Finite Group Databasebeta

← #11787399

Subgroups — #11787399

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#950C211yesmaximal, characteristic
2C2×#63814C211yesmaximal, characteristic, complemented
3C2×#63664C211yesmaximal, characteristic, complemented
4C3×#5234C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6#10589166C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72087—31nomaximal
9#70011—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#950—22no—
15C3×#950—22no—
16C2×C3×#216C411yescharacteristic, complemented
17C2×C3×#215C411yescharacteristic, complemented
18C2×C3×#214C411yescharacteristic, complemented
19C2×C3×#213C411yescharacteristic, complemented
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3711—21no—
24#63814—22no—
25#63814—22no—
26C2×D3×C3⋊C8—21no—
27#63664—22no—
28C3×#830—21no—
29C3×#830—21no—
30#63568—22no—
31C2×C3×#135—31no—
32C2×#950D311yescharacteristic
33C2×#948—31no—
34C2×#901—31no—
35C3×#408—31no—
36C2×#837—31no—
37C2×#837—31no—
38C2×#837—31no—
39C2×#837—61no—
40#5234D311yescharacteristic, complemented
41C2×#825—31no—
42#4558—31no—
43#4552—31no—
44#4550—31no—
45#4550—31no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41—21no—
50C2×C32×Q8C2×C411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4C2×C411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C3×#67—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235D412yes—
60C3×#235D412yes—
61C2×C3×D12C2×C411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6C2×C411yescharacteristic
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—21no—
66#3748—21no—
67#3748D412yes—
68C2×C3⋊(C3⋊C8)—21no—
69C3×#216—22no—
70C3×#215—22no—
71C3×#214—22no—
72C3×#213—22no—
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8C2×C411yescharacteristic
81C2×C3×C3⋊C8C2×C411yescharacteristic
82C2×C3×C3⋊C8D411yescharacteristic
83C2×C3×C3⋊C8D411yescharacteristic
84#3711—24no—
85D3×C3⋊C8—24no—
86#1876—91noSylow
87C2×C3×#41—21no—
88C2×C3×#41—31no—
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×#41C2×D311yescharacteristic
91C2×#235C2×D311yescharacteristic
92C3×#135—62no—
93C3×#135—62no—
94C2×C3×Q16—31no—
95C2×C3×SD16—31no—
96C2×C3×SD16—31no—
97C2×C3×D8—31no—
98C2×C3×M16—31no—
99C22×C3×C8—31no—
100C22×C3×C8—31no—
101#950—22no—
102#950—22no—
103#948—62no—
104#948—62no—
105C2×#216Dic311yescharacteristic, complemented
106C2×#215Dic311yescharacteristic, complemented
107C2×#214Dic311yescharacteristic, complemented
108C2×#213Dic311yescharacteristic, complemented
109C2×C4×Dic3—31no—
110C2×C4×Dic3—31no—
111C2×C4×Dic3—61no—
112C2×#208—31no—
113C2×#208—31no—
114C2×#208—61no—
115C2×#208—61no—
116C2×#208C2×D311yescharacteristic
117C22×C3⋊C8—61no—
118C22×C3⋊C8C2×D311yescharacteristic
119C22×C3⋊C8C2×D311yescharacteristic
120#901—62no—
121#901—62no—
122C2×ΓL(1,𝔽25)—61no—
123C2×D3×C8—61no—
124C3×C22⋊C8—61no—
125C3×C22⋊C8—61no—
126#837—62no—
127#837—62no—
128#837—62no—
129#837—64no—
130#830—21no—
131#830—21no—
132#825—62no—
133C23×C32—21no—
134C23×C32#4111yescharacteristic
135C22×C3×D3—21no—
136C32×Q8—21no—
137C32×Q8—21no—
138C32×D4—21no—
139C32×D4—21no—
140C32×D4—41no—
141C32×D4—41no—
142C2×C32×C4—21no—
143C2×C32×C4—41no—
144C2×C32×C4—41no—
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—41no—
153C2×C3⋊Dic3—41no—
154C3×#67—22no—
155C3×#67—22no—
156C2×C3×Dic3—21no—
157C3×D12—21no—
158C3×D12C22⋊C412yes—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×Dic6—21no—
162C3×Dic6C22⋊C412yes—
163C3⋊(C3⋊C8)—22no—
164C3×C3⋊C8—21no—
165C3×C3⋊C8—21no—
166C3×C3⋊C8—21no—
167C3×C3⋊C8—21no—
168C3×C3⋊C8—41no—
169C2×#135—31no—
170C2×#131—91no—
171C2×#104—91no—
172C2×#104—91no—
173#408—31no—
174#341—91no—
175#336—91no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—21no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—21no—
186C3×#41—32no—
187C3×#41—32no—
188C3×#41—41no—
