Finite Group Databasebeta

← #11807936

Subgroups — #11807936

Order 1152.

1365 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63914C211yesmaximal, characteristic
2#10592350C211yesmaximal, characteristic, complemented
3C3×#4665C212yesmaximal, complemented
4#10591381C212yesmaximal, complemented
5#10591381C212yesmaximal, complemented
6#10591376C212yesmaximal, complemented
7#10591363C212yesmaximal, complemented
8#10591363C212yesmaximal, complemented
9#10591229C211yesmaximal, characteristic, complemented
10#74685—32nomaximal
11C22×C3×D12C2212yes—
12C22×C3×C4×D3C2212yes—
13C22×#625C2211yescharacteristic
14C22×#625C2212yes—
15C22×#625C2211yescharacteristic
16C22×D3×Dic3C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×(C2×D3)⋊Dic3C2212yes—
22C2×(C2×D3)⋊Dic3C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24#63914C418yescomplemented
25C32×#95C2211yescharacteristic
26#63658C2212yes—
27#63658C2212yes—
28#63658C2211yescharacteristic
29C3×C3⋊#95C2212yes—
30#63579C2211yescharacteristic
31#63579C2212yes—
32#63579C2211yescharacteristic
33C2×#940—32no—
34C3×#386—32no—
35#5220—32no—
36#5213—32no—
37#5213—32no—
38#4958—32no—
39#4958—32no—
40#4956—32no—
41#4956—32no—
42#4956—32no—
43#4956—32no—
44#4665—32no—
45#4665D312yescomplemented
46#4651—32no—
47#4651—32no—
48#4651—61no—
49C23×C3×D3C2312yes—
50C23×C3×D3C2312yes—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C2×C3×D12—42no—
59C2×C3×D12—42no—
60C2×C3×D12C2×C418yescomplemented
61C2×C3×C4×D3—42no—
62C2×C3×C4×D3—42no—
63C2×C3×C4×D3—42no—
64C2×#625—41no—
65C2×#625—42no—
66C2×#625—41no—
67C2×#625—41no—
68C2×#625—42no—
69C2×#625—41no—
70C2×#625C2×C414yescomplemented
71C2×#625C2×C418yescomplemented
72C2×#625C2×C414yescomplemented
73C2×D3×Dic3—42no—
74C2×D3×Dic3—42no—
75C2×D3×Dic3—42no—
76C4×C3⋊Dic3C2×C414yescomplemented
77C3×(C2×D3)⋊C4—42no—
78C3×(C2×D3)⋊C4—42no—
79C3×(C2×D3)⋊C4—42no—
80(C2×D3)⋊Dic3—42no—
81(C2×D3)⋊Dic3—42no—
82(C2×D3)⋊Dic3—42no—
83#2380—91noSylow
84C22×C3×D4—32no—
85C23×C3×C4—32no—
86C22×#67—32no—
87C22×#67—32no—
88C22×#67—32no—
89C22×#67—32no—
90C23×Dic3—32no—
91C22×D12C2×D312yes—
92C22×C4×D3—32no—
93C22×C4×D3C2×D312yes—
94C2×C3×C22⋊C4—32no—
95C2×C3×C22⋊C4—32no—
96C2×C3×C22⋊C4—32no—
97C2×#217—32no—
98C2×#217—32no—
99C2×#217—32no—
100#940—316no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4C2×D312yes—
105C2×(C2×D3)⋊C4C2×D312yes—
106C2×(C2×D3)⋊C4C2×D312yes—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—61no—
109C3×#95—21no—
110C3×#95—32no—
111C3×#95C2×D312yes—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—62no—
122C3⋊#95—62no—
123C3⋊#95—61no—
124C3⋊#95C2×D312yes—
125C23×C32C2411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—22no—
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×D3C22×C414yes—
139C22×C3×D3C22×C414yes—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C22×C412yes—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3C22×C412yes—
152C2×C3⋊Dic3C22×C412yes—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C3×D12—48no—
160C3×C4×D3—48no—
161#625—44no—
162#625—48no—
163#625—44no—
164D3×Dic3—48no—
165C2×#127—91no—
166#386—32no—
167#386—92no—
168#386—92no—
169#386—92no—
170#386—92no—
171#386—92no—
172#383—91no—
173#383—91no—
174C24×C3—32no—
175C24×C3—32no—
