Finite Group Databasebeta

← #14739113

Subgroups — #14739113

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079744C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13077697C211yesmaximal, characteristic, complemented
4#13068034C214yesmaximal, complemented
5#13068000C214yesmaximal, complemented
6#13067386C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic
9C2×C11×#477C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×#66995—21no—
13#10623008C2211yescharacteristic
14C11×#477—22no—
15C11×#477C2214yes—
16C2×C11×#107—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#103—21no—
19#10622701C2212yes—
20#10622697—22no—
21#10622692C2212yes—
22#10622644C2212yes—
23#10622641—22no—
24#10622640C2212yes—
25Q8×C11⋊C8—22no—
26Q8×C11⋊C8C2214yes—
27#10622581—22no—
28#10622579—21no—
29#10622538—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622184C2214yes—
34#10622123C2212yes—
35#10622120C2212yes—
36#10622118C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11D411yescharacteristic
39C2×#4339—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2312yes—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11D412yes—
48C4×Q8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4326—22no—
56#66995—44no—
57C2×#4325—22no—
58#66983—21no—
59#66983—21no—
60C2×#4318—21no—
61#66928—21no—
62#66927C2311yescharacteristic
63C4×D44—21no—
64C4×D44—21no—
65#66922C2311yescharacteristic
66C11×#107—24no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×#103—24no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)D412yes—
72#66874—22no—
73#66873—22no—
74#66873—24no—
75#66872—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—24no—
78C4⋊(C11⋊C8)D412yes—
79C4⋊(C11⋊C8)C2312yes—
80C4⋊(C11⋊C8)C2312yes—
81C4×C11⋊C8—21no—
82C4×C11⋊C8—24no—
83C4×C11⋊C8C2312yes—
84#19403—111nomaximal, Sylow
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—41no—
89C2×Q8×C11—82no—
90C2×Q8×C11SD1614yes—
91C2×Q8×C11C2×D412yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C2×C22⋊D11—41no—
99#4339—42no—
100#4339—42no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C2×C8×C11—22no—
107C2×C8×C11—42no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4C2×D412yes—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121C42×C11C2411yescharacteristic
122#4326—44no—
123#4325—44no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128#4318—42no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8C2×D414yes—
132#3227—111no—
133C2×#477D1111yescharacteristic, complemented
134#3037—111no—
135#2982—111no—
136#1678—114no—
137#1672—114no—
138#1570—111no—
139#1548—111no—
140#1540—111no—
141C23×C11#12111yescharacteristic
142C22×D11—41no—
143Q8×C11—22no—
144Q8×C11—24no—
145Q8×C11—82no—
146Q8×C11—82no—
147Q8×C11C2×SD1614yes—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—81no—
155C2×C4×C11—82no—
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11C2×SD1612yes—
160C2×C4×C11#13512yes—
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C2×#4111yescharacteristic
164C22⋊D11—82no—
165C2×Dic11—41no—
166D44—41no—
167D44—41no—
168D44—42no—
169D44—81no—
170C4×D11—82no—
171Dic22—41no—
172Dic22—41no—
173C8×C11—42no—
174C11⋊C8—24no—
175C11⋊C8—42no—
176C11⋊C8—42no—
177C2×#137—221no—
178#532—111no—
179C2×C4⋊Q8C2×D1111yescharacteristic
180C2×C4×Q8C2×D1111yescharacteristic
181#498—112no—
182#486—112no—
183#481—222no—
184#477—22no—
185#477C2×D1114yes—
186#476—222no—
187#464—222no—
188#462—112no—
189#460—112no—
190C8×Q8—114no—
191C8×Q8—222no—
192#431—111no—
193#431—111no—
194#431—222no—
195C2×#107—21no—
196#423—111no—
197C2×C4⋊C8C2×D1111yescharacteristic
198#417—221no—
199C2×#103—21no—
200#334—114no—
201#333—114no—
202#332—112no—
