Finite Group Databasebeta

← #11898314

Subgroups — #11898314

Order 1152.

964 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596024C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591492C212yesmaximal, complemented
6#10591444C212yesmaximal, complemented
7#10590565C212yesmaximal, complemented
8#10590483C212yesmaximal, complemented
9#10590373C211yesmaximal, characteristic, complemented
10#10590367C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#80420—31nomaximal
13#79637—31nomaximal
14C2×#3828—21no—
15C32×C4×D4C2211yescharacteristic
16#64149C2212yes—
17#64139—21no—
18#64102C2212yes—
19#64093—22no—
20#64083C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C2×C3×#214C2212yes—
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63873C2212yes—
27#63869—21no—
28#63847—22no—
29#63844—21no—
30#63843C2212yes—
31C2×#3717C2212yes—
32C2×#3717C2212yes—
33C2×#3717C2212yes—
34C3×#832C2211yescharacteristic
35C3×#810C2212yes—
36C3×#810C2211yescharacteristic
37C3×#808C2211yescharacteristic
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39C3×C4×C3⋊C8C2211yescharacteristic
40#63572C2212yes—
41#63564C2212yes—
42#63553C2212yes—
43#5721—31no—
44#5567—31no—
45#5553—31no—
46#5553—31no—
47#5553—61no—
48C3×#461—31no—
49C3×C4×SD16—31no—
50#5175—32no—
51#5175—32no—
52#5163—32no—
53#5085—31no—
54#5027—31no—
55#5019D311yescharacteristic, complemented
56C4×#214D311yescharacteristic, complemented
57#4852—32no—
58#4848—31no—
59#4830—31no—
60#4818—32no—
61#4818—32no—
62#4788—32no—
63#4762—32no—
64#4693—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#638—22no—
69C2×#638—22no—
70#3828—44no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×C4×C3⋊D3—22no—
75C2×#634D411yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×C3×Dic6C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42C2311yescharacteristic
81#3752—22no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C3×#214—22no—
86C3×#214—42no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3724—22no—
96#3724—22no—
97Dic3⋊Dic3—22no—
98Dic32—22no—
99#3717—24no—
100#3717—42no—
101#3717—42no—
102#3392—91noSylow
103C2×#235—61no—
104C2×#235—61no—
105C2×#235—62no—
106C2×C3×SD16—31no—
107C2×C3×SD16—32no—
108C3×C4⋊Q8—31no—
109C3×C4×Q8—31no—
110C3×C4×D4—21no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113Q8×Dic3—32no—
114#944—32no—
115#944—32no—
116C2×#215—32no—
117C2×#215—32no—
118C2×#215—32no—
119#940—32no—
120#940—32no—
121#940—62no—
122C2×#214C2×D311yescharacteristic
123C2×#214C2×D312yes—
124#930—61no—
125#930—61no—
126#930—62no—
127C2×#204—32no—
128C2×#204—32no—
129C2×#204—32no—
130#893—32no—
131#893—32no—
132#893—62no—
133#890—61no—
134#889—62no—
135#889—62no—
136#887—32no—
137#887—61no—
138#884—62no—
139#884—62no—
140#884—64no—
141#874—31no—
142#874—31no—
143#874—61no—
144#870—61no—
145#869C2×D311yescharacteristic
146C4×Dic6—31no—
147C4×Dic6—31no—
148C4×Dic6—61no—
149C4×Dic6—61no—
150C4×Dic6C2×D311yescharacteristic
151C3×#106—31no—
152C3×C4⋊C8—31no—
153C3×#103—32no—
154C3×#103—31no—
155C3×#102—31no—
156C3×C4×C8—31no—
157#832C2×D311yescharacteristic
158#821—32no—
159Dic3⋊C8—32no—
160Dic3⋊C8—32no—
161C8×Dic3—32no—
162C8×Dic3—32no—
163#810C2×D311yescharacteristic
164#810C2×D312yes—
165#809—32no—
166#808C2×D311yescharacteristic
167C4⋊(C3⋊C8)C2×D311yescharacteristic
168C4×C3⋊C8C2×D311yescharacteristic
169C23×C32—21no—
170C22×C3⋊D3—22no—
171C32×D4—21no—
172C32×D4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—42no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178#638—44no—
179#638—82no—
180C2×C3⋊Dic3C2×D412yes—
181C2×C3⋊Dic3C2×D412yes—
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)—22no—
184C4⋊(C3⋊D3)—42no—
185C4⋊(C3⋊D3)—81no—
186C4×C3⋊D3—44no—
187#634SD1614yescomplemented
