Finite Group Databasebeta

← #11882265

Subgroups — #11882265

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593972C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic, complemented
3C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic, complemented
5C3×#4841C211yesmaximal, characteristic, complemented
6#10590876C212yesmaximal, complemented
7#10590843C212yesmaximal, complemented
8#10590841C212yesmaximal, complemented
9#10590816C212yesmaximal, complemented
10#10590363C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#81070—31nomaximal
13#80438—31nomaximal
14C2×#3798—21no—
15C2×C8×C3⋊D3C2212yes—
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×#204C2212yes—
18C3×C4×D12C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×#869C2211yescharacteristic
22#63919C2211yescharacteristic
23#63916C2211yescharacteristic
24#63916C2211yescharacteristic
25#63915—21no—
26#63914C2211yescharacteristic
27#63912—21no—
28C4×#625—21no—
29#63872—21no—
30#63871—21no—
31#63871C2212yes—
32#63849—21no—
33#63843—21no—
34#63843C2212yes—
35C2×#3715C2212yes—
36C32×C4⋊C8C2211yescharacteristic
37#63641C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C3×#821C2212yes—
40C3×#817C2212yes—
41C3×#816C2212yes—
42#63574C2212yes—
43#63565C2212yes—
44#63562C2212yes—
45#5728—31no—
46#5728—31no—
47#5548—31no—
48#5548—31no—
49C3×#476—31no—
50C3×#461—31no—
51#5171—32no—
52#5163—32no—
53#5084—31no—
54#5083—31no—
55#5019—31no—
56#5008—31no—
57#4864—32no—
58#4854—32no—
59#4842D311yescharacteristic, complemented
60#4841D311yescharacteristic, complemented
61D3×C4⋊C8—31no—
62D3×C4⋊C8—31no—
63D3×C4⋊C8—61no—
64#4807—32no—
65#4791—32no—
66#4778—32no—
67#4762—32no—
68C2×C4×C3⋊D3D411yescharacteristic
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2312yes—
77C2×#627—21no—
78C2×#626—21no—
79C2×#626—21no—
80C2×#625—21no—
81C2×#625—21no—
82#3798—44no—
83C2×C32×C8C2312yes—
84C32×C42C2311yescharacteristic
85C4×C3⋊Dic3D411yescharacteristic
86C4×C3⋊Dic3D411yescharacteristic
87C4×C3⋊Dic3C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2312yes—
89C8×C3⋊D3—42no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2311yescharacteristic
98C3×#204—42no—
99#3724—21no—
100Dic3⋊Dic3—22no—
101Dic3⋊Dic3—22no—
102#3722—22no—
103(C2×D3)⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105Dic32—22no—
106#3715—42no—
107#3246—91noSylow
108C2×#235—61no—
109C2×#235—61no—
110C2×C3×SD16—32no—
111C3×C4⋊Q8—31no—
112C3×C4⋊Q8—31no—
113C3×C4×D4—31no—
114C3×C4×D4—31no—
115#946—32no—
116#946—61no—
117Q8×Dic3—32no—
118Q8×Dic3—61no—
119C2×#215—32no—
120#940—31no—
121#940—31no—
122#938—31no—
123#938—31no—
124C2×#214—32no—
125C4×#67—61no—
126C4×#67—61no—
127C2×#204C2×D312yes—
128C2×D3×C8—32no—
129C2×D3×C8—32no—
130C2×D3×C8—62no—
131#897—32no—
132#897—61no—
133#895—31no—
134#895—31no—
135#892—61no—
136#892—61no—
137#890—61no—
138#890—61no—
139#888—31no—
140#888—31no—
141#887—32no—
142#887—61no—
143#885—61no—
144#885—61no—
145#884—61no—
146#884—61no—
147C4×D12C2×D311yescharacteristic
148C4×D12C2×D311yescharacteristic
149C42×D3—31no—
150C42×D3—31no—
151C42×D3—61no—
152#869C2×D311yescharacteristic
153#869C2×D311yescharacteristic
154C3×#106—32no—
155C3×C4⋊C8—21no—
156C3×C4⋊C8C2×D311yescharacteristic
157C3×C4⋊C8C2×D311yescharacteristic
158C3×#103—32no—
159C3×#102—32no—
160#835—32no—
161#832—32no—
162#821C2×D312yes—
163#817C2×D312yes—
164#816C2×D312yes—
165Dic3⋊C8—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—62no—
168#810—32no—
169#809—32no—
170#808—32no—
171#808—32no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C22×C3⋊D3C2×D411yescharacteristic
176C22×C3×D3—21no—
177C22×C3×D3—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C4×C3⋊D3—21no—
185C4×C3⋊D3—21no—
186C4×C3⋊D3—41no—
187C4×C3⋊D3SD1614yescomplemented
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C3×D12—21no—
