Finite Group Databasebeta

← C3×#71627 #11785275

Subgroups — C3×#71627 #11785275

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic
2C2×C3×#835C212yesmaximal
3C3×#4936C211yesmaximal, characteristic
4C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
5C3×#4529C212yesmaximal
6C3×#1805—31nomaximal
7#71627C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2211yescharacteristic
9C32×C4×Q8—22no—
10C32×C4×Q8C414yescomplemented
11C2×C32×C4⋊C4—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C42—21no—
14C2×C32×C42C2211yescharacteristic
15C2×C3×C4⋊Dic3C2212yes—
16C22×C3×C3⋊C8C2212yes—
17C3×#835—24no—
18C3×C3⋊#95—21no—
19C3×C3⋊#95—21no—
20C3×C4⋊(C3⋊C8)—22no—
21C2×C3×C4×Q8—21no—
22C2×C3×C4×Q8D311yescharacteristic
23C2×C3×C4×Q8C2×C311yescharacteristic
24C2×C3×C4⋊C8—31no—
25C2×C3×#103—32no—
26C3×#382—31no—
27C2×#835C2×C312yes—
28#4936C2×C311yescharacteristic
29C2×C4⋊(C3⋊C8)C2×C311yescharacteristic
30C3×#340—32no—
31#4529C2×C312yes—
32C2×C32×Q8—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8C2×C412yes—
36C2×C32×Q8D412yes—
37C2×C32×Q8Q812yes—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3—22no—
44C32×C4⋊C4—24no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4C2×C412yes—
47C32×C42—24no—
48C32×C42C2×C412yes—
49C32×C42D412yes—
50C3×C4⋊Dic3—22no—
51C3×C4⋊Dic3—22no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—22no—
55#1805—31noSylow
56C22×C3×Q8—21no—
57C22×C3×Q8C2×D311yescharacteristic
58C22×C3×Q8C22×C311yescharacteristic
59C22×C3×C8—32no—
60C3×C4×Q8—24no—
61C3×C4×Q8—22no—
62C3×C4×Q8—22no—
63C3×C4×Q8—24no—
64C3×C4×Q8Dic314yescomplemented
65C3×C4×Q8C3×C414yescomplemented
66C2×C3×C4⋊C4—22no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—32no—
71C2×C3×C4⋊C4C2×D311yescharacteristic
72C2×C3×C4⋊C4C22×C311yescharacteristic
73C2×C3×C42—22no—
74C2×C3×C42—21no—
75C2×C3×C42—21no—
76C2×C3×C42—21no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C22×C311yescharacteristic
79C2×C4⋊Dic3C22×C312yes—
80C22×C3⋊C8C22×C312yes—
81C3×C4⋊C8—62no—
82C3×#103—64no—
83C3×#95—61no—
84C3×#95—61no—
85#835—24no—
86C3⋊#95—21no—
87C3⋊#95—21no—
88C4⋊(C3⋊C8)—22no—
89C23×C32C2×D411yescharacteristic
90C32×Q8—22no—
91C32×Q8—22no—
92C32×Q8—22no—
93C32×Q8C4⋊C414yes—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—42no—
101C2×C32×C4C22⋊C412yes—
102C2×C32×C4C22⋊C412yes—
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×Q811yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×C3⋊C8—42no—
113C2×C4×Q8C3×D311yescharacteristic
114C2×C4⋊C8—31no—
115C2×#103—32no—
116#382—31no—
117#340—32no—
118C2×C3×Q8—22no—
119C2×C3×Q8—22no—
120C2×C3×Q8—22no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8—21no—
126C2×C3×Q8—21no—
127C2×C3×Q8—22no—
128C2×C3×Q8—22no—
129C2×C3×Q8—22no—
130C2×C3×Q8Dic612yes—
131C2×C3×Q8D1212yes—
132C2×C3×Q8C2×Dic312yes—
133C2×C3×Q8C2×C3×C412yes—
134C2×C3×Q8C3×D412yes—
135C2×C3×Q8C3×Q812yes—
136C22×C3×C4—22no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—62no—
146C22×C3×C4#6711yescharacteristic
