Finite Group Databasebeta

← #11860778

Subgroups — #11860778

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2#10594982C211yesmaximal, characteristic
3#10594818C211yesmaximal, characteristic, complemented
4#10592805C211yesmaximal, characteristic, complemented
5C3×#5101C211yesmaximal, characteristic, complemented
6#10591100C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic
8#10590766C214yesmaximal, complemented
9Dic3×#204C214yesmaximal, complemented
10#83843—31nomaximal
11#78572—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15#64135C2211yescharacteristic
16#64135C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#204C418yescomplemented
20C2×C3×#204C2212yes—
21C2×C3×#204C2212yes—
22D3×#217—22no—
23#63955—22no—
24#63898—22no—
25Dic3×D12C2214yes—
26#63843—22no—
27Dic3×Dic6C2214yescomplemented
28#63645C2212yescomplemented
29#63644C2212yescomplemented
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32#63566C2214yescomplemented
33#63563C2214yes—
34C22×C3×SD16—31no—
35#5812—31no—
36#5798—31no—
37C22×#204D311yescharacteristic
38#5521—31no—
39#5516—31no—
40C3×#405—31no—
41#5225—31no—
42#5215—31no—
43#5164—34no—
44Dic3×SD16—34no—
45#5131—31no—
46#5120—31no—
47#5106—31no—
48#5106—31no—
49#5106—61no—
50#5101D311yescharacteristic, complemented
51#4710—34no—
52C4×#204—34no—
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2×C414yescomplemented
63C2×C3×Dic6C2312yes—
64C2×D3×Dic3—24no—
65C2×C32×C8C2×C414yescomplemented
66C2×C32×C8C2311yescharacteristic
67C2×C32×C8C2311yescharacteristic
68#3757—21no—
69#3757—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C4⋊(C3⋊Dic3)C2312yes—
72C4×C3⋊Dic3—21no—
73C4×C3⋊Dic3—21no—
74C3×#217D412yes—
75C3×C4⋊Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C3×#208—22no—
78C2×C3×C3⋊C8C2312yes—
79C3×#204C2×C418yescomplemented
80C3×#204C2×C418yescomplemented
81Dic3⋊Dic3—24no—
82(C2×D3)⋊Dic3—24no—
83Dic32—24no—
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C2×C3×SD16—38no—
90C2×C3×SD16—32no—
91C2×C3×SD16—32no—
92C2×C3×M16—31no—
93C22×C3×C8—21no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C2×D311yescharacteristic
96C3×#117—31no—
97C2×#217—62no—
98Q8×Dic3—34no—
99Q8×Dic3—62no—
100D4×Dic3—34no—
101D4×Dic3—62no—
102#926—31no—
103#926—31no—
104#926—31no—
105#926—31no—
106#926—61no—
107#926—61no—
108#926—62no—
109#926C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111C2×#204Dic318yescomplemented
112C2×#204C2×D312yes—
113C2×#204C2×D312yes—
114#893—62no—
115#887—62no—
116D3×C22⋊C4—62no—
117#877—62no—
118C4×D12—34no—
119C4×Dic6—34no—
120C3×#97—32no—
121C3×C4×C8—32no—
122#835—34no—
123#832—34no—
124#821—34no—
125#818—32no—
126#818—32no—
127#818—62no—
128#817—32no—
129#817—32no—
130#817—62no—
131#816—34no—
132#815C2×D312yescomplemented
133C8×Dic3C2×D312yescomplemented
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—24no—
137C22×C3×D3—82no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3C2×D414yes—
147C3×D12—24no—
148C3×D12—22no—
149C3×D12C22×C414yes—
150C3×Dic6—24no—
151C3×Dic6—22no—
152C3×Dic6C22×C414yes—
153D3×Dic3—84no—
154C32×C8C22×C412yes—
155C32×C8C22×C412yes—
156C3×C3⋊C8—22no—
157C22×SD16—31no—
158#519—91no—
159#518—91no—
160#440—94no—
161C4×SD16—94no—
162#427—91no—
