Finite Group Databasebeta

← C2×#10591206 #11801094

Subgroups — C2×#10591206 #11801094

Order 1152.

1589 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×Dic3C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C212yesmaximal
3C2×#63658C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#10591206C218yesmaximal, direct product factor
7C2×#4936—31nomaximal
8C2×#4650—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2212yes—
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C418yescomplemented
15C2×C3×C4×Dic3C2214yes—
16C2×Dic3⋊Dic3—28no—
17C2×Dic3⋊Dic3C2218yes—
18#63658C2214yes—
19C3×C3⋊#95C2214yes—
20#63579C2218yes—
21C22×C3×C42—31no—
22C22×C4⋊Dic3—32no—
23C22×Dic3⋊C4—32no—
24C22×C4×Dic3D311yescharacteristic
25C2×C3×#95—31no—
26C2×C3⋊#95—31no—
27C2×C3⋊#95—31no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95—61no—
31C2×C3⋊#95D311yescharacteristic
32#4936—38no—
33#4650—38no—
34C24×C32C2311yescharacteristic
35C22×C32×C4—24no—
36C22×C32×C4C2×C414yes—
37C22×C32×C4C2312yes—
38C22×C3⋊Dic3—24no—
39C22×C3⋊Dic3—24no—
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3C2314yes—
42C22×C3×Dic3—24no—
43C22×C3×Dic3—24no—
44C22×C3×Dic3—24no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3C2×C414yes—
47C22×C3×Dic3C2×C414yes—
48C22×C3×Dic3D414yes—
49C22×C3×Dic3Q814yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C3×C4×Dic3C2×C4116yescomplemented
54Dic3⋊Dic3—216no—
55C2×#382—91noSylow
56C23×C3×C4—21no—
57C23×C3×C4—31no—
58C23×C3×C4—31no—
59C23×C3×C4—32no—
60C23×C3×C4C2×D311yescharacteristic
61C23×C3×C4C2×D311yescharacteristic
62C23×Dic3—32no—
63C23×Dic3—32no—
64C23×Dic3—62no—
65C23×Dic3C2×D312yes—
66C23×Dic3C2×D311yescharacteristic
67C23×Dic3C2×D311yescharacteristic
68C2×C3×C42—38no—
69C2×C3×C42—34no—
70C2×C4⋊Dic3—38no—
71C2×C4⋊Dic3—68no—
72C2×Dic3⋊C4—38no—
73C2×Dic3⋊C4—68no—
74C2×C4×Dic3Dic318yescomplemented
75C2×C4×Dic3C2×D314yes—
76C3×#95—34no—
77C3⋊#95—34no—
78C3⋊#95—34no—
79C3⋊#95—38no—
80C3⋊#95—38no—
81C3⋊#95—64no—
82C3⋊#95C2×D314yes—
83C23×C32C22×C412yes—
84C23×C32C2×D412yes—
85C23×C32C2×Q812yes—
86C23×C32#4114yes—
87C23×C32#4114yes—
88C23×C32C2411yescharacteristic
89C2×C32×C4—28no—
90C2×C32×C4—24no—
91C2×C32×C4C22×C414yes—
92C2×C3⋊Dic3—24no—
93C2×C3⋊Dic3—24no—
94C2×C3⋊Dic3—24no—
95C2×C3⋊Dic3—48no—
96C2×C3×Dic3—28no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—48no—
102C2×C3×Dic3C4⋊C4116yes—
103C2×C3×Dic3C22×C414yes—
104C2×C3×Dic3C22×C414yes—
105C2×C3×Dic3C2×D414yes—
106C2×C3×Dic3C2×Q814yes—
107C22×C4⋊C4—92no—
108C22×C42—31no—
109#382—98no—
110C2×#95—31no—
111C2×#95—92no—
112C2×#95—91no—
113C24×C3—21no—
114C24×C3C22×D311yescharacteristic
115C24×C3C22×D311yescharacteristic
116C22×C3×C4—24no—
117C22×C3×C4—24no—
118C22×C3×C4—24no—
119C22×C3×C4—22no—
120C22×C3×C4—34no—
121C22×C3×C4—34no—
122C22×C3×C4—34no—
123C22×C3×C4—32no—
124C22×C3×C4—34no—
125C22×C3×C4—32no—
126C22×C3×C4—34no—
127C22×C3×C4—44no—
128C22×C3×C4—64no—
129C22×C3×C4—64no—
130C22×C3×C4—64no—
131C22×C3×C4—64no—
