Finite Group Databasebeta

← C3×#10593462 #13166831

Subgroups — C3×#10593462 #13166831

Order 1728.

434 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#157C211yesmaximal, characteristic, complemented
2C3×#64221C211yesmaximal, characteristic, complemented
3C3×#63930C211yesmaximal, characteristic, complemented
4C3×#63926C211yesmaximal, characteristic
5C3×#63732C211yesmaximal, characteristic, complemented
6C3×#63730C211yesmaximal, characteristic, complemented
7C3×#63729C211yesmaximal, characteristic, complemented
8#10593462C311yesmaximal, characteristic, direct product factor
9C22×C3×#157—21no—
10C3×D4×C3⋊D3C2211yescharacteristic
11C3×#3802C2211yescharacteristic
12C3×#3797C2211yescharacteristic
13C3×C22⋊#157—21no—
14C3×C4⋊#157C2211yescharacteristic
15C3×C4×#157C2211yescharacteristic
16C3×D32⋊C4—21no—
17C3×D32⋊C4—21no—
18C32×#214—21no—
19C32×#213—21no—
20C3×#3717—21no—
21C3×#3714—21no—
22C3×#3710C2211yescharacteristic
23C3×#3710C2211yescharacteristic
24D4×#157C2×C311yescharacteristic, complemented
25#64221C2×C311yescharacteristic, complemented
26C3×D3×SD16—61no—
27C3×D3×D8—61no—
28#63930C2×C311yescharacteristic, complemented
29#63926C2×C311yescharacteristic
30#63732C2×C311yescharacteristic, complemented
31#63730C2×C311yescharacteristic, complemented
32#63729C2×C311yescharacteristic, complemented
33C22×C3×C3⋊D3—21no—
34C2×C3×D32—21no—
35C2×C3×#157—21no—
36C2×C3×#157—42no—
37C2×C3×#157D411yescharacteristic
38C2×C3×#157D411yescharacteristic
39C33×D4D411yescharacteristic
40C3×#638—21no—
41C3×C4⋊(C3⋊D3)D411yescharacteristic
42C3×C4×C3⋊D3C2311yescharacteristic
43C32×D12—21no—
44C32×Dic6—21no—
45C3×#627—21no—
46C3×#625—21no—
47C3×#624—21no—
48C32×C3⋊C8—21no—
49C32×C3⋊C8—21no—
50C3×#463—91nomaximal
51C22×#157—21no—
52D4×C3⋊D3C22×C311yescharacteristic
53C3×D3×Q8—61no—
54C3×D3×D4—61no—
55C3×D3×D4—61no—
56C3×D3×D4—61no—
57#3802C22×C311yescharacteristic
58#3797C22×C311yescharacteristic
59C22⋊#157—21no—
60C4⋊#157C22×C311yescharacteristic
61C4×#157C22×C311yescharacteristic
62D32⋊C4—21no—
63D32⋊C4—21no—
64C32×SD16—61no—
65C32×D8—61no—
66C3×#215—61no—
67C3×#214—21no—
68C3×#214—21no—
69C3×#214—41no—
70C3×#213—21no—
71C3×#213—21no—
72C3×#213—41no—
73C3×#213—61no—
74C3×D24—61no—
75C3×#204—61no—
76C3×D3×C8—61no—
77C3×D3×C8—61no—
78#3717—21no—
79#3714—21no—
80#3710C22×C311yescharacteristic
81#3710C22×C311yescharacteristic
82C22×C33—21no—
83C2×C3×C3⋊D3—21no—
84C2×C3×C3⋊D3—41no—
85C2×C3×C3⋊D3—41no—
86C2×C3×C3⋊D3C2×D411yescharacteristic
87C2×C32×D3—41no—
88C3×D32—41no—
89C3×D32—41no—
90C3×#157—21no—
91C3×#157—21no—
92C3×#157—41no—
93C33×C4C2×D411yescharacteristic
94C3×C3⋊Dic3#4111yescharacteristic
95C32×Dic3—41no—
96C2×C3×SD16—91no—
97C2×C3×D8—91no—
98C3×#124—91no—
99C3×C4×D4—91no—
100D3×SD16—61no—
101D3×D8—61no—
102C3×C4⋊C8—91no—
103C3×#103—91no—
104C3×#102—91no—
105C22×C3⋊D3—21no—
106C22×C3×D3—121no—
107C22×C3×D3—121no—
108C22×C3×D3—121no—
109C2×D32—21no—
110C2×#157—21no—
111C2×#157—42no—
112C2×#157C3×D411yescharacteristic
113C2×#157C3×D411yescharacteristic
114C32×Q8—61no—
115C32×D4—21no—
116C32×D4—21no—
117C32×D4—41no—
118C32×D4—41no—
119C32×D4—61no—
