Finite Group Databasebeta

← #11868687

Subgroups — #11868687

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595049C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic
3#10592820C211yesmaximal, characteristic, complemented
4C3×#5131C211yesmaximal, characteristic
5C3×#5118C211yesmaximal, characteristic, complemented
6#10591131C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic
8#10590772C212yesmaximal, complemented
9#10590767C212yesmaximal, complemented
10#10590762C212yesmaximal, complemented
11#10590757C212yesmaximal, complemented
12#79059—31nomaximal
13#78917—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3—21no—
16C2×C32×M16C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#63964—21no—
23#63964—21no—
24C2×(C2×D3)⋊Dic3—21no—
25#63918C2211yescharacteristic, complemented
26#63918C2211yescharacteristic, complemented
27C4×#627—21no—
28C4×#627—21no—
29Dic3×D12—21no—
30Dic3×D12—21no—
31Dic3×D12C2212yes—
32Dic3×D12C2212yes—
33#63869C2211yescharacteristic, complemented
34#63869C2211yescharacteristic, complemented
35#63645C2212yescomplemented
36#63644C2212yescomplemented
37C3×#821C2212yes—
38C3×#821C2212yes—
39C3×Dic3⋊C8C2212yescomplemented
40C3×Dic3⋊C8C2212yescomplemented
41#63575C2212yescomplemented
42#63573C2212yescomplemented
43#63563C2212yes—
44#63563C2212yes—
45C2×D4×Dic3—31no—
46#5517—31no—
47C2×C4×D12—31no—
48#5470—31no—
49C3×#423—31no—
50C3×#418—31no—
51#5215—31no—
52#5131—31no—
53#5131D311yescharacteristic
54#5121—31no—
55#5121—31no—
56#5121—31no—
57#5121—61no—
58#5118D311yescharacteristic, complemented
59#4995—31no—
60#4847—32no—
61#4847—32no—
62#4846—32no—
63#4842—32no—
64#4766—32no—
65#4763—32no—
66#4761—32no—
67#4759—32no—
68C23×C3×D3—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C22×C3×Dic3D411yescharacteristic
72C22×C3×Dic3D411yescharacteristic
73C2×C3×D12—21no—
74C2×C3×D12—22no—
75C2×C3×D12Q814yescomplemented
76C2×C3×D12C2312yes—
77C2×#627—21no—
78C2×#627—21no—
79C2×D3×Dic3—22no—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—44no—
82C32×M16—22no—
83C2×C32×C8C2312yes—
84#3757—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C4⋊(C3⋊Dic3)C2312yes—
89C4×C3⋊Dic3—21no—
90C3×#217—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3—21no—
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×#208—22no—
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101#3724—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105Dic3⋊Dic3—21no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3077—91noSylow
109C22×C3×D4—31no—
110C23×Dic3—61no—
111C22×D12C2×D311yescharacteristic
112C22×C4×D3—61no—
113C2×C3×M16—21no—
114C2×C3×M16—31no—
115C2×C3×M16C2×D311yescharacteristic
116C2×C3×M16C2×D311yescharacteristic
117C3×#117—31no—
118C2×C3×C42—31no—
119C2×#217—61no—
120D4×Dic3—32no—
121D4×Dic3—32no—
122D4×Dic3—61no—
123D4×Dic3—61no—
124C2×(C2×D3)⋊C4—61no—
125#926—31no—
126#926—31no—
127#926—61no—
128#926C2×D311yescharacteristic
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—61no—
132#924—61no—
133#924—61no—
134C2×C4×Dic3C2×D311yescharacteristic
135C2×#208C2×D311yescharacteristic
136#890—31no—
137#890—31no—
138#888—31no—
139#888—31no—
140#878—61no—
141#878—61no—
142C4×D12—32no—
143C4×D12—32no—
144C4×D12—61no—
145C4×D12—61no—
146#870—31no—
147#870—31no—
148#869—31no—
149#869—31no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C4×Dic6—61no—
154C3×C4⋊C8—32no—
155C3×C4⋊C8—32no—
156C3×#102—32no—
157C3×#102—32no—
158#832—32no—
159#832—32no—
160#821—32no—
161#821—32no—
162#821C2×D312yes—
163#821C2×D312yes—
164#818—32no—
165#818—32no—
166#818—32no—
167#818—62no—
168#817—32no—
169#817—32no—
170#817—32no—
171#817—62no—
172Dic3⋊C8C2×D312yescomplemented
173Dic3⋊C8C2×D312yescomplemented
174#808—32no—
175#807—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—24no—
178C22×C3×D3—22no—
179C22×C3×D3—42no—
180C22×C3×D3—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×Q812yes—
183C2×C32×C4#4112yes—
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—42no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—24no—
198C3×D12—22no—
199C3×D12C2×Q814yes—
