Finite Group Databasebeta

← #11861564

Subgroups — #11861564

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C2×C3×C4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10591148C214yesmaximal, complemented
5#10590327C212yesmaximal, complemented
6C4×#3710C212yesmaximal, complemented
7#10590297C212yesmaximal, complemented
8#10590254C212yesmaximal, complemented
9#79276—31nomaximal
10C8×#235—31nomaximal
11C2×#3828C411yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C4×#638C412yes—
14C4×#638C2212yes—
15#64135C411yescharacteristic
16C4×C4⋊(C3⋊D3)C411yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18#64081C412yes—
19C42×C3⋊D3C2212yes—
20C4×#634C411yescharacteristic
21C4×#634C2211yescharacteristic
22C22×C3×C3⋊C8C2212yes—
23C2×#3710C2214yes—
24C3×#830C2212yes—
25C3×C4⋊(C3⋊C8)C2212yes—
26C3×C4×C3⋊C8C2212yes—
27C3×C4×C3⋊C8C2211yescharacteristic
28C3×C4×C3⋊C8C2211yescharacteristic
29C3×C4×C3⋊C8C2212yes—
30#63572C2214yes—
31#63557C2214yes—
32#63553C2214yes—
33C4×#235—31no—
34C4×#235—31no—
35C4×#235—61no—
36C3×#431—31no—
37C2×C3×C4×C8—31no—
38C8×#67—34no—
39#4925D311yescharacteristic, complemented
40C2×C4×C3⋊C8D311yescharacteristic, complemented
41#4834—32no—
42#4830—32no—
43#67⋊C8—34no—
44C8×D12—32no—
45#4685—32no—
46#4685—32no—
47C4×D3×C8—32no—
48C4×D3×C8—32no—
49C8×Dic6—32no—
50C22×C32×C4C2×C411yescharacteristic
51C22×C32×C4C2×C411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C2×#638C2×C412yes—
54#3828C818yescomplemented
55C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
56C2×C4×C3⋊D3C2×C412yes—
57C2×C4×C3⋊D3C2×C412yes—
58C2×C4×C3⋊D3C2312yes—
59C2×#634C2×C411yescharacteristic
60C32×C42C2×C411yescharacteristic
61C32×C42C2×C411yescharacteristic
62C32×C42C2311yescharacteristic
63C32×C42C2311yescharacteristic
64#3757C2×C412yes—
65#3752C2×C412yes—
66#3752C2×C412yes—
67C4⋊(C3⋊Dic3)C2×C411yescharacteristic
68C4⋊(C3⋊Dic3)C2×C411yescharacteristic
69#3750C2×C412yes—
70#3750C2×C412yes—
71C4×C3⋊Dic3C2×C412yes—
72C4×C3⋊Dic3C2×C412yes—
73C4×C3⋊Dic3C2312yes—
74C2×C3×C3⋊C8—24no—
75C2×C3×C3⋊C8C2312yes—
76C2×C3×C3⋊C8C2314yes—
77C2×C3×C3⋊C8C2312yes—
78#3710—28no—
79C8×#41—91noSylow
80C2×#235—31no—
81C2×#235—31no—
82C2×#235—61no—
83C22×C3×C8—32no—
84C2×C3×C42—21no—
85C2×C3×C42C2×D311yescharacteristic
86C2×C3×C42C2×D311yescharacteristic
87C4×#67—32no—
88C4×#67—32no—
89C4×#67—32no—
90C4×#67—32no—
91C4×#67—62no—
92C4×#67—62no—
93#926—31no—
94#926—31no—
95#926—61no—
96C22×C3⋊C8C2×D312yes—
97C2×D3×C8—34no—
98C2×D3×C8—34no—
99C4×D12—31no—
100C4×D12—31no—
101C4×D12—31no—
102C4×D12—31no—
103C4×D12—61no—
104C4×D12—61no—
105#872—32no—
106#872—32no—
107#872—62no—
108C42×D3—32no—
109C42×D3—32no—
110C42×D3—62no—
111C4×Dic6—31no—
112C4×Dic6—31no—
113C4×Dic6—31no—
114C4×Dic6—31no—
