Finite Group Databasebeta

← #14657458

Subgroups — #14657458

Order 2816.

460 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 97 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#13078080C211yesmaximal, characteristic
2#13067371C211yesmaximal, characteristic, complemented
3#13067294C211yesmaximal, characteristic, complemented
4#13067066C211yesmaximal, characteristic, complemented
5C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#1800C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66985—21no—
10#10623008C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×#100—21no—
14#10622632—21no—
15#10622629—22no—
16#10622628—21no—
17#10622579—21no—
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×#343—21no—
22D4⋊(C11⋊C8)—21no—
23D4⋊(C11⋊C8)—21no—
24#10622123—21no—
25#10622121—21no—
26#10622121—21no—
27#10622120—21no—
28#10622118—22no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C2×#4339—21no—
32C2×C11×M16—21no—
33C2×C11×M16—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4324—22no—
42#66985—42no—
43#66985—42no—
44C2×#4323—22no—
45#66983—21no—
46#66983—21no—
47C2×#4318—21no—
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44—21no—
54#66922D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×#100—42no—
60#66874—22no—
61#66873—22no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66C4×C11⋊C8—21no—
67C4×C11⋊C8D411yescharacteristic
68C4×C11⋊C8D411yescharacteristic
69#10457—111nomaximal, Sylow
70C24×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11SD1612yes—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—81no—
81C22×C4×C11—81no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C2×C22⋊D11—41no—
86#4339—41no—
87#4339—41no—
88#4339—41no—
89#4339—41no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×C4×D11—41no—
94C2×Dic22—21no—
95C11×M16—41no—
96C11×M16—41no—
97C11×M16—41no—
98C11×M16—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109#4324—44no—
110#4323—44no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115#4318—41no—
116#4318—41no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—81no—
123#3036—111no—
124#1800D1111yescharacteristic, complemented
125#1566—111no—
126#1547—111no—
127#1492—111no—
128C2×D4⋊C8—111no—
129#1292—111no—
130C23×C11—22no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—81no—
134C23×C11—81no—
135C23×C11#12311yescharacteristic
136C22×D11—41no—
137D4×C11—22no—
138D4×C11—22no—
139D4×C11—41no—
140D4×C11—41no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—82no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11#12411yescharacteristic
155C2×C4×C11C2×SD1611yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C22⋊D11—81no—
160C22⋊D11—81no—
161C2×Dic11—41no—
162D44—41no—
163D44—41no—
164D44—41no—
165D44—41no—
166D44—81no—
167C4×D11—81no—
168C4×D11—81no—
169Dic22—41no—
170Dic22—41no—
171C8×C11—81no—
172C8×C11—81no—
173C11⋊C8—22no—
174C11⋊C8—41no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C2×AGL(1,ℤ/8)—221no—
178#532—111no—
179C2×C4×D4C2×D1111yescharacteristic
180#463—222no—
181#461—221no—
182#459—221no—
183#423—111no—
184#423C2×D1111yescharacteristic
185#423C2×D1111yescharacteristic
186C2×C4⋊C8—111no—
187#417—221no—
188C2×#100—21no—
189C2×C4×C8—111no—
190#343—21no—
191#334—222no—
192#332—221no—
193#331—221no—
194D4⋊C8—221no—
195D4⋊C8—221no—
196D4⋊C8—221no—
197D4⋊C8—221no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—42no—
201C22×C11—82no—
202C22×C11—82no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11#39411yescharacteristic
206C22×C11#48111yescharacteristic
207C22×C11#48211yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—81no—
215C4×C11#44911yescharacteristic
216C4×C11#45011yescharacteristic
217C4×C11#46511yescharacteristic
218C4×C11#46911yescharacteristic
