Finite Group Databasebeta

← #76991

Subgroups — #76991

Order 384.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#394C211yesmaximal, characteristic
2#5222C211yesmaximal, characteristic
3#5221C211yesmaximal, characteristic
4#4982C211yesmaximal, characteristic, complemented
5#4980C211yesmaximal, characteristic, complemented
6#4952C211yesmaximal, characteristic, complemented
7#4952C211yesmaximal, characteristic, complemented
8#4949C211yesmaximal, characteristic, complemented
9#4948C211yesmaximal, characteristic, complemented
10#4945C211yesmaximal, characteristic, complemented
11#4945C211yesmaximal, characteristic, complemented
12#4945C211yesmaximal, characteristic, complemented
13#4944C211yesmaximal, characteristic, complemented
14#4657C211yesmaximal, characteristic, complemented
15#4649C211yesmaximal, characteristic, complemented
16#2651—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C2×C3×C4⋊C4C2211yescharacteristic
19C2×C3×C22⋊C4C2211yescharacteristic
20C2×C3×C22⋊C4C2211yescharacteristic
21C2×C3×C22⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×#217C2211yescharacteristic
24C2×#217C2211yescharacteristic
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×C4⋊Dic3C2211yescharacteristic
32C2×C4⋊Dic3C2211yescharacteristic
33C2×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊C4C2211yescharacteristic
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×Dic3⋊C4C2211yescharacteristic
39C2×C4×Dic3C2211yescharacteristic
40C2×C4×Dic3C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42C3×#95C2211yescharacteristic
43C3⋊#95C2211yescharacteristic
44C3⋊#95C2211yescharacteristic
45C3⋊#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52#399—31no—
53#398—31no—
54#398—31no—
55#397—31no—
56#397—31no—
57#396—31no—
58#394—31no—
59#394D311yescharacteristic
60#390—31no—
61#388—31no—
62#388—31no—
63#388—31no—
64#388—31no—
65#387—31no—
66C4×C4⋊C4—31no—
67C24×C3C2311yescharacteristic
68C24×C3C2311yescharacteristic
69C2×C3×D4—22no—
70C2×C3×D4—41no—
71C2×C3×D4—41no—
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×Dic3C2311yescharacteristic
78C22×Dic3C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C3×C4⋊C4—22no—
86C3×C22⋊C4—41no—
87C3×C22⋊C4—41no—
88C3×C22⋊C4—41no—
89C3×C22⋊C4—41no—
90#217—22no—
91#217—22no—
92#217—22no—
93#217—22no—
94#217—41no—
95#217—41no—
96#217—41no—
97#217—41no—
98C4⋊Dic3—41no—
99C4⋊Dic3—41no—
100Dic3⋊C4—22no—
101Dic3⋊C4—22no—
102Dic3⋊C4—41no—
103Dic3⋊C4—41no—
104Dic3⋊C4—41no—
105Dic3⋊C4—41no—
106C4×Dic3—22no—
107C4×Dic3—41no—
108C4×Dic3—41no—
109C22×D4C2×D311yescharacteristic
110C2×C4⋊C4—31no—
111C2×C4⋊C4—31no—
112C2×C4⋊C4—31no—
113C2×C4⋊C4—31no—
114C2×C4⋊C4—31no—
115C2×C4⋊C4—31no—
116C2×C4⋊C4—31no—
117C2×C4⋊C4—31no—
118C2×C4⋊C4C2×D311yescharacteristic
119C2×C22⋊C4—31no—
120C2×C22⋊C4—31no—
121C2×C22⋊C4—31no—
122C2×C22⋊C4—31no—
123C2×C22⋊C4—31no—
124C2×C22⋊C4—31no—
125C2×C22⋊C4—31no—
126C2×C22⋊C4—31no—
127C2×C22⋊C4C2×D311yescharacteristic
128C2×C22⋊C4C2×D311yescharacteristic
129C2×C22⋊C4C2×D311yescharacteristic
130C2×C22⋊C4C2×D311yescharacteristic
131C2×C42—31no—
132C2×C42—31no—
133C2×C42—31no—
134#95—31no—
135#95—31no—
136#95—31no—
137#95—31no—
138#95—31no—
139#95—31no—
140#95—31no—
141#95—31no—
142#95—31no—
143#95C2×D311yescharacteristic
144C23×C3—21no—
145C23×C3—21no—
146C23×C3—21no—
147C23×C3—21no—
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×C3C2411yescharacteristic
159C3×D4—44no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
