Finite Group Databasebeta

← C3×#68264 #11779051

Subgroups — C3×#68264 #11779051

Order 1152.

491 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic
3C3×#4848C211yesmaximal, characteristic
4C3×#4693C211yesmaximal, characteristic
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4456C211yesmaximal, characteristic, complemented
8C3×#1623—31nomaximal
9#68264C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C3×Q8×Dic3—21no—
12C2×C3×#215—21no—
13C2×C3×#204—22no—
14C2×C3×#204—21no—
15C3×#888—22no—
16C3×#888—21no—
17C3×#874C2211yescharacteristic
18C3×#869—21no—
19C3×#869C2211yescharacteristic
20C3×C4×Dic6—21no—
21C3×C4×Dic6C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×C4×C8C2211yescharacteristic
24C3×#821—21no—
25C3×#809—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×Q82—31no—
28Q8×Dic6C2×C311yescharacteristic, complemented
29C3×#492—31no—
30C3×#460—31no—
31C3×#460—31no—
32#5027C2×C311yescharacteristic
33#4848C2×C311yescharacteristic
34#4693C2×C311yescharacteristic
35C3×#333—31no—
36C3×Q8⋊C8—21no—
37C3×Q8⋊C8—31no—
38C3×Q8⋊C8D311yescharacteristic, complemented
39C3×Q8⋊C8C2×C311yescharacteristic, complemented
40#4481C2×C311yescharacteristic, complemented
41#4456C2×C311yescharacteristic, complemented
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6D411yescharacteristic
48C2×C3×Dic6D412yes—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C42—21no—
54C32×C42C2311yescharacteristic
55C3×#215—42no—
56C3×C4⋊Dic3—22no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—22no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C3×#204—44no—
66C3×#204—42no—
67#1623—31noSylow
68C2×C3×SD16—61no—
69C2×C3×SD16—62no—
70C2×C3×SD16—61no—
71C3×C4⋊Q8—31no—
72C3×C4⋊Q8—61no—
73C3×C4⋊Q8—62no—
74C3×C4⋊Q8—61no—
75C3×#127—31no—
76C3×C4×Q8—21no—
77C3×C4×Q8—31no—
78C3×C4×Q8—61no—
79C3×C4×Q8—61no—
80C3×C4×Q8C2×D311yescharacteristic
81C3×C4×Q8C22×C311yescharacteristic
82Q8×Dic3—21no—
83C2×#215—21no—
84C2×#204—22no—
85C2×#204—21no—
86#888—22no—
87#888—21no—
88#874C22×C311yescharacteristic
89#869—21no—
90#869C22×C311yescharacteristic
91C4×Dic6—21no—
92C4×Dic6C22×C311yescharacteristic
93C3×C4⋊C8—21no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8C2×D311yescharacteristic
96C3×C4⋊C8C22×C311yescharacteristic
97C3×#102—61no—
98C3×#102—61no—
99C3×C4×C8—21no—
100C3×C4×C8C2×D311yescharacteristic
101C3×C4×C8C22×C311yescharacteristic
102#821—21no—
103#809—21no—
104C4⋊(C3⋊C8)C22×C311yescharacteristic
105C22×C3×D3—41no—
106C32×Q8—21no—
107C32×Q8SD1612yescomplemented
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3×Dic3—21no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—21no—
116C3×D12—42no—
117C3×D12—41no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×Dic6—21no—
122C3×Dic6—42no—
123C3×Dic6—82no—
124C3×Dic6SD1612yescomplemented
125C32×C8—22no—
126C32×C8—41no—
127C3×C3⋊C8—41no—
128Q82—31no—
129#492—31no—
130#460—31no—
131#460—31no—
132#333—31no—
