Finite Group Databasebeta

← #81359

Subgroups — #81359

Order 384.

328 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5600C211yesmaximal, characteristic
2#5517C211yesmaximal, characteristic, complemented
3C3×#482C211yesmaximal, characteristic
4#5035C211yesmaximal, characteristic
5#4996C211yesmaximal, characteristic, complemented
6#4877C211yesmaximal, characteristic, complemented
7#4876C211yesmaximal, characteristic, complemented
8#4857C211yesmaximal, characteristic, complemented
9#4856C211yesmaximal, characteristic, complemented
10#4766C211yesmaximal, characteristic, complemented
11#4765C211yesmaximal, characteristic, complemented
12#4765C211yesmaximal, characteristic, complemented
13#4763C211yesmaximal, characteristic, complemented
14#4723C211yesmaximal, characteristic, complemented
15#4719C211yesmaximal, characteristic, complemented
16#3240—31nomaximal, Sylow
17C3×#121C2211yescharacteristic
18C3×#117C2211yescharacteristic
19#936C2211yescharacteristic
20#935—21no—
21D4×Dic3—21no—
22D4×Dic3C2211yescharacteristic
23#926C2211yescharacteristic
24#924C2211yescharacteristic
25C2×C4×Dic3C2211yescharacteristic
26#890C2211yescharacteristic
27#890C2211yescharacteristic
28#890C2211yescharacteristic
29#888C2211yescharacteristic
30#888C2211yescharacteristic
31#887C2211yescharacteristic
32#879—21no—
33#878—21no—
34#878—21no—
35#877—21no—
36C4×Dic6—21no—
37C4×Dic6—21no—
38C3×#107C2211yescharacteristic
39C3×#106C2211yescharacteristic
40C3×#102C2211yescharacteristic
41C3×#102C2211yescharacteristic
42C3×C22⋊C8C2211yescharacteristic
43#832C2211yescharacteristic
44#832C2211yescharacteristic
45#830C2211yescharacteristic
46#818C2211yescharacteristic
47#817C2211yescharacteristic
48#816C2211yescharacteristic
49#816C2211yescharacteristic
50#815C2211yescharacteristic
51#815C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53Dic3⋊C8C2211yescharacteristic
54#810C2211yescharacteristic
55#810C2211yescharacteristic
56#808C2211yescharacteristic
57#808C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#533—31no—
61#529—31no—
62#501—31no—
63#501—31no—
64#489—31no—
65#489—31no—
66#485—31no—
67#485—31no—
68#482—31no—
69#482D311yescharacteristic
70#479—31no—
71#479—31no—
72#478—31no—
73#478—31no—
74#432—31no—
75C2×C3×D4—21no—
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×Dic3—21no—
79C22×Dic3D411yescharacteristic
80C22×Dic3D411yescharacteristic
81C2×Dic6—21no—
82C2×Dic6—21no—
83C2×Dic6C2311yescharacteristic
84C2×C3×C8C2311yescharacteristic
85C2×C3×C8C2311yescharacteristic
86C3×C4⋊C4C2311yescharacteristic
87C3×C4⋊C4C2311yescharacteristic
88C3×C4⋊C4C2311yescharacteristic
89C3×C22⋊C4—21no—
90C3×C22⋊C4—21no—
91C3×C42—21no—
92#217—21no—
93#217—21no—
94#217—21no—
95#217—21no—
96#217—21no—
97C4⋊Dic3—21no—
98C4⋊Dic3—21no—
99C4⋊Dic3—21no—
100C4⋊Dic3C2311yescharacteristic
101C4⋊Dic3C2311yescharacteristic
102C4⋊Dic3C2311yescharacteristic
103Dic3⋊C4—21no—
104Dic3⋊C4—21no—
105Dic3⋊C4—21no—
106Dic3⋊C4—21no—
107Dic3⋊C4—21no—
108Dic3⋊C4—21no—
109Dic3⋊C4—21no—
110C4×Dic3—21no—
111C4×Dic3—21no—
112C4×Dic3D411yescharacteristic
113C4×Dic3D411yescharacteristic
114C4×Dic3C2311yescharacteristic
115C4×Dic3C2311yescharacteristic
116C2×C3⋊C8C2311yescharacteristic
117C2×C3⋊C8C2311yescharacteristic
118C4⋊Q8—31no—
119C4⋊Q8—31no—
120#126—61no—
121#125—31no—
122#125—31no—
123#125—31no—
124#124—31no—
125#123—61no—
126C22⋊Q8—31no—
127C22⋊Q8—61no—
128C22⋊Q8—61no—
129#121C2×D311yescharacteristic
130C4×Q8—31no—
131C4×Q8—61no—
132C4×Q8—61no—
133C4×D4—31no—
134C4×D4—61no—
135#117—31no—
136#117—61no—
137#117C2×D311yescharacteristic
138C2×C42—31no—
139#107—31no—
140#107—31no—
141#107—31no—
142#107C2×D311yescharacteristic
143#106—31no—
144#106—31no—
145#106—31no—
146#106C2×D311yescharacteristic
