Finite Group Databasebeta

← #11923092

Subgroups — #11923092

Order 1152.

734 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 77 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×#5945C211yesmaximal, characteristic, complemented
2C2×#64267C211yesmaximal, characteristic, complemented
3#10593665C212yesmaximal, complemented
4#10593663C212yesmaximal, complemented
5#10593657C211yesmaximal, characteristic, complemented
6#85543—33nomaximal
7#84122—31nomaximal
8C3×2−1+4⋊C3—21no—
9C3×2−1+4⋊C3C2211yescharacteristic, complemented
10C3×#994C2211yescharacteristic, complemented
11C2×C3×#41⋊C3—21no—
12C2×C3×#41⋊C3C2211yescharacteristic
13#64267—21no—
14#64267C2212yescomplemented
15C2×C3⋊GL(2,𝔽3)—21no—
16#64158—41nomaximal
17C3⋊GU(2,𝔽3)C2212yescomplemented
18C3×#585D311yescharacteristic, complemented
19#5945D313yescomplemented
20C2×#986—33no—
21#5830—31no—
22C2×#949—31no—
23C2×#949—31no—
24#5431—36no—
25#5429—36no—
26#5423—33no—
27#5245—32no—
28#5245—32no—
29#5241—32no—
30#5241—32no—
31#5237—31no—
32#5236—31no—
33#5236—31no—
34C32×#41—41no—
35C2×C4⋊(C3⋊D3)—41no—
36C3×#41⋊C3—21no—
37C3×#41⋊C3D411yescharacteristic, complemented
38C3×#41⋊C3C2311yescharacteristic
39C2×C3×SL(2,𝔽3)—21no—
40C2×C3×SL(2,𝔽3)D411yescharacteristic, complemented
41C3⋊GL(2,𝔽3)—22no—
42#3755—42no—
43#3753—42no—
44#3748—41no—
45#3021—91noSylow
46C3×2−1+4—21no—
47C3×2−1+4—31no—
48C3×2−1+4C2×D311yescharacteristic, complemented
49C3×H(5,𝔽2)—31no—
50C3×H(5,𝔽2)—61no—
51C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
52C2×C3×#41—21no—
53C2×C3×#41—31no—
54C2×C3×#41—31no—
55C2×C3×#41—61no—
56C2×C3×#41C2×D311yescharacteristic
57C22×D12—31no—
582−1+4⋊C3—23no—
592−1+4⋊C3C2×D313yescomplemented
60#994C2×D313yescomplemented
61C2×#41⋊C3—23no—
62C2×#41⋊C3C2×D313yes—
63#986—36no—
64#986—63no—
65C2×GL(2,𝔽3)—63no—
66#949—32no—
67#949—32no—
68#949—32no—
69#949—32no—
70#949—61no—
71#949—61no—
72#949—61no—
73#949—61no—
74#949—123no—
75#947—32no—
76C2×#215—61no—
77C2×#215—61no—
78#940—32no—
79#937—62no—
80C2×#213—61no—
81C2×#213—61no—
82#930—62no—
83#926—31no—
84C2×#208—31no—
85C2×#208—31no—
86GU(2,𝔽3)—36no—
87#837—32no—
88#837—32no—
89#837—32no—
90#837—32no—
91#836—32no—
92#833—32no—
93C22×C3⋊D3—81no—
94C32×Q8—41no—
95C32×D4—41no—
96C32×D4—81no—
97C2×C32×C4—41no—
98C2×C32×C4—81no—
99C4⋊(C3⋊D3)—42no—
100C4⋊(C3⋊D3)—81no—
101C3×SL(2,𝔽3)C2×D411yescharacteristic
102C3⋊(C3⋊C8)—42no—
103#585C3⋊D311yescharacteristic, complemented
104C2×AGL(1,ℤ/8)—91no—
105C2×AGL(1,ℤ/8)—91no—
106#535—91no—
107#454—92no—
108#454—92no—
109#453—92no—
110#453—92no—
111#421—91no—
112#421—91no—
113#413—91no—
114C23×D3—61no—
115C3×#41—21no—
116C3×#41—31no—
117C3×#41—31no—
118C3×#41—31no—
119C3×#41—31no—
120C3×#41—31no—
121C3×#41—43no—
122C3×#41—61no—
123C3×#41—61no—
124C3×#41—61no—
125C3×#41—61no—
126C3×#41—62no—
127C3×#41—61no—
128C3×#41—61no—
129C3×#41—61no—
130C3×#41—61no—
131C3×#41#6711yescharacteristic
132C3×#41S411yescharacteristic
133C3×#41C22×D311yescharacteristic
134C2×C3×Q8—21no—
135C2×C3×Q8—31no—
136C2×C3×Q8—31no—
137C2×C3×Q8—61no—
138C2×C3×Q8#6711yescharacteristic
139C2×C3×D4—31no—
140C2×C3×D4—31no—
141C2×C3×D4—31no—
