Finite Group Databasebeta

← #11775406

Subgroups — #11775406

Order 1152.

612 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5627C211yesmaximal, characteristic
2#10591295C211yesmaximal, characteristic, complemented
3#10591154C211yesmaximal, characteristic, complemented
4#10589404C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#71709—31nomaximal
9#68337—31nomaximal
10C2×C3×#239C411yescharacteristic, complemented
11C22×C3×C4×D3C2211yescharacteristic
12C32×C22⋊Q8C2211yescharacteristic
13C3×#946C411yescharacteristic, complemented
14C3×#930C2211yescharacteristic
15C3×#895C411yescharacteristic, complemented
16C3×#894—21no—
17C3×#893—21no—
18C3×#892C411yescharacteristic, complemented
19C3×#882—21no—
20C3×#67⋊C4—21no—
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×#3711—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28(C2×D3)⋊(C3⋊C8)—21no—
29C3×#525—31no—
30#5627D311yescharacteristic
31#5212—31no—
32#5207—31no—
33#4726—31no—
34#4667—31no—
35C3×#328—31no—
36#4538—31no—
37#4538—31no—
38#4538—61no—
39#4538D311yescharacteristic, complemented
40#4537—31no—
41#4537—31no—
42#4470—31no—
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8C2×C411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C3×#239—42no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12C2×C411yescharacteristic
55C2×C3×C4×D3—21no—
56C2×C3×C4×D3—42no—
57C2×C3×C4×D3C2×C411yescharacteristic
58C2×C3×C4×D3C2×C411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×C4×D3D411yescharacteristic
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2×C411yescharacteristic
63C32×C22⋊C4—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×C4⋊Dic3C2×C411yescharacteristic
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—42no—
74(C2×D3)⋊Dic3—42no—
75#3711—42no—
76#1513—91noSylow
77C2×C3×#41—31no—
78C23×C3×C4—31no—
79C2×#239Dic311yescharacteristic, complemented
80C22×C4×D3C2×D311yescharacteristic
81C3×#123—61no—
82C3×C22⋊Q8—21no—
83C3×C22⋊Q8—31no—
84C3×C22⋊Q8C2×D311yescharacteristic
85C3×C22⋊Q8C2×D311yescharacteristic
86C3×#121—31no—
87C3×#121—31no—
88C3×#120—61no—
89C3×C4×D4—61no—
90C3×C4×D4—61no—
91C3×#117—31no—
92C2×#217—61no—
93#946Dic311yescharacteristic, complemented
94#930C2×D311yescharacteristic
95C2×(C2×D3)⋊C4—61no—
96C2×C4⋊Dic3—61no—
97C2×Dic3⋊C4—61no—
98C2×#208—61no—
99C2×ΓL(1,𝔽25)—61no—
100#895Dic311yescharacteristic, complemented
101#894—21no—
102#893—21no—
103#892Dic311yescharacteristic, complemented
104#882—21no—
105#67⋊C4—21no—
106C3×C22⋊C8—31no—
107C3×#95—31no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830—31no—
113#830—31no—
114#830—61no—
115#830—61no—
116#830C2×D311yescharacteristic
117(C2×D3)⋊C8—61no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3C22⋊C411yescharacteristic
125C22×C3×D3C22⋊C411yescharacteristic
126C32×Q8—41no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—41no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C3×#67—41no—
136C3×#67—41no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3C22⋊C411yescharacteristic
143C2×C3×Dic3C22⋊C411yescharacteristic
144C3×D12—41no—
145C3×D12—42no—
146C3×D12—42no—
147C3×C4×D3—22no—
148C3×C4×D3—22no—
149C3×C4×D3—41no—
150C3×C4×D3—41no—
151C3×C4×D3—42no—
152C3⋊(C3⋊C8)—41no—
153C3×C3⋊C8—41no—
154#525—31no—
155#407—91no—
156#380—91no—
157#328—31no—
158#328—91no—
159#327—91no—
160#327—91no—
161C24×C3—31no—
162C23×D3#6711yescharacteristic
163C3×#41—122no—
164C2×C3×Q8—21no—
165C2×C3×Q8C4×D311yescharacteristic
166C2×C3×Q8C2×Dic311yescharacteristic
167C2×C3×D4—31no—
168C2×C3×D4—61no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—122no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×#67—21no—
