Finite Group Databasebeta

← #11858321

Subgroups — #11858321

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic
2C2×#63855C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4#10592817C211yesmaximal, characteristic, complemented
5C3×#5118C211yesmaximal, characteristic, complemented
6#10591120C211yesmaximal, characteristic, complemented
7#10591115C211yesmaximal, characteristic, complemented
8#10590695C214yesmaximal, complemented
9#10590694C214yesmaximal, complemented
10#83750—31nomaximal
11#79048—31nomaximal
12C22×C3×C4×D3C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×D3×M16—24no—
20C2×C3×ΓL(1,𝔽25)C2212yes—
21C2×C3×D3×C8C2212yes—
22C2×Dic3⋊Dic3C412yes—
23C2×(C2×D3)⋊Dic3C412yes—
24#63855C411yescharacteristic
25#63855C411yescharacteristic
26#63855C411yescharacteristic
27#63855C411yescharacteristic
28#63855C2212yes—
29#63855C2212yes—
30C2×#3711C2212yes—
31D3×#208—24no—
32C2×D3×C3⋊C8C2212yes—
33#63641C2214yescomplemented
34C3×Dic3⋊C8C2214yescomplemented
35#63572C2214yescomplemented
36Dic3⋊(C3⋊C8)C2214yescomplemented
37C22×C3×M16—31no—
38C2×#926—31no—
39C22×#208—31no—
40C2×D3×M16—31no—
41C2×D3×M16D311yescharacteristic
42C2×#872—31no—
43C3×#423—31no—
44#5119—34no—
45#5118—31no—
46#5118—31no—
47#5118—31no—
48#5118—31no—
49#5118—31no—
50#5118—61no—
51#5118D311yescharacteristic, complemented
52#5102—34no—
53#4924—31no—
54#4839—34no—
55#4839—34no—
56C23×C3×D3C2×C411yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2×C412yes—
59C22×C3×Dic3C2×C412yes—
60C22×C3×Dic3C2×C411yescharacteristic
61C2×C3×C4×D3C2×C411yescharacteristic
62C2×C3×C4×D3C2×C411yescharacteristic
63C2×C3×C4×D3D414yes—
64C2×C3×C4×D3Q814yes—
65C2×C3×C4×D3C2311yescharacteristic
66C2×C3×C4×D3C2311yescharacteristic
67C32×M16—22no—
68C2×C32×C8C2312yes—
69C4×C3⋊Dic3C2×C411yescharacteristic
70C4×C3⋊Dic3C2×C411yescharacteristic
71C4×C3⋊Dic3C2312yes—
72#3748—22no—
73C2×C3⋊(C3⋊C8)C2312yes—
74C3×C4×Dic3C2×C411yescharacteristic
75C3×C4×Dic3C2×C411yescharacteristic
76C3×C4×Dic3C2312yes—
77C3×#208—22no—
78C3×#208—22no—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81C3×ΓL(1,𝔽25)—24no—
82C3×D3×C8—24no—
83Dic3⋊Dic3C2×C412yes—
84Dic3⋊Dic3C2×C412yes—
85Dic3⋊Dic3C2×C412yes—
86Dic3⋊Dic3C2×C412yes—
87(C2×D3)⋊Dic3C2×C412yes—
88(C2×D3)⋊Dic3C2×C412yes—
89(C2×D3)⋊Dic3C2×C412yes—
90(C2×D3)⋊Dic3C2×C412yes—
91#3711—24no—
92D3×C3⋊C8—24no—
93#2905—91noSylow
94C23×C3×C4—31no—
95C22×C4×D3C2×D311yescharacteristic
96C2×C3×M16—21no—
97C2×C3×M16—31no—
98C2×C3×M16—31no—
99C2×C3×M16—32no—
100C2×C3×M16—64no—
101C2×C3×M16C2×D311yescharacteristic
102C2×C3×M16C2×D311yescharacteristic
103C22×C3×C8—32no—
104C2×C3×C42—31no—
105C2×#217—32no—
106C2×(C2×D3)⋊C4—32no—
107#926—31no—
108#926—31no—
109#926—31no—
110#926—31no—
111#926—32no—
112#926—32no—
113C2×C4⋊Dic3—32no—
114C2×Dic3⋊C4—32no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3C2×D311yescharacteristic
