Finite Group Databasebeta

← #11870355

Subgroups — #11870355

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 611 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596304C211yesmaximal, characteristic
2#10594990C211yesmaximal, characteristic, complemented
3C3×#5233C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic, complemented
5#10591561C212yesmaximal, complemented
6#10591553C212yesmaximal, complemented
7#10591425C212yesmaximal, complemented
8#10591419C212yesmaximal, complemented
9#10591131C211yesmaximal, characteristic, complemented
10C2×#63573C211yesmaximal, characteristic, complemented
11#10591073C211yesmaximal, characteristic, complemented
12#78875—31nomaximal
13#78844—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16#64155C2212yes—
17#64148—22no—
18#64147C2212yes—
19#64139—21no—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64133—21no—
22C3×#926C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63952—22no—
27#63900C2212yes—
28#63894—21no—
29#63849C2212yes—
30#63844—21no—
31C3×#835C2211yescharacteristic
32C3×#835C2212yes—
33C3×#835C2211yescharacteristic
34C3×#832C2212yes—
35C3×#832C2211yescharacteristic
36C3×#832C2211yescharacteristic
37#63575C2212yes—
38#63573C2212yes—
39#63573C2212yes—
40#63573C2212yes—
41#63557C2212yes—
42#63557C2212yes—
43#5833—31no—
44#5833—31no—
45#5833—61no—
46#5523—31no—
47#5504—31no—
48C3×#417—31no—
49C3×#416—31no—
50#5233D311yescharacteristic, complemented
51#5232D311yescharacteristic, complemented
52#5129—31no—
53#5121—31no—
54#5110—31no—
55C2×#817—31no—
56#4995—31no—
57C2×#808—31no—
58#4815—32no—
59#4814—32no—
60#4805—32no—
61#4805—32no—
62#4784—32no—
63#4779—32no—
64#4777—32no—
65#4777—32no—
66C32×#41—22no—
67C32×#41—22no—
68C2×C32×Q8C2311yescharacteristic
69C2×C32×D4—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×#638—22no—
74C2×#638D412yes—
75C22×C3⋊Dic3—21no—
76#3828—22no—
77#3828—22no—
78C2×C4⋊(C3⋊D3)D411yescharacteristic
79C2×C4×C3⋊D3C2312yes—
80C2×#634D411yescharacteristic
81C22×C3×Dic3—21no—
82C2×#624—22no—
83#3757—22no—
84#3752—22no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87#3750—22no—
88C3×#217—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3—21no—
94C3×#208—22no—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99#3724—22no—
100#3722—22no—
101Dic32—22no—
102#3099—91noSylow
103C2×C3×#41—21no—
104C2×C3×#41C2×D311yescharacteristic
105C2×C3×#41C2×D311yescharacteristic
106C2×#235—31no—
107C2×#235—31no—
108C2×#235—61no—
109C2×C3×M16—31no—
110C22×C3×C8—31no—
111C3×#117—31no—
112C2×C3×C4⋊C4—31no—
113#946—32no—
114#946—32no—
115#946—62no—
116#939—62no—
117#939—62no—
118#939—64no—
119#938—32no—
120#938—32no—
121#938—62no—
122#930—61no—
123#930—61no—
124#930—62no—
125C4×#67—62no—
126#926C2×D311yescharacteristic
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—61no—
130C2×C4⋊Dic3C2×D311yescharacteristic
131#924—61no—
132#924—61no—
133#924—62no—
134C2×#208C2×D311yescharacteristic
135C22×C3⋊C8C2×D311yescharacteristic
136#893—61no—
137#892—32no—
138#892—32no—
139D3×C4⋊C4—32no—
140D3×C4⋊C4—32no—
141#887—61no—
142#67⋊C4—62no—
143C4×D12—61no—
144C4×Dic6—61no—
145C3×#103—31no—
146C3×#103—31no—
147C3×#103—32no—
148C3×#102—31no—
149C3×#102—32no—
150C3×#102—31no—
151#835C2×D312yes—
152#835C2×D311yescharacteristic
153#835C2×D311yescharacteristic
154#832C2×D312yes—
155#832C2×D311yescharacteristic
156#832C2×D311yescharacteristic
157(C2×D3)⋊C8—32no—
158(C2×D3)⋊C8—32no—
159(C2×D3)⋊C8—32no—
160(C2×D3)⋊C8—32no—
161#818—32no—
162#817—32no—
163#817—32no—
164#817—32no—
165#808—32no—
166#808—32no—
167#808—32no—
168#807—32no—
169C23×C32—21no—
170C23×C32C2×D411yescharacteristic
171C22×C3⋊D3C2×D412yes—
172C32×Q8—21no—
173C32×Q8—21no—
174C32×D4—21no—
175C32×D4—21no—
176C32×D4—42no—
177C2×C32×C4—21no—
178C2×C32×C4—42no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4#4112yes—
181C2×C32×C4#4112yes—
182C2×C32×C4C2411yescharacteristic
183#638—24no—
