Finite Group Databasebeta

← #11861169

Subgroups — #11861169

Order 1152.

967 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
1C3×#5745C211yesmaximal, characteristic, complemented
2#10594786C211yesmaximal, characteristic
3#10594776C211yesmaximal, characteristic, complemented
4#10592823C211yesmaximal, characteristic, complemented
5C2×C3×#825C211yesmaximal, characteristic, complemented
6C2×#63569C211yesmaximal, characteristic, complemented
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590976C214yesmaximal, complemented
9#10590975C214yesmaximal, complemented
10#83811—31nomaximal
11#78980—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#907C2214yescomplemented
20C3×D3×M16—22no—
21C3×#901—22no—
22#63827C412yescomplemented
23#63827C412yescomplemented
24#63823C412yescomplemented
25#63823C412yescomplemented
26#63822C2214yes—
27#63815—22no—
28#63814C2214yescomplemented
29D3×#208—22no—
30#63649C2214yescomplemented
31C3×#825C2212yescomplemented
32C3×#825C2212yescomplemented
33#63569C2212yescomplemented
34#63569C2212yescomplemented
35#63554C2212yescomplemented
36Dic3×C3⋊C8C2212yescomplemented
37C3×#568—31no—
38#5822—31no—
39#5822—31no—
40#5819—31no—
41#5745—31no—
42#5745D311yescharacteristic, complemented
43C2×C3×#104—31no—
44C2×#837—31no—
45#5145—34no—
46#5144—34no—
47C2×#825D311yescharacteristic, complemented
48#5124—31no—
49#5124—31no—
50#5124—61no—
51Dic3×M16—31no—
52C2×#805—31no—
53C4×#208—31no—
54#4824—34no—
55#4823—34no—
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C22×C3×Dic3—21no—
60C3×#235—21no—
61C3×#235—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235C2×C412yes—
65C3×#235C2×C412yes—
66C3×#235C2312yes—
67C3×#235C2312yes—
68C2×C3×D12C2×C411yescharacteristic
69C2×C3×D12C2×C411yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6C2×C411yescharacteristic
73C2×C3×Dic6C2×C411yescharacteristic
74C32×M16—21no—
75C32×M16C2312yes—
76C2×C32×C8—21no—
77#3748—21no—
78#3748C2×C412yes—
79#3748C2×C412yes—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×C4×Dic3—21no—
84C3×C4×Dic3C2311yescharacteristic
85C3×C4×Dic3C2311yescharacteristic
86C3×#208D412yes—
87C3×#208D412yes—
88C2×C3×C3⋊C8C2312yes—
89C3×ΓL(1,𝔽25)—24no—
90C3×D3×C8—24no—
91#3718C2×C414yescomplemented
92#3715C2×C414yescomplemented
93#3715C2×C414yescomplemented
94#3713C2×C414yescomplemented
95#3711—24no—
96D3×C3⋊C8—24no—
97#2956—91noSylow
98C2×C3×#41—31no—
99C2×C3×#41—31no—
100C2×#235C2×D311yescharacteristic
101C2×#235C2×D311yescharacteristic
102C3×#131—34no—
103C3×#131—62no—
104C2×C3×M16—21no—
105C2×C3×M16—31no—
106C2×C3×M16—62no—
107C2×C3×M16C2×D311yescharacteristic
108C2×C3×M16C2×D311yescharacteristic
109C2×C3×C42—31no—
110#951—32no—
111#951—32no—
112#950—34no—
113#950—34no—
114#949—32no—
115#949—32no—
116#948—34no—
117#948—62no—
118#942—32no—
119#942—32no—
120#932—32no—
121#932—32no—
122C2×C4×Dic3C2×D311yescharacteristic
123C2×#208—31no—
124C2×#208—31no—
125C2×#208—31no—
126C2×#208—31no—
