Finite Group Databasebeta

← #11786745

Subgroups — #11786745

Order 1152.

657 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594990C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic
3C3×#5121C211yesmaximal, characteristic, complemented
4#10591230C211yesmaximal, characteristic, complemented
5#10591106C211yesmaximal, characteristic
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70681—31nomaximal
9#69003—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63952—22no—
18#63900—21no—
19#63894—21no—
20#63849—21no—
21#63844—21no—
22#63652C414yescomplemented
23C3×#818—21no—
24C3×#817—21no—
25#63579—22no—
26#63567—21no—
27#63564—21no—
28#5523—31no—
29#5504—31no—
30C3×#428—31no—
31C2×#825—31no—
32C2×#825—31no—
33C2×#825—61no—
34#5133—31no—
35#5121D311yescharacteristic, complemented
36#4977—31no—
37#4977—31no—
38#4966—31no—
39C3×#343—31no—
40#4555—31no—
41#4554D311yescharacteristic, complemented
42#4532—31no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45C22×C3⋊Dic3—21no—
46#3828—21no—
47#3828—21no—
48#3828C2×C412yes—
49#3828Q812yes—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634D411yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3D412yes—
55C2×#624—22no—
56C32×M16—21no—
57C32×M16C2×C412yescomplemented
58C2×C32×C8—21no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3C2×C412yescomplemented
61C3×#217—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×C4⋊Dic3D411yescharacteristic
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72#3724—22no—
73#3722—22no—
74Dic32—22no—
75#1860—91noSylow
76C2×#235—31no—
77C2×#235—31no—
78C2×#235—61no—
79C2×C3×M16—21no—
80C2×C3×M16—31no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C3×#117—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C4×#67—62no—
87#926C2×D311yescharacteristic
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—61no—
93C2×#208C2×D311yescharacteristic
94#893—61no—
95#892—61no—
96#892—61no—
97D3×C4⋊C4—61no—
98D3×C4⋊C4—61no—
99#887—61no—
100#67⋊C4—62no—
101C4×D12—61no—
102C4×Dic6—61no—
103C3×#107—61no—
104C3×#106—61no—
105C3⋊#95—62no—
106C3⋊#95—62no—
107#825—34no—
108#825—34no—
109#825—64no—
110#821—61no—
111#818—21no—
112#817—21no—
113#816—61no—
114#810—61no—
115#809—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q811yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124#638—22no—
125#638—22no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)C4⋊C412yes—
132C4×C3⋊D3—22no—
133C4×C3⋊D3—22no—
134#634—21no—
135#634C4⋊C412yes—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—41no—
142#624—82no—
143C32×C8—22no—
144C3×C3⋊C8—41no—
145#520—91no—
146#428—31no—
147C2×#104—91no—
148#417—91no—
149#382—91no—
150#343—31no—
151#339—91no—
152C22×C3×C4—21no—
153C22×C3×C4—32no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C2×#67—61no—
158C2×#67—61no—
159C2×#67—121no—
160C22×Dic3—21no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—121no—
164C22×Dic3D1212yes—
165#235—32no—
166#235—32no—
167#235—32no—
168#235—32no—
169#235—62no—
170#235—62no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—121no—
176#235—121no—
177C2×D12—31no—
178C2×D12—31no—
179C2×D12—61no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3—62no—
183C2×C4×D3—62no—
184C2×C4×D3—121no—
185C2×Dic6—31no—
186C2×Dic6—31no—
187C2×Dic6—61no—
188C3×M16—21no—
189C3×M16—21no—
190C3×M16—22no—
191C3×M16—41no—
192C3×M16—61no—
193C3×M16—61no—
194C3×M16C4×D312yescomplemented
195C3×M16C4×D312yescomplemented
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—41no—
199C2×C3×C8—61no—
200C3×C4⋊C4—31no—
201C3×C4⋊C4—31no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C42—61no—
208#217—21no—
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3#6711yescharacteristic
216C4⋊Dic3#6711yescharacteristic
217Dic3⋊C4—62no—
218Dic3⋊C4—62no—
219C4×Dic3—21no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—62no—
223C4×Dic3—62no—
224C4×Dic3—62no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—121no—
228#208—21no—
229#208—21no—
230C2×C3⋊C8—21no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32C4×D411yescharacteristic
234C22×C32#12011yescharacteristic
235C22×C32C22⋊Q811yescharacteristic
236C2×C3⋊D3—22no—
237C2×C3⋊D3—41no—
238C2×C3⋊D3—41no—
239C32×C4C2×C4⋊C411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4C22⋊Q811yescharacteristic
242C32×C4#12311yescharacteristic
243C3⋊Dic3—22no—
244C3⋊Dic3—42no—
245C3×Dic3—41no—
246C3×Dic3—41no—
247C3×Dic3—42no—
248C3×Dic3—81no—
249C2×#41—91no—
250C2×M16—31no—
251C2×M16D3211yescharacteristic
252C4×Q8—181no—
253C4×D4—181no—
254C4×D4—182no—
255#117—31no—
256#117—181no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—181no—
260C2×C42—91no—
261#107—61no—
262#106—61no—
263#104—94no—
264#103—181no—
265#102—181no—
266#95—182no—
267C23×C3—21no—
268C23×C3C2×D1211yescharacteristic
269C23×C3D3×D411yescharacteristic
270C22×D3—61no—
