Finite Group Databasebeta

← #49095703

Subgroups — #49095703

Order 35968.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#22582866C211yesmaximal, characteristic
2#31823940C211yesmaximal, characteristic, complemented
3#31823468C211yesmaximal, characteristic
4C2×#22582797C211yesmaximal, characteristic, complemented
5#31823224C211yesmaximal, characteristic, complemented
6#31823222C211yesmaximal, characteristic, complemented
7#418×C281C211yesmaximal, characteristic
8C22×Dic562C2211yescharacteristic
9C2×#17985122C2211yescharacteristic
10#22582866—22no—
11#22582866C414yescomplemented
12C4×Dic562—22no—
13#22582844—22no—
14#22582838C2211yescharacteristic
15#22582835—22no—
16C2×C22⋊Dic281—22no—
17C2×C4×Dic281C2211yescharacteristic
18#22582800—22no—
19#22582797—22no—
20C22×D4×C281C2211yescharacteristic
21C2×M16×C281C2211yescharacteristic
22#117×C281C2211yescharacteristic
23#102×C281—22no—
24C2×Dic562—21no—
25C2×Dic562—21no—
26C2×Dic562—21no—
27C2×Dic562—21no—
28C2×Dic562C2×C412yes—
29C2×Dic562D412yes—
30C22×Dic281—21no—
31C22×Dic281D412yes—
32#17985122—21no—
33#17985122—21no—
34C2×#14555886—21no—
35C4⋊Dic281D412yes—
36#17985117—24no—
37C22⋊Dic281—28no—
38C22⋊Dic281—21no—
39C4×Dic281—24no—
40C4×Dic281—21no—
41C4×Dic281—21no—
42C4×Dic281C2×C412yes—
43C24×C281—21no—
44C2×D4×C281—21no—
45C2×D4×C281—21no—
46C2×D4×C281—21no—
47C2×D4×C281—21no—
48C2×D4×C281—21no—
49C2×D4×C281C2×C412yes—
50C22×C4×C281C2311yescharacteristic
51M16×C281—21no—
52M16×C281—21no—
53C2×C8×C281—21no—
54C4⋊C4×C281D412yes—
55C22⋊C4×C281—21no—
56C42×C281—21no—
57Dic562—22no—
58Dic562—22no—
59Dic562—22no—
60Dic562—22no—
61C2×Dic281—22no—
62C2×Dic281—22no—
63C2×Dic281—22no—
64C2×Dic281—22no—
65C2×Dic281—42no—
66C2×Dic281C22⋊C414yes—
67#14555886—41no—
68C23×C281—22no—
69C23×C281—44no—
70C23×C281—41no—
71C23×C281—41no—
72C23×C281C2×D411yescharacteristic
73D4×C281—22no—
74D4×C281—22no—
75D4×C281—41no—
76D4×C281—41no—
77C2×C4×C281—22no—
78C2×C4×C281C22×C411yescharacteristic
79C2×C4×C281C2×D411yescharacteristic
80C2×C4×C281C2×D411yescharacteristic
81C2×C4×C281C2×D411yescharacteristic
82C2×C4×C281#4111yescharacteristic
83C2×C4×C281#4111yescharacteristic
84C8×C281—41no—
85C22×C281—22no—
86C22×C281—44no—
87C22×C281—42no—
88C22×C281—82no—
89C22×C281—82no—
90C22×C281C2×C22⋊C411yescharacteristic
91C22×C281#12011yescharacteristic
92C22×C281#12311yescharacteristic
93C4×C281—42no—
94C4×C281C4×D411yescharacteristic
95C4×C281C4×D411yescharacteristic
96C4×C281#12111yescharacteristic
97C4×C281#12111yescharacteristic
98Dic281—24no—
99Dic281—42no—
100Dic281—42no—
101C2×C281—21no—
102C2×C281—21no—
103C2×C281—82no—
104C2×C281#38611yescharacteristic
105C2×C281#45412yes—
106C281#188811yescharacteristic, complemented, Sylow
107#1888—2811nomaximal, Sylow
108C2×#124—2811no—
109#519—2811no—
110#418—2811no—
111#418D28111yescharacteristic
112C2×#101—2811no—
113#339—2811no—
114#339—2811no—
115C22×Q8—2811no—
116C22×D4C2×D28111yescharacteristic
117C2×M16—2811no—
118C2×M16C2×D28111yescharacteristic
119#124—2814no—
120#124—5622no—
121C4×Q8—5622no—
122C4×Q8—5622no—
123#117—2811no—
124#117—5622no—
125#117C2×D28111yescharacteristic
126C2×C22⋊C4—5622no—
127C2×C42—2811no—
128#102—22no—
129#102—5622no—
130#101—5622no—
131C24—21no—
132C2×Q8—2812no—
133C2×Q8—2812no—
134C2×Q8—5621no—
135C2×Q8—5621no—
136C2×Q8—5621no—
137C2×Q8—5621no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4C4×D28112yes—
144C22×C4—2812no—
145C22×C4—5621no—
146C22×C4C22×D28111yescharacteristic
147M16—21no—
148M16—21no—
149M16—5621no—
150M16—5621no—
151C2×C8—21no—
152C2×C8—5621no—
153C4⋊C4—2812no—
154C4⋊C4—5624no—
155C4⋊C4C22⋊D28112yes—
156C22⋊C4—21no—
157C22⋊C4—5628no—
158C22⋊C4—5621no—
159C42—21no—
160C42—2812no—
161C42—5624no—
162C42—5621no—
163C42—5621no—
164C23—22no—
165C23—44no—
166C23—41no—
167C23—41no—
168C23D4×D28111yescharacteristic
169Q8—5622no—
170Q8—5622no—
171Q8—5622no—
172Q8—5622no—
173D4—22no—
174D4—22no—
175D4—41no—
176D4—41no—
177C2×C4—22no—
178C2×C4—2814no—
179C2×C4—5622no—
180C2×C4—5622no—
181C2×C4—5622no—
182C2×C4—5622no—
183C2×C4—11242no—
184C2×C4C2×C4×D28111yescharacteristic
185C2×C4D4×D28111yescharacteristic
186C2×C4D4×D28111yescharacteristic
187C2×C4C2×C22⋊D28111yescharacteristic
188C2×C4#1798513711yescharacteristic
189C2×C4#1798513811yescharacteristic
190C8—41no—
191C8—11241no—
192C22—22no—
193C22—44no—
194C22—42no—
195C22—82no—
196C22—82no—
197C22C22⋊C4×D28111yescharacteristic
198C22#2258284711yescharacteristic
199C22#2258286111yescharacteristic
200C4—42no—
201C4—5624no—
202C4—11242no—
203C4—11242no—
204C4#2258283911yescharacteristic
205C4C4×C22⋊D28111yescharacteristic
206C4#2258285011yescharacteristic
207C4#2258285211yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#3182333911yescharacteristic
212C2#3182363412yes—
subgroupG/H
centerC22#22582847
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#418×C281C2
socleC22×C281#120
prime radicalC22×D4×C281C22
cosocleC22×C4×C281C23
hypercenter#418D281
hypocenterC281#1888
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #31823940C2semidirect
4. C2×#22582797C2semidirect
5. #31823224C2semidirect
6. #31823222C2semidirect
11. #22582866C4semidirect
106. C281#1888semidirect

Maximal subgroups

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

subgroupindex
C2×#225828662
#318239402
#318234682
C2×#225827972
#318232242
#318232222
#418×C2812
#1888281