Finite Group Databasebeta

← C3×#71022 #11781280

Subgroups — C3×#71022 #11781280

Order 1152.

384 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#460C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#5021C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1678—31nomaximal
9#71022C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16—21no—
11C32×#127C2211yescharacteristic
12C32×C4×Q8C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×#102—21no—
16C3×#835—21no—
17C3×#832—21no—
18C3×#832—21no—
19C3×#807—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—31no—
27C3×#460—21no—
28C3×#460D311yescharacteristic
29C3×#460C2×C311yescharacteristic
30C3×C8×Q8—31no—
31#5070C2×C311yescharacteristic
32Q8×C3⋊C8C2×C311yescharacteristic, complemented
33#5021C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#333—31no—
36C3×#331—31no—
37#4544C2×C311yescharacteristic
38#4481C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×Q8D411yescharacteristic
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C3×Dic6—21no—
45C32×SD16—42no—
46C2×C32×C8—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1678—31noSylow
58C2×C3×SD16—22no—
59C2×C3×SD16—21no—
60C2×C3×SD16—21no—
61C3×C4⋊Q8—31no—
62C3×#127—21no—
63C3×#127C2×D311yescharacteristic
64C3×#127C22×C311yescharacteristic
65C3×C4×Q8—21no—
66C3×C4×Q8C2×D311yescharacteristic
67C3×C4×Q8C22×C311yescharacteristic
68#869C22×C311yescharacteristic
69C3×#107—61no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—61no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C22×C311yescharacteristic
76C3×#103—61no—
77C3×#102—22no—
78C3×#102—21no—
79C3×#102—21no—
80C3×#102—61no—
81C3×#102—61no—
82C3×C4×C8—31no—
83C3×C4×C8—61no—
84#835—21no—
85#832—21no—
86#832—21no—
87#807—21no—
88C4⋊(C3⋊C8)—21no—
89C4⋊(C3⋊C8)C22×C311yescharacteristic
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4×C3⋊C8—21no—
92C4×C3⋊C8C22×C311yescharacteristic
93C23×C32—41no—
94C32×Q8—21no—
95C32×Q8SD1612yes—
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—81no—
101C2×C32×C4—21no—
102C2×C32×C4—21no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C3×Dic3—41no—
107C3×Dic6—81no—
108C32×C8—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#486—31no—
114#477—31no—
115#460C3×D311yescharacteristic
116C8×Q8—31no—
117#334—31no—
118#333—31no—
119#331—31no—
120C2×C3×Q8—21no—
121C2×C3×Q8—61no—
122C2×C3×Q8#6711yescharacteristic
123C2×C3×Q8C3×D411yescharacteristic
124C2×C3×D4—22no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—41no—
132C2×C3×D4—41no—
133C2×Dic6—21no—
134C3×SD16—44no—
135C3×SD16—42no—
136C3×SD16—42no—
137C2×C3×C8—22no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—31no—
141C2×C3×C8—31no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—41no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
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
158C4⋊Dic3—21no—
159C4⋊Dic3—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8C3×D411yescharacteristic
163C2×C3⋊C8C3×D411yescharacteristic
164C22×C32—81no—
165C22×C32—81no—
166C22×C32—81no—
167C22×C32#12111yescharacteristic
168C32×C4—22no—
169C32×C4—21no—
170C32×C4—41no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13711yescharacteristic
175C3×Dic3—81no—
176C2×SD16—21no—
177C4⋊Q8—31no—
178#127C2×C3×D311yescharacteristic
179C4×Q8C2×C3×D311yescharacteristic
180#107—61no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183C4⋊C8—61no—
184C4⋊C8C2×C3×D311yescharacteristic
185#103—61no—
186#102—21no—
187#102—61no—
188#102—61no—
189C4×C8—31no—
190C4×C8—61no—
191C23×C3—42no—
192C23×C3—41no—
193C23×C3—41no—
194C3×Q8—21no—
195C3×Q8—21no—
