Finite Group Databasebeta

← C2×#10594534 #11903256

Subgroups — C2×#10594534 #11903256

Order 1152.

2549 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×C3×#896C212yesmaximal, complemented
3C2×#63902C211yesmaximal, characteristic
4C2×#63902C211yesmaximal, characteristic
5C2×C4×#625C211yesmaximal, characteristic
6C2×#63896C212yesmaximal, complemented
7C2×#63887C212yesmaximal, complemented
8C2×D3×Dic3⋊C4C212yesmaximal, complemented
9C2×#63873C211yesmaximal, characteristic, complemented
10C2×#63870C211yesmaximal, characteristic, complemented
11C2×#63870C211yesmaximal, characteristic, complemented
12#10594534C2116yesmaximal, direct product factor
13C2×#5636—32nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×Dic6C2212yes—
17C22×#625C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C22×D3×Dic3C2212yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64096C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2212yes—
31C3×#896C22116yescomplemented
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39#63902C2218yes—
40#63902C2218yes—
41C4×#625C2218yes—
42#63896C22116yescomplemented
43#63887C22116yescomplemented
44D3×Dic3⋊C4C22116yescomplemented
45#63873C2218yescomplemented
46#63870C2218yescomplemented
47#63870C2218yescomplemented
48C2×C3×C22⋊Q8—32no—
49C2×#946—32no—
50C2×#944—32no—
51C2×C4×#67—32no—
52C22×Dic3⋊C4—32no—
53#5636—332no—
54C2×#896—32no—
55C2×#896D312yescomplemented
56C2×D3×C4⋊C4—32no—
57C2×#889—32no—
58C2×#889—32no—
59C2×#887—32no—
60C2×#887—61no—
61C2×#67⋊C4—32no—
62C2×#67⋊C4—32no—
63C2×#878—32no—
64C2×#878—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×C3×C4×D3—44no—
79C2×C3×C4×D3C2318yes—
80C2×C3×Dic6—44no—
81C2×C3×Dic6C2318yes—
82C2×#625Q818yescomplemented
83C2×#625C2314yes—
84C2×D3×Dic3—28no—
85C2×D3×Dic3—44no—
86C2×D3×Dic3C2318yes—
87C2×D3×Dic3C2318yes—
88C32×C4⋊C4C2314yes—
89#3750C2314yes—
90#3750C2314yes—
91C4×C3⋊Dic3C2314yes—
92C4×C3⋊Dic3C2314yes—
93C4×C3⋊Dic3C2314yes—
94C3×(C2×D3)⋊C4C2318yes—
95C3×(C2×D3)⋊C4C2318yes—
96C3×Dic3⋊C4C2318yes—
97C3×Dic3⋊C4C2318yes—
98#3724C2314yes—
99#3724C2314yes—
100#3724C2314yes—
101#3724C2318yes—
102Dic3⋊Dic3C2318yes—
103Dic3⋊Dic3C2318yes—
104(C2×D3)⋊Dic3C2318yes—
105C2×#554—91noSylow
106C22×C3×Q8—32no—
107C23×C3×C4—32no—
108C22×#67—32no—
109C23×Dic3—32no—
110C23×Dic3—32no—
111C22×C4×D3—32no—
112C22×C4×D3—32no—
113C22×C4×D3C2×D312yes—
114C22×Dic6—32no—
115C22×Dic6—61no—
116C22×Dic6C2×D312yes—
117C3×C22⋊Q8—316no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—32no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4C2×D312yes—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4—32no—
124C2×#217—32no—
125#946—316no—
126#944—316no—
127C4×#67—316no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4C2×D312yes—
130C2×(C2×D3)⋊C4C2×D312yes—
131C2×C4⋊Dic3—32no—
132C2×C4⋊Dic3—32no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—316no—
143C2×Dic3⋊C4—61no—
144C2×Dic3⋊C4—61no—
145C2×Dic3⋊C4C2×D312yes—
146C2×Dic3⋊C4C2×D312yes—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—61no—
151C2×C4×Dic3—61no—
152C2×C4×Dic3—61no—
153#896—316no—
154#896C2×D3116yescomplemented
155D3×C4⋊C4—316no—
156#889—316no—
157#889—316no—
158#887—316no—
159#887—68no—
160#67⋊C4—316no—
161#67⋊C4—316no—
162#878—316no—
163#878—316no—
164C23×C32C2411yescharacteristic
165C22×C3×D3—24no—
166C22×C3×D3—24no—
167C22×C3×D3C2×Q818yes—
168C22×C3×D3C2414yes—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4C2412yes—
173C2×C32×C4C2412yes—
174C2×C32×C4C2412yes—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3C2×Q814yes—
178C2×C3⋊Dic3#4114yes—
179C2×C3⋊Dic3C2412yes—
180C2×C3⋊Dic3C2412yes—