189C3×#41—41no—
190C3×#41—61no—
191C3×#41—61no—
192C2×C3×Q8—21no—
193C2×C3×Q8—31no—
194C2×C3×Q8C4×D311yescharacteristic
195C2×C3×Q8C2×Dic311yescharacteristic
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—31no—
200C2×C3×D4—41no—
201C2×C3×D4—61no—
202C2×C3×D4C4×D311yescharacteristic
203C2×C3×D4C2×Dic311yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—41no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—21no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3—121no—
215#235—21no—
216#235—21no—
217#235#6712yes—
218#235#6712yes—
219C2×D12C2×Dic311yescharacteristic
220C2×C4×D3—21no—
221C2×Dic6C2×Dic311yescharacteristic
222C3×Q16—62no—
223C3×SD16—62no—
224C3×SD16—62no—
225C3×D8—62no—
226C3×M16—61no—
227C3×M16—61no—
228C2×C3×C8—31no—
229C2×C3×C8—31no—
230C2×C3×C8—31no—
231C2×C3×C8—31no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C2×C3×C8—61no—
237#216—22no—
238#215—22no—
239#214—22no—
240#213—22no—
241C4×Dic3—62no—
242C4×Dic3—61no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—121no—
247#208—21no—
248#208—21no—
249#208—32no—
250#208—32no—
251#208—62no—
252#208—64no—
253#208—61no—
254#208—61no—
255#208—121no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—64no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—121no—
265C2×C3⋊C8C2×Dic311yescharacteristic
266C2×C3⋊C8C2×Dic311yescharacteristic
267C2×C3⋊C8#6711yescharacteristic
268C2×C3⋊C8#6711yescharacteristic
269ΓL(1,𝔽25)—64no—
270D3×C8—64no—
271C22×C32—21no—
272C22×C32—21no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32C4×D411yescharacteristic
277C22×C32#12111yescharacteristic
278C22×C32#12311yescharacteristic
279C2×C3×D3—22no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C32×C4—41no—
283C32×C4C2×C22⋊C411yescharacteristic
284C32×C4C4×D411yescharacteristic
285C32×C4#12011yescharacteristic
286C32×C4#12111yescharacteristic
287C3⋊Dic3—42no—
288C3×Dic3—22no—
289C2×#41—31no—
290C2×#41D3211yescharacteristic
291#135—62no—
292#135—62no—
293C2×Q16—31no—
294C2×SD16—31no—
295C2×SD16—31no—
296C2×D8—31no—
297#131—182no—
298#131—182no—
299C2×M16—31no—
300C2×M16—91no—
301C2×M16—181no—
302C22×C8—31no—
303C22×C8—31no—
304C22×C8—181no—
305C2×C42—91no—
306#104—182no—
307#104—182no—
308C22⋊C8—61no—
309C22⋊C8—61no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—41no—
314C23×C3—61no—
315C23×C3#23511yescharacteristic
316C23×C3#23711yescharacteristic
317C22×D3—21no—
318C3×Q8—22no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—21no—
323C3×Q8—32no—
324C3×Q8—41no—
325C3×Q8—61no—
326C3×D4—22no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—32no—
332C3×D4—41no—
333C3×D4—42no—
334C3×D4—42no—
335C3×D4—41no—
336C3×D4—41no—
337C3×D4—41no—
338C3×D4—41no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—61no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—41no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—61no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4C2×C4×D311yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4#23711yescharacteristic
367C2×C3×C4#23711yescharacteristic
368C2×C3×C4C22×Dic311yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372#67—22no—
373#67—22no—
374C2×Dic3—21no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—122no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384D12—21no—
385D12#21712yes—
386C4×D3—22no—
387C4×D3—22no—
388Dic6—21no—
389Dic6#21712yes—
390C3×C8—61no—
391C3×C8—61no—
392C3×C8—61no—
393C3×C8—61no—
394C3×C8—121no—
395C3⋊C8—21no—
396C3⋊C8—21no—
397C3⋊C8—21no—
398C3⋊C8—21no—
399C3⋊C8—41no—
400C3⋊C8—62no—
401C3⋊C8—62no—
402C3⋊C8—122no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32—81no—
406C2×C32#38611yescharacteristic
407C2×C32#44311yescharacteristic
408C2×C32#44411yescharacteristic
409C3×D3—42no—
410#41—21no—
411#41—21no—
412#41—21no—
413#41—21no—
414#41—32no—
415#41—32no—
