Finite Group Databasebeta

← #11787681

Subgroups — #11787681

Order 1152.

743 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594986C211yesmaximal, characteristic
2C2×#63831C211yesmaximal, characteristic
3#10592819C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic
5#10591213C211yesmaximal, characteristic, complemented
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70365—31nomaximal
9#69004—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17Dic3×#67—22no—
18#63898—21no—
19D3×C4⋊Dic3—21no—
20#63843—21no—
21#63841—21no—
22C2×#3719—21no—
23#63831—22no—
24#63831C414yescomplemented
25C2×#3716—21no—
26#63643—21no—
27#63643—21no—
28C3×#825—22no—
29#63579—22no—
30#5827—31no—
31C2×#951—31no—
32C2×#909—31no—
33#5504—31no—
34C2×C3×#104—31no—
35C2×#825D311yescharacteristic
36#5120—31no—
37#5120—31no—
38#5120—61no—
39#4973—31no—
40#4929—31no—
41C3×#343—31no—
42#4555—31no—
43#4554D311yescharacteristic, complemented
44#4523—31no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634C2×C412yescomplemented
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235C2×C412yes—
59C3×#235D412yes—
60C2×C3×D12D411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6D411yescharacteristic
63C2×D3×Dic3—22no—
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67#3757—21no—
68C4⋊(C3⋊Dic3)D411yescharacteristic
69C4⋊(C3⋊Dic3)D411yescharacteristic
70C4×C3⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C3×#208—21no—
76C3×#208C2×C412yescomplemented
77C2×C3×C3⋊C8—21no—
78Dic3⋊Dic3—22no—
79(C2×D3)⋊Dic3—22no—
80Dic32—22no—
81#3719—24no—
82#3716—24no—
83#1882—91noSylow
84C2×C3×#41—31no—
85C2×#235C2×D311yescharacteristic
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—61no—
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16C2×D311yescharacteristic
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×C4⋊C4—31no—
94C2×C3×C42—31no—
95#951—34no—
96#951—62no—
97Q8×Dic3—61no—
98C2×#216—61no—
99D4×Dic3—61no—
100D4×Dic3—62no—
101C2×#214—61no—
102C4×#67—62no—
103#926—31no—
104#926—31no—
105#926—61no—
106#926—61no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×C4×Dic3C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111#909—34no—
112#909—62no—
113C2×Dic12—61no—
114C2×#204—61no—
115#893—61no—
116#892—61no—
117D3×C4⋊C4—61no—
118#887—61no—
119C3×#104—62no—
120C3⋊#95—62no—
121C3⋊#95—62no—
122#825—22no—
123#816—61no—
124#816—61no—
125#816—61no—
126#816—61no—
127#816—62no—
128#816—62no—
129C23×C32C2×D411yescharacteristic
130C22×C3×D3—21no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142#634—22no—
143#634—22no—
144#634—41no—
145#634—41no—
146C3×#67—22no—
147C3×#67—22no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—42no—
154C3×D12—21no—
155C3×D12C22⋊C412yes—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×Dic6—21no—
159C3×Dic6C22⋊C412yes—
160D3×Dic3—82no—
161C32×C8—41no—
162C3×C3⋊C8—22no—
163C2×#137—91no—
164#520—91no—
165C2×#104—31no—
166#419—91no—
167#391—91no—
168#343—31no—
169#339—91no—
170C3×#41—32no—
171C3×#41—32no—
172C3×#41—61no—
173C3×#41—61no—
174C2×C3×Q8—31no—
175C2×C3×D4—31no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—32no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—21no—
184C22×Dic3—21no—
185C22×Dic3—62no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—121no—
189C22×Dic3D1212yes—
190#235—21no—
191#235—21no—
192#235C4×D312yes—
