Finite Group Databasebeta

← C3×#71137 #11781986

Subgroups — C3×#71137 #11781986

Order 1152.

362 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#476C211yesmaximal, characteristic
2C3×#5078C211yesmaximal, characteristic, complemented
3C3×#5012C211yesmaximal, characteristic
4C3×#5008C211yesmaximal, characteristic
5C3×#4546C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1695—31nomaximal
9#71137C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C2×C3×#208—21no—
13C3×#869C2211yescharacteristic
14C32×#106—21no—
15C32×C4⋊C8C2211yescharacteristic
16C32×#102—21no—
17C3×#832—21no—
18C3×#830—21no—
19C3×#808—21no—
20C3×#807—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#500—31no—
26C3×#476—21no—
27C3×#476—31no—
28C3×#476D311yescharacteristic
29C3×#476C2×C311yescharacteristic
30C3×#436—31no—
31#5078C2×C311yescharacteristic, complemented
32#5012C2×C311yescharacteristic
33#5008C2×C311yescharacteristic
34C3×#334—31no—
35C3×#333—31no—
36C3×#333—31no—
37#4546C2×C311yescharacteristic, complemented
38#4481C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×D4D411yescharacteristic
42C22×C32×C4—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C22⋊C4—21no—
49C32×C42C2311yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×#208—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1695—31noSylow
58C2×C3×M16—61no—
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C22×C311yescharacteristic
63C3×C4×D4—21no—
64C3×C4×D4C2×D311yescharacteristic
65C3×C4×D4C22×C311yescharacteristic
66C2×#208—21no—
67#869C22×C311yescharacteristic
68C3×#107—61no—
69C3×#107—61no—
70C3×#106—22no—
71C3×#106—21no—
72C3×#106—21no—
73C3×#106—61no—
74C3×C4⋊C8—21no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8C2×D311yescharacteristic
78C3×C4⋊C8C22×C311yescharacteristic
79C3×#102—22no—
80C3×#102—21no—
81C3×#102—21no—
82C3×#102—61no—
83C3×C22⋊C8—61no—
84C3×C4×C8—31no—
85#832—21no—
86#830—21no—
87#808—21no—
88#807—21no—
89#807—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4×C3⋊C8C22×C311yescharacteristic
93C23×C32—21no—
94C32×Q8—81no—
95C32×D4—21no—
96C32×D4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3×Dic3—41no—
105C3×Dic6—81no—
106C32×C8—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8SD1612yes—
111#500—31no—
112#476—31no—
113#476C3×D311yescharacteristic
114#436—31no—
115#334—31no—
116#333—31no—
117#333—31no—
118C2×C3×Q8—21no—
119C2×C3×Q8—21no—
120C2×C3×Q8—41no—
121C2×C3×Q8—61no—
122C2×C3×D4—21no—
123C2×C3×D4#6711yescharacteristic
124C2×C3×D4C3×D411yescharacteristic
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—41no—
128C2×Dic6—21no—
129C3×M16—122no—
130C2×C3×C8—22no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—41no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4#6711yescharacteristic
147C3×C4⋊C4C3×D411yescharacteristic
148C3×C22⋊C4—21no—
149C3×C22⋊C4—21no—
150C3×C22⋊C4—41no—
151C3×C42—21no—
152C3×C42C22×D311yescharacteristic
153C3×C42C23×C311yescharacteristic
154C4⋊Dic3—21no—
155C4⋊Dic3—21no—
156#208—42no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8C3×D411yescharacteristic
160C2×C3⋊C8C3×D411yescharacteristic
161C22×C32—41no—
162C22×C32—41no—
163C22×C32—41no—
164C22×C32#12111yescharacteristic
165C32×C4—21no—
166C32×C4—41no—
167C32×C4—81no—
168C32×C4C2×SD1611yescharacteristic
169C32×C4#13711yescharacteristic
170C32×C4#13711yescharacteristic
171C32×C4#13711yescharacteristic
172C3×Dic3—81no—
173C2×M16—61no—
174C4⋊Q8—31no—
175C4⋊Q8C2×C3×D311yescharacteristic
176C4×D4C2×C3×D311yescharacteristic
177#107—61no—
178#107—61no—
179#106—21no—
180#106—61no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183C4⋊C8C2×C3×D311yescharacteristic
184#102—21no—
