Finite Group Databasebeta

← #79595

Subgroups — #79595

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#5562C211yesmaximal, characteristic, complemented
2#5546C211yesmaximal, characteristic, complemented
3C3×C4×D8C211yesmaximal, characteristic, complemented
4#5158C211yesmaximal, characteristic, complemented
5#5150C211yesmaximal, characteristic, complemented
6#5018C211yesmaximal, characteristic, complemented
7#5014C211yesmaximal, characteristic, complemented
8#4882C211yesmaximal, characteristic, complemented
9#4877C211yesmaximal, characteristic, complemented
10#4781C211yesmaximal, characteristic, complemented
11#4777C211yesmaximal, characteristic, complemented
12#4763C211yesmaximal, characteristic, complemented
13#4762C211yesmaximal, characteristic, complemented
14C4×#204C211yesmaximal, characteristic, complemented
15#4690C211yesmaximal, characteristic, complemented
16#3119—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C2×C3×D8C2211yescharacteristic
19C3×C4×D4C2211yescharacteristic
20C3×C4×D4C2211yescharacteristic
21#940C2211yescharacteristic
22#938C2211yescharacteristic
23D4×Dic3C2211yescharacteristic
24C2×#214C2211yescharacteristic
25C2×#213C2211yescharacteristic
26#930—21no—
27#929—21no—
28C4×#67—21no—
29C2×Dic3⋊C4—21no—
30C2×#204C2211yescharacteristic
31#895C2211yescharacteristic
32D3×C4⋊C4C2211yescharacteristic
33#890C2211yescharacteristic
34#887C2211yescharacteristic
35#884—21no—
36#883—21no—
37#67⋊C4—21no—
38#877—21no—
39C4×D12C2211yescharacteristic
40#872C2211yescharacteristic
41C4×Dic6C2211yescharacteristic
42C3×#107C2211yescharacteristic
43C3×#102C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×C4×C8C2211yescharacteristic
46#832C2211yescharacteristic
47#832C2211yescharacteristic
48#821C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#817C2211yescharacteristic
52#816C2211yescharacteristic
53Dic3⋊C8C2211yescharacteristic
54Dic3⋊C8C2211yescharacteristic
55#810C2211yescharacteristic
56#809C2211yescharacteristic
57#808C2211yescharacteristic
58#807C2211yescharacteristic
59#803C2211yescharacteristic
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×D8D311yescharacteristic, complemented
74#433—31no—
75C2×C3×D4C2311yescharacteristic
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C22×Dic3—21no—
84C22×Dic3—21no—
85#237—22no—
86#237—22no—
87C2×D12—21no—
88C2×D12C2311yescharacteristic
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3C2311yescharacteristic
92C2×Dic6C2311yescharacteristic
93C3×D8—22no—
94C2×C3×C8C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C3×C4⋊C4C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C22⋊C4—21no—
99C3×C22⋊C4—21no—
100C3×C42C2311yescharacteristic
101#217—21no—
102#217—21no—
103#214—22no—
104#213—22no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4D411yescharacteristic
108(C2×D3)⋊C4D411yescharacteristic
109C4⋊Dic3—21no—
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116Dic3⋊C4D411yescharacteristic
117Dic3⋊C4D411yescharacteristic
118C4×Dic3—21no—
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123#204—22no—
124C2×#41—31no—
125C2×SD16—31no—
126C2×SD16—31no—
127C2×D8—31no—
128C2×D8C2×D311yescharacteristic
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—61no—
142C4×D4—61no—
143C4×D4C2×D311yescharacteristic
144C4×D4C2×D311yescharacteristic
145#117—31no—
146#117—61no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—61no—
149#107—31no—
150#107C2×D311yescharacteristic
151#106—31no—
152#106—31no—
153C4⋊C8—31no—
154C4⋊C8—31no—
155#103—31no—
156#103—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102C2×D311yescharacteristic
162#102C2×D311yescharacteristic
163C22⋊C8—31no—
164C22⋊C8—31no—
165#97—31no—
