Finite Group Databasebeta

← #81545

Subgroups — #81545

Order 384.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5631C211yesmaximal, characteristic, complemented
2#5532C211yesmaximal, characteristic, complemented
3C3×#485C211yesmaximal, characteristic, complemented
4#5048C211yesmaximal, characteristic, complemented
5#5002C211yesmaximal, characteristic, complemented
6#4888C211yesmaximal, characteristic, complemented
7#4872C211yesmaximal, characteristic, complemented
8#4870C211yesmaximal, characteristic, complemented
9#4864C211yesmaximal, characteristic, complemented
10#4818C211yesmaximal, characteristic, complemented
11#4810C211yesmaximal, characteristic, complemented
12#4804C211yesmaximal, characteristic, complemented
13#4792C211yesmaximal, characteristic, complemented
14#4734C211yesmaximal, characteristic, complemented
15#67⋊C8C211yesmaximal, characteristic, complemented
16#3303—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C3×C22⋊Q8C2211yescharacteristic
20C3×#117C2211yescharacteristic
21#944C2211yescharacteristic
22C2×#215C2211yescharacteristic
23#930C2211yescharacteristic
24C4×#67C2211yescharacteristic
25C22×C3⋊C8C2211yescharacteristic
26C2×D24C2211yescharacteristic
27C2×#204C2211yescharacteristic
28C2×D3×C8C2211yescharacteristic
29#897C2211yescharacteristic
30#895C2211yescharacteristic
31#894—21no—
32#893C2211yescharacteristic
33#893C2211yescharacteristic
34#892C2211yescharacteristic
35D3×C4⋊C4—21no—
36#888C2211yescharacteristic
37#885—21no—
38#884—21no—
39#884—21no—
40#883—21no—
41#875—21no—
42#872—21no—
43C3×#107C2211yescharacteristic
44C3×#106C2211yescharacteristic
45C3×#103C2211yescharacteristic
46C3×#103C2211yescharacteristic
47C3×C22⋊C8C2211yescharacteristic
48#835C2211yescharacteristic
49#821C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#816C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54#810C2211yescharacteristic
55#810C2211yescharacteristic
56#809C2211yescharacteristic
57#809C2211yescharacteristic
58#809C2211yescharacteristic
59#808C2211yescharacteristic
60#555—31no—
61#547—31no—
62#487—31no—
63#485—31no—
64#485D311yescharacteristic, complemented
65#476—31no—
66#465—31no—
67#465—31no—
68#461—31no—
69#449—31no—
70#449—31no—
71C4×D8—31no—
72C8×D4—31no—
73#416—31no—
74#416—31no—
75C2×C3×Q8C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C2×#67—21no—
78C2×#67—21no—
79C2×#67D411yescharacteristic
80#239—22no—
81#239—41no—
82#235—22no—
83#235—41no—
84C2×D12—21no—
85C2×D12—21no—
86C2×D12C2311yescharacteristic
87C2×D12C2311yescharacteristic
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×C4×D3C2311yescharacteristic
93C2×Dic6—21no—
94C2×Dic6C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4—21no—
98C3×C4⋊C4C2311yescharacteristic
99C3×C4⋊C4C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C22⋊C4—21no—
102C3×C22⋊C4—21no—
103C3×C42—21no—
104#217D411yescharacteristic
105#215—41no—
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—
112(C2×D3)⋊C4D411yescharacteristic
113C4⋊Dic3—21no—
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4—21no—
118Dic3⋊C4D411yescharacteristic
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8—41no—
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124D24—22no—
125#204—41no—
126D3×C8—41no—
127C2×#41—31no—
128C2×#41—31no—
129C2×SD16—31no—
130C2×SD16—31no—
131C2×D8—31no—
132C22×C8—31no—
133C22×C8—31no—
134C4⋊Q8—31no—
135C4⋊Q8—31no—
136#124—61no—
137#124—61no—
138#123—61no—
139#123—61no—
140C22⋊Q8—31no—
141C22⋊Q8C2×D311yescharacteristic
142#121—31no—
143#121—31no—
144#121—61no—
145#121—61no—
146C4×D4—31no—
147C4×D4—31no—
148C4×D4—31no—
149#117—31no—
150#117—61no—
151#117C2×D311yescharacteristic
152C2×C4⋊C4—61no—
153#107C2×D311yescharacteristic
154#106—31no—
155#106C2×D311yescharacteristic
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103—31no—
161#103C2×D311yescharacteristic
162#103C2×D311yescharacteristic
163#102—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167C22⋊C8—31no—
