Finite Group Databasebeta

← C3×#71049 #11780226

Subgroups — C3×#71049 #11780226

Order 1152.

460 conjugacy classes of subgroups.

The subgroup lattice has 401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5542C211yesmaximal, characteristic
2C32×#461C211yesmaximal, characteristic
3C3×#5094C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1650—31nomaximal
9#71049C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4×D4C2211yescharacteristic
13C3×#936—21no—
14C3×#926—21no—
15C3×#924—21no—
16C3×#887—21no—
17C3×#879—22no—
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×#103—21no—
22C3×#810—21no—
23C3×#808—21no—
24C3×#807—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#556—31no—
28#5542C2×C311yescharacteristic
29C3×#500—31no—
30C3×#475—31no—
31C3×#461—21no—
32C3×#461D311yescharacteristic
33C3×#461C2×C311yescharacteristic
34#5094C2×C311yescharacteristic, complemented
35#5078C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39D4⋊(C3⋊C8)C2×C311yescharacteristic
40#4484C2×C311yescharacteristic, complemented
41#4482C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C32×SD16—42no—
48C2×C32×C8—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2311yescharacteristic
54C3×#217—22no—
55C3×#217—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D412yes—
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—22no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—22no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1650—31noSylow
66C2×C3×SD16—22no—
67C2×C3×SD16—21no—
68C2×C3×SD16—21no—
69C3×C4⋊Q8—21no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8C2×D311yescharacteristic
72C3×C4⋊Q8C22×C311yescharacteristic
73C3×#126—62no—
74C3×#124—61no—
75C3×C22⋊Q8—61no—
76C3×C4×Q8—31no—
77C3×C4×Q8—61no—
78C3×C4×D4—21no—
79C3×C4×D4C2×D311yescharacteristic
80C3×C4×D4C22×C311yescharacteristic
81C3×#117—61no—
82#936—21no—
83#926—21no—
84#924—21no—
85#887—21no—
86#879—22no—
87#869C22×C311yescharacteristic
88C4×Dic6C22×C311yescharacteristic
89C3×#107—62no—
90C3×#106—61no—
91C3×C4⋊C8—21no—
92C3×C4⋊C8—31no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C22×C311yescharacteristic
95C3×#103—22no—
96C3×#103—21no—
97C3×#103—21no—
98C3×#103—61no—
99C3×C4×C8—31no—
100#810—21no—
101#808—21no—
102#807—22no—
103C4⋊(C3⋊C8)C22×C311yescharacteristic
104C4×C3⋊C8C22×C311yescharacteristic
105C23×C32—21no—
106C32×Q8—41no—
107C32×Q8—41no—
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
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—22no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C32×C8—41no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127#556—31no—
128#500—31no—
129#475—31no—
130#461C3×D311yescharacteristic
131#332—31no—
132Q8⋊C8—31no—
133D4⋊C8—31no—
134C2×C3×Q8—22no—
135C2×C3×Q8—21no—
136C2×C3×Q8—21no—
137C2×C3×Q8—31no—
138C2×C3×Q8—61no—
139C2×C3×D4—21no—
140C2×C3×D4#6711yescharacteristic
141C2×C3×D4C3×D411yescharacteristic
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—41no—
145C2×Dic6—21no—
146C2×Dic6C3×D411yescharacteristic
147C3×SD16—44no—
148C3×SD16—42no—
149C3×SD16—42no—
150C2×C3×C8—22no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—32no—
162C3×C4⋊C4—41no—
163C3×C4⋊C4—41no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4#6711yescharacteristic
168C3×C4⋊C4C3×D411yescharacteristic
169C3×C22⋊C4—21no—
170C3×C22⋊C4—21no—
171C3×C22⋊C4—41no—
172C3×C22⋊C4—62no—
173C3×C22⋊C4—62no—
174C3×C42—21no—
175C3×C42—62no—
176C3×C42—61no—
177C3×C42C22×D311yescharacteristic
178C3×C42C23×C311yescharacteristic
179#217—22no—
180#217—22no—
181C4⋊Dic3—21no—
182C4⋊Dic3C3×D412yes—
183C4⋊Dic3C3×D411yescharacteristic
184Dic3⋊C4—22no—
185Dic3⋊C4—21no—
186C4×Dic3—22no—
187C4×Dic3—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32#12011yescharacteristic
194C32×C4—21no—
195C32×C4—41no—
196C32×C4—81no—
197C32×C4#13511yescharacteristic
198C32×C4#13511yescharacteristic
199C32×C4AGL(1,ℤ/8)11yescharacteristic
200C32×C4#13711yescharacteristic
201C3×Dic3—42no—
202C3×Dic3—41no—
203C3×Dic3—41no—
204C2×SD16—21no—
205C4⋊Q8—31no—
206C4⋊Q8C2×C3×D311yescharacteristic
207#126—62no—
208#124—61no—
209C22⋊Q8—61no—
210C4×Q8—31no—
