Finite Group Databasebeta

← C2×#10594472 #11903392

Subgroups — C2×#10594472 #11903392

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×C3×#898C212yesmaximal, complemented
3C2×#63919C211yesmaximal, characteristic, complemented
4C2×C4×#627C211yesmaximal, characteristic, complemented
5C2×#63915C211yesmaximal, characteristic
6C2×#63915C211yesmaximal, characteristic
7C2×#63902C211yesmaximal, characteristic
8C2×#63896C212yesmaximal, complemented
9C2×#63877C212yesmaximal, complemented
10C2×#63858C212yesmaximal, complemented
11C2×#63838C211yesmaximal, characteristic, complemented
12#10594472C2116yesmaximal, direct product factor
13C2×#5702—32nomaximal
14C22×#634C2211yescharacteristic
15C22×#627C2211yescharacteristic
16C22×#627C2211yescharacteristic
17C22×#625C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64096C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×C4⋊Dic3C2212yes—
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×C4×Dic3C2212yes—
32C3×#898C22116yescomplemented
33C2×#3724C2212yes—
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2212yes—
39#63919C2218yescomplemented
40C4×#627C2218yescomplemented
41#63915C2218yes—
42#63915C2218yes—
43#63902C2218yes—
44#63896C22116yescomplemented
45#63877C22116yescomplemented
46#63858C22116yescomplemented
47#63838C2218yescomplemented
48C2×C3×#126—32no—
49#5702—332no—
50C2×#898—32no—
51C2×#898D312yescomplemented
52C2×#896—32no—
53C2×#888—32no—
54C2×#887—32no—
55C2×#887—32no—
56C2×#887—61no—
57C2×#885—32no—
58C2×#885—32no—
59C2×#67⋊C4—32no—
60C2×#879—32no—
61C2×#878—32no—
62C2×#877—32no—
63C2×#872—32no—
64C2×C4×Dic6—32no—
65C23×C3×D3C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×#634—24no—
74C2×#634C2314yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C2×#627—24no—
79C2×#627—24no—
80C2×#627C2314yes—
81C2×#627C2314yes—
82C2×#625—24no—
83C2×#625C2314yes—
84C2×D3×Dic3—28no—
85C2×D3×Dic3C2318yes—
86C32×C4⋊C4C2314yes—
87#3750C2314yes—
88#3750C2314yes—
89C4×C3⋊Dic3C2314yes—
90C4×C3⋊Dic3C2314yes—
91C4×C3⋊Dic3C2314yes—
92C3×(C2×D3)⋊C4C2318yes—
93C3×(C2×D3)⋊C4C2318yes—
94C3×(C2×D3)⋊C4C2318yes—
95C3×C4⋊Dic3C2318yes—
96C3×Dic3⋊C4C2318yes—
97C3×C4×Dic3C2318yes—
98#3724C2314yes—
99#3724C2318yes—
100Dic3⋊Dic3C2318yes—
101(C2×D3)⋊Dic3C2318yes—
102(C2×D3)⋊Dic3C2318yes—
103Dic32C2318yes—
104C2×#556—91noSylow
105C22×#67—32no—
106C23×Dic3—32no—
107C22×C4×D3—32no—
108C22×Dic6—32no—
109C22×Dic6—32no—
110C22×Dic6—32no—
111C22×Dic6—61no—
112C3×#126—316no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C4⋊C4C2×D312yes—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4—32no—
120C2×C3×C42—32no—
121C2×#217—32no—
122C2×#217—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4C2×D312yes—
126C2×(C2×D3)⋊C4C2×D312yes—
127C2×(C2×D3)⋊C4C2×D312yes—
128C2×C4⋊Dic3—32no—
129C2×C4⋊Dic3C2×D312yes—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—61no—
137C2×Dic3⋊C4—61no—
138C2×Dic3⋊C4C2×D312yes—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—61no—
145C2×C4×Dic3—61no—
146C2×C4×Dic3—61no—
147C2×C4×Dic3C2×D312yes—
148#898—316no—
149#898C2×D3116yescomplemented
150#896—316no—
151#888—316no—
152#887—316no—
153#887—316no—
154#887—68no—
155#885—316no—
156#885—316no—
157#67⋊C4—316no—
158#879—316no—
159#878—316no—
160#877—316no—
161#872—316no—
162C4×Dic6—316no—
163C23×C32C2411yescharacteristic
164C22×C3×D3—24no—
165C22×C3×D3—24no—
166C22×C3×D3—24no—
167C22×C3×D3C2414yes—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4C2412yes—
172C2×C32×C4C2412yes—
