Finite Group Databasebeta

← #81328

Subgroups — #81328

Order 384.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5608C211yesmaximal, characteristic
2#5504C211yesmaximal, characteristic, complemented
3C3×#481C211yesmaximal, characteristic, complemented
4#5035C211yesmaximal, characteristic, complemented
5#4971C211yesmaximal, characteristic, complemented
6#4868C211yesmaximal, characteristic, complemented
7#4862C211yesmaximal, characteristic, complemented
8#4861C211yesmaximal, characteristic, complemented
9D3×#106C211yesmaximal, characteristic, complemented
10#4784C211yesmaximal, characteristic, complemented
11#4777C211yesmaximal, characteristic, complemented
12#4772C211yesmaximal, characteristic, complemented
13#4771C211yesmaximal, characteristic, complemented
14#4727C211yesmaximal, characteristic, complemented
15#4723C211yesmaximal, characteristic, complemented
16#3099—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C3×#121C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21#939—21no—
22#938—21no—
23#938C2211yescharacteristic
24C4×#67—21no—
25C4×#67—21no—
26#926C2211yescharacteristic
27#924C2211yescharacteristic
28C2×ΓL(1,𝔽25)C2211yescharacteristic
29C2×D3×C8C2211yescharacteristic
30#897C2211yescharacteristic
31#893—21no—
32#892C2211yescharacteristic
33#892C2211yescharacteristic
34D3×C4⋊C4C2211yescharacteristic
35D3×C4⋊C4C2211yescharacteristic
36D3×C4⋊C4C2211yescharacteristic
37#887—21no—
38#884—21no—
39#878—21no—
40C3×#106C2211yescharacteristic
41C3×#106C2211yescharacteristic
42C3×#102C2211yescharacteristic
43C3×#102C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45#832C2211yescharacteristic
46#832C2211yescharacteristic
47#830C2211yescharacteristic
48(C2×D3)⋊C8C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50#818C2211yescharacteristic
51#817C2211yescharacteristic
52#816C2211yescharacteristic
53#816C2211yescharacteristic
54#810C2211yescharacteristic
55#810C2211yescharacteristic
56#808C2211yescharacteristic
57#808C2211yescharacteristic
58#808C2211yescharacteristic
59#807C2211yescharacteristic
60#537—31no—
61#520—31no—
62#485—31no—
63#485—31no—
64#483—31no—
65#483—31no—
66#482—31no—
67#482—31no—
68#481—31no—
69#481D311yescharacteristic, complemented
70#428—31no—
71C2×#106—31no—
72#417—31no—
73#416—31no—
74#408—31no—
75C2×C3×D4—21no—
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C22×C3×C4C2311yescharacteristic
79C2×#67—21no—
80C2×#67—21no—
81C2×#67D411yescharacteristic
82C2×#67D411yescharacteristic
83C22×Dic3—21no—
84#237—22no—
85#237—22no—
86#235—22no—
87#235—22no—
88C2×D12D411yescharacteristic
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×C4×D3C2311yescharacteristic
93C2×C4×D3C2311yescharacteristic
94C2×Dic6D411yescharacteristic
95C2×Dic6C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
98C3×C4⋊C4—21no—
99C3×C4⋊C4C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C4⋊C4C2311yescharacteristic
102C3×C22⋊C4—21no—
103#217—21no—
104#217—21no—
105#217—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112C4⋊Dic3C2311yescharacteristic
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120C2×C3⋊C8C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122ΓL(1,𝔽25)—22no—
123D3×C8—22no—
124C2×#41—31no—
125C2×#41—31no—
126C2×M16—31no—
127C22×C8—31no—
128C22⋊Q8—31no—
129C22⋊Q8—31no—
130C22⋊Q8—61no—
131#121—31no—
132#121—61no—
133#121—61no—
134#121—61no—
135#121C2×D311yescharacteristic
136C4×Q8—61no—
137C4×D4—61no—
138C4×D4—61no—
139C4×D4—61no—
140#117—31no—
141#117—31no—
142#117—31no—
143C2×C4⋊C4—31no—
144C2×C4⋊C4—31no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4C2×D311yescharacteristic
147#107—31no—
148#107—31no—
149#106—31no—
150#106—31no—
151#106—31no—
152#106—31no—
153#106C2×D311yescharacteristic
154#106C2×D311yescharacteristic
155#103—31no—
156#103—31no—
157#103—31no—
158#103—31no—
159#102—31no—
160#102—31no—
161#102C2×D311yescharacteristic
162#102C2×D311yescharacteristic
163C22⋊C8—31no—
164C22⋊C8—31no—
165C22⋊C8—31no—
