Finite Group Databasebeta

← C2×#10596003 #11903303

Subgroups — C2×#10596003 #11903303

Order 1152.

3720 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×#64139C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4#10596003C2116yesmaximal, direct product factor
5C2×#64104C211yesmaximal, characteristic, complemented
6C2×#64102C211yesmaximal, characteristic, complemented
7C2×#64101C211yesmaximal, characteristic, complemented
8C2×#64097C211yesmaximal, characteristic, complemented
9C2×#64094C212yesmaximal, complemented
10C2×#64093C212yesmaximal, complemented
11C2×#64084C212yesmaximal, complemented
12C2×#64081C212yesmaximal, complemented
13C2×#5532—34nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×#638C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4⋊(C3⋊D3)C2212yes—
19C22×C4×C3⋊D3C2212yes—
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#634C2212yes—
22C32×#117C2218yescomplemented
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2212yes—
26C2×C32×C42C2212yes—
27C2×#3757C2211yescharacteristic
28#64139C2218yescomplemented
29C4×#638C2218yescomplemented
30C2×#3752C2212yes—
31C2×#3752C2212yes—
32C2×#3752C2211yescharacteristic
33C2×#3752C2212yes—
34C2×#3752C2212yes—
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×#3750C2212yes—
38C2×C4×C3⋊Dic3C2212yes—
39C2×C4×C3⋊Dic3C2211yescharacteristic
40#64104C2218yescomplemented
41#64102C2218yescomplemented
42#64101C2218yescomplemented
43#64097C2218yescomplemented
44#64094C22116yescomplemented
45#64093C22116yescomplemented
46#64084C22116yescomplemented
47#64081C22116yescomplemented
48C2×C3×#117D314yescomplemented
49C2×#930—34no—
50C2×C4×#67—34no—
51#5532—364no—
52C2×#895—34no—
53C2×#893—34no—
54C2×#892—34no—
55C2×#888—34no—
56C2×#885—38no—
57C2×#884—38no—
58C2×#875—38no—
59C2×#872—38no—
60C24×C32C2311yescharacteristic
61C23×C3⋊D3C2312yes—
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4—24no—
64C22×C32×C4C2312yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2314yes—
68C22×C32×C4C2311yescharacteristic
69C2×#638—24no—
70C2×#638—44no—
71C2×#638C2314yes—
72C2×#638C2318yes—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2312yes—
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2311yescharacteristic
77C2×C4⋊(C3⋊D3)—24no—
78C2×C4⋊(C3⋊D3)—44no—
79C2×C4⋊(C3⋊D3)C2314yes—
80C2×C4⋊(C3⋊D3)C2318yes—
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3—28no—
83C2×C4×C3⋊D3C2318yes—
84C2×C4×C3⋊D3C2314yes—
85C2×#634—44no—
86C2×#634C2318yes—
87C32×C4⋊C4C2314yes—
88C32×C4⋊C4C2314yes—
89C32×C22⋊C4C2318yes—
90C32×C42C2318yes—
91#3757C2314yes—
92#3752C2318yes—
93#3752C2318yes—
94#3752C2314yes—
95#3752C2318yes—
96#3752C2318yes—
97C4⋊(C3⋊Dic3)C2314yes—
98#3750C2314yes—
99#3750C2318yes—
100C4×C3⋊Dic3C2318yes—
101C4×C3⋊Dic3C2314yes—
