Finite Group Databasebeta

← C2×#10591227 #11808520

Subgroups — C2×#10591227 #11808520

Order 1152.

1417 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×#63579C212yesmaximal
5C2×#63579C212yesmaximal
6#10591227C218yesmaximal, direct product factor
7C2×#4985—31nomaximal
8C2×#4659—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2212yes—
14C2×#3750—24no—
15C2×#3750C2214yes—
16C2×C3×C4⋊Dic3—24no—
17C2×C3×C4⋊Dic3C2214yes—
18C3×C3⋊#95C2214yes—
19#63579C2218yes—
20#63579C2218yes—
21C22×C3×C4⋊C4—31no—
22C22×C4⋊Dic3D311yescharacteristic
23C22×Dic3⋊C4—31no—
24C22×Dic3⋊C4—31no—
25C22×Dic3⋊C4—61no—
26C2×C3×#95—31no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95D311yescharacteristic
32#4985—38no—
33#4659—38no—
34C24×C32C2311yescharacteristic
35C22×C32×C4—24no—
36C22×C32×C4D414yes—
37C22×C32×C4C2312yes—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3—22no—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3Q814yes—
43C22×C3⋊Dic3C2312yes—
44C22×C3⋊Dic3C2312yes—
45C22×C3×Dic3—24no—
46C22×C3×Dic3—28no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3—24no—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2314yes—
52#3750—28no—
53C3×C4⋊Dic3—28no—
54C2×#400—91noSylow
55C23×C3×C4—21no—
56C23×C3×C4—32no—
57C23×C3×C4—32no—
58C23×C3×C4C2×D311yescharacteristic
59C23×C3×C4C2×D311yescharacteristic
60C23×Dic3—31no—
61C23×Dic3—31no—
62C23×Dic3—31no—
63C23×Dic3—31no—
64C23×Dic3—61no—
65C23×Dic3—61no—
66C23×Dic3C2×D312yes—
67C23×Dic3C2×D312yes—
68C2×C3×C4⋊C4—34no—
69C2×C3×C4⋊C4—64no—
70C2×C4⋊Dic3—24no—
71C2×C4⋊Dic3C2×D314yes—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—34no—
74C2×Dic3⋊C4—64no—
75C2×Dic3⋊C4—68no—
76C2×Dic3⋊C4—64no—
77C2×Dic3⋊C4—64no—
78C3×#95—34no—
79C3⋊#95—38no—
80C3⋊#95—38no—
81C3⋊#95—38no—
82C3⋊#95—38no—
83C3⋊#95C2×D314yes—
84C23×C32C2×D412yes—
85C23×C32C2×Q812yes—
86C23×C32#4114yes—
87C23×C32#4114yes—
88C23×C32#4112yes—
89C23×C32C2411yescharacteristic
90C2×C32×C4—28no—
91C2×C32×C4—24no—
92C2×C32×C4C2×D414yes—
93C2×C3⋊Dic3—28no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—44no—
99C2×C3⋊Dic3C2×Q814yes—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3—28no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—48no—
106C2×C3×Dic3—48no—
107C22×C4⋊C4—31no—
108C22×C4⋊C4—91no—
109#400—98no—
110C2×#95—31no—
111C2×#95—92no—
112C2×#95—92no—
113C24×C3—21no—
114C24×C3C22×D311yescharacteristic
115C24×C3C22×D311yescharacteristic
116C22×C3×C4—24no—
117C22×C3×C4—24no—
118C22×C3×C4—24no—
119C22×C3×C4—22no—
120C22×C3×C4—34no—
121C22×C3×C4—34no—
122C22×C3×C4—44no—
123C22×C3×C4—64no—
124C22×C3×C4—68no—
125C22×C3×C4—64no—
126C22×C3×C4—64no—
127C22×C3×C4—64no—
128C22×C3×C4D1214yes—
129C22×C3×C4#6714yes—
130C22×C3×C4C22×D312yes—
131C22×C3×C4C22×D312yes—
132C22×Dic3—24no—
133C22×Dic3—28no—
