Finite Group Databasebeta

← C2×#10591247 #11801093

Subgroups — C2×#10591247 #11801093

Order 1152.

1633 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×#63579C212yesmaximal
6#10591247C218yesmaximal, direct product factor
7C2×#4650—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×#3750—24no—
14C2×#3750C2214yes—
15C2×#3724—24no—
16C2×#3724C2214yes—
17C2×Dic32C418yescomplemented
18C2×Dic32C2214yes—
19C3×C3⋊#95C2218yes—
20#63579C2218yes—
21C22×Dic3⋊C4—32no—
22C22×Dic3⋊C4—32no—
23C22×Dic3⋊C4—61no—
24C22×C4×Dic3—32no—
25C2×C3×#95—32no—
26C2×C3⋊#95—32no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95D312yes—
29#4650—316no—
30C24×C32C2311yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4—24no—
33C22×C32×C4C2312yes—
34C22×C3⋊Dic3—22no—
35C22×C3⋊Dic3—24no—
36C22×C3⋊Dic3C2×C414yes—
37C22×C3⋊Dic3D414yes—
38C22×C3⋊Dic3Q814yes—
39C22×C3⋊Dic3C2312yes—
40C22×C3⋊Dic3C2312yes—
41C22×C3×Dic3—24no—
42C22×C3×Dic3—24no—
43C22×C3×Dic3—24no—
44C22×C3×Dic3—24no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3C2×C418yes—
47C22×C3×Dic3C2314yes—
48C22×C3×Dic3C2314yes—
49#3750—28no—
50#3724—28no—
51Dic32C2×C4116yescomplemented
52C2×#382—91noSylow
53C23×C3×C4—21no—
54C23×C3×C4—32no—
55C23×C3×C4—32no—
56C23×C3×C4C2×D312yes—
57C23×Dic3—32no—
58C23×Dic3—32no—
59C23×Dic3—61no—
60C23×Dic3—61no—
61C23×Dic3C2×D312yes—
62C23×Dic3C2×D312yes—
63C2×Dic3⋊C4—38no—
64C2×Dic3⋊C4—38no—
65C2×Dic3⋊C4—64no—
66C2×Dic3⋊C4—68no—
67C2×Dic3⋊C4—68no—
68C2×Dic3⋊C4—68no—
69C2×C4×Dic3—316no—
70C2×C4×Dic3—38no—
71C3×#95—38no—
72C3⋊#95—38no—
73C3⋊#95—38no—
74C3⋊#95C2×D318yes—
75C23×C32C22×C412yes—
76C23×C32C2×D412yes—
77C23×C32C2×Q812yes—
78C23×C32#4114yes—
79C23×C32#4114yes—
80C23×C32C2411yescharacteristic
81C2×C32×C4—22no—
82C2×C32×C4—24no—
83C2×C32×C4—44no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—24no—
86C2×C3⋊Dic3—44no—
87C2×C3⋊Dic3C4⋊C4116yes—
88C2×C3⋊Dic3C22×C414yes—
89C2×C3⋊Dic3C2×D414yes—
90C2×C3⋊Dic3C2×Q814yes—
91C2×C3×Dic3—216no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—48no—
98C2×C3×Dic3C22×C418yes—
99C22×C4⋊C4—91no—
100C22×C4⋊C4—91no—
101C22×C42—91no—
102#382—98no—
103C2×#95—32no—
104C2×#95—92no—
105C24×C3—21no—
106C24×C3C22×D312yes—
107C22×C3×C4—24no—
108C22×C3×C4—24no—
109C22×C3×C4—24no—
110C22×C3×C4—24no—
111C22×C3×C4—22no—
112C22×C3×C4—38no—
113C22×C3×C4—34no—
114C22×C3×C4—34no—
115C22×C3×C4—44no—
116C22×C3×C4—64no—
117C22×C3×C4—64no—
118C22×C3×C4—64no—
119C22×C3×C4—64no—
120C22×C3×C4—64no—
121C22×C3×C4C22×D314yes—
122C22×Dic3—24no—
123C22×Dic3—24no—
124C22×Dic3—24no—
125C22×Dic3—24no—
126C22×Dic3—24no—
127C22×Dic3—38no—
128C22×Dic3—38no—
129C22×Dic3—38no—
130C22×Dic3—34no—
131C22×Dic3—34no—
132C22×Dic3—64no—
133C22×Dic3—62no—
134C22×Dic3—64no—
135C22×Dic3—64no—
136C22×Dic3—62no—
137C22×Dic3—64no—
138C22×Dic3—64no—
139C22×Dic3—64no—
140C22×Dic3—64no—
141C22×Dic3—124no—
142C22×Dic3C4×D318yes—
143C22×Dic3C22×D314yes—
144C22×Dic3C22×D314yes—
145Dic3⋊C4—616no—
146Dic3⋊C4—616no—
147Dic3⋊C4—616no—
148C4×Dic3—332no—
149C22×C32C2×C4⋊C414yes—
150C22×C32#11718yes—
151C22×C32#12414yes—
152C22×C32#12414yes—
153C22×C32#12518yes—
154C22×C32C23×C411yescharacteristic
155C22×C32C22×D411yescharacteristic
156C22×C32C22×Q811yescharacteristic
157C22×C32C2×#4112yes—
158C22×C32C2×#4112yes—
159C32×C4—42no—
160C3⋊Dic3—42no—
161C3⋊Dic3C2×C4⋊C418yes—
162C3×Dic3—28no—
163C3×Dic3—44no—
164C23×C4—32no—
165C23×C4—32no—
166C23×C4—91no—
167C23×C4—91no—
168C23×C4D3211yescharacteristic
169C2×C4⋊C4—94no—
170C2×C4⋊C4—94no—
171C2×C4⋊C4—184no—
172C2×C4⋊C4—184no—
173C2×C42—94no—
174C2×C42—98no—
175#95—38no—
176#95—98no—
177C23×C3—21no—
178C23×C3—24no—
179C23×C3—22no—
