Finite Group Databasebeta

← #11860584

Subgroups — #11860584

Order 1152.

1410 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic
2#10595994C211yesmaximal, characteristic
3#10595987C211yesmaximal, characteristic, complemented
4C32×#405C211yesmaximal, characteristic, complemented
5#10592820C211yesmaximal, characteristic, complemented
6#10592812C211yesmaximal, characteristic
7C2×#63643C211yesmaximal, characteristic, complemented
8#10592415C212yesmaximal, complemented
9#10592409C212yesmaximal, complemented
10C4×#3746C212yesmaximal, complemented
11C4×#3744C212yesmaximal, complemented
12#78571—34nomaximal
13C2×#3828C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17C32×#117C2211yescharacteristic
18#64135C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20#64118C418yescomplemented
21C2×#3746C2212yes—
22C2×#3744C2212yes—
23#64101—21no—
24C4⋊C4×C3⋊D3—21no—
25#64096—21no—
26#64096—21no—
27#64090—22no—
28#64086—22no—
29C4×C4⋊(C3⋊D3)C2212yes—
30C4×#634C2212yes—
31C4×#634C2212yes—
32C4×#634C2212yes—
33C32×#97C2212yes—
34C32×C4×C8C2212yes—
35#63648C2211yescharacteristic
36#63648C2211yescharacteristic
37#63645C2212yes—
38#63644C2212yes—
39#63643C2212yes—
40#63643C2212yes—
41#63643C2211yescharacteristic
42#63643C2211yescharacteristic
43C2×#909—34no—
44#5523—34no—
45#5516—34no—
46C3×#405D314yescomplemented
47#5121—34no—
48#5113—34no—
49C2×#816—34no—
50#4716—38no—
51#4710—38no—
52C4×Dic12—38no—
53C4×#204—38no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—21no—
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3—21no—
58#3828—22no—
59#3828C2×C414yes—
60C2×C4⋊(C3⋊D3)C2311yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3—22no—
63C2×#634—21no—
64C2×#634—22no—
65C2×#634C2×C414yescomplemented
66C2×#634C2312yes—
67C2×#634C2311yescharacteristic
68C32×M16C2×C414yescomplemented
69C2×C32×C8—22no—
70C2×C32×C8C2311yescharacteristic
71C2×C32×C8C2311yescharacteristic
72C2×C32×C8C2312yes—
73C32×C4⋊C4D411yescharacteristic
74C32×C4⋊C4D411yescharacteristic
75C32×C22⋊C4D412yes—
76C32×C42C2312yes—
77#3757—21no—
78#3752—22no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2312yes—
83#3750—22no—
84#3750—22no—
85#3750—22no—
86C4×C3⋊Dic3—22no—
87C4×C3⋊Dic3—22no—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3—21no—
90#3746C2×C418yescomplemented
91#3744C2×C418yescomplemented
92#2947—91noSylow
93C2×#235—34no—
94C22×Dic6—34no—
95C2×C3×M16C2×D314yes—
96C22×C3×C8C2×D314yes—
97C3×#117C2×D314yes—
98#926—34no—
99C2×C4⋊Dic3—34no—
100#909—332no—
101C2×Dic12—38no—
102C2×#204—38no—
103#892—64no—
104D3×C4⋊C4—64no—
105#887—64no—
106#887—64no—
107#67⋊C4—68no—
108#877—68no—
109C4×D12—38no—
110C4×Dic6—38no—
111C4×Dic6—38no—
112C4×Dic6—38no—
113C3×#97C2×D318yes—
114C3×C4×C8C2×D318yes—
115#821—34no—
116#821—34no—
117#818—38no—
118#817—38no—
119#816—38no—
120#816—34no—
121#816—38no—
122#816—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—21no—
125C2×C32×C4C22×C412yes—
126C2×C32×C4C2×D412yes—
