Finite Group Databasebeta

← C3×#71150 #11781292

Subgroups — C3×#71150 #11781292

Order 1152.

368 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#477C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic
3C3×#5027C211yesmaximal, characteristic
4C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
5C3×#4546C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1678—31nomaximal
9#71150C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12C2×C3×#215—21no—
13C3×#874C2211yescharacteristic
14C32×#107—21no—
15C32×C4⋊C8C2211yescharacteristic
16C32×#103—21no—
17C3×#809—21no—
18C3×#809—21no—
19C3×#809—21no—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#477—21no—
27C3×#477D311yescharacteristic, complemented
28C3×#477C2×C311yescharacteristic, complemented
29C3×#460—31no—
30C3×C8×Q8—31no—
31#5088C2×C311yescharacteristic
32#5027C2×C311yescharacteristic
33Q8×C3⋊C8C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#333—31no—
36C3×#331—31no—
37#4546C2×C311yescharacteristic, complemented
38#4485C2×C311yescharacteristic
39#4480C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×Q8D411yescharacteristic
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C32×C8—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C42—21no—
51C32×C42C2311yescharacteristic
52C3×#215—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1678—31noSylow
58C2×C3×SD16—61no—
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C22×C311yescharacteristic
62C3×#127—31no—
63C3×C4×Q8—21no—
64C3×C4×Q8C2×D311yescharacteristic
65C3×C4×Q8C22×C311yescharacteristic
66C2×#215—21no—
67#874C22×C311yescharacteristic
68C3×#107—22no—
69C3×#107—21no—
70C3×#107—21no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—61no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×#103—22no—
78C3×#103—21no—
79C3×#103—21no—
80C3×#102—61no—
81C3×#102—61no—
82C3×#102—61no—
83C3×C4×C8—31no—
84C3×C4×C8—61no—
85#809—21no—
86#809—21no—
87#809—21no—
88C4⋊(C3⋊C8)—21no—
89C4⋊(C3⋊C8)C22×C311yescharacteristic
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4×C3⋊C8—21no—
92C4×C3⋊C8C22×C311yescharacteristic
93C22×C3×D3—41no—
94C32×Q8—21no—
95C32×Q8—81no—
96C32×Q8SD1612yes—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—81no—
108C32×C8—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#486—31no—
114#477C3×D311yescharacteristic, complemented
115#460—31no—
116C8×Q8—31no—
117#334—31no—
118#333—31no—
119#331—31no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—41no—
124C2×C3×Q8#6711yescharacteristic
125C2×C3×Q8C3×D411yescharacteristic
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C3×SD16—122no—
133C2×C3×C8—22no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—31no—
137C2×C3×C8—31no—
138C2×C3×C8—61no—
139C2×C3×C8—61no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—41no—
150C3×C4⋊C4#6711yescharacteristic
151C3×C4⋊C4C3×D411yescharacteristic
152C3×C42—21no—
153C3×C42—21no—
154C3×C42—21no—
155C3×C42—41no—
156C3×C42C22×D311yescharacteristic
157C3×C42C23×C311yescharacteristic
158#215—42no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8C3×D411yescharacteristic
162C2×C3⋊C8C3×D411yescharacteristic
163C22×C32#12111yescharacteristic
164C2×C3×D3—81no—
165C2×C3×D3—81no—
166C2×C3×D3—81no—
167C32×C4—22no—
168C32×C4—21no—
169C32×C4—41no—
170C32×C4—81no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13711yescharacteristic
175C2×SD16—61no—
176C4⋊Q8C2×C3×D311yescharacteristic
177#127—31no—
178C4×Q8C2×C3×D311yescharacteristic
179#107—21no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—61no—
183C4⋊C8C2×C3×D311yescharacteristic
184#103—21no—
185#102—61no—
186#102—61no—
187#102—61no—
188C4×C8—31no—
189C4×C8—61no—
190C23×C3—121no—
191C22×D3—41no—
