Finite Group Databasebeta

← C3×#71175 #11778575

Subgroups — C3×#71175 #11778575

Order 1152.

472 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5623C211yesmaximal, characteristic
2C32×#483C211yesmaximal, characteristic
3C3×#4983C211yesmaximal, characteristic
4C3×#4971C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic
7C3×#4467C211yesmaximal, characteristic
8C3×#1611—31nomaximal
9#71175C311yesmaximal, characteristic, direct product factor
10C32×C22⋊Q8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C3×#944—21no—
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4—21no—
15C2×C3×Dic3⋊C4C2211yescharacteristic
16C3×#889—21no—
17C3×#889—21no—
18C3×#888—21no—
19C3×#878—21no—
20C3×#877—21no—
21C32×#106—21no—
22C32×#103—21no—
23C32×C22⋊C8C2211yescharacteristic
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#810—21no—
28C3×#808—21no—
29C3×#544—31no—
30#5623C2×C311yescharacteristic
31C3×#483—21no—
32C3×#483—31no—
33C3×#483D311yescharacteristic
34C3×#483C2×C311yescharacteristic
35C3×#398—31no—
36#4983C2×C311yescharacteristic
37#4971C2×C311yescharacteristic
38C3×#328—31no—
39C3×#328—31no—
40C3×#324—31no—
41#4538C2×C311yescharacteristic
42#4469C2×C311yescharacteristic
43#4467C2×C311yescharacteristic
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6—21no—
51C2×C3×Dic6D411yescharacteristic
52C2×C32×C8—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C3×#217—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—42no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8—21no—
72#1611—31noSylow
73C3×C4⋊Q8—61no—
74C3×C4⋊Q8—61no—
75C3×#125—61no—
76C3×#125—61no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8—31no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×C22⋊Q8C22×C311yescharacteristic
82C3×#117—61no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—61no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C22×C311yescharacteristic
88#944—21no—
89#924C22×C311yescharacteristic
90C2×Dic3⋊C4—21no—
91C2×Dic3⋊C4C22×C311yescharacteristic
92#889—21no—
93#889—21no—
94#888—21no—
95#878—21no—
96#877—21no—
97C3×#106—22no—
98C3×#106—21no—
99C3×#106—21no—
100C3×#106—61no—
101C3×#103—22no—
102C3×#103—21no—
103C3×#103—21no—
104C3×#103—61no—
105C3×C22⋊C8—21no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C22⋊C8C22×C311yescharacteristic
109C3×#95—31no—
110C3×#95—61no—
111C3⋊#95—21no—
112C3⋊#95C22×C311yescharacteristic
113#830C22×C311yescharacteristic
114#810—21no—
115#808—21no—
116C23×C32C2×D411yescharacteristic
117C32×Q8—41no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3SD1612yes—
136C3×Dic6—41no—
137C3×Dic6—81no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#544—31no—
141#483—31no—
142#483C3×D311yescharacteristic
143#398—31no—
144#328—31no—
145#328—31no—
146#324—31no—
147C2×C3×Q8—21no—
148C2×C3×Q8—31no—
149C2×C3×Q8—61no—
150C2×C3×Q8#6711yescharacteristic
151C2×C3×Q8C3×D411yescharacteristic
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—41no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C23×C311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3C3×D411yescharacteristic
163C22×Dic3C3×D411yescharacteristic
164C2×Dic6—21no—
165C2×Dic6C3×D411yescharacteristic
166C2×C3×C8—22no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—31no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—41no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—122no—
190C3×C4⋊C4#6711yescharacteristic
191C3×C4⋊C4C3×D411yescharacteristic
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—41no—
195C3×C22⋊C4—61no—
196C3×C42—61no—
197C3×C42—61no—
198#217—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3C3×D411yescharacteristic
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—42no—
209C4×Dic3—21no—
210C4×Dic3—21no—
211C2×C3⋊C8—21no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32#12011yescharacteristic
215C22×C32C2×SD1611yescharacteristic
216C22×C32#13711yescharacteristic
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—41no—
221C32×C4—81no—
