Finite Group Databasebeta

← #14909624

Subgroups — #14909624

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078271C211yesmaximal, characteristic, complemented
2#13078264C211yesmaximal, characteristic
3#13070825C212yesmaximal, complemented
4#13070808C212yesmaximal, complemented
5#13070729C212yesmaximal, complemented
6#13070712C212yesmaximal, complemented
7#13070547C212yesmaximal, complemented
8#13070535C212yesmaximal, complemented
9C11×#2113C211yesmaximal, characteristic, complemented
10C2×C11×#131C2211yescharacteristic
11#10623361—21no—
12#10623356—21no—
13C22×Dic44C2211yescharacteristic, complemented
14C22×D88C2211yescharacteristic
15C2×C11×M32C2211yescharacteristic, complemented
16C22×C11×C16C2211yescharacteristic, complemented
17#10622750—21no—
18#10622750—21no—
19#10622748—21no—
20#10622748—21no—
21#10622744—21no—
22#10622733—21no—
23#10622729C2212yes—
24#10622729C2212yescomplemented
25#10622728C2212yes—
26#10622728C2212yes—
27#10622719C2211yescharacteristic
28#10622719C2211yescharacteristic, complemented
29C2×#66864C2212yes—
30C2×#66864C2212yes—
31C11×C22⋊C16C2212yes—
32C11×C22⋊C16C2212yescomplemented
33#10622147C2212yes—
34#10622147C2212yes—
35#10622143C2212yescomplemented
36#10622142C2212yescomplemented
37#10622141C2212yescomplemented
38#10622141C2212yescomplemented
39C2×C11×#41D411yescharacteristic
40C22×D44—21no—
41C22×Dic22—21no—
42C11×#131—41no—
43C11×#131—41no—
44C2×C11×M16D411yescharacteristic
45C2×C11×M16D411yescharacteristic
46C2×C11×M16D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50#67000—41no—
51#66997—41no—
52#66993—41no—
53#66990—41no—
54#66990—41no—
55#66989—41no—
56#66988—41no—
57#66988—41no—
58#66983—22no—
59#66983—22no—
60#66979—21no—
61#66979—21no—
62#66977—22no—
63#66977—22no—
64C2×Dic44—21no—
65C2×Dic44—41no—
66C2×Dic44—41no—
67C2×Dic44C2312yes—
68C2×D88—21no—
69C2×D88—41no—
70C2×D88—41no—
71C2×D88C2312yes—
72C11×M32—41no—
73C2×C11×C16—41no—
74C2×C11×C16C2312yes—
75C2×C11×C16C2312yes—
76#66885—22no—
77#66885—22no—
78#66882C2312yes—
79#66882C2312yes—
80#66881—21no—
81#66881—21no—
82#66880—22no—
83#66880—22no—
84#66864—42no—
85#66864—42no—
86#33766—111nomaximal, Sylow
87C23×D11—41no—
88C11×#41—41no—
89C11×#41—41no—
90C2×Q8×C11D811yescharacteristic
91C2×D4×C11D811yescharacteristic
92C2×D4×C11D811yescharacteristic
93C2×D4×C11D811yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—42no—
98C2×C22⋊D11—42no—
99C22×Dic11—41no—
100C2×D44—22no—
101C2×D44—42no—
102C2×D44—42no—
103C2×D44—41no—
104C2×Dic22—22no—
105C2×Dic22—42no—
106C2×Dic22—42no—
107C2×Dic22—41no—
108C11×M16—41no—
109C11×M16—41no—
110C11×M16—41no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2411yescharacteristic
121C22⋊Dic11—42no—
122C22⋊Dic11—42no—
123C22⋊Dic11—41no—
124C22⋊Dic11—41no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129Dic11⋊C4—42no—
130Dic11⋊C4—42no—
131C4×Dic11—41no—
132C4×Dic11—41no—
133Dic44—22no—
134Dic44—22no—
135Dic44—42no—
136D88—22no—
137D88—22no—
138D88—42no—
139C11×C16—22no—
140C11×C16—22no—
141#3059—111no—
142#3058—111no—
143#2237—112no—
144#2234—112no—
145#2220—112no—
146#2217—112no—
147#2187—112no—
148#2185—112no—
149#2113D1111yescharacteristic, complemented
150C23×C11C2×D811yescharacteristic
151C23×C11C2×D811yescharacteristic
152C23×C11C2×D811yescharacteristic
153C22×D11—42no—
154C22×D11—82no—
155C22×D11—162no—
156Q8×C11—41no—
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—41no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C22⋊D11—162no—
171C22⋊D11—162no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—82no—
176D44—42no—
177D44—42no—
178D44—82no—
179Dic22—42no—
180Dic22—42no—
181Dic22—82no—
182C8×C11—21no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11H(5,𝔽2)11yescharacteristic
186C8×C11H(5,𝔽2)11yescharacteristic
187C22×Q16—111no—
188C22×D8—111no—
189C2×#131C2×D1111yescharacteristic
190#536—221no—
191#535—221no—
192C2×SD32—112no—
193C2×SD32—112no—
194C2×M32C2×D1111yescharacteristic, complemented
195C22×C16C2×D1111yescharacteristic, complemented
196#470—221no—
197#470—221no—
198#469—221no—
199#469—221no—
200#467—112no—
201#467—112no—
202#466—112no—
203#466—112no—
204#427—111no—
205#427—111no—
206#419—221no—
207#418—221no—
208#367—112no—
209#366—112no—
210#358—112no—
211#358—112no—
212#357—112no—
213#357—112no—
214C22⋊C16C2×D1112yes—
215C22⋊C16C2×D1112yescomplemented
