Finite Group Databasebeta

← C2×#10591232 #11857530

Subgroups — C2×#10591232 #11857530

Order 1152.

2021 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×C3×#926C212yesmaximal, complemented
3C2×#63581C214yesmaximal, complemented
4#10591232C218yesmaximal, direct product factor
5C2×#5006—32nomaximal
6C23×C32×C4C2211yescharacteristic
7C22×#638C2212yes—
8C2×#3828—22no—
9C2×#3828—22no—
10C2×#3828—24no—
11C2×#3828C414yescomplemented
12C2×#3828C2214yes—
13C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
14C22×C4×C3⋊D3C412yescomplemented
15C22×#634C411yescharacteristic, complemented
16C2×C3×#217C2214yes—
17C3×#926—24no—
18C3×#926C2218yescomplemented
19C2×C3×C4⋊Dic3—22no—
20C2×C3×C4×Dic3—22no—
21#63581C22116yescomplemented
22C22×#235—32no—
23C22×#235—61no—
24C2×C3×#117—32no—
25C2×#926D312yescomplemented
26#5006—316no—
27C2×#806—38no—
28C24×C32C2311yescharacteristic
29C23×C3⋊D3C2×C412yes—
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2×C412yes—
33C22×C32×C4D412yes—
34C22×C32×C4D412yes—
35C22×C32×C4D414yes—
36C22×C32×C4C2312yes—
37C2×#638—24no—
38C2×#638—24no—
39C2×#638C2×C414yes—
40C2×#638C2314yes—
41C22×C3⋊Dic3C2×C412yes—
42#3828—28no—
43#3828—28no—
44#3828—28no—
45#3828—28no—
46C2×C4⋊(C3⋊D3)—22no—
47C2×C4⋊(C3⋊D3)—22no—
48C2×C4⋊(C3⋊D3)C2×C414yescomplemented
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3C2×C418yescomplemented
53C2×#634—22no—
54C2×#634—22no—
55C2×#634C2×C414yescomplemented
56C22×C3×Dic3—24no—
57C3×#217—24no—
58C3×#217C2318yes—
59C3×C4⋊Dic3—28no—
60C3×C4×Dic3—28no—
61C2×#410—91noSylow
62C23×C3×C4—21no—
63C23×C3×C4C2×D312yes—
64C22×#67—34no—
65C22×#67—62no—
66C2×#235—38no—
67C2×#235—38no—
68C2×#235—64no—
69C2×#235—64no—
70C2×#235—64no—
71C2×#235—68no—
72C2×#235—64no—
73C2×#235—62no—
74C2×#235—62no—
75C2×#235—64no—
76C2×#235—62no—
77C2×#235—62no—
78C2×#235—64no—
79C22×D12—32no—
80C22×D12—61no—
81C22×C4×D3—34no—
82C22×C4×D3—62no—
83C22×Dic6—32no—
84C22×Dic6—61no—
85C3×#117—38no—
86C3×#117—64no—
87C2×C3×C4⋊C4—62no—
88C2×C3×C22⋊C4—34no—
89C2×C3×C42—62no—
90C2×#217C2×D314yes—
91#926—24no—
92#926C2×D318yescomplemented
93C2×C4⋊Dic3—22no—
94C2×C4×Dic3—22no—
95#806—332no—
96C23×C32—42no—
97C23×C32C22×C411yescharacteristic
98C23×C32C22×C411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32C2×D412yes—
101C23×C32C2411yescharacteristic
102C22×C3⋊D3—22no—
103C22×C3⋊D3—22no—
104C22×C3⋊D3—44no—
105C22×C3⋊D3C22×C414yes—
106C2×C32×C4C22⋊C412yes—
107C2×C32×C4C22⋊C412yes—
108C2×C32×C4C22⋊C412yes—
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22⋊C414yes—
112C2×C32×C4C22⋊C414yes—
113C2×C32×C4C22×C412yes—
114C2×C32×C4C22×C412yes—
115C2×C32×C4C2×D414yes—
116C2×C32×C4C2×D414yes—
117#638—28no—
118#638—28no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3C22×C414yes—
122C4⋊(C3⋊D3)—28no—
123C4×C3⋊D3—28no—
124C4×C3⋊D3—28no—
125#634—28no—
126C2×C3×Dic3—28no—
127C2×C3×Dic3—48no—
128C22×#41—91no—
129C2×#117—32no—
130#410—98no—
131C2×#99—94no—
132C24×C3—21no—
133C24×C3C22×D312yes—
134C23×D3—34no—
135C23×D3—62no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—24no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—64no—
144C22×C3×C4C4×D312yes—
145C22×C3×C4C4×D312yes—
146C22×C3×C4C4×D314yes—
147C22×C3×C4D1212yes—
148C22×C3×C4D1212yes—
149C22×C3×C4D1214yes—
150C22×C3×C4#6712yes—
151C22×C3×C4#6712yes—
152C22×C3×C4#6714yes—
