Finite Group Databasebeta

← #11869002

Subgroups — #11869002

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594606C211yesmaximal, characteristic
2#10594508C211yesmaximal, characteristic, complemented
3#10592559C211yesmaximal, characteristic, complemented
4C3×#4871C212yesmaximal, complemented
5#10590940C211yesmaximal, characteristic
6#10590757C212yesmaximal, complemented
7#10590701C211yesmaximal, characteristic, complemented
8#10590594C211yesmaximal, characteristic
9#10590582C211yesmaximal, characteristic, complemented
10#10590555C212yesmaximal, complemented
11#10590467C212yesmaximal, complemented
12#81168—32nomaximal
13C2×#3802C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15#64101C2211yescharacteristic
16#64101C2211yescharacteristic
17C3×#893C2212yes—
18C3×#890C2212yescomplemented
19D3×(C2×D3)⋊C4—22no—
20#63919—21no—
21#63918C2212yescomplemented
22#63902—21no—
23C4×#625—21no—
24#63900C2211yescharacteristic
25#63895—22no—
26Dic3×D12C2212yes—
27#63874C2211yescharacteristic
28#63870—21no—
29C2×#3712C2211yescharacteristic
30C32×#106C2211yescharacteristic, complemented
31#63644C2211yescharacteristic, complemented
32#63634C2211yescharacteristic, complemented
33#63634C2211yescharacteristic, complemented
34C3×#821C2212yes—
35C3×Dic3⋊C8C2212yescomplemented
36C3×#809C2212yes—
37C3×#807C2212yescomplemented
38#63573C2212yescomplemented
39Dic3⋊(C3⋊C8)C2212yescomplemented
40#63563C2212yes—
41#63562C2212yes—
42#5689—32no—
43#5545—32no—
44C3×#478—32no—
45#5066—32no—
46#5007—32no—
47#4890—32no—
48#4881—32no—
49#4871D312yescomplemented
50#4860—32no—
51#4860—61no—
52#4842—32no—
53#4839—32no—
54#4770—32no—
55D3×#102—32no—
56#4763—32no—
57#4761—32no—
58C22×D32—21no—
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×D12C2312yes—
61C2×C3×C4×D3—22no—
62C2×#627—22no—
63C2×#625—21no—
64C2×#624—21no—
65C2×D3×Dic3—22no—
66#3802—22no—
67#3802Q814yescomplemented
68C2×C32×C8C2311yescharacteristic
69C32×C4⋊C4C2311yescharacteristic
70C32×C4⋊C4C2311yescharacteristic
71#3752—21no—
72#3752—21no—
73C4⋊(C3⋊Dic3)C2311yescharacteristic
74C4⋊(C3⋊Dic3)C2311yescharacteristic
75C4×C3⋊Dic3—21no—
76C4×C3⋊Dic3—21no—
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C8×C3⋊D3—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3C2312yes—
84C2×C3×C3⋊C8C2312yes—
85#3724—21no—
86#3724D411yescharacteristic
87#3724D411yescharacteristic
88Dic3⋊Dic3—22no—
89#3722D412yes—
90(C2×D3)⋊Dic3—22no—
91#3712—22no—
92#3081—91noSylow
93C2×D3×D4—32no—
94C3×#125—32no—
95C3×C4×D4—32no—
96D4×Dic3—32no—
97C4×#67—62no—
98C2×(C2×D3)⋊C4—62no—
99C2×ΓL(1,𝔽25)—32no—
100C2×D3×C8—32no—
101C2×D3×C8—61no—
102#897—62no—
103#896—62no—
104#893C2×D312yes—
105#892—32no—
106#892—32no—
107#892—61no—
108#892—61no—
109D3×C4⋊C4—32no—
110#890C2×D312yescomplemented
111#889—62no—
112#888—32no—
113#888—62no—
114#67⋊C4—62no—
115D3×C22⋊C4—62no—
116C4×D12—32no—
117#872—32no—
118#869—32no—
119C3×#107—32no—
120C3×#106—21no—
121C3×#106C2×D312yescomplemented
122C3×C4⋊C8—32no—
123C3×#102—32no—
124C3×#102—32no—
125#832—32no—
126#832—32no—
127#821—32no—
128#821C2×D312yes—
129#817—32no—
130#817—32no—
131#817—61no—
132Dic3⋊C8—32no—
133Dic3⋊C8C2×D312yescomplemented
134#809—32no—
135#809C2×D312yes—
136#808—32no—
137#807—32no—
138#807—32no—
139#807—61no—
140#807—61no—
141#807C2×D312yescomplemented
142C4⋊(C3⋊C8)—32no—
143C22×C3⋊D3C2×D411yescharacteristic
