Finite Group Databasebeta

← #11882267

Subgroups — #11882267

Order 1152.

838 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593968C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
6#10590847C212yesmaximal, complemented
7#10590829C212yesmaximal, complemented
8#10590803C212yesmaximal, complemented
9#10590799C212yesmaximal, complemented
10#10590379C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#80438—31nomaximal
13#79027—31nomaximal
14C2×#3798—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×#204C2212yes—
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#63857—21no—
30#63856C2212yes—
31#63852—21no—
32#63844—21no—
33Dic3×Dic6C2212yes—
34#63841—21no—
35C2×#3717C2212yes—
36C32×C4⋊C8C2211yescharacteristic
37#63648C2212yes—
38#63644C2212yes—
39C3×#816C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42#63573C2212yes—
43#63566C2212yes—
44#63563C2212yes—
45#5728—31no—
46#5548—31no—
47#5477—31no—
48#5470—31no—
49C3×#461—31no—
50C2×C3×C4⋊C8—31no—
51#5171—32no—
52#5163—32no—
53#5114—32no—
54#5114—32no—
55#5083—31no—
56#5008—31no—
57#4851—32no—
58#4848—32no—
59#4842—31no—
60#4842—31no—
61#4842—31no—
62#4842—61no—
63#4841—31no—
64#4841D311yescharacteristic, complemented
65D3×C4⋊C8D311yescharacteristic, complemented
66#4807—32no—
67#4791—32no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634—21no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6C2312yes—
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)C2312yes—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3D411yescharacteristic
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97C3×#204—42no—
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#3717—42no—
107#3246—91noSylow
108C2×#235—61no—
109C2×#235—61no—
110C2×C3×SD16—32no—
111C22×C3×C8—32no—
112C3×C4⋊Q8—31no—
113C3×C4×D4—31no—
114C2×C3×C42—31no—
115#946—32no—
116Q8×Dic3—32no—
117C2×#215—32no—
118#940—31no—
119#938—31no—
120#930—31no—
121#930—31no—
122#930—61no—
123C4×#67—61no—
124#926—61no—
125#924—32no—
126#924—61no—
127C2×#204—32no—
128C2×#204C2×D312yes—
129C2×D3×C8C2×D312yes—
130#897—61no—
131#895—31no—
132#892—61no—
133#890—61no—
134#888—31no—
135#887—61no—
136#885—61no—
137#884—61no—
138#875—61no—
139#874—31no—
140C4×D12—31no—
141C4×D12—31no—
142C4×D12—61no—
143C4×D12—61no—
144C4×D12C2×D311yescharacteristic
145C42×D3C2×D311yescharacteristic
146#870—61no—
147#869—31no—
148#869—31no—
149#869—31no—
150#869—61no—
151#869C2×D311yescharacteristic
152C4×Dic6—32no—
153C4×Dic6—61no—
154C3×C4⋊C8—21no—
155C3×C4⋊C8—32no—
156C3×C4⋊C8—31no—
157C3×C4⋊C8C2×D311yescharacteristic
158C3×C4⋊C8C2×D311yescharacteristic
159C3×#103—32no—
160#835—32no—
161#832—32no—
162#821—32no—
163#821—32no—
164#821—32no—
165#821—62no—
166#817—32no—
167#817—32no—
168#817—32no—
169#817—62no—
170#816—32no—
171#816C2×D312yes—
172Dic3⋊C8C2×D312yes—
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—42no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C3×D12—21no—
193C3×D12—21no—
194C3×C4×D3—21no—
195C3×C4×D3—21no—
196C3×C4×D3—41no—
197C3×C4×D3—42no—
198C3×C4×D3SD1614yescomplemented
199C3×Dic6—22no—
200C3×Dic6—22no—
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—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—31no—
