Finite Group Databasebeta

← #11784801

Subgroups — #11784801

Order 1152.

1331 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2#10592906C211yesmaximal, characteristic, complemented
3C3×C4×#217C211yesmaximal, characteristic, complemented
4C2×#63569C214yesmaximal, complemented
5#72138—31nomaximal
6#69454—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×C3×#67—21no—
9C2×C3×#235—21no—
10C2×C3×#235—21no—
11C2×C3×#235—28no—
12C2×C3×#235C412yescomplemented
13C2×C3×#235C2212yes—
14C22×C3×D12C411yescharacteristic, complemented
15C22×C3×C4×D3—21no—
16C22×C3×Dic6C411yescharacteristic, complemented
17C2×#3748C2212yescomplemented
18C2×C3×#217—21no—
19C2×C3×C4×Dic3C2212yescomplemented
20#63657—21no—
21#63657—21no—
22C3×C3⋊#95—21no—
23#63569—28no—
24C22×C3×#41—31no—
25C22×#235D311yescharacteristic
26C3×C4×C22⋊C4—31no—
27C2×#837—34no—
28C4×#217D311yescharacteristic, complemented
29#5207—31no—
30#5207—31no—
31#5207—61no—
32C2×#805—34no—
33C24×C32D411yescharacteristic
34C23×C3×D3—21no—
35C22×C32×C4—24no—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4C2311yescharacteristic
42C2×C3×#67—28no—
43C2×C3×#67—22no—
44C2×C3×#67—22no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—22no—
47C3×#235—28no—
48C3×#235—28no—
49C3×#235—24no—
50C3×#235—24no—
51C3×#235—24no—
52C3×#235D418yes—
53C2×C3×D12—21no—
54C2×C3×D12—24no—
55C2×C3×D12C2×C412yes—
56C2×C3×C4×D3—28no—
57C2×C3×C4×D3—22no—
58C2×C3×C4×D3—22no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—24no—
61C2×C3×Dic6C2×C412yes—
62#3748—24no—
63C2×C3⋊(C3⋊C8)—22no—
64C3×#217—24no—
65C3×C4×Dic3—24no—
66#1789—91noSylow
67C2×C3×#41—32no—
68C2×C3×#41—32no—
69C2×C3×#41—68no—
70C2×C3×#41—61no—
71C2×C3×#41—61no—
72C22×C3×Q8—31no—
73C22×C3×D4—31no—
74C22×C3×D4—61no—
75C23×C3×C4—21no—
76C23×C3×C4—61no—
77C23×C3×C4C2×D311yescharacteristic
78C23×C3×C4C2×D311yescharacteristic
79C22×#67—21no—
80C2×#235—21no—
81C2×#235—21no—
82C2×#235—28no—
83C2×#235Dic312yescomplemented
84C2×#235C2×D312yes—
85C22×D12Dic311yescharacteristic, complemented
86C22×C4×D3—21no—
87C22×Dic6Dic311yescharacteristic, complemented
88C2×C3×C22⋊C4—61no—
89C2×C3×C42—32no—
90C2×#217—21no—
91C2×C4×Dic3C2×D312yescomplemented
92C2×#208—32no—
93C2×#208—32no—
94C2×#208—62no—
95C3×#95—61no—
96#837—68no—
97C3⋊#95—21no—
98#830—62no—
99#830—62no—
100#830—61no—
101#830—61no—
102#830—61no—
103#830—61no—
104#805—68no—
105C23×C32—22no—
106C23×C32—22no—
107C23×C32—41no—
108C23×C32C22⋊C411yescharacteristic
109C23×C32C22⋊C411yescharacteristic
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—24no—
112C22×C3×D3—22no—
113C22×C3×D3—42no—
114C22×C3×D3—42no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4C22⋊C411yescharacteristic
121C2×C32×C4C22⋊C411yescharacteristic
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D414yes—
125C3×#67—28no—
126C3×#67—28no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—42no—
132C3×D12—24no—
133C3×D12—22no—
134C3×D12C22⋊C414yescomplemented
135C3×C4×D3—28no—
136C3×C4×D3—28no—
137C3×Dic6—24no—
138C3×Dic6—22no—
139C3×Dic6C22⋊C414yescomplemented
140C3⋊(C3⋊C8)—42no—
141C22×#41—31no—
142C2×#104—94no—
143#407—91no—
144C4×C22⋊C4—31no—
145C24×C3—21no—
146C24×C3—61no—
147C24×C3#6711yescharacteristic
148C24×C3#6711yescharacteristic
149C23×D3—21no—
150C3×#41—38no—
151C3×#41—64no—
152C3×#41—64no—
153C3×#41—68no—
154C3×#41—68no—
155C3×#41—64no—
156C2×C3×Q8—32no—
157C2×C3×Q8—64no—
158C2×C3×Q8—61no—
159C2×C3×D4—32no—
160C2×C3×D4—64no—
161C2×C3×D4—68no—
162C2×C3×D4—62no—
163C2×C3×D4—62no—
164C2×C3×D4—61no—
165C22×C3×C4—24no—
