Finite Group Databasebeta

← C3×#68154 #11777413

Subgroups — C3×#68154 #11777413

Order 1152.

377 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#214C211yesmaximal, characteristic
2C3×D4×C3⋊C8C211yesmaximal, characteristic
3C3×#4831C211yesmaximal, characteristic, complemented
4C32×D4⋊C8C211yesmaximal, characteristic
5C3×#4480C211yesmaximal, characteristic, complemented
6C3×#4456C211yesmaximal, characteristic, complemented
7C3×#4454C211yesmaximal, characteristic, complemented
8C3×#1582—31nomaximal
9#68154C311yesmaximal, characteristic, direct product factor
10C32×C4×D4C2211yescharacteristic
11C2×C3×#214C411yescharacteristic
12C22×C3×C3⋊C8—21no—
13C3×C4×Dic6C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×C4×C8C2211yescharacteristic
16C3×#832C411yescharacteristic
17C3×#830—21no—
18C3×#815—21no—
19C3×Dic3⋊C8—21no—
20C3×#810C411yescharacteristic
21C3×#808C411yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#446—31no—
26C3×C4×SD16—31no—
27C3×C8×D4—31no—
28C4×#214C2×C311yescharacteristic
29D4×C3⋊C8C2×C311yescharacteristic
30#4831C2×C311yescharacteristic, complemented
31C3×#334—31no—
32C3×Q8⋊C8—31no—
33C3×D4⋊C8—21no—
34C3×D4⋊C8D311yescharacteristic
35C3×D4⋊C8C2×C311yescharacteristic
36C3×#322—31no—
37#4480C2×C311yescharacteristic, complemented
38#4456C2×C311yescharacteristic, complemented
39#4454C2×C311yescharacteristic, complemented
40C2×C32×D4C2×C411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×Dic6C2×C411yescharacteristic
43C2×C32×C8—21no—
44C2×C32×C8—21no—
45C32×C4⋊C4C2×C411yescharacteristic
46C32×C22⋊C4—21no—
47C32×C42C2311yescharacteristic
48C3×#214—22no—
49C3×C4⋊Dic3C2×C411yescharacteristic
50C3×Dic3⋊C4—21no—
51C3×C4×Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—42no—
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C2×C3×C3⋊C8C2×C411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1582—31noSylow
59C2×C3×SD16—31no—
60C22×C3×C8—61no—
61C3×C4×Q8—31no—
62C3×C4×D4—21no—
63C3×C4×D4C2×D311yescharacteristic
64C3×C4×D4C22×C311yescharacteristic
65C2×#214C3×C411yescharacteristic
66C22×C3⋊C8—21no—
67C4×Dic6C22×C311yescharacteristic
68C3×#106—31no—
69C3×C4⋊C8—21no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—61no—
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4⋊C8C22×C311yescharacteristic
74C3×#103—31no—
75C3×#102—31no—
76C3×C22⋊C8—61no—
77C3×#97—61no—
78C3×C4×C8—21no—
79C3×C4×C8—31no—
80C3×C4×C8—31no—
81C3×C4×C8C2×D311yescharacteristic
82C3×C4×C8C22×C311yescharacteristic
83#832C3×C411yescharacteristic
84#830—21no—
85#815—21no—
86Dic3⋊C8—21no—
87#810C3×C411yescharacteristic
88#808C3×C411yescharacteristic
89C4⋊(C3⋊C8)C22×C311yescharacteristic
90C4×C3⋊C8C22×C311yescharacteristic
91C4×C3⋊C8C22×C311yescharacteristic
92C23×C32—21no—
93C32×D4—21no—
94C32×D4M1612yes—
95C2×C32×C4—21no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3×Dic3—21no—
102C2×C3×Dic3—21no—
103C3×Dic6—21no—
104C3×Dic6—21no—
105C32×C8—41no—
106C32×C8—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8SD1612yescomplemented
112#446—31no—
113C4×SD16—31no—
114C8×D4—31no—
115#334—31no—
116Q8⋊C8—31no—
117D4⋊C8C3×D311yescharacteristic
118#322—31no—
119C2×C3×Q8—31no—
120C2×C3×D4—21no—
121C2×C3×D4C4×D311yescharacteristic
122C2×C3×D4C2×C3×C411yescharacteristic
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—41no—
126C2×Dic6C2×C3×C411yescharacteristic
127C3×SD16—62no—
128C2×C3×C8—21no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—31no—
136C2×C3×C8—41no—
137C2×C3×C8—41no—
138C2×C3×C8—61no—
139C2×C3×C8—122no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4C4×D311yescharacteristic
144C3×C4⋊C4C2×C3×C411yescharacteristic
145C3×C22⋊C4—21no—
146C3×C22⋊C4—21no—
147C3×C22⋊C4—41no—
148C3×C42—21no—
149C3×C42—61no—
150C3×C42C22×D311yescharacteristic
151C3×C42C23×C311yescharacteristic
152#214—22no—
153C4⋊Dic3C2×C3×C411yescharacteristic
154Dic3⋊C4—21no—
155C4×Dic3—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—42no—
158C2×C3⋊C8C2×C3×C411yescharacteristic
159C2×C3⋊C8C2×C3×C411yescharacteristic
160C2×C3⋊C8C3×D411yescharacteristic
161C2×C3⋊C8C3×D411yescharacteristic
162C22×C32—22no—
163C22×C32—41no—
164C22×C32—41no—
165C22×C32C4×D411yescharacteristic
166C32×C4—21no—
167C32×C4—41no—
168C32×C4C2×M1611yescharacteristic
