Finite Group Databasebeta

← #11882256

Subgroups — #11882256

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×#5728C211yesmaximal, characteristic, complemented
2#10593968C211yesmaximal, characteristic
3#10592782C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic, complemented
5#10591634C212yesmaximal, complemented
6#10591617C212yesmaximal, complemented
7#10591585C212yesmaximal, complemented
8#10591544C212yesmaximal, complemented
9D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10590300C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#83363—31nomaximal
13#80438—31nomaximal
14C2×#3798—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C2×#3755C2212yes—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#946C2212yes—
19C3×Q8×Dic3C2212yes—
20C2×C3×#215C2212yes—
21C3×#897—21no—
22C3×#892—21no—
23C3×#890—21no—
24C3×#887—21no—
25C3×C4×D12C2211yescharacteristic
26C3×C42×D3C2211yescharacteristic
27C3×#869C2211yescharacteristic
28#63918C2211yescharacteristic
29#63911C2211yescharacteristic
30#63909C2211yescharacteristic
31#63908C2211yescharacteristic
32#63906—21no—
33C4×#626—21no—
34#63852—21no—
35C2×D3×C3⋊C8C2212yes—
36#63662C2212yes—
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
38C3×#835C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63574C2212yes—
41#63573C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63564C2212yes—
44#63562C2212yes—
45C3×#533—31no—
46#5728D311yescharacteristic, complemented
47#5548—31no—
48#5477—31no—
49C3×#461—31no—
50#5171—32no—
51#5163—32no—
52#5084—31no—
53#5084—31no—
54#5083—31no—
55#5083—31no—
56#5083—61no—
57#5083D311yescharacteristic, complemented
58#5048—32no—
59#5048—32no—
60#5027—32no—
61#5020—32no—
62#5008—31no—
63C2×C4⋊(C3⋊C8)—31no—
64#4842—31no—
65D3×C4⋊C8—31no—
66#4807—32no—
67#4791—32no—
68C2×C32×Q8C2312yes—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6—21no—
77C2×#627—21no—
78C2×#626—21no—
79C2×#626—21no—
80C2×#626—21no—
81C2×#625—21no—
82#3798—44no—
83C32×C4⋊C4—21no—
84C32×C4⋊C4—21no—
85C32×C42C2311yescharacteristic
86#3755—42no—
87#3752—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#215—42no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—22no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—21no—
104#3722—21no—
105(C2×D3)⋊Dic3—21no—
106D3×C3⋊C8—42no—
107#3246—91noSylow
108C2×#235—61no—
109C2×#235—61no—
110C2×C3×SD16—32no—
111C3×C4⋊Q8—21no—
112C3×C4⋊Q8—31no—
113C3×C4⋊Q8C2×D311yescharacteristic
114C3×C4⋊Q8C2×D311yescharacteristic
115C3×#125—61no—
116C3×C22⋊Q8—32no—
117C3×C22⋊Q8—61no—
118C3×C4×Q8—32no—
119C3×C4×Q8—61no—
120C3×C4×D4—31no—
121C3×#117—61no—
122C2×C3×C42—31no—
123#946C2×D312yes—
124Q8×Dic3C2×D312yes—
125C2×#215—32no—
126C2×#215—32no—
127C2×#215—62no—
128C2×#215C2×D312yes—
129#940—31no—
130#938—31no—
131#930—31no—
132#930—31no—
133#930—61no—
134C4×#67—61no—
135C22×C3⋊C8—32no—
136C2×D3×C8—32no—
137#897—21no—
138#895—31no—
139#892—21no—
140#890—21no—
141#888—31no—
142#887—21no—
143#885—61no—
144#884—61no—
145#875—61no—
146#874—31no—
147C4×D12—31no—
148C4×D12—31no—
149C4×D12—61no—
150C4×D12—61no—
151C4×D12C2×D311yescharacteristic
152C42×D3C2×D311yescharacteristic
153#869—31no—
154#869C2×D311yescharacteristic
155C3×C4⋊C8—31no—
156C3×#103—32no—
157#835—32no—
158#835—32no—
159#835—62no—
160#835C2×D312yes—
161#832—32no—
162#821—32no—
163#817—32no—
164Dic3⋊C8—32no—
165#809—32no—
166#809—32no—
167#808—32no—
168#808—32no—
169#808—32no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C32×Q8—22no—
179C32×Q8—22no—
180C2×C32×C4—22no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—21no—
185C4⋊(C3⋊D3)—21no—
186C4⋊(C3⋊D3)—21no—
187C4×C3⋊D3—42no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C3×D12—21no—
194C3×D12—21no—
195C3×C4×D3—21no—
196C3×C4×D3—21no—
197C3×C4×D3—41no—
198C3×C4×D3—42no—
199C3×C4×D3SD1614yescomplemented
200C3×Dic6—42no—
201#627—42no—
202#626—42no—
