Finite Group Databasebeta

← #11868816

Subgroups — #11868816

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic, complemented
2#10594954C211yesmaximal, characteristic
3#10592665C211yesmaximal, characteristic
4C3×#4964C211yesmaximal, characteristic, complemented
5#10591139C211yesmaximal, characteristic, complemented
6#10591115C211yesmaximal, characteristic, complemented
7#10591106C211yesmaximal, characteristic
8#10590488C212yesmaximal, complemented
9#10590487C212yesmaximal, complemented
10#10590466C212yesmaximal, complemented
11#10590464C212yesmaximal, complemented
12#83212—31nomaximal
13#79240—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×Dic6—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C3×#888—21no—
24C3×#888—21no—
25C3×#888C2212yes—
26C3×#888C2212yes—
27#63952—21no—
28#63952—21no—
29#63894C2211yescharacteristic
30#63894C2211yescharacteristic
31C4×#624—21no—
32#63874—21no—
33#63844C2211yescharacteristic
34#63844C2211yescharacteristic
35#63637C2212yes—
36#63636C2212yes—
37C3×#808C2212yes—
38C3×#807C2212yes—
39#63576C2212yes—
40#63574C2212yes—
41Dic3⋊(C3⋊C8)C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63567C2212yes—
44#63564C2212yes—
45C2×C3×C4⋊Q8—31no—
46#5522—31no—
47C2×#888D311yescharacteristic, complemented
48C4×#235—31no—
49C3×#428—31no—
50#5133—31no—
51#5118—31no—
52#5094—32no—
53#5091—32no—
54#5087—32no—
55#5084—32no—
56#4995—31no—
57#4966—31no—
58#4966—31no—
59#4966—31no—
60#4966—61no—
61#4964—31no—
62#4964D311yescharacteristic, complemented
63#4924—31no—
64#4890—32no—
65#4875—32no—
66#4870—32no—
67#4854—32no—
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71#3828—22no—
72#3828Q814yescomplemented
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3—21no—
75C2×#634C2311yescharacteristic
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C2×C3×Dic6—22no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6—44no—
82C2×#624—21no—
83C2×#624—21no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86#3748—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
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—21no—
103#3724—21no—
104#3722—21no—
105#3722—21no—
106Dic32—21no—
107Dic32—21no—
108#3079—91noSylow
109C22×C3×Q8—61no—
110C2×#235—31no—
111C2×#235—31no—
112C2×#235—61no—
113C22×Dic6—21no—
114C2×C3×M16—31no—
115C3×C4⋊Q8—32no—
116C3×C4⋊Q8—32no—
117C3×C4⋊Q8—61no—
118C3×C4⋊Q8—61no—
119C3×#117—31no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—61no—
123C2×C3×C4⋊C4C2×D311yescharacteristic
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C42—31no—
126C4×#67—61no—
127C4×#67—61no—
128#926C2×D311yescharacteristic
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3C2×D311yescharacteristic
132C2×#208—31no—
133C2×#208—31no—
134C2×#208—61no—
135C2×#208C2×D311yescharacteristic
136#893—31no—
137#893—31no—
138#888—21no—
139#888—21no—
140#888C2×D312yes—
141#888C2×D312yes—
142#887—31no—
143#887—31no—
144#67⋊C4—61no—
145#67⋊C4—61no—
146C4×D12—31no—
147C4×D12—31no—
148#872—61no—
149#872—61no—
150C42×D3—61no—
151C42×D3—61no—
152C4×Dic6—31no—
153C4×Dic6—31no—
154C3×#107—32no—
155C3×#106—32no—
156#821—32no—
157#816—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160#810—32no—
161#810—32no—
162#810—32no—
163#810—62no—
164#809—32no—
165#809—32no—
166#809—32no—
167#809—62no—
168#808—32no—
169#808—32no—
170#808C2×D312yes—
171#807—32no—
172#807—32no—
173#807C2×D312yes—
174C4⋊(C3⋊C8)—32no—
175C4⋊(C3⋊C8)—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C2×C32×C4—22no—
179C2×C32×C4—42no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×Q812yes—
182C2×C32×C4#4112yes—
183C2×C32×C4C2411yescharacteristic
184#638—24no—
185C2×C3⋊Dic3—21no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)C2×Q812yescomplemented
188C4×C3⋊D3—24no—
189#634—21no—
190#634C2×Q812yescomplemented
