Finite Group Databasebeta

← #11860425

Subgroups — #11860425

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic
2#10594954C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4C3×#5121C211yesmaximal, characteristic, complemented
5C3×Dic3×M16C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591106C211yesmaximal, characteristic
8#10590810C212yesmaximal, complemented
9#10590807C212yesmaximal, complemented
10#10590773C212yesmaximal, complemented
11#10590758C212yesmaximal, complemented
12#79200—31nomaximal
13C4×#909—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17#64118C418yescomplemented
18C2×#3746C2212yes—
19C2×#3744C2212yes—
20C3×#926C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×#3724—21no—
25C2×Dic32—21no—
26#63952—21no—
27#63952—21no—
28#63894C2211yescharacteristic
29#63894C2211yescharacteristic
30C4×#624—21no—
31#63874—21no—
32#63844—21no—
33#63844—21no—
34#63844C2212yes—
35#63844C2212yes—
36#63844C2211yescharacteristic
37#63844C2211yescharacteristic
38C3×#818C2212yes—
39C3×#817C2212yes—
40C3×#815C2212yes—
41C3×C8×Dic3C2212yes—
42#63567C2212yes—
43#63567C2212yes—
44#63567C2212yes—
45#63564C2212yes—
46C2×#909—31no—
47C2×#909—31no—
48C2×#909—61no—
49#5522—31no—
50C2×#887—31no—
51C4×#235—31no—
52C2×C4×Dic6—31no—
53C3×#428—31no—
54C3×C4×M16—31no—
55#5133—31no—
56#5121D311yescharacteristic, complemented
57#5120—31no—
58Dic3×M16D311yescharacteristic, complemented
59#5004—31no—
60#4966—31no—
61#4889—32no—
62#4873—32no—
63#4853—32no—
64#4852—32no—
65#4716—32no—
66#4710—32no—
67C4×Dic12—32no—
68C4×#204—32no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71C22×C3⋊Dic3—21no—
72#3828—22no—
73#3828C2×C414yes—
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C4×C3⋊D3—21no—
76C2×#634—21no—
77C2×#634—22no—
78C2×#634C2×C414yescomplemented
79C2×#634C2312yes—
80C2×#634C2311yescharacteristic
81C22×C3×Dic3—21no—
82C22×C3×Dic3D411yescharacteristic
83C22×C3×Dic3D411yescharacteristic
84C2×#624—21no—
85C2×#624—21no—
86C32×M16C2×C414yescomplemented
87C2×C32×C8C2312yes—
88#3746C2×C418yescomplemented
89#3744C2×C418yescomplemented
90C3×#217—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3—21no—
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C3×#208—22no—
101C2×C3×C3⋊C8C2312yes—
102#3724—22no—
103#3724—22no—
104#3724—21no—
105#3724—21no—
106#3722—21no—
107#3722—21no—
108Dic32—22no—
109Dic32—22no—
110Dic32—21no—
111Dic32—21no—
112C4×#137—91noSylow
113C2×#235—31no—
114C2×#235—31no—
115C2×#235—61no—
116C22×Dic6—31no—
117C22×Dic6—31no—
118C22×Dic6—61no—
119C2×C3×M16—21no—
120C2×C3×M16—31no—
121C2×C3×M16C2×D311yescharacteristic
122C2×C3×M16C2×D311yescharacteristic
123C3×#117—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C42—31no—
126C4×#67—61no—
127C4×#67—61no—
128#926C2×D311yescharacteristic
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×Dic3⋊C4—61no—
131C2×Dic3⋊C4—61no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3—61no—
134C2×C4×Dic3C2×D311yescharacteristic
135C2×#208C2×D311yescharacteristic
136#909—38no—
137#909—38no—
138#909—68no—
139C2×Dic12—32no—
140C2×Dic12—32no—
141C2×Dic12—62no—
142C2×#204—32no—
143C2×#204—32no—
144C2×#204—62no—
145#893—31no—
146#893—31no—
147#887—31no—
148#887—32no—
149#887—32no—
150#887—31no—
151#887—61no—
