Finite Group Databasebeta

← #11807941

Subgroups — #11807941

Order 1152.

1439 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63979C211yesmaximal, characteristic
2#10592912C211yesmaximal, characteristic, complemented
3C3×#5213C212yesmaximal, complemented
4#10591722C211yesmaximal, characteristic, complemented
5#10591721C212yesmaximal, complemented
6#10591364C212yesmaximal, complemented
7#10591363C212yesmaximal, complemented
8#10591275C212yesmaximal, complemented
9#10591248C212yesmaximal, complemented
10#74685—32nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638C2211yescharacteristic
13C22×C3×#67C2212yes—
14C22×#626C2212yes—
15C22×#625C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×#3757C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C3×#217C2212yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23#63979C418yescomplemented
24C2×#3722C2211yescharacteristic
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×Dic32C2211yescharacteristic
27#63658C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#940—32no—
34C3×#386—32no—
35#5220—32no—
36#5213—32no—
37#5213—61no—
38#5213D312yescomplemented
39#4958—32no—
40#4958—32no—
41#4956—32no—
42#4956—32no—
43#4956—32no—
44#4956—32no—
45#4665—32no—
46#4665—32no—
47#4651—32no—
48#4651—32no—
49C24×C32C2311yescharacteristic
50C23×C3⋊D3C2311yescharacteristic
51C23×C3×D3C2312yes—
52C22×C32×C4—42no—
53C22×C32×C4—41no—
54C22×C32×C4C2312yes—
55C2×#638—41no—
56C2×#638—41no—
57C2×#638C2×C414yescomplemented
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C3×#67—42no—
61C2×C3×#67—42no—
62C2×C3×#67C2×C418yescomplemented
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C2×#626—42no—
67C2×#626—42no—
68C2×#626C2×C418yescomplemented
69C2×#625—41no—
70C2×#625—41no—
71C2×#625C2×C414yescomplemented
72C2×#624—42no—
73C2×#624—41no—
74C2×D3×Dic3—42no—
75C2×D3×Dic3—42no—
76C2×D3×Dic3—42no—
77#3757—41no—
78#3752—42no—
79C3×#217—42no—
80C3×(C2×D3)⋊C4—42no—
81C3×(C2×D3)⋊C4—42no—
82#3722—41no—
83(C2×D3)⋊Dic3—42no—
84Dic32C2×C414yescomplemented
85#2380—91noSylow
86C22×C3×D4—32no—
87C23×C3×C4—21no—
88C23×C3×C4C2×D312yes—
89C22×#67—32no—
90C22×#67—32no—
91C22×#67—32no—
92C22×#67—61no—
93C22×#67C2×D312yes—
94C23×Dic3—32no—
95C22×D12—32no—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C2×C3×C22⋊C4—32no—
99C2×C3×C22⋊C4—32no—
100C2×C3×C22⋊C4—32no—
101C2×#217—32no—
102C2×#217—32no—
103C2×#217—61no—
104C2×#217C2×D312yes—
105#940—316no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—62no—
111C2×(C2×D3)⋊C4C2×D312yes—
112C2×(C2×D3)⋊C4C2×D312yes—
113C2×C4×Dic3—32no—
114C3×#95—32no—
115C3×#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—62no—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D312yes—
127C23×C32—21no—
128C23×C32—21no—
129C23×C32—22no—
130C23×C32—22no—
131C23×C32C22×C412yes—
132C23×C32C2411yescharacteristic
133C22×C3⋊D3—21no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3C22×C412yes—
138C22×C3×D3—22no—
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—22no—
144C22×C3×D3C22×C414yes—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—44no—
149#638—44no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3C22×C412yes—
156C3×#67—48no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C22×C414yes—
166#626—48no—
167#625—44no—
168#624—44no—
169D3×Dic3—48no—
170C2×#127—91no—
171#386—32no—
172#386—92no—
173#386—92no—
174#386—91no—
175#386—92no—
176#386—92no—
177#386—91no—
178#383—92no—
179C24×C3—21no—
180C24×C3—32no—
181C24×C3C22×D312yes—
182C23×D3—32no—
183C23×D3—61no—
184C23×D3C22×D312yes—
185C2×C3×D4—38no—
