Finite Group Databasebeta

← #11869383

Subgroups — #11869383

Order 1152.

1081 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 1081 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
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C3×#5043C212yesmaximal, complemented
4#10591553C212yesmaximal, complemented
5#10591552C212yesmaximal, complemented
6#10591152C211yesmaximal, characteristic
7#10591124C212yesmaximal, complemented
8#10590575C212yesmaximal, complemented
9#10590443C212yesmaximal, complemented
10D3×#483—32nomaximal
11C2×Q8×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×#624—21no—
14C32×C22⋊Q8C2211yescharacteristic
15#64155C2211yescharacteristic
16#64133C2211yescharacteristic
17#64106C2211yescharacteristic
18#64105—21no—
19C4⋊C4×C3⋊D3—21no—
20C4⋊C4×C3⋊D3C2211yescharacteristic
21C22⋊C4×C3⋊D3—21no—
22#64087—21no—
23C2×C3×C4⋊Dic3C2212yes—
24C2×#3724—21no—
25#63900—21no—
26#63900—21no—
27#63900C2212yes—
28#63900C2212yes—
29C2×#3710C2212yes—
30C3×#835C2214yescomplemented
31C3×#830C2212yes—
32C3×#808C2214yescomplemented
33#63573C2214yescomplemented
34#63567C2214yescomplemented
35#63557C2212yes—
36D3×C22⋊Q8—32no—
37D3×C22⋊Q8—61no—
38C2×D3×C4⋊C4—32no—
39C3×#483—32no—
40#5043D312yescomplemented
41#4971—32no—
42#4862—34no—
43D3×#106—34no—
44#4805—34no—
45D3×#103—34no—
46D3×C22⋊C8—32no—
47#4721—32no—
48C23×C3⋊D3D411yescharacteristic
49C2×C32×Q8C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52Q8×C3⋊D3—24no—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—21no—
55C2×C4×C3⋊D3—21no—
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×#634—21no—
61C2×#634C2311yescharacteristic
62C22×C3×Dic3—22no—
63C2×#624—22no—
64C2×#624—22no—
65C2×#624—44no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2311yescharacteristic
68C32×C22⋊C4—21no—
69#3757—21no—
70#3752—21no—
71#3752—21no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2311yescharacteristic
74#3750—21no—
75#3750—21no—
76#3750—21no—
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2314yes—
79C2×C3×C3⋊C8C2314yes—
80#3724—22no—
81#3724—22no—
82#3710—24no—
83C2×#483—91noSylow
84C2×D3×Q8—32no—
85C2×D3×Q8—61no—
86C22×C4×D3—32no—
87C22×C4×D3—61no—
88C22×C4×D3—62no—
89C3×C22⋊Q8—21no—
90C3×C22⋊Q8C2×D312yes—
91C2×C3×C4⋊C4—32no—
92#946—32no—
93#946—61no—
94C2×C4⋊Dic3C2×D312yes—
95#924—32no—
96#924—61no—
97C2×Dic3⋊C4—62no—
98C2×D3×C8—34no—
99#897—32no—
100#897—61no—
101#896—62no—
102#896—62no—
103D3×C4⋊C4—32no—
104D3×C4⋊C4—34no—
105D3×C4⋊C4—34no—
106D3×C4⋊C4—61no—
107D3×C4⋊C4—62no—
108D3×C4⋊C4—62no—
109D3×C4⋊C4—62no—
110D3×C4⋊C4—62no—
111D3×C22⋊C4—62no—
112D3×C22⋊C4—62no—
113#878—62no—
114#878—62no—
115C3×#106—34no—
116C3×#103—34no—
117C3×C22⋊C8—32no—
118#835C2×D314yescomplemented
119#830C2×D312yes—
120(C2×D3)⋊C8—34no—
121#817—34no—
122#816—34no—
123#810—34no—
124#808—34no—
125#808C2×D314yescomplemented
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3SD1614yes—
130C22×C3⋊D3C2×D411yescharacteristic
131C22×C3⋊D3C2×D411yescharacteristic
132C32×Q8—22no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—22no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—22no—
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—42no—
