Finite Group Databasebeta

← #11882266

Subgroups — #11882266

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
1#10593968C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
6#10590879C212yesmaximal, complemented
7#10590830C212yesmaximal, complemented
8#10590825C212yesmaximal, complemented
9#10590802C212yesmaximal, complemented
10#10590365C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#81070—31nomaximal
13#79027—31nomaximal
14C2×#3798—21no—
15C2×#3744C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×#869C2211yescharacteristic
22#63918C2211yescharacteristic
23#63911C2211yescharacteristic
24#63909C2211yescharacteristic
25#63908C2211yescharacteristic
26#63906—21no—
27C4×#626—21no—
28#63869—21no—
29#63857C2212yes—
30#63856—21no—
31#63852—21no—
32#63844C2212yes—
33Dic3×Dic6—21no—
34#63841—21no—
35C2×#3716C2212yes—
36C32×C4⋊C8C2211yescharacteristic
37#63643C2212yes—
38C3×#821C2212yes—
39C3×#817C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42#63573C2212yes—
43#63567C2212yes—
44#63564C2212yes—
45#5728—31no—
46#5548—31no—
47#5477—31no—
48#5470—31no—
49C3×#476—31no—
50C2×C3×C4⋊C8—31no—
51#5114—32no—
52#5114—32no—
53#5084—31no—
54#5019—31no—
55#4864—32no—
56#4854—32no—
57#4851—32no—
58#4848—32no—
59#4842—31no—
60#4842D311yescharacteristic, complemented
61#4841—31no—
62#4841—31no—
63#4841—31no—
64#4841—61no—
65D3×C4⋊C8D311yescharacteristic, complemented
66#4778—32no—
67#4762—32no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634C2312yes—
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—
83C2×C32×C8C2312yes—
84C32×C42C2311yescharacteristic
85#3752—21no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89#3744—42no—
90C3×(C2×D3)⋊C4—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C3×D3×C8—42no—
99#3724—22no—
100Dic3⋊Dic3—22no—
101Dic3⋊Dic3—21no—
102#3722—21no—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3—21no—
105Dic32—22no—
106#3716—42no—
107#3246—91noSylow
108C2×#235—61no—
109C2×#235—61no—
110C22×C3×C8—32no—
111C3×C4⋊Q8—31no—
112C3×C4×D4—31no—
113C2×C3×C42—31no—
114#946—61no—
115Q8×Dic3—61no—
116#940—31no—
117#938—31no—
118C2×#214—32no—
119#930—31no—
120#930—31no—
121#930—61no—
122C4×#67—61no—
123#926—61no—
124#924—32no—
125#924—61no—
126C2×#204—32no—
127C2×#204—32no—
128C2×#204—32no—
129C2×#204—62no—
130C2×D3×C8C2×D312yes—
131#897—32no—
132#895—31no—
133#892—61no—
134#890—61no—
135#888—31no—
136#887—32no—
137#885—61no—
138#884—61no—
139#875—61no—
140#874—31no—
141C4×D12—31no—
142C4×D12—31no—
143C4×D12—61no—
144C4×D12—61no—
145C4×D12C2×D311yescharacteristic
146C42×D3C2×D311yescharacteristic
147#870—61no—
148#869—31no—
149#869—31no—
150#869—31no—
151#869—61no—
152#869C2×D311yescharacteristic
153C4×Dic6—32no—
154C4×Dic6—61no—
155C3×#106—32no—
156C3×C4⋊C8—21no—
157C3×C4⋊C8—32no—
158C3×C4⋊C8—31no—
159C3×C4⋊C8C2×D311yescharacteristic
160C3×C4⋊C8C2×D311yescharacteristic
161C3×#102—32no—
162#821—32no—
163#821C2×D312yes—
164#817—32no—
165#817C2×D312yes—
166#816—32no—
167#816—32no—
168#816—32no—
169#816—62no—
170Dic3⋊C8C2×D312yes—
171#810—32no—
172#809—32no—
173#808—32no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)—21no—
185C4×C3⋊D3—42no—
186#634—22no—
187#634—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
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—
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—91no—
216#461—91no—
217#460—92no—
218C2×C4⋊C8—31no—
219C2×C3×Q8—61no—
