Finite Group Databasebeta

← C3×#70855 #11781519

Subgroups — C3×#70855 #11781519

Order 1152.

387 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×C8×D4C211yesmaximal, characteristic
2C3×#5008C211yesmaximal, characteristic
3C3×#5007C211yesmaximal, characteristic
4C3×#4681C211yesmaximal, characteristic, complemented
5C3×#4482C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4458C211yesmaximal, characteristic, complemented
8C3×#1683—31nomaximal
9#70855C311yesmaximal, characteristic, direct product factor
10C22×C32×C8—21no—
11C32×C4×D4C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×C22⋊C8—21no—
16C32×C4×C8C2211yescharacteristic
17C3×#832—21no—
18C3×#832—21no—
19C3×#816—21no—
20C3×#816—21no—
21C3×#808—21no—
22C3×#807—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#487—31no—
26C3×#476—31no—
27C3×#474—31no—
28C3×C8×D4—21no—
29C3×C8×D4D311yescharacteristic
30C3×C8×D4C2×C311yescharacteristic
31#5008C2×C311yescharacteristic
32#5007C2×C311yescharacteristic
33#4681C2×C311yescharacteristic, complemented
34C3×#335—31no—
35C3×#333—31no—
36C3×#332—31no—
37#4482C2×C311yescharacteristic, complemented
38#4481C2×C311yescharacteristic, complemented
39#4458C2×C311yescharacteristic, complemented
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C2×C32×C8—42no—
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C32×C4⋊C4D411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#1683—31noSylow
58C22×C3×C8—22no—
59C22×C3×C8—21no—
60C22×C3×C8—21no—
61C3×C4⋊Q8—31no—
62C3×C4⋊Q8—31no—
63C3×C4×D4—21no—
64C3×C4×D4C2×D311yescharacteristic
65C3×C4×D4C22×C311yescharacteristic
66#869C22×C311yescharacteristic
67#869C22×C311yescharacteristic
68C3×#107—61no—
69C3×#106—61no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8C2×D311yescharacteristic
74C3×C4⋊C8C22×C311yescharacteristic
75C3×#103—61no—
76C3×#103—61no—
77C3×#102—61no—
78C3×#102—61no—
79C3×C22⋊C8—22no—
80C3×C22⋊C8—21no—
81C3×C22⋊C8—21no—
82C3×C4×C8—21no—
83C3×C4×C8C2×D311yescharacteristic
84C3×C4×C8C22×C311yescharacteristic
85#832—21no—
86#832—21no—
87#816—21no—
88#816—21no—
89#808—21no—
90#807—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C23×C32—21no—
94C32×D4—21no—
95C32×D4Q1612yes—
96C2×C32×C4—21no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3×Dic6—81no—
107C32×C8—21no—
108C32×C8—21no—
109C32×C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487—31no—
113#476—31no—
114#474—31no—
115C8×D4C3×D311yescharacteristic
116#335—31no—
117#333—31no—
118#332—31no—
119C2×C3×Q8—61no—
120C2×C3×Q8—61no—
121C2×C3×D4—21no—
122C2×C3×D4D1211yescharacteristic
123C2×C3×D4C3×D411yescharacteristic
124C22×C3×C4—22no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C2×Dic6—21no—
128C2×Dic6—21no—
129C2×C3×C8—22no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—44no—
135C2×C3×C8—42no—
136C2×C3×C8—42no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C2×C3×C8#6711yescharacteristic
140C2×C3×C8#6711yescharacteristic
141C2×C3×C8C3×D411yescharacteristic
142C2×C3×C8C3×D411yescharacteristic
143C3×C4⋊C4—21no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4D1211yescharacteristic
149C3×C4⋊C4C3×D411yescharacteristic
150C3×C22⋊C4—22no—
151C3×C22⋊C4—21no—
152C3×C22⋊C4—21no—
153C3×C42—21no—
154C3×C42C22×D311yescharacteristic
155C3×C42C23×C311yescharacteristic
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C4⋊Dic3—21no—
159C4⋊Dic3—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C22×C32—22no—
163C22×C32—41no—
164C22×C32—41no—
165C22×C32#12111yescharacteristic
166C32×C4—21no—
167C32×C4—41no—
168C32×C4C2×Q1611yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C3×Dic3—81no—
173C3×Dic3—81no—
174C22×C8—21no—
175C4⋊Q8—31no—
176C4⋊Q8—31no—
177C4×D4C2×C3×D311yescharacteristic
178#107—61no—
179#106—61no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8C2×C3×D311yescharacteristic
183#103—61no—
184#103—61no—
185#102—61no—
186#102—61no—
