Finite Group Databasebeta

← C3×#68437 #11780235

Subgroups — C3×#68437 #11780235

Order 1152.

432 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
1C3×#5732C211yesmaximal, characteristic
2C3×#5078C211yesmaximal, characteristic, complemented
3C3×#4851C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic
8C3×#1650—31nomaximal
9#68437C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C3×#947—21no—
12C3×Q8×Dic3—21no—
13C2×C3×#204—21no—
14C3×#898—22no—
15C3×#897—21no—
16C3×#892—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C3×#817—21no—
23C3×#816—21no—
24C3×#816—21no—
25C3×#807—22no—
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#556—31no—
28#5732C2×C311yescharacteristic
29C3×#500—31no—
30C3×#475—31no—
31C3×#461—31no—
32#5078C2×C311yescharacteristic, complemented
33#4851C2×C311yescharacteristic, complemented
34#4841C2×C311yescharacteristic
35C3×#332—21no—
36C3×#332D311yescharacteristic, complemented
37C3×#332C2×C311yescharacteristic, complemented
38C3×Q8⋊C8—31no—
39C3×D4⋊C8—31no—
40#4484C2×C311yescharacteristic, complemented
41#4483C2×C311yescharacteristic
42C2×C32×Q8—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C32×C8—21no—
48C2×C32×C8—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D412yes—
51C32×C42C2311yescharacteristic
52C3×(C2×D3)⋊C4—22no—
53C3×(C2×D3)⋊C4—22no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—22no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C3×#204—42no—
65#1650—31noSylow
66C2×C3×SD16—61no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8—31no—
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4⋊Q8C22×C311yescharacteristic
71C3×#126—62no—
72C3×#124—61no—
73C3×C22⋊Q8—61no—
74C3×C4×Q8—31no—
75C3×C4×Q8—61no—
76C3×C4×D4—31no—
77C3×#117—61no—
78#947—21no—
79Q8×Dic3—21no—
80C2×#204—21no—
81#898—22no—
82#897—21no—
83#892—21no—
84C4×D12C22×C311yescharacteristic
85#869C22×C311yescharacteristic
86C4×Dic6C22×C311yescharacteristic
87C3×#107—62no—
88C3×#106—61no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8—21no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C22×C311yescharacteristic
94C3×C4⋊C8C22×C311yescharacteristic
95C3×#103—61no—
96C3×#103—61no—
97C3×C4×C8—31no—
98#817—21no—
99#816—21no—
100#816—21no—
101#807—22no—
102C4×C3⋊C8C22×C311yescharacteristic
103C22×C3×D3—21no—
104C32×Q8—41no—
105C32×Q8—41no—
106C2×C32×C4—22no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×D12—21no—
115C3×D12—21no—
116C3×C4×D3—41no—
117C3×C4×D3—41no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C32×C8—41no—
123C32×C8—41no—
124C3×C3⋊C8—22no—
125#556—31no—
126#500—31no—
127#475—31no—
128#461—31no—
129#332C3×D311yescharacteristic, complemented
130Q8⋊C8—31no—
131D4⋊C8—31no—
132C2×C3×Q8—21no—
133C2×C3×Q8—21no—
134C2×C3×Q8—31no—
135C2×C3×Q8—41no—
136C2×C3×Q8—61no—
137C2×C3×D4—31no—
138C22×C3×C4—61no—
139C2×D12C3×D411yescharacteristic
140C2×C4×D3—21no—
141C2×Dic6—21no—
142C2×Dic6C3×D411yescharacteristic
143C3×SD16—122no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—41no—
149C2×C3×C8—41no—
150C2×C3×C8—61no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—41no—
157C3×C4⋊C4—62no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4D1212yes—
162C3×C4⋊C4C3×D412yes—
163C3×C22⋊C4—62no—
164C3×C22⋊C4—62no—
165C3×C22⋊C4—61no—
166C3×C42—21no—
167C3×C42—62no—
168C3×C42—61no—
169C3×C42C22×D311yescharacteristic
170C3×C42C23×C311yescharacteristic
171(C2×D3)⋊C4—22no—
172(C2×D3)⋊C4—22no—
173(C2×D3)⋊C4—21no—
174C4⋊Dic3—22no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3C3×D411yescharacteristic
178C4⋊Dic3C3×D411yescharacteristic
179Dic3⋊C4—21no—
180C4×Dic3—22no—
181C4×Dic3—21no—
182C2×C3⋊C8—21no—
183#204—42no—
184C22×C32#12011yescharacteristic
185C2×C3×D3—41no—
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C32×C4—21no—
189C32×C4—42no—
190C32×C4#13511yescharacteristic
191C32×C4#13511yescharacteristic
192C32×C4AGL(1,ℤ/8)11yescharacteristic
193C32×C4#13711yescharacteristic
194C3×Dic3—41no—
195C3×Dic3—41no—
196C3×Dic3—41no—
197C3×Dic3—81no—
198C2×SD16—61no—
199C4⋊Q8—31no—
200C4⋊Q8C2×C3×D311yescharacteristic
201#126—62no—
