Finite Group Databasebeta

← C3×#70486 #11785278

Subgroups — C3×#70486 #11785278

Order 1152.

653 conjugacy classes of subgroups.

The subgroup lattice has 385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C2×C32×C4⋊C8C211yesmaximal, characteristic
3C2×C3×#816C212yesmaximal
4C3×#4936C211yesmaximal, characteristic
5C3×#4551C212yesmaximal
6C3×#1805—31nomaximal
7#70486C311yesmaximal, characteristic, direct product factor
8C22×C3×Dic6C2211yescharacteristic
9C22×C32×C8C2212yes—
10C2×C32×C42C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×Dic3⋊C4—21no—
14C2×C3×C4×Dic3—21no—
15C3×C4×Dic6—22no—
16C3×C4×Dic6C414yescomplemented
17C32×C4⋊C8—22no—
18C3×C3⋊#95—21no—
19C3×C3⋊#95—21no—
20C3×#816—24no—
21C2×C3×C4×Q8—31no—
22C2×C4×Dic6C2×C311yescharacteristic
23C2×C3×C4⋊C8—21no—
24C2×C3×C4⋊C8D311yescharacteristic
25C2×C3×C4⋊C8C2×C311yescharacteristic
26C2×C3×#103—32no—
27C3×#382—31no—
28C2×#816C2×C312yes—
29#4936C2×C311yescharacteristic
30C3×#340—32no—
31#4551C2×C312yes—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3×Dic3—21no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—22no—
38C2×C3×Dic6—21no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6C2×C412yes—
42C2×C3×Dic6D412yes—
43C2×C3×Dic6Q812yes—
44C2×C32×C8—22no—
45C2×C32×C8—22no—
46C2×C32×C8—22no—
47C32×C42C2×C412yes—
48C32×C42D412yes—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—22no—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3C2×C412yes—
53C3×Dic3⋊C4—24no—
54C3×C4×Dic3—24no—
55#1805—31noSylow
56C22×C3×Q8—31no—
57C22×Dic6C22×C311yescharacteristic
58C22×C3×C8—22no—
59C22×C3×C8C2×D312yes—
60C22×C3×C8C22×C312yes—
61C3×C4×Q8—34no—
62C3×C4×Q8—62no—
63C2×C3×C4⋊C4—31no—
64C2×C3×C4⋊C4—32no—
65C2×C3×C4⋊C4—61no—
66C2×C3×C42—21no—
67C2×C3×C42—61no—
68C2×C3×C42C2×D311yescharacteristic
69C2×C3×C42C22×C311yescharacteristic
70C2×C4⋊Dic3C22×C312yes—
71C2×C4⋊Dic3C22×C311yescharacteristic
72C2×Dic3⋊C4—21no—
73C2×C4×Dic3—21no—
74C4×Dic6—22no—
75C4×Dic6C3×C414yescomplemented
76C3×C4⋊C8—24no—
77C3×C4⋊C8—22no—
78C3×C4⋊C8—22no—
79C3×#103—64no—
80C3×#95—61no—
81C3×#95—61no—
82C3⋊#95—21no—
83C3⋊#95—21no—
84#816—24no—
85C23×C32C2×D411yescharacteristic
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4C22⋊C412yes—
89C2×C32×C4C22⋊C412yes—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×Q811yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—42no—
103C2×C3×Dic3—42no—
104C3×Dic6—22no—
105C3×Dic6—22no—
106C3×Dic6—22no—
107C3×Dic6C4⋊C414yes—
108C32×C8—42no—
109C2×C4×Q8—31no—
110C2×C4⋊C8C3×D311yescharacteristic
111C2×#103—32no—
112#382—31no—
113#340—32no—
114C2×C3×Q8—32no—
115C2×C3×Q8—32no—
116C2×C3×Q8—32no—
117C2×C3×Q8—61no—
118C2×C3×Q8—61no—
119C2×C3×Q8—61no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—61no—
124C22×C3×C4—61no—
125C22×C3×C4—62no—
126C22×C3×C4D1211yescharacteristic
127C22×C3×C4D1211yescharacteristic
128C22×C3×C4C3×D411yescharacteristic
129C22×C3×C4C3×D411yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C23×C311yescharacteristic
