Finite Group Databasebeta

← #11792414

Subgroups — #11792414

Order 1152.

835 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 835 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C3×#5748C211yesmaximal, characteristic, complemented
2#10595022C212yesmaximal, complemented
3C3×#5126C211yesmaximal, characteristic, complemented
4#10591110C212yesmaximal, complemented
5#10589423C211yesmaximal, characteristic, complemented
6#72118—31nomaximal
7#69993—31nomaximal
8C2×C3×#235C2212yes—
9C22×C3×C4×D3C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11#64135C2212yes—
12C2×C3×#208C2211yescharacteristic
13C3×#909—22no—
14C3×#908—22no—
15C3×#904—22no—
16#63976—22no—
17#63961—22no—
18#63908—22no—
19C4×#625—24no—
20#63856—22no—
21C3×(C2×D3)⋊C8—22no—
22#63568—24no—
23C3×#575—31no—
24#5828—32no—
25#5791—32no—
26#5748D311yescharacteristic, complemented
27C3×#407—31no—
28#5236—32no—
29#5139—32no—
30#5126D311yescharacteristic, complemented
31#4557—31no—
32#4557—31no—
33#4557—61no—
34C23×C3×D3D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C2×C3×#67—22no—
37C22×C3×Dic3D411yescharacteristic
38C3×#235—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235—22no—
42C2×C3×D12D412yescomplemented
43C2×C3×C4×D3—22no—
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—22no—
46C2×C3×C4×D3—22no—
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D412yescomplemented
49C2×#625—24no—
50C32×M16—22no—
51C2×C32×C8D412yescomplemented
52#3757—22no—
53C4⋊(C3⋊Dic3)—22no—
54C4×C3⋊Dic3D414yescomplemented
55C3×#208—22no—
56C2×C3×C3⋊C8—21no—
57C3×Dic12—22no—
58C3×D24—22no—
59C3×#204—24no—
60#3724—24no—
61(C2×D3)⋊Dic3—24no—
62(C2×D3)⋊Dic3—24no—
63#2010—91noSylow
64C2×C3×#41—32no—
65C23×C3×C4—31no—
66C2×#235C2×D312yes—
67C22×C4×D3C2×D311yescharacteristic
68C3×#137—62no—
69C3×AGL(1,ℤ/8)—62no—
70C3×#135—62no—
71C2×C3×M16—21no—
72C2×C3×M16—31no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C2×D311yescharacteristic
75#953—62no—
76#946—62no—
77#938—62no—
78#937—62no—
79#935—62no—
80#930—62no—
81#929—62no—
82C4×#67—64no—
83C4×#67—64no—
84#926—32no—
85#926—32no—
86#926—62no—
87#924—62no—
88C2×#208C2×D311yescharacteristic
89#909—22no—
90#908—22no—
91#904—22no—
92C3×C22⋊C8—62no—
93#837—64no—
94#825—64no—
95(C2×D3)⋊C8—22no—
96C23×C32C2×D411yescharacteristic
97C22×C3×D3—22no—
98C22×C3×D3—21no—
99C22×C3×D3—22no—
100C22×C3×D3—42no—
101C2×C32×C4C2×D412yes—
102C2×C32×C4C2×D412yes—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3⋊Dic3—24no—
106C3×#67—42no—
107C3×#67—42no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—21no—
111C3×D12—22no—
112C3×D12—22no—
113C3×C4×D3—41no—
114C3×C4×D3—42no—
115C3×C4×D3—42no—
116C3×C4×D3—41no—
117C3×C4×D3—42no—
118C3×Dic6—22no—
119C3×Dic6—22no—
120#625—48no—
121C32×C8—22no—
122C3×C3⋊C8—41no—
123#575—31no—
124#525—92no—
125#421—92no—
126#407—31no—
127H(3,ℤ/4)—91no—
128C24×C3—31no—
129C23×D3D1211yescharacteristic
130C3×#41—62no—
131C3×#41—62no—
132C3×#41—62no—
133C3×#41—62no—
134C2×C3×Q8—32no—
135C2×C3×D4—32no—
