Finite Group Databasebeta

← #11874314

Subgroups — #11874314

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic, complemented
2#10595152C212yesmaximal, complemented
3C2×#63933C212yesmaximal, complemented
4C2×#63807C211yesmaximal, characteristic, complemented
5#10592854C211yesmaximal, characteristic, complemented
6C3×#5151C211yesmaximal, characteristic, complemented
7#10591490C212yesmaximal, complemented
8#10591474C212yesmaximal, complemented
9#10590896C211yesmaximal, characteristic, complemented
10#10590869C211yesmaximal, characteristic, complemented
11D3×C8×Dic3C211yesmaximal, characteristic, complemented
12#83903—31nomaximal
13#81782—31nomaximal
14C2×C3×#237C2212yes—
15C2×#3795C2212yes—
16C2×C32×D8C2211yescharacteristic
17#64145C2212yes—
18C2×#3754C2212yes—
19C2×#3746C2211yescharacteristic
20C3×#940C2212yes—
21C2×C3×#214C2212yes—
22C2×C3×#213C2212yes—
23C3×#912—24no—
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27Dic3×#67—24no—
28#63970—24no—
29#63933—28no—
30C4×D3×Dic3C2211yescharacteristic
31#63866C2212yes—
32#63863C2212yes—
33C2×#3719C2212yes—
34C2×#3716C2212yes—
35C2×#3715C2212yes—
36C2×D3×C3⋊C8C2211yescharacteristic
37#63807—24no—
38C8×C3⋊Dic3C2211yescharacteristic
39C3×C8×Dic3C2211yescharacteristic
40#63553C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
42C2×C3×#135—31no—
43#5832—32no—
44C2×#950—32no—
45C2×#912—32no—
46C2×#912—31no—
47C2×#912D311yescharacteristic, complemented
48C2×#904—31no—
49#5716—32no—
50C3×#493—31no—
51#5191—31no—
52#5183—31no—
53#5175—32no—
54#5168—32no—
55#5155—31no—
56#5155—31no—
57#5155—32no—
58#5155—31no—
59#5155—61no—
60#5151D311yescharacteristic, complemented
61C2×C8×Dic3—31no—
62#5076—32no—
63#4699—31no—
64C4×D3×C8—31no—
65C2×C32×D4C2312yes—
66C2×#634C2312yes—
67C2×C3×#67—22no—
68C2×C3×#67—24no—
69C22×C3×Dic3—22no—
70C3×#237—24no—
71C3×#237—24no—
72C2×C3×D12C2312yes—
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6C2312yes—
75C2×#625—22no—
76C2×D3×Dic3—22no—
77C2×D3×Dic3D412yes—
78#3795—24no—
79#3795—24no—
80C32×D8—22no—
81C2×C32×C8C2311yescharacteristic
82#3757—24no—
83#3754—24no—
84C4×C3⋊Dic3C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3746—22no—
87C3×#214—24no—
88C3×#213—24no—
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×Dic12—22no—
93C3×D24—22no—
94C3×D3×C8D414yescomplemented
95Dic3⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97Dic32D412yes—
98#3719—24no—
99#3716—24no—
100#3715—24no—
101D3×C3⋊C8D414yescomplemented
102#3147—91noSylow
103C2×C3×#41—32no—
104C2×#237—32no—
105C2×#237C2×D312yes—
106C2×#235—32no—
107C3×#135—64no—
108C2×C3×Q16—31no—
109C2×C3×SD16—32no—
110C2×C3×D8—21no—
111C2×C3×D8—32no—
112C2×C3×D8—31no—
113C2×C3×D8C2×D311yescharacteristic
114C2×C3×D8C2×D311yescharacteristic
115C22×C3×C8—31no—
116C3×#127—32no—
