Finite Group Databasebeta

← #49095396

Subgroups — #49095396

Order 35968.

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

normal subgroups only

This group has 300 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
1C2×#22582837C211yesmaximal, characteristic
2C2×#22582791C211yesmaximal, characteristic
3#31823320C211yesmaximal, characteristic
4#31823226C211yesmaximal, characteristic, complemented
5#31823225C211yesmaximal, characteristic, complemented
6#31823225C211yesmaximal, characteristic, complemented
7#340×C281C211yesmaximal, characteristic, complemented
8C22×C4×D281C2211yescharacteristic
9C22×#14555886C2211yescharacteristic
10#22582837—22no—
11#22582837C414yescomplemented
12C2×C4⋊Dic281C2211yescharacteristic
13C2×C4⋊Dic281C2211yescharacteristic
14C2×#17985115—21no—
15C2×#17985115—21no—
16C2×C4×Dic281—21no—
17#22582791—22no—
18#22582786—21no—
19C22×C8×C281C2211yescharacteristic
20C2×C4⋊C4×C281C2211yescharacteristic
21C2×C4⋊C4×C281C2211yescharacteristic
22C23×D281D411yescharacteristic
23C22×Dic281—21no—
24C22×Dic281—21no—
25C22×Dic281D411yescharacteristic
26C2×C4×D281—21no—
27C2×C4×D281—21no—
28C2×C4×D281—21no—
29C2×C4×D281—21no—
30C2×C4×D281C2×C412yes—
31C2×C4×D281D412yes—
32C2×#14555886—21no—
33C2×#14555886—21no—
34C2×#14555886—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281—21no—
38C4⋊Dic281C2×C412yes—
39#17985115—24no—
40#17985115—42no—
41C4×Dic281—24no—
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×C281C2×C412yes—
52C22×D281—21no—
53C22×D281—21no—
54C22×D281—21no—
55C22×D281—21no—
56C22×D281—21no—
57C22×D281—21no—
58C22×D281C22⋊C412yes—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—22no—
62C2×Dic281—41no—
63C2×Dic281—41no—
64C2×Dic281—41no—
65C2×Dic281—41no—
66C2×Dic281—41no—
67C2×Dic281C22⋊C412yes—
68C4×D281—22no—
69C4×D281—22no—
70C4×D281—22no—
71C4×D281—22no—
72#14555886—41no—
73C23×C281C2×D411yescharacteristic
74C2×C4×C281—22no—
75C2×C4×C281—41no—
76C2×C4×C281—41no—
77C2×C4×C281—41no—
78C2×C4×C281—41no—
79C2×C4×C281—41no—
80C2×C4×C281C22×C411yescharacteristic
81C2×C4×C281C2×D411yescharacteristic
82C2×C4×C281#4111yescharacteristic
83C2×C4×C281#4111yescharacteristic
84C2×C4×C281#4111yescharacteristic
85C2×C4×C281#4111yescharacteristic
86C8×C281—41no—
87C22×C281C2×C22⋊C411yescharacteristic
88C22×C281#12311yescharacteristic
89C22×C281#12311yescharacteristic
90C22×C281#13511yescharacteristic
91C22×C281#13511yescharacteristic
92C22×C281AGL(1,ℤ/8)11yescharacteristic
93C22×C281#13711yescharacteristic
94C2×D281—22no—
95C2×D281—22no—
96C2×D281—22no—
97C2×D281—41no—
98C2×D281—41no—
99C2×D281—41no—
100C2×D281—41no—
101C4×C281—42no—
102C4×C281—81no—
103C4×C281#11711yescharacteristic
104C4×C281#11711yescharacteristic
105C4×C281#12311yescharacteristic
106C4×C281#12311yescharacteristic
107Dic281—22no—
108Dic281—42no—
109Dic281—81no—
110C2×C281#38111yescharacteristic
111C2×C281#41611yescharacteristic
112C2×C281#41711yescharacteristic
113C2×C281#48211yescharacteristic
114C2×C281#48211yescharacteristic
115C2×C281#48511yescharacteristic
116C2×C281#48511yescharacteristic
117D281—42no—
