Finite Group Databasebeta

← #11861224

Subgroups — #11861224

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2C2×#63829C211yesmaximal, characteristic
3#10594780C211yesmaximal, characteristic, complemented
4#10592838C211yesmaximal, characteristic, complemented
5C2×C3×#822C211yesmaximal, characteristic, complemented
6#10591110C211yesmaximal, characteristic, complemented
7#10591059C211yesmaximal, characteristic, complemented
8#10590995C214yesmaximal, complemented
9#10590994C214yesmaximal, complemented
10#83812—31nomaximal
11#79249—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15#64135C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#907C2214yescomplemented
20C3×D3×M16—22no—
21C3×#901—22no—
22C2×#3719C411yescharacteristic, complemented
23C2×#3717C411yescharacteristic, complemented
24#63829C412yescomplemented
25#63829C412yescomplemented
26#63829C2212yes—
27#63829C2212yes—
28C2×#3716C411yescharacteristic, complemented
29C2×#3714C411yescharacteristic, complemented
30#63818—22no—
31#63817—22no—
32#63817C2214yescomplemented
33#63652C2214yescomplemented
34C3×#822C2212yescomplemented
35C3×#822C2212yescomplemented
36#63568C2214yescomplemented
37#63555C2212yescomplemented
38#63553C2212yescomplemented
39C3×#568—31no—
40C2×#950—31no—
41#5745—31no—
42#5745—31no—
43#5745D311yescharacteristic, complemented
44C2×#904—31no—
45C2×C3×#108—31no—
46#5236—31no—
47#5145—34no—
48#5144—34no—
49#5139—31no—
50#5139—31no—
51#5139—31no—
52#5139—61no—
53C2×#822D311yescharacteristic, complemented
54#5122—31no—
55#5101—31no—
56#4895—34no—
57#4894—34no—
58C22×C32×C4C2311yescharacteristic
59C2×#638—21no—
60#3828—21no—
61#3828—21no—
62#3828C2×C412yes—
63#3828C2312yes—
64C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×#634C2×C411yescharacteristic
67C2×C3×#67—21no—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235C2×C412yes—
71C3×#235C2312yes—
72C2×C3×D12C2×C411yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6C2×C411yescharacteristic
75C32×M16—21no—
76C32×M16C2312yes—
77C2×C32×C8—21no—
78#3757—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4×C3⋊Dic3C2312yes—
81C3×#208—21no—
82C3×#208D412yes—
83C3×#208D412yes—
84C3×#208C2312yes—
85C2×C3×C3⋊C8—21no—
86C2×C3×C3⋊C8C2×C411yescharacteristic
87C2×C3×C3⋊C8C2×C411yescharacteristic
88C2×C3×C3⋊C8C2×C411yescharacteristic
89C2×C3×C3⋊C8C2×C411yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2312yes—
93C3×ΓL(1,𝔽25)—24no—
94C3×D3×C8—24no—
95#3719C2×C412yes—
96#3719C2×C412yes—
97#3717C2×C412yes—
98#3717C2×C412yes—
99#3716C2×C412yes—
100#3716C2×C412yes—
101#3714C2×C412yes—
102#3714C2×C412yes—
103#3712—24no—
104#3710—24no—
105#2957—91noSylow
106C2×C3×#41—31no—
107C2×#235—31no—
108C2×#235—31no—
109C2×#235—61no—
110C2×#235C2×D311yescharacteristic
111C3×#131—34no—
112C3×#131—62no—
113C2×C3×M16—21no—
114C2×C3×M16—31no—
115C2×C3×M16—31no—
116C2×C3×M16—62no—
117C2×C3×M16C2×D311yescharacteristic
118C2×C3×M16C2×D311yescharacteristic
119C22×C3×C8—31no—
120#950—32no—
121#950—32no—
122#950—32no—
123#950—32no—
124C2×#216—31no—
125C2×#215—31no—
126C2×#214—31no—
127C2×#213—31no—
128#926—31no—
129#926—31no—
130#926—61no—
131C2×#208C2×D311yescharacteristic
132C2×#208C2×D311yescharacteristic
133C22×C3⋊C8C2×D311yescharacteristic
