Finite Group Databasebeta

← C3×#68436 #11780094

Subgroups — C3×#68436 #11780094

Order 1152.

512 conjugacy classes of subgroups.

The subgroup lattice has 421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5726C211yesmaximal, characteristic
2C3×#5078C211yesmaximal, characteristic, complemented
3C3×#4846C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic, complemented
5C32×#332C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic, complemented
8C3×#1647—31nomaximal
9#68436C311yesmaximal, characteristic, direct product factor
10C2×C3×#239—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C3×#946—21no—
13C2×C3×#204—21no—
14C3×#895—21no—
15C3×#894—22no—
16C3×D3×C4⋊C4—21no—
17C3×C4×D12C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C3×#821—21no—
23C3×#818—21no—
24C3×#816—21no—
25C3×#807—22no—
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#547—31no—
28#5726C2×C311yescharacteristic
29C3×#500—31no—
30C3×#474—31no—
31C3×#461—31no—
32#5078C2×C311yescharacteristic, complemented
33#4846C2×C311yescharacteristic, complemented
34#4841C2×C311yescharacteristic, complemented
35C3×#332—21no—
36C3×#332D311yescharacteristic, complemented
37C3×#332C2×C311yescharacteristic, complemented
38C3×D4⋊C8—31no—
39C3×D4⋊C8—31no—
40#4483C2×C311yescharacteristic, complemented
41#4483C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C3×#239—42no—
44C3×#239—42no—
45C2×C3×D12—22no—
46C2×C3×D12D411yescharacteristic
47C2×C3×D12D411yescharacteristic
48C2×C3×C4×D3—22no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D412yes—
56C32×C42C2311yescharacteristic
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—22no—
65C2×C3×C3⋊C8—21no—
66C3×#204—42no—
67#1647—31noSylow
68C2×C3×#41—61no—
69C2×#239—21no—
70C2×C3×SD16—61no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8—31no—
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C22×C311yescharacteristic
75C3×#123—62no—
76C3×C22⋊Q8—61no—
77C3×#121—61no—
78C3×C4×D4—31no—
79C3×C4×D4—31no—
80C2×C3×C4⋊C4—61no—
81#946—21no—
82C2×#204—21no—
83#895—21no—
84#894—22no—
85D3×C4⋊C4—21no—
86C4×D12C22×C311yescharacteristic
87C4×D12C22×C311yescharacteristic
88#869C22×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—
106C22×C3×D3—21no—
107C32×Q8—41no—
108C32×Q8—41no—
109C2×C32×C4—22no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12—21no—
118C3×D12—21no—
119C3×D12—44no—
120C3×D12D812yes—
121C3×C4×D3—44no—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128C32×C8—41no—
129C32×C8—41no—
130C3×C3⋊C8—22no—
131#547—31no—
132#500—31no—
133#474—31no—
134#461—31no—
135#332C3×D311yescharacteristic, complemented
136D4⋊C8—31no—
137D4⋊C8—31no—
138C3×#41—122no—
139C3×#41—122no—
140C2×C3×Q8—21no—
141C2×C3×Q8—21no—
142C2×C3×Q8—41no—
143C2×C3×Q8—61no—
144C2×C3×D4—31no—
145C2×C3×D4—31no—
146C2×C3×D4—62no—
147C22×C3×C4—62no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150#239—42no—
151#239—42no—
152C2×D12—22no—
153C2×D12C3×D411yescharacteristic
154C2×D12C3×D411yescharacteristic
155C2×C4×D3—22no—
156C2×C4×D3—21no—
157C2×C4×D3—21no—
158C2×Dic6—21no—
159C3×SD16—122no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—41no—
165C2×C3×C8—41no—
166C2×C3×C8—61no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—41no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4D1212yes—
177C3×C4⋊C4C3×D412yes—
178C3×C22⋊C4—62no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C42—21no—
182C3×C42C22×D311yescharacteristic
183C3×C42C23×C311yescharacteristic
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—21no—
186(C2×D3)⋊C4—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C4⋊Dic3C3×D411yescharacteristic
190C4⋊Dic3C3×D411yescharacteristic
191Dic3⋊C4—22no—
192C2×C3⋊C8—21no—
193#204—42no—
194C22×C32#12011yescharacteristic
195C2×C3×D3—22no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C32×C4—21no—
202C32×C4—42no—
203C32×C4C2×D811yescharacteristic
204C32×C4#13511yescharacteristic
205C32×C4AGL(1,ℤ/8)11yescharacteristic
206C32×C4#13711yescharacteristic
207C3×Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—81no—
210C2×#41—61no—
211C2×SD16—61no—
212C4⋊Q8—31no—
213C4⋊Q8C2×C3×D311yescharacteristic
214#123—62no—
215C22⋊Q8—61no—
216#121—61no—
217C4×D4—31no—
218C4×D4—31no—
219C2×C4⋊C4—61no—
220#107—61no—
221#107—62no—
222C4⋊C8C2×C3×D311yescharacteristic
223C4⋊C8C2×C3×D311yescharacteristic
224#103—61no—
225#102—61no—
226C4×C8—31no—
