Finite Group Databasebeta

← #11872806

Subgroups — #11872806

Order 1152.

1182 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596169C211yesmaximal, characteristic, complemented
2#10596016C211yesmaximal, characteristic
3C32×#478C211yesmaximal, characteristic, complemented
4#10592765C211yesmaximal, characteristic, complemented
5#10592718C211yesmaximal, characteristic, complemented
6#10592588C211yesmaximal, characteristic, complemented
7#10592587C211yesmaximal, characteristic, complemented
8#10592567C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592540C211yesmaximal, characteristic, complemented
11#10592539C211yesmaximal, characteristic, complemented
12#10592475C211yesmaximal, characteristic
13#10592475C211yesmaximal, characteristic
14#10592457C211yesmaximal, characteristic, complemented
15#10592456C211yesmaximal, characteristic, complemented
16#81147—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C32×#125C2211yescharacteristic, complemented
19C32×C4×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C4×#638—21no—
24C2×#3752—21no—
25C2×#3744C2211yescharacteristic
26C2×#3744C2211yescharacteristic
27#64107—21no—
28#64107—21no—
29#64106C2211yescharacteristic
30#64106C2211yescharacteristic
31#64102C2211yescharacteristic
32#64101C2211yescharacteristic
33#64099—21no—
34#64099—21no—
35#64096C2211yescharacteristic, complemented
36#64096C2211yescharacteristic, complemented
37#64090—21no—
38C22⋊C4×C3⋊D3—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40#64081C2211yescharacteristic
41#64078C2211yescharacteristic, complemented
42C32×#107C2211yescharacteristic, complemented
43C32×#106C2211yescharacteristic, complemented
44C32×C4⋊C8C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63647C2211yescharacteristic
48#63647C2211yescharacteristic
49#63643C2211yescharacteristic, complemented
50#63643C2211yescharacteristic, complemented
51#63642C2211yescharacteristic, complemented
52C8×C3⋊Dic3C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
60#5698—34no—
61#5545—34no—
62C3×#478D314yescomplemented
63#5066—34no—
64#5019—34no—
65#4889—34no—
66#4888—34no—
67#4868—34no—
68#4852—34no—
69#4841—34no—
70#4840—34no—
71#4776—34no—
72#4776—34no—
73#4758—34no—
74#4757—34no—
75C23×C3⋊D3—21no—
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C2×#638—21no—
79C22×C3⋊Dic3—21no—
80D4×C3⋊D3—22no—
81D4×C3⋊D3—22no—
82C2×C4⋊(C3⋊D3)C2311yescharacteristic
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×#634C2311yescharacteristic
87C2×#634C2311yescharacteristic
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90C32×C4⋊C4—21no—
91C32×C4⋊C4—21no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C4⋊C4C2311yescharacteristic
95C32×C22⋊C4—21no—
96C32×C42C2311yescharacteristic
97#3757—21no—
98#3754—22no—
99#3754—22no—
100#3752—21no—
101#3752—21no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752D411yescharacteristic
106#3752D411yescharacteristic
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750D411yescharacteristic
115#3750D411yescharacteristic
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3744—22no—
123#3744—22no—
124#3123—91noSylow
125C2×D3×D4—34no—
126C3×#125C2×D314yescomplemented
127C3×C4×D4C2×D314yes—
128D4×Dic3—34no—
129C2×#214—34no—
130C2×#214—34no—
131C4×#67—64no—
132C2×(C2×D3)⋊C4—64no—
133C2×#204—34no—
134C2×#204—34no—
135#898—64no—
136#898—64no—
137#897—34no—
138#897—34no—
139#893—34no—
140#892—34no—
141#890—64no—
142#890—64no—
143#887—34no—
144#887—34no—
145#67⋊C4—64no—
146D3×C22⋊C4—64no—
147C4×D12—34no—
148#872—34no—
149#869—34no—
150C3×#107C2×D314yescomplemented
151C3×#106C2×D314yescomplemented
152C3×C4⋊C8C2×D314yescomplemented
153C3×#102C2×D314yes—
154C3×#102C2×D314yes—
155(C2×D3)⋊C8—34no—
156(C2×D3)⋊C8—34no—
157#816—34no—
158#816—34no—
159#815—34no—
160C8×Dic3—34no—
161#810—34no—
162#810—34no—
163#809—34no—
