Finite Group Databasebeta

← #11775429

Subgroups — #11775429

Order 1152.

549 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
1C3×#5596C211yesmaximal, characteristic
2#10591223C211yesmaximal, characteristic, complemented
3#10591063C211yesmaximal, characteristic, complemented
4#10589403C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#71813—31nomaximal
9#68281—31nomaximal
10C2×C3×#237—21no—
11C32×#121C2211yescharacteristic
12C3×#940C411yescharacteristic, complemented
13C3×#939—21no—
14C3×D4×Dic3C411yescharacteristic, complemented
15C3×#930C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C3×#893C411yescharacteristic, complemented
18C3×#888C411yescharacteristic, complemented
19C3×#885—21no—
20C3×#67⋊C4—21no—
21#63658C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63579—21no—
26#63579—21no—
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×#532—31no—
30#5596D311yescharacteristic
31#4937—31no—
32#4926—31no—
33#4719—31no—
34#4651—31no—
35C3×#327—31no—
36#4537—31no—
37#4537—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4537D311yescharacteristic, complemented
42#4470—31no—
43#4451—31no—
44C2×C32×D4—21no—
45C2×C32×D4C2×C411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C3×#237—42no—
56C3×#237—42no—
57C2×C3×D12C2×C411yescharacteristic
58C2×C3×C4×D3—21no—
59C2×C3×Dic6—21no—
60C32×C4⋊C4C2×C411yescharacteristic
61C32×C22⋊C4—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C3×#217—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3C2×C411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3C2×C411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C3×C4×Dic3D411yescharacteristic
72C2×C3×C3⋊C8—21no—
73#1514—91noSylow
74C2×C3×#41—61no—
75C2×#237—21no—
76C3×C4⋊Q8—31no—
77C3×#127—31no—
78C3×#124—61no—
79C3×#121—21no—
80C3×#121—31no—
81C3×#121—61no—
82C3×#121C2×D311yescharacteristic
83C3×#121C2×D311yescharacteristic
84C3×C4×D4—31no—
85C3×C4×D4—31no—
86C3×C4×D4—61no—
87C2×C3×C42—31no—
88#940Dic311yescharacteristic, complemented
89#939—21no—
90D4×Dic3Dic311yescharacteristic, complemented
91#930C2×D311yescharacteristic
92C2×C4×Dic3C2×D311yescharacteristic
93#893Dic311yescharacteristic, complemented
94#888Dic311yescharacteristic, complemented
95#885—21no—
96#67⋊C4—21no—
97C3×C22⋊C8—31no—
98C3×#95—31no—
99C3⋊#95—31no—
100C3⋊#95—31no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95C2×D311yescharacteristic
107#830—31no—
108#830—31no—
109#830—61no—
110#830C2×D311yescharacteristic
111#815—61no—
112Dic3⋊C8—61no—
113C4⋊(C3⋊C8)—61no—
114#803—61no—
115C23×C32—21no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C32×D4—41no—
119C32×D4—41no—
120C32×D4—41no—
121C2×C32×C4—21no—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C3×#67—42no—
129C3×#67—42no—
130C3×#67—41no—
131C3×#67—41no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—42no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3C22⋊C411yescharacteristic
142C2×C3×Dic3C22⋊C411yescharacteristic
143C2×C3×Dic3C22⋊C411yescharacteristic
144C3×D12—41no—
145C3×C4×D3—42no—
146C3×Dic6—42no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—41no—
149#532—31no—
150#432—91no—
151#383—91no—
152#327—31no—
153#327—91no—
154#327—91no—
155#327—91no—
156C3×#41—122no—
157C3×#41—122no—
158C2×C3×Q8—61no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—31no—
163C2×C3×D4—41no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4C4×D311yescharacteristic
168C2×C3×D4C2×Dic311yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—21no—
178C2×#67—21no—
179C2×#67—21no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—121no—
185C22×Dic3#6711yescharacteristic
186C22×Dic3#6711yescharacteristic
187#237—42no—
188#237—42no—
189C2×D12C2×Dic311yescharacteristic
190C2×C4×D3—21no—
191C2×Dic6—21no—
192C2×C3×C8—61no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4C4×D311yescharacteristic
197C3×C4⋊C4C2×Dic311yescharacteristic
198C3×C22⋊C4—21no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—41no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C42—31no—
205C3×C42—31no—
206C3×C42—31no—
207C3×C42—31no—
208#217—21no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—21no—
211C4⋊Dic3C2×Dic311yescharacteristic
212Dic3⋊C4—21no—
213C4×Dic3C2×Dic311yescharacteristic
214C4×Dic3C2×Dic311yescharacteristic
215C4×Dic3#6711yescharacteristic
216C4×Dic3#6711yescharacteristic
217C2×C3⋊C8—21no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—121no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32—41no—
224C22×C32—41no—
225C22×C32—41no—
226C22×C32C2×C22⋊C411yescharacteristic
227C22×C32AGL(1,ℤ/8)11yescharacteristic
228C22×C32AGL(1,ℤ/8)11yescharacteristic
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C32×C4—21no—
233C32×C4—21no—
234C32×C4—41no—
235C3⋊Dic3—81no—
236C3×Dic3—21no—
237C3×Dic3—21no—
238C3×Dic3—21no—
239C3×Dic3—21no—
240C3×Dic3—41no—
241C3×Dic3—81no—
242C2×#41—61no—
243C4⋊Q8—31no—
244#127—31no—
245#124—61no—
246#121—31no—
247#121—61no—
248#121D3211yescharacteristic
