Finite Group Databasebeta

← #11868812

Subgroups — #11868812

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3830C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic, complemented
3C3×#5007C212yesmaximal, complemented
4#10591495C212yesmaximal, complemented
5#10591418C212yesmaximal
6#10590582C212yesmaximal, complemented
7#10590432C212yesmaximal, complemented
8#10590340C211yesmaximal, characteristic, complemented
9#10590307C212yesmaximal, complemented
10#80966—32nomaximal
11C2×#3830C2211yescharacteristic
12C2×#3797—21no—
13C32×C4×D4C2211yescharacteristic
14D4×C3⋊Dic3C2211yescharacteristic
15C4×#638—21no—
16C2×C4×C3⋊Dic3—21no—
17#64101C2211yescharacteristic
18#64096C2211yescharacteristic
19#64090—21no—
20#64086—21no—
21C42×C3⋊D3C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#869C2212yes—
24#63919—21no—
25#63919C2212yes—
26#63900—21no—
27#63900C2212yes—
28#63873—21no—
29C2×#3712C2212yes—
30C3×#832C2214yes—
31C3×#807C2214yes—
32C3×C4⋊(C3⋊C8)C2212yes—
33#63573C2214yes—
34#63572C2212yes—
35#63567C2214yes—
36D3×C4⋊Q8—32no—
37C4×#237—32no—
38C4×#237—61no—
39C3×#474—32no—
40#5094—32no—
41#5007D312yescomplemented
42#4881—34no—
43#4875—34no—
44#4851—32no—
45#4837—32no—
46#4771—34no—
47#4761—34no—
48C2×C32×D4C2311yescharacteristic
49C22×C32×C4—21no—
50C2×#638—21no—
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—21no—
53#3830—22no—
54#3830Q814yescomplemented
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3C2311yescharacteristic
58C2×#634C2311yescharacteristic
59C2×C3×Dic6—22no—
60C2×#627—22no—
61C2×#624—22no—
62#3797—44no—
63C32×C4⋊C4C2311yescharacteristic
64C32×C22⋊C4—21no—
65C32×C42C2311yescharacteristic
66#3757—21no—
67#3752—21no—
68C4⋊(C3⋊Dic3)C2311yescharacteristic
69#3750—21no—
70#3750—21no—
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3—21no—
73C4×C3⋊Dic3—21no—
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3D411yescharacteristic
76C4×C3⋊Dic3C2311yescharacteristic
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2314yes—
79C2×C3×C3⋊C8C2314yes—
80#3724—22no—
81#3724—22no—
82#3712—24no—
83#3079—91noSylow
84C2×D3×Q8—62no—
85C2×#237—32no—
86C2×#237—61no—
87C3×C4⋊Q8—32no—
88C3×C4×D4—21no—
89C3×C4×D4C2×D312yes—
90#944—62no—
91D4×Dic3—32no—
92D4×Dic3—61no—
93C4×#67—62no—
94C4×#67—62no—
95C2×C4×Dic3—62no—
96C2×C4×Dic3—62no—
97C2×ΓL(1,𝔽25)—34no—
98#892—32no—
99#892—61no—
100D3×C4⋊C4—34no—
101D3×C4⋊C4—62no—
102#888—34no—
103#888—62no—
104#887—32no—
105#887—61no—
106#67⋊C4—62no—
107#67⋊C4—62no—
108#877—62no—
109#877—62no—
110C42×D3—32no—
111C42×D3—61no—
112#869C2×D312yes—
113C4×Dic6—32no—
114C4×Dic6—61no—
115C3×#107—34no—
116C3×C4⋊C8—32no—
117C3×#102—34no—
118#832C2×D314yes—
119#817—34no—
120#816—34no—
121Dic3⋊C8—34no—
122#810—34no—
123#808—34no—
124#807C2×D314yes—
125C4⋊(C3⋊C8)C2×D312yes—
126C23×C32—21no—
127C22×C3⋊D3C2×D411yescharacteristic
128C32×D4—21no—
129C32×D4C2×Q812yescomplemented
130C2×C32×C4—21no—
131C2×C32×C4—42no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2411yescharacteristic
135#638—24no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—24no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—42no—