196C3×Q8—22no—
197C3×Q8—41no—
198C3×Q8—241no—
199C3×Q8#21412yes—
200C3×Q8C3×SD1612yes—
201C3×D4—42no—
202C3×D4—42no—
203C3×D4—41no—
204C3×D4—41no—
205C3×D4—41no—
206C3×D4—41no—
207C3×D4—41no—
208C3×D4—41no—
209C3×D4—41no—
210C3×D4—41no—
211C3×D4—81no—
212C3×D4—81no—
213C3×D4—81no—
214C3×D4—81no—
215C3×D4—82no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—121no—
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
232C2×Dic3—41no—
233Dic6—81no—
234C3×C8—42no—
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—61no—
238C3×C8—61no—
239C3×C8—121no—
240C3×C8—121no—
241C3⋊C8—21no—
242C3⋊C8—21no—
243C3⋊C8—41no—
244C3⋊C8—41no—
245C2×C32—161no—
246C2×C32#46411yescharacteristic
247C2×C32#46511yescharacteristic
248C2×C32#47211yescharacteristic
249C2×Q8—61no—
250C2×Q8C3×#6711yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254SD16—42no—
255C2×C8—21no—
256C2×C8—31no—
257C2×C8—31no—
258C2×C8—61no—
259C2×C8—61no—
260C4⋊C4—21no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C4⋊C4C3×#6711yescharacteristic
264C42—21no—
265C42C22×C3×D311yescharacteristic
266C22×C3—21no—
267C22×C3—82no—
268C22×C3—82no—
269C22×C3—82no—
270C22×C3—81no—
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3—81no—
275C22×C3—81no—
276C22×C3#93911yescharacteristic
277C22×C3C3×#12111yescharacteristic
278C3×C4—21no—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—42no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—81no—
291C3×C4—241no—
292C3×C4#91511yescharacteristic
293C3×C4#91611yescharacteristic
294C3×C4C2×#21411yescharacteristic
295C3×C4#95011yescharacteristic
296C3×C4C2×C3×SD1611yescharacteristic
297C3×C4C3×#13511yescharacteristic
298C3×C4C3×#13511yescharacteristic
299C3×C4C3×#13711yescharacteristic
300Dic3—81no—
301C32#167811yescharacteristic, complemented, Sylow
302C23—41no—
303Q8—21no—
304Q8—241no—
305Q8C3×#21412yes—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—41no—
310D4—81no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—121no—
314C2×C4C3×D3×D411yescharacteristic
315C2×C4C3×#23711yescharacteristic
316C2×C4C2×C3×#6711yescharacteristic
317C8—41no—
318C8—61no—
319C8—61no—
320C8—121no—
321C8—121no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—162no—
326C2×C3—161no—
327C2×C3—161no—
328C2×C3#504111yescharacteristic
329C2×C3#516611yescharacteristic
330C2×C3#519911yescharacteristic
331C2×C3C3×#46411yescharacteristic
332C2×C3C3×#46511yescharacteristic
333C2×C3C3×#47211yescharacteristic
334C22—81no—
335C22—81no—
336C22—81no—
337C22C3×#93911yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—241no—
342C4C3×#91511yescharacteristic
343C4C3×#91611yescharacteristic
344C4C2×C3×#21411yescharacteristic
345C4C3×#95011yescharacteristic
346C3—21no—
347C3#7102211yescharacteristic, direct product factor
348C3C3×#167811yescharacteristic, complemented
349C2—161no—
350C2C3×#504111yescharacteristic
351C2C3×#516611yescharacteristic
352C2C3×#519911yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#460C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenterC3×#460D3
hypocenterC3C3×#1678
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
3. C3×Q8×C3⋊C8C2semidirect
4. C3×#5021C2semidirect
6. C3×#4481C2semidirect
7. C3×#4480C2semidirect
9. #71022C3direct (N × H)
32. Q8×C3⋊C8C2×C3semidirect
33. #5021C2×C3semidirect
38. #4481C2×C3semidirect
39. #4480C2×C3semidirect
301. C32#1678semidirect
347. C3#71022direct (N × H)
348. C3C3×#1678semidirect

Maximal subgroups

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

subgroupindex
C32×#4602
C3×#50702
C3×Q8×C3⋊C82
C3×#50212
C3×#45442
C3×#44812
C3×#44802
C3×#16783
#710223