166C22×C3×C4—24no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—44no—
174C22×C3×C4—68no—
175C22×C3×C4—61no—
176C22×C3×C4—62no—
177C22×C3×C4—62no—
178C22×C3×C4—62no—
179C22×C3×C4C4×D311yescharacteristic
180C22×C3×C4C4×D311yescharacteristic
181C22×C3×C4D1211yescharacteristic
182C22×C3×C4D1211yescharacteristic
183C22×C3×C4C2×Dic311yescharacteristic
184C22×C3×C4C2×Dic311yescharacteristic
185C22×C3×C4#6711yescharacteristic
186C22×C3×C4#6711yescharacteristic
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—28no—
192C2×#67—22no—
193C2×#67—22no—
194C22×Dic3—21no—
195C22×Dic3—22no—
196#235—28no—
197#235—28no—
198#235—24no—
199#235—24no—
200#235—24no—
201#235#6718yes—
202C2×D12—21no—
203C2×D12—24no—
204C2×D12C2×Dic312yes—
205C2×C4×D3—28no—
206C2×C4×D3—22no—
207C2×C4×D3—22no—
208C2×Dic6—21no—
209C2×Dic6—24no—
210C2×Dic6C2×Dic312yes—
211C3×C22⋊C4—64no—
212C3×C42—64no—
213#217—24no—
214C4×Dic3—24no—
215#208—64no—
216#208—64no—
217#208—124no—
218C2×C3⋊C8—64no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—62no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32—44no—
229C22×C32#10412yescomplemented
230C22×C32C2×C22⋊C411yescharacteristic
231C22×C32#12012yes—
232C2×C3×D3—24no—
233C2×C3×D3—48no—
234C2×C3×D3—42no—
235C2×C3×D3—42no—
236C32×C4—21no—
237C32×C4—21no—
238C32×C4C2×C22⋊C412yes—
239C32×C4#12012yes—
240C3×Dic3—24no—
241C3×Dic3—44no—
242C2×#41—32no—
243C2×#41—32no—
244C2×#41—68no—
245C2×#41—61no—
246C2×#41—61no—
247C22×Q8—31no—
248C22×D4—31no—
249C22×D4—61no—
250C23×C4—61no—
251C23×C4D3211yescharacteristic
252C2×M16—92no—
253C2×C22⋊C4—61no—
254C2×C42—32no—
255#104—188no—
256C22⋊C8—181no—
257C22⋊C8—181no—
258#95—61no—
259C23×C3—22no—
260C23×C3—22no—
261C23×C3—22no—
262C23×C3—22no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—42no—
267C23×C3—42no—
268C23×C3—41no—
269C23×C3—41no—
270C23×C3—42no—
271C23×C3—64no—
272C23×C3—62no—
273C23×C3—122no—
274C23×C3—122no—
275C23×C3(C2×D3)⋊C411yescharacteristic
276C23×C3(C2×D3)⋊C411yescharacteristic
277C23×C3#21711yescharacteristic
278C23×C3#21711yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C23×C3C2×#6711yescharacteristic
281C22×D3—24no—
282C22×D3—22no—
283C22×D3—42no—
284C22×D3—42no—
285C3×Q8—34no—
286C3×Q8—64no—
287C3×Q8—62no—
288C3×D4—34no—
289C3×D4—64no—
290C3×D4—68no—
291C3×D4—68no—
292C3×D4—62no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—24no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—68no—
314C2×C3×C4—64no—
315C2×C3×C4—62no—
316C2×C3×C4—68no—
317C2×C3×C4—64no—
318C2×C3×C4—122no—
319C2×C3×C4—122no—
320C2×C3×C4(C2×D3)⋊C411yescharacteristic
321C2×C3×C4(C2×D3)⋊C411yescharacteristic
322C2×C3×C4#21711yescharacteristic
323C2×C3×C4#21711yescharacteristic
324C2×C3×C4C2×C4×D311yescharacteristic
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4D3×D414yes—
327C2×C3×C4C22×Dic311yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6714yes—
330#67—28no—
331#67—28no—
332C2×Dic3—24no—
333C2×Dic3—22no—
334C2×Dic3—24no—
335C2×Dic3—42no—
336C2×Dic3—42no—
337D12—24no—
338D12—22no—
339D12#21714yescomplemented
340C4×D3—28no—
341C4×D3—28no—
342Dic6—24no—
343Dic6—22no—
344Dic6#21714yescomplemented
345C3⋊C8—124no—
346C3⋊C8—122no—
347C3⋊C8—122no—
348C2×C32—22no—
349C2×C32—22no—
350C2×C32—41no—
351C2×C32#37911yescharacteristic
352C2×C32C2×#10411yescharacteristic
353C2×C32#42111yescharacteristic
354C3×D3—44no—
355C24—61no—
356C24#62511yescharacteristic
357#41—38no—
358#41—64no—
359#41—64no—
360#41—68no—
361#41—68no—
362#41—64no—
363C2×Q8—32no—
364C2×Q8—64no—
365C2×Q8—61no—
366C2×D4—32no—
367C2×D4—64no—
368C2×D4—68no—
369C2×D4—62no—
370C2×D4—62no—
