Finite Group Databasebeta

← C2×#10591317 #11808483

Subgroups — C2×#10591317 #11808483

Order 1152.

2025 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×Dic3⋊Dic3C212yesmaximal, complemented
4C22×(C2×D3)⋊Dic3C212yesmaximal
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6#10591317C218yesmaximal, direct product factor
7C2×#4949—31nomaximal
8C2×#4677—31nomaximal
9C24×C3×D3C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2212yes—
12C23×C3×Dic3C2211yescharacteristic
13C23×C3×Dic3C2212yes—
14C2×C4⋊(C3⋊Dic3)—24no—
15C2×C4⋊(C3⋊Dic3)C2214yescomplemented
16C2×C3×(C2×D3)⋊C4—24no—
17C2×C3×(C2×D3)⋊C4C2214yes—
18C2×Dic3⋊Dic3—28no—
19C2×Dic3⋊Dic3C2218yescomplemented
20C2×(C2×D3)⋊Dic3—28no—
21C2×(C2×D3)⋊Dic3C2218yes—
22C3×C3⋊#95C2214yescomplemented
23C22×C3×C22⋊C4—31no—
24C22×#217—32no—
25C22×(C2×D3)⋊C4—32no—
26C22×(C2×D3)⋊C4D311yescharacteristic
27C22×C4⋊Dic3—31no—
28C22×C4⋊Dic3—31no—
29C22×C4⋊Dic3—32no—
30C22×C4⋊Dic3—61no—
31C22×Dic3⋊C4—32no—
32C2×C3×#95—31no—
33C2×C3⋊#95D311yescharacteristic, complemented
34#4949—38no—
35#4677—38no—
36C24×C32C2311yescharacteristic
37C23×C3×D3—22no—
38C23×C3×D3—24no—
39C23×C3×D3—22no—
40C23×C3×D3—24no—
41C23×C3×D3Q814yes—
42C23×C3×D3C2312yes—
43C22×C32×C4—24no—
44C22×C32×C4D414yes—
45C22×C32×C4C2312yes—
46C22×C3⋊Dic3—24no—
47C22×C3⋊Dic3—24no—
48C22×C3⋊Dic3—24no—
49C22×C3⋊Dic3C2314yes—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—24no—
54C22×C3×Dic3D418yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2314yes—
57C4⋊(C3⋊Dic3)—28no—
58C3×(C2×D3)⋊C4—28no—
59Dic3⋊Dic3—216no—
60(C2×D3)⋊Dic3—216no—
61C2×#399—91noSylow
62C25×C3—31no—
63C24×D3C2×D311yescharacteristic
64C23×C3×C4—21no—
65C23×C3×C4—32no—
66C23×C3×C4—31no—
67C23×C3×C4C2×D311yescharacteristic
68C23×C3×C4C2×D311yescharacteristic
69C23×Dic3—32no—
70C23×Dic3—32no—
71C23×Dic3—62no—
72C23×Dic3C2×D311yescharacteristic
73C23×Dic3C2×D312yes—
74C2×C3×C22⋊C4—34no—
75C2×C3×C22⋊C4—64no—
76C2×#217—38no—
77C2×#217—68no—
78C2×(C2×D3)⋊C4—24no—
79C2×(C2×D3)⋊C4—38no—
80C2×(C2×D3)⋊C4—68no—
81C2×(C2×D3)⋊C4C2×D314yes—
82C2×C4⋊Dic3—34no—
83C2×C4⋊Dic3—34no—
84C2×C4⋊Dic3—38no—
85C2×C4⋊Dic3—64no—
86C2×C4⋊Dic3—68no—
87C2×C4⋊Dic3—68no—
88C2×C4⋊Dic3—64no—
89C2×C4⋊Dic3—64no—
90C2×Dic3⋊C4—38no—
91C2×Dic3⋊C4—68no—
92C3×#95—34no—
93C3⋊#95C2×D314yescomplemented
94C23×C32C2×D414yes—
95C23×C32C2×D412yes—
96C23×C32C2×Q812yes—
97C23×C32#4112yes—
98C23×C32#4114yes—
99C23×C32C2411yescharacteristic
100C22×C3×D3—216no—
101C22×C3×D3—28no—
102C22×C3×D3—24no—
103C22×C3×D3—22no—
104C22×C3×D3—22no—
105C22×C3×D3—24no—
