Finite Group Databasebeta

← C3×#2692 #84556

Subgroups — C3×#2692 #84556

Order 384.

536 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C3×#399C211yesmaximal, characteristic, complemented
4C3×#398C211yesmaximal, characteristic, complemented
5C3×#396C211yesmaximal, characteristic, complemented
6C3×#395C211yesmaximal, characteristic, complemented
7C3×#393C211yesmaximal, characteristic, complemented
8C3×#393C211yesmaximal, characteristic, complemented
9C3×#391C211yesmaximal, characteristic, complemented
10C3×#390C211yesmaximal, characteristic
11C3×#387C211yesmaximal, characteristic, complemented
12C3×#386C211yesmaximal, characteristic
13C3×#386C211yesmaximal, characteristic
14C3×#385C211yesmaximal, characteristic, complemented
15C3×#380C211yesmaximal, characteristic, complemented
16#2692C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q8C2211yescharacteristic
18C22×C3×Q8C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C23×C3×C4C2211yescharacteristic
21C23×C3×C4C2211yescharacteristic
22C3×C22⋊Q8—24no—
23C3×C22⋊Q8—24no—
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C4⋊C4C2211yescharacteristic
29C2×C3×C4⋊C4C2211yescharacteristic
30C2×C3×C4⋊C4C2211yescharacteristic
31C2×C3×C4⋊C4C2211yescharacteristic
32C2×C3×C4⋊C4C2211yescharacteristic
33C2×C3×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊C4C2211yescharacteristic
35C2×C3×C22⋊C4C2211yescharacteristic
36C2×C3×C22⋊C4C2211yescharacteristic
37C2×C3×C22⋊C4C2211yescharacteristic
38C2×C3×C22⋊C4C2211yescharacteristic
39C2×C3×C22⋊C4C2211yescharacteristic
40C2×C3×C22⋊C4C2211yescharacteristic
41C2×C3×C22⋊C4C2211yescharacteristic
42C2×C3×C22⋊C4C2211yescharacteristic
43C2×C3×C42C2211yescharacteristic
44C3×#95C2211yescharacteristic
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C3×#95C2211yescharacteristic
54C2×C22⋊Q8C2×C311yescharacteristic, complemented
55C2×C22⋊Q8C2×C311yescharacteristic, complemented
56#399C2×C311yescharacteristic, complemented
57#398C2×C311yescharacteristic, complemented
58#396C2×C311yescharacteristic, complemented
59#395C2×C311yescharacteristic, complemented
60#393C2×C311yescharacteristic, complemented
61#393C2×C311yescharacteristic, complemented
62#391C2×C311yescharacteristic, complemented
63#390C2×C311yescharacteristic
64#387C2×C311yescharacteristic, complemented
65#386C2×C311yescharacteristic
66#386C2×C311yescharacteristic
67#385C2×C311yescharacteristic, complemented
68#380C2×C311yescharacteristic, complemented
69C24×C3C2311yescharacteristic
70C24×C3C2311yescharacteristic
71C2×C3×Q8—22no—
72C2×C3×Q8—22no—
73C2×C3×Q8—22no—
74C2×C3×Q8—41no—
75C2×C3×Q8—41no—
76C2×C3×Q8—41no—
77C2×C3×D4—41no—
78C2×C3×D4—41no—
79C2×C3×D4Q814yescomplemented
80C22×C3×C4—22no—
81C22×C3×C4—22no—
82C22×C3×C4—22no—
83C22×C3×C4—41no—
84C22×C3×C4—41no—
85C22×C3×C4—41no—
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C22×C3×C4C2311yescharacteristic
95C22×C3×C4C2311yescharacteristic
96C22×C3×C4C2311yescharacteristic
97C22×C3×C4C2311yescharacteristic
98C22×C3×C4C2311yescharacteristic
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—22no—
102C3×C4⋊C4—22no—
103C3×C4⋊C4—41no—
104C3×C4⋊C4—41no—
105C3×C4⋊C4—41no—
106C3×C4⋊C4—41no—
107C3×C4⋊C4D414yescomplemented
108C3×C22⋊C4—22no—
109C3×C22⋊C4—22no—
110C3×C22⋊C4—22no—
111C3×C22⋊C4—22no—
112C3×C22⋊C4—22no—
113C3×C22⋊C4—41no—
114C3×C22⋊C4—41no—
115C3×C22⋊C4—41no—
116C3×C22⋊C4—41no—
117C3×C22⋊C4—41no—
118C3×C42—41no—
119C22×Q8C22×C311yescharacteristic
120C22×Q8C22×C311yescharacteristic
121C22×D4C22×C311yescharacteristic
122C23×C4C22×C311yescharacteristic
123C23×C4C22×C311yescharacteristic
124C22⋊Q8—24no—
125C22⋊Q8—24no—
126C2×C4⋊C4C22×C311yescharacteristic
127C2×C4⋊C4C22×C311yescharacteristic
128C2×C4⋊C4C22×C311yescharacteristic
129C2×C4⋊C4C22×C311yescharacteristic
130C2×C4⋊C4C22×C311yescharacteristic
131C2×C4⋊C4C22×C311yescharacteristic
132C2×C4⋊C4C22×C311yescharacteristic
133C2×C4⋊C4C22×C311yescharacteristic
134C2×C4⋊C4C22×C311yescharacteristic
135C2×C22⋊C4C22×C311yescharacteristic
136C2×C22⋊C4C22×C311yescharacteristic
137C2×C22⋊C4C22×C311yescharacteristic
138C2×C22⋊C4C22×C311yescharacteristic
139C2×C22⋊C4C22×C311yescharacteristic
140C2×C22⋊C4C22×C311yescharacteristic
141C2×C22⋊C4C22×C311yescharacteristic
142C2×C22⋊C4C22×C311yescharacteristic
143C2×C22⋊C4C22×C311yescharacteristic
