Finite Group Databasebeta

← #49096443

Subgroups — #49096443

Order 35968.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#22582878C211yesmaximal, characteristic
2C2×#22582804C211yesmaximal, characteristic
3C2×#22582802C211yesmaximal, characteristic
4#31823368C211yesmaximal, characteristic
5#31823225C211yesmaximal, characteristic
6#31823217C211yesmaximal, characteristic
7#340×C281C211yesmaximal, characteristic
8C22×Dic562—21no—
9C22×Dic562C2211yescharacteristic
10C22×#14555886C2211yescharacteristic
11#22582878—22no—
12#22582878—22no—
13C2×C4⋊Dic281C2211yescharacteristic
14C2×#17985117—21no—
15C2×C4×Dic281C2211yescharacteristic
16#22582804—22no—
17#22582802—22no—
18#22582786—21no—
19#22582786—21no—
20C22×C8×C281C2211yescharacteristic
21C2×C4⋊C4×C281C2211yescharacteristic
22C2×C4⋊C4×C281C2211yescharacteristic
23C2×Dic562—24no—
24C2×Dic562—21no—
25C2×Dic562—21no—
26C2×Dic562—21no—
27C2×Dic562—21no—
28C2×Dic562—21no—
29C2×Dic562—42no—
30C2×Dic562—42no—
31C2×Dic562Q812yescomplemented
32C22×Dic281—21no—
33C22×Dic281—21no—
34C22×Dic281D411yescharacteristic
35C22×Dic281D411yescharacteristic
36C2×#14555886—21no—
37C2×#14555886—21no—
38C2×#14555886—21no—
39C4⋊Dic281—21no—
40C4⋊Dic281D412yes—
41#17985117—24no—
42C4×Dic281—21no—
43C4×Dic281—21no—
44C22×C4×C281—21no—
45C22×C4×C281—21no—
46C22×C4×C281C2311yescharacteristic
47C2×C8×C281—21no—
48C2×C8×C281—21no—
49C2×C8×C281—21no—
50C4⋊C4×C281—21no—
51C4⋊C4×C281—21no—
52C4⋊C4×C281—21no—
53C4⋊C4×C281D412yes—
54Dic562—22no—
55Dic562—22no—
56Dic562—48no—
57Dic562—41no—
58Dic562—41no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—21no—
63C2×Dic281—22no—
64C2×Dic281—22no—
65C2×Dic281—41no—
66C2×Dic281—41no—
67C2×Dic281—41no—
68C2×Dic281—41no—
69C2×Dic281SD1612yes—
70C2×Dic281Q1612yes—
71#14555886—41no—
72C23×C281C2×D411yescharacteristic
73C2×C4×C281—22no—
74C2×C4×C281—41no—
75C2×C4×C281—41no—
76C2×C4×C281—41no—
77C2×C4×C281—41no—
78C2×C4×C281—41no—
79C2×C4×C281C2×D411yescharacteristic
80C2×C4×C281C2×D411yescharacteristic
81C2×C4×C281C2×Q811yescharacteristic
82C2×C4×C281#4111yescharacteristic
83C2×C4×C281#4111yescharacteristic
84C2×C4×C281#4111yescharacteristic
85C8×C281—41no—
86C22×C281#12011yescharacteristic
87C22×C281C22⋊Q811yescharacteristic
88C22×C281#12411yescharacteristic
89C22×C281C2×SD1611yescharacteristic
90C22×C281C2×Q1611yescharacteristic
91C22×C281AGL(1,ℤ/8)11yescharacteristic
92C22×C281#13711yescharacteristic
93C4×C281—42no—
94C4×C281—81no—
95C4×C281C22⋊Q811yescharacteristic
96C4×C281C22⋊Q811yescharacteristic
97C4×C281#12411yescharacteristic
98C4×C281#12411yescharacteristic
99Dic281—22no—
100Dic281—22no—
101Dic281—42no—
102Dic281—42no—
103C2×C281#39311yescharacteristic
104C2×C281#45011yescharacteristic
105C2×C281#45111yescharacteristic
106C2×C281#47511yescharacteristic
107C2×C281#47711yescharacteristic
