Finite Group Databasebeta

← #11921875

Subgroups — #11921875

Order 1152.

568 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 59 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×#64259C211yesmaximal, characteristic, complemented
2C3×#5912C211yesmaximal, characteristic
3A4×#208C211yesmaximal, characteristic, complemented
4#10593180C212yesmaximal, complemented
5#10593177C212yesmaximal, complemented
6#85444—31nomaximal
7#82925—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9C2×C3⋊SL(2,ℤ/4)—21no—
10#64259—21no—
11#64259C2212yes—
12C3×GL(2,ℤ/4)—21no—
13C3×C4⋊S4C2211yescharacteristic
14C3×C4×S4—21no—
15C3×A4⋊Q8C2211yescharacteristic
16#63831—41nomaximal
17A4×C3⋊C8C2212yes—
18#5912D311yescharacteristic
19C2×A4⋊Q8—31no—
20C2×A4⋊Q8—61no—
21C3×#525—31no—
22C2×#951—31no—
23C2×#924—31no—
24C22×#208D311yescharacteristic, complemented
25A4×M16—31no—
26#5401—32no—
27#5398—32no—
28#5232—31no—
29#5052—32no—
30#5051—32no—
31#5042—32no—
32#5041—32no—
33#5004—31no—
34#4995—31no—
35C22×C3×A4D411yescharacteristic
36C2×C3×S4—21no—
37C2×#634—41no—
38C3×#235—41no—
39C3×C4×A4D411yescharacteristic
40C3×C4×A4C2311yescharacteristic
41C3⋊SL(2,ℤ/4)—22no—
42C3×SL(2,ℤ/4)—21no—
43C3×#208—41no—
44#3719—42no—
45#3716—42no—
46#3056—91noSylow
47C2×C3×#41—31no—
48C23×C3×C4C2×D311yescharacteristic
49C22×Dic6—31no—
50C2×C4×A4—21no—
51C2×C4×A4C2×D311yescharacteristic
52GL(2,ℤ/4)—21no—
53C2×SL(2,ℤ/4)—62no—
54C2×SL(2,ℤ/4)—61no—
55C4⋊S4C2×D311yescharacteristic
56C4×S4—21no—
57A4⋊Q8—32no—
58A4⋊Q8—62no—
59A4⋊Q8—62no—
60A4⋊Q8—61no—
61A4⋊Q8C2×D311yescharacteristic
62C3×#123—61no—
63C3×C22⋊Q8—31no—
64C3×C22⋊Q8—31no—
65C3×#121—31no—
66C3×#121—31no—
67C3×#120—61no—
68C3×C4×D4—61no—
69C3×C4×D4—61no—
70C3×#117—31no—
71C2×#217—61no—
72#951—61no—
73#951—62no—
74#951—61no—
75C2×#216—32no—
76C2×#214—32no—
77C2×C4⋊Dic3—31no—
78#924—32no—
79#924—32no—
80#924—61no—
81#924—61no—
82C2×Dic3⋊C4—61no—
83C2×#208—31no—
84C2×#208—31no—
85C2×#208—32no—
86C22×C3⋊C8C2×D312yes—
87#909—121no—
88C8×A4—32no—
89#835—32no—
90#832—32no—
91#810—32no—
92#810—32no—
93#808—32no—
94#807—32no—
95C2×C3×A4—21no—
96C2×C3×A4C2×D411yescharacteristic
97C3×S4—41no—
98C2×C32×C4—41no—
99C2×C3⋊Dic3—81no—
100#634—42no—
101#634—81no—
102C3×#67—81no—
103C3×D12—41no—
104C3×C4×D3—81no—
105C3×Dic6—41no—
106C3×C3⋊C8—42no—
107C2×#137—91no—
108C22×M16—31no—
109#525—31no—
110C2×C22⋊Q8—91no—
111#470—92no—
112#468—92no—
113#467—92no—
114#465—92no—
115#428—91no—
116#419—91no—
117#417—91no—
118C24×C3D1211yescharacteristic
119C22×A4—21no—
120C22×A4#6711yescharacteristic
121C2×S4—21no—
122C3×#41—61no—
123C3×#41—61no—
124C3×#41—61no—
125C3×#41—61no—
126C2×C3×Q8—31no—
127C2×C3×D4—31no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C22×C3×C4—31no—
132C22×C3×C4—31no—
133C22×C3×C4—31no—
134C22×C3×C4—31no—
135C22×C3×C4—61no—
136C22×C3×C4D1211yescharacteristic
137C22×C3×C4C22×D311yescharacteristic
138C22×Dic3—61no—
139C22×Dic3—61no—
140#235—41no—