166C4×C8C2×D311yescharacteristic
167C23×C3—21no—
168C23×C3—21no—
169C22×D3—21no—
170C22×D3C2×D411yescharacteristic
171C3×D4—21no—
172C3×D4—21no—
173C3×D4—21no—
174C3×D4#4112yes—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—81no—
178C2×C3×C4—81no—
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2411yescharacteristic
182#67—24no—
183#67—81no—
184#67—81no—
185#67—81no—
186C2×Dic3—24no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—81no—
191C2×Dic3C2×D411yescharacteristic
192C2×Dic3C2×D411yescharacteristic
193C2×Dic3C2×D411yescharacteristic
194D12—21no—
195D12—21no—
196D12—81no—
197C4×D3—21no—
198C4×D3—21no—
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—61no—
212C2×D4—61no—
213C2×D4—61no—
214C2×D4—61no—
215C2×D4—61no—
216C2×D4C22×D311yescharacteristic
217C2×D4C22×D311yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—31no—
221C22×C4—61no—
222C22×C4—61no—
223C22×C4—61no—
224C22×C4—61no—
225SD16—62no—
226SD16—62no—
227D8—22no—
228D8—62no—
229C2×C8—31no—
230C2×C8—31no—
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⋊C4C22×D311yescharacteristic
243C4⋊C4C22×D311yescharacteristic
244C22⋊C4—21no—
245C22⋊C4—21no—
246C22⋊C4—31no—
247C22⋊C4—31no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C42—31no—
253C42—61no—
254C42—61no—
255C42C22×D311yescharacteristic
256C22×C3—22no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3C22×D411yescharacteristic
263C2×D3—21no—
264C2×D3—21no—
265C2×D3—21no—
266C2×D3—41no—
267C2×D3—41no—
268C2×D3—41no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4C2×#4111yescharacteristic
274C3×C4C2×#4111yescharacteristic
275Dic3—22no—
276Dic3—21no—
277Dic3—21no—
278Dic3—21no—
279Dic3—41no—
280Dic3—41no—
281C23—21no—
282C23—21no—
283C23—31no—
284C23—61no—
285Q8—32no—
286Q8—61no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—64no—
291D4—61no—
292D4—61no—
293D4—241no—
294D4—241no—
295D4—241no—
296D4—241no—
297D4#23512yes—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—31no—
301C2×C4—31no—
302C2×C4—31no—
303C2×C4—64no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—241no—
312C2×C4—241no—
313C2×C4—241no—
314C2×C4D3×D411yescharacteristic
315C2×C4D3×D411yescharacteristic
316C2×C4C23×D311yescharacteristic
317C8—21no—
318C8—21no—
319C8—61no—
320C8—61no—
321C2×C3—42no—
322C2×C3—81no—
323C2×C3#52511yescharacteristic
324C2×C3#57611yescharacteristic
325C2×C3#57711yescharacteristic
326D3—41no—
327D3—81no—
328C22—22no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—61no—
335C22—61no—
336C22—61no—
337C22—121no—
338C22—121no—
339C22—121no—
340C22C2×D3×D411yescharacteristic
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—61no—
346C4—61no—
347C4—61no—
348C4—62no—
349C4—121no—
350C4—121no—
351C4C2×#23511yescharacteristic
352C4D3×#4111yescharacteristic
353C3#311911yescharacteristic, complemented, Sylow
354C2—42no—
355C2—81no—
356C2—121no—
357C2—241no—
358C2#554711yescharacteristic
359C2#575711yescharacteristic
360C2#577011yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×D8C2
socleC22×C3C22×D4
hypercenterC4×D8D3
hypocenterC3#3119
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #5562C2semidirect
2. #5546C2semidirect
3. C3×C4×D8C2semidirect
4. #5158C2semidirect
5. #5150C2semidirect
6. #5018C2semidirect
7. #5014C2semidirect
8. #4882C2semidirect
9. #4877C2semidirect
10. #4781C2semidirect
11. #4777C2semidirect
12. #4763C2semidirect
13. #4762C2semidirect
14. C4×#204C2semidirect
15. #4690C2semidirect
73. C4×D8D3semidirect
353. C3#3119semidirect

Maximal subgroups

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

subgroupindex
#55622
#55462
C3×C4×D82
#51582
#51502
#50182
#50142
#48822
#48772
#47812
#47772
#47632
#47622
C4×#2042
#46902
#31193