Finite Group Databasebeta

← #14317132

Subgroups — #14317132

Order 1920.

332 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 82 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
1D8×Dic15C211yesmaximal, characteristic
2C2×C5×#827C211yesmaximal, characteristic
3C2×C3×#3959C211yesmaximal, characteristic
4#11748041C211yesmaximal, characteristic, complemented
5#11745928C211yesmaximal, characteristic, complemented
6#11745900C211yesmaximal, characteristic, complemented
7#11745898C211yesmaximal, characteristic, complemented
8#10602269—31nomaximal, Hall
9C2×C3×C5×D8C2211yescharacteristic
10D4×Dic15—21no—
11C2×C5×Dic12C2211yescharacteristic
12C2×C3×Dic20C2211yescharacteristic
13#91385—21no—
14C2×#6661—21no—
15#91116—21no—
16#91102C2211yescharacteristic
17C8×Dic15C2211yescharacteristic
18C5×#827—22no—
19C2×C5×C3⋊C16C2211yescharacteristic
20C3×#3959—22no—
21C2×C3×#672C2211yescharacteristic
22#71476—51nomaximal, Hall
23C2×C5×SD32—31no—
24#65470—31no—
25D8×Dic5—31no—
26C2×#3959D311yescharacteristic
27#64784—31no—
28#64723—31no—
29#64721—31no—
30C2×C3×C5×D4—21no—
31C22×Dic15—41no—
32C2×C5×Dic6—21no—
33C2×C3×Dic10—21no—
34C3×C5×D8—21no—
35C3×C5×D8D412yes—
36C2×C3×C5×C8C2311yescharacteristic
37#6719—41no—
38C4⋊Dic15—21no—
39C4×Dic15D411yescharacteristic
40C2×C3⋊#168D411yescharacteristic
41C5×Dic12—21no—
42C5×Dic12—21no—
43C3×Dic20—21no—
44C3×Dic20—21no—
45#6669—41no—
46#6669—41no—
47#6661—42no—
48C3×#672—21no—
49C5×C3⋊C16—21no—
50C2×C3×SD32—51no—
51#5183—51no—
52Dic3×D8—51no—
53C2×#827D511yescharacteristic
54#4564—51no—
55#4503—51no—
56Dic3⋊C16—51no—
57C2×C5×Q16—31no—
58C2×C5×D8C2×D311yescharacteristic
59#4090—61no—
60C2×#689—61no—
61D4×Dic5—61no—
62C2×Dic20C2×D311yescharacteristic
63C5×SD32—62no—
64C2×C5×C16—31no—
65#3964—61no—
66#3959—22no—
67#3950—31no—
68C8×Dic5—31no—
69C2×#672C2×D311yescharacteristic
70#2208—151noSylow
71C23×C3×C5—41no—
72C3×C5×D4—22no—
73C3×C5×D4—41no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×Dic15—41no—
76C2×Dic15—82no—
77C2×Dic15D811yescharacteristic
78C2×Dic15D811yescharacteristic
79C2×C5×Dic3—41no—
80C5×Dic6—41no—
81C5×Dic6—41no—
82C2×C3×Dic5—41no—
83C3×Dic10—41no—
84C3×Dic10—41no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3⋊#168—21no—
88C2×C3×Q16—51no—
89C2×C3×D8C2×D511yescharacteristic
90#944—101no—
91C2×#216—101no—
92D4×Dic3—101no—
93C2×Dic12C2×D511yescharacteristic
94C3×SD32—102no—
95C2×C3×C16—51no—
96#832—101no—
97#827—22no—
98#818—51no—
99C8×Dic3—51no—
100C2×C3⋊C16C2×D511yescharacteristic
101C2×C5×Q8—61no—
102C2×C5×D4—21no—
103C22×Dic5—121no—
104C2×Dic10—21no—
105C5×Q16—61no—
106C5×Q16—61no—
107C5×D8—21no—
108C5×D8#6712yes—
109C2×C5×C8C22×D311yescharacteristic
110C22⋊Dic5—121no—
111#689—122no—
112C4⋊Dic5—61no—
113#683—121no—
114#683—121no—
115C4×Dic5—31no—
116C2×#168—31no—
117Dic20—21no—
118Dic20—21no—
119C5×C16—61no—
120#672—21no—
121C2×SD32—31no—
122C2×SD32—51no—
123#494—151no—
124C4×D8—151no—
125C4⋊C16—151no—
126#358—151no—
127#358—151no—
128C22×C3×C5—42no—
129C22×C3×C5—81no—
130C22×C3×C5—81no—
131C22×C3×C5C2×D811yescharacteristic
132C3×C4×C5#12111yescharacteristic
133C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
134Dic15—21no—
135Dic15—81no—
136Dic15SD3212yescomplemented
137C3×Dic5—81no—
138C5×Dic3—81no—
139C2×C3×Q8—101no—
140C2×C3×D4—21no—
141C22×Dic3—201no—
142C2×Dic6—21no—
143C3×Q16—101no—
144C3×Q16—101no—
145C3×D8—21no—
146C3×D8C22⋊D512yes—
147C2×C3×C8C22×D511yescharacteristic
148#217—201no—
149#216—202no—
150C4⋊Dic3—101no—
151Dic3⋊C4—201no—
