Finite Group Databasebeta

← C2×#10591217 #11808525

Subgroups — C2×#10591217 #11808525

Order 1152.

1417 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic
3C2×C3×C3⋊#95C212yesmaximal
4C2×#63579C212yesmaximal
5C2×#63579C211yesmaximal, characteristic
6#10591217C218yesmaximal, direct product factor
7C2×#4658—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—
17C3×C3⋊#95C2218yes—
18#63579C2214yes—
19#63579C2218yes—
20C22×Dic3⋊C4—32no—
21C22×Dic3⋊C4—32no—
22C22×Dic3⋊C4—61no—
23C2×C3×#95—32no—
24C2×C3⋊#95—32no—
25C2×C3⋊#95—32no—
26C2×C3⋊#95—32no—
27C2×C3⋊#95D312yes—
28#4658—316no—
29C24×C32C2311yescharacteristic
30C22×C32×C4—22no—
31C22×C32×C4—24no—
32C22×C32×C4C2312yes—
33C22×C3⋊Dic3—22no—
34C22×C3⋊Dic3—22no—
35C22×C3⋊Dic3—24no—
36C22×C3⋊Dic3D414yes—
37C22×C3⋊Dic3Q814yes—
38C22×C3⋊Dic3C2312yes—
39C22×C3⋊Dic3C2312yes—
40C22×C3×Dic3—24no—
41C22×C3×Dic3—24no—
42C22×C3×Dic3—24no—
43C22×C3×Dic3—24no—
44C22×C3×Dic3—24no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3C2314yes—
47C22×C3×Dic3C2314yes—
48#3750—28no—
49#3724—28no—
50C2×#400—91noSylow
51C23×C3×C4—21no—
52C23×C3×C4—32no—
53C23×C3×C4—32no—
54C23×C3×C4C2×D312yes—
55C23×Dic3—32no—
56C23×Dic3—32no—
57C23×Dic3—61no—
58C23×Dic3—61no—
59C23×Dic3C2×D312yes—
60C23×Dic3C2×D312yes—
61C2×Dic3⋊C4—38no—
62C2×Dic3⋊C4—38no—
63C2×Dic3⋊C4—64no—
64C2×Dic3⋊C4—68no—
65C2×Dic3⋊C4—68no—
66C2×Dic3⋊C4—68no—
67C3×#95—38no—
68C3⋊#95—38no—
69C3⋊#95—38no—
70C3⋊#95—38no—
71C3⋊#95C2×D318yes—
72C23×C32C2×D412yes—
73C23×C32C2×Q812yes—
74C23×C32#4112yes—
75C23×C32#4114yes—
76C23×C32#4114yes—
77C23×C32C2411yescharacteristic
78C2×C32×C4—22no—
79C2×C32×C4—24no—
80C2×C32×C4—44no—
81C2×C3⋊Dic3—28no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—28no—
85C2×C3⋊Dic3—24no—
86C2×C3⋊Dic3C2×D414yes—
87C2×C3⋊Dic3C2×Q814yes—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—24no—
91C2×C3×Dic3—24no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—48no—
95C2×C3×Dic3—48no—
96C22×C4⋊C4—91no—
97C22×C4⋊C4—91no—
98#400—98no—
99C2×#95—32no—
100C2×#95—92no—
101C2×#95—91no—
102C24×C3—21no—
103C24×C3C22×D312yes—
104C22×C3×C4—24no—
105C22×C3×C4—24no—
106C22×C3×C4—24no—
107C22×C3×C4—24no—
108C22×C3×C4—22no—
109C22×C3×C4—34no—
110C22×C3×C4—34no—
111C22×C3×C4—44no—
112C22×C3×C4—64no—
113C22×C3×C4—64no—
114C22×C3×C4—64no—
115C22×C3×C4—64no—
116C22×C3×C4—64no—
117C22×C3×C4—64no—
118C22×C3×C4C22×D314yes—
119C22×Dic3—24no—
120C22×Dic3—24no—
121C22×Dic3—24no—
122C22×Dic3—24no—
123C22×Dic3—24no—
124C22×Dic3—24no—
125C22×Dic3—38no—
126C22×Dic3—38no—
127C22×Dic3—34no—
128C22×Dic3—34no—
129C22×Dic3—62no—
130C22×Dic3—64no—
131C22×Dic3—64no—
132C22×Dic3—62no—
133C22×Dic3—64no—
134C22×Dic3—64no—
135C22×Dic3—64no—
136C22×Dic3—64no—
137C22×Dic3—64no—
138C22×Dic3—64no—
139C22×Dic3—124no—
140C22×Dic3C22×D314yes—
141C22×Dic3C22×D314yes—
142Dic3⋊C4—616no—
143Dic3⋊C4—616no—
144Dic3⋊C4—616no—
145C22×C32C22⋊Q814yes—
146C22×C32#12314yes—
147C22×C32#12414yes—
148C22×C32#12518yes—
149C22×C32#12618yes—
150C22×C32C22×D411yescharacteristic
151C22×C32C22×Q811yescharacteristic
152C22×C32C2×#4111yescharacteristic
153C22×C32C2×#4112yes—
154C22×C32C2×#4112yes—
155C32×C4—42no—
156C3⋊Dic3—24no—
157C3⋊Dic3—24no—
158C3×Dic3—44no—
159C3×Dic3—44no—
160C23×C4—32no—
161C23×C4—32no—
162C23×C4—91no—
163C23×C4—91no—
164C23×C4D3211yescharacteristic
165C2×C4⋊C4—94no—
166C2×C4⋊C4—94no—
167C2×C4⋊C4—184no—
168C2×C4⋊C4—184no—
169#95—38no—
170#95—94no—
171#95—98no—
172C23×C3—21no—
173C23×C3—24no—
174C23×C3—22no—
175C23×C3—22no—
176C23×C3—24no—
177C23×C3—22no—
178C23×C3#23514yes—
