Finite Group Databasebeta

← C3×#10590033 #13154883

Subgroups — C3×#10590033 #13154883

Order 1728.

380 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 46 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×#63912C211yesmaximal, characteristic
2C3×#63781C211yesmaximal, characteristic, complemented
3C3×#63557C211yesmaximal, characteristic, complemented
4#10590033C311yesmaximal, characteristic, direct product factor
5C22×C3×#157—21no—
6C2×C3×C4×C3⋊D3C2211yescharacteristic
7C2×C3×#626—21no—
8C2×C3×#625C411yescharacteristic, complemented
9C32×(C2×D3)⋊C4—21no—
10C2×C32×C3⋊C8—21no—
11C3×#3724C411yescharacteristic, complemented
12C3×#884—61no—
13#63912C2×C311yescharacteristic
14#63781C2×C311yescharacteristic, complemented
15C3×(C2×D3)⋊C8—61no—
16#63557C2×C311yescharacteristic, complemented
17C22×C3×C3⋊D3D411yescharacteristic
18C22×C32×D3—21no—
19C2×C3×#157—22no—
20C2×C3×#157—41no—
21C2×C3×#157—41no—
22C2×C33×C4D411yescharacteristic
23C2×C3×C3⋊Dic3C2×C411yescharacteristic
24C3×C4×C3⋊D3—41no—
25C2×C32×Dic3—21no—
26C3×#626—41no—
27C3×#626—41no—
28C3×#625—41no—
29C32×C3⋊C8—41no—
30C3×#327—91nomaximal
31C22×#157—21no—
32C2×C4×C3⋊D3C22×C311yescharacteristic
33C2×C3×#67—61no—
34C2×C3×#67—61no—
35C2×C3×D12—61no—
36C2×C3×C4×D3—61no—
37C2×C3×C4×D3—61no—
38C2×#626—21no—
39C2×#625C3×C411yescharacteristic, complemented
40C2×C32×C8—61no—
41C32×C22⋊C4—61no—
42C3×(C2×D3)⋊C4—21no—
43C3×(C2×D3)⋊C4—21no—
44C3×(C2×D3)⋊C4—41no—
45C3×Dic3⋊C4—61no—
46C2×C3×C3⋊C8—21no—
47C2×C3×C3⋊C8—21no—
48C2×C3×C3⋊C8—41no—
49#3724C3×C411yescharacteristic, complemented
50C22×C33C22⋊C411yescharacteristic
51C2×C3×C3⋊D3—21no—
52C2×C3×C3⋊D3—21no—
53C2×C3×C3⋊D3D811yescharacteristic
54C2×C3×C3⋊D3SD1611yescharacteristic
55C2×C32×D3—41no—
56C2×C32×D3—41no—
57C2×C32×D3—41no—
58C3×#157—42no—
59C33×C4—21no—
60C3×C3⋊Dic3—21no—
61C32×Dic3—41no—
62C3×#121—91no—
63#884—61no—
64C3×C22⋊C8—91no—
65C3×#95—91no—
66(C2×D3)⋊C8—61no—
67C23×C32—61no—
68C22×C3⋊D3C3×D411yescharacteristic
69C22×C3×D3—21no—
70C22×C3×D3—21no—
71C22×C3×D3—41no—
72C22×C3×D3—61no—
73C22×C3×D3—61no—
74C2×#157—22no—
75C2×#157—41no—
76C2×#157—41no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4—61no—
82C2×C32×C4C3×D411yescharacteristic
83C2×C3⋊Dic3C2×C3×C411yescharacteristic
84C4×C3⋊D3—41no—
85C3×#67—121no—
86C3×#67—121no—
87C3×#67—122no—
88C2×C3×Dic3—21no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—61no—
92C2×C3×Dic3—61no—
93C3×D12—121no—
94C3×D12—121no—
95C3×C4×D3—122no—
96C3×C4×D3—121no—
97C3×C4×D3—121no—
98#626—41no—
99#626—41no—
100#625—41no—
101C32×C8—121no—
102C3×C3⋊C8—41no—
103C3×C3⋊C8—41no—
