Finite Group Databasebeta

← #11868984

Subgroups — #11868984

Order 1152.

899 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595990C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic
3C3×#5001C211yesmaximal, characteristic
4C3×#4998C211yesmaximal, characteristic, complemented
5#10591131C211yesmaximal, characteristic, complemented
6#10591119C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8#10590474C212yesmaximal, complemented
9#10590473C212yesmaximal, complemented
10#10590472C212yesmaximal, complemented
11#10590471C212yesmaximal, complemented
12#79197—31nomaximal
13#78918—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64135C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18#64099C2212yescomplemented
19#64097C2212yescomplemented
20#64087—22no—
21#64079—21no—
22#64078—21no—
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26D3×#217—22no—
27#63898C2212yes—
28#63898C2212yes—
29Dic3×D12—21no—
30Dic3×D12—21no—
31C3×#809C2212yes—
32C3×#809C2212yes—
33C3×#808C2211yescharacteristic, complemented
34C3×#808C2211yescharacteristic, complemented
35C3×#807C2211yescharacteristic, complemented
36C3×#807C2211yescharacteristic, complemented
37#63575C2212yescomplemented
38#63573C2212yescomplemented
39#63572C2212yescomplemented
40#63572C2212yescomplemented
41#63563C2212yes—
42#63563C2212yes—
43#5798—31no—
44#5521—31no—
45#5519—31no—
46#5519—31no—
47#5519—61no—
48C3×#427—31no—
49C3×#418—31no—
50C2×#832—31no—
51#5121—31no—
52#5119—31no—
53C2×#821—31no—
54#5102—31no—
55#5001D311yescharacteristic
56#4998D311yescharacteristic, complemented
57#4995—31no—
58#4891—32no—
59#4890—32no—
60#4871—32no—
61#4870—32no—
62#4766—32no—
63#4763—32no—
64#4761—32no—
65#4759—32no—
66C23×C3×D3—21no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C2×#634—22no—
70C2×C3×D12—21no—
71C2×C3×D12—22no—
72C2×C3×D12Q814yescomplemented
73C2×C3×D12C2312yes—
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42—21no—
80#3757D412yes—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)D411yescharacteristic
84C4⋊(C3⋊Dic3)D411yescharacteristic
85C4⋊(C3⋊Dic3)C2312yes—
86#3750—22no—
87#3750—22no—
88C4×C3⋊Dic3C2312yes—
89C3×#217—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4×Dic3—21no—
93C3×#208—22no—
94C2×C3×C3⋊C8—22no—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3081—91noSylow
101C22×C3×D4—31no—
102C22×D12C2×D311yescharacteristic
103C2×C3×M16—31no—
104C22×C3×C8—31no—
105C3×#117—21no—
106C3×#117—31no—
107C3×#117C2×D311yescharacteristic
108C3×#117C2×D311yescharacteristic
109C2×#217—62no—
110D4×Dic3—32no—
111D4×Dic3—32no—
112D4×Dic3—61no—
113D4×Dic3—61no—
114#926—31no—
115#926—31no—
116#926—61no—
117#926C2×D311yescharacteristic
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—61no—
121C2×#208C2×D311yescharacteristic
122C22×C3⋊C8C2×D311yescharacteristic
123#893—32no—
124#893—32no—
125#890—32no—
126#890—32no—
127#890—62no—
128#888—32no—
129#888—32no—
130#888—62no—
131D3×C22⋊C4—62no—
132#878—62no—
133#878—62no—
134#878—64no—
135C4×D12—61no—
136C4×D12—61no—
137#870—61no—
138#870—61no—
139#870—62no—
140#869—61no—
141#869—61no—
142#869—62no—
143C3×#107—31no—
144C3×#107—31no—
145C3×#106—31no—
146C3×#106—31no—
147C3×#102—32no—
148C3×#102—32no—
149#832—32no—
150#832—32no—
151#821—32no—
152#821—32no—
153#818—32no—
154#817—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158Dic3⋊C8—32no—
159#809C2×D312yes—
160#809C2×D312yes—
161#808—32no—
162#808C2×D311yescharacteristic, complemented
163#808C2×D311yescharacteristic, complemented
164#807—32no—
165#807C2×D311yescharacteristic, complemented
166#807C2×D311yescharacteristic, complemented
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—22no—
169C22×C3×D3—24no—
170C22×C3×D3—81no—
