Finite Group Databasebeta

← #11860550

Subgroups — #11860550

Order 1152.

1091 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595219C211yesmaximal, characteristic, complemented
2C2×#63927C211yesmaximal, characteristic
3#10594606C211yesmaximal, characteristic, complemented
4#10592471C211yesmaximal, characteristic, complemented
5C3×#4785C212yesmaximal, complemented
6Dic3×#213C212yesmaximal, complemented
7#10590940C211yesmaximal, characteristic, complemented
8#10590747C212yesmaximal, complemented
9#10590703C211yesmaximal, characteristic, complemented
10#10590584C211yesmaximal, characteristic, complemented
11#10590479C212yesmaximal, complemented
12#79866—32nomaximal
13C2×#3830C2211yescharacteristic
14C2×#3802C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16#64101C2211yescharacteristic
17C3×D4×Dic3C2212yescomplemented
18C2×C3×#213C2212yes—
19C3×#893C2212yes—
20C2×#3724—21no—
21#63957—21no—
22#63952—22no—
23#63927C418yescomplemented
24D3×(C2×D3)⋊C4—22no—
25#63902—21no—
26C4×#625—21no—
27#63900C2211yescharacteristic
28Dic3×D12C2212yes—
29#63874C2211yescharacteristic
30#63844C2212yescomplemented
31C2×#3716C2212yes—
32C2×#3712C2211yescharacteristic
33C32×#102C2211yescharacteristic, complemented
34#63659C2211yescharacteristic, complemented
35#63643C2211yescharacteristic, complemented
36#63637C2211yescharacteristic, complemented
37C3×#821C2212yes—
38C3×#815C2212yescomplemented
39C3×#808C2212yescomplemented
40#63575C2212yescomplemented
41#63562C2212yes—
42Dic3×C3⋊C8C2212yescomplemented
43C2×#911—32no—
44#5546—32no—
45#5545—32no—
46C3×#442—32no—
47Dic3×D8—32no—
48C4×#214—32no—
49C4×#213—32no—
50#4861—32no—
51#4852—32no—
52#4785D312yescomplemented
53#4772—32no—
54#4772—61no—
55D3×#102—32no—
56#4757—32no—
57#4710—32no—
58#4708—32no—
59C22×D32—21no—
60C2×C32×D4C2311yescharacteristic
61C2×#638—21no—
62C22×C3⋊Dic3—21no—
63#3830—22no—
64#3830C2×C414yescomplemented
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×#634C2311yescharacteristic
67C22×C3×Dic3—22no—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—22no—
70C2×#625—21no—
71C2×#624—21no—
72C2×D3×Dic3—22no—
73#3802—22no—
74#3802C2×C414yescomplemented
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2311yescharacteristic
77#3752—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4×C3⋊Dic3—21no—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C8×C3⋊D3—22no—
82C3×#217—22no—
83C3×#213C2×C418yescomplemented
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3C2312yes—
86C3×C4×Dic3C2312yes—
87C2×C3×C3⋊C8C2312yes—
88#3724—21no—
89#3724—22no—
90#3724D411yescharacteristic
91#3724D411yescharacteristic
92#3722D412yes—
93(C2×D3)⋊Dic3—22no—
94Dic32—22no—
95#3716C2×C418yescomplemented
96#3712C2×C414yescomplemented
97#2946—91noSylow
98C2×#237—32no—
99C2×#237—61no—
100C2×D3×D4—32no—
101C2×C3×D8—32no—
102C3×C4×D4—32no—
103C3×C4×D4—32no—
104D4×Dic3—32no—