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#4112yes—
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—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3#4112yes—
198C2×Dic3#4112yes—
199C24C22×D311yescharacteristic
200C24C22×D311yescharacteristic
201C2×D4—22no—
202C2×D4—41no—
203C2×D4—41no—
204C22×C4—31no—
205C22×C4—31no—
206C22×C4—31no—
207C22×C4—31no—
208C22×C4—31no—
209C22×C4—31no—
210C22×C4—31no—
211C22×C4—31no—
212C22×C4C22×D311yescharacteristic
213C22×C4C22×D311yescharacteristic
214C22×C4C22×D311yescharacteristic
215C22×C4C22×D311yescharacteristic
216C22×C4C22×D311yescharacteristic
217C4⋊C4—22no—
218C4⋊C4—62no—
219C4⋊C4—62no—
220C4⋊C4—121no—
221C4⋊C4—121no—
222C4⋊C4—121no—
223C4⋊C4—121no—
224C4⋊C4—121no—
225C4⋊C4—121no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—62no—
231C22⋊C4—62no—
232C22⋊C4—62no—
233C22⋊C4—62no—
234C22⋊C4—121no—
235C22⋊C4—121no—
236C22⋊C4—121no—
237C22⋊C4—121no—
238C42—62no—
239C42—121no—
240C42—121no—
241C22×C3—41no—
242C22×C3—41no—
243C22×C3—41no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3—41no—
249C22×C3—41no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3—41no—
255C22×C3C2×#4111yescharacteristic
256C22×C3C2×#4111yescharacteristic
257C22×C3C2×#4111yescharacteristic
258C22×C3H(5,𝔽2)11yescharacteristic
259C22×C3H(5,𝔽2)11yescharacteristic
260C22×C3H(5,𝔽2)11yescharacteristic
261C22×C32−1+411yescharacteristic
262C3×C4—22no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—41no—
267Dic3—22no—
268Dic3—22no—
269Dic3—41no—
270Dic3—41no—
271Dic3—41no—
272Dic3—41no—
273Dic3—41no—
274Dic3—41no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C23×D311yescharacteristic
290D4—44no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—32no—
306C2×C4—32no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
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#23712yes—
330C2×C3—81no—
331C2×C3—81no—
332C2×C3#52911yescharacteristic
333C2×C3#53811yescharacteristic
334C2×C3#53911yescharacteristic
335C2×C3#54011yescharacteristic
336C2×C3#54011yescharacteristic
337C2×C3#54211yescharacteristic
338C2×C3#54211yescharacteristic
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22C2×#23711yescharacteristic
354C22#100411yescharacteristic
355C22#100411yescharacteristic
356C22#100411yescharacteristic
357C22D3×#4111yescharacteristic
358C22D3×#4111yescharacteristic
359C22#101011yescharacteristic
360C4—22no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—62no—
366C4—62no—
367C4—121no—
368C4—121no—
369C4—121no—
370C4—121no—
371C4—121no—
372C4—121no—
373C3#265111yescharacteristic, complemented, Sylow
374C2—81no—
375C2—81no—
376C2#559311yescharacteristic
377C2#560311yescharacteristic
378C2#561511yescharacteristic
379C2#561511yescharacteristic
380C2#566011yescharacteristic
381C2#566211yescharacteristic
382C2#568011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#394C2
prime radicalC22×C3×D4C22
hypercenter#394D3
hypocenterC3#2651
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
4. #4982C2semidirect
5. #4980C2semidirect
6. #4952C2semidirect
7. #4952C2semidirect
8. #4949C2semidirect
9. #4948C2semidirect
10. #4945C2semidirect
11. #4945C2semidirect
12. #4945C2semidirect
13. #4944C2semidirect
14. #4657C2semidirect
15. #4649C2semidirect
373. C3#2651semidirect

Maximal subgroups

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

subgroupindex
C3×#3942
#52222
#52212
#49822
#49802
#49522
#49492
#49482
#49452
#49442
#46572
#46492
#26513