219C4×C11#47111yescharacteristic
220C4×C11#47211yescharacteristic
221Dic11—81no—
222C2×#41—221no—
223C22×D4C22⋊D1111yescharacteristic
224C23×C4—21no—
225AGL(1,ℤ/8)—442no—
226AGL(1,ℤ/8)—442no—
227C2×SD16—222no—
228C2×D8—222no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—221no—
232C22×C8—221no—
233C22×C8—221no—
234C4⋊Q8—111no—
235#127—111no—
236#124—221no—
237#121—221no—
238#121—221no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—221no—
244C4×D4—221no—
245C2×C4⋊C4C22⋊D1111yescharacteristic
246C2×C22⋊C4—21no—
247C2×C42C22×D1111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255C4⋊C8—221no—
256#103—222no—
257#102—222no—
258#100—42no—
259C4×C8—111no—
260C4×C8—111no—
261C4×C8—221no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11—82no—
265C2×C11#203411yescharacteristic
266C2×C11#205011yescharacteristic
267C2×C11#205111yescharacteristic
268D11—161no—
269C24—21no—
270#41—441no—
271#41—441no—
272#41—441no—
273#41—441no—
274C2×Q8—221no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4—221no—
283C2×D4—441no—
284C2×D4#432512yes—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—81no—
289C22×C4—81no—
290C22×C4—441no—
291C22×C4#433911yescharacteristic
292C22×C4#433911yescharacteristic
293C22×C4C2×C22⋊D1111yescharacteristic
294SD16—444no—
295D8—444no—
296M16—41no—
297M16—41no—
298M16—41no—
299M16—41no—
300M16—441no—
301M16—441no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—221no—
305C2×C8—221no—
306C2×C8—222no—
307C2×C8—442no—
308C2×C8—441no—
309C2×C8—881no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C42D4×D1111yescharacteristic
319C42D4×D1111yescharacteristic
320C42D4×D1111yescharacteristic
321C42#434111yescharacteristic
322C11#1045711yescharacteristic, complemented, Sylow
323C23—22no—
324C23—41no—
325C23—41no—
326C23—81no—
327C23—81no—
328C23—441no—
329C23#6698211yescharacteristic
330Q8—441no—
331Q8—441no—
332D4—22no—
333D4—22no—
334D4—41no—
335D4—41no—
336D4—441no—
337D4—441no—
338D4—441no—
339D4—441no—
340D4—881no—
341D4—881no—
342D4—881no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—441no—
352C2×C4—881no—
353C2×C4—881no—
354C2×C4#6693611yescharacteristic
355C2×C4#6693711yescharacteristic
356C2×C4#6693711yescharacteristic
357C2×C4#6693811yescharacteristic
358C2×C4#6698511yescharacteristic
359C2×C4#6699011yescharacteristic
360C2×C4#6699211yescharacteristic
361C2×C4C2×#432511yescharacteristic
362C2×C4#6700211yescharacteristic
363C2×C4#6700311yescharacteristic
364C8—81no—
365C8—81no—
366C8—222no—
367C8—441no—
368C8—442no—
369C8—881no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—82no—
374C22—82no—
375C22—81no—
376C22—81no—
377C22—881no—
378C22—881no—
379C22—881no—
380C22#1062257211yescharacteristic
381C22#1062258111yescharacteristic
382C22#1062261611yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—81no—
387C4—881no—
388C4#1062236111yescharacteristic
389C4#1062236211yescharacteristic
390C4#1062265011yescharacteristic
391C4#1062265211yescharacteristic
392C4#1062265911yescharacteristic
393C4#1062266111yescharacteristic
394C2—21no—
395C2—21no—
396C2—82no—
397C2—1761no—
398C2#1306980511yescharacteristic
399C2#1306990111yescharacteristic
400C2#1306990811yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#394
prime radical#13078080C2
hypercenter#1800D11
hypocenterC11#10457
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #13067371C2semidirect
3. #13067294C2semidirect
4. #13067066C2semidirect
5. C2×D4⋊(C11⋊C8)C2semidirect
6. #13066490C2semidirect
7. C11×#1800C2semidirect
124. #1800D11semidirect
322. C11#10457semidirect

Maximal subgroups

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

subgroupindex
#130780802
#130673712
#130672942
#130670662
C2×D4⋊(C11⋊C8)2
#130664902
C11×#18002
#1045711