Finite Group Databasebeta

← #73353

Subgroups — #73353

Order 384.

440 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#95C211yesmaximal, characteristic
2#5212C211yesmaximal, characteristic
3#5211C211yesmaximal, characteristic
4#5211C211yesmaximal, characteristic
5#5210C211yesmaximal, characteristic
6#5210C211yesmaximal, characteristic
7C4×#217C211yesmaximal, characteristic
8C3⋊#401C211yesmaximal, characteristic, complemented
9#4660C211yesmaximal, characteristic, complemented
10#4659C211yesmaximal, characteristic, complemented
11#4658C211yesmaximal, characteristic, complemented
12#4655C211yesmaximal, characteristic, complemented
13#4653C211yesmaximal, characteristic, complemented
14#4652C211yesmaximal, characteristic, complemented
15#4651C211yesmaximal, characteristic, complemented
16#2493—31nomaximal, Sylow
17C23×C3×C4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C2×#217C2211yescharacteristic
21C2×#217C2211yescharacteristic
22C2×#217C2211yescharacteristic
23C2×#217C2211yescharacteristic
24C2×C4⋊Dic3C2211yescharacteristic
25C2×C4⋊Dic3C2211yescharacteristic
26C2×Dic3⋊C4C2211yescharacteristic
27C2×Dic3⋊C4C2211yescharacteristic
28C2×Dic3⋊C4C2211yescharacteristic
29C2×Dic3⋊C4C2211yescharacteristic
30C2×C4×Dic3C2211yescharacteristic
31C2×C4×Dic3C2211yescharacteristic
32C3×#95C2211yescharacteristic
33C3×#95C2211yescharacteristic
34C3×#95C2211yescharacteristic
35C3×#95C2211yescharacteristic
36C3⋊#95C2211yescharacteristic
37C3⋊#95C2211yescharacteristic
38C3⋊#95C2211yescharacteristic
39C3⋊#95C2211yescharacteristic
40C3⋊#95C2211yescharacteristic
41C3⋊#95C2211yescharacteristic
42C3⋊#95C2211yescharacteristic
43C3⋊#95C2211yescharacteristic
44C3⋊#95C2211yescharacteristic
45C3⋊#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52#401—31no—
53#400—31no—
54#400—31no—
55#400—31no—
56#387—31no—
57#387—31no—
58#387—31no—
59#385—31no—
60#385—31no—
61#383—31no—
62#381—31no—
63#381—31no—
64#380—31no—
65C4×C22⋊C4—31no—
66C2×#95D311yescharacteristic
67C24×C3C2311yescharacteristic
68C22×C3×C4—22no—
69C22×C3×C4—22no—
70C22×C3×C4—22no—
71C22×C3×C4—22no—
72C22×C3×C4—22no—
73C22×C3×C4—22no—
74C22×C3×C4—22no—
75C22×C3×C4—41no—
76C22×C3×C4—41no—
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91#217—22no—
92#217—22no—
93#217—22no—
94#217—22no—
95C4⋊Dic3—22no—
96C4⋊Dic3—41no—
97Dic3⋊C4—22no—
98Dic3⋊C4—22no—
99Dic3⋊C4—41no—
100Dic3⋊C4—41no—
101C4×Dic3—22no—
102C4×Dic3—41no—
103C23×C4C2×D311yescharacteristic
104C23×C4C2×D311yescharacteristic
105C23×C4C2×D311yescharacteristic
106C2×C4⋊C4—31no—
107C2×C4⋊C4—31no—
108C2×C4⋊C4—31no—
109C2×C4⋊C4—31no—
110C2×C4⋊C4—31no—
111C2×C4⋊C4—31no—
112C2×C22⋊C4—31no—
113C2×C22⋊C4—31no—
114C2×C22⋊C4—31no—
115C2×C22⋊C4—31no—
116C2×C42—31no—
117C2×C42—31no—
118#95—31no—
119#95—31no—
120#95—31no—
121#95—31no—
122#95—31no—
123#95—31no—
124#95—31no—
125#95—31no—
126#95—31no—
127#95—31no—
128#95—31no—
129#95—31no—
130#95—31no—
131#95—31no—
132#95—31no—
133#95—31no—
134#95C2×D311yescharacteristic
135#95C2×D311yescharacteristic
136#95C2×D311yescharacteristic
137#95C2×D311yescharacteristic
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—21no—
142C23×C3#4112yes—
143C23×C3#4112yes—
144C23×C3#4112yes—
145C23×C3C2411yescharacteristic
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—44no—
163C2×C3×C4—44no—
164C2×C3×C4—44no—
165C2×C3×C4#4112yes—
166C2×C3×C4#4112yes—
167C2×Dic3—21no—
168C2×Dic3—21no—
169C2×Dic3—21no—
