Finite Group Databasebeta

← #11775581

Subgroups — #11775581

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4#10589150C214yesmaximal, complemented
5#71675—31nomaximal
6#69944—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×C3×#67—21no—
9C22×C3×D12C411yescharacteristic, complemented
10C2×#3757—21no—
11C2×C4⋊(C3⋊Dic3)—21no—
12C3×#930—21no—
13C3×#930—21no—
14C3×#930C412yescomplemented
15C3×#930C2212yes—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C411yescharacteristic, complemented
18C22×C3×C3⋊C8—21no—
19#63658C2212yescomplemented
20C3×#830—21no—
21C3×#830C2212yescomplemented
22C2×C3×#121—31no—
23C2×#930D311yescharacteristic
24C2×C3×C22⋊C8—31no—
25#5212—31no—
26#5212—31no—
27#5212—61no—
28C2×#830D311yescharacteristic, complemented
29#4537—34no—
30#4470—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
40C22×C3⋊Dic3—22no—
41C2×C3×#67—22no—
42C2×C3×#67—22no—
43C2×C3×#67—42no—
44C2×C3×#67—42no—
45C22×C3×Dic3—21no—
46C2×C3×D12—21no—
47C2×C3×D12—42no—
48C2×C3×D12C2×C412yes—
49#3757—42no—
50C4⋊(C3⋊Dic3)—42no—
51C3×(C2×D3)⋊C4—22no—
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3C2×C412yes—
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—42no—
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
65C22×C3×C8—61no—
66C3×#121—32no—
67C3×#121—32no—
68C3×#121—61no—
69C3×#121—61no—
70C2×C3×C4⋊C4—31no—
71C2×C3×C22⋊C4—61no—
72C2×#217—62no—
73C2×#217—61no—
74C2×#217—61no—
75#930—21no—
76#930—21no—
77#930Dic312yescomplemented
78#930C2×D312yes—
79C2×(C2×D3)⋊C4—21no—
80C2×C4⋊Dic3—62no—
81C2×C4⋊Dic3—61no—
82C2×C4⋊Dic3—61no—
83C2×C4⋊Dic3Dic311yescharacteristic, complemented
84C22×C3⋊C8—21no—
85C3×C22⋊C8—32no—
86C3×C22⋊C8—61no—
87C3⋊#95—32no—
88C3⋊#95—32no—
89C3⋊#95—62no—
90#830—21no—
91#830C2×D312yescomplemented
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
113C2×C3⋊Dic3—42no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3—42no—
116C3×#67—44no—
117C3×#67—42no—
118C3×#67—42no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—42no—
121C3×D12—42no—
122C3×D12—42no—
123C3×C3⋊C8—42no—
124C2×#121—31no—
125C2×C22⋊C8—31no—
126#380—91no—
127#327—94no—
128C24×C3—21no—
129C24×C3—61no—
130C24×C3D1211yescharacteristic
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×C4C4×D311yescharacteristic
151C22×C3×C4C4×D311yescharacteristic
152C22×C3×C4D1211yescharacteristic
153C22×C3×C4C2×Dic311yescharacteristic
154C22×C3×C4C2×Dic311yescharacteristic
155C22×C3×C4#6711yescharacteristic
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4#6711yescharacteristic
158C22×C3×C4#6711yescharacteristic
159C22×C3×C4#6711yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—22no—
163C2×#67—22no—
164C2×#67—42no—
165C2×#67—42no—
166C22×Dic3—21no—
167C22×Dic3—64no—
168C22×Dic3—62no—
169C22×Dic3—62no—
170C2×D12—21no—
171C2×D12—42no—
172C2×D12C2×Dic312yes—
173C2×C3×C8—62no—
174C2×C3×C8—122no—
175C3×C4⋊C4—32no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—62no—
178C3×C22⋊C4—62no—
179#217—124no—
180#217—122no—
181#217—122no—
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—22no—
184C4⋊Dic3—21no—
185C4⋊Dic3—124no—
186C4⋊Dic3—122no—
187C4⋊Dic3—122no—
188C4⋊Dic3C2×Dic312yes—
189C2×C3⋊C8—22no—
190C2×C3⋊C8—42no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32—42no—
198C22×C32—42no—
199C22×C32#10212yes—
200C22×C32#10212yes—
201C22×C32C2×C22⋊C411yescharacteristic
202C22×C32C2×D811yescharacteristic
203C22×C32C2×SD1611yescharacteristic
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C2×C3×D3—42no—
207C2×C3×D3—84no—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—21no—
211C32×C4#9912yes—
212C3⋊Dic3—82no—
213C3×Dic3—42no—
214C22×D4—31no—
215C22×D4—61no—
216C23×C4D3211yescharacteristic
217C22×C8—61no—
218#121—32no—
219#121—32no—
220#121—61no—
221#121—61no—
222C2×C4⋊C4—31no—
223C2×C4⋊C4—181no—
224C2×C22⋊C4—61no—
225C2×C22⋊C4—181no—
226C22⋊C8—32no—
227C22⋊C8—61no—
228#95—92no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—41no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3—41no—
238C23×C3—42no—
239C23×C3—42no—
240C23×C3—62no—
241C23×C3—122no—
242C23×C3—122no—
243C23×C3—122no—
244C23×C3#20412yes—
245C23×C3D2412yes—
246C23×C3(C2×D3)⋊C411yescharacteristic
247C23×C3(C2×D3)⋊C411yescharacteristic
248C23×C3#21312yes—
249C23×C3#21412yes—
250C23×C3#21711yescharacteristic
251C23×C3#21711yescharacteristic
252C23×C3C2×D1211yescharacteristic
253C23×C3C2×#6711yescharacteristic
254C22×D3—22no—
255C22×D3—42no—
256C22×D3—42no—