176C23×D3C22×D312yes—
177C23×D3C22×D312yes—
178C2×C3×D4—38no—
179C2×C3×D4—122no—
180C2×C3×D4—122no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—32no—
184C22×C3×C4—32no—
185C22×C3×C4—122no—
186C22×C3×C4—122no—
187C22×C3×C4—122no—
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D312yes—
190C22×C3×C4C22×D312yes—
191C2×#67—38no—
192C2×#67—38no—
193C2×#67—38no—
194C2×#67—38no—
195C2×#67—122no—
196C2×#67—122no—
197C2×#67—122no—
198C2×#67—122no—
199C2×#67—122no—
200C2×#67—122no—
201C2×#67—122no—
202C2×#67—122no—
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—62no—
210C22×Dic3—122no—
211C22×Dic3—122no—
212C22×Dic3—122no—
213C22×Dic3C22×D312yes—
214C22×Dic3C22×D312yes—
215C2×D12—42no—
216C2×D12—42no—
217C2×D12C4×D318yescomplemented
218C2×C4×D3—42no—
219C2×C4×D3—42no—
220C2×C4×D3—42no—
221C2×C4×D3—122no—
222C2×C4×D3—122no—
223C2×C4×D3—122no—
224C3×C22⋊C4—122no—
225C3×C22⋊C4—122no—
226C3×C22⋊C4—122no—
227#217—122no—
228#217—122no—
229#217—122no—
230(C2×D3)⋊C4—42no—
231(C2×D3)⋊C4—42no—
232(C2×D3)⋊C4—42no—
233(C2×D3)⋊C4—122no—
234(C2×D3)⋊C4—122no—
235(C2×D3)⋊C4—122no—
236C4×Dic3—38no—
237C4×Dic3—64no—
238C22×C32C23×C411yescharacteristic
239C22×C32H(5,𝔽2)12yes—
240C22×C32H(5,𝔽2)11yescharacteristic
241C22×C32H(5,𝔽2)12yes—
242C22×C32H(5,𝔽2)11yescharacteristic
243C2×C3×D3—24no—
244C2×C3×D3—24no—
245C2×C3×D3—24no—
246C2×C3×D3—24no—
247C2×C3×D3—24no—
248C2×C3×D3—24no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C32×C4—22no—
258C32×C4—42no—
259C3⋊Dic3—22no—
260C3⋊Dic3—22no—
261C3⋊Dic3—42no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C22×D4—32no—
265C22×D4—91no—
266C22×D4—92no—
267C22×D4—91no—
268C23×C4—32no—
269C23×C4—92no—
270#127—98no—
271C2×C22⋊C4—32no—
272C2×C22⋊C4—32no—
273C2×C22⋊C4—32no—
274C2×C22⋊C4—92no—
275C2×C22⋊C4—92no—
276C2×C22⋊C4—92no—
277C2×C42—91no—
278#95—32no—
279#95—91no—
280#95—92no—
281#95—91no—
282#95—92no—
283#95—92no—
284#95—91no—
285#95D3211yescharacteristic
286C23×C3—21no—
287C23×C3—34no—
288C23×C3—34no—
289C23×C3—62no—
290C23×C3—62no—
291C23×C3—62no—
292C23×C3—62no—
293C23×C3—62no—
294C23×C3—62no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—62no—
299C23×C3—62no—
300C23×C3—62no—
301C23×C3C23×D312yes—
302C22×D3—22no—
303C22×D3—22no—
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—22no—
309C22×D3—22no—
310C22×D3—22no—
311C22×D3—22no—
312C22×D3—22no—
313C22×D3—22no—
314C22×D3C2×C4×D314yes—
315C22×D3C2×C4×D314yes—
316C3×D4—128no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—128no—
337C2×C3×C4C2×C4×D314yes—
338#67—128no—
339#67—128no—
340#67—128no—
341#67—128no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—122no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—122no—
368C2×Dic3—128no—
369D12—48no—
370C4×D3—48no—
371C4×D3—128no—
372C2×C32#51811yescharacteristic
373C2×C32#51811yescharacteristic
374C2×C32#51811yescharacteristic
375C2×C32#56012yes—
376C2×C32#56012yes—
377C3×D3—44no—
378C3×D3—44no—
379C24—32no—
380C24—32no—
381C2×D4—38no—
382C2×D4—94no—
383C2×D4—94no—
384C2×D4—98no—
385C2×D4—122no—
386C2×D4—122no—
387C2×D4—362no—
388C2×D4—362no—
389C2×D4—361no—
390C2×D4—361no—
391C2×D4—361no—
392C2×D4—361no—
393C22×C4—32no—
394C22×C4—32no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—92no—
398C22×C4—122no—
399C22×C4—122no—
