Finite Group Databasebeta

← C3×#71819 #11796364

Subgroups — C3×#71819 #11796364

Order 1152.

671 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic
2C3×#5240C212yesmaximal, complemented
3C3×#4545C212yesmaximal, complemented
4C3×#4541C212yesmaximal, complemented
5C3×#2126—31nomaximal
6#71819C311yesmaximal, characteristic, direct product factor
7C2×C32×#41C411yescharacteristic, complemented
8C2×C32×#41C2211yescharacteristic
9C32×C4⋊Q8C411yescharacteristic, complemented
10C32×#127C2211yescharacteristic
11C32×#124C411yescharacteristic, complemented
12C32×#124C2211yescharacteristic
13C32×#121—22no—
14C32×C4×D4—22no—
15C2×C32×C42C411yescharacteristic, complemented
16C3×#926—22no—
17C3×#834—22no—
18C3×#834C2214yes—
19C3×#532—21no—
20C3×#532D311yescharacteristic
21C3×#532C2×C311yescharacteristic
22C3×#410—32no—
23#5240C2×C312yescomplemented
24C3×#354—32no—
25C3×#353—32no—
26#4545C2×C312yescomplemented
27#4541C2×C312yescomplemented
28C32×#41—41no—
29C32×#41—41no—
30C32×#41—41no—
31C32×#41—41no—
32C2×C32×Q8C2×C411yescharacteristic
33C2×C32×Q8C2×C411yescharacteristic
34C2×C32×D4—21no—
35C2×C32×D4—22no—
36C2×C32×D4C2×C411yescharacteristic
37C2×C32×D4D412yes—
38C2×C32×D4C2311yescharacteristic
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4C2×C411yescharacteristic
42C22×C32×C4D412yes—
43C32×C4⋊C4—22no—
44C32×C22⋊C4—22no—
45C32×C22⋊C4—22no—
46C32×C42—21no—
47C32×C42C2×C411yescharacteristic
48C32×C42C2×C411yescharacteristic
49C3×#217—24no—
50C3×C4⋊Dic3—42no—
51C3×C4×Dic3—42no—
52#2126—31noSylow
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41Dic311yescharacteristic, complemented
56C2×C3×#41C3×C411yescharacteristic, complemented
57C2×C3×#41C2×D311yescharacteristic
58C2×C3×#41C22×C311yescharacteristic
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8Dic311yescharacteristic, complemented
61C3×C4⋊Q8C3×C411yescharacteristic, complemented
62C3×#127—21no—
63C3×#127C2×D311yescharacteristic
64C3×#127C22×C311yescharacteristic
65C3×#124—21no—
66C3×#124—21no—
67C3×#124Dic311yescharacteristic, complemented
68C3×#124C3×C411yescharacteristic, complemented
69C3×#124C2×D311yescharacteristic
70C3×#124C22×C311yescharacteristic
71C3×#121—24no—
72C3×#121—22no—
73C3×#121—22no—
74C3×C4×D4—24no—
75C3×C4×D4—22no—
76C3×C4×D4—22no—
77C3×#117—62no—
78C2×C3×C42—21no—
79C2×C3×C42Dic311yescharacteristic, complemented
80C2×C3×C42C3×C411yescharacteristic, complemented
81#926—22no—
82C3×#99—34no—
83C3×#99—62no—
84#834—22no—
85#834C22×C314yes—
86C23×C32—21no—
87C23×C32C22⋊C411yescharacteristic
88C23×C32C2×D412yes—
89C32×Q8—41no—
90C32×Q8—41no—
91C32×D4—42no—
92C32×D4—41no—
93C32×D4—41no—
94C32×D4—44no—
95C32×D4—42no—
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—42no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4C22⋊C412yes—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22×C411yescharacteristic
109C2×C3×Dic3—44no—
110#532C3×D311yescharacteristic
111#410—32no—
112#354—32no—
113#353—32no—
114C3×#41—41no—
115C3×#41—41no—
116C3×#41—41no—
117C3×#41—41no—
118C3×#41—42no—
119C3×#41—42no—
120C3×#41—42no—
121C3×#41—42no—
122C3×#41—41no—
123C3×#41—41no—
124C3×#41—41no—
125C3×#41—41no—
126C2×C3×Q8—21no—
127C2×C3×Q8—21no—
