Finite Group Databasebeta

← #11870362

Subgroups — #11870362

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic
3C3×#5002C211yesmaximal, characteristic, complemented
4C3×#4995C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6#10591088C211yesmaximal, characteristic, complemented
7#10591073C211yesmaximal, characteristic, complemented
8#10590529C212yesmaximal, complemented
9#10590526C212yesmaximal, complemented
10#10590512C212yesmaximal, complemented
11#10590511C212yesmaximal, complemented
12#79222—31nomaximal
13#78844—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18#64101C2212yes—
19C4⋊C4×C3⋊D3C2212yes—
20#64090—22no—
21C4×C4⋊(C3⋊D3)—21no—
22C4×#634—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63978—22no—
27#63916C2212yes—
28#63909—21no—
29#63871C2212yes—
30#63857—21no—
31C3×#810C2211yescharacteristic
32C3×#810C2211yescharacteristic
33C3×#809C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#808C2212yes—
36C3×#807C2212yes—
37#63573C2212yes—
38#63573C2212yes—
39#63566C2212yes—
40#63563C2212yes—
41#63557C2212yes—
42#63557C2212yes—
43#5833—31no—
44#5523—31no—
45#5523—31no—
46#5523—61no—
47#5510—31no—
48C3×#428—31no—
49C3×#416—31no—
50#5232—31no—
51#5133—31no—
52#5129—31no—
53#5110—31no—
54C2×#817—31no—
55#5002D311yescharacteristic, complemented
56#4995D311yescharacteristic, complemented
57C2×#808—31no—
58#4888—32no—
59#4885—32no—
60#4863—32no—
61#4862—32no—
62#4815—32no—
63#4805—32no—
64#4779—32no—
65#4777—32no—
66C22×C32×C4C2311yescharacteristic
67C2×#638D412yes—
68C22×C3⋊Dic3—21no—
69#3828—22no—
70#3828—22no—
71C2×C4⋊(C3⋊D3)D411yescharacteristic
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3C2312yes—
74C2×#634D411yescharacteristic
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C3×#235—22no—
78C3×#235—22no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C2×#626—22no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86C32×C42—21no—
87#3752—22no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90#3750—22no—
91C4×C3⋊Dic3—22no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×#208—22no—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99Dic3⋊Dic3—22no—
100#3722—22no—
101(C2×D3)⋊Dic3—22no—
102#3099—91noSylow
103C2×C3×#41—31no—
104C2×#235—31no—
105C2×#235—31no—
106C2×#235—61no—
107C2×#235C2×D311yescharacteristic
108C2×C3×M16—31no—
109C22×C3×C8—31no—
110C3×#117—21no—
111C3×#117C2×D311yescharacteristic
112C3×#117C2×D311yescharacteristic
113C2×C3×C4⋊C4—31no—
114#946—32no—
115#939—62no—
116#938—32no—
117#930—61no—
118#930—62no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123#924—61no—
124C2×#208C2×D311yescharacteristic
125C22×C3⋊C8C2×D311yescharacteristic
126#897—32no—
127#897—61no—
128#895—32no—
129#895—61no—
130#892—32no—
131#892—32no—
132#892—62no—
133D3×C4⋊C4—32no—
134D3×C4⋊C4—32no—
135D3×C4⋊C4—62no—
136#67⋊C4—62no—
137#67⋊C4—62no—
138#67⋊C4—64no—
139C4×D12—61no—
140C4×D12—61no—
141C4×D12—62no—
142C4×Dic6—61no—
143C4×Dic6—61no—
144C4×Dic6—62no—
145C3×#107—32no—
146C3×#106—32no—
147C3×#103—31no—
148C3×#103—31no—
149C3×#102—31no—
150C3×#102—31no—
151#835—32no—
152#832—32no—
153#821—32no—
154(C2×D3)⋊C8—32no—
155(C2×D3)⋊C8—32no—
156(C2×D3)⋊C8—32no—
157(C2×D3)⋊C8—32no—
158#817—32no—
159#817—32no—
160#816—32no—
161#810C2×D311yescharacteristic
162#810C2×D311yescharacteristic
163#809C2×D311yescharacteristic
164#809C2×D311yescharacteristic
165#808—32no—
166#808—32no—
167#808C2×D312yes—
168#807C2×D312yes—
169C23×C32C2×D411yescharacteristic
170C22×C3⋊D3C2×D412yes—
171C22×C3×D3—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4#4112yes—
176C2×C32×C4#4112yes—
177C2×C32×C4C2411yescharacteristic
178#638—24no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—81no—
181C2×C3⋊Dic3C2×D412yes—
182C4⋊(C3⋊D3)—22no—
183C4×C3⋊D3—22no—
184C4×C3⋊D3—22no—
185C4×C3⋊D3—82no—
186#634—22no—
187C3×#67—42no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—81no—
191C3×D12—21no—
