Finite Group Databasebeta

← #11776192

Subgroups — #11776192

Order 1152.

456 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic
2D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
3#10590248C211yesmaximal, characteristic
4#10589412C211yesmaximal, characteristic, complemented
5C3×#4546C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71828—31nomaximal
9#68481—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C3×#946C412yes—
12C3×Q8×Dic3C412yes—
13C3×#897—21no—
14C3×#892—21no—
15C3×#890—21no—
16C3×#887—21no—
17C3×C42×D3C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×D3×C3⋊C8—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24Dic3⋊(C3⋊C8)—21no—
25(C2×D3)⋊(C3⋊C8)—21no—
26Dic3×C3⋊C8—21no—
27C3×#533—31no—
28#5728D311yescharacteristic
29#4925—31no—
30C2×C4⋊(C3⋊C8)—31no—
31#4833—31no—
32D3×C4⋊C8—31no—
33C3×#333—31no—
34#4547—31no—
35#4547—31no—
36#4546—31no—
37#4546—31no—
38#4546—61no—
39#4546D311yescharacteristic, complemented
40#4486—31no—
41#4482—31no—
42C2×C32×Q8C2×C412yes—
43C2×C3×C4×D3C2×C411yescharacteristic
44C2×C3×C4×D3D411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×Dic6—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C42C2311yescharacteristic
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3C2×C412yes—
56C3×Dic3⋊C4—22no—
57C3×C4×Dic3—22no—
58C3×C4×Dic3C2×C411yescharacteristic
59C3×C4×Dic3D411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63D3×C3⋊C8—42no—
64#1542—91noSylow
65C3×C4⋊Q8—21no—
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8C2×D311yescharacteristic
68C3×C4⋊Q8C2×D311yescharacteristic
69C3×#125—61no—
70C3×C22⋊Q8—32no—
71C3×C22⋊Q8—61no—
72C3×C4×Q8—32no—
73C3×C4×Q8—61no—
74C3×#117—61no—
75C2×C3×C42—31no—
76#946Dic312yes—
77Q8×Dic3Dic312yes—
78C22×C3⋊C8—61no—
79C2×D3×C8—61no—
80#897—21no—
81#892—21no—
82#890—21no—
83#887—21no—
84C42×D3C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86C3×C4⋊C8—31no—
87C3×C4⋊C8—31no—
88#830—61no—
89(C2×D3)⋊C8—61no—
90Dic3⋊C8—61no—
91C8×Dic3—61no—
92C4⋊(C3⋊C8)—31no—
93C4⋊(C3⋊C8)—31no—
94C4⋊(C3⋊C8)—31no—
95C4⋊(C3⋊C8)—31no—
96C4⋊(C3⋊C8)—61no—
97C4⋊(C3⋊C8)—61no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4×C3⋊C8—61no—
102C22×C3×D3C22⋊C411yescharacteristic
103C32×Q8—42no—
104C2×C32×C4—22no—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3×Dic3—22no—
109C2×C3×Dic3C22⋊C411yescharacteristic
110C2×C3×Dic3C22⋊C411yescharacteristic
111C2×C3×Dic3C22⋊C411yescharacteristic
112C3×C4×D3—21no—
113C3×C4×D3—21no—
114C3×C4×D3—41no—
115C3×C4×D3SD1612yes—
116C3×C4×D3Q1612yes—
117C3×Dic6—41no—
118C3×Dic6—41no—
119C3⋊(C3⋊C8)—41no—
120C3⋊(C3⋊C8)—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8—41no—
123#533—31no—
124#431—91no—
125C2×C4⋊C8—91no—
126#333—31no—
127#333—91no—
128#332—91no—
129#332—91no—
130C2×C3×Q8—22no—
131C2×C3×Q8—61no—
132C2×C3×Q8C4×D312yes—
133C2×C3×Q8C2×Dic312yes—
134C22×C3×C4—31no—
135C22×C3×C4—31no—
136C22×C3×C4—31no—
137C2×C4×D3C2×Dic311yescharacteristic
138C2×C4×D3#6711yescharacteristic
139C2×C4×D3#6711yescharacteristic
140C2×Dic6—21no—
141C2×C3×C8—61no—
142C2×C3×C8—61no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—32no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—41no—
150C3×C4⋊C4—62no—
151C3×C4⋊C4—62no—
152C3×C4⋊C4—61no—
153C3×C22⋊C4—62no—
154C3×C42—21no—
155C3×C42—31no—
156C3×C42—31no—
157C3×C42—31no—
158C3×C42—62no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161(C2×D3)⋊C4—22no—
162C4⋊Dic3—21no—
163C4⋊Dic3—22no—
164C4⋊Dic3C2×Dic312yes—
165Dic3⋊C4—22no—
166C4×Dic3—22no—
167C4×Dic3C2×Dic311yescharacteristic
168C4×Dic3#6711yescharacteristic
169C4×Dic3#6711yescharacteristic
170C2×C3⋊C8—21no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8—61no—
173C2×C3⋊C8—61no—
174C2×C3⋊C8—61no—
175C2×C3⋊C8—61no—
176C2×C3⋊C8—121no—
177C2×C3⋊C8—121no—
178C2×C3⋊C8—122no—
179D3×C8—122no—
180C22×C32C2×C22⋊C411yescharacteristic
181C2×C3×D3—21no—
182C2×C3×D3—21no—
183C2×C3×D3#10312yes—
184C32×C4—21no—
185C32×C4—42no—
186C32×C4C2×SD1611yescharacteristic
187C32×C4C2×Q1611yescharacteristic
188C32×C4#13511yescharacteristic
