Finite Group Databasebeta

← C2×#10591236 #11801730

Subgroups — C2×#10591236 #11801730

Order 1152.

2065 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#627C211yesmaximal, characteristic
2C22×#3750C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×#63579C212yesmaximal
6#10591236C218yesmaximal, direct product factor
7C2×#4646—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C22×#627—24no—
14C22×#627—24no—
15C22×#627C418yescomplemented
16C22×#627C2214yes—
17C2×#3750—24no—
18C2×#3750C2214yes—
19C2×Dic32—24no—
20C2×Dic32C2214yes—
21C3×C3⋊#95C2218yes—
22#63579C2218yes—
23C23×Dic6—32no—
24C22×Dic3⋊C4—32no—
25C22×Dic3⋊C4—61no—
26C22×C4×Dic3—32no—
27C2×C3×#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95D312yes—
31#4646—316no—
32C24×C32C2311yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4—24no—
35C22×C32×C4C2312yes—
36C22×C3⋊Dic3—22no—
37C22×C3⋊Dic3—24no—
38C22×C3⋊Dic3C2×C414yes—
39C22×C3⋊Dic3D414yes—
40C22×C3⋊Dic3D414yes—
41C22×C3⋊Dic3C2312yes—
42C22×C3⋊Dic3C2312yes—
43C22×C3×Dic3—24no—
44C22×C3×Dic3—24no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3—24no—
47C22×C3×Dic3C2×C418yes—
48C22×C3×Dic3Q818yescomplemented
49C22×C3×Dic3C2314yes—
50C22×C3×Dic3C2314yes—
51C2×#627—232no—
52C2×#627—28no—
53C2×#627—28no—
54C2×#627C2×C4116yescomplemented
55#3750—28no—
56Dic32—28no—
57C2×#391—91noSylow
58C23×C3×C4—21no—
59C23×C3×C4—32no—
60C23×C3×C4—32no—
61C23×C3×C4C2×D312yes—
62C23×Dic3—32no—
63C23×Dic3—32no—
64C23×Dic3—61no—
65C23×Dic3—61no—
66C23×Dic3C2×D312yes—
67C23×Dic3C2×D312yes—
68C22×Dic6—316no—
69C22×Dic6—38no—
70C22×Dic6—68no—
71C22×Dic6—68no—
72C2×Dic3⋊C4—38no—
73C2×Dic3⋊C4—64no—
74C2×Dic3⋊C4—68no—
75C2×Dic3⋊C4—68no—
76C2×C4×Dic3—38no—
77C2×C4×Dic3—68no—
78C3×#95—38no—
79C3⋊#95—38no—
80C3⋊#95—38no—
81C3⋊#95C2×D318yes—
82C23×C32C22×C412yes—
83C23×C32C2×D412yes—
84C23×C32C2×D412yes—
85C23×C32C2×Q814yes—
86C23×C32#4114yes—
87C23×C32C2411yescharacteristic
88C2×C32×C4—22no—
89C2×C32×C4—24no—
90C2×C32×C4—44no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—24no—
93C2×C3⋊Dic3—44no—
94C2×C3⋊Dic3C22⋊C4116yes—
95C2×C3⋊Dic3C22×C414yes—
96C2×C3⋊Dic3C2×D414yes—
97C2×C3⋊Dic3C2×D414yes—
98C2×C3×Dic3—216no—
99C2×C3×Dic3—216no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3C22×C418yes—
105C2×C3×Dic3C2×Q818yescomplemented
106#627—232no—
107C23×Q8—91no—
108C22×C4⋊C4—91no—
109C22×C42—91no—
110#391—98no—
111C2×#95—32no—
112C2×#95—92no—
113C24×C3—21no—
114C24×C3C22×D312yes—
115C22×C3×C4—24no—
116C22×C3×C4—24no—
117C22×C3×C4—24no—
118C22×C3×C4—24no—
119C22×C3×C4—22no—
120C22×C3×C4—38no—
121C22×C3×C4—38no—
122C22×C3×C4—34no—
123C22×C3×C4—34no—
124C22×C3×C4—44no—