163#419—91no—
164#418—91no—
165#405—31no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—34no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—62no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C22×C3×C4—21no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—64no—
182C2×D12—21no—
183C2×D12—22no—
184C2×D12C2×Dic314yes—
185C2×D12C22×D312yes—
186C2×C4×D3—64no—
187C2×Dic6—21no—
188C2×Dic6—22no—
189C2×Dic6C2×Dic314yescomplemented
190C2×Dic6C22×D312yes—
191C3×SD16—38no—
192C3×SD16—38no—
193C3×M16—62no—
194C2×C3×C8—24no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—32no—
198C2×C3×C8C4×D314yescomplemented
199C2×C3×C8C2×Dic314yescomplemented
200C2×C3×C8C22×D311yescharacteristic
201C2×C3×C8C22×D311yescharacteristic
202C2×C3×C8C22×D311yescharacteristic
203C2×C3×C8C22×D311yescharacteristic
204C3×C4⋊C4—32no—
205C3×C22⋊C4—32no—
206C3×C42—32no—
207#217—61no—
208#217—61no—
209#217—61no—
210#217—61no—
211#217—64no—
212#217—121no—
213#217—121no—
214#217D1212yes—
215(C2×D3)⋊C4—64no—
216C4⋊Dic3—32no—
217C4⋊Dic3—32no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—64no—
223C4⋊Dic3D1212yes—
224Dic3⋊C4—64no—
225C4×Dic3—64no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C4×Dic3—61no—
230C4×Dic3—64no—
231C4×Dic3—121no—
232C4×Dic3—121no—
233C4×Dic3C22×D312yes—
234#208—22no—
235C2×C3⋊C8C22×D312yes—
236#204C2×Dic318yescomplemented
237#204C2×Dic318yescomplemented
238C22×C32—22no—
239C22×C32C4×D412yes—
240C22×C32C22×D411yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—44no—
243C2×C3×D3—84no—
244C32×C4C4×D412yes—
245C32×C4C23×C411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—42no—
248C3⋊Dic3—42no—
249C3×Dic3—24no—
250C3×Dic3—24no—
251C22×Q8—31no—
252C22×D4—31no—
253C2×SD16—38no—
254C2×SD16—32no—
255C2×SD16—32no—
256C2×M16—31no—
257C22×C8D3211yescharacteristic
258C4×Q8—94no—
259C4×Q8—182no—
260C4×D4—94no—
261C4×D4—182no—
262#117—31no—
263#117—91no—
264#117—91no—
265#117—182no—
266C2×C22⋊C4—182no—
267#107—92no—
268#106—92no—
269#103—94no—
270#102—94no—
271#97—32no—
272C4×C8—32no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—64no—
276C23×C3—242no—
277C23×C3C2×D1211yescharacteristic
278C23×C3D3×D411yescharacteristic
279C22×D3—22no—
280C22×D3—24no—
281C22×D3—82no—
282C3×Q8—34no—
283C3×Q8—64no—
284C3×Q8—62no—
285C3×D4—34no—
286C3×D4—64no—
287C3×D4—62no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—34no—
293C2×C3×C4—64no—
294C2×C3×C4—62no—
295C2×C3×C4C2×C4×D312yes—
296C2×C3×C4C2×D1211yescharacteristic
297C2×C3×C4#23512yes—
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23712yes—
300C2×C3×C4C22×Dic312yes—
301C2×C3×C4C23×D311yescharacteristic
302C2×C3×C4C23×D311yescharacteristic
303C2×Dic3—24no—
304C2×Dic3—22no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3—244no—
312C2×Dic3C2×D1214yes—
313D12—24no—
314D12—22no—
315D12C22×Dic314yes—
316C4×D3—244no—
317Dic6—24no—
318Dic6—22no—
319Dic6C22×Dic314yes—
320C3×C8—22no—
321C3×C8—22no—
322C3×C8—62no—
323C3×C8C2×C4×D312yes—
324C3×C8C2×C4×D312yes—
325C3×C8C22×Dic312yes—
326C3×C8C22×Dic312yes—
327C3⋊C8—22no—
328C2×C32—22no—
329C2×C32C2×C4×D411yescharacteristic
330C2×C32#57712yes—
331C3×D3—44no—
332C24—61no—
333C2×Q8—32no—
334C2×Q8—34no—
335C2×Q8—62no—
336C2×Q8—61no—
337C2×D4—32no—
