Finite Group Databasebeta

← C3×#68204 #11779527

Subgroups — C3×#68204 #11779527

Order 1152.

509 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×#5555C211yesmaximal, characteristic
2C3×#5008C211yesmaximal, characteristic, complemented
3C3×#4842C211yesmaximal, characteristic, complemented
4C3×#4681C211yesmaximal, characteristic, complemented
5C32×D4⋊C8C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1635—31nomaximal
9#68204C311yesmaximal, characteristic, direct product factor
10C2×C3×#237—21no—
11C32×C4×D4C2211yescharacteristic
12C3×#930—21no—
13C2×C3×C4⋊Dic3—21no—
14C3×#897—21no—
15C3×#886—22no—
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4×C8C2211yescharacteristic
21C3×#832—21no—
22C3×#821—21no—
23C3×#817—21no—
24C3×#816—22no—
25C3×#808—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#547—31no—
28#5555C2×C311yescharacteristic
29C3×#487—31no—
30C3×#476—31no—
31C3×#476—31no—
32#5008C2×C311yescharacteristic, complemented
33#4842C2×C311yescharacteristic, complemented
34#4681C2×C311yescharacteristic, complemented
35C3×#332—31no—
36C3×D4⋊C8—21no—
37C3×D4⋊C8—31no—
38C3×D4⋊C8D311yescharacteristic, complemented
39C3×D4⋊C8C2×C311yescharacteristic, complemented
40#4486C2×C311yescharacteristic, complemented
41#4459C2×C311yescharacteristic, complemented
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C3×#67—22no—
45C22×C3×Dic3—22no—
46C3×#237—42no—
47C3×#237—42no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×Dic6—21no—
51C2×C3×Dic6—21no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42C2311yescharacteristic
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—22no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D412yes—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66#1635—31noSylow
67C2×C3×#41—61no—
68C2×#237—21no—
69C3×C4⋊Q8—31no—
70C3×C4⋊Q8—31no—
71C3×#123—62no—
72C3×C22⋊Q8—61no—
73C3×#121—61no—
74C3×C4×D4—21no—
75C3×C4×D4—31no—
76C3×C4×D4C2×D311yescharacteristic
77C3×C4×D4C22×C311yescharacteristic
78C2×C3×C4⋊C4—61no—
79#930—21no—
80C2×C4⋊Dic3—21no—
81#897—21no—
82#886—22no—
83C4×D12C22×C311yescharacteristic
84#869C22×C311yescharacteristic
85#869C22×C311yescharacteristic
86C3×#106—61no—
87C3×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C22×C311yescharacteristic
92C3×#103—62no—
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#816—22no—
102#808—21no—
103C4⋊(C3⋊C8)C22×C311yescharacteristic
104C23×C32—21no—
105C22×C3×D3—21no—
106C32×D4—21no—
107C32×D4SD1612yes—
108C2×C32×C4—21no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C3×#67—44no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—44no—
118C2×C3×Dic3—41no—
119C3×D12—21no—
120C3×D12—21no—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×Dic6—41no—
124C3×Dic6—41no—
125C3×Dic6—42no—
126C32×C8—41no—
127C32×C8—41no—
128C3×C3⋊C8—41no—
129#547—31no—
130#487—31no—
131#476—31no—
132#476—31no—
133#332—31no—
134D4⋊C8—31no—
135D4⋊C8C3×D311yescharacteristic, complemented
136C3×#41—122no—
137C3×#41—122no—
138C2×C3×Q8—61no—
139C2×C3×Q8—61no—
140C2×C3×D4—21no—
141C2×C3×D4—31no—
142C2×C3×D4—62no—
143C2×C3×D4D1211yescharacteristic
144C2×C3×D4C3×D411yescharacteristic
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—41no—
148C22×C3×C4—62no—
149C22×C3×C4—61no—
150C2×#67—22no—
151C22×Dic3—22no—
152#237—42no—
153#237—42no—
154C2×D12C3×D411yescharacteristic
155C2×C4×D3—21no—
156C2×Dic6—21no—
157C2×Dic6—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—41no—
163C2×C3×C8—41no—
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—32no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—62no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4D1211yescharacteristic
173C3×C4⋊C4C3×D411yescharacteristic
174C3×C22⋊C4—21no—
175C3×C22⋊C4—21no—
176C3×C22⋊C4—41no—
177C3×C22⋊C4—62no—
178C3×C22⋊C4—61no—
179C3×C42—21no—
180C3×C42C22×D311yescharacteristic
181C3×C42C23×C311yescharacteristic
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—21no—
184C4⋊Dic3—22no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3C3×D412yes—
189C4⋊Dic3C3×D411yescharacteristic
190C2×C3⋊C8—21no—
191C22×C32—22no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32#12011yescharacteristic
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C32×C4—21no—
199C32×C4—41no—
200C32×C4C2×SD1611yescharacteristic
201C32×C4#13511yescharacteristic
202C32×C4AGL(1,ℤ/8)11yescharacteristic
203C32×C4#13711yescharacteristic
204C3×Dic3—42no—
205C3×Dic3—41no—
206C3×Dic3—81no—
207C2×#41—61no—
208C4⋊Q8—31no—
209C4⋊Q8—31no—
210#123—62no—
211C22⋊Q8—61no—
212#121—61no—
213C4×D4—31no—
