Finite Group Databasebeta

← C3×#71008 #11781605

Subgroups — C3×#71008 #11781605

Order 1152.

434 conjugacy classes of subgroups.

The subgroup lattice has 395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#459C211yesmaximal, characteristic
2C3×#5076C211yesmaximal, characteristic, complemented
3C3×#5012C211yesmaximal, characteristic, complemented
4C3×#5007C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1685—31nomaximal
9#71008C311yesmaximal, characteristic, direct product factor
10C2×C32×D8—21no—
11C32×#127C2211yescharacteristic
12C32×C4×D4C2211yescharacteristic
13C2×C3×#214—21no—
14C2×C3×#214—21no—
15C2×C3×#208—21no—
16C3×#869C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C32×#102—21no—
19C3×#832—21no—
20C3×#830—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#492—31no—
26C3×#474—31no—
27C3×#459—21no—
28C3×#459D311yescharacteristic
29C3×#459C2×C311yescharacteristic
30C3×#436—31no—
31#5076C2×C311yescharacteristic, complemented
32#5012C2×C311yescharacteristic, complemented
33#5007C2×C311yescharacteristic, complemented
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4544C2×C311yescharacteristic, complemented
38#4486C2×C311yescharacteristic, complemented
39#4479C2×C311yescharacteristic, complemented
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C2×C3×Dic6—21no—
46C32×D8—42no—
47C2×C32×C8—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×#214—42no—
52C3×#214—42no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×#208—42no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58C2×C3×C3⋊C8D411yescharacteristic
59C2×C3×C3⋊C8D411yescharacteristic
60#1685—31noSylow
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C2×C3×D8—22no—
64C2×C3×D8—21no—
65C2×C3×D8—21no—
66C2×C3×M16—61no—
67C3×C4⋊Q8—31no—
68C3×#127—21no—
69C3×#127C2×D311yescharacteristic
70C3×#127C22×C311yescharacteristic
71C3×C4×D4—21no—
72C3×C4×D4C2×D311yescharacteristic
73C3×C4×D4C22×C311yescharacteristic
74C2×#214—21no—
75C2×#214—21no—
76C2×#208—21no—
77#869C22×C311yescharacteristic
78C3×#107—61no—
79C3×C4⋊C8—21no—
80C3×C4⋊C8—31no—
81C3×C4⋊C8—31no—
82C3×C4⋊C8C2×D311yescharacteristic
83C3×C4⋊C8C22×C311yescharacteristic
84C3×#102—22no—
85C3×#102—21no—
86C3×#102—21no—
87C3×#102—61no—
88C3×C22⋊C8—61no—
89C3×C4×C8—31no—
90#832—21no—
91#830—21no—
92#807—21no—
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C4⋊(C3⋊C8)C22×C311yescharacteristic
95C4×C3⋊C8C22×C311yescharacteristic
96C23×C32—21no—
97C23×C32—41no—
98C32×D4—21no—
99C32×D4—21no—
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—41no—
103C32×D4—41no—
104C32×D4—81no—
105C2×C32×C4—21no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C3×Dic3—41no—
112C3×Dic6—41no—
113C3×Dic6—41no—
114C32×C8—41no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118C3×C3⋊C8D812yescomplemented
119#492—31no—
120#474—31no—
121#459C3×D311yescharacteristic
122#436—31no—
123#335—31no—
124#332—31no—
125#331—31no—
126C2×C3×Q8—61no—
127C2×C3×D4—22no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—21no—
135C2×C3×D4—41no—
136C2×C3×D4—41no—
137C2×C3×D4#6711yescharacteristic
138C2×C3×D4C3×D411yescharacteristic
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—41no—
142C2×Dic6—21no—
143C3×SD16—122no—
144C3×SD16—122no—
145C3×D8—44no—
146C3×D8—42no—
147C3×D8—42no—
148C3×M16—122no—
149C2×C3×C8—22no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—31no—
153C2×C3×C8—31no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4#6711yescharacteristic
160C3×C4⋊C4C3×D411yescharacteristic
161C3×C22⋊C4—21no—
162C3×C22⋊C4—21no—
163C3×C22⋊C4—41no—
164C3×C42—21no—
165C3×C42C22×D311yescharacteristic
166C3×C42C23×C311yescharacteristic
167#214—42no—
168#214—42no—
169C4⋊Dic3—21no—
170C4⋊Dic3—21no—
171#208—42no—
172C2×C3⋊C8—21no—
173C2×C3⋊C8—21no—
174C2×C3⋊C8C3×D411yescharacteristic
175C2×C3⋊C8C3×D411yescharacteristic
176C22×C32—41no—
177C22×C32—41no—
178C22×C32—41no—
179C22×C32—81no—
180C22×C32—81no—
181C22×C32—81no—
182C22×C32#12111yescharacteristic
183C32×C4—21no—
184C32×C4—41no—
185C32×C4C2×D811yescharacteristic
186C32×C4AGL(1,ℤ/8)11yescharacteristic
187C32×C4AGL(1,ℤ/8)11yescharacteristic
188C32×C4#13711yescharacteristic
189C3×Dic3—81no—
190C2×SD16—61no—
191C2×SD16—61no—
192C2×D8—21no—
193C2×M16—61no—
194C4⋊Q8—31no—
195#127C2×C3×D311yescharacteristic
196C4×D4C2×C3×D311yescharacteristic
197#107—61no—
198C4⋊C8—31no—
199C4⋊C8—31no—
200C4⋊C8C2×C3×D311yescharacteristic