106C22×C3×D3—48no—
107C22×C3×D3—44no—
108C22×C3×D3—44no—
109C22×C3×D3C2×Q814yes—
110C2×C32×C4—28no—
111C2×C32×C4—24no—
112C2×C32×C4C2×D414yes—
113C2×C3⋊Dic3—24no—
114C2×C3⋊Dic3—24no—
115C2×C3⋊Dic3—24no—
116C2×C3⋊Dic3—48no—
117C2×C3×Dic3—216no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—44no—
123C2×C3×Dic3C2×D418yes—
124C22×C4⋊C4—92no—
125C22×C4⋊C4—91no—
126C22×C22⋊C4—31no—
127C22×C22⋊C4—92no—
128#399—98no—
129C2×#95—31no—
130C24×C3—21no—
131C24×C3—34no—
132C24×C3—32no—
133C24×C3—64no—
134C24×C3—62no—
135C24×C3—62no—
136C24×C3—64no—
137C24×C3C22×D311yescharacteristic
138C24×C3C22×D311yescharacteristic
139C23×D3—22no—
140C23×D3—24no—
141C23×D3—24no—
142C23×D3—22no—
143C23×D3Dic614yes—
144C23×D3C22×D312yes—
145C22×C3×C4—28no—
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4—24no—
149C22×C3×C4—22no—
150C22×C3×C4—38no—
151C22×C3×C4—34no—
152C22×C3×C4—32no—
153C22×C3×C4—64no—
154C22×C3×C4—64no—
155C22×C3×C4—64no—
156C22×C3×C4—62no—
157C22×C3×C4D1214yes—
158C22×C3×C4#6714yes—
159C22×C3×C4C22×D312yes—
160C22×C3×C4C22×D312yes—
161C22×Dic3—24no—
162C22×Dic3—24no—
163C22×Dic3—24no—
164C22×Dic3—22no—
165C22×Dic3—34no—
166C22×Dic3—34no—
167C22×Dic3—64no—
168C22×Dic3—68no—
169C22×Dic3—64no—
170C22×Dic3—64no—
171C22×Dic3—64no—
172C22×Dic3—64no—
173C22×Dic3—64no—
174C22×Dic3—64no—
175C22×Dic3—124no—
176C22×Dic3—124no—
177C22×Dic3D1218yes—
178C22×Dic3C22×D312yes—
179C22×Dic3C22×D314yes—
180C3×C22⋊C4—68no—
181#217—616no—
182(C2×D3)⋊C4—28no—
183(C2×D3)⋊C4—616no—
184C4⋊Dic3—616no—
185C4⋊Dic3—616no—
186C4⋊Dic3—68no—
187C4⋊Dic3—68no—
188Dic3⋊C4—616no—
189C22×C32C22⋊Q818yes—
190C22×C32C22⋊Q814yes—
191C22×C32#12318yes—
192C22×C32#12314yes—
193C22×C32#12714yes—
194C22×C32C22×D412yes—
195C22×C32C22×D411yescharacteristic
196C22×C32C22×Q811yescharacteristic
197C22×C32C2×#4111yescharacteristic
198C22×C32C2×#4112yes—
199C2×C3×D3—28no—
200C2×C3×D3—24no—
201C2×C3×D3—44no—
202C2×C3×D3—42no—
203C2×C3×D3—42no—
204C2×C3×D3—416no—
205C32×C4—24no—
206C3⋊Dic3—44no—
207C3×Dic3—28no—
208C3×Dic3—42no—
209C25—31no—
210C23×C4—32no—
211C23×C4—31no—
212C23×C4—92no—
213C23×C4D3211yescharacteristic
214C2×C4⋊C4—98no—
215C2×C4⋊C4—94no—
216C2×C4⋊C4—188no—
217C2×C4⋊C4—184no—
218C2×C22⋊C4—34no—
219C2×C22⋊C4—64no—
220C2×C22⋊C4—98no—
221C2×C22⋊C4—188no—
222#95—34no—
223C23×C3—21no—
224C23×C3—22no—
225C23×C3—22no—
226C23×C3—24no—
227C23×C3—24no—
228C23×C3—22no—
229C23×C3—34no—
230C23×C3—68no—
231C23×C3—616no—
232C23×C3—64no—
233C23×C3—62no—
234C23×C3—62no—
235C23×C3—64no—
236C23×C3—124no—
237C23×C3—128no—
238C23×C3—124no—
