Finite Group Databasebeta

← #11864189

Subgroups — #11864189

Order 1152.

2262 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic
2C2×#64160C211yesmaximal, characteristic, complemented
3C2×#64118C211yesmaximal, characteristic, complemented
4C2×#64106C211yesmaximal, characteristic, complemented
5C32×#417C211yesmaximal, characteristic, complemented
6#10592825C211yesmaximal, characteristic, complemented
7#10592665C211yesmaximal, characteristic, complemented
8#10592508C212yesmaximal, complemented
9#10592507C212yesmaximal, complemented
10#10592482C212yesmaximal, complemented
11#10592475C212yesmaximal, complemented
12#78885—34nomaximal
13C2×C32×#41C2211yescharacteristic
14#41×C3⋊D3—24no—
15#41×C3⋊D3—24no—
16C2×#3832C2211yescharacteristic
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×#3830—21no—
19C2×#3830C2211yescharacteristic
20C2×D4×C3⋊D3—21no—
21C2×D4×C3⋊D3C2211yescharacteristic
22C2×#3828—21no—
23C2×#3828C2211yescharacteristic
24C22×C4×C3⋊D3—21no—
25C22×C4×C3⋊D3C2211yescharacteristic
26C22×#634C2211yescharacteristic, complemented
27C2×C32×M16C2211yescharacteristic, complemented
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29#64160—24no—
30C2×#3756C2212yescomplemented
31C2×#3754C2212yescomplemented
32C2×#3752—21no—
33C2×C4⋊(C3⋊Dic3)—21no—
34C2×#3748C2211yescharacteristic, complemented
35#64118—24no—
36C2×#3746C2212yescomplemented
37C2×#3744C2212yescomplemented
38#64106—21no—
39#64106—21no—
40#64106C2212yes—
41#64106C2212yescomplemented
42C32×#103C2212yescomplemented
43C32×#102C2212yescomplemented
44#63647C2212yes—
45#63647C2212yescomplemented
46#63637C2212yescomplemented
47#63636C2212yescomplemented
48C2×D3×#41—34no—
49C2×#951—34no—
50C2×#909—34no—
51C2×#897—34no—
52C3×#417D314yescomplemented
53#5126—34no—
54#4966—34no—
55#4809—38no—
56#4808—38no—
57#4783—38no—
58#4776—38no—
59C23×C3⋊D3—21no—
60C23×C3⋊D3D411yescharacteristic
61C32×#41—22no—
62C32×#41D414yes—
63C2×C32×Q8C2311yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4C2311yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70C2×#638—21no—
71C2×#638—21no—
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3D411yescharacteristic
75#3832—22no—
76#3832—22no—
77Q8×C3⋊D3—22no—
78Q8×C3⋊D3—22no—
79#3830—28no—
80#3830—22no—
81#3830—22no—
82D4×C3⋊D3—28no—
83D4×C3⋊D3—22no—
84D4×C3⋊D3—22no—
85#3828—28no—
86#3828—22no—
87#3828D414yes—
88C2×C4⋊(C3⋊D3)—21no—
89C2×C4⋊(C3⋊D3)C2311yescharacteristic
90C2×C4×C3⋊D3—28no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3D411yescharacteristic
97C2×C4×C3⋊D3D411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634—21no—
101C2×#634—22no—
102C2×#634—22no—
103C2×#634—21no—
104C2×#634C2312yes—
105C2×#634C2311yescharacteristic
106C32×M16—22no—
107C2×C32×C8C2312yes—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2312yes—
110#3756—24no—
111#3754—24no—
112#3752—22no—
113#3752—22no—
114C4⋊(C3⋊Dic3)—22no—
115C4⋊(C3⋊Dic3)—22no—
116#3748—22no—
117C2×C3⋊(C3⋊C8)C2312yes—
118#3746—24no—
119#3744—24no—
120#3007—91noSylow
121C2×C3×#41C2×D314yes—
122D3×#41—616no—
123D3×#41—616no—
124C2×#239—34no—
125C2×D3×Q8—34no—
126C2×#237—34no—
127C2×#237—64no—
128C2×D3×D4—34no—
129C2×D3×D4—64no—
130C2×#235—34no—
131C2×#235—64no—
