Finite Group Databasebeta

← #76413

Subgroups — #76413

Order 384.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#390C211yesmaximal, characteristic
2#5220C211yesmaximal, characteristic
3#5220C211yesmaximal, characteristic
4#4986C211yesmaximal, characteristic, complemented
5#4982C211yesmaximal, characteristic, complemented
6#4950C211yesmaximal, characteristic, complemented
7#4950C211yesmaximal, characteristic, complemented
8#4949C211yesmaximal, characteristic, complemented
9#4948C211yesmaximal, characteristic, complemented
10#4948C211yesmaximal, characteristic, complemented
11#4948C211yesmaximal, characteristic, complemented
12#4946C211yesmaximal, characteristic, complemented
13#4942C211yesmaximal, characteristic, complemented
14#4933C211yesmaximal, characteristic, complemented
15#4928C211yesmaximal, characteristic, complemented
16#2780—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×Dic3C2211yescharacteristic
19C23×Dic3C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21C2×C3×C22⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C42C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×C4⋊Dic3C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×C4⋊Dic3C2211yescharacteristic
35C2×C4⋊Dic3C2211yescharacteristic
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×Dic3⋊C4C2211yescharacteristic
39C2×Dic3⋊C4C2211yescharacteristic
40C2×Dic3⋊C4C2211yescharacteristic
41C2×Dic3⋊C4C2211yescharacteristic
42C3⋊#95C2211yescharacteristic
43C3⋊#95C2211yescharacteristic
44C3⋊#95C2211yescharacteristic
45C3⋊#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52#400—31no—
53#399—31no—
54#398—31no—
55#396—31no—
56#396—31no—
57#396—31no—
58#390D311yescharacteristic
59#389—31no—
60#387—31no—
61#386—31no—
62#386—31no—
63#385—31no—
64#385—31no—
65#385—31no—
66#380—31no—
67C24×C3C2311yescharacteristic
68C24×C3C2311yescharacteristic
69C2×C3×D4—41no—
70C2×C3×D4—41no—
71C2×C3×D4Q814yes—
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×Dic3—22no—
78C22×Dic3—41no—
79C22×Dic3—41no—
80C22×Dic3—41no—
81C22×Dic3—41no—
82C22×Dic3—41no—
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C3×C4⋊C4—41no—
92C3×C22⋊C4—22no—
93C3×C22⋊C4—22no—
94C3×C22⋊C4—41no—
95C3×C22⋊C4—41no—
96C3×C42—41no—
97#217—22no—
98#217—41no—
99#217—41no—
100#217—41no—
101#217—41no—
102#217—41no—
103C4⋊Dic3—22no—
104C4⋊Dic3—41no—
105C4⋊Dic3—41no—
106C4⋊Dic3—41no—
107Dic3⋊C4—22no—
108Dic3⋊C4—41no—
109Dic3⋊C4—41no—
110Dic3⋊C4—41no—
111Dic3⋊C4—41no—
112Dic3⋊C4—41no—
113C22×D4C2×D311yescharacteristic
114C23×C4—31no—
115C23×C4—31no—
116C2×C4⋊C4—31no—
117C2×C4⋊C4—31no—
118C2×C4⋊C4—31no—
119C2×C4⋊C4—31no—
120C2×C4⋊C4—31no—
121C2×C4⋊C4—31no—
122C2×C4⋊C4—31no—
123C2×C4⋊C4—31no—
124C2×C4⋊C4—31no—
125C2×C4⋊C4—31no—
126C2×C4⋊C4C2×D311yescharacteristic
127C2×C22⋊C4—31no—
128C2×C22⋊C4—31no—
129C2×C22⋊C4—31no—
130C2×C22⋊C4—31no—
131C2×C22⋊C4—31no—
132C2×C22⋊C4—31no—
133C2×C22⋊C4C2×D311yescharacteristic
134C2×C22⋊C4C2×D311yescharacteristic
135C2×C22⋊C4C2×D311yescharacteristic
136C2×C22⋊C4C2×D311yescharacteristic
137C2×C42C2×D311yescharacteristic
138#95—31no—
139#95—31no—
140#95—31no—
141#95—31no—
142#95—31no—
143#95—31no—
144#95—31no—
145#95—31no—
146#95—31no—
147#95—31no—
148C23×C3—21no—
149C23×C3—21no—
150C23×C3—21no—
151C23×C3—21no—
152C23×C3—21no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3C2×Q812yes—
161C23×C3C2×Q812yes—
162C23×C3C2411yescharacteristic
163C3×D4—44no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4C2×Q812yes—