102C2×#555—91noSylow
103C23×C3×C4C2×D314yes—
104C22×#67—34no—
105C22×#67—38no—
106C22×D12—34no—
107C22×D12—38no—
108C22×C4×D3—38no—
109C22×C4×D3—34no—
110C22×Dic6—38no—
111C3×#117C2×D3132yescomplemented
112C2×C3×C4⋊C4C2×D314yes—
113C2×C3×C4⋊C4C2×D314yes—
114C2×C3×C22⋊C4C2×D318yes—
115C2×C3×C42C2×D318yes—
116C2×#217—34no—
117#930—332no—
118C4×#67—332no—
119C2×(C2×D3)⋊C4—38no—
120C2×(C2×D3)⋊C4—38no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4—38no—
123C2×(C2×D3)⋊C4—38no—
124C2×C4⋊Dic3—34no—
125C2×Dic3⋊C4—34no—
126C2×Dic3⋊C4—38no—
127C2×C4×Dic3—38no—
128C2×C4×Dic3—34no—
129#895—332no—
130#893—332no—
131#892—332no—
132#888—332no—
133#885—364no—
134#884—364no—
135#875—364no—
136#872—364no—
137C23×C32—22no—
138C23×C32—22no—
139C23×C32—22no—
140C23×C32C2412yes—
141C23×C32C2411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—24no—
144C22×C3⋊D3—24no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—24no—
148C22×C3⋊D3C2414yes—
149C22×C3⋊D3C2412yes—
150C2×C32×C4—24no—
151C2×C32×C4—22no—
152C2×C32×C4—24no—
153C2×C32×C4—28no—
154C2×C32×C4#4114yes—
155C2×C32×C4C2414yes—
156C2×C32×C4C2412yes—
157C2×C32×C4C2414yes—
158C2×C32×C4C2412yes—
159#638—28no—
160#638—48no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—24no—
164C2×C3⋊Dic3#4114yes—
165C2×C3⋊Dic3C2412yes—
166C2×C3⋊Dic3C2414yes—
167C2×C3⋊Dic3C2412yes—
168C2×C3⋊Dic3C2412yes—
169C4⋊(C3⋊D3)—28no—
170C4⋊(C3⋊D3)—48no—
171C4×C3⋊D3—28no—
172C4×C3⋊D3—216no—
173#634—48no—
174#555—916no—
175C2×C4⋊Q8—91no—
176C2×#124—92no—
177C2×#124—92no—
178C2×#121—91no—
179C2×#121—91no—
180C2×#121—92no—
181C2×C4×D4—91no—
182C2×C4×D4—91no—
183C2×#117—91no—
184C2×#117—92no—
185C2×#117C3⋊D311yescharacteristic, complemented
186C24×C3C22×D314yes—
187C23×D3—34no—
188C23×D3—38no—
189C22×C3×C4—216no—
190C22×C3×C4C22×D318yes—
191C22×C3×C4C22×D314yes—
192C22×C3×C4C22×D318yes—
193C22×C3×C4C22×D3116yes—
194C22×C3×C4C22×D314yes—
195C2×#67—316no—
196C2×#67—332no—
197C2×#67—616no—
198C2×#67—1216no—
199C22×Dic3—34no—
200C22×Dic3—34no—
201C22×Dic3—38no—
202C22×Dic3—34no—
203C2×D12—316no—
204C2×D12—332no—
205C2×D12—616no—
206C2×D12—1216no—
207C2×C4×D3—332no—
208C2×C4×D3—316no—
209C2×C4×D3—632no—
210C2×C4×D3—616no—
211C2×Dic6—332no—
212C2×Dic6—1216no—
213C3×C4⋊C4C22×D3116yes—
214C3×C4⋊C4C22×D3116yes—
215C3×C22⋊C4C22×D3132yes—
216C3×C42C22×D3132yes—
217#217—316no—
218(C2×D3)⋊C4—332no—
219(C2×D3)⋊C4—332no—
220(C2×D3)⋊C4—316no—
221(C2×D3)⋊C4—332no—
222(C2×D3)⋊C4—332no—
223C4⋊Dic3—316no—
224Dic3⋊C4—316no—
225Dic3⋊C4—332no—
226C4×Dic3—332no—
227C4×Dic3—316no—
228C22×C32—22no—
229C22×C32—22no—
230C22×C32—22no—
231C22×C32—44no—
232C22×C32C2×#4112yes—
233C22×C32C2×#4112yes—
234C22×C32H(5,𝔽2)12yes—
235C22×C32C2511yescharacteristic
236C2×C3⋊D3—22no—
237C2×C3⋊D3—24no—
238C2×C3⋊D3—24no—