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C3×Dic6—44no—
202C3×Dic6—44no—
203#624—42no—
204#624—42no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207C2×C4⋊Q8—31no—
208C4×#41—91no—
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—
218C2×C3×Q8—62no—
219C2×C3×Q8—62no—
220C2×C3×Q8—124no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—41no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—61no—
231C2×#67—61no—
232C2×#67—121no—
233C22×Dic3—21no—
234C22×Dic3#6711yescharacteristic
235C22×Dic3#6711yescharacteristic
236#235—34no—
237#235—34no—
238#235—64no—
239#235—62no—
240#235—62no—
241#235—122no—
242C2×D12—31no—
243C2×D12—31no—
244C2×D12—61no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C4×D3—121no—
252C2×Dic6—22no—
253C2×Dic6—22no—
254C2×Dic6—31no—
255C2×Dic6—31no—
256C2×Dic6—44no—
257C2×Dic6—61no—
258C3×M16—62no—
259C2×C3×C8—32no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—31no—
266C3×C4⋊C4—41no—
267C3×C4⋊C4—62no—
268C3×C4⋊C4—62no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4C22×D312yes—
271C3×C4⋊C4C22×D312yes—
272C3×C22⋊C4—61no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42—31no—
276C3×C42—31no—
277C3×C42—61no—
278#217—21no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283C4⋊Dic3—21no—
284C4⋊Dic3C22×D311yescharacteristic
285C4⋊Dic3C22×D312yes—
286C4⋊Dic3C22×D311yescharacteristic
287Dic3⋊C4—22no—
288Dic3⋊C4—22no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293C4×Dic3—21no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3#6711yescharacteristic
299C4×Dic3#6711yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302#208—22no—
303#208—62no—
304#208—62no—
305#208—122no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—62no—
309C2×C3⋊C8C22×D312yes—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32C22⋊Q812yes—
313C22×C32C22×D411yescharacteristic
314C2×C3⋊D3—22no—
315C2×C3⋊D3—41no—
316C2×C3⋊D3—41no—
317C32×C4—42no—
318C32×C4C22⋊Q812yes—
319C32×C4C22×Q811yescharacteristic
320C32×C4C2×#4111yescharacteristic
321C3⋊Dic3—22no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3—41no—
327C3×Dic3AGL(1,ℤ/8)12yes—
328C3×Dic3#13712yes—
329C2×#41—91no—
330C22×Q8—61no—
331C2×M16—31no—
332C2×M16—91no—
333C4⋊Q8—32no—
334C4⋊Q8—32no—
335C4⋊Q8—61no—
336C4⋊Q8—61no—
337C4×Q8—91no—
338C4×Q8—91no—
339C4×D4—91no—
340C4×D4—91no—
341C4×D4—181no—
342C4×D4—181no—
343#117—31no—
344#117—181no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—61no—
347C2×C4⋊C4D3211yescharacteristic
348C2×C42—31no—
349C2×C42—181no—
350#107—32no—
351#107—92no—
352#106—32no—
353#106—92no—
354C4⋊C8—92no—
355C4⋊C8—92no—
356#103—92no—
357#103—92no—
358#102—92no—
359#102—92no—
360C23×C3—21no—
361C23×C3D3×D411yescharacteristic
362C23×C3C2×#6711yescharacteristic
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—121no—
366C3×Q8—124no—
367C3×Q8—124no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—31no—
375C2×C3×C4—31no—
376C2×C3×C4—31no—
377C2×C3×C4—31no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—82no—
387C2×C3×C4—122no—
388C2×C3×C4#23512yes—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×Q812yes—
391C2×C3×C4D3×Q812yes—
392C2×C3×C4#23912yes—
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396#67—64no—
397#67—64no—
398#67—124no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—42no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—121no—
408C2×Dic3C2×#6711yescharacteristic
409C2×Dic3C2×#6711yescharacteristic
410C2×Dic3C2×#6711yescharacteristic
411C2×Dic3C2×#6711yescharacteristic
412D12—32no—
413D12—32no—
414D12—62no—
415D12—61no—
416D12—61no—
417D12—121no—
418C4×D3—64no—
419C4×D3—64no—
420C4×D3—124no—
421C4×D3—122no—
422C4×D3—122no—
423C4×D3—122no—
424C4×D3—122no—
425Dic6—32no—
426Dic6—32no—
427Dic6—44no—
428Dic6—44no—
429Dic6—62no—
430Dic6—61no—
431Dic6—61no—
432Dic6—121no—
433C3×C8—62no—
