Finite Group Databasebeta

← C2×#10594168 #11903264

Subgroups — C2×#10594168 #11903264

Order 1152.

2613 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C2×C3×#878C212yesmaximal, complemented
3C2×#63982C211yesmaximal, characteristic, complemented
4C22×#3724C211yesmaximal, characteristic, complemented
5C2×#63952C212yesmaximal
6C2×#63900C211yesmaximal, characteristic, complemented
7C2×#63888C212yesmaximal, complemented
8C2×#63873C211yesmaximal, characteristic, complemented
9C2×#63865C211yesmaximal, characteristic, complemented
10C2×#63847C212yesmaximal, complemented
11C2×#63838C211yesmaximal, characteristic, complemented
12#10594168C2116yesmaximal, direct product factor
13C2×#5636—32nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C22×C3×Dic6C2212yes—
19C22×#627C2211yescharacteristic
20C22×#624C2212yes—
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64090C2218yes—
26C2×C3×#217C2212yes—
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C3×#878C22116yescomplemented
31#63982C2218yescomplemented
32C2×#3724C2212yes—
33C2×#3724C2212yes—
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×#3724C2218yescomplemented
38C2×Dic3⋊Dic3C2212yes—
39C2×#3722C2212yes—
40C2×Dic32C2212yes—
41#63952C22116yes—
42#63900C2218yescomplemented
43#63888C22116yescomplemented
44#63873C2218yescomplemented
45#63865C2218yescomplemented
46#63847C22116yescomplemented
47#63838C2218yescomplemented
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×#896—32no—
56C2×D3×C4⋊C4—32no—
57C2×#889—32no—
58C2×#889—32no—
59C2×#887—32no—
60C2×#67⋊C4—32no—
61C2×#67⋊C4—32no—
62C2×#67⋊C4—61no—
63C2×#878—32no—
64C2×#878D312yescomplemented
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C2×#638Q818yescomplemented
70C2×#638C2314yes—
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3C2314yes—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C2×C4×C3⋊D3—24no—
77C2×C4×C3⋊D3C2314yes—
78C22×C3×Dic3—44no—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2318yes—
84C2×C3×Dic6—44no—
85C2×C3×Dic6C2318yes—
86C2×#627—24no—
87C2×#627C2314yes—
88C2×#624—44no—
89C2×#624C2318yes—
90C32×C22⋊C4C2314yes—
91#3752C2314yes—
92#3750C2314yes—
93C4×C3⋊Dic3C2314yes—
94C3×#217C2318yes—
95C3×C4⋊Dic3C2318yes—
96C3×Dic3⋊C4C2318yes—
97C3×Dic3⋊C4C2318yes—
98#3724C2314yes—
99#3724C2318yes—
100#3724C2318yes—
101#3724C2314yes—
102#3724C2314yes—
103Dic3⋊Dic3C2318yes—
104#3722C2318yes—
105Dic32C2318yes—
106C2×#554—91noSylow
107C22×C3×Q8—32no—
108C23×C3×C4—32no—
109C22×#67—32no—
110C22×#67—61no—
111C23×Dic3—32no—
112C23×Dic3—61no—
113C23×Dic3C2×D312yes—
114C22×C4×D3—32no—
115C22×C4×D3—32no—
116C22×C4×D3—32no—
117C22×C4×D3—61no—
118C22×Dic6—32no—
119C22×Dic6C2×D312yes—
120C3×C22⋊Q8—316no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4—32no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4C2×D312yes—
127C2×#217C2×D312yes—
128#946—316no—
129#944—316no—
