Finite Group Databasebeta

← C3×#68244 #11779009

Subgroups — C3×#68244 #11779009

Order 1152.

507 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3C3×#4843C211yesmaximal, characteristic
4C3×#4693C211yesmaximal, characteristic, complemented
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1622—31nomaximal
9#68244C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C3×#946—21no—
12C2×C3×#215—21no—
13C2×C3×D24—21no—
14C2×C3×#204—22no—
15C3×#896—22no—
16C3×D3×C4⋊C4—21no—
17C3×#874C2211yescharacteristic
18C3×C4×D12—21no—
19C3×C4×D12C2211yescharacteristic
20C3×#870—21no—
21C3×#869C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×C4×C8C2211yescharacteristic
24C3×#821—21no—
25C3×#809—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#554—31no—
28#5579C2×C311yescharacteristic, complemented
29C3×#492—31no—
30C3×#460—31no—
31C3×#459—31no—
32#5027C2×C311yescharacteristic, complemented
33#4843C2×C311yescharacteristic
34#4693C2×C311yescharacteristic, complemented
35C3×#333—31no—
36C3×Q8⋊C8—21no—
37C3×Q8⋊C8D311yescharacteristic, complemented
38C3×Q8⋊C8C2×C311yescharacteristic, complemented
39C3×D4⋊C8—31no—
40#4481C2×C311yescharacteristic, complemented
41#4459C2×C311yescharacteristic, complemented
42C2×C32×Q8D411yescharacteristic
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×Dic6D412yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C42—21no—
55C32×C42C2311yescharacteristic
56C3×#215—42no—
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—22no—
64C2×C3×C3⋊C8—21no—
65C3×D24—42no—
66C3×#204—44no—
67#1622—31noSylow
68C2×C3×SD16—62no—
69C2×C3×SD16—61no—
70C2×C3×D8—61no—
71C3×C4⋊Q8—31no—
72C3×#127—31no—
73C3×#125—61no—
74C3×C22⋊Q8—62no—
75C3×C22⋊Q8—61no—
76C3×C4×Q8—21no—
77C3×C4×Q8C2×D311yescharacteristic
78C3×C4×Q8C22×C311yescharacteristic
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81C2×C3×C4⋊C4—61no—
82#946—21no—
83C2×#215—21no—
84C2×D24—21no—
85C2×#204—22no—
86#896—22no—
87D3×C4⋊C4—21no—
88#874C22×C311yescharacteristic
89C4×D12—21no—
90C4×D12C22×C311yescharacteristic
91#870—21no—
92#869C22×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—21no—
106C22×C3×D3—41no—
107C32×Q8—21no—
108C32×Q8—21no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C3×D12—21no—
117C3×D12—42no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12SD1612yescomplemented
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×C4×D3—82no—
126C3×Dic6—42no—
127C32×C8—22no—
128C32×C8—41no—
129C3×C3⋊C8—41no—
130#554—31no—
131#492—31no—
132#460—31no—
133#459—31no—
134#333—31no—
135Q8⋊C8C3×D311yescharacteristic, complemented
136D4⋊C8—31no—
137C2×C3×Q8—21no—
138C2×C3×Q8—32no—
139C2×C3×Q8D1211yescharacteristic
140C2×C3×Q8C3×D411yescharacteristic
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×D412yes—
154C3×SD16—124no—
155C3×SD16—122no—
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—31no—
168C3×C4⋊C4—41no—
169C3×C4⋊C4—62no—
170C3×C4⋊C4—62no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4D1211yescharacteristic
174C3×C4⋊C4C3×D411yescharacteristic
175C3×C22⋊C4—62no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42—21no—
180C3×C42—41no—
181C3×C42C22×D311yescharacteristic
182C3×C42C23×C311yescharacteristic
183#215—42no—
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3C3×D411yescharacteristic
189Dic3⋊C4—22no—
190Dic3⋊C4—22no—
191C2×C3⋊C8—21no—
192D24—42no—
193#204—44no—
194C22×C32#12011yescharacteristic
195C2×C3×D3—22no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—81no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C32×C4—21no—
202C32×C4—41no—
203C32×C4—41no—
204C32×C4C2×SD1611yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4#13711yescharacteristic
208C3×Dic3—41no—
209C3×Dic3—42no—
210C2×SD16—62no—
211C2×SD16—61no—
212C2×D8—61no—
213C4⋊Q8—31no—
214#127—31no—
215#125—61no—
216C22⋊Q8—62no—
217C22⋊Q8—61no—
218C4×Q8C2×C3×D311yescharacteristic
219C4×D4—31no—
220C4×D4—61no—
221C2×C4⋊C4—61no—
222C4⋊C8—31no—
223C4⋊C8C2×C3×D311yescharacteristic
224#102—61no—
225#102—61no—
226C4×C8C2×C3×D311yescharacteristic
227C23×C3—61no—
228C23×C3—121no—
229C22×D3—21no—
230C22×D3—41no—
231C3×Q8—22no—
232C3×Q8—21no—
233C3×Q8—21no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—41no—
237C3×Q8—122no—
