Finite Group Databasebeta

← C3×#70846 #11780789

Subgroups — C3×#70846 #11780789

Order 1152.

443 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C8×D4C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic
3C3×#5007C211yesmaximal, characteristic, complemented
4C3×#4693C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4457C211yesmaximal, characteristic, complemented
8C3×#1665—31nomaximal
9#70846C311yesmaximal, characteristic, direct product factor
10C22×C32×C8—21no—
11C32×C4×D4C2211yescharacteristic
12C2×C3×#213—21no—
13C2×C3×#204—21no—
14C2×C3×#204—21no—
15C3×#874C2211yescharacteristic
16C3×#869C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C32×C22⋊C8—21no—
19C32×C4×C8C2211yescharacteristic
20C3×#832—21no—
21C3×#809—21no—
22C3×#807—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#492—31no—
26C3×#474—31no—
27C3×#459—31no—
28C3×C8×D4—21no—
29C3×C8×D4D311yescharacteristic, complemented
30C3×C8×D4C2×C311yescharacteristic, complemented
31#5015C2×C311yescharacteristic
32#5007C2×C311yescharacteristic, complemented
33#4693C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4485C2×C311yescharacteristic, complemented
38#4482C2×C311yescharacteristic, complemented
39#4457C2×C311yescharacteristic, complemented
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C2×C32×C8—42no—
48C2×C32×C8D411yescharacteristic
49C2×C32×C8D411yescharacteristic
50C32×C4⋊C4D411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C42C2311yescharacteristic
53C3×#213—42no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58C3×#204—42no—
59C3×#204—42no—
60#1665—31noSylow
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C2×C3×D8—61no—
64C22×C3×C8—22no—
65C22×C3×C8—21no—
66C22×C3×C8—21no—
67C3×C4⋊Q8—31no—
68C3×#127—31no—
69C3×C4×D4—21no—
70C3×C4×D4C2×D311yescharacteristic
71C3×C4×D4C22×C311yescharacteristic
72C2×#213—21no—
73C2×#204—21no—
74C2×#204—21no—
75#874C22×C311yescharacteristic
76#869C22×C311yescharacteristic
77C3×#107—61no—
78C3×C4⋊C8—21no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8—31no—
81C3×C4⋊C8C2×D311yescharacteristic
82C3×C4⋊C8C22×C311yescharacteristic
83C3×#102—61no—
84C3×#102—61no—
85C3×C22⋊C8—22no—
86C3×C22⋊C8—21no—
87C3×C22⋊C8—21no—
88C3×C4×C8—21no—
89C3×C4×C8C2×D311yescharacteristic
90C3×C4×C8C22×C311yescharacteristic
91#832—21no—
92#809—21no—
93#807—21no—
94C4⋊(C3⋊C8)C22×C311yescharacteristic
95C4⋊(C3⋊C8)C22×C311yescharacteristic
96C23×C32—21no—
97C22×C3×D3—41no—
98C32×D4—21no—
99C32×D4SD1612yescomplemented
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C3×Dic3—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—41no—
111C3×D12—81no—
112C3×Dic6—41no—
113C3×Dic6—41no—
114C32×C8—21no—
115C32×C8—41no—
116C32×C8D812yescomplemented
117C3×C3⋊C8—41no—
118C3×C3⋊C8—41no—
119#492—31no—
120#474—31no—
121#459—31no—
122C8×D4C3×D311yescharacteristic, complemented
123#334—31no—
124#332—31no—
125#331—31no—
126C2×C3×Q8—61no—
127C2×C3×D4—21no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C2×C3×D4D1211yescharacteristic
132C2×C3×D4C3×D411yescharacteristic
133C22×C3×C4—22no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×D12—21no—
139C2×Dic6—21no—
140C3×SD16—122no—
141C3×SD16—122no—
142C3×D8—122no—
143C2×C3×C8—22no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—44no—
149C2×C3×C8—42no—
150C2×C3×C8—42no—
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C2×C3×C8#6711yescharacteristic
154C2×C3×C8#6711yescharacteristic
155C2×C3×C8C3×D411yescharacteristic
156C2×C3×C8C3×D411yescharacteristic
157C3×C4⋊C4—21no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4D1211yescharacteristic
161C3×C4⋊C4C3×D411yescharacteristic
162C3×C22⋊C4—22no—
163C3×C22⋊C4—21no—
164C3×C22⋊C4—21no—
165C3×C42—21no—
166C3×C42C22×D311yescharacteristic
167C3×C42C23×C311yescharacteristic
168#213—42no—
169C4⋊Dic3—21no—
170C4⋊Dic3—21no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8—21no—
173#204—42no—
174#204—42no—
175C22×C32—22no—
176C22×C32—41no—
177C22×C32—41no—
178C22×C32#12111yescharacteristic
179C2×C3×D3—81no—
180C2×C3×D3—81no—
181C2×C3×D3—81no—
182C32×C4—21no—
183C32×C4—41no—
184C32×C4C2×D811yescharacteristic
185C32×C4C2×SD1611yescharacteristic
186C32×C4#13511yescharacteristic
187C32×C4AGL(1,ℤ/8)11yescharacteristic
188C3×Dic3—81no—
189C2×SD16—61no—
190C2×SD16—61no—
191C2×D8—61no—
192C22×C8—21no—
193C4⋊Q8—31no—
194#127—31no—
195C4×D4C2×C3×D311yescharacteristic
196#107—61no—
197C4⋊C8—31no—
198C4⋊C8—31no—
199C4⋊C8C2×C3×D311yescharacteristic
200#102—61no—
201#102—61no—
202C22⋊C8—21no—
203C4×C8C2×C3×D311yescharacteristic
204C23×C3—22no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—121no—
