Finite Group Databasebeta

← #11860951

Subgroups — #11860951

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63809C211yesmaximal, characteristic
2#10593889C212yesmaximal, complemented
3#10592388C211yesmaximal, characteristic, complemented
4C3×C4×#204C212yesmaximal, complemented
5#10590957C212yesmaximal, complemented
6#10590791C211yesmaximal, characteristic, complemented
7#10590775C212yesmaximal, complemented
8#10590741C211yesmaximal, characteristic, complemented
9#10590685C211yesmaximal, characteristic, complemented
10#10590381C211yesmaximal, characteristic, complemented
11#10590344C211yesmaximal, characteristic, complemented
12#79650—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×C4×C8C2211yescharacteristic
31#63642C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33#63630C2211yescharacteristic
34C3×#821C2212yes—
35C3×#817C2212yes—
36C3×#816C2212yes—
37#63574C2211yescharacteristic
38#63574C2211yescharacteristic
39#63565C2212yes—
40#63562C2212yes—
41C2×#916—32no—
42#5574—32no—
43#5546—32no—
44C3×C4×SD16—32no—
45Dic3×SD16—32no—
46#5030—32no—
47#5014—32no—
48D3×#106—32no—
49#4852—32no—
50#4803—32no—
51#4789—32no—
52#4785—32no—
53#4771—32no—
54C4×#204D312yescomplemented
55#4689—32no—
56#4689—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#3752D412yes—
71#3750D412yes—
72C4×C3⋊Dic3C2311yescharacteristic
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75#3743—22no—
76C8×C3⋊D3C2×C414yescomplemented
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3C2312yes—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82C3×#204C2×C418yescomplemented
83#3724—22no—
84Dic3⋊Dic3—22no—
85(C2×D3)⋊Dic3—22no—
86Dic32—22no—
87#3718C2×C414yescomplemented
88#3713C2×C414yescomplemented
89#2952—91noSylow
90C2×#239—32no—
91C2×#237—32no—
92C2×C3×SD16—32no—
93C3×C4×Q8—32no—
94C3×C4×D4—32no—
95Q8×Dic3—32no—
96C2×#216—32no—
97D4×Dic3—32no—
98C2×#213—32no—
99C4×#67—62no—
100C2×Dic3⋊C4—62no—
101#916—316no—
102C2×#204C2×D312yes—
103C2×ΓL(1,𝔽25)—32no—
104C2×ΓL(1,𝔽25)—61no—
105C2×D3×C8—32no—
106C2×D3×C8—61no—
107#893—32no—
108#893—62no—
109D3×C4⋊C4—32no—
110D3×C4⋊C4—32no—
111D3×C4⋊C4—62no—
112#887—32no—
113#67⋊C4—62no—
114#877—62no—
115C4×D12—62no—
116C4×D12C2×D312yes—
117#872—32no—
118#872—61no—
119#872—62no—
120C4×Dic6C2×D312yes—
121C3×#106—32no—
122C3×#103—32no—
123C3×#102—32no—
124C3×C4×C8—21no—
125C3×C4×C8C2×D312yes—
126#835—32no—
127#832—32no—
128#821C2×D312yes—
129#817C2×D312yes—
130#816C2×D312yes—
131#815—32no—
132#815—61no—
133C8×Dic3—32no—
134C8×Dic3—61no—
135#810—32no—
136#809—32no—
137#808—32no—
138#808—32no—
139#803—32no—
140#803—61no—
141C22×C3⋊D3C2×D411yescharacteristic
142C22×C3×D3—22no—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2411yescharacteristic
145C2×C3⋊Dic3C2×D412yes—
146C2×C3⋊Dic3C2×D411yescharacteristic
147C4×C3⋊D3C22×C412yes—
148C4×C3⋊D3#4112yes—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C3×D12—22no—
153C3×D12C22×C414yes—
154C3×C4×D3—82no—
