Finite Group Databasebeta

← #74764

Subgroups — #74764

Order 384.

476 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
1C3×#386C211yesmaximal, characteristic
2#5222C211yesmaximal, characteristic
3#5220C211yesmaximal, characteristic
4#5211C211yesmaximal, characteristic, complemented
5C4×#217C211yesmaximal, characteristic, complemented
6#4947C211yesmaximal, characteristic, complemented
7#4947C211yesmaximal, characteristic, complemented
8#4945C211yesmaximal, characteristic, complemented
9#4944C211yesmaximal, characteristic, complemented
10#4943C211yesmaximal, characteristic, complemented
11Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
12#4658C211yesmaximal, characteristic, complemented
13#4651C211yesmaximal, characteristic, complemented
14#4651C211yesmaximal, characteristic, complemented
15#4646C211yesmaximal, characteristic, complemented
16#2572—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C23×Dic3C2211yescharacteristic
20C22×Dic6C2211yescharacteristic
21C2×C3×C22⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×#217C2211yescharacteristic
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×Dic3⋊C4C2211yescharacteristic
32C2×Dic3⋊C4C2211yescharacteristic
33C2×C4×Dic3C2211yescharacteristic
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#400—31no—
53#394—31no—
54#393—31no—
55#393—31no—
56#391—31no—
57#388—31no—
58#388—31no—
59#386—31no—
60#386D311yescharacteristic
61#383—31no—
62#383—31no—
63#381—31no—
64#381—31no—
65C4×C22⋊C4—31no—
66C4×C22⋊C4—31no—
67C24×C3C2311yescharacteristic
68C24×C3C2311yescharacteristic
69C2×C3×D4—22no—
70C2×C3×D4—22no—
71C2×C3×D4—41no—
72C22×C3×C4—22no—
73C22×C3×C4—22no—
74C22×C3×C4—41no—
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×Dic3—22no—
81C22×Dic3—22no—
82C22×Dic3—41no—
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C2×Dic6—22no—
92C2×Dic6—41no—
93C2×Dic6—41no—
94C3×C22⋊C4—22no—
95C3×C22⋊C4—41no—
96C3×C22⋊C4—41no—
97#217—22no—
98#217—22no—
99#217—22no—
100#217—22no—
101#217—22no—
102#217—41no—
103#217—41no—
104Dic3⋊C4—41no—
105Dic3⋊C4—41no—
106C4×Dic3—22no—
107C4×Dic3—22no—
108C4×Dic3—41no—
109C22×Q8—31no—
110C22×D4C2×D311yescharacteristic
111C23×C4—31no—
112C23×C4C2×D311yescharacteristic
113C2×C4⋊C4—31no—
114C2×C4⋊C4—31no—
115C2×C22⋊C4—31no—
116C2×C22⋊C4—31no—
117C2×C22⋊C4—31no—
118C2×C22⋊C4—31no—
119C2×C22⋊C4—31no—
120C2×C22⋊C4—31no—
121C2×C22⋊C4—31no—
122C2×C22⋊C4C2×D311yescharacteristic
123C2×C22⋊C4C2×D311yescharacteristic
124C2×C22⋊C4C2×D311yescharacteristic
125C2×C42—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#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—21no—
151C23×C3—21no—
152C23×C3—21no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3#4112yes—
157C23×C3#4112yes—
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—44no—
175C2×C3×C4#4112yes—
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—21no—
198C2×Dic3—44no—
199C2×Dic3#4112yes—
200C2×Dic3#4112yes—
201Dic6—44no—
202C24C22×D311yescharacteristic
203C24C22×D311yescharacteristic
204C2×Q8—62no—
205C2×Q8—121no—
206C2×Q8—121no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—41no—
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—31no—
220C22×C4—41no—
221C22×C4—62no—
222C22×C4—62no—
223C22×C4—121no—
224C22×C4C22×D311yescharacteristic
225C22×C4C22×D311yescharacteristic
226C22×C4C22×D311yescharacteristic
227C22×C4C22×D311yescharacteristic
228C22×C4C22×D311yescharacteristic
229C4⋊C4—121no—
230C4⋊C4—121no—
231C22⋊C4—22no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—62no—
235C22⋊C4—62no—
236C22⋊C4—62no—
237C22⋊C4—62no—
238C22⋊C4—62no—
239C22⋊C4—121no—
240C22⋊C4—121no—
241C42—62no—
242C42—62no—
243C42—121no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3—41no—
258C22×C3C2×#4111yescharacteristic
259C22×C3C2×#4111yescharacteristic
260C22×C3C2×#4111yescharacteristic
261C22×C3C2×#4111yescharacteristic
262C22×C3C2×#4111yescharacteristic
263C22×C3H(5,𝔽2)11yescharacteristic
264C22×C3H(5,𝔽2)11yescharacteristic
265C3×C4—22no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4—41no—
270Dic3—22no—
271Dic3—22no—
272Dic3—41no—
273Dic3—41no—
274Dic3—41no—
275Dic3—41no—
276Dic3—41no—
277Dic3—41no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23#23512yes—
291C23#23712yes—
292C23C23×D311yescharacteristic
293Q8—124no—
294D4—44no—
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—32no—
311C2×C4—44no—
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—61no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—124no—
335C2×C4#23712yes—
336C2×C3—42no—
337C2×C3—42no—
338C2×C3#52911yescharacteristic
339C2×C3#52911yescharacteristic
340C2×C3#53811yescharacteristic
341C2×C3#55111yescharacteristic
342C2×C3#55111yescharacteristic
343C2×C3#55111yescharacteristic
344C2×C3#55511yescharacteristic
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22C2×#23511yescharacteristic
360C22C2×#23711yescharacteristic
361C22C2×#23711yescharacteristic
362C22#100411yescharacteristic
363C22#100411yescharacteristic
364C22D3×#4111yescharacteristic
365C22D3×#4111yescharacteristic
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—62no—
372C4—62no—
373C4—121no—
374C4—121no—
375C4—121no—
376C4—121no—
377C4—121no—
378C4—121no—
379C3#257211yescharacteristic, complemented, Sylow
380C2—42no—
381C2—42no—
382C2#549511yescharacteristic
383C2#553811yescharacteristic
384C2#555611yescharacteristic
385C2#558711yescharacteristic
386C2#561311yescharacteristic
387C2#561611yescharacteristic
388C2#564911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
prime radicalC22×C3×D4C22
hypercenter#386D3
hypocenterC3#2572
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
4. #5211C2semidirect
5. C4×#217C2semidirect
6. #4947C2semidirect
7. #4947C2semidirect
8. #4945C2semidirect
9. #4944C2semidirect
10. #4943C2semidirect
11. Dic3×C22⋊C4C2semidirect
12. #4658C2semidirect
13. #4651C2semidirect
14. #4651C2semidirect
15. #4646C2semidirect
379. C3#2572semidirect

Maximal subgroups

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

subgroupindex
C3×#3862
#52222
#52202
#52112
C4×#2172
#49472
#49452
#49442
#49432
Dic3×C22⋊C42
#46582
#46512
#46462
#25723