Finite Group Databasebeta

← #11859116

Subgroups — #11859116

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic
2C3×#5000C212yesmaximal, complemented
3#10591153C212yesmaximal
4#10591066C211yesmaximal, characteristic, complemented
5#10591061C211yesmaximal, characteristic, complemented
6#10590340C211yesmaximal, characteristic, complemented
7#10590331C211yesmaximal, characteristic, complemented
8#10590321C212yesmaximal, complemented
9#10590299C211yesmaximal, characteristic, complemented
10#10590297C211yesmaximal, characteristic, complemented
11#10590257C212yesmaximal, complemented
12#79375—32nomaximal
13C2×#3828C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64102C411yescharacteristic
17#64102C411yescharacteristic
18#64096C411yescharacteristic
19#64096C411yescharacteristic
20#64090C411yescharacteristic
21#64090C411yescharacteristic
22#64090C411yescharacteristic
23#64090C411yescharacteristic
24#64081C2211yescharacteristic
25#64081C2211yescharacteristic
26C42×C3⋊D3C2211yescharacteristic
27C42×C3⋊D3C2211yescharacteristic
28C2×#3712C2212yes—
29C2×#3710C2212yes—
30C3×#830C2212yes—
31C3×#830C2212yes—
32C3×C4⋊(C3⋊C8)C2212yes—
33C3×C4⋊(C3⋊C8)C2212yes—
34C3×#803C2212yes—
35C3×C4×C3⋊C8C2212yes—
36#63572C2211yescharacteristic
37#63572C2211yescharacteristic
38#63572C2211yescharacteristic
39#63572C2211yescharacteristic
40#63557C2212yes—
41#63557C2212yes—
42#63555C2212yes—
43#63553C2212yes—
44#5522—32no—
45#5522—61no—
46C3×#433—32no—
47#5000D312yescomplemented
48#4840—32no—
49#4840—32no—
50#4837—32no—
51D3×C4⋊C8—32no—
52#4727—32no—
53#4727—32no—
54#4719—32no—
55#4718—32no—
56#4708—32no—
57#4705—32no—
58#4689—32no—
59#4685—32no—
60C22×C32×C4C2311yescharacteristic
61C2×#638C2×C411yescharacteristic
62C2×#638C2×C411yescharacteristic
63C22×C3⋊Dic3C2×C411yescharacteristic
64C22×C3⋊Dic3C2×C411yescharacteristic
65#3828—22no—
66#3828—22no—
67C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
68C2×C4×C3⋊D3C2×C411yescharacteristic
69C2×C4×C3⋊D3C2×C411yescharacteristic
70C2×C4×C3⋊D3C2×C411yescharacteristic
71C2×C4×C3⋊D3C2×C411yescharacteristic
72C2×C4×C3⋊D3C2311yescharacteristic
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×#634C2×C411yescharacteristic
75C32×C4⋊C4C2×C411yescharacteristic
76C32×C4⋊C4C2×C411yescharacteristic
77C32×C22⋊C4C2×C411yescharacteristic
78C32×C22⋊C4C2×C411yescharacteristic
79C32×C42C2311yescharacteristic
80C32×C42C2311yescharacteristic
81#3752C2×C411yescharacteristic
82#3752C2×C411yescharacteristic
83#3752C2×C411yescharacteristic
84#3752C2×C411yescharacteristic
85#3750C2×C411yescharacteristic
86#3750C2×C411yescharacteristic
87#3750C2×C411yescharacteristic
88#3750C2×C411yescharacteristic
89C4×C3⋊Dic3C2×C411yescharacteristic
90C4×C3⋊Dic3C2×C411yescharacteristic
91C4×C3⋊Dic3C2×C411yescharacteristic
92C4×C3⋊Dic3C2×C411yescharacteristic
93C4×C3⋊Dic3C2×C411yescharacteristic
94C4×C3⋊Dic3C2×C411yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2312yes—
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2312yes—