203#626—42no—
204#626—42no—
205#625—42no—
206C3⋊(C3⋊C8)—22no—
207C3×C3⋊C8—22no—
208#533—31no—
209#532—91no—
210#476—91no—
211#476—91no—
212#475—92no—
213#465—92no—
214#465—92no—
215#461—31no—
216#461—91no—
217#460—92no—
218C2×C4⋊C8—91no—
219C2×C3×Q8—22no—
220C2×C3×Q8—61no—
221C2×C3×Q8C22×D312yes—
222C2×C3×Q8C22×D312yes—
223C2×C3×D4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—61no—
228C2×#67—61no—
229C2×#67—61no—
230C2×#67—61no—
231C2×#67—61no—
232C2×#67—61no—
233#235—124no—
234#235—124no—
235C2×D12—31no—
236C2×D12—31no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—61no—
240C2×D12—61no—
241C2×D12C22×D311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—121no—
246C2×C4×D3#6711yescharacteristic
247C2×C4×D3#6711yescharacteristic
248C2×C4×D3C22×D311yescharacteristic
249C2×Dic6—21no—
250C2×Dic6—61no—
251C2×Dic6—61no—
252C3×SD16—122no—
253C2×C3×C8—32no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—32no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—41no—
261C3×C4⋊C4—41no—
262C3×C4⋊C4—62no—
263C3×C4⋊C4—62no—
264C3×C4⋊C4—61no—
265C3×C22⋊C4—62no—
266C3×C22⋊C4—61no—
267C3×C42—21no—
268C3×C42—31no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—62no—
272C3×C42C22×D311yescharacteristic
273C3×C42C22×D311yescharacteristic
274#217—61no—
275#215—42no—
276#215—122no—
277#215—122no—
278#215—124no—
279(C2×D3)⋊C4—22no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—61no—
284(C2×D3)⋊C4—61no—
285(C2×D3)⋊C4—61no—
286(C2×D3)⋊C4—121no—
287C4⋊Dic3—21no—
288C4⋊Dic3—22no—
289C4⋊Dic3—31no—
290C4⋊Dic3—31no—
291C4⋊Dic3—61no—
292C4⋊Dic3—61no—
293C4⋊Dic3C22×D311yescharacteristic
294C4⋊Dic3C22×D312yes—
295Dic3⋊C4—22no—
296Dic3⋊C4—61no—
297C4×Dic3—22no—
298C4×Dic3#6711yescharacteristic
299C4×Dic3#6711yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C2×C3⋊C8—32no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—62no—
304C2×C3⋊C8—122no—
305C2×C3⋊C8C22×D312yes—
306D3×C8—122no—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—41no—
309C2×C3⋊D3—41no—
310C2×C3⋊D3—41no—
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—42no—
319C32×C4C2×SD1612yes—
320C32×C4H(5,𝔽2)11yescharacteristic
321C32×C42−1+411yescharacteristic
322C3⋊Dic3—41no—
323C3×Dic3—21no—
324C3×Dic3—21no—
325C3×Dic3—41no—
326C3×Dic3—42no—
327C3×Dic3C2×SD1612yes—
328C2×#41—181no—
329C2×SD16—32no—
330C2×SD16—92no—
331C22×C8—92no—
332C4⋊Q8—31no—
333C4⋊Q8—91no—
334C4⋊Q8D3211yescharacteristic
335#127—91no—
336#125—61no—
337#124—181no—
338C22⋊Q8—32no—
339C22⋊Q8—61no—
340#121—91no—
341#121—91no—
342#121—181no—
343C4×Q8—32no—
344C4×Q8—61no—
345C4×D4—31no—
346C4×D4—91no—
347C4×D4—181no—
348#117—61no—
349C2×C42—31no—
350#106—92no—
351#106—92no—
352C4⋊C8—31no—
353C4⋊C8—92no—
354C4⋊C8—91no—
355#103—32no—
356#103—92no—
357#102—92no—
358#102—92no—
359C23×C3—31no—
360C23×C3—61no—
361C22×D3—21no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—121no—
365C22×D3C2×#6711yescharacteristic
366C3×Q8—22no—
367C3×Q8—22no—
368C3×Q8—22no—
369C3×Q8—22no—
370C3×Q8—42no—
371C3×Q8—42no—
372C3×Q8—122no—
373C3×D4—61no—
374C3×D4—61no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—31no—
381C2×C3×C4—34no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—42no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—62no—
388C2×C3×C4—61no—
389C2×C3×C4—121no—
390C2×C3×C4—122no—
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397#67—122no—
398#67—122no—
399#67—122no—
400#67—122no—
401#67—122no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—121no—
407C2×Dic3C2×#6711yescharacteristic
408C2×Dic3C2×#6711yescharacteristic
409C2×Dic3C2×#6711yescharacteristic
410D12—21no—
411D12—21no—
412D12—62no—
413D12—61no—
414D12—61no—
415D12—61no—
416D12—61no—
417D12—121no—
418D12—122no—
419D12—122no—
420D12—122no—
421C4×D3—21no—
422C4×D3—21no—
423C4×D3—41no—
424C4×D3—42no—
425C4×D3—122no—
426C4×D3—122no—
427C4×D3—242no—
428C4×D3#21514yescomplemented