120C32×D4C3×D411yescharacteristic
121#638—21no—
122C4⋊(C3⋊D3)C3×D411yescharacteristic
123C4×C3⋊D3C23×C311yescharacteristic
124C3×#67—121no—
125C3×#67—121no—
126C3×#67—121no—
127C3×D12—21no—
128C3×D12—21no—
129C3×D12—41no—
130C3×D12—61no—
131C3×D12—61no—
132C3×C4×D3—61no—
133C3×C4×D3—61no—
134C3×C4×D3—121no—
135C3×Dic6—21no—
136C3×Dic6—21no—
137C3×Dic6—41no—
138C3×Dic6—121no—
139#627—21no—
140#625—21no—
141#624—21no—
142C32×C8—61no—
143C32×C8—61no—
144C3×C3⋊C8—21no—
145C3×C3⋊C8—21no—
146C3×C3⋊C8—21no—
147C3×C3⋊C8—21no—
148C3×C3⋊C8—41no—
149C3×C3⋊C8—41no—
150#463—91noSylow
151C2×C33—41no—
152C2×C33#12111yescharacteristic
153C3×C3⋊D3—41no—
154C3×C3⋊D3#13511yescharacteristic
155C3×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
156C32×D3—81no—
157C2×C3×Q8—91no—
158C2×C3×D4—91no—
159C2×C3×D4—91no—
160C22×C3×C4—181no—
161D3×Q8—61no—
162D3×D4—61no—
163D3×D4—61no—
164D3×D4—61no—
165C3×SD16—61no—
166C3×SD16—61no—
167C3×SD16—121no—
168C3×SD16—181no—
169C3×D8—61no—
170C3×D8—61no—
171C3×D8—121no—
172C3×D8—181no—
173C2×C3×C8—91no—
174C2×C3×C8—91no—
175C3×C4⋊C4—91no—
176C3×C22⋊C4—181no—
177C3×C22⋊C4—181no—
178C3×C22⋊C4—181no—
179C3×C42—91no—
180#215—61no—
181#214—21no—
182#213—21no—
183#213—61no—
184D24—61no—
185#204—61no—
186D3×C8—61no—
187D3×C8—61no—
188C22×C32—21no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32—81no—
192C22×C32—81no—
193C22×C32—121no—
194C2×C3⋊D3—21no—
195C2×C3⋊D3—41no—
196C2×C3⋊D3—41no—
197C2×C3⋊D3C2×C3×D411yescharacteristic
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—61no—
201C2×C3×D3—61no—
202C2×C3×D3—81no—
203C2×C3×D3—121no—
204C2×C3×D3—121no—
205C2×C3×D3—241no—
206C2×C3×D3—241no—
207C2×C3×D3—241no—
208C2×C3×D3—241no—
209C2×C3×D3—241no—
210C2×C3×D3—241no—
211D32—41no—
212D32—41no—
213#157—21no—
214#157—21no—
215#157—41no—
216C32×C4—21no—
217C32×C4—21no—
218C32×C4—41no—
219C32×C4—41no—
220C32×C4—121no—
221C32×C4C2×C3×D411yescharacteristic
222C3⋊Dic3C3×#4111yescharacteristic
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—61no—
226C3×Dic3—61no—
227C3×Dic3—81no—
228C2×SD16—91no—
229C2×D8—91no—
230#124—91no—
231C4×D4—91no—
232C4⋊C8—91no—
233#103—91no—
234#102—91no—
235C33#46311yescharacteristic, complemented, Sylow
236C23×C3—181no—
237C23×C3—181no—
238C22×D3—121no—
239C22×D3—121no—
240C22×D3—121no—
241C3×Q8—61no—
242C3×Q8—61no—
243C3×Q8—121no—
244C3×Q8—181no—
245C3×D4—21no—
246C3×D4—21no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—61no—
250C3×D4—61no—
251C3×D4—91no—
252C3×D4—121no—
253C3×D4—181no—
254C3×D4—181no—
255C3×D4GO+(4,𝔽2)11yescharacteristic
256C2×C3×C4—91no—
257C2×C3×C4—91no—
258C2×C3×C4—91no—
259C2×C3×C4—181no—
260C2×C3×C4—181no—
261C2×C3×C4—362no—
262#67—121no—
263#67—121no—
264#67—121no—
265D12—21no—
266D12—61no—
267D12—61no—
268C4×D3—61no—
269C4×D3—61no—
270C4×D3—121no—
271Dic6—21no—
272Dic6—121no—
273C3×C8—61no—
274C3×C8—61no—
275C3×C8—61no—
276C3×C8—61no—
277C3×C8—121no—
278C3×C8—121no—
279C3⋊C8—21no—
280C3⋊C8—21no—
281C2×C32—21no—
282C2×C32—21no—
283C2×C32—41no—
284C2×C32—41no—
285C2×C32—41no—
286C2×C32—81no—
287C2×C32—81no—
288C2×C32—161no—
289C2×C32—161no—
290C2×C32—241no—
