Finite Group Databasebeta

← #11860758

Subgroups — #11860758

Order 1152.

1059 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic
4#10592703C211yesmaximal, characteristic, complemented
5C3×#4998C211yesmaximal, characteristic, complemented
6#10591085C211yesmaximal, characteristic
7#10591055C211yesmaximal, characteristic, complemented
8#10590590C214yesmaximal, complemented
9#10590479C214yesmaximal, complemented
10#82543—31nomaximal
11#79168—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#893C2214yes—
20C3×D3×C22⋊C4—22no—
21C3×C4×D12—22no—
22#63957—22no—
23#63844—22no—
24#63844C2214yescomplemented
25C2×#3716C418yescomplemented
26C2×#3716C2212yes—
27C2×#3716C2212yes—
28#63637C2214yescomplemented
29C3×#808C2212yescomplemented
30C3×#807C2212yescomplemented
31#63562C2214yes—
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C3×#518—31no—
35C22×#214—31no—
36C22×#204—31no—
37#5521D311yescharacteristic
38#5516—31no—
39#5516—31no—
40C3×#427—31no—
41#5215—31no—
42#5101—31no—
43#5018—34no—
44C4×#214—34no—
45#5004—31no—
46#5004—31no—
47#5004—61no—
48#5001—31no—
49#4998D311yescharacteristic, complemented
50#4997—31no—
51#4889—34no—
52#4852—34no—
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634C2×C414yescomplemented
59C2×#634C2312yes—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C32×C4⋊C4C2312yes—
66C32×C22⋊C4—21no—
67C32×C42—21no—
68#3748—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×#217—21no—
71C3×#217D412yes—
72C3×(C2×D3)⋊C4—24no—
73C3×C4⋊Dic3D412yes—
74C3×C4⋊Dic3C2312yes—
75C3×C4×Dic3—21no—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8C2×C414yescomplemented
78C2×C3×C3⋊C8C2311yescharacteristic
79C2×C3×C3⋊C8C2311yescharacteristic
80#3724—24no—
81Dic32—24no—
82#3716C2×C418yescomplemented
83#3716C2×C418yescomplemented
84#2949—91noSylow
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C22×C3×C8—31no—
91C3×C4×D4—34no—
92C3×C4×D4—62no—
93C3×#117—21no—
94C3×#117—31no—
95C3×#117—31no—
96C3×#117C2×D311yescharacteristic
97C3×#117C2×D311yescharacteristic
98C2×C3×C22⋊C4—62no—
99C2×#214—38no—
100C2×#214—32no—
101C2×#214—32no—
102#926C2×D311yescharacteristic
103#926C2×D311yescharacteristic
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108C2×#204—38no—
109C2×#204—32no—
110C2×#204—32no—
111#893C2×D314yes—
112#887—34no—
113#887—62no—
114D3×C22⋊C4—22no—
115#877—62no—
116#877—62no—
117C4×D12—22no—
118C4×Dic6—34no—
119C4×Dic6—62no—
120C3×#107—32no—
121C3×#106—32no—
122#832—34no—
123#815—32no—
124C8×Dic3—32no—
125#810—34no—
126#810—34no—
127#810—64no—
128#809—34no—
129#808C2×D312yescomplemented
130#807C2×D312yescomplemented
131#803—32no—
132C4×C3⋊C8—32no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—24no—
136C22×C3×D3—82no—
137C2×C32×C4—22no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—24no—
143C2×C3⋊Dic3—22no—
144#634—24no—
145#634—22no—
146#634C22×C414yes—
147C2×C3×Dic3—22no—
148C2×C3×Dic3C2×D414yes—
149C3×D12—24no—
150C3×D12—22no—
151C3×D12C22×C414yes—
152C3×C4×D3—84no—
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8C22×C412yes—
155C3×C3⋊C8C22×C412yes—
156C22×SD16—91no—
157#519—91no—
