Finite Group Databasebeta

← #11859360

Subgroups — #11859360

Order 1152.

1205 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
1#10595995C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3C22×#3710C211yesmaximal, characteristic, complemented
4C3×#4999C211yesmaximal, characteristic, complemented
5C3×#4997C211yesmaximal, characteristic, complemented
6#10591074C211yesmaximal, characteristic, complemented
7#10591073C211yesmaximal, characteristic, complemented
8#10590328C214yesmaximal, complemented
9#10590327C214yesmaximal, complemented
10#79073—31nomaximal
11#78553—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C32×#117C2211yescharacteristic
15#64106C412yes—
16#64104C412yes—
17#64095C412yes—
18#64091C412yes—
19C4×C4⋊(C3⋊D3)C2214yes—
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3712C2212yescomplemented
25#63817—24no—
26C2×#3710—24no—
27C2×#3710C2212yes—
28C2×#3710C2212yes—
29C2×#3710C2212yescomplemented
30C3×C4⋊(C3⋊C8)C2214yescomplemented
31C3×#803C2212yescomplemented
32C3×C4×C3⋊C8C2212yescomplemented
33#63557C2214yes—
34#63557C2214yescomplemented
35C2×#907—31no—
36C2×#901—31no—
37C22×D3×C8—31no—
38C22×D3×C8—31no—
39#5524—31no—
40#5524—31no—
41#5524—61no—
42C3×#424—31no—
43C3×#405—31no—
44#5129—31no—
45#5126—31no—
46#5126—31no—
47#5110—31no—
48#4999D311yescharacteristic, complemented
49#4997D311yescharacteristic, complemented
50#4836—34no—
51#4834—34no—
52#4706—34no—
53C8×D12—34no—
54C23×C3⋊D3C2×C411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×#638C2×C412yes—
57C22×C3⋊Dic3C2×C411yescharacteristic
58#3828—22no—
59#3828—22no—
60C2×C4⋊(C3⋊D3)C2×C414yes—
61C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3C2×C412yes—
65C2×C4×C3⋊D3C2312yes—
66C2×C4×C3⋊D3C2312yes—
67C2×#634C2×C411yescharacteristic
68C32×C4⋊C4C2×C412yes—
69C32×C22⋊C4C2×C412yes—
70C32×C42C2312yes—
71#3752C2×C414yes—
72#3752C2×C414yes—
73C4⋊(C3⋊Dic3)C2×C414yes—
74C3×#208—22no—
75C3×#208—22no—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8D414yescomplemented
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83#3712—24no—
84#3710—24no—
85#3710—24no—
86#3710—24no—
87#2929—91noSylow
88C2×#235—31no—
89C2×#235—31no—
90C2×#235—61no—
91C22×C4×D3—31no—
92C22×C4×D3—31no—
93C22×C4×D3—61no—
94C2×C3×M16—31no—
95C2×C3×M16—31no—
96C22×C3×C8—31no—
97C22×C3×C8—31no—
98C3×#117—21no—
99C3×#117C2×D311yescharacteristic
100C3×#117C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102C2×#208C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105#907—64no—
106#901—64no—
107C2×ΓL(1,𝔽25)—32no—
108C2×ΓL(1,𝔽25)—32no—
109C2×D3×C8—32no—
110C2×D3×C8—32no—
111C2×D3×C8—32no—
112C2×D3×C8—32no—
113C2×D3×C8—32no—
114C2×D3×C8—32no—
115C2×D3×C8—64no—
116C2×D3×C8—64no—
117#897—32no—
118#897—32no—
119#897—62no—
120#895—32no—
121#895—32no—
122#895—62no—
123#886—32no—
124#886—32no—
125#886—62no—
126#882—32no—
127#882—32no—
128#882—62no—
129C4×D12—34no—
130C4×D12—34no—
131C4×D12—64no—
132C3×C4⋊C8—34no—
133C3×#97—32no—
134C3×C4×C8—32no—
135(C2×D3)⋊C8—34no—
136(C2×D3)⋊C8—34no—
137(C2×D3)⋊C8—34no—
138(C2×D3)⋊C8—34no—
139C4⋊(C3⋊C8)C2×D314yescomplemented
140#803C2×D312yescomplemented
141C4×C3⋊C8C2×D312yescomplemented
142C23×C32C22×C411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—24no—
145C22×C3⋊D3C22×C412yes—
146C22×C3⋊D3C22×C412yes—
147C2×C32×C4C22×C414yes—
148C2×C32×C4C22×C411yescharacteristic
149C2×C32×C4C2×D412yes—
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152#638—24no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3C22×C412yes—
155C2×C3⋊Dic3C22×C412yes—
156C4⋊(C3⋊D3)—28no—
157C4⋊(C3⋊D3)—22no—
158C4×C3⋊D3—24no—
159C4×C3⋊D3—22no—
160C4×C3⋊D3—22no—
161C4×C3⋊D3—22no—
162C4×C3⋊D3—22no—
163#634—22no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—22no—
