Finite Group Databasebeta

← #14664273

Subgroups — #14664273

Order 2816.

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

normal subgroups only

This group has 622 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#13071952C211yesmaximal, characteristic
2D11×#343C211yesmaximal, characteristic, complemented
3#13066944C211yesmaximal, characteristic, complemented
4#13066646C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic, complemented
6#13066618C211yesmaximal, characteristic, complemented
7C11×#1354C211yesmaximal, characteristic, complemented
8C22×#4343C411yescharacteristic
9C2×M16×D11—21no—
10C2×#66947—21no—
11C2×C4⋊C4×D11C2211yescharacteristic
12C11×#395C2211yescharacteristic
13#10622842C411yescharacteristic
14#10622604C2211yescharacteristic
15#10622602—21no—
16#10622339—21no—
17#10622285C411yescharacteristic
18#10622281—21no—
19#10622278—21no—
20#10622277C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C2×#4343—41no—
29C2×#4343—41no—
30C2×#4343—44no—
31C22×D44—21no—
32C22×D44C2×C411yescharacteristic
33C22×C4×D11—21no—
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×C4×D11D411yescharacteristic
37C2×C11×M16—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2311yescharacteristic
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4C2×C411yescharacteristic
48C2×Dic11⋊C4D411yescharacteristic
49C2×#4318—21no—
50M16×D11—24no—
51M16×D11—42no—
52C2×#4313—41no—
53C2×#4313—41no—
54C2×C8×D11—41no—
55#66947—44no—
56C4⋊C4×D11—41no—
57C4⋊C4×D11—41no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95C2×C411yescharacteristic
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95C2×C411yescharacteristic
64C22⋊(C11⋊C8)—21no—
65(C2×D11)⋊C8—41no—
66#11762—111nomaximal, Sylow
67C23×D11—21no—
68C23×D11C22⋊C411yescharacteristic
69C2×Q8×C11—42no—
70C2×Q8×C11—41no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80#4343—44no—
81#4343—44no—
82#4343—44no—
83#4343—44no—
84C2×D44—24no—
85C2×D44—41no—
86C2×D44—42no—
87C2×D44—42no—
88C2×D44—41no—
89C2×D44—41no—
90C2×C4×D11—22no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C2×C4×D11—42no—
100C2×C4×D11—42no—
101C2×C4×D11—42no—
102C2×C4×D11—42no—
103C2×C4×D11—42no—
104C11×M16—22no—
105C11×M16—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C4⋊Dic11—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—42no—
120#4318—22no—
121#4318—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124#4313—44no—
125#4313—82no—
126C8×D11—44no—
127#2406—111no—
128C2×#343—111no—
129#1463—111no—
130#1354—111no—
131#1354D1111yescharacteristic, complemented
132#1345—111no—
133#1345—111no—
134C23×C11C2×C22⋊C411yescharacteristic
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—22no—
138C22×D11—22no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11#9911yescharacteristic
147C22×D11#9911yescharacteristic
148Q8×C11—42no—
149Q8×C11—42no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—22no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11#13711yescharacteristic
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11#10412yes—
174D44—44no—
175D44—42no—
176D44—42no—
177D44—44no—
178C4×D11—22no—
179C4×D11—22no—
180C4×D11—22no—
181C4×D11—22no—
182C4×D11—42no—
183C4×D11—48no—
184C4×D11—42no—
185C4×D11—42no—
186C4×D11—81no—
187C8×C11—42no—
188C8×C11—81no—
189C11⋊C8—42no—
190C11⋊C8—81no—
191C22×#41—111no—
192C22×M16—221no—
193C2×#123—221no—
194C22×C4⋊C4—111no—
195#407—221no—
196#395—111no—
197#395C2×D1111yescharacteristic
198#394—111no—
199#394—111no—
200#386—221no—
201#385—221no—
202#385—221no—
203#381—111no—
204#343—111no—
205#343—221no—
206#343C2×D1111yescharacteristic
207#324—111no—
208#324—221no—
209#324C2×D1111yescharacteristic
210C22×C11—21no—
211C22×C11—21no—
212C22×C11C2×#9911yescharacteristic
213C22×C11#41711yescharacteristic
