Finite Group Databasebeta

← #11921878

Subgroups — #11921878

Order 1152.

648 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 83 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
1A4×#235C211yesmaximal, characteristic
2#10593643C211yesmaximal, characteristic, complemented
3C2×C3×A4⋊C8C211yesmaximal, characteristic, complemented
4#10593182C212yesmaximal, complemented
5D3×A4⋊C8C212yesmaximal, complemented
6#85511—31nomaximal
7#78600—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9A4×#67C412yes—
10A4×D12C411yescharacteristic
11C4×D3×A4C2212yes—
12A4×Dic6C411yescharacteristic
13#63814—41nomaximal
14C3⋊(A4⋊C8)C2212yes—
15C3×A4⋊C8C2211yescharacteristic
16C3×A4⋊C8C2211yescharacteristic
17C22×#235D311yescharacteristic
18A4×#41—31no—
19C2×#901—31no—
20C2×#901—31no—
21#5409—31no—
22#5409—32no—
23#5409—61no—
24C2×A4⋊C8—32no—
25C2×A4⋊C8D311yescharacteristic, complemented
26C2×C3×C22⋊C8—31no—
27#5207—31no—
28#5110—31no—
29#5110—31no—
30#4727—32no—
31#4727—32no—
32#4726—32no—
33D3×C22⋊C8—32no—
34C22×C3×A4C2×C411yescharacteristic
35C2×D3×A4C2×C412yes—
36C3×#235—41no—
37C3×C4×A4C2×C411yescharacteristic
38C3×C4×A4C2311yescharacteristic
39Dic3×A4C2×C412yes—
40#3748—41no—
41C2×C3×C3⋊C8—41no—
42#3711—42no—
43D3×C3⋊C8—42no—
44#2880—91noSylow
45C23×C3×C4C2×D311yescharacteristic
46C22×#67Dic312yes—
47C2×#235—31no—
48C2×#235—31no—
49C2×#235—31no—
50C2×#235—32no—
51C2×#235—32no—
52C2×#235—31no—
53C22×D12Dic311yescharacteristic
54C22×C4×D3C2×D312yes—
55C22×Dic6Dic311yescharacteristic
56Q8×A4—31no—
57D4×A4—32no—
58D4×A4—31no—
59C2×C4×A4—21no—
60C2×C4×A4—32no—
61C2×C4×A4C2×D311yescharacteristic
62C22×C3×C8—31no—
63C22×C3×C8—31no—
64#948—121no—
65C2×#208—31no—
66C2×#208—31no—
67#901—62no—
68#901—61no—
69#901—61no—
70#901—61no—
71#901—62no—
72#901—61no—
73C2×ΓL(1,𝔽25)—32no—
74C2×ΓL(1,𝔽25)—32no—
75C2×D3×C8—32no—
76C2×D3×C8—32no—
77A4⋊C8—32no—
78A4⋊C8—62no—
79A4⋊C8C2×D311yescharacteristic
80A4⋊C8C2×D311yescharacteristic
81C3×C22⋊C8—31no—
82C3×C22⋊C8—31no—
83C3×C22⋊C8—31no—
84C3×C22⋊C8—31no—
85#830—32no—
86#830—32no—
87(C2×D3)⋊C8—32no—
88(C2×D3)⋊C8—32no—
89(C2×D3)⋊C8—32no—
90(C2×D3)⋊C8—32no—
91C2×C3×A4—21no—
92C2×C3×A4C22×C411yescharacteristic
93D3×A4—22no—
94C2×C32×C4—41no—
95C3×#67—42no—
96C3×D12—41no—
97C3×C4×D3—42no—
98C3×Dic6—41no—
99C3⋊(C3⋊C8)—42no—
100C3×C3⋊C8—41no—
101C3×C3⋊C8—41no—
102C22×#41—31no—
103C2×#131—91no—
104C2×#131—91no—
105#408—92no—
106#408—92no—
107#408—91no—
108#408—91no—
109#407—92no—
110#407—91no—
111C2×C22⋊C8—31no—
112C2×C22⋊C8—92no—
113C24×C3C2×Dic311yescharacteristic
114C23×D3C2×Dic312yes—
115C22×A4—21no—
116C22×A4—32no—
117C22×A4C4×D311yescharacteristic
118C3×#41—121no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4C2×Dic311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C2×#67—32no—
126C2×#67—32no—
127C2×#67—32no—
128C2×#67—32no—
129C22×Dic3C2×Dic312yes—
130#235—31no—
131#235—32no—
132#235—31no—
133#235—32no—
134#235—31no—
135#235—62no—
136#235—61no—
137#235—61no—
138#235—62no—
139#235—61no—
140#235S411yescharacteristic
