Finite Group Databasebeta

← C3×#68270 #11779955

Subgroups — C3×#68270 #11779955

Order 1152.

451 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic, complemented
3C3×#4846C211yesmaximal, characteristic
4C3×#4681C211yesmaximal, characteristic, complemented
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic
8C3×#1644—31nomaximal
9#68270C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C3×#946—21no—
12C2×C3×#216—21no—
13C3×#896—22no—
14C3×D3×C4⋊C4—21no—
15C3×C4×D12—21no—
16C3×C4×D12C2211yescharacteristic
17C3×#870—21no—
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22C3×#821—21no—
23C3×#818—21no—
24C3×#816—22no—
25C3×#810—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#554—31no—
28#5579C2×C311yescharacteristic
29C3×#487—31no—
30C3×#474—31no—
31C3×#462—31no—
32#5031C2×C311yescharacteristic, complemented
33#4846C2×C311yescharacteristic
34#4681C2×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
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—22no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D412yes—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C42—21no—
53C32×C42C2311yescharacteristic
54C3×#216—42no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—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—
65#1644—31noSylow
66C2×C3×Q16—61no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8—31no—
69C3×#125—61no—
70C3×C22⋊Q8—62no—
71C3×C22⋊Q8—61no—
72C3×C4×Q8—21no—
73C3×C4×Q8C2×D311yescharacteristic
74C3×C4×Q8C22×C311yescharacteristic
75C3×C4×D4—31no—
76C3×C4×D4—61no—
77C2×C3×C4⋊C4—61no—
78#946—21no—
79C2×#216—21no—
80#896—22no—
81D3×C4⋊C4—21no—
82C4×D12—21no—
83C4×D12C22×C311yescharacteristic
84#870—21no—
85#869C22×C311yescharacteristic
86#869C22×C311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C22×C311yescharacteristic
92C3×#103—62no—
93C3×#103—61no—
94C3×#102—61no—
95C3×C4×C8—21no—
96C3×C4×C8C2×D311yescharacteristic
97C3×C4×C8C22×C311yescharacteristic
98#821—21no—
99#818—21no—
100#816—22no—
101#810—21no—
102C4⋊(C3⋊C8)C22×C311yescharacteristic
103C22×C3×D3—21no—
104C32×Q8—21no—
105C32×Q8—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3×Dic3—21no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—41no—
114C3×D12—21no—
115C3×D12Q1612yescomplemented
116C3×C4×D3—41no—
117C3×C4×D3—41no—
118C3×C4×D3—82no—
119C3×Dic6—42no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C32×C8—41no—
123C32×C8—41no—
124C3×C3⋊C8—41no—
125#554—31no—
126#487—31no—
127#474—31no—
128#462—31no—
129#333—31no—
130Q8⋊C8C3×D311yescharacteristic, complemented
131D4⋊C8—31no—
132C2×C3×Q8—21no—
133C2×C3×Q8—32no—
134C2×C3×Q8—61no—
135C2×C3×Q8D1211yescharacteristic
136C2×C3×Q8C3×D411yescharacteristic
137C2×C3×D4—31no—
138C22×C3×C4—62no—
139C22×C3×C4—61no—
140C2×D12C3×D411yescharacteristic
141C2×C4×D3—21no—
142C2×C4×D3—22no—
143C2×Dic6—21no—
144C2×Dic6C3×D412yes—
145C3×Q16—122no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—41no—
151C2×C3×C8—41no—
152C2×C3×C8—61no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—41no—
158C3×C4⋊C4—62no—
159C3×C4⋊C4—62no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4D1211yescharacteristic
165C3×C4⋊C4C3×D411yescharacteristic
166C3×C22⋊C4—62no—
167C3×C22⋊C4—61no—
168C3×C42—21no—
169C3×C42—21no—
170C3×C42—21no—
171C3×C42—41no—
172C3×C42C22×D311yescharacteristic
173C3×C42C23×C311yescharacteristic
174#216—42no—
175(C2×D3)⋊C4—22no—
176(C2×D3)⋊C4—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3C3×D411yescharacteristic
182Dic3⋊C4—22no—
183Dic3⋊C4—22no—
184C2×C3⋊C8—21no—
185C22×C32#12011yescharacteristic
186C2×C3×D3—22no—
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C32×C4—21no—
190C32×C4—41no—
191C32×C4—41no—
192C32×C4C2×Q1611yescharacteristic
193C32×C4#13511yescharacteristic
194C32×C4AGL(1,ℤ/8)11yescharacteristic
195C32×C4#13711yescharacteristic
196C3×Dic3—41no—
197C3×Dic3—42no—
198C3×Dic3—81no—
199C2×Q16—61no—
200C4⋊Q8—31no—
201C4⋊Q8—31no—
202#125—61no—
203C22⋊Q8—62no—
204C22⋊Q8—61no—
205C4×Q8C2×C3×D311yescharacteristic
206C4×D4—31no—
207C4×D4—61no—
