Finite Group Databasebeta

← #80766

Subgroups — #80766

Order 384.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5629C211yesmaximal, characteristic
2#5628C211yesmaximal, characteristic, complemented
3C3×#467C211yesmaximal, characteristic, complemented
4#5187C211yesmaximal, characteristic, complemented
5#5186C211yesmaximal, characteristic, complemented
6#5114C211yesmaximal, characteristic, complemented
7#5110C211yesmaximal, characteristic, complemented
8#5052C211yesmaximal, characteristic, complemented
9#5049C211yesmaximal, characteristic, complemented
10#4885C211yesmaximal, characteristic, complemented
11#4884C211yesmaximal, characteristic, complemented
12#4815C211yesmaximal, characteristic, complemented
13#4808C211yesmaximal, characteristic, complemented
14#4806C211yesmaximal, characteristic, complemented
15#4805C211yesmaximal, characteristic, complemented
16#3201—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×D3×Q8C2211yescharacteristic
19C2×#235C2211yescharacteristic
20C2×C3×Q16C2211yescharacteristic
21C22×C3×C8C2211yescharacteristic
22C3×C22⋊Q8C2211yescharacteristic
23C3×C22⋊Q8C2211yescharacteristic
24#946C2211yescharacteristic
25#946C2211yescharacteristic
26C2×#216C2211yescharacteristic
27C2×#215C2211yescharacteristic
28#930C2211yescharacteristic
29#924C2211yescharacteristic
30C2×#208C2211yescharacteristic
31C2×#204C2211yescharacteristic
32#897C2211yescharacteristic
33#896—21no—
34#895—21no—
35#895C2211yescharacteristic
36#894—21no—
37#892C2211yescharacteristic
38D3×C4⋊C4C2211yescharacteristic
39#888—21no—
40#885—21no—
41#884—21no—
42#884—21no—
43#883—21no—
44C3×#107C2211yescharacteristic
45C3×#103C2211yescharacteristic
46C3×#103C2211yescharacteristic
47#835C2211yescharacteristic
48#835C2211yescharacteristic
49#821C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51(C2×D3)⋊C8C2211yescharacteristic
52(C2×D3)⋊C8C2211yescharacteristic
53(C2×D3)⋊C8C2211yescharacteristic
54#817C2211yescharacteristic
55#816C2211yescharacteristic
56#810C2211yescharacteristic
57#809C2211yescharacteristic
58#808C2211yescharacteristic
59#807C2211yescharacteristic
60#537—31no—
61#536—31no—
62#485—31no—
63#484—31no—
64#483—31no—
65#482—31no—
66#470—31no—
67#468—31no—
68#467D311yescharacteristic, complemented
69#465—31no—
70#452—31no—
71#452—31no—
72#451—31no—
73#448—31no—
74#408—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×Q8C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C2×#67D411yescharacteristic
80C2×#67D411yescharacteristic
81#239—41no—
82#239—41no—
83D3×Q8—41no—
84D3×Q8—41no—
85#235—41no—
86#235—41no—
87C2×D12—21no—
88C2×D12—21no—
89C2×D12D411yescharacteristic
90C2×D12C2311yescharacteristic
91C2×C4×D3—21no—
92C2×C4×D3—21no—
93C2×C4×D3—21no—
94C2×C4×D3C2311yescharacteristic
95C2×C4×D3C2311yescharacteristic
96C2×Dic6—21no—
97C2×Dic6D411yescharacteristic
98C2×Dic6C2311yescharacteristic
99C3×Q16—41no—
100C2×C3×C8—41no—
101C2×C3×C8C2311yescharacteristic
102C2×C3×C8C2311yescharacteristic
103C3×C4⋊C4—21no—
104C3×C4⋊C4—21no—
105C3×C4⋊C4C2311yescharacteristic
106C3×C4⋊C4C2311yescharacteristic
107C3×C22⋊C4—21no—
108C3×C22⋊C4—21no—
109#217—21no—
110#216—41no—
111#215—41no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4—21no—
114(C2×D3)⋊C4—21no—
115(C2×D3)⋊C4—21no—
116(C2×D3)⋊C4—21no—
117(C2×D3)⋊C4—21no—
118C4⋊Dic3—21no—
119C4⋊Dic3C2311yescharacteristic
120C4⋊Dic3C2311yescharacteristic
121Dic3⋊C4—21no—
122Dic3⋊C4—21no—
123Dic3⋊C4—21no—
124Dic3⋊C4—21no—
125C4×Dic3—21no—
126#208—41no—
127C2×C3⋊C8C2311yescharacteristic
128C2×C3⋊C8C2311yescharacteristic
129#204—41no—
130C2×#41—31no—
131C2×#41—31no—
132C22×Q8—31no—
133C2×Q16—31no—
134C2×Q16C2×D311yescharacteristic
135C2×SD16—31no—
136C2×SD16—31no—
137C2×M16—31no—
138C22×C8C2×D311yescharacteristic
139C4⋊Q8—61no—
140#124—61no—
141#123—61no—
142#123—61no—
143C22⋊Q8—31no—
144C22⋊Q8—31no—
145C22⋊Q8—31no—
146C22⋊Q8—31no—
147C22⋊Q8—61no—
148C22⋊Q8C2×D311yescharacteristic
149C22⋊Q8C2×D311yescharacteristic
150#121—31no—
151#121—31no—
152#121—61no—
153#121—61no—
154#121—61no—
155#117—31no—
156C2×C4⋊C4—31no—
157#107—31no—
158#107C2×D311yescharacteristic
159#106—31no—
160#106—31no—
161#103—31no—
162#103—31no—
163#103—31no—
164#103—31no—
165#103C2×D311yescharacteristic
