Finite Group Databasebeta

← #11859359

Subgroups — #11859359

Order 1152.

1119 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic, complemented
2#10595023C211yesmaximal, characteristic
3C2×#63817C211yesmaximal, characteristic, complemented
4#10592809C211yesmaximal, characteristic, complemented
5C3×#5102C211yesmaximal, characteristic, complemented
6#10591069C211yesmaximal, characteristic, complemented
7#10591055C211yesmaximal, characteristic, complemented
8#10590727C214yesmaximal, complemented
9#10590720C214yesmaximal, complemented
10#83734—31nomaximal
11#79073—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×D3×C8—24no—
20C2×C3×D3×C8C2212yes—
21C2×C3×D3×C8C2212yes—
22#63977C412yes—
23#63966C412yes—
24#63909C412yes—
25C4×#626C2214yes—
26#63857C412yes—
27C2×#3712C2212yescomplemented
28#63817—24no—
29C2×#3710C2212yescomplemented
30#63647C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32(C2×D3)⋊(C3⋊C8)C2214yes—
33#63554C2212yescomplemented
34Dic3×C3⋊C8C2212yescomplemented
35C23×C3×C8—31no—
36#5791—31no—
37C2×#907—31no—
38C2×#901—31no—
39C22×D3×C8D311yescharacteristic, complemented
40#5524—31no—
41C3×#424—31no—
42#5207—31no—
43#5126—31no—
44#5111—34no—
45#5110—31no—
46#5110—31no—
47#5110—61no—
48C8×#67—34no—
49#5102D311yescharacteristic, complemented
50#5101—31no—
51#4997—31no—
52#4836—34no—
53#4834—34no—
54C23×C3×D3C2×C411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×#638C2×C412yes—
57#3828—22no—
58#3828—22no—
59C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
60C2×C4×C3⋊D3C2312yes—
61C2×#634C2×C411yescharacteristic
62C22×C3×Dic3C2×C411yescharacteristic
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3C2×C412yes—
66C2×C3×C4×D3C2312yes—
67C2×#626C2×C414yes—
68C2×C32×C8—22no—
69C2×C32×C8C2312yes—
70#3748—22no—
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×#217C2×C412yes—
73C3×C4⋊Dic3C2×C412yes—
74C3×C4×Dic3C2312yes—
75C3×#208—22no—
76C2×C3×C3⋊C8D414yescomplemented
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2311yescharacteristic
79C2×C3×C3⋊C8C2311yescharacteristic
80C3×D3×C8—24no—
81C3×D3×C8—24no—
82Dic3⋊Dic3C2×C414yes—
83#3722C2×C414yes—
84(C2×D3)⋊Dic3C2×C414yes—
85#3712—24no—
86#3710—24no—
87#2929—91noSylow
88C23×C3×C4—31no—
89C2×#235—31no—
90C2×#235—31no—
91C2×#235—61no—
92C22×C4×D3C2×D311yescharacteristic
93C2×C3×M16—31no—
94C22×C3×C8—21no—
95C22×C3×C8—31no—
96C22×C3×C8—32no—
97C22×C3×C8—32no—
98C22×C3×C8—64no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C3×#117—31no—
102#953—32no—
103#930—32no—
104#929—32no—
105C4×#67—34no—
106#926C2×D311yescharacteristic
107#924—32no—
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—61no—
111C2×#208C2×D311yescharacteristic
112C22×C3⋊C8C2×D311yescharacteristic
113#907—64no—
114#901—64no—
115C2×ΓL(1,𝔽25)—32no—
116C2×ΓL(1,𝔽25)—32no—
117C2×D3×C8—24no—
118C2×D3×C8—32no—
119C2×D3×C8—32no—
120C2×D3×C8C2×D312yes—
121C2×D3×C8C2×D312yes—
122#897—32no—
123#895—32no—
124#886—32no—
125#882—32no—
126C4×D12—34no—
127C3×C4⋊C8—34no—
128#830—34no—
129(C2×D3)⋊C8—34no—
130(C2×D3)⋊C8—34no—
131(C2×D3)⋊C8—34no—
132(C2×D3)⋊C8—64no—
133#815—32no—
134Dic3⋊C8C2×D314yescomplemented
135C8×Dic3—32no—
136#803—32no—
137C4×C3⋊C8—32no—
138C23×C32C22×C411yescharacteristic
139C22×C3⋊D3C22×C412yes—
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3C22×C412yes—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147#638—24no—
148C2×C3⋊Dic3C22×C412yes—
149C4⋊(C3⋊D3)—22no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152#634—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3C22×C414yes—
155C2×C3×Dic3C22×C412yes—