148C4×C3⋊D3#4114yes—
149#634—22no—
150#634—42no—
151C2×C3×Dic3—24no—
152C2×C3×Dic3—44no—
153#624—44no—
154#624—44no—
155C3×C3⋊C8—24no—
156C2×C22⋊Q8—91no—
157C22×C4⋊C4—91no—
158#483—32no—
159#483—92no—
160#483—92no—
161#483—92no—
162C2×#106—92no—
163C2×#103—92no—
164C2×C22⋊C8—91no—
165C23×D3—32no—
166C23×D3—61no—
167C2×C3×Q8—21no—
168C2×C3×Q8C22×D312yes—
169C22×C3×C4—21no—
170C22×C3×C4—62no—
171C22×C3×C4C22×D312yes—
172C22×Dic3—22no—
173C22×Dic3—32no—
174C22×Dic3—61no—
175D3×Q8—68no—
176D3×Q8—124no—
177C2×C4×D3—32no—
178C2×C4×D3—32no—
179C2×C4×D3—32no—
180C2×C4×D3—32no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—68no—
186C2×C4×D3—64no—
187C2×C4×D3—64no—
188C2×C4×D3—62no—
189C2×C4×D3—62no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—124no—
193C2×C4×D3—128no—
194C2×Dic6—32no—
195C2×Dic6—61no—
196C2×Dic6—62no—
197C2×Dic6—62no—
198C2×C3×C8—34no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—34no—
203C3×C4⋊C4—62no—
204C3×C4⋊C4C22×D312yes—
205C3×C22⋊C4—22no—
206C3×C22⋊C4—22no—
207#217—62no—
208#217—62no—
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—62no—
213C4⋊Dic3—22no—
214C4⋊Dic3—32no—
215C4⋊Dic3—61no—
216C4⋊Dic3—62no—
217C4⋊Dic3—62no—
218C4⋊Dic3C22×D314yes—
219Dic3⋊C4—64no—
220Dic3⋊C4—64no—
221Dic3⋊C4—62no—
222Dic3⋊C4—62no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226Dic3⋊C4—62no—
227C2×C3⋊C8C22×D314yes—
228D3×C8—68no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32C2×SD1612yes—
232C22×C32C22×D411yescharacteristic
233C2×C3⋊D3—21no—
234C2×C3⋊D3—21no—
235C2×C3⋊D3—28no—
236C2×C3⋊D3#12312yes—
237C2×C3⋊D3C2×SD1612yes—
238C2×C3⋊D3C2×SD1612yes—
239C2×C3⋊D3#13712yes—
240C32×C4—21no—
241C32×C4—41no—
242C32×C4—41no—
243C32×C4C2×#4112yes—
244C3⋊Dic3—21no—
245C3⋊Dic3—41no—
246C3⋊Dic3—41no—
247C3⋊Dic3#12312yes—
248C3×Dic3—44no—
249C22×Q8—91no—
250C23×C4—91no—
251C23×C4—181no—
252C22×C8—92no—
253C22⋊Q8—91no—
254C22⋊Q8—91no—
255C22⋊Q8—91no—
256C22⋊Q8—181no—
257C22⋊Q8—181no—
258C22⋊Q8D3211yescharacteristic
259C2×C4⋊C4—32no—
260C2×C4⋊C4—92no—
261C2×C4⋊C4—92no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—181no—
264C2×C4⋊C4—181no—
265C2×C4⋊C4—181no—
266C2×C4⋊C4—181no—
267C2×C22⋊C4—181no—
268#106—34no—
269#106—94no—
270#103—34no—
271#103—94no—
272C22⋊C8—32no—
273C22⋊C8—92no—
274C23×C3—21no—
275C23×C3D3×D412yes—
276C22×D3—32no—
277C22×D3—38no—
278C22×D3—32no—
279C22×D3—61no—
280C22×D3—64no—
281C22×D3—61no—
282C22×D3—64no—
283C22×D3—64no—
284C22×D3—122no—
285C22×D3—122no—
286C3×Q8—24no—
287C3×Q8—42no—
288C2×C3×C4—24no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—42no—
296C2×C3×C4—64no—
297C2×C3×C4—124no—
298C2×C3×C4D3×D412yes—
299C2×C3×C4C23×D312yes—
300C2×Dic3—24no—
301C2×Dic3—32no—
302C2×Dic3—32no—
303C2×Dic3—44no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—64no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—122no—
312C4×D3—38no—
313C4×D3—64no—
314C4×D3—64no—
315C4×D3—64no—
316C4×D3—64no—
317C4×D3—122no—
318C4×D3—122no—
319C4×D3—122no—
320C4×D3—128no—
321C4×D3—128no—
322C4×D3—124no—
323C4×D3—124no—
324C4×D3—124no—
325C4×D3—124no—
326Dic6—64no—
327Dic6—122no—
328Dic6—124no—
329Dic6—124no—
330C3×C8—64no—
331C3⋊C8—24no—
332C2×C32—22no—
