Finite Group Databasebeta

← #82837

Subgroups — #82837

Order 384.

532 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#123C211yesmaximal, characteristic
2#5221C211yesmaximal, characteristic
3#5220C211yesmaximal, characteristic
4#5212C211yesmaximal, characteristic, complemented
5C4×#217C211yesmaximal, characteristic, complemented
6#4984C211yesmaximal, characteristic, complemented
7#4980C211yesmaximal, characteristic, complemented
8#4980C211yesmaximal, characteristic, complemented
9Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
10#4951C211yesmaximal, characteristic, complemented
11#4951C211yesmaximal, characteristic, complemented
12#4951C211yesmaximal, characteristic, complemented
13#4951C211yesmaximal, characteristic, complemented
14#4950C211yesmaximal, characteristic, complemented
15Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
16#2335—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C23×Dic3C2211yescharacteristic
20C3×#123C418yescomplemented
21C2×C3×C4⋊C4C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×C4⋊Dic3C2211yescharacteristic
35C2×C4⋊Dic3C2211yescharacteristic
36C2×C4⋊Dic3C2211yescharacteristic
37C2×C4⋊Dic3C2211yescharacteristic
38C2×C4×Dic3C2211yescharacteristic
39C2×C4×Dic3C2211yescharacteristic
40C2×C4×Dic3C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42C2×C4×Dic3C2211yescharacteristic
43C3⋊#95C2211yescharacteristic
44C3⋊#95C2211yescharacteristic
45C3⋊#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C2×#123D311yescharacteristic
54#390—31no—
55#389—31no—
56#388—31no—
57#388—31no—
58#388—31no—
59#388—31no—
60#387—31no—
61#387—31no—
62#386—31no—
63#385—31no—
64#380—31no—
65C4×C4⋊C4—31no—
66C4×C22⋊C4—31no—
67C4×C22⋊C4—31no—
68C24×C3C2311yescharacteristic
69C24×C3C2311yescharacteristic
70C2×C3×D4—41no—
71C2×C3×D4—41no—
72C2×C3×D4C2×C414yes—
73C22×C3×C4—41no—
74C22×C3×C4—41no—
75C22×C3×C4C2×C414yescomplemented
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×Dic3—22no—
82C22×Dic3—41no—
83C22×Dic3—41no—
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C3×C4⋊C4C2×C414yescomplemented
93C3×C4⋊C4C2×C414yescomplemented
94C3×C22⋊C4C2×C414yes—
95C3×C22⋊C4C2×C414yes—
96C3×C22⋊C4C2×C414yescomplemented
97#217—22no—
98#217—22no—
99#217—22no—
100#217—41no—
101#217—41no—
102#217—41no—
103#217—41no—
104C4⋊Dic3—22no—
105C4⋊Dic3—41no—
106C4⋊Dic3—41no—
107C4⋊Dic3—41no—
108C4⋊Dic3—41no—
109C4×Dic3—22no—
110C4×Dic3—41no—
111C4×Dic3—41no—
112C4×Dic3—41no—
113C4×Dic3—41no—
114C22×D4C2×D311yescharacteristic
115C23×C4—31no—
116C23×C4C2×D311yescharacteristic
117#123Dic318yescomplemented
118C2×C4⋊C4—31no—
119C2×C4⋊C4—31no—
120C2×C4⋊C4—31no—
121C2×C4⋊C4—31no—
122C2×C4⋊C4—31no—
123C2×C4⋊C4C2×D311yescharacteristic
124C2×C4⋊C4C2×D311yescharacteristic
125C2×C22⋊C4—31no—
126C2×C22⋊C4—31no—
127C2×C22⋊C4—31no—
128C2×C22⋊C4—31no—
129C2×C22⋊C4—31no—
130C2×C22⋊C4—31no—
131C2×C22⋊C4—31no—
132C2×C22⋊C4C2×D311yescharacteristic
133C2×C22⋊C4C2×D311yescharacteristic
134C2×C22⋊C4C2×D311yescharacteristic
135C2×C42—31no—
136C2×C42—31no—
137C2×C42—31no—
138C2×C42—31no—
139C2×C42—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—
148#95—31no—
149#95—31no—
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×C3—21no—
161C23×C3—21no—
162C23×C3C22×C412yes—
163C23×C3C22×C412yes—
164C23×C3C2411yescharacteristic
165C3×D4—44no—
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—44no—
177C2×C3×C4C22×C412yes—
178C2×C3×C4C22×C412yes—
179C2×C3×C4C22×C412yes—
180C2×C3×C4C22×C412yes—
181C2×C3×C4C22×C412yes—
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—21no—
203C2×Dic3—21no—
204C2×Dic3—44no—
205C2×Dic3#4112yes—
206C2×Dic3#4112yes—