239C2×C3⋊D3—22no—
240C2×C3⋊D3—22no—
241C2×C3⋊D3—24no—
242C2×C3⋊D3—48no—
243C2×C3⋊D3—44no—
244C32×C4—24no—
245C32×C4—22no—
246C32×C4—24no—
247C32×C4C2×#4114yes—
248C3⋊Dic3—22no—
249C3⋊Dic3—22no—
250C3⋊Dic3—24no—
251C3⋊Dic3C2×#4114yes—
252C22×Q8—92no—
253C22×D4—91no—
254C22×D4—92no—
255C22×D4—91no—
256C22×D4—92no—
257C23×C4—92no—
258C23×C4—91no—
259C23×C4C2×C3⋊D311yescharacteristic
260C4⋊Q8—98no—
261#124—916no—
262#124—916no—
263#121—98no—
264#121—98no—
265#121—916no—
266C4×D4—98no—
267C4×D4—98no—
268#117—98no—
269#117—916no—
270#117C2×C3⋊D318yescomplemented
271C2×C4⋊C4—91no—
272C2×C4⋊C4—92no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4C2×C3⋊D311yescharacteristic
275C2×C4⋊C4C2×C3⋊D311yescharacteristic
276C2×C22⋊C4—91no—
277C2×C22⋊C4—92no—
278C2×C22⋊C4—92no—
279C2×C22⋊C4—92no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—91no—
282C2×C22⋊C4C2×C3⋊D312yes—
283C2×C42—92no—
284C2×C42—91no—
285C2×C42C2×C3⋊D312yes—
286C23×C3—28no—
287C23×C3—28no—
288C23×C3—28no—
289C23×C3C23×D318yes—
290C23×C3C23×D314yes—
291C22×D3—38no—
292C22×D3—316no—
293C22×D3—68no—
294C22×D3—616no—
295C22×D3—616no—
296C22×D3—68no—
297C22×D3—68no—
298C22×D3—616no—
299C2×C3×C4—28no—
300C2×C3×C4—216no—
301C2×C3×C4—216no—
302C2×C3×C4—232no—
303C2×C3×C4#235116yes—
304C2×C3×C4C23×D3116yes—
305C2×C3×C4C23×D318yes—
306C2×C3×C4C23×D3116yes—
307C2×C3×C4C23×D318yes—
308#67—632no—
309#67—1232no—
310C2×Dic3—316no—
311C2×Dic3—38no—
312C2×Dic3—38no—
313C2×Dic3—316no—
314C2×Dic3—38no—
315C2×Dic3—68no—
316C2×Dic3—68no—
317C2×Dic3—616no—
318D12—632no—
319D12—1232no—
320C4×D3—664no—
321C4×D3—632no—
322Dic6—1232no—
323C2×C32—42no—
324C2×C32#55514yescomplemented
325C2×C32C22×#4111yescharacteristic
326C2×C32C22×#4111yescharacteristic
327C2×C32C2×H(5,𝔽2)11yescharacteristic
328C3⋊D3—44no—
329C3⋊D3—42no—
330C24—91no—
331C24—92no—
332C24C22×C3⋊D311yescharacteristic
333C2×Q8—98no—
334C2×Q8—364no—
335C2×D4—94no—
336C2×D4—98no—
337C2×D4—94no—
338C2×D4—98no—
339C2×D4—184no—
340C2×D4—184no—
341C2×D4—364no—
342C2×D4—364no—
343C22×C4—24no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—92no—
348C22×C4—98no—
349C22×C4—94no—
350C22×C4—188no—
351C22×C4—184no—
352C22×C4C22×C3⋊D314yes—
353C22×C4C22×C3⋊D312yes—
354C22×C4C22×C3⋊D311yescharacteristic
355C22×C4C22×C3⋊D312yes—
356C22×C4C22×C3⋊D311yescharacteristic
357C4⋊C4—94no—
358C4⋊C4—98no—
359C4⋊C4—94no—
360C4⋊C4C22×C3⋊D314yes—
361C4⋊C4C22×C3⋊D314yes—
362C22⋊C4—94no—
363C22⋊C4—98no—
364C22⋊C4—98no—
365C22⋊C4—98no—
366C22⋊C4—98no—
367C22⋊C4—94no—
368C22⋊C4C22×C3⋊D318yes—
369C42—98no—
370C42—94no—
371C42C22×C3⋊D318yes—
372C22×C3—28no—
373C22×C3—28no—
374C22×C3—28no—
375C22×C3—416no—
376C22×C3C2×#23518yes—
377C22×C3D3×#4118yes—
378C22×C3#100918yes—
379C22×C3C24×D314yes—
380C2×D3—68no—
381C2×D3—616no—