200#627—42no—
201#627—42no—
202D3×Dic3—44no—
203D3×Dic3—44no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#533—91no—
207C2×C4×D4—91no—
208#478—92no—
209#478—92no—
210#476—92no—
211#474—92no—
212#428—91no—
213#428—91no—
214#423—31no—
215#418—31no—
216#418—91no—
217C24×C3—61no—
218C23×D3—21no—
219C2×C3×D4—34no—
220C2×C3×D4—32no—
221C2×C3×D4—61no—
222C2×C3×D4—62no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—121no—
233C22×Dic3—124no—
234C22×Dic3D1211yescharacteristic
235C22×Dic3D1211yescharacteristic
236C2×D12—21no—
237C2×D12—22no—
238C2×D12Dic614yescomplemented
239C2×D12C22×D312yes—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—124no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—61no—
246C2×Dic6—61no—
247C3×M16—24no—
248C3×M16—22no—
249C3×M16—22no—
250C3×M16—62no—
251C2×C3×C8—22no—
252C2×C3×C8—32no—
253C2×C3×C8C22×D312yes—
254C2×C3×C8C22×D312yes—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—31no—
257C3×C22⋊C4—61no—
258C3×C42—31no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—61no—
263#217—21no—
264#217—61no—
265#217—61no—
266#217—62no—
267#217—62no—
268#217—121no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271C4⋊Dic3—32no—
272C4⋊Dic3—32no—
273C4⋊Dic3—31no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—31no—
277C4⋊Dic3—61no—
278C4⋊Dic3—62no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3—61no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—121no—
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D311yescharacteristic
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—61no—
295Dic3⋊C4—61no—
296Dic3⋊C4—61no—
297C4×Dic3—21no—
298C4×Dic3—61no—
299C4×Dic3—61no—
300C4×Dic3—121no—
301C4×Dic3D1211yescharacteristic
302C4×Dic3D1211yescharacteristic
303C4×Dic3C22×D311yescharacteristic
304C4×Dic3C22×D311yescharacteristic
305#208—22no—
306C2×C3⋊C8C22×D312yes—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C22⋊Q812yes—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—24no—
312C2×C3×D3—48no—
313C2×C3×D3—42no—
314C2×C3×D3—42no—
315C32×C4C22⋊Q812yes—
316C32×C4C22×Q811yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—42no—
319C3⋊Dic3—41no—
320C3⋊Dic3—41no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—41no—
326C3×Dic3AGL(1,ℤ/8)12yes—
327C22×D4—31no—
328C23×C4—181no—
329C2×M16—31no—
330C2×M16D3211yescharacteristic
331C4⋊Q8—91no—
332C4⋊Q8—91no—
333#125—91no—
334#125—91no—
335C22⋊Q8—181no—
336C22⋊Q8—181no—
337C4×Q8—181no—
338C4×Q8—181no—
339C4×D4—92no—
340C4×D4—92no—
341C4×D4—181no—
342C4×D4—181no—
343#117—31no—
344#117—91no—
345C2×C4⋊C4—91no—
346C2×C22⋊C4—181no—
347C2×C42—31no—
348#107—92no—
349#107—92no—
350#106—92no—
351#106—92no—
352C4⋊C8—32no—
353C4⋊C8—32no—
354#102—32no—
355#102—32no—
356#102—92no—
357#102—92no—
358C23×C3—21no—
359C23×C3—64no—
360C23×C3—62no—
361C23×C3—122no—
362C23×C3—122no—
363C23×C3C2×D1211yescharacteristic
364C23×C3D3×D411yescharacteristic
365C22×D3—24no—
366C22×D3—22no—
367C22×D3—42no—
368C22×D3—42no—
369C3×D4—34no—
370C3×D4—64no—
371C3×D4—62no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—31no—
377C2×C3×C4—31no—
378C2×C3×C4—31no—
379C2×C3×C4—31no—
380C2×C3×C4—62no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—121no—
384C2×C3×C4C2×Dic612yes—
385C2×C3×C4C2×D1211yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4#23712yes—
388C2×C3×C4#23712yes—
389C2×C3×C4D3×Q812yes—
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—41no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—62no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—62no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404C2×Dic3—122no—
405C2×Dic3—124no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408C2×Dic3—124no—
409C2×Dic3—242no—
410C2×Dic3C2×D1211yescharacteristic
411C2×Dic3C2×D1211yescharacteristic
412C2×Dic3C2×D1211yescharacteristic
413C2×Dic3C2×D1211yescharacteristic
414D12—24no—
415D12—22no—
416D12C2×Dic614yes—
417C4×D3—124no—
418C4×D3—124no—
419Dic6—122no—
420Dic6—122no—
421Dic6—122no—
422Dic6—122no—
423C3×C8—24no—
424C3×C8—22no—
425C3×C8—22no—
426C3×C8—62no—
427C3⋊C8—22no—
428C2×C32—22no—
