Finite Group Databasebeta

← #11792374

Subgroups — #11792374

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5748C211yesmaximal, characteristic
2#10594855C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic, complemented
4C3×#5120C211yesmaximal, characteristic, complemented
5#10591231C211yesmaximal, characteristic, complemented
6#10591111C211yesmaximal, characteristic, complemented
7#10589422C211yesmaximal, characteristic, complemented
8#72120—31nomaximal
9#70351—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C3×#909—21no—
18C3×#909—21no—
19C3×#908—21no—
20C3×#908—21no—
21C3×#904—22no—
22#63961—22no—
23#63873—21no—
24#63863—21no—
25#63856—22no—
26C2×#3718—21no—
27#63827—22no—
28#63827—22no—
29C2×#3715—21no—
30C3×#816—22no—
31#63580—22no—
32#63569—22no—
33C3×#575—31no—
34#5825—31no—
35C2×#951—31no—
36#5816—31no—
37C2×#942—31no—
38#5748D311yescharacteristic
39C3×#419—31no—
40#5240—31no—
41#5236—31no—
42#5120D311yescharacteristic, complemented
43#5006—31no—
44#5005—31no—
45#4556—31no—
46#4556—31no—
47#4556—61no—
48C22×C32×C4C2311yescharacteristic
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C2×C3×D12D411yescharacteristic
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6D412yes—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6D411yescharacteristic
72C32×M16—21no—
73C32×M16—21no—
74C2×C32×C8D412yes—
75#3757D412yes—
76C4⋊(C3⋊Dic3)—21no—
77C4×C3⋊Dic3—21no—
78#3748—21no—
79#3748D412yes—
80C2×C3⋊(C3⋊C8)—21no—
81C3×#217—21no—
82C3×C4⋊Dic3—21no—
83C3×C4×Dic3—21no—
84C3×Dic12—22no—
85C3×D24—22no—
86C3×#204—22no—
87C3×#204—22no—
88#3724—24no—
89(C2×D3)⋊Dic3—24no—
90#3718—24no—
91#3715—24no—
92#2009—91noSylow
93C2×C3×#41—31no—
94C2×C3×#41—31no—
95C22×C3×Q8—31no—
96C2×#235C2×D311yescharacteristic
97C2×#235C2×D311yescharacteristic
98C22×Dic6C2×D311yescharacteristic
99C3×#137—61no—
100C3×#137—61no—
101C3×AGL(1,ℤ/8)—61no—
102C3×AGL(1,ℤ/8)—61no—
103C3×#135—62no—
104C2×C3×M16—21no—
105C2×C3×M16C2×D311yescharacteristic
106C2×C3×M16C2×D311yescharacteristic
107C3×#117—31no—
108#951—62no—
109#951—62no—
110#947—61no—
111#946—62no—
112#944—61no—
113#944—61no—
114C2×#216—61no—
115C2×#216—61no—
116#942—62no—
117#942—62no—
118C2×#215—61no—
119#936—61no—
120#935—62no—
121C2×#214—61no—
122#929—62no—
123#926—31no—
124#926—31no—
125#926—61no—
126#926C2×D311yescharacteristic
127#924—62no—
128C2×#208—31no—
129C2×#208—31no—
130C2×#208—61no—
131#909—21no—
132#909—21no—
133#908—21no—
134#908—21no—
135#904—22no—
136C3×#103—62no—
137#837—62no—
138#834—62no—
139#816—22no—
140#806—62no—
141#805—62no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—21no—
144C22×C3×D3—21no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C3⋊Dic3—22no—
152C3×#67—41no—
153C3×#67—41no—
154C3×#67—41no—
155C3×#67—41no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—41no—
162C3×D12—21no—
163C3×D12—21no—
164C3×D12—21no—
165C3×D12—21no—
166C3×C4×D3—41no—
167C3×C4×D3—41no—
168C3×C4×D3—41no—
169C3×C4×D3—41no—
170C3×Dic6—22no—
171C3×Dic6—21no—
172C3×Dic6—21no—
173C3×Dic6—21no—
174C3×Dic6—22no—
175C3×Dic6—21no—
176C3×Dic6—41no—
177C3×Dic6—41no—
178C32×C8—22no—
179C3⋊(C3⋊C8)—22no—
180#575—31no—
181C2×#137—91no—
182#536—91no—
183#421—91no—
184#419—31no—
185#410—91no—
186#344—91no—
187C3×#41—61no—
188C3×#41—61no—
189C3×#41—61no—
190C3×#41—61no—
191C3×#41—61no—
192C3×#41—61no—
193C3×#41—61no—
194C3×#41—61no—
195C2×C3×Q8—32no—
196C2×C3×Q8—31no—
197C2×C3×Q8—31no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×D4—31no—