164#809—34no—
165#808—34no—
166#807—34no—
167C4⋊(C3⋊C8)—34no—
168C23×C32—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—24no—
171C22×C3⋊D3—81no—
172C22×C3⋊D3—81no—
173C22×C3⋊D3C2×D411yescharacteristic
174C32×D4—21no—
175C32×D4#4112yes—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—81no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183#638—24no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—81no—
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)#4112yes—
193C4×C3⋊D3—21no—
194C4×C3⋊D3—21no—
195C4×C3⋊D3—81no—
196C4×C3⋊D3—81no—
197#634—21no—
198#634—21no—
199#634—21no—
200#634—21no—
201C32×C8—21no—
202C32×C8—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊C8)—21no—
205#541—91no—
206#518—91no—
207#485—91no—
208#485—91no—
209#478—91no—
210#478C3⋊D311yescharacteristic, complemented
211#461—91no—
212#461—91no—
213#450—91no—
214#450—91no—
215#440—91no—
216#440—91no—
217C4×SD16—91no—
218C4×SD16—91no—
219#433—91no—
220C23×D3—64no—
221C2×C3×D4C22×D314yes—
222C22×C3×C4—24no—
223C2×#67—64no—
224C22×Dic3—64no—
225D3×D4—68no—
226D3×D4—68no—
227C2×D12—34no—
228C2×C4×D3—34no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×Dic6—34no—
232C2×Dic6—34no—
233C2×C3×C8C22×D314yes—
234C2×C3×C8C22×D314yes—
235C3×C4⋊C4—24no—
236C3×C4⋊C4—24no—
237C3×C4⋊C4C22×D314yes—
238C3×C4⋊C4C22×D314yes—
239C3×C4⋊C4C22×D314yes—
240C3×C22⋊C4—24no—
241C3×C42C22×D314yes—
242#217—64no—
243#214—68no—
244#214—68no—
245(C2×D3)⋊C4—34no—
246(C2×D3)⋊C4—34no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252C4⋊Dic3—34no—
253C4⋊Dic3—64no—
254C4⋊Dic3—64no—
255C4⋊Dic3—64no—
256C4⋊Dic3—64no—
257Dic3⋊C4—34no—
258Dic3⋊C4—34no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261C4×Dic3—34no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265C2×C3⋊C8—34no—
266C2×C3⋊C8—34no—
267#204—68no—
268#204—68no—
269C22×C32—22no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—21no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—21no—
276C2×C3⋊D3—21no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—84no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4—41no—
285C32×C4C2×#4111yescharacteristic
286C32×C4C2×#4111yescharacteristic
287C3⋊Dic3—21no—
288C3⋊Dic3—21no—
289C3⋊Dic3—21no—
290C3⋊Dic3—41no—
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C22×D4—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×SD16—91no—
297C2×SD16—91no—
298C4⋊Q8—91no—
299#126—181no—
300#126—181no—
301#125—181no—
302#125—181no—
303#125C2×C3⋊D311yescharacteristic, complemented
304C22⋊Q8—91no—
305C22⋊Q8—91no—
306C4×Q8—91no—
307C4×Q8—91no—
308C4×D4—91no—
309C4×D4—91no—
310C4×D4—91no—
311C4×D4—181no—
312C4×D4—181no—
313C4×D4C2×C3⋊D311yescharacteristic
314#117—91no—
315#117—91no—
316C2×C22⋊C4—181no—
317C2×C22⋊C4—181no—
318#107—91no—
319#107C2×C3⋊D311yescharacteristic, complemented
320#106—91no—
321#106C2×C3⋊D311yescharacteristic, complemented
322C4⋊C8—91no—
323C4⋊C8C2×C3⋊D311yescharacteristic, complemented
324#103—91no—
325#103—91no—
326#103—91no—
327#103—91no—
328#102—91no—
329#102—91no—
330#102C2×C3⋊D311yescharacteristic
331#102C2×C3⋊D311yescharacteristic
332C22⋊C8—91no—
333C22⋊C8—91no—
334#97—91no—
335C4×C8—91no—
336C23×C3—24no—
337C22×D3—34no—
338C22×D3—64no—
339C22×D3—616no—
340C22×D3—244no—
341C22×D3—244no—
342C3×D4—24no—
343C3×D4#23918yes—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—84no—
348C2×C3×C4D3×D414yes—
349C2×C3×C4D3×D414yes—
350C2×C3×C4C23×D314yes—
351#67—616no—
352C2×Dic3—34no—
353C2×Dic3—34no—
354C2×Dic3—34no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—244no—
359D12—38no—
360D12—64no—
361C4×D3—64no—
362C4×D3—64no—
363C4×D3—244no—
364C4×D3—244no—
365Dic6—64no—
366Dic6—64no—
367Dic6—64no—
368Dic6—64no—
369C3×C8—24no—
370C3×C8—24no—
371C3⋊C8—64no—
372C3⋊C8—64no—
373C2×C32—42no—
374C2×C32#52511yescharacteristic
375C2×C32#57711yescharacteristic