127C2×C32×C4C2×D412yes—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4112yes—
130C2×C32×C4C2411yescharacteristic
131#638—24no—
132C2×C3⋊Dic3—24no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—81no—
139C4⋊(C3⋊D3)—21no—
140C4⋊(C3⋊D3)C22×C412yes—
141C4×C3⋊D3—24no—
142C4×C3⋊D3—82no—
143#634—24no—
144#634—22no—
145#634—21no—
146#634C22×C414yes—
147#634C22×C412yes—
148C32×C8—21no—
149C32×C8—21no—
150C32×C8C22×C414yes—
151C2×#137—91no—
152#520—91no—
153#519—91no—
154#441—92no—
155#440—92no—
156C4×Q16—92no—
157C4×SD16—92no—
158#428—91no—
159#416—91no—
160C2×#103—91no—
161#405C3⋊D311yescharacteristic, complemented
162C22×C3×C4C22×D314yes—
163C2×#67—64no—
164C22×Dic3—64no—
165C22×Dic3—64no—
166#235—316no—
167#235—68no—
168C2×D12—34no—
169C2×C4×D3—64no—
170C2×C4×D3—68no—
171C2×Dic6—316no—
172C2×Dic6—38no—
173C2×Dic6—34no—
174C2×Dic6—64no—
175C2×Dic6—68no—
176C3×M16C4×D3116yescomplemented
177C2×C3×C8—28no—
178C2×C3×C8C22×D314yes—
179C2×C3×C8C22×D314yes—
180C2×C3×C8C22×D318yes—
181C3×C4⋊C4D1214yes—
182C3×C4⋊C4D1214yes—
183C3×C22⋊C4D1218yes—
184C3×C42C22×D318yes—
185#217—64no—
186(C2×D3)⋊C4—68no—
187C4⋊Dic3—38no—
188C4⋊Dic3—34no—
189C4⋊Dic3—34no—
190C4⋊Dic3—64no—
191Dic3⋊C4—68no—
192Dic3⋊C4—68no—
193Dic3⋊C4—68no—
194C4×Dic3—68no—
195C4×Dic3—68no—
196C4×Dic3—68no—
197C4×Dic3—64no—
198Dic12—332no—
199#204—332no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32C4×D412yes—
203C22×C32C22×D411yescharacteristic
204C2×C3⋊D3—22no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C32×C4—22no—
208C32×C4—22no—
209C32×C4C4×D412yes—
210C32×C4C23×C411yescharacteristic
211C32×C4C2×#4111yescharacteristic
212C3⋊Dic3—24no—
213C3⋊Dic3—22no—
214C3⋊Dic3—42no—
215C3⋊Dic3—41no—
216C3⋊Dic3—41no—
217C2×#41—91no—
218C22×Q8—91no—
219#137—98no—
220C2×Q16—92no—
221C2×SD16—92no—
222C2×M16C2×C3⋊D311yescharacteristic
223C22×C8C2×C3⋊D311yescharacteristic
224C4×Q8—92no—
225C4×Q8—92no—
226C4×Q8—92no—
227C4×Q8—181no—
228C4×Q8—181no—
229C4×D4—92no—
230C4×D4—182no—
231#117—91no—
232#117—181no—
233#117—182no—
234#117C2×C3⋊D311yescharacteristic
235C2×C4⋊C4—91no—
236C2×C4⋊C4—181no—
237#107—92no—
238#106—92no—
239#103—92no—
240#103—92no—
241#103—91no—
242#103—91no—
243#102—91no—
244#102—91no—
245#97C2×C3⋊D312yes—
246C4×C8C2×C3⋊D312yes—
247C23×C3C2×D1214yes—
248C22×D3—64no—
249C2×C3×C4C2×C4×D318yes—
250C2×C3×C4C2×D1218yes—
251C2×C3×C4C2×D1218yes—
252C2×C3×C4C2×D1214yes—
253C2×C3×C4#23518yes—
254C2×C3×C4C23×D314yes—
255#67—616no—
256C2×Dic3—616no—
257C2×Dic3—68no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—68no—
262C2×Dic3—244no—
263D12—38no—
264D12—64no—
265C4×D3—616no—
266C4×D3—248no—
267Dic6—316no—
268Dic6—38no—
269Dic6—616no—
270Dic6—68no—
271Dic6—64no—
272C3×C8—24no—
273C3×C8—24no—
274C3×C8C2×C4×D3116yes—
275C2×C32—22no—
276C2×C32C2×C4×D411yescharacteristic
277C2×C32#57711yescharacteristic
278C2×C32#57811yescharacteristic
279C3⋊D3—42no—
280#41—94no—
281#41—182no—
282C2×Q8—92no—
283C2×Q8—91no—
284C2×Q8—94no—
285C2×Q8—181no—
