Finite Group Databasebeta

← #11873363

Subgroups — #11873363

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595300C211yesmaximal, characteristic
2#10594374C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic, complemented
4C3×#4760C212yesmaximal, complemented
5#10591487C212yesmaximal, complemented
6#10591416C211yesmaximal, characteristic, complemented
7#10590940C211yesmaximal, characteristic, complemented
8#10590878C212yesmaximal, complemented
9C8×#624C211yesmaximal, characteristic, complemented
10#10590593C211yesmaximal, characteristic, complemented
11#10590548C212yesmaximal, complemented
12D3×#486—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C2×#3811—21no—
15C2×#3811—21no—
16C2×#3802C2211yescharacteristic
17C2×#3797—21no—
18C2×C8×C3⋊D3C2211yescharacteristic
19C4⋊C4×C3⋊D3C2211yescharacteristic
20C3×#940C2212yes—
21C3×#888C2212yescomplemented
22#63979—22no—
23#63918C2212yescomplemented
24#63911C2212yes—
25#63900C2211yescharacteristic
26#63883—21no—
27C4×#624C2211yescharacteristic
28#63839—22no—
29C2×#3710C2211yescharacteristic
30C32×#102C2211yescharacteristic, complemented
31#63659C2211yescharacteristic, complemented
32#63648C2211yescharacteristic, complemented
33#63636C2211yescharacteristic, complemented
34C3×#832C2212yescomplemented
35C3×#821C2212yescomplemented
36C3×C8×Dic3C2212yescomplemented
37C3×#809C2212yescomplemented
38#63564C2212yescomplemented
39#63563C2212yescomplemented
40#63562C2212yescomplemented
41Dic3×C3⋊C8C2212yescomplemented
42D3×C4⋊Q8—32no—
43D3×#127—32no—
44C3×#486—32no—
45#5088—32no—
46#5070—32no—
47D3×#102—32no—
48D3×#102—32no—
49D3×#102—32no—
50D3×#102—32no—
51D3×#102—61no—
52#4760—32no—
53#4760—32no—
54#4760—32no—
55#4760D312yescomplemented
56#4694—32no—
57C4×D3×C8—32no—
58C23×C3⋊D3—21no—
59C22×D32—21no—
60C2×C32×D4C2311yescharacteristic
61C2×#638—21no—
62D4×C3⋊D3—22no—
63D4×C3⋊D3—22no—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C2×C3×D12C2312yes—
70C2×C3×Dic6—22no—
71#3811—44no—
72#3811—44no—
73C2×#627—22no—
74C2×#626—22no—
75C2×#626—22no—
76C2×#625—21no—
77C2×#624—21no—
78C2×#624D411yescharacteristic
79C2×#624D411yescharacteristic
80#3802—22no—
81#3802—22no—
82#3797—44no—
83C2×C32×C8C2311yescharacteristic
84C32×C4⋊C4C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C8×C3⋊D3—22no—
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—22no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3724—21no—
94Dic3⋊Dic3—22no—
95Dic32D412yes—
96#3710—22no—
97C2×#486—91noSylow
98C2×D3×Q8—62no—
99C2×D3×D4—32no—
100C2×D3×D4—32no—
101C2×D3×D4—61no—
102C2×D3×D4—62no—
103C2×D3×D4—62no—
104C3×C4⋊Q8—32no—
105C3×#127—32no—
106#944—62no—
107#940—32no—
108#940—62no—
109#940—62no—
110#940C2×D312yes—
111C2×D3×C8—32no—
112C2×D3×C8—32no—
113C2×D3×C8—61no—
114D3×C4⋊C4—32no—
115D3×C4⋊C4—32no—
116D3×C4⋊C4—61no—
117D3×C4⋊C4—62no—
118#888—32no—
119#888—62no—
120#888C2×D312yescomplemented
121#874—32no—
122C42×D3—32no—
123#869—32no—
124C3×#102—21no—