134C22×Dic3—24no—
135C22×Dic3—24no—
136C22×Dic3—24no—
137C22×Dic3—34no—
138C22×Dic3—34no—
139C22×Dic3—32no—
140C22×Dic3—32no—
141C22×Dic3—32no—
142C22×Dic3—32no—
143C22×Dic3—62no—
144C22×Dic3—64no—
145C22×Dic3—62no—
146C22×Dic3—64no—
147C22×Dic3—64no—
148C22×Dic3—62no—
149C22×Dic3—62no—
150C22×Dic3—62no—
151C22×Dic3—62no—
152C22×Dic3—64no—
153C22×Dic3—62no—
154C22×Dic3—64no—
155C22×Dic3—64no—
156C22×Dic3—62no—
157C22×Dic3—124no—
158C22×Dic3C22×D314yes—
159C22×Dic3C22×D314yes—
160C3×C4⋊C4—68no—
161C4⋊Dic3—28no—
162Dic3⋊C4—616no—
163Dic3⋊C4—68no—
164Dic3⋊C4—68no—
165C22×C32C22⋊Q814yes—
166C22×C32#12314yes—
167C22×C32#12414yes—
168C22×C32#12518yes—
169C22×C32#12618yes—
170C22×C32C22×D411yescharacteristic
171C22×C32C22×Q811yescharacteristic
172C22×C32C2×#4112yes—
173C22×C32C2×#4112yes—
174C22×C32C2×#4111yescharacteristic
175C32×C4—24no—
176C3⋊Dic3—24no—
177C3⋊Dic3—42no—
178C3×Dic3—44no—
179C3×Dic3—44no—
180C23×C4—32no—
181C23×C4—32no—
182C23×C4—91no—
183C23×C4—91no—
184C23×C4D3211yescharacteristic
185C2×C4⋊C4—34no—
186C2×C4⋊C4—64no—
187C2×C4⋊C4—94no—
188C2×C4⋊C4—184no—
189#95—34no—
190#95—98no—
191#95—98no—
192C23×C3—21no—
193C23×C3—24no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—24no—
197C23×C3—22no—
198C23×C3C2×D1212yes—
199C23×C3#23514yes—
200C23×C3#23514yes—
201C23×C3#23714yes—
202C23×C3#23712yes—
203C23×C3#23714yes—
204C23×C3D3×Q812yes—
205C23×C3D3×Q812yes—
206C23×C3#23912yes—
207C23×C3C2×#6712yes—
208C23×C3C23×D311yescharacteristic
209C23×C3C23×D311yescharacteristic
210C2×C3×C4—28no—
211C2×C3×C4—28no—
212C2×C3×C4—24no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—44no—
216C2×C3×C4—48no—
217C2×C3×C4—64no—
218C2×C3×C4—68no—
219C2×C3×C4—64no—
220C2×C3×C4—64no—
221C2×C3×C4—64no—
222C2×C3×C4—128no—
223C2×C3×C4—128no—
224C2×C3×C4C2×D1214yes—
225C2×C3×C4C2×#6714yes—
226C2×Dic3—24no—
227C2×Dic3—28no—
228C2×Dic3—24no—
229C2×Dic3—24no—
230C2×Dic3—24no—
231C2×Dic3—34no—
232C2×Dic3—34no—
233C2×Dic3—48no—
234C2×Dic3—48no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—616no—
239C2×Dic3—68no—
240C2×Dic3—68no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—64no—
246C2×Dic3—62no—
247C2×Dic3—64no—
248C2×Dic3—64no—
249C2×Dic3—62no—
250C2×Dic3—124no—
251C2×Dic3—128no—
252C2×Dic3—124no—
253C2×Dic3—124no—
254C2×C32#40018yescomplemented
255C2×C32C2×C22⋊Q811yescharacteristic
256C2×C32C2×#12311yescharacteristic
257C2×C32C2×#12411yescharacteristic
258C2×C32C2×#12512yes—
259C2×C32C2×#12612yes—
260C24C2×D3211yescharacteristic
261C22×C4—24no—
262C22×C4—34no—
263C22×C4—34no—
264C22×C4—64no—
265C22×C4—68no—
266C22×C4—64no—
267C22×C4—64no—
268C22×C4—64no—
269C22×C4—92no—
270C22×C4—94no—
271C22×C4—92no—
272C22×C4—182no—
273C22×C4—182no—
274C22×C4—184no—
275C22×C4—182no—
276C22×C4#62614yes—
277C22×C4C2×D3212yes—