152#887—61no—
153#67⋊C4—61no—
154#67⋊C4—61no—
155C4×D12—31no—
156C4×D12—31no—
157#872—61no—
158#872—61no—
159C42×D3—61no—
160C42×D3—61no—
161C4×Dic6—32no—
162C4×Dic6—31no—
163C4×Dic6—32no—
164C4×Dic6—31no—
165C4×Dic6—61no—
166C4×Dic6—61no—
167C3×#107—32no—
168C3×#106—32no—
169C3×#97—32no—
170C3×C4×C8—32no—
171#821—32no—
172#818C2×D312yes—
173#817C2×D312yes—
174#816—32no—
175#816—32no—
176#816—32no—
177#815C2×D312yes—
178C8×Dic3C2×D312yes—
179#810—32no—
180#810—32no—
181#810—32no—
182#809—32no—
183C23×C32C2×D411yescharacteristic
184C22×C3⋊D3—21no—
185C2×C32×C4C22×C412yes—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4#4112yes—
188C2×C32×C4C2411yescharacteristic
189#638—24no—
190C2×C3⋊Dic3—24no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—21no—
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)C22×C412yes—
195C4×C3⋊D3—24no—
196#634—24no—
197#634—22no—
198#634—21no—
199#634C22×C414yes—
200#634C22×C412yes—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—41no—
206C2×C3×Dic3—42no—
207C2×C3×Dic3C2×D411yescharacteristic
208C2×C3×Dic3C2×D411yescharacteristic
209C2×C3×Dic3C2×D411yescharacteristic
210C2×C3×Dic3C2×D411yescharacteristic
211#624—42no—
212#624—42no—
213C32×C8C22×C414yes—
214C3×C3⋊C8—22no—
215C2×#137—91no—
216C4×#41—91no—
217C2×C4×Q8—91no—
218#441—92no—
219#440—92no—
220C4×Q16—92no—
221C4×SD16—92no—
222#428—31no—
223#419—91no—
224#417—91no—
225C4×M16—31no—
226C22×C3×C4—21no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—61no—
233C2×#67—61no—
234C2×#67—121no—
235C22×Dic3—21no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—121no—
239C22×Dic3D1211yescharacteristic
240C22×Dic3D1211yescharacteristic
241#235—34no—
242#235—34no—
243#235—64no—
244#235—62no—
245#235—62no—
246#235—122no—
247C2×D12—31no—
248C2×D12—31no—
249C2×D12—61no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—61no—
256C2×C4×D3—121no—
257C2×Dic6—34no—
258C2×Dic6—34no—
259C2×Dic6—32no—
260C2×Dic6—31no—
261C2×Dic6—32no—
262C2×Dic6—31no—
263C2×Dic6—62no—
264C2×Dic6—61no—
265C2×Dic6—64no—
266C2×Dic6—61no—
267C2×Dic6—62no—
268C2×Dic6—61no—
269C2×Dic6—62no—
270C2×Dic6—122no—
271C2×Dic6—121no—
272C3×M16—24no—
273C3×M16—62no—
274C3×M16C4×D314yescomplemented
275C3×M16C4×D314yescomplemented
276C2×C3×C8—22no—
277C2×C3×C8—32no—
278C2×C3×C8C22×D312yes—
279C2×C3×C8C22×D312yes—
280C3×C4⋊C4—32no—
281C3×C4⋊C4—31no—
282C3×C4⋊C4—31no—
283C3×C4⋊C4—61no—
284C3×C22⋊C4—61no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42—31no—
289C3×C42—61no—
290#217—21no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295C4⋊Dic3—21no—
296C4⋊Dic3C22×D311yescharacteristic
297C4⋊Dic3C22×D311yescharacteristic
298C4⋊Dic3C22×D312yes—
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301Dic3⋊C4—61no—
302Dic3⋊C4—61no—
303Dic3⋊C4—61no—
304Dic3⋊C4—61no—
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307C4×Dic3—21no—
308C4×Dic3—62no—
309C4×Dic3—62no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—62no—
315C4×Dic3—62no—
316C4×Dic3D1211yescharacteristic
317C4×Dic3D1211yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C4×Dic3C22×D311yescharacteristic
320#208—22no—
321C2×C3⋊C8C22×D312yes—
322Dic12—38no—
323Dic12—38no—
324Dic12—68no—
325#204—38no—
326#204—38no—
