Finite Group Databasebeta

← #11807922

Subgroups — #11807922

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 497 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63913C211yesmaximal, characteristic
2#10592672C211yesmaximal, characteristic, complemented
3C3×#4989C212yesmaximal, complemented
4#10591381C212yesmaximal
5#10591286C212yesmaximal, complemented
6#10591284C212yesmaximal, complemented
7#10591277C212yesmaximal, complemented
8#10591273C211yesmaximal, characteristic, complemented
9#10591245C212yesmaximal, complemented
10#74402—32nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3C2212yes—
13C22×#625C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4C2212yes—
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×Dic3⋊C4C2212yes—
19C2×#3724C2211yescharacteristic
20C2×Dic3⋊Dic3C2212yes—
21C2×(C2×D3)⋊Dic3C2212yes—
22C2×(C2×D3)⋊Dic3C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×Dic32C2211yescharacteristic
25C2×Dic32C2211yescharacteristic
26#63913C418yescomplemented
27#63658C2212yes—
28#63658C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#885—32no—
34C3×#385—32no—
35#5213—32no—
36#5210—32no—
37#4989—32no—
38#4989D312yescomplemented
39#4977—32no—
40#4973—32no—
41#4973—61no—
42#4956—32no—
43#4951—32no—
44#4945—32no—
45#4670—32no—
46#4669—32no—
47#4650—32no—
48#4646—32no—
49C23×C3×D3C2312yes—
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C2×#634—41no—
56C2×#634—41no—
57C2×#634C2×C414yescomplemented
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C2×C3×C4×D3—42no—
62C2×C3×C4×D3—42no—
63C2×C3×C4×D3—42no—
64C2×#625—41no—
65C2×#625—41no—
66C2×#625C2×C414yes—
67C32×C4⋊C4—41no—
68C4×C3⋊Dic3—41no—
69C3×(C2×D3)⋊C4—42no—
70C3×(C2×D3)⋊C4C2×C418yescomplemented
71C3×Dic3⋊C4—42no—
72#3724—41no—
73Dic3⋊Dic3—42no—
74(C2×D3)⋊Dic3—42no—
75(C2×D3)⋊Dic3—42no—
76(C2×D3)⋊Dic3C2×C418yescomplemented
77Dic32—41no—
78Dic32C2×C414yescomplemented
79#2379—91noSylow
80C23×C3×C4—32no—
81C22×#67—32no—
82C22×C4×D3C2×D312yes—
83C22×Dic6—32no—
84C22×Dic6—61no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—32no—
87C2×C3×C4⋊C4C2×D312yes—
88C2×C3×C22⋊C4—32no—
89C2×C3×C22⋊C4—32no—
90C2×#217—32no—
91C2×#217—32no—
92C2×#217—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4C2×D312yes—
97C2×(C2×D3)⋊C4C2×D312yes—
98C2×C4⋊Dic3—32no—
99C2×Dic3⋊C4—32no—
100C2×Dic3⋊C4—32no—
101C2×Dic3⋊C4C2×D312yes—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—61no—
106#885—316no—
107C3×#95—32no—
108C3×#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—62no—
118C3⋊#95—62no—
119C3⋊#95C2×D312yes—
120C3⋊#95C2×D312yes—
121C23×C32C2411yescharacteristic
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3C22×C414yes—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4C22×C412yes—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3⋊Dic3C22×C412yes—
144#634—44no—
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×Dic3—22no—
153C2×C3×Dic3C22×C414yes—
154C3×C4×D3—48no—
155#625—44no—
156C2×#124—91no—
157#391—91no—
158#391—91no—
