Finite Group Databasebeta

← C2×#10594963 #11900629

Subgroups — C2×#10594963 #11900629

Order 1152.

2713 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#929C212yesmaximal, complemented
3C2×#63982C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic
5C2×#67⋊Dic3C212yesmaximal, complemented
6C2×#63915C211yesmaximal, characteristic, complemented
7C2×#63902C211yesmaximal, characteristic, complemented
8#10594963C2116yesmaximal, direct product factor
9C2×#63878C212yesmaximal, complemented
10C2×#63870C211yesmaximal, characteristic, complemented
11C2×#63862C212yesmaximal, complemented
12C2×#63838C211yesmaximal, characteristic, complemented
13C2×#5649—32nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×#627C2211yescharacteristic
19C22×#625C2211yescharacteristic
20C22×D3×Dic3C2212yes—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2218yescomplemented
26C2×C3×#217C2212yes—
27C3×#929C22116yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×Dic3⋊C4C2212yes—
32#63982C2218yescomplemented
33#63980C2218yes—
34#67⋊Dic3C22116yescomplemented
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×Dic32C2212yes—
42#63915C2218yescomplemented
43#63902C2218yescomplemented
44#63878C22116yescomplemented
45#63870C2218yescomplemented
46#63862C22116yescomplemented
47#63838C2218yescomplemented
48C2×C3×#123—32no—
49C2×#939—32no—
50C2×D4×Dic3—32no—
51C2×#929D312yescomplemented
52C22×C4×Dic3—32no—
53C22×C4×Dic3—61no—
54#5649—332no—
55C2×#898—32no—
56C2×#892—32no—
57C2×#889—32no—
58C2×#887—32no—
59C2×#885—32no—
60C2×#67⋊C4—32no—
61C2×#67⋊C4—32no—
62C2×#879—32no—
63C2×#878—32no—
64C2×#877—32no—
65C24×C32C2311yescharacteristic
66C23×C3×D3C2312yes—
67C22×C32×C4—24no—
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2314yes—
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3—24no—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2314yes—
76C22×C3⋊Dic3C2314yes—
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C2×C3×#67—28no—
80C2×C3×#67C2318yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C2×#627—24no—
85C2×#627C2314yes—
86C2×#625—24no—
87C2×#625C2314yes—
88C2×D3×Dic3—28no—
89C2×D3×Dic3C2318yes—
90C4×C3⋊Dic3C2314yes—
91C4×C3⋊Dic3C2314yes—
92C4×C3⋊Dic3C2314yes—
93C4×C3⋊Dic3C2314yes—
94C3×#217C2318yes—
95C3×(C2×D3)⋊C4C2318yes—
96C3×(C2×D3)⋊C4C2318yes—
97C3×Dic3⋊C4C2318yes—
98C3×Dic3⋊C4C2318yes—
99#3724C2314yes—
100#3724C2314yes—
101Dic3⋊Dic3C2318yes—
102Dic3⋊Dic3C2318yes—
103(C2×D3)⋊Dic3C2318yes—
104(C2×D3)⋊Dic3C2318yes—
105Dic32C2318yes—
106C2×#529—91noSylow
107C22×C3×D4—32no—
108C23×C3×C4—21no—
109C23×C3×C4C2×D312yes—
110C22×#67—32no—
111C22×#67C2×D312yes—
112C23×Dic3—32no—
113C23×Dic3—32no—
114C23×Dic3—32no—
115C23×Dic3—61no—
116C23×Dic3—61no—
117C22×C4×D3—32no—
118C22×Dic6—32no—
119C3×#123—316no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×#217—32no—
126C2×#217—32no—
127C2×#217C2×D312yes—
128#939—316no—
129D4×Dic3—316no—
