Finite Group Databasebeta

← #11899652

Subgroups — #11899652

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic, complemented
2C2×C3×#904C211yesmaximal, characteristic, complemented
3C2×C3×#812C211yesmaximal, characteristic, complemented
4#10590642C212yesmaximal, complemented
5#10590638C212yesmaximal, complemented
6#10590634C212yesmaximal, complemented
7#10590633C212yesmaximal, complemented
8#10590632C214yesmaximal, complemented
9#83894—31nomaximal
10#82009—31nomaximal
11C2×#3828—21no—
12C2×C3×#235—21no—
13C22×C32×C8C2211yescharacteristic
14C2×#3746C2211yescharacteristic, complemented
15#64113—21no—
16#64113—21no—
17#64113C2212yes—
18#64113C2212yescomplemented
19C2×#3745C2211yescharacteristic, complemented
20C2×#3744—21no—
21C2×C3×Dic12C2211yescharacteristic, complemented
22C3×#904—21no—
23C3×#904—21no—
24C3×#904C2212yes—
25C3×#904C2212yescomplemented
26C2×C3×D24C2211yescharacteristic, complemented
27C2×C3×#204—21no—
28C3×#812C2212yescomplemented
29C3×#812C2212yescomplemented
30C2×C3×C3⋊C16C2212yescomplemented
31#63551C2214yescomplemented
32#63549C2214yescomplemented
33#63548C2214yescomplemented
34#63546C2214yescomplemented
35C2×C3×#135—31no—
36C2×#904—31no—
37C2×#904—31no—
38C2×#904—61no—
39C2×#904D311yescharacteristic, complemented
40C2×C3×M32—31no—
41#5195—32no—
42#5194—34no—
43#5193—32no—
44#5179—32no—
45#5147—32no—
46C2×#812D311yescharacteristic, complemented
47#4909—32no—
48#4909—32no—
49#4908—32no—
50#4908—32no—
51#4904—34no—
52C22×C32×C4D411yescharacteristic
53C2×#638—41no—
54#3828—22no—
55#3828—22no—
56#3828—41no—
57#3828—41no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4×C3⋊D3—41no—
60C2×#634—21no—
61C2×C3×#67—41no—
62C3×#235—22no—
63C3×#235—22no—
64C3×#235—41no—
65C3×#235—41no—
66C2×C3×D12—21no—
67C2×C3×C4×D3—41no—
68C2×C3×Dic6—21no—
69C2×C32×C8D411yescharacteristic
70C2×C32×C8D411yescharacteristic
71C2×C32×C8D411yescharacteristic
72C2×C32×C8C2311yescharacteristic
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75#3746—21no—
76#3746C2312yes—
77#3745—21no—
78#3745C2312yes—
79#3744—22no—
80#3744—22no—
81C3×Dic12—21no—
82C3×Dic12C2312yes—
83C3×D24—21no—
84C3×D24C2312yes—
85C3×#204—22no—
86C3×#204—22no—
87C3×C3⋊C16C2314yes—
88#3414—91noSylow
89C2×C3×#41—61no—
90C2×#235—21no—
91C2×#235—62no—
92C2×#235—61no—
93C2×#235—61no—
94C3×#135—32no—
95C3×#135—32no—
96C3×#135—61no—
97C3×#135—61no—
98C2×C3×Q16—31no—
99C2×C3×SD16—61no—
100C2×C3×D8—31no—
101C22×C3×C8—21no—
102C22×C3×C8C2×D311yescharacteristic
103C22×C3×C8C2×D311yescharacteristic
104C2×Dic12—31no—
105C2×Dic12—31no—
106C2×Dic12—61no—
107C2×Dic12C2×D311yescharacteristic, complemented
108#904—21no—
109#904—21no—
110#904—32no—
111#904—32no—
112#904—32no—
113#904—32no—
114#904—62no—
115#904—62no—
116#904—62no—
117#904—62no—
118#904—61no—
119#904—61no—
120#904—61no—
121#904—61no—
122#904C2×D312yes—
123#904C2×D312yescomplemented
124C2×D24—31no—
125C2×D24—31no—
126C2×D24—61no—
127C2×D24C2×D311yescharacteristic, complemented
128C2×#204—21no—
129C2×#204—62no—
130C2×#204—61no—
131C2×#204—61no—
132C3×M32—32no—
133C3×M32—32no—