141C2×Dic6—32no—
142C2×Dic6—61no—
143C2×Dic6—61no—
144C2×Dic6—61no—
145C2×Dic6—61no—
146C2×Dic6—61no—
147C2×Dic6—121no—
148C2×Dic6—241no—
149C4×A4—21no—
150C4×A4—21no—
151C4×A4#6711yescharacteristic
152C4×A4C22×D311yescharacteristic
153SL(2,ℤ/4)—21no—
154SL(2,ℤ/4)—64no—
155SL(2,ℤ/4)—62no—
156C3×M16—121no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C22⋊C4—61no—
164C3×C22⋊C4—61no—
165C3×C22⋊C4—61no—
166C3×C42—61no—
167#217—62no—
168#217—62no—
169#216—62no—
170#216—62no—
171#214—62no—
172#214—62no—
173C4⋊Dic3—32no—
174C4⋊Dic3—61no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177#208—31no—
178#208—32no—
179#208—61no—
180#208S411yescharacteristic, complemented
181C2×C3⋊C8—32no—
182C2×C3⋊C8—32no—
183Dic12—122no—
184#204—122no—
185C22×C32—41no—
186C2×C3×D3—81no—
187C3×A4#13711yescharacteristic, complemented
188C32×C4—41no—
189C32×C4—41no—
190C3⋊Dic3—82no—
191C3×Dic3—81no—
192C2×#41—31no—
193C22×Q8—91no—
194C23×C4D3211yescharacteristic
195#137—181no—
196#137—182no—
197#137—181no—
198C2×Q16—92no—
199C2×SD16—92no—
200C2×M16—91no—
201C2×M16—91no—
202C2×M16—92no—
203C22×C8—32no—
204#123—61no—
205C22⋊Q8—31no—
206C22⋊Q8—31no—
207C22⋊Q8—92no—
208C22⋊Q8—92no—
209C22⋊Q8—181no—
210C22⋊Q8—181no—
211#121—31no—
212#121—31no—
213#120—61no—
214C4×D4—61no—
215C4×D4—61no—
216#117—31no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4—181no—
219C2×C22⋊C4—181no—
220#107—92no—
221#106—92no—
222#103—92no—
223#103—92no—
224#103—92no—
225#102—92no—
226C23×C3—21no—
227C23×C3—31no—
228C23×C3—31no—
229C23×C3—61no—
230C23×C3—61no—
231C23×C3C2×D1211yescharacteristic
232C2×A4—22no—
233C2×A4—21no—
234C2×A4—21no—
235C2×A4C2×#6711yescharacteristic
236S4—41no—
237C3×Q8—61no—
238C3×Q8—61no—
239C3×D4—61no—
240C3×D4—61no—
241C3×D4—121no—
242C3×D4—121no—
243C3×D4—122no—
244C3×D4—121no—
245C3×D4—121no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—31no—
249C2×C3×C4—31no—
250C2×C3×C4—31no—
251C2×C3×C4—31no—
252C2×C3×C4—31no—
253C2×C3×C4—41no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—81no—
259C2×C3×C4—121no—
260C2×C3×C4—121no—
261C2×C3×C4C2×S411yescharacteristic
262#67—81no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—121no—
266C2×Dic3—122no—
267C2×Dic3—121no—
268C2×Dic3—241no—
269C2×Dic3—242no—
270D12—41no—
271C4×D3—81no—
272Dic6—41no—
273Dic6—62no—
274Dic6—62no—
275Dic6—122no—
276Dic6—121no—
277Dic6—121no—
278Dic6—242no—
279Dic6—241no—
280Dic6—242no—
281C3×C8—122no—
282C3⋊C8—32no—
283C3⋊C8C2×S412yes—
284C2×C32—41no—
285C2×C32—81no—
286C3×D3—161no—
287C24#62611yescharacteristic
288#41—61no—
289#41—61no—
290#41—61no—
291#41—61no—
292C2×Q8—31no—
293C2×Q8—92no—
294C2×Q8—181no—
295C2×Q8—181no—
296C2×Q8—181no—
297C2×Q8—181no—
298C2×Q8—181no—
299C2×D4—31no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—61no—
308C22×C4—181no—
309C22×C4—181no—
310C22×C4#62611yescharacteristic
311C22×C4C2×D3211yescharacteristic
312Q16—182no—
313Q16—182no—
314SD16—182no—
315SD16—182no—