158#518—31no—
159#440—94no—
160C4×SD16—94no—
161#427—31no—
162#419—91no—
163#418—91no—
164#405—91no—
165C24×C3—61no—
166C23×D3—21no—
167C2×C3×D4—34no—
168C2×C3×D4—32no—
169C2×C3×D4—61no—
170C2×C3×D4—62no—
171C22×C3×C4—21no—
172C22×C3×C4—64no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—121no—
178C2×D12—22no—
179C2×D12—21no—
180C2×D12C4×D314yes—
181C2×D12C22×D312yes—
182C2×C4×D3—24no—
183C2×Dic6—34no—
184C2×Dic6—34no—
185C2×Dic6—32no—
186C2×Dic6—32no—
187C2×Dic6—62no—
188C2×Dic6—64no—
189C2×Dic6—62no—
190C2×Dic6—61no—
191C2×Dic6—62no—
192C2×Dic6—61no—
193C2×Dic6—122no—
194C2×Dic6—121no—
195C2×C3×C8—34no—
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—32no—
201C3×C4⋊C4C22×D312yes—
202C3×C4⋊C4C22×D312yes—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—32no—
206C3×C22⋊C4—41no—
207C3×C22⋊C4—64no—
208C3×C22⋊C4—61no—
209C3×C42—21no—
210C3×C42—21no—
211C3×C42—32no—
212C3×C42—41no—
213C3×C42—61no—
214#217—21no—
215#217#6712yes—
216#214—38no—
217#214—38no—
218(C2×D3)⋊C4—24no—
219C4⋊Dic3#6712yes—
220C4⋊Dic3C22×D312yes—
221Dic3⋊C4—64no—
222Dic3⋊C4—64no—
223C4×Dic3—21no—
224C4×Dic3—64no—
225C4×Dic3—64no—
226C4×Dic3C22×D312yes—
227#208—62no—
228#208—62no—
229#208—122no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8C4×D314yescomplemented
234C2×C3⋊C8C22×D311yescharacteristic
235C2×C3⋊C8C22×D311yescharacteristic
236#204—38no—
237#204—38no—
238C22×C32—22no—
239C22×C32C4×D412yes—
240C22×C32C22×D411yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—44no—
243C2×C3×D3—84no—
244C32×C4—42no—
245C32×C4C4×D412yes—
246C32×C4C23×C411yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3⋊Dic3—24no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×Q8—91no—
252C22×D4—31no—
253C2×SD16—98no—
254C2×SD16—92no—
255C2×SD16—92no—
256C2×M16—91no—
257C22×C8—31no—
258C4×Q8—94no—
259C4×Q8—182no—
260C4×D4—34no—
261C4×D4—62no—
262#117—31no—
263#117—31no—
264#117—182no—
265#117D3211yescharacteristic
266C2×C22⋊C4—62no—
267#107—32no—
268#106—32no—
269#103—94no—
270#102—94no—
271#97—92no—
272C4×C8—92no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—64no—
276C23×C3—242no—
277C23×C3D3×D411yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C22×D3—22no—
280C22×D3—24no—
281C22×D3—82no—
282C3×D4—34no—
283C3×D4—64no—
284C3×D4—62no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—34no—
292C2×C3×C4—42no—
293C2×C3×C4—62no—
294C2×C3×C4—244no—
295C2×C3×C4C2×C4×D312yes—
296C2×C3×C4C2×C4×D312yes—
297C2×C3×C4#23512yes—
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23912yes—
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C23×D311yescharacteristic
302C2×C3×C4C23×D311yescharacteristic
303C2×Dic3—22no—
304C2×Dic3—64no—
305C2×Dic3—64no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—122no—
309C2×Dic3—124no—
310C2×Dic3C2×#6714yes—
311D12—24no—
312D12—22no—
313D12C2×C4×D314yes—
314C4×D3—84no—
315Dic6—34no—
316Dic6—34no—
317Dic6—64no—
318Dic6—64no—
319Dic6—64no—
320Dic6—62no—
321Dic6—62no—
322Dic6—122no—
323Dic6—124no—
324C3×C8—32no—
325C3×C8—32no—
326C3⋊C8—62no—
327C3⋊C8—62no—
328C3⋊C8—122no—
329C3⋊C8C2×C4×D312yes—
330C3⋊C8C2×C4×D312yes—
331C2×C32—22no—