101#3712—24no—
102#3710—24no—
103#2925—91noSylow
104C2×#235—32no—
105C2×#235—61no—
106C3×#117—21no—
107C3×#117C2×D312yes—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—61no—
110C2×ΓL(1,𝔽25)—32no—
111C2×ΓL(1,𝔽25)—32no—
112C2×D3×C8—32no—
113C2×D3×C8—32no—
114#893—32no—
115#893—32no—
116#893—61no—
117#893—61no—
118#887—32no—
119#887—32no—
120#887—61no—
121#887—61no—
122#67⋊C4—32no—
123#67⋊C4—32no—
124#67⋊C4—32no—
125#67⋊C4—32no—
126#67⋊C4—61no—
127#67⋊C4—61no—
128#67⋊C4—61no—
129#67⋊C4—61no—
130#872—32no—
131#872—32no—
132#872—61no—
133#872—61no—
134C42×D3—32no—
135C42×D3—32no—
136C42×D3—61no—
137C42×D3—61no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8—32no—
140C3×C22⋊C8—32no—
141C3×C22⋊C8—32no—
142C3×#97—32no—
143C3×C4×C8—32no—
144#830C2×D312yes—
145#830C2×D312yes—
146(C2×D3)⋊C8—32no—
147(C2×D3)⋊C8—32no—
148(C2×D3)⋊C8—32no—
149(C2×D3)⋊C8—32no—
150#815—32no—
151#815—32no—
152Dic3⋊C8—32no—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155Dic3⋊C8—32no—
156C8×Dic3—32no—
157C8×Dic3—32no—
158C4⋊(C3⋊C8)C2×D312yes—
159C4⋊(C3⋊C8)C2×D312yes—
160#803C2×D312yes—
161C4×C3⋊C8C2×D312yes—
162C23×C32C22×C411yescharacteristic
163C22×C3⋊D3C22×C411yescharacteristic
164C22×C3⋊D3C22×C411yescharacteristic
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4C22×C411yescharacteristic
169C2×C32×C4C22×C411yescharacteristic
170C2×C32×C4C22×C411yescharacteristic
171C2×C32×C4C22×C411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173#638—22no—
174#638—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—41no—
177C2×C3⋊Dic3C22×C411yescharacteristic
178C2×C3⋊Dic3C22×C411yescharacteristic
179C2×C3⋊Dic3C22×C411yescharacteristic
180C2×C3⋊Dic3C22×C411yescharacteristic
181C2×C3⋊Dic3C22×C411yescharacteristic
182C2×C3⋊Dic3C22×C411yescharacteristic
183C4⋊(C3⋊D3)—22no—
184C4×C3⋊D3—21no—
185C4×C3⋊D3—21no—
186C4×C3⋊D3—22no—
187C4×C3⋊D3—22no—
188C4×C3⋊D3—41no—
189C4×C3⋊D3—41no—
190C4×C3⋊D3#4112yes—
191C4×C3⋊D3#4112yes—
192#634—22no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—22no—
195C3×C3⋊C8—22no—
196C3×C3⋊C8—22no—
197C4×#41—91no—
198#433—32no—
199#433—92no—
200#432—91no—
201#432—91no—
202#431—91no—
203#431—91no—
204#423—91no—
205C2×C4⋊C8—91no—
206#408—92no—
207#405—92no—
208C22×C3×C4—21no—
209C22×C3×C4C22×D312yes—
210C2×#67—32no—
211C2×#67—32no—
212C2×#67—61no—
213C2×#67—61no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218#235—64no—
219#235—64no—
220#235—64no—
221#235—64no—
222C2×D12—32no—
223C2×D12—61no—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3—32no—
227C2×C4×D3—32no—
228C2×C4×D3—32no—
229C2×C4×D3—32no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×Dic6—32no—
237C2×Dic6—61no—
238C2×C3×C8—32no—
239C2×C3×C8—32no—
240C2×C3×C8—32no—
241C2×C3×C8—32no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4C4×D312yes—
245C3×C4⋊C4C4×D312yes—
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4C4×D312yes—
249C3×C22⋊C4C4×D312yes—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42C22×D312yes—
