Finite Group Databasebeta

← #11807571

Subgroups — #11807571

Order 1152.

1275 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64095C211yesmaximal, characteristic
2C3×#4951C212yesmaximal, complemented
3#10591722C211yesmaximal, characteristic
4#10591705C212yesmaximal, complemented
5#10591704C211yesmaximal, characteristic
6#10591271C212yesmaximal, complemented
7Dic3×C4⋊Dic3C212yesmaximal, complemented
8#10591266C212yesmaximal, complemented
9#10591233C212yesmaximal, complemented
10#75488—32nomaximal
11C22×#638C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C22×#624C2211yescharacteristic
14C2×C32×C22⋊C4C2211yescharacteristic
15C2×#3752C2212yes—
16C2×C4⋊(C3⋊Dic3)C2212yes—
17#64095C418yescomplemented
18C2×C3×#217C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×#3724C2211yescharacteristic
23C2×#3722C2212yes—
24C2×#3722C2211yescharacteristic
25C2×Dic32C2212yes—
26C2×Dic32C2212yes—
27C2×Dic32C2211yescharacteristic
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33C2×#886—32no—
34C2×#886—61no—
35C3×#388—32no—
36#4990—32no—
37Dic3×C4⋊C4—32no—
38#4957—32no—
39#4956—32no—
40#4951D312yescomplemented
41Dic3×C22⋊C4—32no—
42Dic3×C22⋊C4—32no—
43C4×(C2×D3)⋊C4—32no—
44C4×C4⋊Dic3—32no—
45#4670—32no—
46#4666—32no—
47#4654—32no—
48#4653—32no—
49C24×C32C2311yescharacteristic
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4C2312yes—
52C2×#638—41no—
53C2×#638—41no—
54C2×#638C2×C414yes—
55C22×C3⋊Dic3—41no—
56C22×C3⋊Dic3—41no—
57C22×C3⋊Dic3C2×C414yescomplemented
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C2×#624—24no—
65C2×#624—41no—
66C32×C22⋊C4C2×C414yescomplemented
67#3752C2×C418yes—
68C4⋊(C3⋊Dic3)C2×C418yescomplemented
69C3×#217—24no—
70C3×#217—24no—
71C3×C4⋊Dic3—24no—
72C3×C4×Dic3—24no—
73#3724—41no—
74#3722—24no—
75#3722—41no—
76Dic32—41no—
77Dic32—42no—
78Dic32—42no—
79#2374—91noSylow
80C22×#67—32no—
81C22×#67—61no—
82C23×Dic3—32no—
83C23×Dic3—61no—
84C22×C4×D3—32no—
85C2×C3×C4⋊C4—32no—
86C2×C3×C22⋊C4—21no—
87C2×C3×C22⋊C4—32no—
88C2×C3×C22⋊C4—32no—
89C2×C3×C22⋊C4C2×D312yes—
90C2×C3×C42—32no—
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×C4⋊Dic3—62no—
102C2×C4⋊Dic3C2×D312yes—
103C2×Dic3⋊C4—32no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—32no—
106C2×C4×Dic3—32no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3C2×D312yes—
110#886—316no—
111#886—68no—
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⋊#95C2×D312yes—
121C3⋊#95C2×D312yes—
122C23×C32—21no—
123C23×C32—21no—
124C23×C32—22no—
125C23×C32—22no—
126C23×C32C22×C412yes—
127C23×C32C2411yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3C22×C412yes—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4C22×C414yes—
136#638—44no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—44no—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3⋊Dic3C22×C414yes—
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×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3#4114yes—
155C2×C3×Dic3#4114yes—
156#624—44no—
157C2×#123—91no—
158#390—91no—
159#388—32no—
160#388—92no—
161#387—92no—
162#386—91no—
163C4×C4⋊C4—92no—
164C4×C22⋊C4—92no—
165C4×C22⋊C4—92no—
166C24×C3—21no—
167C24×C3C22×D312yes—
