Finite Group Databasebeta

← #80506

Subgroups — #80506

Order 384.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5680C211yesmaximal, characteristic, complemented
2C4×#237C211yesmaximal, characteristic, complemented
3C3×#463C211yesmaximal, characteristic, complemented
4#5173C211yesmaximal, characteristic, complemented
5#5164C211yesmaximal, characteristic, complemented
6#5158C211yesmaximal, characteristic
7#5152C211yesmaximal, characteristic, complemented
8#5054C211yesmaximal, characteristic, complemented
9#5009C211yesmaximal, characteristic, complemented
10#4835C211yesmaximal, characteristic, complemented
11#4829C211yesmaximal, characteristic, complemented
12#4815C211yesmaximal, characteristic, complemented
13#4789C211yesmaximal, characteristic, complemented
14#4784C211yesmaximal, characteristic, complemented
15#4757C211yesmaximal, characteristic, complemented
16#3111—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C2×C3×SD16C2211yescharacteristic
19C2×C3×D8C2211yescharacteristic
20C3×#124C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22#946C2211yescharacteristic
23Q8×Dic3C2211yescharacteristic
24C2×#216C2211yescharacteristic
25#938C2211yescharacteristic
26D4×Dic3C2211yescharacteristic
27D4×Dic3C2211yescharacteristic
28C2×#214C2211yescharacteristic
29C4×#67—21no—
30C2×C4×Dic3—21no—
31#892C2211yescharacteristic
32#887C2211yescharacteristic
33#883—21no—
34#67⋊C4—21no—
35#67⋊C4—21no—
36#879—21no—
37#877—21no—
38#877—21no—
39C42×D3C2211yescharacteristic
40#870C2211yescharacteristic
41C4×Dic6C2211yescharacteristic
42C3×C4⋊C8C2211yescharacteristic
43C3×#103C2211yescharacteristic
44C3×#102C2211yescharacteristic
45#835C2211yescharacteristic
46#832C2211yescharacteristic
47#832C2211yescharacteristic
48#832C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#818C2211yescharacteristic
52#817C2211yescharacteristic
53#816C2211yescharacteristic
54#816C2211yescharacteristic
55#815C2211yescharacteristic
56#815C2211yescharacteristic
57#808C2211yescharacteristic
58#807C2211yescharacteristic
59C4⋊(C3⋊C8)C2211yescharacteristic
60#529—31no—
61C4×#41—31no—
62#485—31no—
63#482—31no—
64#479—31no—
65#478—31no—
66#464—31no—
67#463D311yescharacteristic, complemented
68#452—31no—
69#449—31no—
70#442—31no—
71#441—31no—
72#440—31no—
73#440—31no—
74#432—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×D4C2311yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C2×#67—21no—
80C2×#67—21no—
81C22×Dic3—21no—
82C22×Dic3—21no—
83C22×Dic3—21no—
84#237—22no—
85#237—22no—
86C2×C4×D3D411yescharacteristic
87C2×C4×D3D411yescharacteristic
88C2×C4×D3C2311yescharacteristic
89C2×Dic6C2311yescharacteristic
90C3×SD16—22no—
91C3×D8—22no—
92C2×C3×C8C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C3×C4⋊C4C2311yescharacteristic
95C3×C22⋊C4—21no—
96C3×C22⋊C4—21no—
97C3×C22⋊C4—21no—
98C3×C42C2311yescharacteristic
99#217—21no—
100#217—21no—
101#217—21no—
102#216—22no—
103#214—22no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106C4⋊Dic3—21no—
107C4⋊Dic3C2311yescharacteristic
108C4⋊Dic3C2311yescharacteristic
109C4⋊Dic3C2311yescharacteristic
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115C4×Dic3—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3D411yescharacteristic
120C4×Dic3D411yescharacteristic
121C4×Dic3C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124C2×#41—31no—
125C2×Q16—31no—
126C2×SD16—31no—
127C2×SD16C2×D311yescharacteristic
128C2×D8C2×D311yescharacteristic
129#126—61no—
130#125—31no—
131#124C2×D311yescharacteristic
132#123—61no—
133C22⋊Q8—31no—
134#121—31no—
135C4×Q8—31no—
136C4×Q8—31no—
137C4×Q8—31no—
138C4×D4—31no—
139C4×D4—31no—
140C4×D4—61no—
141C4×D4—61no—
142C4×D4—61no—
143C4×D4C2×D311yescharacteristic
144#117—31no—
145#117—61no—
146#117—61no—
147C2×C42—31no—
148C2×C42—61no—
149#107—31no—
150#107—31no—
151#106—31no—
152#106—31no—
153C4⋊C8—31no—
154C4⋊C8C2×D311yescharacteristic
155#103—31no—