183C22×Dic3—21no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—121no—
187C22×Dic3#6711yescharacteristic
188#239—42no—
189C2×D12—21no—
190C2×D12—21no—
191C2×D12C2×Dic311yescharacteristic
192C2×C4×D3—21no—
193C2×C4×D3—42no—
194C2×C4×D3C2×Dic311yescharacteristic
195C2×C4×D3C2×Dic311yescharacteristic
196C2×C4×D3#6711yescharacteristic
197C2×C4×D3#6711yescharacteristic
198C2×C3×C8—61no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—31no—
203C3×C4⋊C4—41no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4C4×D311yescharacteristic
206C3×C4⋊C4C2×Dic311yescharacteristic
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—41no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C42—61no—
215#217—122no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—21no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—21no—
220(C2×D3)⋊C4—122no—
221C4⋊Dic3—122no—
222C4⋊Dic3C2×Dic311yescharacteristic
223Dic3⋊C4—21no—
224Dic3⋊C4—122no—
225C4×Dic3—21no—
226#208—122no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231ΓL(1,𝔽25)—122no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32C2×C22⋊C411yescharacteristic
235C22×C32AGL(1,ℤ/8)11yescharacteristic
236C22×C32#13711yescharacteristic
237C2×C3×D3—21no—
238C2×C3×D3—21no—
239C2×C3×D3—21no—
240C2×C3×D3—21no—
241C2×C3×D3—21no—
242C2×C3×D3—21no—
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C2×C3×D3—41no—
246C2×C3×D3—41no—
247C2×C3×D3—41no—
248C32×C4—21no—
249C32×C4—21no—
250C32×C4—41no—
251C32×C4—41no—
252C3⋊Dic3—81no—
253C3×Dic3—21no—
254C3×Dic3—41no—
255C3×Dic3—81no—
256C3×Dic3#9912yes—
257C2×#41—31no—
258C23×C4—31no—
259C2×M16—181no—
260#123—61no—
261C22⋊Q8—31no—
262C22⋊Q8D3211yescharacteristic
263#121—31no—
264#121—31no—
265#120—61no—
266C4×D4—61no—
267C4×D4—61no—
268#117—31no—
269C2×C4⋊C4—181no—
270C2×C22⋊C4—181no—
271C22⋊C8—31no—
272C22⋊C8—91no—
273C22⋊C8—181no—
274#95—31no—
275#95—91no—
276C23×C3—21no—
277C23×C3—31no—
278C23×C3—31no—
279C23×C3—61no—
280C23×C3—61no—
281C23×C3—61no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3D3×D411yescharacteristic
285C23×C3C2×#6711yescharacteristic
286C22×D3—21no—
287C22×D3—21no—
288C22×D3—21no—
289C22×D3—41no—
290C22×D3—41no—
291C22×D3#21711yescharacteristic
292C22×D3#21711yescharacteristic
293C3×Q8—41no—
294C3×Q8—41no—
295C3×Q8—81no—
296C3×D4—121no—
297C3×D4—122no—
298C3×D4—122no—
299C3×D4—121no—
300C3×D4—121no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—31no—
308C2×C3×C4—31no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—61no—
317C2×C3×C4—81no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—122no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4C2×C4×D311yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4C22×Dic311yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328#67—41no—
329#67—41no—
330C2×Dic3—22no—
331C2×Dic3—21no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—122no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—241no—
343C2×Dic3—241no—
344C2×Dic3#21711yescharacteristic
345C2×Dic3#21711yescharacteristic
346D12—41no—
347D12—42no—
348D12—42no—
349C4×D3—22no—
350C4×D3—22no—
351C4×D3—41no—
352C4×D3—41no—
353C4×D3—42no—
354C3×C8—121no—
355C3⋊C8—41no—
356C3⋊C8—121no—
357C3⋊C8—121no—
358C3⋊C8—241no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32C2×#9911yescharacteristic
362C2×C32#41711yescharacteristic
363C2×C32#42111yescharacteristic
364C3×D3—41no—
365C3×D3—41no—
366C3×D3—81no—
367C24—31no—
368#41—122no—
369C2×Q8D3×Dic311yescharacteristic
370C2×D4—31no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—61no—
374C22×C4—31no—
375C22×C4—31no—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—31no—
