Finite Group Databasebeta

← #79384

Subgroups — #79384

Order 384.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5535C211yesmaximal, characteristic, complemented
2#5523C211yesmaximal, characteristic, complemented
3C3×#433C211yesmaximal, characteristic, complemented
4#4848C211yesmaximal, characteristic, complemented
5#4847C211yesmaximal, characteristic, complemented
6#4843C211yesmaximal, characteristic, complemented
7#4829C211yesmaximal, characteristic, complemented
8#4736C211yesmaximal, characteristic, complemented
9#4735C211yesmaximal, characteristic, complemented
10#4734C211yesmaximal, characteristic, complemented
11#4734C211yesmaximal, characteristic, complemented
12#4711C211yesmaximal, characteristic, complemented
13#4710C211yesmaximal, characteristic, complemented
14C4×D24C211yesmaximal, characteristic, complemented
15C4×#204C211yesmaximal, characteristic, complemented
16#3119—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C3×#117C2211yescharacteristic
19#930C2211yescharacteristic
20#930C2211yescharacteristic
21C2×C4⋊Dic3C2211yescharacteristic
22C2×D24C2211yescharacteristic
23C2×D24C2211yescharacteristic
24C2×#204C2211yescharacteristic
25C2×#204C2211yescharacteristic
26#894—21no—
27#894—21no—
28#892—21no—
29D3×C4⋊C4—21no—
30#884—21no—
31#884—21no—
32#67⋊C4—21no—
33#67⋊C4—21no—
34#874C2211yescharacteristic
35C4×D12C2211yescharacteristic
36C4×D12C2211yescharacteristic
37C4×D12C2211yescharacteristic
38C4×D12C2211yescharacteristic
39#870C2211yescharacteristic
40C4×Dic6C2211yescharacteristic
41C4×Dic6C2211yescharacteristic
42C3×C4⋊C8C2211yescharacteristic
43C3×C4⋊C8C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic
46C3×#97C2211yescharacteristic
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#540—31no—
61#520—31no—
62#481—31no—
63#480—31no—
64#479—31no—
65#478—31no—
66#460—31no—
67#459—31no—
68#449—31no—
69#449—31no—
70#442—31no—
71#440—31no—
72C4×SD16—31no—
73C4×D8—31no—
74#433D311yescharacteristic, complemented
75C22×C3×C4C2311yescharacteristic
76C2×#67—21no—
77C2×#67—21no—
78C2×#67—21no—
79C22×Dic3—21no—
80#235—22no—
81#235—22no—
82C2×D12—21no—
83C2×D12—21no—
84C2×D12C2311yescharacteristic
85C2×D12C2311yescharacteristic
86C2×D12C2311yescharacteristic
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×Dic6C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4D411yescharacteristic
98C3×C4⋊C4D411yescharacteristic
99C3×C22⋊C4D411yescharacteristic
100C3×C22⋊C4D411yescharacteristic
101C3×C42C2311yescharacteristic
102C3×C42C2311yescharacteristic
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—
109C4⋊Dic3—21no—
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112C4⋊Dic3C2311yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120D24—22no—
121D24—22no—
122#204—22no—
123#204—22no—
124C2×#41—31no—
125C2×SD16—31no—
126C2×SD16—31no—
127C2×D8—31no—
128C2×D8—31no—
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×D4—31no—
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—31no—
143C4×D4—61no—
144C4×D4—61no—
145#117—61no—
146#117C2×D311yescharacteristic
147C2×C4⋊C4—31no—
148C2×C4⋊C4—61no—
149#107—31no—
150#107—31no—
151#106—31no—
152#106—31no—
153C4⋊C8C2×D311yescharacteristic
154C4⋊C8C2×D311yescharacteristic
155#103—31no—
156#103—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163C22⋊C8C2×D311yescharacteristic
164C22⋊C8C2×D311yescharacteristic
165#97C2×D311yescharacteristic
166C4×C8C2×D311yescharacteristic
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—24no—
180#67—81no—
181#67—81no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—81no—
188D12—21no—
189D12—21no—
