Finite Group Databasebeta

← #49096404

Subgroups — #49096404

Order 35968.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×Dic1124C211yesmaximal, characteristic
2C22×#17985128C211yesmaximal, characteristic
3C2×#22582877C211yesmaximal, characteristic
4C2×#22582802C211yesmaximal, characteristic
5#31823368C211yesmaximal, characteristic
6#31823217C211yesmaximal, characteristic
7C2×#103×C281C211yesmaximal, characteristic
8C22×Dic562C2211yescharacteristic
9C22×Dic562C2211yescharacteristic
10C2×Dic1124—22no—
11C2×Dic1124—22no—
12C2×Dic1124—22no—
13C2×#17985128—22no—
14C2×#17985128—22no—
15C2×#17985128—22no—
16C22×#14555886C2211yescharacteristic
17#22582877—22no—
18#22582877—22no—
19C2×#17985117—22no—
20C2×C4×Dic281C2211yescharacteristic
21#22582802—22no—
22#22582786—22no—
23C22×Q8×C281C2211yescharacteristic
24C22×C8×C281C2211yescharacteristic
25C2×C4⋊C4×C281C2211yescharacteristic
26#103×C281—22no—
27C2×Dic562—21no—
28C2×Dic562—21no—
29C2×Dic562—21no—
30C2×Dic562—21no—
31C2×Dic562—21no—
32C2×Dic562—21no—
33C2×Dic562—21no—
34C2×Dic562—21no—
35C2×Dic562—21no—
36C2×Dic562—21no—
37C2×Dic562D412yes—
38C2×Dic562D412yes—
39C22×Dic281—21no—
40C22×Dic281—21no—
41C22×Dic281D412yes—
42Dic1124—28no—
43#17985128—28no—
44C2×#14555886—21no—
45C2×#14555886—21no—
46C2×#14555886D412yes—
47#17985117—28no—
48C4×Dic281—21no—
49C4×Dic281—21no—
50C2×Q8×C281—21no—
51C2×Q8×C281—21no—
52C2×Q8×C281—21no—
53C2×Q8×C281—21no—
54C2×Q8×C281—21no—
55C2×Q8×C281D412yes—
56C22×C4×C281—21no—
57C22×C4×C281—21no—
58C22×C4×C281C2311yescharacteristic
59C2×C8×C281—21no—
60C2×C8×C281—21no—
61C2×C8×C281D412yes—
62C4⋊C4×C281—21no—
63C4⋊C4×C281—21no—
64Dic562—22no—
65Dic562—22no—
66Dic562—22no—
67Dic562—22no—
68Dic562—41no—
69Dic562—41no—
70Dic562—41no—
71Dic562—41no—
72C2×Dic281—22no—
73C2×Dic281—22no—
74C2×Dic281—22no—
75C2×Dic281—22no—
76C2×Dic281—41no—
77C2×Dic281—41no—
78C2×Dic281—41no—
79C2×Dic281—41no—
80C2×Dic281Q1614yescomplemented
81#14555886—22no—
82C23×C281C2×D411yescharacteristic
83Q8×C281—22no—
84Q8×C281—22no—
85Q8×C281—41no—
86Q8×C281—41no—
87C2×C4×C281—22no—
88C2×C4×C281—41no—
89C2×C4×C281—41no—
90C2×C4×C281—41no—
91C2×C4×C281—42no—
92C2×C4×C281C2×D411yescharacteristic
93C2×C4×C281C2×D411yescharacteristic
94C2×C4×C281C2×D411yescharacteristic
95C2×C4×C281C2×D411yescharacteristic
96C2×C4×C281C2×D411yescharacteristic
97C2×C4×C281#4111yescharacteristic
98C8×C281—22no—
99C22×C281#12011yescharacteristic
100C22×C281#12111yescharacteristic
101C22×C281#12711yescharacteristic
102C22×C281C2×Q1612yes—
103C22×C281#13712yes—
104C4×C281—42no—
105C4×C281—81no—
106C4×C281#12011yescharacteristic
107C4×C281#12011yescharacteristic
108C4×C281#12111yescharacteristic
109C4×C281#12111yescharacteristic
110Dic281—24no—
111Dic281—42no—
112Dic281—42no—
113C2×C281#39211yescharacteristic
114C2×C281#45112yes—
115C2×C281#46212yes—
116C2×C281#49411yescharacteristic
