Finite Group Databasebeta

← C3×#68461 #11780188

Subgroups — C3×#68461 #11780188

Order 1152.

500 conjugacy classes of subgroups.

The subgroup lattice has 401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2C3×#5078C211yesmaximal, characteristic, complemented
3C3×#4849C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic
8C3×#1649—31nomaximal
9#68461C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C3×#946—21no—
13C2×C3×Dic12—21no—
14C3×#896—22no—
15C3×#893—21no—
16C3×#888—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C3×#821—21no—
23C3×#818—21no—
24C3×#816—21no—
25C3×#807—22no—
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×D4×Q8—31no—
28#5727C2×C311yescharacteristic
29C3×#500—31no—
30C3×#474—31no—
31C3×#462—31no—
32#5078C2×C311yescharacteristic, complemented
33#4849C2×C311yescharacteristic, complemented
34#4846C2×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—
43C3×D3×Q8—42no—
44C3×D3×Q8—42no—
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—22no—
47C2×C3×C4×D3—21no—
48C2×C3×Dic6—22no—
49C2×C3×Dic6—21no—
50C2×C3×Dic6D411yescharacteristic
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D412yes—
55C32×C42C2311yescharacteristic
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C3×Dic12—42no—
67#1649—31noSylow
68C22×C3×Q8—61no—
69C2×D3×Q8—21no—
70C2×C3×Q16—61no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8—31no—
73C3×C4⋊Q8—61no—
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×C4⋊Q8C22×C311yescharacteristic
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—62no—
78C3×C4×Q8—31no—
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81#946—21no—
82C2×Dic12—21no—
83#896—22no—
84#893—21no—
85#888—21no—
86C4×D12C22×C311yescharacteristic
87#869C22×C311yescharacteristic
88C4×Dic6C22×C311yescharacteristic
89C3×#107—61no—
90C3×#107—62no—
91C3×C4⋊C8—21no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C22×C311yescharacteristic
96C3×C4⋊C8C22×C311yescharacteristic
97C3×#103—61no—
98C3×#102—61no—
99C3×C4×C8—31no—
100#821—21no—
101#818—21no—
102#816—21no—
103#807—22no—
104C4×C3⋊C8C22×C311yescharacteristic
105C22×C3×D3—21no—
106C32×Q8—41no—
107C32×Q8—41no—
108C2×C32×C4—22no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12Q1612yescomplemented
118C3×C4×D3—44no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—21no—
122C3×Dic6—44no—
123C3×Dic6—41no—
124C3×Dic6—41no—
125C3×Dic6D812yes—
126C32×C8—41no—
127C32×C8—41no—
128C3×C3⋊C8—22no—
129D4×Q8—31no—
130#500—31no—
131#474—31no—
132#462—31no—
133#332C3×D311yescharacteristic, complemented
134Q8⋊C8—31no—
135D4⋊C8—31no—
136C2×C3×Q8—21no—
137C2×C3×Q8—21no—
138C2×C3×Q8—31no—
139C2×C3×Q8—41no—
140C2×C3×Q8—62no—
141C2×C3×Q8—61no—
142C2×C3×Q8—122no—
143C2×C3×Q8—122no—
144C2×C3×D4—31no—
145C22×C3×C4—62no—
146C22×C3×C4—61no—
147D3×Q8—42no—
148D3×Q8—42no—
149C2×D12C3×D411yescharacteristic
150C2×C4×D3—22no—
151C2×C4×D3—21no—
152C2×Dic6—22no—
153C2×Dic6—21no—
154C2×Dic6C3×D411yescharacteristic
155C3×Q16—122no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—41no—
161C2×C3×C8—41no—
162C2×C3×C8—61no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—41no—
169C3×C4⋊C4—62no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4D1212yes—
174C3×C4⋊C4C3×D412yes—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42—61no—
179C3×C42C22×D311yescharacteristic
180C3×C42C23×C311yescharacteristic
181(C2×D3)⋊C4—22no—
182(C2×D3)⋊C4—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3C3×D411yescharacteristic
186C4⋊Dic3C3×D411yescharacteristic
187Dic3⋊C4—22no—
188Dic3⋊C4—21no—
189C4×Dic3—21no—
190C2×C3⋊C8—21no—
191Dic12—42no—
192C22×C32#12011yescharacteristic
193C2×C3×D3—22no—
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C32×C4—21no—
197C32×C4—42no—
198C32×C4C2×D811yescharacteristic
199C32×C4C2×Q1611yescharacteristic
200C32×C4AGL(1,ℤ/8)11yescharacteristic
201C32×C4#13711yescharacteristic
202C3×Dic3—22no—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C3×Dic3—81no—
206C22×Q8—61no—
207C2×Q16—61no—
208C4⋊Q8—31no—
209C4⋊Q8—61no—
210C4⋊Q8C2×C3×D311yescharacteristic
211C22⋊Q8—61no—
212C22⋊Q8—62no—
213C4×Q8—31no—
214C4×D4—31no—
215C4×D4—61no—
216#107—61no—