125C22×C3×C4—64no—
126C22×C3×C4—64no—
127C22×C3×C4—64no—
128C22×C3×C4—64no—
129C22×C3×C4C22×D314yes—
130C22×Dic3—24no—
131C22×Dic3—24no—
132C22×Dic3—24no—
133C22×Dic3—24no—
134C22×Dic3—38no—
135C22×Dic3—38no—
136C22×Dic3—38no—
137C22×Dic3—34no—
138C22×Dic3—34no—
139C22×Dic3—64no—
140C22×Dic3—62no—
141C22×Dic3—64no—
142C22×Dic3—64no—
143C22×Dic3—62no—
144C22×Dic3—64no—
145C22×Dic3—64no—
146C22×Dic3—64no—
147C22×Dic3—64no—
148C22×Dic3—124no—
149C22×Dic3Dic618yescomplemented
150C22×Dic3C4×D318yes—
151C22×Dic3C22×D314yes—
152C22×Dic3C22×D314yes—
153C2×Dic6—332no—
154C2×Dic6—664no—
155C2×Dic6—616no—
156C2×Dic6—616no—
157Dic3⋊C4—616no—
158Dic3⋊C4—616no—
159C4×Dic3—616no—
160C22×C32C2×C22⋊C414yes—
161C22×C32C4×Q818yes—
162C22×C32C22⋊Q818yes—
163C22×C32#12414yes—
164C22×C32C4⋊Q814yes—
165C22×C32C23×C411yescharacteristic
166C22×C32C22×D411yescharacteristic
167C22×C32C22×D411yescharacteristic
168C22×C32C22×Q812yes—
169C22×C32C2×#4112yes—
170C32×C4—42no—
171C3⋊Dic3—42no—
172C3⋊Dic3C2×C22⋊C418yes—
173C3×Dic3—28no—
174C3×Dic3—28no—
175C22×Q8—94no—
176C22×Q8—98no—
177C22×Q8—184no—
178C22×Q8—184no—
179C23×C4—32no—
180C23×C4—32no—
181C23×C4—91no—
182C23×C4—91no—
183C23×C4D3211yescharacteristic
184C2×C4⋊C4—94no—
185C2×C4⋊C4—184no—
186C2×C42—94no—
187C2×C42—184no—
188#95—38no—
189#95—98no—
190C23×C3—21no—
191C23×C3—24no—
192C23×C3—22no—
193C23×C3—22no—
194C23×C3—24no—
195C23×C3—22no—
196C23×C3C2×Dic614yes—
197C23×C3C2×C4×D314yes—
198C23×C3#23514yes—
199C23×C3D3×D414yes—
200C23×C3D3×D414yes—
201C23×C3#23714yes—
202C23×C3D3×Q814yes—
203C23×C3C23×D312yes—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—38no—
209C2×C3×C4—38no—
210C2×C3×C4—44no—
211C2×C3×C4—48no—
212C2×C3×C4—48no—
213C2×C3×C4—616no—
214C2×C3×C4—616no—
215C2×C3×C4—64no—
216C2×C3×C4—64no—
217C2×C3×C4—64no—
218C2×C3×C4—64no—
219C2×Dic3—216no—
220C2×Dic3—216no—
221C2×Dic3—24no—
222C2×Dic3—24no—
223C2×Dic3—24no—
224C2×Dic3—24no—
225C2×Dic3—332no—
226C2×Dic3—38no—
227C2×Dic3—38no—
228C2×Dic3—38no—
229C2×Dic3—616no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—124no—
238C2×Dic3—128no—
239C2×Dic3—128no—
240C2×Dic3C2×Dic618yescomplemented
241C2×Dic3C2×C4×D318yes—
242Dic6—664no—
243C2×C32#39118yescomplemented
244C2×C32C22×C22⋊C411yescharacteristic
245C2×C32C2×C4×Q812yes—
246C2×C32C2×C22⋊Q812yes—
247C2×C32C2×#12411yescharacteristic
248C2×C32C2×C4⋊Q811yescharacteristic
249C24C2×D3211yescharacteristic
250C2×Q8—916no—
251C2×Q8—188no—
252C2×Q8—188no—
253C2×Q8—1832no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—34no—
257C22×C4—34no—
258C22×C4—38no—
259C22×C4—38no—
260C22×C4—64no—
261C22×C4—64no—
262C22×C4—64no—
263C22×C4—64no—
264C22×C4—92no—