271C22×D3—61no—
272C22×D3—121no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—62no—
282C2×C3×C4—122no—
283C2×C3×C4—122no—
284C2×C3×C4—121no—
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4#23511yescharacteristic
288C2×C3×C4#23511yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4#23711yescharacteristic
293C2×C3×C4D3×Q811yescharacteristic
294C2×C3×C4D3×Q811yescharacteristic
295C2×C3×C4#23911yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297#67—62no—
298#67—62no—
299#67—62no—
300#67—62no—
301#67—122no—
302#67—122no—
303C2×Dic3—22no—
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—42no—
307C2×Dic3—42no—
308C2×Dic3—41no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321D12—32no—
322D12—32no—
323D12—62no—
324D12—61no—
325D12—61no—
326D12—121no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331C4×D3—122no—
332C4×D3—122no—
333C4×D3—242no—
334C4×D3—242no—
335Dic6—32no—
336Dic6—32no—
337Dic6—62no—
338Dic6—61no—
339Dic6—61no—
340Dic6—121no—
341C3×C8—22no—
342C3×C8—22no—
343C3×C8—42no—
344C3×C8—121no—
345C3⋊C8—41no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32#38511yescharacteristic
349C2×C32#45411yescharacteristic
350C2×C32#45511yescharacteristic
351C3⋊D3—42no—
352#41—92no—
353#41—92no—
354#41—181no—
355#41—181no—
356C2×Q8—91no—
357C2×D4—91no—
358C2×D4—181no—
359C22×C4—32no—
360C22×C4—61no—
361C22×C4—182no—
362C22×C4—181no—
363C22×C4—181no—
364C22×C4C2×D3211yescharacteristic
365M16—21no—
366M16—61no—
367M16—61no—
368M16#62412yescomplemented
369C2×C8—21no—
370C2×C8—61no—
371C4⋊C4—31no—
372C4⋊C4—31no—
373C4⋊C4—61no—
374C4⋊C4—61no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—182no—
378C22⋊C4—61no—
379C22⋊C4—182no—
380C42—61no—
381C42—92no—
382C42—182no—
383C42—181no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3C4×D1211yescharacteristic
394C22×C3#88211yescharacteristic
395C22×C3#89311yescharacteristic
396C22×C3#89611yescharacteristic
397C22×C3#89711yescharacteristic
398C22×C3#93711yescharacteristic
399C2×D3—62no—
400C2×D3—62no—
401C2×D3—122no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—121no—
406C2×D3—241no—
407C2×D3—241no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—122no—
413C3×C4—121no—
414C3×C4—121no—
415C3×C4—241no—
416C3×C4#67⋊C411yescharacteristic
417C3×C4#88311yescharacteristic
418C3×C4D3×C4⋊C411yescharacteristic
419C3×C4D3×C4⋊C411yescharacteristic
420C3×C4#89411yescharacteristic
421C3×C4#89611yescharacteristic
422C3×C4C4×#6711yescharacteristic
423C3×C4#94611yescharacteristic
424Dic3—41no—
425Dic3—41no—
426Dic3—42no—
427Dic3—62no—
428Dic3—62no—
429Dic3—81no—
430Dic3—122no—
431Dic3—122no—
432Dic3—122no—
433Dic3—124no—
434C32#186011yescharacteristic, complemented, Sylow
435C23—181no—
436C23D3×D1211yescharacteristic
437Q8—92no—
438Q8—181no—
439D4—92no—
440D4—182no—
441D4—182no—
442D4—181no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—62no—
446C2×C4—122no—
447C2×C4—122no—
448C2×C4—121no—
449C2×C4—181no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4—361no—
454C2×C4—361no—
455C2×C4—722no—
456C2×C4#379711yescharacteristic
457C2×C4#379911yescharacteristic
458C2×C4#380211yescharacteristic
459C2×C4#380411yescharacteristic
460C2×C4C2×#62411yescharacteristic
461C2×C4D3×#6711yescharacteristic
462C8—22no—
463C8—121no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—41no—
472C2×C3—41no—
473C2×C3#466811yescharacteristic
474C2×C3#474611yescharacteristic
475C2×C3#475311yescharacteristic
476C2×C3#498911yescharacteristic
477C2×C3#520111yescharacteristic
478C2×C3#520211yescharacteristic
479D3—122no—
480D3—122no—
481D3—242no—
482C22—21no—
483C22—21no—
484C22—182no—
485C22—361no—
486C22—361no—
487C22#6389411yescharacteristic
488C22#6389511yescharacteristic
489C22#6392211yescharacteristic
490C4—122no—
491C4—121no—
492C4—121no—
493C4—182no—
494C4—241no—
495C4—362no—
496C4#6385411yescharacteristic
497C4#6388811yescharacteristic
498C4#6390011yescharacteristic
499C4#6395211yescharacteristic
500C3—21no—
501C3#6900311yescharacteristic, complemented
502C3#7068111yescharacteristic, complemented
503C2—21no—
504C2—21no—
505C2—362no—
506C2#1059101211yescharacteristic
507C2#1059102011yescharacteristic
508C2#1059137811yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1860
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. C3×#5121C2semidirect
4. #10591230C2semidirect
6. C3×#4554C2semidirect
7. #10589160C2semidirect
22. #63652C4semidirect
35. #5121D3semidirect
41. #4554D3semidirect
57. C32×M16C2×C4semidirect
60. C4×C3⋊Dic3C2×C4semidirect
194. C3×M16C4×D3semidirect
195. C3×M16C4×D3semidirect
368. M16#624semidirect
434. C32#1860semidirect
501. C3#69003semidirect
502. C3#70681semidirect

Maximal subgroups

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

subgroupindex
#105949902
C2×#636522
C3×#51212
#105912302
#105911062
C3×#45542
#105891602
#706813
#690033