156C3×C4×D3—24no—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159#626—28no—
160C32×C8—22no—
161C3⋊(C3⋊C8)—22no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8C2×D412yes—
164C3×C3⋊C8C2×D412yes—
165C2×#131—91no—
166C23×C8—31no—
167#525—91no—
168#435—94no—
169C8×D4—94no—
170#424—31no—
171#408—91no—
172#407—91no—
173#405—91no—
174C24×C3—31no—
175C23×D3C4×D311yescharacteristic
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—62no—
181C22×C3×C4—62no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—32no—
185C2×#67—32no—
186C2×#67—34no—
187C2×#67—62no—
188C22×Dic3C4×D311yescharacteristic
189#235—62no—
190#235—62no—
191#235—62no—
192#235—62no—
193#235—122no—
194#235—122no—
195C2×D12—34no—
196C2×D12—31no—
197C2×D12—31no—
198C2×D12—61no—
199C2×C4×D3—22no—
200C2×C4×D3—22no—
201C2×C4×D3—32no—
202C2×C4×D3—32no—
203C2×C4×D3—62no—
204C2×C4×D3C4×D312yes—
205C2×C4×D3C22×D312yes—
206C2×Dic6—31no—
207C2×Dic6—31no—
208C2×Dic6—61no—
209C3×M16—62no—
210C2×C3×C8—22no—
211C2×C3×C8—22no—
212C2×C3×C8—22no—
213C2×C3×C8—34no—
214C2×C3×C8—31no—
215C2×C3×C8—31no—
216C2×C3×C8—32no—
217C2×C3×C8—42no—
218C2×C3×C8—64no—
219C2×C3×C8—64no—
220C2×C3×C8C22×D312yes—
221C2×C3×C8C22×D312yes—
222C3×C4⋊C4—32no—
223C3×C22⋊C4—32no—
224C3×C42—32no—
225#217—34no—
226#217C4×D312yes—
227(C2×D3)⋊C4—34no—
228(C2×D3)⋊C4—34no—
229(C2×D3)⋊C4—34no—
230C4⋊Dic3—34no—
231C4⋊Dic3C4×D312yes—
232Dic3⋊C4—34no—
233C4×Dic3C22×D312yes—
234#208—22no—
235#208—62no—
236#208—62no—
237#208—122no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8#6714yescomplemented
242C2×C3⋊C8C22×D312yes—
243C2×C3⋊C8C22×D311yescharacteristic
244C2×C3⋊C8C22×D311yescharacteristic
245ΓL(1,𝔽25)—64no—
246ΓL(1,𝔽25)—64no—
247D3×C8—24no—
248D3×C8—24no—
249D3×C8—64no—
250D3×C8—64no—
251C22×C32—22no—
252C22×C32C4×D412yes—
253C22×C32C23×C411yescharacteristic
254C2×C3⋊D3—22no—
255C2×C3⋊D3—24no—
256C2×C3×D3—28no—
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3#13114yescomplemented
260C32×C4C4×D412yes—
261C32×C4C22×D411yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3⋊Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—24no—
266C2×#41—91no—
267C23×C4—31no—
268#131—184no—
269C2×M16—31no—
270C2×M16—92no—
271C2×M16—91no—
272C22×C8—31no—
273C22×C8—32no—
274C22×C8—32no—
275C22×C8—64no—
276C22×C8—92no—
277C22×C8D3211yescharacteristic
278#123—92no—
279C22⋊Q8—92no—
280#121—92no—
281#120—92no—
282C4×D4—94no—
283#117—31no—
284C4⋊C8—34no—
285C22⋊C8—94no—
286C22⋊C8—94no—
287#97—92no—
288C4×C8—92no—
289C23×C3—21no—
290C23×C3—32no—
291C23×C3—64no—
292C23×C3—62no—
293C23×C3C2×C4×D311yescharacteristic
294C23×C3C2×C4×D311yescharacteristic
295C22×D3—22no—
296C22×D3—24no—
297C22×D3—32no—
298C22×D3—32no—
299C22×D3—62no—
300C22×D3C2×C4×D312yes—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—32no—
306C2×C3×C4—34no—
307C2×C3×C4—62no—
308C2×C3×C4—64no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4#23512yes—
314C2×C3×C4D3×D412yes—
315C2×C3×C4#23912yes—
316C2×C3×C4C2×#6712yes—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319#67—68no—
320#67—64no—
321#67—64no—
322#67—124no—
323C2×Dic3—22no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—62no—
327C2×Dic3C2×C4×D314yes—
328C2×Dic3C2×C4×D312yes—
329D12—68no—
330D12—62no—
331D12—62no—
332D12—122no—
333C4×D3—24no—
334C4×D3—22no—
335C4×D3—22no—
336C4×D3—62no—
337C4×D3—62no—
338C4×D3—62no—
339C4×D3—62no—
340C4×D3—122no—
341C4×D3—122no—
342Dic6—62no—
343Dic6—62no—
344Dic6—122no—
345C3×C8—22no—
346C3×C8—22no—
347C3×C8—32no—
348C3×C8—32no—
349C3×C8—42no—
350C3×C8—62no—
351C3⋊C8—22no—
352C3⋊C8—62no—
353C3⋊C8—62no—
354C3⋊C8—122no—
