Finite Group Databasebeta

← #49095519

Subgroups — #49095519

Order 35968.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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#31823940C211yesmaximal, characteristic
2#31823506C211yesmaximal, characteristic
3#31823505C211yesmaximal, characteristic
4C2×#22582797C211yesmaximal, characteristic
5#31823369C211yesmaximal, characteristic
6#31823223C211yesmaximal, characteristic
7#339×C281C211yesmaximal, characteristic
8C22×Dic562C2211yescharacteristic
9C2×#17985122C2211yescharacteristic
10C4×Dic562—21no—
11C4×Dic562—21no—
12#22582844—21no—
13#22582844—21no—
14#22582838C2211yescharacteristic
15#22582835—22no—
16C2×C4⋊Dic281C2211yescharacteristic
17#22582813—21no—
18#22582812—21no—
19#22582811—21no—
20#22582810—21no—
21#22582797C414yescomplemented
22#22582786—22no—
23C2×M16×C281C2211yescharacteristic
24#117×C281C2211yescharacteristic
25C2×C42×C281C2211yescharacteristic
26C2×Dic562—21no—
27C2×Dic562—21no—
28C2×Dic562—21no—
29C2×Dic562—21no—
30C2×Dic562C2×C412yes—
31C2×Dic562Q812yes—
32C22×Dic281—21no—
33C22×Dic281D412yes—
34#17985122—21no—
35#17985122C2×C412yes—
36C2×#14555886—21no—
37C4⋊Dic281—21no—
38C4⋊Dic281—21no—
39C4⋊Dic281D411yescharacteristic
40C4⋊Dic281D411yescharacteristic
41#17985117—22no—
42#17985117—22no—
43C22⋊Dic281—21no—
44C4×Dic281—22no—
45C4×Dic281—22no—
46C4×Dic281—21no—
47C22×C4×C281—21no—
48C22×C4×C281C2311yescharacteristic
49M16×C281—21no—
50M16×C281C2×C412yes—
51C2×C8×C281—21no—
52C4⋊C4×C281D411yescharacteristic
53C4⋊C4×C281D411yescharacteristic
54C22⋊C4×C281—21no—
55C42×C281—21no—
56C42×C281—21no—
57C42×C281—21no—
58Dic562—22no—
59Dic562—22no—
60Dic562—22no—
61Dic562—22no—
62C2×Dic281—22no—
63C2×Dic281—22no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—42no—
67C2×Dic281—41no—
68C2×Dic281C4⋊C414yes—
69#14555886—22no—
70C23×C281C2×D411yescharacteristic
71C2×C4×C281—22no—
72C2×C4×C281—21no—
73C2×C4×C281—21no—
74C2×C4×C281—41no—
75C2×C4×C281—41no—
76C2×C4×C281C22×C411yescharacteristic
77C2×C4×C281C2×D411yescharacteristic
78C2×C4×C281C2×D411yescharacteristic
79C2×C4×C281C2×Q811yescharacteristic
80C2×C4×C281#4111yescharacteristic
81C2×C4×C281#4111yescharacteristic
82C8×C281—22no—
83C22×C281—21no—
84C22×C281—21no—
85C22×C281C2×C4⋊C411yescharacteristic
86C22×C281#12011yescharacteristic
87C22×C281#12311yescharacteristic
88C4×C281—42no—
89C4×C281—41no—
90C4×C281—41no—
91C4×C281C4×D411yescharacteristic
92C4×C281C4×D411yescharacteristic
93C4×C281C22⋊Q811yescharacteristic
94C4×C281C22⋊Q811yescharacteristic
95Dic281—24no—
96Dic281—41no—
97Dic281—41no—
98Dic281—81no—
99C2×C281—21no—
100C2×C281—21no—
101C2×C281#38511yescharacteristic
102C2×C281#45411yescharacteristic
103C2×C281#45611yescharacteristic
104C281#185711yescharacteristic, complemented, Sylow
105#1857—2811nomaximal, Sylow
106#519—2811no—
107#428—2811no—
108#428—2811no—
109C2×#101—2811no—
110#391—2811no—
111#339—2811no—
112#339D28111yescharacteristic
113C22×Q8—2811no—
114C2×M16—2811no—
115C2×M16C2×D28111yescharacteristic
116C4×Q8—5621no—
117C4×Q8—5621no—
118C4×Q8—5621no—
119C4×Q8—5621no—
120#117—2811no—
121#117—5622no—
122#117C2×D28111yescharacteristic
123C2×C4⋊C4—2811no—
124C2×C42C2×D28111yescharacteristic
125#107—5621no—
126#107—5621no—
127#106—5621no—
128#106—5621no—
129#101—2814no—
130#95—5622no—
131C2×Q8—2812no—
132C2×Q8—2812no—
133C2×Q8—5621no—
134C2×Q8—5621no—
135C2×Q8—5621no—
136C2×Q8—5621no—
137C22×C4—21no—
138C22×C4—2812no—
139C22×C4—5621no—
140C22×C4C22×D28111yescharacteristic
141M16—21no—
142M16—2812no—
143M16—5621no—
144M16C4×D28112yes—
145C2×C8—21no—
146C2×C8—5621no—
147C4⋊C4—2811no—
148C4⋊C4—2811no—
149C4⋊C4—5622no—
150C4⋊C4—5622no—
151C4⋊C4—5621no—
152C4⋊C4—5621no—
153C4⋊C4D112411yescharacteristic
154C4⋊C4D112411yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—5621no—
157C42—21no—
158C42—21no—
159C42—21no—
160C42—5622no—
161C42—5622no—
162C42—5621no—
163C23D4×D28111yescharacteristic
164Q8—5622no—
165Q8—5622no—
166Q8—5622no—
167Q8—5622no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—2814no—
174C2×C4—5622no—
175C2×C4—5622no—
176C2×C4—5621no—
177C2×C4—5621no—
178C2×C4—11242no—
179C2×C4—11241no—
180C2×C4C2×C4×D28111yescharacteristic
181C2×C4D4×D28111yescharacteristic
182C2×C4C2×D112411yescharacteristic
183C2×C4Q8×D28111yescharacteristic
184C2×C4#1798513711yescharacteristic
185C2×C4#1798513811yescharacteristic
186C8—22no—
187C8—5622no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D28111yescharacteristic
191C22#2258284911yescharacteristic
192C22#2258286111yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—5624no—
197C4—11241no—
198C4—11241no—
199C4—22481no—
200C4#2258283911yescharacteristic
201C4C4×D112411yescharacteristic
202C4#2258285711yescharacteristic
203C4#2258285911yescharacteristic
204C2—21no—
205C2—21no—
206C2#3182333711yescharacteristic
207C2#3182363711yescharacteristic
208C2#3182364711yescharacteristic
subgroupG/H
centerC22#22582849
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#339×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
cosocleC22×C4×C281C23
hypercenter#339D281
hypocenterC281#1857
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
21. #22582797C4semidirect
104. C281#1857semidirect

Maximal subgroups

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

subgroupindex
#318239402
#318235062
#318235052
C2×#225827972
#318233692
#318232232
#339×C2812
#1857281