Finite Group Databasebeta

← #11878436

Subgroups — #11878436

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596296C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic
4#10591190C212yesmaximal, complemented
5#10591187C212yesmaximal, complemented
6#10591186C212yesmaximal, complemented
7#10591134C212yesmaximal, complemented
8#10591127C212yesmaximal, complemented
9#10591121C212yesmaximal, complemented
10#83413—31nomaximal
11#78682—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15#64153—21no—
16#64145—21no—
17#64144—21no—
18#64144—21no—
19#64135C2211yescharacteristic
20#64133C2212yes—
21#64133C2212yes—
22C3×#944—21no—
23C3×#936—21no—
24C3×#935—21no—
25C3×#935—21no—
26C3×#926C2211yescharacteristic
27C3×#924C2212yes—
28C3×#924C2212yes—
29C2×C3×#208C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31C2×#3719C2212yes—
32C2×#3719C2212yes—
33C3×#830C2212yes—
34C3×#830C2212yes—
35#63575C2212yes—
36#63573C2212yes—
37#63567C2212yes—
38#63567C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41C3×#536—31no—
42#5825—31no—
43#5825—31no—
44#5825—61no—
45#5825D311yescharacteristic
46C3×#408—31no—
47#5234D311yescharacteristic
48#5228—32no—
49#5137—32no—
50#5116—32no—
51#5052—32no—
52#5051—32no—
53#5050—32no—
54#5045—32no—
55#4996—32no—
56#4739—32no—
57#4739—32no—
58#4723—32no—
59#4723—32no—
60C32×#41—41no—
61C32×#41—41no—
62C2×C32×Q8D411yescharacteristic
63C2×C32×D4D411yescharacteristic
64C2×C32×D4D411yescharacteristic
65C2×C32×D4D411yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—21no—
70C2×#634—21no—
71C2×#634—41no—
72C2×#634—41no—
73C2×#634C2312yes—
74C22×C3×Dic3—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6—41no—
77C2×C3×Dic6—41no—
78C2×C3×Dic6C2312yes—
79#3757—22no—
80#3757—22no—
81#3757—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83#3750—22no—
84#3750—22no—
85C4×C3⋊Dic3—21no—
86C3×#217—22no—
87C3×#217—22no—
88C3×#217—21no—
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—21no—
93C3×#208—41no—
94C2×C3×C3⋊C8—41no—
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2312yes—
97#3719—42no—
98#3719—42no—
99#3202—91noSylow
100C2×C3×#41—21no—
101C2×C3×#41C2×D311yescharacteristic
102C2×C3×#41C2×D311yescharacteristic
103C22×C3×Q8—31no—
104C22×Dic6—31no—
105C22×Dic6—31no—
106C22×Dic6—61no—
107C22×Dic6C2×D311yescharacteristic
108C2×C3×M16—31no—
109C22×C3×C8—31no—
110C3×C4⋊Q8—61no—
111C3×#124—61no—
112C3×#123—61no—
113C3×#123—61no—
114C3×C22⋊Q8—32no—
115C3×C22⋊Q8—32no—
116C3×#117—31no—
117#944—21no—
118#944—62no—
119#944—61no—
120#944—61no—
121C2×#216—32no—
122C2×#216—32no—
123#936—21no—
124#936—62no—
125#936—61no—
126#936—61no—
127#935—21no—
128#935—21no—
129#935—62no—
130#935—62no—
131#935—61no—
132#935—61no—
133#935—61no—
134#935—61no—
135#926—31no—
136#926—31no—
137#926—61no—
138#926C2×D311yescharacteristic
139#924—32no—
140#924—32no—
141#924—32no—
142#924—32no—
143#924—62no—
144#924—62no—
145#924C2×D312yes—
146#924C2×D312yes—
147C2×#208C2×D311yescharacteristic
148C22×C3⋊C8C2×D311yescharacteristic
149C2×Dic12—32no—
150C2×Dic12—32no—
151C3×C22⋊C8—32no—
152C3×C22⋊C8—32no—
153#835—32no—
154#835—32no—
155#830C2×D312yes—
156#830C2×D312yes—
157#818—32no—
158#817—32no—
159#816—32no—
160#816—32no—
161#816—32no—
162#816—32no—
163#810—32no—
164#810—32no—
165#808—32no—
166#807—32no—
167C23×C32C2×D411yescharacteristic
168C23×C32C2×D411yescharacteristic
169C23×C32C2×D411yescharacteristic
170C32×Q8—41no—
171C32×D4—41no—
172C32×D4—41no—
173C32×D4—41no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—42no—
187#634—22no—
188#634—22no—