184#638—82no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—81no—
187C2×C3⋊Dic3C2×D412yes—
188C4⋊(C3⋊D3)—22no—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—22no—
191#634—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—81no—
196#624—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—91no—
207C2×#106—91no—
208#417—31no—
209#416—31no—
210#408—91no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—22no—
214C3×#41—22no—
215C3×#41—42no—
216C3×#41—42no—
217C2×C3×Q8—21no—
218C2×C3×Q8C22×D311yescharacteristic
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×D4—22no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4C22×D311yescharacteristic
225C2×C3×D4C22×D311yescharacteristic
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—32no—
234C2×#67—32no—
235C2×#67—62no—
236C2×#67—62no—
237C2×#67—62no—
238C2×#67—64no—
239C22×Dic3—21no—
240C22×Dic3—62no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243#235—62no—
244#235—62no—
245#235—62no—
246#235—62no—
247#235—122no—
248#235—122no—
249C2×D12—31no—
250C2×D12—31no—
251C2×D12—61no—
252C2×C4×D3—32no—
253C2×C4×D3—32no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×C4×D3—62no—
257C2×Dic6—31no—
258C2×Dic6—31no—
259C2×Dic6—61no—
260C3×M16—62no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—32no—
264C2×C3×C8—62no—
265C3×C4⋊C4—31no—
266C3×C4⋊C4—31no—
267C3×C4⋊C4—32no—
268C3×C4⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C42—61no—
271#217—21no—
272#217—62no—
273#217—62no—
274#217—64no—
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—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D312yes—
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—62no—
291Dic3⋊C4—62no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294Dic3⋊C4—64no—
295C4×Dic3—21no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298#208—22no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8C22×D312yes—
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D311yescharacteristic
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32#12312yes—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—22no—
311C2×C3⋊D3—22no—
312C2×C3⋊D3—22no—
313C32×C4—41no—
314C32×C4#12312yes—
315C32×C4C2×#4111yescharacteristic
316C32×C4C2×#4111yescharacteristic
317C3⋊Dic3—22no—
318C3⋊Dic3—42no—
319C3×Dic3—41no—
320C3×Dic3—42no—
321C3×Dic3—41no—
322C2×#41—91no—
323C2×#41D3211yescharacteristic
324C2×M16—31no—
325C22×C8—31no—
326C22⋊Q8—92no—
327C22⋊Q8—181no—
328#121—92no—
329#121—181no—
330#121—182no—
331C4×Q8—181no—
332C4×D4—181no—
333C4×D4—182no—
334#117—31no—
335#117—92no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—92no—
338C2×C4⋊C4—91no—
339#107—92no—
340#106—92no—
341#106—92no—
342#106—92no—
343#103—31no—
344#103—31no—
345#103—32no—
346#102—31no—
347#102—31no—
348#102—32no—
349C22⋊C8—92no—
350C22⋊C8—92no—
351C23×C3—22no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3D3×D411yescharacteristic
356C23×C3D3×D411yescharacteristic
357C22×D3—32no—
358C22×D3—32no—
359C22×D3—62no—
360C3×Q8—21no—
361C3×Q8—21no—
362C3×Q8—21no—
363C3×Q8—21no—
364C3×Q8—41no—
365C3×Q8—41no—
366C3×D4—21no—
367C3×D4—21no—
368C3×D4—21no—
369C3×D4—21no—
370C3×D4—41no—
371C3×D4—41no—
372C3×D4—44no—
373C3×D4—42no—
374C3×D4—42no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—44no—
383C2×C3×C4—42no—
384C2×C3×C4—42no—
385C2×C3×C4—61no—
386C2×C3×C4—62no—
387C2×C3×C4—61no—
388C2×C3×C4—241no—
389C2×C3×C4#23512yes—
390C2×C3×C4#23512yes—
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4#23712yes—
394C2×C3×C4#23712yes—
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397#67—64no—
398#67—64no—
399#67—124no—
400#67—242no—
401#67—242no—
402#67—244no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—22no—
406C2×Dic3—32no—
407C2×Dic3—32no—
408C2×Dic3—62no—
409C2×Dic3—64no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—81no—
413C2×Dic3—241no—
414C2×Dic3—241no—
415C2×Dic3—242no—