253C3×C42C22×D312yes—
254(C2×D3)⋊C4—32no—
255(C2×D3)⋊C4—32no—
256(C2×D3)⋊C4—32no—
257(C2×D3)⋊C4—32no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—61no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262Dic3⋊C4—32no—
263Dic3⋊C4—32no—
264Dic3⋊C4—32no—
265Dic3⋊C4—32no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270C4×Dic3—32no—
271C4×Dic3—32no—
272C4×Dic3—32no—
273C4×Dic3—32no—
274C4×Dic3—32no—
275C4×Dic3—32no—
276C4×Dic3—32no—
277C4×Dic3—32no—
278C4×Dic3—61no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C2×C3⋊C8C22×D312yes—
287C2×C3⋊C8C22×D312yes—
288C2×C3⋊C8C22×D312yes—
289C2×C3⋊C8C22×D312yes—
290ΓL(1,𝔽25)—64no—
291ΓL(1,𝔽25)—64no—
292D3×C8—64no—
293D3×C8—64no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32C23×C411yescharacteristic
298C2×C3⋊D3—21no—
299C2×C3⋊D3—21no—
300C2×C3⋊D3—21no—
301C2×C3⋊D3—21no—
302C2×C3⋊D3—21no—
303C2×C3⋊D3#11712yes—
304C32×C4—21no—
305C32×C4—21no—
306C32×C4—21no—
307C32×C4—21no—
308C32×C4—21no—
309C32×C4C2×#4111yescharacteristic
310C32×C4C2×#4111yescharacteristic
311C3⋊Dic3—21no—
312C3⋊Dic3—21no—
313C3⋊Dic3—21no—
314C3⋊Dic3—21no—
315C3⋊Dic3#11712yes—
316C3⋊Dic3#13112yes—
317C2×#41—91no—
318C2×M16—92no—
319C22×C8—92no—
320C4×Q8—91no—
321C4×Q8—91no—
322C4×D4—91no—
323C4×D4—91no—
324C4×D4—91no—
325C4×D4—91no—
326C4×D4—91no—
327C4×D4—91no—
328#117—91no—
329#117—91no—
330#117D3211yescharacteristic
331C2×C42—91no—
332C2×C42—91no—
333C2×C42—91no—
334C4⋊C8—32no—
335C4⋊C8—32no—
336C4⋊C8—91no—
337C4⋊C8—91no—
338C4⋊C8—91no—
339C4⋊C8—91no—
340C22⋊C8—32no—
341C22⋊C8—32no—
342C22⋊C8—92no—
343C22⋊C8—92no—
344#97—32no—
345#97—92no—
346C4×C8—32no—
347C4×C8—92no—
348C23×C3—21no—
349C23×C3C2×C4×D312yes—
350C22×D3—32no—
351C22×D3—32no—
352C22×D3—61no—
353C22×D3—61no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4C2×C4×D312yes—
365C2×C3×C4C2×C4×D312yes—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4C2×C4×D312yes—
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4C23×D312yes—
370#67—64no—
371#67—64no—
372#67—64no—
373#67—64no—
374C2×Dic3—32no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—64no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3—122no—
390D12—64no—
391D12—64no—
392C4×D3—34no—
393C4×D3—34no—
394C4×D3—62no—
395C4×D3—62no—
396C4×D3—64no—
397C4×D3—64no—
398C4×D3—62no—
399C4×D3—62no—
400C4×D3—62no—
401C4×D3—62no—
402C4×D3—122no—
403C4×D3—122no—
404C4×D3—122no—
405C4×D3—122no—
406C4×D3—122no—
407C4×D3—122no—
408Dic6—64no—
409Dic6—64no—
410C3×C8—62no—
411C3×C8—62no—
412C3×C8—62no—
413C3×C8—62no—
414C3⋊C8—22no—
415C3⋊C8—22no—
416C3⋊C8—22no—
417C3⋊C8—22no—
418C2×C32—41no—
419C2×C32C2×#11711yescharacteristic
420C2×C32C2×#13111yescharacteristic
421C2×C32#56811yescharacteristic
422C3⋊D3—22no—
423C3⋊D3—41no—
424#41—182no—
425#41—182no—
426C2×Q8—91no—
427C2×D4—91no—
428C2×D4—91no—
429C2×D4—91no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—91no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4C2×D3211yescharacteristic
439M16—184no—
440C2×C8—32no—
441C2×C8—32no—
