Finite Group Databasebeta

← #11807611

Subgroups — #11807611

Order 1152.

1505 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63923C211yesmaximal, characteristic
2#10592638C211yesmaximal, characteristic, complemented
3C3×#4940C212yesmaximal, complemented
4#10591399C212yesmaximal, complemented
5#10591384C212yesmaximal, complemented
6#10591380C211yesmaximal, characteristic, complemented
7#10591316C212yesmaximal, complemented
8#10591275C212yesmaximal, complemented
9#10591258C212yesmaximal, complemented
10#75840—32nomaximal
11C23×D32C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×#626C2212yes—
14C22×#624C2211yescharacteristic, complemented
15C2×C32×C42C2211yescharacteristic, complemented
16C2×#3752C2212yes—
17C2×#3752C2212yescomplemented
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yescomplemented
23C2×#3722C2212yes—
24C2×#3722C2211yescharacteristic
25C2×#3722C2211yescharacteristic, complemented
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×Dic32C2212yescomplemented
29#63923C418yescomplemented
30C3×C3⋊#95C2212yescomplemented
31C3×C3⋊#95C2212yescomplemented
32#63579C2212yescomplemented
33C2×#882—32no—
34C3×#388—32no—
35#4990—32no—
36#4988—32no—
37#4957—32no—
38#4956—32no—
39#4955—32no—
40#4955—32no—
41#4951—32no—
42#4940D312yescomplemented
43#4939—32no—
44#4939—61no—
45#4670—32no—
46#4669—32no—
47#4665—32no—
48#4665—32no—
49C23×C3⋊D3C2311yescharacteristic
50C23×C3⋊D3C2311yescharacteristic
51C23×C3×D3C2312yes—
52C22×D32—41no—
53C22×D32—42no—
54C22×D32—41no—
55C22×D32—42no—
56C22×D32C2×C414yescomplemented
57C22×C32×C4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C2×C4⋊(C3⋊D3)—41no—
61C2×C4⋊(C3⋊D3)—41no—
62C2×C4⋊(C3⋊D3)C2×C414yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C2×#626—42no—
67C2×#626—42no—
68C2×#626C2×C418yes—
69C2×#624—41no—
70C2×#624—42no—
71C32×C42—41no—
72#3752—42no—
73#3752—42no—
74C4⋊(C3⋊Dic3)—41no—
75C3×(C2×D3)⋊C4—42no—
76C3×(C2×D3)⋊C4—42no—
77C3×(C2×D3)⋊C4C2×C418yescomplemented
78C3×Dic3⋊C4—42no—
79#3722—42no—
80#3722—41no—
81#3722C2×C414yescomplemented
82(C2×D3)⋊Dic3—42no—
83(C2×D3)⋊Dic3—42no—
84Dic32—42no—
85#2375—91noSylow
86C24×D3—32no—
87C22×#67—32no—
88C22×D12—32no—
89C22×D12—32no—
90C22×D12—61no—
91C22×C4×D3—32no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C22⋊C4—32no—
94C2×C3×C22⋊C4—32no—
95C2×C3×C22⋊C4—32no—
96C2×C3×C42—21no—
97C2×C3×C42C2×D312yescomplemented
98C2×#217—32no—
99C2×#217—32no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—32no—
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)⋊C4—62no—
112C2×(C2×D3)⋊C4C2×D312yes—
113C2×(C2×D3)⋊C4C2×D312yes—
114C2×(C2×D3)⋊C4C2×D312yes—
115C2×C4⋊Dic3—32no—
116C2×C4⋊Dic3—61no—
117C2×Dic3⋊C4C2×D312yescomplemented
118C2×C4×Dic3—32no—
119C2×C4×Dic3—32no—
120#882—316no—
121C3×#95—32no—
122C3×#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95C2×D312yescomplemented
126C3⋊#95C2×D312yescomplemented
127C23×C32C2411yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—21no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—21no—
136C22×C3⋊D3C22×C412yes—
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×D32—48no—
146C2×D32—44no—
147C2×D32—48no—
148C2×D32—44no—
149C2×D32—44no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4C22×C412yes—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C4⋊(C3⋊D3)—44no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C22×C414yes—
169#626—48no—
170#624—44no—
171C2×#120—91no—
172#390—92no—
173#390—91no—
174#388—32no—
175#388—92no—
176#388—92no—
177#386—91no—
178#386—92no—
179#379—92no—
180C24×C3—32no—
181C23×D3—32no—
182C23×D3—32no—
183C23×D3—38no—
184C23×D3—61no—
185C23×D3—61no—
186C23×D3—122no—
187C23×D3—122no—
188C23×D3—122no—
189C23×D3—122no—
190C23×D3—122no—
191C23×D3—122no—
