Finite Group Databasebeta

← C2×#10591344 #11808194

Subgroups — C2×#10591344 #11808194

Order 1152.

1981 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C22×#3724C212yesmaximal
4C2×#63658C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#10591344C218yesmaximal, direct product factor
7C2×#5230—31nomaximal
8C2×#4979—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2212yes—
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2211yescharacteristic
14C22×C3×Dic6—24no—
15C22×C3×Dic6—28no—
16C22×C3×Dic6C2214yes—
17C2×C3×Dic3⋊C4—24no—
18C2×C3×Dic3⋊C4C2214yes—
19C2×#3724—28no—
20C2×#3724C2218yes—
21#63658C2214yes—
22#63579C2218yes—
23C23×C3×Q8—31no—
24C23×Dic6D311yescharacteristic
25C22×C3×C4⋊C4—31no—
26C22×Dic3⋊C4—32no—
27C22×Dic3⋊C4—32no—
28C22×Dic3⋊C4D311yescharacteristic
29#5230—38no—
30C2×C3⋊#95—31no—
31C2×C3⋊#95—31no—
32C2×C3⋊#95—32no—
33C2×C3⋊#95—32no—
34C2×C3⋊#95—61no—
35#4979—38no—
36C24×C32C2311yescharacteristic
37C22×C32×C4—24no—
38C22×C32×C4D414yes—
39C22×C32×C4C2312yes—
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3Q818yescomplemented
43C22×C3⋊Dic3C2314yes—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—24no—
50C22×C3×Dic3D418yes—
51C22×C3×Dic3Q814yescomplemented
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2314yes—
54C22×C3×Dic3C2312yes—
55C2×C3×Dic6—232no—
56C2×C3×Dic6—28no—
57C2×C3×Dic6—216no—
58C3×Dic3⋊C4—28no—
59#3724—216no—
60C2×#395—91noSylow
61C22×C3×Q8—34no—
62C22×C3×Q8—68no—
63C22×C3×Q8—64no—
64C23×C3×C4—21no—
65C23×C3×C4—32no—
66C23×C3×C4—31no—
67C23×C3×C4—31no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C2×D311yescharacteristic
70C23×Dic3—32no—
71C23×Dic3—32no—
72C23×Dic3—62no—
73C23×Dic3C2×D311yescharacteristic
74C23×Dic3C2×D311yescharacteristic
75C23×Dic3C2×D312yes—
76C22×Dic6—24no—
77C22×Dic6—28no—
78C22×Dic6C2×D314yes—
79C2×C3×C4⋊C4—34no—
80C2×C3×C4⋊C4—64no—
81C2×Dic3⋊C4—24no—
82C2×Dic3⋊C4—38no—
83C2×Dic3⋊C4—38no—
84C2×Dic3⋊C4—68no—
85C2×Dic3⋊C4—68no—
86C2×Dic3⋊C4C2×D314yes—
87C3⋊#95—34no—
88C3⋊#95—34no—
89C3⋊#95—38no—
90C3⋊#95—38no—
91C3⋊#95—64no—
92C23×C32C2×D414yes—
93C23×C32C2×D412yes—
94C23×C32C2×Q812yes—
95C23×C32C2×Q814yes—
96C23×C32#4112yes—
97C23×C32C2411yescharacteristic
98C2×C32×C4—28no—
99C2×C32×C4—24no—
100C2×C32×C4C2×D414yes—
101C2×C3⋊Dic3—216no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3C2×Q818yescomplemented
105C2×C3×Dic3—216no—
106C2×C3×Dic3—28no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—44no—
114C2×C3×Dic3C2×D418yes—
115C2×C3×Dic3C2×Q814yescomplemented
116C3×Dic6—232no—
117C23×Q8—31no—
118C22×C4⋊C4—31no—
119C22×C4⋊C4—92no—
120#395—98no—
121C2×#95—92no—
122C2×#95—91no—
123C24×C3—21no—
124C24×C3C22×D311yescharacteristic
125C24×C3C22×D311yescharacteristic
126C2×C3×Q8—616no—
127C2×C3×Q8—632no—
128C2×C3×Q8—68no—
129C22×C3×C4—24no—
130C22×C3×C4—24no—
131C22×C3×C4—24no—
132C22×C3×C4—22no—
133C22×C3×C4—38no—
134C22×C3×C4—34no—
135C22×C3×C4—32no—
136C22×C3×C4—34no—
137C22×C3×C4—32no—
138C22×C3×C4—44no—
139C22×C3×C4—64no—
140C22×C3×C4—62no—
141C22×C3×C4—62no—