147C4⋊C8—31no—
148C4⋊C8—31no—
149#103—31no—
150#103—31no—
151#103—31no—
152#103—31no—
153#102—31no—
154#102—31no—
155#102C2×D311yescharacteristic
156#102C2×D311yescharacteristic
157C22⋊C8—31no—
158C22⋊C8C2×D311yescharacteristic
159#97—31no—
160#97—31no—
161C23×C3—21no—
162C23×C3C2×D411yescharacteristic
163C3×D4—21no—
164C3×D4—21no—
165C3×D4—42no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4C2×D411yescharacteristic
172C2×C3×C4C2411yescharacteristic
173C2×Dic3—21no—
174C2×Dic3—21no—
175C2×Dic3—21no—
176C2×Dic3—21no—
177C2×Dic3—41no—
178C2×Dic3—41no—
179C2×Dic3—42no—
180C2×Dic3C2×D411yescharacteristic
181C2×Dic3C2×D411yescharacteristic
182C2×Dic3C2×D411yescharacteristic
183C2×Dic3C2×D411yescharacteristic
184Dic6—21no—
185Dic6—21no—
186Dic6—42no—
187Dic6—42no—
188C3×C8—21no—
189C3×C8—21no—
190C3⋊C8—21no—
191C3⋊C8—21no—
192C2×Q8—31no—
193C2×Q8—61no—
194C2×Q8—61no—
195C2×D4—21no—
196C2×D4C22×D311yescharacteristic
197C22×C4—31no—
198C22×C4—31no—
199C22×C4—61no—
200C22×C4C22×D311yescharacteristic
201C2×C8—31no—
202C2×C8—31no—
203C2×C8C22×D311yescharacteristic
204C2×C8C22×D311yescharacteristic
205C4⋊C4—31no—
206C4⋊C4—31no—
207C4⋊C4—31no—
208C4⋊C4—61no—
209C4⋊C4—61no—
210C4⋊C4—61no—
211C4⋊C4—61no—
212C4⋊C4—61no—
213C4⋊C4—61no—
214C4⋊C4—61no—
215C4⋊C4—61no—
216C4⋊C4—61no—
217C4⋊C4—61no—
218C4⋊C4C22×D311yescharacteristic
219C4⋊C4C22×D311yescharacteristic
220C4⋊C4C22×D311yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—21no—
223C22⋊C4—61no—
224C22⋊C4—61no—
225C22⋊C4—61no—
226C22⋊C4—61no—
227C22⋊C4—61no—
228C42—21no—
229C42—31no—
230C42—31no—
231C42—31no—
232C42—31no—
233C42—61no—
234C42—61no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—41no—
239C22×C3—41no—
240C22×C3—41no—
241C22×C3C22×D411yescharacteristic
242C3×C4—21no—
243C3×C4—41no—
244C3×C4—41no—
245C3×C4—41no—
246C3×C42−1+411yescharacteristic
247C3×C42−1+411yescharacteristic
248Dic3—21no—
249Dic3—21no—
250Dic3—21no—
251Dic3—21no—
252Dic3—41no—
253Dic3—41no—
254Dic3—41no—
255Dic3—41no—
256C23—21no—
257C23D3×D411yescharacteristic
258Q8—61no—
259Q8—61no—
260Q8—122no—
261Q8—122no—
262D4—21no—
263D4—21no—
264D4—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—31no—
271C2×C4—31no—
272C2×C4—31no—
273C2×C4—31no—
274C2×C4—61no—
275C2×C4—61no—
276C2×C4—61no—
277C2×C4—61no—
278C2×C4—121no—
279C2×C4—121no—
280C2×C4—122no—
281C2×C4D3×D411yescharacteristic
282C2×C4C23×D311yescharacteristic
283C8—21no—
284C8—21no—
285C8—61no—
286C8—61no—
287C2×C3—41no—
288C2×C3—81no—
289C2×C3#53611yescharacteristic
290C2×C3#57511yescharacteristic
291C2×C3#57511yescharacteristic
292C22—21no—
293C22—21no—
294C22—21no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22C2×D3×D411yescharacteristic
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—61no—
304C4—61no—
305C4—61no—
306C4—61no—
307C4—121no—
308C4—121no—
309C4—121no—
310C4—121no—
311C4#101011yescharacteristic
312C4#101011yescharacteristic
313C3#324011yescharacteristic, complemented, Sylow
314C2—41no—
315C2—81no—
316C2#564811yescharacteristic
317C2#576811yescharacteristic
318C2#577311yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#482C2
socleC22×C3C22×D4
prime radicalC3×#121C22
hypercenter#482D3
hypocenterC3#3240
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #5517C2semidirect
5. #4996C2semidirect
6. #4877C2semidirect
7. #4876C2semidirect
8. #4857C2semidirect
9. #4856C2semidirect
10. #4766C2semidirect
11. #4765C2semidirect
12. #4765C2semidirect
13. #4763C2semidirect
14. #4723C2semidirect
15. #4719C2semidirect
313. C3#3240semidirect

Maximal subgroups

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

subgroupindex
#56002
#55172
C3×#4822
#50352
#49962
#48772
#48762
#48572
#48562
#47662
#47652
#47632
#47232
#47192
#32403