192C23×D3C22×D312yes—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D312yes—
201C2×#67—38no—
202C2×#67—122no—
203C2×#67—122no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—62no—
207C22×Dic3C22×D312yes—
208C22×Dic3C22×D312yes—
209C22×Dic3C22×D312yes—
210C2×D12—38no—
211C2×D12—38no—
212C2×D12—64no—
213C2×D12—122no—
214C2×D12—122no—
215C2×D12—122no—
216C2×D12—122no—
217C2×D12—122no—
218C2×D12—122no—
219C2×C4×D3—122no—
220C2×C4×D3—122no—
221C2×C4×D3—122no—
222C3×C4⋊C4—122no—
223C3×C22⋊C4—38no—
224C3×C22⋊C4—122no—
225C3×C22⋊C4—122no—
226C3×C42—42no—
227C3×C42—42no—
228#217—122no—
229#217—122no—
230(C2×D3)⋊C4—38no—
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—
236(C2×D3)⋊C4—122no—
237(C2×D3)⋊C4—122no—
238(C2×D3)⋊C4—122no—
239(C2×D3)⋊C4—122no—
240(C2×D3)⋊C4—122no—
241(C2×D3)⋊C4—122no—
242(C2×D3)⋊C4—124no—
243(C2×D3)⋊C4—124no—
244(C2×D3)⋊C4C4×D318yescomplemented
245C4⋊Dic3—122no—
246C4⋊Dic3—122no—
247Dic3⋊C4—42no—
248C4×Dic3—122no—
249C4×Dic3—122no—
250C22×C32C23×C411yescharacteristic
251C22×C32H(5,𝔽2)11yescharacteristic
252C22×C32H(5,𝔽2)12yes—
253C22×C32H(5,𝔽2)12yes—
254C22×C32H(5,𝔽2)11yescharacteristic
255C2×C3⋊D3—24no—
256C2×C3⋊D3—22no—
257C2×C3⋊D3—22no—
258C2×C3⋊D3—24no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—41no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—41no—
263C2×C3⋊D3—41no—
264C2×C3⋊D3—41no—
265C2×C3×D3—24no—
266C2×C3×D3—24no—
267C2×C3×D3—24no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272D32—416no—
273C32×C4—22no—
274C32×C4—42no—
275C3⋊Dic3—42no—
276C3×Dic3—24no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C25—91no—
280C22×D4—92no—
281C22×D4—91no—
282C23×C4—91no—
283#120—98no—
284C2×C4⋊C4—32no—
285C2×C4⋊C4—91no—
286C2×C22⋊C4—32no—
287C2×C22⋊C4—32no—
288C2×C22⋊C4—32no—
289C2×C22⋊C4—91no—
290C2×C22⋊C4—92no—
291C2×C22⋊C4—91no—
292C2×C22⋊C4—92no—
293C2×C22⋊C4—92no—
294C2×C22⋊C4—92no—
295C2×C22⋊C4—92no—
296C2×C42—92no—
297C2×C42D3211yescharacteristic, complemented
298#95—32no—
299#95—32no—
300#95—92no—
301C23×C3—21no—
302C23×C3—34no—
303C23×C3—62no—
304C23×C3—62no—
305C23×C3—62no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3—62no—
309C23×C3C23×D312yes—
310C22×D3—22no—
311C22×D3—22no—
312C22×D3—22no—
313C22×D3—22no—
314C22×D3—22no—
315C22×D3—22no—
316C22×D3—34no—
317C22×D3—34no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—122no—
333C22×D3—122no—
334C22×D3—121no—
335C22×D3—121no—
336C22×D3—121no—
337C22×D3—121no—
338C22×D3—122no—
339C22×D3—122no—
340C22×D3—128no—
341C22×D3—128no—
342C22×D3—128no—
343C22×D3—128no—
344C22×D3—128no—
345C22×D3—128no—
346C22×D3—128no—
347C22×D3C2×C4×D314yes—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—24no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—34no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4C2×C4×D314yes—
372#67—128no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3—122no—
390C2×Dic3C2×C4×D314yes—
391D12—128no—
392D12—128no—
393D12—128no—
394C4×D3—128no—
395C2×C32#51812yes—
396C2×C32#51811yescharacteristic
397C2×C32#56012yes—
398C2×C32#56011yescharacteristic
399C2×C32H(3,𝔽4)11yescharacteristic
400C3⋊D3—42no—
401C3⋊D3—42no—
402C3×D3—44no—
403C24—32no—
404C24—94no—
405C24—91no—
406C24—91no—
407C24—362no—
408C24—361no—
409C24—362no—
410C24—361no—
411C2×D4—98no—
412C2×D4—94no—
413C2×D4—361no—
414C2×D4—361no—
415C2×D4—362no—
416C2×D4—362no—
417C22×C4—32no—
418C22×C4—32no—
419C22×C4—32no—
420C22×C4—92no—
421C22×C4—362no—
422C22×C4—361no—
423C22×C4C2×D3212yes—
424C22×C4C2×D3211yescharacteristic
425C4⋊C4—122no—
426C4⋊C4—361no—
427C22⋊C4—38no—
428C22⋊C4—94no—
429C22⋊C4—122no—
430C22⋊C4—122no—
431C22⋊C4—362no—
432C22⋊C4—362no—
433C22⋊C4—362no—
434C22⋊C4—361no—
435C22⋊C4—362no—
436C22⋊C4—362no—
437C42—41no—
