Finite Group Databasebeta

← #15617336

Subgroups — #15617336

Order 2816.

4874 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623453C211yesmaximal, characteristic
2C22×#67001C211yesmaximal, characteristic, complemented
3#13077146C218yesmaximal, complemented
4#13077139C218yesmaximal, complemented
5#13077133C216yesmaximal, complemented
6C2×#10622615C216yesmaximal, complemented
7C11×#3428C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9#10623453—28no—
10#10623453C4116yescomplemented
11C2×#67043C2214yes—
12C2×#67042C2214yes—
13C2×#41×D11—24no—
14C2×#67040—21no—
15C2×#67037—23no—
16C22×#4339C2216yes—
17C11×#520C2218yescomplemented
18C11×#519—21no—
19C11×#518—23no—
20C4×C11×#41—24no—
21C2×C11×#117C2216yescomplemented
22C2×#67001—28no—
23C2×#67001C2218yescomplemented
24C22×#4318C2213yescomplemented
25C23×C11⋊C8C2213yescomplemented
26#10622617C22112yescomplemented
27#10622615C2214yescomplemented
28#10622615C22112yescomplemented
29#10622615C22124yescomplemented
30#10622614C22112yescomplemented
31C2×#66874C22112yescomplemented
32#10622579C22124yescomplemented
33C2×#66873C22112yescomplemented
34C2×C11×#41C2×C418yes—
35C2×C11×#41D418yes—
36C2×C11×#41D414yes—
37C2×C11×#41C2314yes—
38C22×Q8×C11D411yescharacteristic
39C22×D4×C11D413yes—
40C23×C4×C11C2313yes—
41C22×C22⋊D11—26no—
42#67043—216no—
43#67043C2×C4132yescomplemented
44#67042—216no—
45#67042C2×C4132yescomplemented
46#41×D11—264no—
47#67040—216no—
48C2×#4343—24no—
49C2×Q8×D11—24no—
50#67037—248no—
51C2×#4341—212no—
52C2×D4×D11—212no—
53C2×#4339—26no—
54C2×#4339—26no—
55C2×#4339—224no—
56C2×#4339C2×C4148yescomplemented
57C2×#4339C23112yes—
58C2×#4339C2314yes—
59C22×D44C2316yes—
60C22×C4×D11—26no—
61C22×Dic22C2316yes—
62C4×Q8×C11—28no—
63C4×D4×C11—224no—
64C11×#117—26no—
65C11×#117—26no—
66C11×#117C2314yes—
67C11×#117C23112yes—
68C2×C11×C4⋊C4C23112yes—
69C2×C11×C22⋊C4—26no—
70C2×C42×C11—26no—
71#67001—232no—
72C2×#4318—212no—
73C2×#4318C23112yes—
74C22×C11⋊C8—212no—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2313yes—
77C22×C11⋊C8C23112yes—
78#66874C23124yes—
79#66874C2318yes—
80#66873C2318yes—
81#66873C23124yes—
82#60086—111nomaximal, Sylow
83C24×C11C2×D413yes—
84C23×D11—26no—
85C11×#41C22⋊C4132yes—
86C11×#41C22×C4116yes—
87C11×#41C2×D4116yes—
88C2×Q8×C11C22⋊C418yes—
89C2×Q8×C11C2×D414yes—
90C2×D4×C11C22⋊C4124yes—
91C2×D4×C11C2×D4112yes—
92C22×C4×C11—212no—
93C22×C4×C11C22×C4112yes—
94C22×C4×C11C2×D416yes—
95C22×C4×C11C2×D413yes—
96C22×C4×C11C2×D4112yes—
97C22×C4×C11C2411yescharacteristic
98C22×C4×C11C2416yes—
99C2×C22⋊D11—248no—
100C2×C22⋊D11—24no—
101C2×C22⋊D11—212no—
102C22×Dic11—26no—
103#4343—232no—
104Q8×D11—232no—
105#4341—296no—
106D4×D11—296no—
107#4339—248no—
108#4339—248no—
109#4339—28no—
110#4339—224no—
111#4339C22×C4116yes—
112#4339C22×C4148yes—
113C2×D44—26no—
114C2×D44—212no—
115C2×D44C22×C4124yes—
116C2×D44C2414yes—
117C2×C4×D11—248no—
118C2×C4×D11—24no—
119C2×C4×D11—212no—
120C2×Dic22—26no—
121C2×Dic22—212no—
122C2×Dic22C22×C4124yes—
123C2×Dic22C2414yes—
124C11×C4⋊C4—212no—
125C11×C4⋊C4C2418yes—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—212no—
128C42×C11—24no—
129C42×C11—212no—