189#634—42no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—42no—
193C3×Dic6—22no—
194C3×Dic6—22no—
195C3×Dic6—42no—
196C3×C3⋊C8—22no—
197C3×C3⋊C8—22no—
198#536—31no—
199#536—91no—
200#485—92no—
201#485—92no—
202#470—92no—
203#467—92no—
204#451—92no—
205#451—92no—
206#408—31no—
207C3×#41—41no—
208C3×#41—41no—
209C3×#41—41no—
210C3×#41—41no—
211C3×#41—42no—
212C3×#41—42no—
213C2×C3×Q8—21no—
214C2×C3×Q8—32no—
215C2×C3×Q8—61no—
216C2×C3×Q8—121no—
217C2×C3×Q8—121no—
218C2×C3×Q8D1211yescharacteristic
219C2×C3×Q8#6711yescharacteristic
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4D1211yescharacteristic
224C2×C3×D4D1211yescharacteristic
225C2×C3×D4D1211yescharacteristic
226C2×C3×D4#6711yescharacteristic
227C2×C3×D4#6711yescharacteristic
228C2×C3×D4#6711yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×Dic3—21no—
240C22×Dic3—62no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C2×Dic6—21no—
244C2×Dic6—32no—
245C2×Dic6—32no—
246C2×Dic6—41no—
247C2×Dic6—41no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—61no—
251C2×Dic6—61no—
252C2×Dic6—121no—
253C2×Dic6—121no—
254C2×Dic6—121no—
255C2×Dic6—121no—
256C2×Dic6—122no—
257C2×Dic6—122no—
258C2×Dic6C22×D312yes—
259C3×M16—121no—
260C2×C3×C8—32no—
261C2×C3×C8—32no—
262C2×C3×C8—121no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—62no—
265C3×C4⋊C4—62no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—62no—
269C3×C42—61no—
270#217—22no—
271#217—22no—
272#217—21no—
273#217—64no—
274#217—64no—
275#217—62no—
276#217—62no—
277#217—62no—
278#217—61no—
279#217—62no—
280#217—62no—
281#217—61no—
282#216—122no—
283#216—122no—
284C4⋊Dic3—32no—
285C4⋊Dic3—32no—
286C4⋊Dic3—62no—
287C4⋊Dic3C22×D312yes—
288Dic3⋊C4—22no—
289Dic3⋊C4—22no—
290Dic3⋊C4—64no—
291Dic3⋊C4—64no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296C4×Dic3—21no—
297C4×Dic3—62no—
298C4×Dic3—61no—
299C4×Dic3—61no—
300#208—41no—
301C2×C3⋊C8—41no—
302C2×C3⋊C8C22×D312yes—
303C2×C3⋊C8C22×D312yes—
304Dic12—122no—
305Dic12—122no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—22no—
310C22×C32—22no—
311C22×C32—22no—
312C22×C32C22×D411yescharacteristic
313C32×C4—21no—
314C32×C4—21no—
315C32×C4—21no—
316C32×C4H(5,𝔽2)11yescharacteristic
317C32×C4H(5,𝔽2)11yescharacteristic
318C3⋊Dic3—42no—
319C3⋊Dic3—42no—
320C3×Dic3—42no—
321C3×Dic3—42no—
322C2×#41D3211yescharacteristic
323C22×Q8—31no—
324C22×Q8—91no—
325C2×Q16—92no—
326C2×Q16—92no—
327C2×M16—31no—
328C22×C8—31no—
329C4⋊Q8—61no—
330C4⋊Q8—181no—
331#124—61no—
332#124—181no—
333#123—61no—
334#123—61no—
335#123—181no—
336#123—181no—
337C22⋊Q8—32no—
338C22⋊Q8—32no—
339C22⋊Q8—92no—
340C22⋊Q8—92no—
341#117—31no—
342#117—91no—
343#107—92no—
344#106—92no—
345#103—92no—
346#103—92no—
347#103—92no—
348#103—92no—
349C22⋊C8—32no—
350C22⋊C8—32no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3C2×D1211yescharacteristic
355C23×C3C2×D1211yescharacteristic
356C23×C3C2×D1211yescharacteristic
357C23×C3C2×#6711yescharacteristic
358C23×C3C2×#6711yescharacteristic
359C23×C3C2×#6711yescharacteristic
360C3×Q8—41no—
361C3×Q8—41no—
362C3×Q8—42no—
363C3×Q8—62no—
364C3×Q8—62no—
365C3×Q8—122no—
366C3×D4—41no—
367C3×D4—41no—
368C3×D4—41no—
369C3×D4—41no—
370C3×D4—41no—
371C3×D4—41no—
372C3×D4—42no—
373C3×D4—42no—
374C3×D4—42no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—122no—
400C2×C3×C4C2×D1211yescharacteristic
401C2×C3×C4C2×D1211yescharacteristic
402C2×C3×C4C2×D1211yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C2×#6711yescharacteristic
405C2×C3×C4C2×#6711yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—42no—