355C3⋊C8C2×#6712yes—
356C3⋊C8C2×#6712yes—
357C2×C32—22no—
358C2×C32C2×C4×D411yescharacteristic
359C2×C32C2×#13112yes—
360C3⋊D3—42no—
361C3×D3—24no—
362C24—31no—
363#41—182no—
364#41—182no—
365C2×Q8—91no—
366C2×D4—94no—
367C2×D4—92no—
368C2×D4—91no—
369C22×C4—31no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—62no—
373C22×C4—62no—
374C22×C4—92no—
375C22×C4C2×D3211yescharacteristic
376M16—62no—
377M16—184no—
378M16—182no—
379C2×C8—22no—
380C2×C8—31no—
381C2×C8—31no—
382C2×C8—34no—
383C2×C8—32no—
384C2×C8—64no—
385C2×C8—64no—
386C2×C8—92no—
387C2×C8—184no—
388C2×C8C2×D3212yes—
389C4⋊C4—32no—
390C4⋊C4—94no—
391C22⋊C4—32no—
392C22⋊C4—94no—
393C22⋊C4—94no—
394C42—32no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—21no—
398C22×C3—22no—
399C22×C3—34no—
400C22×C3—42no—
401C22×C3—68no—
402C22×C3—62no—
403C22×C3—62no—
404C22×C3#89312yes—
405C22×C3C4×#6712yes—
406C22×C3C22×C4×D311yescharacteristic
407C22×C3C22×C4×D311yescharacteristic
408C2×D3—28no—
409C2×D3—22no—
410C2×D3—22no—
411C2×D3—64no—
412C2×D3—64no—
413C2×D3—62no—
414C2×D3—62no—
415C2×D3—122no—
416C2×D3—124no—
417C2×D3#90114yescomplemented
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—22no—
421C3×C4—64no—
422C3×C4—62no—
423C3×C4#89312yes—
424C3×C4C4×#6712yes—
425C3×C4C2×#23511yescharacteristic
426C3×C4C2×D3×D411yescharacteristic
427C3×C4C2×#23911yescharacteristic
428C3×C4C22×#6711yescharacteristic
429Dic3—24no—
430Dic3—22no—
431Dic3—62no—
432Dic3—62no—
433Dic3—122no—
434C32#292911yescharacteristic, complemented, Sylow
435C23—32no—
436C23—64no—
437C23—62no—
438C23—92no—
439C23C4×D3211yescharacteristic
440Q8—182no—
441D4—188no—
442D4—184no—
443D4—182no—
444C2×C4—34no—
445C2×C4—32no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—64no—
450C2×C4—92no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4#379912yes—
454C2×C4C4×D3211yescharacteristic
455C2×C4D3×#6712yes—
456C2×C4C22×D3211yescharacteristic
457C8—22no—
458C8—32no—
459C8—32no—
460C8—62no—
461C8—182no—
462C2×C3—22no—
463C2×C3—22no—
464C2×C3—22no—
465C2×C3—21no—
466C2×C3—42no—
467C2×C3—64no—
468C2×C3C2×#89311yescharacteristic
469C2×C3C2×#90112yes—
470C2×C3D3×#13112yes—
471C2×C3C2×C4×#6711yescharacteristic
472D3—24no—
473D3—122no—
474D3—122no—
475D3—242no—
476C22—22no—
477C22—34no—
478C22—68no—
479C22—62no—
480C22—62no—
481C22—184no—
482C22—182no—
483C22#6390412yes—
484C22C2×C4×D3211yescharacteristic
485C4—64no—
486C4—62no—
487C4—182no—
488C4#6390412yes—
489C4C2×#379911yescharacteristic
490C4C2×D3×#6711yescharacteristic
491C3—21no—
492C3#7907311yescharacteristic, complemented
493C3#8373411yescharacteristic, complemented
494C2—22no—
495C2—64no—
496C2—362no—
497C2D3×#90112yes—
498C2C2×#6390411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC22×C32×C8C22
prime radical#10595023C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×C8C2semidirect
3. C2×#63817C2semidirect
4. #10592809C2semidirect
5. C3×#5102C2semidirect
6. #10591069C2semidirect
7. #10591055C2semidirect
8. #10590727C2semidirect
9. #10590720C2semidirect
27. C2×#3712C22semidirect
29. C2×#3710C22semidirect
30. #63647C22semidirect
31. C3×Dic3⋊C8C22semidirect
33. #63554C22semidirect
34. Dic3×C3⋊C8C22semidirect
39. C22×D3×C8D3semidirect
49. #5102D3semidirect
76. C2×C3×C3⋊C8D4semidirect
134. Dic3⋊C8C2×D3semidirect
241. C2×C3⋊C8#67semidirect
259. C2×C3×D3#131semidirect
417. C2×D3#901semidirect
434. C32#2929semidirect
492. C3#79073semidirect
493. C3#83734semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
#105950232
C2×#638172
#105928092
C3×#51022
#105910692
#105910552
#105907272
#105907202
#837343
#790733