Finite Group Databasebeta

← #79392

Subgroups — #79392

Order 384.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5534C211yesmaximal, characteristic, complemented
2#5525C211yesmaximal, characteristic, complemented
3C3×#433C211yesmaximal, characteristic, complemented
4#4848C211yesmaximal, characteristic, complemented
5#4845C211yesmaximal, characteristic, complemented
6#4844C211yesmaximal, characteristic, complemented
7#4843C211yesmaximal, characteristic, complemented
8#4734C211yesmaximal, characteristic, complemented
9#4733C211yesmaximal, characteristic, complemented
10#4732C211yesmaximal, characteristic, complemented
11#4731C211yesmaximal, characteristic, complemented
12#4714C211yesmaximal, characteristic, complemented
13#4712C211yesmaximal, characteristic, complemented
14#4696C211yesmaximal, characteristic, complemented
15#4694C211yesmaximal, characteristic, complemented
16#3224—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C22×D12C2211yescharacteristic
19C3×#117C2211yescharacteristic
20#930C2211yescharacteristic
21#924C2211yescharacteristic
22C2×Dic12C2211yescharacteristic, complemented
23C2×D24C2211yescharacteristic
24C2×D24C2211yescharacteristic
25C2×D24C2211yescharacteristic, complemented
26C2×#204C2211yescharacteristic
27C2×#204C2211yescharacteristic
28C2×#204C2211yescharacteristic, complemented
29C2×#204C2211yescharacteristic, complemented
30#898—21no—
31#896—21no—
32#895—21no—
33#895—21no—
34#885—21no—
35#883—21no—
36#882—21no—
37#882—21no—
38#875C2211yescharacteristic
39#875C2211yescharacteristic
40#875C2211yescharacteristic, complemented
41#874C2211yescharacteristic
42#874C2211yescharacteristic
43C4×D12C2211yescharacteristic, complemented
44#869C2211yescharacteristic, complemented
45C4×Dic6C2211yescharacteristic, complemented
46C3×C4⋊C8C2211yescharacteristic, complemented
47C3×C4⋊C8C2211yescharacteristic, complemented
48C3×C22⋊C8C2211yescharacteristic
49C3×C22⋊C8C2211yescharacteristic
50C3×#97C2211yescharacteristic, complemented
51C3×C4×C8C2211yescharacteristic, complemented
52#821C2211yescharacteristic
53#821C2211yescharacteristic
54#821C2211yescharacteristic
55#821C2211yescharacteristic
56#821C2211yescharacteristic, complemented
57#821C2211yescharacteristic, complemented
58#816C2211yescharacteristic, complemented
59#816C2211yescharacteristic, complemented
60#542—31no—
61#535—31no—
62#496—31no—
63#495—31no—
64#489—31no—
65#486—31no—
66#464—31no—
67#463—31no—
68#460—31no—
69#459—31no—
70#452—31no—
71#450—31no—
72#449—31no—
73#447—31no—
74#433D311yescharacteristic, complemented
75C23×D3—21no—
76C22×C3×C4C2311yescharacteristic
77C2×#67—21no—
78C2×#67—21no—
79#235—41no—
80#235—41no—
81C2×D12—21no—
82C2×D12—21no—
83C2×D12—21no—
84C2×D12—21no—
85C2×D12—21no—
86C2×D12—41no—
87C2×D12—41no—
88C2×D12C2311yescharacteristic
89C2×D12C2311yescharacteristic
90C2×D12C2311yescharacteristic
91C2×D12C2311yescharacteristic
92C2×C4×D3—21no—
93C2×C4×D3—21no—
94C2×Dic6—21no—
95C2×Dic6C2311yescharacteristic
96C2×Dic6C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
98C2×C3×C8C2311yescharacteristic
99C2×C3×C8C2311yescharacteristic