442C2×C8—32no—
443C2×C8—32no—
444C2×C8—184no—
445C4⋊C4—91no—
446C4⋊C4—91no—
447C4⋊C4—91no—
448C4⋊C4—91no—
449C4⋊C4#62411yescharacteristic
450C4⋊C4#62411yescharacteristic
451C22⋊C4—91no—
452C22⋊C4—91no—
453C22⋊C4—91no—
454C22⋊C4—91no—
455C22⋊C4#62411yescharacteristic
456C22⋊C4#62411yescharacteristic
457C42—91no—
458C42—91no—
459C42—91no—
460C42—91no—
461C42—91no—
462C42—91no—
463C42—91no—
464C42—91no—
465C42C2×D3211yescharacteristic
466C42C2×D3211yescharacteristic
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3C22×C4×D312yes—
475C2×D3—34no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—62no—
483C2×D3—121no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—22no—
490C3×C4—22no—
491C3×C4—22no—
492C3×C4—22no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—41no—
499C3×C4D3×#4112yes—
500C3×C4D3×#4112yes—
501Dic3—34no—
502Dic3—34no—
503Dic3—62no—
504Dic3—62no—
505Dic3—62no—
506Dic3—62no—
507Dic3—62no—
508Dic3—62no—
509Dic3—62no—
510Dic3—62no—
511Dic3—121no—
512Dic3—121no—
513C32#292511yescharacteristic, complemented, Sylow
514C23—91no—
515C23—91no—
516C23C2×#62411yescharacteristic
517Q8—182no—
518D4—182no—
519D4—182no—
520D4—182no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—91no—
524C2×C4—91no—
525C2×C4—92no—
526C2×C4—92no—
527C2×C4—91no—
528C2×C4—91no—
529C2×C4—91no—
530C2×C4—91no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—361no—
537C2×C4—361no—
538C2×C4—361no—
539C2×C4C2×#62411yescharacteristic
540C2×C4C2×#62411yescharacteristic
541C2×C4C2×#62411yescharacteristic
542C2×C4C2×#62411yescharacteristic
543C2×C4C2×#62411yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—62no—
546C8—62no—
547C8—62no—
548C8—62no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—42no—
553C2×C3—42no—
554C2×C3D3×#11712yes—
555C2×C3D3×#13112yes—
556C2×C3#575012yes—
557D3—64no—
558D3—122no—
559D3—122no—
560D3—122no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—92no—
565C22—181no—
566C22—181no—
567C22—181no—
568C22—181no—
569C22—181no—
570C22C22×#62411yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—92no—
577C4—92no—
578C4—181no—
579C4—181no—
580C4—181no—
581C4—181no—
582C4#6430611yescharacteristic
583C4#6430611yescharacteristic
584C3—21no—
585C3#7937512yescomplemented
586C2—41no—
587C2—182no—
588C2—361no—
589C2#1059496911yescharacteristic
590C2#1059544211yescharacteristic
591C2#1059544311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#117C22
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5000C2semidirect
4. #10591066C2semidirect
5. #10591061C2semidirect
6. #10590340C2semidirect
7. #10590331C2semidirect
8. #10590321C2semidirect
9. #10590299C2semidirect
10. #10590297C2semidirect
11. #10590257C2semidirect
47. #5000D3semidirect
513. C32#2925semidirect
585. C3#79375semidirect

Maximal subgroups

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

subgroupindex
#105959932
C3×#50002
#105911532
#105910662
#105910612
#105903402
#105903312
#105903212
#105902992
#105902972
#105902572
#793753