Finite Group Databasebeta

← #87298⋊C3 #11923408

Subgroups — #87298⋊C3 #11923408

Order 1152.

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

normal subgroups only

This group has 714 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
1C3×#5945C211yesmaximal, characteristic, complemented
2C2×C3⋊#994C211yesmaximal, characteristic, complemented
3#5837⋊C3C212yesmaximal, complemented
4#5835⋊C3C212yesmaximal, complemented
5#5819⋊C3C211yesmaximal, characteristic, complemented
6#87298C311yesmaximal, characteristic, complemented
7#3585⋊C3—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
13C3⋊#994—21no—
14C3⋊#994C2212yescomplemented
15C2×C3⋊(#41⋊C3)—21no—
16C3×#951—41nomaximal
17C3⋊(#131⋊C3)C2212yescomplemented
18C3×#585C2×C311yescharacteristic
19C2×#1009C2×C311yescharacteristic, complemented
20#5945—21no—
21#5945D311yescharacteristic, complemented
22C2×#994—31no—
23#5837—32no—
24#5837C2×C312yescomplemented
25#5835—32no—
26#5835C2×C312yescomplemented
27#5822—31no—
28#5822—31no—
29C2×#949—31no—
30C2×#949—31no—
31#5819C2×C311yescharacteristic, complemented
32#577⋊C3—32no—
33#576⋊C3—32no—
34#568⋊C3—31no—
35C32×#41—41no—
36C2×C3×Dic6—41no—
37C3×#41⋊C3—21no—
38C3×#41⋊C3D411yescharacteristic
39C3×#41⋊C3C2311yescharacteristic
40C2×C3×SL(2,𝔽3)—21no—
41C2×C3×SL(2,𝔽3)D411yescharacteristic
42C3⋊(#41⋊C3)—22no—
43C3×#216—42no—
44C3×#214—42no—
45C3×#208—41no—
46#3585—31noSylow
47C3×2−1+4—21no—
48C3×2−1+4—31no—
49C3×2−1+4C22×C311yescharacteristic
50C3×H(5,𝔽2)—31no—
51C3×H(5,𝔽2)—61no—
52C3×H(5,𝔽2)C22×C311yescharacteristic
53C2×C3×#41—21no—
54C2×C3×#41—31no—
55C2×C3×#41—31no—
56C2×C3×#41—61no—
57C2×C3×#41C22×C311yescharacteristic
58#1009—21no—
59#1009—32no—
60#1009—61no—
61#1009C22×C312yes—
62C2×#239—21no—
63C2×D3×D4—61no—
64C2×#235—31no—
65C22×D12—31no—
662−1+4⋊C3—22no—
672−1+4⋊C3—21no—
682−1+4⋊C3—21no—
692−1+4⋊C3C2×D311yescharacteristic, complemented
70#994—21no—
71#994—32no—
72#994—61no—
73#994C2×D311yescharacteristic, complemented
74C2×#41⋊C3—22no—
75C2×#41⋊C3—21no—
76C2×#41⋊C3—21no—
77C2×#41⋊C3—61no—
78C2×#41⋊C3C2×D311yescharacteristic
79C3×#137—121no—
80#951—31no—
81#951A411yescharacteristic
82#950—34no—
83#950—32no—
84#950—32no—
85#949—32no—
86#949—34no—
87#949—31no—
88#949—32no—
89#949—32no—
90#949—31no—
91#948—32no—
92#948C22×C312yes—
93#942—32no—
94#942—32no—
95C2×#215—32no—
96C2×#215—32no—
97#932—32no—
98#932—32no—
99C2×#213—32no—
100C2×#213—32no—
101C2×#208—31no—
102C2×#208—31no—
103#131⋊C3—32no—
104C32×Q8—41no—
105C32×D4—41no—
106C32×D4—81no—
107C2×C32×C4—41no—
108C2×C32×C4—81no—
109C2×C3×Dic3—81no—
110C3×Dic6—42no—
111C3×Dic6—81no—