130#929C2×D3116yescomplemented
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4C2×D312yes—
142C2×Dic3⋊C4C2×D312yes—
143C2×C4×Dic3—316no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—61no—
151C2×C4×Dic3—61no—
152C2×C4×Dic3—61no—
153C2×C4×Dic3—61no—
154C2×C4×Dic3—68no—
155#898—316no—
156#892—316no—
157#889—316no—
158#887—316no—
159#885—316no—
160#67⋊C4—316no—
161#67⋊C4—316no—
162#879—316no—
163#878—316no—
164#877—316no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32#4114yes—
168C23×C32C2412yes—
169C23×C32C2411yescharacteristic
170C22×C3×D3—24no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3C2414yes—
174C2×C32×C4—28no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C2412yes—
178C2×C32×C4C2412yes—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—28no—
182C2×C3⋊Dic3—28no—
183C2×C3⋊Dic3#4114yes—
184C2×C3⋊Dic3#4114yes—
185C2×C3⋊Dic3C2412yes—
186C2×C3⋊Dic3C2412yes—
187C2×C3⋊Dic3C2412yes—
188C2×C3⋊Dic3C2412yes—
189C3×#67—216no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—24no—
192C2×C3×Dic3—24no—
193C2×C3×Dic3C2414yes—
194C2×C3×Dic3C2414yes—
195C2×C3×Dic3C2414yes—
196#627—28no—
197#625—28no—
198D3×Dic3—216no—
199#529—916no—
200C2×#126—92no—
201C2×#125—91no—
202C2×#124—91no—
203C2×#123—32no—
204C2×C22⋊Q8—91no—
205C2×#121—91no—
206C2×C4×Q8—91no—
207C2×C4×D4—91no—
208C2×C4×D4—92no—
209C2×#117—92no—
210C22×C42—91no—
211C24×C3—21no—
212C24×C3—32no—
213C24×C3C22×D312yes—
214C23×D3C22×D312yes—
215C2×C3×D4—38no—
216C2×C3×D4—68no—
217C22×C3×C4—28no—
218C22×C3×C4—28no—
219C22×C3×C4—24no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4C22×D312yes—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D318yes—
228C2×#67—28no—
229C2×#67—38no—
230C2×#67—68no—
231C2×#67C22×D318yes—
232C22×Dic3—32no—
233C22×Dic3—32no—
234C22×Dic3—38no—
235C22×Dic3—38no—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—38no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3—64no—
242C22×Dic3—64no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—68no—
246C22×Dic3—68no—
247C22×Dic3—68no—
248C22×Dic3—68no—
249C22×Dic3—68no—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D312yes—
252C22×Dic3C22×D312yes—
253C2×C4×D3—38no—
254C2×C4×D3—68no—
255C2×Dic6—38no—
256C2×Dic6—68no—
257C3×C4⋊C4—38no—
258C3×C4⋊C4—38no—
259C3×C22⋊C4—38no—
260C3×C22⋊C4—38no—
261C3×C22⋊C4—38no—
262#217—38no—
263#217—38no—
264#217C22×D318yes—
265(C2×D3)⋊C4—38no—
266(C2×D3)⋊C4—38no—
267(C2×D3)⋊C4C22×D318yes—
268(C2×D3)⋊C4C22×D318yes—
269C4⋊Dic3—38no—
270C4⋊Dic3—38no—
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—38no—
282C4×Dic3—38no—
283C4×Dic3—64no—
284C4×Dic3—64no—
285C4×Dic3—64no—
286C4×Dic3—64no—
287C22×C32—28no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32C2×#4114yes—
291C22×C32C2×#4112yes—
292C22×C32C2×#4112yes—
293C22×C32C2×#4112yes—
294C22×C32C2511yescharacteristic
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—24no—
