Finite Group Databasebeta

← #11775211

Subgroups — #11775211

Order 1152.

821 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4#10589150C214yesmaximal, complemented
5#71673—31nomaximal
6#69977—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
18C2×C3×#208—21no—
19#63658C2212yescomplemented
20C3×#830—21no—
21C3×#830C2212yescomplemented
22C2×C3×#121—31no—
23C2×#930D311yescharacteristic
24C3×#407—31no—
25C4×#217—31no—
26C4×#217—31no—
27C4×#217—61no—
28#5207D311yescharacteristic, 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—44no—
44C22×C3×Dic3—21no—
45C2×C3×D12—21no—
46C2×C3×D12—42no—
47C2×C3×D12C2×C412yes—
48#3757—24no—
49C4×C3⋊Dic3—42no—
50C3×(C2×D3)⋊C4—22no—
51C3×(C2×D3)⋊C4—22no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3C2×C412yes—
54C3×#208—42no—
55C2×C3×C3⋊C8—22no—
56#1507—91noSylow
57C22×C3×D4—31no—
58C22×C3×D4—61no—
59C23×C3×C4—21no—
60C23×C3×C4C2×D311yescharacteristic
61C23×C3×C4C2×D311yescharacteristic
62C22×#67—21no—
63C22×D12Dic311yescharacteristic, complemented
64C2×C3×M16—61no—
65C3×#121—32no—
66C3×#121—32no—
67C3×#121—61no—
68C3×#121—61no—
69C2×C3×C4⋊C4—31no—
70C2×C3×C22⋊C4—61no—
71C2×#217—62no—
72C2×#217—61no—
73C2×#217—61no—
74#930—21no—
75#930—21no—
76#930Dic312yescomplemented
77#930C2×D312yes—
78C2×(C2×D3)⋊C4—21no—
79C2×C4⋊Dic3Dic311yescharacteristic, complemented
80C2×C4×Dic3—62no—
81C2×C4×Dic3—61no—
82C2×C4×Dic3—61no—
83C2×#208—21no—
84C3×C22⋊C8—32no—
85C3×C22⋊C8—61no—
86C3⋊#95—32no—
87C3⋊#95—32no—
88C3⋊#95—62no—
89#830—21no—
90#830C2×D312yescomplemented
91C23×C32—22no—
92C23×C32—22no—
93C23×C32—41no—
94C23×C32C22⋊C411yescharacteristic
95C23×C32C22⋊C411yescharacteristic
96C23×C32C2×D411yescharacteristic
97C22×C3×D3—22no—
98C22×C3×D3—42no—
99C22×C3×D3—42no—
100C22×C3×D3—42no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—24no—
112C2×C3⋊Dic3—42no—
113C2×C3⋊Dic3—42no—
114C3×#67—44no—
115C3×#67—44no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—42no—
118C3×D12—42no—
119C3×D12—42no—
120C3×C3⋊C8—42no—
121C2×#121—31no—
122#407—31no—
123C4×C22⋊C4—91no—
124#327—94no—
125C24×C3—21no—
126C24×C3—61no—
127C24×C3D1211yescharacteristic
128C24×C3#6711yescharacteristic
129C23×D3—21no—
130C2×C3×D4—32no—
131C2×C3×D4—62no—
132C2×C3×D4—62no—
133C2×C3×D4—61no—
134C2×C3×D4—122no—
135C2×C3×D4—124no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—42no—
143C22×C3×C4—42no—
144C22×C3×C4—44no—
145C22×C3×C4—61no—
146C22×C3×C4C4×D311yescharacteristic
147C22×C3×C4C4×D311yescharacteristic
148C22×C3×C4D1211yescharacteristic
149C22×C3×C4C2×Dic311yescharacteristic
150C22×C3×C4C2×Dic311yescharacteristic
151C22×C3×C4#6711yescharacteristic
152C22×C3×C4#6711yescharacteristic
153C22×C3×C4#6711yescharacteristic
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4#6711yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—22no—
159C2×#67—22no—
160C2×#67—44no—
161C22×Dic3—21no—
