Finite Group Databasebeta

← C3×#68206 #11779907

Subgroups — C3×#68206 #11779907

Order 1152.

457 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic
3C3×#4851C211yesmaximal, characteristic, complemented
4C3×#4681C211yesmaximal, characteristic, complemented
5C32×D4⋊C8C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4456C211yesmaximal, characteristic, complemented
8C3×#1643—31nomaximal
9#68206C311yesmaximal, characteristic, direct product factor
10C32×C4×D4C2211yescharacteristic
11C3×D4×Dic3—21no—
12C2×C3×#214—21no—
13C2×C3×C4⋊Dic3—21no—
14C3×#924—21no—
15C3×#890—21no—
16C3×#878—22no—
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22C3×#817—21no—
23C3×#816—22no—
24C3×#816—21no—
25C3×#810—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#554—31no—
28#5543C2×C311yescharacteristic
29C3×#487—31no—
30C3×#475—31no—
31C3×#461—31no—
32#5019C2×C311yescharacteristic
33#4851C2×C311yescharacteristic, complemented
34#4681C2×C311yescharacteristic, complemented
35C3×#333—31no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—21no—
38C3×D4⋊C8D311yescharacteristic
39C3×D4⋊C8C2×C311yescharacteristic
40#4481C2×C311yescharacteristic, complemented
41#4456C2×C311yescharacteristic, complemented
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C22×C3×Dic3—22no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D412yes—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C42C2311yescharacteristic
53C3×#217—22no—
54C3×#214—42no—
55C3×C4⋊Dic3—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—22no—
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65#1643—31noSylow
66C2×C3×SD16—61no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8—31no—
69C3×#125—61no—
70C3×C22⋊Q8—62no—
71C3×C22⋊Q8—61no—
72C3×C4×Q8—31no—
73C3×C4×D4—21no—
74C3×C4×D4—61no—
75C3×C4×D4C2×D311yescharacteristic
76C3×C4×D4C22×C311yescharacteristic
77C2×C3×C4⋊C4—61no—
78D4×Dic3—21no—
79C2×#214—21no—
80C2×C4⋊Dic3—21no—
81#924—21no—
82#890—21no—
83#878—22no—
84#869C22×C311yescharacteristic
85#869C22×C311yescharacteristic
86C4×Dic6C22×C311yescharacteristic
87C3×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C22×C311yescharacteristic
92C3×#103—61no—
93C3×#103—62no—
94C3×#103—61no—
95C3×C4×C8—21no—
96C3×C4×C8C2×D311yescharacteristic
97C3×C4×C8C22×C311yescharacteristic
98#817—21no—
99#816—22no—
100#816—21no—
101#810—21no—
102C4⋊(C3⋊C8)C22×C311yescharacteristic
103C23×C32—21no—
104C32×D4—21no—
105C32×D4SD1612yes—
106C2×C32×C4—21no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—82no—
117C3×Dic6—21no—
118C3×Dic6—21no—
119C3×Dic6—42no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C32×C8—41no—
123C32×C8—41no—
124C3×C3⋊C8—41no—
125#554—31no—
126#487—31no—
127#475—31no—
128#461—31no—
129#333—31no—
130Q8⋊C8—31no—
131D4⋊C8C3×D311yescharacteristic
132C2×C3×Q8—31no—
133C2×C3×Q8—32no—
134C2×C3×Q8—61no—
135C2×C3×D4—21no—
136C2×C3×D4D1211yescharacteristic
137C2×C3×D4C3×D411yescharacteristic
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—41no—
141C22×C3×C4—62no—
142C22×Dic3—22no—
143C2×Dic6—21no—
144C2×Dic6C3×D411yescharacteristic
145C2×Dic6C3×D412yes—
146C3×SD16—122no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—41no—
152C2×C3×C8—41no—
153C2×C3×C8—61no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—62no—
157C3×C4⋊C4—62no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4D1211yescharacteristic
164C3×C4⋊C4C3×D411yescharacteristic
165C3×C22⋊C4—21no—
166C3×C22⋊C4—21no—
167C3×C22⋊C4—41no—
168C3×C22⋊C4—62no—
169C3×C42—21no—
170C3×C42—61no—
171C3×C42C22×D311yescharacteristic
172C3×C42C23×C311yescharacteristic
173#217—22no—
174#214—42no—
175C4⋊Dic3—22no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3C3×D411yescharacteristic
181Dic3⋊C4—22no—
182Dic3⋊C4—21no—
183C4×Dic3—21no—
184C2×C3⋊C8—21no—
185C22×C32—22no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32#12011yescharacteristic
189C32×C4—21no—
190C32×C4—41no—
191C32×C4C2×SD1611yescharacteristic
192C32×C4#13511yescharacteristic
193C32×C4#13711yescharacteristic
194C32×C4#13711yescharacteristic
195C3×Dic3—41no—
196C3×Dic3—42no—
