Finite Group Databasebeta

← #49096872

Subgroups — #49096872

Order 35968.

198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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#31823361C211yesmaximal, characteristic
2#31823329C211yesmaximal, characteristic
3#31823226C211yesmaximal, characteristic
4#31823226C211yesmaximal, characteristic
5#31823226C211yesmaximal, characteristic
6#31823226C211yesmaximal, characteristic
7#336×C281C211yesmaximal, characteristic
8C2×C4⋊Dic281C2211yescharacteristic
9C2×C4⋊Dic281C2211yescharacteristic
10C2×C4⋊Dic281C2211yescharacteristic
11C2×C4⋊Dic281C2211yescharacteristic
12C2×#17985117—21no—
13#22582786—21no—
14#22582786—21no—
15#22582786—21no—
16C22×C8×C281C2211yescharacteristic
17C22×C8×C281C2211yescharacteristic
18C2×C42×C281C2211yescharacteristic
19C22×Dic281—21no—
20C22×Dic281—21no—
21C22×Dic281—21no—
22C22×Dic281—21no—
23C4⋊Dic281—21no—
24C4⋊Dic281—21no—
25C4⋊Dic281—21no—
26C4⋊Dic281—21no—
27C4⋊Dic281—21no—
28C4⋊Dic281—21no—
29C4⋊Dic281—21no—
30C4⋊Dic281Q812yes—
31#17985117—42no—
32C22×C4×C281D411yescharacteristic
33C22×C4×C281D411yescharacteristic
34C22×C4×C281C2311yescharacteristic
35C2×C8×C281—21no—
36C2×C8×C281—21no—
37C2×C8×C281—21no—
38C2×C8×C281—21no—
39C2×C8×C281—21no—
40C2×C8×C281—21no—
41C42×C281—21no—
42C42×C281—21no—
43C2×Dic281—22no—
44C2×Dic281—41no—
45C2×Dic281—41no—
46C2×Dic281—41no—
47C2×Dic281—41no—
48C2×Dic281—41no—
49C2×Dic281—41no—
50C2×Dic281—41no—
51C2×Dic281—41no—
52C2×Dic281—41no—
53C2×Dic281—41no—
54C2×Dic281—41no—
55C23×C281C2×D411yescharacteristic
56C2×C4×C281—21no—
57C2×C4×C281—21no—
58C2×C4×C281—21no—
59C2×C4×C281—21no—
60C2×C4×C281—21no—
61C2×C4×C281—21no—
62C2×C4×C281C2×Q811yescharacteristic
63C2×C4×C281#4111yescharacteristic
64C2×C4×C281#4111yescharacteristic
65C2×C4×C281#4111yescharacteristic
66C2×C4×C281#4111yescharacteristic
67C2×C4×C281#4111yescharacteristic
68C8×C281—41no—
69C8×C281—41no—
70C22×C281C22⋊Q811yescharacteristic
71C22×C281#12311yescharacteristic
72C22×C281#12411yescharacteristic
73C22×C281#13511yescharacteristic
74C22×C281#13511yescharacteristic
75C22×C281AGL(1,ℤ/8)11yescharacteristic
76C22×C281#13711yescharacteristic
77C4×C281—41no—
78C4×C281—41no—
79C4×C281#12511yescharacteristic
80C4×C281#12511yescharacteristic
81C4×C281#12611yescharacteristic
82C4×C281#12611yescharacteristic
83Dic281—42no—
84Dic281—81no—
85Dic281—81no—
86Dic281—81no—
87C2×C281#40011yescharacteristic
88C2×C281#47811yescharacteristic
89C2×C281#47911yescharacteristic
90C2×C281#48211yescharacteristic
91C2×C281#48511yescharacteristic
92C2×C281#48811yescharacteristic
93C2×C281#48911yescharacteristic
94C281#210111yescharacteristic, complemented, Sylow
95#2101—2811nomaximal, Sylow
96#389—2811no—
97#382—2811no—
98#340—2811no—
99#340—2811no—
100#340—2811no—
101#340—2811no—
102#336D28111yescharacteristic
103C22×C8C2×D28111yescharacteristic
104C22×C8C2×D28111yescharacteristic
105C2×C4⋊C4—2811no—
106C2×C4⋊C4—2811no—
107C2×C4⋊C4—2811no—
108C2×C4⋊C4—2811no—
109C2×C4⋊C4—5621no—
110C2×C42C2×D28111yescharacteristic
111#95—5621no—
112#95—5621no—
113#95—5621no—
114C22×C4—5621no—
115C22×C4—5621no—
116C22×C4—5621no—
117C22×C4—5621no—
118C22×C4D112411yescharacteristic
119C22×C4D112411yescharacteristic
120C22×C4C22×D28111yescharacteristic
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—21no—
127C4⋊C4—2812no—
128C4⋊C4—5621no—
129C4⋊C4—5621no—
130C4⋊C4—5621no—
131C4⋊C4—5621no—
132C4⋊C4—5621no—
133C4⋊C4—5621no—
134C4⋊C4—5621no—
135C4⋊C4—11242no—
136C42—21no—
137C42—21no—
138C23C2×D112411yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—5622no—
146C2×C4—11241no—
147C2×C4—11241no—
148C2×C4—11241no—
149C2×C4—11241no—
150C2×C4—11241no—
151C2×C4—11241no—
152C2×C4—11241no—
153C2×C4—11241no—
154C2×C4—11241no—
155C2×C4—11241no—
156C2×C4—11241no—
157C2×C4Q8×D28111yescharacteristic
158C2×C4#1798513711yescharacteristic
159C2×C4#1798513711yescharacteristic
160C2×C4#1798513711yescharacteristic
161C2×C4#1798513811yescharacteristic
162C2×C4#1798513811yescharacteristic
163C8—41no—
164C8—41no—
165C22#2258285911yescharacteristic
166C22#2258286311yescharacteristic
167C22#2258286711yescharacteristic
168C22#2258290111yescharacteristic
169C22#2258290111yescharacteristic
170C22#2258290711yescharacteristic
171C22#2258291211yescharacteristic
172C4—41no—
173C4—41no—
174C4—11242no—
175C4—22481no—
176C4—22481no—
177C4—22481no—
178C4#2258286911yescharacteristic
179C4#2258286911yescharacteristic
180C4#2258287211yescharacteristic
181C4#2258287211yescharacteristic
182C2#3182340311yescharacteristic
183C2#3182376411yescharacteristic
184C2#3182377111yescharacteristic
185C2#3182378811yescharacteristic
186C2#3182380511yescharacteristic
187C2#3182381811yescharacteristic
188C2#3182382311yescharacteristic
subgroupG/H
centerC23C2×D1124
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#336×C281C2
socle, prime radicalC23×C281C2×D4
hypercenter#336D281
hypocenterC281#2101
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
94. C281#2101semidirect

Maximal subgroups

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

subgroupindex
#318233612
#318233292
#318232262
#336×C2812
#2101281