Finite Group Databasebeta

← #14739055

Subgroups — #14739055

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079541C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13077697C211yesmaximal, characteristic, complemented
4#13068044C214yesmaximal, complemented
5#13067966C214yesmaximal, complemented
6#13067386C211yesmaximal, characteristic, complemented
7#13067301C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic
9C2×C11×#475C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×#66995—21no—
13#10623008C2211yescharacteristic
14C11×#475—22no—
15C11×#475C2214yes—
16C2×C11×#106—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#103—21no—
19#10622840—22no—
20#10622698C2212yes—
21#10622696—22no—
22#10622694C2212yes—
23#10622644C2212yes—
24#10622641—22no—
25#10622640C2212yes—
26Q8×C11⋊C8—22no—
27Q8×C11⋊C8C2214yes—
28#10622579—21no—
29#10622538—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622185C2214yes—
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—
58C2×#4325—24no—
59#66983—21no—
60#66983—21no—
61C2×#4318—21no—
62#66928—21no—
63#66927C2311yescharacteristic
64C4×D44—21no—
65C4×D44—21no—
66#66922C2311yescharacteristic
67C11×#106—24no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×#103—24no—
71#66899—24no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)D412yes—
74#66874—22no—
75#66873—22no—
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#19397—111nomaximal, Sylow
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—41no—
89C2×Q8×C11—82no—
90C2×Q8×C11SD1614yescomplemented
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#4325—84no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129#4318—42no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8C2×D414yes—
133#3206—111no—
134C2×#475D1111yescharacteristic, complemented
135#3037—111no—
136#2982—111no—
137#1680—114no—
138#1666—114no—
139#1570—111no—
140#1549—111no—
141#1540—111no—
142C23×C11#12111yescharacteristic
143C22×D11—41no—
144Q8×C11—22no—
145Q8×C11—24no—
146Q8×C11—44no—
147Q8×C11—82no—
148Q8×C11C2×SD1614yes—
149C2×C4×C11—22no—
150C2×C4×C11—24no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—81no—
156C2×C4×C11—82no—
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11C2×SD1612yes—
161C2×C4×C11#13512yes—
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C22⋊D11—82no—
166C2×Dic11—41no—
167D44—41no—
168D44—41no—
169D44—42no—
170D44—81no—
171C4×D11—82no—
172Dic22—41no—
173Dic22—41no—
174C8×C11—42no—
175C11⋊C8—24no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178C2×#137—221no—
179#532—111no—
180C2×C4⋊Q8C2×D1111yescharacteristic
181C2×C4×Q8C2×D1111yescharacteristic
182#492—112no—
183#487—112no—
184#475—22no—
185#475C2×D1114yes—
186#464—222no—
187#462—112no—
188#461—222no—
189#460—112no—
190#448—222no—
191C8×Q8—114no—
192C8×Q8—222no—
193#431—111no—
194#431—111no—
195#431—222no—
196C2×#106—21no—
197#423—111no—
198C2×C4⋊C8C2×D1111yescharacteristic
199#417—221no—
200C2×#103—21no—
201#334—114no—
202#332—114no—
203#332—112no—
204#331—112no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11#46512yes—
208C22×C11C2×#12111yescharacteristic
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C4×C11—21no—
213C4×C11—24no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—42no—
217C4×C11—82no—
218C4×C11#46512yes—
219C4×C11C22×SD1611yescharacteristic
220C4×C11C2×#13511yescharacteristic
221C4×C11#57712yes—
222Dic11—81no—
223C2×#41—221no—
224C22×Q8—21no—
225C22×Q8C22⋊D1111yescharacteristic
226#137—444no—
227C2×Q16—222no—
228C2×SD16—224no—
229C2×SD16—222no—
230C2×M16—221no—
231C22×C8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—111no—
236C4⋊Q8C22×D1112yes—
237#127—111no—
238#124—221no—
239#121—221no—
240#121—221no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8C22⋊D1112yes—
244C4×Q8C22×D1112yes—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4C22⋊D1111yescharacteristic
251C2×C42—21no—
252C2×C42C22×D1111yescharacteristic
253#106—24no—
254C4⋊C8—21no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—112no—
258C4⋊C8—224no—
259C4⋊C8—221no—
260C4⋊C8C22×D1112yes—
261#103—24no—
262#103—224no—
263#103—222no—
264#102—222no—
265C22⋊C8—112no—
266C22⋊C8—221no—
267C4×C8—112no—
268C4×C8—224no—
269C4×C8—221no—
270C2×C11—22no—
271C2×C11#304311yescharacteristic
272C2×C11C2×#46511yescharacteristic
273C2×C11#306911yescharacteristic
274D11—161no—
275#41—442no—
276#41—442no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—82no—
282C2×Q8—221no—
283C2×Q8#432514yescomplemented
284C2×Q8C2×C22⋊D1112yes—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—441no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—441no—
293C22×C4D4×D1111yescharacteristic
294C22×C4#434111yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296Q16—444no—
297SD16—444no—
298SD16—884no—
299M16—442no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—114no—
303C2×C8—222no—
304C2×C8—222no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C4⋊C4C2×C22⋊D1112yes—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C42—22no—
318C42—22no—
319C42D4×D1111yescharacteristic
320C42#434111yescharacteristic
321C42C2×C22⋊D1111yescharacteristic
322C42C23×D1111yescharacteristic
323C11#1939711yescharacteristic, complemented, Sylow
324C23—441no—
325C23#6699211yescharacteristic
326Q8—22no—
327Q8—24no—
328Q8—44no—
329Q8—82no—
330Q8—441no—
331Q8—441no—
332Q8C2×#432514yes—
333D4—442no—
334D4—441no—
335D4—441no—
336D4—881no—
337D4—882no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—82no—
346C2×C4—441no—
347C2×C4—882no—
348C2×C4#6699211yescharacteristic
349C2×C4#6699211yescharacteristic
350C2×C4#6699211yescharacteristic
351C2×C4C2×#432512yes—
352C2×C4#6700312yes—
353C2×C4C2×D4×D1111yescharacteristic
354C2×C4C2×#434111yescharacteristic
355C2×C4C22×C22⋊D1111yescharacteristic
356C8—42no—
357C8—224no—
358C8—442no—
359C8—442no—
360C22—21no—
361C22—21no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22#1062266112yes—
366C22C2×#6699211yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—24no—
371C4—42no—
372C4—82no—
373C4—881no—
374C4#1062266112yes—
375C4#1062329312yes—
376C4C22×#432511yescharacteristic
377C4C2×#6700311yescharacteristic
378C2—22no—
379C2—1761no—
380C2#1307813411yescharacteristic
381C2C2×#1062266111yescharacteristic
382C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#475C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#475D11
hypocenterC11#19397
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13077697C2semidirect
4. #13068044C2semidirect
5. #13067966C2semidirect
6. #13067386C2semidirect
7. #13067301C2semidirect
9. C2×C11×#475C2semidirect
90. C2×Q8×C11SD16semidirect
134. C2×#475D11semidirect
283. C2×Q8#4325semidirect
323. C11#19397semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130780882
#130776972
#130680442
#130679662
#130673862
#130673012
#130672662
C2×C11×#4752
#1939711