144C22×C3×D3—22no—
145C2×D32—24no—
146C2×D32—81no—
147C2×D32—81no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3C2×D411yescharacteristic
154C4×C3⋊D3C2×Q812yes—
155C4×C3⋊D3#4112yes—
156C2×C3×Dic3—22no—
157C2×C3×Dic3C2×D412yes—
158C2×C3×Dic3C2×D412yes—
159C3×D12—22no—
160C3×D12C2×Q814yes—
161C3×C4×D3—82no—
162#627—82no—
163#625—24no—
164#624—81no—
165D3×Dic3—82no—
166C32×C8—21no—
167C3⋊(C3⋊C8)—21no—
168C3×C3⋊C8—22no—
169#544—91no—
170#518—91no—
171#478—32no—
172#478—92no—
173#476—92no—
174#474—92no—
175#428—91no—
176#427—91no—
177#424—91no—
178#418—91no—
179C2×#102—91no—
180C23×D3—62no—
181C2×C3×D4—32no—
182C22×C3×C4—62no—
183C2×#67—62no—
184C22×Dic3—62no—
185D3×D4—38no—
186D3×D4—64no—
187C2×D12C22×D312yes—
188C2×C4×D3—22no—
189C2×C4×D3—32no—
190C2×C4×D3—61no—
191C2×C4×D3—62no—
192C2×C4×D3—62no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×C3×C8—21no—
196C2×C3×C8—32no—
197C2×C3×C8C22×D312yes—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—62no—
202C3×C4⋊C4—62no—
203C3×C4⋊C4C22×D312yes—
204C3×C4⋊C4C22×D312yes—
205C3×C22⋊C4—62no—
206C3×C42—32no—
207#217—62no—
208(C2×D3)⋊C4—22no—
209(C2×D3)⋊C4—32no—
210(C2×D3)⋊C4—32no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—62no—
213(C2×D3)⋊C4—62no—
214(C2×D3)⋊C4—121no—
215(C2×D3)⋊C4—121no—
216C4⋊Dic3—22no—
217C4⋊Dic3—32no—
218C4⋊Dic3—32no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—62no—
222C4⋊Dic3C22×D312yes—
223Dic3⋊C4—22no—
224Dic3⋊C4—32no—
225Dic3⋊C4—32no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228C4×Dic3—62no—
229C4×Dic3—62no—
230C4×Dic3—121no—
231C4×Dic3—121no—
232C4×Dic3C22×D312yes—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8C22×D312yes—
236ΓL(1,𝔽25)—64no—
237D3×C8—64no—
238D3×C8—64no—
239C22×C32C22×D411yescharacteristic
240C2×C3⋊D3—21no—
241C2×C3⋊D3—21no—
242C2×C3⋊D3C22⋊Q812yes—
243C2×C3×D3—24no—
244C2×C3×D3—42no—
245C2×C3×D3—42no—
246D32—84no—
247C32×C4—41no—
248C32×C4—41no—
249C32×C4C22×Q811yescharacteristic
250C32×C4C2×#4111yescharacteristic
251C3⋊Dic3—41no—
252C3⋊Dic3—41no—
253C3⋊Dic3C22⋊Q812yes—
254C3×Dic3—22no—
255C3×Dic3—22no—
256C3×Dic3—42no—
257C22×D4—91no—
258C2×M16—91no—
259C22×C8—91no—
260C4⋊Q8—92no—
261C4⋊Q8—181no—
262#125—32no—
263#125—181no—
264C22⋊Q8—182no—
265C4×D4—32no—
266C4×D4—92no—
267C4×D4—181no—
268C4×D4—181no—
269#117—91no—
270#117—91no—
271#117—91no—
272C2×C4⋊C4—91no—
273C2×C22⋊C4—182no—
274#107—32no—
275#107—91no—
276#107—91no—
277#106—92no—
278#106—91no—
279#106D3211yescharacteristic, complemented
280C4⋊C8—32no—
281C4⋊C8—92no—
282#102—32no—
283#102—32no—
284#102—92no—
285#102—92no—
286C23×C3—62no—
287C22×D3—22no—
288C22×D3—32no—
289C22×D3—61no—
290C22×D3—68no—
291C22×D3—242no—
292C22×D3—242no—
293C3×D4—34no—
294C3×D4—62no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—32no—
299C2×C3×C4—32no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—62no—
303C2×C3×C4—242no—
304C2×C3×C4C23×D312yes—
305#67—68no—
306C2×Dic3—22no—
307C2×Dic3—32no—
308C2×Dic3—61no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—242no—
314C2×Dic3D3×D412yes—
315C2×Dic3D3×D412yes—
316D12—22no—
317D12D3×Q814yes—
318C4×D3—34no—
319C4×D3—34no—
320C4×D3—62no—
321C4×D3—62no—
322C4×D3—82no—
323C4×D3—242no—
324C4×D3—242no—
325Dic6—242no—
326Dic6—242no—
327C3×C8—22no—
328C3×C8—22no—
329C3×C8—62no—
330C3⋊C8—22no—
331C3⋊C8—62no—
332C3⋊C8—62no—
