Finite Group Databasebeta

← C3×#71055 #11781479

Subgroups — C3×#71055 #11781479

Order 1152.

386 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#462C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic
3C3×#5027C211yesmaximal, characteristic
4C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1682—31nomaximal
9#71055C311yesmaximal, characteristic, direct product factor
10C2×C32×Q16—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4×Q8C2211yescharacteristic
13C2×C3×#215—21no—
14C3×#874C2211yescharacteristic
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×#462—21no—
27C3×#462D311yescharacteristic, complemented
28C3×#462C2×C311yescharacteristic, complemented
29C3×#460—31no—
30C3×C8×Q8—31no—
31#5088C2×C311yescharacteristic
32#5027C2×C311yescharacteristic
33Q8×C3⋊C8C2×C311yescharacteristic, complemented
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4547C2×C311yescharacteristic, complemented
38#4485C2×C311yescharacteristic
39#4479C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×Q8D411yescharacteristic
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C32×Q16—42no—
46C2×C32×C8—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C42—21no—
52C32×C42C2311yescharacteristic
53C3×#215—42no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1682—31noSylow
59C2×C3×Q16—22no—
60C2×C3×Q16—21no—
61C2×C3×Q16—21no—
62C2×C3×SD16—61no—
63C3×C4⋊Q8—21no—
64C3×C4⋊Q8C2×D311yescharacteristic
65C3×C4⋊Q8C22×C311yescharacteristic
66C3×#127—31no—
67C3×C4×Q8—21no—
68C3×C4×Q8C2×D311yescharacteristic
69C3×C4×Q8C22×C311yescharacteristic
70C2×#215—21no—
71#874C22×C311yescharacteristic
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—61no—
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×#103—22no—
79C3×#103—21no—
80C3×#103—21no—
81C3×#102—61no—
82C3×#102—61no—
83C3×#102—61no—
84C3×C4×C8—31no—
85C3×C4×C8—61no—
86#809—21no—
87#809—21no—
88#809—21no—
89C4⋊(C3⋊C8)—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4×C3⋊C8—21no—
93C4×C3⋊C8C22×C311yescharacteristic
94C22×C3×D3—41no—
95C32×Q8—21no—
96C32×Q8—41no—
97C32×Q8—41no—
98C32×Q8D812yes—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—81no—
110C32×C8—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#486—31no—
116#462C3×D311yescharacteristic, complemented
117#460—31no—
118C8×Q8—31no—
119#335—31no—
120#332—31no—
121#331—31no—
122C2×C3×Q8—22no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8—21no—
126C2×C3×Q8#6711yescharacteristic
127C2×C3×Q8C3×D411yescharacteristic
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C2×D12—21no—
132C2×D12—21no—
133C2×D12—21no—
134C3×Q16—44no—
135C3×Q16—42no—
136C3×Q16—42no—
137C3×SD16—122no—
138C2×C3×C8—22no—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—31no—
142C2×C3×C8—31no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—41no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—41no—
155C3×C4⋊C4#6711yescharacteristic
156C3×C4⋊C4C3×D411yescharacteristic
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—21no—
160C3×C42—41no—
161C3×C42C22×D311yescharacteristic
162C3×C42C23×C311yescharacteristic
163#215—42no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8C3×D411yescharacteristic
167C2×C3⋊C8C3×D411yescharacteristic
168C22×C32#12111yescharacteristic
169C2×C3×D3—81no—
170C2×C3×D3—81no—
171C2×C3×D3—81no—
172C32×C4—22no—
173C32×C4—21no—
174C32×C4—41no—
175C32×C4—81no—
176C32×C4C2×D811yescharacteristic
177C32×C4#13511yescharacteristic
178C32×C4#13511yescharacteristic
179C32×C4#13711yescharacteristic
180C2×Q16—21no—
181C2×SD16—61no—
182C4⋊Q8C2×C3×D311yescharacteristic
183#127—31no—
184C4×Q8C2×C3×D311yescharacteristic
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8—61no—
188C4⋊C8C2×C3×D311yescharacteristic
189#103—21no—
190#102—61no—
191#102—61no—
192#102—61no—
193C4×C8—31no—
194C4×C8—61no—
