Finite Group Databasebeta

← #11860629

Subgroups — #11860629

Order 1152.

1021 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594992C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic, complemented
5C3×#5113C211yesmaximal, characteristic
6C3×#5101C211yesmaximal, characteristic, complemented
7#10591131C211yesmaximal, characteristic, complemented
8#10590794C212yesmaximal, complemented
9#10590793C212yesmaximal, complemented
10#10590747C212yesmaximal, complemented
11#10590744C212yesmaximal, complemented
12#78821—31nomaximal
13#78571—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#67⋊Dic3—22no—
22#63957—22no—
23Dic3×D12C2212yes—
24D3×C4⋊Dic3—21no—
25#63844—21no—
26#63844—21no—
27#63844C2212yes—
28#63844C2212yes—
29Dic3×Dic6C2212yes—
30#63841—21no—
31C2×#3719C2212yes—
32#63831C418yescomplemented
33C2×#3716C2212yes—
34#63643C2212yes—
35#63643C2212yes—
36C3×#821C2211yescharacteristic
37C3×#821C2211yescharacteristic
38C3×#816C2211yescharacteristic
39C3×#816C2211yescharacteristic
40C3×#815C2212yes—
41C3×C8×Dic3C2212yes—
42#63575C2212yes—
43#63573C2212yes—
44#5827—31no—
45C2×#951—31no—
46C2×#909—31no—
47#5523—31no—
48#5516—31no—
49#5516—31no—
50C3×#416—31no—
51C3×#405—31no—
52#5121—31no—
53#5113D311yescharacteristic
54C2×#816—31no—
55C2×#816—31no—
56C2×#816—61no—
57#5101D311yescharacteristic, complemented
58#4995—31no—
59#4790—32no—
60#4789—32no—
61#4758—32no—
62#4757—32no—
63#4716—32no—
64#4710—32no—
65C4×Dic12—32no—
66C4×#204—32no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C22×C3⋊Dic3—21no—
70C2×#634—21no—
71C2×#634—22no—
72C2×#634C2×C414yescomplemented
73C2×#634C2312yes—
74C2×C3×#67—21no—
75C3×#235—22no—
76C3×#235C2×C414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×Dic6C2311yescharacteristic
80C2×D3×Dic3—22no—
81C2×C32×C8—22no—
82C2×C32×C8C2311yescharacteristic
83C2×C32×C8C2311yescharacteristic
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C3×#217—21no—
87C3×#217D412yes—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4×Dic3—21no—
93C3×C4×Dic3C2312yes—
94C3×#208C2×C414yescomplemented
95C2×C3×C3⋊C8C2312yes—
96#3724—22no—
97#3724—22no—
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100Dic32—22no—
101Dic32—22no—
102Dic32—22no—
103#3719C2×C418yescomplemented
104#3716C2×C418yescomplemented
105#2947—91noSylow
106C2×C3×#41—31no—
107C2×#235C2×D311yescharacteristic
108C22×Dic6—31no—
109C22×Dic6—31no—
110C22×Dic6—61no—
111C2×C3×M16—31no—
112C22×C3×C8—21no—
113C22×C3×C8C2×D311yescharacteristic
114C22×C3×C8C2×D311yescharacteristic
115C3×#117—31no—
116C3×#117—31no—
117#951—38no—
118Q8×Dic3—32no—
119C2×#216—32no—
120D4×Dic3—32no—
121D4×Dic3—62no—
122C2×#214—32no—
123#926—61no—
124#926C2×D311yescharacteristic
125#926C2×D311yescharacteristic
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—61no—
129C2×C4⋊Dic3—61no—
130C2×#208C2×D311yescharacteristic
131#909—38no—
132C2×Dic12—32no—
133C2×#204—32no—