201#102—21no—
202#102—61no—
203C22⋊C8—61no—
204C4×C8—31no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—41no—
208C23×C3—42no—
209C23×C3—41no—
210C23×C3—41no—
211C3×Q8—121no—
212C3×Q8—121no—
213C3×D4—22no—
214C3×D4—21no—
215C3×D4—21no—
216C3×D4—21no—
217C3×D4—21no—
218C3×D4—41no—
219C3×D4—42no—
220C3×D4—42no—
221C3×D4—41no—
222C3×D4—41no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—41no—
226C3×D4—41no—
227C3×D4—41no—
228C3×D4—41no—
229C3×D4—81no—
230C3×D4—81no—
231C3×D4—81no—
232C3×D4—81no—
233C3×D4—82no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—81no—
245C2×C3×C4—81no—
246C2×C3×C4—121no—
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4#23711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×C3×C4C2×C3×D411yescharacteristic
251C2×C3×C4C2×C3×D411yescharacteristic
252C2×C3×C4C3×#4111yescharacteristic
253C2×Dic3—41no—
254Dic6—41no—
255Dic6—41no—
256C3×C8—32no—
257C3×C8—42no—
258C3×C8—41no—
259C3×C8—41no—
260C3×C8—61no—
261C3×C8—121no—
262C3×C8—121no—
263C3⋊C8—21no—
264C3⋊C8—41no—
265C3⋊C8—41no—
266C3⋊C8C3×D812yescomplemented
267C2×C32—81no—
268C2×C32—161no—
269C2×C32#45911yescharacteristic
270C2×C32#46811yescharacteristic
271C2×C32#47111yescharacteristic
272C2×Q8—61no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4C3×#6711yescharacteristic
277C22×C4—21no—
278SD16—122no—
279SD16—122no—
280D8—42no—
281M16—122no—
282C2×C8—21no—
283C2×C8—31no—
284C2×C8—31no—
285C2×C8—61no—
286C2×C8—61no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4C3×#6711yescharacteristic
290C22⋊C4—21no—
291C42C22×C3×D311yescharacteristic
292C22×C3—21no—
293C22×C3—42no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—81no—
301C22×C3—81no—
302C22×C3—82no—
303C22×C3—82no—
304C22×C3—82no—
305C22×C3—81no—
306C22×C3—81no—
307C22×C3—81no—
308C22×C3—81no—
309C22×C3—81no—
310C22×C3—81no—
311C22×C3#93911yescharacteristic
312C22×C3C3×#12111yescharacteristic
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—81no—
323C3×C4—241no—
324C3×C4D3×D811yescharacteristic
325C3×C4#91111yescharacteristic
326C3×C4#93211yescharacteristic
327C3×C4#95111yescharacteristic
328C3×C4C2×C3×D811yescharacteristic
329C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
330C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
331C3×C4C3×#13711yescharacteristic
332Dic3—81no—
333C32#168511yescharacteristic, complemented, Sylow
334C23—21no—
335C23—41no—
336Q8—121no—
337Q8—121no—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—41no—
344D4—81no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—121no—
349C2×C4C3×D3×D411yescharacteristic
350C2×C4C3×#23711yescharacteristic
351C2×C4C2×C3×#6711yescharacteristic
352C8—32no—
353C8—41no—
354C8—61no—
355C8—121no—
356C8—121no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—82no—
361C2×C3—81no—
362C2×C3—81no—
363C2×C3—162no—
364C2×C3—161no—
365C2×C3—161no—
366C2×C3#504211yescharacteristic
367C2×C3#515011yescharacteristic
368C2×C3#520011yescharacteristic
369C2×C3C3×#45911yescharacteristic
370C2×C3C3×#46811yescharacteristic
371C2×C3C3×#47111yescharacteristic
372C22—41no—
373C22—41no—
374C22—41no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22C3×#93911yescharacteristic
379C4—21no—
380C4—41no—
381C4—241no—
382C4C3×D3×D811yescharacteristic
383C4C3×#91111yescharacteristic
384C4C3×#93211yescharacteristic
385C4C3×#95111yescharacteristic
386C3—21no—
387C3#7100811yescharacteristic, direct product factor
388C3C3×#168511yescharacteristic, complemented
389C2—81no—
390C2—161no—
391C2C3×#504211yescharacteristic
392C2C3×#515011yescharacteristic
393C2C3×#520011yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
Fitting, prime radicalC32×#459C2
socleC22×C32#121
hypercenterC3×#459D3
hypocenterC3C3×#1685
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
2. C3×#5076C2semidirect
3. C3×#5012C2semidirect
4. C3×#5007C2semidirect
5. C3×#4544C2semidirect
6. C3×#4486C2semidirect
7. C3×#4479C2semidirect
9. #71008C3direct (N × H)
31. #5076C2×C3semidirect
32. #5012C2×C3semidirect
33. #5007C2×C3semidirect
37. #4544C2×C3semidirect
38. #4486C2×C3semidirect
39. #4479C2×C3semidirect
118. C3×C3⋊C8D8semidirect
266. C3⋊C8C3×D8semidirect
333. C32#1685semidirect
387. C3#71008direct (N × H)
388. C3C3×#1685semidirect

Maximal subgroups

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

subgroupindex
C32×#4592
C3×#50762
C3×#50122
C3×#50072
C3×#45442
C3×#44862
C3×#44792
C3×#16853
#710083