Finite Group Databasebeta

← #11783874

Subgroups — #11783874

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic
2C4×Dic32C211yesmaximal, characteristic, complemented
3C2×#63569C211yesmaximal, characteristic
4C2×#63568C211yesmaximal, characteristic
5Dic3×#208C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C4×#837—31nomaximal
9#68728—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#893C412yescomplemented
18C3×#887C412yescomplemented
19C3×#67⋊C4—22no—
20C3×#872—21no—
21C3×C42×D3—21no—
22C2×Dic32—22no—
23#63569C414yescomplemented
24#63568C414yescomplemented
25#63554—21no—
26Dic3×C3⋊C8—21no—
27C3×C4×#41—31no—
28#5522D311yescharacteristic
29C2×#837—31no—
30C2×#837—31no—
31C2×#825—31no—
32Dic3×M16—31no—
33C42×Dic3—31no—
34C42×Dic3—31no—
35C2×#805—31no—
36C4×#208—31no—
37C3×#339—31no—
38#4532—31no—
39#4532—31no—
40#4532—61no—
41#4532D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C3×#67—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3D412yes—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235C2×C412yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—22no—
54C2×C3×Dic6C2×C411yescharacteristic
55C32×C4⋊C4C2×C412yes—
56C32×C22⋊C4—21no—
57C32×C42—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3C2×C412yescomplemented
60#3748—21no—
61#3748C2×C412yescomplemented
62C2×C3⋊(C3⋊C8)—21no—
63C3×(C2×D3)⋊C4—22no—
64C3×Dic3⋊C4—22no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—22no—
67C3×C4×Dic3C2×C412yes—
68C3×C4×Dic3C2×C412yescomplemented
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C3×#208—21no—
72C3×#208C2×C412yescomplemented
73C2×C3×C3⋊C8—21no—
74Dic32—28no—
75C4×#104—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C2×C3×M16—31no—
79C3×C4×Q8—32no—
80C3×C4×D4—32no—
81C3×C4×D4—62no—
82C3×#117—21no—
83C3×#117—61no—
84C3×#117C2×D311yescharacteristic
85C3×#117C2×D311yescharacteristic
86C2×C3×C42—31no—
87C2×C3×C42—31no—
88C2×C3×C42—61no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—61no—
92C2×C4×Dic3—62no—
93C2×C4×Dic3—62no—
94C2×C4×Dic3C2×D311yescharacteristic
95C2×C4×Dic3C2×D311yescharacteristic
96C2×#208—31no—
97C2×#208—31no—
98C2×#208—61no—
99C2×#208C2×D311yescharacteristic
100#893Dic312yescomplemented
101#887Dic312yescomplemented
102#67⋊C4—22no—
103#872—21no—
104C42×D3—21no—
105#837—34no—
106#837—34no—
107#825—34no—
108#815—61no—
109C8×Dic3—61no—
110#805—34no—
111#803—61no—
112C4×C3⋊C8—61no—
113C23×C32C2×D411yescharacteristic
114C22×C3×D3—21no—
115C2×C32×C4—22no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3⋊Dic3—24no—
123C2×C3⋊Dic3—22no—
124C3×#67—22no—
125C3×#67—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3C22⋊C412yes—
131C2×C3×Dic3C22⋊C412yes—
132C3×D12—21no—
133C3×D12C4212yescomplemented
134C3×C4×D3—22no—
135C3×C4×D3—22no—
136C3×C4×D3—44no—
137C3×Dic6—21no—
138C3×Dic6C4212yescomplemented
139C3⋊(C3⋊C8)—22no—
140C3×C3⋊C8—22no—
141C4×#41—31no—
142C2×#104—91no—
143C2×#104—91no—
144C4×M16—91no—
145C43—91no—
146#339—31no—
147#339—91no—
148C3×#41—32no—
149C3×#41—32no—
150C3×#41—61no—
151C3×#41—61no—
152C2×C3×Q8—31no—
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—32no—
157C22×C3×C4—62no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C22×Dic3—21no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—121no—
167C22×Dic3#6712yes—
168#235—21no—
169#235—21no—
170#235C4×D312yes—
171#235C4×D312yes—