214C22×C11C2×#10411yescharacteristic
215C2×D11—21no—
216C2×D11—21no—
217C2×D11—21no—
218C2×D11—21no—
219C2×D11—21no—
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—42no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11AΣL(1,𝔽16)12yes—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—81no—
236Dic11—22no—
237Dic11—41no—
238Dic11—41no—
239Dic11—81no—
240C2×#41—441no—
241C2×#41—441no—
242C2×#41—444no—
243C22×Q8C4×D1111yescharacteristic
244C22×D4—111no—
245C22×D4—221no—
246C23×C4—111no—
247C23×C4—111no—
248C23×C4—111no—
249C23×C4—221no—
250C2×M16—21no—
251C2×M16—224no—
252C2×M16—221no—
253C2×M16—441no—
254C2×M16—441no—
255C2×M16—442no—
256C22×C8—441no—
257#123—444no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—441no—
264C2×C4⋊C4—441no—
265C2×C4⋊C4C22×D1111yescharacteristic
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—221no—
271C22⋊C8—21no—
272C22⋊C8—221no—
273C22⋊C8—441no—
274#95—21no—
275#95—111no—
276#95—221no—
277#95—221no—
278#95C4×D1111yescharacteristic
279C2×C11—21no—
280C2×C11—21no—
281C2×C11#150411yescharacteristic
282C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
283C2×C11#213311yescharacteristic
284D11—22no—
285D11—41no—
286D11—82no—
287C24—111no—
288C24—221no—
289#41—444no—
290#41—444no—
291#41—444no—
292#41—444no—
293C2×Q8—42no—
294C2×Q8—41no—
295C2×D4—224no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—442no—
300C2×D4—442no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—222no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—442no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4—442no—
321C22×C4C2×C4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324M16—22no—
325M16—41no—
326M16—222no—
327M16—444no—
328M16—441no—
329M16—882no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—444no—
333C2×C8—441no—
334C2×C8—441no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—442no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—442no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C11#1176211yescharacteristic, complemented, Sylow
348C23—111no—
349C23—111no—
350C23—222no—
351C23—222no—
352C23—221no—
353C23—221no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23C22⋊C4×D1111yescharacteristic
362Q8—42no—
363Q8—42no—
364D4—444no—
365D4—444no—
366D4—442no—
367D4—442no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—112no—
381C2×C4—222no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—448no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—881no—
399C2×C4#6696711yescharacteristic
400C2×C4#6697111yescharacteristic
401C8—42no—
402C8—81no—
403C8—442no—
404C8—881no—
405C22—21no—
406C22—21no—
407C22—112no—
408C22—221no—
409C22—221no—
410C22—221no—
411C22—221no—
412C22—221no—
413C22—442no—
414C22—442no—
415C22—442no—
416C22—442no—
417C22—442no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22D11×#9911yescharacteristic
423C22#1062241611yescharacteristic
424C22D11×#10411yescharacteristic
425C4—21no—
426C4—21no—
427C4—41no—
428C4—42no—
429C4—41no—
430C4—81no—
431C4—222no—
432C4—441no—
433C4—441no—
434C4—881no—
435C2—21no—
436C2—21no—
437C2—222no—
438C2—441no—
439C2—882no—
440C2#1306711911yescharacteristic
441C2D11×AΣL(1,𝔽16)11yescharacteristic
442C2#1307030411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC22×#4343C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11762
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
2. D11×#343C2semidirect
3. #13066944C2semidirect
4. #13066646C2semidirect
5. #13066620C2semidirect
6. #13066618C2semidirect
7. C11×#1354C2semidirect
131. #1354D11semidirect
347. C11#11762semidirect

Maximal subgroups

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

subgroupindex
#130719522
D11×#3432
#130669442
#130666462
#130666202
#130666182
C11×#13542
#1176211