Finite Group Databasebeta

← #14727681

Subgroups — #14727681

Order 2816.

1220 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 187 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
1C2×#10623041C211yesmaximal, characteristic
2#13079369C212yesmaximal, complemented
3#13067652C214yesmaximal, complemented
4#13067584C214yesmaximal, complemented
5#13067183C212yesmaximal, complemented
6C2×#10622166C211yesmaximal, characteristic, complemented
7C11×#2627C211yesmaximal, characteristic, complemented
8C22×#4339—21no—
9C2×C11×C22⋊Q8C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#66983—21no—
12C2×#66983C2212yes—
13#10623041—22no—
14#10623041—24no—
15#10623041C2214yes—
16C2×#66950—22no—
17C2×#66948—22no—
18C11×#400C2212yescomplemented
19C11×#398—22no—
20C11×#395C2212yescomplemented
21C11×#385—21no—
22C11×#381—21no—
23C11×#380C2211yescharacteristic
24#10622840C2214yescomplemented
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622661—24no—
27#10622659—22no—
28#10622656—22no—
29#10622581C2214yescomplemented
30#10622166C2214yescomplemented
31#10622089C2218yescomplemented
32C22×Q8×C11C2311yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—22no—
37C2×#4339—24no—
38C2×#4339—24no—
39C2×#4339—44no—
40C2×#4339—44no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44D412yes—
44C22×C4×D11—22no—
45C22×Dic22—21no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×#4325—24no—
59#66983—24no—
60#66983—22no—
61#66983—22no—
62#66983—24no—
63#66983D414yes—
64#66983C2314yes—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D412yes—
69C22×C11⋊C8—22no—
70#66950—28no—
71#66950—28no—
72#66948—28no—
73#66948—28no—
74C11×#95—22no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95C2312yes—
78#66899—24no—
79C22⋊(C11⋊C8)—22no—
80C22⋊(C11⋊C8)C2314yes—
81#66873—24no—
82#66872—24no—
83#18293—111nomaximal, Sylow
84C24×C11C2×D411yescharacteristic
85C23×D11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—81no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—81no—
97C22×C4×C11—81no—
98C22×C4×C11SD1614yescomplemented
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2411yescharacteristic
105C2×C22⋊D11—24no—
106C2×C22⋊D11—24no—
107C2×C22⋊D11—44no—
108C2×C22⋊D11—44no—
109C22×Dic11—22no—
110#4339—48no—
111#4339—416no—
112#4339—48no—
113C2×D44—24no—
114C2×D44—24no—
115C2×D44—22no—
116C2×D44—44no—
117C2×D44—82no—
118C2×D44—82no—
119C2×D44C2×D414yes—
120C2×C4×D11—28no—
121C2×C4×D11—48no—
122C2×Dic22—24no—
123C2×Dic22—44no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—81no—
129C11×C4⋊C4—82no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—42no—
133#4325—84no—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—24no—
137C4⋊Dic11—24no—
138C4⋊Dic11—22no—
139C4⋊Dic11C2×D414yes—
140C2×C11⋊C8—24no—
141C2×C11⋊C8—82no—
142C2×#537—111no—
143#3187—112no—
144#2627D1111yescharacteristic, complemented
145#1616—114no—
146#1604—114no—
147#1519—112no—
148C2×#324—111no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#12011yescharacteristic
152C23×C11#12011yescharacteristic
153C23×C11C2×SD1612yes—
154C23×C11AGL(1,ℤ/8)12yes—
155C23×C11C22×D411yescharacteristic
156C22×D11—24no—
157C22×D11—44no—
158C22×D11—44no—
159C22×D11—44no—
160Q8×C11—44no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—81no—
180C2×C4×C11#12012yes—
181C2×C4×C11C2×SD1614yes—
182C2×C4×C11C22×D412yes—
183C22⋊D11—44no—
184C22⋊D11—44no—
185C22⋊D11—48no—
186C2×Dic11—24no—
187C2×Dic11—44no—
188D44—44no—
189D44—48no—
190D44—82no—
191D44—84no—
192C4×D11—416no—
193Dic22—48no—
194C11⋊C8—44no—
195C22×#41—221no—
196#537—114no—
197#537—224no—
198#537—222no—
199C2×C22⋊Q8—222no—
200C2×C22⋊Q8C2×D1111yescharacteristic
201C2×#121—112no—
202C2×#121—222no—
203C2×#121—221no—
204C22×C4⋊C4C2×D1111yescharacteristic
205#483—222no—
206#481—114no—
207#465—224no—
208#450—222no—
209#448—114no—
210C2×C22⋊C8—112no—
211#400C2×D1112yescomplemented
212#398—22no—
213#395C2×D1112yescomplemented
214#385—21no—
215#381—21no—
216#380C2×D1111yescharacteristic
217#327—118no—
218#324—114no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11#45012yes—
228C22×C11#45012yes—
229C22×C11C2×#12011yescharacteristic
230C22×C11C22×SD1611yescharacteristic