104C3×C3⋊C8—42no—
105#327—91noSylow
106C2×C33#9911yescharacteristic
107C2×C33#10211yescharacteristic
108C2×C33#10411yescharacteristic
109C3×C3⋊D3—21no—
110C3×C3⋊D3—21no—
111C32×D3—81no—
112C2×C3×D4—91no—
113C2×C3×D4—181no—
114C22×C3×C4—91no—
115C22×C3×C4—181no—
116C2×#67—61no—
117C2×#67—61no—
118C2×D12—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C3×C8—61no—
122C2×C3×C8—61no—
123C2×C3×C8—121no—
124C3×C4⋊C4—91no—
125C3×C22⋊C4—61no—
126C3×C22⋊C4—61no—
127C3×C22⋊C4—121no—
128(C2×D3)⋊C4—21no—
129Dic3⋊C4—61no—
130C2×C3⋊C8—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—41no—
134C22×C32—41no—
135C22×C32—121no—
136C22×C32—121no—
137C22×C32—121no—
138C22×C32C3×C22⋊C411yescharacteristic
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3C3×D811yescharacteristic
142C2×C3⋊D3C3×SD1611yescharacteristic
143C2×C3×D3—41no—
144C2×C3×D3—41no—
145C2×C3×D3—41no—
146C2×C3×D3—42no—
147C2×C3×D3—41no—
148C2×C3×D3—41no—
149C2×C3×D3—41no—
150C2×C3×D3—61no—
151C2×C3×D3—61no—
152C2×C3×D3—61no—
153C2×C3×D3—61no—
154C2×C3×D3—81no—
155C2×C3×D3—81no—
156C2×C3×D3—121no—
157C2×C3×D3—121no—
158C2×C3×D3—121no—
159C2×C3×D3—121no—
160#157—42no—
161C32×C4—21no—
162C32×C4—21no—
163C32×C4—21no—
164C32×C4—41no—
165C32×C4—41no—
166C32×C4—41no—
167C32×C4—81no—
168C32×C4—121no—
169C3⋊Dic3—21no—
170C3×Dic3—41no—
171C3×Dic3—41no—
172C3×Dic3—62no—
173C3×Dic3—81no—
174C3×Dic3—121no—
175#121—91no—
176C22⋊C8—91no—
177#95—91no—
178C33#32711yescharacteristic, complemented, Sylow
179C23×C3—61no—
180C23×C3—61no—
181C23×C3—91no—
182C23×C3—121no—
183C22×D3—21no—
184C22×D3—61no—
185C22×D3—61no—
186C3×D4—361no—
187C3×D4—361no—
188C3×D4—361no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—61no—
194C2×C3×C4—61no—
195C2×C3×C4—91no—
196C2×C3×C4—121no—
197C2×C3×C4—182no—
198C2×C3×C4—361no—
199C2×C3×C4—361no—
200C2×C3×C4—361no—
201C2×C3×C4GO+(4,𝔽2)11yescharacteristic
202#67—121no—
203#67—121no—
204#67—122no—
205C2×Dic3—21no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208D12—121no—
209D12—121no—
210C4×D3—122no—
211C4×D3—121no—
212C4×D3—121no—
213C3×C8—121no—
214C3×C8—121no—
215C3×C8—122no—
216C3⋊C8—41no—
217C2×C32—21no—
218C2×C32—21no—
219C2×C32—21no—
220C2×C32—21no—
221C2×C32—21no—
222C2×C32—21no—
223C2×C32—41no—
224C2×C32—41no—
225C2×C32—41no—
226C2×C32—41no—
227C2×C32—41no—
228C2×C32—41no—
229C2×C32—241no—
230C2×C32C3×#9911yescharacteristic
231C2×C32C3×#10211yescharacteristic
232C2×C32C3×#10411yescharacteristic
233C3⋊D3—21no—
234C3⋊D3—21no—
235C3×D3—81no—
236C3×D3—82no—
237C3×D3—81no—
238C3×D3—121no—
239C3×D3—121no—
240C3×D3—121no—
241C3×D3—121no—