189C32×C4#13511yescharacteristic
190C3×Dic3—21no—
191C3×Dic3—21no—
192C3×Dic3—42no—
193C3×Dic3#10312yes—
194C22×C8—181no—
195C4⋊Q8—31no—
196C4⋊Q8D3211yescharacteristic
197#125—61no—
198C22⋊Q8—32no—
199C22⋊Q8—61no—
200C4×Q8—32no—
201C4×Q8—61no—
202#117—61no—
203C2×C42—31no—
204C4⋊C8—31no—
205C4⋊C8—31no—
206C4⋊C8—91no—
207C4⋊C8—91no—
208C4⋊C8—181no—
209C22⋊C8—181no—
210C4×C8—181no—
211C23×C3—31no—
212C22×D3#21711yescharacteristic
213C3×Q8—42no—
214C3×Q8—42no—
215C3×Q8—82no—
216C3×Q8—121no—
217C3×Q8—121no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—31no—
224C2×C3×C4—32no—
225C2×C3×C4—32no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—42no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—62no—
232C2×C3×C4—121no—
233C2×C3×C4C2×C4×D311yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4C22×Dic311yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239C2×Dic3—22no—
240C2×Dic3#21711yescharacteristic
241C2×Dic3#21711yescharacteristic
242C2×Dic3#21711yescharacteristic
243C4×D3—21no—
244C4×D3—21no—
245C4×D3—41no—
246C4×D3#21512yes—
247C4×D3#21612yes—
248Dic6—41no—
249Dic6—41no—
250C3×C8—121no—
251C3×C8—121no—
252C3⋊C8—41no—
253C3⋊C8—41no—
254C3⋊C8—121no—
255C3⋊C8—121no—
256C3⋊C8—121no—
257C3⋊C8—121no—
258C3⋊C8—241no—
259C3⋊C8—241no—
260C2×C32#41311yescharacteristic
261C2×C32C2×#10311yescharacteristic
262C2×C32#41611yescharacteristic
263C3×D3—22no—
264C2×Q8—61no—
265C2×Q8D3×Dic312yes—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—31no—
269C2×C8—61no—
270C2×C8—61no—
271C2×C8—181no—
272C2×C8—181no—
273C2×C8—362no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—32no—
277C4⋊C4—62no—
278C4⋊C4—62no—
279C4⋊C4—61no—
280C22⋊C4—62no—
281C42—31no—
282C42—31no—
283C42—31no—
284C42—62no—
285C42C2×D3211yescharacteristic
286C22×C3—21no—
287C22×C3—32no—
288C22×C3—61no—
289C22×C3—61no—
290C22×C3D3×C22⋊C411yescharacteristic
291C22×C3C2×#21711yescharacteristic
292C2×D3—21no—
293C2×D3—21no—
294C2×D3#83512yes—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—32no—
302C3×C4—41no—
303C3×C4—42no—
304C3×C4—42no—
305C3×C4—61no—
306C3×C4—61no—
307C3×C4—82no—
308C3×C4—122no—
309C3×C4D3×SD1611yescharacteristic
310C3×C4#91611yescharacteristic
311C3×C4D3×Q1611yescharacteristic
312C3×C4#91911yescharacteristic
313C3×C4C2×#21511yescharacteristic
314C3×C4C2×#21611yescharacteristic
315C3×C4#95011yescharacteristic
316C3×C4#95011yescharacteristic
317Dic3—21no—
318Dic3—21no—
319Dic3—42no—
320Dic3#83512yes—
321C32#154211yescharacteristic, complemented, Sylow
322C23—31no—
323Q8—42no—
324Q8—121no—
325Q8—121no—
326C2×C4—22no—
327C2×C4—31no—
328C2×C4—32no—
329C2×C4—32no—
330C2×C4—31no—
331C2×C4—31no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—62no—
335C2×C4—121no—
336C2×C4C2×D3×Dic311yescharacteristic
337C2×C4D3×#6711yescharacteristic
338C2×C4D3×#6711yescharacteristic
339C8—121no—
340C8—121no—
341C8—361no—
342C8—361no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—62no—
347C2×C3#474511yescharacteristic
348C2×C3D3×#10311yescharacteristic
349C2×C3#480411yescharacteristic
350C2×C3C2×#83511yescharacteristic
351C2×C3#523311yescharacteristic
352C2×C3#523711yescharacteristic
353D3—22no—
354C22—32no—
355C22—61no—
356C22—61no—
357C22D3×#21711yescharacteristic
358C4—21no—
359C4—32no—
360C4—42no—
361C4—61no—
362C4—61no—
363C4—122no—
364C4D3×#21511yescharacteristic
365C4D3×#21611yescharacteristic
366C4#6394711yescharacteristic
367C4#6394911yescharacteristic
368C3—21no—
369C3#6848111yescharacteristic, complemented
370C3#7182811yescharacteristic, complemented
371C2—62no—
372C2#1059150111yescharacteristic
373C2D3×#83511yescharacteristic
374C2#1059155611yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊Q8D32
hypocenterC32#1542
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10589412C2semidirect
5. C3×#4546C2semidirect
6. #10589093C2semidirect
7. #10589092C2semidirect
39. #4546D3semidirect
321. C32#1542semidirect
369. C3#68481semidirect
370. C3#71828semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
D3×C4⋊(C3⋊C8)2
#105902482
#105894122
C3×#45462
#105890932
#105890922
#718283
#684813