257C22×D3—42no—
258C3×D4—122no—
259C3×D4—124no—
260C3×D4—122no—
261C3×D4—122no—
262C3×D4—122no—
263C2×C3×C4—24no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—62no—
286C2×C3×C4—122no—
287C2×C3×C4(C2×D3)⋊C411yescharacteristic
288C2×C3×C4(C2×D3)⋊C411yescharacteristic
289C2×C3×C4#21711yescharacteristic
290C2×C3×C4#21711yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C22×Dic311yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295#67—44no—
296#67—42no—
297#67—42no—
298C2×Dic3—22no—
299C2×Dic3—42no—
300C2×Dic3—124no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3—124no—
304C2×Dic3—124no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308C2×Dic3—122no—
309D12—42no—
310D12—42no—
311C3×C8—122no—
312C3⋊C8—42no—
313C2×C32—21no—
314C2×C32—21no—
315C2×C32—22no—
316C2×C32—22no—
317C2×C32C2×#9911yescharacteristic
318C2×C32C2×#10211yescharacteristic
319C2×C32#42111yescharacteristic
320C3×D3—82no—
321C24—61no—
322C24#62611yescharacteristic
323C2×D4—32no—
324C2×D4—62no—
325C2×D4—62no—
326C2×D4—61no—
327C2×D4—122no—
328C2×D4—122no—
329C2×D4—122no—
330C22×C4—42no—
331C22×C4—61no—
332C22×C4—182no—
333C22×C4D3×Dic311yescharacteristic
334C22×C4D3×Dic311yescharacteristic
335C22×C4#62511yescharacteristic
336C22×C4#62511yescharacteristic
337C22×C4#62611yescharacteristic
338C22×C4C2×D3211yescharacteristic
339C2×C8—62no—
340C2×C8—122no—
341C4⋊C4—32no—
342C4⋊C4—61no—
343C4⋊C4—362no—
344C22⋊C4—62no—
345C22⋊C4—62no—
346C22⋊C4—362no—
347C22×C3—22no—
348C22×C3—22no—
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—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—44no—
375C22×C3—44no—
376C22×C3—122no—
377C22×C3—122no—
378C22×C3—122no—
379C22×C3—244no—
380C22×C3#82112yes—
381C22×C3#82112yes—
382C22×C3#83212yes—
383C22×C3#83212yes—
384C22×C3C2×#20411yescharacteristic
385C22×C3C2×D2411yescharacteristic
386C22×C3C2×(C2×D3)⋊C411yescharacteristic
387C22×C3C2×#21311yescharacteristic
388C22×C3C2×#21411yescharacteristic
389C22×C3C2×#21711yescharacteristic
390C2×D3—42no—
391C2×D3—42no—
392C2×D3—42no—
393C2×D3—84no—
394C3×C4—22no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—22no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—122no—
405C3×C4#80612yes—
406C3×C4#83412yes—
407Dic3—42no—
408Dic3—244no—
409Dic3—242no—
410Dic3—242no—
411C32#151911yescharacteristic, complemented, Sylow
412C23—41no—
413C23—41no—
414C23—62no—
415C23—122no—
416C23—122no—
417C23—122no—
418C23#371412yes—
419C23#371612yes—
420C23(C2×D3)⋊Dic311yescharacteristic
421C23(C2×D3)⋊Dic311yescharacteristic
422C23C2×#62611yescharacteristic
423D4—122no—
424D4—124no—
425D4—122no—
426D4—122no—
427D4—122no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—62no—
435C2×C4—122no—
436C2×C4—362no—
437C2×C4—362no—
438C2×C4—362no—
439C2×C4(C2×D3)⋊Dic311yescharacteristic
440C2×C4(C2×D3)⋊Dic311yescharacteristic
441C2×C4C2×D3×Dic311yescharacteristic
442C2×C4C2×#62511yescharacteristic
443C8—122no—
444C2×C3—22no—
445C2×C3—22no—
446C2×C3—21no—
447C2×C3—22no—
448C2×C3—22no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—42no—
458C2×C3—42no—
459C2×C3—242no—
460C2×C3C2×#80611yescharacteristic
461C2×C3C2×#82111yescharacteristic
462C2×C3#513911yescharacteristic
463C2×C3C2×#83211yescharacteristic
464C2×C3C2×#83411yescharacteristic
465C2×C3#523611yescharacteristic
466D3—82no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—42no—
474C22—42no—
475C22—122no—
476C22—122no—
477C22—122no—
478C22—244no—
479C22#6356312yes—
480C22#6356312yes—
481C22C2×#371411yescharacteristic
482C22C2×#371611yescharacteristic
483C22C2×(C2×D3)⋊Dic311yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—122no—
488C4—722no—
489C4#6358012yes—
490C3—21no—
491C3#6994411yescharacteristic, complemented
492C3#7167511yescharacteristic, complemented
493C2—21no—
494C2—22no—
495C2—22no—
496C2—21no—
497C2—242no—
498C2C2×#6356311yescharacteristic
499C2#1059111011yescharacteristic
500C2C2×#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. #10592911C2semidirect
3. C2×C3×#830C2semidirect
4. #10589150C2semidirect
9. C22×C3×D12C4semidirect
14. C3×#930C4semidirect
17. C2×C3×C4⋊Dic3C4semidirect
19. #63658C22semidirect
21. C3×#830C22semidirect
28. C2×#830D3semidirect
64. C22×D12Dic3semidirect
77. #930Dic3semidirect
83. C2×C4⋊Dic3Dic3semidirect
91. #830C2×D3semidirect
411. C32#1519semidirect
491. C3#69944semidirect
492. 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
#105929112
C2×C3×#8302
#105891502
#716753
#699443