142C22×C3×C4—64no—
143C22×C3×C4—64no—
144C22×C3×C4—62no—
145C22×C3×C4#6714yes—
146C22×C3×C4#6714yes—
147C22×C3×C4C22×D312yes—
148C22×C3×C4C22×D312yes—
149C22×Dic3—22no—
150C22×Dic3—22no—
151C22×Dic3—24no—
152C22×Dic3—24no—
153C22×Dic3—24no—
154C22×Dic3—22no—
155C22×Dic3—38no—
156C22×Dic3—38no—
157C22×Dic3—34no—
158C22×Dic3—34no—
159C22×Dic3—64no—
160C22×Dic3—68no—
161C22×Dic3—64no—
162C22×Dic3—64no—
163C22×Dic3—64no—
164C22×Dic3—64no—
165C22×Dic3—124no—
166C22×Dic3—124no—
167C22×Dic3Dic614yescomplemented
168C22×Dic3#6718yes—
169C22×Dic3C22×D312yes—
170C22×Dic3C22×D312yes—
171C22×Dic3C22×D314yes—
172C2×Dic6—232no—
173C2×Dic6—28no—
174C2×Dic6—216no—
175C3×C4⋊C4—68no—
176Dic3⋊C4—28no—
177Dic3⋊C4—616no—
178Dic3⋊C4—616no—
179C22×C32#12014yes—
180C22×C32C22⋊Q818yes—
181C22×C32C22⋊Q814yes—
182C22×C32C4⋊Q818yes—
183C22×C32C4⋊Q814yes—
184C22×C32C22×D412yes—
185C22×C32C22×D411yescharacteristic
186C22×C32C22×Q811yescharacteristic
187C22×C32C22×Q812yes—
188C22×C32C2×#4111yescharacteristic
189C32×C4—24no—
190C3⋊Dic3—28no—
191C3×Dic3—28no—
192C3×Dic3—24no—
193C3×Dic3—42no—
194C22×Q8—34no—
195C22×Q8—68no—
196C22×Q8—64no—
197C23×C4—31no—
198C23×C4—32no—
199C23×C4—31no—
200C23×C4—92no—
201C23×C4D3211yescharacteristic
202C2×C4⋊C4—34no—
203C2×C4⋊C4—64no—
204C2×C4⋊C4—98no—
205C2×C4⋊C4—188no—
206#95—98no—
207#95—94no—
208C23×C3—21no—
209C23×C3—22no—
210C23×C3—24no—
211C23×C3—22no—
212C23×C3—22no—
213C23×C3—24no—
214C23×C3C2×Dic612yes—
215C23×C3#23512yes—
216C23×C3D3×D414yes—
217C23×C3D3×Q812yes—
218C23×C3D3×Q814yes—
219C23×C3D3×Q814yes—
220C23×C3#23912yes—
221C23×C3C2×#6712yes—
222C23×C3C2×#6712yes—
223C23×C3C2×#6714yes—
224C23×C3C23×D311yescharacteristic
225C23×C3C23×D311yescharacteristic
226C3×Q8—632no—
227C2×C3×C4—28no—
228C2×C3×C4—28no—
229C2×C3×C4—24no—
230C2×C3×C4—24no—
231C2×C3×C4—24no—
232C2×C3×C4—38no—
233C2×C3×C4—34no—
234C2×C3×C4—44no—
235C2×C3×C4—48no—
236C2×C3×C4—616no—
237C2×C3×C4—68no—
238C2×C3×C4—64no—
239C2×C3×C4—62no—
240C2×C3×C4—62no—
241C2×C3×C4—64no—
242C2×C3×C4—64no—
243C2×C3×C4—62no—
244C2×C3×C4—124no—
245C2×C3×C4C2×#6714yes—
246C2×C3×C4C2×#6714yes—
247C2×Dic3—28no—
248C2×Dic3—216no—
249C2×Dic3—22no—
250C2×Dic3—22no—
251C2×Dic3—24no—
252C2×Dic3—24no—
253C2×Dic3—24no—
254C2×Dic3—22no—
255C2×Dic3—38no—
256C2×Dic3—38no—
257C2×Dic3—44no—
258C2×Dic3—68no—
259C2×Dic3—616no—
260C2×Dic3—616no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—124no—
266C2×Dic3—124no—
267C2×Dic3—1216no—
268C2×Dic3C2×Dic614yescomplemented
269C2×Dic3C2×#6718yes—
270Dic6—232no—
271C2×C32#39518yescomplemented
272C2×C32C2×#12011yescharacteristic
273C2×C32C2×C22⋊Q812yes—
274C2×C32C2×C22⋊Q811yescharacteristic
275C2×C32C2×C4⋊Q812yes—
276C2×C32C2×C4⋊Q811yescharacteristic
277C24C2×D3211yescharacteristic
278C2×Q8—616no—
279C2×Q8—632no—
280C2×Q8—68no—
281C22×C4—24no—
282C22×C4—32no—
283C22×C4—34no—
284C22×C4—34no—
285C22×C4—38no—
286C22×C4—32no—
287C22×C4—62no—
288C22×C4—62no—
289C22×C4—64no—
290C22×C4—64no—
291C22×C4—62no—
292C22×C4—64no—
293C22×C4—94no—
294C22×C4—98no—
295C22×C4—184no—
296C22×C4—184no—
