Finite Group Databasebeta

← #11788627

Subgroups — #11788627

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic, complemented
2C2×#63825C211yesmaximal, characteristic
3C2×#63650C211yesmaximal, characteristic, complemented
4C2×#63564C211yesmaximal, characteristic, complemented
5#10591087C211yesmaximal, characteristic, complemented
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72018—31nomaximal
9#69006—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#907—22no—
18C3×#907—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C2×#3717—21no—
22#63825—22no—
23#63825C414yescomplemented
24C2×#3714—21no—
25#63650—22no—
26#63565—21no—
27#63564—21no—
28#63564—21no—
29#63562—21no—
30C2×C3×#131—31no—
31C2×#949—31no—
32C2×#908—31no—
33C2×#907D311yescharacteristic, complemented
34#5232—31no—
35C2×#823—31no—
36C2×#823—31no—
37C2×#823—61no—
38C2×#821—31no—
39#4966—31no—
40C2×#809—31no—
41C3×#343—31no—
42#4558—31no—
43#4554D311yescharacteristic, complemented
44#4552—31no—
45C23×C3⋊D3—21no—
46C22×C32×C4C2311yescharacteristic
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)C2×C412yes—
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235C2×C412yes—
58C3×#235D412yes—
59C2×C3×D12D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×Dic6D411yescharacteristic
62C32×M16—21no—
63C32×M16D412yes—
64C2×C32×C8—21no—
65#3748—21no—
66#3748—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×#208—21no—
71C3×#208C2×C412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D411yescharacteristic
76C2×C3×C3⋊C8D411yescharacteristic
77C3×ΓL(1,𝔽25)—24no—
78C3×D3×C8—24no—
79#3717—24no—
80#3714—24no—
81#1907—91noSylow
82C2×C3×#41—31no—
83C2×#235C2×D311yescharacteristic
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C3×#131—62no—
88C3×#131—62no—
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—61no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C22×C3×C8—31no—
95C22×C3×C8—61no—
96C2×C3×C4⋊C4—31no—
97#949—34no—
98#949—62no—
99C2×#215—61no—
100C2×#213—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×#208—31no—
103C2×#208—31no—
104C2×#208—61no—
105C2×#208C2×D311yescharacteristic
106C22×C3⋊C8C2×D311yescharacteristic
107#908—34no—
108#908—62no—
109#907—22no—
110#907—22no—
111C2×D24—61no—
112C2×#204—61no—
113C2×ΓL(1,𝔽25)—21no—
114C2×D3×C8—21no—
115#835—61no—
116#832—61no—
117#823—64no—
118#823—62no—
119#823—62no—
120#821—61no—
121#821—61no—
122#810—61no—
123#809—61no—
124#809—61no—
125#809—61no—
126C23×C32#4111yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—81no—
131C22×C3⋊D3—81no—
132C22×C3×D3—21no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—41no—
142C4⋊(C3⋊D3)—41no—
143C3×#67—22no—
144C3×#67—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—81no—
148C3×D12—21no—
149C3×D12C22⋊C412yes—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×Dic6—21no—
153C3×Dic6C22⋊C412yes—
154C32×C8—22no—
155C3⋊(C3⋊C8)—41no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—21no—
158C3×C3⋊C8—21no—
159C2×AGL(1,ℤ/8)—91no—
160C2×#131—31no—
161#417—91no—
162C2×#102—91no—
163C2×#100—91no—
164#343—31no—
165#341—91no—
166C23×D3—62no—
167C23×D3—61no—
168C23×D3—61no—
169C3×#41—32no—
170C3×#41—32no—
171C3×#41—61no—
172C3×#41—61no—
173C2×C3×Q8—31no—
174C2×C3×D4—31no—
175C2×C3×D4—61no—
176C22×C3×C4—21no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—21no—
182C22×Dic3—21no—
183#235—21no—
184#235—21no—
185#235C4×D312yes—
186#235#6712yes—
187C2×D12—32no—