132C22×C4×D3—34no—
133C22×C4×D3—64no—
134C22×Dic6—34no—
135C2×C3×M16C2×D314yescomplemented
136C2×C3×C4⋊C4C2×D314yescomplemented
137#951—616no—
138C2×#216—38no—
139C2×#214—38no—
140C2×(C2×D3)⋊C4—64no—
141C2×C4⋊Dic3—64no—
142C2×#208—34no—
143#909—616no—
144C2×Dic12—38no—
145C2×#204—38no—
146#897—38no—
147#897—38no—
148#897—64no—
149#897—64no—
150C3×#103C2×D318yescomplemented
151C3×#102C2×D318yescomplemented
152(C2×D3)⋊C8—38no—
153(C2×D3)⋊C8—38no—
154#810—38no—
155#809—38no—
156C23×C32—21no—
157C23×C32C2×D411yescharacteristic
158C22×C3⋊D3—24no—
159C22×C3⋊D3—22no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—41no—
163C22×C3⋊D3—42no—
164C22×C3⋊D3—42no—
165C22×C3⋊D3C2×D411yescharacteristic
166C22×C3⋊D3C2×D411yescharacteristic
167C32×Q8—21no—
168C32×Q8C2×D412yes—
169C32×D4—24no—
170C32×D4—21no—
171C32×D4C2×D412yes—
172C2×C32×C4—21no—
173C2×C32×C4—24no—
174C2×C32×C4—22no—
175C2×C32×C4—42no—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2411yescharacteristic
180#638—24no—
181#638—24no—
182#638—24no—
183C2×C3⋊Dic3—24no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—42no—
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C4⋊(C3⋊D3)—24no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)C2×D412yes—
193C4×C3⋊D3—24no—
194C4×C3⋊D3—24no—
195C4×C3⋊D3—22no—
196C4×C3⋊D3—24no—
197C4×C3⋊D3—22no—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—21no—
200C4×C3⋊D3—21no—
201C4×C3⋊D3—21no—
202#634—24no—
203#634—21no—
204#634—22no—
205#634—22no—
206#634—42no—
207#634C2×D412yes—
208C32×C8—22no—
209C3⋊(C3⋊C8)—22no—
210C22×#41—91no—
211C2×#137—91no—
212C2×#137—91no—
213C2×C22⋊Q8—91no—
214#452—92no—
215#452—92no—
216#451—92no—
217#450—92no—
218#417—91no—
219#417C3⋊D311yescharacteristic, complemented
220#407—91no—
221C23×D3—34no—
222C23×D3—64no—
223C3×#41—28no—
224C3×#41D12116yes—
225C2×C3×Q8C22×D314yes—
226C2×C3×D4—24no—
227C2×C3×D4C22×D314yes—
228C22×C3×C4—24no—
229C22×C3×C4—24no—
230C22×C3×C4C22×D314yes—
231C2×#67—64no—
232C2×#67—64no—
233C2×#67—64no—
234C22×Dic3—34no—
235C22×Dic3—64no—
236C22×Dic3—64no—
237#239—68no—
238#239—68no—
239D3×Q8—68no—
240D3×Q8—68no—
241#237—68no—
242#237—632no—
243#237—68no—
244D3×D4—68no—
245D3×D4—632no—
246D3×D4—68no—
247#235—316no—
248#235—632no—
249#235—68no—
250C2×D12—34no—
251C2×D12—64no—
252C2×C4×D3—34no—
253C2×C4×D3—34no—
254C2×C4×D3—34no—
255C2×C4×D3—34no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C2×C4×D3—632no—
259C2×C4×D3—68no—
260C2×C4×D3—68no—
261C2×C4×D3—64no—
262C2×Dic6—34no—
263C2×Dic6—38no—
264C2×Dic6—64no—
265C2×Dic6—68no—
266C2×Dic6—68no—
267C2×Dic6—64no—
268C3×M16—28no—
269C2×C3×C8C22×D318yes—
270C3×C4⋊C4—24no—
271C3×C4⋊C4C22×D318yes—
272#216—616no—
273#214—616no—
274(C2×D3)⋊C4—68no—
275(C2×D3)⋊C4—68no—
276C4⋊Dic3—68no—
277C4⋊Dic3—68no—
278#208—68no—
279C2×C3⋊C8—38no—
280Dic12—616no—
281#204—616no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—22no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32#12012yes—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—21no—
290C2×C3⋊D3—21no—
291C2×C3⋊D3—21no—
292C2×C3⋊D3—22no—
293C2×C3⋊D3—21no—
294C2×C3⋊D3—21no—
295C2×C3⋊D3—44no—
296C2×C3⋊D3—48no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3#13712yescomplemented
