Finite Group Databasebeta

← #11882260

Subgroups — #11882260

Order 1152.

844 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5548C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592718C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591460C212yesmaximal, complemented
6#10591439C212yesmaximal, complemented
7#10590578C212yesmaximal, complemented
8#10590487C212yesmaximal, complemented
9#10590365C211yesmaximal, characteristic, complemented
10D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#83320—31nomaximal
13#81070—31nomaximal
14C2×C3×#235—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3754C2212yes—
17#64078C2211yescharacteristic
18C3×#940C2211yescharacteristic
19C3×#938C2211yescharacteristic
20C3×C4×#67—21no—
21C3×#895C2211yescharacteristic
22C3×#888C2211yescharacteristic
23C3×#885—21no—
24C3×#884—21no—
25C3×C4×D12C2211yescharacteristic
26C3×C42×D3C2211yescharacteristic
27C3×#869C2211yescharacteristic
28#63869—21no—
29#63857C2212yes—
30#63856—21no—
31#63844C2212yes—
32Dic3×Dic6—21no—
33#63841—21no—
34C2×#3716C2212yes—
35C2×D3×C3⋊C8C2212yes—
36#63637C2212yes—
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
38C3×#832C2212yes—
39C3×#808C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63574C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63567C2212yes—
44#63562C2212yes—
45C3×#532—31no—
46#5728—31no—
47#5548D311yescharacteristic
48#5470—31no—
49C3×#476—31no—
50#5094—32no—
51#5084—31no—
52#5075—32no—
53#5041—32no—
54#5041—32no—
55#5019—31no—
56#5019—31no—
57#5019—31no—
58#5019—61no—
59#5008—31no—
60#5008D311yescharacteristic, complemented
61C2×C4⋊(C3⋊C8)—31no—
62#4864—32no—
63#4854—32no—
64#4841—31no—
65D3×C4⋊C8—31no—
66#4778—32no—
67#4762—32no—
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C2×#634C2312yes—
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C3×#235—44no—
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6—21no—
82C2×C3×Dic6—21no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85C32×C42C2311yescharacteristic
86#3754—42no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)—21no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101#3724—22no—
102Dic3⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104Dic32—22no—
105#3716—42no—
106D3×C3⋊C8—42no—
107#3246—91noSylow
108C2×C3×#41—61no—
109C2×#235—21no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8—31no—
112C3×#127—31no—
113C3×#124—61no—
114C3×#121—31no—
115C3×#121—31no—
116C3×#121—61no—
117C3×C4×D4—21no—
118C3×C4×D4—31no—
119C3×C4×D4—61no—
120C3×C4×D4C2×D311yescharacteristic
121C3×C4×D4C2×D311yescharacteristic
122C2×C3×C42—31no—
123#946—61no—
124Q8×Dic3—61no—
125#940C2×D311yescharacteristic
126#938C2×D311yescharacteristic
127C2×#214—32no—
128C2×#214—32no—
129C2×#214—32no—
130C2×#214—62no—
131C4×#67—21no—
132#926—61no—
133#924—32no—
134#924—61no—
135C22×C3⋊C8—32no—
136C2×#204—32no—
137C2×D3×C8—32no—
138#897—32no—
139#895C2×D311yescharacteristic
140#892—61no—
141#890—61no—
142#888C2×D311yescharacteristic
143#887—32no—
144#885—21no—
145#884—21no—
146C4×D12C2×D311yescharacteristic
147C42×D3C2×D311yescharacteristic
148#870—61no—
149#869—31no—
150#869—31no—
151#869—61no—
152#869C2×D311yescharacteristic
153C4×Dic6—32no—
154C4×Dic6—61no—
155C3×#106—32no—
156C3×C4⋊C8—31no—
157C3×#102—32no—
158#832—32no—
159#832C2×D312yes—
160#816—32no—
161Dic3⋊C8—32no—
162#810—32no—
163#810—32no—
164#810—32no—
165#810—62no—
166#809—32no—
167#808—32no—
168#808—32no—
169#808C2×D312yes—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C23×C32—21no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C32×D4—21no—
179C32×D4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—42no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—22no—
186#634—22no—
187#634—22no—
188C3×#67—42no—
189C3×#67—42no—
190C3×#67—42no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—21no—
197C3×D12—21no—
198C3×D12—42no—
199C3×C4×D3—21no—
200C3×C4×D3—21no—
201C3×C4×D3—41no—