125C3×#102—32no—
126C3×#102—32no—
127C3×#102—32no—
128C3×#102C2×D312yescomplemented
129C3×C4×C8—32no—
130#832—32no—
131#832—32no—
132#832—32no—
133#832—61no—
134#832C2×D312yescomplemented
135#821—32no—
136#821—32no—
137#821—32no—
138#821—61no—
139#821C2×D312yescomplemented
140C8×Dic3—32no—
141C8×Dic3C2×D312yescomplemented
142#809—32no—
143#809—32no—
144#809—32no—
145#809—61no—
146#809C2×D312yescomplemented
147C4×C3⋊C8—32no—
148C23×C32—21no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3—42no—
151C22×C3⋊D3—42no—
152C22×C3⋊D3—42no—
153C22×C3⋊D3C2×D411yescharacteristic
154C22×C3×D3—22no—
155C2×D32—42no—
156C2×D32—42no—
157C2×D32—42no—
158C32×D4—21no—
159C32×D4—21no—
160C2×C32×C4—21no—
161C2×C32×C4C2411yescharacteristic
162#638—42no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3C2×D411yescharacteristic
165C4⋊(C3⋊D3)—21no—
166C4⋊(C3⋊D3)—21no—
167C4×C3⋊D3—42no—
168C4×C3⋊D3#4112yes—
169C4×C3⋊D3#4112yes—
170C3×#67—44no—
171C3×#67—44no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D412yes—
175C3×D12—22no—
176C3×D12—22no—
177C3×Dic6—44no—
178#627—44no—
179#626—44no—
180#626—44no—
181#625—42no—
182#624—42no—
183#624D814yes—
184#624SD1614yes—
185C32×C8—21no—
186C3⋊(C3⋊C8)—21no—
187C3×C3⋊C8—22no—
188C2×C4⋊Q8—91no—
189C2×#127—91no—
190#486—32no—
191#486—92no—
192#486—92no—
193#486—92no—
194C2×#102—91no—
195C2×#102—91no—
196C2×#102—91no—
197C2×#102—91no—
198C2×C4×C8—91no—
199C23×D3—62no—
200C23×D3—62no—
201C23×D3—121no—
202C2×C3×Q8—62no—
203C2×C3×D4—21no—
204C2×C3×D4—32no—
205C2×C3×D4—62no—
206C2×C3×D4—62no—
207C2×C3×D4C22×D312yes—
208C2×#67—22no—
209C2×#67—22no—
210C2×#67—62no—
211C2×#67—62no—
212C2×#67—62no—
213C2×#67—62no—
214C2×#67—121no—
215D3×Q8—128no—
216D3×D4—64no—
217D3×D4—64no—
218D3×D4—64no—
219D3×D4—64no—
220D3×D4—64no—
221D3×D4—122no—
222D3×D4—128no—
223D3×D4—128no—
224C2×D12—32no—
225C2×D12—61no—
226C2×D12—62no—
227C2×D12—62no—
228C2×D12C22×D312yes—
229C2×C4×D3—32no—
230C2×C4×D3—32no—
231C2×C4×D3—32no—
232C2×C4×D3—61no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—121no—
236C2×Dic6—22no—
237C2×Dic6—62no—
238C2×Dic6—62no—
239C2×C3×C8—21no—
240C2×C3×C8—32no—
241C2×C3×C8C22×D312yes—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4C22×D312yes—
246C3×C42—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—61no—
249C4⋊Dic3—62no—
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—22no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—121no—
256C4×Dic3—32no—
257C4×Dic3—32no—
258C4×Dic3C22×D312yes—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8C22×D312yes—
262D3×C8—64no—
263D3×C8—64no—
264D3×C8—122no—
265C22×C32—41no—
266C22×C32—41no—
267C22×C32—41no—
268C22×C32C22×D411yescharacteristic
269C2×C3⋊D3—41no—
270C2×C3⋊D3—41no—
271C2×C3⋊D3—41no—
272C2×C3⋊D3—84no—
273C2×C3⋊D3#12412yes—
274C2×C3⋊D3C2×D812yes—
275C2×C3⋊D3C2×SD1612yes—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279D32—84no—
280C32×C4—41no—
281C32×C4C2×#4111yescharacteristic