117#950—68no—
118#947—32no—
119#944—32no—
120C2×#216—32no—
121C2×#215—32no—
122#940C2×D312yes—
123#939—64no—
124#938—64no—
125#936—32no—
126#936—32no—
127#936—32no—
128#936—62no—
129D4×Dic3—64no—
130C2×#214—32no—
131C2×#214—32no—
132C2×#214—32no—
133C2×#214—32no—
134C2×#214—62no—
135C2×#214C2×D312yes—
136C2×#213C2×D312yes—
137C4×#67—64no—
138C2×C4×Dic3—31no—
139C22×C3⋊C8—31no—
140#912—24no—
141#912—68no—
142#912—64no—
143C2×Dic12—32no—
144C2×Dic12—31no—
145C2×Dic12—31no—
146C2×Dic12—61no—
147C2×Dic12C2×D311yescharacteristic
148#904—64no—
149C2×D24C2×D311yescharacteristic
150C2×#204—32no—
151C2×D3×C8—31no—
152C2×D3×C8C2×D311yescharacteristic
153C42×D3—31no—
154#869—32no—
155C3×C4×C8—31no—
156C8×Dic3—31no—
157C8×Dic3—31no—
158C8×Dic3—31no—
159C8×Dic3—31no—
160C8×Dic3—31no—
161C8×Dic3—61no—
162C8×Dic3C2×D311yescharacteristic
163C4×C3⋊C8—31no—
164C23×C32—22no—
165C22×C3×D3—22no—
166C22×C3×D3C2×D411yescharacteristic
167C32×D4—22no—
168C32×D4—22no—
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C2×D412yes—
172#634—22no—
173#634—22no—
174C3×#67—44no—
175C3×#67—48no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—44no—
178C2×C3×Dic3C2×D411yescharacteristic
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12—22no—
182C3×C4×D3C2×D412yes—
183C3×C4×D3C2×D412yes—
184C3×Dic6—22no—
185C3×Dic6—22no—
186#625—44no—
187D3×Dic3—24no—
188D3×Dic3—44no—
189C32×C8C2×D412yes—
190C3⋊(C3⋊C8)C2×D412yes—
191C3×C3⋊C8C2×D412yes—
192C3×C3⋊C8C2×D412yes—
193C2×#135—31no—
194C2×#135—91no—
195C2×#135—92no—
196#532—92no—
197#495—92no—
198#495—91no—
199#495—91no—
200#494—91no—
201#493—31no—
202#492—92no—
203C2×C4×C8—91no—
204C3×#41—64no—
205C3×#41—64no—
206C2×C3×Q8—32no—
207C2×C3×D4—22no—
208C2×C3×D4—32no—
209C2×C3×D4—64no—
210C2×C3×D4—62no—
211C2×C3×D4C22×D312yes—
212C2×C3×D4C22×D312yes—
213C22×C3×C4—31no—
214C22×C3×C4—62no—
215C2×#67—22no—
216C2×#67—24no—
217C2×#67—62no—
218C2×#67—62no—
219C22×Dic3—22no—
220C22×Dic3—32no—
221C22×Dic3—62no—
222#237—24no—
223#237—24no—
224#237—64no—
225#237—64no—
226#235—64no—
227#235—64no—
228C2×D12C22×D312yes—
229C2×C4×D3—32no—
230C2×C4×D3—62no—
231C2×C4×D3C22×D311yescharacteristic
232C2×Dic6—32no—
233C2×Dic6—32no—
234C2×Dic6—62no—
235C2×Dic6C22×D312yes—
236C3×Q16—62no—
237C3×SD16—64no—
238C3×D8—22no—
239C3×D8—22no—
240C3×D8—42no—
241C3×D8—64no—
242C3×D8—62no—
243C2×C3×C8—21no—
244C2×C3×C8—31no—
245C2×C3×C8—31no—
246C2×C3×C8—34no—
247C2×C3×C8C22×D311yescharacteristic
248C2×C3×C8C22×D311yescharacteristic
249C3×C42—31no—
250#217—64no—
251#217—64no—
252#217—64no—
253#217—124no—
254#216—64no—
255#215—64no—
256#214—24no—
257#214—64no—
258#214—64no—
259#214—64no—
260#214—64no—
261#214—124no—
262#213—24no—
263(C2×D3)⋊C4—64no—
264C4⋊Dic3—64no—
265Dic3⋊C4—64no—
266C4×Dic3—31no—