133Q8⋊C8—31no—
134Q8⋊C8C3×D311yescharacteristic, complemented
135C2×C3×Q8—21no—
136C2×C3×Q8—31no—
137C2×C3×Q8—32no—
138C2×C3×Q8—62no—
139C2×C3×Q8D1211yescharacteristic
140C2×C3×Q8C3×D411yescharacteristic
141C2×C3×D4—61no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×D12—21no—
145C2×D12—21no—
146C2×D12—21no—
147C2×Dic6—22no—
148C2×Dic6C3×D411yescharacteristic
149C2×Dic6C3×D412yes—
150C3×SD16—124no—
151C3×SD16—122no—
152C3×SD16—122no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—41no—
158C2×C3×C8—41no—
159C2×C3×C8—61no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—41no—
165C3×C4⋊C4—62no—
166C3×C4⋊C4—62no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4D1211yescharacteristic
171C3×C4⋊C4C3×D411yescharacteristic
172C3×C42—21no—
173C3×C42—21no—
174C3×C42—21no—
175C3×C42—41no—
176C3×C42—62no—
177C3×C42—61no—
178C3×C42C22×D311yescharacteristic
179C3×C42C23×C311yescharacteristic
180#215—42no—
181C4⋊Dic3—22no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3C3×D411yescharacteristic
185Dic3⋊C4—22no—
186Dic3⋊C4—21no—
187C4×Dic3—22no—
188C4×Dic3—21no—
189C2×C3⋊C8—21no—
190#204—44no—
191#204—42no—
192C22×C32#12011yescharacteristic
193C2×C3×D3—81no—
194C2×C3×D3—81no—
195C2×C3×D3—81no—
196C32×C4—22no—
197C32×C4—21no—
198C32×C4—41no—
199C32×C4C2×SD1611yescharacteristic
200C32×C4C2×SD1611yescharacteristic
201C32×C4#13711yescharacteristic
202C32×C4#13711yescharacteristic
203C3×Dic3—22no—
204C3×Dic3—42no—
205C3×Dic3—41no—
206C2×SD16—61no—
207C2×SD16—62no—
208C2×SD16—61no—
209C4⋊Q8—31no—
210C4⋊Q8—61no—
211C4⋊Q8—62no—
212C4⋊Q8—61no—
213#127—31no—
214C4×Q8—31no—
215C4×Q8—61no—
216C4×Q8—61no—
217C4×Q8C2×C3×D311yescharacteristic
218C4⋊C8—31no—
219C4⋊C8C2×C3×D311yescharacteristic
220#102—61no—
221#102—61no—
222C4×C8C2×C3×D311yescharacteristic
223C23×C3—121no—
224C22×D3—41no—
225C3×Q8—21no—
226C3×Q8—21no—
227C3×Q8—22no—
228C3×Q8—32no—
229C3×Q8—41no—
230C3×Q8—61no—
231C3×Q8—122no—
232C3×Q8—242no—
233C3×Q8#20412yescomplemented
234C3×Q8C3×SD1612yescomplemented
235C3×D4—122no—
236C3×D4—121no—
237C3×D4—121no—
238C3×D4—121no—
239C3×D4—121no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—62no—
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4C2×C3×D411yescharacteristic
256C2×C3×C4C2×C3×D411yescharacteristic
257C2×C3×C4C2×C3×D411yescharacteristic
258C2×Dic3—21no—
259C2×Dic3—22no—
260C2×Dic3—21no—
261D12—42no—
262D12—41no—
263D12—41no—
264D12—41no—
265D12—41no—
266Dic6—21no—
267Dic6—42no—
268Dic6—82no—
269Dic6C3×SD1612yescomplemented
270C3×C8—22no—
271C3×C8—22no—
272C3×C8—42no—
273C3×C8—41no—
274C3×C8—41no—
275C3×C8—81no—
276C3×C8—121no—
277C3⋊C8—41no—
278C2×C32#44811yescharacteristic
279C2×C32#44811yescharacteristic
280C2×C32#45311yescharacteristic
281C3×D3—161no—
282C2×Q8—31no—
283C2×Q8—32no—
284C2×Q8—62no—
285C2×Q8C3×D1211yescharacteristic
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—61no—
289SD16—124no—
290SD16—122no—