193C3×D12—21no—
194C3×D12—21no—
195C3×D12—21no—
196C3×C4×D3—42no—
197C3×C4×D3—42no—
198C3×Dic6—22no—
199C3×Dic6—22no—
200C3×Dic6—42no—
201#627—42no—
202#626—42no—
203#626—42no—
204#625—42no—
205#625—42no—
206C32×C8—22no—
207C3⋊(C3⋊C8)—22no—
208#533—91no—
209#532—91no—
210#476—31no—
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—32no—
220C2×C3×Q8—61no—
221C2×C3×D4—31no—
222C2×C3×D4—31no—
223C22×C3×C4—61no—
224C22×C3×C4—61no—
225C2×#67—61no—
226C2×#67—61no—
227C2×#67—61no—
228C2×#67—61no—
229C2×#67—61no—
230C2×#67—61no—
231#235—124no—
232#235—124no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12C22×D311yescharacteristic
236C2×D12C22×D311yescharacteristic
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×C4×D3—31no—
240C2×C4×D3—31no—
241C2×C4×D3—31no—
242C2×C4×D3—31no—
243C2×C4×D3—31no—
244C2×C4×D3—31no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×Dic6—21no—
249C2×Dic6—61no—
250C2×Dic6—61no—
251C2×Dic6C22×D312yes—
252C3×SD16—122no—
253C2×C3×C8—22no—
254C2×C3×C8C22×D312yes—
255C2×C3×C8C22×D312yes—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C22⋊C4—61no—
263C3×C22⋊C4—61no—
264C3×C42—21no—
265C3×C42C22×D311yescharacteristic
266C3×C42C22×D311yescharacteristic
267#217—61no—
268#217—61no—
269#215—122no—
270#214—122no—
271(C2×D3)⋊C4—21no—
272(C2×D3)⋊C4—21no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—62no—
281C4⋊Dic3—62no—
282C4⋊Dic3C22×D311yescharacteristic
283C4⋊Dic3C22×D312yes—
284C4⋊Dic3C22×D311yescharacteristic
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289C4×Dic3—31no—
290C4×Dic3—31no—
291C4×Dic3—31no—
292C4×Dic3—31no—
293C4×Dic3—31no—
294C4×Dic3—31no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—62no—
299C4×Dic3—62no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—62no—
303#204—42no—
304D3×C8—122no—
305D3×C8—122no—
306D3×C8—124no—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—21no—
309C2×C3⋊D3—21no—
310C2×C3⋊D3C2×SD1612yes—
311C2×C3×D3—41no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C32×C4—21no—
318C32×C4C2×SD1612yes—
319C32×C4H(5,𝔽2)11yescharacteristic
320C32×C42−1+411yescharacteristic
321C3⋊Dic3—21no—
322C3⋊Dic3—21no—
323C3⋊Dic3C2×SD1612yes—
324C3×Dic3—42no—
325C3×Dic3—41no—
326C3×Dic3—41no—
327C3×Dic3—42no—
328C2×#41—181no—
329C2×SD16—32no—
330C2×SD16—92no—
331C22×C8—92no—
332C4⋊Q8—31no—
333C4⋊Q8—31no—
334C4⋊Q8—91no—
335#127—91no—
336#125—181no—
337#124—181no—
338C22⋊Q8—92no—
339C22⋊Q8—181no—
340#121—91no—
341#121—91no—
342#121—181no—
343C4×Q8—92no—
344C4×Q8—181no—
345C4×D4—31no—
346C4×D4—31no—
347C4×D4—181no—
348#117—181no—
349C2×C42—91no—
350#106—32no—
351#106—92no—
352C4⋊C8—92no—
353C4⋊C8—91no—
354C4⋊C8D3211yescharacteristic
355#103—32no—
356#103—92no—
357#102—32no—
358#102—92no—
359C23×C3—61no—
360C23×C3—61no—
361C22×D3—21no—
362C22×D3—21no—
363C22×D3—31no—
364C22×D3—31no—
365C22×D3—61no—
366C3×Q8—62no—
367C3×Q8—62no—
368C3×Q8—122no—
369C3×D4—61no—
370C3×D4—61no—
371C3×D4—61no—
372C3×D4—61no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—122no—
381C2×C3×C4—122no—
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388#67—122no—
389#67—122no—
390#67—122no—
391#67—122no—
392#67—122no—
393#67—122no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—31no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—31no—
403C2×Dic3—31no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407D12—21no—
408D12—21no—
409D12—21no—
410D12—21no—
411D12—122no—
412D12—122no—
413C4×D3—34no—
414C4×D3—34no—
415C4×D3—42no—
416C4×D3—42no—
417C4×D3—64no—
418C4×D3—62no—
419C4×D3—62no—
420C4×D3—61no—
421C4×D3—61no—
422C4×D3—61no—
423C4×D3—61no—
424C4×D3—121no—
425C4×D3—121no—
426C4×D3—122no—
427Dic6—22no—
428Dic6—22no—
429Dic6—42no—
430Dic6—122no—
431Dic6—122no—
432C3×C8—22no—
433C3×C8—22no—
434C3×C8—42no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C3⋊C8—122no—