169C32×C4#13111yescharacteristic
170C32×C4C2×SD1611yescharacteristic
171C32×C4#13511yescharacteristic
172C3×Dic3—41no—
173C3×Dic3—41no—
174C2×SD16—31no—
175C22×C8—61no—
176C4×Q8—31no—
177C4×D4C2×C3×D311yescharacteristic
178#106—31no—
179C4⋊C8—31no—
180C4⋊C8—61no—
181C4⋊C8C2×C3×D311yescharacteristic
182#103—31no—
183#102—31no—
184C22⋊C8—61no—
185#97—61no—
186C4×C8—31no—
187C4×C8—31no—
188C4×C8C2×C3×D311yescharacteristic
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—41no—
192C3×Q8—61no—
193C3×Q8—61no—
194C3×D4—21no—
195C3×D4—21no—
196C3×D4—22no—
197C3×D4—41no—
198C3×D4ΓL(1,𝔽25)12yes—
199C3×D4C3×M1612yes—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—61no—
211C2×C3×C4—61no—
212C2×C3×C4—81no—
213C2×C3×C4—81no—
214C2×C3×C4C2×C4×D311yescharacteristic
215C2×C3×C4D3×D411yescharacteristic
216C2×C3×C4#23711yescharacteristic
217C2×C3×C4C22×C3×C411yescharacteristic
218C2×C3×C4C2×C3×D411yescharacteristic
219C2×C3×C4C3×#4111yescharacteristic
220C2×Dic3—21no—
221C2×Dic3—21no—
222Dic6—21no—
223Dic6—21no—
224C3×C8—32no—
225C3×C8—41no—
226C3×C8—41no—
227C3×C8—42no—
228C3×C8—41no—
229C3×C8—41no—
230C3×C8—61no—
231C3×C8—61no—
232C3×C8—61no—
233C3×C8—81no—
234C3×C8—121no—
235C3⋊C8—21no—
236C3⋊C8—21no—
237C3⋊C8—21no—
238C3⋊C8—41no—
239C3⋊C8C3×SD1612yescomplemented
240C2×C32—42no—
241C2×C32#43511yescharacteristic
242C2×C32C4×SD1611yescharacteristic
243C2×C32#44411yescharacteristic
244C2×Q8—31no—
245C2×D4C3×C4×D311yescharacteristic
246C22×C4—21no—
247SD16—62no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—31no—
251C2×C8—31no—
252C2×C8—31no—
253C2×C8—31no—
254C2×C8—61no—
255C2×C8—122no—
256C4⋊C4—31no—
257C4⋊C4—61no—
258C4⋊C4C3×C4×D311yescharacteristic
259C22⋊C4—21no—
260C42—61no—
261C42C22×C3×D311yescharacteristic
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—21no—
265C22×C3—42no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—81no—
271C22×C3—81no—
272C22×C3#67⋊C411yescharacteristic
273C22×C3C3×C4×D411yescharacteristic
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—81no—
284C3×C4—121no—
285C3×C4—121no—
286C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
287C3×C4#90711yescharacteristic
288C3×C4#91211yescharacteristic
289C3×C4D3×SD1611yescharacteristic
290C3×C4C2×C3×M1611yescharacteristic
291C3×C4C3×#13111yescharacteristic
292C3×C4C2×C3×SD1611yescharacteristic
293C3×C4C3×#13511yescharacteristic
294Dic3—41no—
295Dic3—41no—
296C32#158211yescharacteristic, complemented, Sylow
297C23—21no—
298Q8—61no—
299Q8—61no—
300D4—21no—
301D4C3×ΓL(1,𝔽25)12yes—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4C2×C3×C4×D311yescharacteristic
308C2×C4C3×D3×D411yescharacteristic
309C2×C4C3×#23711yescharacteristic
310C8—32no—
311C8—41no—
312C8—41no—
313C8—61no—
314C8—61no—
315C8—61no—
316C8—121no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—42no—
321C2×C3—42no—
322C2×C3—82no—
323C2×C3#473011yescharacteristic
324C2×C3#475811yescharacteristic
325C2×C3#482311yescharacteristic
326C2×C3C3×#43511yescharacteristic
327C2×C3C3×C4×SD1611yescharacteristic
328C2×C3C3×#44411yescharacteristic
329C22—22no—
330C22—41no—
331C22—41no—
332C22C3×#67⋊C411yescharacteristic
333C4—21no—
334C4—41no—
335C4—121no—
336C4—121no—
337C4C2×C3×ΓL(1,𝔽25)11yescharacteristic
338C4C3×#90711yescharacteristic
339C4C3×#91211yescharacteristic
340C4C3×D3×SD1611yescharacteristic
341C3—21no—
342C3#6815411yescharacteristic, direct product factor
343C3C3×#158211yescharacteristic, complemented
344C2—42no—
345C2C3×#473011yescharacteristic
346C2C3×#475811yescharacteristic
347C2C3×#482311yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32C4×D4
prime radicalC2×C32×D4C2×C4
cosocleC3×C42C23×C3
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1582
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
3. C3×#4831C2semidirect
5. C3×#4480C2semidirect
6. C3×#4456C2semidirect
7. C3×#4454C2semidirect
9. #68154C3direct (N × H)
30. #4831C2×C3semidirect
37. #4480C2×C3semidirect
38. #4456C2×C3semidirect
39. #4454C2×C3semidirect
111. C3×C3⋊C8SD16semidirect
239. C3⋊C8C3×SD16semidirect
296. C32#1582semidirect
342. C3#68154direct (N × H)
343. C3C3×#1582semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2142
C3×D4×C3⋊C82
C3×#48312
C32×D4⋊C82
C3×#44802
C3×#44562
C3×#44542
C3×#15823
#681543