Finite Group Databasebeta

← #75759

Subgroups — #75759

Order 384.

378 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#388C211yesmaximal, characteristic
2#4981C211yesmaximal, characteristic, complemented
3#4972C211yesmaximal, characteristic, complemented
4#4952C211yesmaximal, characteristic
5#4952C211yesmaximal, characteristic
6#4948C211yesmaximal, characteristic
7#4948C211yesmaximal, characteristic
8#4945C211yesmaximal, characteristic
9#4945C211yesmaximal, characteristic
10#4933C211yesmaximal, characteristic, complemented
11#4933C211yesmaximal, characteristic, complemented
12#4660C211yesmaximal, characteristic, complemented
13#4652C211yesmaximal, characteristic, complemented
14#4650C211yesmaximal, characteristic, complemented
15#4647C211yesmaximal, characteristic, complemented
16#2772—31nomaximal, Sylow
17C2×C3×C4⋊C4C2211yescharacteristic
18C2×C3×C22⋊C4C2211yescharacteristic
19C2×C3×C22⋊C4C2211yescharacteristic
20C2×C3×C22⋊C4C2211yescharacteristic
21C2×C3×C42C2211yescharacteristic
22C2×#217C2211yescharacteristic
23C2×#217C2211yescharacteristic
24C2×#217C2211yescharacteristic
25C2×#217C2211yescharacteristic
26C2×C4⋊Dic3C2211yescharacteristic
27C2×C4⋊Dic3C2211yescharacteristic
28C2×Dic3⋊C4C2211yescharacteristic
29C2×Dic3⋊C4C2211yescharacteristic
30C2×Dic3⋊C4C2211yescharacteristic
31C2×Dic3⋊C4C2211yescharacteristic
32C2×Dic3⋊C4C2211yescharacteristic
33C2×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊C4C2211yescharacteristic
36C2×C4×Dic3C2211yescharacteristic
37C2×C4×Dic3C2211yescharacteristic
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#400—31no—
53#398—31no—
54#397—31no—
55#397—31no—
56#396—31no—
57#396—31no—
58#389—31no—
59#389—31no—
60#388—31no—
61#388—31no—
62#388D311yescharacteristic
63#387—31no—
64#387—31no—
65#387—31no—
66#382—31no—
67C24×C3C2311yescharacteristic
68C22×C3×C4C2311yescharacteristic
69C22×C3×C4C2311yescharacteristic
70C22×C3×C4C2311yescharacteristic
71C22×C3×C4C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×Dic3C2311yescharacteristic
75C22×Dic3C2311yescharacteristic
76C22×Dic3C2311yescharacteristic
77C22×Dic3C2311yescharacteristic
78C22×Dic3C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C3×C4⋊C4—41no—
83C3×C22⋊C4—22no—
84C3×C22⋊C4—41no—
85C3×C22⋊C4—41no—
86C3×C42—41no—
87#217—22no—
88#217—22no—
89#217—41no—
90#217—41no—
91C4⋊Dic3—22no—
92C4⋊Dic3—41no—
93Dic3⋊C4—22no—
94Dic3⋊C4—22no—
95Dic3⋊C4—22no—
96Dic3⋊C4—22no—
97Dic3⋊C4—41no—
98Dic3⋊C4—41no—
99Dic3⋊C4—41no—
100Dic3⋊C4—41no—
101C4×Dic3—22no—
102C4×Dic3—41no—
103C2×C4⋊C4—31no—
104C2×C4⋊C4—31no—
105C2×C4⋊C4—31no—
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×C4⋊C4—31no—
113C2×C4⋊C4C2×D311yescharacteristic
114C2×C22⋊C4—31no—
115C2×C22⋊C4—31no—
116C2×C22⋊C4—31no—
117C2×C22⋊C4—31no—
118C2×C22⋊C4C2×D311yescharacteristic
119C2×C22⋊C4C2×D311yescharacteristic
120C2×C22⋊C4C2×D311yescharacteristic
121C2×C42—31no—
122C2×C42—31no—
123C2×C42C2×D311yescharacteristic
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#95—31no—
135#95—31no—
136#95C2×D311yescharacteristic
137#95C2×D311yescharacteristic
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—21no—
142C23×C3—21no—
143C23×C3—21no—
144C23×C3—21no—
