Finite Group Databasebeta

← C3×#69654 #11795384

Subgroups — C3×#69654 #11795384

Order 1152.

677 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#390C211yesmaximal, characteristic
2C2×C3×#832C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C3×#4936C211yesmaximal, characteristic, complemented
7C3×#4524C211yesmaximal, characteristic, complemented
8C3×#2092—31nomaximal
9#69654C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4—22no—
13C2×C32×C42C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C3×#832—22no—
19C3×#832—22no—
20C3×C3⋊#95—22no—
21C3×#808—22no—
22C3×#807—22no—
23C2×C3×#107—31no—
24C2×C3×#106—31no—
25C2×C3×#102—31no—
26C2×C3×#102—31no—
27C3×#390—21no—
28C3×#390D311yescharacteristic
29C3×#390C2×C311yescharacteristic
30C3×#382—31no—
31C2×#832C2×C311yescharacteristic
32C2×#832C2×C311yescharacteristic
33C2×#808C2×C311yescharacteristic, complemented
34C2×#807C2×C311yescharacteristic, complemented
35#4936C2×C311yescharacteristic, complemented
36C3×#336—31no—
37#4524C2×C311yescharacteristic, complemented
38C24×C32—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4Q812yes—
45C22×C32×C4—21no—
46C22×C32×C4D412yes—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C22⋊C4—44no—
53C32×C42—21no—
54C32×C42—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8D412yes—
64C2×C3×C3⋊C8D412yes—
65#2092—31noSylow
66C22×C3×D4—21no—
67C22×C3×D4C2×D311yescharacteristic
68C22×C3×D4C22×C311yescharacteristic
69C22×C3×C8—31no—
70C22×C3×C8—31no—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×C3×C4⋊C4C22×C311yescharacteristic
76C2×C3×C22⋊C4—24no—
77C2×C3×C22⋊C4—22no—
78C2×C3×C22⋊C4—22no—
79C2×C3×C42—21no—
80C2×C3×C42C2×D311yescharacteristic
81C2×C3×C42C22×C311yescharacteristic
82C2×C4⋊Dic3C22×C311yescharacteristic
83C2×C4⋊Dic3C22×C311yescharacteristic
84C22×C3⋊C8C22×C311yescharacteristic
85C22×C3⋊C8C22×C311yescharacteristic
86C3×#107—62no—
87C3×#106—62no—
88C3×#102—62no—
89C3×#102—62no—
90C3×#95—62no—
91#832—22no—
92#832—22no—
93C3⋊#95—22no—
94#808—22no—
95#807—22no—
96C23×C32—22no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32—42no—
100C23×C32—42no—
101C23×C32C2×D411yescharacteristic
102C32×D4—22no—
103C32×D4—22no—
104C32×D4—41no—
105C32×D4—41no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—41no—
110C2×C32×C4—42no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×Q811yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C3×C3⋊C8—22no—
122C3×C3⋊C8—22no—
123C2×#107—31no—
124C2×#106—31no—
125C2×#102—31no—
126C2×#102—31no—
127#390C3×D311yescharacteristic
128#382—31no—
129#336—31no—
130C24×C3—22no—
131C24×C3—21no—
132C24×C3—21no—
133C2×C3×D4—22no—
134C2×C3×D4—21no—
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—22no—
145C2×C3×D4—41no—
146C2×C3×D4—41no—
147C2×C3×D4—41no—
148C2×C3×D4—41no—
149C2×C3×D4Dic612yes—
150C2×C3×D4C3×Q812yes—
151C22×C3×C4—22no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—22no—
155C22×C3×C4—21no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4#6712yes—
159C22×C3×C4C3×D412yes—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C23×C311yescharacteristic
162C22×Dic3—21no—
163C22×Dic3—21no—
164C2×C3×C8—32no—
165C2×C3×C8—32no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—41no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C22⋊C4—48no—
181C3×C22⋊C4—44no—
182C3×C22⋊C4—44no—
183C3×C42—21no—
184C3×C42—21no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—41no—
188C3×C42—41no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8C3×D412yes—
198C2×C3⋊C8C3×D412yes—
199C22×C32—42no—
200C22×C32—44no—
201C22×C32—82no—
202C22×C32—81no—
203C22×C32—81no—
204C22×C32C22⋊Q811yescharacteristic
205C22×C32#12311yescharacteristic
206C22×C32#12711yescharacteristic
207C22×C32#13512yes—
208C22×C32AGL(1,ℤ/8)12yes—
209C32×C4—42no—
210C32×C4—81no—
211C32×C4C22⋊Q811yescharacteristic
212C32×C4C22⋊Q811yescharacteristic
213C32×C4#12311yescharacteristic
214C32×C4#12311yescharacteristic
215C3×Dic3—81no—
216C3×Dic3—81no—
217C22×D4C2×C3×D311yescharacteristic
218C22×C8—31no—
219C22×C8—31no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4—31no—
222C2×C4⋊C4C2×C3×D311yescharacteristic
223C2×C22⋊C4—22no—
224C2×C42C2×C3×D311yescharacteristic
225#107—62no—
226#106—62no—
227#102—62no—
228#102—62no—
229#95—62no—
230C23×C3—24no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—21no—
234C23×C3—44no—
235C23×C3—42no—
236C23×C3—42no—
237C23×C3—44no—
238C23×C3—42no—
239C23×C3—41no—
240C23×C3—41no—
241C23×C3—42no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—42no—
245C23×C3—42no—
246C23×C3C2×#6711yescharacteristic
247C23×C3C2×C3×D411yescharacteristic
248C3×D4—22no—
249C3×D4—22no—
250C3×D4—22no—
251C3×D4—22no—
252C3×D4—42no—
