Finite Group Databasebeta

← C2×#10596100 #11901131

Subgroups — C2×#10596100 #11901131

Order 1152.

4920 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3832C211yesmaximal, characteristic, complemented
2C22×#3828C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×#64155C211yesmaximal, characteristic, complemented
5C2×#64139C211yesmaximal, characteristic, complemented
6#10596100C2116yesmaximal, direct product factor
7C2×#64105C212yesmaximal, complemented
8C2×#64104C211yesmaximal, characteristic, complemented
9C2×#64104C212yesmaximal, complemented
10C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
11C2×#64093C212yesmaximal, complemented
12C2×#64093C212yesmaximal, complemented
13C2×#5629—34nomaximal
14C22×C32×Q8C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×#638C2211yescharacteristic
18C22×#638C2212yes—
19C2×#3832—28no—
20C2×#3832C2218yescomplemented
21C2×#3828—28no—
22C2×#3828C2218yescomplemented
23C22×C4⋊(C3⋊D3)C2212yes—
24C22×C4⋊(C3⋊D3)C2211yescharacteristic
25C22×C4⋊(C3⋊D3)C2211yescharacteristic
26C22×C4⋊(C3⋊D3)C2212yes—
27C22×C4×C3⋊D3C2212yes—
28C22×C4×C3⋊D3C2211yescharacteristic
29C22×C4×C3⋊D3C2212yes—
30C22×C4×C3⋊D3C2211yescharacteristic
31C22×#634C2211yescharacteristic
32C32×C22⋊Q8C2218yescomplemented
33C2×C32×C4⋊C4C2211yescharacteristic
34C2×C32×C4⋊C4C2212yes—
35C2×C32×C22⋊C4C2212yes—
36#64155C2218yescomplemented
37#64139C2218yescomplemented
38C2×#3752C2212yes—
39C2×#3752C2212yes—
40C2×#3752C2212yes—
41C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
42C2×#3750C2212yes—
43C2×#3750C2212yes—
44#64105C22116yescomplemented
45#64104C2218yescomplemented
46#64104C22116yescomplemented
47C4⋊C4×C3⋊D3C2218yescomplemented
48#64093C22116yescomplemented
49#64093C22116yescomplemented
50C22×#239—34no—
51C22×#235—34no—
52C2×C3×C22⋊Q8D314yescomplemented
53C2×#946—34no—
54C2×#930—34no—
55#5629—364no—
56C2×#896—38no—
57C2×#895—34no—
58C2×#895—38no—
59C2×D3×C4⋊C4—34no—
60C2×#884—38no—
61C2×#884—38no—
62C24×C32C2311yescharacteristic
63C23×C3⋊D3C2312yes—
64C23×C3⋊D3C2311yescharacteristic
65C23×C3⋊D3C2311yescharacteristic
66C2×C32×Q8—24no—
67C2×C32×Q8C2314yes—
68C22×C32×C4—24no—
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2312yes—
71C22×C32×C4C2312yes—
72C22×C32×C4C2314yes—
73C22×C32×C4C2311yescharacteristic
74C2×#638—24no—
75C2×#638—24no—
76C2×#638—44no—
77C2×#638C2314yes—
78C2×#638C2314yes—
79C2×#638C2318yes—
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2312yes—
