Finite Group Databasebeta

← #11870411

Subgroups — #11870411

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596019C211yesmaximal, characteristic, complemented
2C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4#10592855C211yesmaximal, characteristic, complemented
5#10592849C211yesmaximal, characteristic, complemented
6C4×#3753C211yesmaximal, characteristic, complemented
7C4×#3753C211yesmaximal, characteristic, complemented
8#10592589C211yesmaximal, characteristic, complemented
9#10592581C211yesmaximal, characteristic, complemented
10#10592485C211yesmaximal, characteristic, complemented
11#10592473C211yesmaximal, characteristic, complemented
12#10592472C211yesmaximal, characteristic, complemented
13#10592458C211yesmaximal, characteristic, complemented
14C4×#3745C211yesmaximal, characteristic, complemented
15#10592384C211yesmaximal, characteristic, complemented
16#79590—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C2×#3828—21no—
19C22×C4×C3⋊D3—21no—
20C2×C32×D8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic, complemented
23#64149C2211yescharacteristic, complemented
24#64147C2211yescharacteristic
25D4×C3⋊Dic3C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C2×#3753C2211yescharacteristic
28C4×#638—21no—
29C4×#638—21no—
30C2×#3745C2211yescharacteristic
31#64104C2211yescharacteristic
32#64102C2211yescharacteristic
33C4⋊C4×C3⋊D3C2211yescharacteristic
34#64097C2211yescharacteristic, complemented
35#64094—21no—
36#64093—21no—
37#64090—21no—
38C22⋊C4×C3⋊D3—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
41C42×C3⋊D3C2211yescharacteristic
42C32×#107C2211yescharacteristic, complemented
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic, complemented
45C32×C4×C8C2211yescharacteristic, complemented
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic, complemented
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic, complemented
50#63647C2211yescharacteristic
51#63647C2211yescharacteristic
52#63645C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic, complemented
57#63634C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
60#5548—34no—
61C4×D3×D4—34no—
62C3×C4×D8D314yescomplemented
63#5156—34no—
64#5150—34no—
65C4×#213—34no—
66C4×#213—34no—
67#4890—34no—
68#4882—34no—
69#4786—34no—
70#4774—34no—
71#4773—34no—
72#4759—34no—
73C4×D24—34no—
74#4685—34no—
75C23×C3⋊D3—21no—
76C2×C32×D4C2311yescharacteristic
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C2×#638—21no—
81C2×#638—21no—
82C2×#638—21no—
83C2×#638—21no—
84C22×C3⋊Dic3—21no—
85D4×C3⋊D3—22no—
86D4×C3⋊D3—22no—
87#3828—44no—
88C2×C4⋊(C3⋊D3)—21no—
89C2×C4⋊(C3⋊D3)C2311yescharacteristic
90C2×C4⋊(C3⋊D3)C2311yescharacteristic
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3—44no—
96C2×C4×C3⋊D3D411yescharacteristic
97C2×C4×C3⋊D3D411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634—21no—
100C32×D8—22no—
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C32×C22⋊C4—21no—
106C32×C22⋊C4—21no—
107C32×C42C2311yescharacteristic
108#3757—21no—
109#3757—21no—
110#3753—22no—
111#3753—22no—
112#3752—21no—
113#3752—21no—
114#3752—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3D411yescharacteristic