166#103C2×D311yescharacteristic
167#102—31no—
168#102—31no—
169C22⋊C8—31no—
170C22⋊C8—31no—
171C22⋊C8—31no—
172C22⋊C8—31no—
173C23×C3C2×D411yescharacteristic
174C22×D3—21no—
175C22×D3C2×D411yescharacteristic
176C22×D3C2×D411yescharacteristic
177C3×Q8—21no—
178C3×Q8—21no—
179C3×Q8—21no—
180C3×Q8—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4C2×D411yescharacteristic
188C2×C3×C4C2411yescharacteristic
189#67—41no—
190#67—41no—
191#67—81no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3C2×D411yescharacteristic
196C2×Dic3C2×D411yescharacteristic
197D12—21no—
198D12—21no—
199D12—41no—
200D12—42no—
201D12—81no—
202C4×D3—21no—
203C4×D3—21no—
204C4×D3—21no—
205C4×D3—21no—
206C4×D3—42no—
207C4×D3—42no—
208C4×D3—81no—
209Dic6—21no—
210Dic6—21no—
211Dic6—41no—
212Dic6—42no—
213C3×C8—21no—
214C3×C8—21no—
215C3⋊C8—21no—
216C3⋊C8—21no—
217#41—121no—
218#41—121no—
219#41—121no—
220#41—121no—
221C2×Q8—31no—
222C2×Q8—31no—
223C2×Q8—61no—
224C2×Q8—121no—
225C2×Q8—121no—
226C2×Q8C22×D311yescharacteristic
227C2×Q8C22×D311yescharacteristic
228C2×D4—31no—
229C2×D4—31no—
230C2×D4—31no—
231C2×D4—31no—
232C2×D4—61no—
233C2×D4—61no—
234C2×D4—61no—
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—61no—
238C22×C4—61no—
239C22×C4—61no—
240C22×C4C22×D311yescharacteristic
241Q16—41no—
242Q16—121no—
243SD16—121no—
244SD16—121no—
245M16—121no—
246C2×C8—31no—
247C2×C8—31no—
248C2×C8—41no—
249C2×C8C22×D311yescharacteristic
250C2×C8C22×D311yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—31no—
254C4⋊C4—31no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4—61no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4C22×D311yescharacteristic
261C4⋊C4C22×D311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—61no—
265C22⋊C4—61no—
266C22⋊C4—61no—
267C22⋊C4—61no—
268C22⋊C4—61no—
269C22⋊C4—61no—
270C22⋊C4—61no—
271C42—61no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3C22×D411yescharacteristic
276C2×D3—21no—
277C2×D3—21no—
278C2×D3—21no—
279C2×D3—21no—
280C2×D3—21no—
281C2×D3—21no—
282C2×D3—41no—
283C2×D3—41no—
284C2×D3—41no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4H(5,𝔽2)11yescharacteristic
291C3×C4H(5,𝔽2)11yescharacteristic
292Dic3—21no—
293Dic3—21no—
294Dic3—41no—
295Dic3—41no—
296Dic3—41no—
297C23—31no—
298C23—31no—
299C23—61no—
300C23D3×D411yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—61no—
306Q8—61no—
307Q8—121no—
308Q8—122no—
309D4—61no—
310D4—61no—
311D4—121no—
312D4—122no—
313D4—121no—
314D4—121no—
315D4—241no—
316D4—241no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—31no—
324C2×C4—31no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—122no—
333C2×C4—122no—
334C2×C4—241no—
335C2×C4D3×D411yescharacteristic
336C2×C4C23×D311yescharacteristic
337C8—21no—
338C8—21no—
339C8—61no—
340C8—61no—
341C2×C3—41no—
342C2×C3#53411yescharacteristic
343C2×C3#57711yescharacteristic
344C2×C3#57811yescharacteristic
345D3—41no—
346D3—41no—
347D3—81no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—61no—
352C22—61no—
353C22—61no—
354C22—61no—
355C22—61no—
356C22—61no—
357C22—121no—
358C22—121no—
359C22—121no—
360C22C2×D3×D411yescharacteristic
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—61no—
367C4—61no—
368C4—121no—
369C4—121no—
370C4—121no—
371C4#100411yescharacteristic
372C4#100911yescharacteristic
373C3#320111yescharacteristic, complemented, Sylow
374C2—41no—
375C2—121no—
376C2—121no—
377C2—241no—
378C2#560511yescharacteristic
379C2#576611yescharacteristic
380C2#577011yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#467C2
socleC22×C3C22×D4
prime radical#5629C2
hypercenter#467D3
hypocenterC3#3201
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #5628C2semidirect
3. C3×#467C2semidirect
4. #5187C2semidirect
5. #5186C2semidirect
6. #5114C2semidirect
7. #5110C2semidirect
8. #5052C2semidirect
9. #5049C2semidirect
10. #4885C2semidirect
11. #4884C2semidirect
12. #4815C2semidirect
13. #4808C2semidirect
14. #4806C2semidirect
15. #4805C2semidirect
68. #467D3semidirect
373. C3#3201semidirect

Maximal subgroups

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

subgroupindex
#56292
#56282
C3×#4672
#51872
#51862
#51142
#51102
#50522
#50492
#48852
#48842
#48152
#48082
#48062
#48052
#32013