Finite Group Databasebeta

← #79602

Subgroups — #79602

Order 384.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5562C211yesmaximal, characteristic, complemented
2#5561C211yesmaximal, characteristic, complemented
3C3×C4×D8C211yesmaximal, characteristic, complemented
4#5159C211yesmaximal, characteristic, complemented
5#5154C211yesmaximal, characteristic, complemented
6#5018C211yesmaximal, characteristic, complemented
7#5014C211yesmaximal, characteristic, complemented
8#4886C211yesmaximal, characteristic, complemented
9#4876C211yesmaximal, characteristic, complemented
10#4778C211yesmaximal, characteristic, complemented
11#4775C211yesmaximal, characteristic, complemented
12#4768C211yesmaximal, characteristic, complemented
13#4760C211yesmaximal, characteristic, complemented
14C4×#204C211yesmaximal, characteristic, complemented
15#4689C211yesmaximal, characteristic, complemented
16#3179—31nomaximal, Sylow
17C2×C3×D8C2211yescharacteristic
18C3×C4×D4C2211yescharacteristic
19C3×C4×D4C2211yescharacteristic
20#940C2211yescharacteristic
21#938C2211yescharacteristic
22#938C2211yescharacteristic
23#936C2211yescharacteristic
24C2×#214C2211yescharacteristic
25C2×#213C2211yescharacteristic
26#930—21no—
27#929—21no—
28#929—21no—
29#924—21no—
30C2×#204C2211yescharacteristic
31C2×ΓL(1,𝔽25)C2211yescharacteristic
32C2×D3×C8C2211yescharacteristic
33#897C2211yescharacteristic
34#895C2211yescharacteristic
35#890C2211yescharacteristic
36#888C2211yescharacteristic
37#885—21no—
38#884—21no—
39#883—21no—
40#879—21no—
41C4×D12C2211yescharacteristic
42#872C2211yescharacteristic
43C4×Dic6C2211yescharacteristic
44C3×#107C2211yescharacteristic
45C3×#102C2211yescharacteristic
46C3×#102C2211yescharacteristic
47C3×C4×C8C2211yescharacteristic
48#832C2211yescharacteristic
49#832C2211yescharacteristic
50#821C2211yescharacteristic
51#817C2211yescharacteristic
52#816C2211yescharacteristic
53#815C2211yescharacteristic
54C8×Dic3C2211yescharacteristic
55#810C2211yescharacteristic
56#809C2211yescharacteristic
57#808C2211yescharacteristic
58#807C2211yescharacteristic
59#803C2211yescharacteristic
60#542—31no—
61#540—31no—
62#501—31no—
63#496—31no—
64#488—31no—
65#486—31no—
66#469—31no—
67#468—31no—
68#466—31no—
69#465—31no—
70#442—31no—
71#440—31no—
72C4×SD16—31no—
73C4×D8D311yescharacteristic, complemented
74#405—31no—
75C2×C3×D4C2311yescharacteristic
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C2×D12—21no—
84C2×D12C2311yescharacteristic
85C2×C4×D3—21no—
86C2×C4×D3C2311yescharacteristic
87C2×Dic6—21no—
88C2×Dic6C2311yescharacteristic
89C3×D8—22no—
90C2×C3×C8C2311yescharacteristic
91C2×C3×C8C2311yescharacteristic
92C3×C4⋊C4C2311yescharacteristic
93C3×C4⋊C4C2311yescharacteristic
94C3×C22⋊C4—21no—
95C3×C22⋊C4—21no—
96C3×C42C2311yescharacteristic
97#217—21no—
98#217—21no—
99#217—21no—
100#217—21no—
101#214—22no—
102#213—22no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4D411yescharacteristic
107(C2×D3)⋊C4D411yescharacteristic
108C4⋊Dic3—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4D411yescharacteristic
116Dic3⋊C4D411yescharacteristic
117C4×Dic3—21no—
118C4×Dic3C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121#204—22no—
122ΓL(1,𝔽25)—22no—
123D3×C8—22no—
124C2×SD16—31no—
125C2×SD16—31no—
126C2×D8—31no—
127C2×D8C2×D311yescharacteristic
128C2×M16—31no—
129C22×C8—31no—
130C4⋊Q8—31no—
131#127—31no—
132#126—61no—
133#125—31no—
134#124—31no—
135#124—61no—
136#123—61no—
137#123—61no—
138#123—61no—
139C22⋊Q8—31no—
140C22⋊Q8—61no—
141#121—31no—
142#121—31no—
143#121—31no—
144#121—61no—
145#121—61no—
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4C2×D311yescharacteristic
149C4×D4C2×D311yescharacteristic
150#117—31no—
151#107—31no—
152#107C2×D311yescharacteristic
153#106—31no—
154#106—31no—
155#103—31no—
156#103—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102C2×D311yescharacteristic
