Finite Group Databasebeta

← #49097322

Subgroups — #49097322

Order 35968.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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#31824212C211yesmaximal, characteristic, complemented
2#31823646C211yesmaximal, characteristic, complemented
3#31823636C211yesmaximal, characteristic
4#31823262C211yesmaximal, characteristic, complemented
5#31823261C211yesmaximal, characteristic, complemented
6#31823259C211yesmaximal, characteristic, complemented
7#456×C281C211yesmaximal, characteristic, complemented
8#22582909—21no—
9#22582904—21no—
10#22582877C2211yescharacteristic
11#22582874—21no—
12#22582873—21no—
13#22582869—21no—
14#22582868C2211yescharacteristic
15#22582864—21no—
16#22582857—21no—
17#22582855—21no—
18#22582806—21no—
19#22582806—21no—
20#22582798C2211yescharacteristic
21#22582798C2211yescharacteristic
222−1+4×C281C2211yescharacteristic
23#137×C281—21no—
24C4⋊Q8×C281C2211yescharacteristic
25#104×C281—21no—
26#101×C281C2211yescharacteristic
27C2×Dic562D411yescharacteristic
28C2×D1124D411yescharacteristic
29C2×C4×D281—21no—
30#17985128—41no—
31#17985126—41no—
32#17985125—41no—
33#17985123—41no—
34#17985122—21no—
35#17985122—21no—
36C4⋊Dic281—21no—
37#17985117—21no—
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41#17985117—21no—
42#17985115—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47C4×Dic281D411yescharacteristic
48C4×Dic281D411yescharacteristic
49#41×C281—21no—
50#41×C281—21no—
51#41×C281—21no—
52#41×C281—41no—
53C2×Q8×C281—41no—
54C2×Q8×C281D411yescharacteristic
55C2×Q8×C281C2311yescharacteristic
56Q16×C281—41no—
57SD16×C281—41no—
58M16×C281—21no—
59C4⋊C4×C281—21no—
60C4⋊C4×C281—21no—
61C42×C281D411yescharacteristic
62C22×D281—21no—
63Dic562—41no—
64D1124—41no—
65C2×Dic281—21no—
66C2×Dic281—21no—
67C2×Dic281—21no—
68C4×D281—81no—
69#14555886—41no—
70#14555886—41no—
71Q8×C281—21no—
72Q8×C281—21no—
73Q8×C281—21no—
74Q8×C281—41no—
75Q8×C281—41no—
76D4×C281—21no—
77D4×C281—21no—
78D4×C281—21no—
79D4×C281—41no—
80C2×C4×C281—21no—
81C2×C4×C281—21no—
82C2×C4×C281—41no—
83C2×C4×C281—41no—
84C2×C4×C281—41no—
85C2×C4×C281C2×D411yescharacteristic
86C2×C4×C281C2×D411yescharacteristic
87C2×C4×C281C2×D411yescharacteristic
88C8×C281—41no—
89C22×C281—41no—
90C22×C281#12011yescharacteristic
91C2×D281—42no—
92C2×D281—41no—
93C4×C281—21no—
94C4×C281—21no—
95C4×C281—21no—
96C4×C281—41no—
97C4×C281—41no—
98C4×C281—41no—
99Dic281—41no—
100Dic281—41no—
101Dic281—41no—
102C2×C281—21no—
103C2×C281—81no—
104C2×C281B(4,𝔽2)11yescharacteristic
105D281—81no—
106C281#220311yescharacteristic, complemented, Sylow
107#2203—2811nomaximal, Sylow
108#563—2811no—
109#456—2811no—
110#456D28111yescharacteristic, complemented
111#454—2811no—
112#356—2811no—
113#356—2811no—
114#355—2811no—
1152−1+4C2×D28111yescharacteristic
116#137—21no—
117#137—5621no—
118AGL(1,ℤ/8)—5621no—
119C4⋊Q8—2811no—
120C4⋊Q8C2×D28111yescharacteristic
121#126—5621no—
122#126—5621no—
123#125—5621no—
124#124—2811no—
125#123—5621no—
126C22⋊Q8—5621no—
127C22⋊Q8—5621no—
128#104—21no—
129#104—5621no—
130#104—5621no—
131#101—2811no—
132#101—2811no—
133#101C2×D28111yescharacteristic
134#41—21no—
135#41—21no—
136#41—21no—
137#41—41no—
138C2×Q8—41no—
139C2×Q8—2811no—
140C2×Q8C22⋊D28111yescharacteristic
141C2×Q8C22×D28111yescharacteristic
142C2×D4—2811no—
143C22×C4—5621no—
144Q16—41no—
145Q16—11241no—
146SD16—41no—
147SD16—11241no—
148SD16—11241no—
149D8—11241no—
150M16—21no—
151M16—5621no—
152M16—5621no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—5621no—
156C4⋊C4—5621no—
157C4⋊C4—5621no—
158C4⋊C4—5621no—
159C4⋊C4—5621no—
160C4⋊C4—5621no—
161C22⋊C4—5621no—
162C22⋊C4—5621no—
163C22⋊C4—5621no—
164C22⋊C4—5621no—
165C22⋊C4—5621no—
166C42—2811no—
167C42—2811no—
168C42C22⋊D28111yescharacteristic
169C23—5621no—
170Q8—21no—
171Q8—21no—
172Q8—21no—
173Q8—41no—
174Q8—41no—
175Q8—11241no—
176D4—21no—
177D4—21no—
178D4—21no—
179D4—41no—
180D4—11241no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—5621no—
187C2×C4—5621no—
188C2×C4—5621no—
189C2×C4—22481no—
190C2×C4D4×D28111yescharacteristic
191C2×C4D4×D28111yescharacteristic
192C2×C4C2×C22⋊D28111yescharacteristic
193C8—41no—
194C8—11241no—
195C8—11241no—
196C22—41no—
197C22—11242no—
198C22—11241no—
199C22#2258284711yescharacteristic
200C4—21no—
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—41no—
206C4—11241no—
207C4—11241no—
208C4—11241no—
209C2—21no—
210C2—81no—
211C2—22481no—
212C2#3182364911yescharacteristic
subgroupG/H
centerC2#31823649
commutator, cosocleC2×Q8×C281C23
FrattiniC2×Q8C22×D281
Fitting#456×C281C2
socleC2×C281B(4,𝔽2)
prime radical#31823636C2
hypercenter#456D281
hypocenterC281#2203
LCSG ▷ C2×Q8×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #31824212C2semidirect
2. #31823646C2semidirect
4. #31823262C2semidirect
5. #31823261C2semidirect
6. #31823259C2semidirect
7. #456×C281C2semidirect
106. C281#2203semidirect
110. #456D281semidirect

Maximal subgroups

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

subgroupindex
#318242122
#318236462
#318236362
#318232622
#318232612
#318232592
#456×C2812
#2203281