112C3×SL(2,𝔽3)C2×D411yescharacteristic
113C3×C3⋊C8—42no—
114#585C3×D311yescharacteristic
115C2×H(5,𝔽2)—31no—
116#577—32no—
117#577—92no—
118#576—32no—
119#576—92no—
120#575—91no—
121#575—91no—
122C2×AGL(1,ℤ/8)—91no—
123C2×AGL(1,ℤ/8)—91no—
124#568—31no—
125C23×D3—61no—
126C3×#41—21no—
127C3×#41—31no—
128C3×#41—31no—
129C3×#41—32no—
130C3×#41—31no—
131C3×#41—31no—
132C3×#41—31no—
133C3×#41—41no—
134C3×#41—61no—
135C3×#41—61no—
136C3×#41—61no—
137C3×#41—61no—
138C3×#41—62no—
139C3×#41—61no—
140C3×#41—61no—
141C3×#41—61no—
142C3×#41—81no—
143C3×#41C3×D411yescharacteristic
144C3×#41C2×A411yescharacteristic
145C3×#41C23×C311yescharacteristic
146C2×C3×Q8—21no—
147C2×C3×Q8—31no—
148C2×C3×Q8—31no—
149C2×C3×Q8—61no—
150C2×C3×Q8—121no—
151C2×C3×Q8C3×D411yescharacteristic
152C2×C3×D4—31no—
153C2×C3×D4—31no—
154C2×C3×D4—31no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C2×C3×D4—62no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C22×C3×C4—31no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C2×#67—61no—
164#239—22no—
165#239—62no—
166D3×D4—64no—
167D3×D4—62no—
168D3×D4—62no—
169#235—32no—
170#235—32no—
171#235—61no—
172#235—61no—
173C2×D12—32no—
174C2×D12—31no—
175C2×D12—32no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—61no—
179C2×C4×D3—61no—
180C2×Dic6C2×A411yescharacteristic
181#41⋊C3—22no—
182#41⋊C3—21no—
183#41⋊C3—21no—
184#41⋊C3—21no—
185#41⋊C3—62no—
186#41⋊C3#6711yescharacteristic
187#41⋊C3C22×D311yescharacteristic
188C2×SL(2,𝔽3)—22no—
189C2×SL(2,𝔽3)—21no—
190C2×SL(2,𝔽3)—21no—
191C2×SL(2,𝔽3)#6711yescharacteristic
192C3×Q16—122no—
193C3×SD16—122no—
194C3×M16—121no—
195#216—32no—
196#216C2×A412yes—
197#215—34no—
198#215—32no—
199#215—32no—
200#214—32no—
201#214C2×A412yes—
202#213—34no—
203#213—32no—
204#213—32no—
205#208—31no—
206#208—32no—
207#208—32no—
208#208C2×A411yescharacteristic
209C2×C3⋊C8—32no—
210C2×C3⋊C8—32no—
211C22×C32—41no—
212C22×C32—81no—
213C32×C4—41no—
214C32×C4—41no—
215C32×C4—81no—
216C3×Dic3—82no—
2172−1+4—21no—
2182−1+4—31no—
2192−1+4C2×C3×D311yescharacteristic
220H(5,𝔽2)—31no—
221H(5,𝔽2)—32no—
222H(5,𝔽2)—61no—
223H(5,𝔽2)—61no—
224H(5,𝔽2)—92no—
225H(5,𝔽2)—181no—
226H(5,𝔽2)C2×C3×D311yescharacteristic
227C2×#41—21no—
228C2×#41—31no—
229C2×#41—31no—
230C2×#41—61no—
231C2×#41—61no—
232C2×#41—91no—
233C2×#41C2×C3×D311yescharacteristic
234C22×D4—91no—
235C22×D4—181no—
236#137—31no—
237#137—92no—
238#137—91no—
239#137—92no—
240AGL(1,ℤ/8)—91no—
241AGL(1,ℤ/8)—92no—
242AGL(1,ℤ/8)—92no—
243AGL(1,ℤ/8)—94no—
244AGL(1,ℤ/8)—91no—
245AGL(1,ℤ/8)—92no—
246AGL(1,ℤ/8)—92no—
247AGL(1,ℤ/8)—92no—
248#135—92no—
249#135—92no—
250#135—94no—