298C2×C3×D3—48no—
299C32×C4—22no—
300C32×C4—22no—
301C3⋊Dic3—22no—
302C3⋊Dic3—22no—
303C3⋊Dic3C2×#4114yes—
304C3⋊Dic3C2×#4114yes—
305C3×Dic3—24no—
306C3×Dic3—24no—
307C3×Dic3—24no—
308C22×Q8—91no—
309C22×D4—32no—
310C22×D4—91no—
311C23×C4—92no—
312C23×C4—91no—
313C23×C4—91no—
314C23×C4D3211yescharacteristic
315#126—916no—
316#125—98no—
317#124—98no—
318#123—316no—
319C22⋊Q8—98no—
320#121—98no—
321C4×Q8—98no—
322C4×D4—98no—
323C4×D4—916no—
324#117—916no—
325C2×C4⋊C4—32no—
326C2×C4⋊C4—32no—
327C2×C4⋊C4—92no—
328C2×C4⋊C4—91no—
329C2×C4⋊C4—92no—
330C2×C4⋊C4—91no—
331C2×C22⋊C4—32no—
332C2×C22⋊C4—32no—
333C2×C22⋊C4—32no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4—92no—
336C2×C42—92no—
337C2×C42—91no—
338C2×C42—91no—
339C2×C42—91no—
340C2×C42—91no—
341C2×C42—98no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—22no—
347C23×C3—21no—
348C23×C3—24no—
349C23×C3—34no—
350C23×C3—64no—
351C23×C3—64no—
352C23×C3—64no—
353C23×C3#23718yes—
354C23×C3C23×D314yes—
355C23×C3C23×D312yes—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—24no—
359C22×D3C23×D314yes—
360C3×D4—616no—
361C2×C3×C4—216no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—216no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—34no—
370C2×C3×C4—34no—
371C2×C3×C4—34no—
372C2×C3×C4—64no—
373C2×C3×C4—64no—
374C2×C3×C4—64no—
375C2×C3×C4C23×D314yes—
376C2×C3×C4C23×D314yes—
377#67—216no—
378#67—616no—
379C2×Dic3—24no—
380C2×Dic3—24no—
381C2×Dic3—24no—
382C2×Dic3—38no—
383C2×Dic3—38no—
384C2×Dic3—34no—
385C2×Dic3—34no—
386C2×Dic3—34no—
387C2×Dic3—34no—
388C2×Dic3—64no—
389C2×Dic3—64no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—616no—
395C2×Dic3—616no—
396C2×Dic3—616no—
397C2×Dic3—616no—
398C2×Dic3—616no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3—64no—
402C2×Dic3—64no—
403C2×Dic3C23×D314yes—
404C2×Dic3C23×D314yes—
405C2×Dic3C23×D314yes—
406C4×D3—616no—
407Dic6—616no—
408C2×C32—24no—
409C2×C32#52914yescomplemented
410C2×C32C22×#4111yescharacteristic
411C2×C32C22×#4111yescharacteristic
412C2×C32C22×#4111yescharacteristic
413C3×D3—44no—
414C24—32no—
415C24C2×D3211yescharacteristic
416C2×Q8—94no—
417C2×Q8—184no—
418C2×D4—38no—
419C2×D4—68no—
420C2×D4—94no—
421C2×D4—184no—
422C22×C4—24no—
423C22×C4—32no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—98no—
427C22×C4—91no—
428C22×C4—91no—
429C22×C4—94no—
430C22×C4—94no—
431C22×C4—91no—
432C22×C4—91no—
433C22×C4—188no—
434C22×C4—184no—
435C22×C4—184no—
436C22×C4C2×D3214yes—
437C22×C4C2×D3211yescharacteristic
438C22×C4C2×D3211yescharacteristic
439C4⋊C4—38no—
440C4⋊C4—38no—
441C4⋊C4—98no—
442C4⋊C4—94no—
443C4⋊C4—98no—
444C4⋊C4—94no—
445C22⋊C4—38no—
446C22⋊C4—38no—
447C22⋊C4—38no—
448C22⋊C4—98no—
449C22⋊C4—98no—
450C42—98no—
451C42—94no—
452C42—94no—
453C42—94no—
454C42—94no—
455C22×C3—24no—
456C22×C3—24no—
457C22×C3—216no—
458C22×C3—216no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—24no—
