Finite Group Databasebeta

← C3×#68490 #11779003

Subgroups — C3×#68490 #11779003

Order 1152.

504 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2C3×#5085C211yesmaximal, characteristic, complemented
3C3×#4848C211yesmaximal, characteristic, complemented
4C3×#4843C211yesmaximal, characteristic
5C32×#333C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic, complemented
8C3×#1622—31nomaximal
9#68490C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C3×#946—22no—
12C2×C3×#215—22no—
13C2×C3×D24—21no—
14C2×C3×#204—21no—
15C3×#897—21no—
16C3×#893—21no—
17C3×D3×C4⋊C4—21no—
18C3×#890—21no—
19C3×#874C2211yescharacteristic
20C3×C4×D12C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×C4⋊C8C2211yescharacteristic
24C3×#821—21no—
25C3×#821—21no—
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#554—31no—
28#5730C2×C311yescharacteristic, complemented
29C3×#492—31no—
30C3×#460—31no—
31C3×#459—31no—
32#5085C2×C311yescharacteristic, complemented
33#4848C2×C311yescharacteristic, complemented
34#4843C2×C311yescharacteristic
35C3×#333—21no—
36C3×#333D311yescharacteristic, complemented
37C3×#333C2×C311yescharacteristic, complemented
38C3×Q8⋊C8—31no—
39C3×D4⋊C8—31no—
40#4484C2×C311yescharacteristic, complemented
41#4483C2×C311yescharacteristic, complemented
42C2×C32×Q8D412yes—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—22no—
49C2×C3×Dic6D411yescharacteristic
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C42C2311yescharacteristic
55C3×#215—44no—
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—22no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—22no—
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C3×D24—42no—
66C3×#204—42no—
67#1622—31noSylow
68C2×C3×SD16—61no—
69C2×C3×SD16—62no—
70C2×C3×D8—61no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8C2×D311yescharacteristic
73C3×C4⋊Q8C22×C311yescharacteristic
74C3×#127—31no—
75C3×#125—61no—
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—62no—
78C3×C4×Q8—31no—
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81C2×C3×C4⋊C4—61no—
82#946—22no—
83C2×#215—22no—
84C2×D24—21no—
85C2×#204—21no—
86#897—21no—
87#893—21no—
88D3×C4⋊C4—21no—
89#890—21no—
90#874C22×C311yescharacteristic
91C4×D12C22×C311yescharacteristic
92C4×Dic6C22×C311yescharacteristic
93C3×C4⋊C8—21no—
94C3×C4⋊C8—21no—
95C3×C4⋊C8C2×D311yescharacteristic
96C3×C4⋊C8C2×D311yescharacteristic
97C3×C4⋊C8C22×C311yescharacteristic
98C3×C4⋊C8C22×C311yescharacteristic
99C3×#102—61no—
100C3×#102—61no—
101C3×C4×C8—31no—
102#821—21no—
103#821—21no—
104C4×C3⋊C8C22×C311yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—41no—
107C32×Q8—42no—
108C2×C32×C4—22no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C3×D12—21no—
116C3×D12—42no—
117C3×D12—41no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12SD1612yescomplemented
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×C4×D3—82no—
125C3×Dic6—21no—
126C3×Dic6—21no—
127C32×C8—41no—
128C32×C8—41no—
129C3×C3⋊C8—22no—
130#554—31no—
131#492—31no—
132#460—31no—
133#459—31no—
134#333C3×D311yescharacteristic, complemented
135Q8⋊C8—31no—
136D4⋊C8—31no—
137C2×C3×Q8—22no—
138C2×C3×Q8—31no—
139C2×C3×Q8D1212yes—
140C2×C3×Q8C3×D412yes—
141C2×C3×D4—31no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C22×C3×C4—62no—
146C22×C3×C4—61no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12C3×D411yescharacteristic
151C2×C4×D3—21no—
152C2×C4×D3—22no—
153C2×Dic6C3×D411yescharacteristic
154C3×SD16—122no—
155C3×SD16—124no—
156C3×D8—122no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—41no—
162C2×C3×C8—41no—
163C2×C3×C8—61no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—41no—
171C3×C4⋊C4—41no—
172C3×C4⋊C4—62no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—61no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42—61no—
179C3×C42C22×D311yescharacteristic
180C3×C42C23×C311yescharacteristic
181#215—44no—
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—21no—
184C4⋊Dic3—22no—
185C4⋊Dic3C3×D411yescharacteristic
186C4⋊Dic3C3×D411yescharacteristic
187Dic3⋊C4—22no—
188Dic3⋊C4—21no—
189C4×Dic3—21no—
190C2×C3⋊C8—21no—
191D24—42no—
192#204—42no—
193C22×C32#12011yescharacteristic
194C2×C3×D3—22no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C2×C3×D3—81no—
198C2×C3×D3—81no—
199C2×C3×D3—81no—
200C32×C4—21no—
201C32×C4—42no—
202C32×C4C2×SD1611yescharacteristic
203C32×C4#13511yescharacteristic
204C32×C4AGL(1,ℤ/8)11yescharacteristic
205C32×C4#13711yescharacteristic
206C3×Dic3—41no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C2×SD16—61no—
210C2×SD16—62no—
211C2×D8—61no—
212C4⋊Q8C2×C3×D311yescharacteristic
213#127—31no—
214#125—61no—
215C22⋊Q8—61no—
