Finite Group Databasebeta

← C3×#68958 #11794306

Subgroups — C3×#68958 #11794306

Order 1152.

699 conjugacy classes of subgroups.

The subgroup lattice has 443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5483C211yesmaximal, characteristic
2C3×#4950C212yesmaximal
3C3×#4946C211yesmaximal, characteristic
4C32×#342C211yesmaximal, characteristic
5C3×#4527C212yesmaximal
6C3×#2062—31nomaximal
7#68958C311yesmaximal, characteristic, direct product factor
8C23×C3×Dic3C2211yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×C32×C22⋊C4C2212yes—
11C2×C3×#217C2212yes—
12C2×C3×#217C2211yescharacteristic
13C2×C3×C4⋊Dic3—22no—
14C3×#924—21no—
15C3×#924—21no—
16C2×C3×Dic3⋊C4—21no—
17C3×#878—22no—
18C3×#878—22no—
19C3×C3⋊#95—21no—
20C3×C3⋊#95—22no—
21C3×#543—31no—
22#5483C2×C311yescharacteristic
23C3×#385—31no—
24C3×#385—32no—
25#4950C2×C312yes—
26#4946C2×C311yescharacteristic
27C3×#342—21no—
28C3×#342—32no—
29C3×#342D311yescharacteristic
30C3×#342C2×C311yescharacteristic
31#4527C2×C312yes—
32C24×C32C2311yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—22no—
39C22×C3×Dic3—42no—
40C22×C3×Dic3D412yes—
41C22×C3×Dic3D412yes—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C32×C22⋊C4—22no—
45C32×C22⋊C4—22no—
46C32×C22⋊C4Q814yescomplemented
47C3×#217—22no—
48C3×#217—22no—
49C3×#217—21no—
50C3×#217Q812yescomplemented
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—44no—
54C3×Dic3⋊C4—22no—
55C3×Dic3⋊C4—22no—
56C3×Dic3⋊C4—42no—
57#2062—31noSylow
58C23×C3×C4—31no—
59C23×Dic3C22×C311yescharacteristic
60C3×C22⋊Q8—62no—
61C3×C22⋊Q8—62no—
62C3×C22⋊Q8—61no—
63C3×C22⋊Q8—61no—
64C2×C3×C4⋊C4—62no—
65C2×C3×C4⋊C4—61no—
66C2×C3×C22⋊C4—22no—
67C2×C3×C22⋊C4—21no—
68C2×C3×C22⋊C4—31no—
69C2×C3×C22⋊C4—32no—
70C2×C3×C22⋊C4C2×D311yescharacteristic
71C2×C3×C22⋊C4C2×D312yes—
72C2×C3×C22⋊C4C22×C311yescharacteristic
73C2×C3×C22⋊C4C22×C312yes—
74C2×#217C22×C312yes—
75C2×#217C22×C311yescharacteristic
76C2×C4⋊Dic3—22no—
77#924—21no—
78#924—21no—
79C2×Dic3⋊C4—21no—
80#878—22no—
81#878—22no—
82C3×#95—62no—
83C3×#95—61no—
84C3⋊#95—21no—
85C3⋊#95—22no—
86C23×C32—41no—
87C23×C32—41no—
88C23×C32C2×D411yescharacteristic
89C23×C32C2×D412yes—
90C23×C32C2×Q812yes—
91C23×C32C2×Q811yescharacteristic
92C23×C32#4111yescharacteristic
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—24no—
96C2×C32×C4—42no—
97C2×C32×C4—42no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—42no—
109C2×C3×Dic3—41no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×Dic6—81no—
113C3×Dic6—81no—
114#543—31no—
115#385—31no—
116#385—32no—
117#342—32no—
118#342C3×D311yescharacteristic
119C24×C3—21no—
120C24×C3C22×D311yescharacteristic
121C24×C3C23×C311yescharacteristic
122C2×C3×Q8—61no—
123C2×C3×Q8—61no—
124C22×C3×C4—22no—
125C22×C3×C4—22no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—32no—
129C22×C3×C4—32no—
130C22×C3×C4—42no—
131C22×C3×C4—61no—
132C22×C3×C4—61no—
133C22×C3×C4—62no—
134C22×C3×C4—122no—
135C22×C3×C4D1211yescharacteristic
136C22×C3×C4D1211yescharacteristic
137C22×C3×C4C3×D411yescharacteristic
138C22×C3×C4C3×D411yescharacteristic
139C22×Dic3—21no—
140C22×Dic3—21no—
141C22×Dic3—22no—
142C22×Dic3—42no—
143C22×Dic3C3×D412yes—
144C22×Dic3C3×D412yes—
