Finite Group Databasebeta

← C3×#69594 #11794303

Subgroups — C3×#69594 #11794303

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5483C211yesmaximal, characteristic
2C32×#385C211yesmaximal, characteristic
3C3×#5210C212yesmaximal
4C3×#4527C212yesmaximal
5C3×#4526C211yesmaximal, characteristic
6C3×#2062—31nomaximal
7#69594C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C2×C32×C4⋊C4—21no—
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×C3×#217C2212yes—
13C2×C3×#217C2212yes—
14C3×#924—21no—
15C3×#924—21no—
16C2×C3×Dic3⋊C4—22no—
17C3×#878—22no—
18C3×#878—22no—
19C32×#95—21no—
20C3×C3⋊#95—22no—
21C3×#543—31no—
22#5483C2×C311yescharacteristic
23C3×#385—21no—
24C3×#385—32no—
25C3×#385D311yescharacteristic
26C3×#385C2×C311yescharacteristic
27#5210C2×C312yes—
28C3×#342—31no—
29C3×#342—32no—
30#4527C2×C312yes—
31#4526C2×C311yescharacteristic
32C24×C32C2311yescharacteristic
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4—22no—
36C22×C32×C4—42no—
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C3×Dic3—22no—
40C22×C3×Dic3D412yes—
41C22×C3×Dic3D412yes—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4—42no—
45C32×C22⋊C4—22no—
46C32×C22⋊C4—21no—
47C32×C22⋊C4Q812yescomplemented
48C3×#217—22no—
49C3×#217—22no—
50C3×#217—22no—
51C3×#217Q814yescomplemented
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×Dic3⋊C4—22no—
55C3×Dic3⋊C4—22no—
56C3×Dic3⋊C4—44no—
57#2062—31noSylow
58C23×C3×C4—21no—
59C23×C3×C4C2×D311yescharacteristic
60C23×C3×C4C22×C311yescharacteristic
61C3×C22⋊Q8—62no—
62C3×C22⋊Q8—62no—
63C3×C22⋊Q8—61no—
64C3×C22⋊Q8—61no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—62no—
69C2×C3×C22⋊C4—21no—
70C2×C3×C22⋊C4—21no—
71C2×C3×C22⋊C4—32no—
72C2×C3×C22⋊C4—32no—
73C2×C3×C22⋊C4C2×D311yescharacteristic
74C2×C3×C22⋊C4C2×D311yescharacteristic
75C2×C3×C22⋊C4C22×C311yescharacteristic
76C2×C3×C22⋊C4C22×C311yescharacteristic
77C2×#217C22×C312yes—
78C2×#217C22×C312yes—
79#924—21no—
80#924—21no—
81C2×Dic3⋊C4—22no—
82#878—22no—
83#878—22no—
84C3×#95—22no—
85C3×#95—21no—
86C3×#95—21no—
87C3×#95—62no—
88C3⋊#95—22no—
89C23×C32—41no—
90C23×C32—41no—
91C23×C32C2×D412yes—
92C23×C32C2×D411yescharacteristic
93C23×C32C2×Q811yescharacteristic
94C23×C32C2×Q812yes—
95C23×C32#4111yescharacteristic
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—24no—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4—42no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—42no—
115C3×Dic6—81no—
116C3×Dic6—81no—
117#543—31no—
118#385—32no—
119#385C3×D311yescharacteristic
120#342—31no—
121#342—32no—
122C24×C3—21no—
123C24×C3C22×D311yescharacteristic
124C24×C3C23×C311yescharacteristic
125C2×C3×Q8—61no—
126C2×C3×Q8—61no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—32no—
138C22×C3×C4—32no—
139C22×C3×C4—42no—
140C22×C3×C4—42no—
141C22×C3×C4—42no—
142C22×C3×C4—44no—
143C22×C3×C4—62no—
144C22×C3×C4#6711yescharacteristic
145C22×C3×C4#6711yescharacteristic
146C22×C3×C4C3×D411yescharacteristic
147C22×C3×C4C3×D411yescharacteristic
148C22×Dic3—22no—
149C22×Dic3C3×D412yes—
150C22×Dic3C3×D412yes—
151C2×Dic6—21no—
