Finite Group Databasebeta

← #11787700

Subgroups — #11787700

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 575 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic
2#10594990C211yesmaximal, characteristic
3#10591213C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic
5#10591107C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#69004—31nomaximal
9#68775—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64118—22no—
14#64118C414yescomplemented
15C2×#3746—21no—
16C2×#3744—21no—
17C3×#926C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63952—22no—
22#63900—21no—
23#63894—21no—
24#63849—21no—
25#63844—21no—
26#63579—22no—
27#63570—22no—
28#63567—21no—
29#63567—21no—
30C2×#909—31no—
31C2×#909—31no—
32C2×#909—61no—
33#5523—31no—
34#5504—31no—
35C2×#825—31no—
36#5120—31no—
37#5004—31no—
38#4973—31no—
39#4929—31no—
40C2×#805—31no—
41C3×#343—31no—
42C3×#339—31no—
43#4555D311yescharacteristic, complemented
44#4554D311yescharacteristic, complemented
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48#3828—21no—
49#3828—21no—
50#3828C2×C412yes—
51#3828D412yes—
52C2×C4⋊(C3⋊D3)D411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634C2×C412yescomplemented
60C2×#634D411yescharacteristic
61C22×C3×Dic3—21no—
62C22×C3×Dic3D412yes—
63C2×#624—22no—
64C32×M16—21no—
65C32×M16C2×C412yescomplemented
66C2×C32×C8—21no—
67#3746—24no—
68#3744—24no—
69C3×#217—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3D411yescharacteristic
73C3×C4⋊Dic3D411yescharacteristic
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×#208—21no—
78C3×#208—21no—
79C2×C3×C3⋊C8—21no—
80#3724—22no—
81#3722—22no—
82Dic32—22no—
83#1882—91noSylow
84C2×#235—31no—
85C2×#235—31no—
86C2×#235—61no—
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C2×C3×M16—21no—
91C2×C3×M16—31no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C3×#117—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C42—31no—
97C4×#67—62no—
98#926C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4×Dic3C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102#909—34no—
103#909—34no—
104#909—64no—
105#909—62no—
106#909—62no—
107#909—64no—
108C2×Dic12—61no—
109C2×Dic12—61no—
110C2×Dic12—62no—
111C2×#204—61no—
112C2×#204—61no—
113C2×#204—62no—
114#893—61no—
115#892—61no—
116#892—61no—
117D3×C4⋊C4—61no—
118D3×C4⋊C4—61no—
119#887—61no—
120#67⋊C4—62no—
121C4×D12—61no—
122C4×Dic6—61no—
123C3⋊#95—62no—
124C3⋊#95—62no—
125#825—62no—
126#816—61no—
127#816—61no—
128#810—61no—
129#810—61no—
130#805—62no—
131C23×C32C2×D411yescharacteristic
132C22×C3⋊D3—21no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139#638—22no—
140#638—22no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—41no—
145C4⋊(C3⋊D3)—21no—
146C4⋊(C3⋊D3)C22⋊C412yes—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149#634—22no—
150#634—21no—
151#634—22no—
152#634—41no—
153#634—41no—
154#634C22⋊C412yes—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—42no—
162#624—82no—
163C32×C8—22no—
164C3×C3⋊C8—41no—
165C2×#137—91no—
166#520—91no—
167C2×#104—91no—
168#419—91no—
169#391—91no—
170#343—31no—
171#339—31no—
172C22×C3×C4—21no—
173C22×C3×C4—32no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—121no—
180C22×Dic3—21no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—121no—
184C22×Dic3D1212yes—
185#235—32no—
186#235—32no—
187#235—32no—
188#235—32no—
189#235—62no—
190#235—62no—
191#235—61no—
192#235—61no—
193#235—61no—
194#235—61no—
195#235—121no—
196#235—121no—
197C2×D12—31no—
198C2×D12—31no—