185#102—61no—
186C22⋊C8—61no—
187C4×C8—31no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—41no—
191C3×Q8—81no—
192C3×Q8—81no—
193C3×Q8—82no—
194C3×Q8—241no—
195C3×D4—22no—
196C3×D4—21no—
197C3×D4—21no—
198C3×D4—21no—
199C3×D4—21no—
200C3×D4—41no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—42no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—81no—
215C2×C3×C4—81no—
216C2×C3×C4—121no—
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4#23711yescharacteristic
219C2×C3×C4C2×#6711yescharacteristic
220C2×C3×C4C2×C3×D411yescharacteristic
221C2×C3×C4C2×C3×D411yescharacteristic
222C2×C3×C4C3×#4111yescharacteristic
223C2×Dic3—41no—
224Dic6—81no—
225C3×C8—32no—
226C3×C8—42no—
227C3×C8—41no—
228C3×C8—41no—
229C3×C8—61no—
230C3×C8—121no—
231C3×C8—121no—
232C3⋊C8—21no—
233C3⋊C8—41no—
234C3⋊C8—41no—
235C3⋊C8C3×SD1612yes—
236C2×C32—81no—
237C2×C32#46111yescharacteristic
238C2×C32#47011yescharacteristic
239C2×C32#47211yescharacteristic
240C2×Q8—21no—
241C2×Q8—61no—
242C2×D4C3×#6711yescharacteristic
243C22×C4—21no—
244M16—122no—
245C2×C8—21no—
246C2×C8—31no—
247C2×C8—31no—
248C2×C8—61no—
249C2×C8—61no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—61no—
253C4⋊C4—61no—
254C4⋊C4C3×#6711yescharacteristic
255C22⋊C4—21no—
256C42C22×C3×D311yescharacteristic
257C22×C3—21no—
258C22×C3—42no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—81no—
266C22×C3—81no—
267C22×C3#93911yescharacteristic
268C22×C3C3×#12111yescharacteristic
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—41no—
278C3×C4—81no—
279C3×C4—82no—
280C3×C4—81no—
281C3×C4—81no—
282C3×C4—241no—
283C3×C4D3×SD1611yescharacteristic
284C3×C4#91511yescharacteristic
285C3×C4#94211yescharacteristic
286C3×C4#95111yescharacteristic
287C3×C4C2×C3×SD1611yescharacteristic
288C3×C4C3×#13711yescharacteristic
289C3×C4C3×#13711yescharacteristic
290C3×C4C3×#13711yescharacteristic
291Dic3—81no—
292C32#169511yescharacteristic, complemented, Sylow
293C23—21no—
294Q8—81no—
295Q8—241no—
296D4—21no—
297D4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—121no—
303C2×C4C3×D3×D411yescharacteristic
304C2×C4C3×#23711yescharacteristic
305C2×C4C2×C3×#6711yescharacteristic
306C8—32no—
307C8—41no—
308C8—61no—
309C8—121no—
310C8—121no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—82no—
315C2×C3—81no—
316C2×C3—81no—
317C2×C3#505211yescharacteristic
318C2×C3#516211yescharacteristic
319C2×C3#519911yescharacteristic
320C2×C3C3×#46111yescharacteristic
321C2×C3C3×#47011yescharacteristic
322C2×C3C3×#47211yescharacteristic
323C22—41no—
324C22—41no—
325C22—41no—
326C22C3×#93911yescharacteristic
327C4—21no—
328C4—41no—
329C4—81no—
330C4—241no—
331C4C3×D3×SD1611yescharacteristic
332C4C3×#91511yescharacteristic
333C4C3×#94211yescharacteristic
334C4C3×#95111yescharacteristic
335C3—21no—
336C3#7113711yescharacteristic, direct product factor
337C3C3×#169511yescharacteristic, complemented
338C2—81no—
339C2C3×#505211yescharacteristic
340C2C3×#516211yescharacteristic
341C2C3×#519911yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#476C2
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC3×#476D3
hypocenterC3C3×#1695
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
2. C3×#5078C2semidirect
5. C3×#4546C2semidirect
6. C3×#4481C2semidirect
7. C3×#4480C2semidirect
9. #71137C3direct (N × H)
31. #5078C2×C3semidirect
37. #4546C2×C3semidirect
38. #4481C2×C3semidirect
39. #4480C2×C3semidirect
292. C32#1695semidirect
336. C3#71137direct (N × H)
337. C3C3×#1695semidirect

Maximal subgroups

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

subgroupindex
C32×#4762
C3×#50782
C3×#50122
C3×#50082
C3×#45462
C3×#44812
C3×#44802
C3×#16953
#711373