Finite Group Databasebeta

← C3×#68365 #11775892

Subgroups — C3×#68365 #11775892

Order 1152.

454 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5688C211yesmaximal, characteristic
2C3×#4705C211yesmaximal, characteristic
3C3×D3×#97C211yesmaximal, characteristic
4C32×#330C211yesmaximal, characteristic, complemented
5C3×#4543C211yesmaximal, characteristic, complemented
6C3×#4465C211yesmaximal, characteristic, complemented
7C3×#4465C211yesmaximal, characteristic, complemented
8C3×#1531—31nomaximal
9#68365C311yesmaximal, characteristic, direct product factor
10C32×#125C2211yescharacteristic
11C2×C3×D3×C8—21no—
12C3×#896—21no—
13C3×#896—21no—
14C3×#892C411yescharacteristic
15C3×#892C411yescharacteristic
16C3×#888C411yescharacteristic
17C3×#888C411yescharacteristic
18C3×#887—21no—
19C3×#887—21no—
20C3×C42×D3C2211yescharacteristic
21C3×#870C2211yescharacteristic
22C32×#97C2211yescharacteristic
23C32×#97C2211yescharacteristic
24C3×(C2×D3)⋊C8—21no—
25C3×#815—21no—
26C3×Dic3⋊C8—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29C3×#533—31no—
30#5688C2×C311yescharacteristic
31C3×#432—31no—
32C2×C3×#97—31no—
33#4705C2×C311yescharacteristic
34D3×#97C2×C311yescharacteristic
35C3×#330—21no—
36C3×#330—31no—
37C3×#330—31no—
38C3×#330—31no—
39C3×#330D311yescharacteristic, complemented
40C3×#330C2×C311yescharacteristic, complemented
41#4543C2×C311yescharacteristic, complemented
42#4465C2×C311yescharacteristic, complemented
43#4465C2×C311yescharacteristic, complemented
44C2×C3×C4×D3C2×C411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×Dic6—21no—
48C2×C3×Dic6—21no—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C42C2311yescharacteristic
56C3×(C2×D3)⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
59C3×C4⋊Dic3C2×C411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C3×D3×C8—24no—
72#1531—31noSylow
73C22×C3×C8—61no—
74C3×C4⋊Q8—31no—
75C3×C4⋊Q8—31no—
76C3×#125—21no—
77C3×#125—31no—
78C3×#125C2×D311yescharacteristic
79C3×#125C22×C311yescharacteristic
80C3×C22⋊Q8—61no—
81C3×C22⋊Q8—61no—
82C3×C4×Q8—61no—
83C3×C4×Q8—61no—
84C3×#117—31no—
85C3×#117—31no—
86C2×C3×C42—31no—
87C2×D3×C8—21no—
88#896—21no—
89#896—21no—
90#892C3×C411yescharacteristic
91#892C3×C411yescharacteristic
92#888C3×C411yescharacteristic
93#888C3×C411yescharacteristic
94#887—21no—
95#887—21no—
96C42×D3C22×C311yescharacteristic
97#870C22×C311yescharacteristic
98C3×C4⋊C8—61no—
99C3×C22⋊C8—61no—
100C3×#97—21no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97—31no—
104C3×#97—61no—
105C3×#97C2×D311yescharacteristic
106C3×#97C2×D311yescharacteristic
107C3×#97C22×C311yescharacteristic
108C3×#97C22×C311yescharacteristic
109(C2×D3)⋊C8—21no—
110#815—21no—
111Dic3⋊C8—21no—
112#803C22×C311yescharacteristic
113#803C22×C311yescharacteristic
114C22×C3×D3C22⋊C411yescharacteristic
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3C22⋊C411yescharacteristic
123C2×C3×Dic3C22⋊C411yescharacteristic
124C2×C3×Dic3C22⋊C411yescharacteristic
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×C4×D3—41no—
128C3×Dic6—42no—
129C3×Dic6—42no—
130C32×C8—22no—
131C32×C8—41no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134#533—31no—
135#432—31no—
136C2×#97—31no—
137#330—31no—
138#330—31no—
139#330—31no—
140#330C3×D311yescharacteristic, complemented
141C2×C3×Q8—61no—
142C2×C3×Q8—61no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C22×C3×C4—31no—
146C2×C4×D3C2×C3×C411yescharacteristic
147C2×C4×D3C3×D411yescharacteristic
148C2×C4×D3C3×D411yescharacteristic
149C2×Dic6—21no—
150C2×Dic6—21no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—41no—
156C2×C3×C8—41no—
157C2×C3×C8—64no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—41no—
169C3×C4⋊C4—41no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4C4×D311yescharacteristic
175C3×C4⋊C4C4×D311yescharacteristic
176C3×C4⋊C4C2×C3×C411yescharacteristic
177C3×C4⋊C4C2×C3×C411yescharacteristic
178C3×C22⋊C4—61no—
179C3×C22⋊C4—61no—
180C3×C42—21no—
181C3×C42—31no—
182C3×C42—31no—
183C3×C42—31no—
184C3×C42—61no—
185C3×C42—61no—
186C3×C42C22×D311yescharacteristic
187C3×C42C23×C311yescharacteristic
188(C2×D3)⋊C4—21no—
189(C2×D3)⋊C4—21no—
190C4⋊Dic3C2×C3×C411yescharacteristic
191C4⋊Dic3C2×C3×C411yescharacteristic
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196C4×Dic3—21no—
197C4×Dic3—21no—
198C4×Dic3C2×C3×C411yescharacteristic
199C4×Dic3C3×D411yescharacteristic
200C4×Dic3C3×D411yescharacteristic
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203D3×C8—24no—
