Finite Group Databasebeta

← #11807607

Subgroups — #11807607

Order 1152.

1629 conjugacy classes of subgroups; only the 284 normal subgroups are shown.

normal subgroups only

This group has 1629 conjugacy classes of subgroups — too many to draw. Only its 284 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×C3×#953C211yesmaximal, characteristic
2#10592946C211yesmaximal, characteristic, complemented
3C3×#5247C211yesmaximal, characteristic, complemented
4#10591721C213yesmaximal, complemented
5#10591707C213yesmaximal, complemented
6#10591702C213yesmaximal, complemented
7#10591701C213yesmaximal, complemented
8#82580—31nomaximal
9#73851—31nomaximal
10C25×C32C2211yescharacteristic
11C22×C3×#67C2213yes—
12C22×D3×Dic3C2211yescharacteristic, complemented
13C2×#3757C2213yes—
14C2×#3757C2213yes—
15C3×#953C418yescomplemented
16C2×C3×#217C2213yes—
17C2×C3×#217C2213yes—
18C2×C3×#217C2213yes—
19C2×Dic3⋊Dic3C2213yescomplemented
20C2×(C2×D3)⋊Dic3C2213yescomplemented
21C2×Dic32C2213yescomplemented
22#63579C2213yescomplemented
23#63579C2213yescomplemented
24C2×C3×#120—31no—
25C2×#953D311yescharacteristic
26C3×#379—31no—
27#5247—31no—
28#5247—31no—
29#5247—61no—
30#5247D311yescharacteristic, complemented
31#5221—33no—
32#5220—33no—
33#4957—33no—
34#4956—33no—
35#4951—33no—
36#4951—33no—
37#4945—33no—
38#4944—33no—
39C24×C32—43no—
40C24×C32—43no—
41C24×C32C2×C414yescomplemented
42C24×C32C2313yes—
43C23×C3×D3C2311yescharacteristic
44C22×C3⋊Dic3C2311yescharacteristic
45C22×C3⋊Dic3C2313yes—
46C2×C3×#67—43no—
47C2×C3×#67—43no—
48C2×C3×#67C2×C4112yes—
49C22×C3×Dic3C2311yescharacteristic
50C22×C3×Dic3C2313yes—
51C22×C3×Dic3C2313yes—
52C2×D3×Dic3—43no—
53#3757—43no—
54#3757—43no—
55C3×#217—43no—
56C3×#217—43no—
57C3×#217C2×C4112yescomplemented
58Dic3⋊Dic3—43no—
59(C2×D3)⋊Dic3—43no—
60Dic32—43no—
61#2375—91noSylow
62C25×C3—21no—
63C25×C3C2×D311yescharacteristic
64C25×C3C2×D311yescharacteristic
65C22×C3×D4—33no—
66C22×#67C2×D313yes—
67C23×Dic3—31no—
68C22×C4×D3—31no—
69C3×#120—38no—
70C2×C3×C22⋊C4—33no—
71C2×C3×C22⋊C4—33no—
72C2×C3×C22⋊C4—33no—
73#953Dic318yescomplemented
74C2×#217—33no—
75C2×#217—33no—
76C2×#217—33no—
77C2×#217—33no—
78C2×#217—33no—
79C2×#217—63no—
80C2×#217—63no—
81C2×#217C2×D313yes—
82C2×#217C2×D313yes—
83C2×#217C2×D313yes—
84C2×(C2×D3)⋊C4—33no—
85C2×C4⋊Dic3—33no—
86C2×Dic3⋊C4—33no—
87C2×C4×Dic3—33no—
88C2×C4×Dic3—33no—
89C3⋊#95—33no—
90C3⋊#95—33no—
91C3⋊#95—33no—
92C3⋊#95—33no—
93C23×C32—23no—
94C23×C32—23no—
95C23×C32—23no—
96C23×C32—23no—
97C23×C32—23no—
98C23×C32—23no—
99C23×C32—412no—
100C23×C32—412no—
101C23×C32—44no—
102C23×C32C22×C416yes—
103C23×C32C2411yescharacteristic
104C22×C3×D3—23no—
105C22×C3×D3—23no—
106C22×C3×D3C22×C412yes—
107C2×C3⋊Dic3—23no—
108C2×C3⋊Dic3—23no—
109C2×C3⋊Dic3—23no—
110C2×C3⋊Dic3—23no—
111C3×#67—412no—
112C2×C3×Dic3—23no—
113C2×C3×Dic3—23no—
114C2×C3×Dic3—23no—
115C2×C3×Dic3—23no—
116C2×C3×Dic3—23no—
117C2×C3×Dic3—23no—
118C2×C3×Dic3C22×C416yes—
119D3×Dic3—44no—
120C2×#120—31no—
121#390—93no—
122#388—93no—
123#388—93no—
124#386—93no—
125#379—31no—
126#379—91no—
127C24×C3—24no—
128C24×C3—23no—
129C24×C3—31no—
130C24×C3—43no—
131C24×C3—43no—