219C2×C3×Q8—32no—
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—61no—
247C2×Dic6—61no—
248C2×Dic6—61no—
249C2×Dic6—61no—
250C2×Dic6—121no—
251C2×Dic6C22×D312yes—
252C3×SD16—122no—
253C2×C3×C8—22no—
254C2×C3×C8—32no—
255C2×C3×C8—122no—
256C2×C3×C8C22×D312yes—
257C2×C3×C8C22×D312yes—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C22⋊C4—61no—
262C3×C42—21no—
263C3×C42—31no—
264C3×C42—31no—
265C3×C42—31no—
266C3×C42C22×D311yescharacteristic
267C3×C42C22×D311yescharacteristic
268#217—62no—
269#217—61no—
270#215—122no—
271(C2×D3)⋊C4—21no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—121no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—32no—
282C4⋊Dic3—31no—
283C4⋊Dic3—32no—
284C4⋊Dic3—31no—
285C4⋊Dic3—61no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3—61no—
290C4⋊Dic3—62no—
291C4⋊Dic3—121no—
292C4⋊Dic3C22×D311yescharacteristic
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—61no—
296Dic3⋊C4—62no—
297C4×Dic3—62no—
298C4×Dic3—62no—
299C4×Dic3D1211yescharacteristic
300C4×Dic3D1211yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302C2×C3⋊C8C22×D312yes—
303#204—42no—
304#204—122no—
305D3×C8—42no—
306C22×C32C22×D411yescharacteristic
307C2×C3⋊D3—41no—
308C2×C3⋊D3—41no—
309C2×C3⋊D3—41no—
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3C2×SD1612yes—
316C32×C4—21no—
317C32×C4C2×SD1612yes—
318C32×C4H(5,𝔽2)11yescharacteristic
319C32×C42−1+411yescharacteristic
320C3⋊Dic3—41no—
321C3⋊Dic3—42no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—42no—
325C3×Dic3—41no—
326C3×Dic3C2×SD1612yes—
327C2×#41—181no—
328C2×SD16—32no—
329C2×SD16—92no—
330C22×C8—32no—
331C4⋊Q8—31no—
332C4⋊Q8—91no—
333C4⋊Q8—91no—
334#127—91no—
335#125—181no—
336#124—181no—
337C22⋊Q8—92no—
338C22⋊Q8—181no—
339#121—91no—
340#121—91no—
341#121—181no—
342C4×Q8—92no—
343C4×Q8—181no—
344C4×D4—31no—
345C4×D4—91no—
346C4×D4—181no—
347#117—181no—
348C2×C42—31no—
349#106—92no—
350#106—92no—
351C4⋊C8—32no—
352C4⋊C8—31no—
353C4⋊C8D3211yescharacteristic
354#103—32no—
355#103—92no—
356#102—92no—
357#102—92no—
358C23×C3—31no—
359C23×C3—61no—
360C22×D3—21no—
361C22×D3—61no—
362C22×D3—61no—
363C22×D3—121no—
364C22×D3C2×D1211yescharacteristic
365C3×Q8—62no—
366C3×Q8—62no—
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—122no—
400C2×Dic3—121no—
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—22no—
424Dic6—22no—
425Dic6—122no—
426Dic6—122no—
427Dic6—122no—
428Dic6—122no—
429Dic6—242no—
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—42no—
433C3×C8—62no—
434C3⋊C8—22no—
435C2×C32#53711yescharacteristic
436C2×C32C22×SD1611yescharacteristic
437C2×C32#57511yescharacteristic
438C3⋊D3—81no—
439C3×D3—22no—
440C3×D3—81no—
441#41—364no—
442C2×Q8—32no—
443C2×Q8—181no—
444C2×Q8—181no—
445C2×D4—31no—
446C2×D4—91no—
447C2×D4—181no—
448C2×D4—181no—
449C2×D4—181no—
450C2×D4—181no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—61no—
455C22×C4—181no—
456SD16—122no—
457SD16—362no—
458C2×C8—32no—
459C2×C8—122no—
460C2×C8C2×D3212yes—
461C4⋊C4—31no—
462C4⋊C4—61no—
463C4⋊C4—61no—
464C4⋊C4—92no—
465C4⋊C4—91no—
466C4⋊C4—181no—
467C4⋊C4—182no—
468C4⋊C4—182no—
469C4⋊C4—181no—
470C22⋊C4—61no—
471C22⋊C4—181no—
472C22⋊C4—181no—
