Finite Group Databasebeta

← #11775583

Subgroups — #11775583

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C2×#63657C211yesmaximal, characteristic, complemented
3C3×#5212C211yesmaximal, characteristic, complemented
4#10589149C214yesmaximal, complemented
5#71675—31nomaximal
6#69509—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×C3×#67—21no—
9C22×C3×D12C411yescharacteristic, complemented
10C22×C3⋊(C3⋊C8)—21no—
11C2×C3×#217—21no—
12C3×#930—21no—
13C3×#930—21no—
14C3×#930C412yescomplemented
15C3×#930C2212yes—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3—21no—
18C2×C3×C4⋊Dic3C411yescharacteristic, complemented
19#63657—21no—
20#63657C2212yescomplemented
21C3×C3⋊#95C2212yescomplemented
22C2×C3×#121—31no—
23C2×#930D311yescharacteristic
24C3×#380—31no—
25#5212D311yescharacteristic, complemented
26C2×#830—31no—
27C2×#830—31no—
28C2×#830—61no—
29#4537—34no—
30#4451—34no—
31C24×C32D411yescharacteristic
32C23×C3×D3—21no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—22no—
41C2×C3×#67—22no—
42C2×C3×#67—42no—
43C2×C3×#67—42no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—22no—
46C2×C3×D12—21no—
47C2×C3×D12—42no—
48C2×C3×D12C2×C412yes—
49C2×C3⋊(C3⋊C8)—22no—
50C2×C3⋊(C3⋊C8)—42no—
51C3×#217—42no—
52C3×(C2×D3)⋊C4—22no—
53C3×(C2×D3)⋊C4—22no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—42no—
56C3×C4⋊Dic3C2×C412yes—
57#1519—91noSylow
58C22×C3×D4—31no—
59C22×C3×D4—61no—
60C23×C3×C4—21no—
61C23×C3×C4C2×D311yescharacteristic
62C23×C3×C4C2×D311yescharacteristic
63C22×#67—21no—
64C22×D12Dic311yescharacteristic, complemented
65C3×#121—32no—
66C3×#121—32no—
67C3×#121—61no—
68C3×#121—61no—
69C2×C3×C4⋊C4—31no—
70C2×C3×C4⋊C4—61no—
71C2×C3×C22⋊C4—61no—
72C2×C3×C22⋊C4—61no—
73C2×#217—21no—
74#930—21no—
75#930—21no—
76#930Dic312yescomplemented
77#930C2×D312yes—
78C2×(C2×D3)⋊C4—21no—
79C2×C4⋊Dic3—21no—
80C2×C4⋊Dic3Dic311yescharacteristic, complemented
81C22×C3⋊C8—62no—
82C22×C3⋊C8—61no—
83C22×C3⋊C8—61no—
84C3×#95—32no—
85C3⋊#95C2×D312yescomplemented
86#830—32no—
87#830—32no—
88#830—62no—
89#830—62no—
90#830—61no—
91#830—61no—
92C23×C32—41no—
93C23×C32—41no—
94C23×C32C22⋊C411yescharacteristic
95C23×C32C22⋊C411yescharacteristic
96C23×C32D812yes—
97C23×C32SD1612yes—
98C23×C32C2×D411yescharacteristic
99C22×C3×D3—22no—
100C22×C3×D3—42no—
101C22×C3×D3—42no—
102C22×C3×D3—42no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C3×#67—44no—
114C3×#67—42no—
115C3×#67—42no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—42no—
118C2×C3×Dic3—42no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C3×D12—42no—
122C3×D12—42no—
123C3⋊(C3⋊C8)—42no—
124C2×#121—31no—
125C2×C22⋊C8—91no—
126#380—31no—
127#327—94no—
128C24×C3—21no—
129C24×C3—61no—
130C24×C3#6711yescharacteristic
131C24×C3#6711yescharacteristic
132C23×D3—21no—
133C2×C3×D4—32no—
134C2×C3×D4—62no—
135C2×C3×D4—62no—
136C2×C3×D4—61no—
137C2×C3×D4—122no—
138C2×C3×D4—122no—
139C2×C3×D4—122no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—42no—
147C22×C3×C4—42no—
148C22×C3×C4—44no—
149C22×C3×C4—61no—
150C22×C3×C4—62no—
151C22×C3×C4C4×D311yescharacteristic
152C22×C3×C4C4×D311yescharacteristic
153C22×C3×C4D1211yescharacteristic
154C22×C3×C4D1211yescharacteristic
155C22×C3×C4C2×Dic311yescharacteristic
156C22×C3×C4C2×Dic311yescharacteristic
