Finite Group Databasebeta

← #14655766

Subgroups — #14655766

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#13079538C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic, complemented
3#13067302C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic
5#13066940C211yesmaximal, characteristic, complemented
6#13066511C211yesmaximal, 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—
17C2×#66899—21no—
18#10622706—21no—
19#10622689—21no—
20#10622653—22no—
21#10622634—22no—
22#10622634—22no—
23#10622632—22no—
24C2×#66871—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28D4⋊(C11⋊C8)—22no—
29#10622166—22no—
30#10622124—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×Dic22—21no—
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—
57C22×C11⋊C8—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×#103—22no—
65C11×#102—22no—
66#66899—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—24no—
70#66871—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#10181—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×C11#4111yescharacteristic
99C22×Dic11—41no—
100C2×Dic22—22no—
101C2×Dic22—41no—
102C2×Dic22—82no—
103C11×Q16—44no—
104C11×SD16—44no—
105C11×M16—41no—
106C11×M16—41no—
107C2×C8×C11—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11—41no—
117C42×C11—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122#4324—84no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#3206—111no—
133C2×#477—111no—
134#3037D1111yescharacteristic
135#1549—111no—
136#1480—111no—
137#1461—111no—
138#1301—111no—
139C23×C11—41no—
140C23×C11#12111yescharacteristic
141Q8×C11—22no—
142Q8×C11—22no—
143Q8×C11—41no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—41no—
147D4×C11—42no—
148D4×C11—41no—
149D4×C11—41no—
150D4×C11—42no—
151D4×C11—81no—
152D4×C11—81no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12711yescharacteristic
169C2×C4×C11C2×SD1611yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11#13711yescharacteristic
173C2×Dic11—42no—
174C2×Dic11—82no—
175Dic22—44no—
176Dic22—82no—
177C8×C11—42no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C11⋊C8—81no—
181C2×#137—21no—
182#532C2×D1111yescharacteristic
183C2×C4⋊Q8—111no—
184C2×C4×Q8C2×D1111yescharacteristic
185#492—221no—
186#487—221no—
187#477—222no—
188#477—222no—
189#464—22no—
190#462—21no—
191#461—222no—
192#460—21no—
193#448—222no—
194#431—111no—
195#431—111no—
196C2×#107—221no—
197#423C2×D1111yescharacteristic
198C2×C4⋊C8—111no—
199#417—21no—
200C2×#103—221no—
201#332—222no—
202D4⋊C8—222no—
203#324—222no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11#39211yescharacteristic
210C22×C11#46511yescharacteristic
211C22×C11#46811yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11#44811yescharacteristic
219C4×C11#44911yescharacteristic
220C4×C11#45011yescharacteristic
221C4×C11#45211yescharacteristic
222C4×C11#47312yes—
223Dic11—82no—
224C2×#41—21no—
225C22×Q8—221no—
226C22×Q8C22⋊D1111yescharacteristic
227#137—42no—
228#137—42no—
229C2×Q16—22no—
230C2×SD16—22no—
231C2×SD16—224no—
232C2×M16—21no—
233C22×C8—221no—
234C4⋊Q8—112no—
235C4⋊Q8—221no—
236C4⋊Q8—221no—
237C4⋊Q8—221no—
238C4⋊Q8C22⋊D1111yescharacteristic
239#127C22⋊D1111yescharacteristic
240#124—21no—
241#121—21no—
242#121—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×D4—21no—
248C4×D4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4C22⋊D1111yescharacteristic
253C2×C42—21no—
254C2×C42C22×D1111yescharacteristic
255#107—224no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8C22⋊D1112yes—
262#103—22no—
263#103—224no—
264#103—224no—
265#102—22no—
266C22⋊C8—112no—
267C22⋊C8—221no—
268C4×C8—221no—
269C4×C8—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—161no—
273C2×C11#200011yescharacteristic
274C2×C11#200811yescharacteristic
275C2×C11#202011yescharacteristic
276#41—41no—
277#41—41no—
278#41—41no—
279#41—41no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—222no—
287C2×Q8—441no—
288C2×Q8—882no—
289C2×Q8#432412yescomplemented
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—441no—
298C22×C4D4×D1111yescharacteristic
299C22×C4#434111yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—44no—
302SD16—44no—
303SD16—884no—
304M16—41no—
305M16—41no—
306C2×C8—22no—
307C2×C8—222no—
308C2×C8—222no—
309C2×C8—441no—
310C2×C8—441no—
311C2×C8—441no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C42—41no—
325C42—41no—
326C42D4×D1111yescharacteristic
327C42D4×D1111yescharacteristic
328C42C2×C22⋊D1111yescharacteristic
329C42C2×C22⋊D1111yescharacteristic
330C11#1018111yescharacteristic, complemented, Sylow
331C23—41no—
332C23#6699211yescharacteristic
333Q8—22no—
334Q8—22no—
335Q8—41no—
336Q8—41no—
337Q8—41no—
338Q8—41no—
339Q8—444no—
340Q8—882no—
341D4—42no—
342D4—42no—
343D4—41no—
344D4—41no—
345D4—81no—
346D4—81no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—442no—
358C2×C4—882no—
359C2×C4#6698511yescharacteristic
360C2×C4C2×#432411yescharacteristic
361C2×C4#6699011yescharacteristic
362C2×C4#6699011yescharacteristic
363C2×C4#6699111yescharacteristic
364C2×C4#6699211yescharacteristic
365C2×C4#6699311yescharacteristic
366C2×C4#6700311yescharacteristic
367C2×C4#6700411yescharacteristic
368C2×C4#6700611yescharacteristic
369C8—42no—
370C8—442no—
371C8—442no—
372C8—881no—
373C22—21no—
374C22—21no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1062265411yescharacteristic
379C22#1062265511yescharacteristic
380C22#1062283611yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—42no—
385C4—81no—
386C4—81no—
387C4—882no—
388C4#1062265011yescharacteristic
389C4#1062265311yescharacteristic
390C4#1062281712yes—
391C4#1062283111yescharacteristic
392C4#1062285211yescharacteristic
393C2—21no—
394C2—21no—
395C2—161no—
396C2#1306961911yescharacteristic
397C2#1306966611yescharacteristic
398C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3037C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3037D11
hypocenterC11#10181
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. C2×#10622634C2semidirect
3. #13067302C2semidirect
5. #13066940C2semidirect
6. #13066511C2semidirect
88. C2×Q8×C11SD16semidirect
289. C2×Q8#4324semidirect
330. C11#10181semidirect

Maximal subgroups

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

subgroupindex
#130795382
C2×#106226342
#130673022
#130670152
#130669402
#130665112
C11×#30372
#1018111