171C22×C3×D3—81no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×Q812yes—
176C2×C32×C4#4112yes—
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—81no—
180C2×C3⋊Dic3C2×D412yes—
181C2×C3⋊Dic3C2×D412yes—
182#634—82no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C3×D12—24no—
186C3×D12—22no—
187C3×D12C2×Q814yes—
188D3×Dic3—82no—
189D3×Dic3—82no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193#544—91no—
194#518—91no—
195#478—92no—
196#478—92no—
197#476—92no—
198#474—92no—
199#428—91no—
200#427—31no—
201#424—91no—
202#418—31no—
203C2×#102—91no—
204C24×C3—61no—
205C23×D3—21no—
206C2×C3×D4—34no—
207C2×C3×D4—32no—
208C2×C3×D4—62no—
209C2×C3×D4—61no—
210C22×C3×C4—21no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—62no—
214C22×Dic3—62no—
215C22×Dic3—62no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C2×D12—21no—
219C2×D12—22no—
220C2×D12Dic614yescomplemented
221C2×D12C22×D312yes—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—64no—
227C3×M16—62no—
228C2×C3×C8—32no—
229C2×C3×C8—31no—
230C2×C3×C8—31no—
231C2×C3×C8—62no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C22⋊C4—22no—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—61no—
244C3×C42—22no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—61no—
248#217—21no—
249#217—32no—
250#217—32no—
251#217—62no—
252#217—62no—
253#217—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—32no—
261C4⋊Dic3—32no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3—62no—
268C4⋊Dic3—64no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3C22×D311yescharacteristic
272C4⋊Dic3C22×D311yescharacteristic
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—64no—
278Dic3⋊C4—64no—
279C4×Dic3—21no—
280C4×Dic3—32no—
281C4×Dic3—32no—
282C4×Dic3—62no—
283#208—22no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8C22×D312yes—
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D311yescharacteristic
288C22×C32—21no—
289C22×C32—21no—
290C22×C32C22⋊Q812yes—
291C22×C32C22×D411yescharacteristic
292C2×C3×D3—24no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C2×C3×D3—84no—
296C32×C4—41no—
297C32×C4—41no—
298C32×C4C22⋊Q812yes—
299C32×C4C22×Q811yescharacteristic
300C32×C4C2×#4111yescharacteristic
301C3⋊Dic3—22no—
302C3⋊Dic3—22no—
303C3⋊Dic3—42no—
304C3×Dic3—41no—
305C3×Dic3—41no—
306C22×D4—31no—
307C2×M16—31no—
308C22×C8—31no—
309C4⋊Q8—92no—
310C4⋊Q8—181no—
311#125—92no—
312#125—181no—
313C22⋊Q8—182no—
314C4×D4—92no—
315C4×D4—92no—
316C4×D4—181no—
317C4×D4—181no—
318#117—31no—
319#117—91no—
320#117D3211yescharacteristic
321C2×C4⋊C4—91no—
322C2×C22⋊C4—182no—
323#107—31no—
324#107—31no—
325#107—92no—
326#106—31no—
327#106—31no—
328#106—92no—
329C4⋊C8—92no—
330C4⋊C8—92no—
331#102—32no—
332#102—32no—
333#102—92no—
334#102—92no—
335C23×C3—21no—
336C23×C3—62no—
337C23×C3—64no—
338C23×C3—241no—
339C23×C3—241no—
340C23×C3D3×D411yescharacteristic
341C23×C3D3×D411yescharacteristic
342C22×D3—22no—
343C22×D3—24no—
344C22×D3—81no—
345C22×D3—81no—
346C3×D4—34no—
347C3×D4—64no—
348C3×D4—62no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4C2×Dic612yes—
362C2×C3×C4#23512yes—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4#23712yes—
366C2×C3×C4D3×Q812yes—
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—64no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—242no—
381C2×Dic3—242no—
382C2×Dic3—241no—
383C2×Dic3—241no—
384C2×Dic3—242no—
385D12—24no—
386D12—22no—
387D12C2×Dic614yes—
388C4×D3—242no—
389C4×D3—242no—
390Dic6—242no—
391Dic6—242no—
392Dic6—244no—
393C3×C8—62no—
394C3×C8—61no—
395C3×C8—61no—
396C3⋊C8—21no—
397C3⋊C8—21no—
398C3⋊C8—22no—
399C2×C32—22no—
400C2×C32C2×C22⋊Q811yescharacteristic
401C2×C32#57611yescharacteristic
402C2×C32#57711yescharacteristic
403C3×D3—44no—