172C2×D12C2×Dic311yescharacteristic
173C2×C4×D3—21no—
174C2×C4×D3—22no—
175C2×Dic6C2×Dic311yescharacteristic
176C3×M16—32no—
177C3×M16—61no—
178C2×C3×C8—61no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—62no—
181C3×C4⋊C4C4×D312yes—
182C3×C4⋊C4C2×Dic312yes—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—41no—
186C3×C22⋊C4—62no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—32no—
190C3×C42—31no—
191C3×C42—31no—
192C3×C42—32no—
193C3×C42—41no—
194C3×C42—62no—
195C3×C42—61no—
196(C2×D3)⋊C4—22no—
197Dic3⋊C4—22no—
198C4×Dic3—21no—
199C4×Dic3—22no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—62no—
203C4×Dic3—68no—
204C4×Dic3—68no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—121no—
208C4×Dic3C4×D312yescomplemented
209C4×Dic3C2×Dic312yes—
210C4×Dic3#6711yescharacteristic
211C4×Dic3#6711yescharacteristic
212#208—21no—
213#208—32no—
214#208—32no—
215#208—62no—
216#208—61no—
217#208—61no—
218#208—121no—
219#208C4×D312yescomplemented
220C2×C3⋊C8—21no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—121no—
224C22×C32—22no—
225C22×C32C2×C22⋊C411yescharacteristic
226C22×C32C4×D411yescharacteristic
227C22×C32C4×D411yescharacteristic
228C2×C3×D3—22no—
229C2×C3×D3—42no—
230C32×C4—42no—
231C32×C4C2×C4211yescharacteristic
232C32×C4#11711yescharacteristic
233C32×C4C4×D411yescharacteristic
234C32×C4C4×D411yescharacteristic
235C3⋊Dic3—24no—
236C3×Dic3—24no—
237C3×Dic3—22no—
238C3×Dic3—22no—
239C3×Dic3#10414yescomplemented
240C2×#41—31no—
241C2×M16—31no—
242C2×M16—91no—
243C4×Q8—32no—
244C4×D4—32no—
245C4×D4—62no—
246#117—61no—
247#117D3211yescharacteristic
248C2×C42—31no—
249C2×C42—31no—
250C2×C42—61no—
251C2×C42—91no—
252C2×C42—182no—
253#104—94no—
254#104—94no—
255#97—181no—
256C4×C8—181no—
257C23×C3—21no—
258C23×C3—61no—
259C23×C3D3×D411yescharacteristic
260C23×C3C2×#6711yescharacteristic
261C22×D3—21no—
262C3×Q8—32no—
263C3×Q8—61no—
264C3×D4—32no—
265C3×D4—62no—
266C3×D4—62no—
267C3×D4—61no—
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—21no—
275C2×C3×C4—21no—
276C2×C3×C4—32no—
277C2×C3×C4—32no—
278C2×C3×C4—42no—
279C2×C3×C4—64no—
280C2×C3×C4—64no—
281C2×C3×C4—61no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—124no—
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4#23511yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4#23711yescharacteristic
295C2×C3×C4#23911yescharacteristic
296C2×C3×C4C22×Dic311yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298#67—22no—
299#67—22no—
300C2×Dic3—24no—
301C2×Dic3—22no—
302C2×Dic3—21no—
303C2×Dic3—24no—
304C2×Dic3—64no—
305C2×Dic3—64no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—122no—
309C2×Dic3—124no—
310C2×Dic3#21712yes—
311C2×Dic3#21712yes—
312D12—21no—
313D12C4×Dic312yescomplemented
314C4×D3—22no—
315C4×D3—22no—
316C4×D3—44no—
317Dic6—21no—
318Dic6C4×Dic312yescomplemented
319C3×C8—62no—
320C3⋊C8—22no—
321C3⋊C8—62no—
322C3⋊C8—62no—
323C3⋊C8—122no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32C4×C22⋊C411yescharacteristic
327C2×C32C2×#10412yes—
328C3×D3—42no—
329#41—32no—
330#41—32no—
331#41—61no—
332#41—61no—
333C2×Q8—31no—
334C2×D4—31no—
335C2×D4—61no—
336C22×C4—32no—
337C22×C4—62no—
338C22×C4—61no—
339C22×C4—61no—
340C22×C4—181no—
341C22×C4C2×D3211yescharacteristic
342M16—32no—
343M16—61no—
344M16—92no—
345M16—181no—
346C2×C8—61no—
347C2×C8—181no—
