Finite Group Databasebeta

← #11789952

Subgroups — #11789952

Order 1152.

505 conjugacy classes of subgroups.

The subgroup lattice has 401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5113C211yesmaximal, characteristic
2C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
3#10591116C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic
5#10591070C211yesmaximal, characteristic
6#10589418C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70287—31nomaximal
9#69793—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#821C412yescomplemented
18C3×#816C412yescomplemented
19C3×C8×Dic3—22no—
20Dic3⋊(C3⋊C8)—22no—
21#63569—22no—
22(C2×D3)⋊(C3⋊C8)—22no—
23C3×#416—31no—
24C2×C3×C4×C8—31no—
25C2×#837—31no—
26#5234—31no—
27#5113D311yescharacteristic
28#5110—31no—
29#5102—31no—
30C2×C8×Dic3D311yescharacteristic, complemented
31#4999—31no—
32C2×#805—31no—
33#4552—31no—
34#4552—31no—
35#4552—61no—
36#4532—31no—
37#4523—31no—
38C22×C32×C4C2311yescharacteristic
39C2×C3×#67—21no—
40C22×C3×Dic3—21no—
41C3×#235—21no—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6C2×C411yescharacteristic
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8C2×C412yes—
51#3748—21no—
52#3748—21no—
53#3748—21no—
54#3748—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217—21no—
58C3×C4⋊Dic3C2×C412yes—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3D412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65#1937—91noSylow
66C2×C3×#41—31no—
67C2×#235C2×D311yescharacteristic
68C22×C3×C8—21no—
69C22×C3×C8—31no—
70C22×C3×C8C2×D311yescharacteristic
71C22×C3×C8C2×D311yescharacteristic
72C3×#117—31no—
73C2×C3×C42—31no—
74#926C2×D311yescharacteristic
75C2×C4×Dic3C2×D311yescharacteristic
76C2×#208—31no—
77C2×#208—31no—
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—61no—
81C2×#208—61no—
82C22×C3⋊C8C2×D311yescharacteristic
83C3×#103—32no—
84C3×#102—32no—
85C3×C4×C8—62no—
86#837—62no—
87#830—62no—
88#821Dic312yescomplemented
89(C2×D3)⋊C8—62no—
90#816Dic312yescomplemented
91Dic3⋊C8—62no—
92C8×Dic3—22no—
93#805—62no—
94C4⋊(C3⋊C8)—62no—
95C23×C32#4111yescharacteristic
96C22×C3×D3—21no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C3×#67—41no—
104C3×#67—41no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—21no—
109C3×D12—21no—
110C3×D12—21no—
111C3×C4×D3—41no—
112C3×C4×D3—41no—
113C3×Dic6—21no—
114C3×Dic6—21no—
115C32×C8—22no—
116C3⋊(C3⋊C8)—41no—
117C3⋊(C3⋊C8)—41no—
118C3×C3⋊C8—22no—
119#424—91no—
120C2×#104—91no—
121#416—31no—
122#408—91no—
123C2×C4×C8—31no—
124#341—91no—
125#339—91no—
126C3×#41—61no—
127C3×#41—61no—
128C3×#41—61no—
129C3×#41—61no—
130C2×C3×Q8—31no—
131C2×C3×D4—31no—
132C2×C3×D4—61no—
133C22×C3×C4—21no—
134C22×C3×C4—61no—
135C22×C3×C4—61no—
136C22×C3×C4C22×D311yescharacteristic
137C22×C3×C4C22×D311yescharacteristic
138C2×#67—21no—
139C22×Dic3—21no—
140#235—21no—
141#235—21no—
142#235—21no—
143#235—21no—
144C2×D12C2×Dic311yescharacteristic
145C2×C4×D3—21no—
146C2×Dic6C2×Dic311yescharacteristic
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—22no—
152C2×C3×C8—32no—
153C2×C3×C8—41no—
154C2×C3×C8—41no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C2×C3×C8C4×D312yes—
158C2×C3×C8C2×Dic312yes—
159C3×C4⋊C4—32no—
160C3×C22⋊C4—61no—
161C3×C42—32no—
162C3×C42—61no—
163C3×C42—61no—
164#217—21no—
165C4⋊Dic3C2×Dic312yes—
166C4×Dic3—21no—
167C4×Dic3—21no—
168C4×Dic3#6712yes—
169#208—62no—
170#208—62no—
171#208—61no—
172#208—61no—
173#208—61no—
174#208—61no—
175#208—61no—
176#208—61no—
177#208—61no—
178#208—61no—
179#208—121no—
180#208—121no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—121no—
188C2×C3⋊C8—121no—
189C2×C3⋊C8D1212yes—
190C22×C32—22no—
191C22×C32C4×D411yescharacteristic
192C22×C32#12311yescharacteristic
193C22×C32#12611yescharacteristic
194C2×C3×D3—41no—
195C2×C3×D3—42no—
196C32×C4#11711yescharacteristic
197C32×C4C4×D411yescharacteristic
198C32×C4#12111yescharacteristic
199C32×C4#12411yescharacteristic
200C3×Dic3—24no—
201C3×Dic3—41no—
202C3×Dic3—42no—
203C2×#41—31no—
204C2×M16—91no—
205C2×M16—91no—
206C22×C8—31no—
207C22×C8D3211yescharacteristic
208#117—31no—
209C2×C42—31no—
210C4⋊C8—182no—
211#104—182no—
212#103—32no—
213#102—32no—
214C22⋊C8—182no—
215C4×C8—62no—
