Finite Group Databasebeta

← #11866136

Subgroups — #11866136

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic, complemented
2#10594954C211yesmaximal, characteristic, complemented
3C2×#63860C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic
5C3×#5131C211yesmaximal, characteristic, complemented
6C3×#5118C211yesmaximal, characteristic, complemented
7#10591107C211yesmaximal, characteristic, complemented
8#10590861C214yesmaximal, complemented
9#10590860C214yesmaximal, complemented
10#79058—31nomaximal
11#78943—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64118—24no—
17C2×#3746C2212yescomplemented
18C2×#3744C2212yescomplemented
19C3×#926C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—22no—
23#63952—22no—
24#63894C2212yescomplemented
25C4×#624—21no—
26#63874—21no—
27#63860—21no—
28#63860—21no—
29#63860C2214yes—
30#63844C2212yescomplemented
31#63830—24no—
32C2×#3716C2212yes—
33C2×#3714C2212yes—
34C3×#821C2214yes—
35C3×Dic3⋊C8C2214yescomplemented
36#63567C2214yescomplemented
37C2×#936—31no—
38C2×#932—31no—
39C2×#909—31no—
40C2×#909—31no—
41C2×#909—61no—
42C2×#908—31no—
43#5522—31no—
44C2×#875—31no—
45C4×#235—31no—
46C3×#423—31no—
47C3×#418—31no—
48#5131D311yescharacteristic, complemented
49#5120—31no—
50#5118D311yescharacteristic, complemented
51#5004—31no—
52#4845—34no—
53#4844—34no—
54#4787—34no—
55#4767—34no—
56C23×C3×D3—21no—
57C22×C32×C4C2311yescharacteristic
58C2×#638—21no—
59C22×C3⋊Dic3—21no—
60#3828—22no—
61#3828D414yes—
62C2×C4⋊(C3⋊D3)C2311yescharacteristic
63C2×C4×C3⋊D3—21no—
64C2×#634—22no—
65C2×#634—22no—
66C2×#634—21no—
67C2×#634C2312yes—
68C2×#634C2311yescharacteristic
69C22×C3×Dic3D412yes—
70C2×C3×D12—22no—
71C2×C3×D12—22no—
72C2×C3×D12—21no—
73C2×C3×D12C2312yes—
74C2×#624—22no—
75C32×M16—22no—
76C2×C32×C8C2312yes—
77#3746—24no—
78#3744—24no—
79C3×#217—21no—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3—21no—
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3C2312yes—
85C3×#208—22no—
86C2×C3×C3⋊C8C2312yes—
87#3724—22no—
88#3722—22no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91Dic32—22no—
92#3716—24no—
93#3714—24no—
94#3040—91noSylow
95C22×C3×D4—31no—
96C2×#235—31no—
97C2×#235—31no—
98C2×#235—61no—
99C22×D12C2×D311yescharacteristic
100C22×Dic6—31no—
101C22×Dic6—31no—
102C22×Dic6—61no—
103C2×C3×M16—21no—
104C2×C3×M16—31no—
105C2×C3×M16C2×D311yescharacteristic
106C2×C3×M16C2×D311yescharacteristic
107C3×#117—31no—
108C2×C3×C42—31no—
109C2×#217—62no—
110#936—34no—
111#936—61no—
112#936—61no—
113C2×#214—32no—
114#932—64no—
115C2×#213—32no—
116C4×#67—62no—
117C2×(C2×D3)⋊C4—62no—
118#926C2×D311yescharacteristic
119C2×C4×Dic3C2×D311yescharacteristic
120C2×#208C2×D311yescharacteristic
121#909—64no—
122#909—64no—
123#909—68no—
124#908—64no—
125C2×Dic12—32no—
126C2×Dic12—32no—
127C2×Dic12—62no—
128C2×D24—32no—
129C2×#204—32no—
130C2×#204—32no—
131C2×#204—32no—
132C2×#204—62no—
133#893—32no—
134#887—32no—
135#67⋊C4—62no—
136#875—34no—
137#875—61no—
138#875—61no—
139C4×D12—32no—
140#872—61no—
141#872—61no—
142C42×D3—61no—
143C42×D3—61no—
144C4×Dic6—32no—
145C3×C4⋊C8—34no—
146C3×#102—34no—
147#821C2×D314yes—
148#816—34no—
149Dic3⋊C8C2×D314yescomplemented
150#810—34no—
151C23×C32C2×D411yescharacteristic
152C22×C3⋊D3—21no—
153C22×C3×D3—22no—
154C22×C3×D3—44no—
155C22×C3×D3—42no—
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D412yes—
158C2×C32×C4#4112yes—
159C2×C32×C4C2411yescharacteristic
160#638—24no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—42no—
164C4⋊(C3⋊D3)—21no—
165C4⋊(C3⋊D3)C2×D412yes—
166C4×C3⋊D3—24no—
167#634—22no—
168#634—21no—
169#634—22no—
170#634—42no—
171#634C2×D412yes—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—42no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—22no—
177C3×D12—22no—