327#204—68no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32C4×D412yes—
331C22×C32C22×D411yescharacteristic
332C2×C3⋊D3—22no—
333C2×C3⋊D3—41no—
334C2×C3⋊D3—41no—
335C32×C4C4×D412yes—
336C32×C4C23×C411yescharacteristic
337C32×C4C2×#4111yescharacteristic
338C3⋊Dic3—24no—
339C3⋊Dic3—22no—
340C3×Dic3—21no—
341C3×Dic3—21no—
342C3×Dic3—21no—
343C3×Dic3—41no—
344C3×Dic3—41no—
345C3×Dic3—42no—
346C3×Dic3#13712yescomplemented
347C2×#41—91no—
348C22×Q8—91no—
349#137—98no—
350C2×Q16—92no—
351C2×SD16—92no—
352C2×M16—31no—
353C2×M16D3211yescharacteristic
354C4×Q8—92no—
355C4×Q8—92no—
356C4×Q8—91no—
357C4×Q8—91no—
358C4×Q8—181no—
359C4×Q8—181no—
360C4×D4—91no—
361C4×D4—91no—
362C4×D4—181no—
363C4×D4—181no—
364#117—31no—
365#117—181no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—181no—
368C2×C42—31no—
369C2×C42—181no—
370C2×C42—181no—
371#107—32no—
372#106—32no—
373#103—92no—
374#103—92no—
375#103—92no—
376#102—92no—
377#97—32no—
378C4×C8—32no—
379C23×C3—21no—
380C23×C3C2×D1211yescharacteristic
381C23×C3D3×D411yescharacteristic
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—121no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—121no—
398C2×C3×C4—122no—
399C2×C3×C4C2×C4×D312yes—
400C2×C3×C4C2×C4×D312yes—
401C2×C3×C4C2×D1211yescharacteristic
402C2×C3×C4#23512yes—
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4#23912yes—
405C2×C3×C4C23×D311yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407#67—64no—
408#67—64no—
409#67—124no—
410C2×Dic3—22no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—22no—
414C2×Dic3—41no—
415C2×Dic3—42no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418C2×Dic3—62no—
419C2×Dic3—61no—
420C2×Dic3—62no—
421C2×Dic3—61no—
422C2×Dic3—122no—
423C2×Dic3—124no—
424C2×Dic3—121no—
425C2×Dic3C2×D1211yescharacteristic
426C2×Dic3C2×D1211yescharacteristic
427C2×Dic3C2×D1211yescharacteristic
428C2×Dic3C2×D1211yescharacteristic
429D12—32no—
430D12—32no—
431D12—62no—
432D12—61no—
433D12—61no—
434D12—121no—
435C4×D3—64no—
436C4×D3—64no—
437C4×D3—124no—
438C4×D3—122no—
439C4×D3—122no—
440C4×D3—122no—
441C4×D3—122no—
442Dic6—34no—
443Dic6—34no—
444Dic6—32no—
445Dic6—32no—
446Dic6—64no—
447Dic6—62no—
448Dic6—64no—
449Dic6—64no—
450Dic6—62no—
451Dic6—61no—
452Dic6—62no—
453Dic6—61no—
454Dic6—122no—
455Dic6—124no—
456Dic6—121no—
457C3×C8—24no—
458C3×C8—62no—
459C3×C8C2×C4×D314yes—
460C3×C8C2×C4×D314yes—
461C3⋊C8—22no—
462C2×C32—22no—
463C2×C32C2×C4×D411yescharacteristic
464C2×C32C2×#13711yescharacteristic
465C2×C32#57511yescharacteristic
466C3⋊D3—42no—
467#41—94no—
468#41—182no—
469C2×Q8—92no—
470C2×Q8—91no—
471C2×Q8—94no—
472C2×Q8—182no—
473C2×Q8—181no—
474C2×D4—91no—
475C2×D4—181no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—61no—
479C22×C4—181no—
480C22×C4—181no—
481C22×C4—181no—
482C22×C4—181no—
483C22×C4C2×D3211yescharacteristic
484Q16—98no—
485SD16—98no—
486M16—62no—
487M16#62414yescomplemented
488C2×C8—32no—
489C2×C8C2×D3212yes—
490C4⋊C4—32no—
491C4⋊C4—31no—
492C4⋊C4—31no—
493C4⋊C4—61no—
494C4⋊C4—182no—
495C4⋊C4—182no—
496C4⋊C4—181no—
497C4⋊C4—181no—
498C22⋊C4—61no—
499C22⋊C4—181no—
500C22⋊C4—181no—
501C42—31no—
502C42—31no—
503C42—31no—
504C42—31no—
505C42—61no—
506C42—181no—
507C42—181no—
508C42—182no—
