Finite Group Databasebeta

← #11860885

Subgroups — #11860885

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63809C211yesmaximal, characteristic
2#10593889C212yesmaximal, complemented
3#10592407C211yesmaximal, characteristic, complemented
4C3×#4710C212yesmaximal, complemented
5#10590957C212yesmaximal, complemented
6#10590790C211yesmaximal, characteristic, complemented
7#10590779C212yesmaximal, complemented
8#10590740C211yesmaximal, characteristic, complemented
9#10590687C211yesmaximal, characteristic, complemented
10C4×#3718C211yesmaximal, characteristic, complemented
11C4×#3713C211yesmaximal, characteristic, complemented
12#79778—32nomaximal
13C2×#3796C2212yes—
14C2×#3743C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16#64081C2211yescharacteristic
17C2×C3×#204C2212yes—
18C3×C4×D12C2212yes—
19C3×C4×Dic6C2212yes—
20#63904—22no—
21#63900C2212yes—
22#63898C2212yes—
23#63880—22no—
24#63877—22no—
25D3×Dic3⋊C4—22no—
26#63843C2212yes—
27C2×#3718C2211yescharacteristic
28C2×#3713C2211yescharacteristic
29#63809C418yescomplemented
30C32×#97C2211yescharacteristic
31#63642C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#821C2212yes—
35C3×#818C2212yes—
36C3×#816C2212yes—
37#63576C2211yescharacteristic
38#63576C2211yescharacteristic
39#63565C2212yes—
40#63562C2212yes—
41C2×#916—32no—
42#5574—32no—
43#5546—32no—
44C3×#440—32no—
45#5164—32no—
46C4×#216—32no—
47C4×#213—32no—
48#4889—32no—
49D3×#107—32no—
50#4803—32no—
51#4790—32no—
52#4771—32no—
53#4756—32no—
54#4710D312yescomplemented
55#4708—32no—
56#4708—61no—
57C2×C4×C3⋊D3C2311yescharacteristic
58C2×C3×D12C2312yes—
59C2×C3×C4×D3—22no—
60C2×C3×Dic6C2312yes—
61C2×#626—22no—
62C2×#624—22no—
63C2×D3×Dic3—22no—
64C2×D3×Dic3—22no—
65#3796—24no—
66#3796C2×C418yescomplemented
67C2×C32×C8C2311yescharacteristic
68C2×C32×C8C2311yescharacteristic
69C32×C42C2311yescharacteristic
70#3752D411yescharacteristic
71#3752D411yescharacteristic
72#3750D411yescharacteristic
73#3750D411yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77#3743—22no—
78C8×C3⋊D3C2×C414yescomplemented
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3C2312yes—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×#204C2×C418yescomplemented
85#3724—22no—
86Dic3⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88Dic32—22no—
89#3718C2×C414yescomplemented
90#3713C2×C414yescomplemented
91#2951—91noSylow
92C2×#239—32no—
93C2×#237—32no—
94C2×C3×SD16—32no—
95C3×C4×Q8—32no—
96C3×C4×D4—32no—
97Q8×Dic3—32no—
98C2×#216—32no—
99D4×Dic3—32no—
100C2×#213—32no—
101C4×#67—62no—
102C2×Dic3⋊C4—62no—
103#916—316no—
104C2×#204C2×D312yes—
105C2×ΓL(1,𝔽25)—32no—
106C2×ΓL(1,𝔽25)—61no—
107C2×D3×C8—32no—
108C2×D3×C8—61no—
109#893—32no—
110#893—62no—
111D3×C4⋊C4—32no—
112D3×C4⋊C4—32no—
113D3×C4⋊C4—62no—
114#887—32no—
115#67⋊C4—62no—
116#877—62no—
117C4×D12—62no—
118C4×D12C2×D312yes—
119#872—32no—
120#872—61no—
121#872—62no—
122C4×Dic6C2×D312yes—
123C3×#107—32no—
124C3×#103—32no—
125C3×#102—32no—
126C3×#97—21no—
127C3×#97C2×D312yes—
128#835—32no—
129#832—32no—
130#821C2×D312yes—
131#818C2×D312yes—
132#816C2×D312yes—
133#815—32no—
134#815—61no—
135C8×Dic3—32no—
136C8×Dic3—61no—
137#810—32no—
138#809—32no—
139#807—32no—
140#807—32no—
141C4×C3⋊C8—32no—
142C4×C3⋊C8—61no—