429C2×C32C2×C22⋊Q811yescharacteristic
430C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
431C2×C32#57511yescharacteristic
432C3×D3—44no—
433C24—61no—
434C2×Q8—181no—
435C2×Q8—181no—
436C2×D4—32no—
437C2×D4—34no—
438C2×D4—61no—
439C2×D4—62no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—182no—
443C22×C4—182no—
444C22×C4—181no—
445C22×C4—364no—
446C22×C4C2×D3211yescharacteristic
447M16—22no—
448M16—62no—
449C2×C8—32no—
450C2×C8C2×D3212yes—
451C4⋊C4—31no—
452C4⋊C4—31no—
453C4⋊C4—91no—
454C4⋊C4—91no—
455C4⋊C4—92no—
456C4⋊C4—181no—
457C4⋊C4—181no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C22⋊C4—61no—
464C22⋊C4—182no—
465C22⋊C4—182no—
466C22⋊C4—181no—
467C42—31no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—61no—
472C42—181no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—64no—
482C22×C3—128no—
483C22×C3—122no—
484C22×C3—122no—
485C22×C3#87812yes—
486C22×C3#89712yes—
487C22×C3C22×D1211yescharacteristic
488C22×C3C2×D3×D411yescharacteristic
489C2×D3—24no—
490C2×D3—48no—
491C2×D3—42no—
492C2×D3—42no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—22no—
496C3×C4—32no—
497C3×C4—61no—
498C3×C4—61no—
499C3×C4—61no—
500C3×C4—121no—
501C3×C4—121no—
502C3×C4#87812yes—
503C3×C4#89712yes—
504C3×C4C22×Dic611yescharacteristic
505C3×C4C2×#23711yescharacteristic
506C3×C4C2×#23711yescharacteristic
507C3×C4C2×D3×Q811yescharacteristic
508Dic3—21no—
509Dic3—21no—
510Dic3—21no—
511Dic3—41no—
512Dic3—41no—
513Dic3—121no—
514Dic3—122no—
515Dic3—121no—
516Dic3—121no—
517Dic3—122no—
518Dic3—121no—
519Dic3—242no—
520Dic3—241no—
521Dic3—241no—
522Dic3#90812yes—
523C32#307711yescharacteristic, complemented, Sylow
524C23—62no—
525C23—64no—
526C23—122no—
527C23—122no—
528C23D3×D1211yescharacteristic
529Q8—362no—
530Q8—362no—
531D4—34no—
532D4—62no—
533D4—64no—
534C2×C4—31no—
535C2×C4—31no—
536C2×C4—31no—
537C2×C4—31no—
538C2×C4—62no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—121no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—182no—
545C2×C4—364no—
546C2×C4—364no—
547C2×C4—362no—
548C2×C4D3×Dic612yes—
549C2×C4D3×D1211yescharacteristic
550C2×C4#380512yes—
551C2×C4C22×D3211yescharacteristic
552C8—22no—
553C8—62no—
554C2×C3—22no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—42no—
560C2×C3—124no—
561C2×C3C2×#87811yescharacteristic
562C2×C3C2×#89711yescharacteristic
563C2×C3C2×#90811yescharacteristic
564C2×C3#574811yescharacteristic
565C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
566C2×C3#577311yescharacteristic
567D3—44no—
568C22—21no—
569C22—21no—
570C22—64no—
571C22—128no—
572C22—122no—
573C22—122no—
574C22#6389312yes—
575C22C2×D3×D1211yescharacteristic
576C4—32no—
577C4—61no—
578C4—61no—
579C4—61no—
580C4—121no—
581C4—121no—
582C4—362no—
583C4—361no—
584C4—361no—
585C4#6389312yes—
586C4C2×D3×Dic611yescharacteristic
587C4C2×#380511yescharacteristic
588C3—21no—
589C3#7891711yescharacteristic, complemented
590C3#7905911yescharacteristic, complemented
591C2—22no—
592C2—124no—
593C2D3×#90811yescharacteristic
594C2#1059471211yescharacteristic
595C2C2×#6389311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC2×M16D32
hypocenterC32#3077
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. #10595049C2semidirect
3. #10592820C2semidirect
5. C3×#5118C2semidirect
6. #10591131C2semidirect
8. #10590772C2semidirect
9. #10590767C2semidirect
10. #10590762C2semidirect
11. #10590757C2semidirect
25. #63918C22semidirect
26. #63918C22semidirect
33. #63869C22semidirect
34. #63869C22semidirect
35. #63645C22semidirect
36. #63644C22semidirect
39. C3×Dic3⋊C8C22semidirect
40. C3×Dic3⋊C8C22semidirect
41. #63575C22semidirect
42. #63573C22semidirect
58. #5118D3semidirect
75. C2×C3×D12Q8semidirect
172. Dic3⋊C8C2×D3semidirect
173. Dic3⋊C8C2×D3semidirect
238. C2×D12Dic6semidirect
523. C32#3077semidirect
589. C3#78917semidirect
590. C3#79059semidirect

Maximal subgroups

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

subgroupindex
#105950492
C2×Dic3×D122
#105928202
C3×#51312
C3×#51182
#105911312
#105910862
#105907722
#105907672
#105907622
#105907572
#790593
#789173