Finite Group Databasebeta

← C3×#71145 #11779484

Subgroups — C3×#71145 #11779484

Order 1152.

490 conjugacy classes of subgroups.

The subgroup lattice has 415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5563C211yesmaximal, characteristic
2C32×#476C211yesmaximal, characteristic, complemented
3C3×#5092C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7C3×#4481C211yesmaximal, characteristic, complemented
8C3×#1634—31nomaximal
9#71145C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C2×C3×#216—22no—
13C3×#938—21no—
14C3×#930—21no—
15C3×#926—21no—
16C3×#892—21no—
17C3×#885—22no—
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C32×#106—21no—
21C32×C4⋊C8C2211yescharacteristic
22C32×#102—21no—
23C3×#809—21no—
24C3×#808—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#555—31no—
28#5563C2×C311yescharacteristic
29C3×#494—31no—
30C3×#476—21no—
31C3×#476—31no—
32C3×#476D311yescharacteristic, complemented
33C3×#476C2×C311yescharacteristic, complemented
34#5092C2×C311yescharacteristic, complemented
35#5084C2×C311yescharacteristic, complemented
36C3×#333—31no—
37C3×D4⋊C8—31no—
38C3×D4⋊C8—31no—
39D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
40#4483C2×C311yescharacteristic, complemented
41#4481C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C2×C3×#67—22no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D412yes—
49C2×C32×C8—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C22⋊C4—21no—
54C32×C42C2311yescharacteristic
55C3×#217—22no—
56C3×#216—44no—
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4×Dic3—22no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1634—31noSylow
66C2×C3×Q16—62no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C22×C311yescharacteristic
71C3×#124—62no—
72C3×#121—61no—
73C3×#121—61no—
74C3×C4×D4—21no—
75C3×C4×D4—31no—
76C3×C4×D4C2×D311yescharacteristic
77C3×C4×D4C22×C311yescharacteristic
78C3×#117—61no—
79C3×#117—61no—
80C2×#216—22no—
81#938—21no—
82#930—21no—
83#926—21no—
84#892—21no—
85#885—22no—
86C4×D12C22×C311yescharacteristic
87#869C22×C311yescharacteristic
88C3×#106—22no—
89C3×#106—21no—
90C3×#106—21no—
91C3×#106—61no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8—31no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C22×C311yescharacteristic
96C3×#102—22no—
97C3×#102—21no—
98C3×#102—21no—
99C3×#102—61no—
100C3×C4×C8—31no—
101#809—21no—
102#808—21no—
103C4⋊(C3⋊C8)C22×C311yescharacteristic
104C4×C3⋊C8C22×C311yescharacteristic
105C23×C32—21no—
106C22×C3×D3—21no—
107C32×Q8—42no—
108C32×D4—21no—
109C32×D4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C3×#67—82no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—22no—
120C3×D12—21no—
121C3×D12—21no—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×Dic6—42no—
125C32×C8—41no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—41no—
128#555—31no—
129#494—31no—
130#476—31no—
131#476C3×D311yescharacteristic, complemented
132#333—31no—
133D4⋊C8—31no—
134D4⋊C8—31no—
135C2×C3×Q8—21no—
136C2×C3×Q8—21no—
137C2×C3×Q8—32no—
138C2×C3×Q8—41no—
139C2×C3×D4—21no—
140C2×C3×D4—31no—
141C2×C3×D4—62no—
142C2×C3×D4#6711yescharacteristic
143C2×C3×D4C3×D411yescharacteristic
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—41no—
147C22×C3×C4—61no—
148C2×#67—22no—
149C2×D12C3×D411yescharacteristic
150C2×C4×D3—21no—
151C2×Dic6C3×D412yes—
152C3×Q16—124no—
153C2×C3×C8—22no—
154C2×C3×C8—21no—
155C2×C3×C8—21no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—41no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4#6711yescharacteristic
169C3×C4⋊C4C3×D411yescharacteristic
170C3×C22⋊C4—21no—
171C3×C22⋊C4—21no—
172C3×C22⋊C4—41no—
173C3×C22⋊C4—62no—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—61no—
176C3×C42—21no—
177C3×C42—62no—
178C3×C42C22×D311yescharacteristic
179C3×C42C23×C311yescharacteristic
180#217—22no—
181#216—44no—
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3C3×D411yescharacteristic
187C4×Dic3—22no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32#12011yescharacteristic
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C32×C4—21no—
198C32×C4—41no—
199C32×C4—81no—
200C32×C4#13511yescharacteristic
201C32×C4#13511yescharacteristic
202C32×C4#13711yescharacteristic
203C32×C4#13711yescharacteristic
204C3×Dic3—41no—
205C3×Dic3—42no—
206C2×Q16—62no—
207C4⋊Q8—31no—
208C4⋊Q8C2×C3×D311yescharacteristic
209#124—62no—
210#121—61no—
211#121—61no—
212C4×D4—31no—
213C4×D4C2×C3×D311yescharacteristic
