Finite Group Databasebeta

← C3×#68203 #11779493

Subgroups — C3×#68203 #11779493

Order 1152.

477 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5563C211yesmaximal, characteristic
2C3×#5008C211yesmaximal, characteristic, complemented
3C3×#4842C211yesmaximal, characteristic, complemented
4C3×#4699C211yesmaximal, characteristic, complemented
5C32×D4⋊C8C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1634—31nomaximal
9#68203C311yesmaximal, characteristic, direct product factor
10C32×C4×D4C2211yescharacteristic
11C3×#938—21no—
12C3×#930—21no—
13C3×#926—21no—
14C2×C3×Dic12—22no—
15C3×#892—21no—
16C3×#885—22no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22C3×#832—21no—
23C3×#821—21no—
24C3×#817—21no—
25C3×#808—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#555—31no—
28#5563C2×C311yescharacteristic
29C3×#494—31no—
30C3×#476—31no—
31C3×#476—31no—
32#5008C2×C311yescharacteristic, complemented
33#4842C2×C311yescharacteristic, complemented
34#4699C2×C311yescharacteristic, complemented
35C3×#333—31no—
36C3×D4⋊C8—21no—
37C3×D4⋊C8—31no—
38C3×D4⋊C8D311yescharacteristic, complemented
39C3×D4⋊C8C2×C311yescharacteristic, complemented
40#4481C2×C311yescharacteristic, complemented
41#4459C2×C311yescharacteristic, complemented
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C3×#67—22no—
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D412yes—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2311yescharacteristic
54C3×#217—22no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4×Dic3—22no—
63C2×C3×C3⋊C8—21no—
64C3×Dic12—44no—
65#1634—31noSylow
66C2×C3×Q16—62no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8—31no—
69C3×#124—62no—
70C3×#121—61no—
71C3×#121—61no—
72C3×C4×D4—21no—
73C3×C4×D4—31no—
74C3×C4×D4C2×D311yescharacteristic
75C3×C4×D4C22×C311yescharacteristic
76C3×#117—61no—
77C3×#117—61no—
78#938—21no—
79#930—21no—
80#926—21no—
81C2×Dic12—22no—
82#892—21no—
83#885—22no—
84C4×D12C22×C311yescharacteristic
85#869C22×C311yescharacteristic
86#869C22×C311yescharacteristic
87C3×#106—61no—
88C3×#106—61no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C22×C311yescharacteristic
93C3×#102—61no—
94C3×#102—61no—
95C3×C4×C8—21no—
96C3×C4×C8C2×D311yescharacteristic
97C3×C4×C8C22×C311yescharacteristic
98#832—21no—
99#821—21no—
100#817—21no—
101#808—21no—
102C4⋊(C3⋊C8)C22×C311yescharacteristic
103C23×C32—21no—
104C22×C3×D3—21no—
105C32×D4—21no—
106C32×D4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C3×#67—82no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—41no—
117C3×D12—21no—
118C3×D12—21no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—42no—
122C3×Dic6—42no—
123C32×C8—22no—
124C32×C8—41no—
125C3×C3⋊C8—41no—
126#555—31no—
127#494—31no—
128#476—31no—
129#476—31no—
130#333—31no—
131D4⋊C8—31no—
132D4⋊C8C3×D311yescharacteristic, complemented
133C2×C3×Q8—32no—
134C2×C3×Q8—61no—
135C2×C3×D4—21no—
136C2×C3×D4—31no—
137C2×C3×D4—62no—
138C2×C3×D4D1211yescharacteristic
139C2×C3×D4C3×D411yescharacteristic
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—41no—
143C22×C3×C4—61no—
144C2×#67—22no—
145C2×D12C3×D411yescharacteristic
146C2×C4×D3—21no—
147C2×Dic6—21no—
148C2×Dic6C3×D412yes—
149C3×Q16—124no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—41no—
155C2×C3×C8—41no—
156C2×C3×C8—61no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—31no—
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×C22⋊C4—62no—
170C3×C22⋊C4—61no—
171C3×C42—21no—
172C3×C42—62no—
173C3×C42C22×D311yescharacteristic
174C3×C42C23×C311yescharacteristic
175#217—22no—
176(C2×D3)⋊C4—22no—
177(C2×D3)⋊C4—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3C3×D411yescharacteristic
183C4×Dic3—22no—
184C2×C3⋊C8—21no—
185Dic12—44no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32—41no—
189C22×C32#12011yescharacteristic
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C32×C4—21no—
194C32×C4—41no—
195C32×C4#13511yescharacteristic
196C32×C4#13511yescharacteristic
197C32×C4#13711yescharacteristic
198C32×C4#13711yescharacteristic
199C3×Dic3—41no—
200C3×Dic3—42no—
201C3×Dic3—81no—
202C2×Q16—62no—
203C4⋊Q8—31no—
204C4⋊Q8—31no—
205#124—62no—
206#121—61no—
207#121—61no—
208C4×D4—31no—
209C4×D4C2×C3×D311yescharacteristic
210#117—61no—
211#117—61no—
212#106—61no—