416D12—62no—
417D12—62no—
418D12—122no—
419C4×D3—62no—
420C4×D3—62no—
421C4×D3—62no—
422C4×D3—62no—
423C4×D3—122no—
424C4×D3—122no—
425C4×D3—242no—
426C4×D3—242no—
427Dic6—62no—
428Dic6—62no—
429Dic6—122no—
430C3×C8—61no—
431C3×C8—61no—
432C3×C8—62no—
433C3⋊C8—21no—
434C3⋊C8—21no—
435C3⋊C8—22no—
436C2×C32—22no—
437C2×C32—81no—
438C2×C32C2×#12311yescharacteristic
439C2×C32#57711yescharacteristic
440C2×C32#57711yescharacteristic
441C3⋊D3—42no—
442#41—22no—
443#41—22no—
444#41—182no—
445#41—182no—
446C2×Q8—91no—
447C2×Q8C2×D3211yescharacteristic
448C2×D4—21no—
449C2×D4—92no—
450C2×D4—91no—
451C2×D4—182no—
452C2×D4C2×D3211yescharacteristic
453C22×C4—21no—
454C22×C4—61no—
455C22×C4—92no—
456C22×C4—182no—
457C22×C4—181no—
458C22×C4C2×D3211yescharacteristic
459M16—62no—
460C2×C8—31no—
461C2×C8—31no—
462C2×C8—32no—
463C2×C8—62no—
464C4⋊C4—32no—
465C4⋊C4—31no—
466C4⋊C4—31no—
467C4⋊C4—61no—
468C4⋊C4—92no—
469C4⋊C4—182no—
470C4⋊C4—182no—
471C4⋊C4—181no—
472C22⋊C4—61no—
473C22⋊C4—182no—
474C22⋊C4—182no—
475C22⋊C4—182no—
476C42—61no—
477C42—182no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—22no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3#88312yes—
496C22×C3#88312yes—
497C22×C3C2×D3×D411yescharacteristic
498C22×C3C2×D3×D411yescharacteristic
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—42no—
512C3×C4—41no—
513C3×C4—41no—
514C3×C4—122no—
515C3×C4—121no—
516C3×C4—121no—
517C3×C4#88312yes—
518C3×C4#88312yes—
519C3×C4C2×#23511yescharacteristic
520C3×C4C2×#23511yescharacteristic
521C3×C4C2×#23711yescharacteristic
522C3×C4C2×#23711yescharacteristic
523Dic3—41no—
524Dic3—41no—
525Dic3—42no—
526Dic3—62no—
527Dic3—62no—
528Dic3—122no—
529Dic3—124no—
530Dic3—122no—
531Dic3—122no—
532C32#309911yescharacteristic, complemented, Sylow
533C23—21no—
534C23—92no—
535C23#381111yescharacteristic
536Q8—21no—
537Q8—21no—
538Q8—182no—
539D4—21no—
540D4—21no—
541D4—42no—
542D4—184no—
543D4—182no—
544D4—722no—
545C2×C4—21no—
546C2×C4—42no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—62no—
550C2×C4—92no—
551C2×C4—182no—
552C2×C4—182no—
553C2×C4—182no—
554C2×C4—241no—
555C2×C4—722no—
556C2×C4—721no—
557C2×C4#380412yes—
558C2×C4#380412yes—
559C2×C4#381111yescharacteristic
560C2×C4C22×D3211yescharacteristic
561C8—61no—
562C8—61no—
563C8—62no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—42no—
570C2×C3—82no—
571C2×C3—81no—
572C2×C3—81no—
573C2×C3C2×#88311yescharacteristic
574C2×C3C2×#88311yescharacteristic
575C2×C3#577011yescharacteristic
576C2×C3#577011yescharacteristic
577C2×C3#577511yescharacteristic
578C2×C3#577811yescharacteristic
579D3—122no—
580D3—122no—
581D3—242no—
582C22—21no—
583C22—21no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—182no—
588C22—182no—
589C22—182no—
590C22#6397512yes—
591C22C2×#381111yescharacteristic
592C4—41no—
593C4—122no—
594C4—121no—
595C4—121no—
596C4—182no—
597C4—362no—
598C4#6397512yes—
599C4C2×#380411yescharacteristic
600C4C2×#380411yescharacteristic
601C3—21no—
602C3#7884411yescharacteristic, complemented
603C3#7887511yescharacteristic, complemented
604C2—22no—
605C2—81no—
606C2—362no—
607C2#1059546211yescharacteristic
608C2#1059547311yescharacteristic
609C2C2×#6397511yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radical#10596304C2
hypercenterC2×#41D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594990C2semidirect
3. C3×#5233C2semidirect
4. C3×#5232C2semidirect
5. #10591561C2semidirect
6. #10591553C2semidirect
7. #10591425C2semidirect
8. #10591419C2semidirect
9. #10591131C2semidirect
10. C2×#63573C2semidirect
11. #10591073C2semidirect
50. #5233D3semidirect
51. #5232D3semidirect
532. C32#3099semidirect
602. C3#78844semidirect
603. C3#78875semidirect

Maximal subgroups

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

subgroupindex
#105963042
#105949902
C3×#52332
C3×#52322
#105915612
#105915532
#105914252
#105914192
#105911312
C2×#635732
#105910732
#788753
#788443