434C3⋊C8—22no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C3⋊C8—122no—
438C2×C32—22no—
439C2×C32C2×C22⋊Q811yescharacteristic
440C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
441C2×C32C2×#13711yescharacteristic
442C3⋊D3—42no—
443#41—94no—
444#41—182no—
445C2×Q8—62no—
446C2×Q8—62no—
447C2×Q8—91no—
448C2×Q8—124no—
449C2×D4—91no—
450C2×D4—181no—
451C22×C4—21no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—61no—
455C22×C4—181no—
456C22×C4—181no—
457C22×C4—181no—
458C22×C4C2×D3211yescharacteristic
459M16—62no—
460M16—182no—
461C2×C8—32no—
462C2×C8—92no—
463C4⋊C4—21no—
464C4⋊C4—32no—
465C4⋊C4—31no—
466C4⋊C4—31no—
467C4⋊C4—62no—
468C4⋊C4—62no—
469C4⋊C4—61no—
470C4⋊C4—181no—
471C4⋊C4—181no—
472C4⋊C4C2×D3212yes—
473C22⋊C4—61no—
474C22⋊C4—181no—
475C22⋊C4—181no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—31no—
480C42—61no—
481C42—181no—
482C42—181no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—22no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3#89612yes—
492C22×C3#94612yes—
493C22×C3C2×D3×D411yescharacteristic
494C22×C3C22×#6711yescharacteristic
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—122no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—241no—
503C2×D3—241no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—32no—
508C3×C4—32no—
509C3×C4—42no—
510C3×C4—42no—
511C3×C4—61no—
512C3×C4—61no—
513C3×C4—82no—
514C3×C4—122no—
515C3×C4—121no—
516C3×C4—121no—
517C3×C4#89612yes—
518C3×C4#94612yes—
519C3×C4C2×#23511yescharacteristic
520C3×C4C2×D3×Q811yescharacteristic
521C3×C4C2×D3×Q811yescharacteristic
522C3×C4C2×#23911yescharacteristic
523Dic3—21no—
524Dic3—21no—
525Dic3—41no—
526Dic3—41no—
527Dic3—42no—
528Dic3—62no—
529Dic3—62no—
530Dic3—122no—
531Dic3#93212yes—
532Dic3#94212yes—
533C32#307911yescharacteristic, complemented, Sylow
534C23—181no—
535C23D3×#6711yescharacteristic
536Q8—92no—
537Q8—124no—
538Q8—124no—
539Q8—181no—
540D4—92no—
541D4—184no—
542D4—181no—
543C2×C4—22no—
544C2×C4—31no—
545C2×C4—31no—
546C2×C4—31no—
547C2×C4—31no—
548C2×C4—42no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—62no—
554C2×C4—122no—
555C2×C4—181no—
556C2×C4—184no—
557C2×C4—362no—
558C2×C4—362no—
559C2×C4#379712yes—
560C2×C4#379912yes—
561C2×C4D3×#6711yescharacteristic
562C2×C4C22×D3211yescharacteristic
563C8—62no—
564C8—182no—
565C2×C3—22no—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—42no—
571C2×C3C2×#89611yescharacteristic
572C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
573C2×C3D3×#13711yescharacteristic
574C2×C3C2×#93211yescharacteristic
575C2×C3C2×#94211yescharacteristic
576C2×C3C2×#94611yescharacteristic
577D3—122no—
578D3—122no—
579D3—242no—
580C22—21no—
581C22—21no—
582C22—182no—
583C22—361no—
584C22—361no—
585C22#6388812yes—
586C22C2×D3×#6711yescharacteristic
587C4—32no—
588C4—32no—
589C4—42no—
590C4—61no—
591C4—61no—
592C4—122no—
593C4—121no—
594C4—121no—
595C4—182no—
596C4#6388812yes—
597C4C2×#379711yescharacteristic
598C4C2×#379911yescharacteristic
599C3—21no—
600C3#7924011yescharacteristic, complemented
601C3#8321211yescharacteristic, complemented
602C2—22no—
603C2—362no—
604C2C2×#6388811yescharacteristic
605C2D3×#93211yescharacteristic
606C2D3×#94211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#888C2semidirect
4. C3×#4964C2semidirect
5. #10591139C2semidirect
6. #10591115C2semidirect
8. #10590488C2semidirect
9. #10590487C2semidirect
10. #10590466C2semidirect
11. #10590464C2semidirect
47. C2×#888D3semidirect
62. #4964D3semidirect
72. #3828Q8semidirect
187. C4⋊(C3⋊D3)C2×Q8semidirect
190. #634C2×Q8semidirect
533. C32#3079semidirect
600. C3#79240semidirect
601. C3#83212semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8882
#105949542
#105926652
C3×#49642
#105911392
#105911152
#105911062
#105904882
#105904872
#105904662
#105904642
#832123
#792403