Finite Group Databasebeta

← #49095401

Subgroups — #49095401

Order 35968.

306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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#117×D281C211yesmaximal, characteristic
2#31823426C211yesmaximal, characteristic
3C4×#17985115C211yesmaximal, characteristic
4#31823224C211yesmaximal, characteristic, complemented
5#31823223C211yesmaximal, characteristic, complemented
6#31823222C211yesmaximal, characteristic, complemented
7#339×C281C211yesmaximal, characteristic, complemented
8C22×C4×D281C2211yescharacteristic
9C2×#17985122C2211yescharacteristic
10#22582838C2211yescharacteristic
11#22582837C411yescharacteristic, complemented
12#22582837C411yescharacteristic, complemented
13#22582836—21no—
14#22582835—21no—
15C4⋊C4×D281C411yescharacteristic, complemented
16C4⋊C4×D281C411yescharacteristic, complemented
17C2×#17985115—21no—
18C22⋊C4×D281—21no—
19C2×C4×Dic281C2211yescharacteristic
20C42×D281—21no—
21#22582791—21no—
22#22582791—21no—
23#22582786—21no—
24C2×M16×C281C2211yescharacteristic
25#117×C281C2211yescharacteristic
26C2×C42×C281C2211yescharacteristic
27C23×D281D411yescharacteristic
28C22×Dic281—21no—
29C22×Dic281D411yescharacteristic
30C2×C4×D281—21no—
31C2×C4×D281—21no—
32C2×C4×D281—21no—
33C2×C4×D281—21no—
34C2×C4×D281—21no—
35C2×C4×D281—21no—
36C2×C4×D281C2×C411yescharacteristic
37C2×C4×D281C2×C411yescharacteristic
38C2×C4×D281D411yescharacteristic
39C2×C4×D281D411yescharacteristic
40#17985122—21no—
41#17985122—21no—
42C2×#14555886—21no—
43C4⋊Dic281C2×C411yescharacteristic
44C4⋊Dic281C2×C411yescharacteristic
45#17985117—21no—
46#17985117—21no—
47C22⋊Dic281—21no—
48#17985115—24no—
49#17985115—21no—
50#17985115—21no—
51C4×Dic281—21no—
52C4×Dic281—21no—
53C4×Dic281—21no—
54C4×Dic281—21no—
55C4×Dic281—21no—
56C22×C4×C281—21no—
57C22×C4×C281C2311yescharacteristic
58M16×C281—21no—
59M16×C281—21no—
60C2×C8×C281—21no—
61C4⋊C4×C281C2×C411yescharacteristic
62C4⋊C4×C281C2×C411yescharacteristic
63C22⋊C4×C281—21no—
64C42×C281—21no—
65C42×C281—21no—
66C42×C281—21no—
67C22×D281—21no—
68C22×D281—21no—
69C22×D281—22no—
70C22×D281—41no—
71C22×D281C22⋊C411yescharacteristic
72C22×D281C22⋊C411yescharacteristic
73C2×Dic281—21no—
74C2×Dic281—21no—
75C2×Dic281—22no—
76C2×Dic281—21no—
77C2×Dic281—21no—
78C2×Dic281—41no—
79C2×Dic281—41no—
80C2×Dic281C22⋊C411yescharacteristic
81C2×Dic281C22⋊C411yescharacteristic
82C4×D281—21no—
83C4×D281—21no—
84C4×D281—21no—
85C4×D281—21no—
86C4×D281—21no—
87C4×D281—21no—
88C4×D281—21no—
89C4×D281—21no—
90C4×D281—42no—
91C4×D281—42no—
92#14555886—41no—
93C23×C281C2×D411yescharacteristic
94C2×C4×C281—22no—
95C2×C4×C281—21no—
96C2×C4×C281—21no—
97C2×C4×C281—41no—
98C2×C4×C281—41no—
99C2×C4×C281C22×C411yescharacteristic
100C2×C4×C281C2×D411yescharacteristic
101C2×C4×C281#4111yescharacteristic
102C2×C4×C281#4111yescharacteristic
103C2×C4×C281#4111yescharacteristic
104C2×C4×C281#4111yescharacteristic
105C8×C281—41no—
106C22×C281—21no—
107C22×C281—21no—
108C22×C281C2×C22⋊C411yescharacteristic
109C22×C281#12311yescharacteristic
110C22×C281#12311yescharacteristic
111C2×D281—21no—
112C2×D281—21no—
113C2×D281—21no—
114C2×D281—21no—
115C2×D281—21no—
116C2×D281—42no—
117C2×D281—42no—
118C2×D281#10412yes—
119C4×C281—42no—
120C4×C281—41no—
121C4×C281—41no—
122C4×C281#11711yescharacteristic
123C4×C281#11711yescharacteristic
124C4×C281#12311yescharacteristic
125C4×C281#12311yescharacteristic
126Dic281—21no—
127Dic281—21no—
128Dic281—42no—
129Dic281—41no—
130Dic281—41no—
131C2×C281—21no—
132C2×C281—21no—
133C2×C281#38111yescharacteristic