119C2×#208—31no—
120C2×#208—31no—
121C2×#208—32no—
122C2×#208—61no—
123C2×#208—64no—
124C2×#208C2×D311yescharacteristic
125C2×#208C2×D311yescharacteristic
126C22×C3⋊C8—32no—
127D3×M16—24no—
128D3×M16—64no—
129C2×ΓL(1,𝔽25)—32no—
130C2×ΓL(1,𝔽25)C2×D312yes—
131C2×D3×C8—32no—
132C2×D3×C8C2×D312yes—
133#872—31no—
134#872—31no—
135#872—31no—
136#872—31no—
137#872—32no—
138#872—32no—
139C3×C4⋊C8—34no—
140Dic3⋊C8—34no—
141Dic3⋊C8—34no—
142Dic3⋊C8—34no—
143Dic3⋊C8—34no—
144Dic3⋊C8—34no—
145Dic3⋊C8—64no—
146Dic3⋊C8C2×D314yescomplemented
147C4⋊(C3⋊C8)—34no—
148C23×C32C22×C411yescharacteristic
149C22×C3×D3—42no—
150C22×C3×D3C4⋊C414yes—
151C22×C3×D3C22×C411yescharacteristic
152C22×C3×D3C22×C411yescharacteristic
153C2×C32×C4C22×C411yescharacteristic
154C2×C32×C4C2×D412yes—
155C2×C32×C4C2×Q812yes—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—42no—
158C2×C3⋊Dic3C22×C412yes—
159C2×C3⋊Dic3C22×C412yes—
160C2×C3×Dic3—42no—
161C2×C3×Dic3C4⋊C414yes—
162C2×C3×Dic3C22×C412yes—
163C2×C3×Dic3C22×C412yes—
164C2×C3×Dic3C22×C411yescharacteristic
165C2×C3×Dic3C22×C411yescharacteristic
166C3×C4×D3C4⋊C414yes—
167C3×C4×D3C4⋊C414yes—
168C3×C4×D3C2×D412yes—
169C3×C4×D3C2×D412yes—
170C3×C4×D3C2×Q812yes—
171C3×C4×D3C2×Q812yes—
172C32×C8—22no—
173C3⋊(C3⋊C8)—22no—
174C3×C3⋊C8—22no—
175C3×C3⋊C8—22no—
176C22×M16—31no—
177C22×M16—91no—
178C2×#117—91no—
179#424—94no—
180#424—94no—
181#423—31no—
182#423—91no—
183#423—91no—
184#423—91no—
185C24×C3—31no—
186C23×D3C4×D311yescharacteristic
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—34no—
192C22×C3×C4—34no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—32no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—62no—
201C22×Dic3C4×D312yes—
202C22×Dic3C4×D311yescharacteristic
203C2×C4×D3Dic614yes—
204C2×C4×D3C4×D311yescharacteristic
205C2×C4×D3C4×D311yescharacteristic
206C2×C4×D3#6714yes—
207C2×C4×D3C22×D311yescharacteristic
208C2×C4×D3C22×D311yescharacteristic
209C3×M16—22no—
210C3×M16—22no—
211C3×M16—42no—
212C3×M16—64no—
213C3×M16—62no—
214C3×M16—62no—
215C2×C3×C8—22no—
216C2×C3×C8—32no—
217C2×C3×C8—32no—
218C2×C3×C8—64no—
219C2×C3×C8C22×D312yes—
220C2×C3×C8C22×D312yes—
221C3×C42—31no—
222C3×C42—31no—
223C3×C42—32no—
224#217—32no—
225#217—32no—
226#217—32no—
227#217—32no—
228(C2×D3)⋊C4—32no—
229(C2×D3)⋊C4—32no—
230(C2×D3)⋊C4—32no—
231(C2×D3)⋊C4—32no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236Dic3⋊C4—32no—
237Dic3⋊C4—32no—
238Dic3⋊C4—32no—
239Dic3⋊C4—32no—
240C4×Dic3—31no—
241C4×Dic3—31no—
242C4×Dic3—31no—
243C4×Dic3—31no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—62no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3C4×D311yescharacteristic
250C4×Dic3C4×D311yescharacteristic
251C4×Dic3C22×D312yes—
252#208—22no—
253#208—22no—
254#208—64no—
255#208—62no—
