Finite Group Databasebeta

← C3×#67646 #11771920

Subgroups — C3×#67646 #11771920

Order 1152.

425 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 425 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C32×#393C211yesmaximal, characteristic
2C3×#4526C211yesmaximal, characteristic
3C3×#4525C211yesmaximal, characteristic
4C3×#1351—31nomaximal
5#67646C311yesmaximal, characteristic, direct product factor
6C22×C32×Q8C411yescharacteristic, complemented
7C2×C32×C22⋊C4—21no—
8C2×C32×C22⋊C4C2211yescharacteristic
9C2×C3×#217—21no—
10C32×#95—21no—
11C32×#95C411yescharacteristic, complemented
12C3×#830—21no—
13C3×#393—21no—
14C3×#393D311yescharacteristic
15C3×#393C2×C311yescharacteristic
16C3×#342—31no—
17C3×#323—31no—
18#4526C2×C311yescharacteristic
19#4525C2×C311yescharacteristic
20C24×C32D411yescharacteristic
21C2×C32×Q8—42no—
22C2×C32×Q8—41no—
23C22×C32×C4—21no—
24C22×C32×C4—21no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C3×Dic3—41no—
28C32×C22⋊C4—41no—
29C32×C22⋊C4—42no—
30C3×#217—22no—
31C3×#217—41no—
32C2×C3×C3⋊C8—41no—
33#1351—31noSylow
34C22×C3×Q8—21no—
35C22×C3×Q8Dic311yescharacteristic, complemented
36C22×C3×Q8C3×C411yescharacteristic, complemented
37C2×C3×C22⋊C4—22no—
38C2×C3×C22⋊C4—21no—
39C2×C3×C22⋊C4—21no—
40C2×C3×C22⋊C4—21no—
41C2×C3×C22⋊C4—61no—
42C2×C3×C22⋊C4C2×D311yescharacteristic
43C2×C3×C22⋊C4C22×C311yescharacteristic
44C2×#217—21no—
45C3×C22⋊C8—61no—
46C3×#95—22no—
47C3×#95—21no—
48C3×#95—21no—
49C3×#95—21no—
50C3×#95Dic311yescharacteristic, complemented
51C3×#95C3×C411yescharacteristic, complemented
52#830—21no—
53C23×C32—21no—
54C23×C32—21no—
55C23×C32—41no—
56C23×C32—41no—
57C23×C32C22⋊C411yescharacteristic
58C23×C32SD1611yescharacteristic
59C23×C32Q1611yescharacteristic
60C32×Q8—42no—
61C32×Q8—42no—
62C2×C32×C4—22no—
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4—41no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4—41no—
69C2×C32×C4—41no—
70C2×C32×C4—41no—
71C2×C32×C4—41no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—81no—
74C2×C3×Dic3—81no—
75C3×C3⋊C8—81no—
76#393C3×D311yescharacteristic
77#342—31no—
78#323—31no—
79C24×C3—21no—
80C24×C3#6711yescharacteristic
81C24×C3C3×D411yescharacteristic
82C2×C3×Q8—42no—
83C2×C3×Q8—42no—
84C2×C3×Q8—44no—
85C2×C3×Q8—42no—
86C2×C3×Q8—41no—
87C2×C3×Q8—41no—
88C22×C3×C4—22no—
89C22×C3×C4—21no—
90C22×C3×C4—21no—
91C22×C3×C4—22no—
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—121no—
97C22×C3×C4C2×Dic311yescharacteristic
98C22×C3×C4#6711yescharacteristic
99C22×C3×C4C2×C3×C411yescharacteristic
100C22×C3×C4C3×D411yescharacteristic
101C22×Dic3—41no—
102C2×C3×C8—121no—
103C3×C22⋊C4—41no—
104C3×C22⋊C4—41no—
105C3×C22⋊C4—42no—
106C3×C22⋊C4—42no—
107C3×C22⋊C4—42no—
108C3×C22⋊C4—44no—
109C3×C22⋊C4—62no—
110C3×C22⋊C4—121no—
111#217—22no—
112#217—41no—
113C2×C3⋊C8—41no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32—41no—
119C22×C32—41no—
120C22×C32—41no—
121C22×C32—41no—
122C22×C32—81no—
123C22×C32#9911yescharacteristic
124C22×C32#10311yescharacteristic
125C22×C32#10411yescharacteristic
126C32×C4—42no—
127C32×C4—41no—
128C32×C4—41no—
129C32×C4—81no—
130C3×Dic3—82no—
131C22×Q8C3×Dic311yescharacteristic, complemented
132C2×C22⋊C4—21no—
133C2×C22⋊C4—61no—
134C2×C22⋊C4C2×C3×D311yescharacteristic
135C22⋊C8—61no—
136#95—21no—
137#95C3×Dic311yescharacteristic, complemented
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—21no—
142C23×C3—21no—
143C23×C3—21no—
144C23×C3—21no—
145C23×C3—41no—
146C23×C3—41no—
147C23×C3—41no—
148C23×C3—41no—
149C23×C3—41no—
150C23×C3—41no—
151C23×C3—42no—
152C23×C3—42no—
153C23×C3#21511yescharacteristic
154C23×C3#21611yescharacteristic
155C23×C3#21711yescharacteristic
156C23×C3C3×C22⋊C411yescharacteristic
157C23×C3C3×SD1611yescharacteristic
158C23×C3C3×Q1611yescharacteristic
