Finite Group Databasebeta

← #11923732

Subgroups — #11923732

Order 1152.

1836 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1836 conjugacy classes of subgroups — too many to draw. Only its 187 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×A4×#41C211yesmaximal, characteristic, complemented
2Q8×C3⋊S4C212yesmaximal, complemented
3#10596577C216yesmaximal, complemented
4#10596575C213yesmaximal, complemented
5C2×#64259C213yesmaximal, complemented
6#87490—33nomaximal
7#87264—31nomaximal
8#64367—41nomaximal
9C3×Q8×A4C2211yescharacteristic
10C3×D4×A4C2213yes—
11C2×C3×C4×A4C2213yes—
12#64269C2216yes—
13C2×C3⋊SL(2,ℤ/4)C2216yes—
14C4⋊(C3⋊S4)C2211yescharacteristic
15C4×C3⋊S4C2216yes—
16#64259C2213yes—
17#64259C2216yes—
18C22×C3×#41D311yescharacteristic, complemented
19C2×#1010—31no—
20A4×#41D313yescomplemented
21Q8×S4—36no—
22#5914—318no—
23#5912—39no—
24C2×A4⋊Q8—39no—
25#5833—33no—
26#5831—32no—
27#5827—31no—
28#5825—33no—
29#5824—36no—
30Q8×#67—32no—
31#5806—36no—
32#5791—33no—
33C2×#924—33no—
34C22×C3×A4C2313yes—
35C2×C3⋊S4C2312yes—
36C32×#41—41no—
37Q8×C3⋊D3—42no—
38#3830—46no—
39#3828—43no—
40C2×#634—43no—
41C3×C4×A4C2311yescharacteristic
42C3×C4×A4C2313yes—
43C3⋊SL(2,ℤ/4)C2316yes—
44#3489—91noSylow
45C2×C3×#41—31no—
46C2×C3×#41—33no—
47C2×C3×#41—33no—
48C2×C3×#41—31no—
49C22×C3×Q8C2×D311yescharacteristic
50C22×C3×D4C2×D313yes—
51C23×C3×C4C2×D313yes—
52#1010—61no—
53#1010—63no—
54#1010—63no—
55#1010—61no—
56#1010—123no—
57C2×D3×Q8—32no—
58C2×#237—36no—
59C2×#235—33no—
60C22×Dic6—33no—
61Q8×A4C2×D313yes—
62D4×A4C2×D319yes—
63C2×C4×A4C2×D319yes—
64GL(2,ℤ/4)—318no—
65C2×SL(2,ℤ/4)—318no—
66C4⋊S4—33no—
67C4×S4—318no—
68A4⋊Q8—39no—
69A4⋊Q8—318no—
70#953—36no—
71C2×#217—36no—
72#946—36no—
73Q8×Dic3—32no—
74#944—36no—
75#939—312no—
76#938—36no—
77#936—36no—
78#935—312no—
79D4×Dic3—36no—
80#930—33no—
81#930—31no—
82#929—36no—
83C4×#67—36no—
84C4×#67—36no—
85#926—33no—
86C2×C4⋊Dic3—33no—
87#924—36no—
88#924—36no—
89#924—33no—
90#924—33no—
91#924—36no—
92C2×Dic3⋊C4—36no—
93C2×C3×A4—23no—
94C2×C3×A4C2411yescharacteristic
95C3⋊S4—22no—
96C32×Q8—41no—
97C32×D4—43no—
98C2×C32×C4—43no—
99#638—46no—
100C2×C3⋊Dic3—46no—
101C4⋊(C3⋊D3)—41no—
102C4×C3⋊D3—46no—
103#634—43no—
104#634—46no—
105C2×2−1+4—91no—
106C22×#41C3⋊D311yescharacteristic, complemented
107D4×Q8—92no—
108#548—92no—
109#547—96no—
110#546—96no—
111#537—93no—
112#536—93no—
113#525—93no—
114C2×C22⋊Q8—93no—
115#520—91no—
116C24×C3C22×D313yes—
117C22×A4C22×D319yes—
118C2×S4—36no—
119C3×#41—31no—
120C3×#41—33no—
121C3×#41—33no—
122C3×#41—43no—
123C3×#41—61no—
124C3×#41—63no—
125C3×#41—63no—
126C3×#41S411yescharacteristic, complemented
127C2×C3×Q8—31no—
128C2×C3×Q8—33no—
129C2×C3×D4—33no—
130C2×C3×D4—36no—
131C2×C3×D4—33no—
132C22×C3×C4—33no—
133C22×C3×C4—33no—
134C22×C3×C4—33no—
135C22×C3×C4—33no—
136C22×C3×C4C22×D311yescharacteristic
137C22×C3×C4C22×D313yes—