332C2×C32C2×C4×D411yescharacteristic
333C2×C32#57712yes—
334C3×D3—44no—
335C24—61no—
336C2×Q8—92no—
337C2×Q8—94no—
338C2×Q8—182no—
339C2×Q8—181no—
340C2×D4—32no—
341C2×D4—34no—
342C2×D4—62no—
343C2×D4—61no—
344C22×C4—64no—
345C22×C4—181no—
346C22×C4C2×D3211yescharacteristic
347SD16—98no—
348SD16—98no—
349M16—182no—
350C2×C8—31no—
351C2×C8—31no—
352C2×C8—34no—
353C2×C8—92no—
354C4⋊C4—32no—
355C4⋊C4—32no—
356C4⋊C4—184no—
357C4⋊C4C2×D3212yes—
358C22⋊C4—21no—
359C22⋊C4—32no—
360C22⋊C4—64no—
361C22⋊C4—61no—
362C42—21no—
363C42—32no—
364C42—61no—
365C42—184no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—22no—
370C22×C3—42no—
371C22×C3—64no—
372C22×C3—124no—
373C22×C3—244no—
374C22×C3#89312yes—
375C22×C3C4×#6712yes—
376C22×C3C2×D3×D411yescharacteristic
377C22×C3C22×#6711yescharacteristic
378C2×D3—24no—
379C2×D3—44no—
380C2×D3—84no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—22no—
384C3×C4—42no—
385C3×C4—42no—
386C3×C4—64no—
387C3×C4—82no—
388C3×C4—122no—
389C3×C4#89312yes—
390C3×C4C4×#6712yes—
391C3×C4C22×C4×D311yescharacteristic
392C3×C4C22×C4×D311yescharacteristic
393C3×C4C2×#23511yescharacteristic
394C3×C4C2×#23911yescharacteristic
395Dic3—24no—
396Dic3—42no—
397Dic3—64no—
398Dic3—64no—
399Dic3—124no—
400C32#294911yescharacteristic, complemented, Sylow
401C23—62no—
402C23—64no—
403C23—242no—
404C23D3×#6711yescharacteristic
405Q8—94no—
406Q8—182no—
407Q8—184no—
408D4—34no—
409D4—62no—
410D4—64no—
411C2×C4—22no—
412C2×C4—34no—
413C2×C4—62no—
414C2×C4—182no—
415C2×C4—184no—
416C2×C4—244no—
417C2×C4#379912yes—
418C2×C4C4×D3212yes—
419C2×C4D3×#6711yescharacteristic
420C2×C4C22×D3211yescharacteristic
421C8—32no—
422C8—32no—
423C8—182no—
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—42no—
429C2×C3—124no—
430C2×C3C2×#89311yescharacteristic
431C2×C3#577012yes—
432C2×C3C2×C4×#6711yescharacteristic
433C2×C3#583612yes—
434D3—44no—
435C22—22no—
436C22—64no—
437C22—124no—
438C22—244no—
439C22#6390412yes—
440C22C2×D3×#6711yescharacteristic
441C4—42no—
442C4—64no—
443C4—122no—
444C4—184no—
445C4#6390412yes—
446C4C2×#379911yescharacteristic
447C4C2×C4×D3211yescharacteristic
448C3—21no—
449C3#7916811yescharacteristic, complemented
450C3#8254311yescharacteristic, complemented
451C2—22no—
452C2—124no—
453C2C2×#6390411yescharacteristic
454C2#1059546612yes—
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594828C2semidirect
4. #10592703C2semidirect
5. C3×#4998C2semidirect
7. #10591055C2semidirect
8. #10590590C2semidirect
9. #10590479C2semidirect
24. #63844C22semidirect
25. C2×#3716C4semidirect
28. #63637C22semidirect
29. C3×#808C22semidirect
30. C3×#807C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
49. #4998D3semidirect
58. C2×#634C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
82. #3716C2×C4semidirect
83. #3716C2×C4semidirect
129. #808C2×D3semidirect
130. #807C2×D3semidirect
233. C2×C3⋊C8C4×D3semidirect
400. C32#2949semidirect
449. C3#79168semidirect
450. C3#82543semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105948282
C22×#37162
#105927032
C3×#49982
#105910852
#105910552
#105905902
#105904792
#825433
#791683