152C2×Dic6—21no—
153C3×C4⋊C4—42no—
154C3×C4⋊C4—42no—
155C3×C4⋊C4—44no—
156C3×C4⋊C4—62no—
157C3×C4⋊C4—62no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—124no—
161C3×C22⋊C4—22no—
162C3×C22⋊C4—21no—
163C3×C22⋊C4—22no—
164C3×C22⋊C4—22no—
165C3×C22⋊C4—21no—
166C3×C22⋊C4—22no—
167C3×C22⋊C4—34no—
168C3×C22⋊C4—42no—
169C3×C22⋊C4—62no—
170C3×C22⋊C4—62no—
171C3×C22⋊C4—62no—
172C3×C22⋊C4Dic612yescomplemented
173C3×C22⋊C4C3×Q812yescomplemented
174#217—22no—
175#217—22no—
176#217—22no—
177#217C3×Q814yescomplemented
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180Dic3⋊C4—22no—
181Dic3⋊C4—22no—
182Dic3⋊C4—44no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—22no—
186C22×C32—22no—
187C22×C32—41no—
188C22×C32—42no—
189C22×C32—41no—
190C22×C32#12011yescharacteristic
191C22×C32C22⋊Q812yes—
192C22×C32C22⋊Q811yescharacteristic
193C22×C32C4⋊Q812yes—
194C22×C32C4⋊Q811yescharacteristic
195C32×C4—42no—
196C32×C4—42no—
197C32×C4—41no—
198C32×C4—41no—
199C3×Dic3—44no—
200C3×Dic3—42no—
201C3×Dic3—42no—
202C23×C4C2×C3×D311yescharacteristic
203C22⋊Q8—62no—
204C22⋊Q8—62no—
205C22⋊Q8—61no—
206C22⋊Q8—61no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—62no—
209C2×C22⋊C4—32no—
210C2×C22⋊C4—32no—
211C2×C22⋊C4C2×C3×D311yescharacteristic
212C2×C22⋊C4C2×C3×D311yescharacteristic
213#95—21no—
214#95—62no—
215C23×C3—21no—
216C23×C3—21no—
217C23×C3—22no—
218C23×C3—22no—
219C23×C3—21no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—41no—
223C23×C3—41no—
224C23×C3—42no—
225C23×C3—42no—
226C23×C3C2×Dic611yescharacteristic
227C23×C3#23511yescharacteristic
228C23×C3D3×D412yes—
229C23×C3D3×Q812yes—
230C23×C3C2×#6711yescharacteristic
231C23×C3C2×C3×D412yes—
232C23×C3C2×C3×D411yescharacteristic
233C23×C3C2×C3×Q811yescharacteristic
234C23×C3C2×C3×Q812yes—
235C23×C3C3×#4111yescharacteristic
236C3×Q8—241no—
237C3×Q8—241no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—24no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—24no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—22no—
250C2×C3×C4—44no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—42no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—42no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—42no—
260C2×C3×C4—41no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—41no—
264C2×C3×C4—42no—
265C2×C3×C4—44no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—64no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—122no—
278C2×C3×C4—122no—
279C2×C3×C4—122no—
280C2×C3×C4—122no—
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—24no—
284C2×Dic3—42no—
285C2×Dic3—42no—
286C2×Dic3—42no—
287C2×Dic3—42no—
288Dic6—81no—
289Dic6—81no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—22no—
293C2×C32—22no—
294C2×C32#39511yescharacteristic
295C2×C32B(4,𝔽2)11yescharacteristic
296C2×C32#45811yescharacteristic
297C24C22×C3×D311yescharacteristic
298C2×Q8—61no—
299C2×Q8—61no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—32no—
304C22×C4—32no—
305C22×C4—42no—
306C22×C4—62no—
307C22×C4C3×#6711yescharacteristic
308C22×C4C3×#6711yescharacteristic
