Finite Group Databasebeta

← C3×#71033 #11779042

Subgroups — C3×#71033 #11779042

Order 1152.

520 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2C32×#460C211yesmaximal, characteristic
3C3×#5076C211yesmaximal, characteristic
4C3×#5075C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4481C211yesmaximal, characteristic, complemented
8C3×#1623—31nomaximal
9#71033C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16—21no—
11C32×#127C2211yescharacteristic
12C32×C4×Q8C2211yescharacteristic
13C3×Q8×Dic3—21no—
14C2×C3×#214—21no—
15C2×C3×#214—22no—
16C3×#888—22no—
17C3×#888—21no—
18C3×#869—21no—
19C3×#869C2211yescharacteristic
20C3×C4×Dic6—21no—
21C3×C4×Dic6C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×#102—21no—
24C3×#832—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×Q82—31no—
28Q8×Dic6C2×C311yescharacteristic, complemented
29C3×#492—31no—
30C3×#460—21no—
31C3×#460—31no—
32C3×#460D311yescharacteristic
33C3×#460C2×C311yescharacteristic
34#5076C2×C311yescharacteristic
35#5075C2×C311yescharacteristic
36C3×#333—31no—
37C3×Q8⋊C8—31no—
38C3×Q8⋊C8—31no—
39#4535C2×C311yescharacteristic, complemented
40#4484C2×C311yescharacteristic, complemented
41#4481C2×C311yescharacteristic, complemented
42C2×C32×Q8D411yescharacteristic
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6D411yescharacteristic
48C2×C3×Dic6D412yes—
49C32×SD16—42no—
50C2×C32×C8—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C42—21no—
54C32×C42C2311yescharacteristic
55C3×#214—44no—
56C3×#214—42no—
57C3×C4⋊Dic3—22no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—22no—
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—22no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1623—31noSylow
68C2×C3×SD16—22no—
69C2×C3×SD16—21no—
70C2×C3×SD16—21no—
71C2×C3×SD16—61no—
72C2×C3×SD16—62no—
73C3×C4⋊Q8—31no—
74C3×C4⋊Q8—61no—
75C3×C4⋊Q8—62no—
76C3×C4⋊Q8—61no—
77C3×#127—21no—
78C3×#127C2×D311yescharacteristic
79C3×#127C22×C311yescharacteristic
80C3×C4×Q8—21no—
81C3×C4×Q8—31no—
82C3×C4×Q8—61no—
83C3×C4×Q8—61no—
84C3×C4×Q8C2×D311yescharacteristic
85C3×C4×Q8C22×C311yescharacteristic
86Q8×Dic3—21no—
87C2×#214—21no—
88C2×#214—22no—
89#888—22no—
90#888—21no—
91#869—21no—
92#869C22×C311yescharacteristic
93C4×Dic6—21no—
94C4×Dic6C22×C311yescharacteristic
95C3×C4⋊C8—21no—
96C3×C4⋊C8—31no—
97C3×C4⋊C8C2×D311yescharacteristic
98C3×C4⋊C8C22×C311yescharacteristic
99C3×#102—22no—
100C3×#102—21no—
101C3×#102—21no—
102C3×#102—61no—
103C3×C4×C8—31no—
104#832—21no—
105C4⋊(C3⋊C8)C22×C311yescharacteristic
106C4×C3⋊C8C22×C311yescharacteristic
107C23×C32—41no—
108C32×Q8—21no—
109C32×Q8SD1612yescomplemented
110C32×D4—41no—
111C32×D4—41no—
112C32×D4—42no—
113C32×D4—41no—
114C32×D4—41no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—21no—
123C3×Dic6—21no—
124C3×Dic6—42no—
125C3×Dic6—82no—
126C3×Dic6SD1612yescomplemented
127C32×C8—41no—
128C3×C3⋊C8—22no—
129C3×C3⋊C8—41no—
