Finite Group Databasebeta

← #79661

Subgroups — #79661

Order 384.

382 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#5572C211yesmaximal, characteristic, complemented
2#5562C211yesmaximal, characteristic
3C3×C4×SD16C211yesmaximal, characteristic, complemented
4#5170C211yesmaximal, characteristic, complemented
5#5163C211yesmaximal, characteristic, complemented
6#5026C211yesmaximal, characteristic, complemented
7#5018C211yesmaximal, characteristic, complemented
8#4866C211yesmaximal, characteristic, complemented
9#4857C211yesmaximal, characteristic, complemented
10#4806C211yesmaximal, characteristic, complemented
11#4799C211yesmaximal, characteristic, complemented
12#4779C211yesmaximal, characteristic, complemented
13#4762C211yesmaximal, characteristic, complemented
14C4×#204C211yesmaximal, characteristic, complemented
15#4690C211yesmaximal, characteristic, complemented
16#3126—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×C3×SD16C2211yescharacteristic
19C3×C4×Q8C2211yescharacteristic
20C3×C4×D4C2211yescharacteristic
21Q8×Dic3C2211yescharacteristic
22C2×#215C2211yescharacteristic
23#940C2211yescharacteristic
24#938C2211yescharacteristic
25C2×#214C2211yescharacteristic
26#930—21no—
27#929—21no—
28C2×#204C2211yescharacteristic
29#895C2211yescharacteristic
30#892—21no—
31#892C2211yescharacteristic
32#890C2211yescharacteristic
33#887—21no—
34#887C2211yescharacteristic
35#884—21no—
36#883—21no—
37C4×D12C2211yescharacteristic
38#872—21no—
39#872C2211yescharacteristic
40C4×Dic6—21no—
41C4×Dic6C2211yescharacteristic
42C3×#106C2211yescharacteristic
43C3×#103C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×C4×C8C2211yescharacteristic
46#835C2211yescharacteristic
47#832C2211yescharacteristic
48#821C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#817C2211yescharacteristic
52#816C2211yescharacteristic
53Dic3⋊C8C2211yescharacteristic
54Dic3⋊C8C2211yescharacteristic
55#810C2211yescharacteristic
56#809C2211yescharacteristic
57#807C2211yescharacteristic
58#807C2211yescharacteristic
59#803C2211yescharacteristic
60#540—31no—
61#519—31no—
62#482—31no—
63#482—31no—
64#479—31no—
65#479—31no—
66#460—31no—
67#460—31no—
68#448—31no—
69#448—31no—
70#440—31no—
71#440—31no—
72C4×SD16—31no—
73C4×SD16D311yescharacteristic, complemented
74#433—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C2×#67—21no—
79C2×#67—21no—
80C2×#67—21no—
81D3×Q8—22no—
82D3×Q8—22no—
83C2×D12—21no—
84C2×D12C2311yescharacteristic
85C2×C4×D3—21no—
86C2×C4×D3—21no—
87C2×C4×D3C2311yescharacteristic
88C2×Dic6—21no—
89C2×Dic6C2311yescharacteristic
90C3×SD16—22no—
91C2×C3×C8C2311yescharacteristic
92C2×C3×C8C2311yescharacteristic
93C3×C4⋊C4—21no—
94C3×C4⋊C4C2311yescharacteristic
95C3×C4⋊C4C2311yescharacteristic
96C3×C22⋊C4—21no—
97C3×C42—21no—
98C3×C42C2311yescharacteristic
99#217—21no—
100#215—22no—
101#214—22no—
102(C2×D3)⋊C4—21no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4D411yescharacteristic
106(C2×D3)⋊C4D411yescharacteristic
107C4⋊Dic3—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3C2311yescharacteristic
110C4⋊Dic3C2311yescharacteristic
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4D411yescharacteristic
115Dic3⋊C4D411yescharacteristic
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123#204—22no—
124C22×Q8—31no—
125C2×SD16—31no—
126C2×SD16—31no—
127C2×SD16—31no—
128C2×SD16C2×D311yescharacteristic
129#127—31no—
130#125—31no—
131#123—61no—
132#123—61no—
133#121—31no—
134#121—31no—
135#121—61no—
136#121—61no—
137C4×Q8—31no—
138C4×Q8—31no—
139C4×Q8—31no—
140C4×Q8—61no—
141C4×Q8—61no—
142C4×Q8C2×D311yescharacteristic
143C4×D4—31no—
144C4×D4C2×D311yescharacteristic
145#117—31no—
146#117—31no—
147#117—61no—
148#117—61no—
149#107—31no—
150#107—31no—
151#106—31no—
152#106C2×D311yescharacteristic
153C4⋊C8—31no—
154C4⋊C8—31no—
