Finite Group Databasebeta

← #49095253

Subgroups — #49095253

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#31823447C211yesmaximal, characteristic, complemented
3#31823445C212yesmaximal, complemented
4#31823429C212yesmaximal, complemented
5#408×C281C211yesmaximal, characteristic, complemented
6#22582927—21no—
7#22582926—22no—
8#22582925—22no—
9#22582924—21no—
10#22582924C414yes—
11C2×#17985138—22no—
12C2×#17985138C2212yes—
13#41×D281—24no—
14C2×#17985122C2212yescomplemented
15#22582798—21no—
16#22582797—22no—
17#22582796—21no—
18#22582795—22no—
19#22582791—24no—
20C2×#41×C281C2211yescharacteristic
21C2×M16×C281C2211yescharacteristic, complemented
22C22×C8×C281C2211yescharacteristic, complemented
23C22⋊C8×C281—22no—
24#17985139—24no—
25#17985138—24no—
26#17985138—24no—
27#17985138—24no—
28#17985138—22no—
29#17985138—22no—
30#17985138—22no—
31#17985138—22no—
32#17985137—24no—
33#17985137—28no—
34C2×Dic562—22no—
35C2×Dic562D412yes—
36Q8×D281—24no—
37C2×D1124—22no—
38C2×D1124D412yes—
39C2×C22⋊D281—24no—
40C2×C22⋊D281C2×C414yes—
41D4×D281—24no—
42D4×D281—28no—
43C2×C4×D281—24no—
44C2×C4×D281D414yes—
45#17985122—22no—
46#17985122—22no—
47C2×#14555886—22no—
48#41×C281—22no—
49#41×C281—22no—
50C2×Q8×C281D411yescharacteristic
51C2×D4×C281C2×C412yes—
52C2×D4×C281D411yescharacteristic
53C22×C4×C281D412yes—
54C22×C4×C281C2311yescharacteristic
55M16×C281—22no—
56C2×C8×C281—22no—
57C2×C8×C281—21no—
58C2×C8×C281—21no—
59C22×D281—24no—
60C22×D281C22⋊C414yes—
61Dic562—24no—
62Dic562—22no—
63Dic562—22no—
64D1124—24no—
65D1124—22no—
66D1124—22no—
67C22⋊D281—28no—
68C22⋊D281—24no—
69C22⋊D281—24no—
70C2×Dic281—24no—
71C2×Dic281C22⋊C414yes—
72C4×D281—28no—
73C4×D281—24no—
74C4×D281—24no—
75#14555886—42no—
76C23×C281C22⋊C412yes—
77C23×C281C22×C411yescharacteristic
78Q8×C281—22no—
79D4×C281—24no—
80D4×C281—22no—
81C2×C4×C281—22no—
82C2×C4×C281—22no—
83C2×C4×C281C22⋊C412yes—
84C2×C4×C281C2×D412yes—
85C2×C4×C281C2×D412yes—
86C2×C4×C281C2×D411yescharacteristic
87C2×C4×C281C2×D411yescharacteristic
88C8×C281—41no—
89C8×C281—41no—
90C22×C281—22no—
91C22×C281—41no—
92C22×C281—42no—
93C22×C281C2×C22⋊C412yes—
94C22×C281C2×C22⋊C411yescharacteristic
95C2×D281—24no—
96C2×D281—44no—
97C2×D281—84no—
98C4×C281—22no—
99C4×C281#12011yescharacteristic
100C4×C281#12011yescharacteristic
101C4×C281#12012yes—
102Dic281—24no—
103C2×C281—22no—
104C2×C281—21no—
105C2×C281—42no—
106C2×C281#37911yescharacteristic
107D281—44no—
108C281#179111yescharacteristic, complemented, Sylow
109#1791—2811nomaximal, Sylow
110#585—2811no—
111#413—2811no—
112#413—2812no—
113#408—2812no—
114#408D28111yescharacteristic, complemented
1152−1+4—5622no—
1162−1+4—5621no—
117H(5,𝔽2)—2814no—
118H(5,𝔽2)—5622no—
119H(5,𝔽2)—5621no—
120C2×#41—2812no—
121C2×#41—5624no—
122C2×#41—5622no—
123C2×#41C2×D28111yescharacteristic
124C2×M16—2812no—
125C2×M16C2×D28111yescharacteristic, complemented
126C22×C8C2×D28111yescharacteristic, complemented
127#101—5622no—
128#101—5621no—
129#100—5622no—
130#100—5621no—
131C22⋊C8—22no—
132C22⋊C8—5624no—
133#41—22no—
134#41—22no—
135#41—5624no—
136#41—5624no—
137#41—5628no—
138#41—5624no—
139#41—5624no—
140#41—5624no—
141#41—5622no—
142#41—5622no—
143#41—5622no—
144#41—5622no—
145C2×Q8—2812no—
146C2×Q8—5622no—
147C2×Q8—5624no—
148C2×Q8D112411yescharacteristic
149C2×D4—2814no—
150C2×D4—2812no—
151C2×D4—5622no—
152C2×D4—5628no—
153C2×D4—5624no—
154C2×D4—5624no—
155C2×D4C4×D28112yes—
156C2×D4D112411yescharacteristic
157C22×C4—2814no—
158C22×C4—5624no—
159C22×C4C22⋊D28112yes—
160C22×C4C22×D28111yescharacteristic
161M16—22no—
162M16—5622no—
163M16—5622no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—5622no—
168C23—2814no—
169C23—5624no—
170C23#1798511512yes—
171C23C2×C4×D28111yescharacteristic
172Q8—22no—
173Q8—5624no—
174Q8—5622no—
175Q8—5622no—
176D4—24no—
177D4—22no—
178D4—5624no—
179D4—5628no—
180D4—5624no—
181D4—5624no—
182D4—5622no—
183D4—5622no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—2814no—
187C2×C4—5628no—
188C2×C4—5624no—
189C2×C4—5624no—
190C2×C4—5624no—
191C2×C4#1798511512yes—
192C2×C4D4×D28112yes—
193C2×C4D4×D28112yes—
194C2×C4C2×C22⋊D28111yescharacteristic
195C2×C4C2×D112411yescharacteristic
196C8—41no—
197C8—41no—
198C8—11242no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—5624no—
203C22—11244no—
204C22—22484no—
205C22C22⋊C4×D28112yes—
206C22C2×#1798511511yescharacteristic
207C4—22no—
208C4—5624no—
209C4#2258284711yescharacteristic
210C4#2258284711yescharacteristic
211C4#2258284912yes—
212C2—21no—
213C2—22no—
214C2—42no—
215C2—11244no—
216C2#3182331811yescharacteristic
subgroupG/H
centerC4#22582847
commutatorC23×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#408×C281C2
socleC2×C281#379
prime radical#31824299C2
cosocleC22×C4×C281C23
hypercenter#408D281
hypocenterC281#1791
LCSG ▷ C23×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #31823447C2semidirect
3. #31823445C2semidirect
4. #31823429C2semidirect
5. #408×C281C2semidirect
14. C2×#17985122C22semidirect
21. C2×M16×C281C22semidirect
22. C22×C8×C281C22semidirect
108. C281#1791semidirect
114. #408D281semidirect
125. C2×M16C2×D281semidirect
126. C22×C8C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318242992
#318234472
#318234452
#318234292
#408×C2812
#1791281