220C2×C3×D4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—61no—
225C2×#67—61no—
226C2×#67—61no—
227C2×#67—61no—
228C2×#67—61no—
229C2×#67—61no—
230#235—124no—
231#235—124no—
232C2×D12—31no—
233C2×D12—31no—
234C2×D12—61no—
235C2×D12—61no—
236C2×D12—61no—
237C2×D12—61no—
238C2×D12C22×D311yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—121no—
243C2×C4×D3D1211yescharacteristic
244C2×C4×D3D1211yescharacteristic
245C2×C4×D3C22×D311yescharacteristic
246C2×Dic6—21no—
247C2×Dic6—32no—
248C2×Dic6—32no—
249C2×Dic6—62no—
250C2×Dic6—61no—
251C2×Dic6—61no—
252C2×C3×C8—22no—
253C2×C3×C8—32no—
254C2×C3×C8—122no—
255C2×C3×C8C22×D312yes—
256C2×C3×C8C22×D312yes—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—61no—
260C3×C22⋊C4—61no—
261C3×C42—21no—
262C3×C42—31no—
263C3×C42—31no—
264C3×C42—31no—
265C3×C42C22×D311yescharacteristic
266C3×C42C22×D311yescharacteristic
267#217—62no—
268#217—61no—
269#214—122no—
270(C2×D3)⋊C4—21no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—121no—
278C4⋊Dic3—21no—
279C4⋊Dic3—31no—
280C4⋊Dic3—31no—
281C4⋊Dic3—61no—
282C4⋊Dic3—61no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—62no—
288C4⋊Dic3—121no—
289C4⋊Dic3—121no—
290C4⋊Dic3C22×D311yescharacteristic
291C4⋊Dic3C22×D312yes—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294Dic3⋊C4—61no—
295Dic3⋊C4—62no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C4×Dic3D1211yescharacteristic
299C4×Dic3D1211yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C2×C3⋊C8C22×D312yes—
302#204—122no—
303#204—122no—
304#204—124no—
305#204—122no—
306D3×C8—42no—
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×C4C2×SD1612yes—
319C32×C4H(5,𝔽2)11yescharacteristic
320C32×C42−1+411yescharacteristic
321C3⋊Dic3—42no—
322C3⋊Dic3—41no—
323C3×Dic3—21no—
324C3×Dic3—21no—
325C3×Dic3—41no—
326C3×Dic3—42no—
327C3×Dic3C2×SD1612yes—
328C2×#41—181no—
329C2×SD16—92no—
330C2×SD16—92no—
331C22×C8—32no—
332C4⋊Q8—31no—
333C4⋊Q8—91no—
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—91no—
347C4×D4—181no—
348#117—181no—
349C2×C42—31no—
350#106—32no—
351#106—92no—
352C4⋊C8—32no—
353C4⋊C8—31no—
354C4⋊C8D3211yescharacteristic
355#103—92no—
356#103—92no—
357#102—32no—
358#102—92no—
359C23×C3—31no—
360C23×C3—61no—
361C22×D3—21no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—121no—
365C22×D3C2×D1211yescharacteristic
366C3×Q8—122no—
367C3×D4—61no—
368C3×D4—61no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—31no—
373C2×C3×C4—34no—
374C2×C3×C4—31no—
375C2×C3×C4—31no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4—121no—
381C2×C3×C4—122no—
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4C2×D1211yescharacteristic
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—
393C2×Dic3—22no—
394C2×Dic3—21no—
395C2×Dic3—62no—
396C2×Dic3—61no—
397C2×Dic3—62no—
398C2×Dic3—61no—
399C2×Dic3—121no—
400C2×Dic3—122no—
401C2×Dic3C2×D1211yescharacteristic
402C2×Dic3C2×D1211yescharacteristic
403C2×Dic3C2×D1211yescharacteristic
404D12—21no—
405D12—21no—
406D12—62no—
407D12—61no—
408D12—61no—
409D12—61no—
410D12—61no—
411D12—121no—
412D12—122no—
413D12—122no—
414D12—122no—
415C4×D3—21no—
416C4×D3—21no—
417C4×D3—41no—
418C4×D3—42no—
419C4×D3—122no—
420C4×D3—122no—
421C4×D3—242no—
422C4×D3#20414yescomplemented
423Dic6—42no—
424Dic6—62no—
425Dic6—62no—
426Dic6—62no—
427Dic6—62no—
428Dic6—122no—
429Dic6—122no—
430Dic6—122no—
431Dic6—122no—
432C3×C8—22no—
