Finite Group Databasebeta

← #11873554

Subgroups — #11873554

Order 1152.

1037 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1037 conjugacy classes of subgroups — too many to draw. Only its 164 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⋊D3×#124C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic, complemented
3C3×#5055C212yesmaximal, complemented
4#10591632C212yesmaximal, complemented
5#10591552C212yesmaximal, complemented
6#10591496C212yesmaximal, complemented
7#10591416C212yesmaximal
8#10590322C211yesmaximal, characteristic, complemented
9#10590294C212yesmaximal, complemented
10D3×#489—32nomaximal
11C2×Q8×C3⋊D3C2211yescharacteristic
12C2×D4×C3⋊D3C2211yescharacteristic
13C2×#3797—21no—
14C32×#124C2211yescharacteristic
15#64156C2211yescharacteristic
16#64145C2211yescharacteristic
17#64094—21no—
18#64094—21no—
19C22⋊C4×C3⋊D3—21no—
20C22⋊C4×C3⋊D3—21no—
21#64084C2211yescharacteristic
22C42×C3⋊D3C2211yescharacteristic
23C3×#869C2212yescomplemented
24#63919—21no—
25#63919C2212yescomplemented
26#63900—21no—
27#63900C2212yes—
28#63873—21no—
29C2×#3710C2212yes—
30C3×#835C2214yescomplemented
31C3×#832C2214yes—
32C3×#803C2212yescomplemented
33#63567C2214yescomplemented
34#63564C2214yes—
35#63555C2212yescomplemented
36D3×C4⋊Q8—32no—
37D3×#124—32no—
38D3×#124—61no—
39C3×#489—32no—
40#5089—32no—
41#5055D312yescomplemented
42D3×#103—34no—
43#4794—34no—
44D3×#102—34no—
45#4765—34no—
46#4714—32no—
47D3×#97—32no—
48C23×C3⋊D3—21no—
49C2×C32×Q8C2311yescharacteristic
50C2×C32×D4C2311yescharacteristic
51C2×#638—21no—
52Q8×C3⋊D3—24no—
53D4×C3⋊D3—24no—
54C2×C4⋊(C3⋊D3)C2311yescharacteristic
55C2×C4×C3⋊D3—21no—
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×#634—21no—
60C2×#634C2311yescharacteristic
61C2×C3×Dic6—22no—
62C2×#627—22no—
63C2×#624—22no—
64#3797—44no—
65C32×C22⋊C4—21no—
66C32×C22⋊C4—21no—
67C32×C42C2311yescharacteristic
68#3757—21no—
69#3757—21no—
70#3752—21no—
71#3752—21no—
72#3752—21no—
73#3752—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#3710—24no—
83C2×#489—91noSylow
84C2×D3×Q8—32no—
85C2×D3×Q8—61no—
86C2×D3×Q8—62no—
87C2×D3×D4—32no—
88C2×D3×D4—61no—
89C3×C4⋊Q8—32no—
90C3×#124—21no—
91C3×#124C2×D312yes—
92#947—32no—
93#947—61no—
94#944—62no—
95#936—32no—
96#936—61no—
97C2×D3×C8—34no—
98D3×C4⋊C4—34no—
99D3×C4⋊C4—62no—
100#888—34no—
101#888—62no—
102#885—62no—
103#885—62no—
104#885—62no—
105#885—62no—
106D3×C22⋊C4—62no—
107D3×C22⋊C4—62no—
108D3×C22⋊C4—62no—
109D3×C22⋊C4—62no—
110#875—32no—
111#875—61no—
112C42×D3—32no—
113C42×D3—61no—
114#869C2×D312yescomplemented
115C3×#103—34no—
116C3×#102—34no—
117C3×#97—32no—
118#835C2×D314yescomplemented
119#832C2×D314yes—
120#821—34no—
121#816—34no—
122#815—34no—
123#810—34no—
124#809—34no—
125#803C2×D312yescomplemented
126C23×C32—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—42no—
129C22×C3⋊D3—42no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3C2×D411yescharacteristic
132C32×Q8—22no—
133C32×D4—22no—
134C2×C32×C4—21no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2411yescharacteristic
138#638—42no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C2×C3⋊Dic3C2×D411yescharacteristic
143C4⋊(C3⋊D3)—22no—
