Finite Group Databasebeta

← #11807563

Subgroups — #11807563

Order 1152.

1247 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63975C211yesmaximal, characteristic
2#10592912C211yesmaximal, characteristic
3C3×C4×#217C212yesmaximal, complemented
4#10591704C211yesmaximal, characteristic
5#10591702C212yesmaximal, complemented
6#10591331C212yesmaximal, complemented
7#10591242C212yesmaximal, complemented
8#10591233C212yesmaximal, complemented
9#10591194C212yesmaximal, complemented
10#73479—32nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638C2211yescharacteristic
13C22×#624C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×#3752C2212yes—
16C2×C3×#217C2212yes—
17C2×C3×#217C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20#63975C418yescomplemented
21C2×#3724C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×#3722C2212yes—
25C2×#3722C2211yescharacteristic
26C2×Dic32C2212yes—
27C2×Dic32C2211yescharacteristic
28#63658C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#883—32no—
34C3×C4×C22⋊C4—32no—
35#5213—32no—
36#5213—61no—
37C4×#217D312yescomplemented
38#4957—32no—
39#4951—32no—
40#4945—32no—
41#4940—32no—
42C4×(C2×D3)⋊C4—32no—
43C4×C4⋊Dic3—32no—
44#4933—32no—
45#4670—32no—
46#4666—32no—
47#4654—32no—
48#4649—32no—
49C24×C32C2311yescharacteristic
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4—24no—
52C22×C32×C4—41no—
53C22×C32×C4C2312yes—
54C2×#638—41no—
55C2×#638—41no—
56C2×#638C2×C414yes—
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C2×#624—41no—
64C2×#624—41no—
65C2×#624C2×C414yescomplemented
66#3757—41no—
67#3752—24no—
68C3×#217—24no—
69C3×#217C2×C418yes—
70C3×C4×Dic3—24no—
71C3×C4×Dic3—42no—
72#3724—41no—
73Dic3⋊Dic3—24no—
74Dic3⋊Dic3C2×C418yescomplemented
75#3722—24no—
76#3722C2×C414yescomplemented
77Dic32—41no—
78Dic32—42no—
79#2374—91noSylow
80C23×C3×C4—21no—
81C23×C3×C4C2×D312yes—
82C22×#67—32no—
83C22×#67—61no—
84C22×C4×D3—32no—
85C2×C3×C22⋊C4—32no—
86C2×C3×C22⋊C4—32no—
87C2×C3×C42—32no—
88C2×C3×C42—32no—
89C2×#217—32no—
90C2×#217—61no—
91C2×#217C2×D312yes—
92C2×#217C2×D312yes—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—62no—
99C2×C4⋊Dic3—32no—
100C2×C4⋊Dic3—32no—
101C2×Dic3⋊C4—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—32no—
106C2×C4×Dic3—32no—
107C2×C4×Dic3C2×D312yes—
108C2×C4×Dic3C2×D312yes—
109#883—316no—
110C3×#95—32no—
111C3×#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—62no—
119C3⋊#95C2×D312yes—
120C3⋊#95C2×D312yes—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—22no—
124C23×C32—22no—
125C23×C32C22×C412yes—
126C23×C32C2411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3C22×C412yes—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—44no—
135C2×C32×C4#4114yes—
136#638—44no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3C22×C414yes—
153C2×C3×Dic3C22×C414yes—
154C2×C3×Dic3#4114yes—
155#624—44no—
156C2×#123—91no—
157#390—91no—
158#388—92no—
159#388—92no—
160#387—92no—
161#386—91no—
162C4×C4⋊C4—92no—
163C4×C22⋊C4—32no—
164C4×C22⋊C4—92no—
165C24×C3—21no—
166C24×C3C22×D312yes—
167C23×D3—32no—
