Finite Group Databasebeta

← C2×#10591083 #11857800

Subgroups — C2×#10591083 #11857800

Order 1152.

1753 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×C3×#235C211yesmaximal, characteristic
2C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C2×#63565C212yesmaximal, complemented
5#10591083C218yesmaximal, direct product factor
6C2×#63562C212yesmaximal, complemented
7C2×#5233—31nomaximal
8C2×#5002—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C22×C3×#67—21no—
11C2×C3×#235—24no—
12C2×C3×#235—22no—
13C2×C3×#235C418yescomplemented
14C2×C3×#235C2214yes—
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3—21no—
17C22×C3×Dic6C2211yescharacteristic
18C22×C3⋊(C3⋊C8)—24no—
19C22×C3⋊(C3⋊C8)C2212yes—
20C22×C3⋊(C3⋊C8)C2214yescomplemented
21C2×C3×#217—21no—
22C3×#926—22no—
23C3×#926C2214yescomplemented
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4×Dic3—21no—
26#63565C2218yescomplemented
27#63562C2218yescomplemented
28C22×C3×#41—31no—
29C22×#235D311yescharacteristic
30C2×C3×#117—31no—
31C2×#926D311yescharacteristic, complemented
32C23×C3⋊C8—31no—
33C23×C3⋊C8—31no—
34C23×C3⋊C8—61no—
35#5233—38no—
36C2×#835—32no—
37C2×#832—32no—
38#5002—38no—
39C2×#810—32no—
40C2×#809—32no—
41C24×C32D411yescharacteristic
42C23×C3×D3—21no—
43C22×C32×C4C2×C414yes—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D412yes—
46C22×C32×C4D414yes—
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2312yes—
49C2×C3×#67—28no—
50C2×C3×#67—24no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—22no—
53C3×#235—216no—
54C3×#235—28no—
55C3×#235C2×C4116yescomplemented
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—28no—
61C2×C3×C4×D3—24no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2×C414yes—
65C2×C3×Dic6C2312yes—
66C2×C3⋊(C3⋊C8)—24no—
67C2×C3⋊(C3⋊C8)—28no—
68C2×C3⋊(C3⋊C8)C2314yes—
69C3×#217—24no—
70C3×C4⋊Dic3—22no—
71C3×C4⋊Dic3C2314yes—
72C3×C4×Dic3—24no—
73C2×#416—91noSylow
74C2×C3×#41—38no—
75C2×C3×#41—34no—
76C2×C3×#41—64no—
77C2×C3×#41—62no—
78C22×C3×Q8—31no—
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—21no—
82C23×C3×C4—61no—
83C23×C3×C4C2×D311yescharacteristic
84C23×C3×C4C2×D311yescharacteristic
85C22×#67—21no—
86C2×#235—22no—
87C2×#235—24no—
88C2×#235Dic318yescomplemented
89C2×#235C2×D314yes—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—21no—
92C22×Dic6C2×D311yescharacteristic
93C3×#117—34no—
94C3×#117—62no—
95C2×C3×C4⋊C4—32no—
96C2×C3×C22⋊C4—61no—
97C2×C3×C42—61no—
98C2×#217—21no—
99#926—22no—
100#926C2×D314yescomplemented
101C2×C4⋊Dic3C2×D312yes—
102C2×C4×Dic3—21no—
103C22×C3⋊C8—32no—
104C22×C3⋊C8—32no—
105C22×C3⋊C8—34no—
106C22×C3⋊C8—34no—
107C22×C3⋊C8—62no—
108C22×C3⋊C8—64no—
109C22×C3⋊C8—68no—
110C22×C3⋊C8—64no—
111C22×C3⋊C8—64no—