203#331—112no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#46512yes—
207C22×C11C2×#12111yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—21no—
212C4×C11—24no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—82no—
217C4×C11#46512yes—
218C4×C11C22×SD1611yescharacteristic
219C4×C11C2×#13511yescharacteristic
220C4×C11#57812yes—
221Dic11—81no—
222C2×#41—221no—
223C22×Q8—21no—
224C22×Q8C22⋊D1111yescharacteristic
225#137—444no—
226C2×Q16—222no—
227C2×SD16—222no—
228C2×M16—221no—
229C22×C8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—111no—
234C4⋊Q8C22×D1112yes—
235#127—111no—
236#124—221no—
237#121—221no—
238#121—221no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C22⋊D1112yes—
242C4×Q8C22×D1112yes—
243C4×D4—221no—
244C4×D4—221no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C42—21no—
250C2×C42C22×D1111yescharacteristic
251#107—24no—
252#106—224no—
253C4⋊C8—21no—
254C4⋊C8—112no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—224no—
258C4⋊C8—221no—
259C4⋊C8C22×D1112yes—
260#103—24no—
261#103—222no—
262#102—224no—
263#102—222no—
264C22⋊C8—112no—
265C22⋊C8—221no—
266C4×C8—112no—
267C4×C8—224no—
268C4×C8—221no—
269C2×C11—22no—
270C2×C11#304411yescharacteristic
271C2×C11C2×#46511yescharacteristic
272C2×C11#306811yescharacteristic
273D11—161no—
274#41—442no—
275#41—442no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—82no—
281C2×Q8—221no—
282C2×Q8#432514yes—
283C2×Q8C2×C22⋊D1112yes—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—441no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—441no—
292C22×C4D4×D1111yescharacteristic
293C22×C4#434111yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295Q16—444no—
296SD16—444no—
297M16—442no—
298C2×C8—22no—
299C2×C8—42no—
300C2×C8—114no—
301C2×C8—222no—
302C2×C8—222no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4C2×C22⋊D1112yes—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C42—22no—
316C42—22no—
317C42D4×D1111yescharacteristic
318C42#434111yescharacteristic
319C42C2×C22⋊D1111yescharacteristic
320C42C23×D1111yescharacteristic
321C11#1940311yescharacteristic, complemented, Sylow
322C23—441no—
323C23#6699211yescharacteristic
324Q8—22no—
325Q8—24no—
326Q8—82no—
327Q8—82no—
328Q8—441no—
329Q8—441no—
330Q8C2×#432514yes—
331D4—442no—
332D4—441no—
333D4—441no—
334D4—881no—
335D4—882no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—441no—
345C2×C4—882no—
346C2×C4#6699211yescharacteristic
347C2×C4#6699211yescharacteristic
348C2×C4#6699211yescharacteristic
349C2×C4C2×#432512yes—
350C2×C4#6700312yes—
351C2×C4C2×D4×D1111yescharacteristic
352C2×C4C2×#434111yescharacteristic
353C2×C4C22×C22⋊D1111yescharacteristic
354C8—42no—
355C8—224no—
356C8—442no—
357C8—442no—
358C22—21no—
359C22—21no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22#1062266112yes—
364C22C2×#6699211yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—24no—
369C4—42no—
370C4—82no—
371C4—881no—
372C4#1062266112yes—
373C4#1062329712yes—
374C4C22×#432511yescharacteristic
375C4C2×#6700311yescharacteristic
376C2—22no—
377C2—1761no—
378C2#1307814311yescharacteristic
379C2C2×#1062266111yescharacteristic
380C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#477C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#477D11
hypocenterC11#19403
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13077697C2semidirect
4. #13068034C2semidirect
5. #13068000C2semidirect
6. #13067386C2semidirect
7. #13067297C2semidirect
9. C2×C11×#477C2semidirect
133. C2×#477D11semidirect
321. C11#19403semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130780882
#130776972
#130680342
#130680002
#130673862
#130672972
#130672662
C2×C11×#4772
#1940311