192C3×D12—21no—
193C3×C4×D3—42no—
194C3×Dic6—21no—
195C3×Dic6—21no—
196#626—82no—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199C3×C3⋊C8—22no—
200#537—91no—
201#520—91no—
202#485—92no—
203#483—92no—
204#482—92no—
205#481—92no—
206#428—31no—
207C2×#106—91no—
208#417—91no—
209#416—31no—
210#408—91no—
211C3×#41—62no—
212C3×#41—62no—
213C2×C3×Q8—31no—
214C2×C3×D4—31no—
215C2×C3×D4—61no—
216C22×C3×C4—21no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—21no—
222C2×#67—32no—
223C2×#67—32no—
224C2×#67—62no—
225C2×#67—62no—
226C22×Dic3—21no—
227C22×Dic3—62no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230#235—22no—
231#235—22no—
232#235—64no—
233#235—64no—
234#235—62no—
235#235—62no—
236#235—62no—
237#235—62no—
238C2×D12—31no—
239C2×D12—31no—
240C2×D12—61no—
241C2×D12—62no—
242C2×D12C22×D311yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3—32no—
245C2×C4×D3—32no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—64no—
250C2×Dic6—31no—
251C2×Dic6—31no—
252C2×Dic6—61no—
253C2×Dic6C22×D311yescharacteristic
254C3×M16—62no—
255C2×C3×C8—32no—
256C2×C3×C8—31no—
257C2×C3×C8—31no—
258C2×C3×C8—62no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C4⋊C4C22×D311yescharacteristic
266C3×C4⋊C4C22×D311yescharacteristic
267C3×C22⋊C4—22no—
268C3×C22⋊C4—21no—
269C3×C22⋊C4—21no—
270C3×C42—22no—
271C3×C42—21no—
272C3×C42—21no—
273#217—62no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—64no—
280C4⋊Dic3—21no—
281C4⋊Dic3—32no—
282C4⋊Dic3—32no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3—62no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3C22×D312yes—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291Dic3⋊C4—62no—
292Dic3⋊C4—64no—
293C4×Dic3—62no—
294C4×Dic3—62no—
295C4×Dic3—64no—
296#208—22no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8C22×D312yes—
299C2×C3⋊C8C22×D311yescharacteristic
300C2×C3⋊C8C22×D311yescharacteristic
301C22×C32—21no—
302C22×C32—21no—
303C22×C32#12312yes—
304C22×C32C22×D411yescharacteristic
305C2×C3⋊D3—22no—
306C2×C3⋊D3—22no—
307C2×C3⋊D3—22no—
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3—41no—
311C32×C4—41no—
312C32×C4—41no—
313C32×C4#12312yes—
314C32×C4C2×#4111yescharacteristic
315C32×C4C2×#4111yescharacteristic
316C3⋊Dic3—22no—
317C3⋊Dic3—42no—
318C3×Dic3—41no—
319C3×Dic3—42no—
320C2×#41—31no—
321C2×#41—91no—
322C2×M16—31no—
323C22×C8—31no—
324C22⋊Q8—92no—
325C22⋊Q8—181no—
326#121—92no—
327#121—181no—
328#121—182no—
329C4×Q8—181no—
330C4×D4—181no—
331C4×D4—182no—
332#117—92no—
333#117D3211yescharacteristic
334C2×C4⋊C4—31no—
335C2×C4⋊C4—91no—
336C2×C4⋊C4—92no—
337#107—32no—
338#106—32no—
339#106—92no—
340#106—92no—
341#103—31no—
342#103—31no—
343#103—92no—
344#102—31no—
345#102—31no—
346#102—92no—
347C22⋊C8—92no—
348C22⋊C8—92no—
349C23×C3—21no—
350C23×C3—61no—
351C23×C3D3×D411yescharacteristic
352C23×C3D3×D411yescharacteristic
353C22×D3—21no—
354C22×D3—32no—
355C22×D3—32no—
356C22×D3—62no—
357C3×Q8—61no—
358C3×Q8—61no—
359C3×D4—61no—
360C3×D4—61no—
361C3×D4—122no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—61no—
373C2×C3×C4—62no—
374C2×C3×C4—122no—
375C2×C3×C4—241no—
376C2×C3×C4#23512yes—
377C2×C3×C4#23512yes—
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4#23712yes—
381C2×C3×C4#23912yes—
382C2×C3×C4C23×D311yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384#67—42no—
385#67—68no—
386#67—64no—
387#67—64no—
388#67—242no—
389C2×Dic3—22no—
390C2×Dic3—21no—
391C2×Dic3—32no—
392C2×Dic3—32no—
393C2×Dic3—62no—
394C2×Dic3—64no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—81no—
398C2×Dic3—241no—
399C2×Dic3—241no—
400C2×Dic3—242no—
401D12—21no—
402D12—21no—
403D12—64no—
404D12—62no—
405D12—62no—
406D12—242no—
407C4×D3—42no—
408C4×D3—64no—
409C4×D3—64no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—62no—
414C4×D3—242no—
415C4×D3—242no—
416C4×D3—244no—
417Dic6—21no—
418Dic6—21no—
419Dic6—64no—
420Dic6—62no—
421Dic6—62no—
422C3×C8—62no—