204C2×C3×D4—31no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C22×C3×C4—21no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—21no—
214C2×#67—21no—
215C22×Dic3—21no—
216#235—21no—
217#235—21no—
218#235—21no—
219#235—21no—
220#235—21no—
221#235—21no—
222#235—21no—
223#235—21no—
224C2×D12#6711yescharacteristic
225C2×D12#6711yescharacteristic
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×Dic6—21no—
229C2×Dic6—21no—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6D1212yes—
234C2×Dic6#6711yescharacteristic
235C2×Dic6#6711yescharacteristic
236C3×Q16—62no—
237C3×SD16—62no—
238C3×SD16—62no—
239C3×D8—62no—
240C3×M16—21no—
241C3×M16—21no—
242C3×M16—21no—
243C3×M16—21no—
244C3×M16—41no—
245C3×M16—41no—
246C2×C3×C8—22no—
247C2×C3×C8#6712yes—
248C2×C3×C8#6712yes—
249C3×C4⋊C4—61no—
250C3×C22⋊C4—61no—
251C3×C42—61no—
252#217—21no—
253#217—32no—
254#217—32no—
255#217—62no—
256#217—64no—
257#216—64no—
258#216—64no—
259#215—64no—
260#214—64no—
261(C2×D3)⋊C4—64no—
262C4⋊Dic3—21no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—121no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268C4×Dic3—21no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—121no—
272#208—32no—
273#208—32no—
274#208—62no—
275#208—61no—
276#208—61no—
277#208—121no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—61no—
280C2×C3⋊C8—121no—
281Dic12—22no—
282D24—22no—
283#204—22no—
284#204—22no—
285C22×C32—41no—
286C22×C32#12011yescharacteristic
287C22×C32#12111yescharacteristic
288C22×C32#12711yescharacteristic
289C2×C3×D3—42no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—81no—
293C32×C4#12011yescharacteristic
294C32×C4#12011yescharacteristic
295C32×C4#12111yescharacteristic
296C32×C4#12111yescharacteristic
297C3⋊Dic3—42no—
298C3×Dic3—42no—
299C3×Dic3—41no—
300C3×Dic3—41no—
301C3×Dic3—81no—
302C2×#41—31no—
303C2×#41—31no—
304C22×Q8—31no—
305#137—61no—
306#137—61no—
307#137—182no—
308#137—182no—
309AGL(1,ℤ/8)—61no—
310AGL(1,ℤ/8)—61no—
311#135—62no—
312C2×Q16—181no—
313C2×SD16—181no—
314C2×M16—91no—
315C2×M16D3211yescharacteristic
316C4⋊Q8—181no—
317#124—181no—
318#123—182no—
319C22⋊Q8—182no—
320#117—31no—
321#117—91no—
322#104—182no—
323#103—62no—
324#99—182no—
325C23×C3—21no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3D3×D411yescharacteristic
329C23×C3D3×D411yescharacteristic
330C22×D3—21no—
331C22×D3—21no—
332C3×Q8—61no—
333C3×Q8—61no—
334C3×Q8—62no—
335C3×Q8—61no—
336C3×Q8—61no—
337C3×Q8—62no—
338C3×Q8—121no—
339C3×Q8—121no—
340C3×D4—61no—
341C3×D4—61no—
342C3×D4—61no—
343C3×D4—61no—
344C3×D4—121no—
345C3×D4—121no—
346C3×D4—121no—
347C3×D4—121no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—62no—
357C2×C3×C4—121no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4#23511yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376#67—41no—
377#67—41no—
378#67—41no—
379#67—41no—
380C2×Dic3—22no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—41no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—122no—
389D12—21no—
390D12—21no—
391D12—21no—
392D12—21no—
393C4×D3—41no—
394C4×D3—41no—
395C4×D3—41no—
396C4×D3—41no—
397Dic6—22no—
398Dic6—22no—
399Dic6—21no—
400Dic6—21no—
401Dic6—21no—
402Dic6—21no—
403Dic6—41no—
404Dic6—41no—
405C3×C8—22no—
406C3×C8—22no—
407C3×C8—42no—
408C3⋊C8—62no—
409C3⋊C8—62no—
410C3⋊C8—122no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32#39211yescharacteristic
415C3×D3—81no—
416C3×D3—81no—
417#41—61no—
418#41—61no—
419#41—61no—
420#41—61no—
