Finite Group Databasebeta

← #49093879

Subgroups — #49093879

Order 35968.

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

normal subgroups only

This group has 218 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#31823999C211yesmaximal, characteristic
2#31823513C211yesmaximal, characteristic, complemented
3#31823330C211yesmaximal, characteristic, complemented
4#31823200C211yesmaximal, characteristic, complemented
5#31823198C211yesmaximal, characteristic
6#31823196C211yesmaximal, characteristic
7#328×C281C211yesmaximal, characteristic, complemented
8#22582874—21no—
9#22582870C411yescharacteristic, complemented
10#22582868C411yescharacteristic, complemented
11#22582863—21no—
12#22582853C2211yescharacteristic
13Q8×Dic281C411yescharacteristic, complemented
14#22582841C411yescharacteristic, complemented
15#22582839—21no—
16#22582837—21no—
17C2×C4×Dic281C2211yescharacteristic
18#22582808—21no—
19C22⋊#14555886C2211yescharacteristic
20C8×Dic281—21no—
21#22582786—21no—
22#22582786—21no—
23#22582786C2211yescharacteristic
24C22⋊Q8×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27C2×D1124C2×C411yescharacteristic
28C2×C22⋊D281—21no—
29C22×Dic281—21no—
30C22×Dic281D411yescharacteristic
31C22×Dic281D411yescharacteristic
32C2×C4×D281—21no—
33C2×#14555886—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281C2×C411yescharacteristic
37#17985117—21no—
38#17985115—21no—
39#17985115—21no—
40#17985115—21no—
41#17985115—21no—
42C4×Dic281—21no—
43C4×Dic281C2×C411yescharacteristic
44C4×Dic281C2×C411yescharacteristic
45C4×Dic281D411yescharacteristic
46C4×Dic281D411yescharacteristic
47C2×Q8×C281C2×C411yescharacteristic
48C22×C4×C281—21no—
49C22×C4×C281C2311yescharacteristic
50C2×C8×C281—21no—
51C4⋊C4×C281—21no—
52C4⋊C4×C281C2×C411yescharacteristic
53C22⋊C4×C281—21no—
54C22×D281—21no—
55D1124—41no—
56C22⋊D281—41no—
57C22⋊D281—41no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—41no—
62C2×Dic281—41no—
63C2×Dic281—41no—
64C2×Dic281—41no—
65C2×Dic281C22⋊C411yescharacteristic
66C2×Dic281C22⋊C411yescharacteristic
67C2×Dic281C22⋊C411yescharacteristic
68C2×Dic281C22⋊C411yescharacteristic
69C4×D281—42no—
70#14555886—41no—
71C23×C281C2×D411yescharacteristic
72Q8×C281—41no—
73C2×C4×C281—21no—
74C2×C4×C281—21no—
75C2×C4×C281—41no—
76C2×C4×C281—41no—
77C2×C4×C281—41no—
78C2×C4×C281—41no—
79C2×C4×C281C22×C411yescharacteristic
80C2×C4×C281C2×D411yescharacteristic
81C8×C281—41no—
82C22×C281—21no—
83C22×C281—21no—
84C22×C281C2×C22⋊C411yescharacteristic
85C22×C281#13511yescharacteristic
86C22×C281#13511yescharacteristic
87C2×D281—41no—
88C2×D281—41no—
89C2×D281—41no—
90C4×C281—21no—
91C4×C281—21no—
92C4×C281—41no—
93C4×C281—41no—
94C4×C281—81no—
95Dic281—21no—
96Dic281—21no—
97Dic281—21no—
98Dic281—21no—
99Dic281—41no—
100Dic281—81no—
101C2×C281—21no—
102C2×C281—21no—
103C2×C281#41011yescharacteristic
104C2×C281#41611yescharacteristic
105C2×C281#42111yescharacteristic
106D281—81no—
107C281#152111yescharacteristic, complemented, Sylow
108#1521—2811nomaximal, Sylow
109#529—2811no—
110#431—2811no—
111#383—2811no—
112#328—2811no—
113#328D28111yescharacteristic, complemented
114#327—2811no—
115#327—2811no—
116#126—5621no—
117#125—2811no—
118#124—2811no—
119#123—5621no—
120C22⋊Q8C2×D28111yescharacteristic
121#121—2811no—
122C4×Q8—2811no—
123C4×D4—2811no—
124C4×D4—5621no—
125#117—5621no—
126C2×C42—2811no—
127C4⋊C8—5621no—
128C22⋊C8—2811no—
129C22⋊C8C2×D28111yescharacteristic
130C4×C8—5621no—
131#95—2811no—
132#95—5621no—
133#95—5621no—
134#95C2×D28111yescharacteristic
135C2×Q8C4×D28111yescharacteristic
136C2×D4—2811no—
137C2×D4—5621no—
138C22×C4—21no—
139C22×C4—2811no—
140C22×C4—2811no—
141C22×C4—5621no—
142C22×C4—5621no—
143C22×C4C22×D28111yescharacteristic
144C2×C8—21no—
145C2×C8—5621no—
146C4⋊C4—21no—
147C4⋊C4—2811no—
148C4⋊C4—5621no—
149C4⋊C4—5621no—
150C4⋊C4—5621no—
151C4⋊C4C4×D28111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5621no—
154C22⋊C4—5621no—
155C22⋊C4—5621no—
156C22⋊C4—5621no—
157C42—2811no—
158C42—2811no—
159C42—2811no—
160C42—2811no—
161C42—5621no—
162C23—5621no—
163C23D4×D28111yescharacteristic
164Q8—41no—
165D4—11241no—
166D4—11241no—
167D4—11241no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—2811no—
175C2×C4—2811no—
176C2×C4—2811no—
177C2×C4—2811no—
178C2×C4—5621no—
179C2×C4—5621no—
180C2×C4—5621no—
181C2×C4—11242no—
182C2×C4—11241no—
183C2×C4—11241no—
184C2×C4—11241no—
185C2×C4—11241no—
186C2×C4C2×C4×D28111yescharacteristic
187C2×C4D4×D28111yescharacteristic
188C8—41no—
189C8—11241no—
190C22—21no—
191C22—21no—
192C22—11241no—
193C22—11241no—
194C22—11241no—
195C22C22⋊C4×D28111yescharacteristic
196C22#2258290011yescharacteristic
197C22#2258290211yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—5621no—
204C4—5621no—
205C4—5621no—
206C4—5621no—
207C4—11241no—
208C4—22481no—
209C2—21no—
210C2—21no—
211C2—22481no—
212C2#3182343511yescharacteristic
213C2#3182345811yescharacteristic
214C2#3182347811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D281
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#328×C281C2
socleC22×C281C2×C22⋊C4
prime radical#22582853C22
cosocleC22×C4×C281C23
hypercenter#328D281
hypocenterC281#1521
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #31823513C2semidirect
3. #31823330C2semidirect
4. #31823200C2semidirect
7. #328×C281C2semidirect
9. #22582870C4semidirect
10. #22582868C4semidirect
13. Q8×Dic281C4semidirect
14. #22582841C4semidirect
107. C281#1521semidirect
113. #328D281semidirect

Maximal subgroups

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

subgroupindex
#318239992
#318235132
#318233302
#318232002
#318231982
#318231962
#328×C2812
#1521281