438C2×C32#53711yescharacteristic
439C2×C32C22×SD1611yescharacteristic
440C2×C32#57511yescharacteristic
441C3⋊D3—22no—
442C3×D3—81no—
443C3×D3—81no—
444#41—364no—
445C2×Q8—32no—
446C2×Q8—61no—
447C2×Q8—181no—
448C2×D4—31no—
449C2×D4—31no—
450C2×D4—181no—
451C2×D4—181no—
452C2×D4—181no—
453C2×D4—181no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—91no—
457C22×C4—91no—
458C22×C4—91no—
459SD16—122no—
460SD16—362no—
461C2×C8—92no—
462C2×C8—362no—
463C2×C8C2×D3212yes—
464C4⋊C4—32no—
465C4⋊C4—31no—
466C4⋊C4—31no—
467C4⋊C4—61no—
468C4⋊C4—61no—
469C4⋊C4—61no—
470C4⋊C4—181no—
471C4⋊C4—182no—
472C4⋊C4—182no—
473C22⋊C4—61no—
474C22⋊C4—61no—
475C22⋊C4—182no—
476C22⋊C4—181no—
477C22⋊C4—181no—
478C42—91no—
479C42—91no—
480C42—91no—
481C42—182no—
482C42C2×D3211yescharacteristic
483C22×C3—21no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3C2×D3×D411yescharacteristic
491C22×C3C2×D3×D411yescharacteristic
492C2×D3—32no—
493C2×D3—32no—
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—61no—
504C2×D3—61no—
505C2×D3—61no—
506C2×D3—61no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—22no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—41no—
513C3×C4—121no—
514C3×C4—121no—
515C3×C4—122no—
516C3×C4—122no—
517C3×C4D3×SD1612yes—
518C3×C4D3×SD1612yes—
519C3×C4#100411yescharacteristic
520C3×C4#100711yescharacteristic
521C3×C4#100911yescharacteristic
522C3×C4#101011yescharacteristic
523Dic3—32no—
524Dic3—32no—
525Dic3—41no—
526Dic3—41no—
527Dic3—42no—
528Dic3—42no—
529Dic3—62no—
530Dic3—62no—
531Dic3—61no—
532Dic3—61no—
533Dic3—61no—
534Dic3—61no—
535Dic3—121no—
536C32#324611yescharacteristic, complemented, Sylow
537C23—61no—
538C23—61no—
539C23—91no—
540Q8—62no—
541Q8—62no—
542Q8—122no—
543Q8—362no—
544D4—61no—
545D4—61no—
546D4—61no—
547D4—61no—
548D4—362no—
549D4—362no—
550D4—362no—
551D4—362no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—91no—
557C2×C4—94no—
558C2×C4—91no—
559C2×C4—91no—
560C2×C4—122no—
561C2×C4—122no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—361no—
565C2×C4#380211yescharacteristic
566C2×C4#380211yescharacteristic
567C2×C4C22×D3211yescharacteristic
568C8—22no—
569C8—182no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—241no—
574C2×C3—241no—
575C2×C3#560811yescharacteristic
576C2×C3#562911yescharacteristic
577C2×C3C2×D3×SD1611yescharacteristic
578C2×C3C2×D3×SD1611yescharacteristic
579C2×C3#577311yescharacteristic
580C2×C3#577711yescharacteristic
581D3—64no—
582D3—62no—
583D3—62no—
584D3—81no—
585D3—81no—
586C22—92no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22—181no—
594C22—181no—
595C22C2×#380211yescharacteristic
596C4—21no—
597C4—92no—
598C4—121no—
599C4—121no—
600C4—122no—
601C4—122no—
602C4—181no—
603C4—181no—
604C4#6379612yes—
605C4#6431411yescharacteristic
606C4#6431511yescharacteristic
607C3—21no—
608C3#8043811yescharacteristic, complemented
609C3#8107011yescharacteristic, complemented
610C2—182no—
611C2—241no—
612C2—241no—
613C2#1059452811yescharacteristic
614C2C2×#6379611yescharacteristic
615C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593972C2
hypercenterC4⋊C8D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593866C2semidirect
3. C3⋊D3×C4⋊C8C2semidirect
4. C3×#4842C2semidirect
5. C3×#4841C2semidirect
6. #10590876C2semidirect
7. #10590843C2semidirect
8. #10590841C2semidirect
9. #10590816C2semidirect
10. #10590363C2semidirect
11. #10590266C2semidirect
59. #4842D3semidirect
60. #4841D3semidirect
187. C4×C3⋊D3SD16semidirect
536. C32#3246semidirect
608. C3#80438semidirect
609. C3#81070semidirect

Maximal subgroups

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

subgroupindex
#105939722
#105938662
C3⋊D3×C4⋊C82
C3×#48422
C3×#48412
#105908762
#105908432
#105908412
#105908162
#105903632
#105902662
#810703
#804383