Finite Group Databasebeta

← #11787401

Subgroups — #11787401

Order 1152.

727 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×#63815C211yesmaximal, characteristic, complemented
3#10592933C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6#10589166C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72087—31nomaximal
9#70390—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#950—22no—
15C3×#950—22no—
16C2×C3×#216C411yescharacteristic, complemented
17C2×C3×#215C411yescharacteristic, complemented
18C2×C3×#214C411yescharacteristic, complemented
19C2×C3×#213C411yescharacteristic, complemented
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3711—21no—
24#63815—22no—
25#63815—22no—
26C2×D3×C3⋊C8—21no—
27#63657—21no—
28#63657—21no—
29C3×#837—22no—
30#63569—22no—
31C2×C3×#135—31no—
32C2×#950D311yescharacteristic
33C2×#948—31no—
34C2×#907—31no—
35C2×C3×#104—31no—
36C2×#837—31no—
37C2×#837D311yescharacteristic, complemented
38#5234—31no—
39#5234—31no—
40#5234—61no—
41C2×#805—31no—
42#4558—31no—
43#4552—31no—
44#4550—31no—
45#4524—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
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235D412yes—
60C3×#235D412yes—
61C2×C3×D12C2×C411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6C2×C411yescharacteristic
64#3748—21no—
65#3748—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)D411yescharacteristic
70C2×C3⋊(C3⋊C8)D411yescharacteristic
71C3×#216—22no—
72C3×#215—22no—
73C3×#214—22no—
74C3×#213—22no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×#208—21no—
78C3×#208D412yes—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8C2×C411yescharacteristic
83C2×C3×C3⋊C8C2×C411yescharacteristic
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—
100C2×C3×C42—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×Dic3C2×D311yescharacteristic
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113C2×#208—61no—
114C2×#208C2×D311yescharacteristic
115C22×C3⋊C8—31no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—61no—
118C22×C3⋊C8—61no—
119C22×C3⋊C8C2×D311yescharacteristic
120#907—62no—
121#907—62no—
122C2×ΓL(1,𝔽25)—61no—
123C2×D3×C8—61no—
124C3×#104—62no—
125#837—22no—
126#837—62no—
127#830—61no—
128#830—61no—
129#830—61no—
130#830—61no—
131#830—62no—
132#830—62no—
133#805—62no—
134C23×C32—21no—
135C23×C32#4111yescharacteristic
136C22×C3×D3—21no—
137C32×Q8—21no—
138C32×Q8—21no—
139C32×D4—21no—
140C32×D4—21no—
141C32×D4—41no—
142C32×D4—41no—
143C2×C32×C4—21no—
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4C22×C411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C3×#67—22no—
153C3×#67—22no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C3×D12—21no—
159C3×D12C22⋊C412yes—
160C3×C4×D3—22no—
161C3×C4×D3—22no—
162C3×Dic6—21no—
163C3×Dic6C22⋊C412yes—
164C3⋊(C3⋊C8)—21no—
165C3⋊(C3⋊C8)—21no—
166C3⋊(C3⋊C8)—41no—
167C3×C3⋊C8—21no—
168C3×C3⋊C8—21no—
169C3×C3⋊C8—22no—
170C2×#135—31no—
171C2×#131—91no—
172C2×#104—31no—
173C2×#104—91no—
174#408—91no—
175#341—91no—
176#336—91no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—21no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—32no—
186C3×#41—32no—
187C3×#41—41no—
188C3×#41—41no—
189C3×#41—41no—
190C3×#41—41no—
191C3×#41—61no—
192C3×#41—61no—
193C2×C3×Q8—21no—
194C2×C3×Q8—31no—
195C2×C3×Q8C4×D311yescharacteristic
196C2×C3×Q8C2×Dic311yescharacteristic
197C2×C3×D4—22no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—31no—
202C2×C3×D4—61no—
203C2×C3×D4C4×D311yescharacteristic
204C2×C3×D4C2×Dic311yescharacteristic
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—21no—
214C22×Dic3—21no—
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—32no—
227C3×M16—61no—
228C2×C3×C8—31no—
229C2×C3×C8—31no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C3×C42—61no—
234C3×C42—61no—
235#216—22no—
236#215—22no—
237#214—22no—
238#213—22no—
239C4×Dic3—21no—
240C4×Dic3—21no—
241#208—21no—
242#208—64no—
243#208—61no—
244#208—61no—
245#208—61no—
246#208—61no—
247#208—121no—
248#208—121no—
249#208#6712yes—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—31no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—64no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—121no—
268C2×C3⋊C8—121no—
269C2×C3⋊C8C2×Dic311yescharacteristic
270C2×C3⋊C8C2×Dic311yescharacteristic
271ΓL(1,𝔽25)—64no—
272D3×C8—64no—
273C22×C32—21no—
274C22×C32—21no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C4×D411yescharacteristic
279C22×C32#12111yescharacteristic
280C22×C32#12311yescharacteristic
281C2×C3×D3—22no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C32×C4—41no—
285C32×C4C2×C22⋊C411yescharacteristic
286C32×C4C4×D411yescharacteristic
287C32×C4#12011yescharacteristic
288C32×C4#12111yescharacteristic
289C3×Dic3—22no—
290C3×Dic3—42no—
291C2×#41—31no—
292C2×#41D3211yescharacteristic
293#135—62no—
294#135—62no—
295C2×Q16—31no—
296C2×SD16—31no—
297C2×SD16—31no—
298C2×D8—31no—
299#131—182no—
