Finite Group Databasebeta

← C2×#10591326 #11808306

Subgroups — C2×#10591326 #11808306

Order 1152.

1977 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C22×#3722C212yesmaximal
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×#63579C212yesmaximal, complemented
6#10591326C218yesmaximal, direct product factor
7C2×#4992—31nomaximal
8C2×#4674—31nomaximal
9C24×C3⋊D3C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C23×C3×Dic3C2212yes—
14C2×#3752—24no—
15C2×#3752C2214yes—
16C2×C3×C4⋊Dic3—24no—
17C2×C3×C4⋊Dic3C2214yescomplemented
18C2×#3722—28no—
19C2×#3722C2218yes—
20C3×C3⋊#95C2214yescomplemented
21#63579C2218yescomplemented
22C22×C3×C4⋊C4—31no—
23C22×(C2×D3)⋊C4—31no—
24C22×(C2×D3)⋊C4—31no—
25C22×(C2×D3)⋊C4—32no—
26C22×(C2×D3)⋊C4—32no—
27C22×(C2×D3)⋊C4—61no—
28C22×C4⋊Dic3D311yescharacteristic, complemented
29C2×C3×#95—31no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95—32no—
32C2×C3⋊#95D311yescharacteristic, complemented
33#4992—38no—
34#4674—38no—
35C24×C32C2311yescharacteristic
36C23×C3⋊D3—22no—
37C23×C3⋊D3—22no—
38C23×C3⋊D3—24no—
39C23×C3⋊D3—24no—
40C23×C3⋊D3D414yes—
41C23×C3⋊D3C2312yes—
42C22×C32×C4—24no—
43C22×C32×C4D414yes—
44C22×C32×C4C2312yes—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3—24no—
47C22×C3⋊Dic3C2312yes—
48C22×C3×Dic3—24no—
49C22×C3×Dic3—24no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3—24no—
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2314yes—
56#3752—28no—
57C3×C4⋊Dic3—28no—
58#3722—216no—
59C2×#397—91noSylow
60C24×D3—31no—
61C24×D3—31no—
62C24×D3—61no—
63C23×C3×C4—21no—
64C23×C3×C4—32no—
65C23×C3×C4—32no—
66C23×C3×C4C2×D311yescharacteristic
67C23×C3×C4C2×D311yescharacteristic
68C23×Dic3—31no—
69C23×Dic3—31no—
70C23×Dic3—61no—
71C23×Dic3C2×D312yes—
72C23×Dic3C2×D312yes—
73C2×C3×C4⋊C4—34no—
74C2×C3×C4⋊C4—64no—
75C2×(C2×D3)⋊C4—34no—
76C2×(C2×D3)⋊C4—34no—
77C2×(C2×D3)⋊C4—38no—
78C2×(C2×D3)⋊C4—38no—
79C2×(C2×D3)⋊C4—64no—
80C2×(C2×D3)⋊C4—68no—
81C2×(C2×D3)⋊C4—68no—
82C2×(C2×D3)⋊C4—68no—
83C2×(C2×D3)⋊C4—64no—
84C2×(C2×D3)⋊C4—64no—
85C2×C4⋊Dic3—24no—
86C2×C4⋊Dic3C2×D314yescomplemented
87C3×#95—34no—
88C3⋊#95—38no—
89C3⋊#95—38no—
90C3⋊#95C2×D314yescomplemented
91C23×C32C2×D412yes—
92C23×C32C2×D412yes—
93C23×C32#4114yes—
94C23×C32#4114yes—
95C23×C32#4112yes—
96C23×C32C2411yescharacteristic
97C22×C3⋊D3—28no—
98C22×C3⋊D3—22no—
99C22×C3⋊D3—22no—
100C22×C3⋊D3—216no—
101C22×C3⋊D3—24no—
102C22×C3⋊D3—24no—
103C22×C3⋊D3—44no—
104C22×C3⋊D3—44no—
105C22×C3⋊D3—48no—
106C22×C3⋊D3C2×D414yes—
107C2×C32×C4—28no—
108C2×C32×C4—24no—