192C3×Q8—21no—
193C3×Q8—21no—
194C3×Q8—22no—
195C3×Q8—41no—
196C3×Q8—81no—
197C3×Q8—81no—
198C3×Q8—82no—
199C3×Q8#21512yes—
200C3×Q8C3×SD1612yes—
201C3×D4—121no—
202C3×D4—121no—
203C3×D4—121no—
204C3×D4—121no—
205C3×D4—241no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—42no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4#23711yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×C3×C4C2×C3×D411yescharacteristic
222C2×C3×C4C2×C3×D411yescharacteristic
223C2×C3×C4C3×#4111yescharacteristic
224D12—41no—
225D12—41no—
226D12—41no—
227D12—41no—
228D12—81no—
229C3×C8—42no—
230C3×C8—41no—
231C3×C8—41no—
232C3×C8—61no—
233C3×C8—61no—
234C3×C8—121no—
235C3×C8—121no—
236C3⋊C8—21no—
237C3⋊C8—21no—
238C3⋊C8—41no—
239C3⋊C8—41no—
240C2×C32#46411yescharacteristic
241C2×C32#46511yescharacteristic
242C2×C32#47211yescharacteristic
243C3×D3—161no—
244C2×Q8—21no—
245C2×Q8C3×#6711yescharacteristic
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—61no—
249SD16—122no—
250C2×C8—21no—
251C2×C8—31no—
252C2×C8—31no—
253C2×C8—61no—
254C2×C8—61no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4C3×#6711yescharacteristic
259C42—21no—
260C42C22×C3×D311yescharacteristic
261C22×C3—21no—
262C22×C3—241no—
263C22×C3—241no—
264C22×C3—241no—
265C22×C3#93911yescharacteristic
266C22×C3C3×#12111yescharacteristic
267C2×D3—81no—
268C2×D3—81no—
269C2×D3—81no—
270C3×C4—21no—
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—42no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—81no—
283C3×C4—82no—
284C3×C4—81no—
285C3×C4—81no—
286C3×C4#91811yescharacteristic
287C3×C4#91911yescharacteristic
288C3×C4C2×#21511yescharacteristic
289C3×C4#95011yescharacteristic
290C3×C4C2×C3×SD1611yescharacteristic
291C3×C4C3×#13511yescharacteristic
292C3×C4C3×#13511yescharacteristic
293C3×C4C3×#13711yescharacteristic
294C32#167811yescharacteristic, complemented, Sylow
295C23—121no—
296Q8—21no—
297Q8—81no—
298Q8C3×#21512yes—
299D4—121no—
300D4—121no—
301D4—121no—
302D4—121no—
303D4—241no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4C3×D3×D411yescharacteristic
308C2×C4C3×#23711yescharacteristic
309C2×C4C2×C3×#6711yescharacteristic
310C8—41no—
311C8—61no—
312C8—61no—
313C8—121no—
314C8—121no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—481no—
319C2×C3#504811yescharacteristic
320C2×C3#518511yescharacteristic
321C2×C3#519911yescharacteristic
322C2×C3C3×#46411yescharacteristic
323C2×C3C3×#46511yescharacteristic
324C2×C3C3×#47211yescharacteristic
325D3—161no—
326C22—241no—
327C22—241no—
328C22—241no—
329C22C3×#93911yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—81no—
334C4C3×#91811yescharacteristic
335C4C3×#91911yescharacteristic
336C4C2×C3×#21511yescharacteristic
337C4C3×#95011yescharacteristic
338C3—21no—
339C3#7115011yescharacteristic, direct product factor
340C3C3×#167811yescharacteristic, complemented
341C2—481no—
342C2C3×#504811yescharacteristic
343C2C3×#518511yescharacteristic
344C2C3×#519911yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#477C2
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC3×#477D3
hypocenterC3C3×#1678
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
1. C32×#477C2semidirect
4. C3×Q8×C3⋊C8C2semidirect
5. C3×#4546C2semidirect
7. C3×#4480C2semidirect
9. #71150C3direct (N × H)
27. C3×#477D3semidirect
28. C3×#477C2×C3semidirect
33. Q8×C3⋊C8C2×C3semidirect
37. #4546C2×C3semidirect
39. #4480C2×C3semidirect
114. #477C3×D3semidirect
294. C32#1678semidirect
339. C3#71150direct (N × H)
340. C3C3×#1678semidirect

Maximal subgroups

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

subgroupindex
C32×#4772
C3×#50882
C3×#50272
C3×Q8×C3⋊C82
C3×#45462
C3×#44852
C3×#44802
C3×#16783
#711503