Finite Group Databasebeta

← #11872756

Subgroups — #11872756

Order 1152.

884 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 156 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
1#10593996C211yesmaximal, characteristic, complemented
2#10593984C211yesmaximal, characteristic, complemented
3#10592408C211yesmaximal, characteristic, complemented
4C3×#4711C212yesmaximal, complemented
5#10590945C212yesmaximal, complemented
6#10590782C212yesmaximal, complemented
7#10590749C212yesmaximal, complemented
8#10590652C212yesmaximal, complemented
9C4×#3713C212yesmaximal, complemented
10#79874—32nomaximal
11C2×#3802C2211yescharacteristic
12#64081C2211yescharacteristic
13C2×C3×D24C2212yes—
14C3×C4×D12C2212yes—
15C3×C4×D12C2212yescomplemented
16D3×(C2×D3)⋊C4—22no—
17#63916C2212yes—
18#63914C2211yescharacteristic, complemented
19#63906—22no—
20#63905—22no—
21#63898C2212yes—
22#63879—22no—
23#63872C2211yescharacteristic, complemented
24#63849C2211yescharacteristic
25C2×#3713C2212yes—
26C32×#97C2211yescharacteristic, complemented
27#63647C2212yes—
28#63641C2212yescomplemented
29C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
30C3×#821C2212yes—
31C3×#821C2212yescomplemented
32C3×#817C2212yescomplemented
33#63576C2212yescomplemented
34#63562C2212yes—
35#63562C2212yescomplemented
36#5562—32no—
37#5545—32no—
38C3×#442—32no—
39#5156—32no—
40#5150—32no—
41C4×#213—32no—
42C4×#213—32no—
43#4871—32no—
44#4866—32no—
45#4786—32no—
46#4779—32no—
47#4773—32no—
48#4763—32no—
49#4711D312yescomplemented
50#4709—32no—
51#4709—61no—
52C22×D32—21no—
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×C3×D12C2312yes—
55C2×C3×D12C2312yes—
56C2×C3×C4×D3—22no—
57C2×C3×C4×D3—22no—
58C2×#626—22no—
59C2×#625—21no—
60C2×#625—22no—
61C2×D3×Dic3—22no—
62#3802—24no—
63C2×C32×C8C2312yes—
64C32×C42C2311yescharacteristic
65#3752D412yes—
66#3750D412yes—
67C4×C3⋊Dic3C2311yescharacteristic
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×(C2×D3)⋊C4—22no—
70C3×(C2×D3)⋊C4—22no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C3×D24—24no—
74Dic3⋊Dic3—22no—
75#3722—21no—
76(C2×D3)⋊Dic3—22no—
77(C2×D3)⋊Dic3—22no—
78Dic32—21no—
79#3713—24no—
80#3122—91noSylow
81C2×D3×D4—32no—
82C2×C3×D8—32no—
83C3×C4×D4—32no—
84C3×C4×D4—32no—
85#940—32no—
86#938—32no—
87D4×Dic3—32no—
88C2×#213—32no—
89C2×#213—32no—
90#930—62no—
91#929—62no—
92C4×#67—62no—
93C2×(C2×D3)⋊C4—62no—
94C2×D24C2×D312yes—
95#895—32no—
96#893—32no—
97#892—32no—
98#890—32no—
99#884—62no—
100#883—62no—
101#67⋊C4—62no—
102D3×C22⋊C4—62no—
103C4×D12C2×D312yes—
104C4×D12C2×D312yescomplemented
105#872—32no—
106#872—61no—
107C3×#106—32no—
108C3×#102—32no—
109C3×#102—32no—
110C3×#97—21no—
111C3×#97C2×D312yescomplemented
112#832—32no—
113#832—32no—
114#821C2×D312yes—
115#821C2×D312yescomplemented
116(C2×D3)⋊C8—32no—
117(C2×D3)⋊C8—32no—
118(C2×D3)⋊C8—62no—
119#817C2×D312yescomplemented
120Dic3⋊C8—32no—
121Dic3⋊C8—32no—
122Dic3⋊C8—62no—
123#809—32no—
124#809—32no—
125#807—32no—
126#807—32no—
127C4×C3⋊C8—32no—
128C4×C3⋊C8—61no—
129C22×C3⋊D3C2×D411yescharacteristic
