Finite Group Databasebeta

← #11868040

Subgroups — #11868040

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic, complemented
2C2×C3×#901C211yesmaximal, characteristic, complemented
3#10594795C212yesmaximal, complemented
4C2×C3×#819C211yesmaximal, characteristic, complemented
5#10591078C212yesmaximal, complemented
6#10590932C212yesmaximal, complemented
7#10590931C214yesmaximal, complemented
8#10590927C212yesmaximal, complemented
9#83805—31nomaximal
10#79256—31nomaximal
11C2×#3828C2212yes—
12C2×C3×#235C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×#3746C2211yescharacteristic, complemented
15#64113—21no—
16#64113—21no—
17#64113—21no—
18#64113—21no—
19C2×#3745C2211yescharacteristic, complemented
20C2×#3744C2212yescomplemented
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2212yes—
23C3×#901—21no—
24C3×#901—21no—
25C3×#901C2212yes—
26C3×#901C2212yes—
27C2×C3×ΓL(1,𝔽25)—21no—
28C2×C3×D3×C8—21no—
29#63833—22no—
30#63831C2214yes—
31#63830—22no—
32#63829—24no—
33#63825C2214yes—
34C3×#819C2212yescomplemented
35C3×#819C2212yescomplemented
36#63561C2214yescomplemented
37#63559C2214yescomplemented
38C2×C3×#131—31no—
39#5822—32no—
40#5748—32no—
41C2×#904—31no—
42C2×#904—31no—
43C2×#904—61no—
44C2×#901D311yescharacteristic, complemented
45C2×C3×#108—31no—
46#5143—32no—
47#5142—32no—
48#5141—34no—
49#5132—32no—
50#5132—32no—
51C2×#819D311yescharacteristic, complemented
52#4898—34no—
53#4897—32no—
54#4896—32no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—22no—
57#3828—22no—
58#3828—22no—
59#3828—22no—
60#3828—22no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4×C3⋊D3—22no—
63C2×#634C2312yes—
64C2×C3×#67—21no—
65C3×#235—21no—
66C3×#235—21no—
67C3×#235D412yes—
68C3×#235C2312yes—
69C2×C3×D12D411yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C32×C8D411yescharacteristic
73C2×C32×C8D411yescharacteristic
74C2×C32×C8D411yescharacteristic
75C2×C32×C8D411yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78#3746—21no—
79#3746—21no—
80#3745—21no—
81#3745—21no—
82#3744—22no—
83#3744—22no—
84C3×#208—21no—
85C3×#208—22no—
86C3×#208C2312yes—
87C3×#208C2314yes—
88C2×C3×C3⋊C8—21no—
89C2×C3×C3⋊C8—22no—
90C3×ΓL(1,𝔽25)—22no—
91C3×ΓL(1,𝔽25)—22no—
92C3×D3×C8—22no—
93C3×D3×C8—22no—
94#3719—24no—
95#3717—24no—
96#3716—24no—
97#3714—24no—
98#3067—91noSylow
99C2×C3×#41—31no—
100C2×#235—32no—
101C2×#235—32no—
102C2×#235—62no—
103C2×#235C2×D311yescharacteristic
104C3×#131—32no—
105C3×#131—32no—
106C3×#131—61no—
107C3×#131—61no—
108C2×C3×M16—31no—
109C2×C3×M16—32no—
110C2×C3×M16—61no—
111C22×C3×C8—21no—
112C22×C3×C8—61no—
113C22×C3×C8C2×D311yescharacteristic
114C22×C3×C8C2×D311yescharacteristic
115#951—34no—
116#950—64no—
117#949—34no—
118#942—62no—
119#932—62no—
120C2×#208C2×D311yescharacteristic
121C2×#208C2×D312yes—
122#909—34no—
123#909—62no—
124#908—34no—
125#908—62no—
126C2×Dic12—31no—
127C2×Dic12—31no—
128C2×Dic12—61no—
129#904—62no—
130#904—62no—
131#904—62no—
132#904—62no—
133#904—64no—
134#904—61no—
135#904—61no—
136#904—61no—
137#904—61no—
138#904—61no—
139#904—61no—
140#904—61no—
141#904—61no—
142C2×D24—31no—
143C2×D24—31no—
144C2×D24—61no—
145C2×#204—32no—