159C3×Q8—42no—
160C3×Q8—42no—
161C3×Q8—44no—
162C3×Q8—44no—
163C3×Q8—42no—
164C3×Q8—42no—
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—41no—
174C2×C3×C4—42no—
175C2×C3×C4—41no—
176C2×C3×C4—41no—
177C2×C3×C4—42no—
178C2×C3×C4—42no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—41no—
185C2×C3×C4—42no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—42no—
189C2×C3×C4—42no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—42no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—122no—
196C2×C3×C4—241no—
197C2×C3×C4—241no—
198C2×Dic3—42no—
199C2×Dic3—81no—
200C2×Dic3—81no—
201C3×C8—241no—
202C3⋊C8—81no—
203C2×C32—21no—
204C2×C32—21no—
205C2×C32—41no—
206C2×C32—41no—
207C2×C32#32811yescharacteristic
208C2×C32AΣL(1,𝔽16)11yescharacteristic
209C2×C32#35411yescharacteristic
210C24C3×#6711yescharacteristic
211C2×Q8—42no—
212C2×Q8—41no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—121no—
216C22×C4C2×C3×Dic311yescharacteristic
217C22×C4C3×#6711yescharacteristic
218C2×C8—121no—
219C22⋊C4—41no—
220C22⋊C4—42no—
221C22⋊C4—62no—
222C22⋊C4—121no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—41no—
237C22×C3—41no—
238C22×C3—41no—
239C22×C3—41no—
240C22×C3—41no—
241C22×C3—41no—
242C22×C3—42no—
243C22×C3—42no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3—81no—
249C22×C3—81no—
250C22×C3—81no—
251C22×C3—81no—
252C22×C3—82no—
253C22×C3#83411yescharacteristic
254C22×C3#83511yescharacteristic
255C22×C3#83711yescharacteristic
256C22×C3C3×#9911yescharacteristic
257C22×C3C3×#10311yescharacteristic
258C22×C3C3×#10411yescharacteristic
259C3×C4—44no—
260C3×C4—42no—
261C3×C4—42no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4—42no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4—81no—
268C3×C4—82no—
269C3×C4—81no—
270C3×C4—81no—
271C3×C4—242no—
272Dic3—82no—
273C32#135111yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23C3×#21511yescharacteristic
279C23C3×#21611yescharacteristic
280C23C3×#21711yescharacteristic
281Q8—42no—
282Q8—42no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—122no—
294C2×C4—241no—
295C2×C4—241no—
296C8—241no—
297C2×C3—22no—
298C2×C3—22no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—41no—
307C2×C3—41no—
308C2×C3—41no—
309C2×C3—41no—
310C2×C3—81no—
311C2×C3—81no—
312C2×C3#453611yescharacteristic
313C2×C3#453811yescharacteristic
314C2×C3#454111yescharacteristic
315C2×C3C3×#32811yescharacteristic
316C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
317C2×C3C3×#35411yescharacteristic
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22C3×#83411yescharacteristic
328C22C3×#83511yescharacteristic
329C22C3×#83711yescharacteristic
330C4—42no—
331C4—41no—
332C4—41no—
333C4—81no—
334C4—242no—
335C3—21no—
336C3#6764611yescharacteristic, direct product factor
337C3C3×#135111yescharacteristic, complemented
338C2—21no—
339C2—21no—
340C2—41no—
341C2—41no—
342C2C3×#453611yescharacteristic
343C2C3×#453811yescharacteristic
344C2C3×#454111yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C22⋊C4C2×C3×D3
FittingC32×#393C2
socleC22×C32#99
prime radicalC24×C32D4
cosocleC2×C3×C22⋊C4C22×C3
hypercenterC3×#393D3
hypocenterC3C3×#1351
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C22⋊C4 ◁ C3×#393

Complements

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

NH ≅ G/Ntype
5. #67646C3direct (N × H)
6. C22×C32×Q8C4semidirect
11. C32×#95C4semidirect
35. C22×C3×Q8Dic3semidirect
36. C22×C3×Q8C3×C4semidirect
50. C3×#95Dic3semidirect
51. C3×#95C3×C4semidirect
131. C22×Q8C3×Dic3semidirect
137. #95C3×Dic3semidirect
273. C32#1351semidirect
336. C3#67646direct (N × H)
337. C3C3×#1351semidirect

Maximal subgroups

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

subgroupindex
C32×#3932
C3×#45262
C3×#45252
C3×#13513
#676463