178C2×C3×C4#4112yes—
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—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—44no—
203C2×Dic3—44no—
204C2×Dic3#4112yes—
205C24C22×D311yescharacteristic
206C24C22×D311yescharacteristic
207C2×D4—41no—
208C2×D4—41no—
209C2×D4Dic614yes—
210C22×C4—31no—
211C22×C4—31no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—62no—
219C22×C4—121no—
220C22×C4—121no—
221C22×C4—121no—
222C22×C4—121no—
223C22×C4—121no—
224C22×C4C22×D311yescharacteristic
225C22×C4C22×D311yescharacteristic
226C22×C4C22×D311yescharacteristic
227C22×C4C22×D311yescharacteristic
228C22×C4C22×D311yescharacteristic
229C4⋊C4—41no—
230C4⋊C4—62no—
231C4⋊C4—62no—
232C4⋊C4—121no—
233C4⋊C4—121no—
234C4⋊C4—121no—
235C4⋊C4—121no—
236C4⋊C4—121no—
237C4⋊C4—121no—
238C4⋊C4—121no—
239C4⋊C4—121no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—62no—
245C22⋊C4—121no—
246C22⋊C4—121no—
247C22⋊C4—121no—
248C22⋊C4—121no—
249C22⋊C4—121no—
250C42—41no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—22no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3C22×Q811yescharacteristic
266C22×C3C2×#4111yescharacteristic
267C22×C3C2×#4111yescharacteristic
268C22×C3H(5,𝔽2)11yescharacteristic
269C22×C3H(5,𝔽2)11yescharacteristic
270C22×C3H(5,𝔽2)11yescharacteristic
271C22×C3H(5,𝔽2)11yescharacteristic
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4—41no—
277Dic3—22no—
278Dic3—41no—
279Dic3—41no—
280Dic3—41no—
281Dic3—41no—
282Dic3—41no—
283Dic3—41no—
284Dic3—41no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23C2×Dic612yes—
298C23C2×Dic612yes—
299C23C23×D311yescharacteristic
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—32no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—124no—
339C2×C4—124no—
340C2×C4C2×Dic612yes—
341C2×C4#23712yes—
342C2×C3—42no—
343C2×C3—42no—
344C2×C3#53811yescharacteristic
345C2×C3#54011yescharacteristic
346C2×C3#54311yescharacteristic
347C2×C3#55311yescharacteristic
348C2×C3#55411yescharacteristic
349C2×C3#55411yescharacteristic
350C2×C3#56011yescharacteristic
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22C22×Dic611yescharacteristic
366C22C2×#23711yescharacteristic
367C22#100411yescharacteristic
368C22#100411yescharacteristic
369C22#100411yescharacteristic
370C22D3×#4111yescharacteristic
371C22#100911yescharacteristic
372C4—22no—
373C4—22no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—62no—
378C4—121no—
379C4—121no—
380C4—121no—
381C4—121no—
382C4—121no—
383C4—121no—
384C4—121no—
385C3#278011yescharacteristic, complemented, Sylow
386C2—42no—
387C2—42no—
388C2#548311yescharacteristic
389C2#553911yescharacteristic
390C2#554311yescharacteristic
391C2#560111yescharacteristic
392C2#562011yescharacteristic
393C2#567811yescharacteristic
394C2#571911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#390C2
prime radicalC22×C3×D4C22
hypercenter#390D3
hypocenterC3#2780
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
4. #4986C2semidirect
5. #4982C2semidirect
6. #4950C2semidirect
7. #4950C2semidirect
8. #4949C2semidirect
9. #4948C2semidirect
10. #4948C2semidirect
11. #4948C2semidirect
12. #4946C2semidirect
13. #4942C2semidirect
14. #4933C2semidirect
15. #4928C2semidirect
385. C3#2780semidirect

Maximal subgroups

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

subgroupindex
C3×#3902
#52202
#49862
#49822
#49502
#49492
#49482
#49462
#49422
#49332
#49282
#27803