464C22×C3—22no—
465C22×C3—21no—
466C22×C3—64no—
467C22×C3—64no—
468C22×C3—64no—
469C22×C3—128no—
470C22×C3C2×#23718yes—
471C22×C3C2×#23714yes—
472C22×C3D3×#4114yes—
473C22×C3D3×#4114yes—
474C22×C3C24×D312yes—
475C2×D3—24no—
476C2×D3—24no—
477C2×D3—24no—
478C2×D3—48no—
479C3×C4—24no—
480C3×C4—24no—
481C3×C4—24no—
482C3×C4—24no—
483C3×C4—64no—
484C3×C4—64no—
485C3×C4—64no—
486Dic3—24no—
487Dic3—24no—
488Dic3—24no—
489Dic3—38no—
490Dic3—38no—
491Dic3—64no—
492Dic3—64no—
493Dic3—64no—
494Dic3—64no—
495Dic3—64no—
496Dic3—64no—
497C32C2×#52911yescharacteristic, complemented, Sylow
498C23—22no—
499C23—22no—
500C23—34no—
501C23—64no—
502C23—64no—
503C23—64no—
504C23#380514yes—
505C23C22×D3212yes—
506C23C22×D3211yescharacteristic
507Q8—188no—
508D4—616no—
509D4—188no—
510C2×C4—28no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—34no—
514C2×C4—34no—
515C2×C4—34no—
516C2×C4—64no—
517C2×C4—64no—
518C2×C4—64no—
519C2×C4—94no—
520C2×C4—94no—
521C2×C4—92no—
522C2×C4—92no—
523C2×C4—92no—
524C2×C4—92no—
525C2×C4—1816no—
526C2×C4—188no—
527C2×C4—188no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4C22×D3212yes—
531C2×C4C22×D3212yes—
532C2×C3—28no—
533C2×C3—28no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—24no—
538C2×C3—124no—
539C2×C3#564918yescomplemented
540C2×C3C22×#23712yes—
541C2×C3C2×D3×#4112yes—
542C2×C3C2×D3×#4112yes—
543D3—44no—
544C22—22no—
545C22—22no—
546C22—28no—
547C22—64no—
548C22—64no—
549C22—64no—
550C22—128no—
551C22#6430612yes—
552C22#6430612yes—
553C22C2×#380514yes—
554C22C2×#380512yes—
555C22C23×D3211yescharacteristic
556C4—22no—
557C4—22no—
558C4—64no—
559C4—64no—
560C4—64no—
561C4—94no—
562C4—94no—
563C4—182no—
564C4—182no—
565C3—21no—
566C3C2×#564912yescomplemented
567C2—24no—
568C2—124no—
569C2#1059496314yesdirect product factor
570C2C2×#6430611yescharacteristic
571C2C2×#6430611yescharacteristic
572C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC2×#63980C2
hypercenterC23×C4D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊Dic3C2semidirect
2. C2×C3×#929C2semidirect
3. C2×#63982C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. C2×#63915C2semidirect
7. C2×#63902C2semidirect
8. #10594963C2direct (N × H)
9. C2×#63878C2semidirect
10. C2×#63870C2semidirect
11. C2×#63862C2semidirect
12. C2×#63838C2semidirect
25. C2×C4×C3⋊Dic3C22semidirect
27. C3×#929C22semidirect
32. #63982C22semidirect
34. #67⋊Dic3C22semidirect
42. #63915C22semidirect
43. #63902C22semidirect
44. #63878C22semidirect
45. #63870C22semidirect
46. #63862C22semidirect
47. #63838C22semidirect
51. C2×#929D3semidirect
130. #929C2×D3semidirect
409. C2×C32#529semidirect
497. C32C2×#529semidirect
539. C2×C3#5649semidirect
566. C3C2×#5649semidirect
569. C2#10594963direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C2×C3×#9292
C2×#639822
C2×#639802
C2×#67⋊Dic32
C2×#639152
C2×#639022
#105949632
C2×#638782
C2×#638702
C2×#638622
C2×#638382
C2×#56493