242C2×D4—91no—
243C2×D4—181no—
244C22×C4—91no—
245C22×C4—181no—
246C2×C8—61no—
247C4⋊C4—91no—
248C22⋊C4—61no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—91no—
254C22×C3—91no—
255C22×C3—121no—
256C22×C3—121no—
257C22×C3—121no—
258C22×C3—122no—
259C22×C3—121no—
260C22×C3—121no—
261C22×C3—121no—
262C22×C3—181no—
263C22×C3—181no—
264C22×C3—241no—
265C22×C3—241no—
266C22×C3D32⋊C411yescharacteristic
267C2×D3—41no—
268C2×D3—41no—
269C2×D3—41no—
270C2×D3—61no—
271C2×D3—61no—
272C2×D3—61no—
273C2×D3—61no—
274C2×D3—121no—
275C2×D3—121no—
276C2×D3—121no—
277C2×D3—121no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—81no—
285C3×C4—121no—
286C3×C4—121no—
287C3×C4—181no—
288C3×C4—241no—
289C3×C4—362no—
290Dic3—41no—
291Dic3—62no—
292Dic3—121no—
293C32—21no—
294C32—21no—
295C32—41no—
296C32—41no—
297C32C3×#32711yescharacteristic, complemented
298C23—61no—
299C23—91no—
300D4—361no—
301D4—361no—
302D4—361no—
303C2×C4—61no—
304C2×C4—91no—
305C2×C4—182no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4—361no—
309C2×C4C3×GO+(4,𝔽2)11yescharacteristic
310C8—121no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—41no—
318C2×C3—41no—
319C2×C3—41no—
320C2×C3—41no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3—181no—
324C2×C3—181no—
325C2×C3—241no—
326C2×C3—242no—
327C2×C3—241no—
328C2×C3#6372911yescharacteristic
329C2×C3#6373111yescharacteristic
330C2×C3#6373811yescharacteristic
331D3—81no—
332D3—121no—
333D3—121no—
334D3—121no—
335D3—121no—
336C22—91no—
337C22—91no—
338C22—121no—
339C22—121no—
340C22—121no—
341C22—181no—
342C22—181no—
343C22C3×D32⋊C411yescharacteristic
344C4—21no—
345C4—121no—
346C4—181no—
347C4—362no—
348C3—21no—
349C3—21no—
350C3—41no—
351C3—41no—
352C3#1059003311yescharacteristic, direct product factor
353C2—181no—
354C2—181no—
355C2—241no—
356C2C3×#6372911yescharacteristic
357C2C3×#6373111yescharacteristic
358C2C3×#6373811yescharacteristic
subgroupG/H
centerC22×C3D32⋊C4
commutatorC2×C3⋊Dic3C2×C3×C4
FrattiniC2×C4C3×GO+(4,𝔽2)
FittingC2×C33×C4D4
socleC22×C33C22⋊C4
prime radicalC3×#63912C2
cosocleC2×C4×C3⋊D3C22×C3
hypercenterC2×C3×C4GO+(4,𝔽2)
hypocenterC32C3×#327
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×#63781C2semidirect
3. C3×#63557C2semidirect
4. #10590033C3direct (N × H)
8. C2×C3×#625C4semidirect
11. C3×#3724C4semidirect
14. #63781C2×C3semidirect
16. #63557C2×C3semidirect
39. C2×#625C3×C4semidirect
49. #3724C3×C4semidirect
178. C33#327semidirect
297. C32C3×#327semidirect
352. C3#10590033direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#639122
C3×#637812
C3×#635572
#105900333
C3×#3279