216C23×C3—21no—
217C23×C3—61no—
218C23×C3#23511yescharacteristic
219C23×C3#23711yescharacteristic
220C22×D3—21no—
221C3×Q8—61no—
222C3×Q8—61no—
223C3×D4—61no—
224C3×D4—61no—
225C3×D4—121no—
226C3×D4—121no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—64no—
234C2×C3×C4—62no—
235C2×C3×C4—62no—
236C2×C3×C4—61no—
237C2×C3×C4—121no—
238C2×C3×C4—121no—
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4C2×D1211yescharacteristic
241C2×C3×C4#23511yescharacteristic
242C2×C3×C4#23511yescharacteristic
243C2×C3×C4#23511yescharacteristic
244C2×C3×C4#23511yescharacteristic
245C2×C3×C4#23511yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4#23711yescharacteristic
249C2×C3×C4C22×Dic311yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251#67—41no—
252#67—41no—
253C2×Dic3—24no—
254C2×Dic3—22no—
255C2×Dic3—22no—
256C2×Dic3—21no—
257D12—21no—
258D12—21no—
259C4×D3—41no—
260C4×D3—41no—
261Dic6—21no—
262Dic6—21no—
263C3×C8—22no—
264C3×C8—22no—
265C3×C8—42no—
266C3×C8—62no—
267C3⋊C8—22no—
268C3⋊C8—122no—
269C3⋊C8—122no—
270C3⋊C8—121no—
271C3⋊C8—121no—
272C3⋊C8—121no—
273C3⋊C8—121no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32#38811yescharacteristic
277C2×C32#44312yes—
278C3×D3—81no—
279#41—61no—
280#41—61no—
281#41—61no—
282#41—61no—
283C2×Q8—31no—
284C2×D4—31no—
285C2×D4—61no—
286C22×C4—61no—
287C22×C4—61no—
288C22×C4C2×D3211yescharacteristic
289M16—181no—
290M16—181no—
291M16—181no—
292M16—181no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—32no—
296C2×C8—61no—
297C2×C8—61no—
298C2×C8—181no—
299C2×C8—181no—
300C2×C8D3×Dic312yes—
301C4⋊C4—32no—
302C22⋊C4—61no—
303C42—32no—
304C42—61no—
305C42—61no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—42no—
312C22×C3—121no—
313C22×C3—122no—
314C22×C3C4×D1211yescharacteristic
315C22×C3#87611yescharacteristic
316C22×C3#87911yescharacteristic
317C22×C3#88311yescharacteristic
318C22×C3#92911yescharacteristic
319C22×C3D4×Dic311yescharacteristic
320C2×D3—42no—
321C2×D3—41no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—64no—
327C3×C4—121no—
328C3×C4—122no—
329C3×C4#87211yescharacteristic
330C3×C4#87511yescharacteristic
331C3×C4#88411yescharacteristic
332C3×C4#88511yescharacteristic
333C3×C4#92611yescharacteristic
334C3×C4C4×#6711yescharacteristic
335C3×C4#93011yescharacteristic
336C3×C4D4×Dic311yescharacteristic
337Dic3—24no—
338Dic3—42no—
339Dic3—41no—
340C32#193711yescharacteristic, complemented, Sylow
341C23—61no—
342C23#379511yescharacteristic
343Q8—61no—
344Q8—61no—
345D4—61no—
346D4—61no—
347D4—121no—
348D4—121no—
349C2×C4—64no—
350C2×C4—62no—
351C2×C4—62no—
352C2×C4—61no—
353C2×C4—121no—
354C2×C4—121no—
355C2×C4#379811yescharacteristic
356C2×C4#379811yescharacteristic
357C2×C4D3×D1211yescharacteristic
358C2×C4C2×D3×Dic311yescharacteristic
359C2×C4#380411yescharacteristic
360C2×C4D3×#6711yescharacteristic
361C8—22no—
362C8—62no—
363C8—361no—
364C8—361no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—22no—
371C2×C3—41no—
372C2×C3—41no—
373C2×C3—241no—
374C2×C3#470012yes—
375C2×C3#494011yescharacteristic
376C2×C3#495111yescharacteristic
377C2×C3#519612yes—
378D3—81no—
379C22—22no—
380C22—121no—
381C22—122no—
382C22#6385911yescharacteristic
383C22Dic3×D1211yescharacteristic
384C22#6390511yescharacteristic
385C4—64no—
386C4—121no—
387C4—122no—
388C4#6385211yescharacteristic
389C4#6385511yescharacteristic
390C4#6390611yescharacteristic
391C4Dic3×#6711yescharacteristic
392C3—21no—
393C3#6979311yescharacteristic, complemented
394C3#7028711yescharacteristic, complemented
395C2—21no—
396C2—21no—
397C2—241no—
398C2#1059091512yes—
399C2#1059130511yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1937
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×C8×Dic3C2semidirect
3. #10591116C2semidirect
6. #10589418C2semidirect
7. #10589161C2semidirect
17. C3×#821C4semidirect
18. C3×#816C4semidirect
30. C2×C8×Dic3D3semidirect
88. #821Dic3semidirect
90. #816Dic3semidirect
340. C32#1937semidirect
393. C3#69793semidirect
394. C3#70287semidirect

Maximal subgroups

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

subgroupindex
C3×#51132
C2×C3×C8×Dic32
#105911162
C2×#635692
#105910702
#105894182
#105891612
#702873
#697933