297C22×C4#62514yes—
298C22×C4C2×D3212yes—
299C4⋊C4—68no—
300C4⋊C4—1816no—
301C22×C3—21no—
302C22×C3—22no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—22no—
306C22×C3—28no—
307C22×C3—24no—
308C22×C3—24no—
309C22×C3—28no—
310C22×C3—24no—
311C22×C3#88818yes—
312C22×C3#89618yes—
313C22×C3#92414yes—
314C22×C3#93714yes—
315C22×C3#94418yes—
316C22×C3#94414yes—
317C22×C3#94414yes—
318C22×C3#94614yes—
319C22×C3#94618yes—
320C22×C3#95314yes—
321C22×C3C22×Dic611yescharacteristic
322C22×C3C2×#23511yescharacteristic
323C22×C3C2×D3×D412yes—
324C22×C3C2×D3×Q811yescharacteristic
325C22×C3C2×D3×Q812yes—
326C22×C3C2×D3×Q812yes—
327C22×C3C2×#23911yescharacteristic
328C22×C3C22×#6711yescharacteristic
329C22×C3C22×#6711yescharacteristic
330C22×C3C22×#6712yes—
331C3×C4—24no—
332C3×C4—24no—
333C3×C4—44no—
334C3×C4—68no—
335C3×C4—64no—
336C3×C4—122no—
337Dic3—24no—
338Dic3—28no—
339Dic3—42no—
340Dic3—68no—
341Dic3—68no—
342Dic3—128no—
343C32C2×#39511yescharacteristic, complemented, Sylow
344C23D3×Dic612yes—
345C23#379714yes—
346C23#379912yes—
347C23C2×#62512yes—
348C23D3×#6714yes—
349C23C22×D3211yescharacteristic
350Q8—632no—
351C2×C4—24no—
352C2×C4—28no—
353C2×C4—34no—
354C2×C4—38no—
355C2×C4—62no—
356C2×C4—62no—
357C2×C4—64no—
358C2×C4—64no—
359C2×C4—68no—
360C2×C4—616no—
361C2×C4—62no—
362C2×C4—64no—
363C2×C4—98no—
364C2×C4—124no—
365C2×C4—184no—
366C2×C4—184no—
367C2×C4—1816no—
368C2×C4C2×#62514yes—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—22no—
372C2×C3—28no—
373C2×C3—21no—
374C2×C3—22no—
375C2×C3#497918yescomplemented
376C2×C3#523018yescomplemented
377C2×C3C2×#88812yes—
378C2×C3C2×#89612yes—
379C2×C3C2×#92411yescharacteristic
380C2×C3C2×#93711yescharacteristic
381C2×C3C2×#94411yescharacteristic
382C2×C3C2×#94411yescharacteristic
383C2×C3C2×#94412yes—
384C2×C3C2×#94611yescharacteristic
385C2×C3C2×#94612yes—
386C2×C3C2×#95311yescharacteristic
387C22#6383918yes—
388C22#6385614yes—
389C22#6387314yes—
390C22#6388818yes—
391C22#6397614yes—
392C22C2×D3×Dic611yescharacteristic
393C22C2×#379712yes—
394C22C2×#379911yescharacteristic
395C22C22×#62511yescharacteristic
396C22C2×D3×#6712yes—
397C4—24no—
398C4—64no—
399C4—68no—
400C4—122no—
401C4—188no—
402C3—21no—
403C3C2×#497911yescharacteristic, complemented
404C3C2×#523011yescharacteristic, complemented
405C2#1059134418yesdirect product factor
406C2C2×#6383912yes—
407C2C2×#6385611yescharacteristic
408C2C2×#6387311yescharacteristic
409C2C2×#6388812yes—
410C2C2×#6397611yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591344C2direct (N × H)
42. C22×C3⋊Dic3Q8semidirect
51. C22×C3×Dic3Q8semidirect
104. C2×C3⋊Dic3C2×Q8semidirect
115. C2×C3×Dic3C2×Q8semidirect
167. C22×Dic3Dic6semidirect
268. C2×Dic3C2×Dic6semidirect
271. C2×C32#395semidirect
343. C32C2×#395semidirect
375. C2×C3#4979semidirect
376. C2×C3#5230semidirect
403. C3C2×#4979semidirect
404. C3C2×#5230semidirect
405. C2#10591344direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C22×C3×Dic3⋊C42
C22×#37242
C2×#636582
C2×#635792
#105913442
C2×#52303
C2×#49793