109C2×C32×C4C2×D414yes—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—24no—
112C2×C3⋊Dic3—44no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—48no—
120C2×C3×Dic3—48no—
121C22×C4⋊C4—31no—
122C22×C22⋊C4—92no—
123C22×C22⋊C4—91no—
124#397—98no—
125C2×#95—31no—
126C2×#95—92no—
127C24×C3—21no—
128C24×C3C22×D311yescharacteristic
129C24×C3C22×D311yescharacteristic
130C23×D3—34no—
131C23×D3—34no—
132C23×D3—32no—
133C23×D3—32no—
134C23×D3—64no—
135C23×D3—62no—
136C23×D3—64no—
137C23×D3—64no—
138C23×D3—62no—
139C23×D3—64no—
140C23×D3—64no—
141C23×D3—62no—
142C23×D3—64no—
143C23×D3—62no—
144C23×D3—64no—
145C23×D3—62no—
146C23×D3—124no—
147C23×D3—124no—
148C22×C3×C4—24no—
149C22×C3×C4—24no—
150C22×C3×C4—24no—
151C22×C3×C4—22no—
152C22×C3×C4—34no—
153C22×C3×C4—34no—
154C22×C3×C4—44no—
155C22×C3×C4—64no—
156C22×C3×C4—64no—
157C22×C3×C4—64no—
158C22×C3×C4—64no—
159C22×C3×C4—64no—
160C22×C3×C4—64no—
161C22×C3×C4D1214yes—
162C22×C3×C4#6714yes—
163C22×C3×C4C22×D312yes—
164C22×C3×C4C22×D312yes—
165C22×Dic3—24no—
166C22×Dic3—24no—
167C22×Dic3—24no—
168C22×Dic3—24no—
169C22×Dic3—24no—
170C22×Dic3—24no—
171C22×Dic3—32no—
172C22×Dic3—32no—
173C22×Dic3—62no—
174C22×Dic3—64no—
175C22×Dic3—62no—
176C22×Dic3—64no—
177C22×Dic3—64no—
178C22×Dic3—62no—
179C22×Dic3—124no—
180C22×Dic3C22×D314yes—
181C22×Dic3C22×D314yes—
182C3×C4⋊C4—68no—
183(C2×D3)⋊C4—616no—
184(C2×D3)⋊C4—616no—
185(C2×D3)⋊C4—616no—
186(C2×D3)⋊C4—68no—
187(C2×D3)⋊C4—68no—
188C4⋊Dic3—28no—
189C22×C32#12114yes—
190C22×C32#12318yes—
191C22×C32#12314yes—
192C22×C32#12414yes—
193C22×C32#12618yes—
194C22×C32C22×D411yescharacteristic
195C22×C32C22×D411yescharacteristic
196C22×C32C2×#4112yes—
197C22×C32C2×#4112yes—
198C22×C32C2×#4111yescharacteristic
199C2×C3⋊D3—24no—
200C2×C3⋊D3—28no—
201C2×C3⋊D3—42no—
202C2×C3⋊D3—42no—
203C2×C3⋊D3—44no—
204C2×C3⋊D3—416no—
205C32×C4—24no—
206C3⋊Dic3—42no—
207C3×Dic3—44no—
208C3×Dic3—44no—
209C25—91no—
210C23×C4—32no—
211C23×C4—32no—
212C23×C4—91no—
213C23×C4D3211yescharacteristic
214C2×C4⋊C4—34no—
215C2×C4⋊C4—64no—
216C2×C22⋊C4—98no—
217C2×C22⋊C4—94no—
218C2×C22⋊C4—188no—
219C2×C22⋊C4—184no—
220#95—34no—
221#95—98no—
222C23×C3—21no—
223C23×C3—22no—
224C23×C3—24no—
225C23×C3—22no—
226C23×C3—24no—
227C23×C3—22no—
228C23×C3C2×D1212yes—
229C23×C3#23514yes—
230C23×C3#23514yes—
231C23×C3D3×D412yes—
232C23×C3D3×D412yes—
233C23×C3#23712yes—
234C23×C3#23714yes—
235C23×C3#23912yes—
236C23×C3#23914yes—
237C23×C3C2×#6712yes—
238C23×C3C23×D311yescharacteristic
239C23×C3C23×D311yescharacteristic
240C22×D3—34no—
241C22×D3—34no—
242C22×D3—64no—
243C22×D3—64no—
244C22×D3—64no—
245C22×D3—616no—