132C22×C3×C4C4×D314yes—
133C22×C3×C4C2×Dic314yes—
134C22×C3×C4C22×D312yes—
135C22×C3×C4C22×D312yes—
136C22×Dic3—24no—
137C22×Dic3—24no—
138C22×Dic3—24no—
139C22×Dic3—24no—
140C22×Dic3—34no—
141C22×Dic3—34no—
142C22×Dic3—64no—
143C22×Dic3—68no—
144C22×Dic3—64no—
145C22×Dic3—64no—
146C22×Dic3—64no—
147C22×Dic3—64no—
148C22×Dic3—64no—
149C22×Dic3—64no—
150C22×Dic3—124no—
151C22×Dic3—124no—
152C22×Dic3Dic614yes—
153C22×Dic3D1214yes—
154C22×Dic3C2×Dic314yes—
155C22×Dic3C2×Dic314yes—
156C22×Dic3C22×D314yes—
157C22×Dic3C22×D312yes—
158C22×Dic3C22×D312yes—
159C3×C42—316no—
160C4⋊Dic3—616no—
161Dic3⋊C4—616no—
162C4×Dic3C2×Dic3116yescomplemented
163C22×C32C2×C4⋊C414yes—
164C22×C32#11714yes—
165C22×C32#11714yes—
166C22×C32#12418yes—
167C22×C32#12518yes—
168C22×C32C23×C411yescharacteristic
169C22×C32C22×D411yescharacteristic
170C22×C32C22×Q811yescharacteristic
171C22×C32C2×#4112yes—
172C22×C32C2×#4112yes—
173C32×C4—24no—
174C3⋊Dic3—44no—
175C3×Dic3—24no—
176C3×Dic3—44no—
177C3×Dic3C2×C4⋊C418yes—
178C23×C4—31no—
179C23×C4—31no—
180C23×C4—32no—
181C23×C4—92no—
182C23×C4D3211yescharacteristic
183C2×C4⋊C4—98no—
184C2×C4⋊C4—188no—
185C2×C42—38no—
186C2×C42—34no—
187#95—34no—
188#95—98no—
189#95—94no—
190C23×C3—21no—
191C23×C3—22no—
192C23×C3—24no—
193C23×C3—22no—
194C23×C3—22no—
195C23×C3—24no—
196C23×C3C2×Dic612yes—
197C23×C3C2×C4×D312yes—
198C23×C3C2×D1212yes—
199C23×C3#23514yes—
200C23×C3#23514yes—
201C23×C3#23514yes—
202C23×C3D3×D412yes—
203C23×C3#23714yes—
204C23×C3D3×Q812yes—
205C23×C3C22×Dic312yes—
206C23×C3C23×D311yescharacteristic
207C23×C3C23×D311yescharacteristic
208C2×C3×C4—28no—
209C2×C3×C4—28no—
210C2×C3×C4—24no—
211C2×C3×C4—24no—
212C2×C3×C4—24no—
213C2×C3×C4—316no—
214C2×C3×C4—34no—
215C2×C3×C4—34no—
216C2×C3×C4—34no—
217C2×C3×C4—34no—
218C2×C3×C4—44no—
219C2×C3×C4—48no—
220C2×C3×C4—68no—
221C2×C3×C4—64no—
222C2×C3×C4—64no—
223C2×C3×C4—64no—
224C2×C3×C4—64no—
225C2×C3×C4—128no—
226C2×C3×C4C2×C4×D314yes—
227C2×C3×C4C22×Dic314yes—
228C2×Dic3—28no—
229C2×Dic3—24no—
230C2×Dic3—24no—
231C2×Dic3—24no—
232C2×Dic3—24no—
233C2×Dic3—48no—
234C2×Dic3—68no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—124no—
242C2×Dic3—124no—
243C2×Dic3—1216no—
244C2×Dic3—128no—
245C2×Dic3—128no—
246C2×Dic3C4⋊Dic3116yes—
247C2×Dic3C2×Dic614yes—
248C2×Dic3C2×D1214yes—
249C2×Dic3C22×Dic314yes—
250C2×Dic3C22×Dic314yes—
251C2×C32#38218yescomplemented
252C2×C32C22×C4⋊C411yescharacteristic
253C2×C32C2×#11711yescharacteristic
254C2×C32C2×#11711yescharacteristic
255C2×C32C2×#12412yes—
256C2×C32C2×#12512yes—
257C24C2×D3211yescharacteristic
258C22×C4—24no—
259C22×C4—32no—
260C22×C4—34no—
261C22×C4—34no—
262C22×C4—34no—
263C22×C4—32no—
264C22×C4—34no—
265C22×C4—34no—
266C22×C4—64no—
267C22×C4—64no—
268C22×C4—64no—
269C22×C4—64no—
270C22×C4—94no—
271C22×C4—184no—
272C22×C4—184no—
273C22×C4—184no—
274C22×C4D3×Dic314yes—
275C22×C4C2×D3212yes—
276C4⋊C4—1816no—
277C42—316no—
278C22×C3—21no—