132C22×Dic3—21no—
133C22×Dic3—21no—
134C22×Dic3—22no—
135C2×Dic6—21no—
136C2×Dic6—21no—
137C2×Dic6—21no—
138C2×Dic6C2×C3×C412yes—
139C2×Dic6C3×D412yes—
140C2×Dic6C3×Q812yes—
141C2×C3×C8—24no—
142C2×C3×C8—22no—
143C2×C3×C8—22no—
144C2×C3×C8—22no—
145C2×C3×C8—22no—
146C2×C3×C8—22no—
147C2×C3×C8—22no—
148C2×C3×C8—42no—
149C2×C3×C8—42no—
150C3×C4⋊C4—32no—
151C3×C4⋊C4—64no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—62no—
154C3×C4⋊C4—62no—
155C3×C42—22no—
156C3×C42—22no—
157C3×C42—64no—
158C3×C42C4×D312yes—
159C3×C42#6712yes—
160C3×C42C2×C3×C412yes—
161C3×C42C3×D412yes—
162C4⋊Dic3—21no—
163C4⋊Dic3—22no—
164C4⋊Dic3—22no—
165C4⋊Dic3C2×C3×C412yes—
166Dic3⋊C4—24no—
167C4×Dic3—24no—
168C22×C32C2×C22⋊C411yescharacteristic
169C22×C32#12111yescharacteristic
170C22×C32C22⋊Q811yescharacteristic
171C22×C32#13512yes—
172C22×C32#13712yes—
173C32×C4—22no—
174C32×C4—22no—
175C32×C4C2×C4⋊C411yescharacteristic
176C32×C4#11711yescharacteristic
177C32×C4#12111yescharacteristic
178C32×C4C22⋊Q811yescharacteristic
179C3×Dic3—24no—
180C3×Dic3—42no—
181C3×Dic3—82no—
182C22×Q8—31no—
183C22×C8C2×C3×D312yes—
184C4×Q8—34no—
185C4×Q8—62no—
186C2×C4⋊C4—31no—
187C2×C4⋊C4—32no—
188C2×C4⋊C4—61no—
189C2×C42—61no—
190C2×C42C2×C3×D311yescharacteristic
191C4⋊C8—22no—
192#103—64no—
193#95—61no—
194#95—61no—
195C23×C3—21no—
196C23×C3C2×D1211yescharacteristic
197C23×C3C2×C3×D411yescharacteristic
198C3×Q8—34no—
199C3×Q8—62no—
200C3×Q8—62no—
201C3×Q8—62no—
202C2×C3×C4—24no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—42no—
216C2×C3×C4—62no—
217C2×C3×C4—62no—
218C2×C3×C4—62no—
219C2×C3×C4—62no—
220C2×C3×C4—122no—
221C2×C3×C4—122no—
222C2×C3×C4—122no—
223C2×C3×C4—122no—
224C2×C3×C4(C2×D3)⋊C412yes—
225C2×C3×C4(C2×D3)⋊C412yes—
226C2×C3×C4C3×C22⋊C412yes—
227C2×C3×C4C3×C22⋊C412yes—
228C2×C3×C4C2×C4×D311yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4#23711yescharacteristic
231C2×C3×C4D3×Q811yescharacteristic
232C2×C3×C4#23911yescharacteristic
233C2×C3×C4C2×#6711yescharacteristic
234C2×C3×C4C22×C3×C411yescharacteristic
235C2×C3×C4C2×C3×D411yescharacteristic
236C2×C3×C4C2×C3×D411yescharacteristic
237C2×C3×C4C2×C3×Q811yescharacteristic
238C2×C3×C4C3×#4111yescharacteristic
239C2×C3×C4C3×#4111yescharacteristic
240C2×Dic3—22no—
241C2×Dic3—22no—
242C2×Dic3—22no—
243C2×Dic3—22no—
244C2×Dic3—42no—
245C2×Dic3—42no—
246C2×Dic3—42no—
247C2×Dic3—42no—
248Dic6—22no—
249Dic6—22no—
250Dic6—22no—
251Dic6C3×C4⋊C414yes—
252C3×C8—44no—
253C3×C8—42no—
254C3×C8—42no—
255C2×C32#38011yescharacteristic
256C2×C32#41611yescharacteristic
257C2×C32#41911yescharacteristic
258C2×C32#46412yes—
259C2×C32#47912yes—
260C2×Q8—32no—
261C2×Q8—32no—
262C2×Q8—32no—
263C2×Q8—61no—
264C2×Q8—61no—
265C2×Q8—61no—
266C22×C4—61no—
267C22×C4—61no—
268C22×C4—62no—
269C22×C4C3×D1211yescharacteristic
270C22×C4C3×D1211yescharacteristic
271C22×C4C22×C3×D311yescharacteristic
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C4⋊C4—32no—