214C4×D4C2×C3×D311yescharacteristic
215C2×C4⋊C4—61no—
216#106—61no—
217#106—61no—
218C4⋊C8—31no—
219C4⋊C8C2×C3×D311yescharacteristic
220#103—62no—
221#102—61no—
222#102—61no—
223C4×C8C2×C3×D311yescharacteristic
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—41no—
227C23×C3—61no—
228C22×D3—21no—
229C3×Q8—122no—
230C3×Q8—121no—
231C3×Q8—121no—
232C3×D4—21no—
233C3×D4—21no—
234C3×D4—22no—
235C3×D4—41no—
236C3×D4—61no—
237C3×D4—61no—
238C3×D4—124no—
239C3×D4#20412yes—
240C3×D4C3×SD1612yes—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—61no—
252C2×C3×C4—62no—
253C2×C3×C4—81no—
254C2×C3×C4—81no—
255C2×C3×C4—124no—
256C2×C3×C4—121no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4C2×D1211yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4C2×C3×D411yescharacteristic
263C2×C3×C4C2×C3×D411yescharacteristic
264C2×C3×C4C2×C3×D411yescharacteristic
265#67—44no—
266C2×Dic3—22no—
267C2×Dic3—21no—
268C2×Dic3—44no—
269C2×Dic3—41no—
270D12—21no—
271D12—21no—
272C4×D3—41no—
273C4×D3—41no—
274Dic6—41no—
275Dic6—41no—
276Dic6—42no—
277C3×C8—41no—
278C3×C8—41no—
279C3×C8—42no—
280C3×C8—41no—
281C3×C8—41no—
282C3×C8—81no—
283C3×C8—121no—
284C3⋊C8—41no—
285C2×C32—42no—
286C2×C32#45011yescharacteristic
287C2×C32#45211yescharacteristic
288C2×C32#45411yescharacteristic
289C3×D3—81no—
290#41—122no—
291#41—122no—
292C2×Q8—61no—
293C2×Q8—61no—
294C2×D4—31no—
295C2×D4—62no—
296C2×D4C3×D1211yescharacteristic
297C22×C4—21no—
298C22×C4—62no—
299C22×C4—61no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—61no—
303C4⋊C4—32no—
304C4⋊C4—31no—
305C4⋊C4—62no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—61no—
309C4⋊C4C3×D1211yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—62no—
312C22⋊C4—61no—
313C42C22×C3×D311yescharacteristic
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3—42no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—81no—
323C22×C3—81no—
324C22×C3—121no—
325C22×C3—121no—
326C22×C3—121no—
327C22×C3#88211yescharacteristic
328C22×C3C3×#12011yescharacteristic
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—41no—
340C3×C4—41no—
341C3×C4—81no—
342C3×C4—121no—
343C3×C4—122no—
344C3×C4—241no—
345C3×C4C2×#20411yescharacteristic
346C3×C4#90811yescharacteristic
347C3×C4#91211yescharacteristic
348C3×C4#91511yescharacteristic
349C3×C4C2×C3×SD1611yescharacteristic
350C3×C4C3×#13511yescharacteristic
351C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
352C3×C4C3×#13711yescharacteristic
353Dic3—42no—
354Dic3—41no—
355Dic3—81no—
356C32#163511yescharacteristic, complemented, Sylow
357C23—21no—
358C23—61no—
359Q8—122no—
360Q8—121no—
361Q8—121no—
362D4—21no—
363D4—61no—
364D4—61no—
365D4—124no—
366D4C3×#20412yes—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—61no—
371C2×C4—62no—
372C2×C4—124no—
373C2×C4—121no—
374C2×C4—121no—
375C2×C4—121no—
376C2×C4C2×C3×D1211yescharacteristic
377C2×C4C3×D3×D411yescharacteristic
378C2×C4C3×D3×D411yescharacteristic
379C8—41no—
380C8—41no—
381C8—121no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—42no—
386C2×C3—42no—
387C2×C3—82no—
388C2×C3—241no—
389C2×C3#473111yescharacteristic
390C2×C3#478311yescharacteristic
391C2×C3#482711yescharacteristic
392C2×C3C3×#45011yescharacteristic
393C2×C3C3×#45211yescharacteristic
394C2×C3C3×#45411yescharacteristic
395D3—81no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—121no—
400C22—121no—
401C22—121no—
402C22C3×#88211yescharacteristic
403C4—21no—
404C4—41no—
405C4—121no—
406C4—122no—
407C4—241no—
408C4C2×C3×#20411yescharacteristic
409C4C3×#90811yescharacteristic
410C4C3×#91211yescharacteristic
411C4C3×#91511yescharacteristic
412C3—21no—
413C3#6820411yescharacteristic, direct product factor
414C3C3×#163511yescharacteristic, complemented
415C2—42no—
416C2—241no—
417C2C3×#473111yescharacteristic
418C2C3×#478311yescharacteristic
419C2C3×#482711yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32#120
prime radicalC3×#5555C2
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1635
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×#4681C2semidirect
5. C32×D4⋊C8C2semidirect
6. C3×#4486C2semidirect
7. C3×#4459C2semidirect
9. #68204C3direct (N × H)
32. #5008C2×C3semidirect
33. #4842C2×C3semidirect
34. #4681C2×C3semidirect
38. C3×D4⋊C8D3semidirect
39. C3×D4⋊C8C2×C3semidirect
40. #4486C2×C3semidirect
41. #4459C2×C3semidirect
135. D4⋊C8C3×D3semidirect
356. C32#1635semidirect
413. C3#68204direct (N × H)
414. C3C3×#1635semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C3×#50082
C3×#48422
C3×#46812
C32×D4⋊C82
C3×#44862
C3×#44592
C3×#16353
#682043