278C4⋊C4—68no—
279C4⋊C4—188no—
280C22×C3—22no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—22no—
284C22×C3—21no—
285C22×C3—28no—
286C22×C3—28no—
287C22×C3—24no—
288C22×C3—24no—
289C22×C3—24no—
290C22×C3#87514yes—
291C22×C3#87918yes—
292C22×C3#88614yes—
293C22×C3#88918yes—
294C22×C3#88918yes—
295C22×C3#89714yes—
296C22×C3#89818yes—
297C22×C3#92914yes—
298C22×C3#93614yes—
299C22×C3#94614yes—
300C22×C3C22×D1211yescharacteristic
301C22×C3C2×#23512yes—
302C22×C3C2×#23512yes—
303C22×C3C2×#23712yes—
304C22×C3C2×#23711yescharacteristic
305C22×C3C2×#23712yes—
306C22×C3C2×D3×Q811yescharacteristic
307C22×C3C2×D3×Q811yescharacteristic
308C22×C3C2×#23911yescharacteristic
309C22×C3C22×#6711yescharacteristic
310C3×C4—24no—
311C3×C4—24no—
312C3×C4—44no—
313C3×C4—124no—
314C3×C4—124no—
315Dic3—44no—
316Dic3—44no—
317Dic3—68no—
318Dic3—64no—
319Dic3—64no—
320Dic3—124no—
321Dic3—122no—
322Dic3—122no—
323C32C2×#40011yescharacteristic, complemented, Sylow
324C23#379514yes—
325C23#379612yes—
326C23#379712yes—
327C23#380414yes—
328C23C2×#62612yes—
329C23C22×D3211yescharacteristic
330C2×C4—24no—
331C2×C4—28no—
332C2×C4—64no—
333C2×C4—68no—
334C2×C4—64no—
335C2×C4—64no—
336C2×C4—64no—
337C2×C4—94no—
338C2×C4—128no—
339C2×C4—128no—
340C2×C4—182no—
341C2×C4—182no—
342C2×C4—188no—
343C2×C4—184no—
344C2×C4—182no—
345C2×C4—364no—
346C2×C4C2×#62614yes—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—28no—
353C2×C3#465918yescomplemented
354C2×C3#498518yescomplemented
355C2×C3C2×#87511yescharacteristic
356C2×C3C2×#87912yes—
357C2×C3C2×#88611yescharacteristic
358C2×C3C2×#88912yes—
359C2×C3C2×#88912yes—
360C2×C3C2×#89711yescharacteristic
361C2×C3C2×#89812yes—
362C2×C3C2×#92911yescharacteristic
363C2×C3C2×#93611yescharacteristic
364C2×C3C2×#94611yescharacteristic
365C22#6384718yes—
366C22#6385818yes—
367C22#6386014yes—
368C22#6387114yes—
369C22#6396614yes—
370C22C2×#379512yes—
371C22C2×#379611yescharacteristic
372C22C2×#379711yescharacteristic
373C22C2×#380412yes—
374C22C22×#62611yescharacteristic
375C4—24no—
376C4—124no—
377C4—124no—
378C4—184no—
379C4—362no—
380C3—21no—
381C3C2×#465911yescharacteristic, complemented
382C3C2×#498511yescharacteristic, complemented
383C2#1059122718yesdirect product factor
384C2C2×#6384712yes—
385C2C2×#6385812yes—
386C2C2×#6386011yescharacteristic
387C2C2×#6387111yescharacteristic
388C2C2×#6396611yescharacteristic
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. #10591227C2direct (N × H)
254. C2×C32#400semidirect
323. C32C2×#400semidirect
353. C2×C3#4659semidirect
354. C2×C3#4985semidirect
381. C3C2×#4659semidirect
382. C3C2×#4985semidirect
383. C2#10591227direct (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×C3×C4⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#105912272
C2×#49853
C2×#46593