Finite Group Databasebeta

← C2×#10591356 #11808357

Subgroups — C2×#10591356 #11808357

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×#3750C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic
3C22×Dic3⋊Dic3C212yesmaximal
4C2×C3×C3⋊#95C212yesmaximal
5C2×#63579C211yesmaximal, characteristic
6#10591356C218yesmaximal, direct product factor
7C2×#4657—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×Dic3⋊Dic3—28no—
18C2×Dic3⋊Dic3C2218yes—
19C3×C3⋊#95C2218yes—
20#63579C2214yes—
21C22×C4⋊Dic3—32no—
22C22×Dic3⋊C4—32no—
23C22×Dic3⋊C4—32no—
24C22×Dic3⋊C4—32no—
25C22×Dic3⋊C4—61no—
26C2×C3×#95—32no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95D312yes—
29#4657—316no—
30C24×C32C2311yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4—24no—
33C22×C32×C4C2312yes—
34C22×C3⋊Dic3—22no—
35C22×C3⋊Dic3—22no—
36C22×C3⋊Dic3—24no—
37C22×C3⋊Dic3D414yes—
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—
49#3750—28no—
50#3724—28no—
51Dic3⋊Dic3—216no—
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×C4⋊Dic3—38no—
64C2×C4⋊Dic3—68no—
65C2×Dic3⋊C4—38no—
66C2×Dic3⋊C4—38no—
67C2×Dic3⋊C4—38no—
68C2×Dic3⋊C4—64no—
69C2×Dic3⋊C4—68no—
70C2×Dic3⋊C4—68no—
71C2×Dic3⋊C4—68no—
72C2×Dic3⋊C4—68no—
73C3×#95—38no—
74C3⋊#95—38no—
75C3⋊#95C2×D318yes—
76C23×C32C2×D412yes—
77C23×C32C2×D412yes—
78C23×C32C2×Q814yes—
79C23×C32#4112yes—
80C23×C32#4114yes—
81C23×C32C2411yescharacteristic
82C2×C32×C4—22no—
83C2×C32×C4—24no—
84C2×C32×C4—44no—
85C2×C3⋊Dic3—28no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—28no—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3C2×D414yes—
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—91no—
101C22×C4⋊C4—92no—
102C22×C4⋊C4—91no—
103#398—98no—
104C2×#95—32no—
105C2×#95—91no—
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—22no—
113C22×C3×C4—38no—
114C22×C3×C4—34no—
115C22×C3×C4—34no—
116C22×C3×C4—44no—
117C22×C3×C4—64no—
118C22×C3×C4—64no—
119C22×C3×C4—64no—
120C22×C3×C4—64no—
121C22×C3×C4—64no—
122C22×C3×C4C22×D314yes—
123C22×Dic3—24no—
124C22×Dic3—24no—
125C22×Dic3—24no—
126C22×Dic3—24no—
127C22×Dic3—24no—
128C22×Dic3—38no—
129C22×Dic3—38no—
130C22×Dic3—34no—
131C22×Dic3—34no—
132C22×Dic3—62no—
133C22×Dic3—64no—
134C22×Dic3—64no—
135C22×Dic3—62no—
136C22×Dic3—64no—
137C22×Dic3—64no—
138C22×Dic3—64no—
139C22×Dic3—64no—
140C22×Dic3—64no—
141C22×Dic3—64no—
142C22×Dic3—124no—
143C22×Dic3Dic618yes—
144C22×Dic3C22×D314yes—
145C22×Dic3C22×D314yes—
146C4⋊Dic3—616no—
147Dic3⋊C4—616no—
148Dic3⋊C4—616no—
149Dic3⋊C4—616no—
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×#4111yescharacteristic
160C22×C32C2×#4112yes—
161C32×C4—42no—
162C3⋊Dic3—24no—
163C3⋊Dic3—24no—
164C3×Dic3—28no—
165C3×Dic3—44no—
166C23×C4—32no—
167C23×C4—32no—
168C23×C4—91no—
169C23×C4—91no—
170C23×C4D3211yescharacteristic
171C2×C4⋊C4—94no—
172C2×C4⋊C4—98no—
173C2×C4⋊C4—94no—
174C2×C4⋊C4—184no—
175C2×C4⋊C4—184no—
176C2×C4⋊C4—188no—
177#95—38no—
178#95—94no—
179C23×C3—21no—
180C23×C3—24no—
181C23×C3—22no—
182C23×C3—22no—
183C23×C3—24no—
184C23×C3—22no—
185C23×C3C2×Dic614yes—
186C23×C3#23514yes—