433C3×C8—22no—
434C3×C8—42no—
435C3×C8—62no—
436C3⋊C8—22no—
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—92no—
446C2×Q8—181no—
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—362no—
459SD16—362no—
460C2×C8—32no—
461C2×C8—122no—
462C2×C8C2×D3212yes—
463C4⋊C4—32no—
464C4⋊C4—31no—
465C4⋊C4—61no—
466C4⋊C4—91no—
467C4⋊C4—181no—
468C4⋊C4—182no—
469C4⋊C4—182no—
470C4⋊C4—181no—
471C4⋊C4—181no—
472C22⋊C4—61no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C22⋊C4—182no—
476C22⋊C4—181no—
477C42—31no—
478C42—31no—
479C42—31no—
480C42—182no—
481C42C2×D3211yescharacteristic
482C22×C3—21no—
483C22×C3—32no—
484C22×C3—61no—
485C22×C3—61no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3C22×D1211yescharacteristic
490C22×C3C2×D3×D411yescharacteristic
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×#20412yes—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—32no—
512C3×C4—41no—
513C3×C4—61no—
514C3×C4—61no—
515C3×C4—121no—
516C3×C4—122no—
517C3×C4C2×#20412yes—
518C3×C4D3×SD1612yes—
519C3×C4#100411yescharacteristic
520C3×C4#100711yescharacteristic
521C3×C4#100711yescharacteristic
522C3×C4#100911yescharacteristic
523Dic3—21no—
524Dic3—21no—
525Dic3—41no—
526Dic3—42no—
527Dic3—121no—
528Dic3—121no—
529Dic3—122no—
530Dic3—122no—
531Dic3—242no—
532Dic3—241no—
533Dic3C2×#20412yes—
534C32#324611yescharacteristic, complemented, Sylow
535C23—31no—
536C23—61no—
537C23—181no—
538Q8—122no—
539Q8—182no—
540Q8—182no—
541Q8—362no—
542D4—61no—
543D4—61no—
544D4—181no—
545D4—181no—
546D4—362no—
547D4—362no—
548D4—362no—
549D4—362no—
550C2×C4—31no—
551C2×C4—34no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—62no—
557C2×C4—61no—
558C2×C4—121no—
559C2×C4—122no—
560C2×C4—182no—
561C2×C4—181no—
562C2×C4—362no—
563C2×C4D3×D1211yescharacteristic
564C2×C4D3×D1211yescharacteristic
565C2×C4C22×D3211yescharacteristic
566C8—22no—
567C8—62no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—62no—
572C2×C3—241no—
573C2×C3#551011yescharacteristic
574C2×C3#562911yescharacteristic
575C2×C3C22×#20411yescharacteristic
576C2×C3#574811yescharacteristic
577C2×C3C2×D3×SD1611yescharacteristic
578C2×C3#577311yescharacteristic
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×D1211yescharacteristic
594C4—21no—
595C4—32no—
596C4—61no—
597C4—61no—
598C4—121no—
599C4—122no—
600C4—361no—
601C4—362no—
602C4D3×#20412yes—
603C4#6431411yescharacteristic
604C4#6431611yescharacteristic
605C3—21no—
606C3#7902711yescharacteristic, complemented
607C3#8107011yescharacteristic, complemented
608C2—62no—
609C2—241no—
610C2—721no—
611C2#1059452311yescharacteristic
612C2C2×D3×#20411yescharacteristic
613C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593968C2
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. #10593859C2semidirect
3. #10592540C2semidirect
4. C3×#4842C2semidirect
5. C3×D3×C4⋊C8C2semidirect
6. #10590879C2semidirect
7. #10590830C2semidirect
8. #10590825C2semidirect
9. #10590802C2semidirect
10. #10590365C2semidirect
11. #10590300C2semidirect
60. #4842D3semidirect
65. D3×C4⋊C8D3semidirect
199. C3×C4×D3SD16semidirect
422. C4×D3#204semidirect
534. C32#3246semidirect
606. C3#79027semidirect
607. C3#81070semidirect

Maximal subgroups

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

subgroupindex
#105939682
#105938592
#105925402
C3×#48422
C3×D3×C4⋊C82
#105908792
#105908302
#105908252
#105908022
#105903652
#105903002
#810703
#790273