162C22×Dic3—64no—
163C22×Dic3—62no—
164C22×Dic3—62no—
165C2×D12—21no—
166C2×D12—42no—
167C2×D12C2×Dic312yes—
168C3×M16—122no—
169C2×C3×C8—62no—
170C3×C4⋊C4—32no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—62no—
173C3×C22⋊C4—62no—
174#217—68no—
175#217—64no—
176#217—64no—
177(C2×D3)⋊C4—22no—
178(C2×D3)⋊C4—22no—
179C4⋊Dic3—21no—
180C4⋊Dic3C2×Dic312yes—
181C4×Dic3—124no—
182C4×Dic3—122no—
183C4×Dic3—122no—
184#208—42no—
185C2×C3⋊C8—22no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—44no—
194C22×C32#10412yes—
195C22×C32C2×C22⋊C411yescharacteristic
196C22×C32AGL(1,ℤ/8)12yes—
197C2×C3×D3—42no—
198C2×C3×D3—42no—
199C2×C3×D3—42no—
200C2×C3×D3—84no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—21no—
204C32×C4#9912yes—
205C3⋊Dic3—44no—
206C3×Dic3—42no—
207C22×D4—31no—
208C22×D4—61no—
209C23×C4D3211yescharacteristic
210C2×M16—61no—
211#121—32no—
212#121—32no—
213#121—61no—
214#121—61no—
215C2×C4⋊C4—31no—
216C2×C22⋊C4—61no—
217C2×C22⋊C4—181no—
218C2×C42—181no—
219C22⋊C8—32no—
220C22⋊C8—61no—
221#95—92no—
222C23×C3—24no—
223C23×C3—22no—
224C23×C3—22no—
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—21no—
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—42no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3—42no—
234C23×C3—62no—
235C23×C3—122no—
236C23×C3—122no—
237C23×C3—122no—
238C23×C3(C2×D3)⋊C411yescharacteristic
239C23×C3(C2×D3)⋊C411yescharacteristic
240C23×C3#21711yescharacteristic
241C23×C3#21711yescharacteristic
242C23×C3C2×D1211yescharacteristic
243C23×C3C2×#6711yescharacteristic
244C22×D3—22no—
245C22×D3—42no—
246C22×D3—42no—
247C22×D3—42no—
248C3×D4—122no—
249C3×D4—124no—
250C3×D4—124no—
251C3×D4—122no—
252C2×C3×C4—24no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—62no—
275C2×C3×C4—122no—
276C2×C3×C4(C2×D3)⋊C411yescharacteristic
277C2×C3×C4(C2×D3)⋊C411yescharacteristic
278C2×C3×C4#21711yescharacteristic
279C2×C3×C4#21711yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4C22×Dic311yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284#67—44no—
285#67—44no—
286C2×Dic3—22no—
287C2×Dic3—42no—
288C2×Dic3—68no—
289C2×Dic3—64no—
290C2×Dic3—64no—
291C2×Dic3—124no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294C2×Dic3—124no—
295C2×Dic3—122no—
296C2×Dic3—122no—
297D12—42no—
298D12—42no—
299C3×C8—122no—
300C3⋊C8—42no—
301C2×C32—22no—
302C2×C32—22no—
303C2×C32—41no—
304C2×C32C2×#9911yescharacteristic
305C2×C32#41811yescharacteristic
306C2×C32C2×#10411yescharacteristic
307C3×D3—82no—
308C24—61no—
309C24#62611yescharacteristic
310C2×D4—32no—
311C2×D4—62no—
312C2×D4—62no—
313C2×D4—61no—
314C2×D4—122no—
315C2×D4—124no—
316C22×C4—42no—
317C22×C4—61no—
318C22×C4—182no—
319C22×C4D3×Dic311yescharacteristic
320C22×C4D3×Dic311yescharacteristic
321C22×C4#62511yescharacteristic
322C22×C4#62511yescharacteristic
323C22×C4#62611yescharacteristic
324C22×C4C2×D3211yescharacteristic