199C2×D12—61no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—121no—
205C2×Dic6—31no—
206C2×Dic6—31no—
207C2×Dic6—32no—
208C2×Dic6—32no—
209C2×Dic6—61no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6—62no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—121no—
224C2×Dic6—121no—
225C2×Dic6—121no—
226C3×M16—22no—
227C3×M16—21no—
228C3×M16—21no—
229C3×M16—22no—
230C3×M16—61no—
231C3×M16—61no—
232C3×M16C4×D312yescomplemented
233C3×M16C4×D312yescomplemented
234C2×C3×C8—22no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—61no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C22⋊C4—61no—
243C3×C42—61no—
244C3×C42—61no—
245C3×C42—61no—
246#217—21no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251C4⋊Dic3D1211yescharacteristic
252C4⋊Dic3D1211yescharacteristic
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255C4×Dic3—21no—
256C4×Dic3—21no—
257C4×Dic3—21no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260#208—21no—
261#208—21no—
262C2×C3⋊C8—21no—
263Dic12—64no—
264Dic12—64no—
265Dic12—68no—
266#204—64no—
267#204—64no—
268#204—68no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32C4×D411yescharacteristic
272C22×C32#12011yescharacteristic
273C22×C32#12111yescharacteristic
274C2×C3⋊D3—22no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C32×C4C2×C22⋊C411yescharacteristic
278C32×C4C4×D411yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4#12311yescharacteristic
281C3⋊Dic3—22no—
282C3⋊Dic3—42no—
283C3×Dic3—42no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C2×#41—91no—
288C22×Q8—91no—
289#137—94no—
290#137—182no—
291C2×Q16—181no—
292C2×SD16—181no—
293C2×M16—31no—
294C2×M16D3211yescharacteristic
295C4×Q8—181no—
296C4×D4—181no—
297C4×D4—182no—
298#117—31no—
299#117—181no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—181no—
302C2×C42—31no—
303#104—182no—
304#103—181no—
305#103—181no—
306#95—182no—
307C23×C3—21no—
308C23×C3C2×D1211yescharacteristic
309C23×C3D3×D411yescharacteristic
310C22×D3—61no—
311C22×D3—61no—
312C22×D3—121no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—62no—
322C2×C3×C4—61no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4—122no—
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4#23511yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4#23911yescharacteristic
337C2×C3×C4#23911yescharacteristic
338#67—62no—
339#67—62no—
340#67—62no—
341#67—62no—
342#67—122no—
343#67—122no—
344C2×Dic3—22no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—22no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—42no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—122no—
356C2×Dic3—121no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363D12—32no—
364D12—32no—
365D12—62no—
366D12—61no—
367D12—61no—
368D12—121no—
369C4×D3—62no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—122no—
374C4×D3—122no—
375C4×D3—242no—
376C4×D3—242no—
377Dic6—32no—
378Dic6—32no—
379Dic6—62no—
380Dic6—61no—
381Dic6—61no—
382Dic6—64no—
383Dic6—62no—
384Dic6—62no—
385Dic6—62no—
386Dic6—62no—
387Dic6—122no—
388Dic6—121no—
389Dic6—122no—
390Dic6—122no—
391Dic6—121no—
392Dic6—121no—
393Dic6—121no—
394Dic6—121no—
395C3×C8—24no—
396C3×C8—22no—
397C3×C8—22no—
398C3×C8—121no—
399C3⋊C8—41no—
400C2×C32—21no—
401C2×C32—21no—
402C2×C32#38611yescharacteristic
403C2×C32#45511yescharacteristic
404C2×C32#45611yescharacteristic
405C3⋊D3—42no—
406#41—92no—
407#41—92no—
408#41—181no—
409#41—181no—
410C2×Q8—92no—
411C2×Q8—91no—
412C2×Q8—181no—
413C2×Q8—181no—
414C2×Q8—181no—
415C2×Q8—181no—
416C2×Q8—181no—
417C2×D4—91no—
418C2×D4—181no—
419C22×C4—32no—