105D4×Dic3C2×D312yescomplemented
106C2×#214—32no—
107C2×#213C2×D312yes—
108C4×#67—62no—
109C4×#67—62no—
110C2×(C2×D3)⋊C4—62no—
111C2×Dic3⋊C4—62no—
112#911—316no—
113C2×#204—32no—
114C2×ΓL(1,𝔽25)—32no—
115C2×D3×C8—32no—
116C2×D3×C8—61no—
117#893C2×D312yes—
118#892—32no—
119#892—61no—
120D3×C4⋊C4—32no—
121#887—32no—
122#67⋊C4—62no—
123#67⋊C4—62no—
124D3×C22⋊C4—62no—
125#877—62no—
126C4×D12—32no—
127#872—32no—
128C4×Dic6—32no—
129C3×#106—32no—
130C3×#102—21no—
131C3×#102—32no—
132C3×#102C2×D312yescomplemented
133C3×#97—32no—
134#832—32no—
135#832—32no—
136#832—61no—
137#821C2×D312yes—
138#818—32no—
139#816—32no—
140#816—61no—
141#815C2×D312yescomplemented
142C8×Dic3—32no—
143#810—32no—
144#810—61no—
145#809—32no—
146#808C2×D312yescomplemented
147#807—32no—
148C4×C3⋊C8—32no—
149C23×C32—21no—
150C22×C3⋊D3C2×D411yescharacteristic
151C22×C3×D3—22no—
152C2×D32—24no—
153C2×D32—81no—
154C2×D32—81no—
155C32×D4—21no—
156C32×D4C22×C412yes—
157C2×C32×C4—21no—
158C2×C32×C4C2411yescharacteristic
159#638—24no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—24no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3C2×D411yescharacteristic
164C4×C3⋊D3C22×C412yes—
165C4×C3⋊D3#4112yes—
166#634—21no—
167#634C22×C412yes—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—82no—
170C2×C3×Dic3C2×D412yes—
171C2×C3×Dic3C2×D412yes—
172C3×D12—22no—
173C3×D12C22×C414yes—
174C3×C4×D3—82no—
175#625—24no—
176#624—81no—
177D3×Dic3—82no—
178C32×C8—21no—
179C3⋊(C3⋊C8)—21no—
180C3×C3⋊C8C22×C414yes—
181C2×AGL(1,ℤ/8)—91no—
182#520—91no—
183#518—91no—
184#442—32no—
185#440—92no—
186C4×SD16—92no—
187C4×D8—92no—
188#428—91no—
189#416—91no—
190C2×#102—91no—
191#405—91no—
192C23×D3—62no—
193C2×C3×D4—21no—
194C2×C3×D4—32no—
195C2×C3×D4C22×D312yes—
196C22×C3×C4—62no—
197C22×C3×C4—62no—
198C2×#67—62no—
199C2×#67—62no—
200C2×#67—121no—
201C22×Dic3—22no—
202C22×Dic3—62no—
203C22×Dic3—62no—
204C22×Dic3—121no—
205#237—38no—
206#237—64no—
207#237—64no—
208#237—122no—
209D3×D4—38no—
210D3×D4—64no—
211C2×D12C22×D312yes—
212C2×C4×D3—22no—
213C2×C4×D3—32no—
214C2×C4×D3—61no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×Dic6—32no—
218C2×Dic6—61no—
219C3×D8—38no—
220C2×C3×C8—21no—
221C2×C3×C8—32no—
222C2×C3×C8C22×D312yes—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4C22×D312yes—
226C3×C22⋊C4—62no—
227C3×C22⋊C4—62no—
228C3×C42—32no—
229#217—22no—
230#217—62no—
231#214—38no—
232#213C4×D318yescomplemented
233(C2×D3)⋊C4—22no—
234(C2×D3)⋊C4—32no—
235(C2×D3)⋊C4—32no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—121no—
239C4⋊Dic3—32no—
240C4⋊Dic3—61no—
241C4⋊Dic3C22×D312yes—
242Dic3⋊C4—32no—
243Dic3⋊C4—32no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249C4×Dic3—62no—
250C4×Dic3—121no—
251C4×Dic3C22×D312yes—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8C22×D312yes—
255#204—38no—
256ΓL(1,𝔽25)—38no—
257D3×C8—64no—
258D3×C8—122no—
