Finite Group Databasebeta

← #11921872

Subgroups — #11921872

Order 1152.

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

normal subgroups only

This group has 652 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×C4⋊(C3⋊S4)C211yesmaximal, characteristic, complemented
2C3×#5912C211yesmaximal, characteristic, complemented
3A4×#208C211yesmaximal, characteristic, complemented
4#10593179C212yesmaximal, complemented
5#10593178C212yesmaximal, complemented
6#85443—31nomaximal
7#82924—31nomaximal
8C22×C3⋊S4—21no—
9C2×C3×C4×A4C2211yescharacteristic
10C4⋊(C3⋊S4)—21no—
11C4⋊(C3⋊S4)C2212yes—
12C3×GL(2,ℤ/4)—21no—
13C3×C4⋊S4C2211yescharacteristic, complemented
14C3×C4×S4—21no—
15C3×A4⋊Q8C2211yescharacteristic, complemented
16#63825—41nomaximal
17A4×C3⋊C8C2212yescomplemented
18#5912D311yescharacteristic, complemented
19C2×C4⋊S4—31no—
20C2×C4⋊S4—61no—
21C3×#525—31no—
22C2×#949—31no—
23C2×#930—31no—
24C22×#208D311yescharacteristic, complemented
25A4×M16—31no—
26#5402—32no—
27#5401—32no—
28#5232—31no—
29#5049—32no—
30#5048—32no—
31#5039—32no—
32#5038—32no—
33#5001—31no—
34#4995—31no—
35C22×C3×A4D411yescharacteristic
36C2×C3⋊S4—22no—
37C2×C3⋊S4—42no—
38C2×C3×S4—21no—
39C2×C4⋊(C3⋊D3)—41no—
40C3×#235—41no—
41C3×C4×A4D411yescharacteristic
42C3×C4×A4C2311yescharacteristic
43C3×SL(2,ℤ/4)—21no—
44C3×#208—41no—
45#3717—42no—
46#3714—42no—
47#3055—91noSylow
48C22×S4—62no—
49C22×S4—61no—
50C2×C3×#41—31no—
51C23×C3×C4C2×D311yescharacteristic
52C22×#67—61no—
53C22×D12—31no—
54C2×C4×A4—21no—
55C2×C4×A4C2×D311yescharacteristic
56GL(2,ℤ/4)—21no—
57C4⋊S4—32no—
58C4⋊S4—62no—
59C4⋊S4—62no—
60C4⋊S4—61no—
61C4⋊S4C2×D311yescharacteristic, complemented
62C4×S4—21no—
63A4⋊Q8C2×D311yescharacteristic, complemented
64C3×#123—61no—
65C3×C22⋊Q8—31no—
66C3×C22⋊Q8—31no—
67C3×#121—31no—
68C3×#121—31no—
69C3×#120—61no—
70C3×C4×D4—61no—
71C3×C4×D4—61no—
72C3×#117—31no—
73#949—61no—
74#949—62no—
75#949—61no—
76C2×#215—32no—
77C2×#213—32no—
78#930—32no—
79#930—32no—
80#930—61no—
81#930—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×C4⋊Dic3—31no—
84C2×#208—31no—
85C2×#208—31no—
86C2×#208—32no—
87C22×C3⋊C8C2×D312yescomplemented
88#908—121no—
89C8×A4—32no—
90#835—32no—
91#832—32no—
92#809—32no—
93#809—32no—
94#808—32no—
95#807—32no—
96C22×C3⋊D3—81no—
97C2×C3×A4—21no—
98C2×C3×A4C2×D411yescharacteristic
99C3⋊S4—42no—
100C3×S4—41no—
101C2×C32×C4—41no—
102C4⋊(C3⋊D3)—42no—
103C4⋊(C3⋊D3)—81no—
104C3×#67—81no—
105C3×D12—41no—
106C3×C4×D3—81no—
107C3×Dic6—41no—
108C3×C3⋊C8—42no—
109C2×AGL(1,ℤ/8)—91no—
110C22×M16—31no—
111#525—31no—
112C2×#121—91no—
113#469—92no—
114#468—92no—
115#466—92no—
116#465—92no—
117#428—91no—
118#418—91no—
119#417—91no—
120C24×C3D1211yescharacteristic
121C23×D3—61no—
122C22×A4—21no—
123C22×A4#6711yescharacteristic
124C2×S4—21no—
125C2×S4—64no—
126C2×S4—62no—
127C2×S4—124no—
128C2×S4—122no—
129C3×#41—61no—
130C3×#41—61no—
131C3×#41—61no—
132C3×#41—61no—
133C2×C3×Q8—31no—
134C2×C3×D4—31no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×C3×C4—31no—
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C22×C3×C4—31no—
142C22×C3×C4—61no—
143C22×C3×C4D1211yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C2×#67—62no—
146C2×#67—62no—
147C2×#67—122no—
148C2×#67—122no—
149C22×Dic3—61no—
