Finite Group Databasebeta

← C2×#10593980 #11900640

Subgroups — C2×#10593980 #11900640

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
1C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#872C212yesmaximal, complemented
3C2×C4×#627C211yesmaximal, characteristic, complemented
4C2×#63915C211yesmaximal, characteristic, complemented
5C2×#63912C211yesmaximal, characteristic
6C2×C4×#626C212yesmaximal, complemented
7C2×C4×#625C211yesmaximal, characteristic, complemented
8C2×#63870C211yesmaximal, characteristic, complemented
9C2×#63865C211yesmaximal, characteristic, complemented
10C2×#63862C212yesmaximal, complemented
11C2×#63853C212yesmaximal, complemented
12#10593980C2116yesmaximal, direct product factor
13C2×#5528—32nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×#627C2211yescharacteristic
19C22×#626C2212yes—
20C22×#625C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C42×C3⋊D3C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2212yes—
31C3×#872C22116yescomplemented
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×#3722C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C4×#627C2218yescomplemented
40#63915C2218yescomplemented
41#63912C2218yes—
42C4×#626C22116yescomplemented
43C4×#625C2218yescomplemented
44#63870C2218yescomplemented
45#63865C2218yescomplemented
46#63862C22116yescomplemented
47#63853C22116yescomplemented
48C2×C3×#117—32no—
49C2×C4×#67—32no—
50C2×C4×#67—32no—
51#5528—332no—
52C2×#898—32no—
53C2×#896—32no—
54C2×#894—32no—
55C2×#889—32no—
56C2×#885—32no—
57C2×#884—32no—
58C2×#883—32no—
59C2×#879—32no—
60C2×C4×D12—32no—
61C2×#872D312yescomplemented
62C2×C42×D3—32no—
63C2×C42×D3—61no—
64C2×C4×Dic6—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⋊D3—24no—
75C2×C4×C3⋊D3—24no—
76C2×C4×C3⋊D3C2314yes—
77C2×C4×C3⋊D3C2314yes—
78C2×C4×C3⋊D3C2314yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×C3×C4×D3—28no—
83C2×C3×C4×D3C2318yes—
84C2×#627—24no—
85C2×#627C2314yes—
86C2×#626—28no—
87C2×#626C2318yes—
88C2×#625—24no—
89C2×#625C2314yes—
90C32×C42C2314yes—
91C4×C3⋊Dic3C2314yes—
92C4×C3⋊Dic3C2314yes—
93C4×C3⋊Dic3C2314yes—
94C3×(C2×D3)⋊C4C2318yes—
95C3×(C2×D3)⋊C4C2318yes—
96C3×Dic3⋊C4C2318yes—
97C3×Dic3⋊C4C2318yes—
98C3×C4×Dic3C2318yes—
99#3724C2314yes—
100#3724C2314yes—
101Dic3⋊Dic3C2318yes—
102Dic3⋊Dic3C2318yes—
103#3722C2318yes—
104(C2×D3)⋊Dic3C2318yes—
105(C2×D3)⋊Dic3C2318yes—
106C2×#529—91noSylow
107C23×C3×C4—32no—
108C22×#67—32no—
109C22×#67—32no—
110C22×D12—32no—
111C22×C4×D3—32no—
112C22×C4×D3—32no—
113C22×C4×D3—32no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C22×C4×D3—61no—
117C22×C4×D3C2×D312yes—
118C22×Dic6—32no—
119C3×#117—316no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C42—21no—
125C2×C3×C42—32no—
126C2×C3×C42C2×D312yes—
127C2×#217—32no—
128C2×#217—32no—
129C4×#67—316no—
130C4×#67—316no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4C2×D312yes—
