Finite Group Databasebeta

← C3×#71007 #11781421

Subgroups — C3×#71007 #11781421

Order 1152.

434 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#459C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic, complemented
4C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1681—31nomaximal
9#71007C311yesmaximal, characteristic, direct product factor
10C2×C32×D8—21no—
11C32×#127C2211yescharacteristic
12C32×C4×D4C2211yescharacteristic
13C2×C3×#214—21no—
14C22×C3×C3⋊C8—21no—
15C3×#869C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×#102—21no—
18C3×#832—21no—
19C3×#832—21no—
20C3×#830—21no—
21C3×#810—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#461—31no—
27C3×#459—21no—
28C3×#459D311yescharacteristic
29C3×#459C2×C311yescharacteristic
30C3×C8×D4—31no—
31#5070C2×C311yescharacteristic, complemented
32#5019C2×C311yescharacteristic, complemented
33D4×C3⋊C8C2×C311yescharacteristic, complemented
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4544C2×C311yescharacteristic, complemented
38#4482C2×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×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—42no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59#1681—31noSylow
60C2×C3×SD16—61no—
61C2×C3×D8—22no—
62C2×C3×D8—21no—
63C2×C3×D8—21no—
64C22×C3×C8—61no—
65C3×C4⋊Q8—31no—
66C3×#127—21no—
67C3×#127C2×D311yescharacteristic
68C3×#127C22×C311yescharacteristic
69C3×C4×D4—21no—
70C3×C4×D4C2×D311yescharacteristic
71C3×C4×D4C22×C311yescharacteristic
72C2×#214—21no—
73C22×C3⋊C8—21no—
74#869C22×C311yescharacteristic
75C3×C4⋊C8—21no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4⋊C8C22×C311yescharacteristic
80C3×#103—61no—
81C3×#102—22no—
82C3×#102—21no—
83C3×#102—21no—
84C3×#102—61no—
85C3×#102—61no—
86C3×C22⋊C8—61no—
87C3×C4×C8—31no—
88#832—21no—
89#832—21no—
90#830—21no—
91#810—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C4×C3⋊C8C22×C311yescharacteristic
95C23×C32—21no—
96C23×C32—41no—
97C32×D4—21no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—81no—
103C32×D4D812yes—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C3×Dic3—41no—
111C3×Dic6—41no—
112C3×Dic6—41no—
113C32×C8—41no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118#486—31no—
119#461—31no—
120#459C3×D311yescharacteristic
121C8×D4—31no—
122#335—31no—
123#332—31no—
124#331—31no—
125C2×C3×Q8—61no—
126C2×C3×D4—22no—
127C2×C3×D4—21no—
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—41no—
135C2×C3×D4—41no—
136C2×C3×D4#6711yescharacteristic
137C2×C3×D4C3×D411yescharacteristic
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—41no—
141C2×Dic6—21no—
142C3×SD16—122no—
143C3×D8—44no—
144C3×D8—42no—
145C3×D8—42no—
146C2×C3×C8—22no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—31no—
150C2×C3×C8—31no—
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C2×C3×C8—122no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4#6711yescharacteristic
158C3×C4⋊C4C3×D411yescharacteristic
159C3×C22⋊C4—21no—
160C3×C22⋊C4—21no—
161C3×C22⋊C4—41no—
162C3×C42—21no—
163C3×C42C22×D311yescharacteristic
164C3×C42C23×C311yescharacteristic
165#214—42no—
166C4⋊Dic3—21no—
167C4⋊Dic3—21no—
168C2×C3⋊C8—21no—
169C2×C3⋊C8—21no—
170C2×C3⋊C8—42no—
171C2×C3⋊C8C3×D411yescharacteristic
172C2×C3⋊C8C3×D411yescharacteristic
173C22×C32—22no—
174C22×C32—41no—
175C22×C32—41no—
176C22×C32—81no—
177C22×C32—81no—
178C22×C32—81no—
179C22×C32#12111yescharacteristic
180C32×C4—21no—
181C32×C4—41no—
182C32×C4C2×D811yescharacteristic
183C32×C4#13511yescharacteristic
184C32×C4#13511yescharacteristic
185C32×C4AGL(1,ℤ/8)11yescharacteristic
186C3×Dic3—81no—
187C2×SD16—61no—
188C2×D8—21no—
189C22×C8—61no—
190C4⋊Q8—31no—
191#127C2×C3×D311yescharacteristic
192C4×D4C2×C3×D311yescharacteristic
193C4⋊C8—31no—
194C4⋊C8—31no—
195C4⋊C8C2×C3×D311yescharacteristic
196#103—61no—
197#102—21no—
198#102—61no—
199#102—61no—
200C22⋊C8—61no—
201C4×C8—31no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—41no—
205C23×C3—42no—
206C23×C3—41no—
207C23×C3—41no—
208C3×Q8—121no—
209C3×Q8—121no—
210C3×D4—21no—
211C3×D4—21no—
212C3×D4—22no—
213C3×D4—41no—
214C3×D4—42no—