188C2×C3×Dic3—21no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6—21no—
194C3×Dic6—22no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—22no—
197C3×C3⋊C8#4112yescomplemented
198#557—91no—
199#550—91no—
200#492—91no—
201#492—92no—
202#461—31no—
203#461—92no—
204#460—92no—
205#460—91no—
206C8×Q8—91no—
207C4×SD16—31no—
208C4×SD16—92no—
209C2×C3×Q8—31no—
210C2×C3×Q8—32no—
211C2×C3×D4—21no—
212C2×C3×D4C22×D311yescharacteristic
213C2×C3×D4C22×D311yescharacteristic
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C2×#67—62no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—62no—
221C2×#67—64no—
222C2×#67—64no—
223#235—124no—
224#235—124no—
225#235—128no—
226C2×D12—32no—
227C2×D12—32no—
228C2×D12—62no—
229C2×D12—62no—
230C2×D12—61no—
231C2×D12—61no—
232C2×D12—62no—
233C2×D12—61no—
234C2×D12—61no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—64no—
238C2×Dic6—31no—
239C2×Dic6—31no—
240C2×Dic6—61no—
241C2×Dic6C22×D311yescharacteristic
242C2×Dic6C22×D312yes—
243C3×SD16—62no—
244C3×SD16—122no—
245C2×C3×C8—31no—
246C2×C3×C8—32no—
247C2×C3×C8—31no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C22⋊C4—22no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C42—21no—
259C3×C42—61no—
260C3×C42C22×D311yescharacteristic
261C3×C42C22×D311yescharacteristic
262#215—64no—
263#215—122no—
264#215—122no—
265#214—22no—
266#214—42no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—64no—
270C4⋊Dic3—21no—
271C4⋊Dic3—21no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—61no—
275C4⋊Dic3—62no—
276C4⋊Dic3C22×D311yescharacteristic
277Dic3⋊C4—21no—
278Dic3⋊C4—32no—
279Dic3⋊C4—32no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286C4×Dic3—21no—
287C4×Dic3—32no—
288C4×Dic3—32no—
289C4×Dic3—62no—
290C4×Dic3—62no—
291C4×Dic3—62no—
292C2×C3⋊C8C22×D311yescharacteristic
293C2×C3⋊C8C22×D312yes—
294C2×C3⋊C8C22×D311yescharacteristic
295#204—64no—
296#204—122no—
297#204—122no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32—41no—
301C22×C32C22×D411yescharacteristic
302C2×C3⋊D3—42no—
303C2×C3⋊D3—42no—
304C2×C3⋊D3—42no—
305C32×C4—21no—
306C32×C4—41no—
307C32×C4C2×SD1612yes—
308C32×C4C2×#4111yescharacteristic
309C32×C4H(5,𝔽2)11yescharacteristic
310C3⋊Dic3—22no—
311C3⋊Dic3C2×SD1614yes—
312C3×Dic3—41no—
313C3×Dic3—42no—
314C3×Dic3—41no—
315C2×#41—181no—
316C2×SD16—31no—
317C2×SD16—32no—
318C2×SD16—92no—
319C2×SD16—92no—
320C2×SD16—92no—
321C4⋊Q8—31no—
322C4⋊Q8—92no—
323#127—92no—
324#127—91no—
325#125—181no—
326#125—182no—
327#121—182no—
328#121—181no—
329C4×Q8—31no—
330C4×Q8—91no—
331C4×Q8—92no—
332C4×Q8—181no—
333C4×D4—92no—
334C4×D4D3211yescharacteristic
335#106—31no—
336C4⋊C8—31no—
337C4⋊C8—92no—
338#103—31no—
339#103—32no—
340#102—31no—
341#102—92no—
342C4×C8—31no—
343C4×C8—92no—
344C23×C3—22no—
345C23×C3—21no—
346C23×C3—21no—
347C22×D3—64no—
348C22×D3—62no—
349C22×D3—62no—
350C3×Q8—62no—
351C3×Q8—61no—
352C3×Q8—61no—
353C3×Q8—62no—
354C3×D4—21no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—41no—
359C3×D4—41no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—44no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—61no—
370C2×C3×C4—62no—
371C2×C3×C4—61no—
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378#67—124no—
379#67—124no—
380#67—128no—
381#67—242no—
382#67—242no—
383#67—244no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—32no—
388C2×Dic3—32no—
389C2×Dic3—32no—
390C2×Dic3—32no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393D12—62no—
394D12—62no—
395D12—62no—
396D12—62no—
397D12—122no—
398D12—122no—
399D12—124no—
400D12—122no—
401D12—122no—
402D12—241no—
403D12—241no—
404D12—242no—
405C4×D3—124no—
406C4×D3—124no—
407C4×D3—128no—
408Dic6—21no—
409Dic6—22no—
410Dic6—22no—
411Dic6—21no—
412Dic6—34no—
413Dic6—34no—
414Dic6—64no—
