Finite Group Databasebeta

← C3×#71113 #11779946

Subgroups — C3×#71113 #11779946

Order 1152.

470 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic
2C32×#474C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5090C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4481C211yesmaximal, characteristic, complemented
8C3×#1644—31nomaximal
9#71113C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C2×C3×#216—21no—
13C3×D4×Dic3—21no—
14C2×C3×C4⋊Dic3—21no—
15C3×#924—21no—
16C3×#890—21no—
17C3×#878—22no—
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×#107—21no—
21C32×C4⋊C8C2211yescharacteristic
22C32×#102—21no—
23C3×#835—21no—
24C3×#810—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#554—31no—
28#5543C2×C311yescharacteristic
29C3×#487—31no—
30C3×#474—21no—
31C3×#474D311yescharacteristic
32C3×#474C2×C311yescharacteristic
33C3×#462—31no—
34#5093C2×C311yescharacteristic, complemented
35#5090C2×C311yescharacteristic, complemented
36C3×#333—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39D4⋊(C3⋊C8)C2×C311yescharacteristic
40#4484C2×C311yescharacteristic, complemented
41#4481C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C22×C3×Dic3—22no—
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D412yes—
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×#216—42no—
56C3×C4⋊Dic3—22no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1644—31noSylow
66C2×C3×Q16—61no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C22×C311yescharacteristic
71C3×#125—61no—
72C3×C22⋊Q8—62no—
73C3×C22⋊Q8—61no—
74C3×C4×Q8—31no—
75C3×C4×D4—21no—
76C3×C4×D4—61no—
77C3×C4×D4C2×D311yescharacteristic
78C3×C4×D4C22×C311yescharacteristic
79C2×C3×C4⋊C4—61no—
80C2×#216—21no—
81D4×Dic3—21no—
82C2×C4⋊Dic3—21no—
83#924—21no—
84#890—21no—
85#878—22no—
86#869C22×C311yescharacteristic
87C4×Dic6C22×C311yescharacteristic
88C3×#107—22no—
89C3×#107—21no—
90C3×#107—21no—
91C3×C4⋊C8—21no—
92C3×C4⋊C8—31no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C22×C311yescharacteristic
95C3×#103—62no—
96C3×#103—61no—
97C3×#102—22no—
98C3×#102—21no—
99C3×#102—21no—
100C3×C4×C8—31no—
101#835—21no—
102#810—22no—
103C4⋊(C3⋊C8)C22×C311yescharacteristic
104C4×C3⋊C8C22×C311yescharacteristic
105C23×C32—21no—
106C32×Q8—41no—
107C32×Q8—41no—
108C32×D4—21no—
109C32×D4Q1612yescomplemented
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—
120C2×C3×Dic3—82no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C3×Dic6—42no—
124C32×C8—41no—
125C3×C3⋊C8—41no—
126C3×C3⋊C8—41no—
127#554—31no—
128#487—31no—
129#474C3×D311yescharacteristic
130#462—31no—
131#333—31no—
132Q8⋊C8—31no—
133D4⋊C8—31no—
134C2×C3×Q8—21no—
135C2×C3×Q8—21no—
136C2×C3×Q8—31no—
137C2×C3×Q8—32no—
138C2×C3×Q8—41no—
139C2×C3×D4—21no—
140C2×C3×D4#6711yescharacteristic
141C2×C3×D4C3×D411yescharacteristic
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—41no—
145C22×C3×C4—62no—
146C22×Dic3—22no—
147C2×Dic6C3×D411yescharacteristic
148C2×Dic6C3×D412yes—
149C3×Q16—122no—
150C2×C3×C8—22no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4—41no—
163C3×C4⋊C4—62no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—61no—
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×C42—21no—
175C3×C42—61no—
176C3×C42C22×D311yescharacteristic
177C3×C42C23×C311yescharacteristic
178#217—22no—
179#216—42no—
180C4⋊Dic3—22no—
181C4⋊Dic3—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3C3×D411yescharacteristic
184Dic3⋊C4—22no—
185Dic3⋊C4—21no—
186C4×Dic3—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189C22×C32—22no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32#12011yescharacteristic
193C32×C4—21no—
194C32×C4—41no—
195C32×C4—81no—
196C32×C4C2×Q1611yescharacteristic
197C32×C4#13511yescharacteristic
198C32×C4AGL(1,ℤ/8)11yescharacteristic
199C32×C4#13711yescharacteristic
200C3×Dic3—41no—
201C3×Dic3—42no—
202C3×Dic3—41no—
203C2×Q16—61no—
204C4⋊Q8—31no—
205C4⋊Q8C2×C3×D311yescharacteristic
206#125—61no—
207C22⋊Q8—62no—
208C22⋊Q8—61no—
209C4×Q8—31no—
210C4×D4—61no—
211C4×D4C2×C3×D311yescharacteristic
212C2×C4⋊C4—61no—
213#107—21no—
214C4⋊C8—31no—
215C4⋊C8C2×C3×D311yescharacteristic
216#103—62no—