215C3×D4—42no—
216C3×D4—41no—
217C3×D4—41no—
218C3×D4—41no—
219C3×D4—41no—
220C3×D4—41no—
221C3×D4—41no—
222C3×D4—41no—
223C3×D4—41no—
224C3×D4—81no—
225C3×D4—81no—
226C3×D4—81no—
227C3×D4—81no—
228C3×D4—82no—
229C3×D4#21312yes—
230C3×D4C3×D812yes—
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—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—81no—
242C2×C3×C4—81no—
243C2×C3×C4—121no—
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4#23711yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×C3×C4C2×C3×D411yescharacteristic
248C2×C3×C4C2×C3×D411yescharacteristic
249C2×C3×C4C3×#4111yescharacteristic
250C2×Dic3—41no—
251Dic6—41no—
252Dic6—41no—
253C3×C8—42no—
254C3×C8—41no—
255C3×C8—41no—
256C3×C8—61no—
257C3×C8—61no—
258C3×C8—121no—
259C3×C8—121no—
260C3⋊C8—21no—
261C3⋊C8—21no—
262C3⋊C8—41no—
263C3⋊C8—41no—
264C2×C32—42no—
265C2×C32—161no—
266C2×C32#46311yescharacteristic
267C2×C32#46611yescharacteristic
268C2×C32#47111yescharacteristic
269C2×Q8—61no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4C3×#6711yescharacteristic
274C22×C4—21no—
275SD16—122no—
276D8—42no—
277C2×C8—21no—
278C2×C8—31no—
279C2×C8—31no—
280C2×C8—61no—
281C2×C8—61no—
282C2×C8—122no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4C3×#6711yescharacteristic
286C22⋊C4—21no—
287C42C22×C3×D311yescharacteristic
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—42no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—81no—
297C22×C3—81no—
298C22×C3—82no—
299C22×C3—82no—
300C22×C3—82no—
301C22×C3—81no—
302C22×C3—81no—
303C22×C3—81no—
304C22×C3—81no—
305C22×C3—81no—
306C22×C3—81no—
307C22×C3#93911yescharacteristic
308C22×C3C3×#12111yescharacteristic
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—81no—
319C3×C4—241no—
320C3×C4#91111yescharacteristic
321C3×C4#91211yescharacteristic
322C3×C4C2×#21311yescharacteristic
323C3×C4#95011yescharacteristic
324C3×C4C2×C3×D811yescharacteristic
325C3×C4C3×#13511yescharacteristic
326C3×C4C3×#13511yescharacteristic
327C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
328Dic3—81no—
329C32#168111yescharacteristic, complemented, Sylow
330C23—21no—
331C23—41no—
332Q8—121no—
333Q8—121no—
334D4—21no—
335D4—41no—
336D4—41no—
337D4—41no—
338D4—41no—
339D4—81no—
340D4C3×#21312yes—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—121no—
345C2×C4C3×D3×D411yescharacteristic
346C2×C4C3×#23711yescharacteristic
347C2×C4C2×C3×#6711yescharacteristic
348C8—41no—
349C8—61no—
350C8—61no—
351C8—121no—
352C8—121no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—42no—
357C2×C3—42no—
358C2×C3—82no—
359C2×C3—162no—
360C2×C3—161no—
361C2×C3—161no—
362C2×C3#503811yescharacteristic
363C2×C3#515311yescharacteristic
364C2×C3#520011yescharacteristic
365C2×C3C3×#46311yescharacteristic
366C2×C3C3×#46611yescharacteristic
367C2×C3C3×#47111yescharacteristic
368C22—22no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22C3×#93911yescharacteristic
375C4—21no—
376C4—41no—
377C4—241no—
378C4C3×#91111yescharacteristic
379C4C3×#91211yescharacteristic
380C4C2×C3×#21311yescharacteristic
381C4C3×#95011yescharacteristic
382C3—21no—
383C3#7100711yescharacteristic, direct product factor
384C3C3×#168111yescharacteristic, complemented
385C2—42no—
386C2—161no—
387C2C3×#503811yescharacteristic
388C2C3×#515311yescharacteristic
389C2C3×#520011yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
Fitting, prime radicalC32×#459C2
socleC22×C32#121
hypercenterC3×#459D3
hypocenterC3C3×#1681
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×#5070C2semidirect
3. C3×#5019C2semidirect
4. C3×D4×C3⋊C8C2semidirect
5. C3×#4544C2semidirect
6. C3×#4482C2semidirect
7. C3×#4479C2semidirect
9. #71007C3direct (N × H)
31. #5070C2×C3semidirect
32. #5019C2×C3semidirect
33. D4×C3⋊C8C2×C3semidirect
37. #4544C2×C3semidirect
38. #4482C2×C3semidirect
39. #4479C2×C3semidirect
329. C32#1681semidirect
383. C3#71007direct (N × H)
384. C3C3×#1681semidirect

Maximal subgroups

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

subgroupindex
C32×#4592
C3×#50702
C3×#50192
C3×D4×C3⋊C82
C3×#45442
C3×#44822
C3×#44792
C3×#16813
#710073