150#235—41no—
151C2×D12—32no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—121no—
158C2×D12—241no—
159C4×A4—21no—
160C4×A4—21no—
161C4×A4#6711yescharacteristic
162C4×A4C22×D311yescharacteristic
163SL(2,ℤ/4)—21no—
164C3×M16—121no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C22⋊C4—61no—
171C3×C22⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C42—61no—
175#215—62no—
176#215—62no—
177#213—62no—
178#213—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181C4⋊Dic3—32no—
182C4⋊Dic3—61no—
183#208—31no—
184#208—32no—
185#208—61no—
186#208S411yescharacteristic, complemented
187C2×C3⋊C8—32no—
188C2×C3⋊C8—32no—
189D24—122no—
190#204—122no—
191C22×C32—41no—
192C2×C3⋊D3—82no—
193C2×C3⋊D3—162no—
194C2×C3×D3—81no—
195C3×A4AGL(1,ℤ/8)11yescharacteristic, complemented
196C32×C4—41no—
197C32×C4—41no—
198C3×Dic3—81no—
199C2×#41—31no—
200C22×D4—91no—
201C22×D4—181no—
202C23×C4D3211yescharacteristic
203AGL(1,ℤ/8)—181no—
204AGL(1,ℤ/8)—182no—
205AGL(1,ℤ/8)—181no—
206C2×SD16—92no—
207C2×D8—92no—
208C2×M16—91no—
209C2×M16—91no—
210C2×M16—92no—
211C22×C8—32no—
212#123—61no—
213C22⋊Q8—31no—
214C22⋊Q8—31no—
215#121—31no—
216#121—31no—
217#121—92no—
218#121—92no—
219#121—181no—
220#121—181no—
221#120—61no—
222C4×D4—61no—
223C4×D4—61no—
224#117—31no—
225C2×C4⋊C4—91no—
226C2×C22⋊C4—181no—
227#107—92no—
228#106—92no—
229#103—92no—
230#102—92no—
231#102—92no—
232#102—92no—
233C23×C3—21no—
234C23×C3—31no—
235C23×C3—31no—
236C23×C3—61no—
237C23×C3—61no—
238C23×C3C2×D1211yescharacteristic
239C22×D3—62no—
240C22×D3—121no—
241C22×D3—122no—
242C22×D3—122no—
243C22×D3—121no—
244C22×D3—241no—
245C22×D3—242no—
246C2×A4—22no—
247C2×A4—21no—
248C2×A4—21no—
249C2×A4C2×#6711yescharacteristic
250S4—41no—
251S4—124no—
252S4—122no—
253C3×Q8—61no—
254C3×Q8—61no—
255C3×D4—61no—
256C3×D4—61no—
257C3×D4—121no—
258C3×D4—121no—
259C3×D4—122no—
260C3×D4—121no—
261C3×D4—121no—
262C2×C3×C4—31no—
263C2×C3×C4—31no—
264C2×C3×C4—31no—
265C2×C3×C4—31no—
266C2×C3×C4—31no—
267C2×C3×C4—31no—
268C2×C3×C4—31no—
269C2×C3×C4—41no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—81no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4C2×S411yescharacteristic
278#67—81no—
279#67—122no—
280#67—124no—
281#67—122no—
282C2×Dic3—62no—
283C2×Dic3—122no—
284D12—41no—
285D12—62no—
286D12—62no—
287D12—122no—
288D12—121no—
289D12—121no—
290D12—242no—
291D12—241no—
292D12—242no—
293C4×D3—81no—
294Dic6—41no—
295C3×C8—122no—
296C3⋊C8—32no—
297C3⋊C8C2×S412yescomplemented
298C2×C32—41no—
299C2×C32—81no—
300C3⋊D3—162no—
301C3×D3—161no—
302C24—181no—
303C24#62611yescharacteristic
304#41—61no—
305#41—61no—
306#41—61no—
307#41—61no—
308C2×Q8—31no—
309C2×D4—31no—
310C2×D4—61no—
311C2×D4—61no—
312C2×D4—61no—
313C2×D4—92no—
314C2×D4—181no—
315C2×D4—181no—
316C2×D4—181no—
317C2×D4—181no—
318C2×D4—182no—
319C2×D4—182no—
320C2×D4—181no—
321C2×D4—362no—
322C2×D4—362no—
323C22×C4—31no—
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—61no—
328C22×C4—181no—
329C22×C4#62611yescharacteristic
330C22×C4C2×D3211yescharacteristic
331SD16—182no—
332SD16—182no—
333D8—182no—
334D8—182no—
335M16—31no—
336M16—92no—
337M16—91no—
338M16—181no—
339C2×C8—92no—
340C2×C8—92no—
341C4⋊C4—31no—
342C4⋊C4—31no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C4⋊C4—92no—