222C3×Dic3—22no—
223C3×Dic3—42no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C4⋊Q8—61no—
228C4⋊Q8—61no—
229#125—61no—
230#125—61no—
231C22⋊Q8—31no—
232C22⋊Q8—61no—
233C22⋊Q8C2×C3×D311yescharacteristic
234#117—61no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—61no—
237C2×C4⋊C4C2×C3×D311yescharacteristic
238#106—21no—
239#106—61no—
240#103—21no—
241#103—61no—
242C22⋊C8—31no—
243C22⋊C8C2×C3×D311yescharacteristic
244#95—31no—
245#95—61no—
246C23×C3—21no—
247C23×C3D3×D411yescharacteristic
248C23×C3C2×C3×D411yescharacteristic
249C3×Q8—41no—
250C3×Q8—41no—
251C3×Q8—42no—
252C3×Q8—121no—
253C3×Q8—241no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—32no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—62no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—81no—
280C2×C3×C4—81no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C2×C3×D411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—22no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—41no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3C3×SD1612yes—
298Dic6—41no—
299Dic6—81no—
300C3×C8—42no—
301C3×C8—41no—
302C3×C8—41no—
303C3×C8—121no—
304C3⋊C8—41no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32#44811yescharacteristic
308C2×C32#45611yescharacteristic
309C2×C32#45811yescharacteristic
310C2×Q8—31no—
311C2×Q8—61no—
312C2×Q8C3×#6711yescharacteristic
313C22×C4—21no—
314C22×C4—31no—
315C22×C4—31no—
316C22×C4—61no—
317C22×C4C22×C3×D311yescharacteristic
318C2×C8—21no—
319C2×C8—61no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—31no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—122no—
333C4⋊C4C3×#6711yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—61no—
336C42—61no—
337C42—61no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3D3×SD1611yescharacteristic
348C22×C3#91511yescharacteristic
349C22×C3#93711yescharacteristic
350C22×C3C3×#12011yescharacteristic
351C22×C3C2×C3×SD1611yescharacteristic
352C22×C3C3×#13711yescharacteristic
353C3×C4—22no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—62no—
364C3×C4—81no—
365C3×C4—81no—
366C3×C4—82no—
367C3×C4—81no—
368C3×C4—81no—
369C3×C4—122no—
370C3×C4—121no—
371C3×C4—121no—
372C3×C4—121no—
373Dic3—22no—
374Dic3—42no—
375Dic3—41no—
376Dic3—41no—
377Dic3—41no—
378C32#161111yescharacteristic, complemented, Sylow
379C23C3×D3×D411yescharacteristic
380Q8—41no—
381Q8—121no—
382Q8—241no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—32no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—62no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—121no—
397C2×C4—121no—
398C2×C4—121no—
399C2×C4C3×D3×D411yescharacteristic
400C2×C4C2×C3×#6711yescharacteristic
401C8—41no—
402C8—121no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3#505311yescharacteristic
413C2×C3#517011yescharacteristic
414C2×C3#520511yescharacteristic
415C2×C3C3×#44811yescharacteristic
416C2×C3C3×#45611yescharacteristic
417C2×C3C3×#45811yescharacteristic
418C22—21no—
419C22—21no—
420C22C3×D3×SD1611yescharacteristic
421C22C3×#91511yescharacteristic
422C22C3×#93711yescharacteristic
423C4—21no—
424C4—21no—
425C4—41no—
426C4—41no—
427C4—62no—
428C4—81no—
429C4—122no—
430C4—121no—
431C4—121no—
432C4—121no—
433C3—21no—
434C3#7117511yescharacteristic, direct product factor
435C3C3×#161111yescharacteristic, complemented
436C2—21no—
437C2—21no—
438C2C3×#505311yescharacteristic
439C2C3×#517011yescharacteristic
440C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#483C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC3×#483D3
hypocenterC3C3×#1611
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#483

Complements

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

NH ≅ G/Ntype
9. #71175C3direct (N × H)
378. C32#1611semidirect
434. C3#71175direct (N × H)
435. C3C3×#1611semidirect

Maximal subgroups

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

subgroupindex
C3×#56232
C32×#4832
C3×#49832
C3×#49712
C3×#45382
C3×#44692
C3×#44672
C3×#16113
#711753