134C2×C3×C16—32no—
135#829—34no—
136#828—34no—
137#827—34no—
138#826—34no—
139#812C2×D312yescomplemented
140#812C2×D312yescomplemented
141C2×C3⋊C16C2×D312yescomplemented
142Dic24—34no—
143#800—34no—
144#800—34no—
145D48—34no—
146C23×C32D811yescharacteristic
147C22×C3⋊D3—41no—
148C22×C3×D3—41no—
149C2×C32×C4D811yescharacteristic
150C2×C32×C4D811yescharacteristic
151C2×C32×C4D811yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155#638—42no—
156#638—42no—
157C2×C3⋊Dic3—41no—
158C4⋊(C3⋊D3)—22no—
159C4⋊(C3⋊D3)—41no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3—42no—
162#634—22no—
163#634—41no—
164C3×#67—42no—
165C3×#67—42no—
166C2×C3×Dic3—41no—
167C3×D12—22no—
168C3×D12—41no—
169C3×C4×D3—42no—
170C3×C4×D3—42no—
171C3×Dic6—22no—
172C3×Dic6—41no—
173C32×C8C2×D411yescharacteristic
174C32×C8C2×D411yescharacteristic
175C32×C8C2×D411yescharacteristic
176C32×C8C2411yescharacteristic
177C2×#135—31no—
178C2×#135—91no—
179#510—92no—
180#510—92no—
181#509—92no—
182#509—92no—
183#508—94no—
184C2×M32—31no—
185C3×#41—62no—
186C3×#41—62no—
187C3×#41—121no—
188C3×#41—121no—
189C2×C3×Q8—61no—
190C2×C3×D4—61no—
191C2×C3×D4—121no—
192C22×C3×C4—21no—
193C22×C3×C4—121no—
194C22×C3×C4D1211yescharacteristic
195C22×C3×C4#6711yescharacteristic
196C2×#67—41no—
197C2×#67—122no—
198C2×#67—121no—
199C2×#67—121no—
200#235—22no—
201#235—22no—
202#235—41no—
203#235—41no—
204#235—64no—
205#235—64no—
206#235—62no—
207#235—62no—
208#235—62no—
209#235—62no—
210#235—122no—
211#235—122no—
212#235—121no—
213#235—121no—
214#235—121no—
215#235—121no—
216C2×D12—21no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—61no—
220C2×C4×D3—41no—
221C2×C4×D3—122no—
222C2×C4×D3—121no—
223C2×C4×D3—121no—
224C2×Dic6—21no—
225C2×Dic6—62no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C3×Q16—32no—
229C3×Q16—61no—
230C3×SD16—62no—
231C3×SD16—62no—
232C3×D8—32no—
233C3×D8—61no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8D1211yescharacteristic
241C2×C3×C8D1211yescharacteristic
242C2×C3×C8D1211yescharacteristic
243C2×C3×C8#6711yescharacteristic
244C2×C3×C8#6711yescharacteristic
245C2×C3×C8#6711yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C22×D311yescharacteristic
248C2×C3×C8C22×D311yescharacteristic
249C2×C3×C8C22×D311yescharacteristic
250C2×C3×C8C22×D311yescharacteristic
251C2×C3×C8C22×D311yescharacteristic
252Dic12—21no—
253Dic12—32no—
254Dic12—32no—
255Dic12—62no—
256Dic12—62no—
257Dic12—61no—
258Dic12—61no—
259Dic12C22×D312yes—
260D24—21no—
261D24—32no—
262D24—32no—
263D24—62no—
264D24—62no—
265D24—61no—
266D24—61no—
267D24C22×D312yes—
268#204—22no—
269#204—22no—
270#204—64no—
271#204—64no—
272#204—62no—
273#204—62no—
274#204—62no—
275#204—62no—
276C3×C16—34no—
277C3⋊C16C22×D314yes—
278C22×C32—41no—
279C22×C32C2×D811yescharacteristic
280C22×C32C2×D811yescharacteristic
281C22×C32C2×D811yescharacteristic
282C2×C3⋊D3—42no—
283C2×C3⋊D3—82no—
284C2×C3×D3—42no—
285C2×C3×D3—82no—
286C32×C4C2×D811yescharacteristic
287C32×C4C2×D811yescharacteristic
288C32×C4C2×D811yescharacteristic
289C32×C4C22×D411yescharacteristic