195C23×C3—121no—
196C22×D3—41no—
197C3×Q8—21no—
198C3×Q8—21no—
199C3×Q8—22no—
200C3×Q8—41no—
201C3×Q8—42no—
202C3×Q8—42no—
203C3×Q8—41no—
204C3×Q8—41no—
205C3×Q8—41no—
206C3×Q8—41no—
207C3×Q8#21312yes—
208C3×Q8C3×D812yes—
209C3×D4—121no—
210C3×D4—121no—
211C3×D4—121no—
212C3×D4—121no—
213C3×D4—241no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—42no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4#23711yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×C3×C4C2×C3×D411yescharacteristic
230C2×C3×C4C2×C3×D411yescharacteristic
231C2×C3×C4C3×#4111yescharacteristic
232D12—41no—
233D12—41no—
234D12—41no—
235D12—41no—
236D12—81no—
237C3×C8—42no—
238C3×C8—41no—
239C3×C8—41no—
240C3×C8—61no—
241C3×C8—61no—
242C3×C8—121no—
243C3×C8—121no—
244C3⋊C8—21no—
245C3⋊C8—21no—
246C3⋊C8—41no—
247C3⋊C8—41no—
248C2×C32#46411yescharacteristic
249C2×C32#46611yescharacteristic
250C2×C32#47111yescharacteristic
251C3×D3—161no—
252C2×Q8—21no—
253C2×Q8C3×#6711yescharacteristic
254C2×D4—61no—
255C2×D4—61no—
256C2×D4—61no—
257Q16—42no—
258SD16—122no—
259C2×C8—21no—
260C2×C8—31no—
261C2×C8—31no—
262C2×C8—61no—
263C2×C8—61no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4C3×#6711yescharacteristic
268C42—21no—
269C42C22×C3×D311yescharacteristic
270C22×C3—21no—
271C22×C3—241no—
272C22×C3—241no—
273C22×C3—241no—
274C22×C3#93911yescharacteristic
275C22×C3C3×#12111yescharacteristic
276C2×D3—81no—
277C2×D3—81no—
278C2×D3—81no—
279C3×C4—21no—
280C3×C4—22no—
281C3×C4—22no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—41no—
288C3×C4—42no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—81no—
292C3×C4—82no—
293C3×C4—81no—
294C3×C4—81no—
295C3×C4#91811yescharacteristic
296C3×C4#91911yescharacteristic
297C3×C4C2×#21311yescharacteristic
298C3×C4#95011yescharacteristic
299C3×C4C2×C3×D811yescharacteristic
300C3×C4C3×#13511yescharacteristic
301C3×C4C3×#13511yescharacteristic
302C3×C4C3×#13711yescharacteristic
303C32#168211yescharacteristic, complemented, Sylow
304C23—121no—
305Q8—21no—
306Q8—41no—
307Q8—41no—
308Q8C3×#21312yes—
309D4—121no—
310D4—121no—
311D4—121no—
312D4—121no—
313D4—241no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4C3×D3×D411yescharacteristic
318C2×C4C3×#23711yescharacteristic
319C2×C4C2×C3×#6711yescharacteristic
320C8—41no—
321C8—61no—
322C8—61no—
323C8—121no—
324C8—121no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—481no—
329C2×C3#503811yescharacteristic
330C2×C3#518511yescharacteristic
331C2×C3#520311yescharacteristic
332C2×C3C3×#46411yescharacteristic
333C2×C3C3×#46611yescharacteristic
334C2×C3C3×#47111yescharacteristic
335D3—161no—
336C22—241no—
337C22—241no—
338C22—241no—
339C22C3×#93911yescharacteristic
340C4—21no—
341C4—22no—
342C4—41no—
343C4—81no—
344C4C3×#91811yescharacteristic
345C4C3×#91911yescharacteristic
346C4C2×C3×#21311yescharacteristic
347C4C3×#95011yescharacteristic
348C3—21no—
349C3#7105511yescharacteristic, direct product factor
350C3C3×#168211yescharacteristic, complemented
351C2—481no—
352C2C3×#503811yescharacteristic
353C2C3×#518511yescharacteristic
354C2C3×#520311yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#462C2
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC3×#462D3
hypocenterC3C3×#1682
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
1. C32×#462C2semidirect
4. C3×Q8×C3⋊C8C2semidirect
5. C3×#4547C2semidirect
7. C3×#4479C2semidirect
9. #71055C3direct (N × H)
27. C3×#462D3semidirect
28. C3×#462C2×C3semidirect
33. Q8×C3⋊C8C2×C3semidirect
37. #4547C2×C3semidirect
39. #4479C2×C3semidirect
116. #462C3×D3semidirect
303. C32#1682semidirect
349. C3#71055direct (N × H)
350. C3C3×#1682semidirect

Maximal subgroups

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

subgroupindex
C32×#4622
C3×#50882
C3×#50272
C3×Q8×C3⋊C82
C3×#45472
C3×#44852
C3×#44792
C3×#16823
#710553