Finite Group Databasebeta

← C2×#10591226 #11808519

Subgroups — C2×#10591226 #11808519

Order 1152.

1417 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×#63579C212yesmaximal
5C2×#63579C212yesmaximal
6#10591226C218yesmaximal, direct product factor
7C2×#4986—31nomaximal
8C2×#4659—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2212yes—
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)—24no—
15C2×C4⋊(C3⋊Dic3)C2214yes—
16C2×C3×Dic3⋊C4—24no—
17C2×C3×Dic3⋊C4C2214yes—
18C3×C3⋊#95C2214yes—
19#63579C2218yes—
20#63579C2218yes—
21C22×C3×C4⋊C4—31no—
22C22×C4⋊Dic3—31no—
23C22×C4⋊Dic3—31no—
24C22×C4⋊Dic3—61no—
25C22×Dic3⋊C4D311yescharacteristic
26C2×C3×#95—31no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95D311yescharacteristic
32#4986—38no—
33#4659—38no—
34C24×C32C2311yescharacteristic
35C22×C32×C4—24no—
36C22×C32×C4D414yes—
37C22×C32×C4C2312yes—
38C22×C3⋊Dic3—24no—
39C22×C3⋊Dic3—28no—
40C22×C3⋊Dic3C2314yes—
41C22×C3×Dic3—22no—
42C22×C3×Dic3—22no—
43C22×C3×Dic3—22no—
44C22×C3×Dic3—24no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3Q814yes—
49C22×C3×Dic3C2312yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2312yes—
52C4⋊(C3⋊Dic3)—28no—
53C3×Dic3⋊C4—28no—
54C2×#400—91noSylow
55C23×C3×C4—21no—
56C23×C3×C4—31no—
57C23×C3×C4—32no—
58C23×C3×C4—31no—
59C23×C3×C4C2×D311yescharacteristic
60C23×C3×C4C2×D311yescharacteristic
61C23×Dic3—32no—
62C23×Dic3—32no—
63C23×Dic3—62no—
64C23×Dic3C2×D312yes—
65C23×Dic3C2×D311yescharacteristic
66C23×Dic3C2×D311yescharacteristic
67C2×C3×C4⋊C4—34no—
68C2×C3×C4⋊C4—64no—
69C2×C4⋊Dic3—34no—
70C2×C4⋊Dic3—34no—
71C2×C4⋊Dic3—64no—
72C2×C4⋊Dic3—68no—
73C2×C4⋊Dic3—64no—
74C2×C4⋊Dic3—64no—
75C2×Dic3⋊C4—24no—
76C2×Dic3⋊C4C2×D314yes—
77C3×#95—34no—
78C3⋊#95—38no—
79C3⋊#95—38no—
80C3⋊#95—38no—
81C3⋊#95—38no—
82C3⋊#95C2×D314yes—
83C23×C32C2×D412yes—
84C23×C32C2×Q812yes—
85C23×C32#4112yes—
86C23×C32#4114yes—
87C23×C32#4114yes—
88C23×C32C2411yescharacteristic
89C2×C32×C4—28no—
90C2×C32×C4—24no—
91C2×C32×C4C2×D414yes—
92C2×C3⋊Dic3—24no—
93C2×C3⋊Dic3—28no—
94C2×C3⋊Dic3—48no—
95C2×C3×Dic3—28no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—44no—
104C2×C3×Dic3—48no—
105C2×C3×Dic3C2×Q814yes—
106C22×C4⋊C4—31no—
107C22×C4⋊C4—91no—
108#400—98no—
109C2×#95—31no—
110C2×#95—92no—
111C2×#95—92no—
112C24×C3—21no—
113C24×C3C22×D311yescharacteristic
114C24×C3C22×D311yescharacteristic
115C22×C3×C4—28no—
116C22×C3×C4—24no—
117C22×C3×C4—24no—
118C22×C3×C4—24no—
119C22×C3×C4—22no—
120C22×C3×C4—34no—
121C22×C3×C4—32no—
122C22×C3×C4—34no—
123C22×C3×C4—32no—
124C22×C3×C4—62no—
125C22×C3×C4—62no—
126C22×C3×C4—62no—
127C22×C3×C4—64no—
128C22×C3×C4—64no—
129C22×C3×C4—64no—
130C22×C3×C4—64no—
131C22×C3×C4D1214yes—
132C22×C3×C4#6714yes—
133C22×C3×C4C22×D312yes—