286C2×Q8—182no—
287C2×D4—91no—
288C2×D4—181no—
289C22×C4—181no—
290C22×C4—181no—
291C22×C4—181no—
292C22×C4—182no—
293C22×C4C22×C3⋊D311yescharacteristic
294Q16—98no—
295SD16—98no—
296M16C4×C3⋊D314yescomplemented
297C2×C8—22no—
298C2×C8C22×C3⋊D311yescharacteristic
299C2×C8C22×C3⋊D311yescharacteristic
300C2×C8C22×C3⋊D312yes—
301C4⋊C4—91no—
302C4⋊C4—91no—
303C4⋊C4—92no—
304C4⋊C4—181no—
305C4⋊C4—182no—
306C4⋊C4—182no—
307C4⋊C4—182no—
308C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
309C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
310C22⋊C4—181no—
311C22⋊C4—182no—
312C22⋊C4C4⋊(C3⋊D3)12yes—
313C42—181no—
314C42—182no—
315C42—182no—
316C42—182no—
317C42C22×C3⋊D312yes—
318C22×C3—24no—
319C22×C3—24no—
320C22×C3C4×D1218yes—
321C22×C3C22×D1214yes—
322C2×D3—68no—
323C2×D3—124no—
324C2×D3—124no—
325C3×C4—28no—
326C3×C4—28no—
327C3×C4C4×D1218yes—
328C3×C4C22×C4×D314yes—
329C3×C4C2×#23514yes—
330Dic3—616no—
331Dic3—68no—
332Dic3—128no—
333Dic3—124no—
334Dic3—124no—
335C32#294711yescharacteristic, complemented, Sylow
336C23—181no—
337C23C2×C4⋊(C3⋊D3)11yescharacteristic
338Q8—94no—
339Q8—92no—
340Q8—184no—
341Q8—182no—
342Q8—181no—
343D4—92no—
344D4—184no—
345D4—181no—
346C2×C4—184no—
347C2×C4—181no—
348C2×C4—182no—
349C2×C4—184no—
350C2×C4—181no—
351C2×C4—181no—
352C2×C4—182no—
353C2×C4—722no—
354C2×C4—721no—
355C2×C4C2×C4×C3⋊D312yes—
356C2×C4C2×C4⋊(C3⋊D3)12yes—
357C2×C4C2×C4⋊(C3⋊D3)12yes—
358C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
359C2×C4#382812yes—
360C2×C4C23×C3⋊D311yescharacteristic
361C8—21no—
362C8—21no—
363C8C2×C4×C3⋊D314yes—
364C2×C3—28no—
365C2×C3C2×C4×D1214yes—
366C2×C3#575114yes—
367C2×C3#575314yes—
368D3—128no—
369C22—21no—
370C22—21no—
371C22—182no—
372C22—361no—
373C22—361no—
374C22C4×C4⋊(C3⋊D3)12yes—
375C22C22×C4⋊(C3⋊D3)11yescharacteristic
376C4—22no—
377C4—22no—
378C4—182no—
379C4—184no—
380C4—362no—
381C4—361no—
382C4—361no—
383C4C4×C4⋊(C3⋊D3)12yes—
384C4C22×C4×C3⋊D311yescharacteristic
385C4C2×#382811yescharacteristic
386C3#7857114yescomplemented
387C2—22no—
388C2—362no—
389C2C2×C4×C4⋊(C3⋊D3)11yescharacteristic
390C2#1059622211yescharacteristic
391C2#1059622411yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#405C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#405C3⋊D3
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
3. #10595987C2semidirect
4. C32×#405C2semidirect
5. #10592820C2semidirect
7. C2×#63643C2semidirect
8. #10592415C2semidirect
9. #10592409C2semidirect
10. C4×#3746C2semidirect
11. C4×#3744C2semidirect
20. #64118C4semidirect
46. C3×#405D3semidirect
65. C2×#634C2×C4semidirect
68. C32×M16C2×C4semidirect
90. #3746C2×C4semidirect
91. #3744C2×C4semidirect
161. #405C3⋊D3semidirect
176. C3×M16C4×D3semidirect
296. M16C4×C3⋊D3semidirect
335. C32#2947semidirect
386. C3#78571semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105959942
#105959872
C32×#4052
#105928202
#105928122
C2×#636432
#105924152
#105924092
C4×#37462
C4×#37442
#785713