346C4⋊C4—181no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C22⋊C4—61no—
350C22⋊C4—61no—
351C22⋊C4—61no—
352C22⋊C4—182no—
353C22⋊C4—182no—
354C42—61no—
355C22×C3—31no—
356C22×C3—31no—
357C22×C3—31no—
358C22×C3—41no—
359C22×C3—61no—
360C22×C3—61no—
361C22×C3—61no—
362C22×C3—61no—
363C22×C3—81no—
364C22×C3—121no—
365C22×C3—121no—
366C22×C3—121no—
367C22×C3#90811yescharacteristic, complemented
368C22×C3C4⋊S411yescharacteristic
369C2×D3—81no—
370C2×D3—122no—
371C2×D3—122no—
372C2×D3—122no—
373C2×D3—242no—
374C2×D3—244no—
375C2×D3—242no—
376C2×D3—242no—
377C2×D3—482no—
378C2×D3—484no—
379A4—21no—
380A4#94911yescharacteristic, complemented
381C3×C4—31no—
382C3×C4—31no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—81no—
386C3×C4—81no—
387C3×C4—121no—
388C3×C4—121no—
389C3×C4—121no—
390C3×C4C4⋊S411yescharacteristic
391C3×C4C22×S411yescharacteristic
392Dic3—81no—
393Dic3—122no—
394C32—41noSylow
395C23—21no—
396C23—31no—
397C23—31no—
398C23—61no—
399C23—61no—
400C23—182no—
401C23—361no—
402C23—362no—
403C23—362no—
404C23—361no—
405C23C2×#62611yescharacteristic
406Q8—61no—
407Q8—61no—
408D4—61no—
409D4—61no—
410D4—121no—
411D4—121no—
412D4—122no—
413D4—121no—
414D4—121no—
415D4—182no—
416D4—182no—
417D4—361no—
418D4—362no—
419D4—364no—
420D4—362no—
421D4—361no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—31no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—31no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—182no—
436C2×C4—362no—
437C2×C4D3×S411yescharacteristic
438C8—32no—
439C8—92no—
440C2×C3—21no—
441C2×C3—31no—
442C2×C3—31no—
443C2×C3—41no—
444C2×C3—61no—
445C2×C3—81no—
446C2×C3—82no—
447C2×C3—81no—
448C2×C3—241no—
449C2×C3C2×C4⋊S411yescharacteristic
450D3—161no—
451D3—242no—
452D3—482no—
453D3—484no—
454C22—31no—
455C22—31no—
456C22—31no—
457C22—61no—
458C22—61no—
459C22—61no—
460C22—61no—
461C22—121no—
462C22—121no—
463C22—121no—
464C22—362no—
465C22—362no—
466C22—362no—
467C22—722no—
468C22—722no—
469C22#6382511yescharacteristic, complemented
470C22#6420711yescharacteristic
471C4—31no—
472C4—31no—
473C4—121no—
474C4—121no—
475C4—121no—
476C4—362no—
477C4#6420711yescharacteristic
478C4C2×D3×S411yescharacteristic
479C3—41no—
480C3—81no—
481C3#8544311yescharacteristic, complemented
482C2—21no—
483C2—31no—
484C2—31no—
485C2—61no—
486C2—241no—
487C2—722no—
488C2C2×#6420711yescharacteristic
subgroupG/H
centerC2C2×#64207
commutator, cosocleC3×C4×A4C23
FrattiniC4C2×D3×S4
FittingC23×C3×C4C2×D3
socleC23×C3C2×D12
hypercenterC2×C4D3×S4
hypocenterC3×A4AGL(1,ℤ/8)
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×C4⋊(C3⋊S4)C2semidirect
2. C3×#5912C2semidirect
3. A4×#208C2semidirect
4. #10593179C2semidirect
5. #10593178C2semidirect
13. C3×C4⋊S4C22semidirect
15. C3×A4⋊Q8C22semidirect
17. A4×C3⋊C8C22semidirect
18. #5912D3semidirect
24. C22×#208D3semidirect
61. C4⋊S4C2×D3semidirect
63. A4⋊Q8C2×D3semidirect
87. C22×C3⋊C8C2×D3semidirect
186. #208S4semidirect
195. C3×A4AGL(1,ℤ/8)semidirect
297. C3⋊C8C2×S4semidirect
367. C22×C3#908semidirect
380. A4#949semidirect
469. C22#63825semidirect
481. C3#85443semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊S4)2
C3×#59122
A4×#2082
#105931792
#105931782
#854433
#829243
#638254