208C22×D3—41no—
209C3×Q8—121no—
210C3×Q8—121no—
211C3×D4—22no—
212C3×D4—21no—
213C3×D4—21no—
214C3×D4—22no—
215C3×D4—121no—
216C3×D4—121no—
217C3×D4—121no—
218C3×D4—121no—
219C3×D4—241no—
220C3×D4#20412yescomplemented
221C3×D4C3×SD1612yescomplemented
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—121no—
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4#23511yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×C3×C4C2×C3×D411yescharacteristic
239C2×C3×C4C2×C3×D411yescharacteristic
240C2×C3×C4C3×#4111yescharacteristic
241C2×Dic3—41no—
242D12—41no—
243D12—41no—
244D12—41no—
245D12—41no—
246D12—81no—
247Dic6—41no—
248Dic6—41no—
249C3×C8—21no—
250C3×C8—21no—
251C3×C8—22no—
252C3×C8—41no—
253C3×C8—42no—
254C3×C8—41no—
255C3×C8—41no—
256C3×C8—121no—
257C3×C8—121no—
258C3×C8#21312yescomplemented
259C3×C8C3×D812yescomplemented
260C3⋊C8—41no—
261C3⋊C8—41no—
262C2×C32—42no—
263C2×C32#45911yescharacteristic
264C2×C32#46511yescharacteristic
265C2×C32#47111yescharacteristic
266C3×D3—161no—
267C2×Q8—61no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4—61no—
271C2×D4C3×D1211yescharacteristic
272C22×C4—21no—
273SD16—122no—
274SD16—122no—
275D8—122no—
276C2×C8—21no—
277C2×C8—42no—
278C2×C8—61no—
279C2×C8—61no—
280C2×C8C3×#6711yescharacteristic
281C2×C8C3×#6711yescharacteristic
282C4⋊C4—61no—
283C4⋊C4—61no—
284C4⋊C4C3×D1211yescharacteristic
285C22⋊C4—21no—
286C42C22×C3×D311yescharacteristic
287C22×C3—24no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—42no—
292C22×C3—42no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—241no—
298C22×C3—241no—
299C22×C3—241no—
300C22×C3#93011yescharacteristic
301C22×C3C3×#12111yescharacteristic
302C2×D3—81no—
303C2×D3—81no—
304C2×D3—81no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—42no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—241no—
316C3×C4C2×#20411yescharacteristic
317C3×C4#90411yescharacteristic
318C3×C4C2×#21311yescharacteristic
319C3×C4#94911yescharacteristic
320C3×C4C2×C3×D811yescharacteristic
321C3×C4C2×C3×SD1611yescharacteristic
322C3×C4C3×#13511yescharacteristic
323C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
324Dic3—81no—
325C32#166511yescharacteristic, complemented, Sylow
326C23—21no—
327C23—121no—
328Q8—121no—
329Q8—121no—
330D4—21no—
331D4—121no—
332D4—121no—
333D4—121no—
334D4—121no—
335D4—241no—
336D4C3×#20412yescomplemented
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—121no—
341C2×C4C2×C3×D1211yescharacteristic
342C2×C4C3×#23511yescharacteristic
343C2×C4C2×C3×#6711yescharacteristic
344C8—21no—
345C8—41no—
346C8—121no—
347C8—121no—
348C8C3×#21312yescomplemented
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—44no—
353C2×C3—42no—
354C2×C3—42no—
355C2×C3—481no—
356C2×C3#501511yescharacteristic
357C2×C3#511411yescharacteristic
358C2×C3#514111yescharacteristic
359C2×C3C3×#45911yescharacteristic
360C2×C3C3×#46511yescharacteristic
361C2×C3C3×#47111yescharacteristic
362D3—161no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—241no—
367C22—241no—
368C22—241no—
369C22C3×#93011yescharacteristic
370C4—21no—
371C4—41no—
372C4—241no—
373C4C2×C3×#20411yescharacteristic
374C4C3×#90411yescharacteristic
375C4C2×C3×#21311yescharacteristic
376C4C3×#94911yescharacteristic
377C3—21no—
378C3#7084611yescharacteristic, direct product factor
379C3C3×#166511yescharacteristic, complemented
380C2—42no—
381C2—481no—
382C2C3×#501511yescharacteristic
383C2C3×#511411yescharacteristic
384C2C3×#514111yescharacteristic
subgroupG/H
centerC22×C3#930
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×C8×D4C2
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC3×C8×D4D3
hypocenterC3C3×#1665
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
1. C32×C8×D4C2semidirect
3. C3×#5007C2semidirect
4. C3×#4693C2semidirect
5. C3×#4485C2semidirect
6. C3×#4482C2semidirect
7. C3×#4457C2semidirect
9. #70846C3direct (N × H)
29. C3×C8×D4D3semidirect
30. C3×C8×D4C2×C3semidirect
32. #5007C2×C3semidirect
33. #4693C2×C3semidirect
37. #4485C2×C3semidirect
38. #4482C2×C3semidirect
39. #4457C2×C3semidirect
99. C32×D4SD16semidirect
116. C32×C8D8semidirect
122. C8×D4C3×D3semidirect
220. C3×D4#204semidirect
221. C3×D4C3×SD16semidirect
258. C3×C8#213semidirect
259. C3×C8C3×D8semidirect
325. C32#1665semidirect
336. D4C3×#204semidirect
348. C8C3×#213semidirect
378. C3#70846direct (N × H)
379. C3C3×#1665semidirect

Maximal subgroups

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

subgroupindex
C32×C8×D42
C3×#50152
C3×#50072
C3×#46932
C3×#44852
C3×#44822
C3×#44572
C3×#16653
#708463