376C2×C32#57711yescharacteristic
377C3⋊D3—41no—
378C3⋊D3—42no—
379C24—181no—
380C2×Q8—91no—
381C2×Q8—91no—
382C2×D4—91no—
383C2×D4—181no—
384C2×D4—182no—
385C2×D4—182no—
386C2×D4C22×C3⋊D311yescharacteristic
387C22×C4—21no—
388C22×C4—91no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
392SD16—182no—
393SD16—182no—
394SD16—182no—
395SD16—182no—
396C2×C8—91no—
397C2×C8—91no—
398C2×C8C22×C3⋊D311yescharacteristic
399C2×C8C22×C3⋊D311yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4C22×C3⋊D311yescharacteristic
412C4⋊C4C22×C3⋊D311yescharacteristic
413C4⋊C4C22×C3⋊D311yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—91no—
416C22⋊C4—91no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C42—91no—
424C42—181no—
425C42—181no—
426C42—181no—
427C42C22×C3⋊D311yescharacteristic
428C22×C3—28no—
429C22×C3—44no—
430C22×C3—44no—
431C22×C3C2×D3×D414yes—
432C2×D3—64no—
433C2×D3—64no—
434C2×D3—64no—
435C2×D3—68no—
436C2×D3—124no—
437C2×D3—124no—
438C2×D3—2416no—
439C3×C4—24no—
440C3×C4—24no—
441C3×C4—44no—
442C3×C4—44no—
443C3×C4—44no—
444C3×C4C2×#23914yes—
445C3×C4D3×#4114yes—
446Dic3—64no—
447Dic3—64no—
448Dic3—64no—
449Dic3—124no—
450Dic3—124no—
451Dic3—124no—
452C32#312311yescharacteristic, complemented, Sylow
453C23—21no—
454C23—91no—
455C23—184no—
456C23—181no—
457C23—721no—
458C23—721no—
459Q8—181no—
460Q8—181no—
461Q8—181no—
462Q8—181no—
463D4—21no—
464D4—92no—
465D4—184no—
466D4—181no—
467D4#383212yes—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—81no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—91no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4—721no—
482C2×C4—721no—
483C2×C4D4×C3⋊D311yescharacteristic
484C2×C4D4×C3⋊D311yescharacteristic
485C2×C4C23×C3⋊D311yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—48no—
491C2×C3#562714yes—
492C2×C3#577014yes—
493C2×C3#577514yes—
494D3—124no—
495D3—128no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—181no—
500C22—182no—
501C22—181no—
502C22—181no—
503C22—361no—
504C22—361no—
505C22—724no—
506C22C2×D4×C3⋊D311yescharacteristic
507C4—21no—
508C4—21no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—181no—
513C4—181no—
514C4—181no—
515C4—361no—
516C4—361no—
517C4—361no—
518C4C2×#383211yescharacteristic
519C4#41×C3⋊D311yescharacteristic
520C3#8114714yescomplemented
521C2—42no—
522C2—361no—
523C2—362no—
524C2#1059609811yescharacteristic
525C2#1059624111yescharacteristic
526C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#478C3⋊D3
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10596169C2semidirect
3. C32×#478C2semidirect
4. #10592765C2semidirect
5. #10592718C2semidirect
6. #10592588C2semidirect
7. #10592587C2semidirect
8. #10592567C2semidirect
9. #10592551C2semidirect
10. #10592540C2semidirect
11. #10592539C2semidirect
14. #10592457C2semidirect
15. #10592456C2semidirect
18. C32×#125C22semidirect
35. #64096C22semidirect
36. #64096C22semidirect
41. #64078C22semidirect
42. C32×#107C22semidirect
43. C32×#106C22semidirect
44. C32×C4⋊C8C22semidirect
49. #63643C22semidirect
50. #63643C22semidirect
51. #63642C22semidirect
52. C8×C3⋊Dic3C22semidirect
53. #63637C22semidirect
54. #63637C22semidirect
57. #63635C22semidirect
58. #63634C22semidirect
59. C4⋊(C3⋊(C3⋊C8))C22semidirect
62. C3×#478D3semidirect
126. C3×#125C2×D3semidirect
150. C3×#107C2×D3semidirect
151. C3×#106C2×D3semidirect
152. C3×C4⋊C8C2×D3semidirect
210. #478C3⋊D3semidirect
303. #125C2×C3⋊D3semidirect
319. #107C2×C3⋊D3semidirect
321. #106C2×C3⋊D3semidirect
323. C4⋊C8C2×C3⋊D3semidirect
452. C32#3123semidirect
520. C3#81147semidirect

Maximal subgroups

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

subgroupindex
#105961692
#105960162
C32×#4782
#105927652
#105927182
#105925882
#105925872
#105925672
#105925512
#105925402
#105925392
#105924752
#105924572
#105924562
#811473