132C24×C3—43no—
133C24×C3—43no—
134C24×C3—46no—
135C24×C3—46no—
136C24×C3C4×D314yescomplemented
137C24×C3C2×Dic314yescomplemented
138C24×C3C22×D313yes—
139C24×C3C22×D313yes—
140C23×D3C22×D311yescharacteristic
141C2×C3×D4—312no—
142C2×C3×D4—123no—
143C2×C3×D4—123no—
144C22×C3×C4—33no—
145C22×C3×C4—31no—
146C22×C3×C4—33no—
147C2×#67—43no—
148C2×#67—43no—
149C2×#67C2×Dic3112yes—
150C22×Dic3—31no—
151C22×Dic3—31no—
152C22×Dic3—33no—
153C22×Dic3—33no—
154C22×Dic3—61no—
155C22×Dic3—63no—
156C22×Dic3—123no—
157C22×Dic3C22×D311yescharacteristic
158C22×Dic3C22×D313yes—
159C22×Dic3C22×D313yes—
160C2×C4×D3—123no—
161C3×C22⋊C4—312no—
162C3×C22⋊C4—123no—
163C3×C22⋊C4—123no—
164#217—43no—
165#217—43no—
166#217—123no—
167#217—123no—
168#217—123no—
169#217—123no—
170#217—123no—
171#217—126no—
172#217—126no—
173#217C2×Dic3112yescomplemented
174(C2×D3)⋊C4—123no—
175C4⋊Dic3—123no—
176Dic3⋊C4—123no—
177C4×Dic3—123no—
178C4×Dic3—123no—
179C22×C32—26no—
180C22×C32—26no—
181C22×C32—26no—
182C22×C32—416no—
183C22×C32—43no—
184C22×C32—43no—
185C22×C32—43no—
186C22×C32—43no—
187C22×C32C23×C411yescharacteristic
188C22×C32H(5,𝔽2)13yes—
189C22×C32H(5,𝔽2)13yes—
190C2×C3×D3—26no—
191C2×C3×D3—43no—
192C2×C3×D3—41no—
193C3⋊Dic3—43no—
194C3⋊Dic3—41no—
195C3×Dic3—26no—
196C3×Dic3—43no—
197C3×Dic3—41no—
198C25D3211yescharacteristic
199C22×D4—33no—
200C23×C4—91no—
201#120—38no—
202C2×C4⋊C4—93no—
203C2×C22⋊C4—33no—
204C2×C22⋊C4—33no—
205C2×C22⋊C4—33no—
206C2×C22⋊C4—93no—
207C2×C22⋊C4—93no—
208C2×C22⋊C4—93no—
209C2×C42—93no—
210#95—93no—
211#95—93no—
212C23×C3—26no—
213C23×C3—26no—
214C23×C3—23no—
215C23×C3—23no—
216C23×C3—23no—
217C23×C3—23no—
218C23×C3—23no—
219C23×C3—23no—
220C23×C3—23no—
221C23×C3—23no—
222C23×C3—23no—
223C23×C3—23no—
224C23×C3—23no—
225C23×C3—23no—
226C23×C3—21no—
227C23×C3—26no—
228C23×C3—32no—
229C23×C3—43no—
230C23×C3—43no—
231C23×C3—43no—
232C23×C3—43no—
233C23×C3—412no—
234C23×C3—412no—
235C23×C3—424no—
236C23×C3—424no—
237C23×C3—48no—
238C23×C3—44no—
239C23×C3—44no—
240C23×C3—412no—
241C23×C3—412no—
242C23×C3—63no—
243C23×C3—63no—
244C23×C3C2×C4×D316yes—
245C23×C3C22×Dic316yes—
246C23×C3C23×D311yescharacteristic
247C23×C3C23×D311yescharacteristic
248C22×D3—23no—
249C22×D3—23no—
250C22×D3C22×Dic312yes—
251C3×D4—1212no—
252C2×C3×C4—36no—
253C2×C3×C4—63no—
254C2×C3×C4—63no—
255C2×C3×C4—63no—
256C2×C3×C4—63no—
257C2×C3×C4—63no—
258C2×C3×C4—63no—
259#67—412no—
260C2×Dic3—23no—
261C2×Dic3—23no—
262C2×Dic3—23no—
263C2×Dic3—23no—
264C2×Dic3—23no—
265C2×Dic3—23no—
266C2×Dic3—63no—
267C2×Dic3—63no—
268C2×Dic3—63no—
269C2×Dic3—63no—
270C2×Dic3—63no—
271C2×Dic3—63no—
272C2×Dic3—63no—
273C2×Dic3—63no—
274C2×Dic3—123no—
275C2×Dic3—123no—
276C2×Dic3—123no—
277C2×Dic3—123no—
278C2×Dic3—124no—
279C2×Dic3C22×Dic316yes—
280C4×D3—124no—
281C2×C32—46no—
282C2×C32#51813yes—
283C2×C32#56013yes—
284C2×C32H(3,𝔽4)11yescharacteristic
285C3×D3—42no—
286C24—31no—
287C24—43no—
288C24—43no—
289C24D3×Dic314yescomplemented
290C24C2×D3213yes—
291C2×D4—312no—
292C2×D4—123no—
293C2×D4—123no—
294C22×C4—33no—
295C22×C4—31no—
296C22×C4—33no—
297C22×C4—91no—
298C22×C4—93no—
299C22×C4—363no—
300C4⋊C4—363no—
301C22⋊C4—312no—