256#208—62no—
257#208—122no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8—64no—
262C2×C3⋊C8C22×D312yes—
263C2×C3⋊C8C22×D312yes—
264ΓL(1,𝔽25)—24no—
265ΓL(1,𝔽25)—64no—
266D3×C8—24no—
267D3×C8—64no—
268C22×C32—22no—
269C22×C32C2×C4⋊C412yes—
270C22×C32C23×C411yescharacteristic
271C2×C3×D3—22no—
272C2×C3×D3—22no—
273C2×C3×D3—44no—
274C2×C3×D3C2×C4⋊C412yes—
275C2×C3×D3C2×C4⋊C412yes—
276C32×C4C2×C4⋊C412yes—
277C32×C4C22×D411yescharacteristic
278C32×C4C22×Q811yescharacteristic
279C3⋊Dic3—22no—
280C3⋊Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3C2×C4⋊C412yes—
284C3×Dic3C2×C4⋊C412yes—
285C23×C4—31no—
286C2×M16—31no—
287C2×M16—31no—
288C2×M16—32no—
289C2×M16—64no—
290C2×M16—92no—
291C2×M16—91no—
292C2×M16—184no—
293C2×M16D3211yescharacteristic
294C22×C8—32no—
295C22×C8—92no—
296#117—91no—
297#117—91no—
298#117—91no—
299#117—91no—
300#117—92no—
301#117—92no—
302C2×C4⋊C4—92no—
303C2×C22⋊C4—92no—
304C2×C42—31no—
305C2×C42—91no—
306C4⋊C8—34no—
307C4⋊C8—94no—
308C4⋊C8—94no—
309C4⋊C8—94no—
310C23×C3—21no—
311C23×C3—31no—
312C23×C3—31no—
313C23×C3—34no—
314C23×C3—122no—
315C23×C3C2×C4×D311yescharacteristic
316C23×C3C2×C4×D311yescharacteristic
317C22×D3—42no—
318C22×D3Dic3⋊C414yes—
319C22×D3C2×C4×D311yescharacteristic
320C22×D3C2×C4×D311yescharacteristic
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—34no—
326C2×C3×C4—31no—
327C2×C3×C4—31no—
328C2×C3×C4—34no—
329C2×C3×C4—34no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—122no—
337C2×C3×C4C2×Dic612yes—
338C2×C3×C4C2×C4×D311yescharacteristic
339C2×C3×C4C2×C4×D311yescharacteristic
340C2×C3×C4D3×D412yes—
341C2×C3×C4D3×Q812yes—
342C2×C3×C4C2×#6712yes—
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—42no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3—124no—
355C2×Dic3Dic3⋊C414yes—
356C2×Dic3C2×C4×D312yes—
357C2×Dic3C2×C4×D312yes—
358C2×Dic3C2×C4×D311yescharacteristic
359C2×Dic3C2×C4×D311yescharacteristic
360C4×D3Dic3⋊C414yes—
361C4×D3Dic3⋊C414yes—
362C4×D3C2×Dic612yes—
363C4×D3C2×Dic612yes—
364C4×D3C2×#6712yes—
365C4×D3C2×#6712yes—
366C3×C8—22no—
367C3×C8—22no—
368C3×C8—42no—
369C3×C8—62no—
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—22no—
373C3⋊C8—62no—
374C3⋊C8—62no—
375C3⋊C8—122no—
376C2×C32—22no—
377C2×C32C22×C4⋊C411yescharacteristic
378C2×C32#56812yes—
379C3×D3—22no—
380C3×D3—22no—
381C24—31no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—34no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—34no—
389C22×C4—32no—
390C22×C4—92no—
391C22×C4C2×D3211yescharacteristic
392M16—22no—
393M16—64no—
394M16—62no—
395M16—62no—
396M16—184no—
397M16—182no—
398C2×C8—32no—
399C2×C8—32no—
400C2×C8—64no—
401C2×C8—92no—
402C2×C8—184no—
403C2×C8C2×D3212yes—
404C4⋊C4—92no—
405C4⋊C4—92no—
406C4⋊C4—92no—
407C4⋊C4—92no—
408C22⋊C4—92no—
409C22⋊C4—92no—
410C22⋊C4—92no—
411C22⋊C4—92no—
