Finite Group Databasebeta

← #14656172

Subgroups — #14656172

Order 2816.

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

normal subgroups only

This group has 554 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#13079538C211yesmaximal, characteristic
2#13073828C211yesmaximal, characteristic, complemented
3#13067298C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3037C211yesmaximal, characteristic
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#464—22no—
13C11×#462—21no—
14C11×#460—21no—
15C11×#423C2211yescharacteristic
16C11×#417—21no—
17#10622843—21no—
18#10622706—21no—
19#10622689—21no—
20#10622653—22no—
21#10622632—22no—
22#10622599—22no—
23#10622590—21no—
24C4×C4⋊Dic11C2211yescharacteristic
25#10622542—22no—
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622175—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622119—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×Dic22D412yes—
34C11×#137—42no—
35C11×#137—42no—
36C2×C11×Q16—22no—
37C2×C11×SD16—22no—
38C2×C11×M16—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4324—24no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4×Dic11—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—22no—
66C11×#102—22no—
67C11⋊#95—24no—
68C11⋊#95—24no—
69C11⋊#95D412yes—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#66874—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10244—111nomaximal, Sylow
78C11×#41—41no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11SD1612yescomplemented
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×Dic11—22no—
100C22×Dic11—22no—
101C2×Dic22—22no—
102C2×Dic22—22no—
103C2×Dic22—44no—
104C11×Q16—44no—
105C11×SD16—44no—
106C11×M16—41no—
107C11×M16—41no—
108C2×C8×C11—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11—41no—
118C42×C11—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123#4324—84no—
124C4⋊Dic11—42no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133#3206—111no—
134#3037D1111yescharacteristic
135#2568—111no—
136#1548—111no—
137#1502—111no—
138#1479—111no—
139#1303—111no—
140C23×C11—41no—
141C23×C11#12011yescharacteristic
142Q8×C11—22no—
143Q8×C11—22no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—41no—
147Q8×C11—41no—
148D4×C11—41no—
149D4×C11—41no—
150D4×C11—42no—
151D4×C11—81no—
152D4×C11—81no—
153D4×C11—81no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11C2×SD1611yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11#13711yescharacteristic
174C2×Dic11—42no—
175C2×Dic11—44no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179Dic22—44no—
180Dic22—82no—
181C8×C11—42no—
182C11⋊C8—42no—
183C11⋊C8—81no—
184C2×#137—21no—
185#532C2×D1111yescharacteristic
186C2×C4⋊Q8—111no—
187C2×C4×Q8C2×D1111yescharacteristic
188#492—221no—
189#487—221no—
190#464—22no—
191#462—21no—
192#461—222no—
193#460—21no—
194#448—222no—
195#431—111no—
196#431—111no—
197#423C2×D1111yescharacteristic
198#417—21no—
199#400—222no—
200#391—222no—
201#391—221no—
202#382—221no—
203C4×C4⋊C4—111no—
204#333—222no—
205#327—222no—
206Q8⋊C8—222no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11#39211yescharacteristic
213C22×C11#44811yescharacteristic
214C22×C11#44911yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11#45011yescharacteristic
222C4×C11#45211yescharacteristic
223C4×C11#45512yes—
224C4×C11#46511yescharacteristic
225C4×C11#46811yescharacteristic
226Dic11—82no—
227Dic11—82no—
228C2×#41—21no—
229C22×Q8—112no—
230C22×Q8C22⋊D1111yescharacteristic
231#137—42no—
232#137—42no—
233C2×Q16—22no—
234C2×SD16—22no—
235C2×SD16—224no—
236C2×M16—21no—
237C4⋊Q8—221no—
238C4⋊Q8—221no—
239C4⋊Q8—221no—
240C4⋊Q8—221no—
241C4⋊Q8C22⋊D1111yescharacteristic
242#127C22⋊D1111yescharacteristic
243#124—21no—
244#121—21no—
245#121—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×D4—21no—
251C4×D4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4C22⋊D1111yescharacteristic
257C2×C42—21no—
258C2×C42—221no—
259C2×C42C22×D1111yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—112no—
262C4⋊C8—221no—
263C4⋊C8C22⋊D1112yes—
264#103—22no—
265#103—224no—
266#102—22no—
267C22⋊C8—221no—
268C22⋊C8—221no—
269C4×C8—221no—
270C4×C8—221no—
271#95—112no—
272#95—224no—
273#95—224no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—161no—
277C2×C11#200011yescharacteristic
278C2×C11#200411yescharacteristic
279C2×C11#200911yescharacteristic
280#41—41no—
281#41—41no—
282#41—41no—
283#41—41no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—222no—
291C2×Q8—222no—
292C2×Q8—444no—
293C2×Q8#432412yescomplemented
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—222no—
302C22×C4—222no—
303C22×C4D4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306Q16—44no—
307SD16—44no—
308SD16—884no—
309M16—41no—
310M16—41no—
311C2×C8—22no—
312C2×C8—222no—
313C2×C8—441no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—442no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C42—41no—
328C42—41no—
329C42—441no—
330C42—441no—
331C42D4×D1111yescharacteristic
332C42#434111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C42C2×C22⋊D1111yescharacteristic
335C11#1024411yescharacteristic, complemented, Sylow
336C23—41no—
337C23#6699011yescharacteristic
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—444no—
345Q8—882no—
346D4—42no—
347D4—41no—
348D4—41no—
349D4—81no—
350D4—81no—
351D4—81no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—442no—
363C2×C4—444no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4#6698511yescharacteristic
368C2×C4C2×#432411yescharacteristic
369C2×C4#6699011yescharacteristic
370C2×C4#6699111yescharacteristic
371C2×C4#6699211yescharacteristic
372C2×C4#6699211yescharacteristic
373C2×C4#6699311yescharacteristic
374C2×C4#6700311yescharacteristic
375C2×C4#6700411yescharacteristic
376C2×C4#6700611yescharacteristic
377C8—42no—
378C8—442no—
379C8—881no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#1062265011yescharacteristic
386C22#1062265311yescharacteristic
387C22#1062283611yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—42no—
392C4—81no—
393C4—81no—
394C4—882no—
395C4—882no—
396C4#1062265411yescharacteristic
397C4#1062265511yescharacteristic
398C4#1062281512yes—
399C4#1062283111yescharacteristic
400C4#1062285211yescharacteristic
401C2—21no—
402C2—21no—
403C2—161no—
404C2#1306961911yescharacteristic
405C2#1306964211yescharacteristic
406C2#1306967311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3037C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3037D11
hypocenterC11#10244
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. #13073828C2semidirect
3. #13067298C2semidirect
5. #13067011C2semidirect
6. #13066517C2semidirect
88. C2×Q8×C11SD16semidirect
293. C2×Q8#4324semidirect
335. C11#10244semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130738282
#130672982
#130671112
#130670112
#130665172
C11×#30372
#1024411