Finite Group Databasebeta

← #11869558

Subgroups — #11869558

Order 1152.

1233 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 1233 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595081C211yesmaximal, characteristic
3C3×#4968C212yesmaximal, complemented
4#10591152C211yesmaximal, characteristic, complemented
5#10591092C212yesmaximal, complemented
6#10590593C212yesmaximal, complemented
7#10590575C212yesmaximal, complemented
8#10590511C214yesmaximal, complemented
9D3×#481—32nomaximal
10C22×C4×C3⋊D3—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×#3811—21no—
13C2×#3802C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic, complemented
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
16C2×#3750—21no—
17C4⋊C4×C3⋊D3—21no—
18C4⋊C4×C3⋊D3—21no—
19C4⋊C4×C3⋊D3C2212yes—
20C4⋊C4×C3⋊D3C2212yescomplemented
21C3×#930C2212yes—
22#63980—21no—
23#63921—21no—
24#63916C2212yes—
25#63912—21no—
26#63900C2211yescharacteristic
27C2×#3710C2212yes—
28C3×#830C2212yescomplemented
29C3×#809C2214yescomplemented
30C3×#808C2214yescomplemented
31#63573C2214yescomplemented
32#63563C2214yescomplemented
33#63557C2212yescomplemented
34D3×#121—32no—
35C2×D3×C4⋊C4—32no—
36C2×D3×C4⋊C4—61no—
37C3×#481—32no—
38#5034—32no—
39#4968D312yescomplemented
40#4863—34no—
41D3×#106—34no—
42#4777—34no—
43D3×#102—34no—
44#4735—32no—
45D3×C22⋊C8—32no—
46C23×C3⋊D3D411yescharacteristic
47C22×D32—21no—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3D411yescharacteristic
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3—44no—
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×#67—22no—
61C2×C3×D12C2312yes—
62#3811—44no—
63C2×#626—22no—
64C2×#625—21no—
65C2×#624—21no—
66#3802—24no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4C2312yes—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71#3750—22no—
72#3750—22no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3C2312yes—
75C2×C3×C3⋊C8C2314yes—
76#3724—21no—
77(C2×D3)⋊Dic3—22no—
78#3710—24no—
79C2×#481—91noSylow
80C2×D3×D4—32no—
81C2×D3×D4—62no—
82C22×C4×D3—32no—
83C22×C4×D3—61no—
84C22×C4×D3—62no—
85C22×C4×D3—62no—
86C3×#121—32no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4C2×D312yescomplemented
89#939—62no—
90#938—32no—
91#930C2×D312yes—
92C2×C4⋊Dic3—32no—
93C2×C4⋊Dic3—61no—
94C2×Dic3⋊C4—62no—
95C2×Dic3⋊C4—62no—
96C2×D3×C8—34no—
97#895—32no—
98D3×C4⋊C4—34no—
99D3×C4⋊C4—34no—
100D3×C4⋊C4—32no—
101D3×C4⋊C4—62no—
102D3×C4⋊C4—62no—
103D3×C4⋊C4—62no—
104D3×C4⋊C4—62no—
105D3×C4⋊C4—62no—
106D3×C4⋊C4—62no—
107#884—62no—
108D3×C22⋊C4—62no—
109C3×#106—34no—
110C3×#102—34no—
111C3×C22⋊C8—32no—
112#832—34no—
113#830C2×D312yescomplemented
114#821—34no—
115(C2×D3)⋊C8—34no—
116#817—34no—
117#809C2×D314yescomplemented
118#808—34no—
119#808C2×D314yescomplemented
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—22no—
122C22×C3⋊D3—22no—
123C22×C3⋊D3SD1614yes—
124C22×C3⋊D3C2×D411yescharacteristic
125C22×C3⋊D3C2×D411yescharacteristic
126C22×C3×D3—22no—
127C2×D32—42no—
128C2×D32—42no—
129C2×D32—42no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—42no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—42no—
138C2×C3⋊Dic3C2×D411yescharacteristic
139C2×C3⋊Dic3C2×D411yescharacteristic
140C4×C3⋊D3—22no—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—44no—
144C4×C3⋊D3—44no—
145C4×C3⋊D3#4114yes—
146C3×#67—44no—
147C2×C3×Dic3—22no—