300#131—182no—
301C2×M16—31no—
302C2×M16—91no—
303C2×M16—181no—
304C22×C8—31no—
305C22×C8—91no—
306C22×C8—181no—
307C2×C42—31no—
308#104—62no—
309#104—182no—
310C22⋊C8—181no—
311C22⋊C8—181no—
312C23×C3—22no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—61no—
317C23×C3#23711yescharacteristic
318C23×C3#23711yescharacteristic
319C22×D3—21no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—32no—
325C3×Q8—41no—
326C3×Q8—41no—
327C3×Q8—61no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—32no—
333C3×D4—41no—
334C3×D4—41no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—41no—
338C3×D4—41no—
339C3×D4—41no—
340C3×D4—41no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—61no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
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—42no—
354C2×C3×C4—42no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4C2×C4×D311yescharacteristic
366C2×C3×C4#23511yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4#23711yescharacteristic
373C2×C3×C4C22×Dic311yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376C2×C3×C4C2×#6711yescharacteristic
377#67—22no—
378#67—22no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383D12—21no—
384D12#21712yes—
385C4×D3—22no—
386C4×D3—22no—
387Dic6—21no—
388Dic6#21712yes—
389C3×C8—61no—
390C3×C8—61no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8—21no—
394C3⋊C8—21no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C3⋊C8—61no—
398C3⋊C8—61no—
399C3⋊C8—121no—
400C3⋊C8—121no—
401C3⋊C8—122no—
402C3⋊C8—121no—
403C3⋊C8—121no—
404C2×C32—21no—
405C2×C32—21no—
406C2×C32—81no—
407C2×C32#38611yescharacteristic
408C2×C32#44311yescharacteristic
409C2×C32#44411yescharacteristic
410C3×D3—42no—
411#41—21no—
412#41—21no—
413#41—21no—
414#41—21no—
415#41—32no—
416#41—32no—
417#41—61no—
418#41—61no—
419C2×Q8—31no—
420C2×Q8D3×Dic311yescharacteristic
421C2×D4—21no—
422C2×D4—31no—
423C2×D4—61no—
424C2×D4D3×Dic311yescharacteristic
425C22×C4—21no—
426C22×C4—61no—
427C22×C4—61no—
428C22×C4C2×D3211yescharacteristic
429Q16—62no—
430SD16—62no—
431SD16—62no—
432D8—62no—
433M16—32no—
434M16—61no—
435M16—184no—
436M16—181no—
437M16—181no—
438C2×C8—31no—
439C2×C8—31no—
440C2×C8—61no—
441C2×C8—61no—
442C2×C8—61no—
443C2×C8—91no—
444C2×C8—91no—
445C2×C8—184no—
446C2×C8—181no—
447C2×C8—181no—
448C2×C8—181no—
449C42—61no—
450C42—61no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—62no—
470C22×C3—121no—
471C22×C3—121no—
472C22×C3#67⋊C411yescharacteristic
473C22×C3#88311yescharacteristic
474C22×C3D4×Dic311yescharacteristic
475C22×C3#93511yescharacteristic
476C22×C3#93811yescharacteristic
477C22×C3#93911yescharacteristic
478C2×D3—22no—
479C2×D3—41no—
480C2×D3—41no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—42no—
486C3×C4—41no—
487C3×C4—41no—
488C3×C4—62no—
489C3×C4—122no—
490C3×C4D3×C22⋊C411yescharacteristic
491C3×C4#88411yescharacteristic
492C3×C4C4×#6711yescharacteristic
493C3×C4D4×Dic311yescharacteristic
494C3×C4#93711yescharacteristic
495C3×C4#93711yescharacteristic
496C3×C4#93911yescharacteristic
497C3×C4C2×#21711yescharacteristic
498Dic3—22no—
499Dic3—42no—
500C32#187611yescharacteristic, complemented, Sylow
501C23—21no—
502C23—61no—
503C23#380511yescharacteristic
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—62no—
523C2×C4—121no—
524C2×C4—121no—
525C2×C4C2×D3×Dic311yescharacteristic
526C2×C4#380411yescharacteristic
527C2×C4D3×#6711yescharacteristic
528C2×C4D3×#6711yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4#381111yescharacteristic
531C8—61no—
532C8—61no—
533C8—62no—
534C8—181no—
535C8—181no—
536C8—361no—
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#482311yescharacteristic
551C2×C3#482411yescharacteristic
552C2×C3#495611yescharacteristic
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#6397011yescharacteristic
567C22#67⋊Dic311yescharacteristic
568C4—41no—
569C4—62no—
570C4—122no—
571C4D3×#21711yescharacteristic
572C4#6397111yescharacteristic
573C4Dic3×#6711yescharacteristic
574C4#6398311yescharacteristic
575C3—21no—
576C3#7039011yescharacteristic, complemented
577C3#7208711yescharacteristic, complemented
578C2—21no—
579C2—21no—
580C2—81no—
581C2—122no—
582C2#1059167511yescharacteristic
583C2#1059167611yescharacteristic
584C2#1059172111yescharacteristic
subgroupG/H
centerC2×C4#3811
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×#63815C2semidirect
3. #10592933C2semidirect
4. C2×C3×#837C2semidirect
5. C2×#63569C2semidirect
6. #10589166C2semidirect
7. #10589155C2semidirect
16. C2×C3×#216C4semidirect
17. C2×C3×#215C4semidirect
18. C2×C3×#214C4semidirect
19. C2×C3×#213C4semidirect
37. C2×#837D3semidirect
105. C2×#216Dic3semidirect
106. C2×#215Dic3semidirect
107. C2×#214Dic3semidirect
108. C2×#213Dic3semidirect
500. C32#1876semidirect
576. C3#70390semidirect
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×#638152
#105929332
C2×C3×#8372
C2×#635692
#105891662
#105891552
#720873
#703903