Finite Group Databasebeta

← #81457

Subgroups — #81457

Order 384.

384 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#5643C211yesmaximal, characteristic, complemented
2#5504C211yesmaximal, characteristic, complemented
3C3×#484C211yesmaximal, characteristic, complemented
4#5047C211yesmaximal, characteristic, complemented
5#4967C211yesmaximal, characteristic, complemented
6#4890C211yesmaximal, characteristic, complemented
7#4889C211yesmaximal, characteristic, complemented
8#4875C211yesmaximal, characteristic, complemented
9#4872C211yesmaximal, characteristic, complemented
10#4819C211yesmaximal, characteristic, complemented
11#4817C211yesmaximal, characteristic, complemented
12#4798C211yesmaximal, characteristic, complemented
13#4790C211yesmaximal, characteristic, complemented
14#4734C211yesmaximal, characteristic
15#4720C211yesmaximal, characteristic, complemented
16#3124—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C4⋊C4C2211yescharacteristic
20#947C2211yescharacteristic
21Q8×Dic3C2211yescharacteristic
22C2×#216C2211yescharacteristic
23C2×#215C2211yescharacteristic
24#930C2211yescharacteristic
25C4×#67—21no—
26C4×#67—21no—
27#926C2211yescharacteristic
28C2×D24C2211yescharacteristic
29C2×#204C2211yescharacteristic
30#898—21no—
31#897—21no—
32#893C2211yescharacteristic
33#893C2211yescharacteristic
34#893C2211yescharacteristic
35#892—21no—
36D3×C4⋊C4—21no—
37#888C2211yescharacteristic
38#887C2211yescharacteristic
39#887C2211yescharacteristic
40#885—21no—
41#883—21no—
42C3×#107C2211yescharacteristic
43C3×#107C2211yescharacteristic
44C3×#103C2211yescharacteristic
45C3×#103C2211yescharacteristic
46C3×C22⋊C8C2211yescharacteristic
47#830C2211yescharacteristic
48#821C2211yescharacteristic
49#816C2211yescharacteristic
50#815C2211yescharacteristic
51Dic3⋊C8C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54#810C2211yescharacteristic
55#809C2211yescharacteristic
56#809C2211yescharacteristic
57#809C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#542—31no—
61#520—31no—
62#484D311yescharacteristic, complemented
63#480—31no—
64#477—31no—
65#474—31no—
66#464—31no—
67#463—31no—
68#452—31no—
69#449—31no—
70#440—31no—
71#440—31no—
72C4×Q16—31no—
73C4×D8—31no—
74#433—31no—
75C2×C3×Q8C2311yescharacteristic
76C22×C3×C4—21no—
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C2×#67—21no—
80#235—22no—
81#235—22no—
82C2×D12C2311yescharacteristic
83C2×D12C2311yescharacteristic
84C2×C4×D3—21no—
85C2×C4×D3—21no—
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×Dic6—21no—
89C2×Dic6C2311yescharacteristic
90C2×C3×C8C2311yescharacteristic
91C2×C3×C8C2311yescharacteristic
92C3×C4⋊C4—21no—
93C3×C4⋊C4—21no—
94C3×C4⋊C4C2311yescharacteristic
95C3×C4⋊C4C2311yescharacteristic
96C3×C4⋊C4C2311yescharacteristic
97C3×C22⋊C4—21no—
98#217D411yescharacteristic
99#217D411yescharacteristic
100#216—22no—
101#215—22no—
102(C2×D3)⋊C4—21no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3D411yescharacteristic
110C4⋊Dic3D411yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115C4×Dic3—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3C2311yescharacteristic
119C4×Dic3C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122D24—22no—
123#204—22no—
124C2×#41—31no—
125C2×Q16—31no—
126C2×SD16—31no—
127C2×SD16—31no—
128C2×D8—31no—
129C4⋊Q8—31no—
130#126—61no—
131#124—31no—
132#124—61no—
133#123—61no—
134C22⋊Q8—61no—
135C22⋊Q8C2×D311yescharacteristic
136#121—31no—
137C4×Q8—31no—
138C4×Q8—31no—
139C4×Q8—31no—
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—31no—
143C4×D4—61no—
144C4×D4—61no—
145#117—31no—
146#117—61no—
147C2×C4⋊C4—61no—
148C2×C4⋊C4C2×D311yescharacteristic
149#107—31no—
150#107—31no—
151#107C2×D311yescharacteristic
152#107C2×D311yescharacteristic
153C4⋊C8—31no—
154C4⋊C8—31no—
155#103—31no—
156#103—31no—
157#103C2×D311yescharacteristic
158#103C2×D311yescharacteristic
