Finite Group Databasebeta

← C2×#10591214 #11808351

Subgroups — C2×#10591214 #11808351

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C22×#3724C212yesmaximal
4C2×#63658C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#10591214C218yesmaximal, direct product factor
7C2×#4981—31nomaximal
8C2×#4983—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2212yes—
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3—24no—
15C2×C3×C4⋊Dic3C2214yes—
16C2×C3×Dic3⋊C4—24no—
17C2×C3×Dic3⋊C4C2214yes—
18C2×#3724—28no—
19C2×#3724C2218yes—
20#63658C2214yes—
21#63579C2218yes—
22C22×C3×C4⋊C4—31no—
23C22×C3×C4⋊C4—31no—
24C22×C4⋊Dic3D311yescharacteristic
25C22×Dic3⋊C4—32no—
26C22×Dic3⋊C4—32no—
27C22×Dic3⋊C4D311yescharacteristic
28C2×C3⋊#95—31no—
29C2×C3⋊#95—31no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95—32no—
32C2×C3⋊#95—61no—
33#4983—38no—
34#4981—38no—
35C24×C32C2311yescharacteristic
36C22×C32×C4—24no—
37C22×C32×C4D414yes—
38C22×C32×C4C2312yes—
39C22×C3⋊Dic3—24no—
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3Q818yes—
42C22×C3⋊Dic3C2314yes—
43C22×C3×Dic3—22no—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3—24no—
50C22×C3×Dic3D414yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2314yes—
53C22×C3×Dic3C2312yes—
54C3×C4⋊Dic3—28no—
55C3×Dic3⋊C4—28no—
56#3724—216no—
57C2×#398—91noSylow
58C23×C3×C4—21no—
59C23×C3×C4—31no—
60C23×C3×C4—31no—
61C23×C3×C4—32no—
62C23×C3×C4C2×D311yescharacteristic
63C23×C3×C4C2×D311yescharacteristic
64C23×Dic3—32no—
65C23×Dic3—32no—
66C23×Dic3—62no—
67C23×Dic3C2×D311yescharacteristic
68C23×Dic3C2×D312yes—
69C23×Dic3C2×D311yescharacteristic
70C2×C3×C4⋊C4—34no—
71C2×C3×C4⋊C4—34no—
72C2×C3×C4⋊C4—64no—
73C2×C3×C4⋊C4—64no—
74C2×C4⋊Dic3—24no—
75C2×C4⋊Dic3C2×D314yes—
76C2×Dic3⋊C4—24no—
77C2×Dic3⋊C4—38no—
78C2×Dic3⋊C4—38no—
79C2×Dic3⋊C4—68no—
80C2×Dic3⋊C4—68no—
81C2×Dic3⋊C4C2×D314yes—
82C3⋊#95—34no—
83C3⋊#95—34no—
84C3⋊#95—38no—
85C3⋊#95—38no—
86C3⋊#95—64no—
87C23×C32C2×D412yes—
88C23×C32C2×D412yes—
89C23×C32C2×Q814yes—
90C23×C32#4112yes—
91C23×C32#4114yes—
92C23×C32C2411yescharacteristic
93C2×C32×C4—28no—
94C2×C32×C4—24no—
95C2×C32×C4C2×D414yes—
96C2×C3⋊Dic3—216no—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—24no—
99C2×C3⋊Dic3C2×Q818yes—
100C2×C3×Dic3—28no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—48no—
109C2×C3×Dic3—44no—
110C2×C3×Dic3C2×D414yes—
111C22×C4⋊C4—31no—
112C22×C4⋊C4—31no—
113C22×C4⋊C4—92no—
114#398—98no—
115C2×#95—92no—
116C2×#95—91no—
117C24×C3—21no—
118C24×C3C22×D311yescharacteristic
119C24×C3C22×D311yescharacteristic
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4—22no—
124C22×C3×C4—34no—
125C22×C3×C4—32no—
126C22×C3×C4—32no—
127C22×C3×C4—34no—
128C22×C3×C4—44no—
129C22×C3×C4—62no—
130C22×C3×C4—62no—
131C22×C3×C4—64no—
132C22×C3×C4—64no—
133C22×C3×C4—64no—
134C22×C3×C4—62no—
135C22×C3×C4—64no—