170C2×Dic3—21no—
171C2×Dic3—21no—
172C2×Dic3—21no—
173C2×Dic3—21no—
174C2×Dic3—21no—
175C2×Dic3—21no—
176C2×Dic3—21no—
177C2×Dic3—21no—
178C2×Dic3—21no—
179C2×Dic3—21no—
180C2×Dic3—21no—
181C2×Dic3—21no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C24C22×D311yescharacteristic
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—31no—
200C22×C4—31no—
201C22×C4—31no—
202C22×C4—31no—
203C22×C4—31no—
204C22×C4—31no—
205C22×C4—31no—
206C22×C4—31no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4C22×D311yescharacteristic
210C22×C4C22×D311yescharacteristic
211C22×C4C22×D311yescharacteristic
212C22×C4C22×D311yescharacteristic
213C22×C4C22×D311yescharacteristic
214C22×C4C22×D311yescharacteristic
215C4⋊C4—62no—
216C4⋊C4—62no—
217C4⋊C4—62no—
218C4⋊C4—121no—
219C4⋊C4—121no—
220C4⋊C4—121no—
221C22⋊C4—62no—
222C22⋊C4—62no—
223C22⋊C4—62no—
224C22⋊C4—62no—
225C42—62no—
226C42—121no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—22no—
231C22×C3—22no—
232C22×C3—22no—
233C22×C3#12614yes—
234C22×C3C2×#4111yescharacteristic
235C22×C3C2×#4111yescharacteristic
236C22×C3C2×#4111yescharacteristic
237C22×C3C2×#4111yescharacteristic
238C22×C3C2×#4111yescharacteristic
239C22×C3H(5,𝔽2)11yescharacteristic
240C22×C32−1+411yescharacteristic
241C3×C4—22no—
242C3×C4—22no—
243C3×C4—41no—
244C3×C4—41no—
245C3×C4—41no—
246C3×C4—41no—
247Dic3—41no—
248Dic3—41no—
249Dic3—41no—
250Dic3—41no—
251Dic3—41no—
252Dic3—41no—
253Dic3—41no—
254Dic3—41no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23#23512yes—
260C23#23712yes—
261C23#23712yes—
262C23C23×D311yescharacteristic
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—61no—
283C2×C4—61no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—61no—
288C2×C4—61no—
289C2×C4—61no—
290C2×C4—61no—
291C2×C4—61no—
292C2×C4—61no—
293C2×C4—61no—
294C2×C4—61no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4#23512yes—
307C2×C4#23512yes—
308C2×C3—24no—
309C2×C3C2×#12611yescharacteristic
310C2×C3#52911yescharacteristic
311C2×C3#53911yescharacteristic
312C2×C3#55111yescharacteristic
313C2×C3#55111yescharacteristic
314C2×C3#55211yescharacteristic
315C2×C3#55211yescharacteristic
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22#87914yes—
323C22C2×#23511yescharacteristic
324C22C2×#23511yescharacteristic
325C22C2×#23511yescharacteristic
326C22C2×#23711yescharacteristic
327C22C2×#23711yescharacteristic
328C22#100411yescharacteristic
329C22#100711yescharacteristic
330C4—22no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—121no—
337C4—121no—
338C4—121no—
339C4—121no—
340C4—121no—
341C4—121no—
342C4—121no—
343C4—121no—
344C3#249311yescharacteristic, complemented, Sylow
345C2—24no—
346C2#547911yescharacteristic
347C2C2×#87911yescharacteristic
348C2#549511yescharacteristic
349C2#549511yescharacteristic
350C2#551311yescharacteristic
351C2#551311yescharacteristic
352C2#551511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC2×C3×#95C2
prime radicalC24×C3C23
hypercenterC2×#95D3
hypocenterC3#2493
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
8. C3⋊#401C2semidirect
9. #4660C2semidirect
10. #4659C2semidirect
11. #4658C2semidirect
12. #4655C2semidirect
13. #4653C2semidirect
14. #4652C2semidirect
15. #4651C2semidirect
344. C3#2493semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#952
#52122
#52112
#52102
C4×#2172
C3⋊#4012
#46602
#46592
#46582
#46552
#46532
#46522
#46512
#24933