Finite Group Databasebeta

← C2×#10591273 #11801737

Subgroups — C2×#10591273 #11801737

Order 1152.

2281 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#634C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×#63579C212yesmaximal
6#10591273C218yesmaximal, direct product factor
7C2×#4646—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C22×#634—24no—
12C22×#634—24no—
13C22×#634C418yescomplemented
14C22×#634C2214yes—
15C23×C3×Dic3C2212yes—
16C23×C3×Dic3C2212yes—
17C2×#3724—24no—
18C2×#3724C2214yes—
19C2×Dic32—24no—
20C2×Dic32C2214yes—
21C3×C3⋊#95C2218yes—
22#63579C2218yes—
23C23×Dic6—32no—
24C23×Dic6—61no—
25C22×Dic3⋊C4—32no—
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—22no—
35C22×C32×C4C2×C414yes—
36C22×C32×C4C2312yes—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3C2×C414yes—
40C22×C3⋊Dic3C2×C414yes—
41C22×C3⋊Dic3D414yes—
42C22×C3⋊Dic3D414yes—
43C22×C3⋊Dic3C2312yes—
44C22×C3⋊Dic3C2312yes—
45C2×#634—232no—
46C2×#634—28no—
47C2×#634—28no—
48C2×#634C2×C4116yescomplemented
49C22×C3×Dic3—24no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3—24no—
54C22×C3×Dic3Q818yescomplemented
55C22×C3×Dic3C2314yes—
56C22×C3×Dic3C2314yes—
57#3724—28no—
58Dic32—28no—
59C2×#391—91noSylow
60C23×C3×C4—21no—
61C23×C3×C4—32no—
62C23×C3×C4—32no—
63C23×C3×C4C2×D312yes—
64C23×Dic3—32no—
65C23×Dic3—32no—
66C23×Dic3—61no—
67C23×Dic3—61no—
68C23×Dic3C2×D312yes—
69C23×Dic3C2×D312yes—
70C22×Dic6—316no—
71C22×Dic6—38no—
72C22×Dic6—68no—
73C22×Dic6—64no—
74C22×Dic6—68no—
75C22×Dic6—68no—
76C22×Dic6—68no—
77C22×Dic6—68no—
78C2×Dic3⋊C4—38no—
79C2×Dic3⋊C4—68no—
80C2×C4×Dic3—38no—
81C2×C4×Dic3—68no—
82C3×#95—38no—
83C3⋊#95—38no—
84C3⋊#95—38no—
85C3⋊#95C2×D318yes—
86C23×C32C22×C412yes—
87C23×C32C2×D412yes—
88C23×C32C2×D412yes—
89C23×C32C2×Q814yes—
90C23×C32#4114yes—
91C23×C32C2411yescharacteristic
92C2×C32×C4—28no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4C22×C414yes—
96C2×C3⋊Dic3—28no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3C22⋊C4116yes—
100C2×C3⋊Dic3C22×C414yes—
101C2×C3⋊Dic3C22×C414yes—
102C2×C3⋊Dic3C2×D414yes—
103C2×C3⋊Dic3C2×D414yes—
104#634—232no—
105C2×C3×Dic3—216no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—48no—
112C2×C3×Dic3C2×Q818yescomplemented
113C23×Q8—91no—
114C22×C4⋊C4—91no—
115C22×C42—91no—
116#391—98no—
117C2×#95—32no—
118C2×#95—92no—
119C24×C3—21no—
120C24×C3C22×D312yes—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4—24no—
124C22×C3×C4—24no—
125C22×C3×C4—24no—
126C22×C3×C4—22no—
127C22×C3×C4—38no—
128C22×C3×C4—34no—
129C22×C3×C4—34no—
130C22×C3×C4—64no—
131C22×C3×C4—64no—
132C22×C3×C4—64no—
133C22×C3×C4—64no—
134C22×C3×C4—64no—
135C22×C3×C4C4×D318yes—
136C22×C3×C4C22×D314yes—
