Finite Group Databasebeta

← #11868826

Subgroups — #11868826

Order 1152.

891 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
1C3×#5522C211yesmaximal, characteristic
2C2×#63918C211yesmaximal, characteristic, complemented
3#10592694C211yesmaximal, characteristic, complemented
4C3×#4995C211yesmaximal, characteristic, complemented
5#10591115C211yesmaximal, characteristic, complemented
6#10591088C211yesmaximal, characteristic
7#10591087C211yesmaximal, characteristic
8#10590558C212yesmaximal, complemented
9#10590557C212yesmaximal, complemented
10#10590556C212yesmaximal, complemented
11#10590555C212yesmaximal, complemented
12#82508—31nomaximal
13#79240—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×#627—21no—
16C32×#117C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C3×#67⋊C4—21no—
27C3×#67⋊C4—21no—
28C3×#872—21no—
29C3×C42×D3—21no—
30C2×Dic3⋊Dic3—21no—
31#63918—21no—
32#63918—21no—
33#63918C2212yes—
34#63918C2212yes—
35#63635C2212yes—
36#63634C2212yes—
37C3×#808C2212yes—
38C3×#807C2212yes—
39Dic3⋊(C3⋊C8)C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63566C2212yes—
42#63565C2212yes—
43#63563C2212yes—
44#63562C2212yes—
45C3×C4×#41—31no—
46#5522D311yescharacteristic
47C2×#888—31no—
48C2×#869—31no—
49C3×#428—31no—
50#5232—31no—
51#5232—31no—
52#5133—31no—
53#5118—31no—
54#5021—32no—
55#5020—32no—
56#5008—32no—
57#5007—32no—
58#4995—31no—
59#4995—31no—
60#4995—61no—
61#4995D311yescharacteristic, complemented
62#4966—31no—
63#4924—31no—
64#4890—32no—
65#4875—32no—
66#4870—32no—
67#4854—32no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—21no—
70C2×C3×#67—21no—
71C22×C3×Dic3—21no—
72C22×C3×Dic3D411yescharacteristic
73C22×C3×Dic3D411yescharacteristic
74C3×#235—22no—
75C3×#235Q814yescomplemented
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6C2311yescharacteristic
81C2×#627—22no—
82C2×#627—22no—
83C2×#627—44no—
84C32×C4⋊C4C2311yescharacteristic
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90#3748—22no—
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×#208—22no—
105C2×C3×C3⋊C8C2312yes—
106Dic3⋊Dic3—22no—
107Dic3⋊Dic3—22no—
108#3079—91noSylow
109C2×C3×#41—31no—
110C2×#235C2×D311yescharacteristic
111C22×Dic6—61no—
112C22×Dic6—61no—
113C2×C3×M16—31no—
114C3×C4×Q8—31no—
115C3×C4×Q8—31no—
116C3×C4×D4—31no—
117C3×C4×D4—31no—
118C3×C4×D4—61no—
119C3×C4×D4—61no—
120C3×#117—21no—
121C3×#117—61no—
122C3×#117C2×D311yescharacteristic
123C3×#117C2×D311yescharacteristic
124C2×C3×C4⋊C4—31no—
125C2×C3×C42—31no—
126C2×C3×C42—61no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—61no—
130C2×C4⋊Dic3—61no—
131C2×C4⋊Dic3C2×D311yescharacteristic
132C2×Dic3⋊C4—61no—
133C2×C4×Dic3C2×D311yescharacteristic
134C2×#208—31no—
135C2×#208—31no—
136C2×#208—61no—
137C2×#208C2×D311yescharacteristic
138#893C2×D311yescharacteristic
139#893C2×D311yescharacteristic
140#888—32no—
141#888—32no—
142#888—61no—
143#888—61no—
144#887C2×D311yescharacteristic
145#887C2×D311yescharacteristic
146#67⋊C4—21no—
147#67⋊C4—21no—
148#872—21no—
149C42×D3—21no—
150#869—32no—
151#869—32no—
152#869—61no—
153#869—61no—
154C3×#107—32no—
155C3×#106—32no—
156#835—32no—
157#835—32no—
158#832—32no—
159#832—32no—
160#821—32no—
161#816—32no—
162Dic3⋊C8—32no—
163Dic3⋊C8—32no—
164#810—32no—
165#809—32no—
166#808—32no—
167#808—32no—
168#808—62no—
169#808C2×D312yes—
170#807—32no—
171#807—32no—
172#807—62no—
173#807C2×D312yes—
174C4⋊(C3⋊C8)—32no—
175C4⋊(C3⋊C8)—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×Q812yes—
182C2×C32×C4#4112yes—
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—42no—
186C3×#67—24no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—42no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—21no—
197C3×D12C2×Q812yescomplemented
198C3×C4×D3—24no—
199C3×C4×D3—42no—
200C3×C4×D3—42no—
201C3×Dic6—21no—