291C2×C32C3×#12111yescharacteristic
292C3⋊D3—41no—
293C3⋊D3C3×#13511yescharacteristic
294C3⋊D3C3×AGL(1,ℤ/8)11yescharacteristic
295C3×D3—61no—
296C3×D3—61no—
297C3×D3—61no—
298C3×D3—61no—
299C3×D3—81no—
300C3×D3—81no—
301C3×D3—161no—
302C3×D3—241no—
303C3×D3—241no—
304C2×Q8—91no—
305C2×D4—91no—
306C2×D4—91no—
307C22×C4—181no—
308SD16—61no—
309SD16—181no—
310D8—61no—
311D8—181no—
312C2×C8—91no—
313C2×C8—91no—
314C4⋊C4—91no—
315C22⋊C4—181no—
316C22⋊C4—181no—
317C22⋊C4—181no—
318C42—91no—
319C22×C3—21no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—81no—
323C22×C3—81no—
324C22×C3—91no—
325C22×C3—121no—
326C22×C3—121no—
327C22×C3—181no—
328C22×C3—241no—
329C22×C3—361no—
330C22×C3—361no—
331C22×C3—361no—
332C22×C3—361no—
333C2×D3—41no—
334C2×D3—61no—
335C2×D3—61no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—241no—
339C2×D3—241no—
340C2×D3—241no—
341C2×D3—241no—
342C2×D3—241no—
343C2×D3—241no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—91no—
349C3×C4—121no—
350C3×C4—121no—
351C3×C4—181no—
352C3×C4—181no—
353C3×C4—241no—
354C3×C4—361no—
355C3×C4C2×GO+(4,𝔽2)11yescharacteristic
356Dic3—41no—
357Dic3—61no—
358Dic3—61no—
359C32—21no—
360C32—21no—
361C32—41no—
362C32—41no—
363C32C3×#46311yescharacteristic, complemented
364C23—181no—
365C23—181no—
366Q8—61no—
367Q8—181no—
368D4—61no—
369D4—91no—
370D4—181no—
371D4—181no—
372D4C3×GO+(4,𝔽2)11yescharacteristic
373C2×C4—91no—
374C2×C4—91no—
375C2×C4—91no—
376C2×C4—181no—
377C2×C4—181no—
378C2×C4—362no—
379C8—61no—
380C8—61no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—41no—
384C2×C3—41no—
385C2×C3—41no—
386C2×C3—81no—
387C2×C3—81no—
388C2×C3—91no—
389C2×C3—91no—
390C2×C3—161no—
391C2×C3—161no—
392C2×C3—241no—
393C2×C3—241no—
394C2×C3—361no—
395C2×C3—481no—
396C2×C3#6424211yescharacteristic
397D3—61no—
398D3—61no—
399D3—61no—
400D3—61no—
401D3—81no—
402D3—241no—
403D3—241no—
404C22—21no—
405C22—91no—
406C22—121no—
407C22—181no—
408C22—361no—
409C22—361no—
410C22—361no—
411C22—361no—
412C4—91no—
413C4—121no—
414C4—181no—
415C4—181no—
416C4—361no—
417C4C2×C3×GO+(4,𝔽2)11yescharacteristic
418C3—21no—
419C3—21no—
420C3—41no—
421C3—41no—
422C3#1059346211yescharacteristic, direct product factor
423C2—41no—
424C2—91no—
425C2—91no—
426C2—241no—
427C2—361no—
428C2C3×#6424211yescharacteristic
subgroupG/H
centerC2×C3#64242
commutator, cosocleC4×C3⋊D3C23×C3
FrattiniC4C2×C3×GO+(4,𝔽2)
FittingC33×D4D4
socleC2×C33#121
prime radicalC3×#63926C2
hypercenterC3×D4GO+(4,𝔽2)
hypocenterC32C3×#463
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×#157C2semidirect
2. C3×#64221C2semidirect
3. C3×#63930C2semidirect
5. C3×#63732C2semidirect
6. C3×#63730C2semidirect
7. C3×#63729C2semidirect
8. #10593462C3direct (N × H)
24. D4×#157C2×C3semidirect
25. #64221C2×C3semidirect
28. #63930C2×C3semidirect
30. #63732C2×C3semidirect
31. #63730C2×C3semidirect
32. #63729C2×C3semidirect
235. C33#463semidirect
363. C32C3×#463semidirect
422. C3#10593462direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D4×#1572
C3×#642212
C3×#639302
C3×#639262
C3×#637322
C3×#637302
C3×#637292
#105934623
C3×#4639