Finite Group Databasebeta

← C3×#67651 #11771937

Subgroups — C3×#67651 #11771937

Order 1152.

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

normal subgroups only

This group has 401 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×#399C211yesmaximal, characteristic
2C3×#4526C211yesmaximal, characteristic
3C3×#4525C211yesmaximal, characteristic
4C3×#1352—31nomaximal
5#67651C311yesmaximal, characteristic, direct product factor
6C2×C32×C4⋊C4—21no—
7C2×C32×C4⋊C4C411yescharacteristic, complemented
8C2×C32×C22⋊C4—21no—
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×C3×#217—21no—
11C32×#95C411yescharacteristic, complemented
12C3×#830—21no—
13C3×#399—21no—
14C3×#399D311yescharacteristic
15C3×#399C2×C311yescharacteristic
16C3×#342—31no—
17C3×#323—31no—
18#4526C2×C311yescharacteristic
19#4525C2×C311yescharacteristic
20C24×C32D411yescharacteristic
21C22×C32×C4—21no—
22C22×C32×C4—21no—
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C3×Dic3—41no—
26C32×C4⋊C4—42no—
27C32×C4⋊C4—41no—
28C32×C22⋊C4—41no—
29C32×C22⋊C4—42no—
30C3×#217—22no—
31C3×#217—41no—
32C2×C3×C3⋊C8—41no—
33#1352—31noSylow
34C2×C3×C4⋊C4—22no—
35C2×C3×C4⋊C4—21no—
36C2×C3×C4⋊C4—21no—
37C2×C3×C4⋊C4—21no—
38C2×C3×C4⋊C4Dic311yescharacteristic, complemented
39C2×C3×C4⋊C4C3×C411yescharacteristic, complemented
40C2×C3×C22⋊C4—22no—
41C2×C3×C22⋊C4—21no—
42C2×C3×C22⋊C4—21no—
43C2×C3×C22⋊C4—21no—
44C2×C3×C22⋊C4—61no—
45C2×C3×C22⋊C4C2×D311yescharacteristic
46C2×C3×C22⋊C4C22×C311yescharacteristic
47C2×#217—21no—
48C3×C22⋊C8—61no—
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
60C2×C32×C4—22no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—41no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4—41no—
69C2×C32×C4—41no—
70C2×C3×Dic3—42no—
71C2×C3×Dic3—81no—
72C2×C3×Dic3—81no—
73C3×C3⋊C8—81no—
74#399C3×D311yescharacteristic
75#342—31no—
76#323—31no—
77C24×C3—21no—
78C24×C3#6711yescharacteristic
79C24×C3C3×D411yescharacteristic
80C22×C3×C4—22no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×C3×C4—22no—
84C22×C3×C4—21no—
85C22×C3×C4—21no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C22×C3×C4—121no—
89C22×C3×C4C2×Dic311yescharacteristic
90C22×C3×C4#6711yescharacteristic
91C22×C3×C4C2×C3×C411yescharacteristic
92C22×C3×C4C3×D411yescharacteristic
93C22×Dic3—41no—
94C2×C3×C8—121no—
95C3×C4⋊C4—41no—
96C3×C4⋊C4—41no—
97C3×C4⋊C4—42no—
98C3×C4⋊C4—42no—
99C3×C4⋊C4—42no—
100C3×C4⋊C4—44no—
101C3×C22⋊C4—41no—
102C3×C22⋊C4—41no—
103C3×C22⋊C4—42no—
104C3×C22⋊C4—42no—
105C3×C22⋊C4—42no—
106C3×C22⋊C4—44no—
107C3×C22⋊C4—62no—
108C3×C22⋊C4—121no—
109#217—22no—
110#217—41no—
111C2×C3⋊C8—41no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32—41no—
117C22×C32—41no—
118C22×C32—41no—
119C22×C32—41no—
120C22×C32—81no—
121C22×C32#9911yescharacteristic
122C22×C32#10311yescharacteristic
123C22×C32#10411yescharacteristic
124C32×C4—42no—
125C32×C4—41no—
126C32×C4—41no—
127C32×C4—81no—
128C3×Dic3—82no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4C3×Dic311yescharacteristic, complemented
131C2×C22⋊C4—21no—
132C2×C22⋊C4—61no—
133C2×C22⋊C4C2×C3×D311yescharacteristic
134C22⋊C8—61no—
135#95C3×Dic311yescharacteristic, complemented
136C23×C3—21no—
137C23×C3—21no—
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—21no—
142C23×C3—21no—
143C23×C3—41no—
144C23×C3—41no—
145C23×C3—41no—
146C23×C3—41no—
147C23×C3—41no—
148C23×C3—41no—
149C23×C3—42no—
150C23×C3—42no—
151C23×C3#21511yescharacteristic
152C23×C3#21611yescharacteristic
153C23×C3#21711yescharacteristic
154C23×C3C3×C22⋊C411yescharacteristic
155C23×C3C3×SD1611yescharacteristic
156C23×C3C3×Q1611yescharacteristic