178C3×D12—42no—
179#624—44no—
180C32×C8—22no—
181C3×C3⋊C8—22no—
182C2×#137—91no—
183C2×AGL(1,ℤ/8)—91no—
184C2×#124—91no—
185C4×#41—91no—
186#464—94no—
187#463—94no—
188#423—31no—
189#419—91no—
190#418—31no—
191C24×C3—61no—
192C23×D3—21no—
193C2×C3×D4—32no—
194C2×C3×D4—61no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C22×C3×C4—21no—
198C22×C3×C4—32no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—61no—
202C2×#67—61no—
203C2×#67—121no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3—121no—
207C22×Dic3D1212yes—
208#235—34no—
209#235—34no—
210#235—64no—
211#235—62no—
212#235—62no—
213#235—122no—
214C2×D12—22no—
215C2×D12—22no—
216C2×D12—21no—
217C2×D12—31no—
218C2×D12—31no—
219C2×D12—61no—
220C2×D12C22×D312yes—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—121no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—32no—
229C2×Dic6—32no—
230C2×Dic6—62no—
231C2×Dic6—61no—
232C2×Dic6—64no—
233C2×Dic6—62no—
234C2×Dic6—62no—
235C2×Dic6—62no—
236C2×Dic6—62no—
237C2×Dic6—61no—
238C2×Dic6—61no—
239C2×Dic6—121no—
240C2×Dic6—122no—
241C3×M16—24no—
242C3×M16—22no—
243C3×M16—22no—
244C3×M16—62no—
245C2×C3×C8—22no—
246C2×C3×C8—32no—
247C2×C3×C8C22×D312yes—
248C2×C3×C8C22×D312yes—
249C3×C4⋊C4—32no—
250C3×C22⋊C4—61no—
251C3×C42—31no—
252C3×C42—31no—
253C3×C42—32no—
254C3×C42—61no—
255#217—21no—
256#217—64no—
257#217—64no—
258#214—64no—
259#213—64no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—62no—
264C4⋊Dic3C22×D312yes—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267C4×Dic3—21no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C4×Dic3D1211yescharacteristic
271C4×Dic3D1211yescharacteristic
272C4×Dic3C22×D312yes—
273#208—22no—
274C2×C3⋊C8C22×D312yes—
275Dic12—64no—
276Dic12—64no—
277Dic12—68no—
278D24—64no—
279#204—64no—
280#204—64no—
281#204—68no—
282#204—64no—
283C22×C32—22no—
284C22×C32#12112yes—
285C22×C32C22×D411yescharacteristic
286C2×C3⋊D3—22no—
287C2×C3⋊D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—44no—
290C2×C3×D3—84no—
291C32×C4#12112yes—
292C32×C4C22×D411yescharacteristic
293C32×C4C2×#4111yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—42no—
296C3×Dic3—22no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C2×#41—91no—
300C22×Q8—91no—
301C22×D4—31no—
302#137—184no—
303AGL(1,ℤ/8)—184no—
304C2×Q16—92no—
305C2×SD16—92no—
306C2×SD16—92no—
307C2×D8—92no—
308C2×M16—31no—
309C2×M16D3211yescharacteristic
310#124—94no—
311#124—181no—
312#124—181no—
313C4×Q8—92no—
314C4×D4—92no—
315C4×D4—182no—
316#117—31no—
317#117—181no—
318C2×C22⋊C4—182no—
319C2×C42—31no—
320C2×C42—181no—
321C4⋊C8—34no—
322#103—94no—
323#102—34no—
324C23×C3—21no—
325C23×C3—62no—
326C23×C3—124no—
327C23×C3—122no—
328C23×C3C2×D1211yescharacteristic
329C23×C3D3×D411yescharacteristic
330C22×D3—22no—
331C22×D3—44no—
332C22×D3—42no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—121no—
336C3×D4—62no—
337C3×D4—62no—
338C3×D4—122no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—62no—
346C2×C3×C4—122no—
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4#23512yes—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D412yes—
351C2×C3×C4D3×D412yes—
352C2×C3×C4#23912yes—
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355#67—64no—
356#67—64no—
357#67—124no—
358C2×Dic3—22no—
359C2×Dic3—42no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—122no—
365C2×Dic3—121no—
366C2×Dic3—124no—
367C2×Dic3—122no—
368C2×Dic3—122no—
369C2×Dic3C2×D1212yes—
370C2×Dic3C2×D1212yes—
371D12—22no—
372D12—22no—
373D12—32no—
374D12—32no—
375D12—42no—
376D12—62no—
377D12—61no—
378D12—61no—
379D12—121no—
380C4×D3—64no—
381C4×D3—64no—
382C4×D3—124no—
383C4×D3—124no—
384C4×D3—124no—
385Dic6—32no—
386Dic6—32no—
387Dic6—62no—
388Dic6—61no—
389Dic6—61no—
390Dic6—64no—