404C24—61no—
405C2×Q8—182no—
406C2×D4—32no—
407C2×D4—34no—
408C2×D4—62no—
409C2×D4—61no—
410C22×C4—182no—
411C22×C4—182no—
412C22×C4—181no—
413C22×C4C2×D3211yescharacteristic
414M16—62no—
415C2×C8—32no—
416C2×C8—31no—
417C2×C8—31no—
418C2×C8—62no—
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—91no—
422C4⋊C4—91no—
423C4⋊C4—92no—
424C4⋊C4—182no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C4⋊C4—181no—
428C4⋊C4C2×D3211yescharacteristic
429C4⋊C4C2×D3211yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—61no—
432C22⋊C4—92no—
433C22⋊C4—182no—
434C22⋊C4—182no—
435C42—21no—
436C42—61no—
437C42—92no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—22no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—64no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—244no—
450C22×C3#87812yes—
451C22×C3#89612yes—
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C2×D3×D411yescharacteristic
454C2×D3—24no—
455C2×D3—42no—
456C2×D3—42no—
457C2×D3—84no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4—121no—
468C3×C4—121no—
469C3×C4#87812yes—
470C3×C4#89612yes—
471C3×C4C22×Dic611yescharacteristic
472C3×C4C2×#23511yescharacteristic
473C3×C4C2×#23711yescharacteristic
474C3×C4C2×D3×Q811yescharacteristic
475Dic3—41no—
476Dic3—41no—
477Dic3—62no—
478Dic3—62no—
479Dic3—62no—
480Dic3—62no—
481Dic3—122no—
482Dic3—122no—
483Dic3—124no—
484Dic3—122no—
485Dic3—122no—
486C32#308111yescharacteristic, complemented, Sylow
487C23—62no—
488C23—64no—
489C23—241no—
490C23—241no—
491C23#381111yescharacteristic
492Q8—722no—
493D4—34no—
494D4—62no—
495D4—64no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—92no—
501C2×C4—92no—
502C2×C4—182no—
503C2×C4—722no—
504C2×C4—722no—
505C2×C4—721no—
506C2×C4D3×Dic612yes—
507C2×C4#379512yes—
508C2×C4#381111yescharacteristic
509C2×C4C22×D3211yescharacteristic
510C8—61no—
511C8—61no—
512C8—62no—
513C2×C3—22no—
514C2×C3—22no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—42no—
519C2×C3—124no—
520C2×C3C2×#87811yescharacteristic
521C2×C3C2×#89611yescharacteristic
522C2×C3#576911yescharacteristic
523C2×C3#577011yescharacteristic
524C2×C3#577411yescharacteristic
525C2×C3#577511yescharacteristic
526D3—44no—
527C22—21no—
528C22—21no—
529C22—64no—
530C22—122no—
531C22—122no—
532C22—244no—
533C22#6389612yes—
534C22C2×#381111yescharacteristic
535C4—41no—
536C4—41no—
537C4—121no—
538C4—121no—
539C4—182no—
540C4—182no—
541C4—362no—
542C4#6389612yes—
543C4C2×D3×Dic611yescharacteristic
544C4C2×#379511yescharacteristic
545C3—21no—
546C3#7891811yescharacteristic, complemented
547C3#7919711yescharacteristic, complemented
548C2—22no—
549C2—124no—
550C2C2×#6389611yescharacteristic
551C2#1059546111yescharacteristic
552C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenter#117D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595990C2semidirect
4. C3×#4998C2semidirect
5. #10591131C2semidirect
6. #10591119C2semidirect
8. #10590474C2semidirect
9. #10590473C2semidirect
10. #10590472C2semidirect
11. #10590471C2semidirect
18. #64099C22semidirect
19. #64097C22semidirect
33. C3×#808C22semidirect
34. C3×#808C22semidirect
35. C3×#807C22semidirect
36. C3×#807C22semidirect
37. #63575C22semidirect
38. #63573C22semidirect
39. #63572C22semidirect
40. #63572C22semidirect
56. #4998D3semidirect
72. C2×C3×D12Q8semidirect
162. #808C2×D3semidirect
163. #808C2×D3semidirect
165. #807C2×D3semidirect
166. #807C2×D3semidirect
220. C2×D12Dic6semidirect
486. C32#3081semidirect
546. C3#78918semidirect
547. C3#79197semidirect

Maximal subgroups

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

subgroupindex
#105959902
#105949822
C3×#50012
C3×#49982
#105911312
#105911192
C2×#635632
#105904742
#105904732
#105904722
#105904712
#791973
#789183