429Dic6—42no—
430Dic6—122no—
431Dic6—122no—
432C3×C8—62no—
433C3⋊C8—22no—
434C3⋊C8—62no—
435C3⋊C8—62no—
436C3⋊C8—122no—
437C2×C32#53711yescharacteristic
438C2×C32C22×SD1611yescharacteristic
439C2×C32#57511yescharacteristic
440C3⋊D3—81no—
441C3×D3—22no—
442C3×D3—81no—
443#41—364no—
444C2×Q8—61no—
445C2×Q8—181no—
446C2×Q8C2×D3212yes—
447C2×D4—31no—
448C2×D4—91no—
449C2×D4—181no—
450C2×D4—181no—
451C2×D4—181no—
452C2×D4—181no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—61no—
457C22×C4—181no—
458SD16—122no—
459SD16—362no—
460C2×C8—32no—
461C2×C8—92no—
462C2×C8—362no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—32no—
466C4⋊C4—31no—
467C4⋊C4—62no—
468C4⋊C4—62no—
469C4⋊C4—61no—
470C4⋊C4—91no—
471C4⋊C4—181no—
472C22⋊C4—62no—
473C22⋊C4—61no—
474C22⋊C4—181no—
475C22⋊C4—181no—
476C22⋊C4—181no—
477C42—31no—
478C42—31no—
479C42—31no—
480C42—62no—
481C42C2×D3211yescharacteristic
482C22×C3—21no—
483C22×C3—32no—
484C22×C3—61no—
485C22×C3—61no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3C2×D3×D411yescharacteristic
490C22×C3C22×#6711yescharacteristic
491C2×D3—21no—
492C2×D3—21no—
493C2×D3—41no—
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—122no—
497C2×D3—121no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—121no—
503C2×D3—241no—
504C2×D3—241no—
505C2×D3C2×#21512yes—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—32no—
512C3×C4—41no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—61no—
516C3×C4—61no—
517C3×C4—82no—
518C3×C4—122no—
519C3×C4—121no—
520C3×C4D3×SD1612yes—
521C3×C4C2×#21512yes—
522C3×C4#100411yescharacteristic
523C3×C4#100911yescharacteristic
524C3×C4#101011yescharacteristic
525C3×C4#101011yescharacteristic
526Dic3—21no—
527Dic3—21no—
528Dic3—41no—
529Dic3—42no—
530Dic3—121no—
531Dic3—121no—
532Dic3—241no—
533Dic3C2×#21512yes—
534C32#324611yescharacteristic, complemented, Sylow
535C23—31no—
536C23—61no—
537C23—181no—
538Q8—22no—
539Q8—22no—
540Q8—122no—
541Q8—362no—
542D4—61no—
543D4—61no—
544D4—181no—
545D4—181no—
546D4—362no—
547D4—362no—
548D4—362no—
549D4—362no—
550C2×C4—22no—
551C2×C4—31no—
552C2×C4—34no—
553C2×C4—31no—
554C2×C4—31no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—121no—
560C2×C4—122no—
561C2×C4—181no—
562C2×C4—362no—
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—241no—
573C2×C3#560811yescharacteristic
574C2×C3C2×D3×SD1611yescharacteristic
575C2×C3#577711yescharacteristic
576C2×C3C22×#21511yescharacteristic
577C2×C3#582211yescharacteristic
578C2×C3#583311yescharacteristic
579D3—22no—
580D3—81no—
581D3—242no—
582D3—241no—
583D3—241no—
584C22—32no—
585C22—61no—
586C22—61no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22—361no—
591C22—361no—
592C22—361no—
593C22C2×D3×#6711yescharacteristic
594C4—21no—
595C4—32no—
596C4—42no—
597C4—61no—
598C4—61no—
599C4—121no—
600C4—122no—
601C4—361no—
602C4D3×#21512yes—
603C4#6430911yescharacteristic
604C4#6431411yescharacteristic
605C3—21no—
606C3#8043811yescharacteristic, complemented
607C3#8336311yescharacteristic, complemented
608C2—62no—
609C2—241no—
610C2—721no—
611C2#1059523211yescharacteristic
612C2C2×D3×#21511yescharacteristic
613C2#1059531711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593968C2
hypercenterC4⋊Q8D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. #10592782C2semidirect
4. C3×#5083C2semidirect
5. #10591634C2semidirect
6. #10591617C2semidirect
7. #10591585C2semidirect
8. #10591544C2semidirect
9. D3×C4⋊(C3⋊C8)C2semidirect
10. #10590300C2semidirect
11. #10590266C2semidirect
46. #5728D3semidirect
57. #5083D3semidirect
199. C3×C4×D3SD16semidirect
428. C4×D3#215semidirect
534. C32#3246semidirect
606. C3#80438semidirect
607. C3#83363semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
#105939682
#105927822
C3×#50832
#105916342
#105916172
#105915852
#105915442
D3×C4⋊(C3⋊C8)2
#105903002
#105902662
#833633
#804383