382C2×D3—616no—
383C2×D3—68no—
384C2×D3—68no—
385C2×D3—616no—
386C2×D3—1216no—
387C2×D3—1232no—
388C3×C4—28no—
389C3×C4—216no—
390C3×C4—216no—
391C3×C4C2×#235116yes—
392Dic3—316no—
393Dic3—68no—
394Dic3—68no—
395Dic3—616no—
396C32C2×#55511yescharacteristic, complemented, Sylow
397C23—22no—
398C23—22no—
399C23—22no—
400C23—92no—
401C23—94no—
402C23—182no—
403C23—184no—
404C23—184no—
405C23—182no—
406C23—182no—
407C23—184no—
408C23C23×C3⋊D312yes—
409C23C23×C3⋊D311yescharacteristic
410Q8—368no—
411D4—188no—
412D4—188no—
413D4—368no—
414D4—368no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—28no—
419C2×C4—94no—
420C2×C4—92no—
421C2×C4—92no—
422C2×C4—92no—
423C2×C4—94no—
424C2×C4—1816no—
425C2×C4—182no—
426C2×C4—184no—
427C2×C4—182no—
428C2×C4—188no—
429C2×C4#382814yes—
430C2×C4C23×C3⋊D314yes—
431C2×C4C23×C3⋊D312yes—
432C2×C4C23×C3⋊D314yes—
433C2×C4C23×C3⋊D312yes—
434C2×C3—48no—
435C2×C3#5532116yescomplemented
436C2×C3C22×#23514yes—
437C2×C3C2×D3×#4114yes—
438C2×C3C2×#100914yes—
439D3—128no—
440D3—1216no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—44no—
445C22—182no—
446C22—184no—
447C22—184no—
448C22—182no—
449C22—182no—
450C22—184no—
451C22—364no—
452C22—368no—
453C22C2×#382812yes—
454C22#41×C3⋊D312yes—
455C22#6436612yes—
456C22C24×C3⋊D311yescharacteristic
457C4—22no—
458C4—24no—
459C4—24no—
460C4—94no—
461C4—182no—
462C4—184no—
463C4—182no—
464C4C2×#382814yes—
465C3C2×#553214yescomplemented
466C2—42no—
467C2—362no—
468C2—364no—
469C2#1059600314yesdirect product factor
470C2C22×#382811yescharacteristic
471C2C2×#41×C3⋊D311yescharacteristic
472C2C2×#6436611yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#117C2
socleC23×C32C24
hypercenterC2×#117C3⋊D3
hypocenterC32C2×#555
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
2. C2×#64139C2semidirect
3. C2×C4×#638C2semidirect
4. #10596003C2direct (N × H)
5. C2×#64104C2semidirect
6. C2×#64102C2semidirect
7. C2×#64101C2semidirect
8. C2×#64097C2semidirect
9. C2×#64094C2semidirect
10. C2×#64093C2semidirect
11. C2×#64084C2semidirect
12. C2×#64081C2semidirect
22. C32×#117C22semidirect
28. #64139C22semidirect
29. C4×#638C22semidirect
40. #64104C22semidirect
41. #64102C22semidirect
42. #64101C22semidirect
43. #64097C22semidirect
44. #64094C22semidirect
45. #64093C22semidirect
46. #64084C22semidirect
47. #64081C22semidirect
48. C2×C3×#117D3semidirect
111. C3×#117C2×D3semidirect
185. C2×#117C3⋊D3semidirect
270. #117C2×C3⋊D3semidirect
324. C2×C32#555semidirect
396. C32C2×#555semidirect
435. C2×C3#5532semidirect
465. C3C2×#5532semidirect
469. C2#10596003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×#641392
C2×C4×#6382
#105960032
C2×#641042
C2×#641022
C2×#641012
C2×#640972
C2×#640942
C2×#640932
C2×#640842
C2×#640812
C2×#55323