Finite Group Databasebeta

← #11785926

Subgroups — #11785926

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
1#10594982C211yesmaximal, characteristic
2C2×C3×#823C211yesmaximal, characteristic
3C2×#63558C211yesmaximal, characteristic
4#10589425C211yesmaximal, characteristic, complemented
5C3×#4556C211yesmaximal, characteristic, complemented
6#10589171C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#70067—31nomaximal
9#69026—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17D3×#217C414yes—
18#63898—22no—
19Dic3×D12—22no—
20C3×#823—22no—
21#63558—22no—
22#5798—31no—
23#5521—31no—
24C2×C3×#100—31no—
25C2×#833—31no—
26C2×#823—31no—
27C2×#823D311yescharacteristic
28C3×#344—31no—
29#4559—31no—
30#4559—31no—
31#4559—31no—
32#4559—61no—
33#4556—31no—
34#4556—31no—
35#4556D311yescharacteristic, complemented
36#4533—31no—
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×D3×Dic3—24no—
46C32×M16—21no—
47C32×M16—21no—
48C2×C32×C8—21no—
49#3757C2×C412yes—
50C4⋊(C3⋊Dic3)—21no—
51C4×C3⋊Dic3—21no—
52#3748—21no—
53#3748—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#217C2×C412yes—
56C3×C4⋊Dic3—21no—
57C3×C4×Dic3—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64(C2×D3)⋊Dic3—24no—
65#1829—91noSylow
66C22×C3×D4—31no—
67C22×D12C2×D311yescharacteristic
68C2×C3×M16—21no—
69C2×C3×M16—31no—
70C2×C3×M16—31no—
71C2×C3×M16C2×D311yescharacteristic
72C2×C3×M16C2×D311yescharacteristic
73C3×#117—31no—
74C2×#217—34no—
75D4×Dic3—62no—
76D4×Dic3—62no—
77#926—31no—
78#926—31no—
79#926—61no—
80#926C2×D311yescharacteristic
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86#893—62no—
87D3×C22⋊C4—34no—
88C4×D12—62no—
89C3×#100—62no—
90#833—62no—
91#823—22no—
92#823—62no—
93C23×C32C22×C411yescharacteristic
94C22×C3×D3—22no—
95C22×C3×D3—22no—
96C22×C3×D3—82no—
97C22×C3×D3C22⋊C414yes—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3⋊Dic3—22no—
105C2×C3×Dic3—22no—
106C3×D12—22no—
107C3×D12—22no—
108C3×D12—22no—
109C3×D12—22no—
110D3×Dic3—84no—
111C32×C8—41no—
112C3⋊(C3⋊C8)—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#518—91no—
116C2×#100—31no—
117C2×#100—91no—
118#344—31no—
119#344—91no—
120#344—91no—
121#344—91no—
122C24×C3—32no—
123C23×D3C4×D312yes—
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×C4C22×D311yescharacteristic
132C22×C3×C4C22×D311yescharacteristic
133C22×Dic3—64no—
134C2×D12—21no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×D12D1212yes—
139C2×D12#6712yes—
140C2×C4×D3—64no—
141C3×M16—22no—
142C3×M16—21no—
143C3×M16—21no—
144C3×M16—21no—
145C3×M16—21no—
146C3×M16—41no—
147C3×M16—61no—
148C3×M16—61no—
149C3×M16—61no—
150C3×M16—61no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—41no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C3×C4⋊C4—61no—
157C3×C22⋊C4—32no—
158C3×C42—61no—
159#217—32no—
160#217—32no—
161#217—62no—
162#217—64no—
163#217C4×D312yes—
164(C2×D3)⋊C4—64no—
165C4⋊Dic3—21no—
166C4⋊Dic3—61no—
167C4⋊Dic3—61no—
168C4⋊Dic3—121no—
169C4×Dic3—21no—
170C4×Dic3—61no—
171C4×Dic3—61no—
172C4×Dic3—121no—
173#208—21no—
174#208—21no—
175#208—21no—
176#208—21no—
177#208—61no—
178#208—61no—
179#208—61no—
180#208—61no—
181#208—121no—
182#208—121no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
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#12311yescharacteristic
197C32×C4#12311yescharacteristic
198C32×C4#12311yescharacteristic
199C32×C4#12311yescharacteristic
200C3⋊Dic3—42no—
201C3×Dic3—42no—
202C22×D4—31no—
203C2×M16—31no—
204C2×M16—31no—
205C2×M16—91no—
206C2×M16D3211yescharacteristic
207C4×D4—182no—
208C4×D4—182no—
209#117—31no—
210#117—91no—
211C2×C22⋊C4—94no—
212#100—62no—
213#100—182no—