130#4318—224no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—26no—
133C2×C11⋊C8—224no—
134C2×C11⋊C8C2412yes—
135C2×C11⋊C8C2416yes—
136C2×#585—111no—
137C22×#131—111no—
138#3428D1111yescharacteristic, complemented
139#2898—118no—
140#2897—118no—
141#2896—116no—
142C2×#416—116no—
143C23×C11—46no—
144C23×C11C2×C22⋊C4112yes—
145C23×C11C22×D411yescharacteristic
146C23×C11C22×D416yes—
147C22×D11—24no—
148C22×D11—224no—
149C22×D11—812no—
150Q8×C11C2×C22⋊C4116yes—
151D4×C11C2×C22⋊C4148yes—
152C2×C4×C11—28no—
153C2×C4×C11—812no—
154C2×C4×C11C2×C22⋊C4124yes—
155C2×C4×C11C2×C22⋊C4112yes—
156C2×C4×C11C23×C4112yes—
157C2×C4×C11C23×C412yes—
158C2×C4×C11C22×D412yes—
159C2×C4×C11C22×D4112yes—
160C2×C4×C11C22×D416yes—
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C2511yescharacteristic
163C22⋊D11—216no—
164C22⋊D11—248no—
165C2×Dic11—224no—
166C2×Dic11—24no—
167D44—224no—
168D44—24no—
169D44C23×C418yes—
170C4×D11—216no—
171C4×D11—248no—
172Dic22—224no—
173Dic22—24no—
174Dic22C23×C418yes—
175C11⋊C8—22no—
176C11⋊C8—26no—
177#585—1116no—
178#585—228no—
179C2×2−1+4—114no—
180C2×2−1+4—221no—
181C2×H(5,𝔽2)—114no—
182C2×H(5,𝔽2)—223no—
183C22×#41—116no—
184C22×#41—224no—
185C22×#41C2×D1111yescharacteristic
186C2×#131—118no—
187C2×#131—228no—
188C22×M16—113no—
189C23×C8—113no—
190#520C2×D1118yescomplemented
191#519—21no—
192#518—23no—
193C4×#41—24no—
194C2×#117C2×D1116yescomplemented
195#419—1112no—
196#418—1112no—
197#417—1124no—
198#416—114no—
199#416—1112no—
200#416—1124no—
201C2×#103—1112no—
202C2×#102—1112no—
203C22×C11—212no—
204C22×C11—22no—
205C22×C11—412no—
206C22×C11C22×C22⋊C412yes—
207C22×C11C22×C22⋊C4112yes—
208C22×C11C23×D411yescharacteristic
209C2×D11—28no—
210C2×D11—48no—
211C2×D11—824no—
212C4×C11—48no—
213C4×C11C22×C22⋊C412yes—
214C4×C11C22×C22⋊C4112yes—
215C4×C11C24×C411yescharacteristic
216C4×C11C23×D411yescharacteristic
217Dic11—28no—
2182−1+4—1132no—
2192−1+4—2216no—
2202−1+4—2216no—
221H(5,𝔽2)—1132no—
222H(5,𝔽2)—2216no—
223H(5,𝔽2)—2248no—
224C2×#41—1148no—
225C2×#41—114no—
226C2×#41—1112no—
227C2×#41—2264no—
228C2×#41—224no—
229C2×#41—2212no—
230C2×#41—2224no—
231C2×#41—226no—
232C2×#41—226no—
233C2×#41C4×D1118yes—
234C2×#41D4418yes—
235C2×#41C22⋊D1114yes—
236C2×#41C22×D1114yes—
237C22×Q8—116no—
238C22×Q8—224no—
239C22×Q8C22⋊D1111yescharacteristic
240C22×D4—116no—
241C22×D4—226no—
242C22×D4—2212no—
243C22×D4C22⋊D1113yes—
244C23×C4—226no—
245C23×C4C22×D1113yes—
246#131—2232no—
247C2×M16—1112no—
248C2×M16—2212no—
249C22×C8—111no—
250C22×C8—113no—
251C22×C8—1112no—
252C22×C8—2212no—
253C4×Q8—28no—
254C4×D4—224no—
255#117—26no—
256#117—26no—
257#117C22×D1114yes—
258#117C22×D11112yes—
259C2×C4⋊C4C22×D11112yes—
260C2×C22⋊C4—26no—
261C2×C42—26no—
262#103—118no—
263#103—1124no—
264#102—118no—
265#102—1124no—
266C2×C11—212no—
267C2×C11—22no—
268C2×C11C23×C22⋊C411yescharacteristic
269C2×C11#358412yes—
270D11—48no—
271C24—226no—
272C24C2×C22⋊D1113yes—
273#41—1116no—
274#41—1148no—
275#41—2232no—
276#41—2296no—
277#41—2248no—
278#41—2248no—
279#41—228no—
280#41—2224no—
281#41(C2×D11)⋊C4132yes—
282#41C2×C4×D11116yes—
283#41C2×D44116yes—
284C2×Q8—1124no—
