Finite Group Databasebeta

← #80877

Subgroups — #80877

Order 384.

392 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#5616C211yesmaximal, characteristic, complemented
2#5598C211yesmaximal, characteristic, complemented
3C3×#469C211yesmaximal, characteristic, complemented
4#5158C211yesmaximal, characteristic, complemented
5#5153C211yesmaximal, characteristic, complemented
6#5127C211yesmaximal, characteristic, complemented
7#5120C211yesmaximal, characteristic, complemented
8#5040C211yesmaximal, characteristic, complemented
9#5035C211yesmaximal, characteristic, complemented
10#4868C211yesmaximal, characteristic, complemented
11#4854C211yesmaximal, characteristic, complemented
12#4778C211yesmaximal, characteristic, complemented
13#4772C211yesmaximal, characteristic, complemented
14#4765C211yesmaximal, characteristic, complemented
15#4757C211yesmaximal, characteristic, complemented
16#3321—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C22×Dic6C2211yescharacteristic
19C2×C3×D8C2211yescharacteristic
20C2×C3×M16C2211yescharacteristic
21C3×#121C2211yescharacteristic
22C3×#121C2211yescharacteristic
23#939—21no—
24#939—21no—
25#938C2211yescharacteristic
26#936—21no—
27#936C2211yescharacteristic
28D4×Dic3—21no—
29D4×Dic3C2211yescharacteristic
30C2×#214C2211yescharacteristic
31C2×#214C2211yescharacteristic
32C4×#67C2211yescharacteristic
33#926C2211yescharacteristic
34C2×D3×C8C2211yescharacteristic
35#897C2211yescharacteristic
36#892C2211yescharacteristic
37#888C2211yescharacteristic
38#887C2211yescharacteristic
39#885—21no—
40#885—21no—
41#878—21no—
42#877—21no—
43C3×#106C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×#102C2211yescharacteristic
46#832C2211yescharacteristic
47#832C2211yescharacteristic
48#830C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50#816C2211yescharacteristic
51#816C2211yescharacteristic
52#816C2211yescharacteristic
53#816C2211yescharacteristic
54#815C2211yescharacteristic
55Dic3⋊C8C2211yescharacteristic
56#810C2211yescharacteristic
57#810C2211yescharacteristic
58#808C2211yescharacteristic
59#807C2211yescharacteristic
60#555—31no—
61#548—31no—
62#489—31no—
63#485—31no—
64#482—31no—
65#475—31no—
66#469D311yescharacteristic, complemented
67#465—31no—
68#463—31no—
69#449—31no—
70#448—31no—
71#440—31no—
72#435—31no—
73#419—31no—
74#416—31no—
75C2×C3×D4—21no—
76C2×C3×D4—21no—
77C2×C3×D4C2311yescharacteristic
78C2×C3×D4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C2×#67—21no—
81C2×#67—21no—
82C2×#67D411yescharacteristic
83C22×Dic3—21no—
84C22×Dic3—21no—
85C22×Dic3—21no—
86#237—22no—
87#237—41no—
88C2×C4×D3C2311yescharacteristic
89C2×Dic6—22no—
90C2×Dic6—21no—
91C2×Dic6—21no—
92C2×Dic6—41no—
93C2×Dic6C2311yescharacteristic
94C2×Dic6C2311yescharacteristic
95C3×D8—41no—
96C3×M16—41no—
97C2×C3×C8C2311yescharacteristic
98C2×C3×C8C2311yescharacteristic
99C3×C4⋊C4C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C22⋊C4—21no—
102C3×C22⋊C4—21no—
103#217—21no—
104#217—21no—
105#217—21no—
106#217—21no—
107#217—21no—
108#217D411yescharacteristic
109#214—22no—
110#214—41no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4D411yescharacteristic
114C4⋊Dic3—21no—
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117Dic3⋊C4—21no—
118Dic3⋊C4—21no—
119Dic3⋊C4D411yescharacteristic
120C4×Dic3—21no—
121C4×Dic3—21no—
122C4×Dic3—21no—
123C4×Dic3C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126D3×C8—41no—
127C2×#41—31no—
128C22×Q8—31no—
129C2×SD16—31no—
130C2×SD16—31no—
131C2×D8C2×D311yescharacteristic
132C2×M16C2×D311yescharacteristic
133C22×C8—31no—
134C4⋊Q8—31no—
135#124—31no—
136#124—61no—
137#124—61no—
138#124—61no—
139C22⋊Q8—31no—
140C22⋊Q8—61no—
141#121—31no—
142#121—61no—
143#121—61no—
144#121C2×D311yescharacteristic
145#121C2×D311yescharacteristic
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4—31no—
149C4×D4—61no—
150#117—31no—
151#117—31no—
152#117—61no—
153#107—31no—