168C23×D3—61no—
169C22×C3×C4—24no—
170C22×C3×C4—24no—
171C22×C3×C4—22no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—44no—
177C22×C3×C4—42no—
178C22×C3×C4—42no—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D312yes—
181C2×#67—38no—
182C2×#67—64no—
183C2×#67—122no—
184C2×#67—122no—
185C2×#67—122no—
186C2×#67—122no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—61no—
191C22×Dic3—62no—
192C22×Dic3C22×D312yes—
193C22×Dic3C22×D312yes—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D312yes—
196C2×C4×D3—38no—
197C2×C4×D3—122no—
198C2×C4×D3—122no—
199C3×C22⋊C4—38no—
200C3×C22⋊C4—64no—
201C3×C42—64no—
202C3×C42—122no—
203#217—24no—
204#217—122no—
205#217—122no—
206#217C4×D318yes—
207(C2×D3)⋊C4—38no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—64no—
211(C2×D3)⋊C4—64no—
212(C2×D3)⋊C4—124no—
213C4⋊Dic3—38no—
214C4⋊Dic3—64no—
215Dic3⋊C4—38no—
216Dic3⋊C4—64no—
217Dic3⋊C4—122no—
218C4×Dic3—24no—
219C4×Dic3—42no—
220C4×Dic3—122no—
221C4×Dic3—122no—
222C4×Dic3—122no—
223C22×C32—22no—
224C22×C32—24no—
225C22×C32—41no—
226C22×C32—42no—
227C22×C32—41no—
228C22×C32C23×C411yescharacteristic
229C22×C32C2×#4112yes—
230C22×C32C2×#4112yes—
231C22×C32H(5,𝔽2)11yescharacteristic
232C22×C32H(5,𝔽2)11yescharacteristic
233C2×C3⋊D3—24no—
234C2×C3⋊D3—22no—
235C2×C3⋊D3—41no—
236C2×C3⋊D3—42no—
237C2×C3⋊D3—41no—
238C32×C4—24no—
239C3⋊Dic3—22no—
240C3⋊Dic3—42no—
241C3×Dic3—24no—
242C3×Dic3—24no—
243C3×Dic3—24no—
244C3×Dic3—42no—
245C22×D4—91no—
246C23×C4—91no—
247C23×C4D3211yescharacteristic
248#123—98no—
249C2×C4⋊C4—92no—
250C2×C4⋊C4—92no—
251C2×C4⋊C4—91no—
252C2×C22⋊C4—32no—
253C2×C22⋊C4—32no—
254C2×C22⋊C4—91no—
255C2×C22⋊C4—92no—
256C2×C22⋊C4—92no—
257C2×C22⋊C4—91no—
258C2×C42—32no—
259C2×C42—32no—
260C2×C42—92no—
261C2×C42—91no—
262#95—32no—
263#95—32no—
264#95—92no—
265#95—92no—
266#95—92no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—21no—
276C23×C3—22no—
277C23×C3—42no—
278C23×C3—42no—
279C23×C3C2×C4×D314yes—
280C23×C3C23×D312yes—
281C22×D3—34no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—122no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—122no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—24no—
298C2×C3×C4—34no—
299C2×C3×C4—34no—
300C2×C3×C4—34no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—48no—
304C2×C3×C4—48no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4#23514yes—
315C2×C3×C4#23714yes—
316#67—128no—
317#67—128no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—34no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—122no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3C2×C4×D314yes—
343C2×Dic3C2×C4×D314yes—
344C2×Dic3#23514yes—
345C4×D3—128no—
346C2×C32—42no—
347C2×C32C4×#4112yes—
348C2×C32#51811yescharacteristic
349C2×C32#55111yescharacteristic
350C2×C32#55312yes—
351C2×C32#55911yescharacteristic
352C3⋊D3—42no—
353C24—91no—
354C24C2×D3211yescharacteristic
355C2×D4—94no—
356C2×D4—361no—
357C2×D4—361no—
358C22×C4—24no—
359C22×C4—32no—
360C22×C4—32no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—41no—
364C22×C4—94no—