145C2×Dic6—21no—
146C2×Dic6—21no—
147C3×C4⋊C4—62no—
148C3×C4⋊C4—62no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—122no—
152C3×C4⋊C4—124no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—22no—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—24no—
158C3×C22⋊C4—32no—
159C3×C22⋊C4—42no—
160C3×C22⋊C4—42no—
161C3×C22⋊C4—62no—
162C3×C22⋊C4—62no—
163C3×C22⋊C4—61no—
164C3×C22⋊C4Dic614yescomplemented
165C3×C22⋊C4C3×Q814yescomplemented
166#217—22no—
167#217—22no—
168#217—21no—
169#217C3×Q812yescomplemented
170C4⋊Dic3—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—44no—
173Dic3⋊C4—22no—
174Dic3⋊C4—22no—
175Dic3⋊C4—42no—
176C22×C32—21no—
177C22×C32—22no—
178C22×C32—21no—
179C22×C32—22no—
180C22×C32—42no—
181C22×C32—41no—
182C22×C32—41no—
183C22×C32#12011yescharacteristic
184C22×C32C22⋊Q812yes—
185C22×C32C22⋊Q811yescharacteristic
186C22×C32C4⋊Q811yescharacteristic
187C22×C32C4⋊Q812yes—
188C32×C4—44no—
189C32×C4—41no—
190C32×C4—41no—
191C3×Dic3—42no—
192C3×Dic3—42no—
193C3×Dic3—42no—
194C3×Dic3—42no—
195C23×C4—31no—
196C22⋊Q8—62no—
197C22⋊Q8—62no—
198C22⋊Q8—61no—
199C22⋊Q8—61no—
200C2×C4⋊C4—62no—
201C2×C4⋊C4—61no—
202C2×C22⋊C4—31no—
203C2×C22⋊C4—32no—
204C2×C22⋊C4C2×C3×D311yescharacteristic
205C2×C22⋊C4C2×C3×D312yes—
206#95—62no—
207#95—61no—
208C23×C3—22no—
209C23×C3—21no—
210C23×C3—22no—
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—41no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3—41no—
217C23×C3—81no—
218C23×C3—81no—
219C23×C3C2×Dic612yes—
220C23×C3C2×D1211yescharacteristic
221C23×C3D3×D412yes—
222C23×C3#23711yescharacteristic
223C23×C3D3×Q811yescharacteristic
224C23×C3C2×C3×D411yescharacteristic
225C23×C3C2×C3×D412yes—
226C23×C3C2×C3×Q812yes—
227C23×C3C2×C3×Q811yescharacteristic
228C23×C3C3×#4111yescharacteristic
229C3×Q8—241no—
230C3×Q8—241no—
231C2×C3×C4—24no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—24no—
237C2×C3×C4—44no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—62no—
249C2×C3×C4—64no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—62no—
253C2×C3×C4—82no—
254C2×C3×C4—82no—
255C2×C3×C4—81no—
256C2×C3×C4—81no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4—122no—
261C2×C3×C4—121no—
262C2×C3×C4—122no—
263C2×C3×C4—122no—
264C2×Dic3—22no—
265C2×Dic3—24no—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—41no—
270C2×Dic3—41no—
271C2×Dic3—41no—
272C2×Dic3—42no—
273C2×Dic3—41no—
274C2×Dic3—42no—
275C2×Dic3—42no—
276Dic6—81no—
277Dic6—81no—
278C2×C32—21no—
279C2×C32—22no—
280C2×C32—21no—
281C2×C32—22no—
282C2×C32#39511yescharacteristic
283C2×C32B(4,𝔽2)11yescharacteristic
284C2×C32#45811yescharacteristic
285C24C22×C3×D311yescharacteristic
286C2×Q8—61no—
287C2×Q8—61no—
288C22×C4—22no—
289C22×C4—32no—
290C22×C4—32no—
291C22×C4—61no—
292C22×C4—61no—
293C22×C4—62no—
294C22×C4—122no—
295C22×C4C3×D1211yescharacteristic
296C22×C4C3×D1211yescharacteristic
297C4⋊C4—62no—
298C4⋊C4—62no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4—122no—
302C4⋊C4—124no—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—32no—
306C22⋊C4—62no—
307C22⋊C4—62no—
308C22⋊C4—61no—
309C22⋊C4C3×Dic614yescomplemented
310C22×C3—21no—
311C22×C3—22no—
