Finite Group Databasebeta

← #11785929

Subgroups — #11785929

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2C2×#63558C211yesmaximal, characteristic
3C2×#63558C211yesmaximal, characteristic
4#10589399C211yesmaximal, characteristic, complemented
5C3×#4533C211yesmaximal, characteristic, complemented
6#10589170C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#71648—31nomaximal
9#69026—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#893—22no—
18C3×D3×C22⋊C4C414yes—
19C3×C4×D12—22no—
20#63558—22no—
21#63558—22no—
22C3×#518—31no—
23#5521D311yescharacteristic
24C2×#833—31no—
25C2×#833—31no—
26C2×#823—31no—
27C2×#823—31no—
28C3×#344—31no—
29#4559—31no—
30#4556—31no—
31#4533—31no—
32#4533—31no—
33#4533—31no—
34#4533—31no—
35#4533—61no—
36#4533D311yescharacteristic, complemented
37C23×C3×D3C2×C412yes—
38C22×C32×C4C2311yescharacteristic
39C2×C3×D12—21no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12D412yes—
44C2×C3×D12D412yes—
45C2×C3×C4×D3—24no—
46C32×C4⋊C4—21no—
47C32×C22⋊C4C2×C412yes—
48C32×C42—21no—
49#3748—21no—
50#3748—21no—
51#3748—21no—
52#3748—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#217C2×C412yes—
56C3×(C2×D3)⋊C4—24no—
57C3×C4⋊Dic3—21no—
58C3×C4×Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1829—91noSylow
66C22×C3×D4—31no—
67C22×D12C2×D311yescharacteristic
68C2×C3×M16—31no—
69C2×C3×M16—31no—
70C3×C4×D4—62no—
71C3×C4×D4—62no—
72C3×#117—21no—
73C3×#117—31no—
74C3×#117C2×D311yescharacteristic
75C3×#117C2×D311yescharacteristic
76C2×C3×C22⋊C4—34no—
77#926C2×D311yescharacteristic
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86#893—22no—
87D3×C22⋊C4Dic314yes—
88C4×D12—22no—
89#833—62no—
90#833—62no—
91#823—62no—
92#823—62no—
93C23×C32C22×C411yescharacteristic
94C22×C3×D3—22no—
95C22×C3×D3—22no—
96C22×C3×D3—82no—
97C22×C3×D3C22⋊C414yes—
98C2×C32×C4—22no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3×Dic3—22no—
106C3×D12—22no—
107C3×D12—22no—
108C3×D12—22no—
109C3×D12—22no—
110C3×C4×D3—84no—
111C3⋊(C3⋊C8)—41no—
112C3⋊(C3⋊C8)—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#518—31no—
116C2×#100—91no—
117C2×#100—91no—
118#344—31no—
119#344—91no—
120#344—91no—
121#344—91no—
122C24×C3—32no—
123C23×D3C2×Dic312yes—
124C2×C3×D4—32no—
125C2×C3×D4—32no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C22×C3×C4—21no—
131C22×C3×C4—64no—
132C22×C3×C4C22×D311yescharacteristic
133C22×C3×C4C22×D311yescharacteristic
134C2×D12—21no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×D12#6712yes—
139C2×D12#6712yes—
140C2×C4×D3—24no—
141C3×M16—61no—
142C3×M16—61no—
143C3×M16—61no—
144C3×M16—61no—
145C2×C3×C8—61no—
146C2×C3×C8—61no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—41no—
150C3×C4⋊C4—61no—
151C3×C22⋊C4—22no—
152C3×C22⋊C4—32no—
153C3×C22⋊C4—64no—
154C3×C22⋊C4C4×D312yes—
155C3×C22⋊C4C2×Dic312yes—
156C3×C42—21no—
157C3×C42—21no—
158C3×C42—41no—
159C3×C42—61no—
160#217C2×Dic312yes—
161(C2×D3)⋊C4—24no—
162C4⋊Dic3—21no—
163C4×Dic3—21no—
164#208—21no—
165#208—21no—
166#208—21no—
167#208—21no—
168#208—62no—
169#208—61no—
170#208—61no—
171#208—61no—
172#208—61no—
173#208—61no—
174#208—61no—
175#208—61no—
176#208—61no—
177#208—121no—
178#208—121no—
179#208—121no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—62no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—121no—
188C22×C32—41no—
189C22×C32C2×C22⋊C411yescharacteristic
190C22×C32#11711yescharacteristic
191C22×C32#11711yescharacteristic
192C2×C3×D3—24no—
193C2×C3×D3—44no—
194C2×C3×D3—82no—
195C2×C3×D3—82no—
196C32×C4—42no—
197C32×C4#12311yescharacteristic
198C32×C4#12311yescharacteristic
199C32×C4#12311yescharacteristic
200C32×C4#12311yescharacteristic
201C3×Dic3—42no—
202C22×D4—31no—
203C2×M16—31no—
204C2×M16—31no—
205C2×M16—91no—
206C2×M16—91no—
207C4×D4—62no—
208C4×D4—62no—
209#117—31no—
210#117D3211yescharacteristic