159#102—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163C22⋊C8—31no—
164C22⋊C8C2×D311yescharacteristic
165#97—31no—
166C4×C8—31no—
167C23×C3C2×D411yescharacteristic
168C22×D3—21no—
169C22×D3—21no—
170C3×Q8—21no—
171C3×Q8—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—81no—
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2411yescharacteristic
181#67—24no—
182#67—81no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3C2×D411yescharacteristic
186C2×Dic3C2×D411yescharacteristic
187C2×Dic3C2×D411yescharacteristic
188C2×Dic3C2×D411yescharacteristic
189D12—21no—
190D12—21no—
191D12—21no—
192D12#4112yes—
193C4×D3—24no—
194C4×D3—81no—
195C4×D3—81no—
196C4×D3—81no—
197Dic6—21no—
198Dic6—81no—
199Dic6#4112yes—
200C3×C8—21no—
201C3×C8—21no—
202C3⋊C8—21no—
203C3⋊C8—21no—
204#41—62no—
205#41—62no—
206C2×Q8—31no—
207C2×Q8—61no—
208C2×Q8C22×D311yescharacteristic
209C2×D4—31no—
210C2×D4—31no—
211C2×D4—61no—
212C2×D4—61no—
213C22×C4—21no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4—61no—
217C22×C4—61no—
218C22×C4C22×D311yescharacteristic
219Q16—62no—
220SD16—62no—
221SD16—62no—
222D8—62no—
223C2×C8—31no—
224C2×C8—31no—
225C2×C8C22×D311yescharacteristic
226C2×C8C22×D311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—31no—
230C4⋊C4—31no—
231C4⋊C4—31no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4C22×D311yescharacteristic
237C4⋊C4C22×D311yescharacteristic
238C4⋊C4C22×D311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—31no—
241C22⋊C4—31no—
242C22⋊C4—61no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C42—31no—
249C42—31no—
250C42—61no—
251C42—61no—
252C42—61no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3C22×D411yescharacteristic
257C2×D3—22no—
258C2×D3—41no—
259C2×D3—41no—
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C3×C4—21no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4C2×#4111yescharacteristic
269C3×C4C2×#4111yescharacteristic
270Dic3—22no—
271Dic3—21no—
272Dic3—21no—
273Dic3—21no—
274Dic3—21no—
275Dic3—41no—
276C23—61no—
277C23—61no—
278C23D3×D411yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—32no—
282Q8—61no—
283Q8—241no—
284D4—32no—
285D4—64no—
286D4—61no—
287D4—61no—
288D4—61no—
289D4—241no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—31no—
297C2×C4—31no—
298C2×C4—31no—
299C2×C4—31no—
300C2×C4—64no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—81no—
304C2×C4—241no—
305C2×C4—241no—
306C2×C4—241no—
307C2×C4D3×D411yescharacteristic
308C2×C4C23×D311yescharacteristic
309C8—21no—
310C8—21no—
311C8—61no—
312C8—61no—
313C2×C3—41no—
314C2×C3#52511yescharacteristic
315C2×C3#57611yescharacteristic
316C2×C3#57811yescharacteristic
317D3—42no—
318D3—81no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—62no—
323C22—121no—
324C22—121no—
325C22—121no—
326C22—121no—
327C22—121no—
328C22C2×D3×D411yescharacteristic
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—62no—
335C4—61no—
336C4—61no—
337C4—61no—
338C4—61no—
339C4—121no—
340C4D3×#4111yescharacteristic
341C4D3×#4111yescharacteristic
342C3#312411yescharacteristic, complemented, Sylow
343C2—41no—
344C2—122no—
345C2—241no—
346C2#565611yescharacteristic
347C2#576611yescharacteristic
348C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#484C2
socleC22×C3C22×D4
prime radical#4734C2
hypercenter#484D3
hypocenterC3#3124
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #5643C2semidirect
2. #5504C2semidirect
3. C3×#484C2semidirect
4. #5047C2semidirect
5. #4967C2semidirect
6. #4890C2semidirect
7. #4889C2semidirect
8. #4875C2semidirect
9. #4872C2semidirect
10. #4819C2semidirect
11. #4817C2semidirect
12. #4798C2semidirect
13. #4790C2semidirect
15. #4720C2semidirect
62. #484D3semidirect
342. C3#3124semidirect

Maximal subgroups

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

subgroupindex
#56432
#55042
C3×#4842
#50472
#49672
#48902
#48892
#48752
#48722
#48192
#48172
#47982
#47902
#47342
#47202
#31243