Finite Group Databasebeta

← #14655764

Subgroups — #14655764

Order 2816.

530 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079541C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13067014C211yesmaximal, characteristic
5#13066940C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C2×C11×#477C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66995—21no—
11#10623008C2211yescharacteristic
12C11×#477—22no—
13C11×#477—22no—
14C2×C11×#107—21no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17#10622840—22no—
18#10622698—21no—
19#10622696—22no—
20#10622694—21no—
21#10622644—21no—
22#10622641—22no—
23#10622640—21no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29#10622166—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C2×#4339—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C42×C11—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4326—22no—
50#66995—42no—
51#66995—42no—
52C2×#4325—22no—
53C2×#4325—24no—
54#66983—21no—
55#66983—21no—
56C2×#4318—21no—
57#66928—21no—
58#66927D411yescharacteristic
59C4×D44—21no—
60C4×D44—21no—
61#66922D411yescharacteristic
62C11×#107—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—24no—
66#66899—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—22no—
70#66873—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10181—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×Q8×C11—82no—
86C2×Q8×C11SD1612yescomplemented
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×C22⋊D11—41no—
94#4339—41no—
95#4339—41no—
96#4339—41no—
97#4339—41no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#4326—44no—
121#4325—44no—
122#4325—84no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127#4318—41no—
128#4318—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132#3206—111no—
133C2×#477D1111yescharacteristic, complemented
134#3037—111no—
135#1549—111no—
136#1480—111no—
137#1461—111no—
138#1301—111no—
139C23×C11#12111yescharacteristic
140C22×D11—41no—
141Q8×C11—22no—
142Q8×C11—22no—
143Q8×C11—44no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—82no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—82no—
155C2×C4×C11—81no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C2×C4×C11C2×SD1611yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C22⋊D11—81no—
167C22⋊D11—81no—
168C2×Dic11—41no—
169D44—42no—
170D44—41no—
171D44—41no—
172D44—42no—
173C4×D11—81no—
174C4×D11—81no—
175Dic22—41no—
176Dic22—41no—
177C8×C11—42no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C11⋊C8—81no—
181C2×#137—221no—
182#532—111no—
183C2×C4⋊Q8C2×D1111yescharacteristic
184C2×C4×Q8C2×D1111yescharacteristic
185#492—221no—
186#487—221no—
187#477—22no—
188#477—22no—
189#464—222no—
190#462—221no—
191#461—222no—
192#460—221no—
193#448—222no—
194#431—111no—
195#431—111no—
196C2×#107—21no—
197#423—111no—
198C2×C4⋊C8C2×D1111yescharacteristic
199#417—221no—
200C2×#103—21no—
201#332—222no—
202D4⋊C8—222no—
203#324—222no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#39211yescharacteristic
207C22×C11#46511yescharacteristic
208C22×C11#46811yescharacteristic
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—81no—
217C4×C11—82no—
218C4×C11#44811yescharacteristic
219C4×C11#44911yescharacteristic
220C4×C11#45011yescharacteristic
221C4×C11#45211yescharacteristic
222C4×C11#47312yes—
223Dic11—81no—
224C2×#41—221no—
225C22×Q8—21no—
226C22×Q8C22⋊D1111yescharacteristic
227#137—442no—
228#137—442no—
229C2×Q16—222no—
230C2×SD16—222no—
231C2×SD16—224no—
232C2×M16—221no—
233C22×C8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—111no—
238C4⋊Q8C22⋊D1112yes—
239#127—111no—
240#124—221no—
241#121—221no—
242#121—221no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×D4—221no—
248C4×D4—221no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C22⋊D1111yescharacteristic
253C2×C42—21no—
254C2×C42C22×D1111yescharacteristic
255#107—24no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8C22⋊D1112yes—
262#103—24no—
263#103—222no—
264#103—224no—
265#102—222no—
266C22⋊C8—112no—
267C22⋊C8—221no—
268C4×C8—221no—
269C4×C8—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11#200011yescharacteristic
273C2×C11#200811yescharacteristic
274C2×C11#202011yescharacteristic
275D11—161no—
276#41—441no—
277#41—441no—
278#41—441no—
279#41—441no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—41no—
287C2×Q8—82no—
288C2×Q8—221no—
289C2×Q8#432512yescomplemented
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—441no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—441no—
298C22×C4D4×D1111yescharacteristic
299C22×C4#434111yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—444no—
302SD16—444no—
303SD16—884no—
304M16—441no—
305M16—441no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—222no—
310C2×C8—222no—
311C2×C8—441no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—221no—
321C4⋊C4—221no—
322C22⋊C4—441no—
323C22⋊C4—441no—
324C42—41no—
325C42—41no—
326C42D4×D1111yescharacteristic
327C42D4×D1111yescharacteristic
328C42C2×C22⋊D1111yescharacteristic
329C42C2×C22⋊D1111yescharacteristic
330C11#1018111yescharacteristic, complemented, Sylow
331C23—441no—
332C23#6699211yescharacteristic
333Q8—22no—
334Q8—22no—
335Q8—44no—
336Q8—41no—
337Q8—41no—
338Q8—82no—
339Q8—441no—
340Q8—441no—
341D4—442no—
342D4—442no—
343D4—441no—
344D4—441no—
345D4—881no—
346D4—881no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4—81no—
356C2×C4—441no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4#6699011yescharacteristic
360C2×C4#6699011yescharacteristic
361C2×C4#6699111yescharacteristic
362C2×C4#6699211yescharacteristic
363C2×C4#6699311yescharacteristic
364C2×C4C2×#432511yescharacteristic
365C2×C4#6699511yescharacteristic
366C2×C4#6700211yescharacteristic
367C2×C4#6700311yescharacteristic
368C2×C4#6700611yescharacteristic
369C8—42no—
370C8—442no—
371C8—442no—
372C8—881no—
373C22—21no—
374C22—21no—
375C22—881no—
376C22—881no—
377C22—881no—
378C22#1062266111yescharacteristic
379C22#1062266211yescharacteristic
380C22#1062283611yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—42no—
385C4—82no—
386C4—81no—
387C4—881no—
388C4#1062265911yescharacteristic
389C4#1062266011yescharacteristic
390C4#1062280512yes—
391C4#1062284011yescharacteristic
392C4#1062285111yescharacteristic
393C2—21no—
394C2—21no—
395C2—1761no—
396C2#1306961711yescharacteristic
397C2#1306966711yescharacteristic
398C2#1306973511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#477C2
socleC22×C11#392
prime radical#10623008C22
hypercenterC2×#477D11
hypocenterC11#10181
LCSG ▷ C2×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. #13067301C2semidirect
5. #13066940C2semidirect
6. #13066513C2semidirect
7. C2×C11×#477C2semidirect
86. C2×Q8×C11SD16semidirect
133. C2×#477D11semidirect
289. C2×Q8#4325semidirect
330. C11#10181semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130780882
#130673012
#130670142
#130669402
#130665132
C2×C11×#4772
#1018111