Finite Group Databasebeta

← #49095824

Subgroups — #49095824

Order 35968.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#31824229C211yesmaximal, characteristic
2#31824039C211yesmaximal, characteristic
3#31823473C211yesmaximal, characteristic, complemented
4#31823471C211yesmaximal, characteristic, complemented
5#31823436C211yesmaximal, characteristic
6#31823219C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C281C211yesmaximal, characteristic, complemented
8C2×#17985138C2211yescharacteristic
9C22×Dic562C2211yescharacteristic
10#22582887—22no—
11#22582885—22no—
12C2×#17985122C2211yescharacteristic
13M16×D281—22no—
14#22582879C412yescomplemented
15#22582867C412yescomplemented
16#22582863—22no—
17#22582859—22no—
18#22582838C2211yescharacteristic
19#22582804—22no—
20#22582802—22no—
21#22582793—22no—
22C2×M16×C281C2211yescharacteristic
23#117×C281C2211yescharacteristic
24#117×C281C2211yescharacteristic
25#17985138—21no—
26#17985138—21no—
27#17985138—21no—
28#17985138—21no—
29C2×Dic562—21no—
30C2×Dic562—21no—
31C2×Dic562—21no—
32C2×Dic562—21no—
33C2×Dic562—21no—
34C2×Dic562C2×C412yes—
35C2×Dic562C2×C411yescharacteristic
36C2×D1124C2×C411yescharacteristic
37C2×C22⋊D281D412yes—
38C22×Dic281—21no—
39C2×C4×D281D412yes—
40#17985122—21no—
41#17985122—21no—
42#17985121—24no—
43C2×#14555886D412yes—
44C8×D281—24no—
45C4⋊Dic281—24no—
46C4⋊Dic281—21no—
47C22⋊Dic281—21no—
48#17985115—24no—
49C4×Dic281—21no—
50C22×C4×C281C2311yescharacteristic
51M16×C281—21no—
52M16×C281—21no—
53C2×C8×C281D412yes—
54C4⋊C4×C281—21no—
55C4⋊C4×C281—21no—
56C22⋊C4×C281—21no—
57C22⋊C4×C281—21no—
58C42×C281—21no—
59C42×C281C2×C412yes—
60C22×D281C22⋊C412yes—
61Dic562—21no—
62Dic562—21no—
63Dic562—22no—
64Dic562—22no—
65Dic562—41no—
66Dic562—41no—
67D1124—21no—
68D1124—21no—
69C22⋊D281—22no—
70C22⋊D281—22no—
71C2×Dic281—22no—
72C2×Dic281—41no—
73C2×Dic281—41no—
74C2×Dic281—41no—
75C2×Dic281C22⋊C412yes—
76C4×D281—22no—
77C4×D281—22no—
78#14555886—22no—
79C23×C281C2×D411yescharacteristic
80C2×C4×C281—22no—
81C2×C4×C281—41no—
82C2×C4×C281C22×C411yescharacteristic
83C2×C4×C281C2×D411yescharacteristic
84C2×C4×C281C2×D411yescharacteristic
85C2×C4×C281C2×D411yescharacteristic
86C2×C4×C281#4111yescharacteristic
87C2×C4×C281#4111yescharacteristic
88C8×C281—22no—
89C22×C281—41no—
90C22×C281C2×C22⋊C411yescharacteristic
91C22×C281#12111yescharacteristic
92C22×C281#12111yescharacteristic
93C2×D281—22no—
94C2×D281—42no—
95C4×C281—42no—
96C4×C281—81no—
97C4×C281C4×D411yescharacteristic
98C4×C281C4×D411yescharacteristic
99C4×C281#12011yescharacteristic
100C4×C281#12311yescharacteristic
101Dic281—22no—
102Dic281—42no—
103Dic281—81no—
104C2×C281—21no—
105C2×C281—21no—
106C2×C281—21no—
107C2×C281#38611yescharacteristic
108D281—42no—
109C281#190911yescharacteristic, complemented, Sylow
110#1909—2811nomaximal, Sylow