312C22×C3—21no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—21no—
320C22×C3—22no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—41no—
324C22×C3—42no—
325C22×C3—41no—
326C22×C3—42no—
327C22×C3—42no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—42no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—82no—
334C22×C3—81no—
335C22×C3—81no—
336C22×C3#86911yescharacteristic
337C22×C3#87812yes—
338C22×C3#88211yescharacteristic
339C22×C3#88812yes—
340C22×C3#89711yescharacteristic
341C22×C3C3×#12011yescharacteristic
342C22×C3C3×C22⋊Q812yes—
343C22×C3C3×C22⋊Q811yescharacteristic
344C22×C3C3×C4⋊Q812yes—
345C22×C3C3×C4⋊Q811yescharacteristic
346C3×C4—44no—
347C3×C4—44no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—81no—
353C3×C4—81no—
354C3×C4—84no—
355C3×C4—122no—
356C3×C4—122no—
357C3×C4—122no—
358C3×C4—122no—
359Dic3—42no—
360Dic3—42no—
361Dic3—42no—
362Dic3—42no—
363C32#206211yescharacteristic, complemented, Sylow
364C23—41no—
365C23—41no—
366C23C2×C3×Dic612yes—
367C23C2×C3×D1211yescharacteristic
368C23C3×D3×D412yes—
369C23C3×#23711yescharacteristic
370C23C3×D3×Q811yescharacteristic
371Q8—241no—
372Q8—241no—
373C2×C4—24no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—62no—
381C2×C4—64no—
382C2×C4—62no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—121no—
386C2×C4—121no—
387C2×C4—122no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—122no—
391C2×C4—122no—
392C2×C3—21no—
393C2×C3—22no—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—22no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—22no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—42no—
404C2×C3—41no—
405C2×C3—42no—
406C2×C3—41no—
407C2×C3#465611yescharacteristic
408C2×C3#474111yescharacteristic
409C2×C3#474211yescharacteristic
410C2×C3C3×#39511yescharacteristic
411C2×C3C3×B(4,𝔽2)11yescharacteristic
412C2×C3C3×#45811yescharacteristic
413C22—21no—
414C22—22no—
415C22—21no—
416C22—22no—
417C22—42no—
418C22—41no—
419C22—41no—
420C22C3×#86911yescharacteristic
421C22C3×#87812yes—
422C22C3×#88211yescharacteristic
423C22C3×#88812yes—
424C22C3×#89711yescharacteristic
425C4—44no—
426C4—41no—
427C4—41no—
428C4—122no—
429C4—122no—
430C4—122no—
431C4—122no—
432C3—21no—
433C3#6895811yescharacteristic, direct product factor
434C3C3×#206211yescharacteristic, complemented
435C2—22no—
436C2—21no—
437C2—22no—
438C2—21no—
439C2C3×#465611yescharacteristic
440C2C3×#474111yescharacteristic
441C2C3×#474211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC24×C3C23×C3
FrattiniC24C22×C3×D3
FittingC32×#342C2
socleC22×C32#120
prime radicalC24×C32C23
hypercenterC3×#342D3
hypocenterC3C3×#2062
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#342

Complements

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

NH ≅ G/Ntype
7. #68958C3direct (N × H)
46. C32×C22⋊C4Q8semidirect
50. C3×#217Q8semidirect
164. C3×C22⋊C4Dic6semidirect
165. C3×C22⋊C4C3×Q8semidirect
169. #217C3×Q8semidirect
309. C22⋊C4C3×Dic6semidirect
363. C32#2062semidirect
433. C3#68958direct (N × H)
434. C3C3×#2062semidirect

Maximal subgroups

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

subgroupindex
C3×#54832
C3×#49502
C3×#49462
C32×#3422
C3×#45272
C3×#20623
#689583