188C2×D12—32no—
189C2×D12—62no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—62no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—121no—
202C2×D12—121no—
203C2×D12—121no—
204C2×D12—121no—
205C2×D12D1211yescharacteristic
206C2×C4×D3—21no—
207C2×Dic6D1211yescharacteristic
208C3×M16—21no—
209C3×M16—21no—
210C3×M16—22no—
211C3×M16—32no—
212C3×M16—41no—
213C3×M16—64no—
214C3×M16—61no—
215C3×M16D1212yes—
216C3×M16#6712yes—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—31no—
220C2×C3×C8—31no—
221C2×C3×C8—41no—
222C2×C3×C8—64no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228#215—64no—
229#213—64no—
230C4⋊Dic3—21no—
231C4⋊Dic3—21no—
232#208—21no—
233#208—62no—
234#208—61no—
235#208—61no—
236#208—61no—
237#208—61no—
238#208—121no—
239#208C4×D312yes—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—121no—
246C2×C3⋊C8#6711yescharacteristic
247C2×C3⋊C8#6711yescharacteristic
248D24—64no—
249#204—64no—
250ΓL(1,𝔽25)—24no—
251D3×C8—24no—
252C22×C32—21no—
253C22×C32—21no—
254C22×C32C4×D411yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32#12311yescharacteristic
257C2×C3⋊D3—42no—
258C2×C3⋊D3—82no—
259C2×C3⋊D3—81no—
260C2×C3⋊D3—81no—
261C2×C3⋊D3—82no—
262C2×C3×D3—22no—
263C2×C3×D3—41no—
264C2×C3×D3—41no—
265C32×C4C2×C22⋊C411yescharacteristic
266C32×C4C4×D411yescharacteristic
267C32×C4#12011yescharacteristic
268C32×C4#12111yescharacteristic
269C3×Dic3—22no—
270C3×Dic3—81no—
271C2×#41—31no—
272C22×D4—91no—
273AGL(1,ℤ/8)—94no—
274AGL(1,ℤ/8)—182no—
275C2×SD16—181no—
276C2×D8—181no—
277#131—62no—
278#131—62no—
279C2×M16—31no—
280C2×M16—61no—
281C2×M16—91no—
282C2×M16D3211yescharacteristic
283C22×C8—31no—
284C22×C8—61no—
285C2×C4⋊C4—31no—
286#103—181no—
287#102—181no—
288#102—181no—
289#102—181no—
290#100—182no—
291C23×C3—21no—
292C23×C3—61no—
293C23×C3#23511yescharacteristic
294C23×C3#23511yescharacteristic
295C22×D3—21no—
296C22×D3—64no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—241no—
306C22×D3—241no—
307C22×D3—241no—
308C22×D3—241no—
309C22×D3—242no—
310C22×D3—242no—
311C3×Q8—32no—
312C3×Q8—61no—
313C3×D4—32no—
314C3×D4—62no—
315C3×D4—62no—
316C3×D4—61no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—61no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—121no—
327C2×C3×C4—241no—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4#23911yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340#67—22no—
341#67—22no—
342C2×Dic3—21no—
343C2×Dic3—41no—
344C2×Dic3—81no—
345D12—21no—
346D12—62no—
347D12—62no—
348D12—62no—
349D12—62no—
350D12—122no—
351D12—122no—
352D12—122no—
353D12—122no—
354D12—121no—
355D12—121no—
356D12—121no—
357D12—121no—
358D12(C2×D3)⋊C412yes—
359C4×D3—22no—
360C4×D3—22no—
361Dic6—21no—
362Dic6(C2×D3)⋊C412yes—
363C3×C8—22no—
364C3×C8—22no—
365C3×C8—42no—
366C3×C8—61no—
367C3×C8—61no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C3⋊C8—122no—
373C3⋊C8—121no—
374C3⋊C8—121no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32#38611yescharacteristic
378C2×C32#47111yescharacteristic
379C2×C32#47211yescharacteristic
380C3⋊D3—82no—
381C3×D3—42no—
382C24—181no—
383#41—32no—
384#41—32no—
385#41—61no—
386#41—61no—
387C2×Q8—31no—
388C2×D4—31no—
389C2×D4—61no—
390C2×D4—92no—
391C2×D4—181no—
392C2×D4—181no—
393C2×D4—181no—
394C2×D4—181no—
395C2×D4—181no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4C2×D3211yescharacteristic
399SD16—184no—
400D8—184no—
401M16—21no—
402M16—32no—
403M16—64no—
