Finite Group Databasebeta

← #49096453

Subgroups — #49096453

Order 35968.

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

normal subgroups only

This group has 258 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
1C2×#22582870C211yesmaximal, characteristic
2C2×#22582804C211yesmaximal, characteristic
3C2×#22582802C211yesmaximal, characteristic
4#31823368C211yesmaximal, characteristic
5#31823225C211yesmaximal, characteristic
6#31823217C211yesmaximal, characteristic
7#340×C281C211yesmaximal, characteristic
8C22×Dic562C2211yescharacteristic
9C22×#14555886C2211yescharacteristic
10#22582870—22no—
11#22582870—22no—
12C2×C4⋊Dic281—21no—
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—21no—
24C2×Dic562—21no—
25C2×Dic562—21no—
26C2×Dic562—21no—
27C2×Dic562—21no—
28C2×Dic562Q812yes—
29C22×Dic281—21no—
30C22×Dic281—21no—
31C22×Dic281D411yescharacteristic
32C22×Dic281D411yescharacteristic
33C2×#14555886—21no—
34C2×#14555886—21no—
35C2×#14555886—21no—
36C4⋊Dic281—24no—
37C4⋊Dic281—21no—
38C4⋊Dic281D412yes—
39#17985117—24no—
40C4×Dic281—21no—
41C4×Dic281—21no—
42C22×C4×C281—21no—
43C22×C4×C281—21no—
44C22×C4×C281C2311yescharacteristic
45C2×C8×C281—21no—
46C2×C8×C281—21no—
47C2×C8×C281—21no—
48C4⋊C4×C281—21no—
49C4⋊C4×C281—21no—
50C4⋊C4×C281—21no—
51C4⋊C4×C281D412yes—
52Dic562—22no—
53Dic562—22no—
54Dic562—41no—
55Dic562—41no—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C2×Dic281—22no—
59C2×Dic281—22no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C2×Dic281—21no—
63C2×Dic281—21no—
64C2×Dic281—41no—
65C2×Dic281—41no—
66C2×Dic281—41no—
67C2×Dic281—41no—
68#14555886—41no—
69C23×C281C2×D411yescharacteristic
70C2×C4×C281—22no—
71C2×C4×C281—41no—
72C2×C4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281—41no—
75C2×C4×C281—41no—
76C2×C4×C281C2×D411yescharacteristic
77C2×C4×C281C2×D411yescharacteristic
78C2×C4×C281C2×Q811yescharacteristic
79C2×C4×C281#4111yescharacteristic
80C2×C4×C281#4111yescharacteristic
81C2×C4×C281#4111yescharacteristic
82C8×C281—41no—
83C22×C281#12011yescharacteristic
84C22×C281C22⋊Q811yescharacteristic
85C22×C281#12411yescharacteristic
86C22×C281#13511yescharacteristic
87C22×C281#13511yescharacteristic
88C22×C281#13711yescharacteristic
89C22×C281#13711yescharacteristic
90C4×C281—42no—
91C4×C281—81no—
92C4×C281C22⋊Q811yescharacteristic
93C4×C281C22⋊Q811yescharacteristic
94C4×C281#12411yescharacteristic
95C4×C281#12411yescharacteristic
96Dic281—42no—
97Dic281—41no—
98Dic281—41no—
99Dic281—42no—
100C2×C281#39311yescharacteristic
101C2×C281#45211yescharacteristic
102C2×C281#45211yescharacteristic
103C2×C281#47911yescharacteristic
104C2×C281#47911yescharacteristic
105C2×C281#48811yescharacteristic
106C2×C281#49111yescharacteristic
107C281#202611yescharacteristic, complemented, Sylow
108#2026—2811nomaximal, Sylow
109C2×#125—2811no—
110C2×#103—2811no—
111C2×#103—2811no—
112#391—2811no—
113#340—2811no—
114#340D28111yescharacteristic
115#336—2811no—
116C22×Q8—2811no—
117C22×C8—2811no—
118C22×C8C2×D28111yescharacteristic
119#125—5622no—
120#125—5622no—
121C2×C4⋊C4—2811no—
122C2×C4⋊C4—5621no—
123C2×C4⋊C4—5621no—
124C2×C4⋊C4C2×D28111yescharacteristic
125C2×C4⋊C4C2×D28111yescharacteristic
126C2×C42—2811no—
127#103—5622no—
128#103—5622no—
129#95—5621no—
130#95—5621no—
131C2×Q8—2812no—
132C2×Q8—5621no—
133C2×Q8—5621no—
134C2×Q8—5621no—
135C2×Q8—5621no—
136C2×Q8—5621no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—2811no—
140C22×C4—2811no—
141C22×C4—5621no—
142C22×C4—5621no—
143C22×C4C22×D28111yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—5621no—
148C2×C8—5621no—
149C2×C8—5621no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—2812no—
154C4⋊C4—5624no—
155C4⋊C4—5624no—
156C4⋊C4—5621no—
157C4⋊C4D112412yes—
158C42—5621no—
159C42—5621no—
160C23D4×D28111yescharacteristic
161Q8—5622no—
162Q8—5622no—
163Q8—11241no—
164Q8—11241no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5621no—
172C2×C4—5621no—
173C2×C4—5622no—
174C2×C4—5622no—
175C2×C4—5621no—
176C2×C4—5621no—
177C2×C4—5621no—
178C2×C4—5621no—
179C2×C4—11241no—
180C2×C4—11241no—
181C2×C4—11241no—
182C2×C4—11241no—
183C2×C4D4×D28111yescharacteristic
184C2×C4C2×D112411yescharacteristic
185C2×C4Q8×D28111yescharacteristic
186C2×C4#1798513711yescharacteristic
187C2×C4#1798513811yescharacteristic
188C2×C4#1798513811yescharacteristic
189C8—41no—
190C8—11241no—
191C22#2258284911yescharacteristic
192C22#2258285711yescharacteristic
193C22#2258286511yescharacteristic
194C22#2258289811yescharacteristic
195C22#2258290011yescharacteristic
196C22#2258290811yescharacteristic
197C22#2258291111yescharacteristic
198C4—42no—
199C4—81no—
200C4—11241no—
201C4—11241no—
202C4—11242no—
203C4—11242no—
204C4#2258285711yescharacteristic
205C4#2258285911yescharacteristic
206C4#2258286511yescharacteristic
207C4#2258286711yescharacteristic
208C2#3182337611yescharacteristic
209C2#3182362611yescharacteristic
210C2#3182362811yescharacteristic
211C2#3182376911yescharacteristic
212C2#3182377311yescharacteristic
213C2#3182381611yescharacteristic
214C2#3182383011yescharacteristic
subgroupG/H
centerC23D4×D281
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#340×C281C2
socle, prime radicalC23×C281C2×D4
hypercenter#340D281
hypocenterC281#2026
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
107. C281#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#225828702
C2×#225828042
C2×#225828022
#318233682
#318232252
#318232172
#340×C2812
#2026281