134#907—34no—
135#907—62no—
136#907C2×D314yescomplemented
137D3×M16—22no—
138D3×M16—62no—
139D3×M16—62no—
140C2×Dic12—31no—
141#904—32no—
142#904—32no—
143#904—32no—
144#904—32no—
145C2×D24—31no—
146C2×#204—31no—
147C2×#204—31no—
148#901—22no—
149#901—34no—
150#901—62no—
151C3×#108—32no—
152C3×#108—32no—
153#837—34no—
154#825—34no—
155#825—34no—
156#825—34no—
157#825—64no—
158#822C2×D312yescomplemented
159#822C2×D312yescomplemented
160#815—32no—
161#815—32no—
162C8×Dic3—32no—
163C8×Dic3—32no—
164C23×C32#4111yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4C22×C411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4#4111yescharacteristic
172C2×C32×C4C2411yescharacteristic
173#638—22no—
174#638—22no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—22no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)C22×C412yes—
179C4×C3⋊D3—22no—
180C4×C3⋊D3—22no—
181#634—21no—
182#634C22×C412yes—
183C3×#67—22no—
184C3×#67—22no—
185C2×C3×Dic3—21no—
186C3×D12—21no—
187C3×D12C22×C412yes—
188C3×C4×D3—22no—
189C3×C4×D3—22no—
190C3×Dic6—21no—
191C3×Dic6C22×C412yes—
192C32×C8—22no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8C22×C411yescharacteristic
195C3×C3⋊C8C22×C411yescharacteristic
196C3×C3⋊C8C22×C411yescharacteristic
197C3×C3⋊C8C22×C411yescharacteristic
198C3×C3⋊C8C2×D414yes—
199C2×#135—91no—
200#568—31no—
201#568—91no—
202#444—94no—
203#443—94no—
204C2×#108—31no—
205#421—91no—
206#421—91no—
207#405—91no—
208C3×#41—32no—
209C3×#41—32no—
210C3×#41—61no—
211C3×#41—61no—
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—
220C2×#67—61no—
221C2×#67—61no—
222C2×#67—121no—
223#235—21no—
224#235—21no—
225#235—32no—
226#235—32no—
227#235—32no—
228#235—32no—
229#235—62no—
230#235—62no—
231#235—61no—
232#235—61no—
233#235—61no—
234#235—61no—
235#235—121no—
236#235—121no—
237#235C4×D312yes—
238#235C22×D312yes—
239C2×D12—31no—
240C2×D12—31no—
241C2×D12—61no—
242C2×D12C4×D311yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—121no—
247C2×Dic6—31no—
248C2×Dic6—31no—
249C2×Dic6—61no—
250C2×Dic6C4×D311yescharacteristic
251C3×M16—21no—
252C3×M16—21no—
253C3×M16—22no—
254C3×M16—32no—
255C3×M16—32no—
256C3×M16—32no—
257C3×M16—41no—
258C3×M16—64no—
259C3×M16—61no—
260C3×M16C22×D312yes—
261C3×M16C22×D312yes—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C2×C3×C8—31no—
268C2×C3×C8—31no—
269C2×C3×C8—32no—
270C2×C3×C8—31no—
271C2×C3×C8—41no—
272C2×C3×C8—64no—
273C2×C3×C8—61no—
274#217—61no—
275#217—61no—
276#217—121no—
277#216—32no—
278#216—32no—
279#215—32no—
280#215—32no—
281#214—32no—
282#214—32no—
283#213—32no—
284#213—32no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—121no—
288C4×Dic3—32no—
289C4×Dic3—32no—
290C4×Dic3—62no—
291#208—21no—
292#208#6712yes—
293#208#6712yes—
294#208C22×D312yes—
295C2×C3⋊C8—21no—
296C2×C3⋊C8C4×D311yescharacteristic
297C2×C3⋊C8C4×D311yescharacteristic
298C2×C3⋊C8C4×D311yescharacteristic
299C2×C3⋊C8C4×D311yescharacteristic
300C2×C3⋊C8C22×D311yescharacteristic
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D312yes—
303Dic12—32no—
304Dic12—32no—
305D24—32no—
306D24—32no—
307#204—32no—
308#204—32no—
309#204—32no—
310#204—32no—
311ΓL(1,𝔽25)—24no—
312ΓL(1,𝔽25)—64no—
313ΓL(1,𝔽25)—64no—
314D3×C8—24no—