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C2×D32—24no—
133C2×D32—82no—
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3C2×D411yescharacteristic
137C2×C3⋊Dic3C2×D412yes—
138C4×C3⋊D3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12—22no—
144C3×D12#4114yes—
145C3×C4×D3—82no—
146C3×C4×D3—82no—
147#626—82no—
148#625—24no—
149#625—82no—
150D3×Dic3—82no—
151C32×C8—22no—
152C3⋊(C3⋊C8)—22no—
153#540—91no—
154#518—91no—
155#482—92no—
156#478—92no—
157#459—92no—
158#447—92no—
159#442—32no—
160C4×D8—92no—
161#433—91no—
162C23×D3—62no—
163C2×C3×D4—32no—
164C2×C3×D4—32no—
165C22×C3×C4—62no—
166C22×C3×C4—62no—
167C2×#67—62no—
168C2×#67—62no—
169C2×#67—62no—
170C2×#67—62no—
171C22×Dic3—62no—
172D3×D4—64no—
173D3×D4—64no—
174C2×D12—62no—
175C2×D12C22×D312yes—
176C2×D12C22×D312yes—
177C2×C4×D3—22no—
178C2×C4×D3—22no—
179C2×C4×D3—32no—
180C2×C4×D3—61no—
181C2×C4×D3—62no—
182C3×D8—64no—
183C2×C3×C8—22no—
184C2×C3×C8C22×D312yes—
185C2×C3×C8C22×D312yes—
186C3×C4⋊C4—32no—
187C3×C4⋊C4—32no—
188C3×C22⋊C4—62no—
189C3×C22⋊C4—62no—
190C3×C42—21no—
191C3×C42C22×D312yes—
192#217—62no—
193#217—62no—
194#213—64no—
195#213—64no—
196(C2×D3)⋊C4—22no—
197(C2×D3)⋊C4—22no—
198(C2×D3)⋊C4—32no—
199(C2×D3)⋊C4—32no—
200(C2×D3)⋊C4—62no—
201(C2×D3)⋊C4—62no—
202(C2×D3)⋊C4—62no—
203(C2×D3)⋊C4—62no—
204C4⋊Dic3—62no—
205C4⋊Dic3C22×D312yes—
206C4⋊Dic3C22×D312yes—
207Dic3⋊C4—32no—
208Dic3⋊C4—32no—
209Dic3⋊C4—62no—
210Dic3⋊C4—62no—
211C4×Dic3—32no—
212C4×Dic3—61no—
213C4×Dic3—62no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—32no—
216C2×C3⋊C8—62no—
217D24—24no—
218C22×C32C22×D411yescharacteristic
219C2×C3⋊D3—21no—
220C2×C3⋊D3—22no—
221C2×C3×D3—24no—
222C2×C3×D3—42no—
223C2×C3×D3—42no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227D32—84no—
228C32×C4—22no—
229C32×C4C2×#4112yes—
230C3⋊Dic3—21no—
231C3⋊Dic3—22no—
232C3×Dic3—42no—
233C3×Dic3—42no—
234C22×D4—91no—
235C2×D8—32no—
236C2×D8—92no—
237#127—91no—
238#125—91no—
239#123—182no—
240#121—92no—
241#121—182no—
242C4×D4—32no—
243C4×D4—32no—
244C4×D4—92no—
245C4×D4—182no—
246#117—91no—
247#117—91no—
248C2×C22⋊C4—182no—
249#107—92no—
250#106—32no—
251C4⋊C8—92no—
252#102—32no—
253#102—32no—
254#102—92no—
255#102—92no—
256C22⋊C8—92no—
257#97D3211yescharacteristic, complemented
258C4×C8—91no—
259C23×C3—62no—
260C23×C3—62no—
261C22×D3—22no—
262C22×D3—22no—
263C22×D3—32no—
264C22×D3—61no—
265C22×D3—68no—
266C22×D3—242no—
267C22×D3—242no—
268C3×D4—34no—
269C3×D4—62no—
270C3×D4—62no—
271C3×D4—62no—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—242no—
277C2×C3×C4—242no—
278C2×C3×C4D3×D412yes—
279C2×C3×C4D3×D412yes—
280C2×C3×C4C23×D312yes—
281#67—68no—
282#67—242no—
283#67—242no—
284#67—242no—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—32no—
288C2×Dic3—32no—
289C2×Dic3—32no—
290C2×Dic3—62no—
291C2×Dic3—61no—
292C2×Dic3—242no—
293D12—22no—
294D12—22no—
295D12—22no—
296D12—242no—
297D12#23514yes—
298C4×D3—62no—
299C4×D3—62no—
300C4×D3—82no—
301C4×D3—82no—
302C4×D3—122no—
303C4×D3—242no—
304C3×C8—22no—
305C3×C8—22no—
306C3×C8—42no—
307C3⋊C8—62no—
