Finite Group Databasebeta

← C2×C3×#4979 #11808182

Subgroups — C2×C3×#4979 #11808182

Order 1152.

2025 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic
2C22×C32×C4⋊C4C211yesmaximal, characteristic
3C22×C3×Dic3⋊C4C212yesmaximal
4C2×C3×C3⋊#95C212yesmaximal
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C3×#4979C218yesmaximal, direct product factor
7C2×C3×#395—31nomaximal
8C2×#4979C311yesmaximal, characteristic, direct product factor
9C23×C32×C4C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2212yes—
14C22×C3×Dic6—24no—
15C22×C3×Dic6—28no—
16C22×C3×Dic6C2214yes—
17C2×C32×C4⋊C4—24no—
18C2×C32×C4⋊C4C2214yes—
19C2×C3×Dic3⋊C4—28no—
20C2×C3×Dic3⋊C4C2218yes—
21C3×C3⋊#95C2218yes—
22C3×C3⋊#95C2214yes—
23C23×C3×Q8—31no—
24C23×Dic6C2×C311yescharacteristic
25C22×C3×C4⋊C4—21no—
26C22×C3×C4⋊C4—32no—
27C22×C3×C4⋊C4D311yescharacteristic
28C22×C3×C4⋊C4C2×C311yescharacteristic
29C22×Dic3⋊C4C2×C312yes—
30C3×#395—38no—
31C2×C3×#95—32no—
32C2×C3×#95—31no—
33C2×C3⋊#95C2×C312yes—
34C2×C3⋊#95C2×C311yescharacteristic
35#4979C2×C318yesdirect product factor
36C24×C32C2311yescharacteristic
37C22×C32×C4—22no—
38C22×C32×C4—24no—
39C22×C32×C4—22no—
40C22×C32×C4—22no—
41C22×C32×C4—24no—
42C22×C32×C4D414yes—
43C22×C32×C4Q814yescomplemented
44C22×C32×C4C2312yes—
45C22×C32×C4C2312yes—
46C22×C32×C4C2312yes—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3—24no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3D418yes—
52C22×C3×Dic3Q818yescomplemented
53C22×C3×Dic3C2314yes—
54C22×C3×Dic3C2314yes—
55C2×C3×Dic6—232no—
56C2×C3×Dic6—28no—
57C2×C3×Dic6—216no—
58C32×C4⋊C4—28no—
59C3×Dic3⋊C4—216no—
60C2×#395—31noSylow
61C22×C3×Q8—34no—
62C22×C3×Q8—68no—
63C22×C3×Q8—64no—
64C23×C3×C4—21no—
65C23×C3×C4—21no—
66C23×C3×C4—21no—
67C23×C3×C4—32no—
68C23×C3×C4—32no—
69C23×C3×C4C2×D311yescharacteristic
70C23×C3×C4C2×D311yescharacteristic
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C22×C311yescharacteristic
73C23×C3×C4C22×C311yescharacteristic
74C23×C3×C4C22×C311yescharacteristic
75C23×Dic3C22×C312yes—
76C23×Dic3C22×C312yes—
77C22×Dic6—24no—
78C22×Dic6—28no—
79C22×Dic6C22×C314yes—
80C2×C3×C4⋊C4—28no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—38no—
85C2×C3×C4⋊C4—68no—
86C2×C3×C4⋊C4C2×D314yes—
87C2×C3×C4⋊C4C22×C314yes—
88C2×Dic3⋊C4—28no—
89C2×Dic3⋊C4C22×C318yes—
90C3×#95—34no—
91C3×#95—38no—
92C3⋊#95C22×C318yes—
93C3⋊#95C22×C314yes—
94C23×C32C2×D414yes—
95C23×C32C2×D412yes—
96C23×C32C2×Q812yes—
97C23×C32C2×Q814yes—
98C23×C32#4112yes—
99C23×C32C2411yescharacteristic
100C2×C32×C4—28no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—28no—