411C2×Dic3—64no—
412C2×Dic3—64no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—124no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420Dic6—22no—
421Dic6—22no—
422Dic6—42no—
423Dic6—62no—
424Dic6—62no—
425Dic6—62no—
426Dic6—62no—
427Dic6—122no—
428Dic6—122no—
429Dic6—124no—
430Dic6—122no—
431Dic6—122no—
432C3×C8—62no—
433C3×C8—62no—
434C3⋊C8—22no—
435C3⋊C8—22no—
436C2×C32—41no—
437C2×C32—41no—
438C2×C32—41no—
439C2×C32#53411yescharacteristic
440C2×C32#57812yes—
441#41—41no—
442#41—41no—
443C2×Q8—32no—
444C2×Q8—61no—
445C2×Q8—92no—
446C2×Q8—121no—
447C2×Q8—121no—
448C2×Q8—181no—
449C2×Q8—361no—
450C2×Q8—361no—
451C2×Q8#62611yescharacteristic
452C2×D4#62611yescharacteristic
453C2×D4#62611yescharacteristic
454C2×D4#62611yescharacteristic
455C22×C4—61no—
456C22×C4—181no—
457C22×C4C2×D3211yescharacteristic
458C22×C4C2×D3211yescharacteristic
459C22×C4C2×D3211yescharacteristic
460Q16—362no—
461Q16—362no—
462M16—121no—
463C2×C8—32no—
464C2×C8—32no—
465C2×C8—121no—
466C4⋊C4—32no—
467C4⋊C4—62no—
468C4⋊C4—62no—
469C4⋊C4—92no—
470C4⋊C4—182no—
471C4⋊C4—182no—
472C22⋊C4—61no—
473C22⋊C4—62no—
474C22⋊C4—62no—
475C22⋊C4—181no—
476C22⋊C4—182no—
477C22⋊C4—182no—
478C42—61no—
479C42—181no—
480C22×C3—22no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—21no—
494C22×C3—42no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3C22×D1211yescharacteristic
500C22×C3C22×#6711yescharacteristic
501C3×C4—22no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—41no—
511C3×C4—41no—
512C3×C4—122no—
513C3×C4—122no—
514C3×C4#100411yescharacteristic
515C3×C4#100411yescharacteristic
516C3×C4#100411yescharacteristic
517C3×C4#100411yescharacteristic
518Dic3—42no—
519Dic3—42no—
520Dic3—124no—
521Dic3—124no—
522Dic3—122no—
523Dic3—122no—
524Dic3—122no—
525Dic3—122no—
526C32#320211yescharacteristic, complemented, Sylow
527C23C2×#62611yescharacteristic
528C23C2×#62611yescharacteristic
529C23C2×#62611yescharacteristic
530Q8—41no—
531Q8—62no—
532Q8—62no—
533Q8—122no—
534Q8—182no—
535Q8—182no—
536Q8—362no—
537D4—41no—
538D4—41no—
539D4—41no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—122no—
549C2×C4—182no—
550C2×C4—182no—
551C2×C4—362no—
552C2×C4C2×#62611yescharacteristic
553C2×C4C2×#62611yescharacteristic
554C2×C4C2×#62611yescharacteristic
555C2×C4C22×D3211yescharacteristic
556C8—62no—
557C8—62no—
558C2×C3—22no—
559C2×C3—21no—
560C2×C3—42no—
561C2×C3—41no—
562C2×C3—41no—
563C2×C3—41no—
564C2×C3—41no—
565C2×C3—41no—
566C2×C3—41no—
567C2×C3—81no—
568C2×C3—81no—
569C2×C3#549311yescharacteristic
570C2×C3#575312yes—
571C2×C3#580411yescharacteristic
572C2×C3#583812yes—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22C22×#62611yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—122no—
584C4—122no—
585C4—362no—
586C4—362no—
587C4#6433011yescharacteristic
588C4#6433011yescharacteristic
589C3—21no—
590C3#7868211yescharacteristic, complemented
591C3#8341311yescharacteristic, complemented
592C2—41no—
593C2—41no—
594C2—41no—
595C2#1059545012yes—
596C2#1059551911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3202
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591190C2semidirect
5. #10591187C2semidirect
6. #10591186C2semidirect
7. #10591134C2semidirect
8. #10591127C2semidirect
9. #10591121C2semidirect
526. C32#3202semidirect
590. C3#78682semidirect
591. C3#83413semidirect

Maximal subgroups

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

subgroupindex
#105962962
C3×#58252
C3×#52342
#105911902
#105911872
#105911862
#105911342
#105911272
#105911212
#834133
#786823