Finite Group Databasebeta

← #79393

Subgroups — #79393

Order 384.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5534C211yesmaximal, characteristic, complemented
2#5526C211yesmaximal, characteristic, complemented
3C3×#433C211yesmaximal, characteristic, complemented
4#4849C211yesmaximal, characteristic, complemented
5#4845C211yesmaximal, characteristic, complemented
6#4844C211yesmaximal, characteristic, complemented
7#4841C211yesmaximal, characteristic, complemented
8#4739C211yesmaximal, characteristic, complemented
9#4738C211yesmaximal, characteristic, complemented
10#4734C211yesmaximal, characteristic
11#4733C211yesmaximal, characteristic, complemented
12#4715C211yesmaximal, characteristic, complemented
13#4714C211yesmaximal, characteristic, complemented
14#4696C211yesmaximal, characteristic, complemented
15#4681C211yesmaximal, characteristic, complemented
16#3225—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C22×Dic6C2211yescharacteristic
19C3×#117C2211yescharacteristic
20#930C2211yescharacteristic
21#924C2211yescharacteristic
22C2×Dic12C2211yescharacteristic
23C2×Dic12C2211yescharacteristic
24C2×Dic12C2211yescharacteristic
25C2×D24C2211yescharacteristic
26C2×#204C2211yescharacteristic
27C2×#204C2211yescharacteristic
28C2×#204C2211yescharacteristic
29C2×#204C2211yescharacteristic
30#898—21no—
31#897—21no—
32#897—21no—
33#896—21no—
34#886—21no—
35#886—21no—
36#885—21no—
37#883—21no—
38#875C2211yescharacteristic
39#875C2211yescharacteristic
40#875C2211yescharacteristic
41C4×D12C2211yescharacteristic
42#869C2211yescharacteristic
43#869C2211yescharacteristic
44#869C2211yescharacteristic
45C4×Dic6C2211yescharacteristic
46C3×C4⋊C8C2211yescharacteristic
47C3×C4⋊C8C2211yescharacteristic
48C3×C22⋊C8C2211yescharacteristic
49C3×C22⋊C8C2211yescharacteristic
50C3×#97C2211yescharacteristic
51C3×C4×C8C2211yescharacteristic
52#821C2211yescharacteristic
53#821C2211yescharacteristic
54#816C2211yescharacteristic
55#816C2211yescharacteristic
56#816C2211yescharacteristic
57#816C2211yescharacteristic
58#816C2211yescharacteristic
59#816C2211yescharacteristic
60#542—31no—
61#536—31no—
62#497—31no—
63#495—31no—
64#489—31no—
65#487—31no—
66#464—31no—
67#463—31no—
68#462—31no—
69#461—31no—
70#452—31no—
71#451—31no—
72#449—31no—
73#448—31no—
74#433D311yescharacteristic, complemented
75C22×C3×C4C2311yescharacteristic
76C2×#67—21no—
77C2×#67—21no—
78C22×Dic3—21no—
79#235—41no—
80#235—41no—
81C2×D12C2311yescharacteristic
82C2×D12C2311yescharacteristic
83C2×C4×D3—21no—
84C2×C4×D3—21no—
85C2×Dic6—21no—
86C2×Dic6—21no—
87C2×Dic6—41no—
88C2×Dic6—41no—
89C2×Dic6C2311yescharacteristic
90C2×Dic6C2311yescharacteristic
91C2×Dic6C2311yescharacteristic
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#217—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—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112C4⋊Dic3—21no—
113C4⋊Dic3—21no—
114C4⋊Dic3—21no—
115C4⋊Dic3—21no—
116C4⋊Dic3—21no—
117C4⋊Dic3C2311yescharacteristic
118C4⋊Dic3C2311yescharacteristic
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121C4×Dic3—21no—
122Dic12—41no—
123Dic12—41no—
124Dic12—41no—
125D24—41no—
126#204—41no—
127#204—41no—
128#204—41no—
129#204—41no—
130C2×#41—31no—
131C22×Q8—31no—
132C2×Q16—31no—
133C2×Q16—31no—
134C2×Q16—31no—
135C2×SD16—31no—
136C2×SD16—31no—
137C2×SD16—31no—
138C2×SD16—31no—
139C2×D8—31no—
140C4⋊Q8—31no—
141C4⋊Q8—31no—
142C4⋊Q8—31no—
143#126—61no—
144#124—31no—
145#124—31no—
146#124—31no—
147#124—61no—
148#123—61no—
149#123—61no—
150#123—61no—
151C22⋊Q8—31no—
152C22⋊Q8—61no—
153C22⋊Q8—61no—
154C22⋊Q8—61no—
155#121—31no—
156C4×Q8—31no—
157C4×D4—31no—
158#117C2×D311yescharacteristic
159C4⋊C8C2×D311yescharacteristic
160C4⋊C8C2×D311yescharacteristic
161#103—31no—
162#103—31no—
163#103—31no—
164#103—31no—
165#103—31no—
166#103—31no—
167#102—31no—
168#102—31no—
169C22⋊C8C2×D311yescharacteristic