207C24C22×D311yescharacteristic
208C24C22×D311yescharacteristic
209C2×D4—41no—
210C2×D4—41no—
211C2×D4C2×Dic314yes—
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—41no—
222C22×C4—62no—
223C22×C4—121no—
224C22×C4—121no—
225C22×C4C2×Dic314yescomplemented
226C22×C4C22×D311yescharacteristic
227C22×C4C22×D311yescharacteristic
228C22×C4C22×D311yescharacteristic
229C22×C4C22×D311yescharacteristic
230C22×C4C22×D311yescharacteristic
231C4⋊C4—62no—
232C4⋊C4—121no—
233C4⋊C4—121no—
234C4⋊C4—121no—
235C4⋊C4—121no—
236C4⋊C4C2×Dic314yescomplemented
237C4⋊C4C2×Dic314yescomplemented
238C22⋊C4—62no—
239C22⋊C4—62no—
240C22⋊C4—62no—
241C22⋊C4—121no—
242C22⋊C4—121no—
243C22⋊C4—121no—
244C22⋊C4—121no—
245C22⋊C4C2×Dic314yes—
246C22⋊C4C2×Dic314yes—
247C22⋊C4C2×Dic314yescomplemented
248C42—62no—
249C42—121no—
250C42—121no—
251C42—121no—
252C42—121no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—22no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3C23×C411yescharacteristic
268C22×C3C2×#4111yescharacteristic
269C22×C3C2×#4111yescharacteristic
270C22×C3H(5,𝔽2)11yescharacteristic
271C22×C3H(5,𝔽2)11yescharacteristic
272C22×C3H(5,𝔽2)11yescharacteristic
273C22×C32−1+411yescharacteristic
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279Dic3—22no—
280Dic3—22no—
281Dic3—41no—
282Dic3—41no—
283Dic3—41no—
284Dic3—41no—
285Dic3—41no—
286Dic3—41no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C22×Dic312yes—
300C23C22×Dic312yes—
301C23C23×D311yescharacteristic
302D4—44no—
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—32no—
314C2×C4—32no—
315C2×C4—44no—
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×C4C22×Dic312yes—
340C2×C4C22×Dic312yes—
341C2×C4C22×Dic312yes—
342C2×C4C22×Dic312yes—
343C2×C4C22×Dic312yes—
344C2×C3—42no—
345C2×C3—42no—
346C2×C3C4×#4111yescharacteristic
347C2×C3#51811yescharacteristic
348C2×C3#52011yescharacteristic
349C2×C3#53811yescharacteristic
350C2×C3#53911yescharacteristic
351C2×C3#54011yescharacteristic
352C2×C3#54211yescharacteristic
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22#100411yescharacteristic
368C22#100411yescharacteristic
369C22D3×#4111yescharacteristic
370C22D3×#4111yescharacteristic
371C22#100911yescharacteristic
372C22#101011yescharacteristic
373C22C23×Dic311yescharacteristic
374C4—22no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—62no—
380C4—62no—
381C4—121no—
382C4—121no—
383C4—121no—
384C4—121no—
385C4—121no—
386C4—121no—
387C3#233511yescharacteristic, complemented, Sylow
388C2—42no—
389C2—42no—
390C2#565711yescharacteristic
391C2#566011yescharacteristic
392C2#566211yescharacteristic
393C2#566311yescharacteristic
394C2#579811yescharacteristic
395C2Dic3×#4111yescharacteristic
396C2#582711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC2×C3×#123C2
socle, cosocleC23×C3C24
prime radicalC22×C3×D4C22
hypercenterC2×#123D3
hypocenterC3#2335
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
4. #5212C2semidirect
5. C4×#217C2semidirect
6. #4984C2semidirect
7. #4980C2semidirect
8. #4980C2semidirect
9. Dic3×C4⋊C4C2semidirect
10. #4951C2semidirect
11. #4951C2semidirect
12. #4951C2semidirect
13. #4951C2semidirect
14. #4950C2semidirect
15. Dic3×C22⋊C4C2semidirect
20. C3×#123C4semidirect
75. C22×C3×C4C2×C4semidirect
92. C3×C4⋊C4C2×C4semidirect
93. C3×C4⋊C4C2×C4semidirect
96. C3×C22⋊C4C2×C4semidirect
117. #123Dic3semidirect
225. C22×C4C2×Dic3semidirect
236. C4⋊C4C2×Dic3semidirect
237. C4⋊C4C2×Dic3semidirect
247. C22⋊C4C2×Dic3semidirect
387. C3#2335semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1232
#52212
#52202
#52122
C4×#2172
#49842
#49802
Dic3×C4⋊C42
#49512
#49502
Dic3×C22⋊C42
#23353