157C2×C3×C4—24no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—41no—
166C2×C3×C4—42no—
167C2×C3×C4—41no—
168C2×C3×C4—41no—
169C2×C3×C4—42no—
170C2×C3×C4—42no—
171C2×C3×C4—41no—
172C2×C3×C4—41no—
173C2×C3×C4—41no—
174C2×C3×C4—41no—
175C2×C3×C4—41no—
176C2×C3×C4—41no—
177C2×C3×C4—42no—
178C2×C3×C4—41no—
179C2×C3×C4—41no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—42no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—122no—
188C2×C3×C4—241no—
189C2×C3×C4—241no—
190C2×Dic3—42no—
191C2×Dic3—81no—
192C2×Dic3—81no—
193C3×C8—241no—
194C3⋊C8—81no—
195C2×C32—21no—
196C2×C32—21no—
197C2×C32—41no—
198C2×C32—41no—
199C2×C32#32811yescharacteristic
200C2×C32#35211yescharacteristic
201C2×C32#35311yescharacteristic
202C24C3×#6711yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—121no—
206C22×C4C2×C3×Dic311yescharacteristic
207C22×C4C3×#6711yescharacteristic
208C2×C8—121no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C22⋊C4—41no—
212C22⋊C4—42no—
213C22⋊C4—62no—
214C22⋊C4—121no—
215C22×C3—22no—
216C22×C3—22no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3—41no—
232C22×C3—41no—
233C22×C3—41no—
234C22×C3—42no—
235C22×C3—42no—
236C22×C3—41no—
237C22×C3—41no—
238C22×C3—41no—
239C22×C3—41no—
240C22×C3—81no—
241C22×C3—81no—
242C22×C3—81no—
243C22×C3—81no—
244C22×C3—82no—
245C22×C3#83411yescharacteristic
246C22×C3#83511yescharacteristic
247C22×C3#83711yescharacteristic
248C22×C3C3×#9911yescharacteristic
249C22×C3C3×#10311yescharacteristic
250C22×C3C3×#10411yescharacteristic
251C3×C4—44no—
252C3×C4—42no—
253C3×C4—42no—
254C3×C4—42no—
255C3×C4—41no—
256C3×C4—41no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4—81no—
260C3×C4—82no—
261C3×C4—81no—
262C3×C4—81no—
263C3×C4—242no—
264Dic3—82no—
265C32#135211yescharacteristic, complemented, Sylow
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23C3×#21511yescharacteristic
271C23C3×#21611yescharacteristic
272C23C3×#21711yescharacteristic
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—122no—
284C2×C4—241no—
285C2×C4—241no—
286C8—241no—
287C2×C3—22no—
288C2×C3—22no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—41no—
297C2×C3—41no—
298C2×C3—41no—
299C2×C3—41no—
300C2×C3—81no—
301C2×C3—81no—
302C2×C3#453811yescharacteristic
303C2×C3#453911yescharacteristic
304C2×C3#454511yescharacteristic
305C2×C3C3×#32811yescharacteristic
306C2×C3C3×#35211yescharacteristic
307C2×C3C3×#35311yescharacteristic
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22C3×#83411yescharacteristic
318C22C3×#83511yescharacteristic
319C22C3×#83711yescharacteristic
320C4—42no—
321C4—41no—
322C4—41no—
323C4—81no—
324C4—242no—
325C3—21no—
326C3#6765111yescharacteristic, direct product factor
327C3C3×#135211yescharacteristic, complemented
328C2—21no—
329C2—21no—
330C2—41no—
331C2—41no—
332C2C3×#453811yescharacteristic
333C2C3×#453911yescharacteristic
334C2C3×#454511yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C22⋊C4C2×C3×D3
FittingC32×#399C2
socleC22×C32#99
prime radicalC24×C32D4
cosocleC2×C3×C22⋊C4C22×C3
hypercenterC3×#399D3
hypocenterC3C3×#1352
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C22⋊C4 ◁ C3×#399

Complements

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

NH ≅ G/Ntype
5. #67651C3direct (N × H)
7. C2×C32×C4⋊C4C4semidirect
11. C32×#95C4semidirect
38. C2×C3×C4⋊C4Dic3semidirect
39. C2×C3×C4⋊C4C3×C4semidirect
50. C3×#95Dic3semidirect
51. C3×#95C3×C4semidirect
130. C2×C4⋊C4C3×Dic3semidirect
135. #95C3×Dic3semidirect
265. C32#1352semidirect
326. C3#67651direct (N × H)
327. C3C3×#1352semidirect

Maximal subgroups

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

subgroupindex
C32×#3992
C3×#45262
C3×#45252
C3×#13523
#676513