115C4×Dic6—61no—
116C4×Dic6—61no—
117C3×C4⋊C8—32no—
118C3×C22⋊C8—32no—
119C3×C4×C8—32no—
120C3×C4×C8—31no—
121C3×C4×C8—32no—
122C3×C4×C8—31no—
123#830C2×D312yes—
124(C2×D3)⋊C8—34no—
125(C2×D3)⋊C8—34no—
126Dic3⋊C8—34no—
127Dic3⋊C8—34no—
128C8×Dic3—34no—
129C8×Dic3—34no—
130C4⋊(C3⋊C8)C2×D312yes—
131C4×C3⋊C8C2×D311yescharacteristic
132C4×C3⋊C8C2×D311yescharacteristic
133C4×C3⋊C8C2×D312yes—
134C4×C3⋊C8C2×D312yes—
135C23×C32C22×C411yescharacteristic
136C22×C3⋊D3C22×C412yes—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4C2×C814yescomplemented
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C2411yescharacteristic
146#638C2×C818yescomplemented
147C2×C3⋊Dic3C22×C412yes—
148C2×C3⋊Dic3C22×C412yes—
149C2×C3⋊Dic3C22×C412yes—
150C4⋊(C3⋊D3)C2×C814yescomplemented
151C4×C3⋊D3—24no—
152C4×C3⋊D3—24no—
153C4×C3⋊D3C2×C818yescomplemented
154#634C2×C814yescomplemented
155C3×C3⋊C8—24no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8#4114yescomplemented
158C4×#41—91no—
159C8×Q8—92no—
160C8×D4—92no—
161C8×D4—94no—
162#431—31no—
163#431—92no—
164C2×C4×C8—31no—
165C2×C4×C8—92no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4C4×D311yescharacteristic
170C22×C3×C4C4×D311yescharacteristic
171C22×C3×C4C4×D311yescharacteristic
172C22×C3×C4C4×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—32no—
176C2×#67—32no—
177C2×#67—62no—
178#235—38no—
179#235—38no—
180#235—68no—
181C2×D12—31no—
182C2×D12—31no—
183C2×D12—61no—
184C2×C4×D3—32no—
185C2×C4×D3—32no—
186C2×C4×D3—32no—
187C2×C4×D3—32no—
188C2×C4×D3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—62no—
193C2×Dic6—31no—
194C2×Dic6—31no—
195C2×Dic6—61no—
196C2×C3×C8—32no—
197C2×C3×C8—34no—
198C2×C3×C8—32no—
199C2×C3×C8—64no—
200C3×C42—21no—
201C3×C42—21no—
202C3×C42—21no—
203C3×C42—21no—
204C3×C42C4×D311yescharacteristic
205C3×C42C4×D311yescharacteristic
206C3×C42C4×D311yescharacteristic
207C3×C42C4×D311yescharacteristic
208C3×C42C22×D311yescharacteristic
209C3×C42C22×D311yescharacteristic
210C3×C42C22×D311yescharacteristic
211C3×C42C22×D311yescharacteristic
212#217—32no—
213#217—32no—
214#217—62no—
215(C2×D3)⋊C4—32no—
216(C2×D3)⋊C4—32no—
217(C2×D3)⋊C4—32no—
218(C2×D3)⋊C4—32no—
219(C2×D3)⋊C4—62no—
220(C2×D3)⋊C4—62no—
221C4⋊Dic3—31no—
222C4⋊Dic3—31no—
223C4⋊Dic3—31no—
224C4⋊Dic3—31no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227Dic3⋊C4—32no—
228Dic3⋊C4—32no—
229Dic3⋊C4—32no—
230Dic3⋊C4—32no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233C4×Dic3—32no—
234C4×Dic3—32no—
235C4×Dic3—32no—
236C4×Dic3—32no—
237C4×Dic3—32no—
238C4×Dic3—32no—
239C4×Dic3—62no—
240C4×Dic3—62no—
241C4×Dic3—62no—
242C2×C3⋊C8—24no—
243C2×C3⋊C8C22×D312yes—
244C2×C3⋊C8C22×D314yes—
245C2×C3⋊C8C22×D312yes—
246D3×C8—68no—
247D3×C8—68no—
248C22×C32—21no—