202C3×Dic6C2×Q812yescomplemented
203#627—44no—
204#627—44no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207C2×C4⋊Q8—91no—
208C4×#41—31no—
209#477—92no—
210#476—92no—
211#475—92no—
212#474—92no—
213#428—31no—
214#428—91no—
215#423—91no—
216#417—91no—
217#417—91no—
218C3×#41—34no—
219C3×#41—62no—
220C2×C3×Q8—31no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—21no—
233C22×Dic3—21no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—121no—
237C22×Dic3#6711yescharacteristic
238C22×Dic3#6711yescharacteristic
239#235—22no—
240#235Dic614yescomplemented
241C2×D12C22×D311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C2×Dic6—124no—
250C2×Dic6—124no—
251C2×Dic6C22×D311yescharacteristic
252C3×M16—62no—
253C2×C3×C8—32no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—61no—
268C3×C22⋊C4—61no—
269C3×C42—21no—
270C3×C42—21no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42—41no—
276C3×C42—61no—
277C3×C42—61no—
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—32no—
282C4⋊Dic3—32no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3—62no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3—121no—
289C4⋊Dic3C22×D312yes—
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294C4×Dic3—21no—
295C4×Dic3—21no—
296C4×Dic3#6711yescharacteristic
297C4×Dic3#6711yescharacteristic
298C4×Dic3C22×D311yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300#208—22no—
301#208—64no—
302#208—62no—
303#208—62no—
304C2×C3⋊C8—32no—
305C2×C3⋊C8—32no—
306C2×C3⋊C8—62no—
307C2×C3⋊C8C22×D312yes—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32C22⋊Q812yes—
311C22×C32C22×D411yescharacteristic
312C2×C3×D3—22no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—41no—
316C32×C4—41no—
317C32×C4C22⋊Q812yes—
318C32×C4C22×Q811yescharacteristic
319C32×C4C2×#4111yescharacteristic
320C3⋊Dic3—42no—
321C3×Dic3—22no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—42no—
325C3×Dic3AGL(1,ℤ/8)12yes—
326C3×Dic3#13712yes—
327C2×#41—31no—
328C22×Q8—181no—
329C2×M16—31no—
330C2×M16—91no—
331C4⋊Q8—92no—
332C4⋊Q8—92no—
333C4⋊Q8—181no—
334C4⋊Q8—181no—
335C4×Q8—31no—
336C4×Q8—31no—
337C4×D4—31no—
338C4×D4—31no—
339C4×D4—61no—
340C4×D4—61no—
341#117—61no—
342#117D3211yescharacteristic
343C2×C4⋊C4—31no—
344C2×C4⋊C4—91no—
345C2×C4⋊C4—181no—
346C2×C42—31no—
347C2×C42—61no—
348#107—32no—
349#107—92no—
350#106—32no—
351#106—92no—
352C4⋊C8—92no—
353C4⋊C8—92no—
354#103—92no—
355#103—92no—
356#102—92no—
357#102—92no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3D3×D411yescharacteristic
361C23×C3C2×#6711yescharacteristic
362C22×D3—21no—
363C3×Q8—32no—
364C3×Q8—61no—
365C3×D4—32no—
366C3×D4—64no—
367C3×D4—61no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—31no—
377C2×C3×C4—31no—
378C2×C3×C4—31no—
379C2×C3×C4—31no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—61no—
385C2×C3×C4—64no—
386C2×C3×C4—62no—
387C2×C3×C4—122no—
388C2×C3×C4—122no—
389C2×C3×C4—122no—
390C2×C3×C4C2×Dic612yes—
391C2×C3×C4#23512yes—
392C2×C3×C4#23512yes—
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×Q812yes—
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398#67—24no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—42no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408C2×Dic3—122no—
409C2×Dic3—242no—
410C2×Dic3C2×#6711yescharacteristic
411C2×Dic3C2×#6711yescharacteristic
412C2×Dic3C2×#6711yescharacteristic
413C2×Dic3C2×#6711yescharacteristic
414D12—21no—
415D12C2×Dic612yescomplemented
416C4×D3—24no—
417C4×D3—42no—
418C4×D3—42no—
419Dic6—21no—
420Dic6—124no—
421Dic6—124no—
422Dic6—124no—
423Dic6—124no—
424Dic6C2×Dic612yescomplemented
425C3×C8—62no—
426C3⋊C8—22no—
427C3⋊C8—64no—
428C3⋊C8—62no—
429C3⋊C8—62no—
430C2×C32—22no—
431C2×C32C2×C22⋊Q811yescharacteristic
432C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
