Finite Group Databasebeta

← C3×#68407 #11779809

Subgroups — C3×#68407 #11779809

Order 1152.

542 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic, complemented
3C3×#4849C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic, complemented
8C3×#1641—31nomaximal
9#68407C311yesmaximal, characteristic, direct product factor
10C2×C3×#237—21no—
11C32×#127C2211yescharacteristic
12C3×#940—21no—
13C3×#939—22no—
14C3×#938—21no—
15C3×D4×Dic3—21no—
16C2×C3×Dic12—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C3×#832—22no—
23C3×#821—21no—
24C3×#818—21no—
25C3×#816—21no—
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#550—31no—
28#5718C2×C311yescharacteristic
29C3×#486—31no—
30C3×#474—31no—
31C3×#462—31no—
32#5070C2×C311yescharacteristic, complemented
33#4849C2×C311yescharacteristic, complemented
34#4846C2×C311yescharacteristic, complemented
35C3×#331—21no—
36C3×#331D311yescharacteristic, complemented
37C3×#331C2×C311yescharacteristic, complemented
38C3×Q8⋊C8—31no—
39C3×D4⋊C8—31no—
40#4484C2×C311yescharacteristic, complemented
41#4483C2×C311yescharacteristic, complemented
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4D412yes—
45C2×C3×#67—22no—
46C2×C3×#67—22no—
47C22×C3×Dic3—22no—
48C3×#237—42no—
49C3×#237—42no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57C3×#217—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C3×Dic12—42no—
67#1641—31noSylow
68C2×C3×#41—61no—
69C2×#237—21no—
70C2×C3×Q16—61no—
71C3×C4⋊Q8—31no—
72C3×#127—21no—
73C3×#127—61no—
74C3×#127C2×D311yescharacteristic
75C3×#127C22×C311yescharacteristic
76C3×#121—61no—
77C3×#121—62no—
78C3×C4×Q8—31no—
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81#940—21no—
82#939—22no—
83#938—21no—
84D4×Dic3—21no—
85C2×Dic12—21no—
86C4×D12C22×C311yescharacteristic
87#869C22×C311yescharacteristic
88C4×Dic6C22×C311yescharacteristic
89C3×#107—61no—
90C3×C4⋊C8—21no—
91C3×C4⋊C8—21no—
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C22×C311yescharacteristic
95C3×C4⋊C8C22×C311yescharacteristic
96C3×#103—61no—
97C3×#102—61no—
98C3×#102—62no—
99C3×C4×C8—31no—
100#832—22no—
101#821—21no—
102#818—21no—
103#816—21no—
104C4×C3⋊C8C22×C311yescharacteristic
105C23×C32—22no—
106C22×C3×D3—21no—
107C32×D4—42no—
108C32×D4—41no—
109C32×D4—41no—
110C32×D4—41no—
111C32×D4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C3×#67—44no—
116C3×#67—82no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—44no—
121C2×C3×Dic3—41no—
122C3×D12—21no—
123C3×D12—21no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—21no—
127C3×Dic6—41no—
128C3×Dic6—41no—
129C3×Dic6D812yes—
130C32×C8—41no—
131C32×C8—41no—
132C3×C3⋊C8—41no—
133#550—31no—
134#486—31no—
135#474—31no—
136#462—31no—
137#331C3×D311yescharacteristic, complemented
138Q8⋊C8—31no—
139D4⋊C8—31no—
140C3×#41—122no—
141C3×#41—122no—
142C2×C3×Q8—31no—
143C2×C3×Q8—61no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—22no—
149C2×C3×D4—31no—
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4—62no—
153C2×C3×D4—62no—
154C2×C3×D4D1212yes—
155C2×C3×D4C3×D412yes—
156C22×C3×C4—62no—
157C22×C3×C4—61no—
158C2×#67—22no—
159C2×#67—22no—
160C22×Dic3—22no—
161#237—42no—
162#237—42no—
163C2×D12C3×D411yescharacteristic
164C2×C4×D3—21no—
165C2×Dic6—21no—
166C2×Dic6C3×D411yescharacteristic
167C3×Q16—122no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—41no—
173C2×C3×C8—41no—
174C2×C3×C8—61no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C22⋊C4—62no—
181C3×C22⋊C4—61no—
182C3×C42—21no—
183C3×C42—61no—
184C3×C42C22×D311yescharacteristic
185C3×C42C23×C311yescharacteristic
186#217—22no—
187(C2×D3)⋊C4—21no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3C3×D411yescharacteristic
191C4⋊Dic3C3×D411yescharacteristic
192Dic3⋊C4—21no—
193C4×Dic3—21no—
194C2×C3⋊C8—21no—
195Dic12—42no—
196C22×C32—42no—
197C22×C32—42no—
198C22×C32—42no—
199C22×C32#12011yescharacteristic
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C32×C4—21no—
204C32×C4C2×D811yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4#13711yescharacteristic
208C3×Dic3—22no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211C3×Dic3—81no—
212C2×#41—61no—
213C2×Q16—61no—
214C4⋊Q8—31no—
215#127—61no—
216#127C2×C3×D311yescharacteristic
217#121—61no—
218#121—62no—
219C4×Q8—31no—
220C4×D4—31no—
221C4×D4—61no—
222#107—61no—
223C4⋊C8C2×C3×D311yescharacteristic
224C4⋊C8C2×C3×D311yescharacteristic
225#103—61no—
