Finite Group Databasebeta

← C3×#2335 #84199

Subgroups — C3×#2335 #84199

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
2C3×#390C211yesmaximal, characteristic
3C3×#389C211yesmaximal, characteristic, complemented
4C3×#388C211yesmaximal, characteristic, complemented
5C3×#388C211yesmaximal, characteristic, complemented
6C3×#388C211yesmaximal, characteristic, complemented
7C3×#388C211yesmaximal, characteristic, complemented
8C3×#387C211yesmaximal, characteristic, complemented
9C3×#387C211yesmaximal, characteristic, complemented
10C3×#386C211yesmaximal, characteristic
11C3×#385C211yesmaximal, characteristic, complemented
12C3×#380C211yesmaximal, characteristic, complemented
13C3×C4×C4⋊C4C211yesmaximal, characteristic, complemented
14C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
15C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
16#2335C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C3×#123C418yescomplemented
21C2×C3×C4⋊C4C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C22⋊C4C2211yescharacteristic
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×C3×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊C4C2211yescharacteristic
35C2×C3×C22⋊C4C2211yescharacteristic
36C2×C3×C22⋊C4C2211yescharacteristic
37C2×C3×C22⋊C4C2211yescharacteristic
38C2×C3×C42C2211yescharacteristic
39C2×C3×C42C2211yescharacteristic
40C2×C3×C42C2211yescharacteristic
41C2×C3×C42C2211yescharacteristic
42C2×C3×C42C2211yescharacteristic
43C3×#95C2211yescharacteristic
44C3×#95C2211yescharacteristic
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C2×#123C2×C311yescharacteristic
54#390C2×C311yescharacteristic
55#389C2×C311yescharacteristic, complemented
56#388C2×C311yescharacteristic, complemented
57#388C2×C311yescharacteristic, complemented
58#388C2×C311yescharacteristic, complemented
59#388C2×C311yescharacteristic, complemented
60#387C2×C311yescharacteristic, complemented
61#387C2×C311yescharacteristic, complemented
62#386C2×C311yescharacteristic
63#385C2×C311yescharacteristic, complemented
64#380C2×C311yescharacteristic, complemented
65C4×C4⋊C4C2×C311yescharacteristic, complemented
66C4×C22⋊C4C2×C311yescharacteristic, complemented
67C4×C22⋊C4C2×C311yescharacteristic, complemented
68C24×C3C2311yescharacteristic
69C24×C3C2311yescharacteristic
70C2×C3×D4—41no—
71C2×C3×D4—41no—
72C2×C3×D4C2×C414yes—
73C22×C3×C4—22no—
74C22×C3×C4—41no—
75C22×C3×C4—41no—
76C22×C3×C4—41no—
77C22×C3×C4—41no—
78C22×C3×C4C2×C414yescomplemented
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C3×C4⋊C4—22no—
93C3×C4⋊C4—41no—
94C3×C4⋊C4—41no—
95C3×C4⋊C4—41no—
96C3×C4⋊C4—41no—
97C3×C4⋊C4C2×C414yescomplemented
98C3×C4⋊C4C2×C414yescomplemented
99C3×C22⋊C4—22no—
100C3×C22⋊C4—22no—
101C3×C22⋊C4—22no—
102C3×C22⋊C4—41no—
103C3×C22⋊C4—41no—
104C3×C22⋊C4—41no—
105C3×C22⋊C4—41no—
106C3×C22⋊C4C2×C414yes—
107C3×C22⋊C4C2×C414yes—
108C3×C22⋊C4C2×C414yescomplemented
109C3×C42—22no—
110C3×C42—41no—
111C3×C42—41no—
112C3×C42—41no—
113C3×C42—41no—
114C22×D4C22×C311yescharacteristic
115C23×C4C22×C311yescharacteristic
116C23×C4C22×C311yescharacteristic
117#123C3×C418yescomplemented
118C2×C4⋊C4C22×C311yescharacteristic
119C2×C4⋊C4C22×C311yescharacteristic
120C2×C4⋊C4C22×C311yescharacteristic
121C2×C4⋊C4C22×C311yescharacteristic
122C2×C4⋊C4C22×C311yescharacteristic
123C2×C4⋊C4C22×C311yescharacteristic
124C2×C4⋊C4C22×C311yescharacteristic
125C2×C22⋊C4C22×C311yescharacteristic
126C2×C22⋊C4C22×C311yescharacteristic
127C2×C22⋊C4C22×C311yescharacteristic
128C2×C22⋊C4C22×C311yescharacteristic
129C2×C22⋊C4C22×C311yescharacteristic
130C2×C22⋊C4C22×C311yescharacteristic
131C2×C22⋊C4C22×C311yescharacteristic
132C2×C22⋊C4C22×C311yescharacteristic
133C2×C22⋊C4C22×C311yescharacteristic
134C2×C22⋊C4C22×C311yescharacteristic
135C2×C42C22×C311yescharacteristic
136C2×C42C22×C311yescharacteristic
137C2×C42C22×C311yescharacteristic
138C2×C42C22×C311yescharacteristic
139C2×C42C22×C311yescharacteristic
140#95C22×C311yescharacteristic
141#95C22×C311yescharacteristic