186C2×C3×D4—122no—
187C2×C3×D4—122no—
188C22×C3×C4—22no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4—32no—
192C22×C3×C4—42no—
193C22×C3×C4—42no—
194C22×C3×C4—42no—
195C22×C3×C4—44no—
196C22×C3×C4—42no—
197C22×C3×C4C22×D312yes—
198C22×C3×C4C22×D312yes—
199C2×#67—38no—
200C2×#67—38no—
201C2×#67—38no—
202C2×#67—42no—
203C2×#67—42no—
204C2×#67—64no—
205C2×#67—122no—
206C2×#67—122no—
207C2×#67—122no—
208C2×#67—122no—
209C2×#67—122no—
210C2×#67—122no—
211C2×#67—122no—
212C2×#67—122no—
213C2×#67C4×D318yescomplemented
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—61no—
218C22×Dic3—62no—
219C22×Dic3—122no—
220C22×Dic3—122no—
221C22×Dic3—122no—
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C2×D12—38no—
226C2×D12—122no—
227C2×D12—122no—
228C2×C4×D3—122no—
229C2×C4×D3—122no—
230C2×C4×D3—122no—
231C2×C4×D3—122no—
232C2×C4×D3—122no—
233C2×C4×D3—122no—
234C3×C22⋊C4—122no—
235C3×C22⋊C4—122no—
236C3×C22⋊C4—122no—
237#217—42no—
238#217—122no—
239#217—122no—
240#217—122no—
241(C2×D3)⋊C4—42no—
242(C2×D3)⋊C4—42no—
243(C2×D3)⋊C4—122no—
244(C2×D3)⋊C4—122no—
245(C2×D3)⋊C4—122no—
246(C2×D3)⋊C4—122no—
247(C2×D3)⋊C4—124no—
248C4×Dic3—38no—
249C22×C32—22no—
250C22×C32—24no—
251C22×C32—41no—
252C22×C32—42no—
253C22×C32—41no—
254C22×C32C23×C411yescharacteristic
255C22×C32H(5,𝔽2)12yes—
256C22×C32H(5,𝔽2)11yescharacteristic
257C22×C32H(5,𝔽2)12yes—
258C22×C32H(5,𝔽2)11yescharacteristic
259C2×C3⋊D3—24no—
260C2×C3⋊D3—22no—
261C2×C3⋊D3—41no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—41no—
264C2×C3×D3—24no—
265C2×C3×D3—24no—
266C2×C3×D3—24no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C32×C4—42no—
272C3⋊Dic3—22no—
273C3⋊Dic3—42no—
274C3×Dic3—24no—
275C3×Dic3—42no—
276C3×Dic3—42no—
277C22×D4—32no—
278C22×D4—92no—
279C22×D4—91no—
280C22×D4—91no—
281C23×C4—91no—
282C23×C4—92no—
283C23×C4D3211yescharacteristic
284#127—98no—
285C2×C22⋊C4—32no—
286C2×C22⋊C4—32no—
287C2×C22⋊C4—32no—
288C2×C22⋊C4—91no—
289C2×C22⋊C4—92no—
290C2×C22⋊C4—91no—
291C2×C22⋊C4—92no—
292C2×C42—91no—
293#95—32no—
294#95—32no—
295#95—92no—
296#95—92no—
297#95—92no—
298#95—92no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—21no—
308C23×C3—22no—
309C23×C3—34no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—62no—
313C23×C3—62no—
314C23×C3—62no—
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3C2×C4×D314yes—
319C23×C3C23×D312yes—
320C22×D3—22no—
321C22×D3—22no—
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—34no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—122no—
335C22×D3—121no—
336C22×D3—121no—
337C22×D3—122no—
338C22×D3C2×C4×D314yes—
339C3×D4—128no—
340C2×C3×C4—24no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—34no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—48no—
351C2×C3×C4—48no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360#67—48no—
361#67—128no—
362#67—128no—
363#67—128no—
364#67—128no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—34no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—121no—
384C2×Dic3—121no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3—128no—
389C2×Dic3C2×C4×D314yes—
390D12—128no—
391C4×D3—128no—
392C4×D3—128no—
393C2×C32—42no—
394C2×C32#51812yes—
395C2×C32#51811yescharacteristic
396C2×C32#56012yes—
397C2×C32#56011yescharacteristic
398C2×C32#56011yescharacteristic
399C3⋊D3—42no—
400C3×D3—44no—
401C24—32no—
402C24—91no—
403C24C2×D3211yescharacteristic
404C2×D4—38no—
405C2×D4—98no—
406C2×D4—94no—
407C2×D4—94no—
408C2×D4—122no—
409C2×D4—122no—
410C2×D4—362no—
411C2×D4—362no—
412C2×D4—361no—
413C2×D4—361no—