153C22×C3×C4C22×D314yes—
154C2×#67—38no—
155C2×#67—38no—
156C2×#67—64no—
157C2×#67—64no—
158C2×#67—68no—
159C2×#67—68no—
160C2×#67—64no—
161C2×#67—64no—
162C2×#67—64no—
163C2×#67—64no—
164C22×Dic3—24no—
165C22×Dic3—34no—
166C22×Dic3—62no—
167#235—616no—
168#235—616no—
169#235—616no—
170#235—616no—
171#235—68no—
172#235—68no—
173#235—68no—
174#235—68no—
175#235—68no—
176#235—68no—
177#235—68no—
178#235—68no—
179C2×D12—38no—
180C2×D12—64no—
181C2×D12—64no—
182C2×D12—64no—
183C2×D12—64no—
184C2×D12—62no—
185C2×D12—62no—
186C2×C4×D3—316no—
187C2×C4×D3—68no—
188C2×C4×D3—68no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×C4×D3—68no—
192C2×C4×D3—64no—
193C2×C4×D3—64no—
194C2×Dic6—38no—
195C2×Dic6—64no—
196C2×Dic6—64no—
197C2×Dic6—64no—
198C2×Dic6—64no—
199C2×Dic6—62no—
200C2×Dic6—62no—
201C3×C4⋊C4—68no—
202C3×C22⋊C4—38no—
203C3×C22⋊C4—64no—
204C3×C42—68no—
205#217—24no—
206#217C22×D318yes—
207C4⋊Dic3—28no—
208C4×Dic3—28no—
209C22×C32—22no—
210C22×C32—24no—
211C22×C32—41no—
212C22×C32—42no—
213C22×C32—41no—
214C22×C32C2×C22⋊C411yescharacteristic
215C22×C32C2×C22⋊C412yes—
216C22×C32C2×C22⋊C411yescharacteristic
217C22×C32C23×C411yescharacteristic
218C22×C32C22×D412yes—
219C2×C3⋊D3—24no—
220C2×C3⋊D3—44no—
221C2×C3⋊D3—44no—
222C2×C3⋊D3—44no—
223C32×C4C2×C22⋊C414yes—
224C32×C4C2×C22⋊C412yes—
225C32×C4C2×C22⋊C412yes—
226C3⋊Dic3—24no—
227C3×Dic3—48no—
228C2×#41—94no—
229C2×#41—94no—
230C2×#41—182no—
231C2×#41—184no—
232C2×#41—182no—
233C22×Q8—91no—
234C22×D4—92no—
235C22×D4—91no—
236C23×C4—92no—
237C23×C4D3211yescharacteristic
238#117—38no—
239#117—64no—
240C2×C4⋊C4—62no—
241C2×C22⋊C4—34no—
242C2×C42—62no—
243#99—916no—
244C23×C3—21no—
245C23×C3—21no—
246C23×C3—21no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—44no—
250C23×C3—44no—
251C23×C3C2×C4×D312yes—
252C23×C3C2×C4×D312yes—
253C23×C3C2×D1212yes—
254C23×C3C2×D1212yes—
255C23×C3C2×#6712yes—
256C23×C3C2×#6712yes—
257C23×C3C23×D312yes—
258C22×D3—38no—
259C22×D3—64no—
260C22×D3—64no—
261C22×D3—64no—
262C22×D3—64no—
263C22×D3—64no—
264C22×D3—128no—
265C22×D3—128no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—24no—
276C2×C3×C4—24no—
277C2×C3×C4—68no—
278C2×C3×C4—128no—
279C2×C3×C4(C2×D3)⋊C414yes—
280C2×C3×C4(C2×D3)⋊C412yes—
281C2×C3×C4(C2×D3)⋊C412yes—
282C2×C3×C4(C2×D3)⋊C414yes—
283C2×C3×C4(C2×D3)⋊C412yes—
284C2×C3×C4(C2×D3)⋊C414yes—
285C2×C3×C4(C2×D3)⋊C414yes—
286C2×C3×C4(C2×D3)⋊C414yes—
287C2×C3×C4(C2×D3)⋊C414yes—
288C2×C3×C4(C2×D3)⋊C412yes—
289C2×C3×C4C2×C4×D314yes—
290C2×C3×C4C2×C4×D314yes—
291C2×C3×C4C2×D1214yes—
292C2×C3×C4C2×D1214yes—
293C2×C3×C4C2×#6714yes—
294C2×C3×C4C2×#6714yes—
295#67—616no—
296#67—616no—
297#67—68no—
298#67—68no—
299#67—68no—
300#67—68no—
301C2×Dic3—28no—
302C2×Dic3—38no—
303C2×Dic3—48no—
304C2×Dic3—64no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309D12—616no—
310D12—68no—
311D12—68no—
312C4×D3—616no—
313C4×D3—616no—
314C4×D3—616no—
315C4×D3—616no—
316Dic6—616no—
317Dic6—68no—
318Dic6—68no—
319C2×C32—21no—
320C2×C32—21no—
321C2×C32—22no—
322C2×C32—22no—
323C2×C32#41012yescomplemented
324C2×C32C22×C22⋊C411yescharacteristic
325C3⋊D3—44no—
326C24—92no—
327C24C2×D3211yescharacteristic
328#41—188no—
329#41—188no—
330#41—188no—
331#41—188no—
332C2×Q8—94no—
333C2×Q8—182no—
334C2×Q8—182no—
335C2×D4—94no—
336C2×D4—94no—
337C2×D4—94no—
338C2×D4—184no—