181C2×C3⋊Dic3C2412yes—
182C2×C3⋊Dic3C2412yes—
183#634—28no—
184C2×C3×Dic3—24no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3C2414yes—
188C2×C3×Dic3C2414yes—
189C2×C3×Dic3C2414yes—
190C3×C4×D3—48no—
191C3×Dic6—48no—
192#625C2×Q8116yescomplemented
193D3×Dic3—216no—
194D3×Dic3—48no—
195#554—916no—
196C2×C4⋊Q8—91no—
197C2×#125—91no—
198C2×#125—91no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—92no—
201C2×C22⋊Q8—92no—
202C2×C4×Q8—91no—
203C2×C4×D4—91no—
204C2×C4×D4—91no—
205C2×C4×D4—91no—
206C22×C4⋊C4—92no—
207C24×C3—32no—
208C23×D3C22×D312yes—
209C2×C3×Q8—38no—
210C2×C3×Q8—124no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—38no—
218C22×C3×C4—124no—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D312yes—
221C22×C3×C4C22×D312yes—
222C2×#67—316no—
223C2×#67—38no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—38no—
229C22×Dic3—38no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—68no—
235C22×Dic3—124no—
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C2×C4×D3—38no—
240C2×C4×D3—38no—
241C2×C4×D3—44no—
242C2×C4×D3—68no—
243C2×C4×D3—124no—
244C2×C4×D3C22×D318yes—
245C2×Dic6—38no—
246C2×Dic6—44no—
247C2×Dic6—64no—
248C2×Dic6—68no—
249C2×Dic6—68no—
250C2×Dic6C22×D318yes—
251C3×C4⋊C4—24no—
252C3×C4⋊C4—38no—
253C3×C4⋊C4—38no—
254C3×C4⋊C4C22×D318yes—
255C3×C22⋊C4—38no—
256C3×C22⋊C4—38no—
257#217—38no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4C22×D318yes—
260(C2×D3)⋊C4C22×D318yes—
261C4⋊Dic3—38no—
262C4⋊Dic3—38no—
263Dic3⋊C4—38no—
264Dic3⋊C4—38no—
265Dic3⋊C4—38no—
266Dic3⋊C4—38no—
267Dic3⋊C4—38no—
268Dic3⋊C4—38no—
269Dic3⋊C4—38no—
270Dic3⋊C4—38no—
271Dic3⋊C4—38no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274Dic3⋊C4C22×D318yes—
275Dic3⋊C4C22×D318yes—
276C4×Dic3—38no—
277C4×Dic3—38no—
278C4×Dic3—38no—
279C4×Dic3—64no—
280C4×Dic3—64no—
281C4×Dic3—64no—
282C22×C32C22×Q812yes—
283C22×C32C2×#4112yes—
284C22×C32H(5,𝔽2)12yes—
285C22×C32C2511yescharacteristic
286C2×C3×D3—216no—
287C2×C3×D3—24no—
288C2×C3×D3—24no—
289C2×C3×D3C22×Q818yes—
290C32×C4—22no—
291C32×C4—22no—
292C32×C4—22no—
293C3⋊Dic3—22no—
294C3⋊Dic3—22no—
295C3⋊Dic3C22×Q814yes—
296C3⋊Dic3C2×#4114yes—
297C3×Dic3—24no—
298C3×Dic3—24no—
299C3×Dic3—24no—
300C22×Q8—32no—
301C22×Q8—91no—
302C22×D4—91no—
303C23×C4—32no—
304C23×C4—92no—
305C23×C4—92no—
306C4⋊Q8—98no—
307#125—98no—
308#125—98no—
309C22⋊Q8—316no—
310C22⋊Q8—916no—
311C22⋊Q8—916no—
312C4×Q8—98no—
313C4×D4—98no—
314C4×D4—98no—
315C4×D4—98no—
316C2×C4⋊C4—32no—
317C2×C4⋊C4—32no—
318C2×C4⋊C4—916no—
319C2×C4⋊C4—92no—
320C2×C4⋊C4—92no—
321C2×C4⋊C4—91no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—92no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4D3211yescharacteristic
328C2×C22⋊C4—32no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—92no—
331C2×C42—91no—
332C2×C42—91no—
333C2×C42—91no—
334C23×C3—21no—
335C23×C3—38no—
336C23×C3—34no—
337C23×C3—64no—
338C23×C3—64no—
339C23×C3C23×D312yes—
340C22×D3—24no—
341C22×D3—24no—
342C22×D3D3×Q818yes—
343C22×D3C23×D314yes—
344C3×Q8—128no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—34no—
353C2×C3×C4—34no—
354C2×C3×C4—34no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—64no—
358C2×C3×C4—64no—
359C2×C3×C4—64no—
360C2×C3×C4—128no—
361C2×C3×C4C23×D314yes—
362C2×C3×C4C23×D314yes—
363C2×C3×C4C23×D314yes—
364#67—332no—
365C2×Dic3—24no—
366C2×Dic3—24no—
367C2×Dic3—24no—
368C2×Dic3—38no—
369C2×Dic3—38no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—616no—
381C2×Dic3—64no—
382C2×Dic3—64no—
383C2×Dic3—64no—
384C2×Dic3—122no—
385C2×Dic3—128no—
386C2×Dic3C23×D314yes—
387C2×Dic3C23×D314yes—
388C2×Dic3C23×D314yes—
