Finite Group Databasebeta

← #49097250

Subgroups — #49097250

Order 35968.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#31824260C211yesmaximal, characteristic, complemented
2#31823901C211yesmaximal, characteristic, complemented
3#31823898C211yesmaximal, characteristic, complemented
4#31823717C211yesmaximal, characteristic, complemented
5#31823272C211yesmaximal, characteristic, complemented
6#31823244C211yesmaximal, characteristic, complemented
7#360×C281C211yesmaximal, characteristic, complemented
8#41×D281—21no—
9#22582911—21no—
10#22582908—21no—
11#22582906—21no—
12#22582903—21no—
13#22582901C2211yescharacteristic
14#22582899—21no—
15C2×D2248C2211yescharacteristic, complemented
16C2×#17985121C2211yescharacteristic
17#22582854—21no—
18#22582824—21no—
19#22582822—21no—
20D4496—21no—
21#22582820—21no—
22#22582819C2211yescharacteristic, complemented
23#22582799—21no—
24#135×C281C2211yescharacteristic
25M32×C281C2211yescharacteristic, complemented
26#106×C281C2211yescharacteristic, complemented
27#17985139—21no—
28#17985138—21no—
29#17985138—41no—
30#17985137—21no—
31#17985137—41no—
32Q8×D281—21no—
33C2×D1124—21no—
34C2×D1124—41no—
35D4×D281—21no—
36D4×D281—41no—
37C2×C4×D281—41no—
38C2×C4×D281D411yescharacteristic
39Dic1124D411yescharacteristic, complemented
40#17985128—21no—
41#17985127—21no—
42#17985126—21no—
43#17985125—21no—
44D2248—21no—
45D2248—21no—
46D2248D411yescharacteristic, complemented
47#17985123—21no—
48#17985121—21no—
49#17985121—21no—
50C2×#14555886D411yescharacteristic
51#17985115—41no—
52#17985113—21no—
53#41×C281—21no—
54Q16×C281D411yescharacteristic, complemented
55SD16×C281—21no—
56D8×C281D411yescharacteristic, complemented
57C2×C8×C281C2311yescharacteristic
58C4⋊C4×C281—21no—
59C16×C281—21no—
60C22×D281—41no—
61C22×D281—41no—
62C22×D281D811yescharacteristic
63Dic562—21no—
64Dic562—41no—
65D1124—21no—
66D1124—41no—
67D1124—41no—
68D1124—41no—
69D1124—82no—
70C22⋊D281—41no—
71C22⋊D281—41no—
72C22⋊D281—41no—
73C2×Dic281—41no—
74C2×Dic281D811yescharacteristic
75C4×D281—21no—
76C4×D281—21no—
77C4×D281—41no—
78C4×D281—41no—
79C4×D281—41no—
80#14555886—21no—
81Q8×C281—21no—
82D4×C281—21no—
83D4×C281—41no—
84C2×C4×C281—41no—
85C2×C4×C281—41no—
86C2×C4×C281C2×D411yescharacteristic
87C8×C281C2×D411yescharacteristic
88C8×C281C2×D411yescharacteristic
89C22×C281—41no—
90C22×C281C2×D811yescharacteristic
91C2×D281—21no—
92C2×D281—41no—
93C2×D281—41no—
94C2×D281—82no—
95C2×D281—81no—
96C2×D281—81no—
97C2×D281—81no—
98C4×C281—41no—
99C4×C281—81no—
100C4×C281#12011yescharacteristic
101C4×C281AGL(1,ℤ/8)11yescharacteristic
102Dic281—21no—
103Dic281—41no—
104C2×C281—21no—
105C2×C281—81no—
106C2×C281#44711yescharacteristic
107D281—41no—
108D281—81no—
109D281—161no—
110C281#219011yescharacteristic, complemented, Sylow
111#2190—2811nomaximal, Sylow
112#575—2811no—
113#509—2811no—
114#509—2811no—
115#469—2811no—
116#360—2811no—