127C2×#208—61no—
128C2×#208—61no—
129C2×#208—62no—
130C2×#208C2×D311yescharacteristic
131#907—62no—
132#907C2×D314yescomplemented
133D3×M16—22no—
134D3×M16—62no—
135#901—22no—
136#901—34no—
137C3×#104—32no—
138C3×#104—32no—
139#837—32no—
140#837—32no—
141#825C2×D312yescomplemented
142#825C2×D312yescomplemented
143#822—34no—
144#822—34no—
145#822—64no—
146#815—32no—
147C8×Dic3—32no—
148#805—32no—
149#805—32no—
150#803—32no—
151C4×C3⋊C8—32no—
152C23×C32#4111yescharacteristic
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C2×C32×C4C22×C411yescharacteristic
156C2×C32×C4C22×C411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4#4111yescharacteristic
160C2×C32×C4C2411yescharacteristic
161C3×#67—22no—
162C3×#67—22no—
163C3×#67—22no—
164C3×#67—22no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—42no—
170C3×D12—21no—
171C3×D12—21no—
172C3×D12C22×C412yes—
173C3×D12C22×C412yes—
174C3×C4×D3—22no—
175C3×C4×D3—22no—
176C3×C4×D3—22no—
177C3×C4×D3—22no—
178C3×Dic6—21no—
179C3×Dic6—21no—
180C3×Dic6C22×C412yes—
181C3×Dic6C22×C412yes—
182C32×C8—22no—
183C3⋊(C3⋊C8)—22no—
184C3⋊(C3⋊C8)C22×C414yes—
185C3×C3⋊C8C2×D414yes—
186#575—91no—
187#568—31no—
188#568—91no—
189#444—94no—
190#443—94no—
191#430—91no—
192C2×#104—31no—
193C2×#104—91no—
194C4×M16—91no—
195C3×#41—32no—
196C3×#41—32no—
197C3×#41—32no—
198C3×#41—32no—
199C3×#41—61no—
200C3×#41—61no—
201C3×#41—61no—
202C3×#41—61no—
203C2×C3×Q8—31no—
204C2×C3×Q8—31no—
205C2×C3×D4—31no—
206C2×C3×D4—31no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C22×C3×C4—21no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—21no—
216C2×#67—21no—
217C22×Dic3—21no—
218#235—21no—
219#235—21no—
220#235—21no—
221#235—21no—
222#235C4×D312yes—
223#235C4×D312yes—
224#235C22×D312yes—
225#235C22×D312yes—
226C2×D12C4×D311yescharacteristic
227C2×D12C4×D311yescharacteristic
228C2×C4×D3—21no—
229C2×C4×D3—21no—
230C2×Dic6C4×D311yescharacteristic
231C2×Dic6C4×D311yescharacteristic
232C3×M16—21no—
233C3×M16—21no—
234C3×M16—22no—
235C3×M16—32no—
236C3×M16—32no—
237C3×M16—41no—
238C3×M16—64no—
239C3×M16C22×D312yes—
240C3×M16C22×D312yes—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—32no—
244C2×C3×C8—41no—
245C2×C3×C8—64no—
246C3×C42—31no—
247C3×C42—31no—
248C3×C42—61no—
249#216—34no—
250#216—34no—
251#215—34no—
252#215—34no—
253#214—34no—
254#214—34no—
255#213—34no—
256#213—34no—
257C4×Dic3—21no—
258C4×Dic3C22×D311yescharacteristic
259C4×Dic3C22×D311yescharacteristic
260#208—32no—
261#208—32no—
262#208—32no—
263#208—32no—
264#208—32no—
265#208—32no—
266#208—62no—
267#208—62no—
268#208—62no—
269#208—61no—
270#208—61no—
271#208—64no—
272#208—121no—
273#208#6712yes—
274#208#6712yes—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—61no—
280C2×C3⋊C8—64no—
281C2×C3⋊C8—121no—
282C2×C3⋊C8C22×D312yes—
283ΓL(1,𝔽25)—24no—
284ΓL(1,𝔽25)—64no—
285D3×C8—24no—
286D3×C8—64no—
287C22×C32—41no—
288C22×C32C4×D411yescharacteristic
289C22×C32C4×D411yescharacteristic