282C32×C4C2×#4111yescharacteristic
283C3⋊Dic3—41no—
284C3⋊Dic3#12412yes—
285C3×Dic3—42no—
286C3×Dic3C2×D814yes—
287C3×Dic3C2×SD1614yes—
288C22×Q8—181no—
289C22×D4—91no—
290C22×D4—91no—
291C22×D4—181no—
292C22×D4—181no—
293C22×C8—91no—
294C22×C8—91no—
295C4⋊Q8—32no—
296C4⋊Q8—92no—
297C4⋊Q8—182no—
298#127—32no—
299#127—92no—
300#127—182no—
301C2×C4⋊C4—91no—
302C2×C4⋊C4—91no—
303C2×C4⋊C4—181no—
304C2×C42—91no—
305#102—32no—
306#102—32no—
307#102—32no—
308#102—92no—
309#102—92no—
310#102—92no—
311#102—91no—
312#102—91no—
313#102—91no—
314#102D3211yescharacteristic, complemented
315C4×C8—32no—
316C4×C8—92no—
317C23×C3—22no—
318C23×C3—41no—
319C23×C3—62no—
320C22×D3—22no—
321C22×D3—32no—
322C22×D3—61no—
323C22×D3—62no—
324C22×D3—121no—
325C22×D3—124no—
326C22×D3—124no—
327C22×D3—124no—
328C22×D3—124no—
329C22×D3—124no—
330C22×D3—124no—
331C22×D3—124no—
332C22×D3—242no—
333C22×D3—242no—
334C3×Q8—124no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—41no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—124no—
342C3×D4—124no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—32no—
346C2×C3×C4—32no—
347C2×C3×C4—41no—
348C2×C3×C4—62no—
349C2×C3×C4C23×D312yes—
350#67—44no—
351#67—44no—
352#67—124no—
353#67—124no—
354#67—124no—
355#67—124no—
356#67—124no—
357C2×Dic3—22no—
358C2×Dic3—32no—
359C2×Dic3—61no—
360C2×Dic3—62no—
361C2×Dic3—121no—
362C2×Dic3D3×D412yes—
363C2×Dic3D3×D412yes—
364D12—22no—
365D12—22no—
366D12—62no—
367D12—62no—
368D12—62no—
369D12—121no—
370D12—124no—
371D12—124no—
372C4×D3—34no—
373C4×D3—34no—
374C4×D3—38no—
375C4×D3—38no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—124no—
379C4×D3—124no—
380C4×D3—242no—
381Dic6—44no—
382Dic6—124no—
383Dic6—124no—
384C3×C8—22no—
385C3×C8—41no—
386C3×C8—62no—
387C3⋊C8—22no—
388C3⋊C8—62no—
389C3⋊C8—121no—
390C2×C32—81no—
391C2×C32C2×#12411yescharacteristic
392C2×C32C22×D811yescharacteristic
393C2×C32C22×SD1611yescharacteristic
394C3⋊D3—81no—
395C3⋊D3#48614yescomplemented
396C3×D3—82no—
397C24—181no—
398C24—181no—
399C2×Q8—62no—
400C2×Q8—182no—
401C2×Q8—364no—
402C2×D4—32no—
403C2×D4—62no—
404C2×D4—62no—
405C2×D4—91no—
406C2×D4—182no—
407C2×D4—182no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—182no—
411C2×D4—182no—
412C2×D4—181no—
413C2×D4—181no—
414C2×D4—364no—
415C2×D4—364no—
416C2×D4C2×D3211yescharacteristic
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—181no—
421C22×C4—181no—
422C2×C8—32no—
423C2×C8—91no—
424C2×C8—182no—
425C2×C8—182no—
426C2×C8C2×D3211yescharacteristic
427C4⋊C4—32no—
428C4⋊C4—62no—
429C4⋊C4—91no—
430C4⋊C4—181no—
431C4⋊C4—182no—
432C4⋊C4—181no—
433C4⋊C4C2×D3211yescharacteristic
434C42—32no—
435C42—92no—
436C22×C3—21no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—81no—
442C22×C3—81no—
443C22×C3—122no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3C2×D3×D412yes—
447C2×D3—34no—
448C2×D3—34no—
449C2×D3—34no—
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—241no—
461C2×D3—241no—
462C2×D3—248no—