315D3×C8—64no—
316D3×C8—64no—
317C22×C32—41no—
318C22×C32C4×D411yescharacteristic
319C22×C32C4×D411yescharacteristic
320C22×C32C2×#4111yescharacteristic
321C2×C3⋊D3—22no—
322C2×C3⋊D3—81no—
323C2×C3×D3—22no—
324C2×C3×D3—81no—
325C32×C4C4×D411yescharacteristic
326C32×C4C4×D411yescharacteristic
327C32×C4C23×C411yescharacteristic
328C32×C4C22×D411yescharacteristic
329C3⋊Dic3—22no—
330C3⋊Dic3—42no—
331C3×Dic3—22no—
332C2×#41—31no—
333C2×#41—91no—
334#135—92no—
335#135—92no—
336#135—92no—
337#135—92no—
338C2×Q16—91no—
339C2×SD16—91no—
340C2×SD16—91no—
341C2×D8—91no—
342#131—34no—
343#131—62no—
344#131—94no—
345#131—182no—
346C2×M16—31no—
347C2×M16—31no—
348C2×M16—62no—
349C2×M16—182no—
350C2×M16D3211yescharacteristic
351C22×C8—31no—
352#117—91no—
353#108—32no—
354#108—32no—
355#104—94no—
356#104—94no—
357#97—92no—
358C4×C8—92no—
359C23×C3—21no—
360C23×C3—61no—
361C23×C3#23511yescharacteristic
362C23×C3#23911yescharacteristic
363C22×D3—21no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—121no—
367C3×Q8—32no—
368C3×Q8—61no—
369C3×D4—32no—
370C3×D4—62no—
371C3×D4—62no—
372C3×D4—61no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4C2×C4×D311yescharacteristic
383C2×C3×C4C2×C4×D311yescharacteristic
384C2×C3×C4C2×C4×D311yescharacteristic
385C2×C3×C4C2×C4×D311yescharacteristic
386C2×C3×C4#23511yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4#23911yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394#67—22no—
395#67—22no—
396#67—62no—
397#67—62no—
398#67—62no—
399#67—62no—
400#67—122no—
401#67—122no—
402C2×Dic3—21no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—121no—
408C2×Dic3—122no—
409D12—21no—
410D12—32no—
411D12—32no—
412D12—62no—
413D12—61no—
414D12—61no—
415D12—121no—
416D12C2×C4×D312yes—
417C4×D3—22no—
418C4×D3—22no—
419C4×D3—62no—
420C4×D3—62no—
421C4×D3—62no—
422C4×D3—62no—
423C4×D3—122no—
424C4×D3—122no—
425Dic6—21no—
426Dic6—32no—
427Dic6—32no—
428Dic6—62no—
429Dic6—61no—
430Dic6—61no—
431Dic6—121no—
432Dic6C2×C4×D312yes—
433C3×C8—22no—
434C3×C8—22no—
435C3×C8—31no—
436C3×C8—31no—
437C3×C8—31no—
438C3×C8—31no—
439C3×C8—34no—
440C3×C8—42no—
441C3×C8—62no—
442C3⋊C8—22no—
443C3⋊C8C2×C4×D311yescharacteristic
444C3⋊C8C2×C4×D311yescharacteristic
445C3⋊C8C2×C4×D311yescharacteristic
446C3⋊C8C2×C4×D311yescharacteristic
447C3⋊C8C2×#6714yes—
448C2×C32—21no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32C2×C4×D411yescharacteristic
452C3⋊D3—42no—
453C3×D3—42no—
454#41—32no—
455#41—32no—
456#41—61no—
457#41—61no—
458#41—92no—
459#41—92no—
460#41—181no—
461#41—181no—
462C2×Q8—31no—
463C2×Q8—91no—
464C2×D4—31no—
465C2×D4—61no—
466C2×D4—91no—
467C2×D4—181no—
468C22×C4—61no—
469C22×C4—181no—
470C22×C4C2×D3211yescharacteristic
471Q16—92no—
472Q16—92no—
473SD16—92no—
474SD16—92no—
475SD16—92no—
476SD16—92no—
477D8—92no—
478D8—92no—
479M16—21no—
480M16—32no—
481M16—32no—
482M16—32no—
483M16—64no—
484M16—61no—
485M16—184no—
486M16C2×D3212yes—
487C2×C8—21no—
488C2×C8—31no—
489C2×C8—32no—
490C2×C8—31no—
491C2×C8—31no—
492C2×C8—31no—
493C2×C8—31no—
494C2×C8—31no—
495C2×C8—64no—
496C2×C8—61no—
497C2×C8—184no—
498C4⋊C4—181no—
499C22⋊C4—181no—
500C42—92no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—62no—
507C22×C3—81no—
508C22×C3—241no—