246C22×D3—616no—
247C22×D3—616no—
248C22×D3—68no—
249C22×D3—68no—
250C22×D3—62no—
251C22×D3—64no—
252C22×D3—64no—
253C22×D3—62no—
254C22×D3—64no—
255C22×D3—62no—
256C22×D3—64no—
257C22×D3—62no—
258C22×D3—124no—
259C22×D3—124no—
260C22×D3—1216no—
261C22×D3—1216no—
262C22×D3—128no—
263C22×D3—128no—
264C22×D3—124no—
265C22×D3—124no—
266C22×D3—128no—
267C22×D3—128no—
268C22×D3—124no—
269C22×D3—124no—
270C2×C3×C4—28no—
271C2×C3×C4—28no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—24no—
275C2×C3×C4—44no—
276C2×C3×C4—48no—
277C2×C3×C4—64no—
278C2×C3×C4—64no—
279C2×C3×C4—64no—
280C2×C3×C4—64no—
281C2×C3×C4—64no—
282C2×C3×C4—64no—
283C2×C3×C4—128no—
284C2×C3×C4—128no—
285C2×C3×C4C2×D1214yes—
286C2×C3×C4C2×#6714yes—
287C2×Dic3—24no—
288C2×Dic3—24no—
289C2×Dic3—24no—
290C2×Dic3—24no—
291C2×Dic3—24no—
292C2×Dic3—24no—
293C2×Dic3—48no—
294C2×Dic3—48no—
295C2×Dic3—64no—
296C2×Dic3—62no—
297C2×Dic3—64no—
298C2×Dic3—64no—
299C2×Dic3—62no—
300C2×Dic3—124no—
301C2×Dic3—128no—
302C2×Dic3—124no—
303C2×Dic3—124no—
304C2×C32#39718yescomplemented
305C2×C32C2×#12111yescharacteristic
306C2×C32C2×#12312yes—
307C2×C32C2×#12311yescharacteristic
308C2×C32C2×#12411yescharacteristic
309C2×C32C2×#12612yes—
310C3⋊D3—44no—
311C24—92no—
312C24—94no—
313C24—182no—
314C24—184no—
315C24—184no—
316C24—182no—
317C24C2×D3211yescharacteristic
318C22×C4—24no—
319C22×C4—34no—
320C22×C4—34no—
321C22×C4—64no—
322C22×C4—64no—
323C22×C4—64no—
324C22×C4—64no—
325C22×C4—64no—
326C22×C4—64no—
327C22×C4—92no—
328C22×C4—184no—
329C22×C4—182no—
330C22×C4#62614yes—
331C22×C4C2×D3212yes—
332C4⋊C4—68no—
333C22⋊C4—1816no—
334C22⋊C4—188no—
335C22×C3—21no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—28no—
341C22×C3—28no—
342C22×C3—24no—
343C22×C3—24no—
344C22×C3—24no—
345C22×C3#87514yes—
346C22×C3#88318yes—
347C22×C3#88614yes—
348C22×C3#89418yes—
349C22×C3#89514yes—
350C22×C3#89818yes—
351C22×C3#89818yes—
352C22×C3#92914yes—
353C22×C3#93814yes—
354C22×C3#94714yes—
355C22×C3C22×D1211yescharacteristic
356C22×C3C2×#23512yes—
357C22×C3C2×#23512yes—
358C22×C3C2×D3×D411yescharacteristic
359C22×C3C2×D3×D411yescharacteristic
360C22×C3C2×#23711yescharacteristic
361C22×C3C2×#23712yes—
362C22×C3C2×#23911yescharacteristic
363C22×C3C2×#23912yes—
364C22×C3C22×#6711yescharacteristic
365C2×D3—68no—
366C2×D3—68no—
367C2×D3—68no—
368C2×D3—64no—
369C2×D3—64no—
370C2×D3—128no—
371C2×D3—128no—
372C2×D3—124no—
373C2×D3—1232no—
374C2×D3—124no—
375C2×D3—1216no—
376C2×D3—122no—
377C2×D3—122no—
378C2×D3—1216no—
379C2×D3—124no—
380C2×D3—124no—
381C2×D3—122no—
382C2×D3—122no—