415C3×C8—32no—
416C3×C8—61no—
417C3×C8—62no—
418C3⋊C8—22no—
419C3⋊C8—21no—
420C3⋊C8#23512yescomplemented
421C2×C32—81no—
422C2×C32#55011yescharacteristic
423C2×C32C22×SD1611yescharacteristic
424C2×C32#57711yescharacteristic
425C3⋊D3—82no—
426#41—364no—
427C2×Q8—31no—
428C2×Q8—32no—
429C2×Q8—91no—
430C2×D4—92no—
431C2×D4—182no—
432C2×D4—182no—
433C2×D4—181no—
434C2×D4—181no—
435C2×D4C2×D3211yescharacteristic
436C22×C4—21no—
437C22×C4—182no—
438SD16—62no—
439SD16—122no—
440SD16—184no—
441SD16—362no—
442SD16—362no—
443C2×C8—31no—
444C2×C8—31no—
445C2×C8—32no—
446C4⋊C4—31no—
447C4⋊C4—61no—
448C4⋊C4—61no—
449C4⋊C4—61no—
450C4⋊C4—92no—
451C4⋊C4—91no—
452C4⋊C4—182no—
453C4⋊C4—182no—
454C4⋊C4—182no—
455C4⋊C4C2×D3211yescharacteristic
456C22⋊C4—21no—
457C22⋊C4—182no—
458C42—61no—
459C42—92no—
460C42—182no—
461C42C2×D3211yescharacteristic
462C22×C3—21no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3C2×D3×D411yescharacteristic
473C22×C3C2×D3×D411yescharacteristic
474C2×D3—124no—
475C2×D3—124no—
476C2×D3—124no—
477C2×D3—122no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—122no—
481C2×D3—122no—
482C2×D3—122no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—41no—
489C3×C4—42no—
490C3×C4—41no—
491C3×C4—41no—
492C3×C4—121no—
493C3×C4—122no—
494C3×C4—121no—
495C3×C4D3×SD1612yes—
496C3×C4D3×SD1612yes—
497C3×C4C2×#23511yescharacteristic
498C3×C4#100411yescharacteristic
499C3×C4D3×#4111yescharacteristic
500C3×C4#100911yescharacteristic
501Dic3—34no—
502Dic3—34no—
503Dic3—41no—
504Dic3—41no—
505Dic3—42no—
506Dic3—64no—
507Dic3—62no—
508Dic3—62no—
509Dic3—122no—
510C32#339211yescharacteristic, complemented, Sylow
511C23—21no—
512C23—182no—
513Q8—61no—
514Q8—62no—
515Q8—62no—
516Q8—61no—
517Q8—94no—
518D4—21no—
519D4—21no—
520D4—182no—
521D4—182no—
522D4—364no—
523D4—362no—
524D4—721no—
525D4—722no—
526C2×C4—21no—
527C2×C4—42no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—92no—
532C2×C4—92no—
533C2×C4—364no—
534C2×C4#381111yescharacteristic
535C2×C4#381111yescharacteristic
536C2×C4C22×D3211yescharacteristic
537C8—32no—
538C8—62no—
539C8—61no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—82no—
544C2×C3—81no—
545C2×C3—81no—
546C2×C3#555311yescharacteristic
547C2×C3#559911yescharacteristic
548C2×C3C2×D3×SD1611yescharacteristic
549C2×C3C2×D3×SD1611yescharacteristic
550C2×C3#577011yescharacteristic
551C2×C3#577811yescharacteristic
552D3—244no—
553D3—242no—
554D3—242no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—362no—
559C22—362no—
560C22—362no—
561C22C2×#381111yescharacteristic
562C4—21no—
563C4—41no—
564C4—94no—
565C4—121no—
566C4—122no—
567C4—121no—
568C4—182no—
569C4#6393012yes—
570C4D3×#23511yescharacteristic
571C4#6430711yescharacteristic
572C3—21no—
573C3#7963711yescharacteristic, complemented
574C3#8042011yescharacteristic, complemented
575C2—81no—
576C2—722no—
577C2#1059491911yescharacteristic
578C2C2×#6393011yescharacteristic
579C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10596024C2
hypercenterC4×D4D32
hypocenterC32#3392
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. #10593864C2semidirect
3. C3×#5019C2semidirect
4. C3×C4×#214C2semidirect
5. #10591492C2semidirect
6. #10591444C2semidirect
7. #10590565C2semidirect
8. #10590483C2semidirect
9. #10590373C2semidirect
10. #10590367C2semidirect
11. #10590254C2semidirect
55. #5019D3semidirect
56. C4×#214D3semidirect
187. #634SD16semidirect
197. C3×C3⋊C8#41semidirect
420. C3⋊C8#235semidirect
510. C32#3392semidirect
573. C3#79637semidirect
574. C3#80420semidirect

Maximal subgroups

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

subgroupindex
#105960242
#105938642
C3×#50192
C3×C4×#2142
#105914922
#105914442
#105905652
#105904832
#105903732
#105903672
#105902542
#804203
#796373