400C22×C4—122no—
401C22×C4—362no—
402C22×C4—362no—
403C22×C4—362no—
404C22×C4C2×D3212yes—
405C22×C4C2×D3211yescharacteristic
406C22⋊C4—122no—
407C22⋊C4—122no—
408C22⋊C4—122no—
409C22⋊C4—362no—
410C22⋊C4—362no—
411C22⋊C4—362no—
412C42—94no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—21no—
418C22×C3—64no—
419C22×C3—64no—
420C22×C3—64no—
421C22×C3—64no—
422C22×C3—64no—
423C22×C3—64no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—122no—
431C22×C3—122no—
432C22×C3C22×C4×D312yes—
433C22×C3#100412yes—
434C22×C3#100412yes—
435C22×C3#100412yes—
436C22×C3#100412yes—
437C22×C3#100912yes—
438C22×C3#100912yes—
439C2×D3—24no—
440C2×D3—24no—
441C2×D3—24no—
442C2×D3—24no—
443C2×D3—24no—
444C2×D3—24no—
445C2×D3—42no—
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—42no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—42no—
453C3×C4—24no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—42no—
457C3×C4—82no—
458C3×C4—122no—
459C3×C4—122no—
460Dic3—42no—
461Dic3—42no—
462Dic3—64no—
463Dic3—64no—
464Dic3—122no—
465Dic3—122no—
466Dic3—122no—
467Dic3—122no—
468Dic3—242no—
469C32#238011yescharacteristic, complemented, Sylow
470C23—34no—
471C23—34no—
472C23—62no—
473C23—62no—
474C23—62no—
475C23—62no—
476C23—62no—
477C23—62no—
478C23—62no—
479C23—62no—
480C23—62no—
481C23—62no—
482C23—62no—
483C23—62no—
484C23C22×D3211yescharacteristic
485D4—128no—
486D4—364no—
487D4—364no—
488D4—368no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—92no—
500C2×C4—92no—
501C2×C4—128no—
502C2×C4—182no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—368no—
509C2×C4C4×D3212yes—
510C2×C3—21no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—22no—
514C2×C3—21no—
515C2×C3—124no—
516C2×C3—124no—
517C2×C3#548612yes—
518C2×C3#554512yes—
519C2×C3#554512yes—
520C2×C3#559512yes—
521C2×C3#562012yes—
522C2×C3#562012yes—
523C2×C3#566612yes—
524D3—44no—
525D3—44no—
526C22—64no—
527C22—64no—
528C22—64no—
529C22—64no—
530C22—64no—
531C22—64no—
532C22—122no—
533C22—122no—
534C22—122no—
535C22—122no—
536C22—122no—
537C22—122no—
538C22—122no—
539C22—122no—
540C22C2×C4×D3211yescharacteristic
541C22#6430712yes—
542C22#6431311yescharacteristic
543C22#6431312yes—
544C22#6432011yescharacteristic
545C4—22no—
546C4—42no—
547C4—122no—
548C4—122no—
549C4—182no—
550C4—182no—
551C4—362no—
552C3—21no—
553C3#7468512yescomplemented
554C2—124no—
555C2—124no—
556C2#1059399611yescharacteristic
557C2#1059418111yescharacteristic
558C2#1059423412yes—
559C2#1059460611yescharacteristic
560C2#1059466212yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63914C2
hypercenter#95D32
hypocenterC32#2380
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592350C2semidirect
3. C3×#4665C2semidirect
4. #10591381C2semidirect
5. #10591381C2semidirect
6. #10591376C2semidirect
7. #10591363C2semidirect
8. #10591363C2semidirect
9. #10591229C2semidirect
24. #63914C4semidirect
45. #4665D3semidirect
60. C2×C3×D12C2×C4semidirect
70. C2×#625C2×C4semidirect
71. C2×#625C2×C4semidirect
72. C2×#625C2×C4semidirect
76. C4×C3⋊Dic3C2×C4semidirect
217. C2×D12C4×D3semidirect
469. C32#2380semidirect
553. C3#74685semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
#105923502
C3×#46652
#105913812
#105913762
#105913632
#105912292
#746853