134C2×C281C2×#10411yescharacteristic
135C2×C281#42111yescharacteristic
136D281—22no—
137D281—41no—
138C281#182611yescharacteristic, complemented, Sylow
139#1826—2811nomaximal, Sylow
140C2×#117—2811no—
141#407—2811no—
142C4×C22⋊C4—2811no—
143#339—2811no—
144#339—2811no—
145#339—2811no—
146#339D28111yescharacteristic, complemented
147C23×C4—2811no—
148C2×M16—2811no—
149C2×M16C2×D28111yescharacteristic
150#117—2811no—
151#117—2811no—
152#117—2811no—
153#117—5621no—
154#117—5621no—
155#117C2×D28111yescharacteristic
156C2×C4⋊C4—2811no—
157C2×C4⋊C4—2811no—
158C2×C22⋊C4—5621no—
159C2×C22⋊C4—5621no—
160C2×C42—2811no—
161C2×C42—5621no—
162C2×C42C2×D28111yescharacteristic
163C22⋊C8—5621no—
164C22⋊C8—5621no—
165#95—5621no—
166C24—2811no—
167C22×C4—21no—
168C22×C4—2811no—
169C22×C4—2811no—
170C22×C4—2811no—
171C22×C4—2811no—
172C22×C4—2811no—
173C22×C4—5621no—
174C22×C4—5621no—
175C22×C4—5621no—
176C22×C4—5621no—
177C22×C4—5621no—
178C22×C4—5621no—
179C22×C4—5621no—
180C22×C4C22×D28111yescharacteristic
181M16—21no—
182M16—21no—
183M16—5621no—
184M16—5621no—
185C2×C8—21no—
186C2×C8—5621no—
187C4⋊C4—2811no—
188C4⋊C4—2811no—
189C4⋊C4—5621no—
190C4⋊C4—5621no—
191C4⋊C4C4×D28111yescharacteristic
192C4⋊C4C4×D28111yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—5621no—
195C22⋊C4—5621no—
196C22⋊C4—5624no—
197C22⋊C4—5621no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—5621no—
202C42—5621no—
203C42—5621no—
204C42—5621no—
205C42—5621no—
206C23—2811no—
207C23—2811no—
208C23—5622no—
209C23—5621no—
210C23—5621no—
211C23—11241no—
212C23D4×D28111yescharacteristic
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—2811no—
219C2×C4—2811no—
220C2×C4—5621no—
221C2×C4—5621no—
222C2×C4—5621no—
223C2×C4—5621no—
224C2×C4—5621no—
225C2×C4—5621no—
226C2×C4—5621no—
227C2×C4—5621no—
228C2×C4—5621no—
229C2×C4—5621no—
230C2×C4—5622no—
231C2×C4—5621no—
232C2×C4—5621no—
233C2×C4—11242no—
234C2×C4—11242no—
235C2×C4—11241no—
236C2×C4—11241no—
237C2×C4C2×C4×D28111yescharacteristic
238C2×C4D4×D28111yescharacteristic
239C2×C4#1798513711yescharacteristic
240C2×C4#1798513811yescharacteristic
241C2×C4#1798513811yescharacteristic
242C2×C4#1798513911yescharacteristic
243C8—41no—
244C8—11241no—
245C22—21no—
246C22—21no—
247C22—2812no—
248C22—5621no—
249C22—5621no—
250C22—5621no—
251C22—5621no—
252C22—5621no—
253C22—11242no—
254C22—11242no—
255C22C22⋊C4×D28111yescharacteristic
256C22#2258286111yescharacteristic
257C22#2258286411yescharacteristic
258C4—42no—
259C4—41no—
260C4—41no—
261C4—5621no—
262C4—5621no—
263C4—11242no—
264C4—11241no—
265C4—11241no—
266C4#2258283611yescharacteristic
267C4#2258283711yescharacteristic
268C4#2258286111yescharacteristic
269C4#2258286411yescharacteristic
270C2—21no—
271C2—21no—
272C2—5622no—
273C2—11241no—
274C2#3182332511yescharacteristic
275C2#104×D28111yescharacteristic
276C2#3182347811yescharacteristic
subgroupG/H
centerC2×C4D4×D281
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#339×C281C2
socleC22×C281C2×C22⋊C4
prime radicalC23×D281D4
cosocleC22×C4×C281C23
hypercenter#339D281
hypocenterC281#1826
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #31823224C2semidirect
5. #31823223C2semidirect
6. #31823222C2semidirect
7. #339×C281C2semidirect
11. #22582837C4semidirect
12. #22582837C4semidirect
15. C4⋊C4×D281C4semidirect
16. C4⋊C4×D281C4semidirect
138. C281#1826semidirect
146. #339D281semidirect

Maximal subgroups

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

subgroupindex
#117×D2812
#318234262
C4×#179851152
#318232242
#318232232
#318232222
#339×C2812
#1826281