265C22×C4—94no—
266C22×C4—94no—
267C22×C4—94no—
268C22×C4—92no—
269C22×C4—184no—
270C22×C4—182no—
271C22×C4C2×D3212yes—
272C4⋊C4—188no—
273C42—188no—
274C22×C3—22no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—22no—
278C22×C3—21no—
279C22×C3—28no—
280C22×C3—24no—
281C22×C3—28no—
282C22×C3—24no—
283C22×C3—24no—
284C22×C3C4×Dic618yes—
285C22×C3#87818yes—
286C22×C3D3×C22⋊C418yes—
287C22×C3#88518yes—
288C22×C3#88718yes—
289C22×C3#88818yes—
290C22×C3#89618yes—
291C22×C3C22×Dic612yes—
292C22×C3C22×C4×D312yes—
293C22×C3C2×#23512yes—
294C22×C3C2×D3×D412yes—
295C22×C3C2×D3×D412yes—
296C22×C3C2×#23712yes—
297C22×C3C2×D3×Q812yes—
298C3×C4—44no—
299C3×C4—44no—
300C3×C4—68no—
301C3×C4—68no—
302Dic3—28no—
303Dic3—28no—
304Dic3—316no—
305Dic3—68no—
306Dic3—124no—
307Dic3—124no—
308C32C2×#39111yescharacteristic, complemented, Sylow
309C23D3×Dic614yes—
310C23C4×D3212yes—
311C23#380212yes—
312C23#380414yes—
313C23#381112yes—
314C23C22×D3211yescharacteristic
315Q8—1832no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—38no—
319C2×C4—38no—
320C2×C4—44no—
321C2×C4—64no—
322C2×C4—64no—
323C2×C4—64no—
324C2×C4—64no—
325C2×C4—616no—
326C2×C4—616no—
327C2×C4—94no—
328C2×C4—94no—
329C2×C4—94no—
330C2×C4—916no—
331C2×C4—184no—
332C2×C4—182no—
333C2×C4—364no—
334C2×C3—28no—
335C2×C3—22no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—22no—
339C2×C3—21no—
340C2×C3#4646116yescomplemented
341C2×C3C2×C4×Dic612yes—
342C2×C3C2×#87812yes—
343C2×C3C2×D3×C22⋊C412yes—
344C2×C3C2×#88512yes—
345C2×C3C2×#88712yes—
346C2×C3C2×#88812yes—
347C2×C3C2×#89612yes—
348C22#6383718yes—
349C22#6384014yes—
350C22#6389918yes—
351C22#6392114yes—
352C22#6395314yes—
353C22C2×D3×Dic612yes—
354C22C2×C4×D3211yescharacteristic
355C22C2×#380211yescharacteristic
356C22C2×#380412yes—
357C22C2×#381111yescharacteristic
358C4—42no—
359C4—68no—
360C4—68no—
361C4—98no—
362C4—362no—
363C3—21no—
364C3C2×#464612yescomplemented
365C2#1059123618yesdirect product factor
366C2C2×#6383712yes—
367C2C2×#6384011yescharacteristic
368C2C2×#6389912yes—
369C2C2×#6392111yescharacteristic
370C2C2×#6395311yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#391
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591236C2direct (N × H)
15. C22×#627C4semidirect
48. C22×C3×Dic3Q8semidirect
54. C2×#627C2×C4semidirect
105. C2×C3×Dic3C2×Q8semidirect
149. C22×Dic3Dic6semidirect
240. C2×Dic3C2×Dic6semidirect
243. C2×C32#391semidirect
308. C32C2×#391semidirect
340. C2×C3#4646semidirect
364. C3C2×#4646semidirect
365. C2#10591236direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6272
C22×#37502
C22×Dic322
C2×C3×C3⋊#952
C2×#635792
#105912362
C2×#46463