Finite Group Databasebeta

← C2×#10591215 #11808352

Subgroups — C2×#10591215 #11808352

Order 1152.

1593 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C212yesmaximal
3C22×#3724C211yesmaximal, characteristic
4C2×#63579C212yesmaximal
5C2×#63579C211yesmaximal, characteristic
6#10591215C218yesmaximal, direct product factor
7C2×#4982—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×C4⋊(C3⋊Dic3)—24no—
14C2×C4⋊(C3⋊Dic3)C2214yes—
15C2×C3×Dic3⋊C4—28no—
16C2×C3×Dic3⋊C4C2218yes—
17C2×#3724—24no—
18C2×#3724C2214yes—
19#63579C2218yes—
20#63579C2214yes—
21C22×C3×C4⋊C4—32no—
22C22×C4⋊Dic3—32no—
23C22×C4⋊Dic3—61no—
24C22×Dic3⋊C4—32no—
25C22×Dic3⋊C4D312yes—
26C2×C3⋊#95—32no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—32no—
29#4982—316no—
30C24×C32C2311yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4D414yes—
34C22×C32×C4C2312yes—
35C22×C3⋊Dic3—24no—
36C22×C3⋊Dic3—22no—
37C22×C3⋊Dic3—24no—
38C22×C3⋊Dic3D414yes—
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×Dic3Q818yes—
47C22×C3×Dic3C2314yes—
48C22×C3×Dic3C2314yes—
49C4⋊(C3⋊Dic3)—28no—
50C3×Dic3⋊C4—216no—
51#3724—28no—
52C2×#398—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×C3×C4⋊C4—38no—
64C2×C3×C4⋊C4—68no—
65C2×C4⋊Dic3—38no—
66C2×C4⋊Dic3—64no—
67C2×C4⋊Dic3—68no—
68C2×C4⋊Dic3—68no—
69C2×Dic3⋊C4—28no—
70C2×Dic3⋊C4—38no—
71C2×Dic3⋊C4—68no—
72C2×Dic3⋊C4C2×D318yes—
73C3⋊#95—38no—
74C3⋊#95—38no—
75C3⋊#95—38no—
76C23×C32C2×D412yes—
77C23×C32C2×D412yes—
78C23×C32C2×Q814yes—
79C23×C32#4114yes—
80C23×C32#4112yes—
81C23×C32C2411yescharacteristic
82C2×C32×C4—28no—
83C2×C32×C4—22no—
84C2×C32×C4—22no—
85C2×C32×C4C2×D414yes—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—28no—
88C2×C3⋊Dic3—24no—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3—44no—
91C2×C3⋊Dic3C2×D414yes—
92C2×C3×Dic3—216no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—48no—
99C2×C3×Dic3C2×Q818yes—
100C22×C4⋊C4—32no—
101C22×C4⋊C4—91no—
102C22×C4⋊C4—91no—
103#398—98no—
104C2×#95—91no—
105C2×#95—92no—
106C24×C3—21no—
107C24×C3C22×D312yes—
108C22×C3×C4—24no—
109C22×C3×C4—24no—
110C22×C3×C4—24no—
111C22×C3×C4—24no—
112C22×C3×C4—24no—
113C22×C3×C4—22no—
114C22×C3×C4—38no—
115C22×C3×C4—34no—
116C22×C3×C4—34no—
117C22×C3×C4—64no—
118C22×C3×C4—64no—
119C22×C3×C4—64no—
120C22×C3×C4—64no—
121C22×C3×C4—64no—
122C22×C3×C4#6718yes—
123C22×C3×C4C22×D314yes—
124C22×Dic3—24no—
125C22×Dic3—24no—
126C22×Dic3—24no—
127C22×Dic3—24no—
128C22×Dic3—24no—
129C22×Dic3—38no—
130C22×Dic3—34no—
131C22×Dic3—34no—
132C22×Dic3—64no—
133C22×Dic3—62no—
134C22×Dic3—62no—
135C22×Dic3—64no—
136C22×Dic3—64no—
137C22×Dic3—64no—
138C22×Dic3—64no—
139C22×Dic3—64no—
140C22×Dic3—64no—
141C22×Dic3—124no—
142C22×Dic3—124no—
143C22×Dic3Dic618yes—
144C22×Dic3C22×D314yes—
145C22×Dic3C22×D314yes—
146C3×C4⋊C4—616no—
147C4⋊Dic3—616no—
148C4⋊Dic3—616no—
149Dic3⋊C4—216no—
150Dic3⋊C4—616no—
151C22×C32#12114yes—
152C22×C32C22⋊Q818yes—
153C22×C32#12314yes—
154C22×C32#12518yes—
155C22×C32C4⋊Q814yes—
156C22×C32C22×D411yescharacteristic
157C22×C32C22×D411yescharacteristic
158C22×C32C22×Q812yes—
159C22×C32C2×#4112yes—
160C22×C32C2×#4111yescharacteristic
161C32×C4—24no—
162C3⋊Dic3—24no—
163C3⋊Dic3—42no—
164C3×Dic3—28no—
165C3×Dic3—44no—
166C23×C4—32no—
167C23×C4—32no—
168C23×C4—91no—
169C23×C4—91no—
170C23×C4D3211yescharacteristic
171C2×C4⋊C4—38no—
172C2×C4⋊C4—68no—
173C2×C4⋊C4—94no—
174C2×C4⋊C4—94no—
175C2×C4⋊C4—184no—
176C2×C4⋊C4—184no—
177#95—94no—
178#95—98no—
179C23×C3—21no—
180C23×C3—24no—
181C23×C3—24no—
182C23×C3—22no—
183C23×C3—22no—
184C23×C3—22no—