249C4×D4—31no—
250C4×D4—31no—
251C4×D4—61no—
252C2×C42—31no—
253C4⋊C8—181no—
254C22⋊C8—31no—
255C22⋊C8—91no—
256#97—181no—
257#95—31no—
258#95—91no—
259#95—181no—
260#95—181no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—41no—
265C23×C3—61no—
266C23×C3D3×D411yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C22×D3—21no—
269C3×Q8—122no—
270C3×D4—41no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—81no—
277C3×D4—81no—
278C3×D4—81no—
279C3×D4—121no—
280C3×D4—122no—
281C3×D4—122no—
282C3×D4—121no—
283C3×D4—121no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—31no—
289C2×C3×C4—31no—
290C2×C3×C4—31no—
291C2×C3×C4—31no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—81no—
299C2×C3×C4—122no—
300C2×C3×C4—121no—
301C2×C3×C4—122no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4C22×Dic311yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309#67—42no—
310#67—42no—
311#67—41no—
312#67—41no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—41no—
317C2×Dic3—42no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—122no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—241no—
329C2×Dic3—241no—
330C2×Dic3#21711yescharacteristic
331C2×Dic3#21711yescharacteristic
332C2×Dic3#21711yescharacteristic
333C2×Dic3#21711yescharacteristic
334D12—41no—
335C4×D3—42no—
336Dic6—42no—
337C3×C8—121no—
338C3⋊C8—41no—
339C3⋊C8—121no—
340C3⋊C8—121no—
341C3⋊C8—241no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—81no—
345C2×C32#41011yescharacteristic
346C2×C32#41811yescharacteristic
347C2×C32#42111yescharacteristic
348C3×D3—81no—
349#41—122no—
350#41—122no—
351C2×Q8—61no—
352C2×D4—21no—
353C2×D4—31no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4D3×Dic311yescharacteristic
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—181no—
364C22×C4C2×D3211yescharacteristic
365C2×C8—61no—
366C2×C8—181no—
367C4⋊C4—31no—
368C4⋊C4—61no—
369C4⋊C4D3×Dic311yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C42—31no—
375C42—31no—
376C42—31no—
377C42—31no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—81no—
394C22×C3—81no—
395C22×C3—81no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3—121no—
399C22×C3D3×C22⋊C411yescharacteristic
400C22×C3#91111yescharacteristic
401C22×C3#91411yescharacteristic
402C22×C3#93211yescharacteristic
403C22×C3#93211yescharacteristic
404C22×C3C2×#21711yescharacteristic
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—41no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—61no—
417C3×C4—61no—
418C3×C4—61no—
419C3×C4—61no—
420C3×C4—81no—
421C3×C4—121no—
422C3×C4—241no—
423Dic3—21no—
424Dic3—21no—
425Dic3—21no—
426Dic3—21no—
427Dic3—41no—
428Dic3—81no—
429Dic3—241no—
430Dic3—241no—
431Dic3—242no—
432C32#151411yescharacteristic, complemented, Sylow
433C23—21no—
434C23—61no—
435C23D3×#6711yescharacteristic
436Q8—122no—
437D4—41no—
438D4—41no—
439D4—41no—
440D4—121no—
441D4—122no—
442D4—122no—
443D4—121no—
444D4—121no—
445C2×C4—21no—
446C2×C4—31no—
447C2×C4—31no—
448C2×C4—31no—
449C2×C4—31no—
450C2×C4—41no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—122no—
455C2×C4—121no—
456C2×C4—122no—
457C2×C4—121no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—361no—
461C2×C4—361no—
462C2×C4—361no—
463C2×C4C2×D3×Dic311yescharacteristic
464C2×C4D3×#6711yescharacteristic
465C8—121no—
466C8—361no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—41no—
475C2×C3—41no—
476C2×C3—81no—
477C2×C3—81no—
478C2×C3—161no—
479C2×C3—241no—
480C2×C3#474011yescharacteristic
481C2×C3#477011yescharacteristic
482C2×C3#482111yescharacteristic
483C2×C3#521511yescharacteristic
484C2×C3#523611yescharacteristic
485C2×C3#524011yescharacteristic
486D3—81no—
487C22—21no—
488C22—21no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—121no—
493C22—121no—
494C22—121no—
495C22#6393211yescharacteristic
496C22#6393411yescharacteristic
497C22D3×#21711yescharacteristic
498C4—21no—
499C4—21no—
500C4—41no—
501C4—61no—
502C4—61no—
503C4—61no—
504C4—61no—
505C4—121no—
506C4—241no—
507C4—721no—
508C3—21no—
509C3#6828111yescharacteristic, complemented
510C3#7181311yescharacteristic, complemented
511C2—21no—
512C2—21no—
513C2—81no—
514C2—241no—
515C2#1059142111yescharacteristic
516C2#1059152811yescharacteristic
517C2#1059167011yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5596C2
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32#1514
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10591223C2semidirect
3. #10591063C2semidirect
4. #10589403C2semidirect
5. C3×#4537C2semidirect
6. #10589150C2semidirect
7. #10589149C2semidirect
12. C3×#940C4semidirect
14. C3×D4×Dic3C4semidirect
17. C3×#893C4semidirect
18. C3×#888C4semidirect
41. #4537D3semidirect
88. #940Dic3semidirect
90. D4×Dic3Dic3semidirect
93. #893Dic3semidirect
94. #888Dic3semidirect
432. C32#1514semidirect
509. C3#68281semidirect
510. C3#71813semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
#105912232
#105910632
#105894032
C3×#45372
#105891502
#105891492
#718133
#682813