173C2×C32×C4C2412yes—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3#4114yes—
177C2×C3⋊Dic3#4114yes—
178C2×C3⋊Dic3C2412yes—
179C2×C3⋊Dic3C2412yes—
180C2×C3⋊Dic3C2412yes—
181C2×C3⋊Dic3C2412yes—
182#634—28no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—24no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2414yes—
188C2×C3×Dic3C2414yes—
189#627—28no—
190#627—28no—
191#625—28no—
192D3×Dic3—216no—
193#556—916no—
194C2×C4⋊Q8—91no—
195C2×#126—32no—
196C2×#126—92no—
197C2×#124—91no—
198C2×#124—91no—
199C2×C22⋊Q8—92no—
200C2×C4×Q8—91no—
201C2×C4×Q8—91no—
202C2×C4×Q8—91no—
203C2×C4×D4—91no—
204C2×#117—92no—
205C24×C3—32no—
206C23×D3C22×D312yes—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D312yes—
215C22×C3×C4C22×D312yes—
216C2×#67—38no—
217C2×#67—68no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—38no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—68no—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C2×C4×D3—38no—
232C2×C4×D3—68no—
233C2×Dic6—38no—
234C2×Dic6—38no—
235C2×Dic6—38no—
236C2×Dic6—64no—
237C2×Dic6—68no—
238C2×Dic6—68no—
239C2×Dic6—68no—
240C2×Dic6—68no—
241C3×C4⋊C4—24no—
242C3×C4⋊C4—38no—
243C3×C4⋊C4—38no—
244C3×C4⋊C4C22×D318yes—
245C3×C22⋊C4—38no—
246C3×C22⋊C4—38no—
247C3×C22⋊C4—38no—
248C3×C42—38no—
249#217—38no—
250#217—38no—
251(C2×D3)⋊C4—38no—
252(C2×D3)⋊C4—38no—
253(C2×D3)⋊C4C22×D318yes—
254(C2×D3)⋊C4C22×D318yes—
255(C2×D3)⋊C4C22×D318yes—
256C4⋊Dic3—38no—
257C4⋊Dic3C22×D318yes—
258Dic3⋊C4—38no—
259Dic3⋊C4—38no—
260Dic3⋊C4—38no—
261Dic3⋊C4—38no—
262Dic3⋊C4—38no—
263Dic3⋊C4—38no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4C22×D318yes—
267C4×Dic3—38no—
268C4×Dic3—38no—
269C4×Dic3—38no—
270C4×Dic3—38no—
271C4×Dic3—38no—
272C4×Dic3—64no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C4×Dic3C22×D318yes—
276C22×C32C2×#4112yes—
277C22×C32C2×#4112yes—
278C22×C322−1+412yes—
279C22×C32C2511yescharacteristic
280C2×C3×D3—24no—
281C2×C3×D3—24no—
282C2×C3×D3—24no—
283C2×C3×D3—48no—
284C32×C4—22no—
285C32×C4—22no—
286C32×C4—22no—
287C3⋊Dic3—22no—
288C3⋊Dic3—22no—
289C3⋊Dic3C2×#4114yes—
290C3⋊Dic3C2×#4114yes—
291C3×Dic3—24no—
292C3×Dic3—24no—
293C3×Dic3—24no—
294C22×Q8—91no—
295C22×Q8—91no—
296C22×Q8—91no—
297C22×D4—91no—
298C23×C4—92no—
299C4⋊Q8—98no—
300#126—316no—
301#126—916no—
302#124—98no—
303#124—98no—
304C22⋊Q8—916no—
305C4×Q8—98no—
306C4×Q8—98no—
307C4×Q8—98no—
308C4×D4—98no—
309#117—916no—
310C2×C4⋊C4—32no—
311C2×C4⋊C4—32no—
312C2×C4⋊C4—92no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—92no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4—91no—
317C2×C4⋊C4D3211yescharacteristic
318C2×C22⋊C4—32no—
319C2×C22⋊C4—32no—
320C2×C22⋊C4—32no—
321C2×C22⋊C4—92no—
322C2×C22⋊C4—92no—
323C2×C42—32no—
324C2×C42—92no—
325C2×C42—91no—
326C2×C42—91no—
327C2×C42—91no—
328C23×C3—21no—
329C23×C3—34no—
330C23×C3—64no—
331C23×C3—64no—
332C23×C3—64no—
333C23×C3C23×D312yes—
334C22×D3—24no—
335C22×D3—24no—
336C22×D3—24no—
337C22×D3C23×D314yes—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—34no—
346C2×C3×C4—34no—
347C2×C3×C4—34no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—64no—
351C2×C3×C4—64no—
352C2×C3×C4—64no—
353C2×C3×C4C23×D314yes—
354C2×C3×C4C23×D314yes—
355C2×C3×C4C23×D314yes—
356#67—616no—
357C2×Dic3—24no—
358C2×Dic3—24no—
359C2×Dic3—24no—
360C2×Dic3—38no—
361C2×Dic3—38no—
362C2×Dic3—34no—
363C2×Dic3—34no—
364C2×Dic3—34no—
365C2×Dic3—34no—
366C2×Dic3—64no—
367C2×Dic3—64no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—616no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—122no—