157C22×C3×C4#6711yescharacteristic
158C22×C3×C4#6711yescharacteristic
159C22×C3×C4#6711yescharacteristic
160C22×C3×C4#6711yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67—22no—
164C2×#67—22no—
165C2×#67—42no—
166C2×#67—42no—
167C22×Dic3—21no—
168C22×Dic3—22no—
169C2×D12—21no—
170C2×D12—42no—
171C2×D12C2×Dic312yes—
172C3×C4⋊C4—32no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—122no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—62no—
177C3×C22⋊C4—122no—
178#217—42no—
179(C2×D3)⋊C4—22no—
180(C2×D3)⋊C4—22no—
181C4⋊Dic3—21no—
182C4⋊Dic3—42no—
183C4⋊Dic3C2×Dic312yes—
184C2×C3⋊C8—64no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—62no—
187C2×C3⋊C8—124no—
188C2×C3⋊C8—122no—
189C2×C3⋊C8—122no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—42no—
197C22×C32—42no—
198C22×C32#10212yes—
199C22×C32#10212yes—
200C22×C32C2×C22⋊C411yescharacteristic
201C22×C32C2×D811yescharacteristic
202C22×C32C2×SD1611yescharacteristic
203C2×C3×D3—42no—
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C2×C3×D3—84no—
207C32×C4—21no—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4#9912yes—
211C3×Dic3—42no—
212C3×Dic3—82no—
213C22×D4—31no—
214C22×D4—61no—
215C23×C4D3211yescharacteristic
216C22×C8—181no—
217#121—32no—
218#121—32no—
219#121—61no—
220#121—61no—
221C2×C4⋊C4—31no—
222C2×C4⋊C4—61no—
223C2×C22⋊C4—61no—
224C2×C22⋊C4—61no—
225C22⋊C8—92no—
226C22⋊C8—181no—
227#95—32no—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—21no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—41no—
234C23×C3—41no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3—62no—
240C23×C3—122no—
241C23×C3—122no—
242C23×C3—122no—
243C23×C3(C2×D3)⋊C411yescharacteristic
244C23×C3(C2×D3)⋊C411yescharacteristic
245C23×C3#21312yes—
246C23×C3#21312yes—
247C23×C3#21412yes—
248C23×C3#21512yes—
249C23×C3#21711yescharacteristic
250C23×C3#21711yescharacteristic
251C23×C3C2×#6711yescharacteristic
252C23×C3C2×#6711yescharacteristic
253C22×D3—22no—
254C22×D3—42no—
255C22×D3—42no—
256C22×D3—42no—
257C3×D4—122no—
258C3×D4—124no—
259C3×D4—122no—
260C3×D4—122no—
261C3×D4—122no—
262C2×C3×C4—24no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—62no—
285C2×C3×C4—122no—
286C2×C3×C4—122no—
287C2×C3×C4—122no—
288C2×C3×C4—122no—
289C2×C3×C4(C2×D3)⋊C411yescharacteristic
290C2×C3×C4(C2×D3)⋊C411yescharacteristic
291C2×C3×C4#21711yescharacteristic
292C2×C3×C4#21711yescharacteristic
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×D1211yescharacteristic
295C2×C3×C4C22×Dic311yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297#67—44no—
298#67—42no—
299#67—42no—
300C2×Dic3—22no—
301C2×Dic3—42no—
302C2×Dic3—42no—
303C2×Dic3—42no—
304C2×Dic3—42no—
305D12—42no—
306D12—42no—
307C3⋊C8—124no—
308C3⋊C8—122no—
309C3⋊C8—122no—
310C2×C32—22no—
311C2×C32—21no—
312C2×C32—22no—
313C2×C32—21no—
314C2×C32C2×#9911yescharacteristic
315C2×C32C2×#10211yescharacteristic
316C2×C32#42111yescharacteristic
317C3×D3—82no—
318C24—61no—
319C24#62511yescharacteristic
320C2×D4—32no—
321C2×D4—62no—
322C2×D4—62no—
323C2×D4—61no—
324C2×D4—122no—
325C2×D4—122no—
326C2×D4—122no—
327C22×C4—42no—
328C22×C4—61no—
329C22×C4—62no—
330C22×C4D3×Dic311yescharacteristic
331C22×C4D3×Dic311yescharacteristic
332C22×C4#62511yescharacteristic
333C22×C4#62611yescharacteristic
334C22×C4#62611yescharacteristic