348C4⋊C4—62no—
349C4⋊C4D3×Dic312yes—
350C22⋊C4—21no—
351C22⋊C4—62no—
352C42—21no—
353C42—32no—
354C42—31no—
355C42—31no—
356C42—32no—
357C42—62no—
358C42—61no—
359C42—92no—
360C42—188no—
361C42—181no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—62no—
369C22×C3—122no—
370C22×C3D3×C22⋊C411yescharacteristic
371C22×C3#67⋊C411yescharacteristic
372C22×C3#89311yescharacteristic
373C22×C3C4×#6711yescharacteristic
374C22×C3C4×#6711yescharacteristic
375C22×C3C2×#21711yescharacteristic
376C2×D3—22no—
377C2×D3—42no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—34no—
383C3×C4—42no—
384C3×C4—42no—
385C3×C4—64no—
386C3×C4—62no—
387C3×C4—62no—
388C3×C4—82no—
389C3×C4C42×D311yescharacteristic
390C3×C4#67⋊C411yescharacteristic
391C3×C4#89211yescharacteristic
392C3×C4#89311yescharacteristic
393C3×C4C2×C4×Dic311yescharacteristic
394C3×C4#92611yescharacteristic
395C3×C4C4×#6711yescharacteristic
396C3×C4C4×#6711yescharacteristic
397Dic3—24no—
398Dic3—22no—
399Dic3—22no—
400Dic3—64no—
401Dic3—64no—
402Dic3—124no—
403Dic3#83714yescomplemented
404C32C4×#10411yescharacteristic, complemented, Sylow
405C23—61no—
406C23D3×#6711yescharacteristic
407Q8—32no—
408Q8—61no—
409D4—32no—
410D4—62no—
411D4—62no—
412D4—61no—
413C2×C4—22no—
414C2×C4—32no—
415C2×C4—32no—
416C2×C4—64no—
417C2×C4—64no—
418C2×C4—62no—
419C2×C4—61no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—124no—
423C2×C4—184no—
424C2×C4—182no—
425C2×C4#379511yescharacteristic
426C2×C4#379911yescharacteristic
427C2×C4C4×D3211yescharacteristic
428C2×C4C4×D3211yescharacteristic
429C2×C4C2×D3×Dic311yescharacteristic
430C2×C4D3×#6711yescharacteristic
431C8—62no—
432C8—182no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—22no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—122no—
442C2×C3#466611yescharacteristic
443C2×C3D3×#10412yes—
444C2×C3C4×#21711yescharacteristic
445C2×C3C2×#83712yes—
446D3—42no—
447C22—22no—
448C22—62no—
449C22—122no—
450C22#6387911yescharacteristic
451C22#6390411yescharacteristic
452C22D3×#21711yescharacteristic
453C4—34no—
454C4—42no—
455C4—64no—
456C4—62no—
457C4—62no—
458C4—184no—
459C4#6384111yescharacteristic
460C4C4×D3×Dic311yescharacteristic
461C4#6387911yescharacteristic
462C4#6390411yescharacteristic
463C3—21no—
464C3#6872811yescharacteristic, complemented
465C3C4×#83711yescharacteristic, complemented
466C2—21no—
467C2—21no—
468C2—122no—
469C2#1059123711yescharacteristic
470C2D3×#83712yes—
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32C4×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C4×Dic32C2semidirect
5. Dic3×#208C2semidirect
6. #10589398C2semidirect
7. C3×#4532C2semidirect
17. C3×#893C4semidirect
18. C3×#887C4semidirect
23. #63569C4semidirect
24. #63568C4semidirect
41. #4532D3semidirect
59. C4×C3⋊Dic3C2×C4semidirect
61. #3748C2×C4semidirect
68. C3×C4×Dic3C2×C4semidirect
72. C3×#208C2×C4semidirect
100. #893Dic3semidirect
101. #887Dic3semidirect
133. C3×D12C42semidirect
138. C3×Dic6C42semidirect
208. C4×Dic3C4×D3semidirect
219. #208C4×D3semidirect
239. C3×Dic3#104semidirect
313. D12C4×Dic3semidirect
318. Dic6C4×Dic3semidirect
403. Dic3#837semidirect
404. C32C4×#104semidirect
464. C3#68728semidirect
465. C3C4×#837semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
C4×Dic322
C2×#635692
C2×#635682
Dic3×#2082
#105893982
C3×#45322
C4×#8373
#687283