249C22×C32—21no—
250C22×C32C22×C812yes—
251C22×C32C23×C411yescharacteristic
252C2×C3⋊D3—22no—
253C2×C3⋊D3—22no—
254C2×C3⋊D3C22×C814yes—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4C22×C812yes—
258C32×C4C22×C812yes—
259C32×C4#13112yes—
260C32×C4C2×#4112yes—
261C3⋊Dic3—22no—
262C3⋊Dic3—22no—
263C3⋊Dic3C22×C814yes—
264C2×#41—91no—
265C22×C8—32no—
266C22×C8—94no—
267C4×Q8—91no—
268C4×Q8—91no—
269C4×D4—92no—
270C4×D4—92no—
271C4×D4—91no—
272C4×D4—91no—
273#117—91no—
274#117—92no—
275C2×C42—92no—
276C2×C42D3211yescharacteristic
277C4⋊C8—32no—
278C4⋊C8—94no—
279C22⋊C8—32no—
280C22⋊C8—94no—
281C4×C8—32no—
282C4×C8—31no—
283C4×C8—31no—
284C4×C8—32no—
285C4×C8—94no—
286C23×C3—21no—
287C23×C3C2×C4×D311yescharacteristic
288C23×C3C2×C4×D311yescharacteristic
289C22×D3—32no—
290C22×D3—32no—
291C22×D3—62no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—24no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4D3×C814yescomplemented
306C2×C3×C4D3×C814yescomplemented
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×C4×D311yescharacteristic
309C2×C3×C4C2×C4×D311yescharacteristic
310C2×C3×C4C2×C4×D311yescharacteristic
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319#67—38no—
320#67—38no—
321#67—68no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331D12—34no—
332D12—34no—
333D12—64no—
334C4×D3—38no—
335C4×D3—38no—
336C4×D3—68no—
337C4×D3—64no—
338C4×D3—64no—
339C4×D3—64no—
340C4×D3—64no—
341C4×D3—124no—
342C4×D3—124no—
343Dic6—34no—
344Dic6—34no—
345Dic6—64no—
346C3×C8—34no—
347C3×C8—64no—
348C3×C8—62no—
349C3⋊C8—22no—
350C3⋊C8—24no—
351C3⋊C8#23514yescomplemented
352C2×C32—22no—
353C2×C32C4×#4111yescharacteristic
354C2×C32C23×C811yescharacteristic
355C2×C32C2×#13111yescharacteristic
356C3⋊D3—24no—
357#41—98no—
358C2×Q8—91no—
359C2×D4—92no—
360C2×D4—91no—
361C22×C4—92no—
362C22×C4—92no—
363C22×C4—92no—
364C22×C4#62411yescharacteristic
365C22×C4#62411yescharacteristic
366C22×C4C2×D3211yescharacteristic
367C2×C8—32no—
368C2×C8—32no—
369C2×C8—34no—
370C2×C8—64no—
371C2×C8—188no—
372C4⋊C4—92no—
373C4⋊C4—92no—
374C4⋊C4—91no—
375C4⋊C4—91no—
376C22⋊C4—92no—
377C22⋊C4—92no—
378C22⋊C4—92no—
379C42—92no—
380C42—92no—
381C42—92no—
382C42#62411yescharacteristic
383C42#62411yescharacteristic
384C42C2×D3211yescharacteristic
385C42C2×D3211yescharacteristic
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—22no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3C2×D3×C812yes—
395C22×C3C2×D3×C812yes—
396C22×C3C22×C4×D311yescharacteristic
397C22×C3C22×C4×D311yescharacteristic
398C2×D3—34no—
399C2×D3—34no—
400C2×D3—64no—
401C2×D3—62no—
402C2×D3—62no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—122no—
406C2×D3—122no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—41no—