130C4×#67—316no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—61no—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3C2×D312yes—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—316no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4—61no—
148C2×Dic3⋊C4C2×D312yes—
149C2×Dic3⋊C4C2×D312yes—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—32no—
152C2×C4×Dic3—32no—
153C2×C4×Dic3—61no—
154#896—316no—
155#896—316no—
156D3×C4⋊C4—316no—
157#889—316no—
158#889—316no—
159#887—316no—
160#67⋊C4—316no—
161#67⋊C4—316no—
162#67⋊C4—68no—
163#878—316no—
164#878C2×D3116yescomplemented
165C23×C32—22no—
166C23×C32—22no—
167C23×C32C2×Q814yes—
168C23×C32C2412yes—
169C23×C32C2411yescharacteristic
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3C2×Q814yes—
173C22×C3⋊D3C2412yes—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4C2412yes—
177C2×C32×C4C2412yes—
178#638C2×Q8116yescomplemented
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—28no—
181C2×C3⋊Dic3C2×Q814yes—
182C2×C3⋊Dic3#4114yes—
183C2×C3⋊Dic3C2412yes—
184C2×C3⋊Dic3C2412yes—
185C2×C3⋊Dic3C2412yes—
186C4×C3⋊D3—28no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—48no—
192C2×C3×Dic3C2414yes—
193C2×C3×Dic3C2414yes—
194C2×C3×Dic3C2414yes—
195C2×C3×Dic3C2414yes—
196C3×Dic6—48no—
197#627—28no—
198#624—48no—
199#554—916no—
200C2×C4⋊Q8—91no—
201C2×#125—92no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—91no—
204C2×C22⋊Q8—91no—
205C2×C22⋊Q8—92no—
206C2×C4×Q8—91no—
207C2×C4×D4—92no—
208C2×C4×D4—91no—
209C22×C4⋊C4—91no—
210C22×C4⋊C4—91no—
211C24×C3—21no—
212C24×C3C22×D312yes—
213C23×D3—32no—
214C23×D3—61no—
215C2×C3×Q8—38no—
216C2×C3×Q8—124no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—38no—
224C22×C3×C4—124no—
225C22×C3×C4C22×D312yes—
226C22×C3×C4C22×D312yes—
227C2×#67—316no—
228C2×#67—38no—
229C2×#67—64no—
230C2×#67—68no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—38no—
234C22×Dic3—32no—
235C22×Dic3—44no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—64no—
239C22×Dic3—61no—
240C22×Dic3—68no—
241C22×Dic3—124no—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D312yes—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D318yes—
247C2×C4×D3—38no—
248C2×C4×D3—38no—
249C2×C4×D3—38no—
250C2×C4×D3—64no—
251C2×C4×D3—68no—
252C2×C4×D3—124no—
253C2×C4×D3—124no—
254C2×C4×D3—124no—
255C2×Dic6—38no—
256C2×Dic6—44no—
257C2×Dic6—68no—
258C2×Dic6C22×D318yes—
259C3×C4⋊C4—38no—
260C3×C4⋊C4—38no—
261C3×C4⋊C4—38no—
262C3×C22⋊C4—24no—
263C3×C22⋊C4—38no—
264C3×C22⋊C4C22×D318yes—
265#217C22×D318yes—
266(C2×D3)⋊C4—38no—
267(C2×D3)⋊C4—38no—
268(C2×D3)⋊C4—38no—
269(C2×D3)⋊C4—64no—
270C4⋊Dic3—38no—
271C4⋊Dic3C22×D318yes—
272Dic3⋊C4—38no—
273Dic3⋊C4—38no—
274Dic3⋊C4—38no—
275Dic3⋊C4—38no—
276Dic3⋊C4—38no—
277Dic3⋊C4—38no—
278Dic3⋊C4—38no—
279Dic3⋊C4—38no—
280Dic3⋊C4—38no—
281Dic3⋊C4—64no—
282Dic3⋊C4C22×D318yes—
283Dic3⋊C4C22×D318yes—
284C4×Dic3—38no—
285C4×Dic3—38no—
286C4×Dic3—38no—
287C4×Dic3—64no—
288C22×C32—28no—
289C22×C32—22no—
290C22×C32—22no—
291C22×C32C22×Q814yes—
292C22×C32C22×Q812yes—