121C4×C3⋊Dic3D411yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3745—22no—
126#3100—91noSylow
127C2×D3×D4—34no—
128C2×#235—64no—
129C22×C4×D3—64no—
130C2×C3×D8C2×D314yes—
131C3×C4×D4C2×D314yes—
132C3×C4×D4C2×D314yescomplemented
133#940—34no—
134#938—34no—
135D4×Dic3—34no—
136C2×#213—34no—
137C2×#213—34no—
138C4×#67—64no—
139C4×#67—64no—
140C2×D24—34no—
141#895—34no—
142#893—34no—
143D3×C4⋊C4—34no—
144#888—34no—
145#885—64no—
146#884—64no—
147#67⋊C4—64no—
148D3×C22⋊C4—64no—
149C4×D12—34no—
150C4×D12—34no—
151C42×D3—34no—
152C3×#107C2×D314yescomplemented
153C3×#102C2×D314yes—
154C3×#102C2×D314yescomplemented
155C3×C4×C8C2×D314yescomplemented
156#832—34no—
157#832—34no—
158#821—34no—
159#821—34no—
160(C2×D3)⋊C8—34no—
161(C2×D3)⋊C8—34no—
162#818—34no—
163Dic3⋊C8—34no—
164Dic3⋊C8—34no—
165#809—34no—
166#809—34no—
167#807—34no—
168#807—34no—
169C4×C3⋊C8—34no—
170C23×C32—21no—
171C23×C32—21no—
172C22×C3⋊D3—24no—
173C22×C3⋊D3—21no—
174C22×C3⋊D3—21no—
175C22×C3⋊D3—42no—
176C22×C3⋊D3—42no—
177C22×C3⋊D3C2×D411yescharacteristic
178C32×D4—21no—
179C32×D4—21no—
180C32×D4—21no—
181C32×D4#4112yescomplemented
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—42no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—24no—
190#638—42no—
191#638—42no—
192#638—42no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—42no—
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)—21no—
201C4⋊(C3⋊D3)—21no—
202C4⋊(C3⋊D3)—42no—
203C4⋊(C3⋊D3)#4112yescomplemented
204C4×C3⋊D3—21no—
205C4×C3⋊D3—21no—
206C4×C3⋊D3—41no—
207C4×C3⋊D3—42no—
208C4×C3⋊D3—42no—
209C4×C3⋊D3—42no—
210C4×C3⋊D3—42no—
211C4×C3⋊D3D814yescomplemented
212#634—42no—
213C32×C8—21no—
214C32×C8—21no—
215C3⋊(C3⋊C8)—21no—
216C3⋊(C3⋊C8)—21no—
217#532—91no—
218C2×C4×D4—91no—
219#480—91no—
220#480—91no—
221#474—91no—
222#474—91no—
223#459—91no—
224#459—91no—
225#447—91no—
226#447—91no—
227C4×D8—91no—
228C4×D8—91no—
229C4×D8—91no—
230C4×D8C3⋊D311yescharacteristic, complemented
231#431—91no—
232C23×D3—64no—
233C2×C3×D4C22×D314yes—
234C2×C3×D4C22×D314yes—
235C22×C3×C4—24no—
236C22×C3×C4—24no—
237C2×#67—64no—
238C2×#67—64no—
239C2×#67—64no—
240C2×#67—64no—
241C22×Dic3—64no—
242D3×D4—68no—
243D3×D4—68no—
244#235—1216no—
245C2×D12—34no—
246C2×D12—34no—
247C2×D12—64no—
248C2×C4×D3—34no—
249C2×C4×D3—34no—
250C2×C4×D3—34no—
251C2×C4×D3—64no—
252C2×C4×D3—64no—
253C2×C4×D3—64no—
254C2×C4×D3—64no—
255C2×C4×D3—1216no—
256C2×Dic6—64no—
257C3×D8—28no—
258C2×C3×C8C22×D314yes—
259C2×C3×C8C22×D314yes—
260C3×C4⋊C4C22×D314yes—
261C3×C4⋊C4C22×D314yes—
262C3×C22⋊C4—24no—
263C3×C22⋊C4—24no—
264C3×C42C22×D314yes—
265#217—64no—
266#217—64no—
267#213—68no—
268#213—68no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273C4⋊Dic3—34no—
274C4⋊Dic3—34no—
275Dic3⋊C4—64no—
276Dic3⋊C4—64no—
277C4×Dic3—34no—
278C4×Dic3—34no—
279C4×Dic3—34no—
280C2×C3⋊C8—34no—
281C2×C3⋊C8—34no—
282D24—68no—
283C22×C32—22no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32C22×D411yescharacteristic
290C2×C3⋊D3—21no—
291C2×C3⋊D3—21no—
292C2×C3⋊D3—22no—
293C2×C3⋊D3—48no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—41no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3C2×D812yes—
300C32×C4—21no—
301C32×C4—41no—
302C32×C4—41no—