144C2×C22⋊C4C22×C311yescharacteristic
145C2×C42C22×C311yescharacteristic
146#95C22×C311yescharacteristic
147#95C22×C311yescharacteristic
148#95C22×C311yescharacteristic
149#95C22×C311yescharacteristic
150#95C22×C311yescharacteristic
151#95C22×C311yescharacteristic
152#95C22×C311yescharacteristic
153#95C22×C311yescharacteristic
154#95C22×C311yescharacteristic
155#95C22×C311yescharacteristic
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3C2×Q812yes—
169C23×C3C2×Q812yes—
170C23×C3C2411yescharacteristic
171C3×Q8—44no—
172C3×Q8—44no—
173C3×D4—44no—
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—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—44no—
209C2×C3×C4—44no—
210C2×C3×C4C2×D412yes—
211C2×C3×C4C2×D412yes—
212C2×C3×C4C2×D412yes—
213C2×C3×C4C2×Q812yes—
214C2×C3×C4#4112yes—
215C24C23×C311yescharacteristic
216C24C23×C311yescharacteristic
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4C3×Q814yescomplemented
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4C23×C311yescharacteristic
233C22×C4C23×C311yescharacteristic
234C22×C4C23×C311yescharacteristic
235C22×C4C23×C311yescharacteristic
236C22×C4C23×C311yescharacteristic
237C22×C4C23×C311yescharacteristic
238C22×C4C23×C311yescharacteristic
239C22×C4C23×C311yescharacteristic
240C22×C4C23×C311yescharacteristic
241C22×C4C23×C311yescharacteristic
242C22×C4C23×C311yescharacteristic
243C22×C4C23×C311yescharacteristic
244C22×C4C23×C311yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4C3×D414yescomplemented
254C22⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C42—41no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3C22×D411yescharacteristic
280C22×C3C22×Q811yescharacteristic
281C22×C3C2×#4111yescharacteristic
282C22×C3H(5,𝔽2)11yescharacteristic
283C22×C3H(5,𝔽2)11yescharacteristic
284C22×C3H(5,𝔽2)11yescharacteristic
285C22×C32−1+411yescharacteristic
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—41no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23C2×C3×Q812yes—
312C23C2×C3×Q812yes—
313C23C24×C311yescharacteristic
314Q8—44no—
315Q8—44no—
316D4—44no—
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—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4C2×C3×D412yes—
354C2×C4C2×C3×D412yes—
355C2×C4C2×C3×D412yes—
356C2×C4C2×C3×Q812yes—
357C2×C4C3×#4112yes—
358C2×C3—42no—
359C2×C3—42no—
360C2×C3#53511yescharacteristic
361C2×C3#54211yescharacteristic
362C2×C3#54311yescharacteristic
363C2×C3#54611yescharacteristic
364C2×C3D4×Q811yescharacteristic
365C2×C3#55411yescharacteristic
366C2×C3#56211yescharacteristic
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22C22×C3×D411yescharacteristic
382C22C22×C3×Q811yescharacteristic
383C22C2×C3×#4111yescharacteristic
384C22C3×H(5,𝔽2)11yescharacteristic
385C22C3×H(5,𝔽2)11yescharacteristic
386C22C3×H(5,𝔽2)11yescharacteristic
387C22C3×2−1+411yescharacteristic
388C4—22no—
389C4—22no—
390C4—22no—
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—41no—
401C3#269211yescharacteristic, direct product factor, Sylow
402C2—42no—
403C2—42no—
404C2C3×#53511yescharacteristic
405C2C3×#54211yescharacteristic
406C2C3×#54311yescharacteristic
407C2C3×#54611yescharacteristic
408C2C3×D4×Q811yescharacteristic
409C2C3×#55411yescharacteristic
410C2C3×#56211yescharacteristic
subgroupG/H
center, socleC23×C3C24
commutator, Frattini, cosocleC23C24×C3
prime radicalC22×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C22⋊Q8C2semidirect
2. C2×C3×C22⋊Q8C2semidirect
3. C3×#399C2semidirect
4. C3×#398C2semidirect
5. C3×#396C2semidirect
6. C3×#395C2semidirect
7. C3×#393C2semidirect
8. C3×#393C2semidirect
9. C3×#391C2semidirect
11. C3×#387C2semidirect
14. C3×#385C2semidirect
15. C3×#380C2semidirect
16. #2692C3direct (N × H)
54. C2×C22⋊Q8C2×C3semidirect
55. C2×C22⋊Q8C2×C3semidirect
56. #399C2×C3semidirect
57. #398C2×C3semidirect
58. #396C2×C3semidirect
59. #395C2×C3semidirect
60. #393C2×C3semidirect
61. #393C2×C3semidirect
62. #391C2×C3semidirect
64. #387C2×C3semidirect
67. #385C2×C3semidirect
68. #380C2×C3semidirect
79. C2×C3×D4Q8semidirect
107. C3×C4⋊C4D4semidirect
225. C2×D4C3×Q8semidirect
253. C4⋊C4C3×D4semidirect
401. C3#2692direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C22⋊Q82
C3×#3992
C3×#3982
C3×#3962
C3×#3952
C3×#3932
C3×#3912
C3×#3902
C3×#3872
C3×#3862
C3×#3852
C3×#3802
#26923