147C22×C3×C4#6711yescharacteristic
148C22×C3×C4C3×D411yescharacteristic
149C22×C3×C4C3×D411yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C23×C311yescharacteristic
152C22×Dic3—22no—
153C2×C3×C8—62no—
154C2×C3×C8—62no—
155C2×C3×C8—62no—
156C3×C4⋊C4—28no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—24no—
159C3×C4⋊C4—24no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—62no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4C2×Dic312yes—
166C3×C4⋊C4C2×C3×C412yes—
167C3×C42—28no—
168C3×C42—24no—
169C3×C42—24no—
170C3×C42—22no—
171C3×C42—22no—
172C3×C42C2×Dic312yes—
173C3×C42#6712yes—
174C3×C42C2×C3×C412yes—
175C3×C42C3×D412yes—
176C4⋊Dic3—22no—
177C4⋊Dic3—22no—
178C2×C3⋊C8—22no—
179C2×C3⋊C8—22no—
180C2×C3⋊C8—22no—
181C22×C32C2×C22⋊C411yescharacteristic
182C22×C32#12111yescharacteristic
183C22×C32C22⋊Q811yescharacteristic
184C22×C32#13512yes—
185C22×C32#13712yes—
186C32×C4—24no—
187C32×C4—22no—
188C32×C4—22no—
189C32×C4—42no—
190C32×C4C2×C4⋊C411yescharacteristic
191C32×C4#11711yescharacteristic
192C32×C4#12111yescharacteristic
193C32×C4C22⋊Q811yescharacteristic
194C3×Dic3—82no—
195C22×Q8C2×C3×D311yescharacteristic
196C22×C8—32no—
197C4×Q8—22no—
198C4×Q8C3×Dic314yescomplemented
199C2×C4⋊C4—21no—
200C2×C4⋊C4—32no—
201C2×C4⋊C4C2×C3×D311yescharacteristic
202C2×C42—21no—
203C2×C42C2×C3×D311yescharacteristic
204C4⋊C8—62no—
205#103—64no—
206#95—61no—
207#95—61no—
208C23×C3—21no—
209C23×C3C2×#6711yescharacteristic
210C23×C3C2×C3×D411yescharacteristic
211C3×Q8—24no—
212C3×Q8—24no—
213C3×Q8—24no—
214C3×Q8—22no—
215C3×Q8—22no—
216C3×Q8—22no—
217C3×Q8—22no—
218C3×Q8—22no—
219C3×Q8—22no—
220C3×Q8—24no—
221C3×Q8C4⋊Dic314yes—
222C3×Q8C3×C4⋊C414yes—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—24no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—42no—
249C2×C3×C4—44no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—122no—
253C2×C3×C4—122no—
254C2×C3×C4—122no—
255C2×C3×C4#21712yes—
256C2×C3×C4#21712yes—
257C2×C3×C4C3×C22⋊C412yes—
258C2×C3×C4C3×C22⋊C412yes—
259C2×C3×C4C2×Dic611yescharacteristic
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4#23511yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4C22×Dic311yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×C3×C4C22×C3×C411yescharacteristic
266C2×C3×C4C2×C3×D411yescharacteristic
267C2×C3×C4C2×C3×D411yescharacteristic
268C2×C3×C4C2×C3×Q811yescharacteristic
269C2×C3×C4C3×#4111yescharacteristic
270C2×C3×C4C3×#4111yescharacteristic
271C2×Dic3—42no—
272C2×Dic3—42no—
273C2×Dic3—42no—
274C3×C8—122no—
275C3⋊C8—42no—
276C2×C32#38011yescharacteristic
277C2×C32#41611yescharacteristic
278C2×C32#41911yescharacteristic
279C2×C32#46412yes—
280C2×C32#47912yes—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8C3×Dic612yes—
285C2×Q8C3×D1212yes—
286C2×Q8C2×C3×Dic312yes—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—62no—
290C22×C4C3×#6711yescharacteristic
291C22×C4C3×#6711yescharacteristic
292C22×C4C22×C3×D311yescharacteristic
293C2×C8—62no—
294C2×C8—62no—