180C23×C3—22no—
181C23×C3—24no—
182C23×C3—22no—
183C23×C3C2×C4×D314yes—
184C23×C3#23514yes—
185C23×C3#23514yes—
186C23×C3D3×D414yes—
187C23×C3#23714yes—
188C23×C3#23714yes—
189C23×C3D3×Q814yes—
190C23×C3C23×D312yes—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—38no—
196C2×C3×C4—44no—
197C2×C3×C4—48no—
198C2×C3×C4—48no—
199C2×C3×C4—616no—
200C2×C3×C4—64no—
201C2×C3×C4—64no—
202C2×C3×C4—64no—
203C2×C3×C4—64no—
204C2×C3×C4—64no—
205C2×C3×C4—128no—
206C2×Dic3—216no—
207C2×Dic3—24no—
208C2×Dic3—24no—
209C2×Dic3—24no—
210C2×Dic3—24no—
211C2×Dic3—24no—
212C2×Dic3—332no—
213C2×Dic3—38no—
214C2×Dic3—38no—
215C2×Dic3—38no—
216C2×Dic3—48no—
217C2×Dic3—616no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—64no—
225C2×Dic3—124no—
226C2×Dic3—128no—
227C2×Dic3—128no—
228C2×Dic3C2×C4×D318yes—
229C2×C32#38218yescomplemented
230C2×C32C22×C4⋊C411yescharacteristic
231C2×C32C2×#11712yes—
232C2×C32C2×#12411yescharacteristic
233C2×C32C2×#12411yescharacteristic
234C2×C32C2×#12512yes—
235C24C2×D3211yescharacteristic
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—34no—
239C22×C4—38no—
240C22×C4—34no—
241C22×C4—64no—
242C22×C4—64no—
243C22×C4—64no—
244C22×C4—64no—
245C22×C4—64no—
246C22×C4—92no—
247C22×C4—94no—
248C22×C4—94no—
249C22×C4—94no—
250C22×C4—92no—
251C22×C4—184no—
252C22×C4—182no—
253C22×C4C2×D3212yes—
254C4⋊C4—188no—
255C4⋊C4—188no—
256C42—916no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—28no—
263C22×C3—28no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—24no—
267C22×C3#87218yes—
268C22×C3#87718yes—
269C22×C3#88518yes—
270C22×C3#88518yes—
271C22×C3#88918yes—
272C22×C3#88918yes—
273C22×C3D3×C4⋊C418yes—
274C22×C3C22×C4×D312yes—
275C22×C3C2×#23512yes—
276C22×C3C2×#23512yes—
277C22×C3C2×D3×D412yes—
278C22×C3C2×#23712yes—
279C22×C3C2×#23712yes—
280C22×C3C2×D3×Q812yes—
281C3×C4—44no—
282C3×C4—44no—
283C3×C4—68no—
284C3×C4—124no—
285Dic3—28no—
286Dic3—316no—
287Dic3—44no—
288Dic3—68no—
289Dic3—124no—
290Dic3—124no—
291C32C2×#38211yescharacteristic, complemented, Sylow
292C23#379514yes—
293C23#379712yes—
294C23C4×D3212yes—
295C23#380414yes—
296C23#381112yes—
297C23C22×D3211yescharacteristic
298C2×C4—24no—
299C2×C4—22no—
300C2×C4—38no—
301C2×C4—44no—
302C2×C4—64no—
303C2×C4—64no—
304C2×C4—616no—
305C2×C4—64no—
306C2×C4—64no—
307C2×C4—64no—
308C2×C4—94no—
309C2×C4—94no—
310C2×C4—94no—
311C2×C4—916no—
312C2×C4—128no—
313C2×C4—184no—
314C2×C4—182no—
315C2×C4—364no—
316C2×C3—22no—
317C2×C3—28no—
318C2×C3—22no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3#4650116yescomplemented
323C2×C3C2×#87212yes—
324C2×C3C2×#87712yes—
325C2×C3C2×#88512yes—
326C2×C3C2×#88512yes—
327C2×C3C2×#88912yes—
328C2×C3C2×#88912yes—
329C2×C3C2×D3×C4⋊C412yes—
330C22#6384718yes—
331C22#6387718yes—
332C22#6388314yes—
333C22#6391314yes—
334C22#6395314yes—
335C22C2×#379512yes—
336C22C2×#379711yescharacteristic
337C22C2×C4×D3211yescharacteristic
338C22C2×#380412yes—
339C22C2×#381111yescharacteristic
340C4—42no—
341C4—68no—
342C4—98no—
343C4—124no—
344C4—362no—
345C3—21no—
346C3C2×#465012yescomplemented
347C2#1059124718yesdirect product factor
348C2C2×#6384712yes—
349C2C2×#6387712yes—
350C2C2×#6388311yescharacteristic
351C2C2×#6391311yescharacteristic
352C2C2×#6395311yescharacteristic
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. #10591247C2direct (N × H)
17. C2×Dic32C4semidirect
51. Dic32C2×C4semidirect
229. C2×C32#382semidirect
291. C32C2×#382semidirect
322. C2×C3#4650semidirect
346. C3C2×#4650semidirect
347. C2#10591247direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C22×#37242
C22×Dic322
C2×C3×C3⋊#952
C2×#635792
#105912472
C2×#46503