Finite Group Databasebeta

← #73356

Subgroups — #73356

Order 384.

482 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#95C211yesmaximal, characteristic, complemented
2#5213C211yesmaximal, characteristic
3#5213C211yesmaximal, characteristic
4#5213C211yesmaximal, characteristic
5#5212C211yesmaximal, characteristic, complemented
6#5210C211yesmaximal, characteristic, complemented
7C4×#217C211yesmaximal, characteristic, complemented
8#4675C211yesmaximal, characteristic, complemented
9#4674C211yesmaximal, characteristic, complemented
10#4670C211yesmaximal, characteristic, complemented
11#4669C211yesmaximal, characteristic, complemented
12C3⋊#401C211yesmaximal, characteristic, complemented
13#4660C211yesmaximal, characteristic, complemented
14#4654C211yesmaximal, characteristic, complemented
15#4651C211yesmaximal, characteristic, complemented
16#2510—31nomaximal, Sylow
17C23×C3×C4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C2×#217C2211yescharacteristic
22C2×#217C2211yescharacteristic
23C2×#217C2211yescharacteristic
24C2×(C2×D3)⋊C4C2211yescharacteristic
25C2×(C2×D3)⋊C4C2211yescharacteristic
26C2×(C2×D3)⋊C4C2211yescharacteristic
27C2×(C2×D3)⋊C4C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×C4⋊Dic3C2211yescharacteristic
31C2×C4⋊Dic3C2211yescharacteristic
32C2×Dic3⋊C4C2211yescharacteristic
33C2×Dic3⋊C4C2211yescharacteristic
34C2×C4×Dic3C2211yescharacteristic
35C2×C4×Dic3C2211yescharacteristic
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#397—31no—
55#397—31no—
56#388—31no—
57#388—31no—
58#387—31no—
59#386—31no—
60#386—31no—
61#386—31no—
62#385—31no—
63#383—31no—
64#380—31no—
65C4×C22⋊C4—31no—
66C2×#95D311yescharacteristic, complemented
67C24×C3C2311yescharacteristic
68C23×D3C2311yescharacteristic
69C22×C3×C4—22no—
70C22×C3×C4—22no—
71C22×C3×C4—22no—
72C22×C3×C4—22no—
73C22×C3×C4—22no—
74C22×C3×C4—41no—
75C22×C3×C4—41no—
76C22×C3×C4—41no—
77C22×C3×C4—41no—
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—22no—
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94#217—22no—
95#217—22no—
96#217—22no—
97(C2×D3)⋊C4—22no—
98(C2×D3)⋊C4—22no—
99(C2×D3)⋊C4—41no—
100(C2×D3)⋊C4—41no—
101(C2×D3)⋊C4—41no—
102(C2×D3)⋊C4—41no—
103C4⋊Dic3—22no—
104C4⋊Dic3—41no—
105Dic3⋊C4—41no—
106Dic3⋊C4—41no—
107C4×Dic3—22no—
108C4×Dic3—41no—
109C22×D4—31no—
110C23×C4C2×D311yescharacteristic
111C23×C4C2×D311yescharacteristic
112C23×C4C2×D311yescharacteristic
113C2×C4⋊C4—31no—
114C2×C4⋊C4—31no—
115C2×C4⋊C4—31no—
116C2×C4⋊C4—31no—
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⋊C4—31no—
126C2×C42—31no—
127C2×C42—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#95—31no—
137#95—31no—
138#95—31no—
139#95—31no—
140#95C2×D311yescharacteristic
141#95C2×D311yescharacteristic
142#95C2×D311yescharacteristic
143#95C2×D311yescharacteristic
144C23×C3—21no—
145C23×C3—21no—
146C23×C3—21no—
147C23×C3—21no—
148C23×C3#4112yes—
149C23×C3#4112yes—
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—21no—
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—44no—
177C2×C3×C4—44no—
178C2×C3×C4#4112yes—
179C2×C3×C4#4112yes—
180#67—44no—
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—
202C24—31no—
203C24C22×D311yescharacteristic
204C2×D4—62no—
205C2×D4—62no—