239C23×C3C2×Dic612yes—
240C23×C3C2×D1214yes—
241C23×C3C2×D1212yes—
242C23×C3#23512yes—
243C23×C3D3×D414yes—
244C23×C3#23712yes—
245C23×C3#23714yes—
246C23×C3#23714yes—
247C23×C3D3×Q812yes—
248C23×C3C2×#6712yes—
249C23×C3C23×D311yescharacteristic
250C23×C3C23×D311yescharacteristic
251C22×D3—216no—
252C22×D3—28no—
253C22×D3—22no—
254C22×D3—24no—
255C22×D3—24no—
256C22×D3—22no—
257C22×D3—48no—
258C22×D3—44no—
259C22×D3—44no—
260C22×D3C2×Dic614yes—
261C2×C3×C4—28no—
262C2×C3×C4—216no—
263C2×C3×C4—28no—
264C2×C3×C4—28no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—38no—
269C2×C3×C4—616no—
270C2×C3×C4—64no—
271C2×C3×C4—64no—
272C2×C3×C4—64no—
273C2×C3×C4—62no—
274C2×C3×C4—124no—
275C2×C3×C4C2×D1214yes—
276C2×C3×C4C2×#6714yes—
277C2×Dic3—216no—
278C2×Dic3—24no—
279C2×Dic3—24no—
280C2×Dic3—24no—
281C2×Dic3—22no—
282C2×Dic3—44no—
283C2×Dic3—68no—
284C2×Dic3—64no—
285C2×Dic3—64no—
286C2×Dic3—64no—
287C2×Dic3—64no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—124no—
291C2×Dic3—124no—
292C2×Dic3—1216no—
293C2×Dic3—128no—
294C2×Dic3—128no—
295C2×Dic3C2×D1218yes—
296C2×C32#39918yescomplemented
297C2×C32C2×C22⋊Q812yes—
298C2×C32C2×C22⋊Q811yescharacteristic
299C2×C32C2×#12312yes—
300C2×C32C2×#12311yescharacteristic
301C2×C32C2×#12711yescharacteristic
302C3×D3—44no—
303C24—32no—
304C24—34no—
305C24—62no—
306C24—64no—
307C24—64no—
308C24—62no—
309C24C2×D3211yescharacteristic
310C22×C4—24no—
311C22×C4—34no—
312C22×C4—38no—
313C22×C4—32no—
314C22×C4—64no—
315C22×C4—64no—
316C22×C4—64no—
317C22×C4—62no—
318C22×C4—94no—
319C22×C4—184no—
320C22×C4—184no—
321C22×C4—184no—
322C22×C4#62614yes—
323C22×C4C2×D3212yes—
324C4⋊C4—1816no—
325C4⋊C4—188no—
326C22⋊C4—68no—
327C22⋊C4—1816no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—21no—
333C22×C3—24no—
334C22×C3—28no—
335C22×C3—28no—
336C22×C3—24no—
337C22×C3—24no—
338C22×C3—64no—
339C22×C3—68no—
340C22×C3—1216no—
341C22×C3—122no—
342C22×C3—124no—
343C22×C3—122no—
344C22×C3#87414yes—
345C22×C3#87818yes—
346C22×C3#88318yes—
347C22×C3#88618yes—
348C22×C3#88614yes—
349C22×C3#89714yes—
350C22×C3#89718yes—
351C22×C3#92414yes—
352C22×C3#93514yes—
353C22×C3#94014yes—
354C22×C3C22×Dic611yescharacteristic
355C22×C3C22×D1212yes—
356C22×C3C22×D1211yescharacteristic
357C22×C3C2×#23511yescharacteristic
358C22×C3C2×D3×D412yes—
359C22×C3C2×#23711yescharacteristic
360C22×C3C2×#23712yes—
361C22×C3C2×#23712yes—
362C22×C3C2×D3×Q811yescharacteristic
363C22×C3C22×#6711yescharacteristic
364C2×D3—28no—
365C2×D3—24no—
366C2×D3—416no—
367C2×D3—44no—
368C2×D3—42no—