197C3×Dic3—41no—
198C3×Dic3—81no—
199C2×SD16—61no—
200C4⋊Q8—31no—
201C4⋊Q8—31no—
202#125—61no—
203C22⋊Q8—62no—
204C22⋊Q8—61no—
205C4×Q8—31no—
206C4×D4—61no—
207C4×D4C2×C3×D311yescharacteristic
208C2×C4⋊C4—61no—
209#106—61no—
210C4⋊C8—31no—
211C4⋊C8C2×C3×D311yescharacteristic
212#103—61no—
213#103—62no—
214#103—61no—
215C4×C8C2×C3×D311yescharacteristic
216C23×C3—21no—
217C23×C3—21no—
218C23×C3—41no—
219C3×Q8—61no—
220C3×Q8—61no—
221C3×Q8—122no—
222C3×Q8—121no—
223C3×Q8—121no—
224C3×D4—21no—
225C3×D4—21no—
226C3×D4—22no—
227C3×D4—41no—
228C3×D4#20412yes—
229C3×D4C3×SD1612yes—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—62no—
243C2×C3×C4—81no—
244C2×C3×C4—81no—
245C2×C3×C4—121no—
246C2×C3×C4—242no—
247C2×C3×C4C2×D1211yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4C2×C3×D411yescharacteristic
251C2×C3×C4C2×C3×D411yescharacteristic
252C2×C3×C4C2×C3×D411yescharacteristic
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—22no—
256C2×Dic3—41no—
257C2×Dic3—82no—
258Dic6—21no—
259Dic6—21no—
260Dic6—42no—
261Dic6—41no—
262Dic6—41no—
263C3×C8—41no—
264C3×C8—41no—
265C3×C8—42no—
266C3×C8—41no—
267C3×C8—41no—
268C3×C8—81no—
269C3×C8—121no—
270C3⋊C8—41no—
271C2×C32—42no—
272C2×C32#44811yescharacteristic
273C2×C32#45211yescharacteristic
274C2×C32#45511yescharacteristic
275C2×Q8—31no—
276C2×Q8—32no—
277C2×Q8—61no—
278C2×D4C3×D1211yescharacteristic
279C22×C4—21no—
280C22×C4—62no—
281SD16—122no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—61no—
285C4⋊C4—31no—
286C4⋊C4—62no—
287C4⋊C4—62no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4C3×D1211yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—62no—
296C42—61no—
297C42C22×C3×D311yescharacteristic
298C22×C3—22no—
299C22×C3—22no—
300C22×C3—21no—
301C22×C3—42no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—81no—
307C22×C3—81no—
308C22×C3#88211yescharacteristic
309C22×C3C3×#12011yescharacteristic
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—81no—
320C3×C4—121no—
321C3×C4—121no—
322C3×C4—122no—
323C3×C4—241no—
324C3×C4C2×#20411yescharacteristic
325C3×C4#90911yescharacteristic
326C3×C4#91211yescharacteristic
327C3×C4#91511yescharacteristic
328C3×C4C2×C3×SD1611yescharacteristic
329C3×C4C3×#13511yescharacteristic
330C3×C4C3×#13711yescharacteristic
331C3×C4C3×#13711yescharacteristic
332Dic3—41no—
333Dic3—42no—
334Dic3—41no—
335Dic3—81no—
336C32#164311yescharacteristic, complemented, Sylow
337C23—21no—
338Q8—61no—
339Q8—61no—
340Q8—122no—
341Q8—121no—
342Q8—121no—
343D4—21no—
344D4C3×#20412yes—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—62no—
351C2×C4—121no—
352C2×C4—242no—
353C2×C4C2×C3×D1211yescharacteristic
354C2×C4C3×D3×D411yescharacteristic
355C2×C4C3×D3×D411yescharacteristic
356C8—41no—
357C8—41no—
358C8—121no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—42no—
363C2×C3—42no—
364C2×C3—82no—
365C2×C3#473811yescharacteristic
366C2×C3#478311yescharacteristic
367C2×C3#482511yescharacteristic
368C2×C3C3×#44811yescharacteristic
369C2×C3C3×#45211yescharacteristic
370C2×C3C3×#45511yescharacteristic
371C22—22no—
372C22—41no—
373C22—41no—
374C22C3×#88211yescharacteristic
375C4—21no—
376C4—41no—
377C4—121no—
378C4—121no—
379C4—122no—
380C4—241no—
381C4C2×C3×#20411yescharacteristic
382C4C3×#90911yescharacteristic
383C4C3×#91211yescharacteristic
384C4C3×#91511yescharacteristic
385C3—21no—
386C3#6820611yescharacteristic, direct product factor
387C3C3×#164311yescharacteristic, complemented
388C2—42no—
389C2C3×#473811yescharacteristic
390C2C3×#478311yescharacteristic
391C2C3×#482511yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1643
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
3. C3×#4851C2semidirect
4. C3×#4681C2semidirect
6. C3×#4481C2semidirect
7. C3×#4456C2semidirect
9. #68206C3direct (N × H)
33. #4851C2×C3semidirect
34. #4681C2×C3semidirect
40. #4481C2×C3semidirect
41. #4456C2×C3semidirect
336. C32#1643semidirect
386. C3#68206direct (N × H)
387. C3C3×#1643semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
C3×#50192
C3×#48512
C3×#46812
C32×D4⋊C82
C3×#44812
C3×#44562
C3×#16433
#682063