Finite Group Databasebeta

← C3×#68329 #11778584

Subgroups — C3×#68329 #11778584

Order 1152.

460 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5623C211yesmaximal, characteristic
2C3×#5043C211yesmaximal, characteristic
3C3×#4721C211yesmaximal, characteristic
4C3×#4661C211yesmaximal, characteristic
5C32×#328C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic
7C3×#4452C211yesmaximal, characteristic
8C3×#1611—31nomaximal
9#68329C311yesmaximal, characteristic, direct product factor
10C32×C22⋊Q8C2211yescharacteristic
11C3×#944—21no—
12C2×C3×C4⋊Dic3—21no—
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C3×#924C2211yescharacteristic
15C2×C3×Dic3⋊C4C2211yescharacteristic
16C3×#889—21no—
17C3×#889—21no—
18C3×#888—21no—
19C3×#878—21no—
20C3×#877—21no—
21C32×C22⋊C8C2211yescharacteristic
22C32×#95C2211yescharacteristic
23C3×#835—21no—
24C3×C3⋊#95—21no—
25C3×#830C2211yescharacteristic
26C3×#817—21no—
27C3×#816—21no—
28C3×#808—21no—
29C3×#544—31no—
30#5623C2×C311yescharacteristic
31C3×#483—31no—
32C3×#483—31no—
33C3×#398—31no—
34#5043C2×C311yescharacteristic
35#4721C2×C311yescharacteristic
36#4661C2×C311yescharacteristic
37C3×#328—21no—
38C3×#328—31no—
39C3×#328D311yescharacteristic
40C3×#328C2×C311yescharacteristic
41C3×#324—31no—
42#4469C2×C311yescharacteristic
43#4452C2×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⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—42no—
61C3×C4⋊Dic3D411yescharacteristic
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—21no—
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—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—61no—
86#944—21no—
87C2×C4⋊Dic3—21no—
88C2×C4⋊Dic3C22×C311yescharacteristic
89#924C22×C311yescharacteristic
90C2×Dic3⋊C4C22×C311yescharacteristic
91#889—21no—
92#889—21no—
93#888—21no—
94#878—21no—
95#877—21no—
96C3×#106—61no—
97C3×#106—61no—
98C3×#103—61no—
99C3×#103—61no—
100C3×C22⋊C8—21no—
101C3×C22⋊C8—31no—
102C3×C22⋊C8C2×D311yescharacteristic
103C3×C22⋊C8C22×C311yescharacteristic
104C3×#95—21no—
105C3×#95—61no—
106C3×#95C2×D311yescharacteristic
107C3×#95C22×C311yescharacteristic
108#835—21no—
109C3⋊#95—21no—
110#830C22×C311yescharacteristic
111#817—21no—
112#816—21no—
113#808—21no—
114C23×C32C2×D411yescharacteristic
115C32×Q8—41no—
116C2×C32×C4—22no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3SD1612yes—
134C3×Dic6—41no—
135C3×Dic6—81no—
136C32×C8—41no—
137C3×C3⋊C8—41no—
138#544—31no—
139#483—31no—
140#483—31no—
141#398—31no—
142#328—31no—
143#328C3×D311yescharacteristic
144#324—31no—
145C2×C3×Q8—21no—
146C2×C3×Q8—31no—
147C2×C3×Q8—61no—
148C2×C3×Q8D1211yescharacteristic
149C2×C3×Q8C3×D411yescharacteristic
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—41no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C23×C311yescharacteristic
159C22×Dic3—21no—
160C22×Dic3C3×D411yescharacteristic
161C22×Dic3C3×D411yescharacteristic
162C2×Dic6—21no—
163C2×Dic6C3×D411yescharacteristic
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—41no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—122no—
184C3×C4⋊C4D1211yescharacteristic
185C3×C4⋊C4C3×D411yescharacteristic
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—41no—
189C3×C22⋊C4—61no—
190C3×C42—61no—
191C3×C42—61no—
192#217—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—42no—
197C4⋊Dic3C3×D411yescharacteristic
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C4×Dic3—21no—
206C4×Dic3—21no—
207C2×C3⋊C8—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32#12011yescharacteristic
211C22×C32C2×SD1611yescharacteristic
212C22×C32#13711yescharacteristic
213C32×C4—21no—
214C32×C4—21no—
215C32×C4—42no—
216C32×C4—41no—
217C32×C4—41no—
218C3×Dic3—22no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223C4⋊Q8—61no—
224C4⋊Q8—61no—
