Finite Group Databasebeta

← #73948

Subgroups — #73948

Order 384.

468 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#380C211yesmaximal, characteristic, complemented
2#5213C211yesmaximal, characteristic
3C4×#217C211yesmaximal, characteristic, complemented
4#4992C211yesmaximal, characteristic, complemented
5#4989C211yesmaximal, characteristic, complemented
6#4986C211yesmaximal, characteristic, complemented
7#4980C211yesmaximal, characteristic, complemented
8#4961C211yesmaximal, characteristic
9#4956C211yesmaximal, characteristic
10#4953C211yesmaximal, characteristic, complemented
11#4944C211yesmaximal, characteristic, complemented
12#4670C211yesmaximal, characteristic, complemented
13#4666C211yesmaximal, characteristic, complemented
14#4655C211yesmaximal, characteristic, complemented
15#4651C211yesmaximal, characteristic, complemented
16#2578—31nomaximal, Sylow
17C23×C3×C4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21C2×C3×C4⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×#217C2211yescharacteristic
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×(C2×D3)⋊C4C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×C4⋊Dic3C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×C4×Dic3C2211yescharacteristic
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#397—31no—
54#397—31no—
55#394—31no—
56#388—31no—
57#388—31no—
58#387—31no—
59#387—31no—
60#386—31no—
61#386—31no—
62#385—31no—
63#383—31no—
64#380D311yescharacteristic, complemented
65C4×C22⋊C4—31no—
66C4×C22⋊C4—31no—
67C24×C3C2311yescharacteristic
68C23×D3C2311yescharacteristic
69C22×C3×C4—22no—
70C22×C3×C4—22no—
71C22×C3×C4—41no—
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—22no—
79C2×#67—22no—
80C2×#67—41no—
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C2×C4×D3—22no—
89C2×C4×D3—41no—
90C2×C4×D3—41no—
91C3×C4⋊C4—22no—
92C3×C4⋊C4—41no—
93C3×C22⋊C4—41no—
94C3×C22⋊C4—41no—
95#217—22no—
96#217—22no—
97#217—22no—
98(C2×D3)⋊C4—22no—
99(C2×D3)⋊C4—22no—
100(C2×D3)⋊C4—22no—
101(C2×D3)⋊C4—22no—
102(C2×D3)⋊C4—41no—
103C4⋊Dic3—41no—
104C4⋊Dic3—41no—
105Dic3⋊C4—22no—
106C4×Dic3—22no—
107C4×Dic3—41no—
108C4×Dic3—41no—
109C22×D4—31no—
110C23×C4—31no—
111C23×C4C2×D311yescharacteristic
112C2×C4⋊C4—31no—
113C2×C4⋊C4—31no—
114C2×C4⋊C4—31no—
115C2×C4⋊C4C2×D311yescharacteristic
116C2×C4⋊C4C2×D311yescharacteristic
117C2×C22⋊C4—31no—
118C2×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
126C2×C22⋊C4C2×D311yescharacteristic
127C2×C42—31no—
128C2×C42—31no—
129C2×C42—31no—
130#95—31no—
131#95—31no—
132#95—31no—
133#95—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#95C2×D311yescharacteristic
143#95C2×D311yescharacteristic
144C23×C3—21no—
145C23×C3—21no—
146C23×C3—21no—
147C23×C3—21no—
148C23×C3—21no—
149C23×C3—21no—
150C23×C3#4112yes—
151C23×C3C2411yescharacteristic
152C22×D3—21no—
153C22×D3—21no—
154C22×D3—21no—
155C22×D3—21no—
156C22×D3—21no—
157C22×D3—21no—
158C22×D3#4112yes—
159C2×C3×C4—21no—
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—21no—
175C2×C3×C4—44no—
176C2×C3×C4#4112yes—
177C2×C3×C4#4112yes—
178#67—44no—
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#4112yes—
200C4×D3—44no—
201C24—31no—
202C24C22×D311yescharacteristic
203C2×D4—62no—
204C2×D4—62no—
205C2×D4—121no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—31no—
209C22×C4—31no—
210C22×C4—31no—