185C23×C3C2×Dic614yes—
186C23×C3#23514yes—
187C23×C3D3×D414yes—
188C23×C3#23714yes—
189C23×C3D3×Q814yes—
190C23×C3#23914yes—
191C23×C3C2×#6714yes—
192C23×C3C23×D312yes—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—216no—
196C2×C3×C4—216no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—38no—
201C2×C3×C4—616no—
202C2×C3×C4—64no—
203C2×C3×C4—64no—
204C2×C3×C4—64no—
205C2×C3×C4—64no—
206C2×C3×C4—64no—
207C2×C3×C4—128no—
208C2×C3×C4C2×#6718yes—
209C2×Dic3—216no—
210C2×Dic3—24no—
211C2×Dic3—24no—
212C2×Dic3—24no—
213C2×Dic3—24no—
214C2×Dic3—24no—
215C2×Dic3—38no—
216C2×Dic3—48no—
217C2×Dic3—64no—
218C2×Dic3—616no—
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—124no—
228C2×Dic3—128no—
229C2×Dic3—128no—
230C2×Dic3C2×Dic618yes—
231C2×C32#39818yescomplemented
232C2×C32C2×#12111yescharacteristic
233C2×C32C2×C22⋊Q812yes—
234C2×C32C2×#12311yescharacteristic
235C2×C32C2×#12512yes—
236C2×C32C2×C4⋊Q811yescharacteristic
237C24C2×D3211yescharacteristic
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—34no—
241C22×C4—38no—
242C22×C4—34no—
243C22×C4—64no—
244C22×C4—64no—
245C22×C4—64no—
246C22×C4—64no—
247C22×C4—64no—
248C22×C4—92no—
249C22×C4—94no—
250C22×C4—92no—
251C22×C4—184no—
252C22×C4—184no—
253C22×C4—182no—
254C22×C4#62514yes—
255C22×C4C2×D3212yes—
256C4⋊C4—616no—
257C4⋊C4—188no—
258C4⋊C4—188no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—24no—
265C22×C3—28no—
266C22×C3—28no—
267C22×C3—24no—
268C22×C3—24no—
269C22×C3#88818yes—
270C22×C3#88918yes—
271C22×C3#89018yes—
272C22×C3#89418yes—
273C22×C3#92418yes—
274C22×C3#93918yes—
275C22×C3#94618yes—
276C22×C3C22×Dic612yes—
277C22×C3C2×#23512yes—
278C22×C3C2×D3×D412yes—
279C22×C3C2×#23712yes—
280C22×C3C2×D3×Q812yes—
281C22×C3C2×#23912yes—
282C22×C3C22×#6712yes—
283C3×C4—28no—
284C3×C4—28no—
285C3×C4—68no—
286C3×C4—124no—
287Dic3—28no—
288Dic3—44no—
289Dic3—68no—
290Dic3—124no—
291Dic3—124no—
292Dic3—124no—
293C32C2×#39811yescharacteristic, complemented, Sylow
294C23D3×Dic614yes—
295C23#379914yes—
296C23#380512yes—
297C23C2×#62512yes—
298C23#381112yes—
299C23C22×D3211yescharacteristic
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—28no—
303C2×C4—38no—
304C2×C4—64no—
305C2×C4—64no—
306C2×C4—616no—
307C2×C4—64no—
308C2×C4—64no—
309C2×C4—64no—
310C2×C4—94no—
311C2×C4—128no—
312C2×C4—184no—
313C2×C4—188no—
314C2×C4—184no—
315C2×C4—182no—
316C2×C4—364no—
317C2×C4C2×#62514yes—
318C2×C3—22no—
319C2×C3—22no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—28no—
323C2×C3—21no—
324C2×C3#4982116yescomplemented
325C2×C3C2×#88812yes—
326C2×C3C2×#88912yes—
327C2×C3C2×#89012yes—
328C2×C3C2×#89412yes—
329C2×C3C2×#92412yes—
330C2×C3C2×#93912yes—
331C2×C3C2×#94612yes—
332C22#6384014yes—
333C22#6384518yes—
334C22#6385618yes—
335C22#6389714yes—
336C22#6398014yes—
337C22C2×D3×Dic612yes—
338C22C2×#379912yes—
339C22C2×#380511yescharacteristic
340C22C22×#62511yescharacteristic
341C22C2×#381111yescharacteristic
342C4—24no—
343C4—68no—
344C4—124no—
345C4—184no—
346C4—362no—
347C3—21no—
348C3C2×#498212yescomplemented
349C2#1059121518yesdirect product factor
350C2C2×#6384011yescharacteristic
351C2C2×#6384512yes—
352C2C2×#6385612yes—
353C2C2×#6389711yescharacteristic
354C2C2×#6398011yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591215C2direct (N × H)
231. C2×C32#398semidirect
293. C32C2×#398semidirect
324. C2×C3#4982semidirect
348. C3C2×#4982semidirect
349. C2#10591215direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C22×C3×Dic3⋊C42
C22×#37242
C2×#635792
#105912152
C2×#49823