134C22×C3×C4C22×D312yes—
135C22×Dic3—22no—
136C22×Dic3—22no—
137C22×Dic3—24no—
138C22×Dic3—24no—
139C22×Dic3—24no—
140C22×Dic3—24no—
141C22×Dic3—22no—
142C22×Dic3—34no—
143C22×Dic3—34no—
144C22×Dic3—64no—
145C22×Dic3—68no—
146C22×Dic3—64no—
147C22×Dic3—68no—
148C22×Dic3—68no—
149C22×Dic3—64no—
150C22×Dic3—128no—
151C22×Dic3Dic614yes—
152C22×Dic3C22×D314yes—
153C22×Dic3C22×D312yes—
154C22×Dic3C22×D312yes—
155C3×C4⋊C4—68no—
156C4⋊Dic3—616no—
157C4⋊Dic3—68no—
158C4⋊Dic3—68no—
159Dic3⋊C4—28no—
160C22×C32C22⋊Q814yes—
161C22×C32#12314yes—
162C22×C32#12414yes—
163C22×C32#12518yes—
164C22×C32#12618yes—
165C22×C32C22×D411yescharacteristic
166C22×C32C22×Q811yescharacteristic
167C22×C32C2×#4111yescharacteristic
168C22×C32C2×#4112yes—
169C22×C32C2×#4112yes—
170C32×C4—24no—
171C3⋊Dic3—44no—
172C3×Dic3—24no—
173C3×Dic3—42no—
174C3×Dic3—44no—
175C23×C4—31no—
176C23×C4—31no—
177C23×C4—32no—
178C23×C4—92no—
179C23×C4D3211yescharacteristic
180C2×C4⋊C4—34no—
181C2×C4⋊C4—64no—
182C2×C4⋊C4—94no—
183C2×C4⋊C4—184no—
184#95—34no—
185#95—98no—
186#95—98no—
187C23×C3—21no—
188C23×C3—22no—
189C23×C3—22no—
190C23×C3—24no—
191C23×C3—24no—
192C23×C3—22no—
193C23×C3C2×Dic612yes—
194C23×C3C2×D1212yes—
195C23×C3#23512yes—
196C23×C3#23514yes—
197C23×C3#23712yes—
198C23×C3#23714yes—
199C23×C3#23714yes—
200C23×C3D3×Q812yes—
201C23×C3#23914yes—
202C23×C3C2×#6712yes—
203C23×C3C23×D311yescharacteristic
204C23×C3C23×D311yescharacteristic
205C2×C3×C4—28no—
206C2×C3×C4—216no—
207C2×C3×C4—28no—
208C2×C3×C4—28no—
209C2×C3×C4—24no—
210C2×C3×C4—24no—
211C2×C3×C4—24no—
212C2×C3×C4—34no—
213C2×C3×C4—68no—
214C2×C3×C4—62no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—64no—
218C2×C3×C4—64no—
219C2×C3×C4—64no—
220C2×C3×C4—64no—
221C2×C3×C4—124no—
222C2×C3×C4—128no—
223C2×C3×C4C2×D1214yes—
224C2×C3×C4C2×#6714yes—
225C2×Dic3—28no—
226C2×Dic3—22no—
227C2×Dic3—22no—
228C2×Dic3—24no—
229C2×Dic3—24no—
230C2×Dic3—24no—
231C2×Dic3—24no—
232C2×Dic3—22no—
233C2×Dic3—48no—
234C2×Dic3—44no—
235C2×Dic3—68no—
236C2×Dic3—64no—
237C2×Dic3—68no—
238C2×Dic3—68no—
239C2×Dic3—64no—
240C2×Dic3—128no—
241C2×Dic3—1216no—
242C2×Dic3—128no—
243C2×Dic3—128no—
244C2×Dic3C2×Dic614yes—
245C2×C32#40018yescomplemented
246C2×C32C2×C22⋊Q811yescharacteristic
247C2×C32C2×#12311yescharacteristic
248C2×C32C2×#12411yescharacteristic
249C2×C32C2×#12512yes—
250C2×C32C2×#12612yes—
251C24C2×D3211yescharacteristic
252C22×C4—24no—
253C22×C4—32no—
254C22×C4—34no—
255C22×C4—34no—
256C22×C4—32no—
257C22×C4—62no—
258C22×C4—62no—
259C22×C4—64no—
260C22×C4—64no—
261C22×C4—64no—
262C22×C4—64no—
263C22×C4—62no—
264C22×C4—94no—
265C22×C4—188no—
266C22×C4—184no—
267C22×C4#62614yes—
268C22×C4C2×D3212yes—
269C4⋊C4—68no—