253C3×D4—42no—
254C3×D4—42no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C2×C3×C4—24no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—44no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—42no—
281C2×C3×C4—122no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—122no—
285C2×C3×C4C2×Dic611yescharacteristic
286C2×C3×C4#23511yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4#23711yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4C2×C3×D411yescharacteristic
292C2×C3×C4C2×C3×D411yescharacteristic
293C2×C3×C4C2×C3×Q811yescharacteristic
294C2×C3×C4C3×#4111yescharacteristic
295C2×C3×C4C3×#4111yescharacteristic
296C2×C3×C4C3×#4111yescharacteristic
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—42no—
300C2×Dic3—42no—
301C3×C8—62no—
302C3×C8—62no—
303C3⋊C8—22no—
304C3⋊C8—22no—
305C2×C32—82no—
306C2×C32#39911yescharacteristic
307C2×C32#47812yes—
308C2×C32#48212yes—
309C2×C32#49511yescharacteristic
310C2×C32#49611yescharacteristic
311C24—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4C3×Dic612yes—
318C22×C4—21no—
319C22×C4—61no—
320C22×C4—61no—
321C22×C4C3×#6712yes—
322C22×C4C22×C3×D311yescharacteristic
323C2×C8—32no—
324C2×C8—32no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—61no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C22⋊C4—44no—
336C42—21no—
337C42—21no—
338C22×C3—21no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—22no—
343C22×C3—44no—
344C22×C3—48no—
345C22×C3—42no—
346C22×C3—44no—
347C22×C3—42no—
348C22×C3—44no—
349C22×C3—84no—
350C22×C3—82no—
351C22×C3—82no—
352C22×C3—82no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—82no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3#92411yescharacteristic
359C22×C3#93212yes—
360C22×C3#93511yescharacteristic
361C22×C3#94011yescharacteristic
362C22×C3#95012yes—
363C22×C3C3×C22⋊Q811yescharacteristic
364C22×C3C3×#12311yescharacteristic
365C22×C3C3×#12711yescharacteristic
366C22×C3C3×#13512yes—
367C22×C3C3×AGL(1,ℤ/8)12yes—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—44no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—82no—
376C3×C4—81no—
377C3×C4—81no—
378C3×C4—241no—
379C3×C4—241no—
380C3×C4#87811yescharacteristic
381C3×C4#87811yescharacteristic
382C3×C4#88311yescharacteristic
383C3×C4#88311yescharacteristic
384C3×C4C3×C22⋊Q811yescharacteristic
385C3×C4C3×C22⋊Q811yescharacteristic
386C3×C4C3×#12311yescharacteristic
387C3×C4C3×#12311yescharacteristic
388Dic3—81no—
389Dic3—81no—
390C32#209211yescharacteristic, complemented, Sylow
391C23—22no—
392C23—42no—
393C23—41no—
394C23—41no—
395C23—42no—
396C23C2×C3×#6711yescharacteristic
397D4—22no—
398D4—22no—
399D4—41no—
400D4—41no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—122no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—122no—
410C2×C4C2×C3×Dic611yescharacteristic
411C2×C4C3×#23511yescharacteristic
412C2×C4C3×D3×D411yescharacteristic
413C2×C4C3×D3×D411yescharacteristic
414C2×C4C3×#23711yescharacteristic
415C2×C4C3×#23711yescharacteristic
416C8—62no—
417C8—62no—
418C2×C3—21no—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—84no—
424C2×C3—82no—
425C2×C3—82no—
426C2×C3#494911yescharacteristic
427C2×C3#500912yes—
428C2×C3#503512yes—
429C2×C3#505911yescharacteristic
430C2×C3#507411yescharacteristic
431C2×C3C3×#39911yescharacteristic
432C2×C3C3×#47812yes—
433C2×C3C3×#48212yes—
434C2×C3C3×#49511yescharacteristic
435C2×C3C3×#49611yescharacteristic
436C22—42no—
437C22—44no—
438C22—82no—
439C22—81no—
440C22—81no—
441C22C3×#92411yescharacteristic
442C22C3×#93212yes—
443C22C3×#93511yescharacteristic
444C22C3×#94011yescharacteristic
445C22C3×#95012yes—
446C4—42no—
447C4—81no—
448C4—241no—
449C4—241no—
450C4C3×#87811yescharacteristic
451C4C3×#87811yescharacteristic
452C4C3×#88311yescharacteristic
453C4C3×#88311yescharacteristic
454C3—21no—
455C3#6965411yescharacteristic, direct product factor
456C3C3×#209211yescharacteristic, complemented
457C2—82no—
458C2C3×#494911yescharacteristic
459C2C3×#500912yes—
460C2C3×#503512yes—
461C2C3×#505911yescharacteristic
462C2C3×#507411yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenterC3×#390D3
hypocenterC3C3×#2092
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
4. C2×C3×#808C2semidirect
5. C2×C3×#807C2semidirect
6. C3×#4936C2semidirect
7. C3×#4524C2semidirect
9. #69654C3direct (N × H)
33. C2×#808C2×C3semidirect
34. C2×#807C2×C3semidirect
35. #4936C2×C3semidirect
37. #4524C2×C3semidirect
390. C32#2092semidirect
455. C3#69654direct (N × H)
456. C3C3×#2092semidirect

Maximal subgroups

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

subgroupindex
C32×#3902
C2×C3×#8322
C2×C3×#8082
C2×C3×#8072
C3×#49362
C3×#45242
C3×#20923
#696543