211C22×C4—31no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—41no—
216C22×C4—62no—
217C22×C4—121no—
218C22×C4—121no—
219C22×C4C22×D311yescharacteristic
220C22×C4C22×D311yescharacteristic
221C22×C4C22×D311yescharacteristic
222C22×C4C22×D311yescharacteristic
223C22×C4C22×D311yescharacteristic
224C22×C4C22×D311yescharacteristic
225C4⋊C4—22no—
226C4⋊C4—41no—
227C4⋊C4—62no—
228C4⋊C4—121no—
229C4⋊C4—121no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—62no—
233C22⋊C4—62no—
234C22⋊C4—62no—
235C22⋊C4—62no—
236C22⋊C4—62no—
237C22⋊C4—62no—
238C22⋊C4—62no—
239C22⋊C4—121no—
240C42—62no—
241C42—121no—
242C42—121no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3—41no—
249C22×C3—41no—
250C22×C3C2×#4111yescharacteristic
251C22×C3C2×#4111yescharacteristic
252C22×C3C2×#4111yescharacteristic
253C22×C3C2×#4111yescharacteristic
254C22×C3C2×#4111yescharacteristic
255C22×C3H(5,𝔽2)11yescharacteristic
256C22×C3H(5,𝔽2)11yescharacteristic
257C2×D3—22no—
258C2×D3—22no—
259C2×D3—22no—
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C2×D3—41no—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4—41no—
270Dic3—22no—
271Dic3—41no—
272Dic3—41no—
273Dic3—41no—
274Dic3—41no—
275Dic3—41no—
276Dic3—41no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—32no—
284C23—61no—
285C23—61no—
286C23—61no—
287C23—61no—
288C23—61no—
289C23—61no—
290C23#23912yes—
291C23C23×D311yescharacteristic
292D4—124no—
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—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—32no—
310C2×C4—44no—
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—61no—
330C2×C4—61no—
331C2×C4—124no—
332C2×C4#23512yes—
333C2×C4#23712yes—
334C2×C3—42no—
335C2×C3#52911yescharacteristic
336C2×C3#52911yescharacteristic
337C2×C3#53811yescharacteristic
338C2×C3#55111yescharacteristic
339C2×C3#55111yescharacteristic
340C2×C3#55311yescharacteristic
341C2×C3#55311yescharacteristic
342D3—42no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—62no—
351C22—62no—
352C22—62no—
353C22—121no—
354C22—121no—
355C22—121no—
356C22—121no—
357C22C2×#23511yescharacteristic
358C22C2×#23711yescharacteristic
359C22#100411yescharacteristic
360C22#100411yescharacteristic
361C22C2×#23911yescharacteristic
362C22D3×#4111yescharacteristic
363C22D3×#4111yescharacteristic
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—62no—
371C4—121no—
372C4—121no—
373C4—121no—
374C4—121no—
375C4—121no—
376C4—121no—
377C3#257811yescharacteristic, complemented, Sylow
378C2—42no—
379C2—122no—
380C2#549511yescharacteristic
381C2#551411yescharacteristic
382C2#552811yescharacteristic
383C2#561311yescharacteristic
384C2#561411yescharacteristic
385C2#562411yescharacteristic
386C2#563711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#380C2
prime radicalC22×#67C22
hypercenter#380D3
hypocenterC3#2578
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C3×#380C2semidirect
3. C4×#217C2semidirect
4. #4992C2semidirect
5. #4989C2semidirect
6. #4986C2semidirect
7. #4980C2semidirect
10. #4953C2semidirect
11. #4944C2semidirect
12. #4670C2semidirect
13. #4666C2semidirect
14. #4655C2semidirect
15. #4651C2semidirect
64. #380D3semidirect
377. C3#2578semidirect

Maximal subgroups

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

subgroupindex
C3×#3802
#52132
C4×#2172
#49922
#49892
#49862
#49802
#49612
#49562
#49532
#49442
#46702
#46662
#46552
#46512
#25783