423C3×C8—61no—
424C3×C8—61no—
425C3⋊C8—22no—
426C3⋊C8—21no—
427C3⋊C8—21no—
428C2×C32—22no—
429C2×C32C2×#12311yescharacteristic
430C2×C32#57711yescharacteristic
431C2×C32#57711yescharacteristic
432C3⋊D3—42no—
433C3×D3—81no—
434#41—62no—
435#41—62no—
436#41—182no—
437#41—182no—
438C2×Q8—31no—
439C2×Q8—91no—
440C2×D4—31no—
441C2×D4—61no—
442C2×D4—92no—
443C2×D4—91no—
444C2×D4—182no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4—92no—
448C22×C4—182no—
449C22×C4—181no—
450C22×C4C2×D3211yescharacteristic
451M16—62no—
452C2×C8—31no—
453C2×C8—31no—
454C2×C8—32no—
455C2×C8—62no—
456C4⋊C4—32no—
457C4⋊C4—61no—
458C4⋊C4—92no—
459C4⋊C4—182no—
460C4⋊C4—182no—
461C4⋊C4—181no—
462C4⋊C4C2×D3211yescharacteristic
463C4⋊C4C2×D3211yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—182no—
466C22⋊C4—182no—
467C22⋊C4—182no—
468C42—21no—
469C42—182no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—22no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—121no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3#88312yes—
482C22×C3#89412yes—
483C22×C3C2×D3×D411yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C2×D3—41no—
486C2×D3—41no—
487C2×D3—41no—
488C2×D3—64no—
489C2×D3—62no—
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—122no—
496C2×D3—122no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—22no—
500C3×C4—42no—
501C3×C4—42no—
502C3×C4—41no—
503C3×C4—41no—
504C3×C4—41no—
505C3×C4—41no—
506C3×C4—121no—
507C3×C4—122no—
508C3×C4#88312yes—
509C3×C4#89412yes—
510C3×C4C2×#23511yescharacteristic
511C3×C4C2×#23511yescharacteristic
512C3×C4C2×#23711yescharacteristic
513C3×C4C2×#23911yescharacteristic
514Dic3—41no—
515Dic3—42no—
516Dic3—64no—
517Dic3—62no—
518Dic3—62no—
519Dic3—124no—
520Dic3—122no—
521Dic3—122no—
522C32#309911yescharacteristic, complemented, Sylow
523C23—61no—
524C23—92no—
525C23#381111yescharacteristic
526Q8—61no—
527Q8—61no—
528Q8—182no—
529D4—61no—
530D4—61no—
531D4—122no—
532D4—184no—
533D4—182no—
534D4—722no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—62no—
538C2×C4—61no—
539C2×C4—92no—
540C2×C4—122no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4—241no—
545C2×C4—722no—
546C2×C4—721no—
547C2×C4#379612yes—
548C2×C4#379812yes—
549C2×C4#381111yescharacteristic
550C2×C4C22×D3211yescharacteristic
551C8—61no—
552C8—61no—
553C8—62no—
554C2×C3—22no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—42no—
560C2×C3—241no—
561C2×C3C2×#88311yescharacteristic
562C2×C3C2×#89411yescharacteristic
563C2×C3#577011yescharacteristic
564C2×C3#577011yescharacteristic
565C2×C3#577511yescharacteristic
566C2×C3#577811yescharacteristic
567D3—81no—
568D3—124no—
569D3—122no—
570D3—122no—
571C22—21no—
572C22—21no—
573C22—121no—
574C22—121no—
575C22—121no—
576C22—182no—
577C22—182no—
578C22—182no—
579C22#6385312yes—
580C22C2×#381111yescharacteristic
581C4—41no—
582C4—41no—
583C4—121no—
584C4—122no—
585C4—182no—
586C4—362no—
587C4#6385312yes—
588C4C2×#379611yescharacteristic
589C4C2×#379811yescharacteristic
590C3—21no—
591C3#7884411yescharacteristic, complemented
592C3#7922211yescharacteristic, complemented
593C2—22no—
594C2—241no—
595C2—362no—
596C2C2×#6385311yescharacteristic
597C2#1059546211yescharacteristic
598C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenter#117D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595994C2semidirect
3. C3×#5002C2semidirect
4. C3×#4995C2semidirect
5. C2×#63573C2semidirect
6. #10591088C2semidirect
7. #10591073C2semidirect
8. #10590529C2semidirect
9. #10590526C2semidirect
10. #10590512C2semidirect
11. #10590511C2semidirect
55. #5002D3semidirect
56. #4995D3semidirect
522. C32#3099semidirect
591. C3#78844semidirect
592. C3#79222semidirect

Maximal subgroups

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

subgroupindex
#105959942
#105950432
C3×#50022
C3×#49952
C2×#635732
#105910882
#105910732
#105905292
#105905262
#105905122
#105905112
#792223
#788443