136C22×C3×C4#6714yes—
137C22×C3×C4#6714yes—
138C22×C3×C4C22×D312yes—
139C22×C3×C4C22×D312yes—
140C22×Dic3—22no—
141C22×Dic3—22no—
142C22×Dic3—24no—
143C22×Dic3—24no—
144C22×Dic3—24no—
145C22×Dic3—22no—
146C22×Dic3—24no—
147C22×Dic3—38no—
148C22×Dic3—38no—
149C22×Dic3—34no—
150C22×Dic3—34no—
151C22×Dic3—64no—
152C22×Dic3—68no—
153C22×Dic3—64no—
154C22×Dic3—64no—
155C22×Dic3—64no—
156C22×Dic3—64no—
157C22×Dic3—124no—
158C22×Dic3—124no—
159C22×Dic3D1214yes—
160C22×Dic3C22×D312yes—
161C22×Dic3C22×D314yes—
162C22×Dic3C22×D312yes—
163C3×C4⋊C4—68no—
164C3×C4⋊C4—68no—
165C4⋊Dic3—28no—
166Dic3⋊C4—28no—
167Dic3⋊C4—616no—
168Dic3⋊C4—616no—
169C22×C32#12114yes—
170C22×C32C22⋊Q818yes—
171C22×C32#12314yes—
172C22×C32#12518yes—
173C22×C32C4⋊Q814yes—
174C22×C32C22×D411yescharacteristic
175C22×C32C22×D411yescharacteristic
176C22×C32C22×Q812yes—
177C22×C32C2×#4111yescharacteristic
178C22×C32C2×#4112yes—
179C32×C4—24no—
180C3⋊Dic3—28no—
181C3×Dic3—24no—
182C3×Dic3—44no—
183C3×Dic3—42no—
184C23×C4—31no—
185C23×C4—32no—
186C23×C4—31no—
187C23×C4—92no—
188C23×C4D3211yescharacteristic
189C2×C4⋊C4—34no—
190C2×C4⋊C4—34no—
191C2×C4⋊C4—64no—
192C2×C4⋊C4—64no—
193C2×C4⋊C4—98no—
194C2×C4⋊C4—188no—
195#95—98no—
196#95—94no—
197C23×C3—21no—
198C23×C3—22no—
199C23×C3—24no—
200C23×C3—22no—
201C23×C3—24no—
202C23×C3—22no—
203C23×C3C2×D1212yes—
204C23×C3#23512yes—
205C23×C3#23514yes—
206C23×C3D3×D412yes—
207C23×C3#23712yes—
208C23×C3#23714yes—
209C23×C3D3×Q814yes—
210C23×C3D3×Q814yes—
211C23×C3C2×#6712yes—
212C23×C3C2×#6712yes—
213C23×C3C23×D311yescharacteristic
214C23×C3C23×D311yescharacteristic
215C2×C3×C4—28no—
216C2×C3×C4—28no—
217C2×C3×C4—24no—
218C2×C3×C4—24no—
219C2×C3×C4—24no—
220C2×C3×C4—34no—
221C2×C3×C4—44no—
222C2×C3×C4—48no—
223C2×C3×C4—68no—
224C2×C3×C4—62no—
225C2×C3×C4—62no—
226C2×C3×C4—64no—
227C2×C3×C4—64no—
228C2×C3×C4—64no—
229C2×C3×C4—62no—
230C2×C3×C4—64no—
231C2×C3×C4—124no—
232C2×C3×C4—128no—
233C2×C3×C4C2×#6714yes—
234C2×C3×C4C2×#6714yes—
235C2×Dic3—28no—
236C2×Dic3—22no—
237C2×Dic3—22no—
238C2×Dic3—24no—
239C2×Dic3—24no—
240C2×Dic3—24no—
241C2×Dic3—22no—
242C2×Dic3—24no—
243C2×Dic3—38no—
244C2×Dic3—38no—
245C2×Dic3—44no—
246C2×Dic3—48no—
247C2×Dic3—68no—
248C2×Dic3—616no—
249C2×Dic3—616no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—64no—
254C2×Dic3—124no—
255C2×Dic3—124no—
256C2×Dic3—1216no—
257C2×Dic3C2×D1214yes—
258C2×C32#39818yescomplemented
259C2×C32C2×#12111yescharacteristic
260C2×C32C2×C22⋊Q812yes—
261C2×C32C2×#12311yescharacteristic
262C2×C32C2×#12512yes—
263C2×C32C2×C4⋊Q811yescharacteristic
264C24C2×D3211yescharacteristic
265C22×C4—24no—
266C22×C4—32no—
267C22×C4—34no—
268C22×C4—32no—
269C22×C4—34no—
270C22×C4—62no—
271C22×C4—62no—
272C22×C4—64no—
273C22×C4—64no—
274C22×C4—64no—
275C22×C4—64no—
276C22×C4—62no—
277C22×C4—94no—
278C22×C4—98no—
279C22×C4—184no—
280C22×C4—184no—
281C22×C4#62514yes—