105C2×C32×C4—24no—
106C2×C32×C4—24no—
107C2×C32×C4—44no—
108C2×C32×C4C2×D414yes—
109C2×C32×C4C2×Q814yescomplemented
110C2×C3×Dic3—216no—
111C2×C3×Dic3—216no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3C2×D418yes—
117C2×C3×Dic3C2×Q818yescomplemented
118C3×Dic6—232no—
119C23×Q8—31no—
120C22×C4⋊C4—32no—
121C22×C4⋊C4C3×D311yescharacteristic
122#395—38no—
123C2×#95—32no—
124C2×#95—31no—
125C24×C3—21no—
126C24×C3C22×D311yescharacteristic
127C24×C3C23×C311yescharacteristic
128C2×C3×Q8—616no—
129C2×C3×Q8—632no—
130C2×C3×Q8—68no—
131C22×C3×C4—24no—
132C22×C3×C4—24no—
133C22×C3×C4—22no—
134C22×C3×C4—24no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—24no—
138C22×C3×C4—22no—
139C22×C3×C4—24no—
140C22×C3×C4—24no—
141C22×C3×C4—22no—
142C22×C3×C4—24no—
143C22×C3×C4—22no—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—38no—
150C22×C3×C4—38no—
151C22×C3×C4—34no—
152C22×C3×C4—34no—
153C22×C3×C4—44no—
154C22×C3×C4—44no—
155C22×C3×C4—64no—
156C22×C3×C4—64no—
157C22×C3×C4—64no—
158C22×C3×C4—64no—
159C22×C3×C4Dic614yescomplemented
160C22×C3×C4#6714yes—
161C22×C3×C4C3×D414yes—
162C22×C3×C4C3×Q814yescomplemented
163C22×C3×C4C22×D312yes—
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D312yes—
166C22×C3×C4C23×C312yes—
167C22×C3×C4C23×C312yes—
168C22×C3×C4C23×C312yes—
169C22×Dic3—24no—
170C22×Dic3—24no—
171C22×Dic3—24no—
172C22×Dic3—24no—
173C22×Dic3C3×D418yes—
174C22×Dic3C3×Q818yescomplemented
175C22×Dic3C23×C314yes—
176C22×Dic3C23×C314yes—
177C2×Dic6—232no—
178C2×Dic6—28no—
179C2×Dic6—216no—
180C3×C4⋊C4—216no—
181C3×C4⋊C4—28no—
182C3×C4⋊C4—28no—
183C3×C4⋊C4—616no—
184Dic3⋊C4—216no—
185C22×C32#12014yes—
186C22×C32C22⋊Q818yes—
187C22×C32C22⋊Q814yes—
188C22×C32C4⋊Q818yes—
189C22×C32C4⋊Q814yes—
190C22×C32C22×D412yes—
191C22×C32C22×D411yescharacteristic
192C22×C32C22×Q811yescharacteristic
193C22×C32C22×Q812yes—
194C22×C32C2×#4111yescharacteristic
195C32×C4—24no—
196C32×C4—24no—
197C32×C4—42no—
198C3×Dic3—28no—
199C3×Dic3—28no—
200C22×Q8—34no—
201C22×Q8—68no—
202C22×Q8—64no—
203C23×C4—32no—
204C23×C4—32no—
205C23×C4C2×C3×D311yescharacteristic
206C23×C4C2×C3×D311yescharacteristic
207C23×C4C2×C3×D311yescharacteristic
208C2×C4⋊C4—24no—
209C2×C4⋊C4—38no—
210C2×C4⋊C4—68no—
211C2×C4⋊C4C2×C3×D314yes—
212#95—34no—
213#95—38no—
214C23×C3—21no—
215C23×C3—22no—
216C23×C3—22no—
217C23×C3—24no—
218C23×C3—24no—
219C23×C3—22no—
220C23×C3C2×Dic612yes—
221C23×C3#23512yes—
222C23×C3D3×D414yes—
223C23×C3D3×Q814yes—
224C23×C3C2×#6712yes—
225C23×C3C2×C3×D414yes—
226C23×C3C2×C3×D412yes—
227C23×C3C2×C3×Q812yes—