108C2×C281#48711yescharacteristic
109C2×C281#48911yescharacteristic
110C281#202411yescharacteristic, complemented, Sylow
111#2024—2811nomaximal, Sylow
112C2×C4⋊Q8—2811no—
113C2×#103—2811no—
114C2×#103—2811no—
115#391—2811no—
116#340—2811no—
117#340D28111yescharacteristic
118#336—2811no—
119C22×Q8—2811no—
120C22×Q8—5621no—
121C22×C8—2811no—
122C22×C8C2×D28111yescharacteristic
123C4⋊Q8—5622no—
124C4⋊Q8—5622no—
125C2×C4⋊C4—2811no—
126C2×C4⋊C4—5621no—
127C2×C4⋊C4C2×D28111yescharacteristic
128C2×C4⋊C4C2×D28111yescharacteristic
129C2×C42—2811no—
130#103—5622no—
131#103—5622no—
132#95—5621no—
133#95—5621no—
134C2×Q8—2812no—
135C2×Q8—5624no—
136C2×Q8—5621no—
137C2×Q8—5621no—
138C2×Q8—5621no—
139C2×Q8—5621no—
140C2×Q8—5621no—
141C2×Q8—11242no—
142C2×Q8—11242no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2811no—
146C22×C4—2811no—
147C22×C4—5621no—
148C22×C4—5621no—
149C22×C4C22×D28111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—5621no—
154C2×C8—5621no—
155C2×C8—5621no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—2812no—
160C4⋊C4—5624no—
161C4⋊C4—5621no—
162C4⋊C4D112412yes—
163C42—5621no—
164C42—5621no—
165C23D4×D28111yescharacteristic
166Q8—5622no—
167Q8—5622no—
168Q8—11248no—
169Q8—11241no—
170Q8—11241no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—2812no—
178C2×C4—2812no—
179C2×C4—5621no—
180C2×C4—5621no—
181C2×C4—5621no—
182C2×C4—5621no—
183C2×C4—5622no—
184C2×C4—5622no—
185C2×C4—11241no—
186C2×C4—11241no—
187C2×C4—11241no—
188C2×C4—11241no—
189C2×C4D4×D28111yescharacteristic
190C2×C4C2×D112411yescharacteristic
191C2×C4Q8×D28111yescharacteristic
192C2×C4#1798513711yescharacteristic
193C2×C4#1798513811yescharacteristic
194C2×C4#1798513811yescharacteristic
195C8—41no—
196C8—11241no—
197C22#2258284911yescharacteristic
198C22#2258285711yescharacteristic
199C22#2258286511yescharacteristic
200C22SD16×D28111yescharacteristic
201C22Q16×D28111yescharacteristic
202C22#2258290311yescharacteristic
203C22#2258290811yescharacteristic
204C4—42no—
205C4—81no—
206C4—5622no—
207C4—5622no—
208C4—11242no—
209C4—11242no—
210C4#2258285711yescharacteristic
211C4#2258285911yescharacteristic
212C4#2258286511yescharacteristic
213C4#2258286711yescharacteristic
214C2#3182337611yescharacteristic
215C2#3182361511yescharacteristic
216C2#3182362011yescharacteristic
217C2#3182374711yescharacteristic
218C2#3182375711yescharacteristic
219C2#3182381211yescharacteristic
220C2#3182382111yescharacteristic
subgroupG/H
centerC23D4×D281
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#340×C281C2
socle, prime radicalC23×C281C2×D4
hypercenter#340D281
hypocenterC281#2024
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic562Q8semidirect
110. C281#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#225828782
C2×#225828042
C2×#225828022
#318233682
#318232252
#318232172
#340×C2812
#2024281