302C22⋊C4—123no—
303C22⋊C4—123no—
304C22⋊C4—363no—
305C22⋊C4—363no—
306C22⋊C4—363no—
307C42—363no—
308C22×C3—212no—
309C22×C3—26no—
310C22×C3—26no—
311C22×C3—26no—
312C22×C3—26no—
313C22×C3—26no—
314C22×C3—26no—
315C22×C3—21no—
316C22×C3—23no—
317C22×C3—23no—
318C22×C3—46no—
319C22×C3—46no—
320C22×C3—46no—
321C22×C3—46no—
322C22×C3—46no—
323C22×C3—46no—
324C22×C3—432no—
325C22×C3—416no—
326C22×C3—416no—
327C22×C3—43no—
328C22×C3—43no—
329C22×C3—43no—
330C22×C3—43no—
331C22×C3—43no—
332C22×C3—43no—
333C22×C3—43no—
334C22×C3—43no—
335C22×C3—66no—
336C22×C3—121no—
337C22×C3—123no—
338C22×C3C22×C4×D311yescharacteristic
339C22×C3#100413yes—
340C22×C3#100413yes—
341C22×C3#100413yes—
342C22×C3#100413yes—
343C22×C3C23×Dic311yescharacteristic
344C2×D3—26no—
345C2×D3—41no—
346C2×D3—43no—
347C3×C4—66no—
348C3×C4—121no—
349C3×C4—123no—
350Dic3—26no—
351Dic3—41no—
352Dic3—43no—
353Dic3—121no—
354Dic3—121no—
355Dic3—123no—
356Dic3—123no—
357Dic3—243no—
358Dic3—241no—
359C32#237511yescharacteristic, complemented, Sylow
360C23—23no—
361C23—23no—
362C23—23no—
363C23—23no—
364C23—23no—
365C23—23no—
366C23—32no—
367C23—412no—
368C23—412no—
369C23—44no—
370C23—63no—
371C23—63no—
372C23C2×D3×Dic316yes—
373C23C22×D3211yescharacteristic
374D4—1212no—
375C2×C4—36no—
376C2×C4—63no—
377C2×C4—63no—
378C2×C4—63no—
379C2×C4—63no—
380C2×C4—63no—
381C2×C4—63no—
382C2×C4—183no—
383C2×C4—183no—
384C2×C4—183no—
385C2×C4—183no—
386C2×C4—364no—
387C2×C3—23no—
388C2×C3—23no—
389C2×C3—21no—
390C2×C3—412no—
391C2×C3—46no—
392C2×C3—46no—
393C2×C3—122no—
394C2×C3#548613yes—
395C2×C3#559411yescharacteristic
396C2×C3#559411yescharacteristic
397C2×C3#559513yes—
398C2×C3#559513yes—
399C2×C3#579813yes—
400D3—42no—
401C22—26no—
402C22—26no—
403C22—26no—
404C22—416no—
405C22—43no—
406C22—43no—
407C22—43no—
408C22—43no—
409C22—66no—
410C22—123no—
411C22—121no—
412C22C22×D3×Dic311yescharacteristic
413C22#6433013yes—
414C22#6433013yes—
415C4—66no—
416C4—123no—
417C4—121no—
418C4—363no—
419C4—361no—
420C3—21no—
421C3#7385111yescharacteristic, complemented
422C3#8258011yescharacteristic, complemented
423C2—46no—
424C2—122no—
425C2#1059550513yes—
426C2#1059550613yes—
427C2#1059552911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC25×C32C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#953C2
hypercenterC25D32
hypocenterC32#2375
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
2. #10592946C2semidirect
3. C3×#5247C2semidirect
4. #10591721C2semidirect
5. #10591707C2semidirect
6. #10591702C2semidirect
7. #10591701C2semidirect
12. C22×D3×Dic3C22semidirect
15. C3×#953C4semidirect
19. C2×Dic3⋊Dic3C22semidirect
20. C2×(C2×D3)⋊Dic3C22semidirect
21. C2×Dic32C22semidirect
22. #63579C22semidirect
23. #63579C22semidirect
30. #5247D3semidirect
41. C24×C32C2×C4semidirect
57. C3×#217C2×C4semidirect
73. #953Dic3semidirect
136. C24×C3C4×D3semidirect
137. C24×C3C2×Dic3semidirect
173. #217C2×Dic3semidirect
289. C24D3×Dic3semidirect
359. C32#2375semidirect
421. C3#73851semidirect
422. C3#82580semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9532
#105929462
C3×#52472
#105917212
#105917072
#105917022
#105917012
#825803
#738513