142C2×C3×D4—32no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—62no—
147C22×C3×C4—31no—
148C22×C3×C4—32no—
149C22×C3×C4—61no—
150C2×#67—64no—
151C2×D12—32no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—123no—
158#41⋊C3—23no—
159#41⋊C3#6713yescomplemented
160#41⋊C3C22×D313yes—
161C2×SL(2,𝔽3)—23no—
162C2×SL(2,𝔽3)#6713yescomplemented
163GL(2,𝔽3)—66no—
164#217—61no—
165#215—62no—
166#215—62no—
167#215—62no—
168#215—62no—
169#215—126no—
170#213—62no—
171#213—62no—
172#213—62no—
173#213—62no—
174#213—126no—
175(C2×D3)⋊C4—64no—
176C4⋊Dic3—61no—
177C4×Dic3—32no—
178#208—32no—
179#208—32no—
180#208—61no—
181#208—61no—
182#208—123no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C22×C32—41no—
186C22×C32—81no—
187C2×C3⋊D3—82no—
188C2×C3⋊D3—162no—
189C32×C4—41no—
190C32×C4—41no—
191C32×C4—81no—
1922−1+4—21no—
1932−1+4—31no—
1942−1+4C2×C3⋊D311yescharacteristic, complemented
195H(5,𝔽2)—31no—
196H(5,𝔽2)—61no—
197H(5,𝔽2)C2×C3⋊D311yescharacteristic, complemented
198C2×#41—21no—
199C2×#41—31no—
200C2×#41—31no—
201C2×#41—61no—
202C2×#41C2×C3⋊D311yescharacteristic
203C22×D4—91no—
204AGL(1,ℤ/8)—92no—
205AGL(1,ℤ/8)—92no—
206AGL(1,ℤ/8)—92no—
207AGL(1,ℤ/8)—92no—
208AGL(1,ℤ/8)—181no—
209AGL(1,ℤ/8)—181no—
210AGL(1,ℤ/8)—181no—
211AGL(1,ℤ/8)—181no—
212C2×SD16—181no—
213C2×SD16—181no—
214C2×D8—181no—
215C2×D8—181no—
216C2×M16—91no—
217C2×M16—91no—
218#127—92no—
219#124—92no—
220#121—182no—
221#120—182no—
222#117—91no—
223#104—92no—
224#104—92no—
225#104—92no—
226#104—92no—
227#101—92no—
228#100—92no—
229C23×C3—31no—
230C23×C3—32no—
231C23×C3—61no—
232C22×D3—62no—
233C22×D3—121no—
234C22×D3—121no—
235C22×D3—243no—
236C22×D3—242no—
237C3×Q8—31no—
238C3×Q8—31no—
239C3×Q8—43no—
240C3×Q8—61no—
241C3×Q8—61no—
242C3×Q8C2×#6711yescharacteristic
243C3×Q8C2×S411yescharacteristic
244C3×D4—21no—
245C3×D4—31no—
246C3×D4—31no—
247C3×D4—31no—
248C3×D4—43no—
249C3×D4—61no—
250C3×D4—61no—
251C3×D4—61no—
252C3×D4—61no—
253C3×D4—61no—
254C3×D4—62no—
255C3×D4—61no—
256C3×D4—83no—
257C3×D4C2×S411yescharacteristic
258C2×C3×C4—21no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—31no—
264C2×C3×C4—32no—
265C2×C3×C4—43no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—62no—
270C2×C3×C4—61no—
271C2×C3×C4—83no—
272C2×C3×C4C2×S411yescharacteristic
273#67—244no—
274C2×Dic3—62no—
275D12—62no—
276D12—62no—
277D12—126no—
278D12—121no—
279D12—121no—
280D12—243no—
281SL(2,𝔽3)C2×#6713yes—
282C3⋊C8—62no—
283C3⋊C8—62no—
284C3⋊C8—126no—
285C2×C32—41no—
286C2×C32—81no—
287C2×C32—161no—
288C3⋊D3—162no—
289C24—181no—
290#41—21no—
291#41—31no—
292#41—31no—
293#41—31no—
294#41—31no—
295#41—31no—
296#41—61no—
297#41—61no—
298#41—61no—
299#41—61no—
300#41—62no—
301#41—61no—
302#41—61no—
303#41—61no—
304#41—61no—
305#41#63811yescharacteristic
306#41C3⋊S411yescharacteristic
307#41C22×C3⋊D311yescharacteristic
308C2×Q8—21no—
309C2×Q8—31no—
310C2×Q8—31no—
311C2×Q8—61no—
312C2×Q8#63811yescharacteristic
313C2×D4—31no—
314C2×D4—31no—
315C2×D4—31no—
316C2×D4—32no—
317C2×D4—61no—
318C2×D4—61no—
319C2×D4—61no—
320C2×D4—62no—
321C2×D4—92no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4—181no—
325C2×D4—181no—
326C2×D4—184no—