128C2×C3×Q8C2×Dic311yescharacteristic
129C2×C3×Q8C2×Dic311yescharacteristic
130C2×C3×Q8C2×C3×C411yescharacteristic
131C2×C3×Q8C2×C3×C411yescharacteristic
132C2×C3×D4—24no—
133C2×C3×D4—22no—
134C2×C3×D4—21no—
135C2×C3×D4—21no—
136C2×C3×D4—22no—
137C2×C3×D4—22no—
138C2×C3×D4—21no—
139C2×C3×D4—22no—
140C2×C3×D4—21no—
141C2×C3×D4C2×Dic311yescharacteristic
142C2×C3×D4#6712yes—
143C2×C3×D4C2×C3×C411yescharacteristic
144C2×C3×D4C3×D412yes—
145C2×C3×D4C22×D311yescharacteristic
146C2×C3×D4C23×C311yescharacteristic
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—22no—
155C22×C3×C4C2×Dic311yescharacteristic
156C22×C3×C4#6712yes—
157C22×C3×C4C2×C3×C411yescharacteristic
158C22×C3×C4C3×D412yes—
159C3×C4⋊C4—24no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—122no—
163C3×C22⋊C4—24no—
164C3×C22⋊C4—24no—
165C3×C22⋊C4—22no—
166C3×C22⋊C4—22no—
167C3×C22⋊C4—22no—
168C3×C22⋊C4—22no—
169C3×C22⋊C4—64no—
170C3×C42—22no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42—21no—
174C3×C42—21no—
175C3×C42—122no—
176C3×C42C2×Dic311yescharacteristic
177C3×C42C2×Dic311yescharacteristic
178C3×C42C2×C3×C411yescharacteristic
179C3×C42C2×C3×C411yescharacteristic
180#217—24no—
181C4⋊Dic3—42no—
182C4×Dic3—42no—
183C22×C32—21no—
184C22×C32—22no—
185C22×C32—41no—
186C22×C32—42no—
187C22×C32—42no—
188C22×C32—41no—
189C22×C32C2×C22⋊C411yescharacteristic
190C32×C4—22no—
191C32×C4—21no—
192C32×C4—22no—
193C32×C4—41no—
194C32×C4—41no—
195C32×C4#9911yescharacteristic
196C32×C4#9911yescharacteristic
197C3×Dic3—84no—
198C2×#41C3×Dic311yescharacteristic, complemented
199C2×#41C2×C3×D311yescharacteristic
200C4⋊Q8C3×Dic311yescharacteristic, complemented
201#127C2×C3×D311yescharacteristic
202#124C3×Dic311yescharacteristic, complemented
203#124C2×C3×D311yescharacteristic
204#121—22no—
205C4×D4—22no—
206#117—62no—
207C2×C42C3×Dic311yescharacteristic, complemented
208#99—34no—
209#99—62no—
210C23×C3—22no—
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—21no—
214C23×C3—22no—
215C23×C3#21711yescharacteristic
216C23×C3C3×C22⋊C411yescharacteristic
217C23×C3C2×#6712yes—
218C23×C3C2×C3×D412yes—
219C3×Q8—41no—
220C3×Q8—41no—
221C3×Q8—41no—
222C3×Q8—41no—
223C3×Q8—42no—
224C3×Q8—42no—
225C3×D4—42no—
226C3×D4—42no—
227C3×D4—41no—
228C3×D4—41no—
229C3×D4—41no—
230C3×D4—41no—
231C3×D4—44no—
232C3×D4—44no—
233C3×D4—48no—
234C3×D4—42no—
235C3×D4—42no—
236C3×D4—44no—
237C3×D4—44no—
238C3×D4—42no—
239C3×D4—42no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—22no—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—44no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—124no—
274C2×C3×C4#21712yes—
275C2×C3×C4#21711yescharacteristic
276C2×C3×C4C3×C22⋊C412yes—
277C2×C3×C4C3×C22⋊C411yescharacteristic
278C2×C3×C4C22×Dic311yescharacteristic
279C2×C3×C4C22×C3×C411yescharacteristic
280C2×Dic3—44no—
281C2×C32—21no—
282C2×C32—41no—
283C2×C32—42no—
284C2×C32—81no—
285C2×C32C2×#9911yescharacteristic
286#41—41no—
287#41—41no—
288#41—41no—
289#41—41no—
290C2×Q8C2×C3×Dic311yescharacteristic
291C2×Q8C2×C3×Dic311yescharacteristic
292C2×D4—21no—
293C2×D4—22no—
294C2×D4C2×C3×Dic311yescharacteristic
295C2×D4C3×#6712yes—
296C2×D4C22×C3×D311yescharacteristic
297C22×C4—21no—