412C42—32no—
413C42—31no—
414C42—31no—
415C42—92no—
416C42—91no—
417C42—91no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—32no—
423C22×C3—32no—
424C22×C3—42no—
425C22×C3—62no—
426C22×C3—62no—
427C22×C3—124no—
428C22×C3D3×C4⋊C412yes—
429C22×C3C2×Dic3⋊C412yes—
430C22×C3C22×C4×D311yescharacteristic
431C22×C3C22×C4×D311yescharacteristic
432C2×D3—22no—
433C2×D3—22no—
434C2×D3—44no—
435C2×D3C2×Dic3⋊C412yes—
436C2×D3C2×Dic3⋊C412yes—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—32no—
441C3×C4—32no—
442C3×C4—62no—
443C3×C4—62no—
444C3×C4D3×C4⋊C412yes—
445C3×C4C2×Dic3⋊C412yes—
446C3×C4C22×Dic611yescharacteristic
447C3×C4C2×D3×D411yescharacteristic
448C3×C4C2×D3×Q811yescharacteristic
449C3×C4C22×#6711yescharacteristic
450Dic3—22no—
451Dic3—22no—
452Dic3—64no—
453Dic3—62no—
454Dic3—62no—
455Dic3—62no—
456Dic3—62no—
457Dic3—122no—
458Dic3C2×Dic3⋊C412yes—
459Dic3C2×Dic3⋊C412yes—
460C32#290511yescharacteristic, complemented, Sylow
461C23—31no—
462C23—31no—
463C23—34no—
464C23—122no—
465C23C4×D3211yescharacteristic
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—34no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—32no—
473C2×C4—34no—
474C2×C4—34no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—92no—
478C2×C4—92no—
479C2×C4—122no—
480C2×C4—362no—
481C2×C4D3×Dic612yes—
482C2×C4C4×D3211yescharacteristic
483C2×C4D3×#6712yes—
484C2×C4C22×D3211yescharacteristic
485C8—22no—
486C8—62no—
487C8—62no—
488C8—182no—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—22no—
493C2×C3—42no—
494C2×C3—62no—
495C2×C3—62no—
496C2×C3C2×D3×C4⋊C411yescharacteristic
497C2×C3#574512yes—
498C2×C3#574512yes—
499C2×C3C22×Dic3⋊C411yescharacteristic
500D3—22no—
501D3—22no—
502C22—22no—
503C22—32no—
504C22—32no—
505C22—62no—
506C22—62no—
507C22—124no—
508C22D3×Dic3⋊C412yes—
509C22C2×C4×D3211yescharacteristic
510C4—32no—
511C4—32no—
512C4—62no—
513C4—62no—
514C4—182no—
515C4—182no—
516C4D3×Dic3⋊C412yes—
517C4C2×D3×Dic611yescharacteristic
518C4C2×D3×#6711yescharacteristic
519C3—21no—
520C3#7904811yescharacteristic, complemented
521C3#8375011yescharacteristic, complemented
522C2—22no—
523C2—62no—
524C2—62no—
525C2#1059472212yes—
526C2C2×D3×Dic3⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2905
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10592817C2semidirect
5. C3×#5118C2semidirect
6. #10591120C2semidirect
7. #10591115C2semidirect
8. #10590695C2semidirect
9. #10590694C2semidirect
33. #63641C22semidirect
34. C3×Dic3⋊C8C22semidirect
35. #63572C22semidirect
36. Dic3⋊(C3⋊C8)C22semidirect
51. #5118D3semidirect
146. Dic3⋊C8C2×D3semidirect
460. C32#2905semidirect
520. C3#79048semidirect
521. C3#83750semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
C2×#638552
C2×D3×#2082
#105928172
C3×#51182
#105911202
#105911152
#105906952
#105906942
#837503
#790483