371C2×D4—61no—
372C22×C4—24no—
373C22×C4—68no—
374C22×C4—61no—
375C22×C4—62no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4D3×Dic311yescharacteristic
379C22×C4D3×Dic311yescharacteristic
380C22×C4#62511yescharacteristic
381C22×C4#62611yescharacteristic
382C22×C4#62611yescharacteristic
383C22×C4C2×D3211yescharacteristic
384M16—184no—
385C2×C8—182no—
386C22⋊C4—64no—
387C42—64no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—22no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—22no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—44no—
413C22×C3—44no—
414C22×C3—48no—
415C22×C3—64no—
416C22×C3—128no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3#80512yescomplemented
420C22×C3#83712yescomplemented
421C22×C3C2×(C2×D3)⋊C411yescharacteristic
422C22×C3#93712yes—
423C22×C3C2×#21711yescharacteristic
424C22×C3#95312yes—
425C2×D3—24no—
426C2×D3—48no—
427C2×D3—42no—
428C2×D3—42no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4—64no—
438C3×C4—124no—
439C3×C4D3×C22⋊C412yes—
440C3×C4#88212yes—
441C3×C4C2×#21712yes—
442C3×C4#95312yes—
443Dic3—24no—
444Dic3—44no—
445C32#178911yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—41no—
449C23—64no—
450C23—62no—
451C23—122no—
452C23—122no—
453C23(C2×D3)⋊Dic311yescharacteristic
454C23(C2×D3)⋊Dic311yescharacteristic
455C23C2×#62511yescharacteristic
456Q8—34no—
457Q8—64no—
458Q8—62no—
459D4—34no—
460D4—64no—
461D4—68no—
462D4—68no—
463D4—62no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—68no—
470C2×C4—64no—
471C2×C4—62no—
472C2×C4—68no—
473C2×C4—64no—
474C2×C4—122no—
475C2×C4—122no—
476C2×C4(C2×D3)⋊Dic311yescharacteristic
477C2×C4(C2×D3)⋊Dic311yescharacteristic
478C2×C4C2×D3×Dic311yescharacteristic
479C2×C4C2×#62611yescharacteristic
480C2×C4D3×#6714yes—
481C8—362no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—42no—
490C2×C3—42no—
491C2×C3—42no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—124no—
495C2×C3C2×#80511yescharacteristic
496C2×C3#495511yescharacteristic
497C2×C3#500511yescharacteristic
498C2×C3C2×#83711yescharacteristic
499C2×C3#523611yescharacteristic
500C2×C3#524711yescharacteristic
501D3—44no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—44no—
510C22—64no—
511C22—128no—
512C22—122no—
513C22—122no—
514C22#6356912yescomplemented
515C22C2×(C2×D3)⋊Dic311yescharacteristic
516C22#6397612yes—
517C4—21no—
518C4—21no—
519C4—64no—
520C4—124no—
521C4D3×#21712yes—
522C4#6397712yes—
523C3—21no—
524C3#6945411yescharacteristic, complemented
525C3#7213811yescharacteristic, complemented
526C2—22no—
527C2—22no—
528C2—41no—
529C2—124no—
530C2C2×#6356911yescharacteristic
531C2#1059111111yescharacteristic
532C2#1059170611yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#235C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1789
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592906C2semidirect
3. C3×C4×#217C2semidirect
4. C2×#63569C2semidirect
12. C2×C3×#235C4semidirect
14. C22×C3×D12C4semidirect
16. C22×C3×Dic6C4semidirect
17. C2×#3748C22semidirect
19. C2×C3×C4×Dic3C22semidirect
28. C4×#217D3semidirect
83. C2×#235Dic3semidirect
85. C22×D12Dic3semidirect
87. C22×Dic6Dic3semidirect
91. C2×C4×Dic3C2×D3semidirect
134. C3×D12C22⋊C4semidirect
139. C3×Dic6C22⋊C4semidirect
229. C22×C32#104semidirect
339. D12#217semidirect
344. Dic6#217semidirect
419. C22×C3#805semidirect
420. C22×C3#837semidirect
445. C32#1789semidirect
514. C22#63569semidirect
524. C3#69454semidirect
525. C3#72138semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
#105929062
C3×C4×#2172
C2×#635692
#721383
#694543