473C22⋊C4—182no—
474C22⋊C4—181no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—182no—
479C42C2×D3211yescharacteristic
480C22×C3—21no—
481C22×C3—32no—
482C22×C3—61no—
483C22×C3—61no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3C22×D1211yescharacteristic
488C22×C3C2×D3×D411yescharacteristic
489C2×D3—21no—
490C2×D3—21no—
491C2×D3—41no—
492C2×D3—41no—
493C2×D3—41no—
494C2×D3—122no—
495C2×D3—121no—
496C2×D3—121no—
497C2×D3—121no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—241no—
502C2×D3—241no—
503C2×D3C2×#20412yes—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—32no—
510C3×C4—41no—
511C3×C4—61no—
512C3×C4—61no—
513C3×C4—121no—
514C3×C4—122no—
515C3×C4C2×#20412yes—
516C3×C4D3×SD1612yes—
517C3×C4#100411yescharacteristic
518C3×C4#100411yescharacteristic
519C3×C4#100711yescharacteristic
520C3×C4#101011yescharacteristic
521Dic3—21no—
522Dic3—21no—
523Dic3—41no—
524Dic3—42no—
525Dic3—121no—
526Dic3—122no—
527Dic3—121no—
528Dic3—122no—
529Dic3—242no—
530Dic3—241no—
531Dic3C2×#20412yes—
532C32#324611yescharacteristic, complemented, Sylow
533C23—31no—
534C23—61no—
535C23—181no—
536Q8—62no—
537Q8—62no—
538Q8—362no—
539Q8—362no—
540D4—61no—
541D4—61no—
542D4—181no—
543D4—181no—
544D4—362no—
545D4—362no—
546D4—362no—
547D4—362no—
548C2×C4—31no—
549C2×C4—34no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—62no—
555C2×C4—61no—
556C2×C4—121no—
557C2×C4—122no—
558C2×C4—182no—
559C2×C4—181no—
560C2×C4—362no—
561C2×C4D3×D1211yescharacteristic
562C2×C4D3×D1211yescharacteristic
563C2×C4C22×D3211yescharacteristic
564C8—22no—
565C8—62no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—62no—
570C2×C3—241no—
571C2×C3#551011yescharacteristic
572C2×C3#560811yescharacteristic
573C2×C3C22×#20411yescharacteristic
574C2×C3#574811yescharacteristic
575C2×C3C2×D3×SD1611yescharacteristic
576C2×C3#577711yescharacteristic
577D3—22no—
578D3—81no—
579D3—242no—
580D3—241no—
581D3—241no—
582C22—32no—
583C22—61no—
584C22—61no—
585C22—121no—
586C22—121no—
587C22—121no—
588C22—361no—
589C22—361no—
590C22—361no—
591C22C2×D3×D1211yescharacteristic
592C4—21no—
593C4—32no—
594C4—61no—
595C4—61no—
596C4—121no—
597C4—122no—
598C4—361no—
599C4—362no—
600C4D3×#20412yes—
601C4#6431311yescharacteristic
602C4#6431511yescharacteristic
603C3—21no—
604C3#7902711yescharacteristic, complemented
605C3#8043811yescharacteristic, complemented
606C2—62no—
607C2—241no—
608C2—721no—
609C2#1059452211yescharacteristic
610C2C2×D3×#20411yescharacteristic
611C2#1059471111yescharacteristic
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. #10592541C2semidirect
4. C3×#4841C2semidirect
5. C3×D3×C4⋊C8C2semidirect
6. #10590847C2semidirect
7. #10590829C2semidirect
8. #10590803C2semidirect
9. #10590799C2semidirect
10. #10590379C2semidirect
11. #10590268C2semidirect
64. #4841D3semidirect
65. D3×C4⋊C8D3semidirect
198. C3×C4×D3SD16semidirect
422. C4×D3#204semidirect
532. C32#3246semidirect
604. C3#79027semidirect
605. C3#80438semidirect

Maximal subgroups

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

subgroupindex
#105939682
#105938592
#105925412
C3×#48412
C3×D3×C4⋊C82
#105908472
#105908292
#105908032
#105907992
#105903792
#105902682
#804383
#790273