Finite Group Databasebeta

← #14727900

Subgroups — #14727900

Order 2816.

1058 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 183 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#13079437C212yesmaximal, complemented
2#13073774C211yesmaximal, characteristic
3#13067607C214yesmaximal, complemented
4#13067573C214yesmaximal, complemented
5#13067136C212yesmaximal, complemented
6#13066943C211yesmaximal, characteristic
7C2×C11×#543C211yesmaximal, characteristic
8C11×#543—24no—
9C11×#543—22no—
10C11×#543C2214yes—
11C2×C11×C22⋊Q8—22no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×C22⋊Q8C2212yes—
15C22×C11×C22⋊C4—21no—
16C22×C11×C22⋊C4C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18#10622860—21no—
19#10622841—22no—
20#10622824—21no—
21C4×C22⋊Dic11C2211yescharacteristic
22#10622820C2212yes—
23#10622665—24no—
24#10622663C2214yescomplemented
25#10622656C2214yescomplemented
26#10622584—22no—
27#10622566C2212yes—
28#10622560C2212yes—
29#10622558—22no—
30#10622176C2218yescomplemented
31#10622163C2214yes—
32C25×C11D411yescharacteristic
33C22×Q8×C11—21no—
34C22×Q8×C11D412yes—
35C23×C4×C11—21no—
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×Dic22C2311yescharacteristic
40C11×C22⋊Q8—28no—
41C11×C22⋊Q8—28no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8D414yes—
49C11×C22⋊Q8C2314yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4D412yes—
61C2×C11×C22⋊C4C2312yes—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—22no—
66C2×#4326—24no—
67C2×C4⋊Dic11C2311yescharacteristic
68#66977—22no—
69#66977—22no—
70C2×Dic11⋊C4—21no—
71C2×C4×Dic11—21no—
72C2×#4318—22no—
73#66899—24no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95C2312yes—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)C2314yes—
79#66874—24no—
80#66872—24no—
81#18319—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—24no—
85C24×C11—42no—
86C24×C11—81no—
87C24×C11C2×D411yescharacteristic
88C24×C11C2×D412yes—
89C2×Q8×C11—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—82no—
92C2×Q8×C11—82no—
93C2×Q8×C11C2×D414yes—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—21no—
100C22×C4×C11—42no—
101C22×C4×C11—81no—
102C22×C4×C11—82no—
103C22×C4×C11—82no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—22no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C2×Dic22—22no—
113C2×Dic22—81no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4C2×D414yes—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—24no—
125C22⋊Dic11—42no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—44no—
129C22⋊Dic11—82no—
130#4326—84no—
131C4⋊Dic11—22no—
132Dic11⋊C4—42no—
133C4×Dic11—81no—
134#4318—82no—
135C2×C11⋊C8—24no—
136C2×#543D1111yescharacteristic
137#3195—112no—
138#2561—111no—
139#1608—114no—
140#1602—114no—
141#1508—112no—
142#1462—111no—
143C23×C11—24no—
144C23×C11—24no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—81no—
155C23×C11—81no—
156C23×C11—88no—
157C23×C11#12011yescharacteristic
158C23×C11#12011yescharacteristic
159C23×C11#13714yes—
160C23×C11C22×D411yescharacteristic
161Q8×C11—44no—
162Q8×C11—82no—
163Q8×C11—84no—
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—44no—
172C2×C4×C11—42no—
173C2×C4×C11—44no—
174C2×C4×C11—42no—
175C2×C4×C11—81no—
176C2×C4×C11—84no—
177C2×C4×C11—84no—
178C2×C4×C11#12012yes—
179C2×C4×C11C22×D412yes—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187Dic22—44no—
188C11⋊C8—44no—
189#543—24no—
190#543—22no—
191#543C2×D1114yes—
192C2×C22⋊Q8—22no—
193C2×C22⋊Q8—21no—
194C2×C22⋊Q8—22no—
195C2×C22⋊Q8—111no—
196C2×C22⋊Q8C2×D1112yes—
197C22×C22⋊C4—21no—
198C22×C22⋊C4C2×D1111yescharacteristic
199#483—114no—
200#483—222no—
201#470—224no—
202#451—114no—
203#451—222no—
204#407—112no—
205#397—112no—
206#393—112no—
207#388—222no—
208#381—221no—
209#379—221no—
210C4×C22⋊C4—111no—
211#328—118no—
212#323—114no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—24no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—44no—