167C3×C3⋊C8C2×D412yes—
168C3×C3⋊C8C2×D412yes—
169C2×#131—91no—
170C23×C8—91no—
171#525—91no—
172#435—94no—
173C8×D4—94no—
174#424—31no—
175#408—91no—
176#407—91no—
177#405—31no—
178C23×D3—31no—
179C23×D3—31no—
180C23×D3—61no—
181C22×C3×C4—21no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—32no—
185C2×#67—32no—
186C2×#67—62no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—61no—
190#235—62no—
191#235—62no—
192#235—62no—
193#235—62no—
194#235—122no—
195#235—122no—
196C2×D12—34no—
197C2×D12—34no—
198C2×D12—31no—
199C2×D12—31no—
200C2×D12—64no—
201C2×D12—61no—
202C2×C4×D3—32no—
203C2×C4×D3—32no—
204C2×C4×D3—32no—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—32no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—122no—
216C2×C4×D3—122no—
217C2×Dic6—31no—
218C2×Dic6—31no—
219C2×Dic6—61no—
220C3×M16—62no—
221C3×M16—62no—
222C2×C3×C8—34no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C2×C3×C8—32no—
226C2×C3×C8—32no—
227C2×C3×C8—32no—
228C2×C3×C8—62no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4C4×D312yes—
231C3×C4⋊C4C4×D312yes—
232C3×C22⋊C4—22no—
233C3×C22⋊C4C4×D312yes—
234C3×C22⋊C4C4×D312yes—
235C3×C42—22no—
236C3×C42C22×D312yes—
237C3×C42C22×D312yes—
238(C2×D3)⋊C4—34no—
239(C2×D3)⋊C4—34no—
240(C2×D3)⋊C4—34no—
241(C2×D3)⋊C4—34no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—34no—
245C4⋊Dic3—34no—
246C4⋊Dic3—64no—
247#208—22no—
248#208—22no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8D1214yescomplemented
251C2×C3⋊C8C22×D312yes—
252C2×C3⋊C8C22×D312yes—
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D311yescharacteristic
255C2×C3⋊C8C22×D311yescharacteristic
256ΓL(1,𝔽25)—64no—
257ΓL(1,𝔽25)—64no—
258D3×C8—64no—
259D3×C8—64no—
260D3×C8—64no—
261D3×C8—64no—
262D3×C8—64no—
263D3×C8—64no—
264C22×C32—22no—
265C22×C32C4×D412yes—
266C22×C32C23×C411yescharacteristic
267C2×C3⋊D3—28no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—24no—
272C2×C3⋊D3#13114yescomplemented
273C32×C4—24no—
274C32×C4C4×D412yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3⋊Dic3—22no—
278C3⋊Dic3—22no—
279C2×#41—91no—
280C23×C4—91no—
281#131—184no—
282C2×M16—31no—
283C2×M16—31no—
284C2×M16—92no—
285C22×C8—31no—
286C22×C8—31no—
287C22×C8—92no—
288C22×C8—92no—
289C22×C8—92no—
290C22×C8—184no—
291#123—92no—
292C22⋊Q8—92no—
293#121—92no—
294#120—92no—
295C4×D4—94no—
296#117D3211yescharacteristic
297C4⋊C8—34no—
298C22⋊C8—94no—
299C22⋊C8—94no—
300#97—32no—
301C4×C8—32no—
302C23×C3—21no—
303C23×C3C2×C4×D311yescharacteristic
304C23×C3C2×C4×D311yescharacteristic
305C22×D3—32no—
306C22×D3—32no—
307C22×D3—32no—
308C22×D3—32no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—64no—
312C22×D3—64no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—124no—
316C22×D3—122no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—24no—
322C2×C3×C4C2×C4×D314yes—
323C2×C3×C4C2×C4×D314yes—
324C2×C3×C4C2×C4×D311yescharacteristic
325C2×C3×C4C2×C4×D311yescharacteristic
326C2×C3×C4C2×D1212yes—
327C2×C3×C4#23512yes—
328C2×C3×C4D3×D412yes—
329C2×C3×C4#23912yes—
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332#67—64no—
333#67—64no—
334#67—124no—
335C2×Dic3—32no—
336C2×Dic3—32no—
337C2×Dic3—32no—
338C2×Dic3—32no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—122no—
344D12—68no—
345D12—68no—
346D12—62no—
347D12—62no—
348D12—122no—
349D12—128no—
350C4×D3—64no—
351C4×D3—64no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—62no—
355C4×D3—62no—
356C4×D3—62no—
357C4×D3—62no—
358C4×D3—62no—
359C4×D3—62no—
360C4×D3—122no—
361C4×D3—122no—
362C4×D3—124no—
363C4×D3—122no—
364C4×D3—122no—
365Dic6—62no—
366Dic6—62no—
367Dic6—122no—
368C3×C8—32no—
369C3×C8—32no—
370C3×C8—62no—
371C3×C8—62no—
372C3×C8—62no—
373C3⋊C8—22no—
374C3⋊C8—22no—
