Finite Group Databasebeta

← #83433

Subgroups — #83433

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
1C3×#540C211yesmaximal, characteristic, complemented
2#5534C211yesmaximal, characteristic, complemented
3#5074C211yesmaximal, characteristic, complemented
4#5070C211yesmaximal, characteristic, complemented
5#5068C211yesmaximal, characteristic, complemented
6#5064C211yesmaximal, characteristic, complemented
7#5042C211yesmaximal, characteristic, complemented
8#5041C211yesmaximal, characteristic, complemented
9#5039C211yesmaximal, characteristic, complemented
10#5038C211yesmaximal, characteristic, complemented
11#5018C211yesmaximal, characteristic, complemented
12C4×#214C211yesmaximal, characteristic, complemented
13#5014C211yesmaximal, characteristic, complemented
14C4×#213C211yesmaximal, characteristic, complemented
15#4997C211yesmaximal, characteristic, complemented
16#3179—31nomaximal, Sylow
17C3×#127C2211yescharacteristic
18C3×#125C2211yescharacteristic
19C3×#123—21no—
20C3×#123—21no—
21C3×#121—21no—
22C3×#121—21no—
23C3×#121C2211yescharacteristic
24C3×#121C2211yescharacteristic
25C3×C4×D4C2211yescharacteristic
26C3×C4×D4C2211yescharacteristic
27C3×#117C2211yescharacteristic
28C2×#214C2211yescharacteristic
29C2×#214C2211yescharacteristic
30C2×#213C2211yescharacteristic
31C2×#213C2211yescharacteristic
32#930C2211yescharacteristic
33#924C2211yescharacteristic
34C2×#208C2211yescharacteristic
35C22×C3⋊C8C2211yescharacteristic
36#898—21no—
37#896—21no—
38#885—21no—
39#883—21no—
40#875C2211yescharacteristic
41C4×D12C2211yescharacteristic
42#869C2211yescharacteristic
43C4×Dic6C2211yescharacteristic
44#832C2211yescharacteristic
45#832C2211yescharacteristic
46#832C2211yescharacteristic
47#832C2211yescharacteristic
48#810C2211yescharacteristic
49#810C2211yescharacteristic
50#809C2211yescharacteristic
51#809C2211yescharacteristic
52#808C2211yescharacteristic
53#808C2211yescharacteristic
54#807C2211yescharacteristic
55#807C2211yescharacteristic
56#803C2211yescharacteristic
57#803C2211yescharacteristic
58C4×C3⋊C8C2211yescharacteristic
59C4×C3⋊C8C2211yescharacteristic
60#542—31no—
61#540D311yescharacteristic, complemented
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×D8—31no—
74#405—31no—
75C2×C3×D4—21no—
76C2×C3×D4—21no—
77C2×C3×D4—21no—
78C2×C3×D4—21no—
79C2×C3×D4C2311yescharacteristic
80C2×C3×D4C2311yescharacteristic
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×C3×C4C2311yescharacteristic
84C2×#67—21no—
85C2×D12C2311yescharacteristic
86C2×C4×D3—21no—
87C2×Dic6—21no—
88C2×Dic6C2311yescharacteristic
89C3×C4⋊C4—21no—
90C3×C4⋊C4—21no—
91C3×C4⋊C4D411yescharacteristic
92C3×C4⋊C4D411yescharacteristic
93C3×C4⋊C4C2311yescharacteristic
94C3×C4⋊C4C2311yescharacteristic
95C3×C22⋊C4—21no—
96C3×C22⋊C4—21no—
97C3×C22⋊C4—21no—
98C3×C22⋊C4—21no—
99C3×C22⋊C4D411yescharacteristic
100C3×C22⋊C4D411yescharacteristic
101C3×C42C2311yescharacteristic
102C3×C42C2311yescharacteristic
103#217—21no—
104#214—22no—
105#214—22no—
106#213—22no—
107#213—22no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112C4⋊Dic3—21no—
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117C4×Dic3—21no—
118#208—22no—
119C2×C3⋊C8—22no—
120C2×C3⋊C8C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124C2×SD16—31no—
125C2×SD16—31no—
126C2×D8—31no—
127C2×D8—31no—
128C2×M16—31no—
129C22×C8—31no—
130C4⋊Q8—31no—
131#127C2×D311yescharacteristic
132#126—61no—
133#125C2×D311yescharacteristic
134#124—31no—
135#124—61no—
136#123—21no—
137#123—21no—
138#123—61no—
139C22⋊Q8—31no—
140C22⋊Q8—61no—
141#121—21no—
142#121—21no—
143#121—31no—
144#121C2×D311yescharacteristic
145#121C2×D311yescharacteristic
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4C2×D311yescharacteristic
149C4×D4C2×D311yescharacteristic
150#117C2×D311yescharacteristic
151#107—31no—
152#107—31no—
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#102—31no—