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—21no—
163C2×C3×C4#4112yes—
164C2×Dic3—21no—
165C2×Dic3—21no—
166C2×Dic3—21no—
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#4112yes—
187C2×Dic3#4112yes—
188C24C22×D311yescharacteristic
189C22×C4—31no—
190C22×C4—31no—
191C22×C4—31no—
192C22×C4—31no—
193C22×C4—31no—
194C22×C4—31no—
195C22×C4—31no—
196C22×C4—31no—
197C22×C4C22×D311yescharacteristic
198C22×C4C22×D311yescharacteristic
199C22×C4C22×D311yescharacteristic
200C22×C4C22×D311yescharacteristic
201C22×C4C22×D311yescharacteristic
202C22×C4C22×D311yescharacteristic
203C4⋊C4—41no—
204C4⋊C4—62no—
205C4⋊C4—62no—
206C4⋊C4—62no—
207C4⋊C4—62no—
208C4⋊C4—62no—
209C4⋊C4—121no—
210C4⋊C4—121no—
211C4⋊C4—121no—
212C4⋊C4—121no—
213C4⋊C4—121no—
214C22⋊C4—22no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—62no—
218C22⋊C4—62no—
219C22⋊C4—121no—
220C22⋊C4—121no—
221C42—41no—
222C42—62no—
223C42—121no—
224C22×C3—41no—
225C22×C3—41no—
226C22×C3—41no—
227C22×C3—41no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3C2×#4111yescharacteristic
232C22×C3C2×#4111yescharacteristic
233C22×C3C2×#4111yescharacteristic
234C22×C3H(5,𝔽2)11yescharacteristic
235C22×C3H(5,𝔽2)11yescharacteristic
236C22×C32−1+411yescharacteristic
237C22×C32−1+411yescharacteristic
238C3×C4—22no—
239C3×C4—41no—
240C3×C4—41no—
241C3×C4—41no—
242C3×C4—41no—
243C3×C4—41no—
244Dic3—22no—
245Dic3—22no—
246Dic3—41no—
247Dic3—41no—
248Dic3—41no—
249Dic3—41no—
250Dic3—41no—
251Dic3—41no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23C23×D311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
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—32no—
278C2×C4—32no—
279C2×C4—61no—
280C2×C4—61no—
281C2×C4—61no—
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#23512yes—
302C2×C3—81no—
303C2×C3#54111yescharacteristic
304C2×C3#54211yescharacteristic
305C2×C3#54211yescharacteristic
306C2×C3#55211yescharacteristic
307C2×C3#55311yescharacteristic
308C2×C3#55311yescharacteristic
309C2×C3#56211yescharacteristic
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×#23511yescharacteristic
318C22#100411yescharacteristic
319C22#100411yescharacteristic
320C22D3×#4111yescharacteristic
321C22D3×#4111yescharacteristic
322C22#101011yescharacteristic
323C22#101011yescharacteristic
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—62no—
331C4—62no—
332C4—121no—
333C4—121no—
334C4—121no—
335C4—121no—
336C4—121no—
337C4—121no—
338C3#277211yescharacteristic, complemented, Sylow
339C2—81no—
340C2#552911yescharacteristic
341C2#554011yescharacteristic
342C2#556111yescharacteristic
343C2#562111yescharacteristic
344C2#566111yescharacteristic
345C2#566911yescharacteristic
346C2#570111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#388C2
prime radicalC24×C3C23
hypercenter#388D3
hypocenterC3#2772
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #4981C2semidirect
3. #4972C2semidirect
10. #4933C2semidirect
11. #4933C2semidirect
12. #4660C2semidirect
13. #4652C2semidirect
14. #4650C2semidirect
15. #4647C2semidirect
338. C3#2772semidirect

Maximal subgroups

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

subgroupindex
C3×#3882
#49812
#49722
#49522
#49482
#49452
#49332
#46602
#46522
#46502
#46472
#27723