Finite Group Databasebeta

← C3×#71102 #11781327

Subgroups — C3×#71102 #11781327

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×#474C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic
4C3×D4×C3⋊C8C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1679—31nomaximal
9#71102C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C2×C3×#214—21no—
13C22×C3×C3⋊C8—21no—
14C3×#869C2211yescharacteristic
15C32×#107—21no—
16C32×C4⋊C8C2211yescharacteristic
17C32×#102—21no—
18C3×#835—21no—
19C3×#835—21no—
20C3×#830—21no—
21C3×#810—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#487—31no—
26C3×#474—21no—
27C3×#474D311yescharacteristic
28C3×#474C2×C311yescharacteristic
29C3×#461—31no—
30C3×C8×D4—31no—
31#5079C2×C311yescharacteristic, complemented
32#5019C2×C311yescharacteristic
33D4×C3⋊C8C2×C311yescharacteristic
34C3×#334—31no—
35C3×#332—31no—
36C3×#332—31no—
37#4547C2×C311yescharacteristic, complemented
38#4482C2×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×#214—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—42no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1679—31noSylow
59C2×C3×SD16—61no—
60C22×C3×C8—61no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8—31no—
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×C4⋊Q8C22×C311yescharacteristic
65C3×C4×D4—21no—
66C3×C4×D4C2×D311yescharacteristic
67C3×C4×D4C22×C311yescharacteristic
68C2×#214—21no—
69C22×C3⋊C8—21no—
70#869C22×C311yescharacteristic
71C3×#107—22no—
72C3×#107—21no—
73C3×#107—21no—
74C3×C4⋊C8—21no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8C2×D311yescharacteristic
78C3×C4⋊C8C22×C311yescharacteristic
79C3×#103—61no—
80C3×#103—61no—
81C3×#103—61no—
82C3×#102—22no—
83C3×#102—21no—
84C3×#102—21no—
85C3×C22⋊C8—61no—
86C3×C4×C8—31no—
87#835—21no—
88#835—21no—
89#830—21no—
90#810—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4×C3⋊C8C22×C311yescharacteristic
94C23×C32—21no—
95C32×Q8—41no—
96C32×Q8—41no—
97C32×D4—21no—
98C32×D4SD1612yes—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
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×Dic6—41no—
108C3×Dic6—41no—
109C32×C8—41no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114#487—31no—
115#474C3×D311yescharacteristic
116#461—31no—
117C8×D4—31no—
118#334—31no—
119#332—31no—
120#332—31no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—41no—
124C2×C3×Q8—61no—
125C2×C3×D4—21no—
126C2×C3×D4#6711yescharacteristic
127C2×C3×D4C3×D411yescharacteristic
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—41no—
131C2×Dic6—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—
140C2×C3×C8—122no—
141C3×C4⋊C4—22no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
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×C22⋊C4—21no—
153C3×C22⋊C4—21no—
154C3×C22⋊C4—41no—
155C3×C42—21no—
156C3×C42C22×D311yescharacteristic
157C3×C42C23×C311yescharacteristic
158#214—42no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—42no—
164C2×C3⋊C8C3×D411yescharacteristic
165C2×C3⋊C8C3×D411yescharacteristic
166C22×C32—22no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32#12111yescharacteristic
170C32×C4—21no—
171C32×C4—41no—
172C32×C4—81no—
173C32×C4C2×SD1611yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4#13511yescharacteristic
176C32×C4AGL(1,ℤ/8)11yescharacteristic
177C3×Dic3—81no—
178C2×SD16—61no—
179C22×C8—61no—
180C4⋊Q8—31no—
181C4⋊Q8C2×C3×D311yescharacteristic
182C4×D4C2×C3×D311yescharacteristic
183#107—21no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8C2×C3×D311yescharacteristic
187#103—61no—
188#103—61no—
189#103—61no—
190#102—21no—
191C22⋊C8—61no—