142#95C22×C311yescharacteristic
143#95C22×C311yescharacteristic
144#95C22×C311yescharacteristic
145#95C22×C311yescharacteristic
146#95C22×C311yescharacteristic
147#95C22×C311yescharacteristic
148#95C22×C311yescharacteristic
149#95C22×C311yescharacteristic
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—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—44no—
199C2×C3×C4—44no—
200C2×C3×C4C22×C412yes—
201C2×C3×C4C22×C412yes—
202C2×C3×C4C22×C412yes—
203C2×C3×C4C22×C412yes—
204C2×C3×C4C22×C412yes—
205C2×C3×C4#4112yes—
206C2×C3×C4#4112yes—
207C24C23×C311yescharacteristic
208C24C23×C311yescharacteristic
209C2×D4—41no—
210C2×D4—41no—
211C2×D4C2×C3×C414yes—
212C22×C4—22no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4C2×C3×C414yescomplemented
218C22×C4C23×C311yescharacteristic
219C22×C4C23×C311yescharacteristic
220C22×C4C23×C311yescharacteristic
221C22×C4C23×C311yescharacteristic
222C22×C4C23×C311yescharacteristic
223C22×C4C23×C311yescharacteristic
224C22×C4C23×C311yescharacteristic
225C22×C4C23×C311yescharacteristic
226C22×C4C23×C311yescharacteristic
227C22×C4C23×C311yescharacteristic
228C22×C4C23×C311yescharacteristic
229C22×C4C23×C311yescharacteristic
230C22×C4C23×C311yescharacteristic
231C4⋊C4—22no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4C2×C3×C414yescomplemented
237C4⋊C4C2×C3×C414yescomplemented
238C22⋊C4—22no—
239C22⋊C4—22no—
240C22⋊C4—22no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4C2×C3×C414yes—
246C22⋊C4C2×C3×C414yes—
247C22⋊C4C2×C3×C414yescomplemented
248C42—22no—
249C42—41no—
250C42—41no—
251C42—41no—
252C42—41no—
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—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—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×C3×C412yes—
300C23C22×C3×C412yes—
301C23C24×C311yescharacteristic
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—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4C22×C3×C412yes—
338C2×C4C22×C3×C412yes—
339C2×C4C22×C3×C412yes—
340C2×C4C22×C3×C412yes—
341C2×C4C22×C3×C412yes—
342C2×C4C3×#4112yes—
343C2×C4C3×#4112yes—
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—
367C22C23×C3×C411yescharacteristic
368C22C2×C3×#4111yescharacteristic
369C22C2×C3×#4111yescharacteristic
370C22C3×H(5,𝔽2)11yescharacteristic
371C22C3×H(5,𝔽2)11yescharacteristic
372C22C3×H(5,𝔽2)11yescharacteristic
373C22C3×2−1+411yescharacteristic
374C4—22no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C3#233511yescharacteristic, direct product factor, Sylow
388C2—42no—
389C2—42no—
390C2C3×C4×#4111yescharacteristic
391C2C3×#51811yescharacteristic
392C2C3×#52011yescharacteristic
393C2C3×#53811yescharacteristic
394C2C3×#53911yescharacteristic
395C2C3×#54011yescharacteristic
396C2C3×#54211yescharacteristic
subgroupG/H
center, socleC23×C3C24
commutatorC22C23×C3×C4
Frattini, cosocleC23C24×C3
prime radicalC22×C3×D4C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×#389C2semidirect
4. C3×#388C2semidirect
5. C3×#388C2semidirect
6. C3×#388C2semidirect
7. C3×#388C2semidirect
8. C3×#387C2semidirect
9. C3×#387C2semidirect
11. C3×#385C2semidirect
12. C3×#380C2semidirect
13. C3×C4×C4⋊C4C2semidirect
14. C3×C4×C22⋊C4C2semidirect
15. C3×C4×C22⋊C4C2semidirect
16. #2335C3direct (N × H)
20. C3×#123C4semidirect
55. #389C2×C3semidirect
56. #388C2×C3semidirect
57. #388C2×C3semidirect
58. #388C2×C3semidirect
59. #388C2×C3semidirect
60. #387C2×C3semidirect
61. #387C2×C3semidirect
63. #385C2×C3semidirect
64. #380C2×C3semidirect
65. C4×C4⋊C4C2×C3semidirect
66. C4×C22⋊C4C2×C3semidirect
67. C4×C22⋊C4C2×C3semidirect
78. C22×C3×C4C2×C4semidirect
97. C3×C4⋊C4C2×C4semidirect
98. C3×C4⋊C4C2×C4semidirect
108. C3×C22⋊C4C2×C4semidirect
117. #123C3×C4semidirect
217. C22×C4C2×C3×C4semidirect
236. C4⋊C4C2×C3×C4semidirect
237. C4⋊C4C2×C3×C4semidirect
247. C22⋊C4C2×C3×C4semidirect
387. C3#2335direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1232
C3×#3902
C3×#3892
C3×#3882
C3×#3872
C3×#3862
C3×#3852
C3×#3802
C3×C4×C4⋊C42
C3×C4×C22⋊C42
#23353