303C32×C4C2×D812yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4C2×#4111yescharacteristic
306C3⋊Dic3—21no—
307C3⋊Dic3—21no—
308C3⋊Dic3—41no—
309C3⋊Dic3—41no—
310C3⋊Dic3C2×D812yes—
311C2×#41—181no—
312C22×D4—91no—
313C23×C4—181no—
314C2×D8—91no—
315C2×D8—91no—
316C2×D8—91no—
317C2×D8C2×C3⋊D311yescharacteristic
318C4⋊Q8—91no—
319#127—91no—
320#124—181no—
321#121—91no—
322#121—91no—
323#121—181no—
324C4×D4—91no—
325C4×D4—91no—
326C4×D4—91no—
327C4×D4—91no—
328C4×D4—181no—
329C4×D4—181no—
330C4×D4—181no—
331C4×D4C2×C3⋊D311yescharacteristic
332C4×D4C2×C3⋊D311yescharacteristic, complemented
333C2×C4⋊C4—91no—
334C2×C22⋊C4—181no—
335C2×C42—91no—
336#107—91no—
337#107—91no—
338#107—91no—
339#107C2×C3⋊D311yescharacteristic, complemented
340C4⋊C8—91no—
341C4⋊C8—91no—
342#102—91no—
343#102—91no—
344#102—91no—
345#102—91no—
346#102—91no—
347#102—91no—
348#102C2×C3⋊D311yescharacteristic
349#102C2×C3⋊D311yescharacteristic, complemented
350C22⋊C8—91no—
351C22⋊C8—91no—
352C4×C8—91no—
353C4×C8C2×C3⋊D311yescharacteristic, complemented
354C23×C3—24no—
355C23×C3—24no—
356C22×D3—34no—
357C22×D3—616no—
358C22×D3—64no—
359C22×D3—64no—
360C22×D3—128no—
361C22×D3—128no—
362C3×D4—24no—
363C3×D4—24no—
364C3×D4—24no—
365C3×D4#23518yescomplemented
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—48no—
369C2×C3×C4—48no—
370C2×C3×C4D3×D414yes—
371C2×C3×C4D3×D414yes—
372C2×C3×C4C23×D314yes—
373#67—616no—
374#67—128no—
375#67—128no—
376#67—128no—
377C2×Dic3—34no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—128no—
383D12—38no—
384D12—64no—
385D12—64no—
386D12—64no—
387D12—128no—
388C4×D3—316no—
389C4×D3—64no—
390C4×D3—64no—
391C4×D3—128no—
392C4×D3—124no—
393C4×D3—128no—
394C4×D3—128no—
395C4×D3—128no—
396Dic6—128no—
397C3×C8—24no—
398C3×C8—24no—
399C3⋊C8—64no—
400C3⋊C8—64no—
401C2×C32—42no—
402C2×C32—81no—
403C2×C32#52511yescharacteristic
404C2×C32C22×D811yescharacteristic
405C2×C32#57511yescharacteristic
406C3⋊D3—22no—
407C3⋊D3—42no—
408C3⋊D3—81no—
409C24—181no—
410#41—364no—
411C2×Q8—181no—
412C2×D4—91no—
413C2×D4—91no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4—182no—
419C2×D4—182no—
420C2×D4—181no—
421C2×D4C22×C3⋊D311yescharacteristic
422C2×D4C22×C3⋊D311yescharacteristic
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—91no—
426C22×C4—91no—
427C22×C4—91no—
428C22×C4—181no—
429C22×C4—181no—
430C22×C4—181no—
431C22×C4—181no—
432C22×C4—181no—
433C22×C4—364no—
434D8—22no—
435D8—182no—
436D8—182no—
437D8—182no—
438C2×C8—91no—
439C2×C8—91no—
440C2×C8C22×C3⋊D311yescharacteristic
441C2×C8C22×C3⋊D311yescharacteristic
442C4⋊C4—91no—
443C4⋊C4—91no—
444C4⋊C4—181no—
445C4⋊C4—181no—
446C4⋊C4C22×C3⋊D311yescharacteristic
447C4⋊C4C22×C3⋊D311yescharacteristic
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C22⋊C4—181no—
456C42—91no—
457C42—91no—
458C42—91no—
459C42C22×C3⋊D311yescharacteristic
460C22×C3—28no—
461C22×C3—44no—
462C22×C3—44no—
463C22×C3—44no—
464C22×C3—44no—
465C22×C3—44no—
466C22×C3C2×D3×D414yes—
467C2×D3—38no—
468C2×D3—64no—
469C2×D3—64no—
470C2×D3—68no—
471C2×D3—1232no—
472C2×D3—124no—
473C2×D3—124no—
474C2×D3—124no—
475C2×D3—124no—
476C2×D3—124no—
477C3×C4—24no—
478C3×C4—44no—
479C3×C4—44no—
480C3×C4D3×D818yes—