159#388—92no—
160#388—92no—
161#386—92no—
162#385—32no—
163#385—92no—
164#382—92no—
165C24×C3—32no—
166C23×D3C22×D312yes—
167C22×C3×C4—21no—
168C22×C3×C4—22no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4—32no—
172C22×C3×C4—122no—
173C22×C3×C4—122no—
174C22×C3×C4—122no—
175C22×C3×C4C22×D312yes—
176C22×C3×C4C22×D312yes—
177C22×C3×C4C22×D312yes—
178C2×#67—38no—
179C2×#67—122no—
180C2×#67—122no—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—62no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3C22×D312yes—
189C22×Dic3C22×D312yes—
190C22×Dic3C22×D312yes—
191C2×C4×D3—42no—
192C2×C4×D3—42no—
193C2×C4×D3—42no—
194C2×Dic6—38no—
195C2×Dic6—64no—
196C2×Dic6—122no—
197C2×Dic6—122no—
198C2×Dic6—122no—
199C2×Dic6—122no—
200C3×C4⋊C4—42no—
201C3×C4⋊C4—42no—
202C3×C4⋊C4—122no—
203C3×C22⋊C4—38no—
204C3×C22⋊C4—122no—
205#217—38no—
206#217—122no—
207#217—122no—
208(C2×D3)⋊C4—38no—
209(C2×D3)⋊C4—42no—
210(C2×D3)⋊C4—122no—
211(C2×D3)⋊C4—122no—
212(C2×D3)⋊C4C4×D318yescomplemented
213C4⋊Dic3—122no—
214Dic3⋊C4—42no—
215Dic3⋊C4—122no—
216Dic3⋊C4—122no—
217C4×Dic3—38no—
218C4×Dic3—122no—
219C4×Dic3—122no—
220C4×Dic3—122no—
221C22×C32C23×C411yescharacteristic
222C22×C32H(5,𝔽2)11yescharacteristic
223C22×C32H(5,𝔽2)12yes—
224C22×C32H(5,𝔽2)11yescharacteristic
225C22×C322−1+412yes—
226C2×C3×D3—24no—
227C2×C3×D3—24no—
228C2×C3×D3—24no—
229C2×C3×D3—42no—
230C2×C3×D3—42no—
231C2×C3×D3—42no—
232C2×C3×D3—42no—
233C32×C4—22no—
234C32×C4—42no—
235C3⋊Dic3—22no—
236C3⋊Dic3—22no—
237C3⋊Dic3—42no—
238C3×Dic3—24no—
239C3×Dic3—42no—
240C3×Dic3—42no—
241C22×Q8—91no—
242C22×D4—91no—
243C23×C4—32no—
244#124—98no—
245C2×C4⋊C4—32no—
246C2×C4⋊C4—92no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4D3211yescharacteristic
249C2×C22⋊C4—32no—
250C2×C22⋊C4—32no—
251C2×C22⋊C4—92no—
252C2×C22⋊C4—92no—
253C2×C22⋊C4—92no—
254C2×C42—91no—
255C2×C42—91no—
256C2×C42—91no—
257#95—32no—
258#95—32no—
259#95—92no—
260#95—92no—
261#95—92no—
262#95—92no—
263C23×C3—21no—
264C23×C3—34no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3—62no—
268C23×C3—62no—
269C23×C3—62no—
270C23×C3—62no—
271C23×C3C23×D312yes—
272C22×D3—22no—
273C22×D3—22no—
274C22×D3—22no—
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—22no—
278C22×D3C2×C4×D314yes—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—34no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—128no—
303C2×C3×C4C2×C4×D314yes—
304#67—128no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—34no—
314C2×Dic3—34no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—64no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—122no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—122no—
334C2×Dic3C2×C4×D314yes—
335C4×D3—48no—
336Dic6—128no—
337Dic6—128no—
338C2×C32#51811yescharacteristic
339C2×C32#52012yes—
340C2×C32H(3,𝔽4)11yescharacteristic
341C2×C32#56212yes—
342C2×C32#56311yescharacteristic
343C3×D3—44no—
344C24—32no—
345C2×Q8—94no—
346C2×Q8—361no—
347C2×Q8—361no—
348C2×D4—94no—
349C2×D4—361no—