300C32×C4—22no—
301C32×C4—42no—
302C32×C4#12012yes—
303C32×C4C22×D411yescharacteristic
304C32×C4C22×D411yescharacteristic
305C3⋊Dic3—21no—
306C3⋊Dic3—22no—
307C3⋊Dic3—21no—
308C3⋊Dic3—42no—
309C2×#41—91no—
310C2×#41—91no—
311C2×#41—91no—
312C2×#41—181no—
313C2×#41—181no—
314C2×#41—184no—
315C2×#41—184no—
316C2×#41C2×C3⋊D311yescharacteristic
317C22×Q8—91no—
318C22×Q8—91no—
319C22×D4—91no—
320C22×D4—181no—
321C23×C4—91no—
322C23×C4—181no—
323#137—184no—
324#137—184no—
325C2×Q16—92no—
326C2×Q16—92no—
327C2×SD16—92no—
328C2×SD16—92no—
329C2×M16—91no—
330C2×M16C2×C3⋊D311yescharacteristic, complemented
331C22⋊Q8—92no—
332C22⋊Q8—92no—
333C22⋊Q8—181no—
334C22⋊Q8—181no—
335C2×C4⋊C4—181no—
336C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
337C2×C22⋊C4—181no—
338#103—92no—
339#103C2×C3⋊D312yescomplemented
340#102—92no—
341#102C2×C3⋊D312yescomplemented
342C22⋊C8—92no—
343C22⋊C8—92no—
344C23×C3—24no—
345C23×C3D3×D414yes—
346C22×D3—34no—
347C22×D3—34no—
348C22×D3—68no—
349C22×D3—616no—
350C22×D3—68no—
351C22×D3—64no—
352C22×D3—128no—
353C22×D3—124no—
354C22×D3—128no—
355C3×Q8—24no—
356C3×Q8C2×D1218yes—
357C3×D4—216no—
358C3×D4—24no—
359C3×D4C2×D1218yes—
360C2×C3×C4—24no—
361C2×C3×C4—216no—
362C2×C3×C4—28no—
363C2×C3×C4—48no—
364C2×C3×C4C2×D1218yes—
365C2×C3×C4D3×D414yes—
366C2×C3×C4D3×D418yes—
367C2×C3×C4C23×D314yes—
368#67—616no—
369#67—616no—
370#67—616no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—616no—
374C2×Dic3—68no—
375C2×Dic3—64no—
376C2×Dic3—68no—
377C2×Dic3—128no—
378D12—38no—
379D12—616no—
380D12—64no—
381C4×D3—616no—
382C4×D3—616no—
383C4×D3—68no—
384C4×D3—68no—
385C4×D3—616no—
386C4×D3—64no—
387C4×D3—64no—
388C4×D3—64no—
389C4×D3—64no—
390Dic6—38no—
391Dic6—616no—
392Dic6—64no—
393Dic6—68no—
394Dic6—68no—
395Dic6—128no—
396C3×C8—28no—
397C3⋊C8—68no—
398C2×C32—22no—
399C2×C32—42no—
400C2×C32C2×#12011yescharacteristic
401C2×C32C2×#13711yescharacteristic
402C2×C32#57511yescharacteristic
403C3⋊D3—22no—
404C3⋊D3—41no—
405C3⋊D3—42no—
406C24—91no—
407C24—181no—
408#41—22no—
409#41—94no—
410#41—188no—
411#41—182no—
412#41—188no—
413#41—182no—
414#41—182no—
415#41—182no—
416#41—182no—
417#41C4⋊(C3⋊D3)14yes—
418C2×Q8—91no—
419C2×Q8—92no—
420C2×Q8—181no—
421C2×Q8—182no—
422C2×Q8—182no—
423C2×Q8—181no—
424C2×Q8—182no—
425C2×Q8—182no—
426C2×Q8C22×C3⋊D311yescharacteristic
427C2×D4—21no—
428C2×D4—91no—
429C2×D4—181no—
430C2×D4—181no—
431C2×D4—182no—
432C2×D4—188no—
433C2×D4—181no—
434C2×D4—181no—
435C2×D4—182no—
436C2×D4C22×C3⋊D311yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—188no—
447C22×C4—181no—
448C22×C4—182no—
449C22×C4—182no—
450C22×C4—181no—
451C22×C4—181no—
452C22×C4C22×C3⋊D311yescharacteristic
453Q16—184no—
454Q16—184no—
455SD16—184no—
456SD16—184no—
457M16—22no—
458M16—182no—
459C2×C8—92no—
460C2×C8C22×C3⋊D312yes—
461C4⋊C4—21no—
462C4⋊C4—182no—
463C4⋊C4—182no—
464C4⋊C4C22×C3⋊D312yes—
465C22⋊C4—182no—
466C22⋊C4—182no—
467C22×C3—24no—
468C22×C3—24no—
469C22×C3—28no—
470C22×C3—44no—
471C22×C3—44no—
472C22×C3#88218yes—
473C22×C3C2×D3×D414yes—
474C2×D3—38no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—68no—
478C2×D3—64no—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—1216no—