217#103—61no—
218#102—21no—
219C4×C8—31no—
220C23×C3—21no—
221C23×C3—21no—
222C23×C3—41no—
223C3×Q8—41no—
224C3×Q8—41no—
225C3×Q8—41no—
226C3×Q8—41no—
227C3×Q8—61no—
228C3×Q8—61no—
229C3×Q8—81no—
230C3×Q8—81no—
231C3×Q8—122no—
232C3×D4—21no—
233C3×D4—21no—
234C3×D4—22no—
235C3×D4—41no—
236C3×D4#21612yescomplemented
237C3×D4C3×Q1612yescomplemented
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—42no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—61no—
252C2×C3×C4—61no—
253C2×C3×C4—62no—
254C2×C3×C4—81no—
255C2×C3×C4—81no—
256C2×C3×C4—242no—
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×C3×C4C2×C3×D411yescharacteristic
261C2×C3×C4C2×C3×D411yescharacteristic
262C2×C3×C4C2×C3×D411yescharacteristic
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—22no—
266C2×Dic3—82no—
267Dic6—21no—
268Dic6—21no—
269Dic6—42no—
270C3×C8—42no—
271C3×C8—41no—
272C3×C8—41no—
273C3×C8—121no—
274C3×C8—121no—
275C3⋊C8—41no—
276C3⋊C8—41no—
277C2×C32—42no—
278C2×C32#44911yescharacteristic
279C2×C32#45111yescharacteristic
280C2×C32#45511yescharacteristic
281C2×Q8—21no—
282C2×Q8—31no—
283C2×Q8—32no—
284C2×D4C3×#6711yescharacteristic
285C22×C4—21no—
286C22×C4—62no—
287Q16—122no—
288C2×C8—21no—
289C2×C8—61no—
290C2×C8—61no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—31no—
294C4⋊C4—62no—
295C4⋊C4—62no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4C3×#6711yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—62no—
302C42—61no—
303C42C22×C3×D311yescharacteristic
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—21no—
307C22×C3—42no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—81no—
313C22×C3—81no—
314C22×C3#93711yescharacteristic
315C22×C3C3×#12011yescharacteristic
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—41no—
325C3×C4—81no—
326C3×C4—82no—
327C3×C4—81no—
328C3×C4—81no—
329C3×C4—121no—
330C3×C4—121no—
331C3×C4—122no—
332C3×C4#91111yescharacteristic
333C3×C4#91211yescharacteristic
334C3×C4C2×#21611yescharacteristic
335C3×C4#95111yescharacteristic
336C3×C4C2×C3×Q1611yescharacteristic
337C3×C4C3×#13511yescharacteristic
338C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
339C3×C4C3×#13711yescharacteristic
340Dic3—41no—
341Dic3—42no—
342Dic3—41no—
343C32#164411yescharacteristic, complemented, Sylow
344C23—21no—
345Q8—41no—
346Q8—41no—
347Q8—61no—
348Q8—61no—
349Q8—122no—
350D4—21no—
351D4C3×#21612yescomplemented
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—62no—
359C2×C4—242no—
360C2×C4C3×D3×D411yescharacteristic
361C2×C4C3×D3×D411yescharacteristic
362C2×C4C2×C3×#6711yescharacteristic
363C8—41no—
364C8—121no—
365C8—121no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—42no—
370C2×C3—42no—
371C2×C3—82no—
372C2×C3#505011yescharacteristic
373C2×C3#515811yescharacteristic
374C2×C3#520211yescharacteristic
375C2×C3C3×#44911yescharacteristic
376C2×C3C3×#45111yescharacteristic
377C2×C3C3×#45511yescharacteristic
378C22—22no—
379C22—41no—
380C22—41no—
381C22C3×#93711yescharacteristic
382C4—21no—
383C4—41no—
384C4—81no—
385C4—121no—
386C4—122no—
387C4—121no—
388C4C3×#91111yescharacteristic
389C4C3×#91211yescharacteristic
390C4C2×C3×#21611yescharacteristic
391C4C3×#95111yescharacteristic
392C3—21no—
393C3#7111311yescharacteristic, direct product factor
394C3C3×#164411yescharacteristic, complemented
395C2—42no—
396C2C3×#505011yescharacteristic
397C2C3×#515811yescharacteristic
398C2C3×#520211yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#474C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC3×#474D3
hypocenterC3C3×#1644
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
3. C3×#5093C2semidirect
4. C3×#5090C2semidirect
6. C3×#4484C2semidirect
7. C3×#4481C2semidirect
9. #71113C3direct (N × H)
34. #5093C2×C3semidirect
35. #5090C2×C3semidirect
40. #4484C2×C3semidirect
41. #4481C2×C3semidirect
109. C32×D4Q16semidirect
236. C3×D4#216semidirect
237. C3×D4C3×Q16semidirect
343. C32#1644semidirect
351. D4C3×#216semidirect
393. C3#71113direct (N × H)
394. C3C3×#1644semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
C32×#4742
C3×#50932
C3×#50902
C3×D4⋊(C3⋊C8)2
C3×#44842
C3×#44812
C3×#16443
#711133