379C22×C4—61no—
380C22×C4—61no—
381C22×C4—122no—
382C22×C4—181no—
383C22×C4C2×D3211yescharacteristic
384M16—362no—
385C2×C8—61no—
386C2×C8—181no—
387C4⋊C4—21no—
388C4⋊C4—31no—
389C4⋊C4—61no—
390C4⋊C4—362no—
391C4⋊C4D3×Dic311yescharacteristic
392C22⋊C4—21no—
393C22⋊C4—61no—
394C22⋊C4—61no—
395C22⋊C4—61no—
396C22⋊C4—61no—
397C22⋊C4—362no—
398C42—61no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—61no—
409C22×C3—61no—
410C22×C3—61no—
411C22×C3—61no—
412C22×C3—61no—
413C22×C3—61no—
414C22×C3—122no—
415C22×C3—122no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3D3×C22⋊C411yescharacteristic
420C22×C3#91411yescharacteristic
421C22×C3#91811yescharacteristic
422C22×C3#94911yescharacteristic
423C22×C3#95111yescharacteristic
424C22×C3C2×#21711yescharacteristic
425C2×D3—21no—
426C2×D3—21no—
427C2×D3—21no—
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—21no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—32no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—61no—
448C3×C4—81no—
449C3×C4—81no—
450C3×C4—121no—
451C3×C4—241no—
452Dic3—21no—
453Dic3—41no—
454Dic3—81no—
455Dic3—241no—
456Dic3—241no—
457Dic3—242no—
458Dic3#83412yes—
459C32#151311yescharacteristic, complemented, Sylow
460C23—31no—
461C23—31no—
462C23—61no—
463C23—61no—
464C23—61no—
465C23—121no—
466C23—121no—
467C23D3×#6711yescharacteristic
468Q8—41no—
469D4—121no—
470D4—122no—
471D4—122no—
472D4—121no—
473D4—121no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—31no—
477C2×C4—31no—
478C2×C4—41no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—61no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—122no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—361no—
490C2×C4—361no—
491C2×C4—361no—
492C2×C4C2×D3×Dic311yescharacteristic
493C2×C4D3×#6711yescharacteristic
494C8—121no—
495C8—361no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—41no—
504C2×C3—41no—
505C2×C3—121no—
506C2×C3—121no—
507C2×C3—241no—
508C2×C3D3×#9911yescharacteristic
509C2×C3#480311yescharacteristic
510C2×C3#482111yescharacteristic
511C2×C3C2×#83411yescharacteristic
512C2×C3#523211yescharacteristic
513C2×C3#523611yescharacteristic
514D3—41no—
515D3—41no—
516D3—81no—
517C22—21no—
518C22—21no—
519C22—61no—
520C22—61no—
521C22—61no—
522C22—61no—
523C22—61no—
524C22—61no—
525C22—122no—
526C22—122no—
527C22—121no—
528C22—121no—
529C22—121no—
530C22#6393911yescharacteristic
531C22#6394311yescharacteristic
532C22D3×#21711yescharacteristic
533C4—21no—
534C4—21no—
535C4—32no—
536C4—41no—
537C4—41no—
538C4—61no—
539C4—121no—
540C4—241no—
541C4—721no—
542C3—21no—
543C3#6833711yescharacteristic, complemented
544C3#7170911yescharacteristic, complemented
545C2—21no—
546C2—21no—
547C2—121no—
548C2—121no—
549C2—241no—
550C2D3×#83411yescharacteristic
551C2#1059155011yescharacteristic
552C2#1059167011yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5627C2
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1513
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10591295C2semidirect
3. #10591154C2semidirect
4. #10589404C2semidirect
5. C3×#4538C2semidirect
6. #10589150C2semidirect
7. #10589149C2semidirect
10. C2×C3×#239C4semidirect
13. C3×#946C4semidirect
15. C3×#895C4semidirect
18. C3×#892C4semidirect
39. #4538D3semidirect
79. C2×#239Dic3semidirect
93. #946Dic3semidirect
100. #895Dic3semidirect
103. #892Dic3semidirect
459. C32#1513semidirect
543. C3#68337semidirect
544. C3#71709semidirect

Maximal subgroups

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

subgroupindex
C3×#56272
#105912952
#105911542
#105894042
C3×#45382
#105891502
#105891492
#717093
#683373