193#235#6712yes—
194C2×D12D1211yescharacteristic
195C2×C4×D3—21no—
196C2×C4×D3—62no—
197C2×Dic6—32no—
198C2×Dic6—32no—
199C2×Dic6—62no—
200C2×Dic6—62no—
201C2×Dic6—62no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—121no—
213C2×Dic6—121no—
214C2×Dic6—121no—
215C2×Dic6D1211yescharacteristic
216C3×M16—21no—
217C3×M16—21no—
218C3×M16—21no—
219C3×M16—21no—
220C3×M16—32no—
221C3×M16—41no—
222C3×M16—41no—
223C3×M16—61no—
224C2×C3×C8—22no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—61no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C42—61no—
231C3×C42—61no—
232#217—62no—
233#217—61no—
234#217—61no—
235#217—121no—
236#216—64no—
237#214—64no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248Dic3⋊C4—62no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—121no—
256#208—21no—
257#208C4×D312yescomplemented
258C2×C3⋊C8—21no—
259Dic12—64no—
260#204—64no—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32C4×D411yescharacteristic
264C22×C32#12011yescharacteristic
265C22×C32#12111yescharacteristic
266C2×C3×D3—22no—
267C2×C3×D3—41no—
268C2×C3×D3—41no—
269C32×C4C2×C22⋊C411yescharacteristic
270C32×C4C4×D411yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12311yescharacteristic
273C3⋊Dic3—42no—
274C3⋊Dic3—41no—
275C3⋊Dic3—41no—
276C3×Dic3—22no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C2×#41—31no—
280C22×Q8—91no—
281#137—94no—
282#137—182no—
283C2×Q16—181no—
284C2×SD16—181no—
285C2×M16—31no—
286C2×M16D3211yescharacteristic
287C4×Q8—181no—
288C4×D4—181no—
289C4×D4—182no—
290#117—91no—
291#117—181no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—181no—
294C2×C42—31no—
295#104—62no—
296#103—181no—
297#103—181no—
298#95—182no—
299C23×C3—21no—
300C23×C3—61no—
301C23×C3C2×D1211yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—21no—
304C3×Q8—32no—
305C3×Q8—61no—
306C3×D4—32no—
307C3×D4—62no—
308C3×D4—62no—
309C3×D4—61no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—61no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—122no—
324C2×C3×C4C2×C4×D311yescharacteristic
325C2×C3×C4C2×C4×D311yescharacteristic
326C2×C3×C4C2×D1211yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4#23911yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336#67—22no—
337#67—22no—
338C2×Dic3—21no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—42no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—122no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—122no—
354C2×Dic3—122no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—242no—
360D12—21no—
361D12(C2×D3)⋊C412yes—
362C4×D3—22no—
363C4×D3—22no—
364C4×D3—242no—
365Dic6—21no—
366Dic6—64no—
367Dic6—62no—
368Dic6—62no—
369Dic6—62no—
370Dic6—62no—
371Dic6—122no—
372Dic6—122no—
373Dic6—122no—
374Dic6—121no—
375Dic6—121no—
376Dic6—121no—
377Dic6—121no—
378Dic6(C2×D3)⋊C412yes—
379C3×C8—42no—
380C3×C8—41no—
381C3×C8—41no—
382C3×C8—62no—
383C3⋊C8—22no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32#38611yescharacteristic
387C2×C32#45511yescharacteristic
388C2×C32#45611yescharacteristic
389C3×D3—42no—
390#41—32no—
391#41—32no—
392#41—61no—
393#41—61no—
394C2×Q8—31no—
395C2×Q8—92no—
396C2×Q8—181no—
397C2×Q8—181no—
398C2×Q8—181no—
399C2×Q8—181no—
400C2×Q8—181no—
401C2×D4—31no—
402C2×D4—61no—
403C22×C4—32no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—182no—
407C22×C4—181no—