238C3×D4—32no—
239C3×D4—61no—
240C3×D4—122no—
241C3×D4—121no—
242C3×D4—121no—
243C3×D4—121no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—61no—
255C2×C3×C4—62no—
256C2×C3×C4—121no—
257C2×C3×C4—121no—
258C2×C3×C4—242no—
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4C2×C3×D411yescharacteristic
263C2×C3×C4C2×C3×D411yescharacteristic
264C2×C3×C4C2×C3×D411yescharacteristic
265C2×Dic3—21no—
266C2×Dic3—22no—
267D12—21no—
268D12—42no—
269D12—41no—
270D12—41no—
271D12—41no—
272D12—41no—
273D12C3×SD1612yescomplemented
274C4×D3—41no—
275C4×D3—41no—
276C4×D3—82no—
277Dic6—42no—
278C3×C8—22no—
279C3×C8—22no—
280C3×C8—42no—
281C3×C8—41no—
282C3×C8—41no—
283C3×C8—81no—
284C3×C8—121no—
285C3⋊C8—41no—
286C2×C32#44811yescharacteristic
287C2×C32#44911yescharacteristic
288C2×C32#45311yescharacteristic
289C3×D3—42no—
290C3×D3—161no—
291C2×Q8—32no—
292C2×Q8C3×D1211yescharacteristic
293C2×D4—31no—
294C2×D4—61no—
295C2×D4—61no—
296C2×D4—61no—
297C22×C4—62no—
298C22×C4—61no—
299SD16—124no—
300SD16—122no—
301D8—122no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—61no—
305C4⋊C4—21no—
306C4⋊C4—31no—
307C4⋊C4—62no—
308C4⋊C4—62no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4C3×D1211yescharacteristic
312C22⋊C4—62no—
313C22⋊C4—61no—
314C42—21no—
315C42C22×C3×D311yescharacteristic
316C22×C3—21no—
317C22×C3—62no—
318C22×C3—121no—
319C22×C3—121no—
320C22×C3—241no—
321C22×C3—241no—
322C22×C3—241no—
323C22×C3#88211yescharacteristic
324C22×C3C3×#12011yescharacteristic
325C2×D3—22no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—81no—
329C2×D3—81no—
330C2×D3—81no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—41no—
338C3×C4—42no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—81no—
344C3×C4—121no—
345C3×C4—122no—
346C3×C4#90411yescharacteristic
347C3×C4#90811yescharacteristic
348C3×C4D3×SD1611yescharacteristic
349C3×C4#91811yescharacteristic
350C3×C4C2×C3×SD1611yescharacteristic
351C3×C4C3×#13511yescharacteristic
352C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
353C3×C4C3×#13711yescharacteristic
354Dic3—41no—
355Dic3—42no—
356C32#162211yescharacteristic, complemented, Sylow
357C23—61no—
358C23—121no—
359Q8—21no—
360Q8—21no—
361Q8—122no—
362D4—32no—
363D4—61no—
364D4—122no—
365D4—121no—
366D4—121no—
367D4—121no—
368D4—121no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—61no—
372C2×C4—62no—
373C2×C4—121no—
374C2×C4—121no—
375C2×C4—242no—
376C2×C4C2×C3×D1211yescharacteristic
377C2×C4C3×D3×D411yescharacteristic
378C2×C4C3×D3×D411yescharacteristic
379C8—22no—
380C8—41no—
381C8—121no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—122no—
386C2×C3—481no—
387C2×C3#473411yescharacteristic
388C2×C3#480611yescharacteristic
389C2×C3#482211yescharacteristic
390C2×C3C3×#44811yescharacteristic
391C2×C3C3×#44911yescharacteristic
392C2×C3C3×#45311yescharacteristic
393D3—42no—
394D3—161no—
395C22—62no—
396C22—121no—
397C22—121no—
398C22—241no—
399C22—241no—
400C22—241no—
401C22C3×#88211yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—121no—
406C4—122no—
407C4C3×#90411yescharacteristic
408C4C3×#90811yescharacteristic
409C4C3×D3×SD1611yescharacteristic
410C4C3×#91811yescharacteristic
411C3—21no—
412C3#6824411yescharacteristic, direct product factor
413C3C3×#162211yescharacteristic, complemented
414C2—122no—
415C2—481no—
416C2C3×#473411yescharacteristic
417C2C3×#480611yescharacteristic
418C2C3×#482211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
prime radicalC3×#4843C2
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1622
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×#5579C2semidirect
2. C3×#5027C2semidirect
4. C3×#4693C2semidirect
5. C32×Q8⋊C8C2semidirect
6. C3×#4481C2semidirect
7. C3×#4459C2semidirect
9. #68244C3direct (N × H)
28. #5579C2×C3semidirect
32. #5027C2×C3semidirect
34. #4693C2×C3semidirect
37. C3×Q8⋊C8D3semidirect
38. C3×Q8⋊C8C2×C3semidirect
40. #4481C2×C3semidirect
41. #4459C2×C3semidirect
122. C3×D12SD16semidirect
135. Q8⋊C8C3×D3semidirect
273. D12C3×SD16semidirect
356. C32#1622semidirect
412. C3#68244direct (N × H)
413. C3C3×#1622semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×#50272
C3×#48432
C3×#46932
C32×Q8⋊C82
C3×#44812
C3×#44592
C3×#16223
#682443