335C22×C4C2×D3211yescharacteristic
336C2×C8—182no—
337C2×C8—362no—
338C4⋊C4—32no—
339C4⋊C4—61no—
340C4⋊C4—122no—
341C22⋊C4—62no—
342C22⋊C4—62no—
343C22⋊C4—122no—
344C22×C3—22no—
345C22×C3—22no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—42no—
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3—44no—
372C22×C3—44no—
373C22×C3—122no—
374C22×C3—122no—
375C22×C3—122no—
376C22×C3—244no—
377C22×C3#80912yes—
378C22×C3#80912yes—
379C22×C3#83212yes—
380C22×C3#83212yes—
381C22×C3C2×(C2×D3)⋊C411yescharacteristic
382C22×C3C2×#21311yescharacteristic
383C22×C3C2×#21311yescharacteristic
384C22×C3C2×#21411yescharacteristic
385C22×C3C2×#21511yescharacteristic
386C22×C3C2×#21711yescharacteristic
387C2×D3—42no—
388C2×D3—42no—
389C2×D3—42no—
390C2×D3—84no—
391C3×C4—22no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—22no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4—122no—
402C3×C4—242no—
403C3×C4#80612yes—
404C3×C4#83412yes—
405Dic3—42no—
406Dic3—82no—
407C32#151911yescharacteristic, complemented, Sylow
408C23—41no—
409C23—41no—
410C23—62no—
411C23—122no—
412C23—122no—
413C23—122no—
414C23#371312yes—
415C23#371512yes—
416C23(C2×D3)⋊Dic311yescharacteristic
417C23(C2×D3)⋊Dic311yescharacteristic
418C23C2×#62511yescharacteristic
419D4—122no—
420D4—124no—
421D4—122no—
422D4—122no—
423D4—122no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—62no—
431C2×C4—122no—
432C2×C4—122no—
433C2×C4—122no—
434C2×C4—122no—
435C2×C4(C2×D3)⋊Dic311yescharacteristic
436C2×C4(C2×D3)⋊Dic311yescharacteristic
437C2×C4C2×D3×Dic311yescharacteristic
438C2×C4C2×#62611yescharacteristic
439C8—362no—
440C2×C3—24no—
441C2×C3—21no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—22no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—41no—
453C2×C3—42no—
454C2×C3—41no—
455C2×C3—242no—
456C2×C3C2×#80611yescharacteristic
457C2×C3C2×#80911yescharacteristic
458C2×C3#500511yescharacteristic
459C2×C3C2×#83211yescharacteristic
460C2×C3C2×#83411yescharacteristic
461C2×C3#523611yescharacteristic
462D3—82no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—42no—
470C22—42no—
471C22—122no—
472C22—122no—
473C22—122no—
474C22—244no—
475C22#6356212yes—
476C22#6356212yes—
477C22C2×#371311yescharacteristic
478C22C2×#371511yescharacteristic
479C22C2×(C2×D3)⋊Dic311yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—122no—
484C4—242no—
485C4#6358012yes—
486C3—21no—
487C3#6950911yescharacteristic, complemented
488C3#7167511yescharacteristic, complemented
489C2—21no—
490C2—22no—
491C2—22no—
492C2—21no—
493C2—242no—
494C2C2×#6356211yescharacteristic
495C2#1059111111yescharacteristic
496C2C2×#6358011yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#930C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1519
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63657C2semidirect
3. C3×#5212C2semidirect
4. #10589149C2semidirect
9. C22×C3×D12C4semidirect
14. C3×#930C4semidirect
18. C2×C3×C4⋊Dic3C4semidirect
20. #63657C22semidirect
21. C3×C3⋊#95C22semidirect
25. #5212D3semidirect
64. C22×D12Dic3semidirect
76. #930Dic3semidirect
80. C2×C4⋊Dic3Dic3semidirect
85. C3⋊#95C2×D3semidirect
407. C32#1519semidirect
487. C3#69509semidirect
488. C3#71675semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C2×#636572
C3×#52122
#105891492
#716753
#695093