391Dic6—62no—
392Dic6—62no—
393Dic6—62no—
394Dic6—62no—
395Dic6—122no—
396Dic6—121no—
397Dic6—124no—
398Dic6—122no—
399Dic6—122no—
400C3×C8—24no—
401C3×C8—22no—
402C3×C8—22no—
403C3×C8—62no—
404C3⋊C8—22no—
405C2×C32—22no—
406C2×C32C2×#12111yescharacteristic
407C2×C32#57512yes—
408C3⋊D3—42no—
409C3×D3—82no—
410C24—61no—
411#41—94no—
412#41—182no—
413C2×Q8—91no—
414C2×Q8—92no—
415C2×Q8—181no—
416C2×Q8—182no—
417C2×Q8—182no—
418C2×D4—32no—
419C2×D4—62no—
420C2×D4—61no—
421C2×D4—62no—
422C2×D4—91no—
423C2×D4—181no—
424C22×C4—32no—
425C22×C4—182no—
426C22×C4—181no—
427C22×C4—181no—
428C22×C4C2×D3211yescharacteristic
429Q16—184no—
430SD16—184no—
431SD16—184no—
432D8—184no—
433M16—22no—
434M16—62no—
435C2×C8—32no—
436C2×C8C2×D3212yes—
437C4⋊C4—32no—
438C4⋊C4—182no—
439C22⋊C4—61no—
440C22⋊C4—182no—
441C22⋊C4—184no—
442C22⋊C4—184no—
443C42—32no—
444C42—31no—
445C42—31no—
446C42—61no—
447C42—182no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3—22no—
452C22×C3—42no—
453C22×C3—124no—
454C22×C3—122no—
455C22×C3—244no—
456C22×C3#88412yes—
457C22×C3#89512yes—
458C22×C3C22×D1211yescharacteristic
459C22×C3C2×D3×D411yescharacteristic
460C2×D3—42no—
461C2×D3—44no—
462C2×D3—62no—
463C2×D3—62no—
464C2×D3—84no—
465C2×D3—122no—
466C2×D3—122no—
467C2×D3—122no—
468C2×D3—242no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—22no—
472C3×C4—62no—
473C3×C4—62no—
474C3×C4—122no—
475C3×C4#88412yes—
476C3×C4#89512yes—
477C3×C4C2×#23511yescharacteristic
478C3×C4C2×D3×D411yescharacteristic
479C3×C4C2×D3×D411yescharacteristic
480C3×C4C2×#23911yescharacteristic
481Dic3—22no—
482Dic3—22no—
483Dic3—42no—
484Dic3—62no—
485Dic3—62no—
486Dic3—122no—
487Dic3—124no—
488Dic3—122no—
489Dic3—122no—
490C32#304011yescharacteristic, complemented, Sylow
491C23—62no—
492C23—124no—
493C23—122no—
494C23—181no—
495C23D3×D1211yescharacteristic
496Q8—92no—
497Q8—181no—
498Q8—182no—
499Q8—182no—
500Q8—362no—
501D4—62no—
502D4—62no—
503D4—92no—
504D4—122no—
505D4—184no—
506D4—181no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—62no—
510C2×C4—122no—
511C2×C4—181no—
512C2×C4—184no—
513C2×C4—182no—
514C2×C4—364no—
515C2×C4—362no—
516C2×C4#379912yes—
517C2×C4D3×D1211yescharacteristic
518C2×C4#381112yes—
519C2×C4C22×D3211yescharacteristic
520C8—22no—
521C8—62no—
522C2×C3—22no—
523C2×C3—22no—
524C2×C3—22no—
525C2×C3—21no—
526C2×C3—42no—
527C2×C3—242no—
528C2×C3C2×#88411yescharacteristic
529C2×C3C2×#89511yescharacteristic
530C2×C3#574812yes—
531C2×C3#577312yes—
532D3—82no—
533D3—122no—
534D3—122no—
535D3—242no—
536C22—22no—
537C22—124no—
538C22—122no—
539C22—182no—
540C22—244no—
541C22—362no—
542C22#6391012yes—
543C22C2×D3×D1211yescharacteristic
544C4—62no—
545C4—62no—
546C4—122no—
547C4—182no—
548C4—362no—
549C4#6391012yes—
550C4C2×#379911yescharacteristic
551C4C2×#381111yescharacteristic
552C3—21no—
553C3#7894311yescharacteristic, complemented
554C3#7905811yescharacteristic, complemented
555C2—22no—
556C2—242no—
557C2—362no—
558C2#1059471212yes—
559C2C2×#6391011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#63830C2
hypercenterC2×M16D32
hypocenterC32#3040
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
2. #10594954C2semidirect
3. C2×#63860C2semidirect
5. C3×#5131C2semidirect
6. C3×#5118C2semidirect
7. #10591107C2semidirect
8. #10590861C2semidirect
9. #10590860C2semidirect
17. C2×#3746C22semidirect
18. C2×#3744C22semidirect
24. #63894C22semidirect
30. #63844C22semidirect
35. C3×Dic3⋊C8C22semidirect
36. #63567C22semidirect
48. #5131D3semidirect
50. #5118D3semidirect
149. Dic3⋊C8C2×D3semidirect
490. C32#3040semidirect
553. C3#78943semidirect
554. C3#79058semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105949542
C2×#638602
C2×#638302
C3×#51312
C3×#51182
#105911072
#105908612
#105908602
#790583
#789433