438C42—362no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—64no—
445C22×C3—64no—
446C22×C3—64no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3C22×C4×D312yes—
452C22×C3#100412yes—
453C22×C3#100412yes—
454C22×C3#100912yes—
455C22×C3#100912yes—
456C22×C3#100912yes—
457C22×C3#100912yes—
458C2×D3—24no—
459C2×D3—24no—
460C2×D3—24no—
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—42no—
464C2×D3—42no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—64no—
468C2×D3—64no—
469C2×D3—64no—
470C2×D3—64no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—124no—
474C2×D3—124no—
475C2×D3—1232no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—122no—
481C2×D3—122no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—242no—
485C2×D3—242no—
486C2×D3—241no—
487C2×D3—241no—
488C2×D3—241no—
489C2×D3—241no—
490C3×C4—24no—
491C3×C4—24no—
492C3×C4—44no—
493C3×C4—42no—
494C3×C4—42no—
495C3×C4—64no—
496C3×C4—122no—
497C3×C4—122no—
498Dic3—24no—
499Dic3—42no—
500Dic3—42no—
501Dic3—122no—
502Dic3—122no—
503Dic3—242no—
504C32#237511yescharacteristic, complemented, Sylow
505C23—34no—
506C23—62no—
507C23—62no—
508C23—62no—
509C23—62no—
510C23—62no—
511C23—62no—
512C23—92no—
513C23—92no—
514C23—182no—
515C23—182no—
516C23—182no—
517C23—182no—
518C23—181no—
519C23—181no—
520C23—181no—
521C23—181no—
522C23—368no—
523C23—364no—
524C23—368no—
525C23—364no—
526C23—364no—
527C23C22×D3211yescharacteristic
528D4—364no—
529D4—368no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—34no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—182no—
547C2×C4—364no—
548C2×C4C4×D3212yes—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—124no—
555C2×C3#552112yes—
556C2×C3#554512yes—
557C2×C3#554512yes—
558C2×C3#562012yes—
559C2×C3#566612yes—
560C2×C3#568312yes—
561C2×C3#571112yes—
562D3—44no—
563D3—124no—
564D3—124no—
565D3—242no—
566D3—242no—
567C22—64no—
568C22—64no—
569C22—64no—
570C22—122no—
571C22—122no—
572C22—122no—
573C22—122no—
574C22—184no—
575C22—184no—
576C22—182no—
577C22—182no—
578C22—3616no—
579C22—362no—
580C22—362no—
581C22—361no—
582C22—361no—
583C22—361no—
584C22—361no—
585C22C2×C4×D3211yescharacteristic
586C22#6430712yes—
587C22#6430812yes—
588C22#6430811yescharacteristic
589C22#6433011yescharacteristic
590C4—22no—
591C4—42no—
592C4—64no—
593C4—122no—
594C4—122no—
595C4—362no—
596C3—21no—
597C3#7584012yescomplemented
598C2—124no—
599C2—362no—
600C2—362no—
601C2#1059399412yes—
602C2#1059402111yescharacteristic
603C2#1059402311yescharacteristic
604C2#1059505811yescharacteristic
605C2#1059509012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63923C2
hypercenterC2×C42D32
hypocenterC32#2375
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592638C2semidirect
3. C3×#4940C2semidirect
4. #10591399C2semidirect
5. #10591384C2semidirect
6. #10591380C2semidirect
7. #10591316C2semidirect
8. #10591275C2semidirect
9. #10591258C2semidirect
14. C22×#624C22semidirect
15. C2×C32×C42C22semidirect
17. C2×#3752C22semidirect
18. C2×C4⋊(C3⋊Dic3)C22semidirect
22. C2×C3×Dic3⋊C4C22semidirect
25. C2×#3722C22semidirect
28. C2×Dic32C22semidirect
29. #63923C4semidirect
30. C3×C3⋊#95C22semidirect
31. C3×C3⋊#95C22semidirect
32. #63579C22semidirect
42. #4940D3semidirect
56. C22×D32C2×C4semidirect
77. C3×(C2×D3)⋊C4C2×C4semidirect
81. #3722C2×C4semidirect
97. C2×C3×C42C2×D3semidirect
117. C2×Dic3⋊C4C2×D3semidirect
125. C3⋊#95C2×D3semidirect
126. C3⋊#95C2×D3semidirect
244. (C2×D3)⋊C4C4×D3semidirect
297. C2×C42D32semidirect
504. C32#2375semidirect
597. C3#75840semidirect

Maximal subgroups

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

subgroupindex
C2×#639232
#105926382
C3×#49402
#105913992
#105913842
#105913802
#105913162
#105912752
#105912582
#758403