179C23×C3#23514yes—
180C23×C3#23514yes—
181C23×C3D3×D414yes—
182C23×C3#23714yes—
183C23×C3#23714yes—
184C23×C3D3×Q814yes—
185C23×C3C23×D312yes—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—44no—
191C2×C3×C4—48no—
192C2×C3×C4—48no—
193C2×C3×C4—64no—
194C2×C3×C4—64no—
195C2×C3×C4—64no—
196C2×C3×C4—64no—
197C2×C3×C4—64no—
198C2×C3×C4—64no—
199C2×C3×C4—128no—
200C2×C3×C4—128no—
201C2×Dic3—24no—
202C2×Dic3—24no—
203C2×Dic3—24no—
204C2×Dic3—24no—
205C2×Dic3—24no—
206C2×Dic3—24no—
207C2×Dic3—38no—
208C2×Dic3—38no—
209C2×Dic3—48no—
210C2×Dic3—48no—
211C2×Dic3—64no—
212C2×Dic3—64no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215C2×Dic3—616no—
216C2×Dic3—616no—
217C2×Dic3—616no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—124no—
223C2×Dic3—128no—
224C2×C32#40018yescomplemented
225C2×C32C2×C22⋊Q811yescharacteristic
226C2×C32C2×#12311yescharacteristic
227C2×C32C2×#12411yescharacteristic
228C2×C32C2×#12512yes—
229C2×C32C2×#12612yes—
230C24C2×D3211yescharacteristic
231C22×C4—24no—
232C22×C4—22no—
233C22×C4—34no—
234C22×C4—34no—
235C22×C4—64no—
236C22×C4—64no—
237C22×C4—64no—
238C22×C4—64no—
239C22×C4—64no—
240C22×C4—64no—
241C22×C4—92no—
242C22×C4—92no—
243C22×C4—94no—
244C22×C4—94no—
245C22×C4—182no—
246C22×C4—184no—
247C22×C4—182no—
248C22×C4C2×D3212yes—
249C4⋊C4—188no—
250C4⋊C4—188no—
251C22×C3—22no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—22no—
255C22×C3—21no—
256C22×C3—28no—
257C22×C3—28no—
258C22×C3—24no—
259C22×C3—24no—
260C22×C3—24no—
261C22×C3#87618yes—
262C22×C3#87918yes—
263C22×C3#88318yes—
264C22×C3#88518yes—
265C22×C3#88918yes—
266C22×C3#88918yes—
267C22×C3#89618yes—
268C22×C3C2×#23512yes—
269C22×C3C2×#23512yes—
270C22×C3C2×#23512yes—
271C22×C3C2×D3×D412yes—
272C22×C3C2×#23712yes—
273C22×C3C2×#23712yes—
274C22×C3C2×D3×Q812yes—
275C3×C4—44no—
276C3×C4—44no—
277C3×C4—124no—
278C3×C4—124no—
279Dic3—44no—
280Dic3—44no—
281Dic3—68no—
282Dic3—68no—
283Dic3—68no—
284Dic3—124no—
285C32C2×#40011yescharacteristic, complemented, Sylow
286C23#379514yes—
287C23#379712yes—
288C23#379812yes—
289C23#380414yes—
290C23#381112yes—
291C23C22×D3211yescharacteristic
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—44no—
295C2×C4—64no—
296C2×C4—64no—
297C2×C4—64no—
298C2×C4—64no—
299C2×C4—64no—
300C2×C4—64no—
301C2×C4—94no—
302C2×C4—94no—
303C2×C4—128no—
304C2×C4—128no—
305C2×C4—182no—
306C2×C4—184no—
307C2×C4—182no—
308C2×C4—188no—
309C2×C4—188no—
310C2×C3—22no—
311C2×C3—22no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—28no—
316C2×C3#4658116yescomplemented
317C2×C3C2×#87612yes—
318C2×C3C2×#87912yes—
319C2×C3C2×#88312yes—
320C2×C3C2×#88512yes—
321C2×C3C2×#88912yes—
322C2×C3C2×#88912yes—
323C2×C3C2×#89612yes—
324C22#6384718yes—
325C22#6385918yes—
326C22#6386514yes—
327C22#6391314yes—
328C22#6397514yes—
329C22C2×#379512yes—
330C22C2×#379711yescharacteristic
331C22C2×#379811yescharacteristic
332C22C2×#380412yes—
333C22C2×#381111yescharacteristic
334C4—42no—
335C4—124no—
336C4—124no—
337C4—184no—
338C4—184no—
339C3—21no—
340C3C2×#465812yescomplemented
341C2#1059121718yesdirect product factor
342C2C2×#6384712yes—
343C2C2×#6385912yes—
344C2C2×#6386511yescharacteristic
345C2C2×#6391311yescharacteristic
346C2C2×#6397511yescharacteristic
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. #10591217C2direct (N × H)
224. C2×C32#400semidirect
285. C32C2×#400semidirect
316. C2×C3#4658semidirect
340. C3C2×#4658semidirect
341. C2#10591217direct (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
C2×C3×C3⋊#952
C2×#635792
#105912172
C2×#46583