187C23×C3#23514yes—
188C23×C3D3×D414yes—
189C23×C3D3×D414yes—
190C23×C3#23714yes—
191C23×C3D3×Q814yes—
192C23×C3C23×D312yes—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—38no—
198C2×C3×C4—44no—
199C2×C3×C4—48no—
200C2×C3×C4—48no—
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×Dic3—216no—
209C2×Dic3—24no—
210C2×Dic3—24no—
211C2×Dic3—24no—
212C2×Dic3—24no—
213C2×Dic3—24no—
214C2×Dic3—38no—
215C2×Dic3—38no—
216C2×Dic3—48no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—616no—
222C2×Dic3—616no—
223C2×Dic3—616no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3—124no—
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—24no—
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—92no—
250C22×C4—94no—
251C22×C4—94no—
252C22×C4—182no—
253C22×C4—184no—
254C22×C4—182no—
255C22×C4C2×D3212yes—
256C4⋊C4—188no—
257C4⋊C4—188no—
258C4⋊C4—1816no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—21no—
264C22×C3—24no—
265C22×C3—28no—
266C22×C3—28no—
267C22×C3—24no—
268C22×C3—24no—
269C22×C3#87018yes—
270C22×C3#87818yes—
271C22×C3#88318yes—
272C22×C3#88418yes—
273C22×C3#88818yes—
274C22×C3#88918yes—
275C22×C3#89618yes—
276C22×C3C22×Dic612yes—
277C22×C3C2×#23512yes—
278C22×C3C2×#23512yes—
279C22×C3C2×D3×D412yes—
280C22×C3C2×D3×D412yes—
281C22×C3C2×#23712yes—
282C22×C3C2×D3×Q812yes—
283C3×C4—44no—
284C3×C4—44no—
285C3×C4—68no—
286C3×C4—124no—
287Dic3—28no—
288Dic3—44no—
289Dic3—68no—
290Dic3—68no—
291Dic3—68no—
292Dic3—124no—
293C32C2×#39811yescharacteristic, complemented, Sylow
294C23D3×Dic614yes—
295C23#379812yes—
296C23#380212yes—
297C23#380414yes—
298C23#381112yes—
299C23C22×D3211yescharacteristic
300C2×C4—24no—
301C2×C4—22no—
302C2×C4—38no—
303C2×C4—44no—
304C2×C4—64no—
305C2×C4—64no—
306C2×C4—616no—
307C2×C4—64no—
308C2×C4—64no—
309C2×C4—64no—
310C2×C4—94no—
311C2×C4—94no—
312C2×C4—128no—
313C2×C4—182no—
314C2×C4—184no—
315C2×C4—182no—
316C2×C4—188no—
317C2×C4—188no—
318C2×C3—22no—
319C2×C3—22no—
320C2×C3—28no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3#4657116yescomplemented
325C2×C3C2×#87012yes—
326C2×C3C2×#87812yes—
327C2×C3C2×#88312yes—
328C2×C3C2×#88412yes—
329C2×C3C2×#88812yes—
330C2×C3C2×#88912yes—
331C2×C3C2×#89612yes—
332C22#6384014yes—
333C22#6386718yes—
334C22#6389918yes—
335C22#6391214yes—
336C22#6397514yes—
337C22C2×D3×Dic612yes—
338C22C2×#379811yescharacteristic
339C22C2×#380211yescharacteristic
340C22C2×#380412yes—
341C22C2×#381111yescharacteristic
342C4—42no—
343C4—68no—
344C4—124no—
345C4—184no—
346C4—184no—
347C3—21no—
348C3C2×#465712yescomplemented
349C2#1059135618yesdirect product factor
350C2C2×#6384011yescharacteristic
351C2C2×#6386712yes—
352C2C2×#6389912yes—
353C2C2×#6391211yescharacteristic
354C2C2×#6397511yescharacteristic
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. #10591356C2direct (N × H)
231. C2×C32#398semidirect
293. C32C2×#398semidirect
324. C2×C3#4657semidirect
348. C3C2×#4657semidirect
349. C2#10591356direct (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×Dic3⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#105913562
C2×#46573