Finite Group Databasebeta

← #11866367

Subgroups — #11866367

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic, complemented
2#10595042C211yesmaximal, characteristic
3#10594828C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic, complemented
6C3×#5119C211yesmaximal, characteristic, complemented
7#10591105C211yesmaximal, characteristic, complemented
8#10590879C214yesmaximal, complemented
9#10590861C214yesmaximal, complemented
10#79099—31nomaximal
11#78945—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64118—24no—
17C2×#3746C2212yescomplemented
18C2×#3744C2212yescomplemented
19C3×#926C2211yescharacteristic
20C3×#926C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63977—22no—
23#63957—22no—
24#63916—22no—
25#63911C2212yes—
26#63860C2212yes—
27#63844—22no—
28#63844C2214yescomplemented
29C2×#3716—24no—
30C2×#3716C2214yes—
31C3×#821C2214yes—
32C3×Dic3⋊C8C2214yescomplemented
33#63567C2212yescomplemented
34#63564C2212yescomplemented
35#5805—31no—
36C22×#214—31no—
37C2×#909—31no—
38C2×#909—31no—
39C2×#909—61no—
40C22×#204—31no—
41#5525—31no—
42#5516—31no—
43#5516—31no—
44C3×#424—31no—
45C3×#418—31no—
46#5131D311yescharacteristic, complemented
47#5119D311yescharacteristic, complemented
48#5113—31no—
49#5002—31no—
50#4848—34no—
51#4845—34no—
52#4767—34no—
53#4762—34no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57C22×C3⋊Dic3—21no—
58#3828—22no—
59#3828—22no—
60C2×C4⋊(C3⋊D3)C2311yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×#634—21no—
63C2×#634—22no—
64C2×#634D414yescomplemented
65C2×#634C2311yescharacteristic
66C2×#634C2312yes—
67C2×C3×D12—22no—
68C2×C3×D12—22no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×#626—24no—
72C32×M16—22no—
73C2×C32×C8C2312yes—
74#3746—24no—
75#3744—24no—
76C3×#217—21no—
77C3×#217D412yes—
78C3×C4⋊Dic3D412yes—
79C3×C4⋊Dic3C2312yes—
80C3×C4×Dic3—21no—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84#3724—24no—
85(C2×D3)⋊Dic3—24no—
86Dic32—24no—
87#3716—28no—
88#3043—91noSylow
89C22×C3×D4—31no—
90C2×#235—31no—
91C2×#235—31no—
92C2×#235—61no—
93C22×D12C2×D311yescharacteristic
94C22×Dic6—31no—
95C22×Dic6—31no—
96C22×Dic6—61no—
97C2×C3×M16—21no—
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×M16C2×D311yescharacteristic
100C22×C3×C8—31no—
101C3×#117—31no—
102C3×#117—31no—
103#953—62no—
104#940—32no—
105#938—62no—
106#936—32no—
107C2×#214—34no—
108C2×#214—64no—
109#926C2×D311yescharacteristic
110#926C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112#909—64no—
113#909—64no—
114#909—68no—
115C2×Dic12—32no—
116C2×Dic12—32no—
117C2×Dic12—62no—
118C2×#204—34no—
119C2×#204—32no—
120C2×#204—32no—
121C2×#204—62no—
122C2×#204—64no—
123#895—62no—
124#887—34no—
125#887—62no—
126#882—62no—
127#877—62no—
128#877—62no—
129#875—32no—
130#874—32no—
131C4×Dic6—34no—
132C4×Dic6—62no—
133C3×C4⋊C8—34no—
134C3×#102—34no—
135#821—32no—
136#821C2×D314yes—
137#816—32no—
138Dic3⋊C8C2×D314yescomplemented
139#810—32no—
140#809—32no—
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—21no—
143C22×C3×D3—22no—
144C22×C3×D3—42no—
145C22×C3×D3—82no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D412yes—
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150#638—42no—
151C2×C3⋊Dic3—24no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—21no—
154C4⋊(C3⋊D3)—21no—
155C4⋊(C3⋊D3)—21no—
156C4×C3⋊D3—42no—
157#634—21no—
158#634—24no—
159#634—22no—
160#634—21no—
161#634C2×D414yes—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D414yes—
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—42no—