138C2×#67—36no—
139C2×#67—32no—
140C2×#67—36no—
141C22×Dic3—36no—
142C22×Dic3—36no—
143D3×Q8—66no—
144D3×Q8—62no—
145D3×Q8—126no—
146#237—612no—
147#237—66no—
148#237—66no—
149#237—1218no—
150#235—63no—
151#235—63no—
152#235—63no—
153#235—63no—
154#235—129no—
155C2×D12—31no—
156C2×C4×D3—36no—
157C2×Dic6—33no—
158C2×Dic6—36no—
159C2×Dic6—63no—
160C2×Dic6—63no—
161C2×Dic6—63no—
162C2×Dic6—63no—
163C2×Dic6—129no—
164C4×A4C22×D313yes—
165C4×A4C22×D319yes—
166SL(2,ℤ/4)—318no—
167#217—312no—
168#217—36no—
169#217—36no—
170#217—36no—
171(C2×D3)⋊C4—32no—
172(C2×D3)⋊C4—36no—
173C4⋊Dic3—33no—
174C4⋊Dic3—31no—
175C4⋊Dic3—36no—
176Dic3⋊C4—36no—
177Dic3⋊C4—312no—
178Dic3⋊C4—36no—
179C4×Dic3—36no—
180C22×C32—43no—
181C2×C3⋊D3—42no—
182C3×A42−1+411yescharacteristic, complemented
183C32×C4—41no—
184C32×C4—43no—
185C3⋊Dic3—46no—
1862−1+4—183no—
1872−1+4—181no—
1882−1+4—183no—
1892−1+4—181no—
190C2×#41—31no—
191C2×#41—33no—
192C2×#41—33no—
193C2×#41—31no—
194C2×#41—93no—
195C2×#41—96no—
196C22×Q8—93no—
197C22×Q8—92no—
198C22×Q8C2×C3⋊D311yescharacteristic
199C22×D4C2×C3⋊D313yes—
200C23×C4C2×C3⋊D313yes—
201C4⋊Q8—96no—
202#124—96no—
203#123—96no—
204#123—912no—
205C22⋊Q8—96no—
206C22⋊Q8—96no—
207C22⋊Q8—93no—
208C22⋊Q8—96no—
209C22⋊Q8—93no—
210C22⋊Q8—96no—
211#121—93no—
212#121—912no—
213#121—96no—
214#121—91no—
215#120—96no—
216C4×Q8—92no—
217C4×D4—96no—
218C4×D4—96no—
219C4×D4—96no—
220#117—93no—
221C2×C4⋊C4—93no—
222C2×C4⋊C4—96no—
223C2×C22⋊C4—96no—
224C23×C3—23no—
225C23×C3—33no—
226C23×C3—33no—
227C23×C3—63no—
228C23×C3C23×D311yescharacteristic
229C22×D3—32no—
230C2×A4—29no—
231C2×A4C23×D313yes—
232S4—66no—
233C3×Q8—33no—
234C3×Q8—43no—
235C3×Q8—61no—
236C3×Q8C2×S411yescharacteristic
237C3×D4—36no—
238C3×D4—33no—
239C3×D4—49no—
240C3×D4—63no—
241C3×D4C2×S413yes—
242C2×C3×C4—33no—
243C2×C3×C4—33no—
244C2×C3×C4—31no—
245C2×C3×C4—33no—
246C2×C3×C4—33no—
247C2×C3×C4—31no—
248C2×C3×C4—33no—
249C2×C3×C4—49no—
250C2×C3×C4—63no—
251C2×C3×C4C2×S413yes—
252#67—66no—
253#67—62no—
254#67—62no—
255#67—66no—
256#67—1218no—
257#67—126no—
258C2×Dic3—32no—
259C2×Dic3—36no—
260C2×Dic3—36no—
261C2×Dic3—66no—
262C2×Dic3—66no—
263C2×Dic3—1218no—
264C2×Dic3—126no—
265D12—61no—
266D12—61no—
267D12—123no—
268C4×D3—66no—
269C4×D3—66no—
270C4×D3—1218no—
271Dic6—63no—
272Dic6—66no—
273Dic6—63no—
274Dic6—66no—
275Dic6—129no—
276Dic6—1218no—
277C2×C32—41no—
278C2×C32—83no—
279C3⋊D3—82no—
280C24C22×C3⋊D313yes—
281#41—31no—
282#41—33no—
283#41—33no—
284#41—61no—
285#41—63no—
286#41—63no—
287#41—183no—
288#41—183no—
289#41—183no—
290#41—1812no—
291#41—186no—
292#41—186no—
293#41—183no—
294#41C3⋊S411yescharacteristic, complemented
295C2×Q8—31no—
296C2×Q8—33no—
297C2×Q8—93no—
298C2×Q8—96no—
299C2×Q8—183no—
300C2×Q8—183no—
301C2×Q8—183no—
302C2×Q8—186no—
303C2×Q8—182no—
304C2×Q8—183no—
305C2×D4—33no—
306C2×D4—36no—
307C2×D4—33no—
308C2×D4—91no—
309C2×D4—96no—