259C22×C32—22no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32C22×D411yescharacteristic
263C2×C3⋊D3—21no—
264C2×C3⋊D3—21no—
265C2×C3⋊D3C4×D412yes—
266C2×C3×D3—24no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269D32—84no—
270C32×C4—41no—
271C32×C4C23×C411yescharacteristic
272C32×C4C2×#4111yescharacteristic
273C3⋊Dic3—22no—
274C3⋊Dic3—41no—
275C3⋊Dic3C4×D412yes—
276C3×Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C2×#41—91no—
280C22×D4—91no—
281AGL(1,ℤ/8)—98no—
282C2×SD16—92no—
283C2×D8—32no—
284C2×M16—91no—
285C22×C8—91no—
286C4×Q8—92no—
287C4×D4—32no—
288C4×D4—32no—
289C4×D4—92no—
290C4×D4—181no—
291C4×D4—182no—
292C4×D4—181no—
293#117—91no—
294#117—91no—
295#117—181no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—181no—
298C2×C22⋊C4—182no—
299#107—92no—
300#106—32no—
301#103—91no—
302#103—91no—
303#102—32no—
304#102—92no—
305#102—91no—
306#102D3211yescharacteristic, complemented
307#97—32no—
308C4×C8—92no—
309C23×C3—22no—
310C23×C3—41no—
311C23×C3—62no—
312C22×D3—22no—
313C22×D3—32no—
314C22×D3—61no—
315C22×D3—68no—
316C22×D3—242no—
317C22×D3—242no—
318C3×D4—22no—
319C3×D4—22no—
320C3×D4—34no—
321C3×D4—41no—
322C3×D4—62no—
323C3×D4C2×C4×D314yes—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—41no—
329C2×C3×C4—62no—
330C2×C3×C4—242no—
331C2×C3×C4—242no—
332C2×C3×C4C23×D312yes—
333#67—68no—
334#67—68no—
335#67—124no—
336C2×Dic3—22no—
337C2×Dic3—32no—
338C2×Dic3—61no—
339C2×Dic3—68no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—82no—
343C2×Dic3—124no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—242no—
347C2×Dic3D3×D412yes—
348C2×Dic3D3×D412yes—
349D12—22no—
350D12C2×C4×D314yes—
351C4×D3—34no—
352C4×D3—34no—
353C4×D3—62no—
354C4×D3—62no—
355C4×D3—82no—
356C4×D3—242no—
357C4×D3—242no—
358Dic6—34no—
359Dic6—62no—
360Dic6—62no—
361Dic6—121no—
362C3×C8—22no—
363C3×C8—34no—
364C3×C8—41no—
365C3⋊C8—62no—
366C3⋊C8—121no—
367C3⋊C8C2×C4×D314yes—
368C2×C32—42no—
369C2×C32C2×C4×D411yescharacteristic
370C2×C32#57611yescharacteristic
371C2×C32#57711yescharacteristic
372C3⋊D3—22no—
373C3×D3—44no—
374C24—181no—
375#41—94no—
376#41—182no—
377C2×Q8—91no—
378C2×D4—32no—
379C2×D4—94no—
380C2×D4—182no—
381C2×D4—181no—
382C2×D4—181no—
383C2×D4C2×D3211yescharacteristic
384C22×C4—62no—
385C22×C4—62no—
386C22×C4—91no—
387C22×C4—182no—
388C22×C4—181no—
389C22×C4—181no—
390SD16—98no—
391D8—38no—
392M16—94no—
393C2×C8—32no—
394C2×C8—91no—
395C2×C8—182no—
396C2×C8C2×D3211yescharacteristic
397C4⋊C4—32no—
398C4⋊C4—91no—
399C4⋊C4—91no—
400C4⋊C4—91no—
401C4⋊C4—182no—
402C4⋊C4—181no—
403C4⋊C4C2×D3211yescharacteristic
404C22⋊C4—62no—
405C22⋊C4—62no—
406C22⋊C4—92no—
407C22⋊C4—181no—
408C22⋊C4—182no—
409C42—32no—
410C42—181no—
411C42—182no—
412C22×C3—24no—
413C22×C3—21no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—64no—
418C22×C3—81no—
419C22×C3—81no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3C2×D3×D412yes—