117C2×C281#49711yescharacteristic
118C281#201611yescharacteristic, complemented, Sylow
119#2016—2811nomaximal, Sylow
120C22×Q16—2811no—
121C22×Q16—2811no—
122C2×C4⋊Q8—2811no—
123C2×#103—2811no—
124C2×#103D28111yescharacteristic
125#391—2811no—
126#336—2811no—
127C22×Q8—2811no—
128C22×Q8—2811no—
129C22×Q8C2×D28111yescharacteristic
130C2×Q16—5622no—
131C2×Q16—5622no—
132C2×Q16—5622no—
133C2×Q16—5622no—
134C2×Q16—5622no—
135C2×Q16—5622no—
136C22×C8—2811no—
137C22×C8C2×D28111yescharacteristic
138C4⋊Q8—5622no—
139C4⋊Q8—5622no—
140C2×C4⋊C4—5622no—
141C2×C4⋊C4C2×D28111yescharacteristic
142C2×C42—2811no—
143#103—22no—
144#103—5622no—
145#95—5622no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—2812no—
152C2×Q8—2812no—
153C2×Q8—5621no—
154C2×Q8—5621no—
155C2×Q8—5621no—
156C2×Q8—5621no—
157C2×Q8—5621no—
158C2×Q8—5621no—
159C2×Q8—5621no—
160C2×Q8—5621no—
161C2×Q8—5621no—
162C2×Q8—5621no—
163C2×Q8D112412yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—2812no—
167C22×C4—5621no—
168C22×C4—5621no—
169C22×C4C22×D28111yescharacteristic
170Q16—5628no—
171Q16—5628no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—2812no—
175C2×C8—5621no—
176C2×C8—5621no—
177C2×C8C22⋊D28112yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—5628no—
181C42—5621no—
182C42—5621no—
183C23D4×D28111yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8—5622no—
189Q8—5622no—
190Q8—5622no—
191Q8—5622no—
192Q8—11241no—
193Q8—11241no—
194Q8—11241no—
195Q8—11241no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—2814no—
202C2×C4—5622no—
203C2×C4—5622no—
204C2×C4—5622no—
205C2×C4—5622no—
206C2×C4—11241no—
207C2×C4—11241no—
208C2×C4—11241no—
209C2×C4—11241no—
210C2×C4D4×D28111yescharacteristic
211C2×C4D4×D28111yescharacteristic
212C2×C4D4×D28111yescharacteristic
213C2×C4C2×C22⋊D28111yescharacteristic
214C2×C4C2×D112411yescharacteristic
215C2×C4#1798513811yescharacteristic
216C8—22no—
217C8—5622no—
218C22#2258284911yescharacteristic
219C22#2258285211yescharacteristic
220C22#2258287511yescharacteristic
221C22Q16×D28112yes—
222C22#2258290812yes—
223C4—42no—
224C4—81no—
225C4—5624no—
226C4—11242no—
227C4—11242no—
228C4#2258284711yescharacteristic
229C4#2258284911yescharacteristic
230C4#2258285211yescharacteristic
231C4#2258285311yescharacteristic
232C2#3182337211yescharacteristic
233C2#3182362012yes—
234C2#3182367212yes—
235C2#3182384111yescharacteristic
236C2#3182385411yescharacteristic
subgroupG/H
centerC23D4×D281
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
FittingC2×#103×C281C2
socle, prime radicalC23×C281C2×D4
hypercenterC2×#103D281
hypocenterC281#2016
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
80. C2×Dic281Q16semidirect
118. C281#2016semidirect

Maximal subgroups

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

subgroupindex
C22×Dic11242
C22×#179851282
C2×#225828772
C2×#225828022
#318233682
#318232172
C2×#103×C2812
#2016281