311yescharacteristic
117#126—5661no—
118#125—2831no—
119#124—2831no—
120#123—5661no—
121C22⋊Q8—2831no—
122#121C2×D28311yescharacteristic
123C4×Q8—2831no—
124C4×D4—2831no—
125C4×D4—5661no—
126#117—5661no—
127C2×C4⋊C4—5661no—
128C2×C42—2831no—
129C4⋊C8—5661no—
130C22⋊C8—2831no—
131C22⋊C8C2×D28311yescharacteristic
132#97—5661no—
133#95—2831no—
134#95—5661no—
135#95C2×D28311yescharacteristic
136C2×Q8—2831no—
137C2×D4—21no—
138C2×D4C4×D28311yescharacteristic
139C22×C4—21no—
140C22×C4—2831no—
141C22×C4—2831no—
142C22×C4—5661no—
143C22×C4—5661no—
144C22×C4C22×D28311yescharacteristic
145C2×C8—21no—
146C2×C8—5661no—
147C4⋊C4—2831no—
148C4⋊C4—5661no—
149C4⋊C4—5661no—
150C4⋊C4—5661no—
151C4⋊C4—5661no—
152C4⋊C4—11322no—
153C4⋊C4C4×D28311yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—5661no—
156C22⋊C4—5661no—
157C22⋊C4—5661no—
158C22⋊C4—5661no—
159C42—2831no—
160C42—2831no—
161C42—2831no—
162C42—2831no—
163C42—5661no—
164C23—21no—
165C23D4×D28311yescharacteristic
166Q8—11321no—
167D4—41no—
168D4—41no—
169D4—41no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—2831no—
176C2×C4—2831no—
177C2×C4—2831no—
178C2×C4—2831no—
179C2×C4—5661no—
180C2×C4—5661no—
181C2×C4—5661no—
182C2×C4—5661no—
183C2×C4—11321no—
184C2×C4—11322no—
185C2×C4—11321no—
186C2×C4—11321no—
187C2×C4—11321no—
188C2×C4C2×C4×D28311yescharacteristic
189C2×C4D4×D28311yescharacteristic
190C8—41no—
191C8—11321no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22C22⋊C4×D28311yescharacteristic
198C22#2258363411yescharacteristic
199C22#2258363911yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—81no—
204C4—5661no—
205C4—5661no—
206C4—5661no—
207C4—5661no—
208C4—11321no—
209C4—11321no—
210C4—22641no—
211C2—21no—
212C2—21no—
213C2—81no—
214C2#3182643711yescharacteristic
215C2#3182646311yescharacteristic
216C2#3182648011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#327×C283C2
socleC22×C283C2×C22⋊C4
prime radical#121×C283C22
cosocleC22×C4×C283C23
hypercenter#327D283
hypocenterC283#1512
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31826519C2semidirect
3. #31826329C2semidirect
4. #31826203C2semidirect
5. #31826201C2semidirect
9. #22583601C4semidirect
10. #22583597C4semidirect
13. #22583575C4semidirect
15. D4×Dic283C4semidirect
108. C283#1512semidirect

Maximal subgroups

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

subgroupindex
#318269962
#318265192
#318263292
#318262032
#318262012
#318261992
#327×C2832
#1512283