509C22×C3#89311yescharacteristic
510C22×C3#89311yescharacteristic
511C22×C3C4×#6711yescharacteristic
512C22×C3C4×#6711yescharacteristic
513C22×C3C2×#23511yescharacteristic
514C22×C3C2×#23911yescharacteristic
515C2×D3—22no—
516C2×D3—62no—
517C2×D3—62no—
518C2×D3—81no—
519C2×D3—122no—
520C2×D3—241no—
521C2×D3—241no—
522C2×D3—242no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—62no—
528C3×C4#89311yescharacteristic
529C3×C4#89311yescharacteristic
530C3×C4C4×#6711yescharacteristic
531C3×C4C4×#6711yescharacteristic
532C3×C4C22×C4×D311yescharacteristic
533C3×C4C22×C4×D311yescharacteristic
534C3×C4C2×D3×D411yescharacteristic
535C3×C4C22×#6711yescharacteristic
536Dic3—22no—
537Dic3—62no—
538Dic3—62no—
539Dic3—122no—
540Dic3—122no—
541Dic3—122no—
542Dic3—242no—
543C32#295711yescharacteristic, complemented, Sylow
544C23—61no—
545C23—181no—
546C23#379911yescharacteristic
547Q8—32no—
548Q8—61no—
549Q8—92no—
550Q8—181no—
551D4—32no—
552D4—62no—
553D4—62no—
554D4—61no—
555D4—92no—
556D4—182no—
557D4—182no—
558D4—181no—
559C2×C4—61no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—181no—
563C2×C4—182no—
564C2×C4—182no—
565C2×C4—182no—
566C2×C4#379911yescharacteristic
567C2×C4C4×D3211yescharacteristic
568C2×C4C4×D3211yescharacteristic
569C2×C4D3×#6711yescharacteristic
570C2×C4D3×#6711yescharacteristic
571C2×C4C22×D3211yescharacteristic
572C8—22no—
573C8—31no—
574C8—31no—
575C8—31no—
576C8—31no—
577C8—34no—
578C8—62no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—41no—
587C2×C3—41no—
588C2×C3—41no—
589C2×C3—122no—
590C2×C3C2×#89311yescharacteristic
591C2×C3C2×C4×#6711yescharacteristic
592D3—42no—
593D3—122no—
594D3—122no—
595D3—242no—
596C22—41no—
597C22—62no—
598C22—182no—
599C22—241no—
600C22—721no—
601C22#6390411yescharacteristic
602C22#6390411yescharacteristic
603C22C2×#379911yescharacteristic
604C4—62no—
605C4—182no—
606C4—362no—
607C4#6390411yescharacteristic
608C4#6390411yescharacteristic
609C4C2×C4×D3211yescharacteristic
610C4C2×D3×#6711yescharacteristic
611C3—21no—
612C3#7924911yescharacteristic, complemented
613C3#8381211yescharacteristic, complemented
614C2—21no—
615C2—21no—
616C2—21no—
617C2—122no—
618C2—362no—
619C2C2×#6390411yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×C4×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2957
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. #10594780C2semidirect
4. #10592838C2semidirect
5. C2×C3×#822C2semidirect
6. #10591110C2semidirect
7. #10591059C2semidirect
8. #10590995C2semidirect
9. #10590994C2semidirect
19. C3×#907C22semidirect
22. C2×#3719C4semidirect
23. C2×#3717C4semidirect
24. #63829C4semidirect
25. #63829C4semidirect
28. C2×#3716C4semidirect
29. C2×#3714C4semidirect
32. #63817C22semidirect
33. #63652C22semidirect
34. C3×#822C22semidirect
35. C3×#822C22semidirect
36. #63568C22semidirect
37. #63555C22semidirect
38. #63553C22semidirect
43. #5745D3semidirect
53. C2×#822D3semidirect
136. #907C2×D3semidirect
158. #822C2×D3semidirect
159. #822C2×D3semidirect
543. C32#2957semidirect
612. C3#79249semidirect
613. C3#83812semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
C2×#638292
#105947802
#105928382
C2×C3×#8222
#105911102
#105910592
#105909952
#105909942
#838123
#792493