141C2×D12—31no—
142C2×D12—32no—
143C2×D12—31no—
144C2×C4×D3—32no—
145C2×C4×D3—32no—
146C2×C4×D3—32no—
147C2×C4×D3—32no—
148C2×Dic6—31no—
149C2×Dic6—31no—
150C2×Dic6—32no—
151C4×A4—21no—
152C4×A4—21no—
153C4×A4—32no—
154C4×A4C4×D311yescharacteristic
155C4×A4C22×D311yescharacteristic
156C2×C3×C8—31no—
157C2×C3×C8—31no—
158C2×C3×C8—31no—
159C2×C3×C8—31no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164#208—61no—
165#208—61no—
166#208—61no—
167#208—61no—
168#208—122no—
169#208—121no—
170#208—241no—
171C2×C3⋊C8—32no—
172C2×C3⋊C8—32no—
173C2×C3⋊C8—41no—
174C2×C3⋊C8—122no—
175ΓL(1,𝔽25)—62no—
176ΓL(1,𝔽25)—62no—
177ΓL(1,𝔽25)—62no—
178ΓL(1,𝔽25)—62no—
179D3×C8—62no—
180D3×C8—62no—
181D3×C8—62no—
182D3×C8—62no—
183C22×C32—41no—
184C2×C3×D3—42no—
185C3×A4#13111yescharacteristic, complemented
186C32×C4—41no—
187C32×C4—41no—
188C3×Dic3—42no—
189C2×#41—91no—
190C2×#41—91no—
191C2×#41—92no—
192C2×#41—91no—
193C2×#41—92no—
194C2×#41—91no—
195C22×Q8—31no—
196C22×D4—32no—
197C22×D4—31no—
198C23×C4—32no—
199C23×C4D3211yescharacteristic
200#131—181no—
201#131—182no—
202#131—182no—
203#131—181no—
204#131—181no—
205#131—181no—
206C2×M16—92no—
207C2×M16—92no—
208C2×M16—91no—
209C2×M16—91no—
210C22×C8—31no—
211C22×C8—31no—
212C22×C8—92no—
213C22×C8—92no—
214C22⋊C8—31no—
215C22⋊C8—31no—
216C22⋊C8—31no—
217C22⋊C8—31no—
218C22⋊C8—92no—
219C22⋊C8—92no—
220C22⋊C8—92no—
221C22⋊C8—92no—
222C22⋊C8—92no—
223C22⋊C8—92no—
224C23×C3—21no—
225C23×C3—31no—
226C23×C3—31no—
227C23×C3—61no—
228C23×C3C22×Dic311yescharacteristic
229C22×D3—22no—
230C22×D3—32no—
231C22×D3—32no—
232C22×D3—62no—
233C2×A4—21no—
234C2×A4—21no—
235C2×A4—41no—
236C2×A4—62no—
237C2×A4C2×C4×D311yescharacteristic
238C3×Q8—121no—
239C3×D4—121no—
240C3×D4—122no—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—41no—
249C2×C3×C4—61no—
250C2×C3×C4—81no—
251C2×C3×C4—122no—
252C2×C3×C4C2×S411yescharacteristic
253#67—32no—
254#67—32no—
255#67—32no—
256#67—62no—
257#67SL(2,ℤ/4)12yes—
258C2×Dic3—32no—
259C2×Dic3—32no—
260D12—32no—
261D12—31no—
262D12—61no—
263D12SL(2,ℤ/4)11yescharacteristic
264C4×D3—32no—
265C4×D3—32no—
266C4×D3—32no—
267C4×D3—62no—
268C4×D3C2×S412yes—
269Dic6—31no—
270Dic6—32no—
271Dic6—61no—
272Dic6SL(2,ℤ/4)11yescharacteristic
273C3×C8—61no—
274C3×C8—61no—
275C3×C8—61no—
276C3×C8—61no—
277C3⋊C8—41no—
278C3⋊C8—41no—
279C3⋊C8—62no—
280C3⋊C8—62no—
281C3⋊C8—122no—
282C3⋊C8—242no—
283C2×C32—41no—
284C2×C32—81no—
285C3×D3—82no—
286C24—32no—
287C24D3×Dic311yescharacteristic
288#41—31no—
289#41—92no—
290#41—92no—
291#41—91no—
292#41—91no—
293#41—91no—
294#41—181no—
295#41—181no—
296#41—181no—
297#41—182no—
298#41—182no—
299C2×Q8—91no—
300C2×Q8—91no—
301C2×Q8—92no—
302C2×D4—91no—
303C2×D4—91no—
304C2×D4—92no—
305C2×D4—92no—
306C2×D4—92no—
307C2×D4—92no—
308C2×D4—92no—
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—31no—
313C22×C4—32no—
314C22×C4—92no—
315C22×C4—92no—
316C22×C4—92no—
317C22×C4—92no—
318C22×C4D3×Dic311yescharacteristic
319C22×C4C2×D3211yescharacteristic
320M16—182no—
321M16—182no—
322M16—182no—