144C4×C3⋊D3—22no—
145C4×C3⋊D3—22no—
146C4×C3⋊D3—42no—
147C4×C3⋊D3#4114yes—
148#634—22no—
149#634—42no—
150C2×C3×Dic3—24no—
151C3×Dic6—44no—
152#627—44no—
153#624—44no—
154C3×C3⋊C8—24no—
155C2×C4⋊Q8—91no—
156C2×#124—91no—
157#489—32no—
158#489—92no—
159#489—92no—
160#489—92no—
161C2×#103—92no—
162C2×#102—92no—
163C2×#97—91no—
164C23×D3—62no—
165C23×D3—62no—
166C2×C3×Q8—21no—
167C2×C3×Q8—62no—
168C2×C3×Q8C22×D312yes—
169C2×C3×D4—21no—
170C2×C3×D4C22×D312yes—
171C2×#67—62no—
172C2×#67—62no—
173D3×Q8—68no—
174D3×Q8—124no—
175D3×Q8—128no—
176D3×D4—68no—
177D3×D4—124no—
178C2×D12—32no—
179C2×D12—61no—
180C2×C4×D3—32no—
181C2×C4×D3—32no—
182C2×C4×D3—32no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—64no—
187C2×C4×D3—62no—
188C2×C4×D3—62no—
189C2×Dic6—22no—
190C2×Dic6—32no—
191C2×Dic6—61no—
192C2×Dic6—64no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×C3×C8—34no—
196C3×C4⋊C4—34no—
197C3×C4⋊C4—62no—
198C3×C22⋊C4—22no—
199C3×C22⋊C4—22no—
200C3×C22⋊C4—22no—
201C3×C22⋊C4—22no—
202C3×C42—21no—
203C3×C42C22×D312yes—
204#217—62no—
205#217—62no—
206#217—62no—
207#217—62no—
208(C2×D3)⋊C4—62no—
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—62no—
213(C2×D3)⋊C4—62no—
214(C2×D3)⋊C4—62no—
215(C2×D3)⋊C4—62no—
216C4⋊Dic3—22no—
217C4⋊Dic3C22×D314yes—
218Dic3⋊C4—64no—
219Dic3⋊C4—64no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C2×C3⋊C8C22×D314yes—
227D3×C8—68no—
228C22×C32—41no—
229C22×C32—41no—
230C22×C32—41no—
231C22×C32C22×D411yescharacteristic
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C2×C3⋊D3—84no—
236C2×C3⋊D3#12412yes—
237C2×C3⋊D3AGL(1,ℤ/8)12yes—
238C2×C3⋊D3#13712yes—
239C32×C4—21no—
240C32×C4—21no—
241C32×C4—41no—
242C32×C4C2×#4112yes—
243C3⋊Dic3—21no—
244C3⋊Dic3—21no—
245C3⋊Dic3—41no—
246C3⋊Dic3#12412yes—
247C3×Dic3—44no—
248C22×Q8—91no—
249C22×Q8—181no—
250C22×D4—91no—
251C22×C8—92no—
252C4⋊Q8—32no—
253C4⋊Q8—92no—
254C4⋊Q8—181no—
255C4⋊Q8—181no—
256#124—91no—
257#124—91no—
258#124—91no—
259#124—181no—
260#124—181no—
261#124D3211yescharacteristic
262C2×C4⋊C4—92no—
263C2×C4⋊C4—181no—
264C2×C22⋊C4—181no—
265C2×C22⋊C4—181no—
266C2×C42—91no—
267#103—34no—
268#103—94no—
269#102—34no—
270#102—94no—
271#97—32no—
272#97—92no—
273C23×C3—22no—
274C23×C3—22no—
275C22×D3—32no—
276C22×D3—61no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—124no—
280C22×D3—124no—
281C22×D3—124no—
282C22×D3—124no—
283C22×D3—124no—
284C22×D3—124no—
285C3×Q8—24no—
286C3×Q8—42no—
287C3×Q8—124no—
288C3×D4—24no—
289C3×D4—42no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—64no—
296C2×C3×C4D3×D412yes—
297C2×C3×C4D3×D412yes—
298C2×C3×C4C23×D312yes—
299#67—124no—
300#67—124no—
301C2×Dic3—24no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310D12—64no—
311D12—122no—
312C4×D3—38no—
313C4×D3—64no—
314C4×D3—64no—
315C4×D3—64no—
316C4×D3—122no—
317C4×D3—122no—
318C4×D3—128no—
319C4×D3—124no—
320C4×D3—124no—
321Dic6—44no—
322Dic6—64no—
323Dic6—122no—
324Dic6—124no—
325Dic6—128no—
326Dic6—124no—
327C3×C8—64no—
328C3⋊C8—24no—
329C2×C32—81no—
330C2×C32C2×#12411yescharacteristic
331C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
332C2×C32C2×#13711yescharacteristic
333C3⋊D3—81no—