136C2×(C2×D3)⋊C4C2×D312yes—
137C2×C4⋊Dic3—32no—
138C2×C4⋊Dic3—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4C2×D312yes—
144C2×Dic3⋊C4C2×D312yes—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—61no—
149C2×C4×Dic3—61no—
150C2×C4×Dic3—61no—
151C2×C4×Dic3C2×D312yes—
152#898—316no—
153#896—316no—
154#894—316no—
155#889—316no—
156#885—316no—
157#884—316no—
158#883—316no—
159#879—316no—
160C4×D12—316no—
161#872C2×D3116yescomplemented
162C42×D3—316no—
163C42×D3—68no—
164C4×Dic6—316no—
165C23×C32C2411yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3#4114yes—
169C22×C3⋊D3C2412yes—
170C22×C3×D3—24no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3C2414yes—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4#4114yes—
177C2×C32×C4C2412yes—
178C2×C32×C4C2412yes—
179C2×C32×C4C2412yes—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3#4114yes—
183C2×C3⋊Dic3C2412yes—
184C2×C3⋊Dic3C2412yes—
185C2×C3⋊Dic3C2412yes—
186C4×C3⋊D3—28no—
187C4×C3⋊D3—28no—
188C4×C3⋊D3—28no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—24no—
192C2×C3×Dic3C2414yes—
193C2×C3×Dic3C2414yes—
194C2×C3×Dic3C2414yes—
195C3×C4×D3—216no—
196#627—28no—
197#626—216no—
198#625—28no—
199#529—916no—
200C2×#126—92no—
201C2×#125—91no—
202C2×#124—91no—
203C2×#123—92no—
204C2×C22⋊Q8—91no—
205C2×#121—91no—
206C2×C4×Q8—91no—
207C2×C4×D4—92no—
208C2×C4×D4—91no—
209C2×#117—32no—
210C22×C42—91no—
211C24×C3—32no—
212C23×D3—32no—
213C23×D3—61no—
214C23×D3C22×D312yes—
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—68no—
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D312yes—
225C22×C3×C4C22×D312yes—
226C2×#67—38no—
227C2×#67—38no—
228C2×#67—68no—
229C2×#67—68no—
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—68no—
241C2×C4×D3—28no—
242C2×C4×D3—38no—
243C2×C4×D3—38no—
244C2×C4×D3—38no—
245C2×C4×D3—64no—
246C2×C4×D3—64no—
247C2×C4×D3—64no—
248C2×C4×D3—68no—
249C2×C4×D3—68no—
250C2×C4×D3—68no—
251C2×C4×D3—68no—
252C2×C4×D3—68no—
253C2×C4×D3—68no—
254C2×C4×D3C22×D318yes—
255C2×Dic6—38no—
256C2×Dic6—68no—
257C3×C4⋊C4—38no—
258C3×C4⋊C4—38no—
259C3×C22⋊C4—38no—
260C3×C22⋊C4—38no—
261C3×C42—24no—
262C3×C42—38no—
263C3×C42C22×D318yes—
264#217—38no—
265#217—38no—
266(C2×D3)⋊C4—38no—
267(C2×D3)⋊C4—38no—
268(C2×D3)⋊C4—38no—
269(C2×D3)⋊C4—38no—
270(C2×D3)⋊C4C22×D318yes—
271(C2×D3)⋊C4C22×D318yes—
272C4⋊Dic3—38no—
273C4⋊Dic3—38no—
274Dic3⋊C4—38no—
275Dic3⋊C4—38no—
276Dic3⋊C4—38no—
277Dic3⋊C4—38no—
278Dic3⋊C4C22×D318yes—
279Dic3⋊C4C22×D318yes—
280C4×Dic3—38no—
281C4×Dic3—38no—
282C4×Dic3—38no—
283C4×Dic3—64no—
284C4×Dic3—64no—
285C4×Dic3—64no—
286C4×Dic3C22×D318yes—
287C22×C32C2×#4112yes—
288C22×C32C2×#4112yes—
289C22×C32C2×#4112yes—
290C22×C32C2511yescharacteristic
291C2×C3⋊D3—28no—
292C2×C3⋊D3—22no—
293C2×C3⋊D3—22no—
294C2×C3⋊D3C2×#4114yes—
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—24no—
298C2×C3×D3—48no—