170C22⋊C8C2×D311yescharacteristic
171#97C2×D311yescharacteristic
172C4×C8C2×D311yescharacteristic
173C23×C3C2×D411yescharacteristic
174C22×D3—21no—
175C22×D3—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2411yescharacteristic
184#67—42no—
185#67—81no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—42no—
193D12—21no—
194D12—21no—
195D12—21no—
196D12—21no—
197C4×D3—42no—
198C4×D3—81no—
199Dic6—21no—
200Dic6—21no—
201Dic6—21no—
202Dic6—21no—
203Dic6—21no—
204Dic6—21no—
205Dic6—21no—
206Dic6—21no—
207Dic6—42no—
208Dic6—81no—
209C3×C8—21no—
210C3×C8—21no—
211C3×C8—21no—
212C3×C8—21no—
213#41—121no—
214#41—121no—
215C2×Q8—31no—
216C2×Q8—31no—
217C2×Q8—31no—
218C2×Q8—31no—
219C2×Q8—61no—
220C2×Q8—61no—
221C2×Q8—121no—
222C2×Q8—121no—
223C2×D4—31no—
224C2×D4—31no—
225C2×D4—61no—
226C2×D4—61no—
227C22×C4—61no—
228C22×C4—61no—
229C22×C4—61no—
230C22×C4C22×D311yescharacteristic
231Q16—121no—
232Q16—121no—
233Q16—121no—
234SD16—121no—
235SD16—121no—
236SD16—121no—
237SD16—121no—
238D8—121no—
239C2×C8C22×D311yescharacteristic
240C2×C8C22×D311yescharacteristic
241C2×C8C22×D311yescharacteristic
242C2×C8C22×D311yescharacteristic
243C4⋊C4—31no—
244C4⋊C4—31no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—61no—
249C4⋊C4—61no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4D1211yescharacteristic
253C4⋊C4D1211yescharacteristic
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C22⋊C4—61no—
261C22⋊C4—61no—
262C22⋊C4—61no—
263C22⋊C4D1211yescharacteristic
264C22⋊C4D1211yescharacteristic
265C42—61no—
266C42C22×D311yescharacteristic
267C42C22×D311yescharacteristic
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3C22×D411yescharacteristic
272C2×D3—41no—
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—41no—
276C2×D3—41no—
277C2×D3—41no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4H(5,𝔽2)11yescharacteristic
284C3×C4H(5,𝔽2)11yescharacteristic
285Dic3—41no—
286Dic3—41no—
287Dic3—41no—
288Dic3—41no—
289Dic3—41no—
290Dic3—41no—
291C23—61no—
292C23—61no—
293C23C2×D1211yescharacteristic
294Q8—61no—
295Q8—61no—
296Q8—61no—
297Q8—61no—
298Q8—61no—
299Q8—61no—
300Q8—61no—
301Q8—61no—
302Q8—122no—
303Q8—241no—
304D4—61no—
305D4—61no—
306D4—61no—
307D4—61no—
308D4—122no—
309D4—241no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4—241no—
321C2×C4C2×D1211yescharacteristic
322C2×C4C2×D1211yescharacteristic
323C2×C4C2×D1211yescharacteristic
324C2×C4C2×D1211yescharacteristic
325C2×C4C2×D1211yescharacteristic
326C2×C4C23×D311yescharacteristic
327C8—21no—
328C8—21no—
329C8—21no—
330C8—21no—
331C2×C3—41no—
332C2×C3#53511yescharacteristic
333C2×C3#57711yescharacteristic
334C2×C3#57811yescharacteristic
335D3—81no—
336D3—81no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—121no—
341C22—121no—
342C22—121no—
343C22—121no—
344C22—121no—
345C22—121no—
346C22C22×D1211yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—121no—
353C4—121no—
354C4—121no—
355C4—121no—
356C4—121no—
357C4—121no—
358C4#100911yescharacteristic
359C4#100911yescharacteristic
360C3#322511yescharacteristic, complemented, Sylow
361C2—41no—
362C2—241no—
363C2—241no—
364C2#552511yescharacteristic
365C2#575111yescharacteristic
366C2#575311yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#433C2
socleC22×C3C22×D4
prime radical#4734C2
hypercenter#433D3
hypocenterC3#3225
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. #5526C2semidirect
3. C3×#433C2semidirect
4. #4849C2semidirect
5. #4845C2semidirect
6. #4844C2semidirect
7. #4841C2semidirect
8. #4739C2semidirect
9. #4738C2semidirect
11. #4733C2semidirect
12. #4715C2semidirect
13. #4714C2semidirect
14. #4696C2semidirect
15. #4681C2semidirect
74. #433D3semidirect
360. C3#3225semidirect

Maximal subgroups

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

subgroupindex
#55342
#55262
C3×#4332
#48492
#48452
#48442
#48412
#47392
#47382
#47342
#47332
#47152
#47142
#46962
#46812
#32253