295C2×C8—62no—
296C4⋊C4—24no—
297C4⋊C4—21no—
298C4⋊C4—62no—
299C4⋊C4—62no—
300C4⋊C4C2×C3×Dic312yes—
301C42—24no—
302C42C2×C3×Dic312yes—
303C42C3×#6712yes—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3#92411yescharacteristic
310C22×C3#93011yescharacteristic
311C22×C3#94212yes—
312C22×C3#95012yes—
313C22×C3C2×#21711yescharacteristic
314C22×C3C2×C3×C22⋊C411yescharacteristic
315C22×C3C3×#12111yescharacteristic
316C22×C3C3×C22⋊Q811yescharacteristic
317C22×C3C3×#13512yes—
318C22×C3C3×#13712yes—
319C3×C4—28no—
320C3×C4—24no—
321C3×C4—24no—
322C3×C4—22no—
323C3×C4—22no—
324C3×C4—24no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—42no—
332C3×C4—44no—
333C3×C4—42no—
334C3×C4—42no—
335C3×C4—242no—
336C3×C4#92411yescharacteristic
337C3×C4C2×C4⋊Dic311yescharacteristic
338C3×C4#92611yescharacteristic
339C3×C4#93011yescharacteristic
340C3×C4C2×C3×C4⋊C411yescharacteristic
341C3×C4C3×#11711yescharacteristic
342C3×C4C3×#12111yescharacteristic
343C3×C4C3×C22⋊Q811yescharacteristic
344Dic3—82no—
345C32#180511yescharacteristic, complemented, Sylow
346C23C2×C3×#6711yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—22no—
350Q8C3×C4⋊Dic314yes—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—42no—
358C2×C4—122no—
359C2×C4—122no—
360C2×C4—122no—
361C2×C4C3×#21712yes—
362C2×C4C3×#21712yes—
363C2×C4C2×C3×Dic611yescharacteristic
364C2×C4C2×C3×D1211yescharacteristic
365C2×C4C3×#23511yescharacteristic
366C2×C4C3×#23511yescharacteristic
367C2×C4C22×C3×Dic311yescharacteristic
368C2×C4C2×C3×#6711yescharacteristic
369C8—122no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—22no—
374C2×C3—22no—
375C2×C3#502212yes—
376C2×C3#502812yes—
377C2×C3#521211yescharacteristic
378C2×C3#522511yescharacteristic
379C2×C3#523311yescharacteristic
380C2×C3C3×#38011yescharacteristic
381C2×C3C3×#41611yescharacteristic
382C2×C3C3×#41911yescharacteristic
383C2×C3C3×#46412yes—
384C2×C3C3×#47912yes—
385C22C3×#92411yescharacteristic
386C22C3×#93011yescharacteristic
387C22C3×#94212yes—
388C22C3×#95012yes—
389C22C2×C3×#21711yescharacteristic
390C4—24no—
391C4—22no—
392C4—22no—
393C4—42no—
394C4—242no—
395C4C3×#92411yescharacteristic
396C4C2×C3×C4⋊Dic311yescharacteristic
397C4C3×#92611yescharacteristic
398C4C3×#93011yescharacteristic
399C3—21no—
400C3#7162711yescharacteristic, direct product factor
401C3C3×#180511yescharacteristic, complemented
402C2C3×#502212yes—
403C2C3×#502812yes—
404C2C3×#521211yescharacteristic
405C2C3×#522511yescharacteristic
406C2C3×#523311yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×Q8C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#1805
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
7. #71627C3direct (N × H)
10. C32×C4×Q8C4semidirect
64. C3×C4×Q8Dic3semidirect
65. C3×C4×Q8C3×C4semidirect
198. C4×Q8C3×Dic3semidirect
345. C32#1805semidirect
400. C3#71627direct (N × H)
401. C3C3×#1805semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×C3×#8352
C3×#49362
C2×C3×C4⋊(C3⋊C8)2
C3×#45292
C3×#18053
#716273