100C2×C3×C8C2311yescharacteristic
101C3×C4⋊C4D411yescharacteristic
102C3×C4⋊C4D411yescharacteristic
103C3×C22⋊C4D411yescharacteristic
104C3×C22⋊C4D411yescharacteristic
105C3×C42C2311yescharacteristic
106C3×C42C2311yescharacteristic
107#217—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4—21no—
114(C2×D3)⋊C4—21no—
115(C2×D3)⋊C4—21no—
116C4⋊Dic3—21no—
117C4⋊Dic3C2311yescharacteristic
118C4⋊Dic3C2311yescharacteristic
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121C4×Dic3—21no—
122Dic12—41no—
123D24—41no—
124D24—41no—
125D24—41no—
126#204—41no—
127#204—41no—
128#204—41no—
129#204—41no—
130C2×#41—31no—
131C22×D4—31no—
132C2×Q16—31no—
133C2×SD16—31no—
134C2×SD16—31no—
135C2×SD16—31no—
136C2×SD16—31no—
137C2×D8—31no—
138C2×D8—31no—
139C2×D8—31no—
140C4⋊Q8—31no—
141#127—31no—
142#127—31no—
143#126—61no—
144#124—31no—
145#124—31no—
146#124—31no—
147#124—61no—
148#123—61no—
149C22⋊Q8—31no—
150C22⋊Q8—61no—
151#121—31no—
152#121—61no—
153#121—61no—
154#120—61no—
155#120—61no—
156C4×Q8—31no—
157C4×D4—31no—
158#117C2×D311yescharacteristic
159C4⋊C8C2×D311yescharacteristic, complemented
160C4⋊C8C2×D311yescharacteristic, complemented
161#103—31no—
162#103—31no—
163#102—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167#102—31no—
168#102—31no—
169C22⋊C8C2×D311yescharacteristic
170C22⋊C8C2×D311yescharacteristic
171#97C2×D311yescharacteristic, complemented
172C4×C8C2×D311yescharacteristic, complemented
173C23×C3C2×D411yescharacteristic
174C22×D3—21no—
175C22×D3—21no—
176C22×D3—21no—
177C22×D3—21no—
178C22×D3—42no—
179C22×D3—81no—
180C22×D3—81no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2×D411yescharacteristic
188C2×C3×C4C2411yescharacteristic
189#67—42no—
190#67—81no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195D12—21no—
196D12—21no—
197D12—21no—
198D12—21no—
199D12—21no—
200D12—21no—
201D12—21no—
202D12—21no—
203D12—42no—
204D12—81no—
205D12—81no—
206D12—81no—
207D12—81no—
208C4×D3—42no—
209C4×D3—81no—
210Dic6—21no—
211Dic6—21no—
212Dic6—21no—
213Dic6—21no—
214Dic6—81no—
215C3×C8—21no—
216C3×C8—21no—
217C3×C8—21no—
218C3×C8—21no—
219C24—61no—
220#41—121no—
221#41—121no—
222C2×Q8—31no—
223C2×Q8—31no—
224C2×Q8—61no—
225C2×D4—31no—
226C2×D4—31no—
227C2×D4—31no—
228C2×D4—31no—
229C2×D4—61no—
230C2×D4—61no—
231C2×D4—61no—
232C2×D4—61no—
233C2×D4—61no—
234C2×D4—61no—
235C2×D4—61no—
236C2×D4—121no—
237C2×D4—121no—
238C22×C4—61no—
239C22×C4—61no—
240C22×C4C22×D311yescharacteristic
241Q16—121no—
242SD16—121no—
243SD16—121no—
244SD16—121no—
245SD16—121no—
246D8—121no—
247D8—121no—
248D8—121no—
249C2×C8C22×D311yescharacteristic
250C2×C8C22×D311yescharacteristic
251C2×C8C22×D311yescharacteristic
252C2×C8C22×D311yescharacteristic
253C4⋊C4—31no—
254C4⋊C4—31no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4—61no—
258C4⋊C4D1211yescharacteristic
259C4⋊C4D1211yescharacteristic
260C22⋊C4—61no—
261C22⋊C4—61no—
262C22⋊C4—61no—
263C22⋊C4—61no—
264C22⋊C4—61no—
265C22⋊C4—61no—
266C22⋊C4—61no—
267C22⋊C4—61no—
268C22⋊C4—61no—
269C22⋊C4D1211yescharacteristic
270C22⋊C4D1211yescharacteristic
271C42—61no—
272C42C22×D311yescharacteristic
273C42C22×D311yescharacteristic