228C23×C3C2×C3×Q814yes—
229C23×C3C3×#4112yes—
230C23×C3C23×D311yescharacteristic
231C23×C3C24×C311yescharacteristic
232C3×Q8—632no—
233C2×C3×C4—24no—
234C2×C3×C4—216no—
235C2×C3×C4—24no—
236C2×C3×C4—28no—
237C2×C3×C4—28no—
238C2×C3×C4—28no—
239C2×C3×C4—28no—
240C2×C3×C4—22no—
241C2×C3×C4—24no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—24no—
245C2×C3×C4—22no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—22no—
249C2×C3×C4—24no—
250C2×C3×C4—22no—
251C2×C3×C4—24no—
252C2×C3×C4—24no—
253C2×C3×C4—38no—
254C2×C3×C4—38no—
255C2×C3×C4—48no—
256C2×C3×C4—44no—
257C2×C3×C4—44no—
258C2×C3×C4—48no—
259C2×C3×C4—44no—
260C2×C3×C4—44no—
261C2×C3×C4—616no—
262C2×C3×C4—616no—
263C2×C3×C4—64no—
264C2×C3×C4—64no—
265C2×C3×C4—64no—
266C2×C3×C4—64no—
267C2×C3×C4C2×Dic614yescomplemented
268C2×C3×C4C2×#6714yes—
269C2×C3×C4C2×C3×D414yes—
270C2×C3×C4C2×C3×Q814yescomplemented
271C2×Dic3—216no—
272C2×Dic3—216no—
273C2×Dic3—24no—
274C2×Dic3—24no—
275C2×Dic3—24no—
276C2×Dic3—24no—
277C2×Dic3C2×C3×D418yes—
278C2×Dic3C2×C3×Q818yescomplemented
279Dic6—232no—
280C2×C32#39518yescomplemented
281C2×C32C2×#12011yescharacteristic
282C2×C32C2×C22⋊Q812yes—
283C2×C32C2×C22⋊Q811yescharacteristic
284C2×C32C2×C4⋊Q812yes—
285C2×C32C2×C4⋊Q811yescharacteristic
286C24C22×C3×D311yescharacteristic
287C2×Q8—616no—
288C2×Q8—632no—
289C2×Q8—68no—
290C22×C4—22no—
291C22×C4—24no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—22no—
295C22×C4—34no—
296C22×C4—34no—
297C22×C4—38no—
298C22×C4—38no—
299C22×C4—64no—
300C22×C4—64no—
301C22×C4—64no—
302C22×C4—64no—
303C22×C4C3×Dic614yescomplemented
304C22×C4C3×#6714yes—
305C22×C4C22×C3×D312yes—
306C22×C4C22×C3×D312yes—
307C22×C4C22×C3×D312yes—
308C4⋊C4—28no—
309C4⋊C4—616no—
310C22×C3—28no—
311C22×C3—28no—
312C22×C3—24no—
313C22×C3—24no—
314C22×C3—24no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—21no—
320C22×C3#88818yes—
321C22×C3#89618yes—
322C22×C3#92414yes—
323C22×C3#93714yes—
324C22×C3#94414yes—
325C22×C3C3×#12014yes—
326C22×C3C3×C22⋊Q818yes—
327C22×C3C3×C22⋊Q814yes—
328C22×C3C3×C4⋊Q818yes—
329C22×C3C3×C4⋊Q814yes—
330C22×C3C22×Dic611yescharacteristic
331C22×C3C2×#23511yescharacteristic
332C22×C3C2×D3×D412yes—
333C22×C3C2×D3×Q812yes—
334C22×C3C22×#6711yescharacteristic
335C22×C3C22×C3×D412yes—
336C22×C3C22×C3×D411yescharacteristic
337C22×C3C22×C3×Q811yescharacteristic
338C22×C3C22×C3×Q812yes—
339C22×C3C2×C3×#4111yescharacteristic
340C3×C4—28no—
341C3×C4—24no—
342C3×C4—24no—
343C3×C4—24no—
344C3×C4—24no—
345C3×C4—44no—
346C3×C4—44no—
347C3×C4—42no—
348C3×C4—42no—
349C3×C4—68no—
350C3×C4—68no—
351Dic3—28no—
