Finite Group Databasebeta

← #11803862

Subgroups — #11803862

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63914C211yesmaximal, characteristic
2C2×#63879C212yesmaximal, complemented
3#10592349C211yesmaximal, characteristic, complemented
4C3×#4665C212yesmaximal, complemented
5#10591386C212yesmaximal, complemented
6#10591381C212yesmaximal, complemented
7#10591376C212yesmaximal, complemented
8#10591363C212yesmaximal, complemented
9#10591252C211yesmaximal, characteristic, complemented
10#74667—32nomaximal
11C22×C3×D12C2212yes—
12C22×C3×C4×D3C2212yes—
13C22×#625C2212yes—
14C22×#625C2211yescharacteristic
15C22×#625C2211yescharacteristic
16C22×D3×Dic3C2212yes—
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×(C2×D3)⋊Dic3C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×Dic32C2211yescharacteristic
26C2×Dic32C2211yescharacteristic
27#63914C418yescomplemented
28#63879—28no—
29C32×#95C2211yescharacteristic
30#63658C2212yes—
31#63658C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34C2×#940—32no—
35C2×C4×#67—32no—
36C2×#67⋊C4—32no—
37C3×#386—32no—
38#5220—32no—
39#5213—32no—
40#4958—32no—
41#4957—32no—
42#4957—32no—
43#4956—32no—
44#4956—32no—
45#4665—32no—
46#4665D312yescomplemented
47#4650—32no—
48#4650—61no—
49#4648—32no—
50C23×C3×D3C2312yes—
51C23×C3×D3C2312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C2×C3×D12—42no—
60C2×C3×D12—42no—
61C2×C3×D12C2×C418yescomplemented
62C2×C3×C4×D3—24no—
63C2×C3×C4×D3—42no—
64C2×C3×C4×D3—42no—
65C2×#625—24no—
66C2×#625—24no—
67C2×#625—42no—
68C2×#625—42no—
69C2×#625C2×C418yescomplemented
70C2×#625C2×C414yescomplemented
71C2×#625C2×C414yescomplemented
72C2×D3×Dic3—24no—
73C2×D3×Dic3—42no—
74C2×D3×Dic3—42no—
75#3750—24no—
76C4×C3⋊Dic3C2×C414yescomplemented
77C3×(C2×D3)⋊C4—24no—
78C3×(C2×D3)⋊C4—42no—
79C3×(C2×D3)⋊C4—42no—
80(C2×D3)⋊Dic3—24no—
81(C2×D3)⋊Dic3—42no—
82(C2×D3)⋊Dic3—42no—
83Dic32—22no—
84Dic32D414yescomplemented
85#2328—91noSylow
86C22×C3×D4—32no—
87C23×C3×C4—32no—
88C22×#67—32no—
89C22×#67—32no—
90C22×#67—32no—
91C22×#67—32no—
92C23×Dic3—32no—
93C22×D12C2×D312yes—
94C22×C4×D3—32no—
95C22×C4×D3C2×D312yes—
96C2×C3×C22⋊C4—32no—
97C2×C3×C22⋊C4—32no—
98C2×C3×C22⋊C4—32no—
99C2×#217—32no—
100C2×#217—32no—
101C2×#217—32no—
102#940—316no—
103C4×#67—68no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—32no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4C2×D312yes—
108C2×(C2×D3)⋊C4C2×D312yes—
109C2×(C2×D3)⋊C4C2×D312yes—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—62no—
113C2×C4×Dic3—32no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3—32no—
116C2×C4×Dic3—61no—
117#67⋊C4—68no—
118C3×#95—21no—
119C3×#95—32no—
120C3×#95C2×D312yes—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—62no—
127C3⋊#95—61no—
128C3⋊#95C2×D312yes—
129C23×C32C2411yescharacteristic
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—22no—
138C22×C3×D3—22no—
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3C22×C414yes—
143C22×C3×D3C22×C414yes—
144C2×C32×C4—22no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4C22×C412yes—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3C22×C412yes—
154C2×C3⋊Dic3C22×C412yes—
155C2×C3⋊Dic3C2×D412yes—
156C2×C3⋊Dic3#4112yes—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3C2×D414yes—
163C3×D12—48no—
164C3×C4×D3—48no—
165#625—216no—
166#625—44no—
167#625—44no—
168D3×Dic3—48no—
169C2×#127—91no—
170C2×C4×D4—92no—
171#390—92no—
172#386—32no—
173#386—92no—
174#386—92no—
175#386—92no—
176#382—91no—