134#892—61no—
135D3×C4⋊C4—61no—
136#887—32no—
137#887—32no—
138#887—61no—
139#887—61no—
140#67⋊C4—62no—
141#877—62no—
142#877—62no—
143C4×D12—32no—
144C4×Dic6—32no—
145C4×Dic6—32no—
146C4×Dic6—32no—
147C4×Dic6—61no—
148C4×Dic6—61no—
149C3×#103—31no—
150C3×#103—31no—
151C3×#102—31no—
152C3×#102—31no—
153C3×#97—32no—
154C3×C4×C8—32no—
155#821C2×D311yescharacteristic
156#821C2×D311yescharacteristic
157#818—32no—
158#817—32no—
159#816—32no—
160#816—32no—
161#816—32no—
162#816—32no—
163#816—62no—
164#816—62no—
165#816C2×D311yescharacteristic
166#816C2×D311yescharacteristic
167#815C2×D312yes—
168C8×Dic3C2×D312yes—
169#808—32no—
170#807—32no—
171C23×C32C2×D411yescharacteristic
172C22×C3×D3—21no—
173C2×C32×C4C22×C412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4#4112yes—
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—24no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—81no—
181#634—24no—
182#634—22no—
183#634C22×C414yes—
184C3×#67—24no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D412yes—
189C2×C3×Dic3C2×D412yes—
190C3×D12—21no—
191C3×D12C22×C412yes—
192C3×C4×D3—24no—
193C3×Dic6—21no—
194C3×Dic6C22×C412yes—
195D3×Dic3—82no—
196C32×C8—21no—
197C32×C8—21no—
198C3×C3⋊C8C22×C414yes—
199C2×#137—91no—
200#520—91no—
201#519—91no—
202#441—92no—
203#440—92no—
204C4×Q16—92no—
205C4×SD16—92no—
206#428—91no—
207#416—31no—
208C2×#103—91no—
209#405—31no—
210C3×#41—34no—
211C3×#41—62no—
212C2×C3×Q8—31no—
213C2×C3×D4—31no—
214C2×C3×D4—61no—
215C22×C3×C4—21no—
216C22×C3×C4—61no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C2×#67—21no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—62no—
225C22×Dic3—121no—
226C22×Dic3—121no—
227#235—22no—
228#235C4×D314yes—
229C2×D12C22×D311yescharacteristic
230C2×C4×D3—21no—
231C2×C4×D3—62no—
232C2×Dic6—34no—
233C2×Dic6—34no—
234C2×Dic6—32no—
235C2×Dic6—32no—
236C2×Dic6—62no—
237C2×Dic6—64no—
238C2×Dic6—61no—
239C2×Dic6—62no—
240C2×Dic6—61no—
241C2×Dic6—62no—
242C2×Dic6—121no—
243C2×Dic6—122no—
244C2×Dic6C22×D311yescharacteristic
245C3×M16—34no—
246C2×C3×C8—22no—
247C2×C3×C8—22no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—32no—
251C2×C3×C8—42no—
252C2×C3×C8C22×D311yescharacteristic
253C2×C3×C8C22×D311yescharacteristic
254C2×C3×C8C22×D311yescharacteristic
255C2×C3×C8C22×D311yescharacteristic
256C3×C4⋊C4—31no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—31no—
260C3×C22⋊C4—32no—
261C3×C22⋊C4—61no—
262C3×C42—32no—
263C3×C42—61no—
264#217—21no—
265#217—62no—
266#217D1212yes—
267#216—38no—
268#214—38no—
269(C2×D3)⋊C4—62no—
270C4⋊Dic3—32no—
271C4⋊Dic3—32no—
272C4⋊Dic3—62no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3—62no—
276C4⋊Dic3—121no—
277C4⋊Dic3D1211yescharacteristic
278C4⋊Dic3D1211yescharacteristic
279C4⋊Dic3C22×D311yescharacteristic
280C4⋊Dic3C22×D311yescharacteristic
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286C4×Dic3—21no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3—62no—