365C22×C4—91no—
366C22×C4—92no—
367C22×C4—361no—
368C22×C4—361no—
369C22×C4C2×D3212yes—
370C4⋊C4—98no—
371C4⋊C4—184no—
372C4⋊C4—361no—
373C22⋊C4—38no—
374C22⋊C4—64no—
375C22⋊C4—94no—
376C22⋊C4—184no—
377C22⋊C4—184no—
378C22⋊C4—361no—
379C42—64no—
380C42—122no—
381C42—361no—
382C42—362no—
383C22×C3—24no—
384C22×C3—24no—
385C22×C3—24no—
386C22×C3—24no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—22no—
391C22×C3—21no—
392C22×C3—44no—
393C22×C3—42no—
394C22×C3—44no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3C22×C4×D312yes—
401C22×C3C2×#23512yes—
402C22×C3C2×#23512yes—
403C22×C3C2×#23712yes—
404C22×C3#100412yes—
405C22×C3D3×#4112yes—
406C22×C3#100912yes—
407C2×D3—64no—
408C2×D3—64no—
409C2×D3—64no—
410C2×D3—122no—
411C2×D3—124no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—242no—
417C2×D3—241no—
418C2×D3—241no—
419C3×C4—24no—
420C3×C4—24no—
421C3×C4—44no—
422C3×C4—64no—
423C3×C4—64no—
424C3×C4—64no—
425C3×C4—122no—
426Dic3—24no—
427Dic3—24no—
428Dic3—24no—
429Dic3—42no—
430Dic3—64no—
431Dic3—122no—
432Dic3—122no—
433Dic3—122no—
434Dic3—242no—
435C32#237411yescharacteristic, complemented, Sylow
436C23—22no—
437C23—21no—
438C23—22no—
439C23—21no—
440C23—92no—
441C23—182no—
442C23—181no—
443C23—182no—
444C23—181no—
445C23C4×D3212yes—
446C23C22×D3211yescharacteristic
447D4—364no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—34no—
451C2×C4—34no—
452C2×C4—34no—
453C2×C4—44no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—92no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—182no—
467C2×C4—182no—
468C2×C4—182no—
469C2×C4—364no—
470C2×C4#380414yes—
471C2×C3—22no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—44no—
477C2×C3—44no—
478C2×C3C4×#23512yes—
479C2×C3#549512yes—
480C2×C3#553012yes—
481C2×C3C4×#23712yes—
482C2×C3#554512yes—
483C2×C3#555912yes—
484C2×C3#556512yes—
485D3—124no—
486D3—242no—
487C22—24no—
488C22—22no—
489C22—42no—
490C22—41no—
491C22—41no—
492C22—184no—
493C22—182no—
494C22—362no—
495C22—361no—
496C22—361no—
497C22C2×C4×D3211yescharacteristic
498C22D3×#23512yes—
499C22#6430811yescharacteristic
500C22C2×#380412yes—
501C22#6433011yescharacteristic
502C4—24no—
503C4—64no—
504C4—64no—
505C4—64no—
506C4—122no—
507C4—182no—
508C4—362no—
509C3—21no—
510C3#7347912yescomplemented
511C2—42no—
512C2—362no—
513C2C4×#380412yes—
514C2#1059494612yes—
515C2#1059503011yescharacteristic
516C2#1059505811yescharacteristic
517C2#1059547611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2374
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C3×C4×#217C2semidirect
5. #10591702C2semidirect
6. #10591331C2semidirect
7. #10591242C2semidirect
8. #10591233C2semidirect
9. #10591194C2semidirect
20. #63975C4semidirect
37. C4×#217D3semidirect
65. C2×#624C2×C4semidirect
74. Dic3⋊Dic3C2×C4semidirect
76. #3722C2×C4semidirect
435. C32#2374semidirect
510. C3#73479semidirect

Maximal subgroups

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

subgroupindex
C2×#639752
#105929122
C3×C4×#2172
#105917042
#105917022
#105913312
#105912422
#105912332
#105911942
#734793