112#835—38no—
113#832—38no—
114#810—38no—
115#809—38no—
116C23×C32—24no—
117C23×C32C22⋊C414yes—
118C23×C32C2×D412yes—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—24no—
121C22×C3×D3—22no—
122C22×C3×D3—44no—
123C2×C32×C4C22⋊C414yes—
124C2×C32×C4C22⋊C418yes—
125C2×C32×C4C22×C412yes—
126C2×C32×C4C22×C414yes—
127C2×C32×C4C2×D412yes—
128C2×C32×C4C2×D414yes—
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2411yescharacteristic
132C3×#67—216no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—44no—
137C3×D12—24no—
138C3×D12—22no—
139C3×D12C22×C414yes—
140C3×C4×D3—216no—
141C3×Dic6—24no—
142C3×Dic6—22no—
143C3×Dic6C22×C414yes—
144C3⋊(C3⋊C8)—24no—
145C22×#41—31no—
146C23×C8—91no—
147C2×#117—31no—
148#416—98no—
149C2×#103—92no—
150C2×#102—92no—
151C24×C3—21no—
152C24×C3—61no—
153C24×C3#6711yescharacteristic
154C24×C3#6711yescharacteristic
155C23×D3—21no—
156C3×#41—316no—
157C3×#41—616no—
158C3×#41—68no—
159C2×C3×Q8—34no—
160C2×C3×Q8—32no—
161C2×C3×Q8—62no—
162C2×C3×Q8—61no—
163C2×C3×D4—34no—
164C2×C3×D4—32no—
165C2×C3×D4—68no—
166C2×C3×D4—64no—
167C2×C3×D4—62no—
168C2×C3×D4—61no—
169C22×C3×C4—24no—
170C22×C3×C4—22no—
171C22×C3×C4—21no—
172C22×C3×C4—24no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—61no—
176C22×C3×C4—68no—
177C22×C3×C4—64no—
178C22×C3×C4—62no—
179C22×C3×C4C4×D314yes—
180C22×C3×C4D1214yes—
181C22×C3×C4C2×Dic314yes—
182C22×C3×C4#6712yes—
183C22×C3×C4#6712yes—
184C22×C3×C4#6711yescharacteristic
185C22×C3×C4#6711yescharacteristic
186C22×C3×C4#6714yes—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D312yes—
191C2×#67—28no—
192C2×#67—24no—
193C22×Dic3—21no—
194C22×Dic3—22no—
195#235—216no—
196#235—28no—
197#235C2×Dic3116yescomplemented
198C2×D12—21no—
199C2×D12—22no—
200C2×D12C2×Dic314yes—
201C2×D12C22×D312yes—
202C2×C4×D3—28no—
203C2×C4×D3—24no—
204C2×Dic6—21no—
205C2×Dic6—22no—
206C2×Dic6C2×Dic314yes—
207C2×Dic6C22×D312yes—
208C3×C4⋊C4—34no—
209C3×C4⋊C4—62no—
210C3×C22⋊C4—64no—
211C3×C42—64no—
212#217—24no—
213C4⋊Dic3—22no—
214C4⋊Dic3C22×D314yes—
215C4×Dic3—24no—
216C2×C3⋊C8—34no—
217C2×C3⋊C8—34no—
218C2×C3⋊C8—64no—
219C2×C3⋊C8—68no—
220C2×C3⋊C8—616no—
221C2×C3⋊C8—64no—
222C2×C3⋊C8—68no—
223C2×C3⋊C8—64no—
224C2×C3⋊C8—68no—
225C22×C32—24no—
226C22×C32—28no—
227C22×C32C2×C22⋊C414yes—
228C22×C32C2×C22⋊C412yes—
229C22×C32#13514yes—
230C22×C32C22×D411yescharacteristic
231C2×C3×D3—24no—
232C2×C3×D3—44no—
233C2×C3×D3—48no—
234C32×C4C2×C22⋊C412yes—
235C32×C4C2×C22⋊C414yes—
236C32×C4C23×C411yescharacteristic
237C32×C4C22×D411yescharacteristic
238C3×Dic3—24no—
239C3×Dic3—44no—
240C2×#41—38no—
241C2×#41—34no—
242C2×#41—62no—
243C2×#41—64no—
244C22×Q8—31no—
245C22×D4—31no—
246C22×D4—61no—
247C23×C4—61no—
248C23×C4D3211yescharacteristic