323M16—182no—
324M16—181no—
325M16—181no—
326M16—181no—
327M16—181no—
328C2×C8—31no—
329C2×C8—31no—
330C2×C8—31no—
331C2×C8—31no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—61no—
335C2×C8—61no—
336C2×C8—92no—
337C2×C8—92no—
338C2×C8—182no—
339C2×C8—182no—
340C2×C8—182no—
341C2×C8—182no—
342C22×C3—31no—
343C22×C3—31no—
344C22×C3—31no—
345C22×C3—41no—
346C22×C3—61no—
347C22×C3—61no—
348C22×C3—61no—
349C22×C3—61no—
350C22×C3—81no—
351C22×C3—122no—
352C22×C3#94811yescharacteristic, complemented
353C22×C3C2×SL(2,ℤ/4)11yescharacteristic
354C2×D3—32no—
355C2×D3—62no—
356C2×D3—62no—
357C2×D3—62no—
358C2×D3—62no—
359C2×D3C2×SL(2,ℤ/4)12yes—
360A4—21no—
361A4#90111yescharacteristic, complemented
362C3×C4—31no—
363C3×C4—31no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—81no—
367C3×C4—81no—
368C3×C4—122no—
369C3×C4C2×SL(2,ℤ/4)11yescharacteristic
370C3×C4C22×S411yescharacteristic
371Dic3—32no—
372Dic3C2×SL(2,ℤ/4)12yes—
373C32—41noSylow
374C23—21no—
375C23—31no—
376C23—31no—
377C23—61no—
378C23—62no—
379C23—92no—
380C23—92no—
381C23—182no—
382C23C2×D3×Dic311yescharacteristic
383Q8—31no—
384Q8—92no—
385Q8—91no—
386Q8—181no—
387D4—32no—
388D4—31no—
389D4—92no—
390D4—92no—
391D4—92no—
392D4—92no—
393D4—91no—
394D4—181no—
395D4—182no—
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—31no—
399C2×C4—32no—
400C2×C4—31no—
401C2×C4—31no—
402C2×C4—31no—
403C2×C4—31no—
404C2×C4—61no—
405C2×C4—92no—
406C2×C4—92no—
407C2×C4—92no—
408C2×C4—92no—
409C2×C4—92no—
410C2×C4—182no—
411C2×C4D3×S411yescharacteristic
412C8—61no—
413C8—61no—
414C8—61no—
415C8—61no—
416C8—182no—
417C8—182no—
418C2×C3—21no—
419C2×C3—31no—
420C2×C3—31no—
421C2×C3—41no—
422C2×C3—61no—
423C2×C3—81no—
424C2×C3—81no—
425C2×C3—161no—
426C2×C3—242no—
427C2×C3C22×SL(2,ℤ/4)11yescharacteristic
428D3—22no—
429D3—62no—
430C22—31no—
431C22—31no—
432C22—31no—
433C22—32no—
434C22—61no—
435C22—61no—
436C22—61no—
437C22—61no—
438C22—92no—
439C22—182no—
440C22—182no—
441C22—182no—
442C22—182no—
443C22#6381411yescharacteristic, complemented
444C22D3×SL(2,ℤ/4)11yescharacteristic
445C4—31no—
446C4—31no—
447C4—32no—
448C4—92no—
449C4D3×SL(2,ℤ/4)11yescharacteristic
450C4C2×D3×S411yescharacteristic
451C3—41no—
452C3—81no—
453C3#8551111yescharacteristic, complemented
454C2—21no—
455C2—31no—
456C2—31no—
457C2—61no—
458C2—62no—
459C2—182no—
460C2C2×D3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC4C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC23×C3C22×Dic3
prime radicalA4×#235C2
cosocleC3×C4×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4#131
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #10593643C2semidirect
3. C2×C3×A4⋊C8C2semidirect
4. #10593182C2semidirect
5. D3×A4⋊C8C2semidirect
25. C2×A4⋊C8D3semidirect
185. C3×A4#131semidirect
352. C22×C3#948semidirect
361. A4#901semidirect
443. C22#63814semidirect
453. C3#85511semidirect

Maximal subgroups

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

subgroupindex
A4×#2352
#105936432
C2×C3×A4⋊C82
#105931822
D3×A4⋊C82
#855113
#786003
#638144