308C3⋊C8—62no—
309C3⋊C8—122no—
310C2×C32#52511yescharacteristic
311C2×C32#57612yes—
312C3⋊D3—41no—
313C3×D3—44no—
314C3×D3—82no—
315C24—181no—
316C2×D4—32no—
317C2×D4—32no—
318C2×D4—182no—
319C2×D4—181no—
320C2×D4—182no—
321C2×D4—184no—
322C22×C4—62no—
323C22×C4—62no—
324C22×C4—91no—
325C22×C4—182no—
326D8—64no—
327D8—184no—
328C2×C8—92no—
329C2×C8C2×D3212yes—
330C4⋊C4—32no—
331C4⋊C4—32no—
332C4⋊C4—92no—
333C4⋊C4—182no—
334C22⋊C4—62no—
335C22⋊C4—62no—
336C22⋊C4—92no—
337C22⋊C4—181no—
338C22⋊C4—182no—
339C22⋊C4—182no—
340C42—91no—
341C42—181no—
342C42C2×D3211yescharacteristic
343C22×C3—21no—
344C22×C3—64no—
345C22×C3—122no—
346C22×C3—122no—
347C22×C3—122no—
348C22×C3—122no—
349C22×C3—122no—
350C22×C3C2×D3×D412yes—
351C2×D3—24no—
352C2×D3—42no—
353C2×D3—42no—
354C2×D3—42no—
355C2×D3—42no—
356C2×D3—42no—
357C2×D3—62no—
358C2×D3—62no—
359C2×D3—62no—
360C2×D3—121no—
361C2×D3—122no—
362C2×D3—248no—
363C3×C4—22no—
364C3×C4—22no—
365C3×C4—22no—
366C3×C4—42no—
367C3×C4—122no—
368C3×C4—122no—
369C3×C4C2×#23512yes—
370C3×C4D3×#4112yes—
371Dic3—42no—
372Dic3—42no—
373Dic3—62no—
374Dic3—62no—
375Dic3—62no—
376Dic3—121no—
377Dic3—122no—
378C32#312211yescharacteristic, complemented, Sylow
379C23—62no—
380C23—62no—
381C23—91no—
382C23—184no—
383C23—722no—
384D4—34no—
385D4—62no—
386D4—62no—
387D4—62no—
388D4—184no—
389D4—722no—
390D4—722no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—92no—
394C2×C4—91no—
395C2×C4—182no—
396C2×C4—242no—
397C2×C4—242no—
398C2×C4—722no—
399C2×C4#380212yes—
400C2×C4C22×D3211yescharacteristic
401C8—22no—
402C8—182no—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—124no—
406C2×C3—242no—
407C2×C3#554712yes—
408C2×C3#577412yes—
409C2×C3#577412yes—
410D3—44no—
411D3—82no—
412D3—122no—
413D3—241no—
414C22—64no—
415C22—122no—
416C22—122no—
417C22—122no—
418C22—122no—
419C22—122no—
420C22—182no—
421C22—181no—
422C22—724no—
423C22C2×#380211yescharacteristic
424C4—22no—
425C4—122no—
426C4—122no—
427C4—182no—
428C4—181no—
429C4D3×#23512yes—
430C3—21no—
431C3#7987412yescomplemented
432C2—124no—
433C2—242no—
434C2—361no—
435C2#1059400611yescharacteristic
436C2#1059472012yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593996C2semidirect
2. #10593984C2semidirect
3. #10592408C2semidirect
4. C3×#4711C2semidirect
5. #10590945C2semidirect
6. #10590782C2semidirect
7. #10590749C2semidirect
8. #10590652C2semidirect
9. C4×#3713C2semidirect
15. C3×C4×D12C22semidirect
18. #63914C22semidirect
23. #63872C22semidirect
26. C32×#97C22semidirect
28. #63641C22semidirect
29. C4×C3⋊(C3⋊C8)C22semidirect
31. C3×#821C22semidirect
32. C3×#817C22semidirect
33. #63576C22semidirect
35. #63562C22semidirect
49. #4711D3semidirect
104. C4×D12C2×D3semidirect
111. C3×#97C2×D3semidirect
115. #821C2×D3semidirect
119. #817C2×D3semidirect
257. #97D32semidirect
378. C32#3122semidirect
431. C3#79874semidirect

Maximal subgroups

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

subgroupindex
#105939962
#105939842
#105924082
C3×#47112
#105909452
#105907822
#105907492
#105906522
C4×#37132
#798743