509C42—182no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—22no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3C4×D1212yes—
519C22×C3#89312yes—
520C22×C3C22×D1211yescharacteristic
521C22×C3C2×D3×D411yescharacteristic
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—122no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—241no—
530C2×D3—241no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—22no—
534C3×C4—32no—
535C3×C4—61no—
536C3×C4—61no—
537C3×C4—61no—
538C3×C4—121no—
539C3×C4—121no—
540C3×C4—122no—
541C3×C4C4×D1212yes—
542C3×C4#89312yes—
543C3×C4C22×C4×D311yescharacteristic
544C3×C4C22×C4×D311yescharacteristic
545C3×C4C2×#23511yescharacteristic
546C3×C4C2×#23911yescharacteristic
547Dic3—21no—
548Dic3—21no—
549Dic3—21no—
550Dic3—41no—
551Dic3—42no—
552Dic3—41no—
553Dic3—64no—
554Dic3—62no—
555Dic3—64no—
556Dic3—62no—
557Dic3—124no—
558Dic3—122no—
559Dic3#90912yescomplemented
560C32C4×#13711yescharacteristic, complemented, Sylow
561C23—181no—
562C23D3×D1211yescharacteristic
563Q8—94no—
564Q8—92no—
565Q8—182no—
566Q8—181no—
567Q8—184no—
568D4—92no—
569D4—184no—
570D4—181no—
571C2×C4—31no—
572C2×C4—31no—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—62no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—62no—
579C2×C4—121no—
580C2×C4—122no—
581C2×C4—181no—
582C2×C4—182no—
583C2×C4—184no—
584C2×C4—184no—
585C2×C4—362no—
586C2×C4—362no—
587C2×C4#379912yes—
588C2×C4D3×D1211yescharacteristic
589C2×C4C2×#62412yes—
590C2×C4C22×D3211yescharacteristic
591C8—62no—
592C8C2×#62414yes—
593C2×C3—22no—
594C2×C3—22no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—42no—
599C2×C3C2×C4×D1211yescharacteristic
600C2×C3C2×#89311yescharacteristic
601C2×C3C2×#90911yescharacteristic
602C2×C3#574811yescharacteristic
603C2×C3#577311yescharacteristic
604C2×C3D3×#13711yescharacteristic
605D3—122no—
606D3—122no—
607D3—242no—
608C22—21no—
609C22—21no—
610C22—182no—
611C22—361no—
612C22—361no—
613C22#6389412yes—
614C22C2×D3×D1211yescharacteristic
615C4—32no—
616C4—61no—
617C4—61no—
618C4—61no—
619C4—121no—
620C4—122no—
621C4—121no—
622C4—182no—
623C4—184no—
624C4#6389412yes—
625C4C2×#379911yescharacteristic
626C4C22×#62411yescharacteristic
627C3—21no—
628C3C4×#90911yescharacteristic, complemented
629C3#7920011yescharacteristic, complemented
630C2—22no—
631C2—362no—
632C2D3×#90911yescharacteristic
633C2#1059471211yescharacteristic
634C2C2×#6389411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C4×#137
LCSG ▷ 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
3. C2×#63844C2semidirect
4. C3×#5121C2semidirect
5. C3×Dic3×M16C2semidirect
6. #10591107C2semidirect
8. #10590810C2semidirect
9. #10590807C2semidirect
10. #10590773C2semidirect
11. #10590758C2semidirect
17. #64118C4semidirect
56. #5121D3semidirect
58. Dic3×M16D3semidirect
78. C2×#634C2×C4semidirect
86. C32×M16C2×C4semidirect
88. #3746C2×C4semidirect
89. #3744C2×C4semidirect
274. C3×M16C4×D3semidirect
275. C3×M16C4×D3semidirect
346. C3×Dic3#137semidirect
487. M16#624semidirect
559. Dic3#909semidirect
560. C32C4×#137semidirect
628. C3C4×#909semidirect
629. C3#79200semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105949542
C2×#638442
C3×#51212
C3×Dic3×M162
#105911072
#105911062
#105908102
#105908072
#105907732
#105907582
#792003
C4×#9093