279C22×C3—22no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—22no—
283C22×C3—28no—
284C22×C3—24no—
285C22×C3—28no—
286C22×C3—24no—
287C22×C3—24no—
288C22×C3#87018yes—
289C22×C3#87214yes—
290C22×C3#87518yes—
291C22×C3#87714yes—
292C22×C3#88518yes—
293C22×C3#88918yes—
294C22×C3D3×C4⋊C414yes—
295C22×C3C2×C4⋊Dic314yes—
296C22×C3#92614yes—
297C22×C3#92614yes—
298C22×C3C22×Dic611yescharacteristic
299C22×C3C22×C4×D311yescharacteristic
300C22×C3C22×D1211yescharacteristic
301C22×C3C2×#23512yes—
302C22×C3C2×#23512yes—
303C22×C3C2×#23512yes—
304C22×C3C2×D3×D411yescharacteristic
305C22×C3C2×#23712yes—
306C22×C3C2×D3×Q811yescharacteristic
307C22×C3C23×Dic311yescharacteristic
308C3×C4—24no—
309C3×C4—24no—
310C3×C4—38no—
311C3×C4—44no—
312C3×C4—64no—
313C3×C4—124no—
314Dic3—24no—
315Dic3—44no—
316Dic3—128no—
317Dic3—124no—
318Dic3—124no—
319Dic3C2×C4⋊Dic318yes—
320C32C2×#38211yescharacteristic, complemented, Sylow
321C23D3×Dic612yes—
322C23#379814yes—
323C23D3×D1212yes—
324C23C2×D3×Dic312yes—
325C23#380414yes—
326C23C22×D3211yescharacteristic
327C2×C4—24no—
328C2×C4—28no—
329C2×C4—34no—
330C2×C4—34no—
331C2×C4—34no—
332C2×C4—316no—
333C2×C4—34no—
334C2×C4—64no—
335C2×C4—68no—
336C2×C4—64no—
337C2×C4—64no—
338C2×C4—64no—
339C2×C4—128no—
340C2×C4—184no—
341C2×C4—184no—
342C2×C4—184no—
343C2×C4—368no—
344C2×C4C2×D3×Dic314yes—
345C2×C3—22no—
346C2×C3—21no—
347C2×C3—22no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—28no—
351C2×C3#465018yescomplemented
352C2×C3#493618yescomplemented
353C2×C3C2×#87012yes—
354C2×C3C2×#87211yescharacteristic
355C2×C3C2×#87512yes—
356C2×C3C2×#87711yescharacteristic
357C2×C3C2×#88512yes—
358C2×C3C2×#88912yes—
359C2×C3C2×D3×C4⋊C411yescharacteristic
360C2×C3C22×C4⋊Dic311yescharacteristic
361C2×C3C2×#92611yescharacteristic
362C2×C3C2×#92611yescharacteristic
363C22#6385218yes—
364C22#6385514yes—
365C22#6386718yes—
366C22D3×C4⋊Dic314yes—
367C22#6395514yes—
368C22C2×D3×Dic611yescharacteristic
369C22C2×#379812yes—
370C22C2×D3×D1211yescharacteristic
371C22C22×D3×Dic311yescharacteristic
372C22C2×#380412yes—
373C4—24no—
374C4—38no—
375C4—64no—
376C4—124no—
377C4—364no—
378C3—21no—
379C3C2×#465011yescharacteristic, complemented
380C3C2×#493611yescharacteristic, complemented
381C2#1059120618yesdirect product factor
382C2C2×#6385212yes—
383C2C2×#6385511yescharacteristic
384C2C2×#6386712yes—
385C2C2×D3×C4⋊Dic311yescharacteristic
386C2C2×#6395511yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#382
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591206C2direct (N × H)
14. C2×C3×C4×Dic3C4semidirect
53. C3×C4×Dic3C2×C4semidirect
74. C2×C4×Dic3Dic3semidirect
162. C4×Dic3C2×Dic3semidirect
251. C2×C32#382semidirect
320. C32C2×#382semidirect
351. C2×C3#4650semidirect
352. C2×C3#4936semidirect
379. C3C2×#4650semidirect
380. C3C2×#4936semidirect
381. C2#10591206direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×Dic32
C22×Dic3⋊Dic32
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#105912062
C2×#49363
C2×#46503