143C22×C3⋊D3C2×D411yescharacteristic
144C22×C3×D3—22no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C4×C3⋊D3C22×C412yes—
152C4×C3⋊D3#4112yes—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C3×D12—22no—
157C3×D12C22×C414yes—
158C3×C4×D3—82no—
159C3×Dic6—22no—
160C3×Dic6C22×C414yes—
161#626—28no—
162#624—82no—
163D3×Dic3—28no—
164D3×Dic3—82no—
165C32×C8—21no—
166C32×C8C22×C412yes—
167C3⋊(C3⋊C8)—21no—
168C3⋊(C3⋊C8)C22×C412yes—
169C2×#135—91no—
170#520—92no—
171#440—32no—
172#440—92no—
173C4×Q16—91no—
174C4×Q16—91no—
175C4×D8—91no—
176C4×D8—91no—
177C2×#107—91no—
178#417—92no—
179#405—91no—
180C2×C3×Q8—32no—
181C2×C3×D4—32no—
182C22×C3×C4—62no—
183C2×#67—62no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186#239—38no—
187#239—64no—
188#237—38no—
189#237—64no—
190C2×D12—62no—
191C2×D12C22×D312yes—
192C2×C4×D3—22no—
193C2×C4×D3—32no—
194C2×C4×D3—61no—
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×Dic6C22×D312yes—
200C3×SD16—38no—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8C22×D312yes—
204C2×C3×C8C22×D312yes—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—62no—
208C3×C22⋊C4—62no—
209C3×C42—21no—
210C3×C42—62no—
211C3×C42C22×D312yes—
212#217—62no—
213#216—38no—
214#213—38no—
215(C2×D3)⋊C4—22no—
216(C2×D3)⋊C4—32no—
217(C2×D3)⋊C4—32no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3C22×D312yes—
223C4⋊Dic3C22×D312yes—
224Dic3⋊C4—22no—
225Dic3⋊C4—32no—
226Dic3⋊C4—32no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232C4×Dic3—22no—
233C4×Dic3—32no—
234C4×Dic3—61no—
235C4×Dic3—62no—
236C4×Dic3—62no—
237C2×C3⋊C8—32no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241#204C4×D318yescomplemented
242ΓL(1,𝔽25)—64no—
243ΓL(1,𝔽25)—64no—
244D3×C8—38no—
245D3×C8—64no—
246C22×C32C22×D411yescharacteristic
247C2×C3⋊D3—21no—
248C2×C3⋊D3—21no—
249C2×C3⋊D3C4×D412yes—
250C2×C3×D3—24no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C32×C4—21no—
254C32×C4—21no—
255C32×C4C23×C411yescharacteristic
256C32×C4C2×#4111yescharacteristic
257C3⋊Dic3—21no—
258C3⋊Dic3—21no—
259C3⋊Dic3C4×D412yes—
260C3×Dic3—24no—
261C3×Dic3—42no—
262C3×Dic3—42no—
263C2×#41—92no—
264#135—98no—
265C2×Q16—91no—
266C2×SD16—32no—
267C2×D8—91no—
268C2×M16—91no—
269C22×C8—91no—
270C4×Q8—32no—
271C4×Q8—92no—
272C4×D4—32no—
273C4×D4—92no—
274C4×D4—182no—
275C4×D4—182no—
276#117—91no—
277#117—182no—
278C2×C4⋊C4—92no—
279C2×C4⋊C4—182no—
280#107—32no—
281#107—91no—
282#107—91no—
283#103—32no—
284#103—92no—
285#102—32no—
286#102—92no—
287#97—91no—
288#97D3211yescharacteristic
289C4×C8—91no—
290C4×C8—91no—
291C23×C3—62no—
292C22×D3—22no—
293C22×D3—32no—
294C22×D3—61no—
295C3×Q8—34no—
296C3×Q8—62no—
297C3×D4—34no—
298C3×D4—62no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—242no—
306C2×C3×C4D3×D412yes—
307C2×C3×C4D3×D412yes—
308C2×C3×C4C23×D312yes—
309#67—68no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—32no—
314C2×Dic3—32no—
315C2×Dic3—32no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—68no—
320C2×Dic3—242no—
321D12—22no—
322D12—68no—
323D12C2×C4×D314yes—
324C4×D3—34no—
325C4×D3—34no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—68no—
329C4×D3—82no—
330C4×D3—242no—
331C4×D3—242no—
332C4×D3—242no—
333Dic6—22no—
334Dic6C2×C4×D314yes—
335C3×C8—22no—
336C3×C8—22no—