290C3⋊Dic3—42no—
291C3×Dic3—42no—
292C2×#41—61no—
293C2×#41—181no—
294#135—32no—
295#135—32no—
296#135—61no—
297#135—61no—
298#135—92no—
299#135—92no—
300#135—181no—
301#135—181no—
302C2×Q16—31no—
303C2×Q16—91no—
304C2×SD16—61no—
305C2×SD16—181no—
306C2×D8—31no—
307C2×D8—91no—
308C22×C8D3211yescharacteristic
309Q32—94no—
310SD32—94no—
311SD32—94no—
312D16—94no—
313M32—32no—
314M32—32no—
315C2×C16—32no—
316C23×C3—21no—
317C23×C3—121no—
318C23×C3D2411yescharacteristic
319C23×C3#21311yescharacteristic
320C22×D3—41no—
321C22×D3—122no—
322C22×D3—121no—
323C22×D3—121no—
324C3×Q8—62no—
325C3×Q8—121no—
326C3×D4—62no—
327C3×D4—122no—
328C3×D4—122no—
329C3×D4—121no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—121no—
337C2×C3×C4—122no—
338C2×C3×C4—122no—
339C2×C3×C4D2411yescharacteristic
340C2×C3×C4D2411yescharacteristic
341C2×C3×C4D2411yescharacteristic
342C2×C3×C4#21311yescharacteristic
343C2×C3×C4#21311yescharacteristic
344C2×C3×C4#21311yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351#67—42no—
352#67—42no—
353#67—124no—
354#67—124no—
355#67—122no—
356#67—122no—
357#67—122no—
358#67—122no—
359C2×Dic3—41no—
360C2×Dic3—122no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363D12—22no—
364D12—41no—
365D12—64no—
366D12—62no—
367D12—62no—
368D12—122no—
369D12—121no—
370D12—121no—
371C4×D3—42no—
372C4×D3—42no—
373C4×D3—124no—
374C4×D3—124no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—122no—
379Dic6—22no—
380Dic6—41no—
381Dic6—64no—
382Dic6—62no—
383Dic6—62no—
384Dic6—122no—
385Dic6—121no—
386Dic6—121no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—21no—
391C3×C8C2×D1211yescharacteristic
392C3×C8C2×D1211yescharacteristic
393C3×C8C2×D1211yescharacteristic
394C3×C8C2×#6711yescharacteristic
395C3×C8C2×#6711yescharacteristic
396C3×C8C2×#6711yescharacteristic
397C3×C8C23×D311yescharacteristic
398C3×C8C23×D311yescharacteristic
399C2×C32—21no—
400C2×C32—21no—
401C2×C32—21no—
402C2×C32C22×D811yescharacteristic
403C3⋊D3—82no—
404C3×D3—82no—
405#41—62no—
406#41—62no—
407#41—121no—
408#41—121no—
409#41—182no—
410#41—182no—
411#41—361no—
412#41—361no—
413C2×Q8—61no—
414C2×Q8—181no—
415C2×D4—61no—
416C2×D4—121no—
417C2×D4—181no—
418C2×D4—361no—
419C22×C4—121no—
420C22×C4—361no—
421C22×C4#62611yescharacteristic
422Q16—32no—
423Q16—61no—
424Q16—92no—
425Q16—181no—
426SD16—62no—
427SD16—62no—
428SD16—182no—
429SD16—182no—
430D8—32no—
431D8—61no—
432D8—92no—
433D8—181no—
434C2×C8#62611yescharacteristic
435C2×C8#62611yescharacteristic
436C2×C8#62611yescharacteristic
437C2×C8C2×D3211yescharacteristic
438C2×C8C2×D3211yescharacteristic
439C2×C8C2×D3211yescharacteristic
440C16—34no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—42no—
447C22×C3—122no—
448C22×C3—242no—
449C22×C3C2×D2411yescharacteristic
450C22×C3C2×D2411yescharacteristic
451C22×C3C2×D2411yescharacteristic
452C22×C3C2×#21311yescharacteristic
453C22×C3C2×#21311yescharacteristic
454C22×C3C2×#21311yescharacteristic
455C2×D3—42no—
456C2×D3—82no—
457C2×D3—124no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—244no—
