Finite Group Databasebeta

← #11802004

Subgroups — #11802004

Order 1152.

2779 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×Dic3C211yesmaximal, characteristic, complemented
2C2×#64162C211yesmaximal, characteristic
3C2×#63952C213yesmaximal, complemented
4C3×#5247C211yesmaximal, characteristic, complemented
5#10591711C213yesmaximal, complemented
6Dic3×#217C213yesmaximal, complemented
7#10591693C213yesmaximal, complemented
8C4×#953—31nomaximal
9#73818—31nomaximal
10C25×C32C2211yescharacteristic
11C22×#638C2213yes—
12C23×C3×Dic3—212no—
13C23×C3×Dic3C2213yes—
14C23×C3×Dic3C2213yes—
15C22×#624C2211yescharacteristic, complemented
16#64162C418yescomplemented
17C2×#3757C2213yes—
18C2×C3×#217C2213yes—
19C2×C3×#217C2213yes—
20C2×#3724C2213yescomplemented
21C2×#3722C2213yescomplemented
22C2×Dic32C2213yescomplemented
23#63952—212no—
24#63579C2216yescomplemented
25C24×C3×C4—31no—
26C24×Dic3D311yescharacteristic, complemented
27C2×#953—31no—
28C2×#953—31no—
29C2×#953—61no—
30C2×C4×#67—33no—
31C2×#67⋊C4—33no—
32C3×#379—31no—
33#5247D311yescharacteristic, complemented
34#5213—33no—
35#5210—33no—
36C4×#217—33no—
37#4958—33no—
38#4946—33no—
39Dic3×C22⋊C4—33no—
40C24×C32—26no—
41C24×C32—26no—
42C24×C32C2×C414yescomplemented
43C24×C32C2313yes—
44C23×C3⋊D3C2311yescharacteristic
45C2×#638—26no—
46C2×#638—26no—
47C2×#638C2×C4112yescomplemented
48C22×C3⋊Dic3C2313yes—
49C22×C3×Dic3—232no—
50C22×C3×Dic3—26no—
51C22×C3×Dic3—212no—
52C22×C3×Dic3—212no—
53C22×C3×Dic3D4112yescomplemented
54C22×C3×Dic3C2311yescharacteristic
55C22×C3×Dic3C2313yes—
56C22×C3×Dic3C2313yes—
57C22×C3×Dic3C2311yescharacteristic
58C2×#624—26no—
59#3757C2×C4112yescomplemented
60C3×#217—26no—
61C3×#217—26no—
62#3724—26no—
63#3722—26no—
64Dic32—26no—
65C4×#120—91noSylow
66C25×C3—21no—
67C25×C3C2×D311yescharacteristic
68C25×C3C2×D311yescharacteristic
69C23×C3×C4—33no—
70C23×C3×C4—33no—
71C23×C3×C4—612no—
72C22×#67—33no—
73C22×#67—33no—
74C22×#67—63no—
75C23×Dic3—212no—
76C23×Dic3C2×D313yes—
77C23×Dic3C2×D313yes—
78C22×C4×D3—31no—
79C22×C4×D3—31no—
80C2×C3×C22⋊C4—33no—
81C2×C3×C22⋊C4—33no—
82#953—38no—
83#953—38no—
84#953—68no—
85C2×#217—33no—
86C2×#217—33no—
87C2×#217—63no—
88C2×#217C2×D313yes—
89C2×#217C2×D313yes—
90C4×#67—612no—
91C2×(C2×D3)⋊C4—33no—
92C2×(C2×D3)⋊C4—33no—
93C2×Dic3⋊C4—33no—
94C2×Dic3⋊C4—33no—
95C2×C4×Dic3—33no—
96C2×C4×Dic3—33no—
97#67⋊C4—612no—
98C3⋊#95—36no—
99C3⋊#95—36no—
100C23×C32—224no—
101C23×C32—28no—
102C23×C32—224no—
103C23×C32—26no—