202C3×C4×D3—42no—
203C3×C4×D3SD1614yescomplemented
204C3×Dic6—42no—
205C3×Dic6—42no—
206C3⋊(C3⋊C8)—22no—
207C3×C3⋊C8—22no—
208#533—91no—
209#532—31no—
210#476—31no—
211#476—91no—
212#475—92no—
213#465—92no—
214#465—92no—
215#461—91no—
216#461—91no—
217#460—92no—
218C2×C4⋊C8—91no—
219C3×#41—124no—
220C2×C3×Q8—61no—
221C2×C3×Q8—61no—
222C2×C3×D4—21no—
223C2×C3×D4—31no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C2×C3×D4C22×D311yescharacteristic
229C2×C3×D4C22×D311yescharacteristic
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—41no—
236C22×C3×C4—61no—
237C2×#67—21no—
238C2×#67—21no—
239C2×#67—21no—
240#235—44no—
241C2×D12—21no—
242C2×D12C22×D311yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3#6711yescharacteristic
245C2×C4×D3#6711yescharacteristic
246C2×C4×D3C22×D311yescharacteristic
247C2×Dic6—21no—
248C2×Dic6—21no—
249C2×Dic6—32no—
250C2×Dic6—32no—
251C2×Dic6—62no—
252C2×C3×C8—32no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4C22×D311yescharacteristic
259C3×C4⋊C4C22×D311yescharacteristic
260C3×C22⋊C4—21no—
261C3×C22⋊C4—21no—
262C3×C22⋊C4—41no—
263C3×C22⋊C4—61no—
264C3×C22⋊C4—61no—
265C3×C22⋊C4—61no—
266C3×C42—21no—
267C3×C42—31no—
268C3×C42—31no—
269C3×C42—31no—
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D311yescharacteristic
272#217—21no—
273#217—62no—
274#214—122no—
275#214—122no—
276#214—122no—
277#214—124no—
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—21no—
280(C2×D3)⋊C4—62no—
281C4⋊Dic3—21no—
282C4⋊Dic3—61no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—62no—
287C4⋊Dic3—121no—
288C4⋊Dic3—121no—
289C4⋊Dic3C22×D311yescharacteristic
290C4⋊Dic3C22×D312yes—
291Dic3⋊C4—21no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295C4×Dic3—62no—
296C4×Dic3—62no—
297C4×Dic3#6711yescharacteristic
298C4×Dic3#6711yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C2×C3⋊C8—32no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—122no—
304C2×C3⋊C8C22×D312yes—
305#204—122no—
306D3×C8—122no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3C2×SD1612yes—
317C32×C4—21no—
318C32×C4—41no—
319C32×C4C2×SD1612yes—
320C32×C4H(5,𝔽2)11yescharacteristic
321C32×C42−1+411yescharacteristic
322C3⋊Dic3—42no—
323C3×Dic3—21no—
324C3×Dic3—21no—
325C3×Dic3—41no—
326C3×Dic3—42no—
327C3×Dic3C2×SD1612yes—
328C2×#41—61no—
329C2×SD16—92no—
330C2×SD16—92no—
331C22×C8—92no—
332C4⋊Q8—31no—
333C4⋊Q8—31no—
334C4⋊Q8—91no—
335#127—31no—
336#125—181no—
337#124—61no—
338C22⋊Q8—92no—
339C22⋊Q8—181no—
340#121—31no—
341#121—31no—
342#121—61no—
343C4×Q8—92no—
344C4×Q8—181no—
345C4×D4—31no—
346C4×D4—61no—
347C4×D4D3211yescharacteristic
348#117—181no—
349C2×C42—31no—
350#106—32no—
351#106—92no—
352C4⋊C8—31no—
353C4⋊C8—92no—
354C4⋊C8—91no—
355#103—92no—
356#103—92no—
357#102—32no—
358#102—92no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—31no—
362C23×C3—41no—
363C23×C3—61no—
364C22×D3—21no—
365C22×D3C2×#6711yescharacteristic
366C3×Q8—122no—
367C3×Q8—122no—
368C3×D4—22no—
369C3×D4—21no—
370C3×D4—21no—
371C3×D4—21no—
372C3×D4—21no—
373C3×D4—41no—
374C3×D4—61no—
375C3×D4—61no—
376C3×D4—122no—
377C3×D4—122no—
378C3×D4—122no—
379C3×D4—122no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—31no—
386C2×C3×C4—34no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—41no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—62no—
396C2×C3×C4—82no—
397C2×C3×C4—121no—
398C2×C3×C4—122no—
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—42no—
406#67—42no—
407#67—42no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—122no—
413C2×Dic3C2×#6711yescharacteristic
414C2×Dic3C2×#6711yescharacteristic
415C2×Dic3C2×#6711yescharacteristic
416D12—21no—
417D12—21no—
418D12—42no—
419C4×D3—21no—
420C4×D3—21no—
421C4×D3—41no—
422C4×D3—42no—
423C4×D3#21414yescomplemented
424Dic6—42no—
425Dic6—42no—
426Dic6—62no—
427Dic6—62no—
428Dic6—62no—
429Dic6—62no—
430Dic6—122no—
431Dic6—122no—
432C3×C8—62no—
433C3⋊C8—22no—
434C3⋊C8—62no—
435C3⋊C8—62no—