187C22⋊C8—21no—
188C4×C8C2×C3×D311yescharacteristic
189C23×C3—22no—
190C23×C3—21no—
191C23×C3—21no—
192C3×Q8—121no—
193C3×Q8—121no—
194C3×Q8—241no—
195C3×D4—22no—
196C3×D4—21no—
197C3×D4—21no—
198C3×D4—22no—
199C3×D4Dic1212yes—
200C3×D4C3×Q1612yes—
201C2×C3×C4—22no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—42no—
208C2×C3×C4—42no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215C2×C3×C4C2×D1211yescharacteristic
216C2×C3×C4#23511yescharacteristic
217C2×C3×C4C2×#6711yescharacteristic
218C2×C3×C4C2×C3×D411yescharacteristic
219C2×C3×C4C2×C3×D411yescharacteristic
220C2×C3×C4C3×#4111yescharacteristic
221C2×Dic3—41no—
222C2×Dic3—41no—
223Dic6—41no—
224Dic6—41no—
225Dic6—81no—
226C3×C8—22no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8—21no—
230C3×C8—21no—
231C3×C8—41no—
232C3×C8—42no—
233C3×C8—41no—
234C3×C8—41no—
235C3×C8—121no—
236C3×C8—121no—
237C3⋊C8—41no—
238C3⋊C8—41no—
239C2×C32—42no—
240C2×C32#46311yescharacteristic
241C2×C32#46711yescharacteristic
242C2×C32#47111yescharacteristic
243C2×Q8—61no—
244C2×Q8—61no—
245C2×D4C3×D1211yescharacteristic
246C22×C4—21no—
247C2×C8—21no—
248C2×C8—42no—
249C2×C8—61no—
250C2×C8—61no—
251C2×C8C3×#6711yescharacteristic
252C2×C8C3×#6711yescharacteristic
253C4⋊C4—61no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4C3×D1211yescharacteristic
258C22⋊C4—21no—
259C42C22×C3×D311yescharacteristic
260C22×C3—24no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—21no—
264C22×C3—42no—
265C22×C3—42no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3#93011yescharacteristic
271C22×C3C3×#12111yescharacteristic
272C3×C4—21no—
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—241no—
283C3×C4—241no—
284C3×C4#90411yescharacteristic
285C3×C4C2×Dic1211yescharacteristic
286C3×C4#93211yescharacteristic
287C3×C4#95011yescharacteristic
288C3×C4C2×C3×Q1611yescharacteristic
289C3×C4C3×#13511yescharacteristic
290C3×C4C3×#13511yescharacteristic
291C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
292Dic3—81no—
293Dic3—81no—
294C32#168311yescharacteristic, complemented, Sylow
295C23—21no—
296Q8—121no—
297Q8—121no—
298Q8—241no—
299D4—21no—
300D4C3×Dic1212yes—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—121no—
305C2×C4—121no—
306C2×C4C2×C3×D1211yescharacteristic
307C2×C4C3×#23511yescharacteristic
308C2×C4C2×C3×#6711yescharacteristic
309C8—21no—
310C8—21no—
311C8—41no—
312C8—121no—
313C8—121no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—44no—
318C2×C3—42no—
319C2×C3—42no—
320C2×C3#501611yescharacteristic
321C2×C3#511611yescharacteristic
322C2×C3#514111yescharacteristic
323C2×C3C3×#46311yescharacteristic
324C2×C3C3×#46711yescharacteristic
325C2×C3C3×#47111yescharacteristic
326C22—22no—
327C22—41no—
328C22—41no—
329C22C3×#93011yescharacteristic
330C4—21no—
331C4—41no—
332C4—241no—
333C4—241no—
334C4C3×#90411yescharacteristic
335C4C2×C3×Dic1211yescharacteristic
336C4C3×#93211yescharacteristic
337C4C3×#95011yescharacteristic
338C3—21no—
339C3#7085511yescharacteristic, direct product factor
340C3C3×#168311yescharacteristic, complemented
341C2—42no—
342C2C3×#501611yescharacteristic
343C2C3×#511611yescharacteristic
344C2C3×#514111yescharacteristic
subgroupG/H
centerC22×C3#930
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×C8×D4C2
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC3×C8×D4D3
hypocenterC3C3×#1683
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
4. C3×#4681C2semidirect
5. C3×#4482C2semidirect
6. C3×#4481C2semidirect
7. C3×#4458C2semidirect
9. #70855C3direct (N × H)
33. #4681C2×C3semidirect
37. #4482C2×C3semidirect
38. #4481C2×C3semidirect
39. #4458C2×C3semidirect
294. C32#1683semidirect
339. C3#70855direct (N × H)
340. C3C3×#1683semidirect

Maximal subgroups

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

subgroupindex
C32×C8×D42
C3×#50082
C3×#50072
C3×#46812
C3×#44822
C3×#44812
C3×#44582
C3×#16833
#708553