211C4×Q8—61no—
212C4×D4C2×C3×D311yescharacteristic
213#117—61no—
214#107—62no—
215#106—61no—
216C4⋊C8—31no—
217C4⋊C8C2×C3×D311yescharacteristic
218#103—21no—
219#103—61no—
220C4×C8—31no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—41no—
224C3×Q8—42no—
225C3×Q8—42no—
226C3×Q8—41no—
227C3×Q8—41no—
228C3×Q8—41no—
229C3×Q8—41no—
230C3×Q8—61no—
231C3×Q8—61no—
232C3×Q8—121no—
233C3×Q8—121no—
234C3×D4—22no—
235C3×D4—21no—
236C3×D4—21no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—41no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—42no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—61no—
254C2×C3×C4—62no—
255C2×C3×C4—61no—
256C2×C3×C4—81no—
257C2×C3×C4—81no—
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4C2×#6711yescharacteristic
261C2×C3×C4C2×C3×D411yescharacteristic
262C2×C3×C4C2×C3×D411yescharacteristic
263C2×C3×C4C2×C3×D411yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—22no—
267Dic6—21no—
268Dic6—21no—
269Dic6—41no—
270Dic6—41no—
271C3×C8—42no—
272C3×C8—41no—
273C3×C8—41no—
274C3×C8—62no—
275C3×C8—121no—
276C3⋊C8—22no—
277C3⋊C8—41no—
278C2×C32—81no—
279C2×C32#44911yescharacteristic
280C2×C32#45211yescharacteristic
281C2×C32#45611yescharacteristic
282C2×Q8—21no—
283C2×Q8—31no—
284C2×Q8—61no—
285C2×D4C3×#6711yescharacteristic
286C22×C4—21no—
287SD16—42no—
288C2×C8—21no—
289C2×C8—61no—
290C2×C8—61no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—31no—
294C4⋊C4—32no—
295C4⋊C4—62no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4C3×#6711yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C42—62no—
303C42—61no—
304C42C22×C3×D311yescharacteristic
305C22×C3—21no—
306C22×C3—42no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—81no—
314C22×C3—81no—
315C22×C3#93711yescharacteristic
316C22×C3C3×#12011yescharacteristic
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—41no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—81no—
327C3×C4—82no—
328C3×C4—81no—
329C3×C4—81no—
330C3×C4—121no—
331C3×C4—121no—
332C3×C4—122no—
333C3×C4#91511yescharacteristic
334C3×C4#91611yescharacteristic
335C3×C4#93211yescharacteristic
336C3×C4#95011yescharacteristic
337C3×C4C3×#13511yescharacteristic
338C3×C4C3×#13511yescharacteristic
339C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
340C3×C4C3×#13711yescharacteristic
341Dic3—42no—
342Dic3—41no—
343Dic3—41no—
344C32#165011yescharacteristic, complemented, Sylow
345C23—21no—
346Q8—41no—
347Q8—41no—
348Q8—61no—
349Q8—61no—
350Q8—121no—
351Q8—121no—
352D4—21no—
353D4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—61no—
359C2×C4—62no—
360C2×C4—61no—
361C2×C4C3×D3×D411yescharacteristic
362C2×C4C3×D3×D411yescharacteristic
363C2×C4C2×C3×#6711yescharacteristic
364C8—41no—
365C8—62no—
366C8—121no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—82no—
371C2×C3—81no—
372C2×C3—81no—
373C2×C3#503711yescharacteristic
374C2×C3#517311yescharacteristic
375C2×C3#520511yescharacteristic
376C2×C3C3×#44911yescharacteristic
377C2×C3C3×#45211yescharacteristic
378C2×C3C3×#45611yescharacteristic
379C22—41no—
380C22—41no—
381C22—41no—
382C22C3×#93711yescharacteristic
383C4—21no—
384C4—41no—
385C4—81no—
386C4—121no—
387C4—121no—
388C4—122no—
389C4C3×#91511yescharacteristic
390C4C3×#91611yescharacteristic
391C4C3×#93211yescharacteristic
392C4C3×#95011yescharacteristic
393C3—21no—
394C3#7104911yescharacteristic, direct product factor
395C3C3×#165011yescharacteristic, complemented
396C2—81no—
397C2C3×#503711yescharacteristic
398C2C3×#517311yescharacteristic
399C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#461C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC3×#461D3
hypocenterC3C3×#1650
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
3. C3×#5094C2semidirect
4. C3×#5078C2semidirect
6. C3×#4484C2semidirect
7. C3×#4482C2semidirect
9. #71049C3direct (N × H)
34. #5094C2×C3semidirect
35. #5078C2×C3semidirect
40. #4484C2×C3semidirect
41. #4482C2×C3semidirect
344. C32#1650semidirect
394. C3#71049direct (N × H)
395. C3C3×#1650semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
C32×#4612
C3×#50942
C3×#50782
C3×D4⋊(C3⋊C8)2
C3×#44842
C3×#44822
C3×#16503
#710493