208C2×C4⋊C4—61no—
209#107—61no—
210C4⋊C8—31no—
211C4⋊C8C2×C3×D311yescharacteristic
212#103—62no—
213#103—61no—
214#102—61no—
215C4×C8C2×C3×D311yescharacteristic
216C23×C3—61no—
217C22×D3—21no—
218C3×Q8—22no—
219C3×Q8—21no—
220C3×Q8—21no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×Q8—41no—
224C3×Q8—122no—
225C3×Q8—121no—
226C3×Q8—121no—
227C3×D4—32no—
228C3×D4—61no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—61no—
239C2×C3×C4—62no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4—242no—
244C2×C3×C4C2×D1211yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4C2×C3×D411yescharacteristic
248C2×C3×C4C2×C3×D411yescharacteristic
249C2×C3×C4C2×C3×D411yescharacteristic
250C2×Dic3—21no—
251C2×Dic3—22no—
252C2×Dic3—41no—
253D12—21no—
254D12C3×Q1612yescomplemented
255C4×D3—41no—
256C4×D3—41no—
257C4×D3—82no—
258Dic6—42no—
259Dic6—41no—
260Dic6—41no—
261C3×C8—41no—
262C3×C8—41no—
263C3×C8—42no—
264C3×C8—41no—
265C3×C8—41no—
266C3×C8—81no—
267C3×C8—121no—
268C3⋊C8—41no—
269C2×C32#44911yescharacteristic
270C2×C32#45111yescharacteristic
271C2×C32#45511yescharacteristic
272C3×D3—42no—
273C2×Q8—32no—
274C2×Q8—61no—
275C2×Q8C3×D1211yescharacteristic
276C2×D4—31no—
277C22×C4—62no—
278C22×C4—61no—
279Q16—122no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—61no—
283C4⋊C4—21no—
284C4⋊C4—31no—
285C4⋊C4—62no—
286C4⋊C4—62no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4C3×D1211yescharacteristic
292C22⋊C4—62no—
293C22⋊C4—61no—
294C42—21no—
295C42C22×C3×D311yescharacteristic
296C22×C3—21no—
297C22×C3—62no—
298C22×C3—121no—
299C22×C3—121no—
300C22×C3#88211yescharacteristic
301C22×C3C3×#12011yescharacteristic
302C2×D3—22no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—42no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—81no—
318C3×C4—121no—
319C3×C4—122no—
320C3×C4—241no—
321C3×C4#90411yescharacteristic
322C3×C4#90811yescharacteristic
323C3×C4#91511yescharacteristic
324C3×C4D3×Q1611yescharacteristic
325C3×C4C2×C3×Q1611yescharacteristic
326C3×C4C3×#13511yescharacteristic
327C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
328C3×C4C3×#13711yescharacteristic
329Dic3—41no—
330Dic3—42no—
331Dic3—81no—
332C32#164411yescharacteristic, complemented, Sylow
333C23—61no—
334Q8—21no—
335Q8—21no—
336Q8—122no—
337Q8—121no—
338Q8—121no—
339D4—32no—
340D4—61no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—61no—
344C2×C4—62no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4—121no—
348C2×C4—242no—
349C2×C4C2×C3×D1211yescharacteristic
350C2×C4C3×D3×D411yescharacteristic
351C2×C4C3×D3×D411yescharacteristic
352C8—41no—
353C8—41no—
354C8—121no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—122no—
359C2×C3#473411yescharacteristic
360C2×C3#480911yescharacteristic
361C2×C3#482511yescharacteristic
362C2×C3C3×#44911yescharacteristic
363C2×C3C3×#45111yescharacteristic
364C2×C3C3×#45511yescharacteristic
365D3—42no—
366C22—62no—
367C22—121no—
368C22—121no—
369C22C3×#88211yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—121no—
374C4—122no—
375C4—241no—
376C4C3×#90411yescharacteristic
377C4C3×#90811yescharacteristic
378C4C3×#91511yescharacteristic
379C4C3×D3×Q1611yescharacteristic
380C3—21no—
381C3#6827011yescharacteristic, direct product factor
382C3C3×#164411yescharacteristic, complemented
383C2—122no—
384C2C3×#473411yescharacteristic
385C2C3×#480911yescharacteristic
386C2C3×#482511yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1644
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
2. C3×#5031C2semidirect
4. C3×#4681C2semidirect
5. C32×Q8⋊C8C2semidirect
6. C3×#4481C2semidirect
9. #68270C3direct (N × H)
32. #5031C2×C3semidirect
34. #4681C2×C3semidirect
37. C3×Q8⋊C8D3semidirect
38. C3×Q8⋊C8C2×C3semidirect
40. #4481C2×C3semidirect
115. C3×D12Q16semidirect
130. Q8⋊C8C3×D3semidirect
254. D12C3×Q16semidirect
332. C32#1644semidirect
381. C3#68270direct (N × H)
382. C3C3×#1644semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×#50312
C3×#48462
C3×#46812
C32×Q8⋊C82
C3×#44812
C3×#44592
C3×#16443
#682703