310C2×D4—92no—
311C2×D4—96no—
312C22×C4—33no—
313C22×C4—33no—
314C22×C4—33no—
315C22×C4—33no—
316C22×C4—96no—
317C22×C4—96no—
318C22×C4—96no—
319C22×C4C22×C3⋊D313yes—
320C22×C4C22×C3⋊D311yescharacteristic
321C4⋊C4—93no—
322C4⋊C4—96no—
323C4⋊C4—96no—
324C4⋊C4—912no—
325C4⋊C4—91no—
326C4⋊C4—96no—
327C22⋊C4—92no—
328C22⋊C4—96no—
329C22⋊C4—912no—
330C22⋊C4—96no—
331C22⋊C4—96no—
332C22⋊C4—96no—
333C42—96no—
334C22×C3—31no—
335C22×C3—31no—
336C22×C3—33no—
337C22×C3—49no—
338C22×C3—63no—
339C22×C3—63no—
340C22×C3—63no—
341C22×C3—63no—
342C22×C3#101011yescharacteristic, complemented
343C22×C3C22×S413yes—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—126no—
348A4#101013yescomplemented
349C3×C4—31no—
350C3×C4—33no—
351C3×C4—43no—
352C3×C4—49no—
353C3×C4C22×S411yescharacteristic
354C3×C4C22×S413yes—
355Dic3—66no—
356Dic3—62no—
357Dic3—66no—
358Dic3—1218no—
359C32—41noSylow
360C23—23no—
361C23—33no—
362C23—33no—
363C23—63no—
364C23—92no—
365C23C23×C3⋊D311yescharacteristic
366Q8—33no—
367Q8—61no—
368Q8—183no—
369Q8—186no—
370Q8—183no—
371Q8—186no—
372Q8C2×C3⋊S411yescharacteristic
373D4—36no—
374D4—33no—
375D4—63no—
376D4—181no—
377D4—186no—
378D4—182no—
379D4—182no—
380D4—186no—
381D4—181no—
382D4—366no—
383D4C2×C3⋊S413yes—
384C2×C4—33no—
385C2×C4—33no—
386C2×C4—31no—
387C2×C4—33no—
388C2×C4—33no—
389C2×C4—31no—
390C2×C4—33no—
391C2×C4—63no—
392C2×C4—92no—
393C2×C4—96no—
394C2×C4—96no—
395C2×C4—186no—
396C2×C4—186no—
397C2×C4—186no—
398C2×C4—186no—
399C2×C4—366no—
400C2×C4C2×C3⋊S413yes—
401C2×C3—23no—
402C2×C3—31no—
403C2×C3—31no—
404C2×C3—43no—
405C2×C3—63no—
406C2×C3—89no—
407C2×C3C23×S411yescharacteristic
408D3—122no—
409D3—246no—
410C22—31no—
411C22—31no—
412C22—33no—
413C22—63no—
414C22—63no—
415C22—63no—
416C22—63no—
417C22—182no—
418C22—182no—
419C22—182no—
420C22#6436711yescharacteristic, complemented
421C22C22×C3⋊S413yes—
422C4—31no—
423C4—33no—
424C4—186no—
425C4—182no—
426C4—186no—
427C4C22×C3⋊S411yescharacteristic
428C4C22×C3⋊S413yes—
429C3—43no—
430C3#8749011yescharacteristic, complemented
431C2—23no—
432C2—31no—
433C2—31no—
434C2—63no—
435C2—362no—
436C2C23×C3⋊S411yescharacteristic
subgroupG/H
center, FrattiniC2C23×C3⋊S4
commutator, cosocleC2×C3×A4C24
FittingC22×C3×#41D3
socleC23×C3C23×D3
hypercenter#41C3⋊S4
hypocenterC3×A42−1+4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×A4×#41C2semidirect
2. Q8×C3⋊S4C2semidirect
3. #10596577C2semidirect
4. #10596575C2semidirect
5. C2×#64259C2semidirect
18. C22×C3×#41D3semidirect
20. A4×#41D3semidirect
106. C22×#41C3⋊D3semidirect
126. C3×#41S4semidirect
182. C3×A42−1+4semidirect
294. #41C3⋊S4semidirect
342. C22×C3#1010semidirect
348. A4#1010semidirect
420. C22#64367semidirect
430. C3#87490semidirect

Maximal subgroups

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

subgroupindex
C3×A4×#412
Q8×C3⋊S42
#105965772
#105965752
C2×#642592
#874903
#872643
#643674