404M16—61no—
405M16—181no—
406M16—181no—
407M16#62612yes—
408C2×C8—21no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8—64no—
412C2×C8—61no—
413C2×C8—61no—
414C2×C8—61no—
415C2×C8—181no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—62no—
428C22×C3—121no—
429C22×C3—121no—
430C22×C3C4×D1211yescharacteristic
431C22×C3#88411yescharacteristic
432C22×C3#89411yescharacteristic
433C22×C3C4×#6711yescharacteristic
434C22×C3#92911yescharacteristic
435C22×C3#93011yescharacteristic
436C2×D3—22no—
437C2×D3—41no—
438C2×D3—41no—
439C2×D3—124no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—242no—
443C2×D3—242no—
444C2×D3—242no—
445C2×D3—242no—
446C2×D3—244no—
447C2×D3—241no—
448C2×D3—241no—
449C2×D3—241no—
450C2×D3—241no—
451C2×D3—242no—
452C2×D3—242no—
453C2×D3—244no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—62no—
459C3×C4—241no—
460C3×C4D3×C22⋊C411yescharacteristic
461C3×C4#88211yescharacteristic
462C3×C4#89311yescharacteristic
463C3×C4#89511yescharacteristic
464C3×C4C2×(C2×D3)⋊C411yescharacteristic
465C3×C4C4×#6711yescharacteristic
466C3×C4#93011yescharacteristic
467C3×C4#95311yescharacteristic
468Dic3—22no—
469Dic3—81no—
470C32#190711yescharacteristic, complemented, Sylow
471C23—61no—
472C23—182no—
473C23—361no—
474C23—361no—
475C23—721no—
476C23—721no—
477C23#379811yescharacteristic
478Q8—32no—
479Q8—61no—
480D4—32no—
481D4—62no—
482D4—62no—
483D4—61no—
484D4—182no—
485D4—182no—
486D4—361no—
487D4—361no—
488C2×C4—61no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—121no—
492C2×C4—241no—
493C2×C4#379911yescharacteristic
494C2×C4C4×D3211yescharacteristic
495C2×C4D3×D1211yescharacteristic
496C2×C4C2×#62611yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C2×C4D3×#6711yescharacteristic
499C8—22no—
500C8—62no—
501C8—61no—
502C8—61no—
503C8—361no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—41no—
512C2×C3—41no—
513C2×C3—122no—
514C2×C3#466511yescharacteristic
515C2×C3#474911yescharacteristic
516C2×C3#475411yescharacteristic
517C2×C3#514111yescharacteristic
518C2×C3#514211yescharacteristic
519C2×C3#521311yescharacteristic
520D3—42no—
521D3—244no—
522D3—242no—
523D3—242no—
524C22—21no—
525C22—21no—
526C22—62no—
527C22—121no—
528C22—121no—
529C22—362no—
530C22—722no—
531C22—722no—
532C22—721no—
533C22—721no—
534C22#6385011yescharacteristic
535C22C4×#62611yescharacteristic
536C22#6390611yescharacteristic
537C4—62no—
538C4—241no—
539C4#6390411yescharacteristic
540C4#6390911yescharacteristic
541C4D3×(C2×D3)⋊C411yescharacteristic
542C4#6397711yescharacteristic
543C3—21no—
544C3#6900611yescharacteristic, complemented
545C3#7201811yescharacteristic, complemented
546C2—21no—
547C2—21no—
548C2—122no—
549C2—722no—
550C2#1059099711yescharacteristic
551C2#1059099811yescharacteristic
552C2#1059138211yescharacteristic
subgroupG/H
centerC22#63906
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#63825C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1907
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
1. C2×C3×#907C2semidirect
3. C2×#63650C2semidirect
4. C2×#63564C2semidirect
5. #10591087C2semidirect
6. C3×#4554C2semidirect
7. #10589166C2semidirect
23. #63825C4semidirect
33. C2×#907D3semidirect
43. #4554D3semidirect
470. C32#1907semidirect
544. C3#69006semidirect
545. C3#72018semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
C2×#638252
C2×#636502
C2×#635642
#105910872
C3×#45542
#105891662
#720183
#690063