249C22×C8—92no—
250C22×C8—94no—
251C22×C8—184no—
252#117—34no—
253#117—62no—
254C2×C4⋊C4—32no—
255C2×C22⋊C4—61no—
256C2×C42—61no—
257#103—98no—
258#102—98no—
259C23×C3—28no—
260C23×C3—24no—
261C23×C3—24no—
262C23×C3—24no—
263C23×C3—22no—
264C23×C3—21no—
265C23×C3—64no—
266C23×C3—62no—
267C23×C3—124no—
268C23×C3(C2×D3)⋊C414yes—
269C23×C3#21714yes—
270C23×C3C2×#6712yes—
271C23×C3C2×#6712yes—
272C23×C3C2×#6711yescharacteristic
273C23×C3C2×#6711yescharacteristic
274C22×D3—24no—
275C22×D3—22no—
276C22×D3—44no—
277C3×Q8—34no—
278C3×Q8—64no—
279C3×Q8—62no—
280C3×D4—34no—
281C3×D4—616no—
282C3×D4—64no—
283C3×D4—62no—
284C2×C3×C4—21no—
285C2×C3×C4—24no—
286C2×C3×C4—28no—
287C2×C3×C4—22no—
288C2×C3×C4—24no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—24no—
293C2×C3×C4—64no—
294C2×C3×C4—62no—
295C2×C3×C4—616no—
296C2×C3×C4—64no—
297C2×C3×C4—124no—
298C2×C3×C4(C2×D3)⋊C414yes—
299C2×C3×C4(C2×D3)⋊C418yes—
300C2×C3×C4#21714yes—
301C2×C3×C4#21718yes—
302C2×C3×C4C2×C4×D312yes—
303C2×C3×C4C2×C4×D314yes—
304C2×C3×C4C2×D1212yes—
305C2×C3×C4C2×D1214yes—
306C2×C3×C4C22×Dic312yes—
307C2×C3×C4C22×Dic314yes—
308C2×C3×C4C2×#6712yes—
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6712yes—
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6712yes—
313C2×C3×C4C2×#6714yes—
314C2×C3×C4C23×D311yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316#67—216no—
317C2×Dic3—24no—
318C2×Dic3—22no—
319C2×Dic3—24no—
320C2×Dic3—44no—
321D12—24no—
322D12—22no—
323D12C22×Dic314yes—
324C4×D3—216no—
325Dic6—24no—
326Dic6—22no—
327Dic6C22×Dic314yes—
328C3⋊C8—68no—
329C3⋊C8—64no—
330C3⋊C8—64no—
331C2×C32—24no—
332C2×C32#41614yescomplemented
333C2×C32C22×C22⋊C411yescharacteristic
334C2×C32C2×#13512yes—
335C3×D3—44no—
336C24—61no—
337C24#62511yescharacteristic
338#41—316no—
339#41—616no—
340#41—68no—
341C2×Q8—32no—
342C2×Q8—34no—
343C2×Q8—61no—
344C2×Q8—62no—
345C2×D4—32no—
346C2×D4—34no—
347C2×D4—68no—
348C2×D4—64no—
349C2×D4—61no—
350C2×D4—62no—
351C22×C4—61no—
352C22×C4—68no—
353C22×C4—64no—
354C22×C4—62no—
355C22×C4D3×Dic314yes—
356C22×C4#62512yes—
357C22×C4#62511yescharacteristic
358C22×C4#62614yes—
359C22×C4C2×D3211yescharacteristic
360C22×C4C2×D3212yes—
361C2×C8—94no—
362C2×C8—184no—
363C2×C8—188no—
364C4⋊C4—34no—
365C4⋊C4—62no—
366C22⋊C4—64no—
367C42—64no—
368C22×C3—216no—
369C22×C3—28no—
370C22×C3—28no—
371C22×C3—28no—
372C22×C3—24no—
373C22×C3—24no—
374C22×C3—21no—
375C22×C3—24no—
376C22×C3—24no—
377C22×C3—22no—
378C22×C3—64no—
379C22×C3—128no—
380C22×C3—124no—
381C22×C3C2×(C2×D3)⋊C414yes—
382C22×C3C2×(C2×D3)⋊C412yes—
383C22×C3#95014yes—
384C22×C3#95014yes—
385C22×C3C2×#21714yes—
386C22×C3C2×#21712yes—
387C22×C3C22×#6711yescharacteristic
388C22×C3C22×#6711yescharacteristic
389C2×D3—24no—
