Finite Group Databasebeta

← C3×#71065 #11780179

Subgroups — C3×#71065 #11780179

Order 1152.

522 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic
2C32×#462C211yesmaximal, characteristic, complemented
3C3×#5087C211yesmaximal, characteristic
4C3×#5078C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1649—31nomaximal
9#71065C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8—21no—
11C2×C32×Q16—21no—
12C32×C4⋊Q8C2211yescharacteristic
13C32×C4×Q8C2211yescharacteristic
14C3×#897—21no—
15C3×#897—22no—
16C3×C4×D12—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869—21no—
19C3×#869C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×#103—21no—
22C3×#809—21no—
23C3×#807—22no—
24C3×#807—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×D4×Q8—31no—
28Q8×D12C2×C311yescharacteristic
29C3×#500—31no—
30C3×#474—31no—
31C3×#462—21no—
32C3×#462D311yescharacteristic, complemented
33C3×#462C2×C311yescharacteristic, complemented
34#5087C2×C311yescharacteristic
35#5078C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39#4535C2×C311yescharacteristic, complemented
40#4483C2×C311yescharacteristic
41#4482C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×Q8D411yescharacteristic
44C3×D3×Q8—42no—
45C3×D3×Q8—42no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—22no—
48C2×C3×C4×D3—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6—21no—
51C32×Q16—42no—
52C2×C32×C8—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C42—21no—
58C32×C42C2311yescharacteristic
59C3×(C2×D3)⋊C4—22no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—22no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D412yes—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1649—31noSylow
68C22×C3×Q8—61no—
69C2×D3×Q8—21no—
70C2×C3×Q16—22no—
71C2×C3×Q16—21no—
72C2×C3×Q16—21no—
73C3×C4⋊Q8—21no—
74C3×C4⋊Q8—31no—
75C3×C4⋊Q8—61no—
76C3×C4⋊Q8C2×D311yescharacteristic
77C3×C4⋊Q8C22×C311yescharacteristic
78C3×C22⋊Q8—62no—
79C3×C22⋊Q8—61no—
80C3×C4×Q8—21no—
81C3×C4×Q8C2×D311yescharacteristic
82C3×C4×Q8C22×C311yescharacteristic
83C3×C4×D4—31no—
84C3×C4×D4—61no—
85#897—21no—
86#897—22no—
87C4×D12—21no—
88C4×D12C22×C311yescharacteristic
89#869—21no—
90#869C22×C311yescharacteristic
91C3×#107—61no—
92C3×#107—62no—
93C3×C4⋊C8—21no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8C2×D311yescharacteristic
96C3×C4⋊C8C22×C311yescharacteristic
97C3×#103—22no—
98C3×#103—21no—
99C3×#103—21no—
100C3×#102—61no—
101C3×C4×C8—31no—
102#809—21no—
103#807—22no—
104#807—21no—
105C4⋊(C3⋊C8)C22×C311yescharacteristic
106C4×C3⋊C8C22×C311yescharacteristic
107C22×C3×D3—21no—
108C32×Q8—21no—
109C32×Q8—41no—
110C32×Q8—41no—
111C32×Q8D812yes—
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3×Dic3—21no—
119C2×C3×Dic3—22no—
120C3×D12—21no—
121C3×D12Q1612yescomplemented
122C3×C4×D3—44no—
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×Dic6—44no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128C32×C8—41no—
129C3×C3⋊C8—22no—
130C3×C3⋊C8—41no—
131D4×Q8—31no—
132#500—31no—
133#474—31no—
134#462C3×D311yescharacteristic, complemented
135#332—31no—
136Q8⋊C8—31no—
137D4⋊C8—31no—
138C2×C3×Q8—22no—
139C2×C3×Q8—21no—
140C2×C3×Q8—21no—
141C2×C3×Q8—21no—
142C2×C3×Q8—62no—
143C2×C3×Q8—61no—
144C2×C3×Q8—122no—
145C2×C3×Q8—122no—
146C2×C3×Q8#6711yescharacteristic
147C2×C3×Q8C3×D411yescharacteristic
148C2×C3×D4—31no—
149C22×C3×C4—62no—
150C22×C3×C4—61no—
151D3×Q8—42no—
152D3×Q8—42no—
153C2×D12C3×D411yescharacteristic
154C2×C4×D3—22no—
155C2×C4×D3—21no—
156C2×Dic6—22no—
157C2×Dic6—21no—
158C3×Q16—44no—
159C3×Q16—42no—
160C3×Q16—42no—
161C2×C3×C8—22no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—32no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—41no—
177C3×C4⋊C4—41no—
178C3×C4⋊C4—62no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4#6711yescharacteristic
181C3×C4⋊C4C3×D411yescharacteristic
182C3×C22⋊C4—62no—
183C3×C22⋊C4—61no—
184C3×C42—21no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—41no—
188C3×C42C22×D311yescharacteristic
189C3×C42C23×C311yescharacteristic
190(C2×D3)⋊C4—22no—
191(C2×D3)⋊C4—21no—
192C4⋊Dic3—22no—
193C4⋊Dic3—21no—
194C4⋊Dic3C3×D411yescharacteristic
195C4⋊Dic3C3×D412yes—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C22×C32#12011yescharacteristic
199C2×C3×D3—22no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4—22no—
203C32×C4—21no—
204C32×C4—41no—
205C32×C4—81no—
206C32×C4C2×D811yescharacteristic
207C32×C4C2×Q1611yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C32×C4#13711yescharacteristic
