Finite Group Databasebeta

← #79093

Subgroups — #79093

Order 384.

358 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#5535C211yesmaximal, characteristic, complemented
2#5534C211yesmaximal, characteristic, complemented
3C3×#424C211yesmaximal, characteristic, complemented
4#5135C211yesmaximal, characteristic, complemented
5#5134C211yesmaximal, characteristic, complemented
6#5115C211yesmaximal, characteristic, complemented
7#5114C211yesmaximal, characteristic, complemented
8#4848C211yesmaximal, characteristic, complemented
9#4847C211yesmaximal, characteristic, complemented
10#4846C211yesmaximal, characteristic, complemented
11#4844C211yesmaximal, characteristic, complemented
12#4844C211yesmaximal, characteristic, complemented
13#4843C211yesmaximal, characteristic, complemented
14#4842C211yesmaximal, characteristic, complemented
15#4829C211yesmaximal, characteristic, complemented
16#3257—31nomaximal, Sylow
17C2×C3×M16C2211yescharacteristic
18C22×C3×C8C2211yescharacteristic
19C3×#117C2211yescharacteristic
20#930C2211yescharacteristic
21#930C2211yescharacteristic
22#930C2211yescharacteristic
23#924C2211yescharacteristic
24C2×D24C2211yescharacteristic
25C2×D24C2211yescharacteristic
26C2×#204C2211yescharacteristic
27C2×#204C2211yescharacteristic
28#898—21no—
29#896—21no—
30#894—21no—
31#894—21no—
32#885—21no—
33#884—21no—
34#884—21no—
35#883—21no—
36#875C2211yescharacteristic
37#874C2211yescharacteristic
38C4×D12C2211yescharacteristic
39C4×D12C2211yescharacteristic
40C4×D12C2211yescharacteristic
41#870C2211yescharacteristic
42#869C2211yescharacteristic
43C4×Dic6C2211yescharacteristic
44C3×C4⋊C8C2211yescharacteristic
45C3×C4⋊C8C2211yescharacteristic
46C3×C4⋊C8C2211yescharacteristic
47C3×C4⋊C8C2211yescharacteristic
48#821C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51#821C2211yescharacteristic
52#821C2211yescharacteristic
53#821C2211yescharacteristic
54#818C2211yescharacteristic
55#818C2211yescharacteristic
56#817C2211yescharacteristic
57#817C2211yescharacteristic
58#816C2211yescharacteristic
59#816C2211yescharacteristic
60#542—31no—
61#540—31no—
62#479—31no—
63#478—31no—
64#476—31no—
65#474—31no—
66#469—31no—
67#468—31no—
68#466—31no—
69#465—31no—
70#463—31no—
71#463—31no—
72#460—31no—
73#459—31no—
74#424D311yescharacteristic, complemented
75C22×C3×C4C2311yescharacteristic
76C2×#67—21no—
77C2×#67—21no—
78C2×#67—21no—
79C2×D12—21no—
80C2×D12—21no—
81C2×D12C2311yescharacteristic
82C2×D12C2311yescharacteristic
83C2×D12C2311yescharacteristic
84C2×C4×D3—21no—
85C2×C4×D3—21no—
86C2×C4×D3—21no—
87C2×Dic6—21no—
88C2×Dic6C2311yescharacteristic
89C3×M16—41no—
90C2×C3×C8—41no—
91C2×C3×C8C2311yescharacteristic
92C2×C3×C8C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C3×C4⋊C4D411yescharacteristic
96C3×C4⋊C4D411yescharacteristic
97C3×C22⋊C4D411yescharacteristic
98C3×C22⋊C4D411yescharacteristic
99C3×C42C2311yescharacteristic
100C3×C42C2311yescharacteristic
101#217—21no—
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—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3C2311yescharacteristic
112C4⋊Dic3C2311yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4—21no—
118Dic3⋊C4—21no—
119C4×Dic3—21no—
120D24—41no—
121D24—41no—
122#204—41no—
123#204—41no—
124C2×SD16—31no—
125C2×SD16—31no—
126C2×D8—31no—
127C2×D8—31no—
128C2×M16C2×D311yescharacteristic
129C22×C8C2×D311yescharacteristic
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×D4—31no—
149C4×D4—31no—
150#117C2×D311yescharacteristic
151#107—31no—
152#107—31no—
153#106—31no—
154#106—31no—
155C4⋊C8C2×D311yescharacteristic
156C4⋊C8C2×D311yescharacteristic
157C4⋊C8C2×D311yescharacteristic
158C4⋊C8C2×D311yescharacteristic
159#103—31no—
160#103—31no—
161#102—31no—
162#102—31no—