290C22×C32C2×#4111yescharacteristic
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3—81no—
294C2×C3×D3—81no—
295C32×C4C4×D411yescharacteristic
296C32×C4C4×D411yescharacteristic
297C32×C4C23×C411yescharacteristic
298C32×C4C22×D411yescharacteristic
299C3×Dic3—22no—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3—41no—
303C2×#41—31no—
304C2×#41—31no—
305#137—92no—
306#137—92no—
307AGL(1,ℤ/8)—92no—
308AGL(1,ℤ/8)—92no—
309#135—94no—
310#131—34no—
311#131—62no—
312#131—94no—
313#131—182no—
314C2×M16—31no—
315C2×M16—62no—
316C2×M16—91no—
317C2×M16—91no—
318C2×M16—182no—
319C2×M16D3211yescharacteristic
320C2×C42—31no—
321#108—94no—
322#104—32no—
323#104—32no—
324#104—92no—
325#104—92no—
326#97—92no—
327C4×C8—92no—
328C23×C3—21no—
329C23×C3—61no—
330C23×C3—61no—
331C23×C3#23511yescharacteristic
332C23×C3#23711yescharacteristic
333C22×D3—21no—
334C22×D3—21no—
335C3×Q8—32no—
336C3×Q8—32no—
337C3×Q8—61no—
338C3×Q8—61no—
339C3×D4—32no—
340C3×D4—32no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—62no—
344C3×D4—62no—
345C3×D4—61no—
346C3×D4—61no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—61no—
361C2×C3×C4—122no—
362C2×C3×C4C2×C4×D311yescharacteristic
363C2×C3×C4C2×C4×D311yescharacteristic
364C2×C3×C4C2×C4×D311yescharacteristic
365C2×C3×C4C2×C4×D311yescharacteristic
366C2×C3×C4#23511yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4#23711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—22no—
375#67—22no—
376#67—22no—
377#67—22no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—42no—
383D12—21no—
384D12—21no—
385D12C2×C4×D312yes—
386D12C2×C4×D312yes—
387C4×D3—22no—
388C4×D3—22no—
389C4×D3—22no—
390C4×D3—22no—
391Dic6—21no—
392Dic6—21no—
393Dic6C2×C4×D312yes—
394Dic6C2×C4×D312yes—
395C3×C8—22no—
396C3×C8—22no—
397C3×C8—34no—
398C3×C8—42no—
399C3⋊C8—34no—
400C3⋊C8—34no—
401C3⋊C8—64no—
402C3⋊C8—62no—
403C3⋊C8—62no—
404C3⋊C8—122no—
405C3⋊C8C2×#6714yes—
406C2×C32—21no—
407C2×C32—21no—
408C2×C32—21no—
409C2×C32C2×C4×D411yescharacteristic
410C3×D3—42no—
411C3×D3—42no—
412#41—32no—
413#41—32no—
414#41—32no—
415#41—32no—
416#41—61no—
417#41—61no—
418#41—61no—
419#41—61no—
420C2×Q8—31no—
421C2×Q8—31no—
422C2×D4—31no—
423C2×D4—31no—
424C2×D4—61no—
425C2×D4—61no—
426C22×C4—61no—
427C22×C4—61no—
428C22×C4—61no—
429C22×C4C2×D3211yescharacteristic
430Q16—94no—
431SD16—94no—
432SD16—94no—
433D8—94no—
434M16—21no—
435M16—32no—
436M16—32no—
437M16—64no—
438M16—92no—
439M16—92no—
440M16—92no—
441M16—184no—
442M16—181no—
443M16C2×D3212yes—
444C2×C8—21no—
445C2×C8—32no—
446C2×C8—64no—
447C2×C8—92no—
448C2×C8—184no—
449C2×C8—181no—
450C42—31no—
451C42—31no—
452C42—61no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—62no—
459C22×C3—62no—
460C22×C3—81no—
461C22×C3—241no—
462C22×C3—241no—
463C22×C3#67⋊C411yescharacteristic
464C22×C3#67⋊C411yescharacteristic
465C22×C3C4×#6711yescharacteristic
466C22×C3C4×#6711yescharacteristic
467C22×C3C2×#23511yescharacteristic