327C2×D4—181no—
328C22×C4—31no—
329C22×C4—32no—
330C22×C4—61no—
331SD16—182no—
332SD16—182no—
333SD16—182no—
334SD16—182no—
335D8—182no—
336D8—182no—
337D8—182no—
338D8—182no—
339M16—92no—
340M16—92no—
341M16—181no—
342M16—181no—
343C2×C8—181no—
344C2×C8—181no—
345C4⋊C4—181no—
346C22⋊C4—184no—
347C22⋊C4—181no—
348C42—92no—
349C22×C3—21no—
350C22×C3—31no—
351C22×C3—31no—
352C22×C3—43no—
353C22×C3—61no—
354C22×C3—83no—
355C22×C3—121no—
356C22×C3—122no—
357C22×C3—241no—
358C22×C3GL(2,ℤ/4)11yescharacteristic
359C2×D3—124no—
360C2×D3—122no—
361C2×D3—246no—
362C2×D3—242no—
363C2×D3—242no—
364C2×D3—486no—
365C3×C4—21no—
366C3×C4—31no—
367C3×C4—31no—
368C3×C4—43no—
369C3×C4—43no—
370C3×C4—61no—
371C3×C4—83no—
372C3×C4GL(2,ℤ/4)11yescharacteristic
373C3×C4C22×S411yescharacteristic
374Dic3—122no—
375C32—41noSylow
376C23—31no—
377C23—32no—
378C23—61no—
379C23—182no—
380C23—361no—
381C23—361no—
382C23—722no—
383Q8—31no—
384Q8—31no—
385Q8—61no—
386Q8—61no—
387Q8C2×#63811yescharacteristic
388Q8C2×C3⋊S411yescharacteristic
389D4—21no—
390D4—31no—
391D4—31no—
392D4—31no—
393D4—61no—
394D4—61no—
395D4—61no—
396D4—61no—
397D4—61no—
398D4—62no—
399D4—61no—
400D4—182no—
401D4—182no—
402D4—361no—
403D4—361no—
404D4—724no—
405D4C2×C3⋊S411yescharacteristic
406C2×C4—21no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—32no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—62no—
417C2×C4—61no—
418C2×C4—182no—
419C2×C4C2×C3⋊S411yescharacteristic
420C8—182no—
421C8—182no—
422C2×C3—21no—
423C2×C3—41no—
424C2×C3—43no—
425C2×C3—61no—
426C2×C3—61no—
427C2×C3—83no—
428C2×C3—121no—
429C2×C3—163no—
430C2×C3C2×GL(2,ℤ/4)11yescharacteristic
431D3—242no—
432D3—486no—
433C22—21no—
434C22—31no—
435C22—31no—
436C22—61no—
437C22—121no—
438C22—122no—
439C22—241no—
440C22—364no—
441C22—362no—
442C22—722no—
443C22—722no—
444C22#6426911yescharacteristic
445C4—21no—
446C4—31no—
447C4—31no—
448C4—61no—
449C4—362no—
450C4#6426911yescharacteristic
451C4C22×C3⋊S411yescharacteristic
452C3—43no—
453C3#8554311yescharacteristic, complemented
454C2—21no—
455C2—41no—
456C2—61no—
457C2—61no—
458C2—121no—
459C2—722no—
460C2C2×#6426911yescharacteristic
subgroupG/H
centerC2C2×#64269
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C22×C3⋊S4
FittingC3×#585D3
socleC2×C3C2×GL(2,ℤ/4)
hypercenter#41C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×#5945C2semidirect
2. C2×#64267C2semidirect
3. #10593665C2semidirect
4. #10593663C2semidirect
5. #10593657C2semidirect
9. C3×2−1+4⋊C3C22semidirect
10. C3×#994C22semidirect
14. #64267C22semidirect
17. C3⋊GU(2,𝔽3)C22semidirect
18. C3×#585D3semidirect
19. #5945D3semidirect
37. C3×#41⋊C3D4semidirect
40. C2×C3×SL(2,𝔽3)D4semidirect
48. C3×2−1+4C2×D3semidirect
51. C3×H(5,𝔽2)C2×D3semidirect
59. 2−1+4⋊C3C2×D3semidirect
60. #994C2×D3semidirect
103. #585C3⋊D3semidirect
159. #41⋊C3#67semidirect
162. C2×SL(2,𝔽3)#67semidirect
194. 2−1+4C2×C3⋊D3semidirect
197. H(5,𝔽2)C2×C3⋊D3semidirect
453. C3#85543semidirect

Maximal subgroups

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

subgroupindex
C3×#59452
C2×#642672
#105936652
#105936632
#105936572
#855433
#841223
#641584