Finite Group Databasebeta

← #49094391

Subgroups — #49094391

Order 35968.

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

normal subgroups only

This group has 256 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#31824118C211yesmaximal, characteristic, complemented
2#31823809C211yesmaximal, characteristic, complemented
3#31823655C211yesmaximal, characteristic, complemented
4#31823208C211yesmaximal, characteristic, complemented
5D4⋊#14555886C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#459×C281C211yesmaximal, characteristic, complemented
8C2×#17985138—21no—
9C2×#17985123—21no—
10#22582879C2211yescharacteristic
11#22582861—22no—
12#22582858—21no—
13#22582850—21no—
14C4×D1124C2211yescharacteristic
15C4⋊C4×D281—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—
25#17985138—42no—
26#17985138—42no—
27C2×Dic562—21no—
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—22no—
30C2×C4×D281—22no—
31C2×C4×D281—21no—
32#17985123—42no—
33C2×#14555886—21no—
34C2×#14555886—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281D411yescharacteristic
37C4⋊Dic281D412yes—
38#17985117—22no—
39C22⋊Dic281—22no—
40#17985115—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
51C22×D281—21no—
52Dic562—41no—
53Dic562—41no—
54D1124—21no—
55D1124D812yescomplemented
56C22⋊D281—44no—
57C2×Dic281—21no—
58C2×Dic281—22no—
59C4×D281—44no—
60C4×D281—41no—
61C4×D281—41no—
62#14555886—41no—
63#14555886—41no—
64C23×C281—21no—
65C23×C281—41no—
66D4×C281—21no—
67D4×C281—21no—
68D4×C281—42no—
69D4×C281—41no—
70D4×C281—41no—
71D4×C281—41no—
72D4×C281—41no—
73C2×C4×C281—21no—
74C2×C4×C281—41no—
75C2×C4×C281—41no—
76C2×C4×C281C2×D411yescharacteristic
77C2×C4×C281C2×D411yescharacteristic
78C2×C4×C281C2×D411yescharacteristic
79C8×C281—41no—
80C22×C281—41no—
81C22×C281—41no—
82C22×C281—41no—
83C22×C281—81no—
84C22×C281—81no—
85C22×C281—81no—
86C22×C281#12011yescharacteristic
87C2×D281—22no—
88C2×D281—41no—
89C2×D281—41no—
90C4×C281—21no—
91C4×C281—41no—
92C4×C281C2×D811yescharacteristic
93C4×C281#13511yescharacteristic
94C4×C281AGL(1,ℤ/8)11yescharacteristic
95C4×C281AGL(1,ℤ/8)11yescharacteristic
96Dic281—42no—
97Dic281—41no—
98C2×C281—81no—
99C2×C281—161no—
100C2×C281#44711yescharacteristic
101C2×C281#44911yescharacteristic
102C2×C281#45411yescharacteristic
103D281—42no—
104C281#162511yescharacteristic, complemented, Sylow
105#1625—2811nomaximal, Sylow
106#547—2811no—
107#486—2811no—
108#459—2811no—
109#459D28111yescharacteristic, complemented
110#332—2811no—
111D4⋊C8—2811no—
112D4⋊C8—2811no—
113C2×#41—5621no—
114C2×D8—21no—
115C2×D8—5621no—
116C4⋊Q8—2811no—
117#127C2×D28111yescharacteristic
118#123—5622no—
119C22⋊Q8—5621no—
120#121—5621no—
121C4×D4—2811no—
122C4×D4C2×D28111yescharacteristic
123C2×C4⋊C4—5621no—
124C4⋊C8—2811no—
125C4⋊C8C2×D28111yescharacteristic
126#102—21no—
127#102—5621no—
128#102—5622no—
129C4×C8—2811no—
130#41—11242no—
131#41—11242no—
132C2×Q8—5621no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—2811no—
137C2×D4—5622no—
138C2×D4C22⋊D28111yescharacteristic
139C22×C4—21no—
140C22×C4—5622no—
141C22×C4—5621no—
142D8—42no—
143D8—11242no—
144C2×C8—21no—
145C2×C8—5621no—
146C2×C8—5621no—
147C4⋊C4—2811no—
148C4⋊C4—2812no—
149C4⋊C4—5622no—
150C4⋊C4—5621no—
151C4⋊C4C22⋊D28111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5622no—
154C22⋊C4—5621no—
155C42C22×D28111yescharacteristic
156C23—21no—
157C23—41no—
158C23—5621no—
159Q8—11241no—
160Q8—11241no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—2812no—
169D4—5621no—
170D4—11244no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5621no—
175C2×C4—5622no—
176C2×C4—11244no—
177C2×C4—11241no—
178C2×C4—11241no—
179C2×C4D4×D28111yescharacteristic
180C2×C4D4×D28111yescharacteristic
181C2×C4C2×C22⋊D28111yescharacteristic
182C8—41no—
183C8—11241no—
184C8—11241no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—5622no—
192C22—11241no—
193C22—11241no—
194C22#2258284711yescharacteristic
195C4—21no—
196C4—41no—
197C4—11242no—
198C4—11241no—
199C4D8×D28111yescharacteristic
200C4#2258289911yescharacteristic
201C4#2258290311yescharacteristic
202C4#2258290511yescharacteristic
203C2—81no—
204C2—161no—
205C2—11242no—
206C2#3182359511yescharacteristic
207C2#3182360611yescharacteristic
208C2#3182363411yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#459×C281C2
socleC22×C281#120
hypercenter#459D281
hypocenterC281#1625
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. #31824118C2semidirect
2. #31823809C2semidirect
3. #31823655C2semidirect
4. #31823208C2semidirect
5. D4⋊#14555886C2semidirect
6. #31823190C2semidirect
7. #459×C281C2semidirect
55. D1124D8semidirect
104. C281#1625semidirect
109. #459D281semidirect

Maximal subgroups

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

subgroupindex
#318241182
#318238092
#318236552
#318232082
D4⋊#145558862
#318231902
#459×C2812
#1625281