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C2×C3⋊Dic3C2×D411yescharacteristic
143C4×C3⋊D3—22no—
144C4×C3⋊D3—22no—
145C4×C3⋊D3C2×Q812yes—
146C4×C3⋊D3#4112yes—
147#634—21no—
148#634C2×Q812yescomplemented
149C2×C3×Dic3—24no—
150C3×Dic6—44no—
151#627—44no—
152#624—44no—
153C3×C3⋊C8—24no—
154C2×C4⋊Q8—91no—
155C4×#41—91no—
156#477—92no—
157#476—92no—
158#475—92no—
159#474—32no—
160#428—92no—
161#423—91no—
162#417—92no—
163C2×C3×Q8—62no—
164C2×C3×D4—21no—
165C2×C3×D4C22×D312yes—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C2×#67—62no—
169C2×#67—62no—
170C22×Dic3—62no—
171C22×Dic3—62no—
172C22×Dic3—62no—
173C22×Dic3—62no—
174D3×Q8—128no—
175#237—38no—
176#237—64no—
177#237—64no—
178#237—64no—
179C2×C4×D3—32no—
180C2×C4×D3—32no—
181C2×C4×D3—32no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—64no—
186C2×Dic6—22no—
187C2×Dic6—32no—
188C2×Dic6—61no—
189C2×Dic6—64no—
190C2×C3×C8—34no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—34no—
193C3×C4⋊C4—62no—
194C3×C4⋊C4C22×D312yes—
195C3×C22⋊C4—22no—
196C3×C22⋊C4—22no—
197C3×C42—21no—
198C3×C42C22×D312yes—
199#217—62no—
200#217—62no—
201(C2×D3)⋊C4—62no—
202(C2×D3)⋊C4—62no—
203C4⋊Dic3—22no—
204C4⋊Dic3—32no—
205C4⋊Dic3—61no—
206C4⋊Dic3C22×D314yes—
207Dic3⋊C4—64no—
208Dic3⋊C4—64no—
209Dic3⋊C4—62no—
210Dic3⋊C4—62no—
211Dic3⋊C4—62no—
212Dic3⋊C4—62no—
213C4×Dic3—32no—
214C4×Dic3—32no—
215C4×Dic3—32no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—61no—
219C4×Dic3—62no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C4×Dic3—62no—
223C4×Dic3—62no—
224C4×Dic3—62no—
225C2×C3⋊C8C22×D314yes—
226ΓL(1,𝔽25)—68no—
227C22×C32—22no—
228C22×C32—41no—
229C22×C32—41no—
230C22×C32C22×D411yescharacteristic
231C2×C3⋊D3—21no—
232C2×C3⋊D3—21no—
233C2×C3⋊D3C22⋊Q812yes—
234C32×C4—21no—
235C32×C4—41no—
236C32×C4AGL(1,ℤ/8)12yes—
237C32×C4C22×Q811yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3⋊Dic3—22no—
240C3⋊Dic3—21no—
241C3⋊Dic3—41no—
242C3⋊Dic3C22⋊Q812yes—
243C3⋊Dic3#13712yes—
244C3×Dic3—44no—
245C2×#41—91no—
246C22×Q8—181no—
247C2×M16—92no—
248C4⋊Q8—32no—
249C4⋊Q8—92no—
250C4⋊Q8—181no—
251C4⋊Q8—181no—
252C4×Q8—91no—
253C4×Q8—91no—
254C4×D4—91no—
255C4×D4—181no—
256C4×D4—181no—
257C4×D4D3211yescharacteristic
258#117—91no—
259#117—181no—
260C2×C4⋊C4—92no—
261C2×C4⋊C4—181no—
262C2×C42—91no—
263C2×C42—181no—
264#107—34no—
265#106—94no—
266C4⋊C8—32no—
267C4⋊C8—92no—
268#103—94no—
269#102—34no—
270C23×C3—22no—
271C23×C3—22no—
272C22×D3—32no—
273C22×D3—61no—
274C3×Q8—124no—
275C3×D4—22no—
276C3×D4—22no—
277C3×D4—22no—
278C3×D4D3×Q814yescomplemented
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—44no—
285C2×C3×C4—44no—
286C2×C3×C4—64no—
287C2×C3×C4D3×D412yes—
288C2×C3×C4D3×D412yes—
289C2×C3×C4C23×D312yes—
290#67—68no—
291#67—68no—
292C2×Dic3—24no—
293C2×Dic3—32no—
294C2×Dic3—32no—
295C2×Dic3—32no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—68no—
300C2×Dic3—62no—
301C2×Dic3—68no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—124no—
306C2×Dic3—124no—
307C4×D3—34no—
308C4×D3—34no—
309C4×D3—62no—
310C4×D3—62no—
311C4×D3—64no—
312C4×D3—64no—
313C4×D3—122no—
314C4×D3—122no—
315C4×D3—128no—
316Dic6—34no—
317Dic6—44no—
318Dic6—62no—