155C3×Dic6—22no—
156C3×Dic6C22×C414yes—
157#626—28no—
158#624—82no—
159D3×Dic3—28no—
160D3×Dic3—82no—
161C32×C8—21no—
162C32×C8C22×C412yes—
163C3⋊(C3⋊C8)—21no—
164C3⋊(C3⋊C8)C22×C412yes—
165C2×#135—91no—
166#520—92no—
167#442—91no—
168#442—91no—
169#441—91no—
170#441—91no—
171C4×SD16—32no—
172C4×SD16—92no—
173C2×#106—91no—
174#417—92no—
175#405—91no—
176C2×C3×Q8—32no—
177C2×C3×D4—32no—
178C22×C3×C4—62no—
179C2×#67—62no—
180C22×Dic3—62no—
181C22×Dic3—62no—
182#239—38no—
183#239—64no—
184#237—38no—
185#237—64no—
186C2×D12—62no—
187C2×D12C22×D312yes—
188C2×C4×D3—22no—
189C2×C4×D3—32no—
190C2×C4×D3—61no—
191C2×C4×D3—62no—
192C2×C4×D3—62no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×Dic6C22×D312yes—
196C3×SD16—38no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8C22×D312yes—
200C2×C3×C8C22×D312yes—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—62no—
204C3×C22⋊C4—62no—
205C3×C42—21no—
206C3×C42—62no—
207C3×C42C22×D312yes—
208#217—62no—
209#216—38no—
210#213—38no—
211(C2×D3)⋊C4—22no—
212(C2×D3)⋊C4—32no—
213(C2×D3)⋊C4—32no—
214(C2×D3)⋊C4—62no—
215(C2×D3)⋊C4—62no—
216C4⋊Dic3—62no—
217C4⋊Dic3C22×D312yes—
218C4⋊Dic3C22×D312yes—
219Dic3⋊C4—22no—
220Dic3⋊C4—32no—
221Dic3⋊C4—32no—
222Dic3⋊C4—62no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226C4×Dic3—22no—
227C4×Dic3—32no—
228C4×Dic3—61no—
229C4×Dic3—62no—
230C4×Dic3—62no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235#204C4×D318yescomplemented
236ΓL(1,𝔽25)—64no—
237ΓL(1,𝔽25)—64no—
238D3×C8—38no—
239D3×C8—64no—
240C22×C32C22×D411yescharacteristic
241C2×C3⋊D3—22no—
242C2×C3⋊D3C4×D412yes—
243C2×C3×D3—24no—
244C2×C3×D3—42no—
245C2×C3×D3—42no—
246C32×C4—22no—
247C32×C4C23×C411yescharacteristic
248C32×C4C2×#4111yescharacteristic
249C3⋊Dic3—22no—
250C3⋊Dic3C4×D412yes—
251C3×Dic3—24no—
252C3×Dic3—42no—
253C3×Dic3—42no—
254C2×#41—92no—
255#135—98no—
256C2×Q16—91no—
257C2×SD16—32no—
258C2×D8—91no—
259C2×M16—91no—
260C22×C8—91no—
261C4×Q8—32no—
262C4×Q8—92no—
263C4×D4—32no—
264C4×D4—92no—
265C4×D4—182no—
266C4×D4—182no—
267#117—91no—
268#117—182no—
269C2×C4⋊C4—92no—
270C2×C4⋊C4—182no—
271#106—32no—
272#106—91no—
273#106—91no—
274#103—32no—
275#103—92no—
276#102—32no—
277#102—92no—
278#97—91no—
279#97—91no—
280C4×C8—91no—
281C4×C8D3211yescharacteristic
282C23×C3—62no—
283C22×D3—22no—
284C22×D3—32no—
285C22×D3—61no—
286C3×Q8—34no—
287C3×Q8—62no—
288C3×D4—34no—
289C3×D4—62no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—242no—
296C2×C3×C4D3×D412yes—
297C2×C3×C4D3×D412yes—
298C2×C3×C4C23×D312yes—
299#67—68no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—61no—
307C2×Dic3—62no—
308C2×Dic3—68no—
309C2×Dic3—242no—
310D12—22no—
311D12—68no—
312D12C2×C4×D314yes—
313C4×D3—34no—
314C4×D3—34no—
315C4×D3—62no—
316C4×D3—62no—
317C4×D3—68no—
318C4×D3—82no—
319C4×D3—242no—
320C4×D3—242no—
321C4×D3—242no—
322Dic6—22no—
323Dic6C2×C4×D314yes—
324C3×C8—22no—
325C3×C8—22no—
326C3×C8—22no—
327C3×C8C2×C4×D314yes—
328C3⋊C8—34no—