204C22×C32C2×C22⋊C411yescharacteristic
205C2×C3×D3—21no—
206C2×C3×D3—21no—
207C2×C3×D3#10112yes—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—21no—
211C32×C4—41no—
212C32×C4—41no—
213C3×Dic3—21no—
214C3×Dic3—21no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3#10412yes—
218C22×C8—61no—
219C4⋊Q8—31no—
220C4⋊Q8—31no—
221#125—31no—
222#125C2×C3×D311yescharacteristic
223C22⋊Q8—61no—
224C22⋊Q8—61no—
225C4×Q8—61no—
226C4×Q8—61no—
227#117—31no—
228#117—31no—
229C2×C42—31no—
230C4⋊C8—61no—
231C22⋊C8—61no—
232#97—31no—
233#97—31no—
234#97—61no—
235#97C2×C3×D311yescharacteristic
236#97C2×C3×D311yescharacteristic
237C23×C3—31no—
238C22×D3C3×C22⋊C411yescharacteristic
239C3×Q8—122no—
240C3×Q8—122no—
241C2×C3×C4—21no—
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—31no—
249C2×C3×C4—31no—
250C2×C3×C4—31no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—121no—
258C2×C3×C4C2×C4×D311yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4C22×C3×C411yescharacteristic
262C2×C3×C4C2×C3×D411yescharacteristic
263C2×C3×C4C2×C3×D411yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3C3×C22⋊C411yescharacteristic
267C2×Dic3C3×C22⋊C411yescharacteristic
268C2×Dic3C3×C22⋊C411yescharacteristic
269C4×D3—22no—
270C4×D3—22no—
271C4×D3—41no—
272Dic6—42no—
273Dic6—42no—
274C3×C8—22no—
275C3×C8—22no—
276C3×C8—42no—
277C3×C8—41no—
278C3×C8—41no—
279C3×C8—42no—
280C3×C8—62no—
281C3×C8—121no—
282C3⋊C8—22no—
283C3⋊C8—41no—
284C2×C32C2×#10111yescharacteristic
285C2×C32C2×#10411yescharacteristic
286C2×C32#42111yescharacteristic
287C3×D3—22no—
288C2×Q8—61no—
289C2×Q8—61no—
290C22×C4—31no—
291C22×C4—31no—
292C22×C4—31no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—64no—
296C2×C8—61no—
297C2×C8—61no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C4⋊C4—61no—
305C4⋊C4—61no—
306C4⋊C4C3×C4×D311yescharacteristic
307C4⋊C4C3×C4×D311yescharacteristic
308C22⋊C4—61no—
309C22⋊C4—61no—
310C42—31no—
311C42—31no—
312C42—31no—
313C42—61no—
314C42—61no—
315C42C22×C3×D311yescharacteristic
316C22×C3—21no—
317C22×C3—32no—
318C22×C3—61no—
319C22×C3—61no—
320C22×C3D3×C22⋊C411yescharacteristic
321C22×C3C2×C3×C22⋊C411yescharacteristic
322C2×D3—21no—
323C2×D3—21no—
324C2×D3C3×#10112yes—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—32no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—41no—
335C3×C4—41no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4—61no—
340C3×C4—61no—
341C3×C4—81no—
342C3×C4—81no—
343C3×C4—121no—
344C3×C4—121no—
345Dic3—21no—
346Dic3—21no—
347Dic3—41no—
348Dic3—41no—
349Dic3C3×#10412yes—
350C32#153111yescharacteristic, complemented, Sylow
351C23—31no—
352Q8—122no—
353Q8—122no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—31no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—121no—
364C2×C4C2×C3×C4×D311yescharacteristic
365C2×C4C3×D3×D411yescharacteristic
366C2×C4C3×D3×D411yescharacteristic
367C8—22no—
368C8—41no—
369C8—62no—
370C8—121no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—62no—
375C2×C3D3×#10111yescharacteristic
376C2×C3D3×#10411yescharacteristic
377C2×C3#482111yescharacteristic
378C2×C3C2×C3×#10111yescharacteristic
379C2×C3C2×C3×#10411yescharacteristic
380C2×C3C3×#42111yescharacteristic
381D3—22no—
382C22—32no—
383C22—61no—
384C22—61no—
385C22C3×D3×C22⋊C411yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—32no—
390C4—41no—
391C4—41no—
392C4—61no—
393C4—61no—
394C4—121no—
395C4—121no—
396C3—21no—
397C3#6836511yescharacteristic, direct product factor
398C3C3×#153111yescharacteristic, complemented
399C2—62no—
400C2C3×D3×#10111yescharacteristic
401C2C3×D3×#10411yescharacteristic
402C2C3×#482111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#330C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC3×C42C23×C3
hypercenterC3×#330D3
hypocenterC3C3×#1531
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#330

Complements

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

NH ≅ G/Ntype
4. C32×#330C2semidirect
5. C3×#4543C2semidirect
6. C3×#4465C2semidirect
7. C3×#4465C2semidirect
9. #68365C3direct (N × H)
39. C3×#330D3semidirect
40. C3×#330C2×C3semidirect
41. #4543C2×C3semidirect
42. #4465C2×C3semidirect
43. #4465C2×C3semidirect
140. #330C3×D3semidirect
350. C32#1531semidirect
397. C3#68365direct (N × H)
398. C3C3×#1531semidirect

Maximal subgroups

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

subgroupindex
C3×#56882
C3×#47052
C3×D3×#972
C32×#3302
C3×#45432
C3×#44652
C3×#15313
#683653