276C4⋊C4—64no—
277C4⋊C4—61no—
278C4⋊C4—62no—
279C4⋊C4—62no—
280C42—64no—
281C42C3×C4×D312yes—
282C42C3×#6712yes—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—21no—
288C22×C3#89511yescharacteristic
289C22×C3#89711yescharacteristic
290C22×C3#90412yes—
291C22×C3#90912yes—
292C22×C3C2×(C2×D3)⋊C411yescharacteristic
293C22×C3C2×C3×C22⋊C411yescharacteristic
294C22×C3C3×#12111yescharacteristic
295C22×C3C3×C22⋊Q811yescharacteristic
296C22×C3C3×#13512yes—
297C22×C3C3×#13712yes—
298C3×C4—24no—
299C3×C4—22no—
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—42no—
308C3×C4—64no—
309C3×C4—122no—
310C3×C4—242no—
311C3×C4D3×C4⋊C411yescharacteristic
312C3×C4#89211yescharacteristic
313C3×C4#93811yescharacteristic
314C3×C4#94611yescharacteristic
315C3×C4C2×C3×C4⋊C411yescharacteristic
316C3×C4C3×#11711yescharacteristic
317C3×C4C3×#12111yescharacteristic
318C3×C4C3×C22⋊Q811yescharacteristic
319Dic3—24no—
320Dic3—42no—
321Dic3—82no—
322C32#180511yescharacteristic, complemented, Sylow
323C23C2×C3×D1211yescharacteristic
324Q8—34no—
325Q8—62no—
326Q8—62no—
327Q8—62no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—62no—
331C2×C4—62no—
332C2×C4—62no—
333C2×C4—62no—
334C2×C4—122no—
335C2×C4—122no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4C3×(C2×D3)⋊C412yes—
339C2×C4C3×(C2×D3)⋊C412yes—
340C2×C4C2×C3×C4×D311yescharacteristic
341C2×C4C3×D3×D411yescharacteristic
342C2×C4C3×#23711yescharacteristic
343C2×C4C3×D3×Q811yescharacteristic
344C2×C4C3×#23911yescharacteristic
345C2×C4C2×C3×#6711yescharacteristic
346C8—42no—
347C2×C3—21no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3#482912yes—
353C2×C3#484512yes—
354C2×C3#498711yescharacteristic
355C2×C3#511311yescharacteristic
356C2×C3#512011yescharacteristic
357C2×C3C3×#38011yescharacteristic
358C2×C3C3×#41611yescharacteristic
359C2×C3C3×#41911yescharacteristic
360C2×C3C3×#46412yes—
361C2×C3C3×#47912yes—
362C22C3×#89511yescharacteristic
363C22C3×#89711yescharacteristic
364C22C3×#90412yes—
365C22C3×#90912yes—
366C22C2×C3×(C2×D3)⋊C411yescharacteristic
367C4—22no—
368C4—22no—
369C4—64no—
370C4—122no—
371C4—242no—
372C4C3×D3×C4⋊C411yescharacteristic
373C4C3×#89211yescharacteristic
374C4C3×#93811yescharacteristic
375C4C3×#94611yescharacteristic
376C3—21no—
377C3#7048611yescharacteristic, direct product factor
378C3C3×#180511yescharacteristic, complemented
379C2C3×#482912yes—
380C2C3×#484512yes—
381C2C3×#498711yescharacteristic
382C2C3×#511311yescharacteristic
383C2C3×#512011yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4⋊C8C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C3×#1805
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
7. #70486C3direct (N × H)
16. C3×C4×Dic6C4semidirect
75. C4×Dic6C3×C4semidirect
322. C32#1805semidirect
377. C3#70486direct (N × H)
378. C3C3×#1805semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C2×C32×C4⋊C82
C2×C3×#8162
C3×#49362
C3×#45512
C3×#18053
#704863