Finite Group Databasebeta

← C2×#10594569 #11901717

Subgroups — C2×#10594569 #11901717

Order 1152.

2429 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2C2×C3×#896C212yesmaximal, complemented
3C2×#63915C211yesmaximal, characteristic, complemented
4C2×#63912C211yesmaximal, characteristic
5C2×#63907C212yesmaximal, complemented
6C2×C4×#625C211yesmaximal, characteristic, complemented
7C2×#63873C211yesmaximal, characteristic, complemented
8C2×#63865C211yesmaximal, characteristic, complemented
9C2×#63861C212yesmaximal, complemented
10C2×#63850C212yesmaximal, complemented
11C2×#63838C211yesmaximal, characteristic, complemented
12#10594569C2116yesmaximal, direct product factor
13C2×#5640—32nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×Dic6C2212yes—
17C22×#627C2211yescharacteristic
18C22×#626C2212yes—
19C22×#625C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64101C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2212yes—
31C3×#896C22116yescomplemented
32C2×#3724C2212yes—
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3722C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2212yes—
39#63915C2218yescomplemented
40#63912C2218yes—
41#63907C22116yescomplemented
42C4×#625C2218yescomplemented
43#63873C2218yescomplemented
44#63865C2218yescomplemented
45#63861C22116yescomplemented
46#63850C22116yescomplemented
47#63838C2218yescomplemented
48C2×C3×C22⋊Q8—32no—
49C2×#947—32no—
50C2×#944—32no—
51C2×#929—32no—
52C2×C4×#67—32no—
53#5640—332no—
54C2×#898—32no—
55C2×#896—32no—
56C2×#896D312yescomplemented
57C2×#894—32no—
58C2×#892—32no—
59C2×#892—61no—
60C2×#887—32no—
61C2×#885—32no—
62C2×#885—32no—
63C2×#884—32no—
64C2×#879—32no—
65C23×C3⋊D3C2311yescharacteristic
66C23×C3×D3C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4×C3⋊D3—24no—
74C2×C4×C3⋊D3C2314yes—
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×#627—24no—
83C2×#627C2314yes—
84C2×#626—44no—
85C2×#626C2318yes—
86C2×#625—24no—
87C2×#625C2314yes—
88C32×C4⋊C4C2314yes—
89#3752C2314yes—
90#3752C2314yes—
91C4⋊(C3⋊Dic3)C2314yes—
92C4×C3⋊Dic3C2314yes—
93C4×C3⋊Dic3C2314yes—
94C3×(C2×D3)⋊C4C2318yes—
95C3×(C2×D3)⋊C4C2318yes—
96C3×Dic3⋊C4C2318yes—
97C3×Dic3⋊C4C2318yes—
98#3724C2314yes—
99#3724C2318yes—
100#3724C2314yes—
101#3722C2318yes—
102(C2×D3)⋊Dic3C2318yes—
103(C2×D3)⋊Dic3C2318yes—
104Dic32C2318yes—
105C2×#542—91noSylow
106C22×C3×Q8—32no—
107C23×C3×C4—32no—
108C22×#67—32no—
109C22×#67—32no—
110C22×D12—32no—
111C22×C4×D3—32no—
112C22×C4×D3—61no—
113C22×C4×D3C2×D312yes—
114C22×Dic6—32no—
115C22×Dic6C2×D312yes—
116C3×C22⋊Q8—316no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C4⋊C4—32no—
120C2×C3×C4⋊C4C2×D312yes—
121C2×C3×C22⋊C4—32no—
122C2×C3×C22⋊C4—32no—
123C2×#217—32no—
124C2×#217—32no—
125#947—316no—
126#944—316no—
127#929—316no—
128C4×#67—316no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—61no—
136C2×(C2×D3)⋊C4—61no—
137C2×(C2×D3)⋊C4C2×D312yes—
138C2×(C2×D3)⋊C4C2×D312yes—
139C2×C4⋊Dic3—32no—
140C2×C4⋊Dic3—61no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4C2×D312yes—
146C2×Dic3⋊C4C2×D312yes—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—61no—
152C2×C4×Dic3—61no—
153#898—316no—
154#896—316no—
155#896C2×D3116yescomplemented
156#894—316no—
157#892—316no—
158#892—68no—
159#887—316no—
160#885—316no—
161#885—316no—
162#884—316no—
163#879—316no—
164C23×C32C2411yescharacteristic
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3C2412yes—
169C22×C3×D3—24no—
170C22×C3×D3—24no—
171C22×C3×D3—24no—
172C22×C3×D3C2414yes—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4C2412yes—
177C2×C32×C4C2412yes—
178C2×C32×C4C2412yes—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3#4114yes—
182C2×C3⋊Dic3C2412yes—
183C2×C3⋊Dic3C2412yes—