433C2×C32C2×#13711yescharacteristic
434C3×D3—42no—
435#41—34no—
436#41—62no—
437C2×Q8—31no—
438C2×Q8—182no—
439C2×Q8—182no—
440C2×Q8—364no—
441C2×D4—31no—
442C2×D4—61no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4—61no—
448C22×C4—61no—
449C22×C4—181no—
450C22×C4C2×D3211yescharacteristic
451M16—62no—
452M16—182no—
453C2×C8—32no—
454C2×C8—92no—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—92no—
460C4⋊C4—182no—
461C4⋊C4—182no—
462C4⋊C4—181no—
463C4⋊C4C2×D3211yescharacteristic
464C4⋊C4C2×D3211yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—61no—
467C22⋊C4—61no—
468C42—21no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—31no—
473C42—61no—
474C42—61no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—22no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—62no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3#89612yes—
487C22×C3#92412yes—
488C22×C3C2×D3×D411yescharacteristic
489C22×C3C22×#6711yescharacteristic
490C2×D3—22no—
491C2×D3—41no—
492C2×D3—41no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—22no—
496C3×C4—32no—
497C3×C4—32no—
498C3×C4—41no—
499C3×C4—41no—
500C3×C4—41no—
501C3×C4—41no—
502C3×C4—62no—
503C3×C4—61no—
504C3×C4—61no—
505C3×C4—81no—
506C3×C4—81no—
507C3×C4—122no—
508C3×C4#89612yes—
509C3×C4#92412yes—
510C3×C4C22×Dic611yescharacteristic
511C3×C4C2×#23511yescharacteristic
512C3×C4C2×#23511yescharacteristic
513C3×C4C2×D3×Q811yescharacteristic
514Dic3—22no—
515Dic3—21no—
516Dic3—21no—
517Dic3—42no—
518Dic3—122no—
519Dic3—122no—
520Dic3—242no—
521Dic3#94912yes—
522Dic3#95112yes—
523C32#307911yescharacteristic, complemented, Sylow
524C23—61no—
525C23D3×#6711yescharacteristic
526Q8—32no—
527Q8—61no—
528Q8—364no—
529Q8—364no—
530D4—32no—
531D4—64no—
532D4—61no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—31no—
536C2×C4—31no—
537C2×C4—31no—
538C2×C4—31no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—61no—
542C2×C4—64no—
543C2×C4—62no—
544C2×C4—122no—
545C2×C4—122no—
546C2×C4—122no—
547C2×C4—182no—
548C2×C4—362no—
549C2×C4D3×Dic612yes—
550C2×C4#379812yes—
551C2×C4D3×#6711yescharacteristic
552C2×C4C22×D3211yescharacteristic
553C8—62no—
554C8—182no—
555C2×C3—22no—
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—42no—
561C2×C3—122no—
562C2×C3C2×#89611yescharacteristic
563C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
564C2×C3D3×#13711yescharacteristic
565C2×C3C2×#92411yescharacteristic
566C2×C3C2×#94911yescharacteristic
567C2×C3C2×#95111yescharacteristic
568D3—42no—
569C22—21no—
570C22—21no—
571C22—62no—
572C22—121no—
573C22—121no—
574C22#6385112yes—
575C22C2×D3×#6711yescharacteristic
576C4—32no—
577C4—32no—
578C4—41no—
579C4—41no—
580C4—62no—
581C4—61no—
582C4—61no—
583C4—122no—
584C4—362no—
585C4#6385112yes—
586C4C2×D3×Dic611yescharacteristic
587C4C2×#379811yescharacteristic
588C3—21no—
589C3#7924011yescharacteristic, complemented
590C3#8250811yescharacteristic, complemented
591C2—22no—
592C2—122no—
593C2C2×#6385111yescharacteristic
594C2D3×#94911yescharacteristic
595C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenter#117D32
hypocenterC32#3079
LCSG ▷ C2×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. C2×#63918C2semidirect
3. #10592694C2semidirect
4. C3×#4995C2semidirect
5. #10591115C2semidirect
8. #10590558C2semidirect
9. #10590557C2semidirect
10. #10590556C2semidirect
11. #10590555C2semidirect
61. #4995D3semidirect
75. C3×#235Q8semidirect
197. C3×D12C2×Q8semidirect
202. C3×Dic6C2×Q8semidirect
240. #235Dic6semidirect
415. D12C2×Dic6semidirect
424. Dic6C2×Dic6semidirect
523. C32#3079semidirect
589. C3#79240semidirect
590. C3#82508semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
C2×#639182
#105926942
C3×#49952
#105911152
#105910882
#105910872
#105905582
#105905572
#105905562
#105905552
#825083
#792403