192C4×C8—31no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—41no—
196C3×Q8—41no—
197C3×Q8—41no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×Q8—81no—
201C3×Q8—81no—
202C3×Q8—121no—
203C3×Q8—121no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—22no—
207C3×D4—41no—
208C3×D4#21512yes—
209C3×D4C3×SD1612yes—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—42no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—81no—
224C2×C3×C4—81no—
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—41no—
234Dic6—41no—
235C3×C8—42no—
236C3×C8—41no—
237C3×C8—41no—
238C3×C8—61no—
239C3×C8—61no—
240C3×C8—121no—
241C3×C8—121no—
242C3⋊C8—21no—
243C3⋊C8—21no—
244C3⋊C8—41no—
245C3⋊C8—41no—
246C2×C32—42no—
247C2×C32#46311yescharacteristic
248C2×C32#46511yescharacteristic
249C2×C32#47311yescharacteristic
250C2×Q8—21no—
251C2×Q8—61no—
252C2×D4C3×#6711yescharacteristic
253C22×C4—21no—
254SD16—122no—
255C2×C8—21no—
256C2×C8—31no—
257C2×C8—31no—
258C2×C8—61no—
259C2×C8—61no—
260C2×C8—122no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—61no—
264C4⋊C4—61no—
265C4⋊C4C3×#6711yescharacteristic
266C22⋊C4—21no—
267C42C22×C3×D311yescharacteristic
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—21no—
271C22×C3—42no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—81no—
277C22×C3—81no—
278C22×C3#93911yescharacteristic
279C22×C3C3×#12111yescharacteristic
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—81no—
290C3×C4—82no—
291C3×C4—81no—
292C3×C4—81no—
293C3×C4—241no—
294C3×C4#91111yescharacteristic
295C3×C4#91211yescharacteristic
296C3×C4C2×#21511yescharacteristic
297C3×C4#95011yescharacteristic
298C3×C4C2×C3×SD1611yescharacteristic
299C3×C4C3×#13511yescharacteristic
300C3×C4C3×#13511yescharacteristic
301C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
302Dic3—81no—
303C32#167911yescharacteristic, complemented, Sylow
304C23—21no—
305Q8—41no—
306Q8—41no—
307Q8—121no—
308Q8—121no—
309D4—21no—
310D4C3×#21512yes—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—121no—
316C2×C4C3×D3×D411yescharacteristic
317C2×C4C3×#23711yescharacteristic
318C2×C4C2×C3×#6711yescharacteristic
319C8—41no—
320C8—61no—
321C8—61no—
322C8—121no—
323C8—121no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—42no—
328C2×C3—42no—
329C2×C3—82no—
330C2×C3#504811yescharacteristic
331C2×C3#515311yescharacteristic
332C2×C3#520411yescharacteristic
333C2×C3C3×#46311yescharacteristic
334C2×C3C3×#46511yescharacteristic
335C2×C3C3×#47311yescharacteristic
336C22—22no—
337C22—41no—
338C22—41no—
339C22C3×#93911yescharacteristic
340C4—21no—
341C4—41no—
342C4—81no—
343C4—241no—
344C4C3×#91111yescharacteristic
345C4C3×#91211yescharacteristic
346C4C2×C3×#21511yescharacteristic
347C4C3×#95011yescharacteristic
348C3—21no—
349C3#7110211yescharacteristic, direct product factor
350C3C3×#167911yescharacteristic, complemented
351C2—42no—
352C2C3×#504811yescharacteristic
353C2C3×#515311yescharacteristic
354C2C3×#520411yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#474C2
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC3×#474D3
hypocenterC3C3×#1679
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
2. C3×#5079C2semidirect
5. C3×#4547C2semidirect
6. C3×#4482C2semidirect
7. C3×#4480C2semidirect
9. #71102C3direct (N × H)
31. #5079C2×C3semidirect
37. #4547C2×C3semidirect
38. #4482C2×C3semidirect
39. #4480C2×C3semidirect
303. C32#1679semidirect
349. C3#71102direct (N × H)
350. C3C3×#1679semidirect

Maximal subgroups

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

subgroupindex
C32×#4742
C3×#50792
C3×#50192
C3×D4×C3⋊C82
C3×#45472
C3×#44822
C3×#44802
C3×#16793
#711023