267C4×Dic3—31no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—61no—
271C4×Dic3C22×D311yescharacteristic
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—34no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278Dic12—22no—
279Dic12—64no—
280Dic12—62no—
281Dic12—62no—
282Dic12—122no—
283D24—22no—
284#204—64no—
285D3×C8—34no—
286D3×C8#6714yescomplemented
287C22×C32—42no—
288C22×C32—44no—
289C22×C32C22×D411yescharacteristic
290C2×C3×D3—22no—
291C2×C3×D3—42no—
292C2×C3×D3—44no—
293C2×C3×D3#12712yes—
294C32×C4C22×D411yescharacteristic
295C32×C4C22×D411yescharacteristic
296C3⋊Dic3—22no—
297C3⋊Dic3—42no—
298C3×Dic3—42no—
299C3×Dic3#12712yes—
300C3×Dic3#13514yescomplemented
301C2×#41—32no—
302C2×#41—92no—
303#135—64no—
304#135—184no—
305#135—188no—
306C2×Q16—31no—
307C2×Q16—92no—
308C2×Q16—91no—
309C2×SD16—32no—
310C2×SD16—92no—
311C2×SD16—92no—
312C2×SD16—92no—
313C2×D8—32no—
314C2×D8—31no—
315C2×D8D3211yescharacteristic
316C22×C8—31no—
317C22×C8—91no—
318C4⋊Q8—92no—
319#127—32no—
320#124—92no—
321#124—92no—
322#121—184no—
323C4×D4—184no—
324C2×C42—91no—
325C4×C8—31no—
326C4×C8—91no—
327C4×C8—91no—
328C4×C8—91no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—31no—
332C23×C3—42no—
333C23×C3—62no—
334C22×D3—22no—
335C22×D3D3×D411yescharacteristic
336C3×Q8—62no—
337C3×Q8—62no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—42no—
343C3×D4—42no—
344C3×D4—62no—
345C3×D4—62no—
346C3×D4—128no—
347C3×D4—124no—
348C2×C3×C4—21no—
349C2×C3×C4—31no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—62no—
354C2×C3×C4—124no—
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357#67—44no—
358#67—48no—
359#67—124no—
360#67—124no—
361C2×Dic3—22no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—44no—
365C2×Dic3—62no—
366C2×Dic3—64no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—122no—
370C2×Dic3—124no—
371C2×Dic3D3×D412yes—
372C2×Dic3D3×D411yescharacteristic
373D12—22no—
374D12—22no—
375C4×D3—64no—
376C4×D3—124no—
377C4×D3D3×D412yes—
378C4×D3C2×#6712yes—
379Dic6—22no—
380Dic6—22no—
381Dic6—62no—
382Dic6—62no—
383Dic6—62no—
384Dic6—62no—
385Dic6—122no—
386Dic6—122no—
387C3×C8—22no—
388C3×C8—32no—
389C3×C8—32no—
390C3×C8D3×D412yes—
391C3×C8C2×#6712yes—
392C3⋊C8—32no—
393C3⋊C8—32no—
394C3⋊C8—62no—
395C3⋊C8D3×D412yes—
396C3⋊C8C2×#6712yes—
397C2×C32—82no—
398C2×C32C2×#12711yescharacteristic
399C2×C32C2×#13512yes—
400C3×D3—22no—
401C3×D3—82no—
402#41—64no—
403#41—64no—
404#41—184no—
405#41—184no—
406C2×Q8—32no—
407C2×Q8—92no—
408C2×D4—32no—
409C2×D4—64no—
410C2×D4—62no—
411C2×D4—182no—
412C2×D4C2×D3212yes—
413C22×C4—31no—
414C22×C4—62no—
415C22×C4—92no—
416C22×C4—182no—
417Q16—62no—
418Q16—184no—
419Q16—182no—
420SD16—64no—
421SD16—184no—
422SD16—184no—
423SD16—184no—
424D8—22no—
425D8—64no—
426D8—62no—
427C2×C8—31no—
428C2×C8—31no—
429C2×C8—34no—