168C23×D3—32no—
169C23×D3—61no—
170C22×C3×C4—22no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4C22×D312yes—
176C22×C3×C4C22×D312yes—
177C2×#67—38no—
178C2×#67—64no—
179C2×#67—122no—
180C2×#67—122no—
181C2×#67—122no—
182C2×#67—122no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—38no—
187C22×Dic3—64no—
188C22×Dic3—61no—
189C22×Dic3—62no—
190C22×Dic3—122no—
191C22×Dic3—122no—
192C22×Dic3—122no—
193C22×Dic3—122no—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D312yes—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D312yes—
198C2×C4×D3—64no—
199C2×C4×D3—64no—
200C2×C4×D3—122no—
201C3×C4⋊C4—64no—
202C3×C22⋊C4—24no—
203C3×C22⋊C4—64no—
204C3×C22⋊C4—64no—
205C3×C22⋊C4C4×D318yescomplemented
206C3×C42—64no—
207#217—24no—
208#217—24no—
209(C2×D3)⋊C4—38no—
210(C2×D3)⋊C4—38no—
211(C2×D3)⋊C4—68no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—122no—
215C4⋊Dic3—24no—
216C4⋊Dic3—38no—
217C4⋊Dic3—38no—
218C4⋊Dic3—68no—
219Dic3⋊C4—122no—
220C4×Dic3—24no—
221C4×Dic3—122no—
222C4×Dic3—122no—
223C4×Dic3—122no—
224C4×Dic3—122no—
225C4×Dic3—122no—
226C22×C32—22no—
227C22×C32—24no—
228C22×C32—41no—
229C22×C32—42no—
230C22×C32—41no—
231C22×C32C23×C411yescharacteristic
232C22×C32C2×#4112yes—
233C22×C32C2×#4112yes—
234C22×C32H(5,𝔽2)11yescharacteristic
235C22×C32H(5,𝔽2)11yescharacteristic
236C2×C3⋊D3—24no—
237C2×C3⋊D3—22no—
238C2×C3⋊D3—41no—
239C2×C3⋊D3—42no—
240C2×C3⋊D3—41no—
241C32×C4—24no—
242C3⋊Dic3—24no—
243C3⋊Dic3—22no—
244C3×Dic3—24no—
245C3×Dic3—24no—
246C3×Dic3—42no—
247C3×Dic3—42no—
248C22×D4—91no—
249C23×C4—91no—
250C23×C4—91no—
251#123—98no—
252C2×C4⋊C4—32no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—91no—
255C2×C22⋊C4—32no—
256C2×C22⋊C4—32no—
257C2×C22⋊C4—92no—
258C2×C22⋊C4—92no—
259C2×C22⋊C4—91no—
260C2×C22⋊C4D3211yescharacteristic
261C2×C42—32no—
262C2×C42—92no—
263C2×C42—92no—
264C2×C42—91no—
265#95—32no—
266#95—32no—
267#95—92no—
268#95—92no—
269#95—92no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3—21no—
279C23×C3—22no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3C2×C4×D314yes—
283C23×C3C23×D312yes—
284C22×D3—34no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—122no—
295C22×D3—122no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—34no—
302C2×C3×C4—34no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
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—62no—
315C2×C3×C4C2×C4×D314yes—
316C2×C3×C4C2×C4×D314yes—
317#67—128no—
318#67—128no—
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—22no—
328C2×Dic3—22no—
329C2×Dic3—34no—
330C2×Dic3—34no—
331C2×Dic3—34no—
332C2×Dic3—62no—
333C2×Dic3—64no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—128no—
345C2×Dic3—128no—
346C2×Dic3#23714yes—
347C2×Dic3#23714yes—
348C4×D3—128no—
349C2×C32—42no—
350C2×C32C4×#4112yes—
351C2×C32#51811yescharacteristic
352C2×C32#55111yescharacteristic
353C2×C32#55312yes—
354C2×C32#55911yescharacteristic
355C3⋊D3—42no—
356C24—91no—
357C24C2×D3211yescharacteristic
358C2×D4—94no—
359C2×D4—361no—
360C2×D4—361no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—32no—
365C22×C4—92no—
366C22×C4—91no—
367C22×C4—94no—
368C22×C4—184no—