177#376—91no—
178C24×C3—32no—
179C24×C3—32no—
180C23×D3C22×D312yes—
181C23×D3C22×D312yes—
182C2×C3×D4—38no—
183C2×C3×D4—122no—
184C2×C3×D4—122no—
185C22×C3×C4—21no—
186C22×C3×C4—22no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4—64no—
190C22×C3×C4—122no—
191C22×C3×C4—122no—
192C22×C3×C4C22×D312yes—
193C22×C3×C4C22×D312yes—
194C22×C3×C4C22×D312yes—
195C2×#67—38no—
196C2×#67—38no—
197C2×#67—38no—
198C2×#67—38no—
199C2×#67—64no—
200C2×#67—64no—
201C2×#67—64no—
202C2×#67—64no—
203C2×#67—122no—
204C2×#67—122no—
205C2×#67—122no—
206C2×#67—122no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—32no—
210C22×Dic3—32no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—62no—
214C22×Dic3—64no—
215C22×Dic3—122no—
216C22×Dic3—122no—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C2×D12—42no—
220C2×D12—42no—
221C2×D12C4×D318yescomplemented
222C2×C4×D3—24no—
223C2×C4×D3—42no—
224C2×C4×D3—42no—
225C2×C4×D3—64no—
226C2×C4×D3—122no—
227C2×C4×D3—122no—
228C3×C22⋊C4—64no—
229C3×C22⋊C4—122no—
230C3×C22⋊C4—122no—
231#217—64no—
232#217—122no—
233#217—122no—
234(C2×D3)⋊C4—24no—
235(C2×D3)⋊C4—42no—
236(C2×D3)⋊C4—42no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—122no—
239(C2×D3)⋊C4—122no—
240Dic3⋊C4—64no—
241Dic3⋊C4—64no—
242Dic3⋊C4—124no—
243C4×Dic3—38no—
244C4×Dic3—38no—
245C4×Dic3—64no—
246C4×Dic3—64no—
247C22×C32C23×C411yescharacteristic
248C22×C32C22×D411yescharacteristic
249C22×C32C2×#4111yescharacteristic
250C22×C32H(5,𝔽2)12yes—
251C22×C32H(5,𝔽2)12yes—
252C2×C3×D3—24no—
253C2×C3×D3—24no—
254C2×C3×D3—24no—
255C2×C3×D3—24no—
256C2×C3×D3—24no—
257C2×C3×D3—24no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C32×C4—22no—
267C32×C4—42no—
268C3⋊Dic3—22no—
269C3⋊Dic3—42no—
270C3⋊Dic3C4×D414yes—
271C3×Dic3—24no—
272C3×Dic3—42no—
273C22×D4—32no—
274C22×D4—92no—
275C22×D4—91no—
276C22×D4—91no—
277C23×C4—32no—
278C23×C4—92no—
279#127—98no—
280C4×D4—188no—
281C2×C4⋊C4—92no—
282C2×C22⋊C4—32no—
283C2×C22⋊C4—32no—
284C2×C22⋊C4—32no—
285C2×C22⋊C4—92no—
286C2×C22⋊C4—92no—
287C2×C22⋊C4—92no—
288C2×C42—91no—
289C2×C42—91no—
290C2×C42—91no—
291#95—32no—
292#95—92no—
293#95—92no—
294#95—91no—
295#95D3211yescharacteristic
296C23×C3—21no—
297C23×C3—34no—
298C23×C3—34no—
299C23×C3—62no—
300C23×C3—62no—
301C23×C3—62no—
302C23×C3—62no—
303C23×C3—62no—
304C23×C3—62no—
305C23×C3—62no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3—62no—
309C23×C3—62no—
310C23×C3—62no—
311C23×C3C23×D312yes—
312C22×D3—22no—
313C22×D3—22no—
314C22×D3—22no—
315C22×D3—22no—
316C22×D3—22no—
317C22×D3—22no—
318C22×D3—22no—
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—22no—
322C22×D3—22no—
323C22×D3—22no—
324C22×D3C2×C4×D314yes—
325C22×D3C2×C4×D314yes—
326C3×D4—128no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—34no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—128no—
347C2×C3×C4C2×C4×D314yes—
348#67—616no—
349#67—616no—
350#67—128no—
351#67—128no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—34no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—122no—
374C2×Dic3—122no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—128no—
378C2×Dic3D3×D414yes—
379D12—48no—
380C4×D3—48no—
381C4×D3—128no—
382C2×C32C2×C4×D411yescharacteristic
383C2×C32#51811yescharacteristic
384C2×C32#51811yescharacteristic
385C2×C32#53512yes—
386C2×C32#54012yes—
387C3×D3—44no—
388C3×D3—44no—
389C24—32no—
390C24—32no—
391C2×D4—38no—
392C2×D4—98no—
393C2×D4—94no—
394C2×D4—94no—
395C2×D4—122no—
396C2×D4—122no—
397C2×D4—184no—
398C2×D4—184no—
