Finite Group Databasebeta

← #49094405

Subgroups — #49094405

Order 35968.

250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic562C211yesmaximal, characteristic, complemented
2#31823809C211yesmaximal, characteristic, complemented
3#31823660C211yesmaximal, characteristic, complemented
4#31823208C211yesmaximal, characteristic, complemented
5#31823193C211yesmaximal, characteristic, complemented
6D4⋊#14555886C211yesmaximal, characteristic, complemented
7#459×C281C211yesmaximal, characteristic
8C22×Dic562—21no—
9C2×#17985126—21no—
10#22582879C2211yescharacteristic
11#22582878—21no—
12#22582858—21no—
13#22582856—22no—
14C4×Dic562C2211yescharacteristic
15D4×Dic281—21no—
16C4⋊#14555886C2211yescharacteristic
17#22582800—21no—
18#22582800—22no—
19C4×#14555886C2211yescharacteristic
20C2×D8×C281—21no—
21#127×C281C2211yescharacteristic
22C4×D4×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24#102×C281—21no—
25C2×Dic562—22no—
26C2×Dic562—21no—
27C2×Dic562—42no—
28C2×Dic562—42no—
29C2×Dic562D411yescharacteristic
30C22×Dic281—22no—
31#17985126—42no—
32C2×#14555886—21no—
33C2×#14555886—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281D411yescharacteristic
36C4⋊Dic281D412yes—
37#17985117—22no—
38#17985117—21no—
39C22⋊Dic281—22no—
40C4×Dic281—21no—
41C2×D4×C281—21no—
42C2×D4×C281—21no—
43C2×D4×C281—21no—
44C2×D4×C281D411yescharacteristic
45C22×C4×C281—21no—
46D8×C281—42no—
47C2×C8×C281—21no—
48C4⋊C4×C281D411yescharacteristic
49C22⋊C4×C281—21no—
50C42×C281C2311yescharacteristic
51Dic562—21no—
52Dic562—44no—
53Dic562—41no—
54Dic562—41no—
55Dic562D812yescomplemented
56C2×Dic281—21no—
57C2×Dic281—21no—
58C2×Dic281—22no—
59C2×Dic281—44no—
60#14555886—41no—
61#14555886—41no—
62C23×C281—21no—
63C23×C281—41no—
64D4×C281—21no—
65D4×C281—42no—
66D4×C281—41no—
67D4×C281—41no—
68D4×C281—41no—
69D4×C281—41no—
70D4×C281SD1612yescomplemented
71C2×C4×C281—21no—
72C2×C4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281C2×D411yescharacteristic
75C2×C4×C281C2×D411yescharacteristic
76C2×C4×C281C2×D411yescharacteristic
77C8×C281—41no—
78C22×C281—22no—
79C22×C281—41no—
80C22×C281—41no—
81C22×C281—81no—
82C22×C281—81no—
83C22×C281—81no—
84C22×C281#12011yescharacteristic
85C4×C281—21no—
86C4×C281—41no—
87C4×C281C2×D811yescharacteristic
88C4×C281C2×SD1611yescharacteristic
89C4×C281AGL(1,ℤ/8)11yescharacteristic
90C4×C281#13711yescharacteristic
91Dic281—22no—
92Dic281—42no—
93Dic281—41no—
94C2×C281—42no—
95C2×C281—161no—
96C2×C281#44711yescharacteristic
97C2×C281#44811yescharacteristic
98C2×C281#45411yescharacteristic
99C281#162711yescharacteristic, complemented, Sylow
100#1627—2811nomaximal, Sylow
101D4×Q8—2811no—
102#486—2811no—
103#460—2811no—
104#459D28111yescharacteristic
105#332—2811no—
106Q8⋊C8—2811no—
107D4⋊C8—2811no—
108C22×Q8—5621no—
109C2×SD16—5621no—
110C2×D8—21no—
111C4⋊Q8—2811no—
112C4⋊Q8—5621no—
113#127C2×D28111yescharacteristic
114C22⋊Q8—5622no—
115C22⋊Q8—5621no—
116C4×Q8—2811no—
117C4×D4—5621no—
118C4×D4C2×D28111yescharacteristic
119C4⋊C8—2811no—
120C4⋊C8C2×D28111yescharacteristic
121#102—21no—
122#102—5621no—
123#102—5622no—
124C4×C8—2811no—
125C2×Q8—2811no—
126C2×Q8—5622no—
127C2×Q8—5621no—
128C2×Q8—11242no—
129C2×Q8—11242no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D28111yescharacteristic
134C22×C4—21no—
135C22×C4—5622no—
136SD16—11242no—
137D8—42no—
138C2×C8—21no—
139C2×C8—5621no—
140C2×C8—5621no—
141C4⋊C4—2811no—
142C4⋊C4—2812no—
143C4⋊C4—5622no—
144C4⋊C4—5621no—
145C4⋊C4—5621no—
146C4⋊C4C22⋊D28111yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—5622no—
149C42—5621no—
150C42C22×D28111yescharacteristic
151C23—21no—
152C23—41no—
153Q8—2812no—
154Q8—5621no—
155Q8—11244no—
156Q8—11241no—
157Q8—11241no—
158D4—21no—
159D4—42no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4#1798512612yescomplemented
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—5621no—
169C2×C4—5621no—
170C2×C4—5622no—
171C2×C4—11244no—
172C2×C4D4×D28111yescharacteristic
173C2×C4D4×D28111yescharacteristic
174C2×C4C2×C22⋊D28111yescharacteristic
175C8—41no—
176C8—11241no—
177C8—11241no—
178C22—22no—
179C22—41no—
180C22—41no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22#2258284711yescharacteristic
185C4—21no—
186C4—41no—
187C4—5622no—
188C4—11241no—
189C4—11242no—
190C4D8×D28111yescharacteristic
191C4C2×#1798512611yescharacteristic
192C4#2258290311yescharacteristic
193C4#2258290911yescharacteristic
194C2—42no—
195C2—161no—
196C2#3182359511yescharacteristic
197C2#3182360111yescharacteristic
198C2#3182363411yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting, prime radical#459×C281C2
socleC22×C281#120
hypercenter#459D281
hypocenterC281#1627
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. D4×Dic562C2semidirect
2. #31823809C2semidirect
3. #31823660C2semidirect
4. #31823208C2semidirect
5. #31823193C2semidirect
6. D4⋊#14555886C2semidirect
55. Dic562D8semidirect
70. D4×C281SD16semidirect
99. C281#1627semidirect
164. D4#17985126semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5622
#318238092
#318236602
#318232082
#318231932
D4⋊#145558862
#459×C2812
#1627281