167#626—84no—
168C32×C8—22no—
169C3×C3⋊C8—22no—
170C2×#137—91no—
171C22×SD16—91no—
172#535—91no—
173#519—91no—
174#464—94no—
175#460—94no—
176#424—31no—
177#418—31no—
178#416—91no—
179C24×C3—61no—
180C23×D3—21no—
181C2×C3×D4—32no—
182C2×C3×D4—61no—
183C2×C3×D4—62no—
184C2×C3×D4—62no—
185C22×C3×C4—21no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—61no—
189C2×#67—61no—
190C2×#67—64no—
191C2×#67—121no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—121no—
195#235—64no—
196#235—62no—
197#235—62no—
198#235—62no—
199#235—62no—
200#235—122no—
201C2×D12—22no—
202C2×D12—22no—
203C2×D12—21no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—61no—
207C2×D12—64no—
208C2×D12C22×D312yes—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—121no—
212C2×Dic6—34no—
213C2×Dic6—34no—
214C2×Dic6—32no—
215C2×Dic6—32no—
216C2×Dic6—31no—
217C2×Dic6—31no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—64no—
221C2×Dic6—61no—
222C2×Dic6—62no—
223C2×Dic6—61no—
224C2×Dic6—62no—
225C2×Dic6—122no—
226C2×Dic6—121no—
227C3×M16—24no—
228C3×M16—22no—
229C3×M16—22no—
230C2×C3×C8—22no—
231C2×C3×C8—32no—
232C2×C3×C8—62no—
233C2×C3×C8C22×D312yes—
234C2×C3×C8C22×D312yes—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—32no—
237C3×C22⋊C4—32no—
238C3×C22⋊C4—61no—
239C3×C42—32no—
240C3×C42—61no—
241#217—21no—
242#217—64no—
243#217D1212yes—
244#214—68no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3D1212yes—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250C4×Dic3—21no—
251C4×Dic3—64no—
252C4×Dic3—64no—
253C4×Dic3C22×D312yes—
254C2×C3⋊C8—22no—
255C2×C3⋊C8C22×D312yes—
256Dic12—64no—
257Dic12—64no—
258Dic12—68no—
259#204—64no—
260#204—64no—
261#204—68no—
262#204—68no—
263C22×C32—22no—
264C22×C32#12112yes—
265C22×C32C22×D411yescharacteristic
266C2×C3⋊D3—41no—
267C2×C3⋊D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—44no—
270C2×C3×D3—84no—
271C32×C4#12112yes—
272C32×C4C22×D411yescharacteristic
273C32×C4C2×#4111yescharacteristic
274C3⋊Dic3—24no—
275C3⋊Dic3—41no—
276C3×Dic3—24no—
277C3×Dic3—42no—
278C2×#41—91no—
279C22×Q8—91no—
280C22×D4—31no—
281#137—184no—
282C2×Q16—92no—
283C2×SD16—94no—
284C2×SD16—92no—
285C2×SD16—184no—
286C2×M16D3211yescharacteristic
287C22×C8—31no—
288#127—92no—
289#124—92no—
290#121—182no—
291#120—182no—
292C4×Q8—94no—
293C4×Q8—182no—
294#117—31no—
295#117—31no—
296#117—182no—
297C4⋊C8—34no—
298#103—92no—
299#102—34no—
300#102—92no—
301C23×C3—21no—
302C23×C3—62no—
303C23×C3—122no—
304C23×C3—242no—
305C23×C3C2×D1211yescharacteristic
306C23×C3D3×D411yescharacteristic
307C22×D3—22no—
308C22×D3—42no—
309C22×D3—61no—
310C22×D3—61no—
311C22×D3—82no—
312C22×D3—121no—
313C3×D4—62no—
314C3×D4—62no—
315C3×D4—122no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—34no—
321C2×C3×C4—62no—
322C2×C3×C4C2×D1211yescharacteristic
323C2×C3×C4#23512yes—
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D412yes—
326C2×C3×C4D3×D412yes—
327C2×C3×C4#23912yes—
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330#67—124no—
331#67—122no—
332#67—122no—
333#67—244no—
334C2×Dic3—22no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—122no—
342C2×Dic3—124no—
343C2×Dic3—121no—
344C2×Dic3C2×D1214yes—
345D12—22no—
346D12—22no—
347D12—42no—
348D12—62no—
349D12—61no—
350D12—61no—
351D12—61no—
352D12—61no—
353D12—121no—
354D12—244no—
355C4×D3—124no—
356C4×D3—122no—
357C4×D3—122no—
358Dic6—34no—
359Dic6—34no—
360Dic6—64no—
361Dic6—64no—
362Dic6—64no—
363Dic6—62no—
364Dic6—62no—
365Dic6—62no—
366Dic6—61no—
367Dic6—61no—
368Dic6—61no—
369Dic6—61no—
370Dic6—122no—