154#106—31no—
155#106C2×D311yescharacteristic
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103—31no—
161#103—31no—
162#103—31no—
163#102—31no—
164#102—31no—
165#102C2×D311yescharacteristic
166#102C2×D311yescharacteristic
167C22⋊C8—31no—
168C22⋊C8—31no—
169#97—31no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3C2×D411yescharacteristic
173C22×D3C2×D411yescharacteristic
174C3×D4—21no—
175C3×D4—21no—
176C3×D4—21no—
177C3×D4—21no—
178C3×D4—42no—
179C3×D4—81no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2411yescharacteristic
186#67—41no—
187#67—42no—
188#67—81no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—42no—
194C2×Dic3—42no—
195C2×Dic3—42no—
196C2×Dic3C2×D411yescharacteristic
197C2×Dic3C2×D411yescharacteristic
198C2×Dic3C2×D411yescharacteristic
199C4×D3—21no—
200C4×D3—21no—
201Dic6—21no—
202Dic6—21no—
203Dic6—21no—
204Dic6—42no—
205Dic6—81no—
206Dic6#4112yes—
207C3×C8—21no—
208C3×C8—21no—
209C3⋊C8—21no—
210C3⋊C8—21no—
211#41—62no—
212#41—121no—
213C2×Q8—31no—
214C2×Q8—31no—
215C2×Q8—61no—
216C2×Q8—62no—
217C2×Q8—61no—
218C2×Q8—121no—
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—31no—
222C2×D4—61no—
223C2×D4—61no—
224C2×D4C22×D311yescharacteristic
225C2×D4C22×D311yescharacteristic
226C22×C4—31no—
227C22×C4—61no—
228C22×C4—61no—
229C22×C4—61no—
230C22×C4C22×D311yescharacteristic
231SD16—62no—
232SD16—121no—
233D8—41no—
234M16—41no—
235C2×C8—31no—
236C2×C8—31no—
237C2×C8—121no—
238C2×C8C22×D311yescharacteristic
239C2×C8C22×D311yescharacteristic
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—31no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4C22×D311yescharacteristic
247C4⋊C4C22×D311yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—21no—
250C22⋊C4—31no—
251C22⋊C4—31no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C42—31no—
260C42—61no—
261C42—61no—
262C42—61no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3C22×D411yescharacteristic
273C2×D3—21no—
274C2×D3—21no—
275C2×D3—21no—
276C3×C4—21no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4C2×#4111yescharacteristic
280C3×C4H(5,𝔽2)11yescharacteristic
281Dic3—22no—
282Dic3—21no—
283Dic3—21no—
284Dic3—21no—
285Dic3—41no—
286Dic3—41no—
287Dic3—41no—
288C23—21no—
289C23—21no—
290C23—31no—
291C23D3×D411yescharacteristic
292Q8—32no—
293Q8—61no—
294Q8—61no—
295Q8—61no—
296Q8—122no—
297Q8—241no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—81no—
304D4—121no—
305D4—122no—
306D4—241no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—61no—
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—81no—
331C2×C3—81no—
332C2×C3#54611yescharacteristic
333C2×C3#57511yescharacteristic
334C2×C3#57711yescharacteristic
335D3—41no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—61no—
346C22—61no—
347C22—61no—
348C22C2×D3×D411yescharacteristic
349C4—21no—
350C4—41no—
351C4—41no—
352C4—61no—
353C4—61no—
354C4—61no—
355C4—62no—
356C4—121no—
357C4—121no—
358C4—121no—
359C4#100411yescharacteristic
360C4D3×#4111yescharacteristic
361C3#332111yescharacteristic, complemented, Sylow
362C2—41no—
363C2—81no—
364C2—81no—
365C2—121no—
366C2#561011yescharacteristic
367C2#577311yescharacteristic
368C2#577511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#469C2
socleC22×C3C22×D4
hypercenter#469D3
hypocenterC3#3321
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #5616C2semidirect
2. #5598C2semidirect
3. C3×#469C2semidirect
4. #5158C2semidirect
5. #5153C2semidirect
6. #5127C2semidirect
7. #5120C2semidirect
8. #5040C2semidirect
9. #5035C2semidirect
10. #4868C2semidirect
11. #4854C2semidirect
12. #4778C2semidirect
13. #4772C2semidirect
14. #4765C2semidirect
15. #4757C2semidirect
66. #469D3semidirect
361. C3#3321semidirect

Maximal subgroups

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

subgroupindex
#56162
#55982
C3×#4692
#51582
#51532
#51272
#51202
#50402
#50352
#48682
#48542
#47782
#47722
#47652
#47572
#33213