319Dic6—62no—
320Dic6—62no—
321Dic6—128no—
322C3×C8—64no—
323C3⋊C8—24no—
324C2×C32—42no—
325C2×C32C2×C22⋊Q811yescharacteristic
326C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
327C2×C32C2×#13711yescharacteristic
328C3⋊D3—22no—
329#41—94no—
330#41—182no—
331C2×Q8—62no—
332C2×Q8—91no—
333C2×Q8—182no—
334C2×Q8—364no—
335C2×D4—181no—
336C2×D4C2×D3211yescharacteristic
337C22×C4—21no—
338C22×C4—91no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4—182no—
342C22×C4—181no—
343C22×C4—181no—
344M16—184no—
345C2×C8—34no—
346C4⋊C4—34no—
347C4⋊C4—62no—
348C4⋊C4—91no—
349C4⋊C4—181no—
350C4⋊C4—182no—
351C4⋊C4—182no—
352C4⋊C4—181no—
353C4⋊C4C2×D3211yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C42—91no—
358C42—91no—
359C42—91no—
360C42—181no—
361C42—181no—
362C42—181no—
363C42C2×D3211yescharacteristic
364C22×C3—24no—
365C22×C3—24no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3C2×D3×D412yes—
372C2×D3—34no—
373C2×D3—62no—
374C2×D3—62no—
375C2×D3—62no—
376C2×D3—121no—
377C2×D3—121no—
378C3×C4—22no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—22no—
382C3×C4—41no—
383C3×C4—42no—
384C3×C4—42no—
385C3×C4—124no—
386C3×C4#91114yes—
387C3×C4C2×D3×Q812yes—
388C3×C4D3×#4112yes—
389Dic3—34no—
390Dic3—34no—
391Dic3—44no—
392Dic3—62no—
393Dic3—62no—
394Dic3—64no—
395Dic3—62no—
396Dic3—64no—
397Dic3—121no—
398Dic3—122no—
399Dic3—122no—
400C32#307911yescharacteristic, complemented, Sylow
401C23—21no—
402C23—91no—
403Q8—92no—
404Q8—124no—
405Q8—181no—
406Q8—364no—
407D4—21no—
408D4—184no—
409D4#379712yescomplemented
410C2×C4—21no—
411C2×C4—42no—
412C2×C4—64no—
413C2×C4—91no—
414C2×C4—91no—
415C2×C4—92no—
416C2×C4—92no—
417C2×C4—91no—
418C2×C4—182no—
419C2×C4—184no—
420C2×C4—181no—
421C2×C4—182no—
422C2×C4—181no—
423C2×C4—362no—
424C2×C4—364no—
425C2×C4#381111yescharacteristic
426C2×C4#381111yescharacteristic
427C2×C4C22×D3211yescharacteristic
428C8—64no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—44no—
433C2×C3—44no—
434C2×C3D3×C22⋊Q812yes—
435C2×C3C2×#91112yes—
436C2×C3D3×#13712yes—
437D3—64no—
438D3—122no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—92no—
443C22—181no—
444C22—181no—
445C22C2×#381111yescharacteristic
446C4—21no—
447C4—41no—
448C4—92no—
449C4—92no—
450C4—124no—
451C4—181no—
452C4—182no—
453C4—361no—
454C4#6392712yes—
455C4C2×#379711yescharacteristic
456C4#6430611yescharacteristic
457C3—21no—
458C3#8096612yescomplemented
459C2—42no—
460C2—182no—
461C2#1059492511yescharacteristic
462C2C2×#6392711yescharacteristic
463C2#1059546811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#3830C22
hypercenterC4×D4D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593909C2semidirect
3. C3×#5007C2semidirect
4. #10591495C2semidirect
6. #10590582C2semidirect
7. #10590432C2semidirect
8. #10590340C2semidirect
9. #10590307C2semidirect
41. #5007D3semidirect
54. #3830Q8semidirect
129. C32×D4C2×Q8semidirect
148. #634C2×Q8semidirect
278. C3×D4D3×Q8semidirect
400. C32#3079semidirect
409. D4#3797semidirect
458. C3#80966semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
#105939092
C3×#50072
#105914952
#105914182
#105905822
#105904322
#105903402
#105903072
#809663