231C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
232C2×D11—44no—
233C2×D11—44no—
234C2×D11—44no—
235C2×D11—88no—
236C4×C11—24no—
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—42no—
240C4×C11—82no—
241C4×C11—81no—
242C4×C11—81no—
243Dic11—44no—
244C2×#41—224no—
245C2×#41—224no—
246C2×#41—444no—
247C2×#41—444no—
248C22×Q8—221no—
249C22×Q8C22×D1111yescharacteristic
250C22×D4—112no—
251C22×D4—221no—
252C22×D4—221no—
253C22×D4—222no—
254C23×C4—222no—
255C23×C4C22⋊D1111yescharacteristic
256C23×C4C22⋊D1111yescharacteristic
257C23×C4C22×D1111yescharacteristic
258C2×SD16—224no—
259C22×C8—222no—
260C22⋊Q8—22no—
261C22⋊Q8—22no—
262C22⋊Q8—228no—
263C22⋊Q8—228no—
264#121—114no—
265#121—114no—
266#121—228no—
267#121—228no—
268#121—224no—
269#121—222no—
270#121—222no—
271#121—224no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4C22⋊D1112yes—
280C2×C4⋊C4C22×D1111yescharacteristic
281C2×C4⋊C4C22×D1112yes—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—222no—
285C2×C22⋊C4—222no—
286#106—224no—
287#103—224no—
288#102—224no—
289C22⋊C8—114no—
290C22⋊C8—222no—
291#95—22no—
292#95—22no—
293#95—22no—
294#95C22×D1112yes—
295C2×C11—21no—
296C2×C11—22no—
297C2×C11—21no—
298C2×C11—22no—
299C2×C11C2×#45011yescharacteristic
300C2×C11#302011yescharacteristic
301C2×C11#302611yescharacteristic
302D11—84no—
303C24—222no—
304C24C2×C22⋊D1111yescharacteristic
305#41—448no—
306#41—4416no—
307#41—448no—
308C2×Q8—22no—
309C2×Q8—81no—
310C2×Q8—224no—
311C2×Q8—444no—
312C2×D4—114no—
313C2×D4—224no—
314C2×D4—224no—
315C2×D4—224no—
316C2×D4—224no—
317C2×D4—222no—
318C2×D4—444no—
319C2×D4—444no—
320C2×D4—444no—
321C2×D4—882no—
322C2×D4—882no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—81no—
332C22×C4—81no—
333C22×C4—228no—
334C22×C4—222no—
335C22×C4—448no—
336C22×C4#432514yescomplemented
337C22×C4D4×D1112yes—
338C22×C4D4×D1112yes—
339C22×C4C2×C22⋊D1112yes—
340C22×C4C2×C22⋊D1112yes—
341C22×C4C2×C22⋊D1111yescharacteristic
342C22×C4C23×D1111yescharacteristic
343SD16—884no—
344C2×C8—224no—
345C2×C8—882no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—22no—
349C4⋊C4—42no—
350C4⋊C4—81no—
351C4⋊C4—82no—
352C4⋊C4—114no—
353C4⋊C4—224no—
354C4⋊C4—222no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—42no—
358C22⋊C4—228no—
359C22⋊C4—224no—
360C22⋊C4—224no—
361C11#1829311yescharacteristic, complemented, Sylow
362C23—41no—
363C23—41no—
364C23—224no—
365C23—444no—
366C23—444no—
367C23—444no—
368C23#6699011yescharacteristic
369C23#6699011yescharacteristic
370C23C2×#432512yes—
371C23#6700212yes—
372C23C22×C22⋊D1111yescharacteristic
373Q8—44no—
374Q8—448no—
375D4—444no—
376D4—448no—
377D4—444no—
378D4—444no—
379D4—448no—
380D4—882no—
381D4—884no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—81no—
401C2×C4—224no—
402C2×C4—4416no—
403C2×C4—444no—
404C2×C4#6699012yes—
405C2×C4C2×#432514yes—
406C2×C4C2×D4×D1112yes—
407C8—444no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22—444no—
417C22—444no—
418C22—444no—
419C22—888no—
420C22#1062265912yes—
421C22#1062265912yes—
422C22C2×#6699011yescharacteristic
423C22C22×#432511yescharacteristic
424C22C2×#6700211yescharacteristic
425C4—24no—
426C4—22no—
427C4—22no—
428C4—42no—
429C4—82no—
430C4—81no—
431C4—81no—
432C4—444no—
433C2—21no—
434C2—22no—
435C2—21no—
436C2—22no—
437C2—884no—
438C2C2×#1062265911yescharacteristic
439C2#1307797911yescharacteristic
440C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2627C2
socleC22×C11C2×#120
prime radicalC2×#10623041C2
hypercenter#2627D11
hypocenterC11#18293
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
2. #13079369C2semidirect
3. #13067652C2semidirect
4. #13067584C2semidirect
5. #13067183C2semidirect
6. C2×#10622166C2semidirect
7. C11×#2627C2semidirect
18. C11×#400C22semidirect
20. C11×#395C22semidirect
24. #10622840C22semidirect
29. #10622581C22semidirect
30. #10622166C22semidirect
31. #10622089C22semidirect
98. C22×C4×C11SD16semidirect
144. #2627D11semidirect
211. #400C2×D11semidirect
213. #395C2×D11semidirect
336. C22×C4#4325semidirect
361. C11#18293semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
#130793692
#130676522
#130675842
#130671832
C2×#106221662
C11×#26272
#1829311