82C22×C3⋊Dic3C2311yescharacteristic
83#3832—232no—
84#3828—232no—
85C2×C4⋊(C3⋊D3)—24no—
86C2×C4⋊(C3⋊D3)—28no—
87C2×C4⋊(C3⋊D3)—24no—
88C2×C4⋊(C3⋊D3)—44no—
89C2×C4⋊(C3⋊D3)C2318yes—
90C2×C4⋊(C3⋊D3)C2314yes—
91C2×C4⋊(C3⋊D3)C2314yes—
92C2×C4⋊(C3⋊D3)C2318yes—
93C2×C4×C3⋊D3—24no—
94C2×C4×C3⋊D3—28no—
95C2×C4×C3⋊D3—44no—
96C2×C4×C3⋊D3D418yescomplemented
97C2×C4×C3⋊D3C2318yes—
98C2×C4×C3⋊D3C2314yes—
99C2×C4×C3⋊D3C2318yes—
100C2×C4×C3⋊D3C2314yes—
101C2×#634—24no—
102C2×#634C2314yes—
103C32×C4⋊C4C2314yes—
104C32×C4⋊C4C2318yes—
105C32×C22⋊C4C2318yes—
106#3752C2318yes—
107#3752C2318yes—
108#3752C2318yes—
109C4⋊(C3⋊Dic3)C2314yes—
110#3750C2318yes—
111#3750C2318yes—
112C2×#537—91noSylow
113C22×C3×Q8C2×D314yes—
114C23×C3×C4C2×D314yes—
115C22×#67—34no—
116C22×#67—34no—
117C22×#67—38no—
118C2×#239—332no—
119C2×#239—632no—
120C2×#235—332no—
121C2×#235—632no—
122C22×D12—34no—
123C22×D12—38no—
124C22×D12—34no—
125C22×D12—38no—
126C22×C4×D3—34no—
127C22×C4×D3—34no—
128C22×C4×D3—38no—
129C22×C4×D3—38no—
130C22×Dic6—34no—
131C3×C22⋊Q8C2×D3132yescomplemented
132C2×C3×C4⋊C4C2×D314yes—
133C2×C3×C4⋊C4C2×D318yes—
134C2×C3×C22⋊C4C2×D318yes—
135#946—332no—
136#930—332no—
137C2×(C2×D3)⋊C4—38no—
138C2×(C2×D3)⋊C4—38no—
139C2×(C2×D3)⋊C4—38no—
140C2×C4⋊Dic3—34no—
141C2×Dic3⋊C4—38no—
142C2×Dic3⋊C4—38no—
143#896—364no—
144#895—332no—
145#895—364no—
146D3×C4⋊C4—332no—
147#884—364no—
148#884—364no—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32C2412yes—
153C23×C32C2411yescharacteristic
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—24no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3—24no—
160C22×C3⋊D3—24no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3C2×D414yes—
163C22×C3⋊D3C2414yes—
164C22×C3⋊D3C2412yes—
165C22×C3⋊D3C2412yes—
166C32×Q8—28no—
167C2×C32×C4—22no—
168C2×C32×C4—24no—
169C2×C32×C4—24no—
170C2×C32×C4—28no—
171C2×C32×C4C2×D414yes—
172C2×C32×C4C2414yes—
173C2×C32×C4C2414yes—
174C2×C32×C4C2412yes—
175C2×C32×C4C2412yes—
176#638—28no—
177#638—28no—
178#638—48no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—24no—
181C2×C3⋊Dic3C2×D414yes—
182C2×C3⋊Dic3C2414yes—
183C2×C3⋊Dic3C2412yes—
184C2×C3⋊Dic3C2412yes—
185C4⋊(C3⋊D3)—28no—
186C4⋊(C3⋊D3)—216no—
187C4⋊(C3⋊D3)—28no—
188C4⋊(C3⋊D3)—48no—
189C4×C3⋊D3—28no—
190C4×C3⋊D3—216no—
191C4×C3⋊D3—48no—
192C4×C3⋊D3C2×D4116yescomplemented
193#634—28no—
194C22×#41—91no—
195C22×#41—91no—
196#537—916no—
197C2×C22⋊Q8—91no—
198C2×C22⋊Q8—92no—
199C2×C22⋊Q8C3⋊D311yescharacteristic, complemented