117#360D28111yescharacteristic, complemented
118#349—2811no—
119C2×#41—5621no—
120#137—5621no—
121#137—5621no—
122AGL(1,ℤ/8)—5621no—
123AGL(1,ℤ/8)—5621no—
124#135—2811no—
125#135—5621no—
126#135C2×D28111yescharacteristic
127C2×D8—2811no—
128C2×M16—2811no—
129#121—5621no—
130SD32—5621no—
131SD32—5621no—
132D16—5621no—
133D16—5621no—
134M32—2811no—
135M32C2×D28111yescharacteristic, complemented
136#106C2×D28111yescharacteristic, complemented
137#102—5621no—
138#41—21no—
139#41—5621no—
140#41—5621no—
141#41—5621no—
142#41—11241no—
143#41—11241no—
144C2×Q8—5621no—
145C2×D4—5621no—
146C2×D4—5621no—
147C2×D4—11241no—
148C2×D4—11241no—
149C22×C4—2811no—
150C22×C4—11241no—
151Q16—2811no—
152Q16—5621no—
153Q16D112411yescharacteristic, complemented
154SD16—21no—
155SD16—5621no—
156SD16—5621no—
157SD16—5621no—
158D8—2811no—
159D8—5621no—
160D8—5621no—
161D8—5621no—
162D8D112411yescharacteristic, complemented
163M16—5621no—
164M16—5621no—
165C2×C8—2811no—
166C2×C8C22×D28111yescharacteristic
167C4⋊C4—21no—
168C22⋊C4—11241no—
169C16—21no—
170C16—5621no—
171C23—2811no—
172C23—11241no—
173C23—11241no—
174Q8—21no—
175Q8—5621no—
176Q8—11241no—
177D4—21no—
178D4—41no—
179D4—5621no—
180D4—11241no—
181D4—11241no—
182D4—11241no—
183D4—11241no—
184D4—11241no—
185D4—11241no—
186D4—22482no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2811no—
190C2×C4—5621no—
191C2×C4—5621no—
192C2×C4—11241no—
193C2×C4—11241no—
194C2×C4—11241no—
195C2×C4—11241no—
196C2×C4D4×D28111yescharacteristic
197C8—5621no—
198C8D4×D28111yescharacteristic
199C8C2×D112411yescharacteristic
200C22—41no—
201C22—5621no—
202C22—11241no—
203C22—11241no—
204C22—22481no—
205C22—22481no—
206C22—22482no—
207C22—22481no—
208C22D8×D28111yescharacteristic
209C4—41no—
210C4—81no—
211C4—5621no—
212C4—11241no—
213C4#2258284911yescharacteristic
214C4#2258290611yescharacteristic
215C2—21no—
216C2—81no—
217C2—11241no—
218C2—44961no—
219C2—22481no—
220C2#3182359811yescharacteristic
subgroupG/H
centerC2#31823598
commutator, cosocleC2×C8×C281C23
FrattiniC2×C8C22×D281
Fitting#360×C281C2
socleC2×C281#447
hypercenter#360D281
hypocenterC281#2190
LCSG ▷ C2×C8×C281 ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
1. #31824260C2semidirect
2. #31823901C2semidirect
3. #31823898C2semidirect
4. #31823717C2semidirect
5. #31823272C2semidirect
6. #31823244C2semidirect
7. #360×C281C2semidirect
15. C2×D2248C22semidirect
22. #22582819C22semidirect
25. M32×C281C22semidirect
26. #106×C281C22semidirect
39. Dic1124D4semidirect
46. D2248D4semidirect
54. Q16×C281D4semidirect
56. D8×C281D4semidirect
110. C281#2190semidirect
117. #360D281semidirect
135. M32C2×D281semidirect
136. #106C2×D281semidirect
153. Q16D1124semidirect
162. D8D1124semidirect

Maximal subgroups

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

subgroupindex
#318242602
#318239012
#318238982
#318237172
#318232722
#318232442
#360×C2812
#2190281