299C32×C4—22no—
300C32×C4—22no—
301C32×C4C2×#4114yes—
302C3⋊Dic3—22no—
303C3⋊Dic3—22no—
304C3⋊Dic3C2×#4114yes—
305C3×Dic3—24no—
306C3×Dic3—24no—
307C3×Dic3—24no—
308C22×Q8—91no—
309C22×D4—92no—
310C22×D4—91no—
311C23×C4—32no—
312C23×C4—91no—
313C23×C4—91no—
314C23×C4—91no—
315#126—916no—
316#125—98no—
317#124—98no—
318#123—916no—
319C22⋊Q8—98no—
320#121—98no—
321C4×Q8—98no—
322C4×D4—916no—
323C4×D4—98no—
324#117—316no—
325C2×C4⋊C4—32no—
326C2×C4⋊C4—32no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—92no—
329C2×C4⋊C4—91no—
330C2×C4⋊C4—92no—
331C2×C22⋊C4—32no—
332C2×C22⋊C4—32no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4—92no—
336C2×C42—32no—
337C2×C42—91no—
338C2×C42—91no—
339C2×C42—91no—
340C2×C42—98no—
341C2×C42D3211yescharacteristic
342C23×C3—21no—
343C23×C3—34no—
344C23×C3—64no—
345C23×C3—64no—
346C23×C3—64no—
347C23×C3C23×D312yes—
348C22×D3—24no—
349C22×D3—24no—
350C22×D3—24no—
351C22×D3—38no—
352C22×D3—34no—
353C22×D3—64no—
354C22×D3—62no—
355C22×D3—64no—
356C22×D3—64no—
357C22×D3—64no—
358C22×D3—64no—
359C22×D3C23×D314yes—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—24no—
368C2×C3×C4—34no—
369C2×C3×C4—34no—
370C2×C3×C4—34no—
371C2×C3×C4—64no—
372C2×C3×C4—64no—
373C2×C3×C4—64no—
374C2×C3×C4—616no—
375C2×C3×C4#23518yes—
376C2×C3×C4C23×D314yes—
377C2×C3×C4C23×D314yes—
378C2×C3×C4C23×D314yes—
379#67—616no—
380#67—616no—
381C2×Dic3—24no—
382C2×Dic3—24no—
383C2×Dic3—24no—
384C2×Dic3—38no—
385C2×Dic3—34no—
386C2×Dic3—34no—
387C2×Dic3—34no—
388C2×Dic3—64no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—64no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3—64no—
396C2×Dic3C23×D314yes—
397C2×Dic3C23×D314yes—
398C2×Dic3C23×D314yes—
399D12—616no—
400C4×D3—216no—
401C4×D3—616no—
402C4×D3—616no—
403C4×D3—616no—
404C4×D3—616no—
405C4×D3—616no—
406C4×D3—616no—
407Dic6—616no—
408C2×C32#52914yescomplemented
409C2×C32C22×#4111yescharacteristic
410C2×C32C22×#4111yescharacteristic
411C2×C32C22×#4111yescharacteristic
412C3⋊D3—24no—
413C3×D3—44no—
414C24—32no—
415C24—91no—
416C2×Q8—94no—
417C2×Q8—184no—
418C2×D4—98no—
419C2×D4—94no—
420C2×D4—188no—
421C2×D4—184no—
422C22×C4—32no—
423C22×C4—32no—
424C22×C4—32no—
425C22×C4—38no—
426C22×C4—68no—
427C22×C4—91no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—94no—
431C22×C4—94no—
432C22×C4—94no—
433C22×C4—184no—
434C22×C4—184no—
435C22×C4—184no—
436C22×C4C2×D3211yescharacteristic
437C22×C4C2×D3211yescharacteristic
438C22×C4C2×D3211yescharacteristic
439C4⋊C4—38no—
440C4⋊C4—38no—
441C4⋊C4—94no—
442C4⋊C4—98no—
443C4⋊C4—94no—
444C4⋊C4—98no—
445C22⋊C4—38no—
446C22⋊C4—38no—
447C22⋊C4—98no—
448C22⋊C4—98no—
449C22⋊C4—98no—
450C42—38no—
451C42—94no—
452C42—94no—
453C42—94no—
454C42C2×D3214yes—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—21no—
459C22×C3—64no—
460C22×C3—64no—
461C22×C3—64no—
462C22×C3—128no—
463C22×C3C2×#23514yes—
464C22×C3D3×#4114yes—