214#117—61no—
215#117—61no—
216#106—21no—
217#106—61no—
218C4⋊C8—31no—
219C4⋊C8C2×C3×D311yescharacteristic
220#102—21no—
221#102—61no—
222C4×C8—31no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—41no—
226C23×C3—61no—
227C22×D3—21no—
228C3×Q8—42no—
229C3×Q8—42no—
230C3×Q8—82no—
231C3×Q8—122no—
232C3×D4—22no—
233C3×D4—21no—
234C3×D4—21no—
235C3×D4—21no—
236C3×D4—21no—
237C3×D4—41no—
238C3×D4—61no—
239C3×D4—61no—
240C3×D4—242no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—42no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—61no—
255C2×C3×C4—62no—
256C2×C3×C4—81no—
257C2×C3×C4—81no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×C3×C4C2×C3×D411yescharacteristic
264C2×C3×C4C2×C3×D411yescharacteristic
265C2×C3×C4C2×C3×D411yescharacteristic
266#67—82no—
267C2×Dic3—21no—
268C2×Dic3—22no—
269D12—21no—
270D12—21no—
271C4×D3—41no—
272C4×D3—41no—
273Dic6—42no—
274C3×C8—42no—
275C3×C8—41no—
276C3×C8—41no—
277C3×C8—62no—
278C3×C8—121no—
279C3⋊C8—22no—
280C3⋊C8—41no—
281C2×C32—81no—
282C2×C32#45211yescharacteristic
283C2×C32#45211yescharacteristic
284C2×C32#45311yescharacteristic
285C3×D3—81no—
286C2×Q8—21no—
287C2×Q8—32no—
288C2×D4—31no—
289C2×D4—62no—
290C2×D4C3×#6711yescharacteristic
291C22×C4—21no—
292C22×C4—61no—
293Q16—124no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—61no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—31no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4C3×#6711yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—62no—
305C22⋊C4—62no—
306C22⋊C4—61no—
307C42—62no—
308C42C22×C3×D311yescharacteristic
309C22×C3—21no—
310C22×C3—42no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—81no—
318C22×C3—81no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3—121no—
322C22×C3#93711yescharacteristic
323C22×C3C3×#12011yescharacteristic
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—41no—
334C3×C4—41no—
335C3×C4—41no—
336C3×C4—81no—
337C3×C4—82no—
338C3×C4—81no—
339C3×C4—81no—
340C3×C4—122no—
341C3×C4—121no—
342C3×C4#91511yescharacteristic
343C3×C4#91611yescharacteristic
344C3×C4#94211yescharacteristic
345C3×C4#95011yescharacteristic
346C3×C4C3×#13511yescharacteristic
347C3×C4C3×#13511yescharacteristic
348C3×C4C3×#13711yescharacteristic
349C3×C4C3×#13711yescharacteristic
350Dic3—41no—
351Dic3—42no—
352C32#163411yescharacteristic, complemented, Sylow
353C23—21no—
354C23—61no—
355Q8—42no—
356Q8—122no—
357D4—21no—
358D4—21no—
359D4—61no—
360D4—61no—
361D4—242no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—61no—
367C2×C4—62no—
368C2×C4—121no—
369C2×C4—121no—
370C2×C4C3×D3×D411yescharacteristic
371C2×C4C3×D3×D411yescharacteristic
372C2×C4C2×C3×#6711yescharacteristic
373C8—41no—
374C8—62no—
375C8—121no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—82no—
380C2×C3—81no—
381C2×C3—81no—
382C2×C3—241no—
383C2×C3#504711yescharacteristic
384C2×C3#517311yescharacteristic
385C2×C3#519811yescharacteristic
386C2×C3C3×#45211yescharacteristic
387C2×C3C3×#45211yescharacteristic
388C2×C3C3×#45311yescharacteristic
389D3—81no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—121no—
394C22—121no—
395C22—121no—
396C22C3×#93711yescharacteristic
397C4—21no—
398C4—41no—
399C4—81no—
400C4—122no—
401C4—121no—
402C4C3×#91511yescharacteristic
403C4C3×#91611yescharacteristic
404C4C3×#94211yescharacteristic
405C4C3×#95011yescharacteristic
406C3—21no—
407C3#7114511yescharacteristic, direct product factor
408C3C3×#163411yescharacteristic, complemented
409C2—81no—
410C2—241no—
411C2C3×#504711yescharacteristic
412C2C3×#517311yescharacteristic
413C2C3×#519811yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#476C2
socleC22×C32#120
prime radicalC3×#5563C2
hypercenterC3×#476D3
hypocenterC3C3×#1634
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
2. C32×#476C2semidirect
3. C3×#5092C2semidirect
4. C3×#5084C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. C3×#4483C2semidirect
7. C3×#4481C2semidirect
9. #71145C3direct (N × H)
32. C3×#476D3semidirect
33. C3×#476C2×C3semidirect
34. #5092C2×C3semidirect
35. #5084C2×C3semidirect
39. D4⋊(C3⋊C8)C2×C3semidirect
40. #4483C2×C3semidirect
41. #4481C2×C3semidirect
131. #476C3×D3semidirect
352. C32#1634semidirect
407. C3#71145direct (N × H)
408. C3C3×#1634semidirect

Maximal subgroups

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

subgroupindex
C3×#55632
C32×#4762
C3×#50922
C3×#50842
C3×D4⋊(C3⋊C8)2
C3×#44832
C3×#44812
C3×#16343
#711453