377C2×Dic3C23×D314yes—
378C2×Dic3C23×D314yes—
379C2×Dic3C23×D314yes—
380C4×D3—616no—
381Dic6—616no—
382Dic6—616no—
383Dic6—616no—
384Dic6—616no—
385C2×C32#55614yescomplemented
386C2×C32C22×#4111yescharacteristic
387C2×C32C22×#4111yescharacteristic
388C2×C32C2×2−1+411yescharacteristic
389C3×D3—44no—
390C24—32no—
391C2×Q8—94no—
392C2×Q8—94no—
393C2×Q8—94no—
394C2×Q8—184no—
395C2×Q8—184no—
396C2×Q8—184no—
397C2×D4—94no—
398C2×D4—184no—
399C22×C4—32no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—98no—
403C22×C4—91no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—188no—
408C22×C4C2×D3211yescharacteristic
409C22×C4C2×D3211yescharacteristic
410C22×C4C2×D3211yescharacteristic
411C4⋊C4—38no—
412C4⋊C4—38no—
413C4⋊C4—98no—
414C4⋊C4—94no—
415C4⋊C4—98no—
416C4⋊C4—94no—
417C4⋊C4—94no—
418C4⋊C4C2×D3214yes—
419C22⋊C4—38no—
420C22⋊C4—38no—
421C22⋊C4—38no—
422C22⋊C4—98no—
423C22⋊C4—98no—
424C42—38no—
425C42—98no—
426C42—94no—
427C42—94no—
428C42—94no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—64no—
434C22×C3—64no—
435C22×C3—64no—
436C22×C3—128no—
437C22×C3D3×#4114yes—
438C22×C3D3×#4114yes—
439C22×C3#101014yes—
440C22×C3C24×D312yes—
441C2×D3—24no—
442C2×D3—24no—
443C2×D3—24no—
444C2×D3—48no—
445C3×C4—24no—
446C3×C4—24no—
447C3×C4—24no—
448C3×C4—24no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—64no—
452C3×C4—64no—
453C3×C4—64no—
454Dic3—24no—
455Dic3—24no—
456Dic3—24no—
457Dic3—38no—
458Dic3—38no—
459Dic3—64no—
460Dic3—64no—
461Dic3—64no—
462Dic3—64no—
463Dic3—64no—
464Dic3—122no—
465C32C2×#55611yescharacteristic, complemented, Sylow
466C23—34no—
467C23—64no—
468C23—64no—
469C23—64no—
470C23C22×D3211yescharacteristic
471Q8—188no—
472Q8—188no—
473Q8—188no—
474D4—188no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—34no—
479C2×C4—34no—
480C2×C4—34no—
481C2×C4—64no—
482C2×C4—64no—
483C2×C4—64no—
484C2×C4—94no—
485C2×C4—94no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—1816no—
491C2×C4—182no—
492C2×C4—182no—
493C2×C4C22×D3212yes—
494C2×C4C22×D3212yes—
495C2×C4C22×D3212yes—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—24no—
500C2×C3—124no—
501C2×C3#570218yescomplemented
502C2×C3C2×D3×#4112yes—
503C2×C3C2×D3×#4112yes—
504C2×C3C2×#101012yes—
505D3—44no—
506C22—64no—
507C22—64no—
508C22—64no—
509C22—128no—
510C22#6430612yes—
511C22#6430912yes—
512C22#6431912yes—
513C22C23×D3211yescharacteristic
514C4—22no—
515C4—22no—
516C4—22no—
517C4—64no—
518C4—64no—
519C4—64no—
520C4—94no—
521C4—94no—
522C4—182no—
523C4—182no—
524C3—21no—
525C3C2×#570212yescomplemented
526C2—124no—
527C2#1059447214yesdirect product factor
528C2C2×#6430611yescharacteristic
529C2C2×#6430911yescharacteristic
530C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64096C2semidirect
2. C2×C3×#898C2semidirect
3. C2×#63919C2semidirect
4. C2×C4×#627C2semidirect
8. C2×#63896C2semidirect
9. C2×#63877C2semidirect
10. C2×#63858C2semidirect
11. C2×#63838C2semidirect
12. #10594472C2direct (N × H)
25. #64096C22semidirect
32. C3×#898C22semidirect
39. #63919C22semidirect
40. C4×#627C22semidirect
44. #63896C22semidirect
45. #63877C22semidirect
46. #63858C22semidirect
47. #63838C22semidirect
51. C2×#898D3semidirect
149. #898C2×D3semidirect
385. C2×C32#556semidirect
465. C32C2×#556semidirect
501. C2×C3#5702semidirect
525. C3C2×#5702semidirect
527. C2#10594472direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×C3×#8982
C2×#639192
C2×C4×#6272
C2×#639152
C2×#639022
C2×#638962
C2×#638772
C2×#638582
C2×#638382
#105944722
C2×#57023