463C2×D3—248no—
464C2×D3—248no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—34no—
468C3×C4—34no—
469C3×C4—42no—
470C3×C4—81no—
471C3×C4—122no—
472C3×C4D3×#4112yes—
473C3×C4D3×#4112yes—
474Dic3—34no—
475Dic3—42no—
476Dic3—62no—
477Dic3—122no—
478Dic3—241no—
479Dic3D3×D814yes—
480Dic3D3×SD1614yes—
481C32C2×#48611yescharacteristic, complemented, Sylow
482C23—21no—
483C23—62no—
484C23—91no—
485C23—181no—
486C23—362no—
487C23—362no—
488C23—362no—
489C23—362no—
490C23—362no—
491C23—362no—
492Q8—124no—
493Q8—364no—
494D4—21no—
495D4—21no—
496D4—62no—
497D4—62no—
498D4—124no—
499D4—124no—
500D4—181no—
501D4—181no—
502D4—364no—
503D4—364no—
504D4—362no—
505D4—362no—
506C2×C4—21no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—62no—
510C2×C4—94no—
511C2×C4—94no—
512C2×C4—91no—
513C2×C4—92no—
514C2×C4—92no—
515C2×C4—181no—
516C2×C4—362no—
517C2×C4—362no—
518C2×C4C22×D3211yescharacteristic
519C8—21no—
520C8—62no—
521C8—181no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—82no—
526C2×C3—82no—
527C2×C3—242no—
528C2×C3D3×#12412yes—
529C2×C3C2×D3×D812yes—
530C2×C3C2×D3×SD1612yes—
531D3—38no—
532D3—64no—
533D3—82no—
534D3—242no—
535D3—242no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—92no—
540C22—92no—
541C22—92no—
542C22—122no—
543C22—122no—
544C22—122no—
545C22—361no—
546C22—361no—
547C22—361no—
548C22—724no—
549C22—724no—
550C22D32×D411yescharacteristic
551C4—34no—
552C4—34no—
553C4—41no—
554C4—92no—
555C4—122no—
556C4—361no—
557C4#6430611yescharacteristic
558C4#6431211yescharacteristic
559C3—21no—
560C3D3×#48612yescomplemented
561C2—81no—
562C2—94no—
563C2—242no—
564C2—721no—
565C2#1059428811yescharacteristic
566C2D32×D811yescharacteristic
567C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595300C2
hypercenter#102D32
hypocenterC32C2×#486
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594374C2semidirect
3. C3⋊D3×#102C2semidirect
4. C3×#4760C2semidirect
5. #10591487C2semidirect
6. #10591416C2semidirect
7. #10590940C2semidirect
8. #10590878C2semidirect
9. C8×#624C2semidirect
10. #10590593C2semidirect
11. #10590548C2semidirect
21. C3×#888C22semidirect
23. #63918C22semidirect
30. C32×#102C22semidirect
31. #63659C22semidirect
32. #63648C22semidirect
33. #63636C22semidirect
34. C3×#832C22semidirect
35. C3×#821C22semidirect
36. C3×C8×Dic3C22semidirect
37. C3×#809C22semidirect
38. #63564C22semidirect
39. #63563C22semidirect
40. #63562C22semidirect
41. Dic3×C3⋊C8C22semidirect
55. #4760D3semidirect
120. #888C2×D3semidirect
128. C3×#102C2×D3semidirect
134. #832C2×D3semidirect
139. #821C2×D3semidirect
141. C8×Dic3C2×D3semidirect
146. #809C2×D3semidirect
314. #102D32semidirect
395. C3⋊D3#486semidirect
481. C32C2×#486semidirect
560. C3D3×#486semidirect

Maximal subgroups

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

subgroupindex
#105953002
#105943742
C3⋊D3×#1022
C3×#47602
#105914872
#105914162
#105909402
#105908782
C8×#6242
#105905932
#105905482
D3×#4863