213#106—61no—
214C4⋊C8—31no—
215C4⋊C8C2×C3×D311yescharacteristic
216#102—61no—
217#102—61no—
218C4×C8C2×C3×D311yescharacteristic
219C23×C3—21no—
220C23×C3—21no—
221C23×C3—41no—
222C23×C3—61no—
223C22×D3—21no—
224C3×Q8—122no—
225C3×Q8—122no—
226C3×D4—22no—
227C3×D4—21no—
228C3×D4—21no—
229C3×D4—21no—
230C3×D4—21no—
231C3×D4—41no—
232C3×D4—61no—
233C3×D4—61no—
234C3×D4—242no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—61no—
246C2×C3×C4—62no—
247C2×C3×C4—81no—
248C2×C3×C4—81no—
249C2×C3×C4—121no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4C2×C3×D411yescharacteristic
256C2×C3×C4C2×C3×D411yescharacteristic
257C2×C3×C4C2×C3×D411yescharacteristic
258#67—82no—
259C2×Dic3—21no—
260C2×Dic3—22no—
261C2×Dic3—41no—
262D12—21no—
263D12—21no—
264C4×D3—41no—
265C4×D3—41no—
266Dic6—42no—
267Dic6—42no—
268C3×C8—22no—
269C3×C8—22no—
270C3×C8—42no—
271C3×C8—41no—
272C3×C8—41no—
273C3×C8—81no—
274C3×C8—121no—
275C3⋊C8—41no—
276C2×C32—81no—
277C2×C32#45211yescharacteristic
278C2×C32#45211yescharacteristic
279C2×C32#45311yescharacteristic
280C3×D3—81no—
281C2×Q8—32no—
282C2×Q8—61no—
283C2×D4—31no—
284C2×D4—62no—
285C2×D4C3×D1211yescharacteristic
286C22×C4—21no—
287C22×C4—61no—
288Q16—124no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—61no—
292C4⋊C4—31no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4C3×D1211yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—61no—
302C42—62no—
303C42C22×C3×D311yescharacteristic
304C22×C3—21no—
305C22×C3—42no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—81no—
313C22×C3—81no—
314C22×C3—121no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3#88211yescharacteristic
318C22×C3C3×#12011yescharacteristic
319C2×D3—41no—
320C2×D3—41no—
321C2×D3—41no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—81no—
332C3×C4—121no—
333C3×C4—122no—
334C3×C4—241no—
335C3×C4#90411yescharacteristic
336C3×C4#90911yescharacteristic
337C3×C4#91211yescharacteristic
338C3×C4#91511yescharacteristic
339C3×C4C3×#13511yescharacteristic
340C3×C4C3×#13511yescharacteristic
341C3×C4C3×#13711yescharacteristic
342C3×C4C3×#13711yescharacteristic
343Dic3—41no—
344Dic3—42no—
345Dic3—81no—
346C32#163411yescharacteristic, complemented, Sylow
347C23—21no—
348C23—61no—
349Q8—122no—
350Q8—122no—
351D4—21no—
352D4—21no—
353D4—61no—
354D4—61no—
355D4—242no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—61no—
360C2×C4—62no—
361C2×C4—121no—
362C2×C4—121no—
363C2×C4—121no—
364C2×C4C2×C3×D1211yescharacteristic
365C2×C4C3×D3×D411yescharacteristic
366C2×C4C3×D3×D411yescharacteristic
367C8—22no—
368C8—41no—
369C8—121no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—82no—
374C2×C3—81no—
375C2×C3—81no—
376C2×C3—241no—
377C2×C3#473311yescharacteristic
378C2×C3#478311yescharacteristic
379C2×C3#482211yescharacteristic
380C2×C3C3×#45211yescharacteristic
381C2×C3C3×#45211yescharacteristic
382C2×C3C3×#45311yescharacteristic
383D3—81no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—121no—
388C22—121no—
389C22—121no—
390C22C3×#88211yescharacteristic
391C4—21no—
392C4—41no—
393C4—121no—
394C4—122no—
395C4—241no—
396C4C3×#90411yescharacteristic
397C4C3×#90911yescharacteristic
398C4C3×#91211yescharacteristic
399C4C3×#91511yescharacteristic
400C3—21no—
401C3#6820311yescharacteristic, direct product factor
402C3C3×#163411yescharacteristic, complemented
403C2—81no—
404C2—241no—
405C2C3×#473311yescharacteristic
406C2C3×#478311yescharacteristic
407C2C3×#482211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32#120
prime radicalC3×#5563C2
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1634
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
2. C3×#5008C2semidirect
3. C3×#4842C2semidirect
4. C3×#4699C2semidirect
5. C32×D4⋊C8C2semidirect
6. C3×#4481C2semidirect
7. C3×#4459C2semidirect
9. #68203C3direct (N × H)
32. #5008C2×C3semidirect
33. #4842C2×C3semidirect
34. #4699C2×C3semidirect
38. C3×D4⋊C8D3semidirect
39. C3×D4⋊C8C2×C3semidirect
40. #4481C2×C3semidirect
41. #4459C2×C3semidirect
132. D4⋊C8C3×D3semidirect
346. C32#1634semidirect
401. C3#68203direct (N × H)
402. C3C3×#1634semidirect

Maximal subgroups

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

subgroupindex
C3×#55632
C3×#50082
C3×#48422
C3×#46992
C32×D4⋊C82
C3×#44812
C3×#44592
C3×#16343
#682033