227C23×C3—61no—
228C23×C3—61no—
229C22×D3—21no—
230C22×D3—21no—
231C3×Q8—41no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—41no—
235C3×Q8—81no—
236C3×Q8—81no—
237C3×Q8—121no—
238C3×Q8—121no—
239C3×D4—32no—
240C3×D4—61no—
241C3×D4—61no—
242C3×D4—61no—
243C3×D4—124no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—42no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—124no—
253C2×C3×C4—121no—
254C2×C3×C4—121no—
255C2×C3×C4—121no—
256C2×C3×C4—121no—
257C2×C3×C4—121no—
258C2×C3×C4C2×D1211yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4C2×C3×D411yescharacteristic
262C2×C3×C4C2×C3×D411yescharacteristic
263C2×C3×C4C2×C3×D411yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—41no—
267D12—21no—
268D12—21no—
269D12—21no—
270D12—44no—
271D12C3×D812yes—
272C4×D3—44no—
273C4×D3—41no—
274C4×D3—41no—
275C4×D3—41no—
276C4×D3—41no—
277Dic6—41no—
278Dic6—41no—
279C3×C8—41no—
280C3×C8—41no—
281C3×C8—41no—
282C3×C8—41no—
283C3×C8—62no—
284C3×C8—81no—
285C3×C8—81no—
286C3⋊C8—22no—
287C2×C32#44711yescharacteristic
288C2×C32#45211yescharacteristic
289C2×C32#45611yescharacteristic
290C3×D3—42no—
291C3×D3—81no—
292#41—122no—
293#41—122no—
294C2×Q8—21no—
295C2×Q8—61no—
296C2×D4—31no—
297C2×D4—31no—
298C2×D4—62no—
299C22×C4—62no—
300C22×C4—61no—
301C22×C4—61no—
302SD16—122no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—61no—
306C4⋊C4—21no—
307C4⋊C4—31no—
308C4⋊C4—31no—
309C4⋊C4—62no—
310C4⋊C4—61no—
311C4⋊C4—61no—
312C4⋊C4C3×D1212yes—
313C22⋊C4—62no—
314C22⋊C4—61no—
315C22⋊C4—61no—
316C42C22×C3×D311yescharacteristic
317C22×C3—21no—
318C22×C3—62no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3—121no—
322C22×C3—121no—
323C22×C3—121no—
324C22×C3#88211yescharacteristic
325C22×C3C3×#12011yescharacteristic
326C2×D3—22no—
327C2×D3—41no—
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—41no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—42no—
340C3×C4—42no—
341C3×C4—82no—
342C3×C4—121no—
343C3×C4—121no—
344C3×C4—241no—
345C3×C4D3×D811yescharacteristic
346C3×C4#91411yescharacteristic
347C3×C4#91611yescharacteristic
348C3×C4#91811yescharacteristic
349C3×C4C2×C3×D811yescharacteristic
350C3×C4C3×#13511yescharacteristic
351C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
352C3×C4C3×#13711yescharacteristic
353Dic3—41no—
354Dic3—41no—
355Dic3—81no—
356C32#164711yescharacteristic, complemented, Sylow
357C23—61no—
358C23—61no—
359Q8—41no—
360Q8—41no—
361Q8—121no—
362Q8—121no—
363D4—32no—
364D4—61no—
365D4—61no—
366D4—61no—
367D4—124no—
368C2×C4—22no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—124no—
372C2×C4—121no—
373C2×C4—121no—
374C2×C4—121no—
375C2×C4—121no—
376C2×C4—121no—
377C2×C4C2×C3×D1211yescharacteristic
378C2×C4C3×D3×D411yescharacteristic
379C2×C4C3×D3×D411yescharacteristic
380C8—41no—
381C8—41no—
382C8—62no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—122no—
387C2×C3—241no—
388C2×C3#475211yescharacteristic
389C2×C3#477311yescharacteristic
390C2×C3#480811yescharacteristic
391C2×C3C3×#44711yescharacteristic
392C2×C3C3×#45211yescharacteristic
393C2×C3C3×#45611yescharacteristic
394D3—42no—
395D3—81no—
396C22—62no—
397C22—121no—
398C22—121no—
399C22—121no—
400C22—121no—
401C22—121no—
402C22C3×#88211yescharacteristic
403C4—21no—
404C4—42no—
405C4—121no—
406C4—121no—
407C4—241no—
408C4C3×D3×D811yescharacteristic
409C4C3×#91411yescharacteristic
410C4C3×#91611yescharacteristic
411C4C3×#91811yescharacteristic
412C3—21no—
413C3#6843611yescharacteristic, direct product factor
414C3C3×#164711yescharacteristic, complemented
415C2—122no—
416C2—241no—
417C2C3×#475211yescharacteristic
418C2C3×#477311yescharacteristic
419C2C3×#480811yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32#120
prime radicalC3×#5726C2
hypercenterC3×#332D3
hypocenterC3C3×#1647
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×#4846C2semidirect
4. C3×#4841C2semidirect
5. C32×#332C2semidirect
6. C3×#4483C2semidirect
7. C3×#4483C2semidirect
9. #68436C3direct (N × H)
32. #5078C2×C3semidirect
33. #4846C2×C3semidirect
34. #4841C2×C3semidirect
36. C3×#332D3semidirect
37. C3×#332C2×C3semidirect
40. #4483C2×C3semidirect
41. #4483C2×C3semidirect
135. #332C3×D3semidirect
356. C32#1647semidirect
413. C3#68436direct (N × H)
414. C3C3×#1647semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
C3×#50782
C3×#48462
C3×#48412
C32×#3322
C3×#44832
C3×#16473
#684363