333C2×C32C2×#12311yescharacteristic
334C2×C32C22×SD1611yescharacteristic
335C2×C32C2×#13711yescharacteristic
336C3⋊D3—22no—
337C3⋊D3#48314yescomplemented
338C24—91no—
339C2×Q8—91no—
340C2×Q8—181no—
341C2×Q8—184no—
342C2×Q8C2×D3211yescharacteristic
343C22×C4—62no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—184no—
350C22×C4—181no—
351C22×C4—181no—
352C22×C4—182no—
353C22×C4—182no—
354C22×C4—364no—
355C22×C4C2×D3211yescharacteristic
356C2×C8—34no—
357C2×C8—184no—
358C4⋊C4—21no—
359C4⋊C4—34no—
360C4⋊C4—62no—
361C4⋊C4—91no—
362C4⋊C4—181no—
363C4⋊C4—181no—
364C4⋊C4—181no—
365C4⋊C4—182no—
366C4⋊C4—182no—
367C4⋊C4—181no—
368C4⋊C4C2×D3211yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—181no—
371C22⋊C4—181no—
372C22⋊C4—181no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3D3×SD1614yes—
380C22×C3C2×D3×D412yes—
381C2×D3—34no—
382C2×D3—34no—
383C2×D3—34no—
384C2×D3—34no—
385C2×D3—62no—
386C2×D3—62no—
387C2×D3—62no—
388C2×D3—62no—
389C2×D3—616no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—128no—
393C2×D3—121no—
394C2×D3—121no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—41no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—42no—
401C3×C4—42no—
402C3×C4—124no—
403C3×C4D3×#4114yes—
404Dic3—34no—
405Dic3—44no—
406Dic3—62no—
407Dic3—62no—
408Dic3—121no—
409Dic3—122no—
410Dic3—122no—
411Dic3—122no—
412Dic3—122no—
413C32C2×#48311yescharacteristic, complemented, Sylow
414C23—91no—
415C23—91no—
416C23—94no—
417C23—182no—
418C23—182no—
419C23#381111yescharacteristic
420Q8—22no—
421Q8—182no—
422Q8—362no—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—64no—
427C2×C4—91no—
428C2×C4—94no—
429C2×C4—91no—
430C2×C4—124no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—362no—
438C2×C4—362no—
439C2×C4—364no—
440C2×C4—364no—
441C2×C4#381111yescharacteristic
442C2×C4C22×D3211yescharacteristic
443C8—64no—
444C2×C3—24no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—42no—
449C2×C3D3×#12312yes—
450C2×C3C2×D3×SD1612yes—
451C2×C3D3×#13712yes—
452D3—38no—
453D3—64no—
454D3—64no—
455D3—122no—
456C22—21no—
457C22—21no—
458C22—92no—
459C22—92no—
460C22—92no—
461C22—92no—
462C22—188no—
463C22—181no—
464C22—181no—
465C22#6394012yes—
466C22C2×#381111yescharacteristic
467C4—21no—
468C4—41no—
469C4—41no—
470C4—92no—
471C4—124no—
472C4—181no—
473C4—361no—
474C4—361no—
475C4#6431212yes—
476C3—21no—
477C3D3×#48312yescomplemented
478C2—22no—
479C2—94no—
480C2—182no—
481C2#1059516911yescharacteristic
482C2C2×#6394011yescharacteristic
483C2#1059546811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC22⋊Q8D32
hypocenterC32C2×#483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5043C2semidirect
4. #10591553C2semidirect
5. #10591552C2semidirect
7. #10591124C2semidirect
8. #10590575C2semidirect
9. #10590443C2semidirect
30. C3×#835C22semidirect
32. C3×#808C22semidirect
33. #63573C22semidirect
34. #63567C22semidirect
40. #5043D3semidirect
118. #835C2×D3semidirect
125. #808C2×D3semidirect
337. C3⋊D3#483semidirect
413. C32C2×#483semidirect
477. C3D3×#483semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
C2×#639002
C3×#50432
#105915532
#105915522
#105911522
#105911242
#105905752
#105904432
D3×#4833