130Q82—31no—
131#492—31no—
132#460—31no—
133#460C3×D311yescharacteristic
134#333—31no—
135Q8⋊C8—31no—
136Q8⋊C8—31no—
137C2×C3×Q8—21no—
138C2×C3×Q8—31no—
139C2×C3×Q8—32no—
140C2×C3×Q8—62no—
141C2×C3×Q8#6711yescharacteristic
142C2×C3×Q8C3×D411yescharacteristic
143C2×C3×D4—22no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×Dic6—22no—
153C2×Dic6C3×D411yescharacteristic
154C2×Dic6C3×D412yes—
155C3×SD16—44no—
156C3×SD16—42no—
157C3×SD16—42no—
158C3×SD16—124no—
159C3×SD16—122no—
160C2×C3×C8—22no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—41no—
170C3×C4⋊C4—62no—
171C3×C4⋊C4—62no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4#6711yescharacteristic
176C3×C4⋊C4C3×D411yescharacteristic
177C3×C42—21no—
178C3×C42—21no—
179C3×C42—21no—
180C3×C42—41no—
181C3×C42—62no—
182C3×C42—61no—
183C3×C42C22×D311yescharacteristic
184C3×C42C23×C311yescharacteristic
185#214—44no—
186#214—42no—
187C4⋊Dic3—22no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3C3×D411yescharacteristic
191Dic3⋊C4—22no—
192Dic3⋊C4—21no—
193C4×Dic3—22no—
194C4×Dic3—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C22×C32—81no—
198C22×C32—81no—
199C22×C32—81no—
200C22×C32#12011yescharacteristic
201C32×C4—22no—
202C32×C4—21no—
203C32×C4—41no—
204C32×C4C2×SD1611yescharacteristic
205C32×C4C2×SD1611yescharacteristic
206C32×C4#13711yescharacteristic
207C32×C4#13711yescharacteristic
208C3×Dic3—22no—
209C3×Dic3—42no—
210C3×Dic3—41no—
211C2×SD16—21no—
212C2×SD16—61no—
213C2×SD16—62no—
214C4⋊Q8—31no—
215C4⋊Q8—61no—
216C4⋊Q8—62no—
217C4⋊Q8—61no—
218#127C2×C3×D311yescharacteristic
219C4×Q8—31no—
220C4×Q8—61no—
221C4×Q8—61no—
222C4×Q8C2×C3×D311yescharacteristic
223C4⋊C8—31no—
224C4⋊C8C2×C3×D311yescharacteristic
225#102—21no—
226#102—61no—
227C4×C8—31no—
228C23×C3—42no—
229C23×C3—41no—
230C23×C3—41no—
231C3×Q8—21no—
232C3×Q8—21no—
233C3×Q8—22no—
234C3×Q8—32no—
235C3×Q8—41no—
236C3×Q8—61no—
237C3×Q8—122no—
238C3×Q8—242no—
239C3×Q8#21412yescomplemented
240C3×Q8C3×SD1612yescomplemented
241C3×D4—42no—
242C3×D4—42no—
243C3×D4—42no—
244C3×D4—42no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—81no—
254C3×D4—81no—
255C3×D4—82no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—62no—
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×C3×D411yescharacteristic
272C2×C3×C4C2×C3×D411yescharacteristic
273C2×C3×C4C2×C3×D411yescharacteristic
274C2×Dic3—21no—
275C2×Dic3—22no—
276C2×Dic3—21no—
277Dic6—21no—
278Dic6—42no—
279Dic6—82no—
280Dic6C3×SD1612yescomplemented
281C3×C8—42no—
282C3×C8—41no—
283C3×C8—41no—
284C3×C8—62no—
285C3×C8—121no—
286C3⋊C8—22no—
287C3⋊C8—41no—
288C2×C32—161no—
289C2×C32#44811yescharacteristic
290C2×C32#44811yescharacteristic
291C2×C32#45311yescharacteristic
292C2×Q8—31no—
293C2×Q8—32no—
294C2×Q8—62no—
295C2×Q8C3×#6711yescharacteristic
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299SD16—42no—
300SD16—124no—
301SD16—122no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—61no—