293C22×C32C2×#4112yes—
294C22×C32H(5,𝔽2)12yes—
295C22×C32C2511yescharacteristic
296C2×C3⋊D3—28no—
297C2×C3⋊D3—22no—
298C2×C3⋊D3—22no—
299C2×C3⋊D3C22×Q814yes—
300C32×C4—22no—
301C32×C4—22no—
302C3⋊Dic3—22no—
303C3⋊Dic3C22×Q814yes—
304C3⋊Dic3C2×#4114yes—
305C3×Dic3—24no—
306C3×Dic3—24no—
307C3×Dic3—24no—
308C3×Dic3—24no—
309C22×Q8—32no—
310C22×Q8—91no—
311C22×D4—91no—
312C23×C4—32no—
313C23×C4—92no—
314C23×C4—91no—
315C23×C4—91no—
316C4⋊Q8—98no—
317#125—916no—
318C22⋊Q8—316no—
319C22⋊Q8—98no—
320C22⋊Q8—98no—
321C22⋊Q8—916no—
322C4×Q8—98no—
323C4×D4—916no—
324C4×D4—98no—
325C2×C4⋊C4—32no—
326C2×C4⋊C4—32no—
327C2×C4⋊C4—32no—
328C2×C4⋊C4—98no—
329C2×C4⋊C4—91no—
330C2×C4⋊C4—92no—
331C2×C4⋊C4—91no—
332C2×C4⋊C4—91no—
333C2×C4⋊C4—98no—
334C2×C4⋊C4—92no—
335C2×C4⋊C4—92no—
336C2×C4⋊C4—91no—
337C2×C22⋊C4—32no—
338C2×C22⋊C4—92no—
339C2×C22⋊C4—91no—
340C2×C22⋊C4D3211yescharacteristic
341C2×C42—92no—
342C2×C42—91no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—22no—
346C23×C3—21no—
347C23×C3—24no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3D3×Q818yes—
351C23×C3C23×D314yes—
352C23×C3C23×D312yes—
353C22×D3—38no—
354C22×D3—34no—
355C22×D3—64no—
356C22×D3—62no—
357C22×D3—64no—
358C22×D3—64no—
359C22×D3—122no—
360C22×D3—122no—
361C3×Q8—128no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—34no—
367C2×C3×C4—34no—
368C2×C3×C4—34no—
369C2×C3×C4—34no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—64no—
373C2×C3×C4—64no—
374C2×C3×C4—64no—
375C2×C3×C4—64no—
376C2×C3×C4—128no—
377C2×C3×C4C23×D314yes—
378C2×C3×C4C23×D314yes—
379#67—332no—
380#67—616no—
381C2×Dic3—24no—
382C2×Dic3—24no—
383C2×Dic3—24no—
384C2×Dic3—24no—
385C2×Dic3—38no—
386C2×Dic3—38no—
387C2×Dic3—34no—
388C2×Dic3—34no—
389C2×Dic3—34no—
390C2×Dic3—48no—
391C2×Dic3—64no—
392C2×Dic3—64no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—616no—
397C2×Dic3—64no—
398C2×Dic3—128no—
399C2×Dic3—122no—
400C2×Dic3C23×D314yes—
401C2×Dic3C23×D314yes—
402C2×Dic3C23×D314yes—
403C2×Dic3C23×D314yes—
404C4×D3—616no—
405C4×D3—128no—
406C4×D3—128no—
407C4×D3—128no—
408Dic6—48no—
409Dic6—616no—
410C2×C32—24no—
411C2×C32#55414yescomplemented
412C2×C32C23×Q811yescharacteristic
413C2×C32C22×#4111yescharacteristic
414C2×C32C2×H(5,𝔽2)11yescharacteristic
415C3⋊D3—24no—
416C24—91no—
417C24C2×D3211yescharacteristic
418C2×Q8—38no—
419C2×Q8—94no—
420C2×Q8—124no—
421C2×Q8—184no—
422C2×D4—94no—
423C2×D4—98no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—32no—
427C22×C4—32no—
428C22×C4—38no—
429C22×C4—98no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—94no—
433C22×C4—91no—
434C22×C4—94no—
435C22×C4—124no—
436C22×C4—184no—
437C22×C4—184no—
438C22×C4—364no—
439C22×C4C2×D3211yescharacteristic
440C22×C4C2×D3211yescharacteristic
441C4⋊C4—38no—
442C4⋊C4—38no—
443C4⋊C4—38no—
444C4⋊C4—94no—
445C4⋊C4—98no—
446C4⋊C4—94no—
447C4⋊C4—94no—
448C4⋊C4—98no—
449C4⋊C4—98no—
450C4⋊C4—94no—
451C22⋊C4—38no—
452C22⋊C4—98no—
453C22⋊C4—94no—
454C22⋊C4C2×D3214yes—