190D12—21no—
191D12—21no—
192D12—21no—
193D12—81no—
194D12—81no—
195D12#4112yes—
196C4×D3—24no—
197C4×D3—81no—
198C4×D3—81no—
199C4×D3—81no—
200C4×D3—81no—
201Dic6—21no—
202Dic6#4112yes—
203C3×C8—21no—
204C3×C8—21no—
205C3×C8—21no—
206C3×C8—21no—
207#41—62no—
208#41—62no—
209C2×Q8—31no—
210C2×D4—31no—
211C2×D4—31no—
212C2×D4—31no—
213C2×D4—61no—
214C2×D4—61no—
215C2×D4—61no—
216C2×D4—61no—
217C2×D4—61no—
218C22×C4—61no—
219C22×C4—61no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4—61no—
223C22×C4—61no—
224C22×C4C22×D311yescharacteristic
225SD16—62no—
226SD16—62no—
227D8—62no—
228D8—62no—
229C2×C8C22×D311yescharacteristic
230C2×C8C22×D311yescharacteristic
231C2×C8C22×D311yescharacteristic
232C2×C8C22×D311yescharacteristic
233C4⋊C4—31no—
234C4⋊C4—31no—
235C4⋊C4—31no—
236C4⋊C4—31no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4D1211yescharacteristic
243C4⋊C4D1211yescharacteristic
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4D1211yescharacteristic
251C22⋊C4D1211yescharacteristic
252C42—61no—
253C42—61no—
254C42C22×D311yescharacteristic
255C42C22×D311yescharacteristic
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3C22×D411yescharacteristic
260C2×D3—22no—
261C2×D3—41no—
262C2×D3—41no—
263C2×D3—41no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C2×D3—41no—
268C2×D3—41no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4C2×#4111yescharacteristic
275C3×C4C2×#4111yescharacteristic
276Dic3—22no—
277Dic3—41no—
278Dic3—41no—
279Dic3—41no—
280Dic3—41no—
281C23—61no—
282C23—61no—
283C23—61no—
284C23C2×D1211yescharacteristic
285Q8—32no—
286Q8—61no—
287D4—32no—
288D4—64no—
289D4—61no—
290D4—61no—
291D4—61no—
292D4—61no—
293D4—61no—
294D4—241no—
295D4—241no—
296D4—241no—
297D4—241no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—64no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—241no—
307C2×C4—241no—
308C2×C4—241no—
309C2×C4—241no—
310C2×C4—241no—
311C2×C4C2×D1211yescharacteristic
312C2×C4C2×D1211yescharacteristic
313C2×C4C2×D1211yescharacteristic
314C2×C4C2×D1211yescharacteristic
315C2×C4C2×D1211yescharacteristic
316C2×C4C23×D311yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8—21no—
321C2×C3—41no—
322C2×C3#52511yescharacteristic
323C2×C3#57611yescharacteristic
324C2×C3#57711yescharacteristic
325D3—42no—
326D3—81no—
327D3—81no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—62no—
332C22—121no—
333C22—121no—
334C22—121no—
335C22—121no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22—121no—
340C22C22×D1211yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—62no—
347C4—121no—
348C4—121no—
349C4—121no—
350C4—121no—
351C4D3×#4111yescharacteristic
352C4D3×#4111yescharacteristic
353C3#311911yescharacteristic, complemented, Sylow
354C2—41no—
355C2—122no—
356C2—241no—
357C2—241no—
358C2#552411yescharacteristic
359C2#575111yescharacteristic
360C2#575211yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#433C2
socleC22×C3C22×D4
hypercenter#433D3
hypocenterC3#3119
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #5535C2semidirect
2. #5523C2semidirect
3. C3×#433C2semidirect
4. #4848C2semidirect
5. #4847C2semidirect
6. #4843C2semidirect
7. #4829C2semidirect
8. #4736C2semidirect
9. #4735C2semidirect
10. #4734C2semidirect
11. #4734C2semidirect
12. #4711C2semidirect
13. #4710C2semidirect
14. C4×D24C2semidirect
15. C4×#204C2semidirect
74. #433D3semidirect
353. C3#3119semidirect

Maximal subgroups

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

subgroupindex
#55352
#55232
C3×#4332
#48482
#48472
#48432
#48292
#47362
#47352
#47342
#47112
#47102
C4×D242
C4×#2042
#31193