305C4⋊C4—21no—
306C4⋊C4—31no—
307C4⋊C4—62no—
308C4⋊C4—62no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4—61no—
312C4⋊C4C3×#6711yescharacteristic
313C42—21no—
314C42—62no—
315C42—61no—
316C42C22×C3×D311yescharacteristic
317C22×C3—21no—
318C22×C3—82no—
319C22×C3—82no—
320C22×C3—82no—
321C22×C3—81no—
322C22×C3—81no—
323C22×C3—81no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3—81no—
327C22×C3#93711yescharacteristic
328C22×C3C3×#12011yescharacteristic
329C3×C4—21no—
330C3×C4—22no—
331C3×C4—22no—
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—62no—
342C3×C4—81no—
343C3×C4—122no—
344C3×C4—121no—
345C3×C4D3×SD1611yescharacteristic
346C3×C4#91511yescharacteristic
347C3×C4C2×#21411yescharacteristic
348C3×C4#95111yescharacteristic
349C3×C4C2×C3×SD1611yescharacteristic
350C3×C4C2×C3×SD1611yescharacteristic
351C3×C4C3×#13711yescharacteristic
352C3×C4C3×#13711yescharacteristic
353Dic3—22no—
354Dic3—42no—
355Dic3—41no—
356C32#162311yescharacteristic, complemented, Sylow
357C23—41no—
358Q8—21no—
359Q8—32no—
360Q8—61no—
361Q8—122no—
362Q8—242no—
363Q8C3×#21412yescomplemented
364D4—42no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—62no—
374C2×C4C3×D3×D411yescharacteristic
375C2×C4C3×D3×D411yescharacteristic
376C2×C4C2×C3×#6711yescharacteristic
377C8—41no—
378C8—62no—
379C8—121no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—162no—
384C2×C3—161no—
385C2×C3—161no—
386C2×C3#504011yescharacteristic
387C2×C3#517011yescharacteristic
388C2×C3#519811yescharacteristic
389C2×C3C3×#44811yescharacteristic
390C2×C3C3×#44811yescharacteristic
391C2×C3C3×#45311yescharacteristic
392C22—81no—
393C22—81no—
394C22—81no—
395C22C3×#93711yescharacteristic
396C4—21no—
397C4—22no—
398C4—41no—
399C4—62no—
400C4—122no—
401C4—121no—
402C4C3×D3×SD1611yescharacteristic
403C4C3×#91511yescharacteristic
404C4C2×C3×#21411yescharacteristic
405C4C3×#95111yescharacteristic
406C3—21no—
407C3#7103311yescharacteristic, direct product factor
408C3C3×#162311yescharacteristic, complemented
409C2—161no—
410C2C3×#504011yescharacteristic
411C2C3×#517011yescharacteristic
412C2C3×#519811yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#460C2
socleC22×C32#120
prime radicalC32×#127C22
hypercenterC3×#460D3
hypocenterC3C3×#1623
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
1. C3×Q8×Dic6C2semidirect
5. C3×#4535C2semidirect
6. C3×#4484C2semidirect
7. C3×#4481C2semidirect
9. #71033C3direct (N × H)
28. Q8×Dic6C2×C3semidirect
39. #4535C2×C3semidirect
40. #4484C2×C3semidirect
41. #4481C2×C3semidirect
109. C32×Q8SD16semidirect
126. C3×Dic6SD16semidirect
239. C3×Q8#214semidirect
240. C3×Q8C3×SD16semidirect
280. Dic6C3×SD16semidirect
356. C32#1623semidirect
363. Q8C3×#214semidirect
407. C3#71033direct (N × H)
408. 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
C32×#4602
C3×#50762
C3×#50752
C3×#45352
C3×#44842
C3×#44812
C3×#16233
#710333