389C4×D3—48no—
390C4×D3—616no—
391C4×D3—128no—
392Dic6—48no—
393Dic6—616no—
394Dic6—616no—
395C2×C32#55414yescomplemented
396C2×C32C23×Q811yescharacteristic
397C2×C32C22×#4111yescharacteristic
398C2×C32C2×H(5,𝔽2)11yescharacteristic
399C3×D3—28no—
400C24—32no—
401C2×Q8—38no—
402C2×Q8—94no—
403C2×Q8—124no—
404C2×Q8—184no—
405C2×D4—94no—
406C2×D4—98no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—32no—
410C22×C4—38no—
411C22×C4—98no—
412C22×C4—98no—
413C22×C4—91no—
414C22×C4—91no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—124no—
418C22×C4—188no—
419C22×C4—364no—
420C22×C4C2×D3211yescharacteristic
421C22×C4C2×D3211yescharacteristic
422C22×C4C2×D3211yescharacteristic
423C4⋊C4—38no—
424C4⋊C4—38no—
425C4⋊C4—98no—
426C4⋊C4—98no—
427C4⋊C4—94no—
428C4⋊C4—94no—
429C4⋊C4—94no—
430C4⋊C4—98no—
431C4⋊C4—94no—
432C4⋊C4—94no—
433C4⋊C4C2×D3214yes—
434C22⋊C4—38no—
435C22⋊C4—38no—
436C22⋊C4—98no—
437C42—94no—
438C42—94no—
439C42—94no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—38no—
445C22×C3—616no—
446C22×C3—64no—
447C22×C3—64no—
448C22×C3#100414yes—
449C22×C3C2×D3×Q814yes—
450C22×C3D3×#4114yes—
451C22×C3C24×D312yes—
452C2×D3—216no—
453C2×D3—24no—
454C2×D3—24no—
455C2×D3C2×D3×Q818yes—
456C3×C4—24no—
457C3×C4—24no—
458C3×C4—24no—
459C3×C4—24no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—64no—
463C3×C4—64no—
464C3×C4—64no—
465Dic3—24no—
466Dic3—24no—
467Dic3—24no—
468Dic3—38no—
469Dic3—38no—
470Dic3—64no—
471Dic3—64no—
472Dic3—64no—
473Dic3—64no—
474Dic3—64no—
475Dic3—122no—
476C32C2×#55411yescharacteristic, complemented, Sylow
477C23—38no—
478C23—34no—
479C23—64no—
480C23—64no—
481C23C22×D3211yescharacteristic
482Q8—128no—
483Q8—188no—
484D4—916no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—34no—
489C2×C4—34no—
490C2×C4—34no—
491C2×C4—64no—
492C2×C4—64no—
493C2×C4—64no—
494C2×C4—94no—
495C2×C4—94no—
496C2×C4—92no—
497C2×C4—92no—
498C2×C4—92no—
499C2×C4—92no—
500C2×C4—128no—
501C2×C4—1816no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—368no—
505C2×C4C22×D3212yes—
506C2×C4C22×D3212yes—
507C2×C4C22×D3212yes—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—24no—
512C2×C3—68no—
513C2×C3#563618yescomplemented
514C2×C3C2×#100412yes—
515C2×C3C22×D3×Q812yes—
516C2×C3C2×D3×#4112yes—
517D3—28no—
518C22—38no—
519C22—64no—
520C22—64no—
521C22—616no—
522C22#6430612yes—
523C22#6431312yes—
524C22D32×Q812yes—
525C22C23×D3211yescharacteristic
526C4—22no—
527C4—22no—
528C4—22no—
529C4—64no—
530C4—64no—
531C4—64no—
532C4—94no—
533C4—94no—
534C4—182no—
535C4—182no—
536C3—21no—
537C3C2×#563612yescomplemented
538C2—68no—
539C2#1059453414yesdirect product factor
540C2C2×#6430611yescharacteristic
541C2C2×#6431311yescharacteristic
542C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#554
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×#896C2semidirect
6. C2×#63896C2semidirect
7. C2×#63887C2semidirect
8. C2×D3×Dic3⋊C4C2semidirect
9. C2×#63873C2semidirect
10. C2×#63870C2semidirect
11. C2×#63870C2semidirect
12. #10594534C2direct (N × H)
26. #64096C22semidirect
31. C3×#896C22semidirect
42. #63896C22semidirect
43. #63887C22semidirect
44. D3×Dic3⋊C4C22semidirect
45. #63873C22semidirect
46. #63870C22semidirect
47. #63870C22semidirect
55. C2×#896D3semidirect
82. C2×#625Q8semidirect
154. #896C2×D3semidirect
192. #625C2×Q8semidirect
395. C2×C32#554semidirect
476. C32C2×#554semidirect
513. C2×C3#5636semidirect
537. C3C2×#5636semidirect
539. C2#10594534direct (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×#8962
C2×#639022
C2×C4×#6252
C2×#638962
C2×#638872
C2×D3×Dic3⋊C42
C2×#638732
C2×#638702
#105945342
C2×#56363