Finite Group Databasebeta

← C3×#70287 #11789940

Subgroups — C3×#70287 #11789940

Order 1152.

539 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
1C32×#416C211yesmaximal, characteristic
2C2×C3×#837C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic
4C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
5C3×#4999C211yesmaximal, characteristic, complemented
6C3×#4552C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C3×#1937—31nomaximal
9#70287C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C32×#103C412yescomplemented
18C32×#102C412yescomplemented
19C3×#837—22no—
20C3×#830—22no—
21C3×C8×Dic3—22no—
22C3×C4⋊(C3⋊C8)—22no—
23C3×#424—31no—
24C2×C3×#104—31no—
25C3×#416—21no—
26C3×#416D311yescharacteristic
27C3×#416C2×C311yescharacteristic
28C3×#408—31no—
29C2×C3×C4×C8—31no—
30C2×#837C2×C311yescharacteristic
31#5234C2×C311yescharacteristic
32C2×C8×Dic3C2×C311yescharacteristic, complemented
33#4999C2×C311yescharacteristic, complemented
34C3×#341—31no—
35C3×#339—31no—
36#4552C2×C311yescharacteristic, complemented
37#4532C2×C311yescharacteristic, complemented
38C32×#41—21no—
39C32×#41—21no—
40C32×#41—21no—
41C32×#41—21no—
42C2×C32×Q8C2×C411yescharacteristic
43C2×C32×D4—21no—
44C2×C32×D4C2×C411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8C2×C412yes—
51C32×C4⋊C4C2×C412yes—
52C32×C22⋊C4—21no—
53C32×C42—21no—
54C3×C4×Dic3—21no—
55C3×C4×Dic3D412yes—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65#1937—31noSylow
66C2×C3×#41—21no—
67C2×C3×#41C2×D311yescharacteristic
68C2×C3×#41C22×C311yescharacteristic
69C2×C3×M16—31no—
70C2×C3×M16—31no—
71C22×C3×C8—21no—
72C22×C3×C8—31no—
73C22×C3×C8C2×D311yescharacteristic
74C22×C3×C8C22×C311yescharacteristic
75C3×#117—21no—
76C3×#117C2×D311yescharacteristic
77C3×#117C22×C311yescharacteristic
78C2×C3×C42—31no—
79C2×C4×Dic3C22×C311yescharacteristic
80C2×#208C22×C311yescharacteristic
81C2×#208C22×C311yescharacteristic
82C22×C3⋊C8C22×C311yescharacteristic
83C3×C4⋊C8—62no—
84C3×#104—62no—
85C3×#103—22no—
86C3×#103Dic312yescomplemented
87C3×#103C3×C412yescomplemented
88C3×#102—22no—
89C3×#102Dic312yescomplemented
90C3×#102C3×C412yescomplemented
91C3×C22⋊C8—62no—
92C3×C4×C8—62no—
93#837—22no—
94#830—22no—
95C8×Dic3—22no—
96C4⋊(C3⋊C8)—22no—
97C23×C32—21no—
98C23×C32#4111yescharacteristic
99C32×Q8—21no—
100C32×Q8—21no—
101C32×D4—21no—
102C32×D4—21no—
103C32×D4—41no—
104C32×D4—41no—
105C2×C32×C4—22no—
106C2×C32×C4—21no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3×Dic3—24no—
116C2×C3×Dic3—22no—
117C32×C8—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120C3×C3⋊C8—41no—
121#424—31no—
122C2×#104—31no—
123#416C3×D311yescharacteristic
124#408—31no—
125C2×C4×C8—31no—
126#341—31no—
127#339—31no—
128C3×#41—22no—
129C3×#41—22no—
130C3×#41—21no—
131C3×#41—21no—
132C3×#41—21no—
133C3×#41—21no—
134C3×#41—21no—
135C3×#41—21no—
136C3×#41—21no—
137C3×#41—21no—
138C3×#41—41no—
139C3×#41—41no—
140C2×C3×Q8—21no—
141C2×C3×Q8C2×Dic311yescharacteristic
142C2×C3×Q8C2×C3×C411yescharacteristic
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—41no—
147C2×C3×D4C2×Dic311yescharacteristic
148C2×C3×D4C2×C3×C411yescharacteristic
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—41no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C23×C311yescharacteristic
156C22×Dic3—21no—
157C3×M16—61no—
158C3×M16—61no—
159C3×M16—61no—
160C3×M16—61no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—22no—
166C2×C3×C8—32no—
167C2×C3×C8—41no—
168C2×C3×C8—41no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8C2×Dic312yes—
174C2×C3×C8C2×C3×C412yes—
175C3×C4⋊C4—22no—
176C3×C4⋊C4C2×Dic312yes—
177C3×C4⋊C4C2×C3×C412yes—
178C3×C22⋊C4—21no—
179C3×C22⋊C4—21no—
180C3×C22⋊C4—41no—
181C3×C42—21no—
182C3×C42—21no—
183C3×C42—32no—
184C3×C42—41no—
185C3×C42—61no—
186C4×Dic3—21no—
187C4×Dic3C3×D412yes—
188#208—21no—
189#208—21no—
190#208—21no—
191#208—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8C3×D412yes—
197C22×C32—22no—
198C22×C32—41no—
199C22×C32—42no—
200C22×C32C4×D411yescharacteristic
201C22×C32#12311yescharacteristic
202C22×C32#12611yescharacteristic
203C32×C4—41no—
204C32×C4—42no—
205C32×C4#11711yescharacteristic
206C32×C4C4×D411yescharacteristic
207C32×C4#12111yescharacteristic
208C32×C4#12411yescharacteristic
209C3×Dic3—24no—
210C2×#41C2×C3×D311yescharacteristic
211C2×M16—31no—
212C2×M16—31no—
213C22×C8—31no—
214C22×C8C2×C3×D311yescharacteristic
215#117C2×C3×D311yescharacteristic
216C2×C42—31no—
217C4⋊C8—62no—
218#104—62no—
219#103C3×Dic312yescomplemented
220#102C3×Dic312yescomplemented
221C22⋊C8—62no—
222C4×C8—62no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—41no—