148C3×D12—24no—
149#626—44no—
150#625—42no—
151#624—42no—
152C3×C3⋊C8—24no—
153C2×#121—91no—
154C22×C4⋊C4—91no—
155#481—32no—
156#481—92no—
157#481—94no—
158C2×#106—92no—
159C2×#102—92no—
160C2×C22⋊C8—91no—
161C23×D3—32no—
162C23×D3—61no—
163C23×D3—62no—
164C2×C3×D4—32no—
165C2×C3×D4—62no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—21no—
169C22×C3×C4C22×D312yes—
170C2×#67—22no—
171C2×#67—62no—
172C2×#67—62no—
173C22×Dic3—32no—
174C22×Dic3—61no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177D3×D4—68no—
178D3×D4—128no—
179C2×D12—62no—
180C2×D12C22×D312yes—
181C2×C4×D3—32no—
182C2×C4×D3—32no—
183C2×C4×D3—32no—
184C2×C4×D3—32no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—68no—
190C2×C4×D3—68no—
191C2×C4×D3—62no—
192C2×C4×D3—64no—
193C2×C4×D3—64no—
194C2×C4×D3—64no—
195C2×C4×D3—64no—
196C2×C4×D3—128no—
197C2×C4×D3—128no—
198C2×C3×C8—34no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4C22×D314yes—
204C3×C22⋊C4—62no—
205#217—62no—
206(C2×D3)⋊C4—22no—
207(C2×D3)⋊C4—62no—
208C4⋊Dic3—34no—
209C4⋊Dic3—62no—
210C4⋊Dic3—62no—
211C4⋊Dic3—62no—
212C4⋊Dic3C22×D312yes—
213Dic3⋊C4—62no—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216Dic3⋊C4—64no—
217Dic3⋊C4—64no—
218C2×C3⋊C8C22×D314yes—
219D3×C8—68no—
220C22×C32—21no—
221C22×C32—21no—
222C22×C32C2×SD1612yes—
223C22×C32C22×D411yescharacteristic
224C2×C3⋊D3—21no—
225C2×C3⋊D3—21no—
226C2×C3⋊D3—28no—
227C2×C3⋊D3#12312yes—
228C2×C3⋊D3C2×SD1612yes—
229C2×C3⋊D3C2×SD1612yes—
230C2×C3⋊D3AGL(1,ℤ/8)12yes—
231C2×C3×D3—42no—
232C2×C3×D3—42no—
233C2×C3×D3—42no—
234D32—84no—
235C32×C4—21no—
236C32×C4—42no—
237C32×C4C2×#4112yes—
238C3⋊Dic3—21no—
239C3⋊Dic3—42no—
240C3⋊Dic3#12312yes—
241C3×Dic3—42no—
242C22×D4—91no—
243C22×D4—181no—
244C23×C4—91no—
245C23×C4—181no—
246C22×C8—92no—
247#121—32no—
248#121—92no—
249#121—181no—
250#121—181no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4—181no—
256C2×C4⋊C4—181no—
257C2×C4⋊C4—181no—
258C2×C4⋊C4D3211yescharacteristic, complemented
259C2×C22⋊C4—181no—
260#106—34no—
261#106—94no—
262#102—34no—
263#102—94no—
264C22⋊C8—32no—
265C22⋊C8—92no—
266C23×C3—21no—
267C23×C3—62no—
268C23×C3D3×D412yes—
269C22×D3—22no—
270C22×D3—32no—
271C22×D3—38no—
272C22×D3—32no—
273C22×D3—64no—
274C22×D3—61no—
275C22×D3—61no—
276C22×D3—64no—
277C22×D3—64no—
278C22×D3—64no—
279C22×D3—64no—
280C22×D3—124no—
281C22×D3—124no—
282C22×D3—124no—
283C3×D4—64no—
284C3×D4—124no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—24no—
288C2×C3×C4—24no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—44no—
292C2×C3×C4—44no—
293C2×C3×C4—62no—
294C2×C3×C4D3×D412yes—
295C2×C3×C4C23×D312yes—
296#67—44no—
297#67—124no—
298#67—124no—
299C2×Dic3—22no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—64no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—124no—
309C2×Dic3—124no—
310D12—24no—
311D12—124no—
312C4×D3—38no—
313C4×D3—64no—
314C4×D3—64no—
315C4×D3—64no—
316C4×D3—64no—
317C4×D3—64no—
318C4×D3—64no—
319C4×D3—64no—
320C4×D3—124no—
321C4×D3—128no—
322C4×D3—128no—
323C4×D3—128no—
324C4×D3—128no—
325C3×C8—64no—
326C3⋊C8—24no—
327C2×C32—22no—
328C2×C32C2×#12311yescharacteristic
329C2×C32C22×SD1611yescharacteristic
330C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
331C3⋊D3—22no—
332C3⋊D3#48114yescomplemented
333C3×D3—82no—
334C24—91no—
335C24—181no—
336C2×D4—32no—
337C2×D4—62no—
338C2×D4—182no—
339C2×D4—184no—
