Finite Group Databasebeta

← #49094264

Subgroups — #49094264

Order 35968.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#31824060C211yesmaximal, characteristic
2#31823619C211yesmaximal, characteristic, complemented
3#31823602C211yesmaximal, characteristic
4#31823199C211yesmaximal, characteristic, complemented
5#31823196C211yesmaximal, characteristic
6#31823189C211yesmaximal, characteristic, complemented
7#395×C281C211yesmaximal, characteristic, complemented
8C2×#17985128—21no—
9C2×#17985125—21no—
10#22582874—21no—
11#22582869—21no—
12#22582864—21no—
13#22582862—21no—
14#22582858C2211yescharacteristic
15#22582857—21no—
16#22582853C2211yescharacteristic
17C4×C22⋊D281—21no—
18#22582803—21no—
19#22582803—21no—
20C22⋊#14555886C2211yescharacteristic
21C22⋊#14555886C2211yescharacteristic
22C22×Q8×C281C2211yescharacteristic
23C2×C4⋊C4×C281—21no—
24C2×C4⋊C4×C281C2211yescharacteristic
25#95×C281—21no—
26#95×C281C2211yescharacteristic
27C2×Dic562D411yescharacteristic
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—21no—
30C2×C4×D281—21no—
31#17985128—42no—
32#17985125—42no—
33C2×#14555886—21no—
34C2×#14555886—21no—
35C4⋊Dic281D411yescharacteristic
36C4⋊Dic281D411yescharacteristic
37#17985117—21no—
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41C22⋊Dic281—21no—
42#17985115—21no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46C4×Dic281—21no—
47C2×Q8×C281—21no—
48C2×Q8×C281—21no—
49C2×Q8×C281—42no—
50C22×C4×C281—21no—
51C22×C4×C281—21no—
52C22×C4×C281D411yescharacteristic
53C22×C4×C281D411yescharacteristic
54C22×C4×C281C2311yescharacteristic
55C4⋊C4×C281—21no—
56C4⋊C4×C281—21no—
57C4⋊C4×C281—42no—
58C22×D281—21no—
59Dic562—41no—
60D1124—41no—
61C22⋊D281—41no—
62C22⋊D281—41no—
63C2×Dic281—21no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C4×D281—81no—
67#14555886—41no—
68#14555886—41no—
69C23×C281C2×D411yescharacteristic
70Q8×C281—22no—
71Q8×C281—22no—
72Q8×C281—41no—
73Q8×C281—41no—
74C2×C4×C281—22no—
75C2×C4×C281—22no—
76C2×C4×C281—21no—
77C2×C4×C281—21no—
78C2×C4×C281—21no—
79C2×C4×C281—21no—
80C2×C4×C281—41no—
81C2×C4×C281—41no—
82C2×C4×C281—41no—
83C2×C4×C281—41no—
84C2×C4×C281—41no—
85C2×C4×C281—41no—
86C2×C4×C281C2×D411yescharacteristic
87C2×C4×C281C2×D411yescharacteristic
88C22×C281—21no—
89C22×C281—21no—
90C22×C281#12011yescharacteristic
91C22×C281#13511yescharacteristic
92C22×C281#13711yescharacteristic
93C2×D281—41no—
94C2×D281—41no—
95C2×D281—41no—
96C4×C281—21no—
97C4×C281—21no—
98C4×C281—42no—
99C4×C281—41no—
100C4×C281—42no—
101C4×C281—41no—
102Dic281—41no—
103Dic281—41no—
104Dic281—41no—
105C2×C281—21no—
106C2×C281—21no—
107C2×C281#45211yescharacteristic
108C2×C281#45611yescharacteristic
109C2×C281B(4,𝔽2)11yescharacteristic
110D281—81no—
111C281#160311yescharacteristic, complemented, Sylow
112#1603—2811nomaximal, Sylow
113#539—2811no—
114#451—2811no—
115#448—2811no—
116#395D28111yescharacteristic, complemented
117#328—2811no—
118#327—2811no—
119#324—2811no—
120C22×Q8C2×D28111yescharacteristic
121C2×Q16—5621no—
122C2×SD16—5621no—
123#126—5621no—
124#125—5621no—
125#123—5621no—
126#123—5621no—
127C22⋊Q8—2811no—
128C22⋊Q8—5621no—
129#121—2811no—
130C4×D4—5621no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4C2×D28111yescharacteristic
133#103—5621no—
134#103—5621no—
135C22⋊C8—2811no—
136C22⋊C8—2811no—
137#95—21no—
138#95C2×D28111yescharacteristic
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8—2811no—
143C2×D4—2811no—
144C2×D4—5621no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—5621no—
148C22×C4C22⋊D28111yescharacteristic
149C22×C4C22⋊D28111yescharacteristic
150C22×C4C22×D28111yescharacteristic
151Q16—11242no—
152SD16—11242no—
153C2×C8—5621no—
154C2×C8—5621no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—42no—
158C4⋊C4—2811no—
159C4⋊C4—2811no—
160C4⋊C4—5621no—
161C4⋊C4—5621no—
162C4⋊C4—5621no—
163C4⋊C4—5621no—
164C22⋊C4—5621no—
165C22⋊C4—5621no—
166C22⋊C4—5621no—
167C22⋊C4—5621no—
168C22⋊C4—5621no—
169C42—5621no—
170C23—5621no—
171C23C2×C22⋊D28111yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—11241no—
177D4—11241no—
178D4—11241no—
179D4—11241no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—5621no—
193C2×C4—5621no—
194C2×C4—5621no—
195C2×C4—22481no—
196C2×C4D4×D28111yescharacteristic
197C2×C4D4×D28111yescharacteristic
198C8—11241no—
199C8—11241no—
200C22—21no—
201C22—21no—
202C22—11241no—
203C22—11241no—
204C22—11241no—
205C22#2258284711yescharacteristic
206C22#2258289911yescharacteristic
207C22#2258291011yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—42no—
213C4—41no—
214C4—11241no—
215C4—11241no—
216C4—11241no—
217C2—21no—
218C2—21no—
219C2—22481no—
220C2#3182362311yescharacteristic
221C2#3182364511yescharacteristic
222C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#395×C281C2
socleC22×C281#120
prime radical#22582853C22
hypercenter#395D281
hypocenterC281#1603
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #31823619C2semidirect
4. #31823199C2semidirect
6. #31823189C2semidirect
7. #395×C281C2semidirect
111. C281#1603semidirect
116. #395D281semidirect

Maximal subgroups

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

subgroupindex
#318240602
#318236192
#318236022
#318231992
#318231962
#318231892
#395×C2812
#1603281