118C281#182511yescharacteristic, complemented, Sylow
119#1825—2811nomaximal, Sylow
120C2×#117—2811no—
121C2×C22⋊C8—2811no—
122#380—2811no—
123#340—2811no—
124#340—2811no—
125#340—2811no—
126#340D28111yescharacteristic, complemented
127C23×C4—2811no—
128C22×C8—2811no—
129C22×C8C2×D28111yescharacteristic
130#117—2814no—
131#117—5622no—
132C2×C4⋊C4—2811no—
133C2×C4⋊C4—2811no—
134C2×C4⋊C4C2×D28111yescharacteristic
135C2×C4⋊C4C2×D28111yescharacteristic
136C2×C22⋊C4—5621no—
137C2×C22⋊C4—5621no—
138C2×C42—5621no—
139C22⋊C8—5622no—
140#95—5621no—
141C24—2811no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—2811no—
145C22×C4—2812no—
146C22×C4—2812no—
147C22×C4—5621no—
148C22×C4—5621no—
149C22×C4—5621no—
150C22×C4—5621no—
151C22×C4—5621no—
152C22×C4—5621no—
153C22×C4C22×D28111yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—5621no—
158C2×C8—5621no—
159C2×C8—5621no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—2812no—
164C4⋊C4—5621no—
165C4⋊C4—5621no—
166C4⋊C4—5621no—
167C4⋊C4C4×D28112yes—
168C22⋊C4—5624no—
169C22⋊C4—11242no—
170C42—5624no—
171C23—2812no—
172C23—5621no—
173C23—5621no—
174C23—5621no—
175C23—5621no—
176C23—5621no—
177C23—5621no—
178C23D4×D28111yescharacteristic
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—2812no—
186C2×C4—5621no—
187C2×C4—5621no—
188C2×C4—5622no—
189C2×C4—5622no—
190C2×C4—5622no—
191C2×C4—5622no—
192C2×C4—5622no—
193C2×C4—11241no—
194C2×C4—11241no—
195C2×C4—11241no—
196C2×C4—11241no—
197C2×C4—11241no—
198C2×C4C2×C4×D28111yescharacteristic
199C2×C4D4×D28111yescharacteristic
200C2×C4#1798513711yescharacteristic
201C2×C4#1798513811yescharacteristic
202C2×C4#1798513811yescharacteristic
203C2×C4#1798513911yescharacteristic
204C8—41no—
205C8—11241no—
206C22—5622no—
207C22—5622no—
208C22—5622no—
209C22—11241no—
210C22—11241no—
211C22—11241no—
212C22—11241no—
213C22C22⋊C4×D28111yescharacteristic
214C22#2258286111yescharacteristic
215C22#2258286411yescharacteristic
216C22#2258289811yescharacteristic
217C22#2258290011yescharacteristic
218C22#2258290611yescharacteristic
219C22#2258291111yescharacteristic
220C4—42no—
221C4—81no—
222C4—5622no—
223C4—11242no—
224C4—22481no—
225C4#2258283611yescharacteristic
226C4#2258283711yescharacteristic
227C4#2258286111yescharacteristic
228C4#2258286411yescharacteristic
229C2—11242no—
230C2#3182332511yescharacteristic
231C2#3182345611yescharacteristic
232C2#3182346311yescharacteristic
233C2#3182378511yescharacteristic
234C2#3182378911yescharacteristic
235C2#3182380211yescharacteristic
236C2#3182380611yescharacteristic
subgroupG/H
centerC23D4×D281
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#340×C281C2
socleC23×C281C2×D4
prime radicalC23×D281D4
cosocleC22×C4×C281C23
hypercenter#340D281
hypocenterC281#1825
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
4. #31823226C2semidirect
5. #31823225C2semidirect
6. #31823225C2semidirect
7. #340×C281C2semidirect
11. #22582837C4semidirect
118. C281#1825semidirect
126. #340D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828372
C2×#225827912
#318233202
#318232262
#318232252
#340×C2812
#1825281