Finite Group Databasebeta

← #49094368

Subgroups — #49094368

Order 35968.

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

normal subgroups only

This group has 278 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#31823839C211yesmaximal, characteristic, complemented
2#31823663C211yesmaximal, characteristic, complemented
3#31823658C211yesmaximal, characteristic, complemented
4#31823207C211yesmaximal, characteristic, complemented
5Q8⋊#14555886C211yesmaximal, characteristic, complemented
6D4⋊#14555886C211yesmaximal, characteristic, complemented
7#550×C281C211yesmaximal, characteristic, complemented
8C2×#17985125—21no—
9C2×#17985123—21no—
10C2×#17985123—22no—
11#22582876C2211yescharacteristic
12C4⋊#14555886C2211yescharacteristic
13C4⋊#14555886C2211yescharacteristic
14#22582799—21no—
15#22582799—21no—
16C4×#14555886C2211yescharacteristic
17C2×#41×C281—21no—
18#127×C281—21no—
19#127×C281C2211yescharacteristic
20#121×C281—22no—
21#121×C281—21no—
22C4×Q8×C281C2211yescharacteristic
23C4×D4×C281—21no—
24C4×D4×C281C2211yescharacteristic
25C2×D1124—21no—
26C2×D1124—21no—
27C2×D1124—21no—
28#17985125—42no—
29#17985123—42no—
30#17985123—44no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C2×#14555886—21no—
34#41×C281—42no—
35#41×C281—42no—
36C2×Q8×C281D411yescharacteristic
37C2×D4×C281—22no—
38C2×D4×C281—22no—
39C2×D4×C281—21no—
40C2×D4×C281—21no—
41C2×D4×C281D411yescharacteristic
42C2×D4×C281D412yes—
43C22×C4×C281—22no—
44C22×C4×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281D411yescharacteristic
47C4⋊C4×C281D411yescharacteristic
48C22⋊C4×C281—22no—
49C22⋊C4×C281—21no—
50C42×C281—21no—
51C42×C281C2311yescharacteristic
52C22×D281—41no—
53D1124—42no—
54D1124—41no—
55D1124—41no—
56D1124—41no—
57D1124—41no—
58#14555886—22no—
59#14555886—41no—
60#14555886—41no—
61C23×C281—21no—
62C23×C281—22no—
63Q8×C281—21no—
64Q8×C281D812yescomplemented
65D4×C281—21no—
66D4×C281—21no—
67D4×C281—42no—
68D4×C281—44no—
69D4×C281—41no—
70D4×C281—41no—
71D4×C281—41no—
72D4×C281—41no—
73D4×C281—82no—
74C2×C4×C281—21no—
75C2×C4×C281—21no—
76C2×C4×C281—21no—
77C2×C4×C281—44no—
78C2×C4×C281—41no—
79C2×C4×C281—41no—
80C2×C4×C281C2×D411yescharacteristic
81C2×C4×C281C2×D411yescharacteristic
82C2×C4×C281C2×D411yescharacteristic
83C22×C281—42no—
84C22×C281—41no—
85C22×C281—41no—
86C22×C281—42no—
87C22×C281—42no—
88C22×C281—41no—
89C22×C281#12011yescharacteristic
90C2×D281—81no—
91C2×D281—81no—
92C2×D281—81no—
93C4×C281—22no—
94C4×C281—21no—
95C4×C281—41no—
96C4×C281—41no—
97C4×C281C2×D811yescharacteristic
98C4×C281#13511yescharacteristic
99C4×C281AGL(1,ℤ/8)11yescharacteristic
100C4×C281AGL(1,ℤ/8)11yescharacteristic
101C2×C281—81no—
102C2×C281—82no—
103C2×C281#44711yescharacteristic
104C2×C281#44911yescharacteristic
105C2×C281#45311yescharacteristic
106D281—161no—
107C281#162111yescharacteristic, complemented, Sylow
108#1621—2811nomaximal, Sylow
109#550D28111yescharacteristic, complemented
110#493—2811no—
111#460—2811no—
112#459—2811no—
113#331—2811no—
114Q8⋊C8—2811no—
115D4⋊C8—2811no—
116C2×#41—21no—
117C2×SD16—5621no—
118C2×D8—5621no—
119C2×D8—5622no—
120#127—21no—
121#127—2811no—
122#127C2×D28111yescharacteristic
123#121—22no—
124#121—21no—
125C4×Q8C2×D28111yescharacteristic
126C4×D4—21no—
127C4×D4C2×D28111yescharacteristic
128C4⋊C8—2811no—
129C4⋊C8—2811no—
130#102—5621no—
131#102—5621no—
132C4×C8—2811no—
133#41—42no—
134#41—42no—
135C2×Q8C22⋊D28111yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—5621no—
141C2×D4—5621no—
142C2×D4—5621no—
143C2×D4C22⋊D28111yescharacteristic
144C2×D4C22⋊D28112yes—
145C22×C4—22no—
146C22×C4—21no—
147SD16—11242no—
148D8—11244no—
149D8—11242no—
150C2×C8—5621no—
151C2×C8—5621no—
152C2×C8—5621no—
153C4⋊C4—21no—
154C4⋊C4C22⋊D28111yescharacteristic
155C4⋊C4C22⋊D28111yescharacteristic
156C22⋊C4—22no—
157C22⋊C4—21no—
158C42—21no—
159C42C22×D28111yescharacteristic
160C23—22no—
161C23—21no—
162C23—11241no—
163Q8—21no—
164Q8#1798512312yescomplemented
165D4—21no—
166D4—21no—
167D4—42no—
168D4—44no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—82no—
174D4—11242no—
175D4—11241no—
176D4—11241no—
177D4—11241no—
178D4—11241no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—44no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4C2×C22⋊D28111yescharacteristic
186C2×C4C2×C22⋊D28111yescharacteristic
187C2×C4C2×C22⋊D28111yescharacteristic
188C8—5622no—
189C8—11241no—
190C8—11241no—
191C22—42no—
192C22—41no—
193C22—42no—
194C22—41no—
195C22—41no—
196C22—42no—
197C22—22481no—
198C22—22481no—
199C22—22481no—
200C22#2258284811yescharacteristic
201C4—21no—
202C4—22no—
203C4—41no—
204C4—41no—
205C4C2×#1798512311yescharacteristic
206C4#2258289911yescharacteristic
207C4#2258290411yescharacteristic
208C4#2258290511yescharacteristic
209C2—82no—
210C2—81no—
211C2—44961no—
212C2#3182359711yescharacteristic
213C2#3182360811yescharacteristic
214C2#3182363111yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#550×C281C2
socleC22×C281#120
hypercenter#550D281
hypocenterC281#1621
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #31823839C2semidirect
2. #31823663C2semidirect
3. #31823658C2semidirect
4. #31823207C2semidirect
5. Q8⋊#14555886C2semidirect
6. D4⋊#14555886C2semidirect
7. #550×C281C2semidirect
64. Q8×C281D8semidirect
107. C281#1621semidirect
109. #550D281semidirect
164. Q8#17985123semidirect

Maximal subgroups

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

subgroupindex
#318238392
#318236632
#318236582
#318232072
Q8⋊#145558862
D4⋊#145558862
#550×C2812
#1621281