290C4×Dic3—62no—
291C4×Dic3—62no—
292C4×Dic3—62no—
293C4×Dic3C22×D312yes—
294#208C4×D314yescomplemented
295C2×C3⋊C8C22×D312yes—
296Dic12—38no—
297#204—38no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32C4×D412yes—
301C22×C32C22×D411yescharacteristic
302C2×C3×D3—22no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C32×C4C4×D412yes—
306C32×C4C23×C411yescharacteristic
307C32×C4C2×#4111yescharacteristic
308C3⋊Dic3—24no—
309C3⋊Dic3—42no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C3×Dic3—41no—
314C3×Dic3—41no—
315C2×#41—31no—
316C22×Q8—91no—
317#137—98no—
318C2×Q16—92no—
319C2×SD16—92no—
320C2×M16—31no—
321C22×C8D3211yescharacteristic
322C4×Q8—92no—
323C4×Q8—92no—
324C4×Q8—92no—
325C4×Q8—181no—
326C4×Q8—181no—
327C4×D4—92no—
328C4×D4—182no—
329#117—31no—
330#117—31no—
331#117—182no—
332#117—181no—
333C2×C4⋊C4—91no—
334C2×C4⋊C4—181no—
335#107—92no—
336#106—92no—
337#103—31no—
338#103—31no—
339#103—92no—
340#103—92no—
341#102—31no—
342#102—31no—
343#97—32no—
344C4×C8—32no—
345C23×C3—21no—
346C23×C3—61no—
347C23×C3C2×D1211yescharacteristic
348C23×C3D3×D411yescharacteristic
349C22×D3—21no—
350C3×Q8—32no—
351C3×Q8—61no—
352C3×D4—32no—
353C3×D4—64no—
354C3×D4—61no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—32no—
360C2×C3×C4—32no—
361C2×C3×C4—61no—
362C2×C3×C4—64no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4C2×C4×D312yes—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4#23512yes—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23712yes—
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—24no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—64no—
378C2×Dic3—64no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—124no—
385C2×Dic3—122no—
386C2×Dic3—242no—
387C2×Dic3—241no—
388C2×Dic3—241no—
389C2×Dic3—242no—
390C2×Dic3C2×D1212yes—
391C2×Dic3C2×D1212yes—
392D12—21no—
393D12C2×C4×D312yes—
394C4×D3—24no—
395C4×D3—242no—
396Dic6—21no—
397Dic6—34no—
398Dic6—34no—
399Dic6—64no—
400Dic6—64no—
401Dic6—64no—
402Dic6—62no—
403Dic6—62no—
404Dic6—122no—
405Dic6—124no—
406Dic6C2×C4×D312yes—
407C3×C8—21no—
408C3×C8—21no—
409C3×C8—21no—
410C3×C8—21no—
411C3×C8—34no—
412C3×C8—41no—
413C3×C8—41no—
414C3⋊C8C2×C4×D314yes—
415C2×C32—22no—
416C2×C32C2×C4×D411yescharacteristic
417C2×C32#57711yescharacteristic
418C2×C32#57811yescharacteristic
419C3×D3—42no—
420#41—34no—
421#41—62no—
422C2×Q8—31no—
423C2×Q8—92no—
424C2×Q8—94no—
425C2×Q8—181no—
426C2×Q8—182no—
427C2×D4—31no—
428C2×D4—61no—
429C22×C4—61no—
430C22×C4—182no—
431C22×C4—181no—
432C22×C4—181no—
433C22×C4C2×D3211yescharacteristic
434Q16—98no—
435SD16—98no—
436M16—34no—
437C2×C8—22no—
438C2×C8—32no—
439C2×C8C2×D3211yescharacteristic
440C2×C8C2×D3211yescharacteristic
441C4⋊C4—31no—
442C4⋊C4—31no—
443C4⋊C4—31no—
444C4⋊C4—31no—
445C4⋊C4—92no—
446C4⋊C4—182no—
447C4⋊C4—182no—
448C4⋊C4—182no—
449C4⋊C4—181no—