146C2×#204—32no—
147C2×#204—62no—
148#901—21no—
149#901—21no—
150#901C2×D312yes—
151#901C2×D312yes—
152C2×ΓL(1,𝔽25)—21no—
153C2×D3×C8—21no—
154C3×#108—32no—
155C3×#108—32no—
156#824—34no—
157#824—34no—
158#823—34no—
159#823—34no—
160#819C2×D312yescomplemented
161#819C2×D312yescomplemented
162C23×C32#4111yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4#4111yescharacteristic
170C2×C32×C4C2411yescharacteristic
171#638—42no—
172#638—42no—
173C2×C3⋊Dic3—22no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—22no—
176C4×C3⋊D3—42no—
177C4×C3⋊D3—42no—
178#634—22no—
179#634—22no—
180C3×#67—22no—
181C3×#67—22no—
182C2×C3×Dic3—21no—
183C3×D12—21no—
184C3×D12C2×D412yes—
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187C3×Dic6—21no—
188C3×Dic6C2×D412yes—
189C32×C8C2×D411yescharacteristic
190C32×C8C2×D411yescharacteristic
191C32×C8C2×D411yescharacteristic
192C32×C8C2×D411yescharacteristic
193C3×C3⋊C8—24no—
194C3×C3⋊C8—22no—
195#575—92no—
196C2×#135—91no—
197C2×#131—31no—
198#473—92no—
199#472—92no—
200#471—94no—
201C2×#108—31no—
202#413—92no—
203C3×#41—32no—
204C3×#41—32no—
205C3×#41—61no—
206C3×#41—61no—
207C2×C3×Q8—31no—
208C2×C3×D4—31no—
209C2×C3×D4—61no—
210C22×C3×C4—21no—
211C22×C3×C4—61no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—21no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—122no—
218#235—21no—
219#235—21no—
220#235—64no—
221#235—64no—
222#235—62no—
223#235—62no—
224#235—62no—
225#235—62no—
226#235—62no—
227#235—62no—
228#235—62no—
229#235—62no—
230#235—122no—
231#235—122no—
232#235D1212yes—
233#235C22×D312yes—
234C2×D12—32no—
235C2×D12—32no—
236C2×D12—62no—
237C2×D12D1211yescharacteristic
238C2×C4×D3—21no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—122no—
242C2×Dic6—32no—
243C2×Dic6—32no—
244C2×Dic6—62no—
245C2×Dic6D1211yescharacteristic
246C3×M16—32no—
247C3×M16—34no—
248C3×M16—62no—
249C3×M16—61no—
250C3×M16—62no—
251C3×M16—62no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—62no—
259C2×C3×C8—61no—
260C2×C3×C8—62no—
261C2×C3×C8—62no—
262C2×C3×C8D1211yescharacteristic
263C2×C3×C8D1211yescharacteristic
264C2×C3×C8D1211yescharacteristic
265C2×C3×C8D1211yescharacteristic
266C2×C3×C8#6711yescharacteristic
267C2×C3×C8#6711yescharacteristic
268C2×C3×C8#6711yescharacteristic
269C2×C3×C8#6711yescharacteristic
270C2×C3×C8C22×D311yescharacteristic
271C2×C3×C8C22×D311yescharacteristic
272C2×C3×C8C22×D311yescharacteristic
273C2×C3×C8C22×D311yescharacteristic
274#216—64no—
275#215—64no—
276#214—64no—
277#213—64no—
278#208—22no—
279#208—21no—
280#208C22×D314yes—
281#208C22×D312yes—
282C2×C3⋊C8—22no—
283C2×C3⋊C8—21no—
284Dic12—62no—
285Dic12—62no—
286Dic12—64no—
287Dic12—61no—
288Dic12—61no—
289Dic12—61no—
290Dic12—61no—
291D24—62no—
292D24—62no—
293D24—64no—
294D24—61no—
295D24—61no—
296D24—61no—
297D24—61no—
298#204—64no—
299#204—64no—
300#204—64no—
301#204—64no—
302#204—62no—
303#204—62no—
304#204—62no—
305#204—62no—
306ΓL(1,𝔽25)—22no—
307ΓL(1,𝔽25)—22no—
308D3×C8—22no—
309D3×C8—22no—
310C22×C32—41no—
311C22×C32#12111yescharacteristic
312C22×C32#12111yescharacteristic
313C22×C32C2×#4111yescharacteristic
314C2×C3⋊D3—42no—