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11C22×D811yescharacteristic
223C2×D11—82no—
224C2×D11—82no—
225C2×D11—82no—
226C2×D11—164no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11#53411yescharacteristic
231C4×C11#57511yescharacteristic
232Dic11—82no—
233Dic11—82no—
234Dic11—82no—
235C2×#41D4411yescharacteristic
236C22×Q8—221no—
237C22×D4—221no—
238C2×Q16—112no—
239C2×Q16—221no—
240C2×Q16—441no—
241C2×Q16—441no—
242C2×D8—112no—
243C2×D8—221no—
244C2×D8—441no—
245C2×D8—441no—
246#131—41no—
247#131—41no—
248C2×M16D4411yescharacteristic
249C2×M16D4411yescharacteristic
250C2×M16D4411yescharacteristic
251C22×C8C22×D1111yescharacteristic
252C22×C8C22×D1111yescharacteristic
253C22×C8C22×D1111yescharacteristic
254C4⋊Q8—441no—
255#127—441no—
256#124—441no—
257#124—441no—
258#123—441no—
259#123—441no—
260C22⋊Q8—222no—
261C22⋊Q8—222no—
262#121—222no—
263#121—222no—
264#120—441no—
265#120—441no—
266#117—221no—
267#117—221no—
268SD32—442no—
269SD32—442no—
270M32—41no—
271C2×C16—41no—
272C2×C16C22×D1112yes—
273C2×C16C22×D1112yes—
274#107—112no—
275#107—112no—
276#106—221no—
277#106—221no—
278#103—222no—
279#103—222no—
280#102—222no—
281#102—222no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11—41no—
285C2×C11#318611yescharacteristic
286C2×C11#341612yes—
287D11—162no—
288C24—441no—
289#41—41no—
290#41—41no—
291C2×Q8—222no—
292C2×Q8—442no—
293C2×Q8—442no—
294C2×Q8—441no—
295C2×Q8D8811yescharacteristic
296C2×D4—222no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—442no—
300C2×D4—442no—
301C2×D4—441no—
302C2×D4D8811yescharacteristic
303C2×D4D8811yescharacteristic
304C2×D4D8811yescharacteristic
305C22×C4—441no—
306C22×C4C2×D4411yescharacteristic
307C22×C4C2×D4411yescharacteristic
308C22×C4C2×D4411yescharacteristic
309Q16—222no—
310Q16—222no—
311Q16—442no—
312D8—222no—
313D8—222no—
314D8—442no—
315M16—41no—
316M16—41no—
317M16—41no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8C2×D4411yescharacteristic
325C2×C8C2×D4411yescharacteristic
326C2×C8C2×D4411yescharacteristic
327C2×C8C23×D1111yescharacteristic
328C4⋊C4—222no—
329C4⋊C4—222no—
330C4⋊C4—442no—
331C4⋊C4—442no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—442no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C22⋊C4—442no—
338C42—441no—
339C42—441no—
340C16—22no—
341C16—22no—
342C11#3376611yescharacteristic, complemented, Sylow
343C23—442no—
344C23—882no—
345C23—1762no—
346C23C2×D8811yescharacteristic
347C23C2×D8811yescharacteristic
348C23C2×D8811yescharacteristic
349Q8—41no—
350Q8—442no—
351Q8—442no—
352Q8—882no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—442no—
357D4—442no—
358D4—882no—
359D4—1762no—
360D4—1762no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—882no—
371C2×C4C2×D8811yescharacteristic
372C2×C4C2×D8811yescharacteristic
373C2×C4C2×D8811yescharacteristic
374C2×C4C22×D4411yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8#6703711yescharacteristic
379C8#6703711yescharacteristic
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—882no—
387C22—882no—
388C22—882no—
389C22—1764no—
390C22C22×D8811yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—882no—
395C4—882no—
396C4—882no—
397C4#1062302411yescharacteristic
398C4#1062327911yescharacteristic
399C2—41no—
400C2—41no—
401C2—41no—
402C2—1762no—
403C2#1307936711yescharacteristic
404C2#1308176412yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2113C2
socleC22×C11C22×D8
prime radical#13078264C2
hypercenter#2113D11
hypocenterC11#33766
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
1. #13078271C2semidirect
3. #13070825C2semidirect
4. #13070808C2semidirect
5. #13070729C2semidirect
6. #13070712C2semidirect
7. #13070547C2semidirect
8. #13070535C2semidirect
9. C11×#2113C2semidirect
13. C22×Dic44C22semidirect
15. C2×C11×M32C22semidirect
16. C22×C11×C16C22semidirect
24. #10622729C22semidirect
28. #10622719C22semidirect
32. C11×C22⋊C16C22semidirect
35. #10622143C22semidirect
36. #10622142C22semidirect
37. #10622141C22semidirect
38. #10622141C22semidirect
149. #2113D11semidirect
194. C2×M32C2×D11semidirect
195. C22×C16C2×D11semidirect
215. C22⋊C16C2×D11semidirect
342. C11#33766semidirect

Maximal subgroups

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

subgroupindex
#130782712
#130782642
#130708252
#130708082
#130707292
#130707122
#130705472
#130705352
C11×#21132
#3376611