Finite Group Databasebeta

← #11788173

Subgroups — #11788173

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595022C211yesmaximal, characteristic
2C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic, complemented
4C3×#5126C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70382—31nomaximal
9#69965—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C32×M16C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63976—21no—
19#63961—21no—
20C2×Dic32—21no—
21#63908C412yescomplemented
22C4×#625—22no—
23C4×D3×Dic3—22no—
24C4×D3×Dic3—22no—
25#63856C412yescomplemented
26C3×#825—22no—
27C3×(C2×D3)⋊C8—22no—
28#63568—22no—
29#5828—31no—
30#5791—31no—
31C22×C4×Dic3—31no—
32C2×C42×D3—31no—
33C2×C3×#104—31no—
34C3×#407—31no—
35C2×#837—31no—
36C2×#825—31no—
37C2×#825D311yescharacteristic, complemented
38#5126D311yescharacteristic, complemented
39#4555—31no—
40#4555—31no—
41#4555—31no—
42#4555—61no—
43#4523—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C2×C3×D12C2×C411yescharacteristic, complemented
55C2×C3×C4×D3—21no—
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3C2×C412yes—
61C2×C3×C4×D3D412yes—
62C2×C3×Dic6C2×C411yescharacteristic, complemented
63C2×#625—22no—
64C2×D3×Dic3—28no—
65C2×D3×Dic3—24no—
66C32×M16—21no—
67C32×M16—21no—
68C2×C32×C8—21no—
69#3757—21no—
70C4⋊(C3⋊Dic3)C2×C412yescomplemented
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3—21no—
73C4×C3⋊Dic3D412yescomplemented
74C3×C4×Dic3—21no—
75C3×C4×Dic3D412yescomplemented
76C3×#208—21no—
77C3×#208—21no—
78C2×C3×C3⋊C8—21no—
79#3724—22no—
80(C2×D3)⋊Dic3—22no—
81(C2×D3)⋊Dic3—22no—
82Dic32—24no—
83#1896—91noSylow
84C2×C3×#41—31no—
85C23×C3×C4—31no—
86C23×Dic3—61no—
87C2×#235C2×D311yescharacteristic
88C22×C4×D3—61no—
89C22×C4×D3C2×D311yescharacteristic
90C2×C3×M16—21no—
91C2×C3×M16—31no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×C42—31no—
95#953—61no—
96#946—32no—
97#938—32no—
98#937—61no—
99#935—61no—
100#930—32no—
101#929—61no—
102C4×#67—62no—
103C4×#67—62no—
104#926—31no—
105#926—31no—
106#926—61no—
107#924—32no—
108C2×C4×Dic3—31no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3—62no—
112C2×C4×Dic3—61no—
113C2×C4×Dic3—61no—
114C2×C4×Dic3—62no—
115C2×C4×Dic3C2×D311yescharacteristic
116C2×#208C2×D311yescharacteristic
117C42×D3—62no—
118C42×D3—62no—
119C3×#104—62no—
120C3×C22⋊C8—62no—
121#837—62no—
122#825—22no—
123#825—62no—
124(C2×D3)⋊C8—22no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—24no—
129C22×C3×D3—21no—
130C22×C3×D3C22⋊C412yes—
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—24no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—24no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3C22⋊C412yes—
148C3×D12—21no—
149C3×D12—21no—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×C4×D3—22no—
153C3×C4×D3—22no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×Dic6—21no—
157C3×Dic6—21no—
158#625—44no—
159D3×Dic3—216no—
160C32×C8—41no—
161C3×C3⋊C8—41no—
162#525—91no—
163C22×C42—91no—
164C2×#104—31no—
165C2×#104—91no—
166#407—31no—
167#339—91no—
168#339—91no—
169C24×C3—31no—
170C23×D3D1211yescharacteristic
171C3×#41—61no—
172C3×#41—61no—
173C3×#41—61no—
174C3×#41—61no—
175C2×C3×Q8—31no—
176C2×C3×D4—31no—
177C2×C3×D4—61no—
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—21no—
191C2×#67—62no—
192C2×#67—62no—
193C22×Dic3—21no—
194C22×Dic3—64no—
195C22×Dic3—68no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—121no—
199C22×Dic3D1211yescharacteristic
200#235—21no—
201#235—21no—
202#235—21no—
203#235—21no—