222C22×C11—44no—
223C22×C11—48no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—82no—
227C22×C11—84no—
228C22×C11#45512yes—
229C22×C11C2×#12011yescharacteristic
230C22×C11C2×#13712yes—
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—42no—
234C4×C11—44no—
235C4×C11—44no—
236Dic11—82no—
237Dic11—81no—
238Dic11—81no—
239C25C22⋊D1111yescharacteristic
240C22×Q8—21no—
241C22×Q8—111no—
242C22×Q8C22⋊D1112yes—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4C22⋊D1111yescharacteristic
246C23×C4C22×D1111yescharacteristic
247C2×Q16—224no—
248C2×M16—222no—
249C22⋊Q8—28no—
250C22⋊Q8—28no—
251C22⋊Q8—24no—
252C22⋊Q8—28no—
253C22⋊Q8—24no—
254C22⋊Q8—22no—
255C22⋊Q8—22no—
256C22⋊Q8—28no—
257C22⋊Q8—222no—
258C22⋊Q8—222no—
259C22⋊Q8C22⋊D1114yes—
260C22⋊Q8C22×D1114yes—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4C22⋊D1112yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—221no—
274C2×C22⋊C4—221no—
275C2×C22⋊C4—222no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4C22⋊D1112yes—
278C2×C22⋊C4C22×D1112yes—
279C2×C42—221no—
280#106—224no—
281#103—224no—
282#103—224no—
283C22⋊C8—114no—
284C22⋊C8—222no—
285#95—112no—
286#95—222no—
287#95—222no—
288C2×C11—22no—
289C2×C11—22no—
290C2×C11—41no—
291C2×C11—44no—
292C2×C11#300411yescharacteristic
293C2×C11C2×#45511yescharacteristic
294C2×C11#302611yescharacteristic
295C24—21no—
296C24—24no—
297C24—21no—
298C24—42no—
299C24—81no—
300C24C2×C22⋊D1111yescharacteristic
301C24C2×C22⋊D1112yes—
302C2×Q8—24no—
303C2×Q8—22no—
304C2×Q8—82no—
305C2×Q8—82no—
306C2×Q8—222no—
307C2×Q8—881no—
308C2×Q8C2×C22⋊D1114yes—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—81no—
317C22×C4—82no—
318C22×C4—82no—
319C22×C4—222no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1111yescharacteristic
324C22×C4C2×C22⋊D1112yes—
325C22×C4C2×C22⋊D1112yes—
326C22×C4C23×D1111yescharacteristic
327Q16—884no—
328M16—882no—
329C2×C8—224no—
330C4⋊C4—24no—
331C4⋊C4—28no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—222no—
336C4⋊C4—442no—
337C4⋊C4C2×C22⋊D1114yes—
338C22⋊C4—28no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—442no—
344C22⋊C4—444no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—882no—
348C42—881no—
349C11#1831911yescharacteristic, complemented, Sylow
350C23—24no—
351C23—24no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—41no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—81no—
362C23—81no—
363C23—88no—
364C23#6699514yes—
365C23#6700611yescharacteristic
366C23#6700611yescharacteristic
367C23C22×C22⋊D1111yescharacteristic
368Q8—44no—
369Q8—82no—
370Q8—84no—
371Q8—444no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—81no—
384C2×C4—84no—
385C2×C4—84no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4#6700612yes—
394C2×C4C22×C22⋊D1112yes—
395C8—444no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—24no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—44no—
405C22—44no—
406C22—48no—
407C22—42no—
408C22—42no—
409C22—82no—
410C22—84no—
411C22#1062285512yes—
412C22C2×#6699512yes—
413C22C2×#6700611yescharacteristic
414C4—22no—
415C4—22no—
416C4—42no—
417C4—44no—
418C4—44no—
419C4—882no—
420C4—881no—
421C4—881no—
422C2—22no—
423C2—22no—
424C2—41no—
425C2—44no—
426C2#1307785011yescharacteristic
427C2C2×#1062285511yescharacteristic
428C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#543C2
socleC22×C11C2×#120
prime radicalC25×C11D4
hypercenterC2×#543D11
hypocenterC11#18319
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #13079437C2semidirect
3. #13067607C2semidirect
4. #13067573C2semidirect
5. #13067136C2semidirect
24. #10622663C22semidirect
25. #10622656C22semidirect
30. #10622176C22semidirect
349. C11#18319semidirect

Maximal subgroups

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

subgroupindex
#130794372
#130737742
#130676072
#130675732
#130671362
#130669432
C2×C11×#5432
#1831911