136C2×C3×D4—62no—
137C22×C3×C4—21no—
138C22×C3×C4—31no—
139C22×C3×C4—62no—
140C22×C3×C4—62no—
141C22×C3×C4—61no—
142C22×C3×C4—61no—
143C22×C3×C4—62no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C2×#67—22no—
147C2×#67—64no—
148C2×#67—64no—
149C22×Dic3D1211yescharacteristic
150#235—22no—
151#235—22no—
152#235—22no—
153#235—22no—
154C2×D12#6712yescomplemented
155C2×C4×D3—21no—
156C2×C4×D3—22no—
157C2×C4×D3—22no—
158C2×C4×D3—22no—
159C2×C4×D3—21no—
160C2×Dic6#6712yescomplemented
161C3×Q16—62no—
162C3×SD16—64no—
163C3×D8—62no—
164C3×M16—22no—
165C3×M16—22no—
166C3×M16—42no—
167C3×M16—62no—
168C2×C3×C8—22no—
169C2×C3×C8—61no—
170C2×C3×C8#6712yescomplemented
171C2×C3×C8#6712yescomplemented
172#217—64no—
173#217—64no—
174#217—62no—
175#217—62no—
176#217—122no—
177(C2×D3)⋊C4—64no—
178(C2×D3)⋊C4—64no—
179C4⋊Dic3—62no—
180C4⋊Dic3—62no—
181C4⋊Dic3—122no—
182Dic3⋊C4—64no—
183Dic3⋊C4—64no—
184C4×Dic3—34no—
185C4×Dic3—34no—
186C4×Dic3—64no—
187#208—22no—
188C2×C3⋊C8—21no—
189Dic12—22no—
190D24—22no—
191#204—24no—
192C22×C32—41no—
193C22×C32#12012yes—
194C22×C32#12111yescharacteristic
195C2×C3×D3—24no—
196C2×C3×D3—22no—
197C2×C3×D3—42no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—44no—
201C2×C3×D3—42no—
202C32×C4#12011yescharacteristic
203C32×C4#12112yes—
204C32×C4#12711yescharacteristic
205C3⋊Dic3—44no—
206C3×Dic3—42no—
207C3×Dic3—41no—
208C2×#41—32no—
209C23×C4—31no—
210#137—62no—
211AGL(1,ℤ/8)—62no—
212#135—62no—
213C2×M16—31no—
214C2×M16D3211yescharacteristic
215#123—182no—
216C22⋊Q8—182no—
217#121—182no—
218#120—182no—
219C4×D4—184no—
220#117—92no—
221#104—184no—
222C22⋊C8—62no—
223C23×C3—21no—
224C23×C3—62no—
225C23×C3—61no—
226C23×C3—62no—
227C23×C3—122no—
228C23×C3C2×D1211yescharacteristic
229C23×C3D3×D411yescharacteristic
230C22×D3—22no—
231C22×D3—21no—
232C22×D3—22no—
233C22×D3—42no—
234C3×Q8—62no—
235C3×Q8—62no—
236C3×D4—62no—
237C3×D4—62no—
238C3×D4—122no—
239C3×D4—122no—
240C2×C3×C4—21no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—22no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—61no—
247C2×C3×C4—122no—
248C2×C3×C4—122no—
249C2×C3×C4—121no—
250C2×C3×C4—122no—
251C2×C3×C4—121no—
252C2×C3×C4#23511yescharacteristic
253C2×C3×C4D3×D412yes—
254C2×C3×C4D3×D412yes—
255C2×C3×C4D3×D412yes—
256C2×C3×C4#23711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259C2×C3×C4C2×#6712yes—
260#67—42no—
261#67—42no—
262#67—128no—
263#67—128no—
264C2×Dic3—22no—
265C2×Dic3—21no—
266C2×Dic3—22no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—124no—
270D12—22no—
271D12—22no—
272C4×D3—42no—
273C4×D3—41no—
274C4×D3—42no—
275C4×D3—41no—
276C4×D3—42no—
277Dic6—22no—
278Dic6—22no—
279C3×C8—22no—
280C3×C8—22no—
281C3×C8—42no—
282C3×C8—121no—
283C3⋊C8—41no—
284C2×C32—22no—
285C2×C32—21no—
286C2×C32#39211yescharacteristic
287C3×D3—42no—
288C3×D3—82no—
289C24—31no—
290#41—62no—
291#41—62no—
292#41—62no—
293#41—62no—
294C2×Q8—32no—
295C2×D4—32no—
296C2×D4—62no—
297C2×D4—184no—
298C22×C4—31no—
299C22×C4—61no—
300C22×C4—62no—