416#41—61no—
417#41—61no—
418C2×Q8—31no—
419C2×Q8D3×Dic311yescharacteristic
420C2×D4—21no—
421C2×D4—31no—
422C2×D4—61no—
423C2×D4D3×Dic311yescharacteristic
424C22×C4—21no—
425C22×C4—61no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428Q16—62no—
429SD16—62no—
430SD16—62no—
431D8—62no—
432M16—61no—
433M16—61no—
434M16—92no—
435M16—184no—
436M16—181no—
437C2×C8—31no—
438C2×C8—31no—
439C2×C8—31no—
440C2×C8—31no—
441C2×C8—61no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8—184no—
447C2×C8—181no—
448C42—181no—
449C42—181no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—42no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—62no—
467C22×C3—81no—
468C22×C3—81no—
469C22×C3—121no—
470C22×C3—121no—
471C22×C3#88311yescharacteristic
472C22×C3#88411yescharacteristic
473C22×C3C4×#6711yescharacteristic
474C22×C3D4×Dic311yescharacteristic
475C22×C3#93511yescharacteristic
476C22×C3#93911yescharacteristic
477C2×D3—22no—
478C2×D3—41no—
479C2×D3—41no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—42no—
485C3×C4—41no—
486C3×C4—41no—
487C3×C4—62no—
488C3×C4D3×C22⋊C411yescharacteristic
489C3×C4#67⋊C411yescharacteristic
490C3×C4D4×Dic311yescharacteristic
491C3×C4#93711yescharacteristic
492C3×C4#93711yescharacteristic
493C3×C4#93811yescharacteristic
494C3×C4#93911yescharacteristic
495C3×C4C2×#21711yescharacteristic
496Dic3—22no—
497Dic3—122no—
498Dic3—122no—
499Dic3—124no—
500C32#187611yescharacteristic, complemented, Sylow
501C23—21no—
502C23—61no—
503C23#380411yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—32no—
507Q8—61no—
508D4—21no—
509D4—21no—
510D4—32no—
511D4—41no—
512D4—41no—
513D4—62no—
514D4—62no—
515D4—61no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—61no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—182no—
523C2×C4—361no—
524C2×C4—361no—
525C2×C4C2×D3×Dic311yescharacteristic
526C2×C4#380511yescharacteristic
527C2×C4D3×#6711yescharacteristic
528C2×C4D3×#6711yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4#381111yescharacteristic
531C8—61no—
532C8—61no—
533C8—61no—
534C8—61no—
535C8—121no—
536C8—182no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—41no—
545C2×C3—41no—
546C2×C3—82no—
547C2×C3—81no—
548C2×C3—81no—
549C2×C3—122no—
550C2×C3#495611yescharacteristic
551C2×C3#514411yescharacteristic
552C2×C3#514511yescharacteristic
553C2×C3#519611yescharacteristic
554C2×C3#519711yescharacteristic
555C2×C3#522011yescharacteristic
556D3—42no—
557C22—21no—
558C22—21no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—62no—
563C22—121no—
564C22—121no—
565C22#6396911yescharacteristic
566C22#6397111yescharacteristic
567C22Dic3×#6711yescharacteristic
568C4—41no—
569C4—62no—
570C4—362no—
571C4D3×#21711yescharacteristic
572C4#6397011yescharacteristic
573C4#67⋊Dic311yescharacteristic
574C4#6398311yescharacteristic
575C3—21no—
576C3#7001111yescharacteristic, complemented
577C3#7208711yescharacteristic, complemented
578C2—21no—
579C2—21no—
580C2—81no—
581C2—122no—
582C2#1059167311yescharacteristic
583C2#1059167411yescharacteristic
584C2#1059172111yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C4×D4
prime radicalC2×C3×#950C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1876
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63814C2semidirect
3. C2×#63664C2semidirect
4. C3×#5234C2semidirect
5. C2×#63568C2semidirect
6. #10589166C2semidirect
7. #10589156C2semidirect
16. C2×C3×#216C4semidirect
17. C2×C3×#215C4semidirect
18. C2×C3×#214C4semidirect
19. C2×C3×#213C4semidirect
40. #5234D3semidirect
105. C2×#216Dic3semidirect
106. C2×#215Dic3semidirect
107. C2×#214Dic3semidirect
108. C2×#213Dic3semidirect
500. C32#1876semidirect
576. C3#70011semidirect
577. C3#72087semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9502
C2×#638142
C2×#636642
C3×#52342
C2×#635682
#105891662
#105891562
#720873
#700113