Finite Group Databasebeta

← #49095269

Subgroups — #49095269

Order 35968.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#31824299C211yesmaximal, characteristic
2#31823481C212yesmaximal, complemented
3#31823457C212yesmaximal, complemented
4#31823430C211yesmaximal, characteristic, complemented
5#410×C281C211yesmaximal, characteristic, complemented
6#22582927C412yescomplemented
7#22582926—22no—
8#22582925—22no—
9#22582924—22no—
10#22582924C412yescomplemented
11C2×#17985138—22no—
12C2×#17985138C2212yes—
13#41×D281—24no—
14C2×#17985122C2211yescharacteristic, complemented
15C22×#14555886C2211yescharacteristic, complemented
16#22582807—24no—
17#22582802—22no—
18#22582799—22no—
19C22⋊#14555886—22no—
20C2×#41×C281C2211yescharacteristic
21#117×C281C2212yescomplemented
22#99×C281—22no—
23#17985139—24no—
24#17985138—24no—
25#17985138—24no—
26#17985138—24no—
27#17985138—22no—
28#17985138—22no—
29#17985138C2×C414yes—
30#17985138D414yes—
31#17985137—28no—
32#17985137—24no—
33C2×Dic562—22no—
34C2×Dic562D412yes—
35Q8×D281—24no—
36C2×D1124—22no—
37C2×D1124D412yes—
38C2×C22⋊D281—24no—
39C2×C22⋊D281—22no—
40D4×D281—28no—
41D4×D281—24no—
42C2×C4×D281—24no—
43C2×C4×D281—22no—
44#17985122—22no—
45C2×#14555886—21no—
46C2×#14555886—21no—
47C2×#14555886—22no—
48#41×C281—22no—
49#41×C281—22no—
50C2×Q8×C281C2×C411yescharacteristic
51C2×D4×C281C2×C411yescharacteristic
52C2×D4×C281D412yes—
53C22×C4×C281D412yes—
54C22×C4×C281C2311yescharacteristic
55C4⋊C4×C281—22no—
56C22⋊C4×C281—22no—
57C42×C281—22no—
58C22×D281—24no—
59C22×D281—22no—
60Dic562—24no—
61Dic562—22no—
62Dic562C22⋊C414yes—
63D1124—24no—
64D1124—22no—
65D1124C22⋊C414yes—
66C22⋊D281—28no—
67C22⋊D281—24no—
68C22⋊D281—24no—
69C2×Dic281—24no—
70C2×Dic281—22no—
71C4×D281—28no—
72C4×D281—24no—
73C4×D281—24no—
74#14555886—41no—
75#14555886—41no—
76C23×C281C22⋊C412yes—
77C23×C281C2×D411yescharacteristic
78Q8×C281—22no—
79D4×C281—24no—
80D4×C281—22no—
81C2×C4×C281—22no—
82C2×C4×C281—22no—
83C2×C4×C281—42no—
84C2×C4×C281C22⋊C412yes—
85C2×C4×C281C22×C411yescharacteristic
86C2×C4×C281C2×D412yes—
87C2×C4×C281C2×D412yes—
88C2×C4×C281C2×D411yescharacteristic
89C22×C281—22no—
90C22×C281—41no—
91C22×C281—42no—
92C22×C281C2×C22⋊C411yescharacteristic
93C22×C281#12012yes—
94C2×D281—24no—
95C2×D281—82no—
96C2×D281—84no—
97C4×C281—22no—
98C4×C281—82no—
99C4×C281C2×C22⋊C412yes—
100C4×C281#12011yescharacteristic
101C4×C281#12011yescharacteristic
102Dic281—24no—
103C2×C281—22no—
104C2×C281—21no—
105C2×C281—42no—
106C2×C281#37911yescharacteristic
107D281—44no—
108C281#179411yescharacteristic, complemented, Sylow
109#1794—2811nomaximal, Sylow
110#585—2811no—
111#421—2812no—
112#416—2812no—
113#410D28111yescharacteristic, complemented
114#408—2811no—
1152−1+4—2812no—
1162−1+4—5622no—
117H(5,𝔽2)—2812no—
118H(5,𝔽2)—5622no—
119H(5,𝔽2)—5622no—
120C2×#41—2812no—
121C2×#41—5624no—
122C2×#41—5622no—
123C2×#41C2×D28111yescharacteristic
124C2×M16—2811no—
125C22×C8—2811no—
126#117C2×D28112yescomplemented
127#104—5624no—
128#103—5622no—
129#102—5622no—
130#99—22no—
131C22⋊C8—5622no—
132#41—22no—
133#41—22no—
134#41—2814no—
135#41—2814no—
136#41—5624no—
137#41—5624no—
138#41—5624no—
139#41—5628no—
140#41—5624no—
141#41—5624no—
142#41—5622no—
143#41—5622no—
144C2×Q8—2812no—
145C2×Q8—5622no—
146C2×Q8—5624no—
147C2×Q8C4×D28111yescharacteristic
148C2×D4—2812no—
149C2×D4—5622no—
150C2×D4—5624no—
151C2×D4—5628no—
152C2×D4—5624no—
153C2×D4—5622no—
154C2×D4C4×D28111yescharacteristic
155C2×D4C22⋊D28112yes—
156C22×C4—5624no—
157C22×C4—5622no—
158C22×C4D112412yes—
159C22×C4C22×D28111yescharacteristic
160M16—5622no—
161C2×C8—5622no—
162C2×C8—5621no—
163C2×C8—5621no—
164C4⋊C4—22no—
165C22⋊C4—22no—
166C42—22no—
167C23—5624no—
168C23—5622no—
169C23#1798511512yes—
170C23C2×C22⋊D28111yescharacteristic
171Q8—22no—
172Q8—2814no—
173Q8—5624no—
174Q8—5622no—
175D4—24no—
176D4—22no—
177D4—2814no—
178D4—5624no—
179D4—5628no—
180D4—5624no—
181D4—5624no—
182D4—5622no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—5628no—
187C2×C4—5624no—
188C2×C4—5622no—
189C2×C4—5624no—
190C2×C4—5624no—
191C2×C4#1798511512yes—
192C2×C4C2×C4×D28111yescharacteristic
193C2×C4D4×D28112yes—
194C2×C4D4×D28112yes—
195C2×C4C2×D112411yescharacteristic
196C8—11241no—
197C8—11241no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—5624no—
202C22—22482no—
203C22—22484no—
204C22C2×#1798511511yescharacteristic
205C22#2258284712yes—
206C4—22no—
207C4—82no—
208C4—5624no—
209C4C22⋊C4×D28112yes—
210C4#2258284911yescharacteristic
211C4#2258284911yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—11244no—
216C2#3182331811yescharacteristic
subgroupG/H
centerC4#22582849
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#410×C281C2
socleC2×C281#379
prime radical#31824299C2
cosocleC22×C4×C281C23
hypercenter#410D281
hypocenterC281#1794
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #31823481C2semidirect
3. #31823457C2semidirect
4. #31823430C2semidirect
5. #410×C281C2semidirect
6. #22582927C4semidirect
10. #22582924C4semidirect
14. C2×#17985122C22semidirect
15. C22×#14555886C22semidirect
21. #117×C281C22semidirect
108. C281#1794semidirect
113. #410D281semidirect
126. #117C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318242992
#318234812
#318234572
#318234302
#410×C2812
#1794281