333C2×C32C2×C22⋊Q811yescharacteristic
334C2×C32#57611yescharacteristic
335C2×C32#57711yescharacteristic
336C3⋊D3—22no—
337C3×D3—44no—
338C24—181no—
339C2×Q8—182no—
340C2×D4—32no—
341C2×D4—94no—
342C2×D4—182no—
343C2×D4—181no—
344C22×C4—62no—
345C22×C4—91no—
346C22×C4—182no—
347C22×C4—181no—
348M16—182no—
349C2×C8—32no—
350C2×C8—91no—
351C2×C8—182no—
352C2×C8C2×D3211yescharacteristic
353C4⋊C4—32no—
354C4⋊C4—62no—
355C4⋊C4—62no—
356C4⋊C4—91no—
357C4⋊C4—91no—
358C4⋊C4—91no—
359C4⋊C4—91no—
360C4⋊C4—182no—
361C4⋊C4—181no—
362C4⋊C4C2×D3211yescharacteristic
363C4⋊C4C2×D3211yescharacteristic
364C22⋊C4—62no—
365C22⋊C4—92no—
366C22⋊C4—181no—
367C22⋊C4—181no—
368C22⋊C4—182no—
369C42—32no—
370C42—181no—
371C42—181no—
372C22×C3—21no—
373C22×C3—64no—
374C22×C3—122no—
375C22×C3—122no—
376C22×C3C2×D3×D412yes—
377C2×D3—24no—
378C2×D3—34no—
379C2×D3—42no—
380C2×D3—42no—
381C2×D3—62no—
382C2×D3—62no—
383C2×D3—62no—
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—248no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—62no—
392C3×C4—62no—
393C3×C4—81no—
394C3×C4—81no—
395C3×C4—122no—
396C3×C4C2×D3×Q812yes—
397C3×C4D3×#4112yes—
398Dic3—22no—
399Dic3—22no—
400Dic3—34no—
401Dic3—42no—
402Dic3—62no—
403Dic3—122no—
404Dic3—122no—
405Dic3—241no—
406Dic3—241no—
407C32#308111yescharacteristic, complemented, Sylow
408C23—62no—
409C23—91no—
410C23—184no—
411C23—721no—
412C23—721no—
413Q8—722no—
414D4—34no—
415D4—62no—
416D4—184no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—32no—
420C2×C4—32no—
421C2×C4—62no—
422C2×C4—91no—
423C2×C4—92no—
424C2×C4—92no—
425C2×C4—181no—
426C2×C4—181no—
427C2×C4—242no—
428C2×C4—722no—
429C2×C4—721no—
430C2×C4C22×D3211yescharacteristic
431C8—21no—
432C8—62no—
433C8—181no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—124no—
438C2×C3D3×C22⋊Q812yes—
439C2×C3#577012yes—
440C2×C3#577412yes—
441D3—44no—
442D3—64no—
443D3—122no—
444C22—64no—
445C22—92no—
446C22—122no—
447C22—122no—
448C22—181no—
449C22—181no—
450C22—724no—
451C22D32×D411yescharacteristic
452C4—41no—
453C4—41no—
454C4—62no—
455C4—62no—
456C4—92no—
457C4—122no—
458C4—361no—
459C4—361no—
460C4#6430611yescharacteristic
461C4D32×Q811yescharacteristic
462C3—21no—
463C3#8116812yescomplemented
464C2—124no—
465C2—182no—
466C2#1059462411yescharacteristic
467C2#1059475011yescharacteristic
468C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#106D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594508C2semidirect
3. #10592559C2semidirect
4. C3×#4871C2semidirect
6. #10590757C2semidirect
7. #10590701C2semidirect
9. #10590582C2semidirect
10. #10590555C2semidirect
11. #10590467C2semidirect
18. C3×#890C22semidirect
21. #63918C22semidirect
30. C32×#106C22semidirect
31. #63644C22semidirect
32. #63634C22semidirect
33. #63634C22semidirect
35. C3×Dic3⋊C8C22semidirect
37. C3×#807C22semidirect
38. #63573C22semidirect
39. Dic3⋊(C3⋊C8)C22semidirect
49. #4871D3semidirect
67. #3802Q8semidirect
110. #890C2×D3semidirect
121. C3×#106C2×D3semidirect
133. Dic3⋊C8C2×D3semidirect
141. #807C2×D3semidirect
279. #106D32semidirect
407. C32#3081semidirect
463. C3#81168semidirect

Maximal subgroups

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

subgroupindex
#105946062
#105945082
#105925592
C3×#48712
#105909402
#105907572
#105907012
#105905942
#105905822
#105905552
#105904672
#811683