Finite Group Databasebeta

← #11808834

Subgroups — #11808834

Order 1152.

1512 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C2×#64096C211yesmaximal, characteristic
3C32×#398C211yesmaximal, characteristic
4#10592682C211yesmaximal, characteristic
5#10592678C211yesmaximal, characteristic
6#10592678C212yesmaximal
7C4⋊C4×C3⋊Dic3C212yesmaximal
8#10592356C212yesmaximal
9#10592355C211yesmaximal, characteristic
10#10592348C212yesmaximal
11#10592347C211yesmaximal, characteristic
12#77740—34nomaximal
13C22×#634C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2212yes—
18C2×C4⋊(C3⋊Dic3)C2212yes—
19C2×#3750C2212yes—
20C2×#3750C2212yes—
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2212yes—
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C4×C3⋊Dic3C2212yes—
29#64096—24no—
30#64096—24no—
31C32×#95C2211yescharacteristic
32C32×#95C2212yes—
33#63658C2212yes—
34#63658C2211yescharacteristic
35#63658C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38C2×#887—34no—
39C2×#887—34no—
40C3×#398D314yes—
41#4983—34no—
42#4979—38no—
43#4979—34no—
44Dic3×C4⋊C4—38no—
45#4657—38no—
46#4656—34no—
47#4649—38no—
48#4648—34no—
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C2×#634—22no—
61C2×#634—22no—
62C2×#634—22no—
63C2×#634—22no—
64C2×#634—24no—
65C32×C4⋊C4—22no—
66C32×C4⋊C4—22no—
67C32×C4⋊C4—24no—
68C4⋊(C3⋊Dic3)—24no—
69#3750—22no—
70#3750—24no—
71#3750—22no—
72#3750—24no—
73#3750—24no—
74C4×C3⋊Dic3—22no—
75C4×C3⋊Dic3—24no—
76C4×C3⋊Dic3—22no—
77C4×C3⋊Dic3D414yes—
78C4×C3⋊Dic3Q818yescomplemented
79#2399—91noSylow
80C22×Dic6—34no—
81C22×Dic6—34no—
82C2×C3×C4⋊C4C2×D318yes—
83C2×C3×C4⋊C4C2×D314yes—
84C2×C3×C4⋊C4C2×D314yes—
85C2×C4⋊Dic3—38no—
86C2×Dic3⋊C4—38no—
87C2×Dic3⋊C4—38no—
88C2×Dic3⋊C4—34no—
89C2×Dic3⋊C4—34no—
90C2×Dic3⋊C4—38no—
91C2×C4×Dic3—38no—
92C2×C4×Dic3—34no—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—38no—
95C2×C4×Dic3—34no—
96#887—616no—
97#887—616no—
98C3×#95C2×D314yes—
99C3×#95C2×D318yes—
100C3⋊#95—38no—
101C3⋊#95—34no—
102C3⋊#95—38no—
103C3⋊#95—38no—
104C3⋊#95—38no—
105C23×C32C2411yescharacteristic
106C2×C32×C4—21no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4C2×D412yes—
117C2×C32×C4C2×Q814yes—
118C2×C32×C4#4112yes—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C2×D412yes—
130C2×C3⋊Dic3C2×D412yes—
131C2×C3⋊Dic3C2×Q814yes—
132C2×C3⋊Dic3C2×Q814yes—
133C2×C3⋊Dic3#4112yes—
134C2×C3⋊Dic3#4114yes—
135#634—28no—
136#634—28no—
137C2×C4×Q8—91no—
138C2×C4×Q8—91no—
139#398—91no—
140#398—92no—
141#398C3⋊D311yescharacteristic
142#395—92no—
143#395—91no—
144#395—91no—
145C4×C4⋊C4—92no—
146C4×C4⋊C4—92no—
147#376—91no—
148C22×C3×C4C22×D318yes—
149C22×C3×C4C22×D314yes—
150C22×C3×C4C22×D314yes—
151C22×C3×C4C22×D314yes—
152C22×C3×C4C22×D318yes—
153C22×Dic3—34no—
154C22×Dic3—38no—
155C22×Dic3—34no—
156C22×Dic3—34no—
157C22×Dic3—38no—
158C22×Dic3—34no—
159C2×Dic6—68no—
160C2×Dic6—68no—
161C2×Dic6—616no—
162C2×Dic6—68no—
163C2×Dic6—68no—
164C3×C4⋊C4—28no—
165C3×C4⋊C4—28no—
166C3×C4⋊C4—216no—
167C4⋊Dic3—616no—
168Dic3⋊C4—616no—
169Dic3⋊C4—68no—
170Dic3⋊C4—616no—
171Dic3⋊C4—616no—
172Dic3⋊C4—68no—
173C4×Dic3—316no—
174C4×Dic3—332no—
175C4×Dic3—68no—
176C4×Dic3—616no—
177C4×Dic3—68no—
178C22×C32C22×D411yescharacteristic
179C22×C32C22×Q812yes—
180C22×C32C2×#4111yescharacteristic
181C22×C32C2×#4112yes—
182C22×C32C2×#4111yescharacteristic
183C32×C4—22no—
184C32×C4—22no—
185C32×C4—24no—
186C32×C4—41no—
187C32×C4—42no—
188C3⋊Dic3—22no—
189C3⋊Dic3—24no—
190C3⋊Dic3—22no—
191C3⋊Dic3—24no—
192C3⋊Dic3—41no—
193C3⋊Dic3C4⋊Q814yes—