211C2×C22⋊C4—34no—
212#100—182no—
213#100—182no—
214C23×C3—21no—
215C23×C3—34no—
216C23×C3—62no—
217C23×C3—62no—
218C23×C3—242no—
219C23×C3C2×C4×D311yescharacteristic
220C23×C3C22×Dic311yescharacteristic
221C22×D3—22no—
222C22×D3—22no—
223C22×D3—82no—
224C22×D3#21714yes—
225C3×D4—62no—
226C3×D4—62no—
227C3×D4—62no—
228C3×D4—62no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—62no—
239C2×C3×C4—244no—
240C2×C3×C4#23511yescharacteristic
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×C4#23911yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×Dic3—22no—
253D12—22no—
254D12—22no—
255D12—22no—
256D12—22no—
257C4×D3—84no—
258C3×C8—121no—
259C3×C8—121no—
260C3⋊C8—41no—
261C3⋊C8—41no—
262C3⋊C8—122no—
263C3⋊C8—122no—
264C3⋊C8—121no—
265C3⋊C8—121no—
266C3⋊C8—121no—
267C3⋊C8—121no—
268C2×C32—21no—
269C2×C32—21no—
270C2×C32—21no—
271C2×C32#38111yescharacteristic
272C3×D3—44no—
273C24—32no—
274C2×D4—32no—
275C2×D4—32no—
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—61no—
279C2×D4—61no—
280C22×C4—64no—
281C22×C4C2×D3211yescharacteristic
282M16—61no—
283M16—61no—
284M16—61no—
285M16—61no—
286M16—181no—
287M16—181no—
288M16—181no—
289M16—181no—
290C2×C8—61no—
291C2×C8—61no—
292C2×C8—181no—
293C2×C8—181no—
294C4⋊C4—21no—
295C4⋊C4—61no—
296C22⋊C4—32no—
297C22⋊C4—64no—
298C22⋊C4D3×Dic312yes—
299C42—21no—
300C42—61no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—64no—
307C22×C3—81no—
308C22×C3—124no—
309C22×C3—242no—
310C22×C3—242no—
311C22×C3#87211yescharacteristic
312C22×C3D3×C22⋊C411yescharacteristic
313C22×C3#89211yescharacteristic
314C22×C3#92611yescharacteristic
315C22×C3#92611yescharacteristic
316C22×C3C2×#21711yescharacteristic
317C2×D3—24no—
318C2×D3—44no—
319C2×D3—82no—
320C2×D3—82no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—42no—
326C3×C4—42no—
327C3×C4—82no—
328C3×C4—122no—
329C3×C4#88311yescharacteristic
330C3×C4#88311yescharacteristic
331C3×C4#89411yescharacteristic
332C3×C4#89411yescharacteristic
333C3×C4#92911yescharacteristic
334C3×C4#92911yescharacteristic
335C3×C4#92911yescharacteristic
336C3×C4#92911yescharacteristic
337Dic3—42no—
338C32#182911yescharacteristic, complemented, Sylow
339C23—34no—
340C23—62no—
341C23—62no—
342C23—242no—
343C23C2×D3×Dic311yescharacteristic
344D4—62no—
345D4—62no—
346D4—62no—
347D4—62no—
348C2×C4—22no—
349C2×C4—62no—
350C2×C4—244no—
351C2×C4#379511yescharacteristic
352C2×C4#379811yescharacteristic
353C2×C4#379811yescharacteristic
354C2×C4#379911yescharacteristic
355C2×C4D3×#6711yescharacteristic
356C2×C4D3×#6711yescharacteristic
357C8—121no—
358C8—121no—
359C8—361no—
360C8—361no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—41no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—124no—
372C2×C3#466411yescharacteristic
373C2×C3#521111yescharacteristic
374D3—44no—
375C22—41no—
376C22—64no—
377C22—124no—
378C22—242no—
379C22—242no—
380C22#6384111yescharacteristic
381C22#6385511yescharacteristic
382C22D3×#21711yescharacteristic
383C4—42no—
384C4—122no—
385C4#6385011yescharacteristic
386C4#6385011yescharacteristic
387C4#6390511yescharacteristic
388C4#6390511yescharacteristic
389C3—21no—
390C3#6902611yescharacteristic, complemented
391C3#7164811yescharacteristic, complemented
392C2—21no—
393C2—21no—
394C2—21no—
395C2—124no—
396C2#1059129411yescharacteristic
subgroupG/H
centerC2#10591294
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#381
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1829
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10589399C2semidirect
5. C3×#4533C2semidirect
6. #10589170C2semidirect
7. #10589169C2semidirect
36. #4533D3semidirect
338. C32#1829semidirect
390. C3#69026semidirect
391. C3#71648semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
C2×#635582
#105893992
C3×#45332
#105891702
#105891692
#716483
#690263