214C23×C3—21no—
215C23×C3—34no—
216C23×C3—62no—
217C23×C3—62no—
218C23×C3—242no—
219C23×C3C2×C4×D311yescharacteristic
220C23×C3C2×C4×D311yescharacteristic
221C22×D3—22no—
222C22×D3—22no—
223C22×D3—82no—
224C22×D3(C2×D3)⋊C414yes—
225C3×D4—62no—
226C3×D4—62no—
227C3×D4—62no—
228C3×D4—62no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—62no—
236C2×C3×C4C2×D1211yescharacteristic
237C2×C3×C4#23511yescharacteristic
238C2×C3×C4#23511yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4#23711yescharacteristic
242C2×C3×C4#23711yescharacteristic
243C2×C3×C4#23711yescharacteristic
244C2×C3×C4#23711yescharacteristic
245C2×C3×C4#23711yescharacteristic
246C2×C3×C4#23911yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×Dic3—22no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—122no—
252C2×Dic3—244no—
253D12—22no—
254D12—22no—
255D12—22no—
256D12—22no—
257C4×D3—244no—
258C3×C8—42no—
259C3×C8—41no—
260C3×C8—41no—
261C3×C8—121no—
262C3×C8—121no—
263C3⋊C8—41no—
264C3⋊C8—41no—
265C3⋊C8—122no—
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—184no—
281C22×C4C2×D3211yescharacteristic
282M16—21no—
283M16—21no—
284M16—61no—
285M16—61no—
286M16—61no—
287M16—61no—
288M16—181no—
289M16—181no—
290C2×C8—21no—
291C2×C8—61no—
292C2×C8—61no—
293C2×C8—181no—
294C4⋊C4—61no—
295C4⋊C4—181no—
296C22⋊C4—32no—
297C22⋊C4—92no—
298C22⋊C4—184no—
299C42—61no—
300C42—181no—
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×C3#87711yescharacteristic
313C22×C3#87711yescharacteristic
314C22×C3D3×C22⋊C411yescharacteristic
315C22×C3#89211yescharacteristic
316C22×C3C2×(C2×D3)⋊C411yescharacteristic
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—122no—
326C3×C4#88311yescharacteristic
327C3×C4#88311yescharacteristic
328C3×C4#88611yescharacteristic
329C3×C4#88611yescharacteristic
330C3×C4#89411yescharacteristic
331C3×C4#89411yescharacteristic
332C3×C4#93511yescharacteristic
333C3×C4#93511yescharacteristic
334Dic3—42no—
335Dic3—122no—
336Dic3—122no—
337Dic3—242no—
338C32#182911yescharacteristic, complemented, Sylow
339C23—34no—
340C23—62no—
341C23—62no—
342C23—242no—
343C23C4×D3211yescharacteristic
344D4—62no—
345D4—62no—
346D4—62no—
347D4—62no—
348C2×C4—62no—
349C2×C4—182no—
350C2×C4—724no—
351C2×C4#379511yescharacteristic
352C2×C4#379611yescharacteristic
353C2×C4D3×D1211yescharacteristic
354C2×C4#380411yescharacteristic
355C2×C4#380511yescharacteristic
356C2×C4D3×#6711yescharacteristic
357C8—41no—
358C8—121no—
359C8—121no—
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#494311yescharacteristic
374D3—44no—
375C22—41no—
376C22—64no—
377C22—124no—
378C22—242no—
379C22—242no—
380C22#6387711yescharacteristic
381C22#6387811yescharacteristic
382C22D3×(C2×D3)⋊C411yescharacteristic
383C4—122no—
384C4—362no—
385C4#6388411yescharacteristic
386C4#6389011yescharacteristic
387C4#6389111yescharacteristic
388C4#6396911yescharacteristic
389C3—21no—
390C3#6902611yescharacteristic, complemented
391C3#7006711yescharacteristic, complemented
392C2—21no—
393C2—21no—
394C2—21no—
395C2—124no—
396C2#1059136211yescharacteristic
subgroupG/H
centerC2#10591362
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#381
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1829
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10589425C2semidirect
5. C3×#4556C2semidirect
6. #10589171C2semidirect
7. #10589169C2semidirect
35. #4556D3semidirect
338. C32#1829semidirect
390. C3#69026semidirect
391. C3#70067semidirect

Maximal subgroups

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

subgroupindex
#105949822
C2×C3×#8232
C2×#635582
#105894252
C3×#45562
#105891712
#105891692
#700673
#690263