329C3⋊C8—62no—
330C3⋊C8—62no—
331C3⋊C8—62no—
332C2×C32C2×C4×D411yescharacteristic
333C2×C32#57712yes—
334C3⋊D3—22no—
335C3×D3—44no—
336#41—98no—
337#41—184no—
338C2×Q8—32no—
339C2×D4—32no—
340C2×D4—182no—
341C22×C4—62no—
342C22×C4—91no—
343C22×C4—182no—
344C22×C4—182no—
345C22×C4—182no—
346Q16—94no—
347SD16—38no—
348D8—94no—
349M16—182no—
350C2×C8—91no—
351C2×C8—94no—
352C2×C8—91no—
353C2×C8C2×D3211yescharacteristic
354C2×C8C2×D3211yescharacteristic
355C4⋊C4—32no—
356C4⋊C4—32no—
357C4⋊C4—62no—
358C4⋊C4—92no—
359C4⋊C4—182no—
360C4⋊C4—182no—
361C22⋊C4—62no—
362C22⋊C4—92no—
363C22⋊C4—182no—
364C42—62no—
365C42—91no—
366C42—182no—
367C42C2×D3211yescharacteristic
368C22×C3—21no—
369C22×C3—64no—
370C22×C3—122no—
371C22×C3—122no—
372C22×C3C2×D3×D412yes—
373C2×D3—24no—
374C2×D3—34no—
375C2×D3—42no—
376C2×D3—42no—
377C2×D3—62no—
378C2×D3—62no—
379C2×D3—62no—
380C2×D3—122no—
381C3×C4—22no—
382C3×C4—22no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—42no—
386C3×C4—64no—
387C3×C4—122no—
388C3×C4—122no—
389C3×C4C22×C4×D312yes—
390C3×C4D3×#4112yes—
391Dic3—24no—
392Dic3—34no—
393Dic3—42no—
394Dic3—42no—
395Dic3—62no—
396Dic3—62no—
397Dic3—62no—
398Dic3—122no—
399C32#295211yescharacteristic, complemented, Sylow
400C23—62no—
401C23—91no—
402Q8—34no—
403Q8—62no—
404D4—34no—
405D4—62no—
406D4—188no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—91no—
411C2×C4—92no—
412C2×C4—92no—
413C2×C4—92no—
414C2×C4—188no—
415C2×C4—242no—
416C2×C4—722no—
417C2×C4—722no—
418C2×C4#380212yes—
419C2×C4C22×D3211yescharacteristic
420C8—21no—
421C8—92no—
422C8—181no—
423C8C4×D3212yes—
424C2×C3—22no—
425C2×C3—21no—
426C2×C3—124no—
427C2×C3C4×D3×D412yes—
428C2×C3#576212yes—
429C2×C3#577012yes—
430D3—44no—
431D3—64no—
432D3—122no—
433C22—64no—
434C22—92no—
435C22—122no—
436C22—122no—
437C22—182no—
438C22C2×#380211yescharacteristic
439C4—22no—
440C4—64no—
441C4—92no—
442C4—122no—
443C4—122no—
444C4—182no—
445C4C2×C4×D3211yescharacteristic
446C4#6430611yescharacteristic
447C3—21no—
448C3#7965012yescomplemented
449C2—124no—
450C2—182no—
451C2C4×#380211yescharacteristic
452C2#1059468612yes—
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63809C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593889C2semidirect
3. #10592388C2semidirect
4. C3×C4×#204C2semidirect
5. #10590957C2semidirect
6. #10590791C2semidirect
7. #10590775C2semidirect
8. #10590741C2semidirect
9. #10590685C2semidirect
10. #10590381C2semidirect
11. #10590344C2semidirect
29. #63809C4semidirect
54. C4×#204D3semidirect
66. #3796C2×C4semidirect
76. C8×C3⋊D3C2×C4semidirect
82. C3×#204C2×C4semidirect
87. #3718C2×C4semidirect
88. #3713C2×C4semidirect
235. #204C4×D3semidirect
399. C32#2952semidirect
448. C3#79650semidirect

Maximal subgroups

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

subgroupindex
C2×#638092
#105938892
#105923882
C3×C4×#2042
#105909572
#105907912
#105907752
#105907412
#105906852
#105903812
#105903442
#796503