204C2×D12C4×D311yescharacteristic, complemented
205C2×C4×D3—21no—
206C2×C4×D3—21no—
207C2×C4×D3—21no—
208C2×C4×D3—21no—
209C2×C4×D3—21no—
210C2×C4×D3—64no—
211C2×C4×D3—68no—
212C2×C4×D3C4×D312yes—
213C2×C4×D3#6712yes—
214C2×Dic6C4×D311yescharacteristic, complemented
215C3×M16—22no—
216C3×M16—21no—
217C3×M16—21no—
218C3×M16—21no—
219C3×M16—21no—
220C3×M16—41no—
221C3×M16—61no—
222C3×M16—61no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—41no—
226C2×C3×C8—61no—
227C3×C42—32no—
228C3×C42—61no—
229#217—62no—
230#217—61no—
231#217—61no—
232#217—62no—
233#217—121no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236C4⋊Dic3—32no—
237C4⋊Dic3—32no—
238C4⋊Dic3—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241C4×Dic3—21no—
242C4×Dic3—32no—
243C4×Dic3—32no—
244C4×Dic3—62no—
245C4×Dic3—64no—
246C4×Dic3—64no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—121no—
252C4×Dic3—121no—
253C4×Dic3#6712yescomplemented
254#208—21no—
255#208—21no—
256C2×C3⋊C8—21no—
257C22×C32—22no—
258C22×C32C2×C22⋊C411yescharacteristic
259C22×C32#12011yescharacteristic
260C22×C32#12311yescharacteristic
261C2×C3×D3—24no—
262C2×C3×D3—24no—
263C2×C3×D3—22no—
264C2×C3×D3—22no—
265C2×C3×D3—41no—
266C2×C3×D3—42no—
267C2×C3×D3#10414yescomplemented
268C32×C4C4×D411yescharacteristic
269C32×C4C4×D411yescharacteristic
270C32×C4#12111yescharacteristic
271C32×C4#12111yescharacteristic
272C3⋊Dic3—24no—
273C3⋊Dic3—42no—
274C3×Dic3—24no—
275C3×Dic3—22no—
276C3×Dic3—41no—
277C2×#41—31no—
278C23×C4—31no—
279C23×C4—181no—
280C2×M16—31no—
281C2×M16D3211yescharacteristic
282#123—181no—
283C22⋊Q8—92no—
284#121—92no—
285#120—181no—
286C4×D4—182no—
287#117—91no—
288C2×C42—31no—
289C2×C42—91no—
290C2×C42—182no—
291C2×C42—182no—
292C2×C42—181no—
293#104—62no—
294#104—182no—
295C22⋊C8—62no—
296C23×C3—21no—
297C23×C3—32no—
298C23×C3—64no—
299C23×C3—61no—
300C23×C3—61no—
301C23×C3—61no—
302C23×C3C2×D1211yescharacteristic
303C23×C3D3×D411yescharacteristic
304C22×D3—21no—
305C22×D3—21no—
306C22×D3—24no—
307C22×D3—21no—
308C22×D3(C2×D3)⋊C412yes—
309C3×Q8—61no—
310C3×Q8—61no—
311C3×D4—61no—
312C3×D4—61no—
313C3×D4—121no—
314C3×D4—121no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—64no—
323C2×C3×C4—62no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—61no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4#23511yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4#23711yescharacteristic
342C2×C3×C4#23711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345#67—41no—
346#67—41no—
347#67—124no—
348#67—124no—
349C2×Dic3—24no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—21no—
354C2×Dic3—616no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—122no—
362C2×Dic3—124no—
363C2×Dic3—122no—
364C2×Dic3(C2×D3)⋊C412yes—
365D12—21no—
366D12—21no—
367C4×D3—22no—
368C4×D3—22no—
369C4×D3—22no—
370C4×D3—22no—
371C4×D3—41no—
372C4×D3—41no—
373C4×D3—616no—
374Dic6—21no—
375Dic6—21no—
376C3×C8—42no—
377C3×C8—41no—
378C3×C8—41no—
379C3×C8—121no—
380C3⋊C8—41no—
381C2×C32—21no—
382C2×C32—21no—
383C2×C32#38611yescharacteristic
384C2×C32C2×#10412yes—
385C3×D3—24no—
386C3×D3—81no—
387C24—31no—
388#41—61no—
389#41—61no—
390#41—61no—
391#41—61no—
392C2×Q8—31no—
393C2×D4—31no—
394C2×D4—61no—
395C2×D4—182no—
396C22×C4—31no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—184no—
406C22×C4—188no—
407C22×C4—181no—
408C22×C4C2×D3211yescharacteristic
409M16—21no—
410M16—21no—
411M16—61no—
412M16—61no—
413C2×C8—21no—
414C2×C8—61no—
415C4⋊C4—92no—
416C4⋊C4—182no—
417C22⋊C4—182no—
418C22⋊C4—182no—