337C3×C8—22no—
338C3×C8C2×C4×D314yes—
339C3⋊C8—34no—
340C3⋊C8—62no—
341C3⋊C8—62no—
342C3⋊C8—62no—
343C2×C32C2×C4×D411yescharacteristic
344C2×C32#57611yescharacteristic
345C2×C32#57811yescharacteristic
346C3⋊D3—22no—
347C3×D3—44no—
348#41—98no—
349#41—184no—
350C2×Q8—32no—
351C2×D4—32no—
352C2×D4—182no—
353C22×C4—62no—
354C22×C4—91no—
355C22×C4—182no—
356C22×C4—182no—
357C22×C4—182no—
358Q16—94no—
359SD16—38no—
360D8—94no—
361M16—182no—
362C2×C8—91no—
363C2×C8—94no—
364C2×C8—91no—
365C2×C8C2×D3211yescharacteristic
366C2×C8C2×D3211yescharacteristic
367C4⋊C4—32no—
368C4⋊C4—32no—
369C4⋊C4—62no—
370C4⋊C4—91no—
371C4⋊C4—91no—
372C4⋊C4—182no—
373C4⋊C4—182no—
374C22⋊C4—62no—
375C22⋊C4—91no—
376C22⋊C4—91no—
377C22⋊C4—182no—
378C42—62no—
379C42—91no—
380C42—182no—
381C42C2×D3211yescharacteristic
382C22×C3—21no—
383C22×C3—64no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3C2×D3×D412yes—
387C2×D3—24no—
388C2×D3—34no—
389C2×D3—42no—
390C2×D3—42no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—62no—
394C2×D3—121no—
395C2×D3—121no—
396C3×C4—22no—
397C3×C4—22no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—64no—
403C3×C4—122no—
404C3×C4—122no—
405C3×C4C22×C4×D312yes—
406C3×C4D3×#4112yes—
407Dic3—24no—
408Dic3—34no—
409Dic3—42no—
410Dic3—42no—
411Dic3—62no—
412Dic3—62no—
413Dic3—62no—
414Dic3—121no—
415Dic3—121no—
416C32#295111yescharacteristic, complemented, Sylow
417C23—62no—
418C23—91no—
419Q8—34no—
420Q8—62no—
421D4—34no—
422D4—62no—
423D4—188no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—91no—
428C2×C4—92no—
429C2×C4—92no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—188no—
433C2×C4—242no—
434C2×C4—722no—
435C2×C4—722no—
436C2×C4#380211yescharacteristic
437C2×C4#380211yescharacteristic
438C2×C4C22×D3211yescharacteristic
439C8—21no—
440C8—92no—
441C8—181no—
442C8C4×D3212yes—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—124no—
447C2×C3C4×D3×D412yes—
448C2×C3#577412yes—
449C2×C3#577912yes—
450D3—44no—
451D3—64no—
452D3—122no—
453C22—64no—
454C22—92no—
455C22—122no—
456C22—122no—
457C22—181no—
458C22—181no—
459C22C2×#380211yescharacteristic
460C4—21no—
461C4—21no—
462C4—64no—
463C4—92no—
464C4—122no—
465C4—122no—
466C4—181no—
467C4—181no—
468C4C2×C4×D3211yescharacteristic
469C4#6430611yescharacteristic
470C3—21no—
471C3#7977812yescomplemented
472C2—124no—
473C2—182no—
474C2C4×#380211yescharacteristic
475C2#1059472011yescharacteristic
476C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#63809C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593889C2semidirect
3. #10592407C2semidirect
4. C3×#4710C2semidirect
5. #10590957C2semidirect
6. #10590790C2semidirect
7. #10590779C2semidirect
8. #10590740C2semidirect
9. #10590687C2semidirect
10. C4×#3718C2semidirect
11. C4×#3713C2semidirect
29. #63809C4semidirect
54. #4710D3semidirect
66. #3796C2×C4semidirect
78. C8×C3⋊D3C2×C4semidirect
84. C3×#204C2×C4semidirect
89. #3718C2×C4semidirect
90. #3713C2×C4semidirect
241. #204C4×D3semidirect
416. C32#2951semidirect
471. C3#79778semidirect

Maximal subgroups

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

subgroupindex
C2×#638092
#105938892
#105924072
C3×#47102
#105909572
#105907902
#105907792
#105907402
#105906872
C4×#37182
C4×#37132
#797783