163#102—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167C23×C3C2×D411yescharacteristic
168C22×D3—21no—
169C22×D3—21no—
170C22×D3—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4C2×D411yescharacteristic
174C2×C3×C4C2×D411yescharacteristic
175C2×C3×C4C2×D411yescharacteristic
176C2×C3×C4C2×D411yescharacteristic
177C2×C3×C4C2×D411yescharacteristic
178C2×C3×C4C2411yescharacteristic
179#67—81no—
180#67—81no—
181#67—81no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187D12—21no—
188D12—21no—
189D12—21no—
190D12—21no—
191D12—21no—
192D12—21no—
193D12—81no—
194D12—81no—
195C4×D3—81no—
196C4×D3—81no—
197C4×D3—81no—
198Dic6—21no—
199Dic6—21no—
200Dic6—81no—
201C3×C8—21no—
202C3×C8—21no—
203C3×C8—21no—
204C3×C8—21no—
205C2×Q8—31no—
206C2×Q8—61no—
207C2×D4—31no—
208C2×D4—31no—
209C2×D4—31no—
210C2×D4—61no—
211C2×D4—61no—
212C2×D4—61no—
213C2×D4—61no—
214C2×D4—61no—
215C22×C4—61no—
216C22×C4—61no—
217C22×C4—61no—
218C22×C4C22×D311yescharacteristic
219SD16—121no—
220SD16—121no—
221D8—121no—
222D8—121no—
223M16—41no—
224C2×C8—41no—
225C2×C8C22×D311yescharacteristic
226C2×C8C22×D311yescharacteristic
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⋊C4D1211yescharacteristic
239C4⋊C4D1211yescharacteristic
240C22⋊C4—61no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4D1211yescharacteristic
250C22⋊C4D1211yescharacteristic
251C42—61no—
252C42C22×D311yescharacteristic
253C42C22×D311yescharacteristic
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3C22×D411yescharacteristic
258C2×D3—41no—
259C2×D3—41no—
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C2×D3—41no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4H(5,𝔽2)11yescharacteristic
273C3×C42−1+411yescharacteristic
274Dic3—41no—
275Dic3—41no—
276Dic3—41no—
277Dic3—41no—
278Dic3—41no—
279C23—61no—
280C23—61no—
281C23—61no—
282C23C2×D1211yescharacteristic
283Q8—61no—
284Q8—61no—
285Q8—241no—
286D4—61no—
287D4—61no—
288D4—61no—
289D4—61no—
290D4—61no—
291D4—61no—
292D4—241no—
293D4—241no—
294D4—241no—
295D4—241no—
296D4—241no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—241no—
305C2×C4—241no—
306C2×C4—241no—
307C2×C4C2×D1211yescharacteristic
308C2×C4C2×D1211yescharacteristic
309C2×C4C2×D1211yescharacteristic
310C2×C4C2×D1211yescharacteristic
311C2×C4C2×D1211yescharacteristic
312C2×C4C23×D311yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—21no—
317C2×C3—41no—
318C2×C3#53711yescharacteristic
319C2×C3#57611yescharacteristic
320C2×C3#57711yescharacteristic
321D3—81no—
322D3—81no—
323D3—81no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—121no—
328C22—121no—
329C22—121no—
330C22—121no—
331C22—121no—
332C22—121no—
333C22—121no—
334C22—121no—
335C22—121no—
336C22C22×D1211yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—121no—
343C4—121no—
344C4—121no—
345C4—121no—
346C4—121no—
347C4#100411yescharacteristic
348C4#100711yescharacteristic
349C3#325711yescharacteristic, complemented, Sylow
350C2—41no—
351C2—241no—
352C2—241no—
353C2—241no—
354C2#551011yescharacteristic
355C2#575111yescharacteristic
356C2#575211yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#424C2
socleC22×C3C22×D4
hypercenter#424D3
hypocenterC3#3257
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #5535C2semidirect
2. #5534C2semidirect
3. C3×#424C2semidirect
4. #5135C2semidirect
5. #5134C2semidirect
6. #5115C2semidirect
7. #5114C2semidirect
8. #4848C2semidirect
9. #4847C2semidirect
10. #4846C2semidirect
11. #4844C2semidirect
12. #4844C2semidirect
13. #4843C2semidirect
14. #4842C2semidirect
15. #4829C2semidirect
74. #424D3semidirect
349. C3#3257semidirect

Maximal subgroups

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

subgroupindex
#55352
#55342
C3×#4242
#51352
#51342
#51152
#51142
#48482
#48472
#48462
#48442
#48432
#48422
#48292
#32573