450C22⋊C4—32no—
451C22⋊C4—61no—
452C22⋊C4—182no—
453C42—32no—
454C42—61no—
455C42—182no—
456C42—182no—
457C42—182no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—62no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3C4×D1212yes—
470C22×C3#67⋊C412yes—
471C22×C3C22×D1211yescharacteristic
472C22×C3C2×D3×D411yescharacteristic
473C2×D3—22no—
474C2×D3—41no—
475C2×D3—41no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—62no—
480C3×C4—62no—
481C3×C4—62no—
482C3×C4—121no—
483C3×C4—121no—
484C3×C4C4×D1212yes—
485C3×C4#67⋊C412yes—
486C3×C4C22×C4×D311yescharacteristic
487C3×C4C22×C4×D311yescharacteristic
488C3×C4C2×#23511yescharacteristic
489C3×C4C2×#23711yescharacteristic
490Dic3—22no—
491Dic3—22no—
492Dic3—22no—
493Dic3—41no—
494Dic3—41no—
495Dic3—64no—
496Dic3—64no—
497Dic3—124no—
498Dic3—122no—
499Dic3—122no—
500Dic3—242no—
501C32#294711yescharacteristic, complemented, Sylow
502C23—61no—
503C23D3×D1211yescharacteristic
504Q8—32no—
505Q8—61no—
506Q8—94no—
507Q8—182no—
508Q8—184no—
509D4—32no—
510D4—64no—
511D4—61no—
512C2×C4—32no—
513C2×C4—32no—
514C2×C4—61no—
515C2×C4—64no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—182no—
519C2×C4—184no—
520C2×C4—182no—
521C2×C4—722no—
522C2×C4—721no—
523C2×C4C4×D3212yes—
524C2×C4D3×D1211yescharacteristic
525C2×C4#380412yes—
526C2×C4C22×D3211yescharacteristic
527C8—21no—
528C8—21no—
529C8—34no—
530C2×C3—24no—
531C2×C3—22no—
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—122no—
537C2×C3C2×C4×D1211yescharacteristic
538C2×C3C2×#67⋊C411yescharacteristic
539C2×C3#575111yescharacteristic
540C2×C3#575311yescharacteristic
541C2×C3#577011yescharacteristic
542C2×C3#577111yescharacteristic
543D3—42no—
544C22—21no—
545C22—21no—
546C22—62no—
547C22—121no—
548C22—121no—
549C22#6388012yes—
550C22C2×D3×D1211yescharacteristic
551C4—62no—
552C4—62no—
553C4—62no—
554C4—121no—
555C4—121no—
556C4—184no—
557C4—362no—
558C4#6388012yes—
559C4C2×C4×D3211yescharacteristic
560C4C2×#380411yescharacteristic
561C3—21no—
562C3#7857111yescharacteristic, complemented
563C3#7882111yescharacteristic, complemented
564C2—22no—
565C2—122no—
566C2#1059467911yescharacteristic
567C2#1059469211yescharacteristic
568C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594828C2semidirect
4. C2×#63643C2semidirect
6. C3×#5101C2semidirect
7. #10591131C2semidirect
8. #10590794C2semidirect
9. #10590793C2semidirect
10. #10590747C2semidirect
11. #10590744C2semidirect
32. #63831C4semidirect
57. #5101D3semidirect
72. C2×#634C2×C4semidirect
94. C3×#208C2×C4semidirect
103. #3719C2×C4semidirect
104. #3716C2×C4semidirect
294. #208C4×D3semidirect
501. C32#2947semidirect
562. C3#78571semidirect
563. C3#78821semidirect

Maximal subgroups

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

subgroupindex
#105949922
#105948282
C2×#638312
C2×#636432
C3×#51132
C3×#51012
#105911312
#105907942
#105907932
#105907472
#105907442
#788213
#785713