301C22×C4—62no—
302C22×C4—61no—
303C22×C4—62no—
304C22×C4C2×D3211yescharacteristic
305Q16—62no—
306SD16—64no—
307D8—62no—
308M16—22no—
309M16—62no—
310C2×C8—61no—
311C2×C8#62512yescomplemented
312C4⋊C4—184no—
313C4⋊C4—182no—
314C22⋊C4—184no—
315C22⋊C4—184no—
316C22⋊C4—182no—
317C42—94no—
318C22×C3—21no—
319C22×C3—22no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—64no—
323C22×C3—62no—
324C22×C3—81no—
325C22×C3—122no—
326C22×C3—121no—
327C22×C3—124no—
328C22×C3—121no—
329C22×C3—122no—
330C22×C3#88212yes—
331C22×C3#93011yescharacteristic
332C22×C3#93712yes—
333C22×C3#93811yescharacteristic
334C2×D3—24no—
335C2×D3—22no—
336C2×D3—42no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—44no—
340C2×D3—42no—
341C3×C4—22no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—122no—
345C3×C4—121no—
346C3×C4#88412yes—
347C3×C4#93711yescharacteristic
348C3×C4#93912yes—
349C3×C4#94011yescharacteristic
350C3×C4#94011yescharacteristic
351C3×C4#95311yescharacteristic
352Dic3—41no—
353Dic3—42no—
354Dic3—124no—
355Dic3—124no—
356Dic3—244no—
357C32#201011yescharacteristic, complemented, Sylow
358C23—61no—
359C23—62no—
360C23—62no—
361C23—122no—
362C23D3×D1211yescharacteristic
363Q8—62no—
364Q8—62no—
365D4—62no—
366D4—62no—
367D4—122no—
368D4—122no—
369D4—368no—
370C2×C4—61no—
371C2×C4—62no—
372C2×C4—62no—
373C2×C4—122no—
374C2×C4—122no—
375C2×C4—121no—
376C2×C4—122no—
377C2×C4—121no—
378C2×C4—184no—
379C2×C4#379511yescharacteristic
380C2×C4#380212yes—
381C2×C4C2×#62511yescharacteristic
382C2×C4D3×#6712yes—
383C8—22no—
384C8—121no—
385C2×C3—22no—
386C2×C3—21no—
387C2×C3—22no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—42no—
391C2×C3—41no—
392C2×C3—122no—
393C2×C3—242no—
394C2×C3#496011yescharacteristic
395C2×C3#522311yescharacteristic
396D3—42no—
397D3—82no—
398C22—41no—
399C22—64no—
400C22—62no—
401C22—122no—
402C22—121no—
403C22—124no—
404C22—121no—
405C22—122no—
406C22#6390811yescharacteristic
407C22#6392212yes—
408C4—121no—
409C4—122no—
410C4—364no—
411C4#6388512yes—
412C4#6391411yescharacteristic
413C4#6397611yescharacteristic
414C3—21no—
415C3#6999311yescharacteristic, complemented
416C3#7211811yescharacteristic, complemented
417C2—22no—
418C2—21no—
419C2—122no—
420C2—242no—
421C2#1059138911yescharacteristic
subgroupG/H
centerC4#63914
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#392
hypercenterC2×M16D32
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5748C2semidirect
2. #10595022C2semidirect
3. C3×#5126C2semidirect
4. #10591110C2semidirect
5. #10589423C2semidirect
26. #5748D3semidirect
30. #5126D3semidirect
42. C2×C3×D12D4semidirect
48. C2×C3×Dic6D4semidirect
51. C2×C32×C8D4semidirect
54. C4×C3⋊Dic3D4semidirect
154. C2×D12#67semidirect
160. C2×Dic6#67semidirect
170. C2×C3×C8#67semidirect
171. C2×C3×C8#67semidirect
311. C2×C8#625semidirect
357. C32#2010semidirect
415. C3#69993semidirect
416. C3#72118semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
#105950222
C3×#51262
#105911102
#105894232
#721183
#699933