137C22×Dic3—24no—
138C22×Dic3—24no—
139C22×Dic3—24no—
140C22×Dic3—24no—
141C22×Dic3—24no—
142C22×Dic3—38no—
143C22×Dic3—38no—
144C22×Dic3—38no—
145C22×Dic3—34no—
146C22×Dic3—38no—
147C22×Dic3—34no—
148C22×Dic3—64no—
149C22×Dic3—64no—
150C22×Dic3—64no—
151C22×Dic3—64no—
152C22×Dic3—62no—
153C22×Dic3—62no—
154C22×Dic3—64no—
155C22×Dic3—64no—
156C22×Dic3—64no—
157C22×Dic3—64no—
158C22×Dic3Dic618yescomplemented
159C22×Dic3C22×D314yes—
160C22×Dic3C22×D314yes—
161C2×Dic6—332no—
162C2×Dic6—616no—
163C2×Dic6—664no—
164C2×Dic6—616no—
165C2×Dic6—616no—
166C2×Dic6—664no—
167C2×Dic6—616no—
168C2×Dic6—616no—
169Dic3⋊C4—616no—
170C4×Dic3—616no—
171C22×C32C2×C22⋊C414yes—
172C22×C32C4×Q818yes—
173C22×C32C22⋊Q818yes—
174C22×C32#12414yes—
175C22×C32C4⋊Q814yes—
176C22×C32C23×C411yescharacteristic
177C22×C32C22×D411yescharacteristic
178C22×C32C22×D411yescharacteristic
179C22×C32C22×Q812yes—
180C22×C32C2×#4112yes—
181C32×C4—24no—
182C3⋊Dic3—24no—
183C3⋊Dic3C2×C22⋊C418yes—
184C3×Dic3—28no—
185C3×Dic3—44no—
186C22×Q8—98no—
187C22×Q8—94no—
188C22×Q8—184no—
189C22×Q8—184no—
190C23×C4—32no—
191C23×C4—32no—
192C23×C4—91no—
193C23×C4—91no—
194C23×C4D3211yescharacteristic
195C2×C4⋊C4—94no—
196C2×C4⋊C4—184no—
197C2×C42—94no—
198C2×C42—184no—
199#95—38no—
200#95—98no—
201C23×C3—21no—
202C23×C3—24no—
203C23×C3—24no—
204C23×C3—22no—
205C23×C3—22no—
206C23×C3—22no—
207C23×C3C2×Dic614yes—
208C23×C3C2×C4×D314yes—
209C23×C3#23514yes—
210C23×C3D3×D414yes—
211C23×C3D3×D414yes—
212C23×C3#23714yes—
213C23×C3D3×Q814yes—
214C23×C3C23×D312yes—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—216no—
218C2×C3×C4—216no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—38no—
223C2×C3×C4—616no—
224C2×C3×C4—64no—
225C2×C3×C4—64no—
226C2×C3×C4—64no—
227C2×C3×C4—64no—
228C2×C3×C4—64no—
229C2×C3×C4—128no—
230C2×C3×C4C2×C4×D318yes—
231C2×Dic3—216no—
232C2×Dic3—24no—
233C2×Dic3—24no—
234C2×Dic3—24no—
235C2×Dic3—24no—
236C2×Dic3—24no—
237C2×Dic3—332no—
238C2×Dic3—38no—
239C2×Dic3—38no—
240C2×Dic3—38no—
241C2×Dic3—38no—
242C2×Dic3—48no—
243C2×Dic3—616no—
244C2×Dic3—64no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—64no—
249C2×Dic3—64no—
250C2×Dic3—616no—
251C2×Dic3—616no—
252C2×Dic3—64no—
253C2×Dic3—64no—
254C2×Dic3C2×Dic618yescomplemented
255Dic6—664no—
256Dic6—664no—
257C2×C32#39118yescomplemented
258C2×C32C22×C22⋊C411yescharacteristic
259C2×C32C2×C4×Q812yes—
260C2×C32C2×C22⋊Q812yes—
261C2×C32C2×#12411yescharacteristic
262C2×C32C2×C4⋊Q811yescharacteristic
263C24C2×D3211yescharacteristic
264C2×Q8—916no—
265C2×Q8—188no—
266C2×Q8—188no—
267C2×Q8—1832no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—34no—
271C22×C4—38no—
272C22×C4—34no—
273C22×C4—64no—
274C22×C4—64no—