111#568—2811no—
112#536—2811no—
113#419—2811no—
114#419—2811no—
115#410—2811no—
116H(3,ℤ/4)—2811no—
117H(3,ℤ/4)D28111yescharacteristic, complemented
118C2×#41—2811no—
119C22×Q8—2811no—
120#131—5622no—
121#131—5622no—
122C2×M16—2811no—
123C2×M16—5622no—
124C2×M16C2×D28111yescharacteristic
125C4⋊Q8—2812no—
126#124—2812no—
127#123—5622no—
128C22⋊Q8—5622no—
129#117—2811no—
130#117C2×D28111yescharacteristic
131#117C2×D28111yescharacteristic
132#103—5622no—
133#103—5622no—
134#99—5622no—
135#41—5621no—
136#41—5621no—
137#41—5621no—
138#41—5621no—
139C2×Q8—2811no—
140C2×Q8—2812no—
141C2×Q8—5621no—
142C2×Q8—5621no—
143C2×Q8—5621no—
144C2×Q8—5621no—
145C2×Q8—5621no—
146C2×D4—2812no—
147C2×D4—2811no—
148C22×C4—2812no—
149C22×C4—5621no—
150C22×C4C22×D28111yescharacteristic
151M16—21no—
152M16—21no—
153M16—5624no—
154M16—5621no—
155M16—5621no—
156C2×C8—2812no—
157C2×C8—5624no—
158C2×C8D112412yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—5624no—
162C4⋊C4—5621no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—5624no—
166C22⋊C4—5621no—
167C42—21no—
168C42—5621no—
169C42C4×D28112yes—
170C23—2812no—
171C23D4×D28111yescharacteristic
172Q8—5621no—
173Q8—5621no—
174Q8—5622no—
175Q8—5622no—
176Q8—11241no—
177Q8—11241no—
178D4—5622no—
179D4—5622no—
180D4—5621no—
181D4—5621no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—2812no—
185C2×C4—5622no—
186C2×C4—5622no—
187C2×C4—5622no—
188C2×C4—11241no—
189C2×C4—11241no—
190C2×C4—11241no—
191C2×C4C2×C4×D28111yescharacteristic
192C2×C4D4×D28111yescharacteristic
193C2×C4D4×D28111yescharacteristic
194C2×C4C2×D112411yescharacteristic
195C2×C4#1798513811yescharacteristic
196C2×C4#1798513911yescharacteristic
197C8—22no—
198C8—5622no—
199C22—41no—
200C22—5622no—
201C22—11242no—
202C22C22⋊C4×D28111yescharacteristic
203C22#2258285211yescharacteristic
204C22#2258285411yescharacteristic
205C4—42no—
206C4—81no—
207C4—5622no—
208C4—11242no—
209C4—22481no—
210C4#2258284111yescharacteristic
211C4C4×D112411yescharacteristic
212C4#2258284911yescharacteristic
213C4#2258286411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—11242no—
218C2#3182334111yescharacteristic
subgroupG/H
centerC2#31823341
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
FittingH(3,ℤ/4)×C281C2
socleC2×C281#386
prime radicalC2×#17985138C22
cosocleC22×C4×C281C23
hypercenterH(3,ℤ/4)D281
hypocenterC281#1909
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
3. #31823473C2semidirect
4. #31823471C2semidirect
6. #31823219C2semidirect
7. H(3,ℤ/4)×C281C2semidirect
14. #22582879C4semidirect
15. #22582867C4semidirect
109. C281#1909semidirect
117. H(3,ℤ/4)D281semidirect

Maximal subgroups

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

subgroupindex
#318242292
#318240392
#318234732
#318234712
#318234362
#318232192
H(3,ℤ/4)×C2812
#1909281