210C3×Dic3—41no—
211C3×Dic3—42no—
212C22×Q8—61no—
213C2×Q16—21no—
214C4⋊Q8—31no—
215C4⋊Q8—61no—
216C4⋊Q8C2×C3×D311yescharacteristic
217C22⋊Q8—62no—
218C22⋊Q8—61no—
219C4×Q8C2×C3×D311yescharacteristic
220C4×D4—31no—
221C4×D4—61no—
222#107—61no—
223#107—62no—
224C4⋊C8—31no—
225C4⋊C8C2×C3×D311yescharacteristic
226#103—21no—
227#102—61no—
228C4×C8—31no—
229C23×C3—61no—
230C22×D3—21no—
231C3×Q8—21no—
232C3×Q8—21no—
233C3×Q8—22no—
234C3×Q8—41no—
235C3×Q8—42no—
236C3×Q8—42no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—41no—
240C3×Q8—41no—
241C3×Q8—124no—
242C3×Q8—121no—
243C3×Q8—121no—
244C3×Q8#21312yes—
245C3×Q8C3×D812yes—
246C3×D4—32no—
247C3×D4—61no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—62no—
261C2×C3×C4—61no—
262C2×C3×C4—124no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C2×C3×D411yescharacteristic
269C2×C3×C4C2×C3×D411yescharacteristic
270C2×C3×C4C2×C3×D411yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—22no—
273D12—21no—
274D12C3×Q1612yescomplemented
275C4×D3—44no—
276C4×D3—41no—
277C4×D3—41no—
278Dic6—44no—
279Dic6—41no—
280Dic6—41no—
281C3×C8—42no—
282C3×C8—41no—
283C3×C8—41no—
284C3×C8—62no—
285C3×C8—121no—
286C3⋊C8—22no—
287C3⋊C8—41no—
288C2×C32#44711yescharacteristic
289C2×C32#45111yescharacteristic
290C2×C32#45611yescharacteristic
291C3×D3—42no—
292C2×Q8—21no—
293C2×Q8—62no—
294C2×Q8—61no—
295C2×Q8—122no—
296C2×Q8—122no—
297C2×Q8C3×#6711yescharacteristic
298C2×D4—31no—
299C22×C4—62no—
300C22×C4—61no—
301Q16—42no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—61no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—31no—
309C4⋊C4—32no—
310C4⋊C4—62no—
311C4⋊C4—61no—
312C4⋊C4C3×#6711yescharacteristic
313C22⋊C4—62no—
314C22⋊C4—61no—
315C42—21no—
316C42C22×C3×D311yescharacteristic
317C22×C3—21no—
318C22×C3—62no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3#93711yescharacteristic
322C22×C3C3×#12011yescharacteristic
323C2×D3—22no—
324C2×D3—41no—
325C2×D3—41no—
326C3×C4—21no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—42no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—81no—
339C3×C4—82no—
340C3×C4—81no—
341C3×C4—81no—
342C3×C4—122no—
343C3×C4—121no—
344C3×C4D3×Q1611yescharacteristic
345C3×C4#91811yescharacteristic
346C3×C4C2×#21311yescharacteristic
347C3×C4#94911yescharacteristic
348C3×C4C2×C3×D811yescharacteristic
349C3×C4C2×C3×Q1611yescharacteristic
350C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
351C3×C4C3×#13711yescharacteristic
352Dic3—41no—
353Dic3—42no—
354C32#164911yescharacteristic, complemented, Sylow
355C23—61no—
356Q8—21no—
357Q8—41no—
358Q8—41no—
359Q8—124no—
360Q8—121no—
361Q8—121no—
362Q8C3×#21312yes—
363D4—32no—
364D4—61no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—62no—
369C2×C4—61no—
370C2×C4—124no—
371C2×C4—121no—
372C2×C4—121no—
373C2×C4C3×D3×D411yescharacteristic
374C2×C4C3×D3×D411yescharacteristic
375C2×C4C2×C3×#6711yescharacteristic
376C8—41no—
377C8—62no—
378C8—121no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—122no—
383C2×C3#503611yescharacteristic
384C2×C3#518611yescharacteristic
385C2×C3#520511yescharacteristic
386C2×C3C3×#44711yescharacteristic
387C2×C3C3×#45111yescharacteristic
388C2×C3C3×#45611yescharacteristic
389D3—42no—
390C22—62no—
391C22—121no—
392C22—121no—
393C22C3×#93711yescharacteristic
394C4—21no—
395C4—22no—
396C4—41no—
397C4—81no—
398C4—122no—
399C4—121no—
400C4C3×D3×Q1611yescharacteristic
401C4C3×#91811yescharacteristic
402C4C2×C3×#21311yescharacteristic
403C4C3×#94911yescharacteristic
404C3—21no—
405C3#7106511yescharacteristic, direct product factor
406C3C3×#164911yescharacteristic, complemented
407C2—122no—
408C2C3×#503611yescharacteristic
409C2C3×#518611yescharacteristic
410C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#462C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×#462D3
hypocenterC3C3×#1649
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
2. C32×#462C2semidirect
4. C3×#5078C2semidirect
5. C3×#4535C2semidirect
7. C3×#4482C2semidirect
9. #71065C3direct (N × H)
32. C3×#462D3semidirect
33. C3×#462C2×C3semidirect
35. #5078C2×C3semidirect
39. #4535C2×C3semidirect
41. #4482C2×C3semidirect
121. C3×D12Q16semidirect
134. #462C3×D3semidirect
274. D12C3×Q16semidirect
354. C32#1649semidirect
405. C3#71065direct (N × H)
406. C3C3×#1649semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
C32×#4622
C3×#50872
C3×#50782
C3×#45352
C3×#44832
C3×#44822
C3×#16493
#710653