309C4⋊C4—42no—
310C4⋊C4—62no—
311C4⋊C4—62no—
312C4⋊C4—61no—
313C4⋊C4—61no—
314C4⋊C4—124no—
315C22⋊C4—21no—
316C22⋊C4—22no—
317C22⋊C4—34no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—62no—
321C22⋊C4C3×Dic612yescomplemented
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—22no—
326C22×C3—21no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—42no—
342C22×C3—41no—
343C22×C3—42no—
344C22×C3—41no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—44no—
348C22×C3#88812yes—
349C22×C3#89612yes—
350C22×C3#92411yescharacteristic
351C22×C3#93711yescharacteristic
352C22×C3#94411yescharacteristic
353C22×C3C3×#12011yescharacteristic
354C22×C3C3×C22⋊Q812yes—
355C22×C3C3×C22⋊Q811yescharacteristic
356C22×C3C3×C4⋊Q812yes—
357C22×C3C3×C4⋊Q811yescharacteristic
358C3×C4—44no—
359C3×C4—44no—
360C3×C4—42no—
361C3×C4—42no—
362C3×C4—42no—
363C3×C4—41no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—42no—
367C3×C4—41no—
368C3×C4—81no—
369C3×C4—81no—
370C3×C4—124no—
371C3×C4—122no—
372C3×C4—122no—
373Dic3—44no—
374Dic3—42no—
375Dic3—42no—
376C32#206211yescharacteristic, complemented, Sylow
377C23—41no—
378C23—41no—
379C23C2×C3×Dic611yescharacteristic
380C23C3×#23511yescharacteristic
381C23C3×D3×D412yes—
382C23C3×D3×Q812yes—
383C23C2×C3×#6711yescharacteristic
384Q8—241no—
385Q8—241no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—64no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—122no—
402C2×C4—122no—
403C2×C4—122no—
404C2×C4—122no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—22no—
413C2×C3—22no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—42no—
419C2×C3—42no—
420C2×C3#497911yescharacteristic
421C2×C3#503211yescharacteristic
422C2×C3#505311yescharacteristic
423C2×C3C3×#39511yescharacteristic
424C2×C3C3×B(4,𝔽2)11yescharacteristic
425C2×C3C3×#45811yescharacteristic
426C22—21no—
427C22—22no—
428C22—21no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22—42no—
433C22C3×#88812yes—
434C22C3×#89612yes—
435C22C3×#92411yescharacteristic
436C22C3×#93711yescharacteristic
437C22C3×#94411yescharacteristic
438C4—42no—
439C4—42no—
440C4—41no—
441C4—41no—
442C4—124no—
443C4—122no—
444C4—122no—
445C3—21no—
446C3#6959411yescharacteristic, direct product factor
447C3C3×#206211yescharacteristic, complemented
448C2—21no—
449C2—22no—
450C2—22no—
451C2—21no—
452C2C3×#497911yescharacteristic
453C2C3×#503211yescharacteristic
454C2C3×#505311yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC24×C3C23×C3
FrattiniC24C22×C3×D3
FittingC32×#385C2
socleC22×C32#120
prime radicalC24×C32C23
hypercenterC3×#385D3
hypocenterC3C3×#2062
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
7. #69594C3direct (N × H)
47. C32×C22⋊C4Q8semidirect
51. C3×#217Q8semidirect
172. C3×C22⋊C4Dic6semidirect
173. C3×C22⋊C4C3×Q8semidirect
177. #217C3×Q8semidirect
321. C22⋊C4C3×Dic6semidirect
376. C32#2062semidirect
446. C3#69594direct (N × H)
447. C3C3×#2062semidirect

Maximal subgroups

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

subgroupindex
C3×#54832
C32×#3852
C3×#52102
C3×#45272
C3×#45262
C3×#20623
#695943