375C3⋊C8—22no—
376C3⋊C8C2×D1212yes—
377C3⋊C8C2×D1212yes—
378C2×C32—22no—
379C2×C32C2×C4×D411yescharacteristic
380C2×C32C2×#13112yes—
381C3⋊D3—24no—
382C3⋊D3—42no—
383C24—91no—
384#41—182no—
385#41—182no—
386C2×Q8—91no—
387C2×D4—92no—
388C2×D4—94no—
389C2×D4—91no—
390C22×C4—91no—
391C22×C4—92no—
392C22×C4—92no—
393C22×C4—92no—
394C22×C4—182no—
395C22×C4—182no—
396C22×C4C2×D3211yescharacteristic
397M16—62no—
398M16—62no—
399M16—184no—
400C2×C8—31no—
401C2×C8—31no—
402C2×C8—34no—
403C2×C8—32no—
404C2×C8—32no—
405C2×C8—32no—
406C2×C8—62no—
407C2×C8—184no—
408C2×C8—184no—
409C2×C8—184no—
410C4⋊C4—94no—
411C4⋊C4#62412yes—
412C22⋊C4—94no—
413C22⋊C4—94no—
414C22⋊C4#62412yes—
415C42C2×D3212yes—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—42no—
421C22×C3C4×D1212yes—
422C22×C3#89312yes—
423C22×C3C22×C4×D311yescharacteristic
424C22×C3C22×C4×D311yescharacteristic
425C2×D3—34no—
426C2×D3—34no—
427C2×D3—64no—
428C2×D3—68no—
429C2×D3—68no—
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—64no—
436C2×D3—64no—
437C2×D3—62no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—128no—
441C2×D3—122no—
442C2×D3—124no—
443C3×C4—24no—
444C3×C4—24no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—44no—
449C3×C4C4×D1212yes—
450C3×C4#89312yes—
451C3×C4C22×D1211yescharacteristic
452C3×C4C2×#23511yescharacteristic
453C3×C4C2×D3×D411yescharacteristic
454C3×C4C2×#23911yescharacteristic
455Dic3—62no—
456Dic3—62no—
457Dic3—62no—
458Dic3—62no—
459Dic3—122no—
460Dic3—122no—
461C32#292911yescharacteristic, complemented, Sylow
462C23—92no—
463C23—92no—
464C23—184no—
465C23—182no—
466C23C2×#62411yescharacteristic
467Q8—182no—
468D4—188no—
469D4—184no—
470D4—182no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—182no—
474C2×C4—182no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—182no—
478C2×C4—184no—
479C2×C4#379912yes—
480C2×C4D3×D1212yes—
481C2×C4C2×#62414yes—
482C2×C4C2×#62411yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—32no—
485C8—32no—
486C8—62no—
487C8—62no—
488C8—62no—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—22no—
493C2×C3—42no—
494C2×C3C2×C4×D1211yescharacteristic
495C2×C3C2×#89311yescharacteristic
496C2×C3D3×#13112yes—
497C2×C3D3×#13112yes—
498D3—64no—
499D3—64no—
500D3—124no—
501D3—122no—
502D3—122no—
503D3—242no—
504C22—22no—
505C22—94no—
506C22—188no—
507C22—182no—
508C22—182no—
509C22—182no—
510C22—184no—
511C22#6389412yes—
512C22C22×#62411yescharacteristic
513C4—24no—
514C4—182no—
515C4—182no—
516C4#6389412yes—
517C4C2×#379911yescharacteristic
518C4C2×D3×D1211yescharacteristic
519C3—21no—
520C3#7855311yescharacteristic, complemented
521C3#7907311yescharacteristic, complemented
522C2—22no—
523C2—184no—
524C2—362no—
525C2C2×#6389411yescharacteristic
526C2#1059544212yes—
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#117C22
prime radical#10595995C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C22×#3710C2semidirect
4. C3×#4999C2semidirect
5. C3×#4997C2semidirect
6. #10591074C2semidirect
7. #10591073C2semidirect
8. #10590328C2semidirect
9. #10590327C2semidirect
24. C2×#3712C22semidirect
29. C2×#3710C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. C3×#803C22semidirect
32. C3×C4×C3⋊C8C22semidirect
34. #63557C22semidirect
48. #4999D3semidirect
49. #4997D3semidirect
77. C2×C3×C3⋊C8D4semidirect
139. C4⋊(C3⋊C8)C2×D3semidirect
140. #803C2×D3semidirect
141. C4×C3⋊C8C2×D3semidirect
250. C2×C3⋊C8D12semidirect
272. C2×C3⋊D3#131semidirect
461. C32#2929semidirect
520. C3#78553semidirect
521. C3#79073semidirect

Maximal subgroups

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

subgroupindex
#105959952
C2×#638172
C22×#37102
C3×#49992
C3×#49972
#105910742
#105910732
#105903282
#105903272
#790733
#785533