Finite Group Databasebeta

← #14642227

Subgroups — #14642227

Order 2816.

568 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 109 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#13076957C211yesmaximal, characteristic
2#13068308C211yesmaximal, characteristic
3D11×#336C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic, complemented
5#13066440C211yesmaximal, characteristic, complemented
6#13066438C211yesmaximal, characteristic, complemented
7C11×#1272C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic
9C22×#4313—21no—
10C22×C8×D11—21no—
11C2×C42×D11C2211yescharacteristic
12C11×#391C2211yescharacteristic
13#10622843C411yescharacteristic
14#10622600C411yescharacteristic
15#10622598C411yescharacteristic
16#10622541C2211yescharacteristic
17#10622281—21no—
18#10622277—21no—
19#10622267—21no—
20#10622265—21no—
21C11×#336C2211yescharacteristic
22C11×#336C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11C2×C411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35#66999—42no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48C2×#4313—24no—
49C2×#4313—42no—
50C2×#4313—42no—
51C2×C8×D11—24no—
52C2×C8×D11—42no—
53C2×C8×D11—42no—
54C42×D11—42no—
55C11×#95—21no—
56C11×#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62#7681—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11—22no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—41no—
88C2×C4×D11SD1612yes—
89C2×C4×D11Q1612yes—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—41no—
97C42×C11—41no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—41no—
103C4⋊Dic11—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—41no—
108C4×Dic11—41no—
109C4×Dic11—41no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#4313—48no—
117C8×D11—48no—
118#2855—111no—
119#1728—111no—
120C2×#336—111no—
121#1272—111no—
122#1272D1111yescharacteristic, complemented
123#1271—111no—
124#1271—111no—
125C23×C11C2×C22⋊C411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11#9912yes—
131C22×D11#10312yes—
132C22×D11#10412yes—
133Q8×C11—81no—
134Q8×C11—81no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11#13111yescharacteristic
148C2×C4×C11#13111yescharacteristic
149C2×C4×C11C2×SD1611yescharacteristic
150C2×C4×C11C2×Q1611yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11#10312yes—
167C2×Dic11#10412yes—
168C4×D11—24no—
169C4×D11—24no—
170C4×D11—24no—
171C4×D11—24no—
172C4×D11—42no—
173C4×D11—42no—
174C8×C11—42no—
175C8×C11—42no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178C22×M16—221no—
179C23×C8—221no—
180C2×C22⋊Q8—111no—
181C22×C42—111no—
182#391—111no—
183#391C2×D1111yescharacteristic
184#389—111no—
185#389—111no—
186#387—221no—
187#387—221no—
188#385—221no—
189#381—221no—
190#380—111no—
191#336—111no—
192#336—111no—
193#336—221no—
194#336—221no—
195#336C2×D1111yescharacteristic
196#336C2×D1111yescharacteristic
197C22×C11#40811yescharacteristic
198C22×C11C2×#9911yescharacteristic
199C22×C11#41311yescharacteristic
200C22×C11C2×#10311yescharacteristic
201C22×C11#41711yescharacteristic
202C22×C11C2×#10411yescharacteristic
203C22×C11C2×#10411yescharacteristic
204C2×D11—22no—
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—22no—
210C2×D11#32814yes—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—81no—
218C4×C11—81no—
219Dic11—22no—
220Dic11—22no—
221Dic11—41no—
222Dic11—81no—
223Dic11—81no—
224C22×Q8C4×D1111yescharacteristic
225C23×C4—111no—
226C23×C4—111no—
227C23×C4—111no—
228C2×M16—224no—
229C2×M16—442no—
230C2×M16—442no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—224no—
234C22×C8—221no—
235C22×C8—221no—
236C22×C8—442no—
237C22×C8—442no—
238C22⋊Q8—442no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4C4×D1111yescharacteristic
245C2×C22⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C42—111no—
248C2×C42—111no—
249C2×C42—111no—
250C2×C42—442no—
251C2×C42C22×D1111yescharacteristic
252#95—21no—
253#95—21no—
254#95—221no—
255#95—221no—
256#95—221no—
257#95—221no—
258#95—221no—
259C2×C11#146811yescharacteristic
260C2×C11#148311yescharacteristic
261C2×C11#149311yescharacteristic
262C2×C11C2×#32811yescharacteristic
263C2×C11#150411yescharacteristic
264C2×C11#152411yescharacteristic
265C2×C11#155011yescharacteristic
266D11—24no—
267C24—111no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—41no—
271C2×Q8—41no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—112no—
277C22×C4—112no—
278C22×C4—111no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—222no—
283C22×C4—222no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—441no—
291C22×C4C2×C4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294M16—448no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—222no—
302C2×C8—222no—
303C2×C8—448no—
304C2×C8—441no—
305C2×C8—441no—
306C2×C8—441no—
307C2×C8—441no—
308C4⋊C4—41no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—441no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C22⋊C4—442no—
317C22⋊C4—442no—
318C42—41no—
319C42—441no—
320C42—441no—
321C42—441no—
322C11#768111yescharacteristic, complemented, Sylow
323C23—112no—
324C23—112no—
325C23—112no—
326C23—221no—
327C23—221no—
328C23—221no—
329C23—221no—
330C23C22⋊C4×D1111yescharacteristic
331Q8—81no—
332Q8—81no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—224no—
348C2×C4—224no—
349C2×C4—224no—
350C2×C4—224no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4#6695411yescharacteristic
367C2×C4#6696011yescharacteristic
368C2×C4SD16×D1111yescharacteristic
369C2×C4#6696711yescharacteristic
370C2×C4Q16×D1111yescharacteristic
371C2×C4#6697111yescharacteristic
372C8—42no—
373C8—42no—
374C8—442no—
375C8—442no—
376C22—114no—
377C22—222no—
378C22—222no—
379C22—222no—
380C22—222no—
381C22—222no—
382C22—222no—
383C22#1062234011yescharacteristic
384C22D11×#9911yescharacteristic
385C22#1062235811yescharacteristic
386C22D11×#10311yescharacteristic
387C22#1062241611yescharacteristic
388C22D11×#10411yescharacteristic
389C22D11×#10411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—81no—
398C4—222no—
399C4—222no—
400C4—441no—
401C4—881no—
402C4—881no—
403C2—224no—
404C2#1306696111yescharacteristic
405C2#1306702811yescharacteristic
406C2#1306706911yescharacteristic
407C2D11×#32811yescharacteristic
408C2#1306711911yescharacteristic
409C2#1306720111yescharacteristic
410C2#1306730311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1272D11
hypocenterC11#7681
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #13066442C2semidirect
5. #13066440C2semidirect
6. #13066438C2semidirect
7. C11×#1272C2semidirect
122. #1272D11semidirect
322. C11#7681semidirect

Maximal subgroups

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

subgroupindex
#130769572
#130683082
D11×#3362
#130664422
#130664402
#130664382
C11×#12722
#768111