315C2×C3⋊D3—82no—
316C2×C3×D3—22no—
317C2×C3×D3—42no—
318C32×C4#12111yescharacteristic
319C32×C4#12111yescharacteristic
320C32×C4C22×D411yescharacteristic
321C32×C4C22×D411yescharacteristic
322C3⋊Dic3—42no—
323C3×Dic3—22no—
324C2×#41—31no—
325C2×#41—92no—
326#137—94no—
327#137—182no—
328AGL(1,ℤ/8)—94no—
329AGL(1,ℤ/8)—182no—
330#135—184no—
331#135—181no—
332#135—181no—
333#135—181no—
334#135—181no—
335C2×Q16—91no—
336C2×SD16—92no—
337C2×D8—91no—
338#131—32no—
339#131—32no—
340#131—61no—
341#131—61no—
342C2×M16—31no—
343C2×M16—32no—
344C2×M16—61no—
345C22×C8—61no—
346C22×C8D3211yescharacteristic
347#108—32no—
348#108—32no—
349#101—94no—
350#100—94no—
351C23×C3—21no—
352C23×C3—61no—
353C23×C3#23511yescharacteristic
354C23×C3#23911yescharacteristic
355C22×D3—21no—
356C22×D3—62no—
357C22×D3—62no—
358C22×D3—122no—
359C3×Q8—32no—
360C3×Q8—61no—
361C3×D4—32no—
362C3×D4—62no—
363C3×D4—62no—
364C3×D4—61no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4C2×D1211yescharacteristic
375C2×C3×C4C2×D1211yescharacteristic
376C2×C3×C4C2×D1211yescharacteristic
377C2×C3×C4C2×D1211yescharacteristic
378C2×C3×C4#23511yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4#23911yescharacteristic
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C2×#6711yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386#67—22no—
387#67—22no—
388#67—124no—
389#67—124no—
390#67—122no—
391#67—122no—
392#67—122no—
393#67—122no—
394C2×Dic3—21no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—122no—
398D12—21no—
399D12—64no—
400D12—62no—
401D12—62no—
402D12—62no—
403D12—62no—
404D12—122no—
405D12C2×D1212yes—
406C4×D3—22no—
407C4×D3—22no—
408C4×D3—124no—
409C4×D3—124no—
410C4×D3—122no—
411C4×D3—122no—
412C4×D3—122no—
413C4×D3—122no—
414Dic6—21no—
415Dic6—64no—
416Dic6—62no—
417Dic6—62no—
418Dic6—62no—
419Dic6—62no—
420Dic6—122no—
421Dic6C2×D1212yes—
422C3×C8—21no—
423C3×C8—21no—
424C3×C8—21no—
425C3×C8—21no—
426C3×C8—64no—
427C3×C8—62no—
428C3×C8C2×D1211yescharacteristic
429C3×C8C2×D1211yescharacteristic
430C3×C8C2×D1211yescharacteristic
431C3×C8C2×D1211yescharacteristic
432C3×C8C2×#6711yescharacteristic
433C3×C8C2×#6711yescharacteristic
434C3×C8C2×#6711yescharacteristic
435C3×C8C2×#6711yescharacteristic
436C3⋊C8—24no—
437C3⋊C8—22no—
438C2×C32—21no—
439C2×C32—21no—
440C2×C32—21no—
441C2×C32C2×#12111yescharacteristic
442C3⋊D3—82no—
443C3×D3—42no—
444#41—32no—
445#41—32no—
446#41—61no—
447#41—61no—
448#41—182no—
449#41—182no—
450#41—182no—
451#41—182no—
452C2×Q8—31no—
453C2×Q8—92no—
454C2×D4—31no—
455C2×D4—61no—
456C2×D4—92no—
457C2×D4—182no—
458C22×C4—61no—
459C22×C4—182no—
460C22×C4C2×D3211yescharacteristic
461Q16—184no—
462Q16—181no—
463Q16—181no—
464SD16—184no—
465SD16—184no—
466SD16—182no—
467SD16—182no—
468D8—184no—
469D8—181no—
470D8—181no—
471M16—32no—
472M16—34no—
473M16—62no—
474M16—61no—
475M16—62no—
476M16—62no—
477C2×C8—62no—
478C2×C8—61no—
479C2×C8—62no—
480C2×C8—62no—
481C2×C8#62611yescharacteristic
482C2×C8#62611yescharacteristic
483C2×C8#62611yescharacteristic
484C2×C8#62611yescharacteristic
485C2×C8C2×D3211yescharacteristic
486C2×C8C2×D3211yescharacteristic