408C22×C4C2×D3211yescharacteristic
409Q16—184no—
410SD16—184no—
411M16—21no—
412M16—21no—
413M16—32no—
414M16—61no—
415C2×C8—21no—
416C2×C8—61no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—91no—
420C4⋊C4—91no—
421C4⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—181no—
424C42—61no—
425C42—61no—
426C42—182no—
427C42—181no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—62no—
438C22×C3—121no—
439C22×C3—121no—
440C22×C3C4×D1211yescharacteristic
441C22×C3#67⋊C411yescharacteristic
442C22×C3#88211yescharacteristic
443C22×C3#88211yescharacteristic
444C22×C3#89511yescharacteristic
445C22×C3#93911yescharacteristic
446C2×D3—22no—
447C2×D3—41no—
448C2×D3—41no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—62no—
454C3×C4—122no—
455C3×C4—122no—
456C3×C4D3×C22⋊C411yescharacteristic
457C3×C4#67⋊C411yescharacteristic
458C3×C4#88411yescharacteristic
459C3×C4#88611yescharacteristic
460C3×C4#89311yescharacteristic
461C3×C4#89411yescharacteristic
462C3×C4C2×(C2×D3)⋊C411yescharacteristic
463C3×C4#93911yescharacteristic
464Dic3—22no—
465Dic3—42no—
466Dic3—42no—
467Dic3—124no—
468Dic3—122no—
469Dic3—122no—
470Dic3—121no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474Dic3—241no—
475Dic3—241no—
476C32#188211yescharacteristic, complemented, Sylow
477C23—61no—
478C23D3×D1211yescharacteristic
479Q8—32no—
480Q8—61no—
481Q8—182no—
482Q8—182no—
483Q8—361no—
484Q8—361no—
485D4—32no—
486D4—62no—
487D4—62no—
488D4—61no—
489C2×C4—61no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—122no—
497C2×C4—182no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4—722no—
503C2×C4#379611yescharacteristic
504C2×C4C4×D3211yescharacteristic
505C2×C4D3×D1211yescharacteristic
506C2×C4#380411yescharacteristic
507C2×C4D3×#6711yescharacteristic
508C2×C4#381111yescharacteristic
509C8—41no—
510C8—62no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—41no—
519C2×C3—41no—
520C2×C3—122no—
521C2×C3#466511yescharacteristic
522C2×C3#474611yescharacteristic
523C2×C3#475211yescharacteristic
524C2×C3#482511yescharacteristic
525C2×C3#482611yescharacteristic
526C2×C3#495811yescharacteristic
527D3—42no—
528C22—21no—
529C22—21no—
530C22—62no—
531C22—121no—
532C22—121no—
533C22#6388011yescharacteristic
534C22#6388611yescharacteristic
535C22#6392311yescharacteristic
536C4—62no—
537C4—122no—
538C4—122no—
539C4—361no—
540C4—361no—
541C4—362no—
542C4#6388111yescharacteristic
543C4#6389011yescharacteristic
544C4D3×(C2×D3)⋊C411yescharacteristic
545C4#6397111yescharacteristic
546C3—21no—
547C3#6900411yescharacteristic, complemented
548C3#7036511yescharacteristic, complemented
549C2—21no—
550C2—21no—
551C2—122no—
552C2#1059101611yescharacteristic
553C2#1059102111yescharacteristic
554C2#1059136411yescharacteristic
subgroupG/H
centerC22#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×C3×#235C22
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. #10592819C2semidirect
5. #10591213C2semidirect
6. C3×#4554C2semidirect
7. #10589162C2semidirect
24. #63831C4semidirect
43. #4554D3semidirect
52. C2×#634C2×C4semidirect
76. C3×#208C2×C4semidirect
257. #208C4×D3semidirect
476. C32#1882semidirect
547. C3#69004semidirect
548. C3#70365semidirect

Maximal subgroups

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

subgroupindex
#105949862
C2×#638312
#105928192
C2×C3×#8252
#105912132
C3×#45542
#105891622
#703653
#690043