200C2×#121—91no—
201C2×#121—91no—
202C2×#121—92no—
203C2×#121—92no—
204C2×#121—92no—
205C22×C4⋊C4—91no—
206C24×C3C22×D314yes—
207C23×D3—34no—
208C23×D3—38no—
209C23×D3—34no—
210C2×C3×Q8—216no—
211C2×C3×Q8C22×D3116yes—
212C22×C3×C4—216no—
213C22×C3×C4C22×D318yes—
214C22×C3×C4C22×D318yes—
215C22×C3×C4C22×D314yes—
216C22×C3×C4C22×D3116yes—
217C22×C3×C4C22×D314yes—
218C2×#67—316no—
219C2×#67—316no—
220C2×#67—332no—
221C2×#67—616no—
222C2×#67—616no—
223C2×#67—1216no—
224C22×Dic3—34no—
225C22×Dic3—38no—
226C22×Dic3—34no—
227#239—6128no—
228#235—6128no—
229C2×D12—332no—
230C2×D12—316no—
231C2×D12—316no—
232C2×D12—332no—
233C2×D12—616no—
234C2×D12—632no—
235C2×D12—616no—
236C2×D12—1216no—
237C2×C4×D3—332no—
238C2×C4×D3—316no—
239C2×C4×D3—332no—
240C2×C4×D3—316no—
241C2×C4×D3—332no—
242C2×C4×D3—632no—
243C2×C4×D3—616no—
244C2×C4×D3—1216no—
245C2×Dic6—316no—
246C2×Dic6—616no—
247C3×C4⋊C4C22×D3116yes—
248C3×C4⋊C4C22×D3132yes—
249C3×C22⋊C4C22×D3132yes—
250(C2×D3)⋊C4—332no—
251(C2×D3)⋊C4—332no—
252(C2×D3)⋊C4—332no—
253C4⋊Dic3—316no—
254Dic3⋊C4—332no—
255Dic3⋊C4—332no—
256C22×C32—22no—
257C22×C32—22no—
258C22×C32—22no—
259C22×C32—44no—
260C22×C32C22×D412yes—
261C22×C32H(5,𝔽2)12yes—
262C22×C322−1+412yes—
263C22×C32C2511yescharacteristic
264C2×C3⋊D3—28no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—22no—
267C2×C3⋊D3—24no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—24no—
271C2×C3⋊D3—24no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—48no—
274C2×C3⋊D3—44no—
275C2×C3⋊D3C22×D414yes—
276C32×C4—22no—
277C32×C4—24no—
278C32×C4—24no—
279C32×C4C22×D414yes—
280C3⋊Dic3—22no—
281C3⋊Dic3—24no—
282C3⋊Dic3C22×D414yes—
283C2×#41—98no—
284C2×#41—98no—
285C2×#41—188no—
286C2×#41—188no—
287C22×Q8—91no—
288C22×Q8C2×C3⋊D311yescharacteristic
289C22×D4—91no—
290C22×D4—91no—
291C22×D4—92no—
292C22×D4—91no—
293C22×D4—92no—
294C22×D4—91no—
295C22×D4—92no—
296C23×C4—91no—
297C23×C4—92no—
298C23×C4—91no—
299C23×C4—92no—
300C23×C4C2×C3⋊D311yescharacteristic
301C22⋊Q8—98no—
302C22⋊Q8—916no—
303C22⋊Q8C2×C3⋊D318yescomplemented
304#121—98no—
305#121—98no—
306#121—916no—
307#121—916no—
308#121—916no—
309C2×C4⋊C4—92no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—92no—
312C2×C4⋊C4—98no—
313C2×C4⋊C4C2×C3⋊D311yescharacteristic
314C2×C4⋊C4C2×C3⋊D312yes—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—92no—
318C2×C22⋊C4C2×C3⋊D312yes—
319C23×C3—28no—
320C23×C3—28no—
321C23×C3—28no—
322C23×C3C23×D318yes—
323C23×C3C23×D314yes—