227C23×C3#23711yescharacteristic
228C23×C3C3×#4111yescharacteristic
229C3×Q8—22no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—21no—
233C3×Q8—21no—
234C3×Q8—41no—
235C3×D4—22no—
236C3×D4—21no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—21no—
240C3×D4—41no—
241C3×D4—42no—
242C3×D4—42no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—22no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—41no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—64no—
266C2×C3×C4—62no—
267C2×C3×C4#23511yescharacteristic
268C2×C3×C4#23511yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4C22×Dic311yescharacteristic
273C2×C3×C4C22×C3×C411yescharacteristic
274C2×C3×C4C2×C3×D411yescharacteristic
275C2×C3×C4C2×C3×D411yescharacteristic
276C2×C3×C4C3×#4111yescharacteristic
277C2×C3×C4C3×#4111yescharacteristic
278C2×C3×C4C3×#4111yescharacteristic
279C2×Dic3—24no—
280C2×Dic3—22no—
281C3×C8—22no—
282C3×C8—22no—
283C3×C8—42no—
284C3×C8—62no—
285C3×C8—121no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—41no—
289C3⋊C8—41no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—81no—
293C2×C32#38811yescharacteristic
294C2×C32#44312yes—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299C2×Q8C2×C3×Dic311yescharacteristic
300C2×D4—21no—
301C2×D4C2×C3×Dic311yescharacteristic
302C22×C4—21no—
303C22×C4—61no—
304C22×C4C22×C3×D311yescharacteristic
305M16—61no—
306M16—61no—
307M16—61no—
308M16—61no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—32no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8C2×C3×Dic312yes—
317C4⋊C4C2×C3×Dic312yes—
318C22⋊C4—21no—
319C42—21no—
320C42—32no—
321C42—61no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3—42no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—42no—
333C22×C3—82no—
334C22×C3#87911yescharacteristic
335C22×C3#88311yescharacteristic
336C22×C3D4×Dic311yescharacteristic
337C22×C3C3×C4×D411yescharacteristic
338C22×C3C3×#12311yescharacteristic
339C22×C3C3×#12611yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—42no—
345C3×C4—42no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—42no—
349C3×C4—64no—
350C3×C4—82no—
351C3×C4#88411yescharacteristic
352C3×C4#88511yescharacteristic
353C3×C4#92611yescharacteristic
354C3×C4D4×Dic311yescharacteristic
355C3×C4C3×#11711yescharacteristic
356C3×C4C3×C4×D411yescharacteristic
357C3×C4C3×#12111yescharacteristic
358C3×C4C3×#12411yescharacteristic
359Dic3—24no—
360C32#193711yescharacteristic, complemented, Sylow
361C23—21no—
362C23C3×#23711yescharacteristic
363Q8—21no—
364Q8—21no—
365D4—21no—
366D4—21no—
367D4—41no—
368D4—41no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—64no—
374C2×C4—62no—
375C2×C4C3×#23511yescharacteristic
376C2×C4C3×#23511yescharacteristic
377C2×C4C3×D3×D411yescharacteristic
378C2×C4C3×D3×D411yescharacteristic
379C2×C4C3×#23711yescharacteristic
380C2×C4C22×C3×Dic311yescharacteristic
381C8—22no—
382C8—62no—
383C8—121no—
384C8—121no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—22no—
390C2×C3—21no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3—82no—
394C2×C3—81no—
395C2×C3—81no—
396C2×C3#495111yescharacteristic
397C2×C3#519612yes—
398C2×C3C3×#38811yescharacteristic
399C2×C3C3×#44312yes—
400C22—22no—
401C22—42no—
402C22—41no—
403C22C3×#87911yescharacteristic
404C22C3×#88311yescharacteristic
405C22C3×D4×Dic311yescharacteristic
406C4—42no—
407C4—41no—
408C4—64no—
409C4C3×#88411yescharacteristic
410C4C3×#88511yescharacteristic
411C4C3×#92611yescharacteristic
412C4C3×D4×Dic311yescharacteristic
413C3—21no—
414C3#7028711yescharacteristic, direct product factor
415C3C3×#193711yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—81no—
419C2C3×#495111yescharacteristic
420C2C3×#519612yes—
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#416C2
socleC22×C32C4×D4
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#416D3
hypocenterC3C3×#1937
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
4. C2×C3×C8×Dic3C2semidirect
5. C3×#4999C2semidirect
6. C3×#4552C2semidirect
7. C3×#4532C2semidirect
9. #70287C3direct (N × H)
17. C32×#103C4semidirect
18. C32×#102C4semidirect
32. C2×C8×Dic3C2×C3semidirect
33. #4999C2×C3semidirect
36. #4552C2×C3semidirect
37. #4532C2×C3semidirect
86. C3×#103Dic3semidirect
87. C3×#103C3×C4semidirect
89. C3×#102Dic3semidirect
90. C3×#102C3×C4semidirect
219. #103C3×Dic3semidirect
220. #102C3×Dic3semidirect
360. C32#1937semidirect
414. C3#70287direct (N × H)
415. C3C3×#1937semidirect

Maximal subgroups

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

subgroupindex
C32×#4162
C2×C3×#8372
C3×#52342
C2×C3×C8×Dic32
C3×#49992
C3×#45522
C3×#45322
C3×#19373
#702873