369C22×C4—361no—
370C22×C4—361no—
371C22×C4—361no—
372C22×C4C2×D3212yes—
373C4⋊C4—64no—
374C4⋊C4—98no—
375C4⋊C4—361no—
376C22⋊C4—64no—
377C22⋊C4—64no—
378C22⋊C4—98no—
379C22⋊C4—184no—
380C22⋊C4—361no—
381C22⋊C4#62414yescomplemented
382C42—64no—
383C42—361no—
384C42—362no—
385C42—362no—
386C22×C3—24no—
387C22×C3—24no—
388C22×C3—24no—
389C22×C3—24no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—44no—
396C22×C3—44no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3C22×C4×D312yes—
404C22×C3C2×#23712yes—
405C22×C3C2×#23712yes—
406C22×C3D3×#4112yes—
407C22×C3D3×#4112yes—
408C22×C3#100912yes—
409C22×C3#100912yes—
410C2×D3—64no—
411C2×D3—64no—
412C2×D3—64no—
413C2×D3—122no—
414C2×D3—124no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—242no—
420C2×D3—241no—
421C2×D3—241no—
422C3×C4—24no—
423C3×C4—24no—
424C3×C4—44no—
425C3×C4—64no—
426C3×C4—64no—
427C3×C4—122no—
428C3×C4—122no—
429Dic3—24no—
430Dic3—24no—
431Dic3—42no—
432Dic3—42no—
433Dic3—64no—
434Dic3—64no—
435Dic3—64no—
436Dic3—124no—
437Dic3—122no—
438C32#237411yescharacteristic, complemented, Sylow
439C23—21no—
440C23—21no—
441C23—22no—
442C23—22no—
443C23—92no—
444C23—181no—
445C23—181no—
446C23—182no—
447C23—182no—
448C23C2×#62412yes—
449C23C22×D3211yescharacteristic
450D4—364no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—34no—
454C2×C4—34no—
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—62no—
464C2×C4—62no—
465C2×C4—94no—
466C2×C4—92no—
467C2×C4—182no—
468C2×C4—182no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—364no—
472C2×C4—364no—
473C2×C4C2×#62414yes—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—22no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—44no—
480C2×C3—44no—
481C2×C3#552112yes—
482C2×C3C4×#23712yes—
483C2×C3C4×#23712yes—
484C2×C3#561812yes—
485C2×C3#565812yes—
486C2×C3#568112yes—
487C2×C3#570912yes—
488D3—124no—
489D3—242no—
490C22—24no—
491C22—22no—
492C22—42no—
493C22—41no—
494C22—41no—
495C22—184no—
496C22—182no—
497C22—362no—
498C22—361no—
499C22—361no—
500C22#6430811yescharacteristic
501C22#6430811yescharacteristic
502C22D3×#23712yes—
503C22D3×#23712yes—
504C22C22×#62411yescharacteristic
505C4—24no—
506C4—64no—
507C4—64no—
508C4—122no—
509C4—122no—
510C4—184no—
511C4—182no—
512C3—21no—
513C3#7548812yescomplemented
514C2—42no—
515C2—362no—
516C2#1059412512yes—
517C2#1059414211yescharacteristic
518C2#1059430311yescharacteristic
519C2#1059499611yescharacteristic
520C2#1059519012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2374
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4951C2semidirect
4. #10591705C2semidirect
6. #10591271C2semidirect
7. Dic3×C4⋊Dic3C2semidirect
8. #10591266C2semidirect
9. #10591233C2semidirect
17. #64095C4semidirect
40. #4951D3semidirect
57. C22×C3⋊Dic3C2×C4semidirect
66. C32×C22⋊C4C2×C4semidirect
68. C4⋊(C3⋊Dic3)C2×C4semidirect
205. C3×C22⋊C4C4×D3semidirect
381. C22⋊C4#624semidirect
438. C32#2374semidirect
513. C3#75488semidirect

Maximal subgroups

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

subgroupindex
C2×#640952
C3×#49512
#105917222
#105917052
#105917042
#105912712
Dic3×C4⋊Dic32
#105912662
#105912332
#754883