Finite Group Databasebeta

← #49094341

Subgroups — #49094341

Order 35968.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#31824040C211yesmaximal, characteristic
2#31823782C211yesmaximal, characteristic, complemented
3#31823779C211yesmaximal, characteristic, complemented
4#31823403C211yesmaximal, characteristic, complemented
5#31823196C211yesmaximal, characteristic, complemented
6#31823188C211yesmaximal, characteristic, complemented
7#327×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9#22582857—21no—
10#22582856—21no—
11#22582853C2211yescharacteristic
12#22582852—21no—
13#22582851—21no—
14#22582851—21no—
15C2×C4⋊Dic281C2211yescharacteristic
16C2×#17985117C2211yescharacteristic
17#22582811—21no—
18#22582810—21no—
19#22582801—21no—
20#22582800—21no—
21C22⋊#14555886C2211yescharacteristic
22#22582786—21no—
23#22582786—21no—
24#121×C281C2211yescharacteristic
25C22⋊C8×C281C2211yescharacteristic
26#95×C281C2211yescharacteristic
27#17985137—42no—
28#17985137—42no—
29C2×Dic562—21no—
30C2×D1124D411yescharacteristic
31C2×C22⋊D281—21no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281—21no—
34C22×Dic281—21no—
35C22×Dic281—21no—
36C22×Dic281D411yescharacteristic
37C22×Dic281D411yescharacteristic
38C2×C4×D281—21no—
39C2×#14555886—21no—
40C4⋊Dic281—21no—
41C4⋊Dic281—21no—
42C4⋊Dic281D411yescharacteristic
43#17985117—21no—
44#17985117—21no—
45#17985117—21no—
46C22⋊Dic281—21no—
47#17985115—21no—
48#17985115—21no—
49C2×D4×C281—21no—
50C2×D4×C281D411yescharacteristic
51C22×C4×C281—21no—
52C22×C4×C281C2311yescharacteristic
53C2×C8×C281—21no—
54C4⋊C4×C281D411yescharacteristic
55C22⋊C4×C281—21no—
56C22×D281—21no—
57Dic562—42no—
58D1124—41no—
59C22⋊D281—42no—
60C22⋊D281—41no—
61C22⋊D281—41no—
62C22⋊D281—81no—
63C2×Dic281—21no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—21no—
67C2×Dic281—42no—
68C2×Dic281—41no—
69C2×Dic281—42no—
70C2×Dic281—41no—
71C2×Dic281SD1612yes—
72C4×D281—42no—
73#14555886—41no—
74C23×C281—21no—
75C23×C281C2×D411yescharacteristic
76D4×C281—41no—
77D4×C281—41no—
78D4×C281—41no—
79C2×C4×C281—21no—
80C2×C4×C281—41no—
81C2×C4×C281—41no—
82C2×C4×C281—41no—
83C2×C4×C281—41no—
84C2×C4×C281C2×D411yescharacteristic
85C2×C4×C281C2×D411yescharacteristic
86C8×C281—41no—
87C22×C281—21no—
88C22×C281—21no—
89C22×C281—41no—
90C22×C281—41no—
91C22×C281—41no—
92C22×C281#12011yescharacteristic
93C22×C281C2×SD1611yescharacteristic
94C22×C281AGL(1,ℤ/8)11yescharacteristic
95C2×D281—41no—
96C2×D281—41no—
97C2×D281—41no—
98C4×C281—21no—
99C4×C281—21no—
100C4×C281—41no—
101C4×C281—81no—
102Dic281—22no—
103Dic281—41no—
104Dic281—41no—
105Dic281—81no—
106C2×C281—21no—
107C2×C281—21no—
108C2×C281—81no—
109C2×C281#45011yescharacteristic
110C2×C281#45411yescharacteristic
111C2×C281#45811yescharacteristic
112D281—81no—
113C281#161611yescharacteristic, complemented, Sylow
114#1616—2811nomaximal, Sylow
115#537—2811no—
116#481—2811no—
117#481—2811no—
118#400—2811no—
119#327—2811no—
120#327D28111yescharacteristic, complemented
121#324—2811no—
122C2×#41—5621no—
123C22⋊Q8—5621no—
124C22⋊Q8—5621no—
125#121—2811no—
126#121—5621no—
127#121—5621no—
128#121—5621no—
129#121C2×D28111yescharacteristic
130C2×C4⋊C4—2811no—
131C2×C4⋊C4—2811no—
132#106—5621no—
133#106—5621no—
134#102—5621no—
135#102—5621no—
136C22⋊C8—2811no—
137C22⋊C8C2×D28111yescharacteristic
138#95—5621no—
139#95—5621no—
140#95C2×D28111yescharacteristic
141#41—11242no—
142#41—11242no—
143C2×Q8—5621no—
144C2×D4—21no—
145C2×D4—2811no—
146C2×D4—5621no—
147C2×D4—5621no—
148C2×D4—5621no—
149C2×D4D112411yescharacteristic
150C22×C4—21no—
151C22×C4—2811no—
152C22×C4—2811no—
153C22×C4—5621no—
154C22×C4—5621no—
155C22×C4—5621no—
156C22×C4C22×D28111yescharacteristic
157C2×C8—21no—
158C2×C8—5621no—
159C4⋊C4—2811no—
160C4⋊C4—5621no—
161C4⋊C4—5621no—
162C4⋊C4—5621no—
163C4⋊C4—5621no—
164C4⋊C4—5621no—
165C4⋊C4D112411yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—5621no—
168C22⋊C4—5621no—
169C22⋊C4—5621no—
170C23—21no—
171C23—5621no—
172C23D4×D28111yescharacteristic
173Q8—11242no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—11241no—
178D4—11242no—
179D4—11241no—
180D4—11241no—
181D4—22481no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—2812no—
188C2×C4—5621no—
189C2×C4—5621no—
190C2×C4—5621no—
191C2×C4—5621no—
192C2×C4—11242no—
193C2×C4—11242no—
194C2×C4—11241no—
195C2×C4—11242no—
196C2×C4—11241no—
197C2×C4D4×D28111yescharacteristic
198C2×C4C2×D112411yescharacteristic
199C8—41no—
200C8—11241no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—11241no—
207C22—11241no—
208C22—11241no—
209C22#2258284911yescharacteristic
210C22SD16×D28111yescharacteristic
211C22#2258290311yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—5622no—
217C4—11241no—
218C4—11241no—
219C4—22481no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—22481no—
224C2#3182361511yescharacteristic
225C2#3182363711yescharacteristic
226C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#327×C281C2
socleC22×C281#120
prime radical#31824040C2
hypercenter#327D281
hypocenterC281#1616
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31823782C2semidirect
3. #31823779C2semidirect
4. #31823403C2semidirect
5. #31823196C2semidirect
6. #31823188C2semidirect
7. #327×C281C2semidirect
113. C281#1616semidirect
120. #327D281semidirect

Maximal subgroups

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

subgroupindex
#318240402
#318237822
#318237792
#318234032
#318231962
#318231882
#327×C2812
#1616281