436C3⋊C8—122no—
437C2×C32—81no—
438C2×C32#53711yescharacteristic
439C2×C32C22×SD1611yescharacteristic
440C2×C32#57511yescharacteristic
441C3×D3—22no—
442C3×D3—81no—
443#41—124no—
444C2×Q8—61no—
445C2×Q8—61no—
446C2×Q8—92no—
447C2×D4—31no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4C2×D3211yescharacteristic
453C22×C4—21no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—61no—
458SD16—362no—
459SD16—362no—
460C2×C8—32no—
461C2×C8—92no—
462C2×C8—362no—
463C4⋊C4—32no—
464C4⋊C4—31no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—182no—
468C4⋊C4—182no—
469C4⋊C4—181no—
470C4⋊C4—181no—
471C4⋊C4C2×D3211yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—61no—
474C22⋊C4—61no—
475C22⋊C4—61no—
476C22⋊C4—182no—
477C42—31no—
478C42—31no—
479C42—31no—
480C42—182no—
481C42C2×D3211yescharacteristic
482C22×C3—21no—
483C22×C3—32no—
484C22×C3—42no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—61no—
492C22×C3—61no—
493C22×C3—81no—
494C22×C3—81no—
495C22×C3—121no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3C2×D3×D411yescharacteristic
499C22×C3C22×#6711yescharacteristic
500C2×D3—21no—
501C2×D3—21no—
502C2×D3—41no—
503C2×D3—41no—
504C2×D3—41no—
505C2×D3C2×#21412yes—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—32no—
512C3×C4—41no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—61no—
516C3×C4—61no—
517C3×C4—81no—
518C3×C4—121no—
519C3×C4—122no—
520C3×C4D3×SD1612yes—
521C3×C4C2×#21412yes—
522C3×C4#100711yescharacteristic
523C3×C4#100911yescharacteristic
524C3×C4#100911yescharacteristic
525C3×C4#101011yescharacteristic
526Dic3—21no—
527Dic3—21no—
528Dic3—42no—
529Dic3—41no—
530Dic3—122no—
531Dic3—122no—
532Dic3—242no—
533Dic3C2×#21412yes—
534C32#324611yescharacteristic, complemented, Sylow
535C23—21no—
536C23—31no—
537C23—61no—
538Q8—122no—
539Q8—122no—
540Q8—182no—
541Q8—182no—
542D4—21no—
543D4—21no—
544D4—61no—
545D4—61no—
546D4—122no—
547D4—122no—
548D4—122no—
549D4—122no—
550C2×C4—21no—
551C2×C4—31no—
552C2×C4—34no—
553C2×C4—31no—
554C2×C4—31no—
555C2×C4—42no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—62no—
559C2×C4—61no—
560C2×C4—121no—
561C2×C4—122no—
562C2×C4—182no—
563C2×C4D3×#6711yescharacteristic
564C2×C4D3×#6711yescharacteristic
565C2×C4C22×D3211yescharacteristic
566C8—62no—
567C8—182no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—62no—
572C2×C3—82no—
573C2×C3—81no—
574C2×C3—81no—
575C2×C3—241no—
576C2×C3#562911yescharacteristic
577C2×C3C2×D3×SD1611yescharacteristic
578C2×C3#577311yescharacteristic
579C2×C3C22×#21411yescharacteristic
580C2×C3#582211yescharacteristic
581C2×C3#583311yescharacteristic
582D3—22no—
583D3—81no—
584C22—32no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—61no—
589C22—61no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22C2×D3×#6711yescharacteristic
594C4—21no—
595C4—32no—
596C4—41no—
597C4—61no—
598C4—61no—
599C4—121no—
600C4—122no—
601C4—362no—
602C4D3×#21412yes—
603C4#6429711yescharacteristic
604C4#6430811yescharacteristic
605C3—21no—
606C3#8107011yescharacteristic, complemented
607C3#8332011yescharacteristic, complemented
608C2—62no—
609C2—81no—
610C2—241no—
611C2#1059489411yescharacteristic
612C2C2×D3×#21411yescharacteristic
613C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5548C2
hypercenterC4×D4D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593859C2semidirect
3. #10592718C2semidirect
4. C3×#5008C2semidirect
5. #10591460C2semidirect
6. #10591439C2semidirect
7. #10590578C2semidirect
8. #10590487C2semidirect
9. #10590365C2semidirect
10. D3×C4⋊(C3⋊C8)C2semidirect
11. #10590266C2semidirect
60. #5008D3semidirect
203. C3×C4×D3SD16semidirect
423. C4×D3#214semidirect
534. C32#3246semidirect
606. C3#81070semidirect
607. C3#83320semidirect

Maximal subgroups

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

subgroupindex
C3×#55482
#105938592
#105927182
C3×#50082
#105914602
#105914392
#105905782
#105904872
#105903652
D3×C4⋊(C3⋊C8)2
#105902662
#833203
#810703