482C2×D3—1232no—
483C2×D3—124no—
484C2×D3—124no—
485C3×C4—28no—
486C3×C4—48no—
487C3×C4#88218yes—
488C3×C4C22×D1214yes—
489C3×C4C2×D3×D414yes—
490Dic3—68no—
491Dic3—64no—
492Dic3—64no—
493Dic3—128no—
494C32#300711yescharacteristic, complemented, Sylow
495C23—21no—
496C23—91no—
497C23—91no—
498C23—182no—
499C23—184no—
500C23—182no—
501C23—181no—
502C23—361no—
503C23—362no—
504C23—362no—
505C23D4×C3⋊D311yescharacteristic
506Q8—21no—
507Q8—92no—
508Q8—184no—
509Q8—181no—
510Q8—182no—
511Q8—182no—
512Q8—362no—
513Q8C2×C4⋊(C3⋊D3)12yes—
514D4—24no—
515D4—21no—
516D4—92no—
517D4—184no—
518D4—184no—
519D4—184no—
520D4—184no—
521D4—181no—
522D4C2×C4⋊(C3⋊D3)12yes—
523C2×C4—21no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—42no—
527C2×C4—91no—
528C2×C4—91no—
529C2×C4—184no—
530C2×C4—184no—
531C2×C4—184no—
532C2×C4—182no—
533C2×C4—181no—
534C2×C4—182no—
535C2×C4—182no—
536C2×C4—184no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—182no—
542C2×C4—362no—
543C2×C4C2×C4⋊(C3⋊D3)12yes—
544C2×C4D4×C3⋊D311yescharacteristic
545C2×C4D4×C3⋊D312yes—
546C2×C4C23×C3⋊D311yescharacteristic
547C8—22no—
548C8—182no—
549C2×C3—28no—
550C2×C3—48no—
551C2×C3C2×#88214yes—
552C2×C3#577314yes—
553C2×C3D3×#13714yes—
554D3—68no—
555D3—124no—
556D3—128no—
557C22—21no—
558C22—21no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—92no—
563C22—181no—
564C22—181no—
565C22—182no—
566C22—181no—
567C22—181no—
568C22—181no—
569C22—364no—
570C22—368no—
571C22—361no—
572C22—361no—
573C22#6409112yes—
574C22C2×D4×C3⋊D311yescharacteristic
575C4—22no—
576C4—42no—
577C4—181no—
578C4—181no—
579C4—182no—
580C4—362no—
581C4#6409112yes—
582C4C22×C4⋊(C3⋊D3)11yescharacteristic
583C4C2×D4×C3⋊D311yescharacteristic
584C3#7888514yescomplemented
585C2—22no—
586C2—42no—
587C2—182no—
588C2—361no—
589C2—362no—
590C2C2×#6409111yescharacteristic
591C2#1059624411yescharacteristic
592C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#417C2
socleC22×C32C22×D4
prime radicalC2×#41×C3⋊D3C2
hypercenter#417C3⋊D3
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#64160C2semidirect
3. C2×#64118C2semidirect
4. C2×#64106C2semidirect
5. C32×#417C2semidirect
6. #10592825C2semidirect
7. #10592665C2semidirect
8. #10592508C2semidirect
9. #10592507C2semidirect
10. #10592482C2semidirect
11. #10592475C2semidirect
26. C22×#634C22semidirect
27. C2×C32×M16C22semidirect
28. C2×C32×C4⋊C4C22semidirect
30. C2×#3756C22semidirect
31. C2×#3754C22semidirect
34. C2×#3748C22semidirect
36. C2×#3746C22semidirect
37. C2×#3744C22semidirect
41. #64106C22semidirect
42. C32×#103C22semidirect
43. C32×#102C22semidirect
45. #63647C22semidirect
46. #63637C22semidirect
47. #63636C22semidirect
52. C3×#417D3semidirect
135. C2×C3×M16C2×D3semidirect
136. C2×C3×C4⋊C4C2×D3semidirect
150. C3×#103C2×D3semidirect
151. C3×#102C2×D3semidirect
219. #417C3⋊D3semidirect
299. C2×C3⋊D3#137semidirect
330. C2×M16C2×C3⋊D3semidirect
336. C2×C4⋊C4C2×C3⋊D3semidirect
339. #103C2×C3⋊D3semidirect
341. #102C2×C3⋊D3semidirect
494. C32#3007semidirect
584. C3#78885semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×#641602
C2×#641182
C2×#641062
C32×#4172
#105928252
#105926652
#105925082
#105925072
#105924822
#105924752
#788853