168C22⋊C8C2×D311yescharacteristic
169C4×C8—31no—
170C23×C3C2×D411yescharacteristic
171C22×D3—21no—
172C22×D3—21no—
173C22×D3C2×D411yescharacteristic
174C3×Q8—21no—
175C3×Q8—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2411yescharacteristic
184#67—22no—
185#67—42no—
186#67—81no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3C2×D411yescharacteristic
190C2×Dic3C2×D411yescharacteristic
191C2×Dic3C2×D411yescharacteristic
192D12—21no—
193D12—21no—
194D12—21no—
195D12—42no—
196D12—81no—
197D12#4112yes—
198C4×D3—21no—
199C4×D3—21no—
200C4×D3—42no—
201C4×D3—42no—
202C4×D3—42no—
203C4×D3—42no—
204Dic6—21no—
205Dic6—21no—
206Dic6—81no—
207C3×C8—21no—
208C3×C8—21no—
209C3⋊C8—21no—
210C3⋊C8—21no—
211#41—62no—
212#41—62no—
213#41—121no—
214#41—121no—
215C2×Q8—31no—
216C2×Q8—61no—
217C2×Q8C22×D311yescharacteristic
218C2×D4—31no—
219C2×D4—31no—
220C2×D4—31no—
221C2×D4—61no—
222C2×D4—61no—
223C2×D4—61no—
224C2×D4—61no—
225C22×C4—31no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229C22×C4—61no—
230C22×C4C22×D311yescharacteristic
231SD16—121no—
232SD16—121no—
233D8—62no—
234C2×C8—31no—
235C2×C8—31no—
236C2×C8—121no—
237C2×C8—121no—
238C2×C8C22×D311yescharacteristic
239C2×C8C22×D311yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—31no—
242C4⋊C4—31no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4C22×D311yescharacteristic
248C4⋊C4C22×D311yescharacteristic
249C4⋊C4C22×D311yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—31no—
253C22⋊C4—31no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C42—21no—
261C42—31no—
262C42—61no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3C22×D411yescharacteristic
267C2×D3—21no—
268C2×D3—22no—
269C2×D3—21no—
270C2×D3—21no—
271C2×D3—41no—
272C2×D3—41no—
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—41no—
276C3×C4—21no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4C2×#4111yescharacteristic
282C3×C4H(5,𝔽2)11yescharacteristic
283Dic3—21no—
284Dic3—21no—
285Dic3—41no—
286Dic3—41no—
287Dic3#13512yes—
288C23—31no—
289C23—61no—
290C23—61no—
291C23D3×D411yescharacteristic
292Q8—21no—
293Q8—21no—
294Q8—61no—
295Q8—61no—
296Q8—241no—
297D4—32no—
298D4—62no—
299D4—61no—
300D4—61no—
301D4—61no—
302D4—122no—
303D4—122no—
304D4—241no—
305D4—241no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—31no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—122no—
320C2×C4—122no—
321C2×C4—122no—
322C2×C4—122no—
323C2×C4D3×D411yescharacteristic
324C2×C4C23×D311yescharacteristic
325C8—21no—
326C8—21no—
327C8—61no—
328C8—61no—
329C2×C3—41no—
330C2×C3#54611yescharacteristic
331C2×C3C2×#13511yescharacteristic
332C2×C3#57711yescharacteristic
333D3—41no—
334D3—42no—
335D3—81no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—61no—
340C22—62no—
341C22—61no—
342C22—61no—
343C22—121no—
344C22—121no—
345C22—121no—
346C22—121no—
347C22—121no—
348C22C2×D3×D411yescharacteristic
349C4—21no—
350C4—32no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—61no—
356C4—61no—
357C4—121no—
358C4—121no—
359C4D3×#4111yescharacteristic
360C4#100911yescharacteristic
361C3#330311yescharacteristic, complemented, Sylow
362C2—41no—
363C2—121no—
364C2—122no—
365C2—241no—
366C2#565411yescharacteristic
367C2D3×#13511yescharacteristic
368C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#485C2
socleC22×C3C22×D4
hypercenter#485D3
hypocenterC3#3303
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #5631C2semidirect
2. #5532C2semidirect
3. C3×#485C2semidirect
4. #5048C2semidirect
5. #5002C2semidirect
6. #4888C2semidirect
7. #4872C2semidirect
8. #4870C2semidirect
9. #4864C2semidirect
10. #4818C2semidirect
11. #4810C2semidirect
12. #4804C2semidirect
13. #4792C2semidirect
14. #4734C2semidirect
15. #67⋊C8C2semidirect
64. #485D3semidirect
361. C3#3303semidirect

Maximal subgroups

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

subgroupindex
#56312
#55322
C3×#4852
#50482
#50022
#48882
#48722
#48702
#48642
#48182
#48102
#48042
#47922
#47342
#67⋊C82
#33033