216C22⋊Q8—62no—
217C4×Q8—31no—
218C4×D4—31no—
219C4×D4—61no—
220C2×C4⋊C4—61no—
221C4⋊C8C2×C3×D311yescharacteristic
222C4⋊C8C2×C3×D311yescharacteristic
223#102—61no—
224#102—61no—
225C4×C8—31no—
226C23×C3—61no—
227C23×C3—121no—
228C22×D3—21no—
229C22×D3—41no—
230C3×Q8—42no—
231C3×Q8—42no—
232C3×Q8—61no—
233C3×Q8—61no—
234C3×Q8—82no—
235C3×D4—32no—
236C3×D4—61no—
237C3×D4—122no—
238C3×D4—121no—
239C3×D4—121no—
240C3×D4—121no—
241C3×D4—121no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—42no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4—242no—
254C2×C3×C4C2×D1211yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4C2×C3×D411yescharacteristic
258C2×C3×C4C2×C3×D411yescharacteristic
259C2×C3×C4C2×C3×D411yescharacteristic
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—21no—
263D12—21no—
264D12—42no—
265D12—41no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12C3×SD1612yescomplemented
270C4×D3—41no—
271C4×D3—41no—
272C4×D3—82no—
273Dic6—21no—
274Dic6—21no—
275C3×C8—41no—
276C3×C8—41no—
277C3×C8—41no—
278C3×C8—41no—
279C3×C8—62no—
280C3×C8—81no—
281C3×C8—81no—
282C3⋊C8—22no—
283C2×C32#44811yescharacteristic
284C2×C32#44911yescharacteristic
285C2×C32#45311yescharacteristic
286C3×D3—42no—
287C3×D3—161no—
288C2×Q8—31no—
289C2×Q8C3×D1212yes—
290C2×D4—31no—
291C2×D4—61no—
292C2×D4—61no—
293C2×D4—61no—
294C22×C4—62no—
295C22×C4—61no—
296SD16—122no—
297SD16—124no—
298D8—122no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—61no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—31no—
305C4⋊C4—31no—
306C4⋊C4—62no—
307C4⋊C4—62no—
308C4⋊C4—61no—
309C22⋊C4—62no—
310C22⋊C4—61no—
311C42—61no—
312C42C22×C3×D311yescharacteristic
313C22×C3—21no—
314C22×C3—62no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3—241no—
318C22×C3—241no—
319C22×C3—241no—
320C22×C3#88211yescharacteristic
321C22×C3C3×#12011yescharacteristic
322C2×D3—22no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—81no—
326C2×D3—81no—
327C2×D3—81no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—42no—
336C3×C4—42no—
337C3×C4—82no—
338C3×C4—121no—
339C3×C4—121no—
340C3×C4—121no—
341C3×C4D3×SD1611yescharacteristic
342C3×C4#91411yescharacteristic
343C3×C4#91811yescharacteristic
344C3×C4#91911yescharacteristic
345C3×C4C2×C3×SD1611yescharacteristic
346C3×C4C3×#13511yescharacteristic
347C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
348C3×C4C3×#13711yescharacteristic
349Dic3—41no—
350Dic3—41no—
351Dic3—41no—
352C32#162211yescharacteristic, complemented, Sylow
353C23—61no—
354C23—121no—
355Q8—42no—
356Q8—61no—
357Q8—61no—
358D4—32no—
359D4—61no—
360D4—122no—
361D4—121no—
362D4—121no—
363D4—121no—
364D4—121no—
365C2×C4—22no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—121no—
370C2×C4—121no—
371C2×C4—242no—
372C2×C4C2×C3×D1211yescharacteristic
373C2×C4C3×D3×D411yescharacteristic
374C2×C4C3×D3×D411yescharacteristic
375C8—41no—
376C8—41no—
377C8—62no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—122no—
382C2×C3—481no—
383C2×C3#474711yescharacteristic
384C2×C3#480611yescharacteristic
385C2×C3#481011yescharacteristic
386C2×C3C3×#44811yescharacteristic
387C2×C3C3×#44911yescharacteristic
388C2×C3C3×#45311yescharacteristic
389D3—42no—
390D3—161no—
391C22—62no—
392C22—121no—
393C22—121no—
394C22—241no—
395C22—241no—
396C22—241no—
397C22C3×#88211yescharacteristic
398C4—21no—
399C4—42no—
400C4—121no—
401C4—121no—
402C4—121no—
403C4C3×D3×SD1611yescharacteristic
404C4C3×#91411yescharacteristic
405C4C3×#91811yescharacteristic
406C4C3×#91911yescharacteristic
407C3—21no—
408C3#6849011yescharacteristic, direct product factor
409C3C3×#162211yescharacteristic, complemented
410C2—122no—
411C2—481no—
412C2C3×#474711yescharacteristic
413C2C3×#480611yescharacteristic
414C2C3×#481011yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#333C2
socleC22×C32#120
prime radicalC3×#4843C2
hypercenterC3×#333D3
hypocenterC3C3×#1622
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#333

Complements

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

NH ≅ G/Ntype
1. C3×#5730C2semidirect
2. C3×#5085C2semidirect
3. C3×#4848C2semidirect
5. C32×#333C2semidirect
6. C3×#4484C2semidirect
7. C3×#4483C2semidirect
9. #68490C3direct (N × H)
28. #5730C2×C3semidirect
32. #5085C2×C3semidirect
33. #4848C2×C3semidirect
36. C3×#333D3semidirect
37. C3×#333C2×C3semidirect
40. #4484C2×C3semidirect
41. #4483C2×C3semidirect
121. C3×D12SD16semidirect
134. #333C3×D3semidirect
269. D12C3×SD16semidirect
352. C32#1622semidirect
408. C3#68490direct (N × H)
409. C3C3×#1622semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×#50852
C3×#48482
C3×#48432
C32×#3332
C3×#44842
C3×#44832
C3×#16223
#684903