340C2×D4—181no—
341C2×D4—364no—
342C22×C4—21no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—184no—
349C22×C4—182no—
350C22×C4—182no—
351C22×C4—181no—
352C22×C4—181no—
353C22×C4—364no—
354C22×C4C2×D3211yescharacteristic
355C2×C8—34no—
356C2×C8—184no—
357C4⋊C4—21no—
358C4⋊C4—32no—
359C4⋊C4—92no—
360C4⋊C4—182no—
361C4⋊C4—182no—
362C4⋊C4—181no—
363C4⋊C4—181no—
364C4⋊C4C2×D3212yes—
365C22⋊C4—62no—
366C22⋊C4—182no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—21no—
372C22×C3—22no—
373C22×C3—122no—
374C22×C3—122no—
375C22×C3—122no—
376C22×C3D3×SD1614yes—
377C22×C3C2×D3×D412yes—
378C2×D3—34no—
379C2×D3—34no—
380C2×D3—34no—
381C2×D3—34no—
382C2×D3—42no—
383C2×D3—42no—
384C2×D3—42no—
385C2×D3—62no—
386C2×D3—62no—
387C2×D3—62no—
388C2×D3—62no—
389C2×D3—616no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—616no—
393C2×D3—62no—
394C2×D3—62no—
395C2×D3—248no—
396C3×C4—22no—
397C3×C4—22no—
398C3×C4—22no—
399C3×C4—44no—
400C3×C4—44no—
401C3×C4—122no—
402C3×C4D3×#4114yes—
403Dic3—34no—
404Dic3—42no—
405Dic3—62no—
406Dic3—62no—
407Dic3—62no—
408Dic3—124no—
409Dic3—124no—
410C32C2×#48111yescharacteristic, complemented, Sylow
411C23—62no—
412C23—91no—
413C23—91no—
414C23—94no—
415C23—182no—
416C23—182no—
417C23—362no—
418C23—362no—
419C23—362no—
420C23#381111yescharacteristic
421D4—64no—
422D4—124no—
423D4—362no—
424D4—364no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—42no—
428C2×C4—62no—
429C2×C4—91no—
430C2×C4—94no—
431C2×C4—91no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4—182no—
436C2×C4—182no—
437C2×C4—364no—
438C2×C4—364no—
439C2×C4—362no—
440C2×C4—362no—
441C2×C4#381111yescharacteristic
442C2×C4C22×D3211yescharacteristic
443C8—64no—
444C2×C3—24no—
445C2×C3—24no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—242no—
450C2×C3D3×#12312yes—
451C2×C3C2×D3×SD1612yes—
452C2×C3D3×AGL(1,ℤ/8)12yes—
453D3—38no—
454D3—64no—
455D3—64no—
456D3—64no—
457D3—82no—
458C22—21no—
459C22—21no—
460C22—92no—
461C22—92no—
462C22—92no—
463C22—92no—
464C22—122no—
465C22—122no—
466C22—122no—
467C22—188no—
468C22—181no—
469C22—181no—
470C22—724no—
471C22#6394012yes—
472C22C2×#381111yescharacteristic
473C4—21no—
474C4—42no—
475C4—92no—
476C4—122no—
477C4—181no—
478C4—362no—
479C4#6430612yes—
480C3—21no—
481C3D3×#48112yescomplemented
482C2—22no—
483C2—94no—
484C2—182no—
485C2—242no—
486C2#1059507911yescharacteristic
487C2#1059510011yescharacteristic
488C2C2×#6394011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10595081C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#481
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
3. C3×#4968C2semidirect
4. #10591152C2semidirect
5. #10591092C2semidirect
6. #10590593C2semidirect
7. #10590575C2semidirect
8. #10590511C2semidirect
14. C2×C32×C4⋊C4C22semidirect
15. C2×C4⋊(C3⋊Dic3)C22semidirect
20. C4⋊C4×C3⋊D3C22semidirect
28. C3×#830C22semidirect
29. C3×#809C22semidirect
30. C3×#808C22semidirect
31. #63573C22semidirect
32. #63563C22semidirect
33. #63557C22semidirect
39. #4968D3semidirect
88. C2×C3×C4⋊C4C2×D3semidirect
113. #830C2×D3semidirect
117. #809C2×D3semidirect
119. #808C2×D3semidirect
258. C2×C4⋊C4D32semidirect
332. C3⋊D3#481semidirect
410. C32C2×#481semidirect
481. C3D3×#481semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
#105950812
C3×#49682
#105911522
#105910922
#105905932
#105905752
#105905112
D3×#4813