226#102—61no—
227#102—62no—
228C4×C8—31no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—42no—
232C23×C3—61no—
233C22×D3—21no—
234C3×Q8—32no—
235C3×Q8—61no—
236C3×Q8—121no—
237C3×Q8—121no—
238C3×D4—42no—
239C3×D4—42no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—61no—
249C3×D4—61no—
250C3×D4—81no—
251C3×D4—81no—
252C3×D4—81no—
253C3×D4—81no—
254C3×D4—82no—
255C3×D4—124no—
256C3×D4—242no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—124no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×C3×D411yescharacteristic
271C2×C3×C4C2×C3×D411yescharacteristic
272C2×C3×C4C2×C3×D411yescharacteristic
273#67—44no—
274#67—82no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—44no—
279C2×Dic3—41no—
280D12—21no—
281D12—21no—
282C4×D3—41no—
283C4×D3—41no—
284Dic6—21no—
285Dic6—41no—
286Dic6—41no—
287Dic6C3×D812yes—
288C3×C8—41no—
289C3×C8—41no—
290C3×C8—41no—
291C3×C8—41no—
292C3×C8—81no—
293C3×C8—81no—
294C3×C8—121no—
295C3⋊C8—41no—
296C2×C32—82no—
297C2×C32#44711yescharacteristic
298C2×C32#45211yescharacteristic
299C2×C32#45511yescharacteristic
300C3×D3—81no—
301#41—122no—
302#41—122no—
303C2×Q8—31no—
304C2×Q8—61no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—31no—
308C2×D4—62no—
309C2×D4—62no—
310C2×D4C3×D1212yes—
311C22×C4—62no—
312C22×C4—61no—
313Q16—122no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—61no—
317C4⋊C4—31no—
318C4⋊C4—31no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C22⋊C4—62no—
323C22⋊C4—61no—
324C42—61no—
325C42C22×C3×D311yescharacteristic
326C22×C3—21no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3—42no—
330C22×C3—42no—
331C22×C3—42no—
332C22×C3—42no—
333C22×C3—82no—
334C22×C3—82no—
335C22×C3—82no—
336C22×C3—121no—
337C22×C3—121no—
338C22×C3—121no—
339C22×C3#88211yescharacteristic
340C22×C3C3×#12011yescharacteristic
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—62no—
352C3×C4—121no—
353C3×C4—121no—
354C3×C4—241no—
355C3×C4D3×D811yescharacteristic
356C3×C4#91211yescharacteristic
357C3×C4#91411yescharacteristic
358C3×C4#91511yescharacteristic
359C3×C4C2×C3×D811yescharacteristic
360C3×C4C3×#13511yescharacteristic
361C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
362C3×C4C3×#13711yescharacteristic
363Dic3—22no—
364Dic3—41no—
365Dic3—41no—
366Dic3—81no—
367C32#164111yescharacteristic, complemented, Sylow
368C23—22no—
369C23—61no—
370Q8—32no—
371Q8—61no—
372Q8—121no—
373Q8—121no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—61no—
380D4—61no—
381D4—124no—
382D4—242no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—124no—
387C2×C4—121no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4C2×C3×D1211yescharacteristic
391C2×C4C3×D3×D411yescharacteristic
392C2×C4C3×D3×D411yescharacteristic
393C8—41no—
394C8—41no—
395C8—121no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—82no—
400C2×C3—82no—
401C2×C3—162no—
402C2×C3—241no—
403C2×C3#474611yescharacteristic
404C2×C3#477311yescharacteristic
405C2×C3#478311yescharacteristic
406C2×C3C3×#44711yescharacteristic
407C2×C3C3×#45211yescharacteristic
408C2×C3C3×#45511yescharacteristic
409D3—81no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—121no—
414C22—121no—
415C22—121no—
416C22C3×#88211yescharacteristic
417C4—21no—
418C4—62no—
419C4—121no—
420C4—121no—
421C4—241no—
422C4C3×D3×D811yescharacteristic
423C4C3×#91211yescharacteristic
424C4C3×#91411yescharacteristic
425C4C3×#91511yescharacteristic
426C3—21no—
427C3#6840711yescharacteristic, direct product factor
428C3C3×#164111yescharacteristic, complemented
429C2—82no—
430C2—241no—
431C2C3×#474611yescharacteristic
432C2C3×#477311yescharacteristic
433C2C3×#478311yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#120
prime radicalC3×#5718C2
hypercenterC3×#331D3
hypocenterC3C3×#1641
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
2. C3×#5070C2semidirect
3. C3×#4849C2semidirect
4. C3×#4846C2semidirect
5. C32×#331C2semidirect
6. C3×#4484C2semidirect
7. C3×#4483C2semidirect
9. #68407C3direct (N × H)
32. #5070C2×C3semidirect
33. #4849C2×C3semidirect
34. #4846C2×C3semidirect
36. C3×#331D3semidirect
37. C3×#331C2×C3semidirect
40. #4484C2×C3semidirect
41. #4483C2×C3semidirect
137. #331C3×D3semidirect
367. C32#1641semidirect
427. C3#68407direct (N × H)
428. C3C3×#1641semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
C3×#50702
C3×#48492
C3×#48462
C32×#3312
C3×#44842
C3×#44832
C3×#16413
#684073