339C2×D4—184no—
340C2×D4—182no—
341C2×D4—182no—
342C22×C4—64no—
343C22×C4—92no—
344C22×C4—98no—
345C22×C4—184no—
346C22×C4—182no—
347C22×C4—182no—
348C22×C4#62411yescharacteristic
349C22×C4#62412yes—
350C22×C4#62411yescharacteristic
351C22×C4#62612yes—
352C22×C4#62614yes—
353C22×C4#62612yes—
354C22×C4C2×D3212yes—
355C4⋊C4—68no—
356C22⋊C4—38no—
357C22⋊C4—64no—
358C42—68no—
359C22×C3—24no—
360C22×C3—24no—
361C22×C3—24no—
362C22×C3—24no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—44no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—44no—
376C22×C3C2×(C2×D3)⋊C412yes—
377C22×C3C2×(C2×D3)⋊C412yes—
378C22×C3C2×(C2×D3)⋊C412yes—
379C22×C3C2×(C2×D3)⋊C412yes—
380C22×C3C22×C4×D312yes—
381C22×C3C22×D1212yes—
382C22×C3C22×#6712yes—
383C2×D3—68no—
384C2×D3—68no—
385C2×D3—128no—
386C2×D3—128no—
387C2×D3—128no—
388C2×D3—128no—
389C2×D3—128no—
390C2×D3—128no—
391C3×C4—24no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—128no—
395C3×C4C2×(C2×D3)⋊C414yes—
396C3×C4C2×(C2×D3)⋊C414yes—
397C3×C4C2×(C2×D3)⋊C414yes—
398C3×C4C2×(C2×D3)⋊C414yes—
399Dic3—48no—
400Dic3—68no—
401Dic3—68no—
402C32C2×#41011yescharacteristic, complemented, Sylow
403C23—42no—
404C23—94no—
405C23—182no—
406C23—182no—
407C23—364no—
408C23C2×#62411yescharacteristic
409C23C2×#62411yescharacteristic
410C23C2×#62612yes—
411C23C2×#62612yes—
412C23C22×D3211yescharacteristic
413Q8—188no—
414D4—188no—
415D4—188no—
416D4—188no—
417C2×C4—68no—
418C2×C4—94no—
419C2×C4—128no—
420C2×C4—182no—
421C2×C4—182no—
422C2×C4—188no—
423C2×C4—188no—
424C2×C4#372211yescharacteristic
425C2×C4#372212yes—
426C2×C4#372212yes—
427C2×C4#372212yes—
428C2×C4#372214yes—
429C2×C4#372214yes—
430C2×C4#372211yescharacteristic
431C2×C4C2×#62412yes—
432C2×C4C2×#62412yes—
433C2×C4C2×#62614yes—
434C2×C4C2×#62614yes—
435C2×C3—22no—
436C2×C3—22no—
437C2×C3—22no—
438C2×C3—22no—
439C2×C3—22no—
440C2×C3—22no—
441C2×C3—22no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—21no—
445C2×C3—42no—
446C2×C3—42no—
447C2×C3#500614yescomplemented
448C2×C3C22×(C2×D3)⋊C412yes—
449D3—128no—
450D3—128no—
451C22—24no—
452C22—22no—
453C22—41no—
454C22—41no—
455C22—42no—
456C22—184no—
457C22—364no—
458C22—364no—
459C22—364no—
460C22C2×#372211yescharacteristic
461C22C2×#372212yes—
462C22C2×#372211yescharacteristic
463C22C22×#62411yescharacteristic
464C22C22×#62612yes—
465C4—128no—
466C4—184no—
467C4C2×#372212yes—
468C4C2×#372212yes—
469C4C2×#372214yes—
470C3—21no—
471C3C2×#500612yescomplemented
472C2—22no—
473C2—21no—
474C2—21no—
475C2—22no—
476C2—364no—
477C2#1059123212yesdirect product factor
478C2C22×#372211yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3828C2
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#410
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×#63581C2semidirect
4. #10591232C2direct (N × H)
11. C2×#3828C4semidirect
13. C22×C4⋊(C3⋊D3)C4semidirect
14. C22×C4×C3⋊D3C4semidirect
15. C22×#634C4semidirect
18. C3×#926C22semidirect
21. #63581C22semidirect
25. C2×#926D3semidirect
48. C2×C4⋊(C3⋊D3)C2×C4semidirect
52. C2×C4×C3⋊D3C2×C4semidirect
55. C2×#634C2×C4semidirect
92. #926C2×D3semidirect
323. C2×C32#410semidirect
402. C32C2×#410semidirect
447. C2×C3#5006semidirect
471. C3C2×#5006semidirect
477. C2#10591232direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×#9262
C2×#635812
#105912322
C2×#50063