184C2×C3⋊Dic3C2412yes—
185C4×C3⋊D3—28no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3C2414yes—
190C2×C3×Dic3C2414yes—
191C2×C3×Dic3C2414yes—
192C3×C4×D3—48no—
193C3×Dic6—48no—
194#627—28no—
195#626—48no—
196#625—28no—
197#542—916no—
198C2×C4⋊Q8—91no—
199C2×#126—92no—
200C2×#124—91no—
201C2×#124—92no—
202C2×#123—92no—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—91no—
205C2×#121—91no—
206C2×C4×Q8—91no—
207C2×C4×D4—91no—
208C2×#117—91no—
209C24×C3—32no—
210C23×D3—32no—
211C23×D3—61no—
212C23×D3C22×D312yes—
213C2×C3×Q8—38no—
214C2×C3×Q8—124no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—38no—
222C22×C3×C4—124no—
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D312yes—
225C22×C3×C4C22×D312yes—
226C2×#67—38no—
227C2×#67—38no—
228C2×#67—68no—
229C2×#67—124no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C2×D12—38no—
240C2×D12—124no—
241C2×C4×D3—38no—
242C2×C4×D3—44no—
243C2×C4×D3—64no—
244C2×C4×D3—68no—
245C2×C4×D3—68no—
246C2×C4×D3C22×D318yes—
247C2×Dic6—38no—
248C2×Dic6—44no—
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#217—38no—
259(C2×D3)⋊C4—38no—
260(C2×D3)⋊C4—38no—
261(C2×D3)⋊C4—38no—
262(C2×D3)⋊C4—38no—
263(C2×D3)⋊C4—38no—
264(C2×D3)⋊C4—38no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4C22×D318yes—
268(C2×D3)⋊C4C22×D318yes—
269C4⋊Dic3—38no—
270C4⋊Dic3—64no—
271Dic3⋊C4—38no—
272Dic3⋊C4—38no—
273Dic3⋊C4—38no—
274Dic3⋊C4—38no—
275Dic3⋊C4C22×D318yes—
276Dic3⋊C4C22×D318yes—
277C4×Dic3—38no—
278C4×Dic3—38no—
279C4×Dic3—38no—
280C4×Dic3—38no—
281C4×Dic3—64no—
282C4×Dic3—64no—
283C22×C32C2×#4112yes—
284C22×C32H(5,𝔽2)12yes—
285C22×C322−1+412yes—
286C22×C32C2511yescharacteristic
287C2×C3⋊D3—22no—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—44no—
291C2×C3×D3—24no—
292C2×C3×D3—24no—
293C2×C3×D3—24no—
294C2×C3×D3—48no—
295C32×C4—22no—
296C32×C4—22no—
297C32×C4—22no—
298C3⋊Dic3—22no—
299C3⋊Dic3—22no—
300C3⋊Dic3C2×#4114yes—
301C3×Dic3—24no—
302C3×Dic3—24no—
303C3×Dic3—24no—
304C22×Q8—32no—
305C22×Q8—91no—
306C22×D4—92no—
307C22×D4—91no—
308C23×C4—32no—
309C23×C4—91no—
310C4⋊Q8—98no—
311#126—916no—
312#124—98no—
313#124—916no—
314#123—916no—
315C22⋊Q8—316no—
316C22⋊Q8—98no—
317#121—98no—
318C4×Q8—98no—
319C4×D4—98no—
320#117—98no—
321C2×C4⋊C4—32no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4D3211yescharacteristic
328C2×C22⋊C4—32no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—92no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—91no—
334C2×C22⋊C4—91no—
335C2×C42—92no—
336C2×C42—91no—
337C2×C42—91no—
338C23×C3—21no—
339C23×C3—34no—
340C23×C3—64no—
341C23×C3—64no—
342C23×C3—64no—
343C23×C3C23×D312yes—
344C22×D3—24no—
345C22×D3—24no—
346C22×D3—24no—
347C22×D3—34no—
348C22×D3—62no—
349C22×D3—64no—
350C22×D3—64no—
351C22×D3—64no—
352C22×D3—64no—
353C22×D3—122no—
354C22×D3—122no—
355C22×D3C23×D314yes—
356C3×Q8—128no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—34no—
365C2×C3×C4—34no—
366C2×C3×C4—34no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—64no—
370C2×C3×C4—64no—
371C2×C3×C4—64no—
372C2×C3×C4—128no—
373C2×C3×C4C23×D314yes—
374C2×C3×C4C23×D314yes—
375C2×C3×C4C23×D314yes—
376#67—616no—
377#67—128no—
378C2×Dic3—24no—
379C2×Dic3—24no—
380C2×Dic3—24no—
381C2×Dic3—38no—
382C2×Dic3—34no—
383C2×Dic3—34no—
384C2×Dic3—34no—
385C2×Dic3—64no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—64no—
390C2×Dic3—64no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3C23×D314yes—
394C2×Dic3C23×D314yes—
395C2×Dic3C23×D314yes—
396D12—128no—
397C4×D3—48no—
398C4×D3—616no—
399C4×D3—616no—
400Dic6—48no—
401Dic6—616no—
402C2×C32#54214yescomplemented
403C2×C32C22×#4111yescharacteristic
404C2×C32C2×H(5,𝔽2)11yescharacteristic
405C2×C32C2×2−1+411yescharacteristic
406C3⋊D3—42no—