350C2×D4—361no—
351C22×C4—32no—
352C22×C4—32no—
353C22×C4—32no—
354C22×C4—91no—
355C22×C4—91no—
356C22×C4—92no—
357C22×C4—122no—
358C22×C4—122no—
359C22×C4—122no—
360C22×C4C2×D3212yes—
361C22×C4C2×D3211yescharacteristic
362C4⋊C4—41no—
363C4⋊C4—122no—
364C4⋊C4—361no—
365C4⋊C4—362no—
366C22⋊C4—38no—
367C22⋊C4—98no—
368C22⋊C4—122no—
369C22⋊C4—362no—
370C22⋊C4—362no—
371C42—94no—
372C42—361no—
373C42—361no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3—64no—
380C22×C3—64no—
381C22×C3—64no—
382C22×C3—122no—
383C22×C3—122no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3C22×C4×D312yes—
387C22×C3#100412yes—
388C22×C3#100412yes—
389C22×C3#100412yes—
390C22×C3#100712yes—
391C22×C3#100912yes—
392C22×C3#101012yes—
393C2×D3—24no—
394C2×D3—24no—
395C2×D3—24no—
396C2×D3—42no—
397C2×D3—42no—
398C2×D3—42no—
399C2×D3—42no—
400C3×C4—24no—
401C3×C4—24no—
402C3×C4—42no—
403C3×C4—42no—
404C3×C4—64no—
405C3×C4—82no—
406C3×C4—122no—
407C3×C4—122no—
408Dic3—24no—
409Dic3—42no—
410Dic3—42no—
411Dic3—64no—
412Dic3—64no—
413Dic3—122no—
414Dic3—122no—
415Dic3—124no—
416Dic3—122no—
417Dic3—122no—
418C32#237911yescharacteristic, complemented, Sylow
419C23—34no—
420C23—62no—
421C23—62no—
422C23—62no—
423C23—62no—
424C23—62no—
425C23—62no—
426C23C22×D3211yescharacteristic
427Q8—364no—
428D4—364no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—34no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—92no—
444C2×C4—92no—
445C2×C4—128no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4C4×D3212yes—
454C2×C3—22no—
455C2×C3—22no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—124no—
460C2×C3#550412yes—
461C2×C3#554512yes—
462C2×C3#554612yes—
463C2×C3#559412yes—
464C2×C3#564612yes—
465C2×C3#564712yes—
466C2×C3#566712yes—
467D3—44no—
468C22—64no—
469C22—64no—
470C22—64no—
471C22—122no—
472C22—122no—
473C22—122no—
474C22—122no—
475C22C2×C4×D3211yescharacteristic
476C22#6430811yescharacteristic
477C22#6431312yes—
478C22#6431512yes—
479C22#6433011yescharacteristic
480C4—22no—
481C4—42no—
482C4—64no—
483C4—122no—
484C4—122no—
485C4—182no—
486C4—182no—
487C4—362no—
488C3—21no—
489C3#7440212yescomplemented
490C2—124no—
491C2#1059435912yes—
492C2#1059459012yes—
493C2#1059505811yescharacteristic
494C2#1059525611yescharacteristic
495C2#1059541611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2379
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592672C2semidirect
3. C3×#4989C2semidirect
5. #10591286C2semidirect
6. #10591284C2semidirect
7. #10591277C2semidirect
8. #10591273C2semidirect
9. #10591245C2semidirect
26. #63913C4semidirect
38. #4989D3semidirect
57. C2×#634C2×C4semidirect
70. C3×(C2×D3)⋊C4C2×C4semidirect
76. (C2×D3)⋊Dic3C2×C4semidirect
78. Dic32C2×C4semidirect
212. (C2×D3)⋊C4C4×D3semidirect
418. C32#2379semidirect
489. C3#74402semidirect

Maximal subgroups

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

subgroupindex
C2×#639132
#105926722
C3×#49892
#105913812
#105912862
#105912842
#105912772
#105912732
#105912452
#744023