369C2×D3—42no—
370C3×C4—28no—
371C3×C4—24no—
372C3×C4—24no—
373C3×C4—68no—
374C3×C4—122no—
375Dic3—28no—
376Dic3—42no—
377Dic3—128no—
378Dic3—124no—
379Dic3—124no—
380C32C2×#39911yescharacteristic, complemented, Sylow
381C23—34no—
382C23—62no—
383C23—64no—
384C23—64no—
385C23—62no—
386C23—68no—
387C23—616no—
388C23—128no—
389C23—124no—
390C23—124no—
391C23D3×Dic612yes—
392C23#379512yes—
393C23D3×D1214yes—
394C23#380514yes—
395C23C2×#62612yes—
396C23C22×D3211yescharacteristic
397C2×C4—24no—
398C2×C4—28no—
399C2×C4—38no—
400C2×C4—64no—
401C2×C4—64no—
402C2×C4—616no—
403C2×C4—64no—
404C2×C4—62no—
405C2×C4—124no—
406C2×C4—184no—
407C2×C4—184no—
408C2×C4—184no—
409C2×C4—368no—
410C2×C4C2×#62614yes—
411C2×C3—21no—
412C2×C3—28no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—124no—
418C2×C3#467718yescomplemented
419C2×C3#494918yescomplemented
420C2×C3C2×#87411yescharacteristic
421C2×C3C2×#87812yes—
422C2×C3C2×#88312yes—
423C2×C3C2×#88612yes—
424C2×C3C2×#88611yescharacteristic
425C2×C3C2×#89711yescharacteristic
426C2×C3C2×#89712yes—
427C2×C3C2×#92411yescharacteristic
428C2×C3C2×#93511yescharacteristic
429C2×C3C2×#94011yescharacteristic
430D3—44no—
431C22—64no—
432C22—68no—
433C22—1216no—
434C22—124no—
435C22—122no—
436C22—122no—
437C22#6385714yes—
438C22#6389118yes—
439C22#6389318yes—
440C22#6391114yes—
441C22#6396214yes—
442C22C2×D3×Dic611yescharacteristic
443C22C2×#379511yescharacteristic
444C22C2×D3×D1212yes—
445C22C2×#380512yes—
446C22C22×#62611yescharacteristic
447C4—24no—
448C4—68no—
449C4—122no—
450C4—364no—
451C3—21no—
452C3C2×#467711yescharacteristic, complemented
453C3C2×#494911yescharacteristic, complemented
454C2—124no—
455C2#1059131718yesdirect product factor
456C2C2×#6385711yescharacteristic
457C2C2×#6389112yes—
458C2C2×#6389312yes—
459C2C2×#6391111yescharacteristic
460C2C2×#6396211yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32C2×#399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊(C3⋊Dic3)C2semidirect
3. C22×Dic3⋊Dic3C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. #10591317C2direct (N × H)
15. C2×C4⋊(C3⋊Dic3)C22semidirect
19. C2×Dic3⋊Dic3C22semidirect
22. C3×C3⋊#95C22semidirect
33. C2×C3⋊#95D3semidirect
93. C3⋊#95C2×D3semidirect
296. C2×C32#399semidirect
380. C32C2×#399semidirect
418. C2×C3#4677semidirect
419. C2×C3#4949semidirect
452. C3C2×#4677semidirect
453. C3C2×#4949semidirect
455. C2#10591317direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C22×C3×(C2×D3)⋊C42
C22×Dic3⋊Dic32
C22×(C2×D3)⋊Dic32
C2×C3×C3⋊#952
#105913172
C2×#49493
C2×#46773