104C23×C32—26no—
105C23×C32C22×C416yes—
106C23×C32C2×D416yes—
107C23×C32#4116yes—
108C23×C32C2411yescharacteristic
109C22×C3⋊D3—23no—
110C22×C3⋊D3—23no—
111C22×C3⋊D3C22×C412yescomplemented
112#638—224no—
113C2×C3⋊Dic3—23no—
114C2×C3⋊Dic3—23no—
115C2×C3⋊Dic3C22×C416yescomplemented
116C2×C3×Dic3—224no—
117C2×C3×Dic3—26no—
118C2×C3×Dic3—224no—
119C2×C3×Dic3—23no—
120C2×C3×Dic3—23no—
121C2×C3×Dic3—26no—
122C2×C3×Dic3C2×D416yes—
123C2×C3×Dic3C2×D416yes—
124#624—44no—
125C24×C4—31no—
126C2×#120—91no—
127C2×C4×D4—93no—
128#386—93no—
129#385—93no—
130#379—31no—
131C4×C22⋊C4—93no—
132C24×C3—26no—
133C24×C3—26no—
134C24×C3—26no—
135C24×C3—26no—
136C24×C3—24no—
137C24×C3—23no—
138C24×C3—46no—
139C24×C3—46no—
140C24×C3C4×D314yescomplemented
141C24×C3C4×D314yescomplemented
142C24×C3C22×D313yes—
143C24×C3C22×D313yes—
144C23×D3—31no—
145C23×D3—31no—
146C23×D3—61no—
147C22×C3×C4—31no—
148C22×C3×C4—312no—
149C22×C3×C4—33no—
150C22×C3×C4—33no—
151C22×C3×C4—31no—
152C22×C3×C4—612no—
153C22×C3×C4—612no—
154C22×C3×C4—632no—
155C22×C3×C4—66no—
156C2×#67—312no—
157C2×#67—312no—
158C2×#67—612no—
159C2×#67—66no—
160C2×#67—66no—
161C2×#67—66no—
162C2×#67—66no—
163C2×#67—126no—
164C2×#67—126no—
165C22×Dic3—232no—
166C22×Dic3—26no—
167C22×Dic3—212no—
168C22×Dic3—212no—
169C22×Dic3—33no—
170C22×Dic3—33no—
171C22×Dic3—63no—
172C22×Dic3#67112yescomplemented
173C22×Dic3C22×D313yes—
174C22×Dic3C22×D311yescharacteristic
175C22×Dic3C22×D313yes—
176C22×Dic3C22×D311yescharacteristic
177C2×C4×D3—66no—
178C2×C4×D3—66no—
179C3×C22⋊C4—66no—
180C3×C22⋊C4—66no—
181#217—26no—
182#217—26no—
183#217—312no—
184#217—312no—
185#217—612no—
186(C2×D3)⋊C4—66no—
187(C2×D3)⋊C4—66no—
188Dic3⋊C4—66no—
189Dic3⋊C4—66no—
190C4×Dic3—66no—
191C4×Dic3—66no—
192C22×C32—232no—
193C22×C32—212no—
194C22×C32—26no—
195C22×C32—26no—
196C22×C32—212no—
197C22×C32C4×D4112yescomplemented
198C22×C32C23×C411yescharacteristic
199C22×C32C22×D413yes—
200C22×C32C2×#4113yes—
201C2×C3⋊D3—26no—
202C2×C3⋊D3—41no—
203C2×C3⋊D3—43no—
204C3⋊Dic3—26no—
205C3×Dic3—26no—
206C3×Dic3—41no—
207C3×Dic3—43no—
208C3×Dic3#12014yescomplemented
209C25D3211yescharacteristic
210C22×D4—93no—
211C23×C4—33no—
212C23×C4—33no—
213C23×C4—612no—
214C23×C4—91no—
215#120—98no—
216C4×D4—1812no—
217C2×C4⋊C4—93no—
218C2×C22⋊C4—33no—
219C2×C22⋊C4—33no—
220C2×C22⋊C4—93no—
221C2×C22⋊C4—93no—
222C2×C42—93no—
223#95—96no—
224C23×C3—28no—
225C23×C3—28no—
226C23×C3—224no—
227C23×C3—224no—
228C23×C3—224no—
229C23×C3—224no—