414C2×D4—361no—
415C2×D4—361no—
416C22×C4—32no—
417C22×C4—32no—
418C22×C4—32no—
419C22×C4—41no—
420C22×C4—42no—
421C22×C4—91no—
422C22×C4—92no—
423C22×C4—362no—
424C22×C4—361no—
425C22×C4—362no—
426C22×C4—362no—
427C22×C4—362no—
428C22×C4C2×D3212yes—
429C22⋊C4—122no—
430C22⋊C4—122no—
431C22⋊C4—122no—
432C22⋊C4—362no—
433C22⋊C4—361no—
434C22⋊C4—362no—
435C22⋊C4—361no—
436C42—94no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—44no—
447C22×C3—42no—
448C22×C3—44no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—64no—
455C22×C3—64no—
456C22×C3—64no—
457C22×C3—122no—
458C22×C3—122no—
459C22×C3—122no—
460C22×C3—122no—
461C22×C3C22×C4×D312yes—
462C22×C3#100412yes—
463C22×C3#100412yes—
464C22×C3#100412yes—
465C22×C3#100412yes—
466C22×C3#100912yes—
467C22×C3#100912yes—
468C2×D3—24no—
469C2×D3—24no—
470C2×D3—24no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—64no—
478C2×D3—122no—
479C2×D3—124no—
480C2×D3—122no—
481C2×D3—122no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—242no—
485C2×D3—241no—
486C2×D3—241no—
487C3×C4—44no—
488C3×C4—42no—
489C3×C4—42no—
490C3×C4—64no—
491C3×C4—122no—
492C3×C4—122no—
493Dic3—24no—
494Dic3—42no—
495Dic3—42no—
496Dic3—64no—
497Dic3—122no—
498Dic3—122no—
499Dic3—122no—
500Dic3—242no—
501C32#238011yescharacteristic, complemented, Sylow
502C23—22no—
503C23—21no—
504C23—22no—
505C23—21no—
506C23—34no—
507C23—62no—
508C23—62no—
509C23—62no—
510C23—62no—
511C23—62no—
512C23—62no—
513C23—92no—
514C23—182no—
515C23—181no—
516C23—182no—
517C23—181no—
518C23C4×D3212yes—
519C23C22×D3211yescharacteristic
520D4—128no—
521D4—368no—
522D4—364no—
523D4—364no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—34no—
528C2×C4—44no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—92no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4—364no—
544C2×C4—368no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—44no—
551C2×C3—44no—
552C2×C3—124no—
553C2×C3#548612yes—
554C2×C3#554512yes—
555C2×C3#554512yes—
556C2×C3#559512yes—
557C2×C3#562012yes—
558C2×C3#562012yes—
559C2×C3#566612yes—
560D3—44no—
561D3—124no—
562D3—242no—
563C22—24no—
564C22—22no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—64no—
569C22—64no—
570C22—64no—
571C22—122no—
572C22—122no—
573C22—122no—
574C22—122no—
575C22—184no—
576C22—182no—
577C22—362no—
578C22—361no—
579C22—361no—
580C22C2×C4×D3211yescharacteristic
581C22#6430712yes—
582C22#6430811yescharacteristic
583C22#6433012yes—
584C22#6433011yescharacteristic
585C4—42no—
586C4—64no—
587C4—122no—
588C4—122no—
589C4—182no—
590C4—362no—
591C3—21no—
592C3#7468512yescomplemented
593C2—42no—
594C2—124no—
595C2—362no—
596C2#1059505612yes—
597C2#1059505811yescharacteristic
598C2#1059509012yes—
599C2#1059509111yescharacteristic
600C2#1059550511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63979C2
hypercenterC23×C4D32
hypocenterC32#2380
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592912C2semidirect
3. C3×#5213C2semidirect
4. #10591722C2semidirect
5. #10591721C2semidirect
6. #10591364C2semidirect
7. #10591363C2semidirect
8. #10591275C2semidirect
9. #10591248C2semidirect
23. #63979C4semidirect
38. #5213D3semidirect
57. C2×#638C2×C4semidirect
62. C2×C3×#67C2×C4semidirect
68. C2×#626C2×C4semidirect
71. C2×#625C2×C4semidirect
84. Dic32C2×C4semidirect
213. C2×#67C4×D3semidirect
501. C32#2380semidirect
592. C3#74685semidirect

Maximal subgroups

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

subgroupindex
C2×#639792
#105929122
C3×#52132
#105917222
#105917212
#105913642
#105913632
#105912752
#105912482
#746853