430C2×C8—94no—
431C2×C8—91no—
432C2×C8C2×D3211yescharacteristic
433C4⋊C4—184no—
434C22⋊C4—184no—
435C22⋊C4—184no—
436C42—31no—
437C42—92no—
438C42—91no—
439C22×C3—21no—
440C22×C3—32no—
441C22×C3—42no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3—42no—
445C22×C3—62no—
446C22×C3—82no—
447C22×C3—84no—
448C22×C3—124no—
449C22×C3—122no—
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—22no—
453C2×D3—42no—
454C2×D3—44no—
455C2×D3#94012yes—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—32no—
459C3×C4—34no—
460C3×C4—122no—
461C3×C4C2×D3×D411yescharacteristic
462C3×C4C2×D3×D411yescharacteristic
463C3×C4C2×D3×D411yescharacteristic
464C3×C4C22×#6711yescharacteristic
465Dic3—42no—
466Dic3—62no—
467Dic3—62no—
468Dic3—122no—
469Dic3—122no—
470Dic3—122no—
471Dic3—242no—
472Dic3#91214yescomplemented
473Dic3#94012yes—
474C32#314711yescharacteristic, complemented, Sylow
475C23—22no—
476C23—31no—
477C23—62no—
478Q8—62no—
479Q8—62no—
480Q8—182no—
481Q8—182no—
482D4—22no—
483D4—22no—
484D4—62no—
485D4—62no—
486D4—128no—
487D4—124no—
488D4—364no—
489C2×C4—32no—
490C2×C4—31no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—62no—
494C2×C4—92no—
495C2×C4—124no—
496C2×C4—184no—
497C2×C4—182no—
498C2×C4—364no—
499C2×C4C22×D3211yescharacteristic
500C8—32no—
501C8—32no—
502C8—92no—
503C8D3×#6712yes—
504C2×C3—22no—
505C2×C3—21no—
506C2×C3—62no—
507C2×C3—82no—
508C2×C3—82no—
509C2×C3—162no—
510C2×C3—242no—
511C2×C3D3×#12711yescharacteristic
512C2×C3C2×#91212yes—
513C2×C3D3×#13512yes—
514C2×C3C2×#94011yescharacteristic
515D3—22no—
516D3—82no—
517C22—32no—
518C22—44no—
519C22—42no—
520C22—62no—
521C22—124no—
522C22—122no—
523C22D32×D411yescharacteristic
524C4—34no—
525C4—32no—
526C4—122no—
527C4—182no—
528C4—362no—
529C4D32×D411yescharacteristic
530C4C2×D3×#6711yescharacteristic
531C3—21no—
532C3#8178211yescharacteristic, complemented
533C3#8390311yescharacteristic, complemented
534C2—62no—
535C2—82no—
536C2—242no—
537C2D3×#91212yes—
538C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3147
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#912C2semidirect
2. #10595152C2semidirect
3. C2×#63933C2semidirect
4. C2×#63807C2semidirect
5. #10592854C2semidirect
6. C3×#5151C2semidirect
7. #10591490C2semidirect
8. #10591474C2semidirect
9. #10590896C2semidirect
10. #10590869C2semidirect
11. D3×C8×Dic3C2semidirect
47. C2×#912D3semidirect
60. #5151D3semidirect
94. C3×D3×C8D4semidirect
101. D3×C3⋊C8D4semidirect
286. D3×C8#67semidirect
300. C3×Dic3#135semidirect
472. Dic3#912semidirect
474. C32#3147semidirect
532. C3#81782semidirect
533. C3#83903semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
#105951522
C2×#639332
C2×#638072
#105928542
C3×#51512
#105914902
#105914742
#105908962
#105908692
D3×C8×Dic32
#839033
#817823