383C3×C4—24no—
384C3×C4—24no—
385C3×C4—44no—
386C3×C4—124no—
387C3×C4—124no—
388Dic3—44no—
389Dic3—44no—
390Dic3—124no—
391Dic3—122no—
392Dic3—122no—
393C32C2×#39711yescharacteristic, complemented, Sylow
394C23—94no—
395C23—182no—
396C23—184no—
397C23—184no—
398C23—182no—
399C23—1816no—
400C23—188no—
401C23—368no—
402C23—364no—
403C23—364no—
404C23#379612yes—
405C23#379914yes—
406C23#380212yes—
407C23#380414yes—
408C23C2×#62612yes—
409C23C22×D3211yescharacteristic
410C2×C4—24no—
411C2×C4—28no—
412C2×C4—64no—
413C2×C4—64no—
414C2×C4—64no—
415C2×C4—64no—
416C2×C4—64no—
417C2×C4—64no—
418C2×C4—128no—
419C2×C4—128no—
420C2×C4—184no—
421C2×C4—182no—
422C2×C4—364no—
423C2×C4C2×#62614yes—
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—21no—
427C2×C3—28no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3#467418yescomplemented
431C2×C3#499218yescomplemented
432C2×C3C2×#87511yescharacteristic
433C2×C3C2×#88312yes—
434C2×C3C2×#88611yescharacteristic
435C2×C3C2×#89412yes—
436C2×C3C2×#89511yescharacteristic
437C2×C3C2×#89812yes—
438C2×C3C2×#89812yes—
439C2×C3C2×#92911yescharacteristic
440C2×C3C2×#93811yescharacteristic
441C2×C3C2×#94711yescharacteristic
442D3—128no—
443D3—124no—
444D3—124no—
445C22—188no—
446C22—184no—
447C22—364no—
448C22—362no—
449C22—3616no—
450C22—362no—
451C22#6384818yes—
452C22#6385418yes—
453C22#6386414yes—
454C22#6391614yes—
455C22#6396614yes—
456C22C2×#379611yescharacteristic
457C22C2×#379912yes—
458C22C2×#380211yescharacteristic
459C22C2×#380412yes—
460C22C22×#62611yescharacteristic
461C4—24no—
462C4—124no—
463C4—124no—
464C4—362no—
465C3—21no—
466C3C2×#467411yescharacteristic, complemented
467C3C2×#499211yescharacteristic, complemented
468C2—364no—
469C2#1059132618yesdirect product factor
470C2C2×#6384812yes—
471C2C2×#6385412yes—
472C2C2×#6386411yescharacteristic
473C2C2×#6391611yescharacteristic
474C2C2×#6396611yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32C2×#397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. C2×#63579C2semidirect
6. #10591326C2direct (N × H)
17. C2×C3×C4⋊Dic3C22semidirect
20. C3×C3⋊#95C22semidirect
21. #63579C22semidirect
28. C22×C4⋊Dic3D3semidirect
32. C2×C3⋊#95D3semidirect
86. C2×C4⋊Dic3C2×D3semidirect
90. C3⋊#95C2×D3semidirect
304. C2×C32#397semidirect
393. C32C2×#397semidirect
430. C2×C3#4674semidirect
431. C2×C3#4992semidirect
466. C3C2×#4674semidirect
467. C3C2×#4992semidirect
469. C2#10591326direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37522
C22×C3×C4⋊Dic32
C22×#37222
C2×C3×C3⋊#952
C2×#635792
#105913262
C2×#49923
C2×#46743