156#103—31no—
157#103—31no—
158#103C2×D311yescharacteristic
159#102—31no—
160#102—31no—
161#102—31no—
162#102C2×D311yescharacteristic
163C22⋊C8—31no—
164C22⋊C8—31no—
165#97—31no—
166#97—31no—
167C23×C3—21no—
168C23×C3—21no—
169C22×D3C2×D411yescharacteristic
170C3×Q8—21no—
171C3×Q8—21no—
172C3×D4—21no—
173C3×D4—21no—
174C3×D4—21no—
175C3×D4#4112yes—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—42no—
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2411yescharacteristic
182#67—24no—
183#67—42no—
184C2×Dic3—24no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—42no—
190C2×Dic3—42no—
191C2×Dic3C2×D411yescharacteristic
192C2×Dic3C2×D411yescharacteristic
193C2×Dic3C2×D411yescharacteristic
194C4×D3—21no—
195C4×D3—21no—
196C4×D3—41no—
197C4×D3—41no—
198Dic6—21no—
199Dic6#4112yes—
200C3×C8—21no—
201C3×C8—21no—
202C3⋊C8—21no—
203C3⋊C8—21no—
204#41—62no—
205#41—62no—
206C2×Q8—31no—
207C2×Q8C22×D311yescharacteristic
208C2×D4—61no—
209C2×D4—61no—
210C2×D4C22×D311yescharacteristic
211C2×D4C22×D311yescharacteristic
212C22×C4—21no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—61no—
217C22×C4—61no—
218C22×C4—61no—
219Q16—62no—
220SD16—22no—
221SD16—62no—
222D8—22no—
223C2×C8—31no—
224C2×C8—31no—
225C2×C8C22×D311yescharacteristic
226C2×C8C22×D311yescharacteristic
227C4⋊C4—31no—
228C4⋊C4—31no—
229C4⋊C4—31no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4C22×D311yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—61no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C42—31no—
246C42—31no—
247C42—31no—
248C42—61no—
249C42—61no—
250C42—61no—
251C42—61no—
252C42C22×D311yescharacteristic
253C22×C3—22no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3C22×D411yescharacteristic
260C2×D3—21no—
261C2×D3—21no—
262C2×D3—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4C2×#4111yescharacteristic
268C3×C4C2×#4111yescharacteristic
269Dic3—22no—
270Dic3—21no—
271Dic3—21no—
272Dic3—21no—
273Dic3—41no—
274Dic3—41no—
275Dic3—41no—
276C23—21no—
277C23—21no—
278C23—31no—
279Q8—21no—
280Q8—21no—
281Q8—32no—
282Q8—61no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—64no—
287D4—122no—
288D4#23712yes—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—31no—
292C2×C4—31no—
293C2×C4—31no—
294C2×C4—42no—
295C2×C4—64no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—121no—
303C2×C4—121no—
304C2×C4—122no—
305C2×C4—122no—
306C2×C4D3×D411yescharacteristic
307C2×C4D3×D411yescharacteristic
308C2×C4C23×D311yescharacteristic
309C8—21no—
310C8—21no—
311C8—61no—
312C8—61no—
313C2×C3—42no—
314C2×C3—81no—
315C2×C3#52511yescharacteristic
316C2×C3#57511yescharacteristic
317C2×C3#57511yescharacteristic
318D3—41no—
319C22—22no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—61no—
326C22—61no—
327C22—61no—
328C22C2×D3×D411yescharacteristic
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—61no—
334C4—61no—
335C4—61no—
336C4—62no—
337C4—121no—
338C4—121no—
339C4—121no—
340C4C2×#23711yescharacteristic
341C4D3×#4111yescharacteristic
342C3#311111yescharacteristic, complemented, Sylow
343C2—42no—
344C2—81no—
345C2—121no—
346C2#560611yescharacteristic
347C2#576811yescharacteristic
348C2#577311yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#463C2
socleC22×C3C22×D4
prime radical#5158C2
hypercenter#463D3
hypocenterC3#3111
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #5680C2semidirect
2. C4×#237C2semidirect
3. C3×#463C2semidirect
4. #5173C2semidirect
5. #5164C2semidirect
7. #5152C2semidirect
8. #5054C2semidirect
9. #5009C2semidirect
10. #4835C2semidirect
11. #4829C2semidirect
12. #4815C2semidirect
13. #4789C2semidirect
14. #4784C2semidirect
15. #4757C2semidirect
67. #463D3semidirect
342. C3#3111semidirect

Maximal subgroups

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

subgroupindex
#56802
C4×#2372
C3×#4632
#51732
#51642
#51582
#51522
#50542
#50092
#48352
#48292
#48152
#47892
#47842
#47572
#31113