455C42—98no—
456C42—94no—
457C22×C3—216no—
458C22×C3—24no—
459C22×C3—24no—
460C22×C3—22no—
461C22×C3—24no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—48no—
468C22×C3#100414yes—
469C22×C3C2×D3×Q818yes—
470C22×C3C2×D3×Q814yes—
471C22×C3D3×#4114yes—
472C22×C3C24×D312yes—
473C2×D3—38no—
474C2×D3—64no—
475C2×D3—616no—
476C2×D3—64no—
477C2×D3—64no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—128no—
481C3×C4—24no—
482C3×C4—24no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—64no—
486C3×C4—64no—
487C3×C4—64no—
488C3×C4—64no—
489Dic3—24no—
490Dic3—24no—
491Dic3—24no—
492Dic3—24no—
493Dic3—38no—
494Dic3—38no—
495Dic3—64no—
496Dic3—64no—
497Dic3—64no—
498Dic3—122no—
499C32C2×#55411yescharacteristic, complemented, Sylow
500C23—22no—
501C23—22no—
502C23—94no—
503C23—92no—
504C23—182no—
505C23—182no—
506C23#379714yes—
507C23C22×D3212yes—
508C23C22×D3211yescharacteristic
509Q8—128no—
510Q8—188no—
511D4—916no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—34no—
515C2×C4—34no—
516C2×C4—34no—
517C2×C4—34no—
518C2×C4—64no—
519C2×C4—64no—
520C2×C4—64no—
521C2×C4—64no—
522C2×C4—94no—
523C2×C4—94no—
524C2×C4—92no—
525C2×C4—92no—
526C2×C4—92no—
527C2×C4—128no—
528C2×C4—188no—
529C2×C4—188no—
530C2×C4—182no—
531C2×C4—368no—
532C2×C4C22×D3212yes—
533C2×C4C22×D3212yes—
534C2×C3—28no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—24no—
539C2×C3—44no—
540C2×C3#563618yescomplemented
541C2×C3C2×#100412yes—
542C2×C3C22×D3×Q812yes—
543C2×C3C2×D3×#4112yes—
544D3—68no—
545D3—124no—
546C22—22no—
547C22—22no—
548C22—28no—
549C22—94no—
550C22—182no—
551C22—182no—
552C22—188no—
553C22C2×#379714yes—
554C22C2×#379712yes—
555C22#6431212yes—
556C22#6431312yes—
557C22C23×D3211yescharacteristic
558C4—22no—
559C4—22no—
560C4—64no—
561C4—64no—
562C4—64no—
563C4—64no—
564C4—94no—
565C4—94no—
566C4—182no—
567C3—21no—
568C3C2×#563612yescomplemented
569C2—24no—
570C2—184no—
571C2#1059416814yesdirect product factor
572C2C22×#379711yescharacteristic
573C2C2×#6431211yescharacteristic
574C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#878C2semidirect
3. C2×#63982C2semidirect
4. C22×#3724C2semidirect
6. C2×#63900C2semidirect
7. C2×#63888C2semidirect
8. C2×#63873C2semidirect
9. C2×#63865C2semidirect
10. C2×#63847C2semidirect
11. C2×#63838C2semidirect
12. #10594168C2direct (N × H)
30. C3×#878C22semidirect
31. #63982C22semidirect
37. C2×#3724C22semidirect
42. #63900C22semidirect
43. #63888C22semidirect
44. #63873C22semidirect
45. #63865C22semidirect
46. #63847C22semidirect
47. #63838C22semidirect
64. C2×#878D3semidirect
69. C2×#638Q8semidirect
164. #878C2×D3semidirect
178. #638C2×Q8semidirect
411. C2×C32#554semidirect
499. C32C2×#554semidirect
540. C2×C3#5636semidirect
568. C3C2×#5636semidirect
571. C2#10594168direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640902
C2×C3×#8782
C2×#639822
C22×#37242
C2×#639522
C2×#639002
C2×#638882
C2×#638732
C2×#638652
C2×#638472
C2×#638382
#105941682
C2×#56363