419C22⋊C4—181no—
420C42—32no—
421C42—61no—
422C42—92no—
423C42—184no—
424C42—181no—
425C42—181no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—34no—
432C22×C3—42no—
433C22×C3—64no—
434C22×C3—64no—
435C22×C3—62no—
436C22×C3—62no—
437C22×C3—122no—
438C22×C3—121no—
439C22×C3D3×C22⋊C411yescharacteristic
440C22×C3#88211yescharacteristic
441C22×C3#88311yescharacteristic
442C22×C3#88611yescharacteristic
443C22×C3C2×(C2×D3)⋊C411yescharacteristic
444C22×C3#93711yescharacteristic
445C2×D3—24no—
446C2×D3—24no—
447C2×D3—22no—
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—42no—
451C2×D3#82514yescomplemented
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—64no—
457C3×C4—62no—
458C3×C4—121no—
459C3×C4#67⋊C411yescharacteristic
460C3×C4#67⋊C411yescharacteristic
461C3×C4#67⋊C411yescharacteristic
462C3×C4#88411yescharacteristic
463C3×C4C4×#6711yescharacteristic
464C3×C4#93811yescharacteristic
465C3×C4#93911yescharacteristic
466C3×C4#93911yescharacteristic
467Dic3—24no—
468Dic3—22no—
469Dic3—41no—
470Dic3—64no—
471Dic3—64no—
472Dic3—124no—
473Dic3—122no—
474Dic3—122no—
475Dic3—242no—
476C32#189611yescharacteristic, complemented, Sylow
477C23—32no—
478C23—64no—
479C23—61no—
480C23—61no—
481C23—61no—
482C23D3×D1211yescharacteristic
483Q8—61no—
484Q8—61no—
485D4—61no—
486D4—61no—
487D4—121no—
488D4—121no—
489D4—364no—
490C2×C4—32no—
491C2×C4—64no—
492C2×C4—61no—
493C2×C4—62no—
494C2×C4—61no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—1816no—
503C2×C4—184no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4#379511yescharacteristic
507C2×C4C4×D3211yescharacteristic
508C2×C4#380211yescharacteristic
509C2×C4#380511yescharacteristic
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C8—41no—
513C8—121no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—22no—
519C2×C3—21no—
520C2×C3—41no—
521C2×C3—41no—
522C2×C3—64no—
523C2×C3—241no—
524C2×C3D3×#10412yes—
525C2×C3#495611yescharacteristic
526C2×C3#495811yescharacteristic
527C2×C3C2×#82512yes—
528D3—24no—
529D3—81no—
530C22—22no—
531C22—34no—
532C22—64no—
533C22—64no—
534C22—62no—
535C22—62no—
536C22—122no—
537C22—121no—
538C22#6389111yescharacteristic
539C22D3×(C2×D3)⋊C411yescharacteristic
540C22#6392211yescharacteristic
541C4—64no—
542C4—62no—
543C4—121no—
544C4—184no—
545C4—362no—
546C4#6387911yescharacteristic
547C4#6388511yescharacteristic
548C4#6390211yescharacteristic
549C4#6397011yescharacteristic
550C3—21no—
551C3#6996511yescharacteristic, complemented
552C3#7038211yescharacteristic, complemented
553C2—21no—
554C2—21no—
555C2—64no—
556C2—241no—
557C2D3×#82512yes—
558C2#1059136311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595022C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×Dic3C2semidirect
3. C2×C3×#825C2semidirect
4. C3×#5126C2semidirect
5. C2×#63568C2semidirect
6. #10589421C2semidirect
7. #10589162C2semidirect
21. #63908C4semidirect
25. #63856C4semidirect
37. C2×#825D3semidirect
38. #5126D3semidirect
54. C2×C3×D12C2×C4semidirect
62. C2×C3×Dic6C2×C4semidirect
70. C4⋊(C3⋊Dic3)C2×C4semidirect
73. C4×C3⋊Dic3D4semidirect
75. C3×C4×Dic3D4semidirect
204. C2×D12C4×D3semidirect
214. C2×Dic6C4×D3semidirect
253. C4×Dic3#67semidirect
267. C2×C3×D3#104semidirect
451. C2×D3#825semidirect
476. C32#1896semidirect
551. C3#69965semidirect
552. C3#70382semidirect

Maximal subgroups

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

subgroupindex
#105950222
C2×C4×D3×Dic32
C2×C3×#8252
C3×#51262
C2×#635682
#105894212
#105891622
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