399C2×D4—362no—
400C2×D4—362no—
401C22×C4—32no—
402C22×C4—32no—
403C22×C4—64no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—92no—
407C22×C4—122no—
408C22×C4—122no—
409C22×C4—184no—
410C22×C4—362no—
411C22×C4—362no—
412C22×C4C2×D3212yes—
413C22×C4C2×D3211yescharacteristic
414C4⋊C4—184no—
415C22⋊C4—64no—
416C22⋊C4—122no—
417C22⋊C4—122no—
418C22⋊C4—184no—
419C22⋊C4—362no—
420C22⋊C4—362no—
421C42—94no—
422C42—94no—
423C42—182no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—22no—
428C22×C3—21no—
429C22×C3—64no—
430C22×C3—64no—
431C22×C3—64no—
432C22×C3—64no—
433C22×C3—64no—
434C22×C3—64no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3C22×C4×D312yes—
444C22×C3C2×D3×D412yes—
445C22×C3#100412yes—
446C22×C3#100412yes—
447C22×C3#100412yes—
448C22×C3D3×#4112yes—
449C22×C3#100912yes—
450C2×D3—24no—
451C2×D3—24no—
452C2×D3—24no—
453C2×D3—24no—
454C2×D3—24no—
455C2×D3—24no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—42no—
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—42no—
464C3×C4—24no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—64no—
469C3×C4—82no—
470C3×C4—122no—
471Dic3—24no—
472Dic3—38no—
473Dic3—42no—
474Dic3—64no—
475Dic3—64no—
476Dic3—122no—
477Dic3—122no—
478Dic3—122no—
479Dic3—242no—
480C32#232811yescharacteristic, complemented, Sylow
481C23—34no—
482C23—34no—
483C23—62no—
484C23—62no—
485C23—62no—
486C23—62no—
487C23—62no—
488C23—62no—
489C23—62no—
490C23—62no—
491C23—62no—
492C23—62no—
493C23—62no—
494C23—62no—
495C23C22×D3211yescharacteristic
496D4—128no—
497D4—1816no—
498D4—364no—
499D4—364no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—34no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—92no—
511C2×C4—92no—
512C2×C4—92no—
513C2×C4—92no—
514C2×C4—128no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—182no—
519C2×C4—368no—
520C2×C4C4×D3212yes—
521C2×C3—22no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—22no—
526C2×C3—124no—
527C2×C3—124no—
528C2×C3#548612yes—
529C2×C3C4×D3×D412yes—
530C2×C3#554512yes—
531C2×C3#559212yes—
532C2×C3#560712yes—
533C2×C3#561512yes—
534C2×C3#566312yes—
535D3—44no—
536D3—44no—
537C22—64no—
538C22—64no—
539C22—64no—
540C22—64no—
541C22—64no—
542C22—64no—
543C22—122no—
544C22—122no—
545C22—122no—
546C22—122no—
547C22—122no—
548C22—122no—
549C22—122no—
550C22—122no—
551C22C2×C4×D3211yescharacteristic
552C22#6430712yes—
553C22D32×D411yescharacteristic
554C22#6431312yes—
555C22#6431911yescharacteristic
556C4—22no—
557C4—42no—
558C4—64no—
559C4—94no—
560C4—122no—
561C4—182no—
562C4—362no—
563C3—21no—
564C3#7466712yescomplemented
565C2—124no—
566C2—124no—
567C2#1059399611yescharacteristic
568C2#1059418111yescharacteristic
569C2#1059426912yes—
570C2#1059458012yes—
571C2#1059460511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63914C2
hypercenter#95D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63879C2semidirect
3. #10592349C2semidirect
4. C3×#4665C2semidirect
5. #10591386C2semidirect
6. #10591381C2semidirect
7. #10591376C2semidirect
8. #10591363C2semidirect
9. #10591252C2semidirect
27. #63914C4semidirect
46. #4665D3semidirect
61. C2×C3×D12C2×C4semidirect
69. C2×#625C2×C4semidirect
70. C2×#625C2×C4semidirect
71. C2×#625C2×C4semidirect
76. C4×C3⋊Dic3C2×C4semidirect
84. Dic32D4semidirect
221. C2×D12C4×D3semidirect
480. C32#2328semidirect
564. C3#74667semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
C2×#638792
#105923492
C3×#46652
#105913862
#105913812
#105913762
#105913632
#105912522
#746673