194C22×Q8—91no—
195C22×Q8—91no—
196C4×Q8—184no—
197C4×Q8—184no—
198C2×C4⋊C4—92no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—91no—
201C2×C4⋊C4—92no—
202C2×C4⋊C4—92no—
203C2×C4⋊C4—92no—
204C2×C4⋊C4C2×C3⋊D311yescharacteristic
205C2×C4⋊C4C2×C3⋊D311yescharacteristic
206C2×C4⋊C4C2×C3⋊D312yes—
207C2×C42—91no—
208C2×C42—92no—
209C2×C42—92no—
210C2×C42—91no—
211C2×C42—91no—
212#95—91no—
213#95—92no—
214#95—92no—
215#95—92no—
216#95—92no—
217#95C2×C3⋊D311yescharacteristic
218#95C2×C3⋊D312yes—
219C23×C3C23×D314yes—
220C2×C3×C4—24no—
221C2×C3×C4—28no—
222C2×C3×C4—28no—
223C2×C3×C4—28no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—28no—
227C2×C3×C4—28no—
228C2×C3×C4—28no—
229C2×C3×C4—28no—
230C2×C3×C4D3×D418yes—
231C2×C3×C4#23718yes—
232C2×C3×C4D3×Q8116yes—
233C2×Dic3—38no—
234C2×Dic3—316no—
235C2×Dic3—38no—
236C2×Dic3—316no—
237C2×Dic3—38no—
238C2×Dic3—316no—
239C2×Dic3—68no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—68no—
244C2×Dic3—68no—
245C2×Dic3—68no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—68no—
249Dic6—632no—
250Dic6—632no—
251C2×C32#52511yescharacteristic
252C2×C32#52511yescharacteristic
253C2×C32C2×C4⋊Q811yescharacteristic
254C2×C32#53312yes—
255C2×C32#53312yes—
256C2×Q8—182no—
257C2×Q8—184no—
258C2×Q8—182no—
259C2×Q8—182no—
260C2×Q8—182no—
261C22×C4—91no—
262C22×C4—92no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—92no—
266C22×C4—91no—
267C22×C4C22×C3⋊D312yes—
268C22×C4C22×C3⋊D311yescharacteristic
269C22×C4C22×C3⋊D311yescharacteristic
270C22×C4C22×C3⋊D311yescharacteristic
271C22×C4C22×C3⋊D312yes—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—24no—
275C4⋊C4—184no—
276C4⋊C4—182no—
277C4⋊C4—184no—
278C4⋊C4—184no—
279C4⋊C4—184no—
280C4⋊C4—182no—
281C42—94no—
282C42—98no—
283C42—182no—
284C42—182no—
285C42—184no—
286C22×C3C2×D3×D414yes—
287C22×C3C2×#23714yes—
288C22×C3C2×D3×Q818yes—
289C22×C3D3×#4118yes—
290C22×C3D3×#4114yes—
291C3×C4—28no—
292C3×C4—28no—
293C3×C4—216no—
294C3×C4—44no—
295C3×C4—48no—
296Dic3—316no—
297Dic3—616no—
298Dic3—616no—
299Dic3—68no—
300Dic3—68no—
301Dic3—124no—
302C32#239911yescharacteristic, complemented, Sylow
303C23C23×C3⋊D311yescharacteristic
304Q8—188no—
305Q8—188no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—92no—
317C2×C4—94no—
318C2×C4—92no—
319C2×C4—94no—
320C2×C4—94no—
321C2×C4—92no—
322C2×C4—182no—
323C2×C4—181no—
324C2×C4—181no—
325C2×C4—181no—
326C2×C4—182no—
327C2×C4—182no—
328C2×C4—182no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—182no—
332C2×C4D4×C3⋊D312yes—
333C2×C4#383012yes—
334C2×C4Q8×C3⋊D314yes—
335C2×C3#560614yes—
336C2×C3#562218yes—
337C2×C3#565614yes—
338C2×C3#568818yes—
339C2×C3D3×C4⋊Q814yes—
340C22C2×D4×C3⋊D311yescharacteristic
341C22C2×#383011yescharacteristic
342C22C2×Q8×C3⋊D312yes—
343C22#41×C3⋊D312yes—
344C22#41×C3⋊D311yescharacteristic
345C4—22no—
346C4—22no—
347C4—24no—
348C4—41no—
349C4—42no—
350C4—94no—
351C4—184no—
352C4—184no—
353C4—182no—
354C4—182no—
355C4—361no—
356C3#7774014yescomplemented
357C2#1059607711yescharacteristic
358C2#1059609312yes—
359C2#1059612711yescharacteristic
360C2#1059615912yes—
361C2C3⋊D3×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, prime radical, cosocleC23×C32C24
FittingC32×#398C2
hypercenter#398C3⋊D3
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
78. C4×C3⋊Dic3Q8semidirect
302. C32#2399semidirect
356. C3#77740semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C32×#3982
#105926822
#105926782
C4⋊C4×C3⋊Dic32
#105923562
#105923552
#105923482
#105923472
#777403