285C2×Q8—114no—
286C2×Q8—2232no—
287C2×Q8—2212no—
288C2×Q8—226no—
289C2×Q8(C2×D11)⋊C418yes—
290C2×Q8C2×C22⋊D1114yes—
291C2×D4—1124no—
292C2×D4—114no—
293C2×D4—2248no—
294C2×D4—224no—
295C2×D4—2212no—
296C2×D4—2296no—
297C2×D4—2212no—
298C2×D4—226no—
299C2×D4(C2×D11)⋊C4124yes—
300C2×D4C2×C22⋊D11112yes—
301C22×C4—212no—
302C22×C4—226no—
303C22×C4—2248no—
304C22×C4—2212no—
305C22×C4—224no—
306C22×C4C2×C4×D11112yes—
307C22×C4C2×D44112yes—
308C22×C4C2×C22⋊D1113yes—
309C22×C4C2×C22⋊D1116yes—
310C22×C4C23×D1116yes—
311C22×C4C23×D1111yescharacteristic
312M16—2224no—
313C2×C8—112no—
314C2×C8—116no—
315C2×C8—222no—
316C2×C8—226no—
317C2×C8—2224no—
318C4⋊C4—212no—
319C4⋊C4C23×D1118yes—
320C22⋊C4—24no—
321C22⋊C4—212no—
322C42—212no—
323C42—24no—
324C11#6008611yescharacteristic, complemented, Sylow
325C23—46no—
326C23—224no—
327C23—2224no—
328C23—8812no—
329C23C2×(C2×D11)⋊C4112yes—
330C23C22×C22⋊D1111yescharacteristic
331C23C22×C22⋊D1116yes—
332Q8—118no—
333Q8—2224no—
334Q8—224no—
335Q8C2×(C2×D11)⋊C4116yes—
336D4—118no—
337D4—2248no—
338D4—2216no—
339D4—2224no—
340D4—224no—
341D4C2×(C2×D11)⋊C4148yes—
342C2×C4—28no—
343C2×C4—812no—
344C2×C4—2224no—
345C2×C4—224no—
346C2×C4—2216no—
347C2×C4—2248no—
348C2×C4C2×(C2×D11)⋊C4124yes—
349C2×C4C2×(C2×D11)⋊C4112yes—
350C2×C4C22×C4×D1112yes—
351C2×C4C22×C4×D11112yes—
352C2×C4C22×D4412yes—
353C2×C4C22×D44112yes—
354C2×C4C22×C22⋊D1116yes—
355C2×C4C22×C22⋊D1111yescharacteristic
356C2×C4C24×D1111yescharacteristic
357C8—222no—
358C8—226no—
359C22—212no—
360C22—22no—
361C22—412no—
362C22—228no—
363C22—448no—
364C22—8824no—
365C22C22×(C2×D11)⋊C4112yes—
366C22C22×(C2×D11)⋊C412yes—
367C22C23×C22⋊D1111yescharacteristic
368C4—48no—
369C4—228no—
370C4C22×(C2×D11)⋊C412yes—
371C4C22×(C2×D11)⋊C4112yes—
372C4C23×C4×D1111yescharacteristic
373C4C23×D4411yescharacteristic
374C2—22no—
375C2—212no—
376C2—448no—
377C2C23×(C2×D11)⋊C411yescharacteristic
378C2#1308338712yes—
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#3428C2
socleC22×C11C23×D4
prime radicalC2×#10623453C2
cosocleC2×C4×C11C25
hypercenter#3428D11
hypocenterC11#60086
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×#41 ◁ #3428

Complements

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

NH ≅ G/Ntype
2. C22×#67001C2semidirect
3. #13077146C2semidirect
4. #13077139C2semidirect
5. #13077133C2semidirect
6. C2×#10622615C2semidirect
7. C11×#3428C2semidirect
10. #10623453C4semidirect
17. C11×#520C22semidirect
21. C2×C11×#117C22semidirect
23. C2×#67001C22semidirect
24. C22×#4318C22semidirect
25. C23×C11⋊C8C22semidirect
26. #10622617C22semidirect
27. #10622615C22semidirect
28. #10622615C22semidirect
29. #10622615C22semidirect
30. #10622614C22semidirect
31. C2×#66874C22semidirect
32. #10622579C22semidirect
33. C2×#66873C22semidirect
43. #67043C2×C4semidirect
45. #67042C2×C4semidirect
56. C2×#4339C2×C4semidirect
138. #3428D11semidirect
190. #520C2×D11semidirect
194. C2×#117C2×D11semidirect
324. C11#60086semidirect

Maximal subgroups

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

subgroupindex
C2×#106234532
C22×#670012
#130771462
#130771392
#130771332
C2×#106226152
C11×#34282
#6008611