217#107—62no—
218C4⋊C8C2×C3×D311yescharacteristic
219C4⋊C8C2×C3×D311yescharacteristic
220#103—61no—
221#102—61no—
222C4×C8—31no—
223C23×C3—61no—
224C22×D3—21no—
225C3×Q8—32no—
226C3×Q8—41no—
227C3×Q8—41no—
228C3×Q8—41no—
229C3×Q8—41no—
230C3×Q8—61no—
231C3×Q8—81no—
232C3×Q8—81no—
233C3×Q8—124no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×D4—32no—
237C3×D4—61no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—42no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—124no—
248C2×C3×C4—121no—
249C2×C3×C4—121no—
250C2×C3×C4—121no—
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4C2×C3×D411yescharacteristic
255C2×C3×C4C2×C3×D411yescharacteristic
256C2×C3×C4C2×C3×D411yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—41no—
261D12—21no—
262D12C3×Q1612yescomplemented
263C4×D3—44no—
264C4×D3—41no—
265C4×D3—41no—
266Dic6—21no—
267Dic6—44no—
268Dic6—41no—
269Dic6—41no—
270Dic6C3×D812yes—
271C3×C8—41no—
272C3×C8—41no—
273C3×C8—41no—
274C3×C8—41no—
275C3×C8—62no—
276C3×C8—81no—
277C3×C8—81no—
278C3⋊C8—22no—
279C2×C32#44711yescharacteristic
280C2×C32#45111yescharacteristic
281C2×C32#45611yescharacteristic
282C3×D3—42no—
283C2×Q8—21no—
284C2×Q8—31no—
285C2×Q8—62no—
286C2×Q8—61no—
287C2×Q8—122no—
288C2×Q8—122no—
289C2×D4—31no—
290C22×C4—62no—
291C22×C4—61no—
292Q16—122no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—61no—
296C4⋊C4—21no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—62no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—61no—
303C4⋊C4C3×D1212yes—
304C22⋊C4—62no—
305C22⋊C4—61no—
306C42—61no—
307C42C22×C3×D311yescharacteristic
308C22×C3—21no—
309C22×C3—62no—
310C22×C3—121no—
311C22×C3—121no—
312C22×C3#88211yescharacteristic
313C22×C3C3×#12011yescharacteristic
314C2×D3—22no—
315C2×D3—41no—
316C2×D3—41no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—41no—
324C3×C4—42no—
325C3×C4—42no—
326C3×C4—62no—
327C3×C4—82no—
328C3×C4—121no—
329C3×C4—121no—
330C3×C4—241no—
331C3×C4D3×D811yescharacteristic
332C3×C4#91411yescharacteristic
333C3×C4#91511yescharacteristic
334C3×C4D3×Q1611yescharacteristic
335C3×C4C2×C3×D811yescharacteristic
336C3×C4C2×C3×Q1611yescharacteristic
337C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
338C3×C4C3×#13711yescharacteristic
339Dic3—22no—
340Dic3—41no—
341Dic3—41no—
342Dic3—81no—
343C32#164911yescharacteristic, complemented, Sylow
344C23—61no—
345Q8—32no—
346Q8—41no—
347Q8—41no—
348Q8—61no—
349Q8—124no—
350Q8—121no—
351Q8—121no—
352D4—32no—
353D4—61no—
354C2×C4—22no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—124no—
359C2×C4—121no—
360C2×C4—121no—
361C2×C4—121no—
362C2×C4C2×C3×D1211yescharacteristic
363C2×C4C3×D3×D411yescharacteristic
364C2×C4C3×D3×D411yescharacteristic
365C8—41no—
366C8—41no—
367C8—62no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—122no—
372C2×C3#475211yescharacteristic
373C2×C3#477311yescharacteristic
374C2×C3#480911yescharacteristic
375C2×C3C3×#44711yescharacteristic
376C2×C3C3×#45111yescharacteristic
377C2×C3C3×#45611yescharacteristic
378D3—42no—
379C22—62no—
380C22—121no—
381C22—121no—
382C22C3×#88211yescharacteristic
383C4—21no—
384C4—42no—
385C4—62no—
386C4—121no—
387C4—121no—
388C4—241no—
389C4C3×D3×D811yescharacteristic
390C4C3×#91411yescharacteristic
391C4C3×#91511yescharacteristic
392C4C3×D3×Q1611yescharacteristic
393C3—21no—
394C3#6846111yescharacteristic, direct product factor
395C3C3×#164911yescharacteristic, complemented
396C2—122no—
397C2C3×#475211yescharacteristic
398C2C3×#477311yescharacteristic
399C2C3×#480911yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×#332D3
hypocenterC3C3×#1649
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×#4849C2semidirect
5. C32×#332C2semidirect
6. C3×#4484C2semidirect
9. #68461C3direct (N × H)
32. #5078C2×C3semidirect
33. #4849C2×C3semidirect
36. C3×#332D3semidirect
37. C3×#332C2×C3semidirect
40. #4484C2×C3semidirect
117. C3×D12Q16semidirect
133. #332C3×D3semidirect
262. D12C3×Q16semidirect
343. C32#1649semidirect
394. C3#68461direct (N × H)
395. C3C3×#1649semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C3×#50782
C3×#48492
C3×#48462
C32×#3322
C3×#44842
C3×#44832
C3×#16493
#684613