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—
166C4×C8C2×D311yescharacteristic
167C23×C3—21no—
168C22×D3—21no—
169C22×D3C2×D411yescharacteristic
170C3×Q8—21no—
171C3×Q8#4112yes—
172C3×D4—21no—
173C3×D4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—81no—
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2411yescharacteristic
181#67—81no—
182#67—81no—
183#67—81no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3C2×D411yescharacteristic
188C2×Dic3C2×D411yescharacteristic
189C2×Dic3C2×D411yescharacteristic
190D12—21no—
191D12—21no—
192D12—81no—
193C4×D3—24no—
194C4×D3—21no—
195C4×D3—21no—
196C4×D3—81no—
197Dic6—24no—
198Dic6—21no—
199Dic6#4112yes—
200C3×C8—21no—
201C3×C8—21no—
202C3⋊C8—21no—
203C3⋊C8—21no—
204C2×Q8—31no—
205C2×Q8—61no—
206C2×Q8—62no—
207C2×Q8—62no—
208C2×Q8C22×D311yescharacteristic
209C2×D4—31no—
210C2×D4—61no—
211C2×D4—61no—
212C2×D4—61no—
213C2×D4—61no—
214C2×D4C22×D311yescharacteristic
215C22×C4—21no—
216C22×C4—31no—
217C22×C4—61no—
218C22×C4—61no—
219SD16—22no—
220SD16—62no—
221SD16—62no—
222SD16—62no—
223C2×C8—31no—
224C2×C8—31no—
225C2×C8C22×D311yescharacteristic
226C2×C8C22×D311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—31no—
229C4⋊C4—31no—
230C4⋊C4—31no—
231C4⋊C4—31no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
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—
246C42—21no—
247C42—31no—
248C42—61no—
249C42—61no—
250C42—61no—
251C42—61no—
252C42C22×D311yescharacteristic
253C22×C3—41no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3C22×D411yescharacteristic
257C2×D3—21no—
258C2×D3—21no—
259C2×D3—21no—
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C3×C4—22no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4C2×#4111yescharacteristic
269C3×C4C2×#4111yescharacteristic
270Dic3—21no—
271Dic3—22no—
272Dic3—21no—
273Dic3—21no—
274Dic3—41no—
275Dic3—41no—
276C23—21no—
277C23—31no—
278C23—61no—
279Q8—21no—
280Q8—32no—
281Q8—64no—
282Q8—61no—
283Q8#23512yes—
284D4—21no—
285D4—21no—
286D4—61no—
287D4—61no—
288D4—241no—
289D4—241no—
290D4—241no—
291D4—241no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—31no—
296C2×C4—31no—
297C2×C4—31no—
298C2×C4—64no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—81no—
305C2×C4—241no—
306C2×C4D3×D411yescharacteristic
307C2×C4D3×D411yescharacteristic
308C2×C4C23×D311yescharacteristic
309C8—21no—
310C8—21no—
311C8—61no—
312C8—61no—
313C2×C3—81no—
314C2×C3#52511yescharacteristic
315C2×C3#57711yescharacteristic
316C2×C3#57711yescharacteristic
317D3—41no—
318D3—81no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—61no—
323C22—61no—
324C22—61no—
325C22—121no—
326C22—121no—
327C22—121no—
328C22C2×D3×D411yescharacteristic
329C4—21no—
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—61no—
335C4—61no—
336C4—61no—
337C4—62no—
338C4—121no—
339C4—121no—
340C4C2×#23511yescharacteristic
341C4D3×#4111yescharacteristic
342C3#312611yescharacteristic, complemented, Sylow
343C2—81no—
344C2—121no—
345C2—241no—
346C2#554711yescharacteristic
347C2#576211yescharacteristic
348C2#577011yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×SD16C2
socleC22×C3C22×D4
prime radical#5562C2
hypercenterC4×SD16D3
hypocenterC3#3126
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #5572C2semidirect
3. C3×C4×SD16C2semidirect
4. #5170C2semidirect
5. #5163C2semidirect
6. #5026C2semidirect
7. #5018C2semidirect
8. #4866C2semidirect
9. #4857C2semidirect
10. #4806C2semidirect
11. #4799C2semidirect
12. #4779C2semidirect
13. #4762C2semidirect
14. C4×#204C2semidirect
15. #4690C2semidirect
73. C4×SD16D3semidirect
342. C3#3126semidirect

Maximal subgroups

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

subgroupindex
#55722
#55622
C3×C4×SD162
#51702
#51632
#50262
#50182
#48662
#48572
#48062
#47992
#47792
#47622
C4×#2042
#46902
#31263