465C22×C3D3×#4114yes—
466C22×C3C24×D312yes—
467C2×D3—24no—
468C2×D3—24no—
469C2×D3—24no—
470C2×D3—38no—
471C2×D3—48no—
472C2×D3—64no—
473C2×D3—64no—
474C2×D3—64no—
475C2×D3—616no—
476C2×D3—64no—
477C2×D3—64no—
478C2×D3—616no—
479C3×C4—24no—
480C3×C4—24no—
481C3×C4—24no—
482C3×C4—24no—
483C3×C4—24no—
484C3×C4—64no—
485C3×C4—64no—
486C3×C4—64no—
487C3×C4C2×#23518yes—
488Dic3—24no—
489Dic3—24no—
490Dic3—24no—
491Dic3—38no—
492Dic3—64no—
493Dic3—64no—
494Dic3—64no—
495Dic3—64no—
496Dic3—64no—
497C32C2×#52911yescharacteristic, complemented, Sylow
498C23—34no—
499C23—64no—
500C23—64no—
501C23—64no—
502C23—94no—
503C23—92no—
504C23—182no—
505C23—182no—
506C23C22×D3211yescharacteristic
507Q8—188no—
508D4—1816no—
509D4—188no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—34no—
513C2×C4—34no—
514C2×C4—34no—
515C2×C4—64no—
516C2×C4—64no—
517C2×C4—64no—
518C2×C4—616no—
519C2×C4—94no—
520C2×C4—92no—
521C2×C4—92no—
522C2×C4—92no—
523C2×C4—188no—
524C2×C4—188no—
525C2×C4—182no—
526C2×C4—182no—
527C2×C4—188no—
528C2×C4#379814yes—
529C2×C4C22×D3212yes—
530C2×C4C22×D3212yes—
531C2×C4C22×D3212yes—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—24no—
536C2×C3—124no—
537C2×C3#552818yescomplemented
538C2×C3C22×#23512yes—
539C2×C3C2×D3×#4112yes—
540C2×C3C2×D3×#4112yes—
541D3—44no—
542D3—68no—
543D3—68no—
544C22—64no—
545C22—64no—
546C22—64no—
547C22—94no—
548C22—128no—
549C22—182no—
550C22—182no—
551C22—188no—
552C22C2×#379812yes—
553C22#6430612yes—
554C22#6430612yes—
555C22C23×D3211yescharacteristic
556C4—22no—
557C4—22no—
558C4—64no—
559C4—64no—
560C4—64no—
561C4—94no—
562C4—182no—
563C4—182no—
564C4C2×#379814yes—
565C3—21no—
566C3C2×#552812yescomplemented
567C2—124no—
568C2—184no—
569C2#1059398014yesdirect product factor
570C2C22×#379811yescharacteristic
571C2C2×#6430611yescharacteristic
572C2C2×#6430611yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC2×#63912C2
hypercenterC2×C42D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C42×C3⋊D3C2semidirect
2. C2×C3×#872C2semidirect
3. C2×C4×#627C2semidirect
4. C2×#63915C2semidirect
6. C2×C4×#626C2semidirect
7. C2×C4×#625C2semidirect
8. C2×#63870C2semidirect
9. C2×#63865C2semidirect
10. C2×#63862C2semidirect
11. C2×#63853C2semidirect
12. #10593980C2direct (N × H)
25. C42×C3⋊D3C22semidirect
31. C3×#872C22semidirect
39. C4×#627C22semidirect
40. #63915C22semidirect
42. C4×#626C22semidirect
43. C4×#625C22semidirect
44. #63870C22semidirect
45. #63865C22semidirect
46. #63862C22semidirect
47. #63853C22semidirect
61. C2×#872D3semidirect
161. #872C2×D3semidirect
408. C2×C32#529semidirect
497. C32C2×#529semidirect
537. C2×C3#5528semidirect
566. C3C2×#5528semidirect
569. C2#10593980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×C3×#8722
C2×C4×#6272
C2×#639152
C2×#639122
C2×C4×#6262
C2×C4×#6252
C2×#638702
C2×#638652
C2×#638622
C2×#638532
#105939802
C2×#55283