390C2×D3—48no—
391C2×D3—44no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—24no—
395C3×C4—22no—
396C3×C4—64no—
397C3×C4—124no—
398C3×C4C2×(C2×D3)⋊C414yes—
399C3×C4C2×(C2×D3)⋊C412yes—
400C3×C4C2×#21712yes—
401C3×C4C2×#21714yes—
402C3×C4C22×C4×D311yescharacteristic
403C3×C4C22×D1211yescharacteristic
404C3×C4C23×Dic311yescharacteristic
405C3×C4C22×#6711yescharacteristic
406Dic3—24no—
407Dic3—44no—
408C32C2×#41611yescharacteristic, complemented, Sylow
409C23—24no—
410C23—62no—
411C23—64no—
412C23—124no—
413C23(C2×D3)⋊Dic314yes—
414C23C2×#62512yes—
415C23C2×#62511yescharacteristic
416Q8—34no—
417Q8—62no—
418Q8—64no—
419D4—34no—
420D4—616no—
421D4—62no—
422D4—64no—
423C2×C4—62no—
424C2×C4—64no—
425C2×C4—616no—
426C2×C4—64no—
427C2×C4—124no—
428C2×C4(C2×D3)⋊Dic314yes—
429C2×C4(C2×D3)⋊Dic318yes—
430C2×C4C2×D3×Dic312yes—
431C2×C4C2×D3×Dic314yes—
432C2×C4C2×#62512yes—
433C2×C4C2×#62511yescharacteristic
434C2×C4C2×#62612yes—
435C2×C4C2×#62614yes—
436C2×C4C22×D3211yescharacteristic
437C8—184no—
438C2×C3—28no—
439C2×C3—24no—
440C2×C3—24no—
441C2×C3—24no—
442C2×C3—21no—
443C2×C3—22no—
444C2×C3—124no—
445C2×C3#500214yescomplemented
446C2×C3#523314yescomplemented
447C2×C3C22×(C2×D3)⋊C411yescharacteristic
448C2×C3C2×#95012yes—
449C2×C3C2×#95012yes—
450C2×C3C22×#21711yescharacteristic
451D3—44no—
452C22—28no—
453C22—24no—
454C22—64no—
455C22—128no—
456C22—124no—
457C22#6382214yes—
458C22C2×(C2×D3)⋊Dic314yes—
459C22C2×(C2×D3)⋊Dic312yes—
460C22C22×#62511yescharacteristic
461C4—64no—
462C4—124no—
463C4C2×(C2×D3)⋊Dic314yes—
464C4C2×(C2×D3)⋊Dic312yes—
465C4C22×D3×Dic311yescharacteristic
466C4C22×#62611yescharacteristic
467C3—21no—
468C3C2×#500211yescharacteristic, complemented
469C3C2×#523311yescharacteristic, complemented
470C2—24no—
471C2—124no—
472C2#1059108314yesdirect product factor
473C2C2×#6382212yes—
474C2C22×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC22×C4#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC22×C3×#235C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C23×C3⋊(C3⋊C8)C2semidirect
3. C2×C3×#926C2semidirect
4. C2×#63565C2semidirect
5. #10591083C2direct (N × H)
6. C2×#63562C2semidirect
13. C2×C3×#235C4semidirect
20. C22×C3⋊(C3⋊C8)C22semidirect
23. C3×#926C22semidirect
26. #63565C22semidirect
27. #63562C22semidirect
31. C2×#926D3semidirect
55. C3×#235C2×C4semidirect
88. C2×#235Dic3semidirect
100. #926C2×D3semidirect
197. #235C2×Dic3semidirect
332. C2×C32#416semidirect
408. C32C2×#416semidirect
445. C2×C3#5002semidirect
446. C2×C3#5233semidirect
468. C3C2×#5002semidirect
469. C3C2×#5233semidirect
472. C2#10591083direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C23×C3⋊(C3⋊C8)2
C2×C3×#9262
C2×#635652
#105910832
C2×#635622
C2×#52333
C2×#50023