230C23×C3—26no—
231C23×C3—26no—
232C23×C3—26no—
233C23×C3—26no—
234C23×C3—21no—
235C23×C3—26no—
236C23×C3—26no—
237C23×C3—26no—
238C23×C3—46no—
239C23×C3—46no—
240C23×C3—424no—
241C23×C3—48no—
242C23×C3—424no—
243C23×C3C2×C4×D316yes—
244C23×C3C2×C4×D316yes—
245C23×C3#23516yes—
246C23×C3D3×D416yes—
247C23×C3#23716yes—
248C23×C3C2×#6716yes—
249C23×C3C23×D311yescharacteristic
250C23×C3C23×D311yescharacteristic
251C22×D3—32no—
252C22×D3—32no—
253C22×D3—62no—
254C22×D3—63no—
255C22×D3—63no—
256C22×D3—63no—
257C22×D3—63no—
258C22×D3—123no—
259C22×D3—123no—
260C2×C3×C4—36no—
261C2×C3×C4—36no—
262C2×C3×C4—624no—
263C2×C3×C4—624no—
264C2×C3×C4—66no—
265C2×C3×C4—66no—
266C2×C3×C4—63no—
267C2×C3×C4—63no—
268#67—624no—
269#67—624no—
270#67—1224no—
271C2×Dic3—224no—
272C2×Dic3—26no—
273C2×Dic3—224no—
274C2×Dic3—23no—
275C2×Dic3—23no—
276C2×Dic3—26no—
277C2×Dic3—36no—
278C2×Dic3—36no—
279C2×Dic3—66no—
280C2×Dic3—63no—
281C2×Dic3—63no—
282C2×Dic3—63no—
283C2×Dic3—63no—
284C2×Dic3—123no—
285C2×Dic3—123no—
286C2×Dic3C2×#6716yes—
287C2×Dic3C2×#6716yes—
288C4×D3—124no—
289C4×D3—124no—
290C2×C32—212no—
291C2×C32C2×C4×D413yes—
292C2×C32C2×#12011yescharacteristic
293C2×C32#52513yes—
294C3⋊D3—42no—
295C24—26no—
296C24—26no—
297C24—91no—
298C24#62414yescomplemented
299C24C2×D3213yes—
300C2×D4—912no—
301C2×D4—186no—
302C2×D4—186no—
303C22×C4—31no—
304C22×C4—33no—
305C22×C4—312no—
306C22×C4—33no—
307C22×C4—31no—
308C22×C4—612no—
309C22×C4—612no—
310C22×C4—632no—
311C22×C4—66no—
312C22×C4—93no—
313C22×C4—186no—
314C4⋊C4—186no—
315C22⋊C4—66no—
316C22⋊C4—66no—
317C22⋊C4—912no—
318C22⋊C4—186no—
319C42—186no—
320C22×C3—232no—
321C22×C3—232no—
322C22×C3—212no—
323C22×C3—212no—
324C22×C3—212no—
325C22×C3—26no—
326C22×C3—26no—
327C22×C3—26no—
328C22×C3—212no—
329C22×C3—26no—
330C22×C3—23no—
331C22×C3—21no—
332C22×C3—23no—
333C22×C3—212no—
334C22×C3—412no—
335C22×C3—412no—
336C22×C3—46no—
337C22×C3—46no—
338C22×C3—432no—
339C22×C3#67⋊C4112yescomplemented
340C22×C3C4×#67112yescomplemented
341C22×C3C22×C4×D311yescharacteristic
342C22×C3C22×C4×D311yescharacteristic
343C22×C3C2×#23513yes—
344C22×C3C2×D3×D413yes—
345C22×C3C2×#23713yes—
346C22×C3C22×#6713yes—
347C2×D3—66no—
348C2×D3—66no—
349C2×D3—126no—
350C2×D3—123no—
351C2×D3—121no—
352C2×D3—123no—
353C2×D3—121no—
354C2×D3—243no—
355C2×D3—241no—
356C3×C4—34no—
357C3×C4—66no—
358C3×C4—123no—
359C3×C4—121no—
360Dic3—26no—
361Dic3—43no—
362Dic3—41no—
363Dic3—66no—
364Dic3—66no—
365Dic3—126no—