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—42no—
493C22×C3—62no—
494C22×C3—122no—
495C22×C3#89511yescharacteristic
496C22×C3#89511yescharacteristic
497C22×C3#93011yescharacteristic
498C22×C3#93011yescharacteristic
499C22×C3C2×#23511yescharacteristic
500C22×C3C2×#23911yescharacteristic
501C2×D3—22no—
502C2×D3—42no—
503C2×D3—124no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—244no—
507C2×D3—242no—
508C2×D3—242no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—62no—
514C3×C4#89511yescharacteristic
515C3×C4#89511yescharacteristic
516C3×C4#93011yescharacteristic
517C3×C4#93011yescharacteristic
518C3×C4C22×D1211yescharacteristic
519C3×C4C22×D1211yescharacteristic
520C3×C4C2×D3×D411yescharacteristic
521C3×C4C22×#6711yescharacteristic
522Dic3—22no—
523Dic3—124no—
524Dic3—122no—
525Dic3—122no—
526C32#306711yescharacteristic, complemented, Sylow
527C23—61no—
528C23—182no—
529C23#379911yescharacteristic
530Q8—32no—
531Q8—61no—
532Q8—182no—
533Q8—182no—
534D4—32no—
535D4—62no—
536D4—62no—
537D4—61no—
538D4—182no—
539D4—182no—
540D4—362no—
541D4—362no—
542C2×C4—61no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—182no—
546C2×C4—362no—
547C2×C4—362no—
548C2×C4#379911yescharacteristic
549C2×C4D3×D1211yescharacteristic
550C2×C4D3×D1211yescharacteristic
551C2×C4C2×#62611yescharacteristic
552C2×C4C2×#62611yescharacteristic
553C2×C4C22×D3211yescharacteristic
554C8—64no—
555C8—62no—
556C8C2×#62611yescharacteristic
557C8C2×#62611yescharacteristic
558C8C2×#62611yescharacteristic
559C8C2×#62611yescharacteristic
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—41no—
569C2×C3—41no—
570C2×C3—122no—
571C2×C3C2×#89511yescharacteristic
572C2×C3C2×#93011yescharacteristic
573D3—42no—
574D3—244no—
575D3—242no—
576D3—242no—
577C22—41no—
578C22—62no—
579C22—122no—
580C22—362no—
581C22—722no—
582C22#6390911yescharacteristic
583C22#6390911yescharacteristic
584C22C2×#379911yescharacteristic
585C4—62no—
586C4—362no—
587C4#6390911yescharacteristic
588C4#6390911yescharacteristic
589C4C2×D3×D1211yescharacteristic
590C4C22×#62611yescharacteristic
591C3—21no—
592C3#7925611yescharacteristic, complemented
593C3#8380511yescharacteristic, complemented
594C2—21no—
595C2—21no—
596C2—21no—
597C2—122no—
598C2—722no—
599C2C2×#6390911yescharacteristic
subgroupG/H
centerC4#63909
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC2×C32C2×#121
hypercenterC22×C8D32
hypocenterC32#3067
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64113C2semidirect
2. C2×C3×#901C2semidirect
3. #10594795C2semidirect
4. C2×C3×#819C2semidirect
5. #10591078C2semidirect
6. #10590932C2semidirect
7. #10590931C2semidirect
8. #10590927C2semidirect
14. C2×#3746C22semidirect
19. C2×#3745C22semidirect
20. C2×#3744C22semidirect
34. C3×#819C22semidirect
35. C3×#819C22semidirect
36. #63561C22semidirect
37. #63559C22semidirect
44. C2×#901D3semidirect
51. C2×#819D3semidirect
160. #819C2×D3semidirect
161. #819C2×D3semidirect
526. C32#3067semidirect
592. C3#79256semidirect
593. C3#83805semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C2×C3×#9012
#105947952
C2×C3×#8192
#105910782
#105909322
#105909312
#105909272
#838053
#792563