166C22⋊C8C2×D311yescharacteristic
167C23×C3—21no—
168C23×C3C2×D411yescharacteristic
169C22×D3C2×D411yescharacteristic
170C22×D3C2×D411yescharacteristic
171C3×D4—21no—
172C3×D4—21no—
173C3×D4—81no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—81no—
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2411yescharacteristic
182#67—22no—
183#67—22no—
184#67—42no—
185#67—81no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—42no—
191C2×Dic3C2×D411yescharacteristic
192C2×Dic3C2×D411yescharacteristic
193D12—22no—
194C4×D3—21no—
195C4×D3—21no—
196C4×D3—81no—
197C4×D3—81no—
198C4×D3—81no—
199C4×D3#4112yes—
200C4×D3#4112yes—
201Dic6—22no—
202Dic6—21no—
203Dic6—21no—
204C3×C8—21no—
205C3×C8—21no—
206C3⋊C8—21no—
207C3⋊C8—21no—
208#41—62no—
209#41—62no—
210#41—62no—
211#41—62no—
212C2×Q8—31no—
213C2×Q8—31no—
214C2×D4—21no—
215C2×D4—31no—
216C2×D4—31no—
217C2×D4—31no—
218C2×D4—61no—
219C2×D4—61no—
220C2×D4C22×D311yescharacteristic
221C22×C4—21no—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—61no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4C22×D311yescharacteristic
229M16—62no—
230C2×C8—31no—
231C2×C8—31no—
232C2×C8—62no—
233C2×C8C22×D311yescharacteristic
234C2×C8C22×D311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—31no—
237C4⋊C4—31no—
238C4⋊C4—31no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4C22×D311yescharacteristic
245C4⋊C4C22×D311yescharacteristic
246C4⋊C4C22×D311yescharacteristic
247C22⋊C4—21no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C42—61no—
255C42—61no—
256C42—61no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3C22×D411yescharacteristic
264C2×D3—21no—
265C2×D3—21no—
266C2×D3—21no—
267C2×D3—21no—
268C2×D3—21no—
269C2×D3#12312yes—
270C3×C4—21no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4C2×#4111yescharacteristic
275C3×C4C2×#4111yescharacteristic
276Dic3—21no—
277Dic3—41no—
278Dic3—41no—
279Dic3—41no—
280Dic3—41no—
281Dic3#12312yes—
282C23—21no—
283C23—31no—
284C23—31no—
285C23D3×D411yescharacteristic
286Q8—62no—
287Q8—61no—
288Q8—61no—
289D4—21no—
290D4—21no—
291D4—62no—
292D4—62no—
293D4—62no—
294D4—81no—
295D4—122no—
296D4—241no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—31no—
303C2×C4—32no—
304C2×C4—32no—
305C2×C4—31no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—81no—
313C2×C4—122no—
314C2×C4—241no—
315C2×C4—241no—
316C2×C4—241no—
317C2×C4D3×D411yescharacteristic
318C2×C4C23×D311yescharacteristic
319C8—21no—
320C8—21no—
321C8—61no—
322C8—61no—
323C2×C3—41no—
324C2×C3—81no—
325C2×C3C2×#12311yescharacteristic
326C2×C3#57711yescharacteristic
327C2×C3#57711yescharacteristic
328D3—22no—
329D3—41no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—32no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—61no—
338C22—61no—
339C22—61no—
340C22—61no—
341C22—61no—
342C22C2×D3×D411yescharacteristic
343C4—21no—
344C4—32no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—61no—
349C4—121no—
350C4—121no—
351C4—121no—
352C4—121no—
353C4D3×#4111yescharacteristic
354C4D3×#4111yescharacteristic
355C3#309911yescharacteristic, complemented, Sylow
356C2—41no—
357C2—62no—
358C2—81no—
359C2—121no—
360C2D3×#12311yescharacteristic
361C2#576211yescharacteristic
362C2#577511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#481C2
socleC22×C3C22×D4
prime radical#5608C2
hypercenter#481D3
hypocenterC3#3099
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #5504C2semidirect
3. C3×#481C2semidirect
4. #5035C2semidirect
5. #4971C2semidirect
6. #4868C2semidirect
7. #4862C2semidirect
8. #4861C2semidirect
9. D3×#106C2semidirect
10. #4784C2semidirect
11. #4777C2semidirect
12. #4772C2semidirect
13. #4771C2semidirect
14. #4727C2semidirect
15. #4723C2semidirect
69. #481D3semidirect
355. C3#3099semidirect

Maximal subgroups

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

subgroupindex
#56082
#55042
C3×#4812
#50352
#49712
#48682
#48622
#48612
D3×#1062
#47842
#47772
#47722
#47712
#47272
#47232
#30993