371Dic6—124no—
372Dic6—121no—
373C3×C8—24no—
374C3×C8—22no—
375C3×C8—22no—
376C3×C8—62no—
377C3⋊C8—22no—
378C2×C32—22no—
379C2×C32C2×#12111yescharacteristic
380C2×C32#57712yes—
381C3⋊D3—81no—
382C3×D3—82no—
383C24—61no—
384#41—182no—
385#41—182no—
386C2×Q8—92no—
387C2×Q8—91no—
388C2×Q8—94no—
389C2×Q8—182no—
390C2×Q8—181no—
391C2×D4—32no—
392C2×D4—62no—
393C2×D4—61no—
394C2×D4—62no—
395C2×D4—91no—
396C2×D4—184no—
397C2×D4—181no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4C2×D3211yescharacteristic
401Q16—184no—
402SD16—184no—
403SD16—188no—
404M16—22no—
405C2×C8—32no—
406C2×C8—62no—
407C2×C8C2×D3212yes—
408C4⋊C4—32no—
409C4⋊C4—32no—
410C4⋊C4—184no—
411C22⋊C4—32no—
412C22⋊C4—61no—
413C22⋊C4—184no—
414C42—32no—
415C42—61no—
416C42—184no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3—22no—
421C22×C3—42no—
422C22×C3—124no—
423C22×C3—122no—
424C22×C3—244no—
425C22×C3#88412yes—
426C22×C3#89512yes—
427C22×C3C22×D1211yescharacteristic
428C22×C3C2×D3×D411yescharacteristic
429C2×D3—42no—
430C2×D3—44no—
431C2×D3—84no—
432C2×D3—122no—
433C2×D3—121no—
434C2×D3—122no—
435C2×D3—121no—
436C2×D3—122no—
437C2×D3—242no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—64no—
442C3×C4—122no—
443C3×C4#88412yes—
444C3×C4#89512yes—
445C3×C4C2×#23511yescharacteristic
446C3×C4C2×D3×D411yescharacteristic
447C3×C4C2×D3×D411yescharacteristic
448C3×C4C2×#23911yescharacteristic
449Dic3—24no—
450Dic3—42no—
451Dic3—64no—
452Dic3—64no—
453Dic3—124no—
454Dic3—122no—
455Dic3—121no—
456Dic3—121no—
457C32#304311yescharacteristic, complemented, Sylow
458C23—62no—
459C23—122no—
460C23—181no—
461C23—242no—
462C23D3×D1211yescharacteristic
463Q8—94no—
464Q8—182no—
465Q8—184no—
466Q8—181no—
467Q8—181no—
468D4—62no—
469D4—62no—
470D4—122no—
471D4—181no—
472D4—181no—
473D4—362no—
474D4—724no—
475C2×C4—34no—
476C2×C4—62no—
477C2×C4—182no—
478C2×C4—184no—
479C2×C4—181no—
480C2×C4—362no—
481C2×C4#379912yes—
482C2×C4D3×D1211yescharacteristic
483C2×C4#381112yes—
484C2×C4C22×D3211yescharacteristic
485C8—22no—
486C8—62no—
487C2×C3—22no—
488C2×C3—22no—
489C2×C3—22no—
490C2×C3—21no—
491C2×C3—42no—
492C2×C3—242no—
493C2×C3C2×#88411yescharacteristic
494C2×C3C2×#89511yescharacteristic
495C2×C3#575112yes—
496C2×C3#577512yes—
497D3—82no—
498D3—242no—
499D3—241no—
500D3—241no—
501C22—22no—
502C22—124no—
503C22—122no—
504C22—244no—
505C22—362no—
506C22—361no—
507C22#6391012yes—
508C22C2×D3×D1211yescharacteristic
509C4—64no—
510C4—122no—
511C4—184no—
512C4—361no—
513C4#6391012yes—
514C4C2×#379911yescharacteristic
515C4C2×#381111yescharacteristic
516C3—21no—
517C3#7894511yescharacteristic, complemented
518C3#7909911yescharacteristic, complemented
519C2—22no—
520C2—242no—
521C2—721no—
522C2#1059471312yes—
523C2C2×#6391011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10595042C2
hypercenterC2×M16D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64118C2semidirect
3. #10594828C2semidirect
4. C22×#3716C2semidirect
5. C3×#5131C2semidirect
6. C3×#5119C2semidirect
7. #10591105C2semidirect
8. #10590879C2semidirect
9. #10590861C2semidirect
17. C2×#3746C22semidirect
18. C2×#3744C22semidirect
28. #63844C22semidirect
32. C3×Dic3⋊C8C22semidirect
33. #63567C22semidirect
34. #63564C22semidirect
46. #5131D3semidirect
47. #5119D3semidirect
64. C2×#634D4semidirect
138. Dic3⋊C8C2×D3semidirect
457. C32#3043semidirect
517. C3#78945semidirect
518. C3#79099semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105950422
#105948282
C22×#37162
C3×#51312
C3×#51192
#105911052
#105908792
#105908612
#790993
#789453