421#41—61no—
422#41—61no—
423#41—61no—
424#41—61no—
425C2×Q8—32no—
426C2×Q8—31no—
427C2×Q8—31no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—61no—
431C2×Q8—61no—
432C2×Q8—61no—
433C2×D4—31no—
434C2×D4—31no—
435C2×D4—61no—
436C2×D4—61no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4C2×D3211yescharacteristic
441Q16—62no—
442Q16—184no—
443SD16—62no—
444SD16—62no—
445SD16—184no—
446D8—62no—
447M16—21no—
448M16—21no—
449M16—92no—
450M16—181no—
451C2×C8—181no—
452C2×C8#62512yes—
453C4⋊C4—61no—
454C4⋊C4—184no—
455C4⋊C4—181no—
456C22⋊C4—61no—
457C22⋊C4—92no—
458C22⋊C4—184no—
459C42—61no—
460C42—181no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—81no—
467C22×C3—122no—
468C22×C3—121no—
469C22×C3—121no—
470C22×C3—241no—
471C22×C3#88211yescharacteristic
472C22×C3#88411yescharacteristic
473C22×C3#93711yescharacteristic
474C22×C3#93911yescharacteristic
475C22×C3#94011yescharacteristic
476C22×C3#94011yescharacteristic
477C2×D3—42no—
478C2×D3—41no—
479C2×D3—41no—
480C2×D3—81no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—121no—
486C3×C4—121no—
487C3×C4—122no—
488C3×C4—241no—
489C3×C4#88211yescharacteristic
490C3×C4#88411yescharacteristic
491C3×C4#93011yescharacteristic
492C3×C4#93711yescharacteristic
493C3×C4#93711yescharacteristic
494C3×C4#93811yescharacteristic
495C3×C4#93911yescharacteristic
496C3×C4#95311yescharacteristic
497Dic3—42no—
498Dic3—41no—
499Dic3—41no—
500Dic3—81no—
501Dic3—122no—
502Dic3—122no—
503Dic3—242no—
504C32#200911yescharacteristic, complemented, Sylow
505C23—61no—
506C23—61no—
507C23#380211yescharacteristic
508Q8—61no—
509Q8—62no—
510Q8—62no—
511Q8—61no—
512Q8—61no—
513Q8—61no—
514Q8—121no—
515Q8—121no—
516D4—61no—
517D4—61no—
518D4—61no—
519D4—61no—
520D4—121no—
521D4—121no—
522D4—121no—
523D4—121no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—61no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4—182no—
535C2×C4#379511yescharacteristic
536C2×C4D3×D1211yescharacteristic
537C2×C4#380211yescharacteristic
538C2×C4C2×#62511yescharacteristic
539C2×C4D3×#6711yescharacteristic
540C2×C4D3×#6711yescharacteristic
541C8—22no—
542C8—182no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—41no—
551C2×C3—41no—
552C2×C3—41no—
553C2×C3—241no—
554C2×C3—241no—
555C2×C3#496011yescharacteristic
556C2×C3#522311yescharacteristic
557D3—81no—
558D3—81no—
559C22—41no—
560C22—122no—
561C22—121no—
562C22—121no—
563C22—241no—
564C22#6388511yescharacteristic
565C22#6391411yescharacteristic
566C22#6392211yescharacteristic
567C4—121no—
568C4—121no—
569C4—122no—
570C4—241no—
571C4—362no—
572C4#6388511yescharacteristic
573C4#6390811yescharacteristic
574C4#6392211yescharacteristic
575C4#6397611yescharacteristic
576C3—21no—
577C3#7035111yescharacteristic, complemented
578C3#7212011yescharacteristic, complemented
579C2—21no—
580C2—21no—
581C2—21no—
582C2—241no—
583C2—241no—
584C2#1059138911yescharacteristic
subgroupG/H
centerC2#10591389
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#392
prime radicalC3×#5748C2
hypercenterC2×M16D32
hypocenterC32#2009
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594855C2semidirect
3. C2×#63827C2semidirect
4. C3×#5120C2semidirect
5. #10591231C2semidirect
6. #10591111C2semidirect
7. #10589422C2semidirect
42. #5120D3semidirect
504. C32#2009semidirect
577. C3#70351semidirect
578. C3#72120semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
#105948552
C2×#638272
C3×#51202
#105912312
#105911112
#105894222
#721203
#703513