162#102C2×D311yescharacteristic
163#97—31no—
164#97—31no—
165C4×C8—31no—
166C4×C8C2×D311yescharacteristic
167C23×C3—21no—
168C23×C3—21no—
169C22×D3—21no—
170C22×D3C2×D411yescharacteristic
171C3×D4—21no—
172C3×D4—21no—
173C3×D4—21no—
174C3×D4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—81no—
178C2×C3×C4—81no—
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2411yescharacteristic
182#67—81no—
183#67—81no—
184#67—81no—
185#67—81no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3C2×D411yescharacteristic
190C2×Dic3C2×D411yescharacteristic
191C2×Dic3C2×D411yescharacteristic
192D12—21no—
193D12—21no—
194D12—81no—
195C4×D3—21no—
196C4×D3—21no—
197C4×D3—81no—
198Dic6—21no—
199Dic6—21no—
200Dic6—81no—
201C3×C8—21no—
202C3×C8#4112yes—
203C3⋊C8—21no—
204C3⋊C8#4112yes—
205C2×Q8—31no—
206C2×Q8—61no—
207C2×D4—31no—
208C2×D4—61no—
209C2×D4—61no—
210C2×D4—61no—
211C2×D4—61no—
212C2×D4—61no—
213C2×D4C22×D311yescharacteristic
214C2×D4C22×D311yescharacteristic
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—31no—
218C22×C4—61no—
219SD16—62no—
220SD16—62no—
221D8—22no—
222D8—62no—
223M16—62no—
224C2×C8—31no—
225C2×C8—31no—
226C2×C8—62no—
227C2×C8C22×D311yescharacteristic
228C2×C8C22×D311yescharacteristic
229C4⋊C4—31no—
230C4⋊C4—31no—
231C4⋊C4—31no—
232C4⋊C4—31no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4C22×D311yescharacteristic
239C4⋊C4C22×D311yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4—31no—
243C22⋊C4—31no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C42—31no—
252C42—61no—
253C42C22×D311yescharacteristic
254C22×C3—41no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3C22×D411yescharacteristic
261C2×D3—21no—
262C2×D3—21no—
263C2×D3—21no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4C2×#4111yescharacteristic
272C3×C4C2×#4111yescharacteristic
273Dic3—21no—
274Dic3—21no—
275Dic3—21no—
276Dic3—41no—
277Dic3—41no—
278Dic3—41no—
279C23—21no—
280C23—21no—
281C23—31no—
282C23—61no—
283Q8—61no—
284Q8—61no—
285Q8—241no—
286D4—21no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—61no—
291D4—61no—
292D4—241no—
293D4—241no—
294D4—241no—
295D4—241no—
296D4—241no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—31no—
300C2×C4—31no—
301C2×C4—31no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—241no—
310C2×C4D3×D411yescharacteristic
311C2×C4D3×D411yescharacteristic
312C2×C4C23×D311yescharacteristic
313C8—21no—
314C8—32no—
315C8—61no—
316C8#23512yes—
317C2×C3—81no—
318C2×C3—81no—
319C2×C3#53211yescharacteristic
320C2×C3#57611yescharacteristic
321C2×C3#57711yescharacteristic
322D3—41no—
323D3—81no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—61no—
331C22—61no—
332C22—61no—
333C22—121no—
334C22—121no—
335C22—121no—
336C22C2×D3×D411yescharacteristic
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—61no—
342C4—61no—
343C4—61no—
344C4—121no—
345C4—121no—
346C4—121no—
347C4C2×#23511yescharacteristic
348C4D3×#4111yescharacteristic
349C3#317911yescharacteristic, complemented, Sylow
350C2—81no—
351C2—81no—
352C2—121no—
353C2—241no—
354C2#554811yescharacteristic
355C2#575711yescharacteristic
356C2#577011yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×D8C2
socleC22×C3C22×D4
hypercenterC4×D8D3
hypocenterC3#3179
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #5562C2semidirect
2. #5561C2semidirect
3. C3×C4×D8C2semidirect
4. #5159C2semidirect
5. #5154C2semidirect
6. #5018C2semidirect
7. #5014C2semidirect
8. #4886C2semidirect
9. #4876C2semidirect
10. #4778C2semidirect
11. #4775C2semidirect
12. #4768C2semidirect
13. #4760C2semidirect
14. C4×#204C2semidirect
15. #4689C2semidirect
73. C4×D8D3semidirect
349. C3#3179semidirect

Maximal subgroups

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

subgroupindex
#55622
#55612
C3×C4×D82
#51592
#51542
#50182
#50142
#48862
#48762
#47782
#47752
#47682
#47602
C4×#2042
#46892
#31793