324C22×D3—316no—
325C22×D3—38no—
326C22×D3—316no—
327C22×D3—38no—
328C22×D3—68no—
329C22×D3—68no—
330C22×D3—616no—
331C22×D3—68no—
332C22×D3—616no—
333C22×D3—68no—
334C22×D3—68no—
335C22×D3—616no—
336C3×Q8—232no—
337C2×C3×C4—28no—
338C2×C3×C4—216no—
339C2×C3×C4—216no—
340C2×C3×C4—232no—
341C2×C3×C4D3×D4116yes—
342C2×C3×C4C23×D3116yes—
343C2×C3×C4C23×D3116yes—
344C2×C3×C4C23×D318yes—
345C2×C3×C4C23×D318yes—
346#67—632no—
347#67—632no—
348#67—1232no—
349C2×Dic3—316no—
350C2×Dic3—38no—
351C2×Dic3—316no—
352C2×Dic3—38no—
353C2×Dic3—68no—
354C2×Dic3—616no—
355D12—632no—
356D12—664no—
357D12—632no—
358D12—1232no—
359C4×D3—364no—
360C4×D3—664no—
361C4×D3—632no—
362C4×D3—1232no—
363Dic6—632no—
364C2×C32—42no—
365C2×C32#53714yescomplemented
366C2×C32C23×D411yescharacteristic
367C2×C32C2×H(5,𝔽2)11yescharacteristic
368C2×C32C2×2−1+411yescharacteristic
369C3⋊D3—24no—
370C3⋊D3—44no—
371C3⋊D3—42no—
372C24—91no—
373C24—91no—
374C24—92no—
375C24C22×C3⋊D311yescharacteristic
376#41—1832no—
377#41—1832no—
378C2×Q8—24no—
379C2×Q8—94no—
380C2×Q8—184no—
381C2×Q8C22×C3⋊D314yes—
382C2×D4—94no—
383C2×D4—94no—
384C2×D4—98no—
385C2×D4—94no—
386C2×D4—98no—
387C2×D4—94no—
388C2×D4—98no—
389C2×D4—184no—
390C2×D4—188no—
391C2×D4—184no—
392C2×D4—184no—
393C2×D4—184no—
394C2×D4—364no—
395C2×D4—364no—
396C22×C4—24no—
397C22×C4—91no—
398C22×C4—94no—
399C22×C4—98no—
400C22×C4—92no—
401C22×C4—91no—
402C22×C4—98no—
403C22×C4—94no—
404C22×C4—98no—
405C22×C4—188no—
406C22×C4—184no—
407C22×C4—364no—
408C22×C4C22×C3⋊D314yes—
409C22×C4C22×C3⋊D311yescharacteristic
410C22×C4C22×C3⋊D312yes—
411C22×C4C22×C3⋊D312yes—
412C22×C4C22×C3⋊D311yescharacteristic
413C4⋊C4—98no—
414C4⋊C4—94no—
415C4⋊C4—98no—
416C4⋊C4C22×C3⋊D314yes—
417C4⋊C4C22×C3⋊D318yes—
418C22⋊C4—98no—
419C22⋊C4—98no—
420C22⋊C4—98no—
421C22⋊C4C22×C3⋊D318yes—
422C22×C3—28no—
423C22×C3—28no—
424C22×C3—28no—
425C22×C3—416no—
426C22×C3C2×D3×D418yes—
427C22×C3#100718yes—
428C22×C3#100918yes—
429C22×C3C24×D314yes—
430C2×D3—316no—
431C2×D3—68no—
432C2×D3—68no—
433C2×D3—632no—
434C2×D3—616no—
435C2×D3—68no—
436C2×D3—616no—
437C2×D3—68no—
438C2×D3—68no—
439C2×D3—616no—
440C2×D3—1232no—
441C2×D3—1216no—
442C3×C4—28no—
443C3×C4—216no—
444C3×C4—216no—
445C3×C4C2×D3×D4116yes—
446Dic3—316no—
447Dic3—68no—
448Dic3—616no—
449C32C2×#53711yescharacteristic, complemented, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—94no—
454C23—92no—
455C23—92no—
456C23—94no—
457C23—182no—
458C23—182no—
459C23—184no—
460C23—182no—
