Finite Group Databasebeta

← #49095705

Subgroups — #49095705

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×#22582867C211yesmaximal, characteristic
2#31823940C211yesmaximal, characteristic, complemented
3#31823469C211yesmaximal, characteristic
4#31823467C211yesmaximal, characteristic
5C2×#22582797C211yesmaximal, characteristic, complemented
6#31823223C211yesmaximal, characteristic, complemented
7#339×C281C211yesmaximal, characteristic, complemented
8C22×Dic562C2211yescharacteristic
9C22×D1124C2211yescharacteristic
10C2×#17985122C2211yescharacteristic
11#22582867—22no—
12#22582867C414yescomplemented
13C4×Dic562—22no—
14#22582844—22no—
15#22582838C2211yescharacteristic
16#22582835—22no—
17C2×#17985115—22no—
18#22582801—22no—
19#22582799—22no—
20#22582797—22no—
21C2×M16×C281C2211yescharacteristic
22#117×C281C2211yescharacteristic
23C2×C42×C281C2211yescharacteristic
24C23×D281—21no—
25C2×Dic562—21no—
26C2×Dic562—21no—
27C2×Dic562—21no—
28C2×Dic562—21no—
29C2×Dic562C2×C412yes—
30C2×Dic562D412yes—
31C2×D1124—21no—
32C2×D1124—21no—
33C2×D1124—21no—
34C2×D1124—21no—
35C2×D1124—21no—
36C2×D1124C2×C412yes—
37C22×Dic281D412yes—
38#17985122—21no—
39#17985122—21no—
40C2×#14555886—21no—
41C4⋊Dic281D412yes—
42#17985117—24no—
43C22⋊Dic281—21no—
44#17985115—28no—
45C4×Dic281—24no—
46C4×Dic281—21no—
47C22×C4×C281—21no—
48C22×C4×C281C2311yescharacteristic
49M16×C281—21no—
50M16×C281—21no—
51C2×C8×C281—21no—
52C4⋊C4×C281D412yes—
53C22⋊C4×C281—21no—
54C42×C281—21no—
55C42×C281—21no—
56C42×C281C2×C412yes—
57C22×D281—22no—
58C22×D281—44no—
59C22×D281—41no—
60C22×D281—41no—
61Dic562—22no—
62Dic562—22no—
63Dic562—22no—
64Dic562—22no—
65D1124—22no—
66D1124—22no—
67D1124—41no—
68D1124—41no—
69C2×Dic281—22no—
70C2×Dic281—22no—
71C2×Dic281—22no—
72C2×Dic281C22⋊C414yes—
73#14555886—41no—
74C23×C281C2×D411yescharacteristic
75C2×C4×C281—22no—
76C2×C4×C281—22no—
77C2×C4×C281—42no—
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×C281C2×C22⋊C411yescharacteristic
87C22×C281#12011yescharacteristic
88C22×C281#12311yescharacteristic
89C2×D281—44no—
90C2×D281—42no—
91C2×D281—82no—
92C2×D281—82no—
93C4×C281—42no—
94C4×C281—42no—
95C4×C281C4×D411yescharacteristic
96C4×C281C4×D411yescharacteristic
97C4×C281#12111yescharacteristic
98C4×C281#12111yescharacteristic
99Dic281—24no—
100Dic281—42no—
101C2×C281—21no—
102C2×C281—21no—
103C2×C281#38611yescharacteristic
104C2×C281#45412yes—
105D281—82no—
106C281#188811yescharacteristic, complemented, Sylow
107#1888—2811nomaximal, Sylow
108C2×#124—2811no—
109#519—2811no—
110#418—2811no—
111#418—2811no—
112C2×#101—2811no—
113#339—2811no—
114#339D28111yescharacteristic, complemented
115C22×Q8—2811no—
116C22×D4—2811no—
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×C42C2×D28111yescharacteristic
128#102—5622no—
129#102—5622no—
130#101—5622no—
131C24—5621no—
132C2×Q8—2812no—
133C2×Q8—2812no—
134C2×Q8—5621no—
135C2×Q8—5621no—
136C2×Q8—5621no—
137C2×Q8—5621no—
138C2×D4—2812no—
139C2×D4—5621no—
140C2×D4—5621no—
141C2×D4—5621no—
142C2×D4—5621no—
143C2×D4—5621no—
144C22×C4—21no—
145C22×C4—2812no—
146C22×C4C22×D28111yescharacteristic
147M16—21no—
148M16—21no—
149M16—5621no—
150M16—5621no—
151C2×C8—21no—
152C2×C8—5621no—
153C4⋊C4—2812no—
154C4⋊C4—5624no—
155C4⋊C4D112412yes—
156C22⋊C4—21no—
157C22⋊C4—5628no—
158C22⋊C4—5621no—
159C42—21no—
160C42—21no—
161C42—5624no—
162C42—5621no—
163C42C4×D28112yes—
164C23—5622no—
165C23—11244no—
166C23—11241no—
167C23—11241no—
168C23D4×D28111yescharacteristic
169Q8—5622no—
170Q8—5622no—
171Q8—5622no—
172Q8—5622no—
173D4—5622no—
174D4—5622no—
175D4—11241no—
176D4—11241no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—2814no—
181C2×C4—5622no—
182C2×C4—5622no—
183C2×C4—5622no—
184C2×C4C2×C4×D28111yescharacteristic
185C2×C4D4×D28111yescharacteristic
186C2×C4D4×D28111yescharacteristic
187C2×C4C2×D112411yescharacteristic
188C2×C4#1798513811yescharacteristic
189C2×C4#1798513911yescharacteristic
190C8—41no—
191C8—11241no—
192C22—22no—
193C22—11244no—
194C22—11242no—
195C22—22482no—
196C22—22482no—
197C22C22⋊C4×D28111yescharacteristic
198C22#2258284911yescharacteristic
199C22#2258286411yescharacteristic
200C4—42no—
201C4—42no—
202C4—5624no—
203C4—11242no—
204C4#2258284111yescharacteristic
205C4C4×D112411yescharacteristic
206C4#2258285211yescharacteristic
207C4#2258285411yescharacteristic
208C2—21no—
209C2—21no—
210C2—22482no—
211C2#3182334111yescharacteristic
212C2#3182363712yes—
subgroupG/H
centerC22#22582849
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#339×C281C2
socleC22×C281#120
prime radicalC22×D1124C22
cosocleC22×C4×C281C23
hypercenter#339D281
hypocenterC281#1888
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #31823940C2semidirect
5. C2×#22582797C2semidirect
6. #31823223C2semidirect
7. #339×C281C2semidirect
12. #22582867C4semidirect
106. C281#1888semidirect
114. #339D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828672
#318239402
#318234692
#318234672
C2×#225827972
#318232232
#339×C2812
#1888281