225#125—61no—
226#125—61no—
227C22⋊Q8—31no—
228C22⋊Q8—61no—
229C22⋊Q8C2×C3×D311yescharacteristic
230#117—61no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—61no—
234#106—61no—
235#106—61no—
236#103—61no—
237#103—61no—
238C22⋊C8—31no—
239C22⋊C8C2×C3×D311yescharacteristic
240#95—61no—
241#95C2×C3×D311yescharacteristic
242C23×C3—21no—
243C23×C3D3×D411yescharacteristic
244C23×C3C2×C3×D411yescharacteristic
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—81no—
248C3×Q8—121no—
249C3×Q8—241no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—32no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—42no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—81no—
274C2×C3×C4—81no—
275C2×C3×C4—81no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4C2×C3×D411yescharacteristic
283C2×C3×C4C2×C3×D411yescharacteristic
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—41no—
293C2×Dic3C3×SD1612yes—
294Dic6—41no—
295Dic6—81no—
296C3×C8—41no—
297C3×C8—41no—
298C3×C8—81no—
299C3×C8—121no—
300C3⋊C8—41no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32#44811yescharacteristic
304C2×C32#45611yescharacteristic
305C2×C32#45811yescharacteristic
306C2×Q8—31no—
307C2×Q8—61no—
308C2×Q8C3×D1211yescharacteristic
309C22×C4—21no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—61no—
313C22×C4C22×C3×D311yescharacteristic
314C2×C8—21no—
315C2×C8—61no—
316C4⋊C4—21no—
317C4⋊C4—31no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—122no—
329C4⋊C4C3×D1211yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—61no—
332C42—61no—
333C42—61no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3#88211yescharacteristic
344C22×C3D3×SD1611yescharacteristic
345C22×C3#91811yescharacteristic
346C22×C3C3×#12011yescharacteristic
347C22×C3C2×C3×SD1611yescharacteristic
348C22×C3C3×#13711yescharacteristic
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—42no—
356C3×C4—42no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—62no—
362C3×C4—81no—
363C3×C4—81no—
364C3×C4—82no—
365C3×C4—121no—
366C3×C4—121no—
367C3×C4—121no—
368C3×C4—241no—
369Dic3—22no—
370Dic3—41no—
371Dic3—41no—
372Dic3—41no—
373Dic3—81no—
374C32#161111yescharacteristic, complemented, Sylow
375C23C3×D3×D411yescharacteristic
376Q8—41no—
377Q8—121no—
378Q8—241no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—32no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—121no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—121no—
395C2×C4C2×C3×D1211yescharacteristic
396C2×C4C3×D3×D411yescharacteristic
397C8—41no—
398C8—121no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—41no—
407C2×C3—41no—
408C2×C3#474211yescharacteristic
409C2×C3#480611yescharacteristic
410C2×C3#482611yescharacteristic
411C2×C3C3×#44811yescharacteristic
412C2×C3C3×#45611yescharacteristic
413C2×C3C3×#45811yescharacteristic
414C22—21no—
415C22—21no—
416C22C3×#88211yescharacteristic
417C22C3×D3×SD1611yescharacteristic
418C22C3×#91811yescharacteristic
419C4—21no—
420C4—21no—
421C4—42no—
422C4—41no—
423C4—41no—
424C4—62no—
425C4—121no—
426C4—121no—
427C4—121no—
428C4—241no—
429C3—21no—
430C3#6832911yescharacteristic, direct product factor
431C3C3×#161111yescharacteristic, complemented
432C2—21no—
433C2—21no—
434C2C3×#474211yescharacteristic
435C2C3×#480611yescharacteristic
436C2C3×#482611yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#328C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC3×#328D3
hypocenterC3C3×#1611
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
9. #68329C3direct (N × H)
374. C32#1611semidirect
430. C3#68329direct (N × H)
431. C3C3×#1611semidirect

Maximal subgroups

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

subgroupindex
C3×#56232
C3×#50432
C3×#47212
C3×#46612
C32×#3282
C3×#44692
C3×#44522
C3×#16113
#683293