325M16—122no—
326C2×C8—62no—
327C4⋊C4—32no—
328C4⋊C4—61no—
329C22⋊C4—62no—
330C22⋊C4—62no—
331C22⋊C4—184no—
332C42—362no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—21no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—44no—
358C22×C3—44no—
359C22×C3—48no—
360C22×C3—122no—
361C22×C3—122no—
362C22×C3—122no—
363C22×C3—244no—
364C22×C3#82512yes—
365C22×C3#83712yes—
366C22×C3#90812yes—
367C22×C3C2×(C2×D3)⋊C411yescharacteristic
368C22×C3#93212yes—
369C22×C3C2×#21711yescharacteristic
370C2×D3—42no—
371C2×D3—42no—
372C2×D3—42no—
373C2×D3—84no—
374C3×C4—22no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—22no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—122no—
385C3×C4#80612yes—
386C3×C4#83412yes—
387Dic3—42no—
388Dic3—128no—
389Dic3—124no—
390Dic3—124no—
391C32#150711yescharacteristic, complemented, Sylow
392C23—22no—
393C23—22no—
394C23—41no—
395C23—62no—
396C23—122no—
397C23—122no—
398C23—122no—
399C23(C2×D3)⋊Dic311yescharacteristic
400C23(C2×D3)⋊Dic311yescharacteristic
401C23C2×#62611yescharacteristic
402D4—122no—
403D4—124no—
404D4—124no—
405D4—122no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—62no—
413C2×C4—122no—
414C2×C4—184no—
415C2×C4—362no—
416C2×C4—362no—
417C2×C4(C2×D3)⋊Dic311yescharacteristic
418C2×C4(C2×D3)⋊Dic311yescharacteristic
419C2×C4C2×D3×Dic311yescharacteristic
420C2×C4C2×#62511yescharacteristic
421C8—122no—
422C2×C3—24no—
423C2×C3—22no—
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—42no—
431C2×C3—42no—
432C2×C3—41no—
433C2×C3—41no—
434C2×C3—242no—
435C2×C3C2×#80611yescharacteristic
436C2×C3#513111yescharacteristic
437C2×C3C2×#82511yescharacteristic
438C2×C3#521511yescharacteristic
439C2×C3C2×#83411yescharacteristic
440C2×C3C2×#83711yescharacteristic
441D3—82no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—44no—
450C22—122no—
451C22—122no—
452C22—122no—
453C22—244no—
454C22#6356812yes—
455C22#6383012yes—
456C22C2×(C2×D3)⋊Dic311yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—122no—
461C4—364no—
462C4#6358012yes—
463C3—21no—
464C3#6997711yescharacteristic, complemented
465C3#7167311yescharacteristic, complemented
466C2—22no—
467C2—22no—
468C2—41no—
469C2—242no—
470C2#1059108611yescharacteristic
471C2C2×#6356811yescharacteristic
472C2C2×#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#1507
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. C4×#3757C2semidirect
3. C3×#5207C2semidirect
4. #10589150C2semidirect
9. C22×C3×D12C4semidirect
14. C3×#930C4semidirect
17. C2×C3×C4⋊Dic3C4semidirect
19. #63658C22semidirect
21. C3×#830C22semidirect
28. #5207D3semidirect
63. C22×D12Dic3semidirect
76. #930Dic3semidirect
79. C2×C4⋊Dic3Dic3semidirect
90. #830C2×D3semidirect
391. C32#1507semidirect
464. C3#69977semidirect
465. C3#71673semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C4×#37572
C3×#52072
#105891502
#716733
#699773