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3C22×D411yescharacteristic
278C2×D3—41no—
279C2×D3—41no—
280C2×D3—41no—
281C2×D3—41no—
282C2×D3—41no—
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—41no—
287C2×D3—41no—
288C2×D3—41no—
289C2×D3—41no—
290C2×D3—84no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4H(5,𝔽2)11yescharacteristic
297C3×C4H(5,𝔽2)11yescharacteristic
298Dic3—41no—
299Dic3—41no—
300Dic3—41no—
301Dic3—41no—
302C23—61no—
303C23—61no—
304C23—61no—
305C23—61no—
306C23—122no—
307C23—241no—
308C23—241no—
309C23C2×D1211yescharacteristic
310Q8—61no—
311Q8—61no—
312Q8—61no—
313Q8—61no—
314Q8—241no—
315D4—61no—
316D4—61no—
317D4—61no—
318D4—61no—
319D4—61no—
320D4—61no—
321D4—61no—
322D4—61no—
323D4—122no—
324D4—122no—
325D4—241no—
326D4—241no—
327D4—241no—
328D4—241no—
329D4—241no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—122no—
337C2×C4—241no—
338C2×C4C2×D1211yescharacteristic
339C2×C4C2×D1211yescharacteristic
340C2×C4C2×D1211yescharacteristic
341C2×C4C2×D1211yescharacteristic
342C2×C4C2×D1211yescharacteristic
343C2×C4C23×D311yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C2×C3—41no—
349C2×C3#53511yescharacteristic
350C2×C3#57611yescharacteristic
351C2×C3#57711yescharacteristic
352D3—81no—
353D3—81no—
354D3—81no—
355D3—81no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—121no—
360C22—121no—
361C22—121no—
362C22—121no—
363C22—121no—
364C22—121no—
365C22—121no—
366C22—121no—
367C22—121no—
368C22—121no—
369C22—121no—
370C22—121no—
371C22—244no—
372C22C22×D1211yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—121no—
379C4—121no—
380C4—121no—
381C4—121no—
382C4#100911yescharacteristic
383C4#100911yescharacteristic
384C3#322411yescharacteristic, complemented, Sylow
385C2—41no—
386C2—241no—
387C2—241no—
388C2—241no—
389C2—241no—
390C2#552511yescharacteristic
391C2#575111yescharacteristic
392C2#575211yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#433C2
socleC22×C3C22×D4
hypercenter#433D3
hypocenterC3#3224
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. #5534C2semidirect
2. #5525C2semidirect
3. C3×#433C2semidirect
4. #4848C2semidirect
5. #4845C2semidirect
6. #4844C2semidirect
7. #4843C2semidirect
8. #4734C2semidirect
9. #4733C2semidirect
10. #4732C2semidirect
11. #4731C2semidirect
12. #4714C2semidirect
13. #4712C2semidirect
14. #4696C2semidirect
15. #4694C2semidirect
22. C2×Dic12C22semidirect
25. C2×D24C22semidirect
28. C2×#204C22semidirect
29. C2×#204C22semidirect
40. #875C22semidirect
43. C4×D12C22semidirect
44. #869C22semidirect
45. C4×Dic6C22semidirect
46. C3×C4⋊C8C22semidirect
47. C3×C4⋊C8C22semidirect
50. C3×#97C22semidirect
51. C3×C4×C8C22semidirect
56. #821C22semidirect
57. #821C22semidirect
58. #816C22semidirect
59. #816C22semidirect
74. #433D3semidirect
159. C4⋊C8C2×D3semidirect
160. C4⋊C8C2×D3semidirect
171. #97C2×D3semidirect
172. C4×C8C2×D3semidirect
384. C3#3224semidirect

Maximal subgroups

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

subgroupindex
#55342
#55252
C3×#4332
#48482
#48452
#48442
#48432
#47342
#47332
#47322
#47312
#47142
#47122
#46962
#46942
#32243