298C22×C4—21no—
299C22×C4C2×C3×Dic311yescharacteristic
300C22×C4C3×#6712yes—
301C4⋊C4—22no—
302C4⋊C4—122no—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—64no—
306C42—21no—
307C42—122no—
308C42C2×C3×Dic311yescharacteristic
309C42C2×C3×Dic311yescharacteristic
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—21no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—42no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—44no—
324C22×C3—44no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3C2×#21711yescharacteristic
330C22×C3C2×C3×C22⋊C411yescharacteristic
331C3×C4—22no—
332C3×C4—24no—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—21no—
337C3×C4—22no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—42no—
342C3×C4—42no—
343C3×C4—42no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—244no—
349C3×C4#83411yescharacteristic
350C3×C4#83411yescharacteristic
351C3×C4C3×#9911yescharacteristic
352C3×C4C3×#9911yescharacteristic
353Dic3—84no—
354C32#212611yescharacteristic, complemented, Sylow
355C23—21no—
356C23C3×#21711yescharacteristic
357C23C2×C3×#6712yes—
358Q8—41no—
359Q8—41no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—44no—
364D4—42no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—124no—
376C2×C4C3×#21712yes—
377C2×C4C3×#21711yescharacteristic
378C2×C4C22×C3×Dic311yescharacteristic
379C2×C3—22no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—42no—
384C2×C3—42no—
385C2×C3—41no—
386C2×C3—42no—
387C2×C3—41no—
388C2×C3—82no—
389C2×C3—82no—
390C2×C3—81no—
391C2×C3—81no—
392C2×C3C2×#83411yescharacteristic
393C2×C3C2×C3×#9911yescharacteristic
394C22—22no—
395C22—21no—
396C22—41no—
397C22—42no—
398C22—42no—
399C22—41no—
400C22C2×C3×#21711yescharacteristic
401C4—22no—
402C4—22no—
403C4—21no—
404C4—41no—
405C4—41no—
406C4—244no—
407C4C3×#83411yescharacteristic
408C4C3×#83411yescharacteristic
409C3—21no—
410C3#7181911yescharacteristic, direct product factor
411C3C3×#212611yescharacteristic, complemented
412C2—21no—
413C2—42no—
414C2—41no—
415C2—81no—
416C2C2×C3×#83411yescharacteristic
subgroupG/H
centerC3×C4#834
commutatorC2×C3×C4C22×C3×C4
FrattiniC2×D4C22×C3×D3
Fitting, prime radicalC32×#532C2
socleC2×C32C2×#99
cosocleC2×C3×D4C23×C3
hypercenterC3×#532D3
hypocenterC3C3×#2126
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#532

Complements

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

NH ≅ G/Ntype
2. C3×#5240C2semidirect
3. C3×#4545C2semidirect
4. C3×#4541C2semidirect
6. #71819C3direct (N × H)
7. C2×C32×#41C4semidirect
9. C32×C4⋊Q8C4semidirect
11. C32×#124C4semidirect
15. C2×C32×C42C4semidirect
23. #5240C2×C3semidirect
26. #4545C2×C3semidirect
27. #4541C2×C3semidirect
55. C2×C3×#41Dic3semidirect
56. C2×C3×#41C3×C4semidirect
60. C3×C4⋊Q8Dic3semidirect
61. C3×C4⋊Q8C3×C4semidirect
67. C3×#124Dic3semidirect
68. C3×#124C3×C4semidirect
79. C2×C3×C42Dic3semidirect
80. C2×C3×C42C3×C4semidirect
198. C2×#41C3×Dic3semidirect
200. C4⋊Q8C3×Dic3semidirect
202. #124C3×Dic3semidirect
207. C2×C42C3×Dic3semidirect
354. C32#2126semidirect
410. C3#71819direct (N × H)
411. C3C3×#2126semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
C3×#52402
C3×#45452
C3×#45412
C3×#21263
#718193