162#102—31no—
163#97—31no—
164#97—31no—
165C4×C8—31no—
166C4×C8—31no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3C2×D411yescharacteristic
170C22×D3—21no—
171C3×D4—21no—
172C3×D4—21no—
173C3×D4—21no—
174C3×D4—21no—
175C3×D4—81no—
176C3×D4—81no—
177C3×D4—81no—
178C3×D4—81no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—81no—
184C2×C3×C4—81no—
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2×D411yescharacteristic
188C2×C3×C4C2×D411yescharacteristic
189C2×C3×C4C2×D411yescharacteristic
190C2×C3×C4C2411yescharacteristic
191#67—81no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195D12—21no—
196D12—21no—
197C4×D3—81no—
198Dic6—21no—
199Dic6—21no—
200Dic6—81no—
201C3⋊C8—21no—
202C3⋊C8—21no—
203C3⋊C8#4112yes—
204C3⋊C8#4112yes—
205C2×Q8—31no—
206C2×Q8—61no—
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—31no—
212C2×D4—61no—
213C2×D4C22×D311yescharacteristic
214C2×D4C22×D311yescharacteristic
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—61no—
218C22×C4C22×D311yescharacteristic
219SD16—62no—
220SD16—62no—
221D8—62no—
222D8—62no—
223M16—62no—
224C2×C8—31no—
225C2×C8—31no—
226C2×C8—31no—
227C2×C8—31no—
228C2×C8—62no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—31no—
232C4⋊C4—31no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4#6711yescharacteristic
237C4⋊C4#6711yescharacteristic
238C4⋊C4C22×D311yescharacteristic
239C4⋊C4C22×D311yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4—21no—
243C22⋊C4—21no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4#6711yescharacteristic
250C22⋊C4#6711yescharacteristic
251C42—61no—
252C42C22×D311yescharacteristic
253C42C22×D311yescharacteristic
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3C22×D411yescharacteristic
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×C4—41no—
273C3×C4—41no—
274C3×C4C2×#4111yescharacteristic
275C3×C4C2×#4111yescharacteristic
276Dic3—41no—
277Dic3—41no—
278Dic3—41no—
279C23—21no—
280C23—21no—
281C23—61no—
282C23C2×#6711yescharacteristic
283Q8—61no—
284Q8—61no—
285Q8—241no—
286D4—21no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—61no—
291D4—61no—
292D4—81no—
293D4—81no—
294D4—81no—
295D4—81no—
296D4—241no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—241no—
307C2×C4C2×#6711yescharacteristic
308C2×C4C2×#6711yescharacteristic
309C2×C4C2×#6711yescharacteristic
310C2×C4C2×#6711yescharacteristic
311C2×C4C2×#6711yescharacteristic
312C2×C4C23×D311yescharacteristic
313C8—32no—
314C8—32no—
315C8—61no—
316C8—61no—
317C2×C3—41no—
318C2×C3—81no—
319C2×C3—81no—
320C2×C3#53211yescharacteristic
321C2×C3#57611yescharacteristic
322C2×C3#57711yescharacteristic
323D3—81no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—121no—
334C22—121no—
335C22—121no—
336C22C22×#6711yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—121no—
345C4—121no—
346C4—121no—
347C4D3×#4111yescharacteristic
348C4D3×#4111yescharacteristic
349C3#317911yescharacteristic, complemented, Sylow
350C2—41no—
351C2—81no—
352C2—81no—
353C2—241no—
354C2#583211yescharacteristic
355C2#583511yescharacteristic
356C2#583611yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#540C2
socleC22×C3C22×D4
hypercenter#540D3
hypocenterC3#3179
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. C3×#540C2semidirect
2. #5534C2semidirect
3. #5074C2semidirect
4. #5070C2semidirect
5. #5068C2semidirect
6. #5064C2semidirect
7. #5042C2semidirect
8. #5041C2semidirect
9. #5039C2semidirect
10. #5038C2semidirect
11. #5018C2semidirect
12. C4×#214C2semidirect
13. #5014C2semidirect
14. C4×#213C2semidirect
15. #4997C2semidirect
61. #540D3semidirect
349. C3#3179semidirect

Maximal subgroups

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

subgroupindex
C3×#5402
#55342
#50742
#50702
#50682
#50642
#50422
#50412
#50392
#50382
#50182
C4×#2142
#50142
C4×#2132
#49972
#31793