352Dic3—28no—
353C32C2×#39511yescharacteristic, complemented, Sylow
354C23C2×C3×Dic612yes—
355C23C3×#23512yes—
356C23C3×D3×D414yes—
357C23C3×D3×Q814yes—
358C23C2×C3×#6712yes—
359C23C23×C3×D311yescharacteristic
360Q8—632no—
361C2×C4—28no—
362C2×C4—28no—
363C2×C4—22no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—38no—
369C2×C4—38no—
370C2×C4—44no—
371C2×C4—616no—
372C2×C4—616no—
373C2×C4—64no—
374C2×C4—64no—
375C2×C4—64no—
376C2×C4—64no—
377C2×C4C2×C3×Dic614yescomplemented
378C2×C4C2×C3×#6714yes—
379C2×C3—22no—
380C2×C3—22no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—28no—
385C2×C3#497918yesdirect product factor
386C2×C3C3×#39518yescomplemented
387C2×C3C2×#88812yes—
388C2×C3C2×#89612yes—
389C2×C3C2×#92411yescharacteristic
390C2×C3C2×#93711yescharacteristic
391C2×C3C2×#94411yescharacteristic
392C2×C3C2×C3×#12011yescharacteristic
393C2×C3C2×C3×C22⋊Q812yes—
394C2×C3C2×C3×C22⋊Q811yescharacteristic
395C2×C3C2×C3×C4⋊Q812yes—
396C2×C3C2×C3×C4⋊Q811yescharacteristic
397C22C3×#88818yes—
398C22C3×#89618yes—
399C22C3×#92414yes—
400C22C3×#93714yes—
401C22C3×#94414yes—
402C22C22×C3×Dic611yescharacteristic
403C22C2×C3×#23511yescharacteristic
404C22C2×C3×D3×D412yes—
405C22C2×C3×D3×Q812yes—
406C22C22×C3×#6711yescharacteristic
407C4—24no—
408C4—24no—
409C4—42no—
410C4—68no—
411C4—68no—
412C3—21no—
413C3C2×#497911yescharacteristic, direct product factor
414C3C2×C3×#39511yescharacteristic, complemented
415C2C3×#497918yesdirect product factor
416C2C2×C3×#88812yes—
417C2C2×C3×#89612yes—
418C2C2×C3×#92411yescharacteristic
419C2C2×C3×#93711yescharacteristic
420C2C2×C3×#94411yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC22×C32×C4⋊C4C2
socle, prime radicalC24×C32C23
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#395
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. C3×#4979C2direct (N × H)
8. C2×#4979C3direct (N × H)
35. #4979C2×C3direct (N × H)
43. C22×C32×C4Q8semidirect
52. C22×C3×Dic3Q8semidirect
109. C2×C32×C4C2×Q8semidirect
117. C2×C3×Dic3C2×Q8semidirect
159. C22×C3×C4Dic6semidirect
162. C22×C3×C4C3×Q8semidirect
174. C22×Dic3C3×Q8semidirect
267. C2×C3×C4C2×Dic6semidirect
270. C2×C3×C4C2×C3×Q8semidirect
278. C2×Dic3C2×C3×Q8semidirect
280. C2×C32#395semidirect
303. C22×C4C3×Dic6semidirect
353. C32C2×#395semidirect
377. C2×C4C2×C3×Dic6semidirect
385. C2×C3#4979direct (N × H)
386. C2×C3C3×#395semidirect
413. C3C2×#4979direct (N × H)
414. C3C2×C3×#395semidirect
415. C2C3×#4979direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C22×C32×C4⋊C42
C22×C3×Dic3⋊C42
C2×C3×C3⋊#952
C3×#49792
C2×C3×#3953
C2×#49793