334C3⋊D3#48914yescomplemented
335C24—181no—
336C2×Q8—62no—
337C2×Q8—91no—
338C2×Q8—181no—
339C2×Q8—182no—
340C2×Q8—184no—
341C2×Q8—364no—
342C2×Q8C2×D3211yescharacteristic
343C2×D4—91no—
344C2×D4—184no—
345C2×D4—181no—
346C2×D4C2×D3211yescharacteristic
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—91no—
350C22×C4—181no—
351C22×C4—182no—
352C2×C8—34no—
353C2×C8—184no—
354C4⋊C4—34no—
355C4⋊C4—62no—
356C4⋊C4—182no—
357C4⋊C4—182no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—181no—
361C22⋊C4—181no—
362C22⋊C4—181no—
363C22⋊C4—181no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C42—91no—
367C42—91no—
368C42—91no—
369C42C2×D3211yescharacteristic
370C22×C3—21no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3C2×D3×D412yes—
378C2×D3—34no—
379C2×D3—34no—
380C2×D3—34no—
381C2×D3—62no—
382C2×D3—62no—
383C2×D3—62no—
384C2×D3—122no—
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—248no—
391C2×D3—248no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—22no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—124no—
400C3×C4D3×#4114yes—
401Dic3—34no—
402Dic3—44no—
403Dic3—62no—
404Dic3—62no—
405Dic3—62no—
406Dic3—121no—
407Dic3—121no—
408Dic3—122no—
409Dic3—122no—
410C32C2×#48911yescharacteristic, complemented, Sylow
411C23—21no—
412C23—91no—
413C23—181no—
414C23—362no—
415C23—362no—
416C23—362no—
417Q8—22no—
418Q8—124no—
419Q8—182no—
420Q8—362no—
421Q8—364no—
422D4—22no—
423D4—182no—
424D4—362no—
425C2×C4—21no—
426C2×C4—64no—
427C2×C4—91no—
428C2×C4—94no—
429C2×C4—91no—
430C2×C4—91no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4—181no—
434C2×C4—362no—
435C2×C4—364no—
436C2×C4#381111yescharacteristic
437C2×C4#381111yescharacteristic
438C2×C4C22×D3211yescharacteristic
439C8—64no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—82no—
444C2×C3—82no—
445C2×C3D3×#12412yes—
446C2×C3D3×AGL(1,ℤ/8)12yes—
447C2×C3D3×#13712yes—
448D3—38no—
449D3—64no—
450D3—242no—
451D3—242no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—92no—
456C22—92no—
457C22—92no—
458C22—361no—
459C22—361no—
460C22—361no—
461C22—724no—
462C22C2×#381111yescharacteristic
463C4—21no—
464C4—21no—
465C4—41no—
466C4—92no—
467C4—124no—
468C4—181no—
469C4—181no—
470C4—361no—
471C4#6431212yes—
472C3—21no—
473C3D3×#48912yescomplemented
474C2—81no—
475C2—94no—
476C2—721no—
477C2#1059517011yescharacteristic
478C2#1059545811yescharacteristic
479C2#1059546811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#124D32
hypocenterC32C2×#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593909C2semidirect
3. C3×#5055C2semidirect
4. #10591632C2semidirect
5. #10591552C2semidirect
6. #10591496C2semidirect
8. #10590322C2semidirect
9. #10590294C2semidirect
23. C3×#869C22semidirect
25. #63919C22semidirect
30. C3×#835C22semidirect
32. C3×#803C22semidirect
33. #63567C22semidirect
35. #63555C22semidirect
41. #5055D3semidirect
114. #869C2×D3semidirect
118. #835C2×D3semidirect
125. #803C2×D3semidirect
334. C3⋊D3#489semidirect
410. C32C2×#489semidirect
473. C3D3×#489semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1242
#105939092
C3×#50552
#105916322
#105915522
#105914962
#105914162
#105903222
#105902942
D3×#4893