251C2×SD16—92no—
252C2×SD16—92no—
253C2×D8—92no—
254C2×D8—92no—
255#131—32no—
256#131—92no—
257C2×M16—91no—
258C2×M16—91no—
259C23×C3—31no—
260C23×C3—61no—
261C23×C3—61no—
262C22×D3—61no—
263C22×D3—62no—
264C22×D3—62no—
265C22×D3—242no—
266C3×Q8—31no—
267C3×Q8—31no—
268C3×Q8—41no—
269C3×Q8—61no—
270C3×Q8—61no—
271C3×Q8—81no—
272C3×Q8—122no—
273C3×Q8—241no—
274C3×Q8C2×C3×D411yescharacteristic
275C3×Q8C22×A411yescharacteristic
276C3×D4—21no—
277C3×D4—31no—
278C3×D4—31no—
279C3×D4—32no—
280C3×D4—31no—
281C3×D4—41no—
282C3×D4—61no—
283C3×D4—61no—
284C3×D4—61no—
285C3×D4—61no—
286C3×D4—62no—
287C3×D4—61no—
288C3×D4—81no—
289C3×D4—82no—
290C3×D4—81no—
291C3×D4C22×A411yescharacteristic
292C2×C3×C4—21no—
293C2×C3×C4—31no—
294C2×C3×C4—31no—
295C2×C3×C4—31no—
296C2×C3×C4—31no—
297C2×C3×C4—31no—
298C2×C3×C4—41no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—62no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—81no—
306C2×C3×C4—82no—
307C2×C3×C4—81no—
308C2×C3×C4—241no—
309C2×C3×C4C22×A411yescharacteristic
310#67—62no—
311#67—62no—
312C2×Dic3—21no—
313D12—32no—
314D12—62no—
315D12—62no—
316D12—61no—
317C4×D3—62no—
318C4×D3—62no—
319Dic6—21no—
320Dic6C22×A412yes—
321SL(2,𝔽3)—21no—
322SL(2,𝔽3)C2×#6711yescharacteristic
323C3×C8—122no—
324C3⋊C8—32no—
325C3⋊C8C22×A412yes—
326C2×C32—41no—
327C2×C32—81no—
328C2×C32—161no—
329C24—181no—
330#41—21no—
331#41—31no—
332#41—31no—
333#41—32no—
334#41—31no—
335#41—31no—
336#41—31no—
337#41—61no—
338#41—61no—
339#41—61no—
340#41—61no—
341#41—62no—
342#41—61no—
343#41—61no—
344#41—61no—
345#41—62no—
346#41—92no—
347#41—92no—
348#41—181no—
349#41—181no—
350#41—182no—
351#41C3×#6711yescharacteristic
352#41D3×A411yescharacteristic
353#41C22×C3×D311yescharacteristic
354C2×Q8—21no—
355C2×Q8—31no—
356C2×Q8—31no—
357C2×Q8—31no—
358C2×Q8—61no—
359C2×Q8C3×#6711yescharacteristic
360C2×D4—31no—
361C2×D4—31no—
362C2×D4—31no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—62no—
366C2×D4—61no—
367C2×D4—61no—
368C2×D4—92no—
369C2×D4—92no—
370C2×D4—91no—
371C2×D4—181no—
372C2×D4—181no—
373C2×D4—181no—
374C2×D4—181no—
375C2×D4—184no—
376C2×D4—182no—
377C2×D4—182no—
378C22×C4—31no—
379C22×C4—61no—
380C22×C4—61no—
381C22×C4—181no—
382Q16—32no—
383Q16—92no—
384SD16—32no—
385SD16—92no—
386SD16—92no—
387SD16—94no—
388SD16—92no—
389D8—92no—
390D8—94no—
391D8—92no—
392M16—31no—
393M16—92no—
394M16—91no—
395M16—92no—
396C2×C8—92no—
397C2×C8—92no—
398C22×C3—21no—
399C22×C3—31no—
400C22×C3—31no—
401C22×C3—41no—
402C22×C3—61no—
403C22×C3—81no—
404C22×C3—82no—
405C22×C3—81no—
406C22×C3—121no—
407C22×C3—241no—
408C22×C3—241no—
