Finite Group Databasebeta

← #11775153

Subgroups — #11775153

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C211yesmaximal, characteristic
2#10591239C211yesmaximal, characteristic, complemented
3#10591063C211yesmaximal, characteristic, complemented
4#10589403C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#71812—31nomaximal
9#68278—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—
21C2×Dic32—21no—
22#63658C2211yescharacteristic
23#63657C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×#532—31no—
30#5596D311yescharacteristic
31#4932—31no—
32#4926—31no—
33#4719—31no—
34#4648—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—
73Dic32—24no—
74#1505—91noSylow
75C2×C3×#41—61no—
76C2×#237—21no—
77C3×C4⋊Q8—31no—
78C3×#127—31no—
79C3×#124—61no—
80C3×#121—21no—
81C3×#121—31no—
82C3×#121—61no—
83C3×#121C2×D311yescharacteristic
84C3×#121C2×D311yescharacteristic
85C3×C4×D4—31no—
86C3×C4×D4—31no—
87C3×C4×D4—61no—
88C2×C3×C42—31no—
89#940Dic311yescharacteristic, complemented
90#939—21no—
91D4×Dic3Dic311yescharacteristic, complemented
92#930C2×D311yescharacteristic
93C2×C4×Dic3—61no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3C2×D311yescharacteristic
96#893Dic311yescharacteristic, complemented
97#888Dic311yescharacteristic, complemented
98#885—21no—
99#67⋊C4—21no—
100C3×C22⋊C8—31no—
101C3×#95—31no—
102C3⋊#95—31no—
103C3⋊#95—31no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107C3⋊#95C2×D311yescharacteristic
108#830—31no—
109#830—31no—
110#830—61no—
111#830C2×D311yescharacteristic
112#815—61no—
113Dic3⋊C8—61no—
114C4⋊(C3⋊C8)—61no—
115#803—61no—
116C23×C32—21no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C32×D4—41no—
120C32×D4—41no—
121C32×D4—41no—
122C2×C32×C4—21no—
123C2×C32×C4—41no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C3×#67—42no—
130C3×#67—41no—
131C3×#67—41no—
132C3×#67—42no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3C22⋊C411yescharacteristic
142C2×C3×Dic3C22⋊C411yescharacteristic
143C2×C3×Dic3C22⋊C411yescharacteristic
144C2×C3×Dic3C22⋊C411yescharacteristic
145C3×D12—41no—
146C3×C4×D3—42no—
147C3×Dic6—42no—
148C3⋊(C3⋊C8)—41no—
149C3×C3⋊C8—41no—
150#532—31no—
151#432—91no—
152#376—91no—
153#327—31no—
154#327—91no—
155#327—91no—
156#327—91no—
157C3×#41—122no—
158C3×#41—122no—
159C2×C3×Q8—61no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—31no—
164C2×C3×D4—41no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4C4×D311yescharacteristic
169C2×C3×D4C2×Dic311yescharacteristic
170C22×C3×C4—21no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C2×#67—21no—
179C2×#67—21no—
180C2×#67—21no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—121no—
186C22×Dic3#6711yescharacteristic
187C22×Dic3#6711yescharacteristic
188#237—42no—
189#237—42no—
190C2×D12C2×Dic311yescharacteristic
191C2×C4×D3—21no—
192C2×Dic6—21no—
193C2×C3×C8—61no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—31no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4C4×D311yescharacteristic
198C3×C4⋊C4C2×Dic311yescharacteristic
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—41no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C42—31no—
206C3×C42—31no—
207C3×C42—31no—
208C3×C42—31no—
209#217—21no—
210(C2×D3)⋊C4—21no—
211(C2×D3)⋊C4—21no—
212C4⋊Dic3C2×Dic311yescharacteristic
213Dic3⋊C4—21no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C4×Dic3C2×Dic311yescharacteristic
217C4×Dic3C2×Dic311yescharacteristic
218C4×Dic3#6711yescharacteristic
219C4×Dic3#6711yescharacteristic
220C2×C3⋊C8—21no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—121no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32—41no—
227C22×C32—41no—
228C22×C32—41no—
229C22×C32C2×C22⋊C411yescharacteristic
230C22×C32AGL(1,ℤ/8)11yescharacteristic
231C22×C32AGL(1,ℤ/8)11yescharacteristic
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C2×C3×D3—41no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—41no—
238C3⋊Dic3—42no—
239C3×Dic3—21no—
240C3×Dic3—21no—
241C3×Dic3—21no—
242C3×Dic3—42no—
243C3×Dic3—41no—
244C3×Dic3#10412yes—
245C2×#41—61no—
246C4⋊Q8—31no—
247#127—31no—
248#124—61no—
249#121—31no—
250#121—61no—
251#121D3211yescharacteristic
252C4×D4—31no—
253C4×D4—31no—
254C4×D4—61no—
255C2×C42—31no—
256C2×C42—181no—
257C4⋊C8—181no—
258C22⋊C8—31no—
259C22⋊C8—91no—
260#97—181no—
261#95—31no—
262#95—91no—
263#95—181no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—41no—
268C23×C3—61no—
269C23×C3D3×D411yescharacteristic
270C23×C3C2×#6711yescharacteristic
271C22×D3—21no—
272C3×Q8—122no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4—41no—
279C3×D4—81no—
280C3×D4—81no—