270C4⋊C4—188no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—21no—
276C22×C3—28no—
277C22×C3—24no—
278C22×C3—28no—
279C22×C3—24no—
280C22×C3—24no—
281C22×C3#87514yes—
282C22×C3#87918yes—
283C22×C3#88614yes—
284C22×C3#88918yes—
285C22×C3#89018yes—
286C22×C3#89714yes—
287C22×C3#89818yes—
288C22×C3#92414yes—
289C22×C3#93514yes—
290C22×C3#94714yes—
291C22×C3C22×Dic611yescharacteristic
292C22×C3C22×D1211yescharacteristic
293C22×C3C2×#23511yescharacteristic
294C22×C3C2×#23512yes—
295C22×C3C2×#23711yescharacteristic
296C22×C3C2×#23712yes—
297C22×C3C2×#23712yes—
298C22×C3C2×D3×Q811yescharacteristic
299C22×C3C2×#23912yes—
300C22×C3C22×#6711yescharacteristic
301C3×C4—28no—
302C3×C4—24no—
303C3×C4—24no—
304C3×C4—64no—
305C3×C4—122no—
306C3×C4—124no—
307Dic3—24no—
308Dic3—44no—
309Dic3—42no—
310Dic3—128no—
311Dic3—124no—
312Dic3—124no—
313C32C2×#40011yescharacteristic, complemented, Sylow
314C23D3×Dic612yes—
315C23#379512yes—
316C23#379914yes—
317C23#380514yes—
318C23C2×#62612yes—
319C23C22×D3211yescharacteristic
320C2×C4—24no—
321C2×C4—28no—
322C2×C4—34no—
323C2×C4—62no—
324C2×C4—62no—
325C2×C4—68no—
326C2×C4—64no—
327C2×C4—64no—
328C2×C4—64no—
329C2×C4—64no—
330C2×C4—62no—
331C2×C4—128no—
332C2×C4—124no—
333C2×C4—188no—
334C2×C4—184no—
335C2×C4—368no—
336C2×C4C2×#62614yes—
337C2×C3—22no—
338C2×C3—21no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—28no—
343C2×C3#465918yescomplemented
344C2×C3#498618yescomplemented
345C2×C3C2×#87511yescharacteristic
346C2×C3C2×#87912yes—
347C2×C3C2×#88611yescharacteristic
348C2×C3C2×#88912yes—
349C2×C3C2×#89012yes—
350C2×C3C2×#89711yescharacteristic
351C2×C3C2×#89812yes—
352C2×C3C2×#92411yescharacteristic
353C2×C3C2×#93511yescharacteristic
354C2×C3C2×#94711yescharacteristic
355C22#6384518yes—
356C22#6385714yes—
357C22#6386118yes—
358C22#6386414yes—
359C22#6396214yes—
360C22C2×D3×Dic611yescharacteristic
361C22C2×#379511yescharacteristic
362C22C2×#379912yes—
363C22C2×#380512yes—
364C22C22×#62611yescharacteristic
365C4—24no—
366C4—64no—
367C4—124no—
368C4—122no—
369C4—364no—
370C3—21no—
371C3C2×#465911yescharacteristic, complemented
372C3C2×#498611yescharacteristic, complemented
373C2#1059122618yesdirect product factor
374C2C2×#6384512yes—
375C2C2×#6385711yescharacteristic
376C2C2×#6386112yes—
377C2C2×#6386411yescharacteristic
378C2C2×#6396211yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#400
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591226C2direct (N × H)
245. C2×C32#400semidirect
313. C32C2×#400semidirect
343. C2×C3#4659semidirect
344. C2×C3#4986semidirect
371. C3C2×#4659semidirect
372. C3C2×#4986semidirect
373. C2#10591226direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C22×C3×Dic3⋊C42
C2×C3×C3⋊#952
C2×#635792
#105912262
C2×#49863
C2×#46593