481C3×C4C2×#23514yes—
482C3×C4D3×#4114yes—
483Dic3—38no—
484Dic3—64no—
485Dic3—64no—
486Dic3—124no—
487Dic3—124no—
488C32#310011yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—91no—
492C23—184no—
493C23—181no—
494C23—181no—
495C23—362no—
496C23—362no—
497Q8—362no—
498D4—21no—
499D4—21no—
500D4—21no—
501D4—92no—
502D4—184no—
503D4—181no—
504D4—181no—
505D4—181no—
506D4—362no—
507D4—362no—
508D4—362no—
509D4—362no—
510D4#382812yescomplemented
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—91no—
516C2×C4—94no—
517C2×C4—91no—
518C2×C4—91no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—361no—
524C2×C4—362no—
525C2×C4—362no—
526C2×C4—362no—
527C2×C4—362no—
528C2×C4—362no—
529C2×C4D4×C3⋊D311yescharacteristic
530C2×C4D4×C3⋊D311yescharacteristic
531C2×C4C23×C3⋊D311yescharacteristic
532C8—21no—
533C8—21no—
534C8—181no—
535C8—181no—
536C2×C3—48no—
537C2×C3—84no—
538C2×C3#554714yes—
539C2×C3C2×D3×D814yes—
540C2×C3#576814yes—
541D3—68no—
542D3—128no—
543D3—244no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—92no—
551C22—181no—
552C22—181no—
553C22—182no—
554C22—368no—
555C22—361no—
556C22—361no—
557C22—361no—
558C22—361no—
559C22—361no—
560C22C2×D4×C3⋊D311yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—92no—
565C4—181no—
566C4—181no—
567C4—361no—
568C4—361no—
569C4D8×C3⋊D312yes—
570C4C2×#382811yescharacteristic
571C4#41×C3⋊D311yescharacteristic
572C3#7959014yescomplemented
573C2—42no—
574C2—81no—
575C2—182no—
576C2—362no—
577C2—721no—
578C2#1059601811yescharacteristic
579C2C2×D8×C3⋊D311yescharacteristic
580C2#1059623911yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
hypercenterC4×D8C3⋊D3
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10596019C2semidirect
2. C4×D4×C3⋊D3C2semidirect
3. C32×C4×D8C2semidirect
4. #10592855C2semidirect
5. #10592849C2semidirect
6. C4×#3753C2semidirect
7. C4×#3753C2semidirect
8. #10592589C2semidirect
9. #10592581C2semidirect
10. #10592485C2semidirect
11. #10592473C2semidirect
12. #10592472C2semidirect
13. #10592458C2semidirect
14. C4×#3745C2semidirect
15. #10592384C2semidirect
22. C32×C4×D4C22semidirect
23. #64149C22semidirect
34. #64097C22semidirect
40. C4×C4⋊(C3⋊D3)C22semidirect
42. C32×#107C22semidirect
44. C32×#102C22semidirect
45. C32×C4×C8C22semidirect
47. #63659C22semidirect
49. #63648C22semidirect
52. #63645C22semidirect
53. #63641C22semidirect
54. #63641C22semidirect
56. #63636C22semidirect
57. #63634C22semidirect
58. #63634C22semidirect
59. C4×C3⋊(C3⋊C8)C22semidirect
62. C3×C4×D8D3semidirect
132. C3×C4×D4C2×D3semidirect
152. C3×#107C2×D3semidirect
154. C3×#102C2×D3semidirect
155. C3×C4×C8C2×D3semidirect
181. C32×D4#41semidirect
203. C4⋊(C3⋊D3)#41semidirect
211. C4×C3⋊D3D8semidirect
230. C4×D8C3⋊D3semidirect
332. C4×D4C2×C3⋊D3semidirect
339. #107C2×C3⋊D3semidirect
349. #102C2×C3⋊D3semidirect
353. C4×C8C2×C3⋊D3semidirect
365. C3×D4#235semidirect
488. C32#3100semidirect
510. D4#3828semidirect
572. C3#79590semidirect

Maximal subgroups

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

subgroupindex
#105960192
C4×D4×C3⋊D32
C32×C4×D82
#105928552
#105928492
C4×#37532
#105925892
#105925812
#105924852
#105924732
#105924722
#105924582
C4×#37452
#105923842
#795903