420C22×C4—61no—
421C22×C4—182no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4C2×D3211yescharacteristic
425Q16—184no—
426SD16—184no—
427M16—21no—
428M16—61no—
429M16—61no—
430M16#62412yescomplemented
431C2×C8—21no—
432C2×C8—61no—
433C4⋊C4—31no—
434C4⋊C4—31no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C4⋊C4—182no—
438C22⋊C4—61no—
439C22⋊C4—182no—
440C42—61no—
441C42—61no—
442C42—61no—
443C42—182no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3C4×D1211yescharacteristic
454C22×C3#88211yescharacteristic
455C22×C3#88211yescharacteristic
456C22×C3#88411yescharacteristic
457C22×C3#89311yescharacteristic
458C22×C3#89511yescharacteristic
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—122no—
462C2×D3—121no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—241no—
467C2×D3—241no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—122no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4—122no—
476C3×C4C4×D1211yescharacteristic
477C3×C4D3×C22⋊C411yescharacteristic
478C3×C4D3×C22⋊C411yescharacteristic
479C3×C4#88411yescharacteristic
480C3×C4#89311yescharacteristic
481C3×C4#89411yescharacteristic
482C3×C4#89411yescharacteristic
483C3×C4#89511yescharacteristic
484Dic3—42no—
485Dic3—42no—
486Dic3—41no—
487Dic3—41no—
488Dic3—62no—
489Dic3—62no—
490Dic3—122no—
491Dic3—124no—
492Dic3—122no—
493Dic3—122no—
494C32#188211yescharacteristic, complemented, Sylow
495C23—181no—
496C23D3×D1211yescharacteristic
497Q8—92no—
498Q8—181no—
499Q8—182no—
500Q8—182no—
501Q8—361no—
502Q8—361no—
503D4—92no—
504D4—182no—
505D4—182no—
506D4—181no—
507C2×C4—62no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—122no—
514C2×C4—181no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—361no—
519C2×C4—361no—
520C2×C4—722no—
521C2×C4#379911yescharacteristic
522C2×C4#379911yescharacteristic
523C2×C4D3×D1211yescharacteristic
524C2×C4C2×#62411yescharacteristic
525C2×C4#381111yescharacteristic
526C2×C4#381111yescharacteristic
527C8—22no—
528C8—121no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—41no—
537C2×C3—41no—
538C2×C3#466511yescharacteristic
539C2×C3#466511yescharacteristic
540C2×C3#474611yescharacteristic
541C2×C3#475211yescharacteristic
542C2×C3#482511yescharacteristic
543C2×C3#482611yescharacteristic
544D3—122no—
545D3—122no—
546D3—242no—
547C22—21no—
548C22—21no—
549C22—182no—
550C22—361no—
551C22—361no—
552C22#6389411yescharacteristic
553C22#6391011yescharacteristic
554C22#6392311yescharacteristic
555C4—122no—
556C4—122no—
557C4—121no—
558C4—121no—
559C4—182no—
560C4—362no—
561C4#6389411yescharacteristic
562C4#6389711yescharacteristic
563C4#6391011yescharacteristic
564C4#6397411yescharacteristic
565C3—21no—
566C3#6877511yescharacteristic, complemented
567C3#6900411yescharacteristic, complemented
568C2—21no—
569C2—21no—
570C2—362no—
571C2#1059101611yescharacteristic
572C2#1059102111yescharacteristic
573C2#1059138011yescharacteristic
subgroupG/H
centerC22#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1882
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #10591213C2semidirect
5. #10591107C2semidirect
6. C3×#4555C2semidirect
7. C3×#4554C2semidirect
14. #64118C4semidirect
43. #4555D3semidirect
44. #4554D3semidirect
59. C2×#634C2×C4semidirect
65. C32×M16C2×C4semidirect
232. C3×M16C4×D3semidirect
233. C3×M16C4×D3semidirect
430. M16#624semidirect
494. C32#1882semidirect
566. C3#68775semidirect
567. C3#69004semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105949902
#105912132
C2×#635702
#105911072
C3×#45552
C3×#45542
#690043
#687753