423C2×D3—24no—
424C2×D3—34no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—248no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—42no—
436C3×C4—62no—
437C3×C4—62no—
438C3×C4—81no—
439C3×C4—122no—
440C3×C4C22×C4×D312yes—
441C3×C4D3×#4112yes—
442Dic3—22no—
443Dic3—22no—
444Dic3—34no—
445Dic3—42no—
446Dic3—62no—
447Dic3—64no—
448Dic3—122no—
449Dic3—122no—
450Dic3—241no—
451C32#294611yescharacteristic, complemented, Sylow
452C23—21no—
453C23—62no—
454C23—91no—
455C23—184no—
456C23—721no—
457C23—721no—
458Q8—92no—
459Q8—181no—
460D4—21no—
461D4—34no—
462D4—62no—
463D4—184no—
464D4—184no—
465D4C4×D3212yes—
466C2×C4—21no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—62no—
470C2×C4—91no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—184no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—242no—
477C2×C4—242no—
478C2×C4—722no—
479C2×C4—721no—
480C2×C4C22×D3211yescharacteristic
481C8—21no—
482C8—34no—
483C8—181no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—44no—
488C2×C3—82no—
489C2×C3—124no—
490C2×C3C4×D3×D412yes—
491C2×C3#577412yes—
492C2×C3#577512yes—
493D3—44no—
494D3—64no—
495D3—122no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—64no—
500C22—92no—
501C22—122no—
502C22—122no—
503C22—181no—
504C22—181no—
505C22—724no—
506C22D32×D411yescharacteristic
507C4—41no—
508C4—62no—
509C4—62no—
510C4—92no—
511C4—122no—
512C4—182no—
513C4—361no—
514C4C2×C4×D3211yescharacteristic
515C4#6431211yescharacteristic
516C3—21no—
517C3#7986612yescomplemented
518C2—42no—
519C2—124no—
520C2—182no—
521C2#1059425511yescharacteristic
522C2#1059473311yescharacteristic
523C2#1059475011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63927C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595219C2semidirect
3. #10594606C2semidirect
4. #10592471C2semidirect
5. C3×#4785C2semidirect
6. Dic3×#213C2semidirect
7. #10590940C2semidirect
8. #10590747C2semidirect
9. #10590703C2semidirect
10. #10590584C2semidirect
11. #10590479C2semidirect
17. C3×D4×Dic3C22semidirect
23. #63927C4semidirect
30. #63844C22semidirect
33. C32×#102C22semidirect
34. #63659C22semidirect
35. #63643C22semidirect
36. #63637C22semidirect
38. C3×#815C22semidirect
39. C3×#808C22semidirect
40. #63575C22semidirect
42. Dic3×C3⋊C8C22semidirect
52. #4785D3semidirect
64. #3830C2×C4semidirect
74. #3802C2×C4semidirect
83. C3×#213C2×C4semidirect
95. #3716C2×C4semidirect
96. #3712C2×C4semidirect
105. D4×Dic3C2×D3semidirect
132. C3×#102C2×D3semidirect
141. #815C2×D3semidirect
146. #808C2×D3semidirect
232. #213C4×D3semidirect
306. #102D32semidirect
451. C32#2946semidirect
517. C3#79866semidirect

Maximal subgroups

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

subgroupindex
#105952192
C2×#639272
#105946062
#105924712
C3×#47852
Dic3×#2132
#105909402
#105907472
#105907032
#105905842
#105904792
#798663