206C2×D4—62no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—31no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4C22×D311yescharacteristic
224C22×C4C22×D311yescharacteristic
225C22×C4C22×D311yescharacteristic
226C22×C4C22×D311yescharacteristic
227C22×C4C22×D311yescharacteristic
228C22×C4C22×D311yescharacteristic
229C4⋊C4—62no—
230C4⋊C4—121no—
231C4⋊C4—121no—
232C4⋊C4—121no—
233C22⋊C4—62no—
234C22⋊C4—62no—
235C22⋊C4—62no—
236C22⋊C4—62no—
237C22⋊C4—62no—
238C22⋊C4—121no—
239C22⋊C4—121no—
240C22⋊C4—121no—
241C22⋊C4—121no—
242C42—62no—
243C42—121no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3#12614yes—
251C22×C3C2×#4111yescharacteristic
252C22×C3C2×#4111yescharacteristic
253C22×C3C2×#4111yescharacteristic
254C22×C3C2×#4111yescharacteristic
255C22×C3C2×#4111yescharacteristic
256C22×C3H(5,𝔽2)11yescharacteristic
257C22×C3H(5,𝔽2)11yescharacteristic
258C2×D3—41no—
259C2×D3—41no—
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C2×D3—41no—
264C2×D3—41no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4—41no—
270C3×C4—41no—
271Dic3—41no—
272Dic3—41no—
273Dic3—41no—
274Dic3—41no—
275Dic3—41no—
276Dic3—41no—
277Dic3—41no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—61no—
283C23—61no—
284C23—61no—
285C23—61no—
286C23—61no—
287C23—61no—
288C23—61no—
289C23#23512yes—
290C23#23712yes—
291C23#23912yes—
292C23C23×D311yescharacteristic
293D4—124no—
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—21no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—44no—
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—61no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4#23512yes—
335C2×C4#23512yes—
336C2×C3—24no—
337C2×C3C2×#12611yescharacteristic
338C2×C3#52911yescharacteristic
339C2×C3#53811yescharacteristic
340C2×C3#55111yescharacteristic
341C2×C3#55111yescharacteristic
342C2×C3#55311yescharacteristic
343C2×C3#55311yescharacteristic
344D3—81no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22—121no—
352C22—121no—
353C22—121no—
354C22—121no—
355C22—121no—
356C22—121no—
357C22—121no—
358C22#89814yes—
359C22C2×#23511yescharacteristic
360C22C2×#23511yescharacteristic
361C22C2×#23511yescharacteristic
362C22C2×#23711yescharacteristic
363C22#100411yescharacteristic
364C22#100411yescharacteristic
365C22C2×#23911yescharacteristic
366C4—22no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—121no—
373C4—121no—
374C4—121no—
375C4—121no—
376C4—121no—
377C4—121no—
378C4—121no—
379C3#251011yescharacteristic, complemented, Sylow
380C2—24no—
381C2—241no—
382C2#547911yescharacteristic
383C2#549411yescharacteristic
384C2#549511yescharacteristic
385C2#549511yescharacteristic
386C2C2×#89811yescharacteristic
387C2#551411yescharacteristic
388C2#551411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC2×C3×#95C2
prime radicalC22×#67C22
hypercenterC2×#95D3
hypocenterC3#2510
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C2×C3×#95C2semidirect
5. #5212C2semidirect
6. #5210C2semidirect
7. C4×#217C2semidirect
8. #4675C2semidirect
9. #4674C2semidirect
10. #4670C2semidirect
11. #4669C2semidirect
12. C3⋊#401C2semidirect
13. #4660C2semidirect
14. #4654C2semidirect
15. #4651C2semidirect
66. C2×#95D3semidirect
379. C3#2510semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#952
#52132
#52122
#52102
C4×#2172
#46752
#46742
#46702
#46692
C3⋊#4012
#46602
#46542
#46512
#25103