Finite Group Databasebeta

← #49095261

Subgroups — #49095261

Order 35968.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22582927C211yesmaximal, characteristic
2C2×#22582807C212yesmaximal, complemented
3#31823462C212yesmaximal, complemented
4C2×#22582798C211yesmaximal, characteristic, complemented
5#391×C281C211yesmaximal, characteristic, complemented
6#22582927—24no—
7#22582927—22no—
8#22582927C414yescomplemented
9C2×#17985139—22no—
10C2×#17985138—22no—
11C2×#17985138C2212yes—
12C2×Q8×D281—22no—
13C2×#17985122C2212yes—
14#22582807—24no—
15#22582802—22no—
16#22582799—22no—
17#22582798—22no—
18C22×Q8×C281C2211yescharacteristic
19C2×C4⋊C4×C281C2211yescharacteristic
20C2×C42×C281C2211yescharacteristic
21#95×C281—22no—
22#17985139—28no—
23#17985139—28no—
24#17985138—28no—
25#17985138—28no—
26#17985138—22no—
27#17985138—22no—
28#17985138C2×C414yes—
29#17985138D414yes—
30C2×Dic562—22no—
31C2×Dic562D412yes—
32Q8×D281—28no—
33Q8×D281—28no—
34C2×D1124—22no—
35C2×D1124D412yes—
36C2×C22⋊D281—22no—
37C2×C4×D281—24no—
38C2×C4×D281—22no—
39#17985122—22no—
40#17985122—22no—
41C2×#14555886—22no—
42C2×Q8×C281—22no—
43C2×Q8×C281—22no—
44C2×Q8×C281C2×C412yes—
45C2×Q8×C281D412yes—
46C22×C4×C281—21no—
47C22×C4×C281—21no—
48C22×C4×C281D412yes—
49C22×C4×C281C2311yescharacteristic
50C4⋊C4×C281—22no—
51C42×C281—22no—
52C22×D281—22no—
53Dic562—28no—
54Dic562—22no—
55Dic562C22⋊C414yes—
56D1124—28no—
57D1124—22no—
58D1124C22⋊C414yes—
59C22⋊D281—24no—
60C22⋊D281—24no—
61C2×Dic281—22no—
62C4×D281—216no—
63C4×D281—24no—
64C4×D281—24no—
65#14555886—42no—
66C23×C281C2×D411yescharacteristic
67Q8×C281—24no—
68Q8×C281—24no—
69C2×C4×C281—22no—
70C2×C4×C281—22no—
71C2×C4×C281—22no—
72C2×C4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281—42no—
75C2×C4×C281—41no—
76C2×C4×C281C22⋊C414yes—
77C2×C4×C281C22×C411yescharacteristic
78C2×C4×C281C2×D412yes—
79C2×C4×C281C2×D412yes—
80C2×C4×C281C2×D411yescharacteristic
81C22×C281—21no—
82C22×C281—21no—
83C22×C281C2×C22⋊C411yescharacteristic
84C22×C281#12011yescharacteristic
85C22×C281#12011yescharacteristic
86C2×D281—24no—
87C2×D281—42no—
88C2×D281—42no—
89C4×C281—24no—
90C4×C281—42no—
91C4×C281—81no—
92C4×C281C2×C22⋊C412yes—
93C4×C281#12012yes—
94Dic281—24no—
95C2×C281—21no—
96C2×C281—21no—
97C2×C281#37911yescharacteristic
98C2×C281#45411yescharacteristic
99C2×C281#45611yescharacteristic
100D281—44no—
101C281#179311yescharacteristic, complemented, Sylow
102#1793—2811nomaximal, Sylow
103C2×2−1+4—2811no—
104C2×#104—2812no—
105#417—2812no—
106C2×#101—2811no—
107#391D28111yescharacteristic, complemented
1082−1+4—2814no—
1092−1+4—5624no—
1102−1+4—5622no—
111C2×#41—2812no—
112C2×#41—5622no—
113C2×#41—5622no—
114C22×Q8—5622no—
115C22×Q8C2×D28111yescharacteristic
116C2×M16—2812no—
117C2×C4⋊C4C2×D28111yescharacteristic
118C2×C42C2×D28111yescharacteristic
119#104—5624no—
120#103—5622no—
121#102—5622no—
122#101—5622no—
123#95—22no—
124#41—2814no—
125#41—2814no—
126#41—5628no—
127#41—5628no—
128#41—5628no—
129#41—5628no—
130#41—5622no—
131#41—5622no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—2812no—
135C2×Q8—5622no—
136C2×Q8—5628no—
137C2×Q8—5628no—
138C2×Q8C4×D28112yes—
139C2×Q8D112412yes—
140C2×D4—2812no—
141C2×D4—5622no—
142C2×D4—5622no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—5624no—
146C22×C4—5622no—
147C22×C4C22⋊D28112yes—
148C22×C4C22×D28111yescharacteristic
149M16—5622no—
150M16—5622no—
151C2×C8—5622no—
152C4⋊C4—22no—
153C42—22no—
154C23—5622no—
155C23C2×C22⋊D28111yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—2814no—
159Q8—5628no—
160Q8—5622no—
161D4—2814no—
162D4—5628no—
163D4—5624no—
164D4—5624no—
165D4—5622no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—56216no—
174C2×C4—5622no—
175C2×C4—5624no—
176C2×C4—5624no—
177C2×C4#1798511514yes—
178C2×C4C2×C4×D28111yescharacteristic
179C2×C4D4×D28112yes—
180C2×C4D4×D28112yes—
181C2×C4C2×D112411yescharacteristic
182C8—11242no—
183C22—21no—
184C22—21no—
185C22—5624no—
186C22—11242no—
187C22—11242no—
188C22C2×#1798511511yescharacteristic
189C22#2258284711yescharacteristic
190C22#2258284711yescharacteristic
191C4—24no—
192C4—42no—
193C4—81no—
194C4—5624no—
195C4C22⋊C4×D28112yes—
196C4#2258284912yes—
197C2—21no—
198C2—21no—
199C2—11244no—
200C2#3182331811yescharacteristic
201C2#3182363511yescharacteristic
202C2#3182364511yescharacteristic
subgroupG/H
centerC22#22582847
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#391×C281C2
socleC22×C281#120
prime radicalC2×#22582927C2
cosocleC22×C4×C281C23
hypercenter#391D281
hypocenterC281#1793
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#22582807C2semidirect
3. #31823462C2semidirect
4. C2×#22582798C2semidirect
5. #391×C281C2semidirect
8. #22582927C4semidirect
101. C281#1793semidirect
107. #391D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225829272
C2×#225828072
#318234622
C2×#225827982
#391×C2812
#1793281