281C3×D4—81no—
282C3×D4—121no—
283C3×D4—122no—
284C3×D4—122no—
285C3×D4—121no—
286C3×D4—121no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—31no—
292C2×C3×C4—31no—
293C2×C3×C4—31no—
294C2×C3×C4—31no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—62no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—62no—
302C2×C3×C4—61no—
303C2×C3×C4—81no—
304C2×C3×C4—122no—
305C2×C3×C4—122no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4C2×C4×D311yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4C22×Dic311yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312#67—42no—
313#67—41no—
314#67—41no—
315#67—42no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—21no—
321C2×Dic3—42no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—122no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—241no—
332C2×Dic3—241no—
333C2×Dic3#21711yescharacteristic
334C2×Dic3#21711yescharacteristic
335C2×Dic3#21711yescharacteristic
336C2×Dic3#21711yescharacteristic
337D12—41no—
338C4×D3—42no—
339Dic6—42no—
340C3×C8—121no—
341C3⋊C8—41no—
342C3⋊C8—121no—
343C3⋊C8—121no—
344C3⋊C8—241no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—81no—
348C2×C32#41011yescharacteristic
349C2×C32#41811yescharacteristic
350C2×C32C2×#10411yescharacteristic
351C3×D3—81no—
352#41—122no—
353#41—122no—
354C2×Q8—61no—
355C2×D4—21no—
356C2×D4—31no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4D3×Dic311yescharacteristic
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—61no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368C2×C8—61no—
369C2×C8—181no—
370C4⋊C4—31no—
371C4⋊C4—61no—
372C4⋊C4D3×Dic311yescharacteristic
373C22⋊C4—21no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C42—31no—
378C42—31no—
379C42—31no—
380C42—31no—
381C42—184no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—81no—
398C22×C3—81no—
399C22×C3—81no—
400C22×C3—121no—
401C22×C3—121no—
402C22×C3—121no—
403C22×C3D3×C22⋊C411yescharacteristic
404C22×C3#91111yescharacteristic
405C22×C3#91411yescharacteristic
406C22×C3#93211yescharacteristic
407C22×C3#93211yescharacteristic
408C22×C3C2×#21711yescharacteristic
409C2×D3—41no—
410C2×D3—41no—
411C2×D3—41no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—32no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—41no—
420C3×C4—41no—
421C3×C4—61no—
422C3×C4—61no—
423C3×C4—61no—
424C3×C4—81no—
425C3×C4—122no—
426C3×C4—121no—
427Dic3—21no—
428Dic3—21no—
429Dic3—21no—
430Dic3—42no—
431Dic3—41no—
432Dic3—122no—
433Dic3—122no—
434Dic3—242no—
435Dic3#83712yes—
436C32#150511yescharacteristic, complemented, Sylow
437C23—21no—
438C23—61no—
439C23D3×#6711yescharacteristic
440Q8—122no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—121no—
445D4—122no—
446D4—122no—
447D4—121no—
448D4—121no—
449C2×C4—21no—
450C2×C4—31no—
451C2×C4—31no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—41no—
455C2×C4—62no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—62no—
459C2×C4—61no—
460C2×C4—122no—
461C2×C4—122no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—182no—
465C2×C4—361no—
466C2×C4—361no—
467C2×C4C2×D3×Dic311yescharacteristic
468C2×C4D3×#6711yescharacteristic
469C8—121no—
470C8—361no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—41no—
479C2×C3—41no—
480C2×C3—81no—
481C2×C3—81no—
482C2×C3—161no—
483C2×C3—241no—
484C2×C3#474011yescharacteristic
485C2×C3#477011yescharacteristic
486C2×C3D3×#10411yescharacteristic
487C2×C3#521511yescharacteristic
488C2×C3C2×#83711yescharacteristic
489C2×C3#524011yescharacteristic
490D3—81no—
491C22—21no—
492C22—21no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—121no—
497C22—121no—
498C22—121no—
499C22#6393211yescharacteristic
500C22#6393411yescharacteristic
501C22D3×#21711yescharacteristic
502C4—21no—
503C4—21no—
504C4—32no—
505C4—41no—
506C4—61no—
507C4—61no—
508C4—61no—
509C4—122no—
510C4—121no—
511C4—362no—
512C3—21no—
513C3#6827811yescharacteristic, complemented
514C3#7181211yescharacteristic, complemented
515C2—21no—
516C2—21no—
517C2—81no—
518C2—241no—
519C2#1059142111yescharacteristic
520C2#1059152811yescharacteristic
521C2D3×#83711yescharacteristic
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#1505
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. #10591239C2semidirect
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
89. #940Dic3semidirect
91. D4×Dic3Dic3semidirect
96. #893Dic3semidirect
97. #888Dic3semidirect
436. C32#1505semidirect
513. C3#68278semidirect
514. C3#71812semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
#105912392
#105910632
#105894032
C3×#45372
#105891502
#105891492
#718123
#682783