316M16—31no—
317M16—92no—
318M16—91no—
319M16—181no—
320C2×C8—92no—
321C2×C8—92no—
322C4⋊C4—31no—
323C4⋊C4—31no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—92no—
327C4⋊C4—181no—
328C4⋊C4—182no—
329C4⋊C4—182no—
330C22⋊C4—61no—
331C22⋊C4—61no—
332C22⋊C4—61no—
333C22⋊C4—61no—
334C22⋊C4—61no—
335C22⋊C4—182no—
336C22⋊C4—182no—
337C42—61no—
338C22×C3—31no—
339C22×C3—31no—
340C22×C3—31no—
341C22×C3—41no—
342C22×C3—61no—
343C22×C3—61no—
344C22×C3—61no—
345C22×C3—61no—
346C22×C3—81no—
347C22×C3—121no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3#90911yescharacteristic, complemented
351C22×C3C4⋊S411yescharacteristic
352C2×D3—81no—
353A4—21no—
354A4#95111yescharacteristic, complemented
355C3×C4—31no—
356C3×C4—31no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—81no—
360C3×C4—81no—
361C3×C4—121no—
362C3×C4—121no—
363C3×C4—121no—
364C3×C4C4⋊S411yescharacteristic
365C3×C4C22×S411yescharacteristic
366Dic3—81no—
367Dic3—122no—
368Dic3—122no—
369Dic3—242no—
370Dic3—244no—
371C32—41noSylow
372C23—21no—
373C23—31no—
374C23—31no—
375C23—61no—
376C23—61no—
377C23C2×#62611yescharacteristic
378Q8—61no—
379Q8—61no—
380Q8—182no—
381Q8—182no—
382Q8—361no—
383Q8—361no—
384D4—61no—
385D4—61no—
386D4—121no—
387D4—121no—
388D4—122no—
389D4—121no—
390D4—121no—
391C2×C4—31no—
392C2×C4—31no—
393C2×C4—31no—
394C2×C4—31no—
395C2×C4—31no—
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—182no—
405C2×C4—182no—
406C2×C4—361no—
407C2×C4—362no—
408C2×C4—361no—
409C2×C4D3×S411yescharacteristic
410C8—32no—
411C8—92no—
412C2×C3—21no—
413C2×C3—31no—
414C2×C3—31no—
415C2×C3—41no—
416C2×C3—61no—
417C2×C3—81no—
418C2×C3—82no—
419C2×C3—81no—
420C2×C3—241no—
421C2×C3C2×C4⋊S411yescharacteristic
422D3—161no—
423C22—31no—
424C22—31no—
425C22—31no—
426C22—61no—
427C22—61no—
428C22—61no—
429C22—61no—
430C22—121no—
431C22—121no—
432C22—121no—
433C22#6383111yescharacteristic, complemented
434C22#6420711yescharacteristic
435C4—31no—
436C4—31no—
437C4—121no—
438C4—121no—
439C4—121no—
440C4—362no—
441C4—362no—
442C4#6420711yescharacteristic
443C4C2×D3×S411yescharacteristic
444C3—41no—
445C3—81no—
446C3#8544411yescharacteristic, complemented
447C2—21no—
448C2—31no—
449C2—31no—
450C2—61no—
451C2—241no—
452C2C2×#6420711yescharacteristic
subgroupG/H
centerC2C2×#64207
commutator, cosocleC3×C4×A4C23
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC23×C3C2×D12
prime radicalC3×#5912C2
hypercenterC2×C4D3×S4
hypocenterC3×A4#137
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64259C2semidirect
3. A4×#208C2semidirect
4. #10593180C2semidirect
5. #10593177C2semidirect
24. C22×#208D3semidirect
180. #208S4semidirect
187. C3×A4#137semidirect
350. C22×C3#909semidirect
354. A4#951semidirect
433. C22#63831semidirect
446. C3#85444semidirect

Maximal subgroups

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

subgroupindex
C2×#642592
C3×#59122
A4×#2082
#105931802
#105931772
#854443
#829253
#638314