Finite Group Databasebeta

← #14664291

Subgroups — #14664291

Order 2816.

488 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 73 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#13074090C211yesmaximal, characteristic
2D11×#343C211yesmaximal, characteristic, complemented
3#13066944C211yesmaximal, characteristic, complemented
4#13066644C211yesmaximal, characteristic, complemented
5#13066642C211yesmaximal, characteristic, complemented
6#13066619C211yesmaximal, characteristic, complemented
7C11×#1345C211yesmaximal, characteristic, complemented
8C2×#66991C411yescharacteristic
9C2×M16×D11—21no—
10C2×C4⋊C4×D11C2211yescharacteristic
11C11×#394C2211yescharacteristic
12#10622835C411yescharacteristic
13#10622599C2211yescharacteristic
14#10622569—21no—
15#10622569—21no—
16#10622564—21no—
17#10622557—21no—
18#10622339—21no—
19#10622279C411yescharacteristic
20#10622272C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×M16—21no—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39#66991—41no—
40#66991—41no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4C2×C411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11—21no—
47C2×#4318—21no—
48M16×D11—24no—
49M16×D11—42no—
50C2×#4313—41no—
51C2×#4313—41no—
52C2×C8×D11—41no—
53C4⋊C4×D11—41no—
54C4⋊C4×D11—41no—
55C11×C22⋊C8—21no—
56C11×#95C2×C411yescharacteristic
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11766—111nomaximal, Sylow
65C24×C11—21no—
66C23×D11C22⋊C411yescharacteristic
67C2×D4×C11—41no—
68C2×D4×C11—81no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—42no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C2×C4×D11—22no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—81no—
92C2×C4×D11—81no—
93C11×M16—22no—
94C11×M16—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—81no—
101C22⋊Dic11—42no—
102C22⋊Dic11—42no—
103C22⋊Dic11—81no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—81no—
110#4318—22no—
111#4318—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#4313—44no—
115#4313—82no—
116C8×D11—44no—
117#2591—111no—
118C2×#343—111no—
119#1463—111no—
120#1353—111no—
121#1353—111no—
122#1345—111no—
123#1345D1111yescharacteristic, complemented
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11C2×C22⋊C411yescharacteristic
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—22no—
135C22×D11—41no—
136C22×D11#9911yescharacteristic
137C22×D11#9911yescharacteristic
138D4×C11—82no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C22⋊D11—82no—
151C22⋊D11—82no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11#10412yes—
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—22no—
168C4×D11—22no—
169C4×D11—42no—
170C4×D11—81no—
171C4×D11—81no—
172C4×D11—81no—
173C8×C11—42no—
174C8×C11—81no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C22×M16—221no—
178C2×#121—111no—
179C22×C4⋊C4—111no—
180#407—221no—
181#400—111no—
182#400—111no—
183#394—111no—
184#394C2×D1111yescharacteristic
185#388—221no—
186#388—221no—
187#386—221no—
188#386—221no—
189C4×C22⋊C4—111no—
190#343—111no—
191#343—221no—
192#343C2×D1111yescharacteristic
193#324—111no—
194#324—221no—
195#324C2×D1111yescharacteristic
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11C2×#9911yescharacteristic
206C22×C11#41711yescharacteristic
207C22×C11C2×#10411yescharacteristic
208C2×D11—21no—
209C2×D11—21no—
210C2×D11—21no—
211C2×D11—21no—
212C2×D11—21no—
213C2×D11—42no—
214C2×D11—42no—
215C2×D11#35512yes—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—81no—
221Dic11—22no—
222Dic11—41no—
223Dic11—41no—
224Dic11—81no—
225Dic11—81no—
226C22×D4—221no—
227C22×D4C4×D1111yescharacteristic
228C23×C4—111no—
229C23×C4—111no—
230C23×C4—111no—
231C2×M16—21no—
232C2×M16—224no—
233C2×M16—221no—
234C2×M16—441no—
235C2×M16—441no—
236C2×M16—442no—
237C22×C8—441no—
238#121—441no—
239#121—441no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—441no—
245C2×C4⋊C4—441no—
246C2×C4⋊C4C22×D1111yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C42—221no—
254C22⋊C8—21no—
255C22⋊C8—221no—
256C22⋊C8—441no—
257#95—111no—
258#95—221no—
259#95—221no—
260#95—221no—
261#95—221no—
262#95C4×D1111yescharacteristic
263C2×C11—21no—
264C2×C11—21no—
265C2×C11—161no—
266C2×C11#150411yescharacteristic
267C2×C11#212111yescharacteristic
268C2×C11C2×#35511yescharacteristic
269D11—22no—
270D11—41no—
271C24—21no—
272C24—111no—
273C2×D4—41no—
274C2×D4—81no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—442no—
278C2×D4—442no—
279C22×C4—21no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—111no—
283C22×C4—222no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—881no—
295C22×C4—881no—
296C22×C4C2×C4×D1111yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299M16—22no—
300M16—41no—
301M16—222no—
302M16—444no—
303M16—441no—
304M16—882no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—444no—
308C2×C8—441no—
309C2×C8—441no—
310C4⋊C4—41no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4—441no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—81no—
318C22⋊C4—442no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4—881no—
322C42—881no—
323C11#1176611yescharacteristic, complemented, Sylow
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—111no—
332C23—111no—
333C23—222no—
334C23—221no—
335C23—221no—
336C23—441no—
337C23C22⋊C4×D1111yescharacteristic
338D4—82no—
339D4—882no—
340D4—882no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—112no—
351C2×C4—222no—
352C2×C4—222no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—442no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4—881no—
371C2×C4#6696411yescharacteristic
372C2×C4#6696811yescharacteristic
373C8—42no—
374C8—81no—
375C8—442no—
376C8—881no—
377C22—21no—
378C22—21no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—112no—
387C22—221no—
388C22—221no—
389C22—221no—
390C22—221no—
391C22—221no—
392C22—442no—
393C22—442no—
394C22D11×#9911yescharacteristic
395C22#1062238411yescharacteristic
396C22D11×#10411yescharacteristic
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—81no—
402C4—222no—
403C4—441no—
404C4—441no—
405C4—881no—
406C4—881no—
407C2—21no—
408C2—21no—
409C2—161no—
410C2—222no—
411C2—441no—
412C2#1306711711yescharacteristic
413C2#1307025911yescharacteristic
414C2D11×#35511yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1345C2
socleC22×C11C2×#99
prime radicalC2×#66991C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1345D11
hypocenterC11#11766
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. D11×#343C2semidirect
3. #13066944C2semidirect
4. #13066644C2semidirect
5. #13066642C2semidirect
6. #13066619C2semidirect
7. C11×#1345C2semidirect
123. #1345D11semidirect
323. C11#11766semidirect

Maximal subgroups

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

subgroupindex
#130740902
D11×#3432
#130669442
#130666442
#130666422
#130666192
C11×#13452
#1176611