152Dic3⋊C4—201no—
153C4×Dic3—51no—
154C2×C3⋊C8—51no—
155Dic12—21no—
156Dic12—21no—
157C3×C16—101no—
158C3⋊C16—21no—
159C23×C5—41no—
160C5×Q8—121no—
161C5×Q8—121no—
162C5×D4—22no—
163C5×D4—41no—
164C2×C4×C5—121no—
165C2×C4×C5D3×D411yescharacteristic
166C2×Dic5—31no—
167C2×Dic5—31no—
168C2×Dic5—41no—
169C2×Dic5—121no—
170C2×Dic5—242no—
171Dic10—41no—
172Dic10—41no—
173C5×C8#23711yescharacteristic
174C5×C8C2×#6711yescharacteristic
175#168—61no—
176C2×Q16—31no—
177C2×Q16—51no—
178C2×Q16—301no—
179C2×D8D3×D511yescharacteristic
180C4⋊Q8—301no—
181C4×D4—301no—
182SD32—62no—
183SD32—102no—
184C2×C16—31no—
185C2×C16—51no—
186#107—151no—
187#102—301no—
188C4×C8—151no—
189C2×C3×C5—82no—
190C2×C3×C5#45911yescharacteristic
191C2×C3×C5C2×SD3211yescharacteristic
192C2×C3×C5#51011yescharacteristic
193C23×C3—41no—
194C3×Q8—201no—
195C3×Q8—201no—
196C3×D4—22no—
197C3×D4—41no—
198C2×C3×C4—201no—
199C2×C3×C4D4×D511yescharacteristic
200C2×Dic3—41no—
201C2×Dic3—51no—
202C2×Dic3—51no—
203C2×Dic3—201no—
204C2×Dic3—402no—
205Dic6—41no—
206Dic6—41no—
207C3×C8#71111yescharacteristic
208C3×C8C2×C22⋊D511yescharacteristic
209C3⋊C8—101no—
210C22×C5—42no—
211C22×C5—81no—
212C22×C5—81no—
213C22×C5D3×D811yescharacteristic
214C4×C5—241no—
215C4×C5#91111yescharacteristic
216C4×C5#93911yescharacteristic
217Dic5—32no—
218Dic5—61no—
219Dic5—81no—
220Dic5—241no—
221C2×Q8—61no—
222C2×Q8—101no—
223C2×D4—21no—
224C22×C4—601no—
225Q16—61no—
226Q16—61no—
227Q16—101no—
228Q16—101no—
229Q16—602no—
230D8—21no—
231D8#120112yes—
232C2×C8—151no—
233C2×C8C2×D3×D511yescharacteristic
234C4⋊C4—301no—
235C4⋊C4—601no—
236C4⋊C4—601no—
237C22⋊C4—601no—
238C42—151no—
239C16—61no—
240C16—101no—
241C3×C5#220811yescharacteristic, complemented, Hall
242C22×C3—42no—
243C22×C3—81no—
244C22×C3—81no—
245C22×C3D5×D811yescharacteristic
246C3×C4—401no—
247C3×C4#405711yescharacteristic
248C3×C4#408511yescharacteristic
249Dic3—52no—
250Dic3—81no—
251Dic3—101no—
252Dic3—401no—
253C2×C5—82no—
254C2×C5D3×SD3211yescharacteristic
255C2×C5#491511yescharacteristic
256C2×C5#515011yescharacteristic
257C23—41no—
258Q8—121no—
259Q8—121no—
260Q8—201no—
261Q8—201no—
262D4—22no—
263D4—41no—
264C2×C4—121no—
265C2×C4—151no—
266C2×C4—151no—
267C2×C4—201no—
268C2×C4—601no—
269C2×C4—1202no—
270C2×C4#679011yescharacteristic
271C8—301no—
272C8#678011yescharacteristic
273C8C2×#120111yescharacteristic
274C2×C3—82no—
275C2×C3D5×SD3211yescharacteristic
276C2×C3#6520411yescharacteristic
277C2×C3#6543911yescharacteristic
278C5#7147611yescharacteristic, complemented, Sylow
279C22—42no—
280C22—81no—
281C22—81no—
282C22#9148111yescharacteristic
283C4—152no—
284C4—241no—
285C4—301no—
286C4—401no—
287C4—1201no—
288C4#9148211yescharacteristic
289C4#9157111yescharacteristic
290C3#1060226911yescharacteristic, complemented, Sylow
291C2—82no—
292C2#1174827411yescharacteristic
293C2#1174827511yescharacteristic
294C2#1174910011yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
Fitting, prime radicalC2×C3×C5×D8C22
socleC22×C3×C5C2×D8
hypercenterC2×D8D3×D5
hypocenterC3×C5#2208
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
4. #11748041C2semidirect
5. #11745928C2semidirect
6. #11745900C2semidirect
7. #11745898C2semidirect
136. Dic15SD32semidirect
241. C3×C5#2208semidirect
278. C5#71476semidirect
290. C3#10602269semidirect

Maximal subgroups

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

subgroupindex
D8×Dic152
C2×C5×#8272
C2×C3×#39592
#117480412
#117459282
#117459002
#117458982
#106022693
#714765