275C22×C4—64no—
276C22×C4—64no—
277C22×C4—64no—
278C22×C4—92no—
279C22×C4—94no—
280C22×C4—94no—
281C22×C4—94no—
282C22×C4—92no—
283C22×C4—94no—
284C22×C4—182no—
285C22×C4—182no—
286C22×C4#62414yes—
287C22×C4C2×D3212yes—
288C4⋊C4—188no—
289C42—188no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—24no—
296C22×C3—28no—
297C22×C3—28no—
298C22×C3—24no—
299C22×C3—24no—
300C22×C3C4×Dic618yes—
301C22×C3#87818yes—
302C22×C3D3×C22⋊C418yes—
303C22×C3#88518yes—
304C22×C3#88718yes—
305C22×C3#88818yes—
306C22×C3#89618yes—
307C22×C3C22×Dic612yes—
308C22×C3C22×C4×D312yes—
309C22×C3C2×#23512yes—
310C22×C3C2×D3×D412yes—
311C22×C3C2×D3×D412yes—
312C22×C3C2×#23712yes—
313C22×C3C2×D3×Q812yes—
314C3×C4—28no—
315C3×C4—28no—
316C3×C4—68no—
317C3×C4—124no—
318Dic3—28no—
319Dic3—316no—
320Dic3—44no—
321Dic3—68no—
322Dic3—68no—
323Dic3—68no—
324C32C2×#39111yescharacteristic, complemented, Sylow
325C23D3×Dic614yes—
326C23#379514yes—
327C23C2×#62412yes—
328C23#381112yes—
329C23#381112yes—
330C23C22×D3211yescharacteristic
331Q8—1832no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—28no—
335C2×C4—38no—
336C2×C4—64no—
337C2×C4—64no—
338C2×C4—616no—
339C2×C4—64no—
340C2×C4—64no—
341C2×C4—64no—
342C2×C4—94no—
343C2×C4—94no—
344C2×C4—94no—
345C2×C4—916no—
346C2×C4—94no—
347C2×C4—128no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—188no—
351C2×C4C2×#62414yes—
352C2×C3—22no—
353C2×C3—28no—
354C2×C3—22no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3#4646116yescomplemented
359C2×C3C2×C4×Dic612yes—
360C2×C3C2×#87812yes—
361C2×C3C2×D3×C22⋊C412yes—
362C2×C3C2×#88512yes—
363C2×C3C2×#88712yes—
364C2×C3C2×#88812yes—
365C2×C3C2×#89612yes—
366C22#6384014yes—
367C22#6384418yes—
368C22#6389618yes—
369C22#6391314yes—
370C22#6397414yes—
371C22C2×D3×Dic612yes—
372C22C2×#379512yes—
373C22C22×#62411yescharacteristic
374C22C2×#381111yescharacteristic
375C22C2×#381111yescharacteristic
376C4—24no—
377C4—68no—
378C4—98no—
379C4—124no—
380C4—184no—
381C3—21no—
382C3C2×#464612yescomplemented
383C2#1059127318yesdirect product factor
384C2C2×#6384011yescharacteristic
385C2C2×#6384412yes—
386C2C2×#6389612yes—
387C2C2×#6391311yescharacteristic
388C2C2×#6397411yescharacteristic
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. #10591273C2direct (N × H)
13. C22×#634C4semidirect
48. C2×#634C2×C4semidirect
54. C22×C3×Dic3Q8semidirect
112. C2×C3×Dic3C2×Q8semidirect
158. C22×Dic3Dic6semidirect
254. C2×Dic3C2×Dic6semidirect
257. C2×C32#391semidirect
324. C32C2×#391semidirect
358. C2×C3#4646semidirect
382. C3C2×#4646semidirect
383. C2#10591273direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6342
C22×#37242
C22×Dic322
C2×C3×C3⋊#952
C2×#635792
#105912732
C2×#46463