468C22×C3C2×#23711yescharacteristic
469C2×D3—22no—
470C2×D3—22no—
471C2×D3—81no—
472C2×D3—81no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—62no—
478C3×C4—62no—
479C3×C4—62no—
480C3×C4—121no—
481C3×C4#67⋊C411yescharacteristic
482C3×C4#67⋊C411yescharacteristic
483C3×C4C4×#6711yescharacteristic
484C3×C4C4×#6711yescharacteristic
485C3×C4C22×C4×D311yescharacteristic
486C3×C4C22×C4×D311yescharacteristic
487C3×C4C2×D3×D411yescharacteristic
488C3×C4C22×#6711yescharacteristic
489Dic3—22no—
490Dic3—22no—
491Dic3—22no—
492Dic3—41no—
493C32#295611yescharacteristic, complemented, Sylow
494C23—61no—
495C23—61no—
496C23#379511yescharacteristic
497Q8—32no—
498Q8—32no—
499Q8—61no—
500Q8—61no—
501D4—32no—
502D4—32no—
503D4—62no—
504D4—62no—
505D4—62no—
506D4—62no—
507D4—61no—
508D4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—61no—
517C2×C4—122no—
518C2×C4#379511yescharacteristic
519C2×C4C4×D3211yescharacteristic
520C2×C4C4×D3211yescharacteristic
521C2×C4D3×#6711yescharacteristic
522C2×C4D3×#6711yescharacteristic
523C2×C4C22×D3211yescharacteristic
524C8—22no—
525C8—34no—
526C8—94no—
527C8—182no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—41no—
536C2×C3—41no—
537C2×C3—41no—
538C2×C3—122no—
539C2×C3—122no—
540C2×C3C2×#67⋊C411yescharacteristic
541C2×C3C2×C4×#6711yescharacteristic
542D3—42no—
543D3—42no—
544C22—41no—
545C22—62no—
546C22—62no—
547C22—241no—
548C22—241no—
549C22#6387911yescharacteristic
550C22#6387911yescharacteristic
551C22C2×#379511yescharacteristic
552C4—62no—
553C4—62no—
554C4—62no—
555C4—121no—
556C4#6387911yescharacteristic
557C4#6387911yescharacteristic
558C4C2×C4×D3211yescharacteristic
559C4C2×D3×#6711yescharacteristic
560C3—21no—
561C3#7898011yescharacteristic, complemented
562C3#8381111yescharacteristic, complemented
563C2—21no—
564C2—21no—
565C2—21no—
566C2—122no—
567C2—122no—
568C2C2×#6387911yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×C4×D4
prime radical#10594786C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5745C2semidirect
3. #10594776C2semidirect
4. #10592823C2semidirect
5. C2×C3×#825C2semidirect
6. C2×#63569C2semidirect
7. Dic3×#208C2semidirect
8. #10590976C2semidirect
9. #10590975C2semidirect
19. C3×#907C22semidirect
22. #63827C4semidirect
23. #63827C4semidirect
24. #63823C4semidirect
25. #63823C4semidirect
28. #63814C22semidirect
30. #63649C22semidirect
31. C3×#825C22semidirect
32. C3×#825C22semidirect
33. #63569C22semidirect
34. #63569C22semidirect
35. #63554C22semidirect
36. Dic3×C3⋊C8C22semidirect
42. #5745D3semidirect
47. C2×#825D3semidirect
91. #3718C2×C4semidirect
92. #3715C2×C4semidirect
93. #3715C2×C4semidirect
94. #3713C2×C4semidirect
132. #907C2×D3semidirect
141. #825C2×D3semidirect
142. #825C2×D3semidirect
493. C32#2956semidirect
561. C3#78980semidirect
562. C3#83811semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105947862
#105947762
#105928232
C2×C3×#8252
C2×#635692
Dic3×#2082
#105909762
#105909752
#838113
#789803