416C3×C4—41no—
417C3×C4C2×D3×C812yes—
418C3×C4C2×D3×C812yes—
419C3×C4C2×D3×C812yes—
420C3×C4C2×D3×C812yes—
421C3×C4#90112yes—
422C3×C4#90712yes—
423C3×C4C2×#23512yes—
424C3×C4D3×#4112yes—
425Dic3—34no—
426Dic3—34no—
427Dic3—64no—
428Dic3—62no—
429Dic3—62no—
430Dic3—62no—
431Dic3—62no—
432Dic3—122no—
433Dic3—122no—
434C32C8×#4111yescharacteristic, complemented, Sylow
435C23—92no—
436C23C2×#62411yescharacteristic
437Q8—94no—
438D4—98no—
439D4—94no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—92no—
443C2×C4—98no—
444C2×C4—92no—
445C2×C4—92no—
446C2×C4—184no—
447C2×C4—184no—
448C2×C4#371014yescomplemented
449C2×C4C2×#62411yescharacteristic
450C2×C4C2×#62411yescharacteristic
451C2×C4C2×#62411yescharacteristic
452C2×C4C2×#62411yescharacteristic
453C2×C4C2×#62411yescharacteristic
454C2×C4C22×D3211yescharacteristic
455C8—34no—
456C8—62no—
457C8—64no—
458C2×C3—22no—
459C2×C3—22no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—42no—
464C2×C3C4×#23511yescharacteristic
465C2×C3#552211yescharacteristic
466C2×C3C22×D3×C811yescharacteristic
467C2×C3C22×D3×C811yescharacteristic
468C2×C3C2×#90111yescharacteristic
469C2×C3C2×#90711yescharacteristic
470D3—64no—
471D3—64no—
472D3—124no—
473C22—21no—
474C22—21no—
475C22—94no—
476C22—182no—
477C22—182no—
478C22C2×#371012yes—
479C22C22×#62411yescharacteristic
480C4—21no—
481C4—21no—
482C4—94no—
483C4—182no—
484C4—182no—
485C4C2×#371012yes—
486C4C2×#371012yes—
487C4#6381712yes—
488C4D3×#23512yes—
489C3—21no—
490C3C8×#23511yescharacteristic, complemented
491C3#7927611yescharacteristic, complemented
492C2—22no—
493C2—184no—
494C2C22×#371011yescharacteristic
495C2C2×#6381711yescharacteristic
496C2#1059495411yescharacteristic
subgroupG/H
centerC42C2×D32
commutatorC2×C32C23×C8
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C23×C4
prime radicalC2×#3828C4
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C8×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C42 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. C2×C3×C4×C3⋊C8C2semidirect
4. #10591148C2semidirect
5. #10590327C2semidirect
6. C4×#3710C2semidirect
7. #10590297C2semidirect
8. #10590254C2semidirect
39. #4925D3semidirect
40. C2×C4×C3⋊C8D3semidirect
54. #3828C8semidirect
139. C2×C32×C4C2×C8semidirect
146. #638C2×C8semidirect
150. C4⋊(C3⋊D3)C2×C8semidirect
153. C4×C3⋊D3C2×C8semidirect
154. #634C2×C8semidirect
157. C3×C3⋊C8#41semidirect
305. C2×C3×C4D3×C8semidirect
306. C2×C3×C4D3×C8semidirect
351. C3⋊C8#235semidirect
434. C32C8×#41semidirect
448. C2×C4#3710semidirect
490. C3C8×#235semidirect
491. C3#79276semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×#49252
C2×C3×C4×C3⋊C82
#105911482
#105903272
C4×#37102
#105902972
#105902542
#792763
C8×#2353