291SD16—122no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—61no—
295C4⋊C4—21no—
296C4⋊C4—31no—
297C4⋊C4—62no—
298C4⋊C4—62no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4C3×D1211yescharacteristic
303C42—21no—
304C42—62no—
305C42—61no—
306C42C22×C3×D311yescharacteristic
307C22×C3—21no—
308C22×C3—241no—
309C22×C3—241no—
310C22×C3—241no—
311C22×C3#88211yescharacteristic
312C22×C3C3×#12011yescharacteristic
313C2×D3—81no—
314C2×D3—81no—
315C2×D3—81no—
316C3×C4—22no—
317C3×C4—22no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—41no—
325C3×C4—42no—
326C3×C4—41no—
327C3×C4—41no—
328C3×C4—62no—
329C3×C4—81no—
330C3×C4—122no—
331C3×C4—121no—
332C3×C4C2×#20411yescharacteristic
333C3×C4#90911yescharacteristic
334C3×C4D3×SD1611yescharacteristic
335C3×C4#91811yescharacteristic
336C3×C4C2×C3×SD1611yescharacteristic
337C3×C4C2×C3×SD1611yescharacteristic
338C3×C4C3×#13711yescharacteristic
339C3×C4C3×#13711yescharacteristic
340Dic3—22no—
341Dic3—42no—
342Dic3—41no—
343C32#162311yescharacteristic, complemented, Sylow
344C23—121no—
345Q8—21no—
346Q8—32no—
347Q8—61no—
348Q8—122no—
349Q8—242no—
350Q8C3×#20412yescomplemented
351D4—122no—
352D4—121no—
353D4—121no—
354D4—121no—
355D4—121no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—62no—
361C2×C4C2×C3×D1211yescharacteristic
362C2×C4C3×D3×D411yescharacteristic
363C2×C4C3×D3×D411yescharacteristic
364C8—22no—
365C8—41no—
366C8—121no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—481no—
371C2×C3#473811yescharacteristic
372C2×C3#480611yescharacteristic
373C2×C3#482211yescharacteristic
374C2×C3C3×#44811yescharacteristic
375C2×C3C3×#44811yescharacteristic
376C2×C3C3×#45311yescharacteristic
377D3—161no—
378C22—241no—
379C22—241no—
380C22—241no—
381C22C3×#88211yescharacteristic
382C4—22no—
383C4—21no—
384C4—41no—
385C4—62no—
386C4—122no—
387C4—121no—
388C4C2×C3×#20411yescharacteristic
389C4C3×#90911yescharacteristic
390C4C3×D3×SD1611yescharacteristic
391C4C3×#91811yescharacteristic
392C3—21no—
393C3#6826411yescharacteristic, direct product factor
394C3C3×#162311yescharacteristic, complemented
395C2—481no—
396C2C3×#473811yescharacteristic
397C2C3×#480611yescharacteristic
398C2C3×#482211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1623
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×Q8×Dic6C2semidirect
5. C32×Q8⋊C8C2semidirect
6. C3×#4481C2semidirect
7. C3×#4456C2semidirect
9. #68264C3direct (N × H)
28. Q8×Dic6C2×C3semidirect
38. C3×Q8⋊C8D3semidirect
39. C3×Q8⋊C8C2×C3semidirect
40. #4481C2×C3semidirect
41. #4456C2×C3semidirect
107. C32×Q8SD16semidirect
124. C3×Dic6SD16semidirect
134. Q8⋊C8C3×D3semidirect
233. C3×Q8#204semidirect
234. C3×Q8C3×SD16semidirect
269. Dic6C3×SD16semidirect
343. C32#1623semidirect
350. Q8C3×#204semidirect
393. C3#68264direct (N × H)
394. C3C3×#1623semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
C3×#50272
C3×#48482
C3×#46932
C32×Q8⋊C82
C3×#44812
C3×#44562
C3×#16233
#682643