461C23—182no—
462C23—184no—
463C23—182no—
464C23—184no—
465C23C23×C3⋊D312yes—
466C23C23×C3⋊D311yescharacteristic
467Q8—28no—
468Q8—188no—
469D4—188no—
470D4—1816no—
471D4—188no—
472D4—188no—
473D4—188no—
474D4—368no—
475D4—368no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—28no—
480C2×C4—94no—
481C2×C4—92no—
482C2×C4—916no—
483C2×C4—94no—
484C2×C4—92no—
485C2×C4—1816no—
486C2×C4—182no—
487C2×C4—184no—
488C2×C4—188no—
489C2×C4—368no—
490C2×C4D4×C3⋊D314yes—
491C2×C4C23×C3⋊D312yes—
492C2×C4C23×C3⋊D314yes—
493C2×C4C23×C3⋊D314yes—
494C2×C4C23×C3⋊D312yes—
495C2×C3—48no—
496C2×C3#5629116yescomplemented
497C2×C3C22×D3×D414yes—
498C2×C3C2×#100714yes—
499C2×C3C2×#100914yes—
500D3—616no—
501D3—1216no—
502D3—128no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—44no—
507C22—94no—
508C22—188no—
509C22—182no—
510C22—182no—
511C22—184no—
512C22—182no—
513C22—182no—
514C22—184no—
515C22—182no—
516C22—184no—
517C22—368no—
518C22—364no—
519C22C2×D4×C3⋊D312yes—
520C22#6436412yes—
521C22#6436612yes—
522C22C24×C3⋊D311yescharacteristic
523C4—22no—
524C4—24no—
525C4—24no—
526C4—94no—
527C4—182no—
528C4—184no—
529C4C2×D4×C3⋊D314yes—
530C3C2×#562914yescomplemented
531C2—42no—
532C2—184no—
533C2—364no—
534C2—362no—
535C2#1059610014yesdirect product factor
536C2C22×D4×C3⋊D311yescharacteristic
537C2C2×#6436411yescharacteristic
538C2C2×#6436611yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C22×#3828C2semidirect
3. C2×C32×C22⋊Q8C2semidirect
4. C2×#64155C2semidirect
5. C2×#64139C2semidirect
6. #10596100C2direct (N × H)
7. C2×#64105C2semidirect
8. C2×#64104C2semidirect
9. C2×#64104C2semidirect
10. C2×C4⋊C4×C3⋊D3C2semidirect
11. C2×#64093C2semidirect
12. C2×#64093C2semidirect
20. C2×#3832C22semidirect
22. C2×#3828C22semidirect
32. C32×C22⋊Q8C22semidirect
36. #64155C22semidirect
37. #64139C22semidirect
44. #64105C22semidirect
45. #64104C22semidirect
46. #64104C22semidirect
47. C4⋊C4×C3⋊D3C22semidirect
48. #64093C22semidirect
49. #64093C22semidirect
52. C2×C3×C22⋊Q8D3semidirect
96. C2×C4×C3⋊D3D4semidirect
131. C3×C22⋊Q8C2×D3semidirect
192. C4×C3⋊D3C2×D4semidirect
199. C2×C22⋊Q8C3⋊D3semidirect
303. C22⋊Q8C2×C3⋊D3semidirect
365. C2×C32#537semidirect
449. C32C2×#537semidirect
496. C2×C3#5629semidirect
530. C3C2×#5629semidirect
535. C2#10596100direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38322
C22×#38282
C2×C32×C22⋊Q82
C2×#641552
C2×#641392
#105961002
C2×#641052
C2×#641042
C2×C4⋊C4×C3⋊D32
C2×#640932
C2×#56293