Finite Group Databasebeta

← #14655820

Subgroups — #14655820

Order 2816.

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

normal subgroups only

This group has 518 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#13079744C211yesmaximal, characteristic
2#13078088C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic, complemented
4#13067014C211yesmaximal, characteristic
5#13066940C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C2×C11×#475C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66995—21no—
11#10623008C2211yescharacteristic
12C11×#475—22no—
13C11×#475—22no—
14C2×C11×#106—21no—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17#10622701—21no—
18#10622697—22no—
19#10622692—21no—
20#10622644—21no—
21#10622641—22no—
22#10622640—21no—
23#10622581—22no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622184—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—
53#66983—21no—
54#66983—21no—
55C2×#4318—21no—
56#66928—21no—
57#66927D411yescharacteristic
58C4×D44—21no—
59C4×D44—21no—
60#66922D411yescharacteristic
61C11×#106—24no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#103—24no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)D412yes—
67#66874—22no—
68#66873—22no—
69#66873—24no—
70#66872—24no—
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#10189—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×C11SD1612yes—
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—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
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(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126#4318—41no—
127#4318—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131#3227—111no—
132C2×#475D1111yescharacteristic, complemented
133#3037—111no—
134#1548—111no—
135#1480—111no—
136#1461—111no—
137#1301—111no—
138C23×C11#12111yescharacteristic
139C22×D11—41no—
140Q8×C11—22no—
141Q8×C11—22no—
142Q8×C11—41no—
143Q8×C11—41no—
144Q8×C11—82no—
145Q8×C11—82no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11—81no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12711yescharacteristic
161C2×C4×C11C2×SD1611yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11#13711yescharacteristic
165C22⋊D11—81no—
166C22⋊D11—81no—
167C2×Dic11—41no—
168D44—42no—
169D44—41no—
170D44—41no—
171D44—42no—
172C4×D11—81no—
173C4×D11—81no—
174Dic22—41no—
175Dic22—41no—
176C8×C11—42no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C11⋊C8—81no—
180C2×#137—221no—
181#532—111no—
182C2×C4⋊Q8C2×D1111yescharacteristic
183C2×C4×Q8C2×D1111yescharacteristic
184#498—221no—
185#486—221no—
186#481—222no—
187#476—222no—
188#475—22no—
189#475—22no—
190#464—222no—
191#462—221no—
192#460—221no—
193#431—111no—
194#431—111no—
195C2×#106—21no—
196#423—111no—
197C2×C4⋊C8C2×D1111yescharacteristic
198#417—221no—
199C2×#103—21no—
200#333—222no—
201D4⋊C8—222no—
202#324—222no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11#39211yescharacteristic
206C22×C11#46511yescharacteristic
207C22×C11#46811yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—81no—
216C4×C11—82no—
217C4×C11#44811yescharacteristic
218C4×C11#44911yescharacteristic
219C4×C11#45011yescharacteristic
220C4×C11#45211yescharacteristic
221C4×C11#47112yes—
222Dic11—81no—
223C2×#41—221no—
224C22×Q8—21no—
225C22×Q8C22⋊D1111yescharacteristic
226#137—442no—
227#137—442no—
228C2×Q16—222no—
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×Q8—21no—
244C4×Q8—21no—
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—
254#106—224no—
255C4⋊C8—21no—
256C4⋊C8—112no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8C22⋊D1112yes—
261#103—24no—
262#103—222no—
263#102—222no—
264#102—224no—
265C22⋊C8—112no—
266C22⋊C8—221no—
267C4×C8—221no—
268C4×C8—221no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11#200011yescharacteristic
272C2×C11#200911yescharacteristic
273C2×C11#201911yescharacteristic
274D11—161no—
275#41—441no—
276#41—441no—
277#41—441no—
278#41—441no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—22no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—41no—
286C2×Q8—82no—
287C2×Q8—221no—
288C2×Q8#432512yes—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—441no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—441no—
297C22×C4D4×D1111yescharacteristic
298C22×C4#434111yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300Q16—444no—
301SD16—444no—
302M16—441no—
303M16—441no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—222no—
308C2×C8—222no—
309C2×C8—441no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C42—41no—
323C42—41no—
324C42D4×D1111yescharacteristic
325C42D4×D1111yescharacteristic
326C42C2×C22⋊D1111yescharacteristic
327C42C2×C22⋊D1111yescharacteristic
328C11#1018911yescharacteristic, complemented, Sylow
329C23—441no—
330C23#6699211yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—41no—
334Q8—41no—
335Q8—82no—
336Q8—82no—
337Q8—441no—
338Q8—441no—
339D4—442no—
340D4—442no—
341D4—441no—
342D4—441no—
343D4—881no—
344D4—881no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4—81no—
354C2×C4—441no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4#6699011yescharacteristic
358C2×C4#6699011yescharacteristic
359C2×C4#6699111yescharacteristic
360C2×C4#6699211yescharacteristic
361C2×C4#6699311yescharacteristic
362C2×C4C2×#432511yescharacteristic
363C2×C4#6699511yescharacteristic
364C2×C4#6700211yescharacteristic
365C2×C4#6700311yescharacteristic
366C2×C4#6700611yescharacteristic
367C8—42no—
368C8—442no—
369C8—442no—
370C8—881no—
371C22—21no—
372C22—21no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22#1062266111yescharacteristic
377C22#1062266211yescharacteristic
378C22#1062283611yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—81no—
384C4—82no—
385C4—881no—
386C4#1062265911yescharacteristic
387C4#1062266011yescharacteristic
388C4#1062279012yes—
389C4#1062284011yescharacteristic
390C4#1062285111yescharacteristic
391C2—21no—
392C2—21no—
393C2—1761no—
394C2#1306961711yescharacteristic
395C2#1306967411yescharacteristic
396C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#475C2
socleC22×C11#392
prime radical#10623008C22
hypercenterC2×#475D11
hypocenterC11#10189
LCSG ▷ C2×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. #13067297C2semidirect
5. #13066940C2semidirect
6. #13066513C2semidirect
7. C2×C11×#475C2semidirect
132. C2×#475D11semidirect
328. C11#10189semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130780882
#130672972
#130670142
#130669402
#130665132
C2×C11×#4752
#1018911