282C22×C4C2×D3212yes—
283C4⋊C4—68no—
284C4⋊C4—68no—
285C4⋊C4—1816no—
286C22×C3—21no—
287C22×C3—22no—
288C22×C3—21no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—28no—
292C22×C3—24no—
293C22×C3—28no—
294C22×C3—24no—
295C22×C3—24no—
296C22×C3#88918yes—
297C22×C3#88918yes—
298C22×C3#89618yes—
299C22×C3#89718yes—
300C22×C3#92914yes—
301C22×C3#93014yes—
302C22×C3#93514yes—
303C22×C3#93814yes—
304C22×C3#94414yes—
305C22×C3#94414yes—
306C22×C3C22×D1211yescharacteristic
307C22×C3C2×#23511yescharacteristic
308C22×C3C2×#23512yes—
309C22×C3C2×D3×D411yescharacteristic
310C22×C3C2×#23711yescharacteristic
311C22×C3C2×#23712yes—
312C22×C3C2×D3×Q812yes—
313C22×C3C2×D3×Q812yes—
314C22×C3C22×#6711yescharacteristic
315C22×C3C22×#6711yescharacteristic
316C3×C4—24no—
317C3×C4—24no—
318C3×C4—44no—
319C3×C4—64no—
320C3×C4—122no—
321C3×C4—124no—
322Dic3—24no—
323Dic3—42no—
324Dic3—44no—
325Dic3—68no—
326Dic3—68no—
327Dic3—128no—
328C32C2×#39811yescharacteristic, complemented, Sylow
329C23#379512yes—
330C23#379714yes—
331C23D3×D1212yes—
332C23#380414yes—
333C23C2×#62512yes—
334C23C22×D3211yescharacteristic
335C2×C4—24no—
336C2×C4—28no—
337C2×C4—34no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—68no—
341C2×C4—64no—
342C2×C4—64no—
343C2×C4—64no—
344C2×C4—62no—
345C2×C4—64no—
346C2×C4—98no—
347C2×C4—128no—
348C2×C4—124no—
349C2×C4—184no—
350C2×C4—184no—
351C2×C4—1816no—
352C2×C4C2×#62514yes—
353C2×C3—22no—
354C2×C3—21no—
355C2×C3—22no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—28no—
359C2×C3#498118yescomplemented
360C2×C3#498318yescomplemented
361C2×C3C2×#88912yes—
362C2×C3C2×#88912yes—
363C2×C3C2×#89612yes—
364C2×C3C2×#89712yes—
365C2×C3C2×#92911yescharacteristic
366C2×C3C2×#93011yescharacteristic
367C2×C3C2×#93511yescharacteristic
368C2×C3C2×#93811yescharacteristic
369C2×C3C2×#94411yescharacteristic
370C2×C3C2×#94411yescharacteristic
371C22#6384718yes—
372C22#6387314yes—
373C22#6389518yes—
374C22#6390814yes—
375C22#6396114yes—
376C22C2×#379511yescharacteristic
377C22C2×#379712yes—
378C22C2×D3×D1211yescharacteristic
379C22C2×#380412yes—
380C22C22×#62511yescharacteristic
381C4—24no—
382C4—64no—
383C4—122no—
384C4—124no—
385C4—188no—
386C3—21no—
387C3C2×#498311yescharacteristic, complemented
388C3C2×#498111yescharacteristic, complemented
389C2#1059121418yesdirect product factor
390C2C2×#6384712yes—
391C2C2×#6387311yescharacteristic
392C2C2×#6389512yes—
393C2C2×#6390811yescharacteristic
394C2C2×#6396111yescharacteristic
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. #10591214C2direct (N × H)
258. C2×C32#398semidirect
328. C32C2×#398semidirect
359. C2×C3#4981semidirect
360. C2×C3#4983semidirect
387. C3C2×#4983semidirect
388. C3C2×#4981semidirect
389. C2#10591214direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C22×#37242
C2×#636582
C2×#635792
#105912142
C2×#49813
C2×#49833