338C2×D4—34no—
339C2×D4—62no—
340C2×D4—61no—
341C22×C4—61no—
342C22×C4—184no—
343C22×C4C2×D3211yescharacteristic
344SD16—38no—
345SD16—38no—
346M16—62no—
347C2×C8—32no—
348C2×C8D3×Dic314yescomplemented
349C2×C8C2×D3211yescharacteristic
350C2×C8C2×D3211yescharacteristic
351C4⋊C4—32no—
352C4⋊C4—92no—
353C4⋊C4—92no—
354C4⋊C4—184no—
355C22⋊C4—32no—
356C22⋊C4—184no—
357C22⋊C4—181no—
358C22⋊C4—181no—
359C42—32no—
360C42—184no—
361C42—181no—
362C42—181no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—42no—
368C22×C3—64no—
369C22×C3—124no—
370C22×C3—244no—
371C22×C3C4×D1212yes—
372C22×C3D4×Dic312yes—
373C22×C3C22×D1211yescharacteristic
374C22×C3C2×D3×D411yescharacteristic
375C2×D3—24no—
376C2×D3—44no—
377C2×D3—84no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—22no—
381C3×C4—64no—
382C3×C4—64no—
383C3×C4C4×D1212yes—
384C3×C4D4×Dic312yes—
385C3×C4C22×C4×D311yescharacteristic
386C3×C4C2×#23511yescharacteristic
387C3×C4C2×#23711yescharacteristic
388C3×C4C23×Dic311yescharacteristic
389Dic3—24no—
390Dic3—24no—
391Dic3—122no—
392Dic3—122no—
393Dic3—122no—
394Dic3—122no—
395Dic3—242no—
396Dic3—242no—
397C32#294911yescharacteristic, complemented, Sylow
398C23—62no—
399C23—64no—
400C23—242no—
401C23D3×D1211yescharacteristic
402Q8—34no—
403Q8—62no—
404Q8—64no—
405D4—34no—
406D4—62no—
407D4—64no—
408C2×C4—34no—
409C2×C4—62no—
410C2×C4—64no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4—724no—
414C2×C4#379512yes—
415C2×C4D3×D1211yescharacteristic
416C2×C4C2×D3×Dic312yes—
417C2×C4C22×D3211yescharacteristic
418C8—62no—
419C8C2×D3×Dic312yes—
420C8C2×D3×Dic312yes—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—21no—
424C2×C3—22no—
425C2×C3—42no—
426C2×C3—124no—
427C2×C3C2×C4×D1211yescharacteristic
428C2×C3#575112yes—
429C2×C3#576212yes—
430C2×C3C2×D4×Dic311yescharacteristic
431D3—44no—
432C22—22no—
433C22—64no—
434C22—124no—
435C22—244no—
436C22Dic3×D1212yes—
437C22C2×D3×D1211yescharacteristic
438C4—64no—
439C4—64no—
440C4—362no—
441C4—362no—
442C4Dic3×D1212yes—
443C4C2×#379511yescharacteristic
444C4C22×D3×Dic311yescharacteristic
445C3—21no—
446C3#7857211yescharacteristic, complemented
447C3#8384311yescharacteristic, complemented
448C2—22no—
449C2—124no—
450C2#1059467712yes—
451C2C2×Dic3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. #10594818C2semidirect
4. #10592805C2semidirect
5. C3×#5101C2semidirect
6. #10591100C2semidirect
8. #10590766C2semidirect
9. Dic3×#204C2semidirect
19. C2×C3×#204C4semidirect
27. Dic3×Dic6C22semidirect
28. #63645C22semidirect
29. #63644C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. #63566C22semidirect
50. #5101D3semidirect
62. C2×C3×Dic6C2×C4semidirect
65. C2×C32×C8C2×C4semidirect
79. C3×#204C2×C4semidirect
80. C3×#204C2×C4semidirect
111. C2×#204Dic3semidirect
132. #815C2×D3semidirect
133. C8×Dic3C2×D3semidirect
189. C2×Dic6C2×Dic3semidirect
198. C2×C3×C8C4×D3semidirect
199. C2×C3×C8C2×Dic3semidirect
236. #204C2×Dic3semidirect
237. #204C2×Dic3semidirect
348. C2×C8D3×Dic3semidirect
397. C32#2949semidirect
446. C3#78572semidirect
447. C3#83843semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
#105949822
#105948182
#105928052
C3×#51012
#105911002
#105910862
#105907662
Dic3×#2042
#838433
#785723