409C22×C3D4×A411yescharacteristic
410C2×D3—62no—
411C2×D3—122no—
412C2×D3—242no—
413C2×D3—242no—
414C3×C4—21no—
415C3×C4—31no—
416C3×C4—31no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—61no—
420C3×C4—81no—
421C3×C4—82no—
422C3×C4—81no—
423C3×C4—81no—
424C3×C4—242no—
425C3×C4D4×A411yescharacteristic
426C3×C4C23×A411yescharacteristic
427Dic3—22no—
428C32—41noSylow
429C23—31no—
430C23—61no—
431C23—61no—
432C23—182no—
433C23—182no—
434C23—181no—
435C23—722no—
436Q8—31no—
437Q8—32no—
438Q8—31no—
439Q8—61no—
440Q8—61no—
441Q8—61no—
442Q8C2×C3×#6711yescharacteristic
443Q8C2×D3×A411yescharacteristic
444D4—21no—
445D4—31no—
446D4—31no—
447D4—32no—
448D4—31no—
449D4—61no—
450D4—61no—
451D4—61no—
452D4—61no—
453D4—62no—
454D4—61no—
455D4—92no—
456D4—182no—
457D4—182no—
458D4—182no—
459D4—182no—
460D4—181no—
461D4C2×D3×A411yescharacteristic
462C2×C4—21no—
463C2×C4—31no—
464C2×C4—31no—
465C2×C4—31no—
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—62no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4C2×D3×A411yescharacteristic
478C8—32no—
479C8—92no—
480C2×C3—21no—
481C2×C3—41no—
482C2×C3—41no—
483C2×C3—61no—
484C2×C3—61no—
485C2×C3—81no—
486C2×C3—81no—
487C2×C3—121no—
488C2×C3—161no—
489C2×C3—161no—
490C2×C3—162no—
491C2×C3C2×D4×A411yescharacteristic
492D3—122no—
493C22—21no—
494C22—31no—
495C22—31no—
496C22—61no—
497C22—121no—
498C22—182no—
499C22—241no—
500C22—241no—
501C22—362no—
502C22—722no—
503C22—722no—
504C22A4×#6711yescharacteristic
505C4—21no—
506C4—31no—
507C4—31no—
508C4—61no—
509C4—62no—
510C4A4×#6711yescharacteristic
511C4C22×D3×A411yescharacteristic
512C3—41no—
513C3—81no—
514C3#3585⋊C311yescharacteristic, complemented
515C2—21no—
516C2—41no—
517C2—61no—
518C2—61no—
519C2—121no—
520C2—362no—
521C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC2C2×A4×#67
commutator, cosocleC3×#41C23×C3
FrattiniC4C22×D3×A4
FittingC3×#585C2×C3
socleC2×C3C2×D4×A4
hypercenter#41D3×A4
hypocenterC3×Q8C2×C3×D4
LCSG ▷ C3×#41 ▷ C3×Q8
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×#5945C2semidirect
2. C2×C3⋊#994C2semidirect
3. #5837⋊C3C2semidirect
4. #5835⋊C3C2semidirect
5. #5819⋊C3C2semidirect
6. #87298C3semidirect
9. C3×2−1+4⋊C3C22semidirect
10. C3×#994C22semidirect
14. C3⋊#994C22semidirect
17. C3⋊(#131⋊C3)C22semidirect
19. C2×#1009C2×C3semidirect
21. #5945D3semidirect
24. #5837C2×C3semidirect
26. #5835C2×C3semidirect
31. #5819C2×C3semidirect
69. 2−1+4⋊C3C2×D3semidirect
73. #994C2×D3semidirect
514. C3#3585⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#59452
C2×C3⋊#9942
#5837⋊C32
#5835⋊C32
#5819⋊C32
#872983
#3585⋊C33
C3×#9514