461C2×D3—242no—
462C2×D3—242no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—122no—
468C3×C4C2×D2411yescharacteristic
469C3×C4C2×D2411yescharacteristic
470C3×C4C2×D2411yescharacteristic
471C3×C4C2×#21311yescharacteristic
472C3×C4C2×#21311yescharacteristic
473C3×C4C2×#21311yescharacteristic
474C3×C4C22×D1211yescharacteristic
475C3×C4C22×#6711yescharacteristic
476Dic3—42no—
477Dic3—124no—
478Dic3—122no—
479Dic3—122no—
480C32#341411yescharacteristic, complemented, Sylow
481C23—121no—
482C23—361no—
483C23#371411yescharacteristic
484Q8—62no—
485Q8—121no—
486Q8—182no—
487Q8—361no—
488D4—62no—
489D4—122no—
490D4—122no—
491D4—121no—
492D4—182no—
493D4—362no—
494D4—362no—
495D4—361no—
496C2×C4—121no—
497C2×C4—122no—
498C2×C4—122no—
499C2×C4—361no—
500C2×C4—362no—
501C2×C4—362no—
502C2×C4#371411yescharacteristic
503C2×C4#371411yescharacteristic
504C2×C4#371411yescharacteristic
505C2×C4C2×#62611yescharacteristic
506C2×C4C2×#62611yescharacteristic
507C2×C4C2×#62611yescharacteristic
508C8C2×#62611yescharacteristic
509C8C2×#62611yescharacteristic
510C8C2×#62611yescharacteristic
511C8C22×D3211yescharacteristic
512C2×C3—22no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—41no—
521C2×C3—41no—
522C2×C3—242no—
523C2×C3C22×D2411yescharacteristic
524C2×C3C22×#21311yescharacteristic
525D3—82no—
526D3—244no—
527D3—242no—
528D3—242no—
529C22—41no—
530C22—122no—
531C22—242no—
532C22—362no—
533C22—722no—
534C22C2×#371411yescharacteristic
535C22C2×#371411yescharacteristic
536C22C2×#371411yescharacteristic
537C4—122no—
538C4—362no—
539C4C2×#371411yescharacteristic
540C4C2×#371411yescharacteristic
541C4C2×#371411yescharacteristic
542C4C22×#62611yescharacteristic
543C3—21no—
544C3#8200911yescharacteristic, complemented
545C3#8389411yescharacteristic, complemented
546C2—21no—
547C2—21no—
548C2—21no—
549C2—242no—
550C2—722no—
551C2C22×#371411yescharacteristic
subgroupG/H
centerC4C2×#3714
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC22×C32×C8C22
socleC2×C32C22×D8
hypercenterC22×C8D32
hypocenterC32#3414
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64113C2semidirect
2. C2×C3×#904C2semidirect
3. C2×C3×#812C2semidirect
4. #10590642C2semidirect
5. #10590638C2semidirect
6. #10590634C2semidirect
7. #10590633C2semidirect
8. #10590632C2semidirect
14. C2×#3746C22semidirect
18. #64113C22semidirect
19. C2×#3745C22semidirect
21. C2×C3×Dic12C22semidirect
25. C3×#904C22semidirect
26. C2×C3×D24C22semidirect
28. C3×#812C22semidirect
29. C3×#812C22semidirect
30. C2×C3×C3⋊C16C22semidirect
31. #63551C22semidirect
32. #63549C22semidirect
33. #63548C22semidirect
34. #63546C22semidirect
39. C2×#904D3semidirect
46. C2×#812D3semidirect
107. C2×Dic12C2×D3semidirect
123. #904C2×D3semidirect
127. C2×D24C2×D3semidirect
139. #812C2×D3semidirect
140. #812C2×D3semidirect
141. C2×C3⋊C16C2×D3semidirect
480. C32#3414semidirect
544. C3#82009semidirect
545. C3#83894semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C2×C3×#9042
C2×C3×#8122
#105906422
#105906382
#105906342
#105906332
#105906322
#838943
#820093