202#124—61no—
203C22⋊Q8—61no—
204C4×Q8—31no—
205C4×Q8—61no—
206C4×D4—31no—
207#117—61no—
208#107—62no—
209#106—61no—
210C4⋊C8C2×C3×D311yescharacteristic
211C4⋊C8C2×C3×D311yescharacteristic
212#103—61no—
213#103—61no—
214C4×C8—31no—
215C23×C3—61no—
216C22×D3—21no—
217C3×Q8—41no—
218C3×Q8—41no—
219C3×Q8—41no—
220C3×Q8—41no—
221C3×Q8—61no—
222C3×Q8—61no—
223C3×Q8—81no—
224C3×Q8—81no—
225C3×Q8—121no—
226C3×Q8—121no—
227C3×D4—61no—
228C3×D4—61no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—42no—
235C2×C3×C4—61no—
236C2×C3×C4—61no—
237C2×C3×C4—61no—
238C2×C3×C4—121no—
239C2×C3×C4—121no—
240C2×C3×C4—121no—
241C2×C3×C4C2×D1211yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4C2×C3×D411yescharacteristic
245C2×C3×C4C2×C3×D411yescharacteristic
246C2×C3×C4C2×C3×D411yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—41no—
251D12—21no—
252D12—21no—
253C4×D3—41no—
254C4×D3—41no—
255Dic6—21no—
256Dic6—21no—
257Dic6—41no—
258Dic6—41no—
259C3×C8—41no—
260C3×C8—41no—
261C3×C8—41no—
262C3×C8—41no—
263C3×C8—62no—
264C3×C8—81no—
265C3×C8—81no—
266C3⋊C8—22no—
267C2×C32#44911yescharacteristic
268C2×C32#45211yescharacteristic
269C2×C32#45611yescharacteristic
270C3×D3—81no—
271C2×Q8—21no—
272C2×Q8—31no—
273C2×Q8—61no—
274C2×D4—31no—
275C22×C4—61no—
276SD16—122no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—61no—
280C4⋊C4—21no—
281C4⋊C4—31no—
282C4⋊C4—31no—
283C4⋊C4—62no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4C3×D1212yes—
288C22⋊C4—62no—
289C22⋊C4—62no—
290C22⋊C4—61no—
291C42—62no—
292C42—61no—
293C42C22×C3×D311yescharacteristic
294C22×C3—21no—
295C22×C3—121no—
296C22×C3—121no—
297C22×C3—121no—
298C22×C3#88211yescharacteristic
299C22×C3C3×#12011yescharacteristic
300C2×D3—41no—
301C2×D3—41no—
302C2×D3—41no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—41no—
310C3×C4—42no—
311C3×C4—42no—
312C3×C4—82no—
313C3×C4—121no—
314C3×C4—121no—
315C3×C4—121no—
316C3×C4—241no—
317C3×C4#91111yescharacteristic
318C3×C4#91611yescharacteristic
319C3×C4#91611yescharacteristic
320C3×C4#91811yescharacteristic
321C3×C4C3×#13511yescharacteristic
322C3×C4C3×#13511yescharacteristic
323C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
324C3×C4C3×#13711yescharacteristic
325Dic3—41no—
326Dic3—41no—
327Dic3—41no—
328Dic3—81no—
329C32#165011yescharacteristic, complemented, Sylow
330C23—61no—
331Q8—41no—
332Q8—41no—
333Q8—61no—
334Q8—61no—
335Q8—121no—
336Q8—121no—
337D4—61no—
338D4—61no—
339C2×C4—22no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—121no—
344C2×C4—121no—
345C2×C4—121no—
346C2×C4C2×C3×D1211yescharacteristic
347C2×C4C3×D3×D411yescharacteristic
348C2×C4C3×D3×D411yescharacteristic
349C8—41no—
350C8—41no—
351C8—62no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—241no—
356C2×C3#475211yescharacteristic
357C2×C3#478111yescharacteristic
358C2×C3#480811yescharacteristic
359C2×C3C3×#44911yescharacteristic
360C2×C3C3×#45211yescharacteristic
361C2×C3C3×#45611yescharacteristic
362D3—81no—
363C22—121no—
364C22—121no—
365C22—121no—
366C22C3×#88211yescharacteristic
367C4—21no—
368C4—42no—
369C4—121no—
370C4—121no—
371C4—121no—
372C4—241no—
373C4C3×#91111yescharacteristic
374C4C3×#91611yescharacteristic
375C4C3×#91611yescharacteristic
376C4C3×#91811yescharacteristic
377C3—21no—
378C3#6843711yescharacteristic, direct product factor
379C3C3×#165011yescharacteristic, complemented
380C2—241no—
381C2C3×#475211yescharacteristic
382C2C3×#478111yescharacteristic
383C2C3×#480811yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×#332D3
hypocenterC3C3×#1650
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
2. C3×#5078C2semidirect
3. C3×#4851C2semidirect
5. C32×#332C2semidirect
6. C3×#4484C2semidirect
9. #68437C3direct (N × H)
32. #5078C2×C3semidirect
33. #4851C2×C3semidirect
36. C3×#332D3semidirect
37. C3×#332C2×C3semidirect
40. #4484C2×C3semidirect
129. #332C3×D3semidirect
329. C32#1650semidirect
378. C3#68437direct (N × H)
379. C3C3×#1650semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
C3×#50782
C3×#48512
C3×#48412
C32×#3322
C3×#44842
C3×#44832
C3×#16503
#684373