407C3×D3—44no—
408C24—32no—
409C24—91no—
410C2×Q8—38no—
411C2×Q8—94no—
412C2×Q8—124no—
413C2×Q8—184no—
414C2×D4—98no—
415C2×D4—94no—
416C2×D4—184no—
417C2×D4—364no—
418C22×C4—32no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—38no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—94no—
426C22×C4—124no—
427C22×C4—184no—
428C22×C4C2×D3211yescharacteristic
429C22×C4C2×D3211yescharacteristic
430C22×C4C2×D3211yescharacteristic
431C4⋊C4—38no—
432C4⋊C4—38no—
433C4⋊C4—94no—
434C4⋊C4—94no—
435C4⋊C4—98no—
436C4⋊C4—94no—
437C4⋊C4C2×D3214yes—
438C22⋊C4—38no—
439C22⋊C4—38no—
440C22⋊C4—98no—
441C22⋊C4—98no—
442C22⋊C4—98no—
443C22⋊C4—94no—
444C22⋊C4—94no—
445C42—98no—
446C42—94no—
447C42—94no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—21no—
452C22×C3—64no—
453C22×C3—64no—
454C22×C3—64no—
455C22×C3—128no—
456C22×C3#100414yes—
457C22×C3#100714yes—
458C22×C3D3×#4114yes—
459C22×C3C24×D312yes—
460C2×D3—24no—
461C2×D3—24no—
462C2×D3—24no—
463C2×D3—48no—
464C2×D3—64no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—64no—
468C2×D3—122no—
469C2×D3—122no—
470C2×D3—128no—
471C2×D3—128no—
472C3×C4—24no—
473C3×C4—24no—
474C3×C4—24no—
475C3×C4—24no—
476C3×C4—42no—
477C3×C4—42no—
478C3×C4—64no—
479C3×C4—64no—
480C3×C4—64no—
481Dic3—24no—
482Dic3—24no—
483Dic3—24no—
484Dic3—38no—
485Dic3—64no—
486Dic3—64no—
487Dic3—64no—
488Dic3—122no—
489Dic3—122no—
490C32C2×#54211yescharacteristic, complemented, Sylow
491C23—34no—
492C23—64no—
493C23—64no—
494C23—64no—
495C23—92no—
496C23—182no—
497C23—182no—
498C23—182no—
499C23C22×D3211yescharacteristic
500Q8—128no—
501Q8—188no—
502D4—188no—
503D4—368no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—34no—
508C2×C4—34no—
509C2×C4—34no—
510C2×C4—64no—
511C2×C4—64no—
512C2×C4—64no—
513C2×C4—94no—
514C2×C4—92no—
515C2×C4—92no—
516C2×C4—92no—
517C2×C4—128no—
518C2×C4—188no—
519C2×C4—182no—
520C2×C4—182no—
521C2×C4C22×D3212yes—
522C2×C4C22×D3212yes—
523C2×C4C22×D3212yes—
524C2×C3—24no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—124no—
529C2×C3#564018yescomplemented
530C2×C3C2×#100412yes—
531C2×C3C2×#100712yes—
532C2×C3C2×D3×#4112yes—
533D3—44no—
534D3—124no—
535D3—124no—
536C22—64no—
537C22—64no—
538C22—64no—
539C22—128no—
540C22—182no—
541C22—182no—
542C22—182no—
543C22—364no—
544C22#6430612yes—
545C22#6431312yes—
546C22#6431612yes—
547C22C23×D3211yescharacteristic
548C4—22no—
549C4—22no—
550C4—22no—
551C4—64no—
552C4—64no—
553C4—64no—
554C4—94no—
555C4—182no—
556C4—182no—
557C3—21no—
558C3C2×#564012yescomplemented
559C2—124no—
560C2—362no—
561C2#1059456914yesdirect product factor
562C2C2×#6430611yescharacteristic
563C2C2×#6431311yescharacteristic
564C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63912C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#542
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×#64101C2semidirect
2. C2×C3×#896C2semidirect
3. C2×#63915C2semidirect
5. C2×#63907C2semidirect
6. C2×C4×#625C2semidirect
7. C2×#63873C2semidirect
8. C2×#63865C2semidirect
9. C2×#63861C2semidirect
10. C2×#63850C2semidirect
11. C2×#63838C2semidirect
12. #10594569C2direct (N × H)
26. #64101C22semidirect
31. C3×#896C22semidirect
39. #63915C22semidirect
41. #63907C22semidirect
42. C4×#625C22semidirect
43. #63873C22semidirect
44. #63865C22semidirect
45. #63861C22semidirect
46. #63850C22semidirect
47. #63838C22semidirect
56. C2×#896D3semidirect
155. #896C2×D3semidirect
402. C2×C32#542semidirect
490. C32C2×#542semidirect
529. C2×C3#5640semidirect
558. C3C2×#5640semidirect
561. C2#10594569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641012
C2×C3×#8962
C2×#639152
C2×#639122
C2×#639072
C2×C4×#6252
C2×#638732
C2×#638652
C2×#638612
C2×#638502
C2×#638382
#105945692
C2×#56403