366Dic3#95314yescomplemented
367C32C4×#12011yescharacteristic, complemented, Sylow
368C23—28no—
369C23—224no—
370C23—26no—
371C23—26no—
372C23—224no—
373C23—92no—
374C23—183no—
375C23—183no—
376C23#380416yes—
377C23C2×#62416yes—
378C23D3×#6716yes—
379C23C22×D3211yescharacteristic
380D4—1824no—
381C2×C4—36no—
382C2×C4—36no—
383C2×C4—624no—
384C2×C4—624no—
385C2×C4—66no—
386C2×C4—66no—
387C2×C4—63no—
388C2×C4—63no—
389C2×C4—96no—
390C2×C4—183no—
391C2×C4—183no—
392C2×C4—364no—
393C2×C3—212no—
394C2×C3—212no—
395C2×C3—23no—
396C2×C3—23no—
397C2×C3—21no—
398C2×C3—412no—
399C2×C3C2×#67⋊C413yes—
400C2×C3#558613yes—
401C2×C3D3×#12011yescharacteristic
402C2×C3C2×C4×#6713yes—
403C2×C3#579113yes—
404C2×C3C2×#95311yescharacteristic
405D3—122no—
406D3—122no—
407D3—242no—
408C22—232no—
409C22—212no—
410C22—212no—
411C22—26no—
412C22—26no—
413C22—186no—
414C22—363no—
415C22—361no—
416C22#63952112yescomplemented
417C22C2×#380413yes—
418C22C22×#62411yescharacteristic
419C22C2×D3×#6713yes—
420C4—34no—
421C4—66no—
422C4—123no—
423C4—121no—
424C4—186no—
425C3—21no—
426C3#7381811yescharacteristic, complemented
427C3C4×#95311yescharacteristic, complemented
428C2—212no—
429C2—362no—
430C2C2×#6395213yes—
431C2#1059549813yes—
432C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC25×C32C22
socle, cosocleC23×C32C24
prime radicalC2×#64162C2
hypercenterC25D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C24×C3×Dic3C2semidirect
3. C2×#63952C2semidirect
4. C3×#5247C2semidirect
5. #10591711C2semidirect
6. Dic3×#217C2semidirect
7. #10591693C2semidirect
15. C22×#624C22semidirect
16. #64162C4semidirect
20. C2×#3724C22semidirect
21. C2×#3722C22semidirect
22. C2×Dic32C22semidirect
24. #63579C22semidirect
26. C24×Dic3D3semidirect
33. #5247D3semidirect
42. C24×C32C2×C4semidirect
47. C2×#638C2×C4semidirect
53. C22×C3×Dic3D4semidirect
59. #3757C2×C4semidirect
111. C22×C3⋊D3C22×C4semidirect
115. C2×C3⋊Dic3C22×C4semidirect
140. C24×C3C4×D3semidirect
141. C24×C3C4×D3semidirect
172. C22×Dic3#67semidirect
197. C22×C32C4×D4semidirect
208. C3×Dic3#120semidirect
298. C24#624semidirect
339. C22×C3#67⋊C4semidirect
340. C22×C3C4×#67semidirect
366. Dic3#953semidirect
367. C32C4×#120semidirect
416. C22#63952semidirect
426. C3#73818semidirect
427. C3C4×#953semidirect

Maximal subgroups

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

subgroupindex
C24×C3×Dic32
C2×#641622
C2×#639522
C3×#52472
#105917112
Dic3×#2172
#105916932
C4×#9533
#738183