Finite Group Databasebeta

← #14726816

Subgroups — #14726816

Order 2816.

1338 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1338 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
1#13082380C211yesmaximal, characteristic, complemented
2#13078616C212yesmaximal, complemented
3#13067601C214yesmaximal, complemented
4#13067533C214yesmaximal, complemented
5#13067175C212yesmaximal, complemented
6#13066937C211yesmaximal, characteristic, complemented
7C11×#2535C211yesmaximal, characteristic, complemented
8C2×#67037—21no—
9C2×C11×#121—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic, complemented
12C2×#66983—22no—
13#10623086—22no—
14#10623085—24no—
15D4×D44—22no—
16#10623041—21no—
17#10623024C2214yes—
18#10623008C2212yes—
19C11×#397C2212yescomplemented
20C11×#392C2212yescomplemented
21C11×#386—22no—
22C11×#382C2211yescharacteristic, complemented
23C11×#380—21no—
24#10622830C2214yescomplemented
25#10622628—22no—
26C4×#4323—24no—
27#10622620—22no—
28#10622580C2214yescomplemented
29#10622538C2212yescomplemented
30#10622163C2214yescomplemented
31#10622089C2218yescomplemented
32C22×D4×C11—22no—
33C22×D4×C11D411yescharacteristic
34C22×D4×C11C2311yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11D412yes—
37C22×C22⋊D11—24no—
38#67037—44no—
39#67037—44no—
40C2×#4341—24no—
41C2×D4×D11—24no—
42C2×#4339—22no—
43C22×D44—22no—
44C11×#121—44no—
45C4×D4×C11—22no—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×#4323—24no—
58#66983—24no—
59#66983—24no—
60#66983—22no—
61#66983—24no—
62#66983C2314yes—
63C2×(C2×D11)⋊C4—24no—
64C2×C4⋊Dic11—22no—
65#66950—24no—
66#66948—24no—
67#66939—28no—
68#66935—28no—
69#66928—22no—
70#66927D412yescomplemented
71C4×D44—22no—
72C4×D44D414yescomplemented
73#66922D412yescomplemented
74C11×#95—22no—
75C11×#95—21no—
76C11×#95C2312yes—
77#66896—24no—
78C22⋊(C11⋊C8)C2314yes—
79#66873—24no—
80#66871—24no—
81C4⋊(C11⋊C8)—22no—
82C4×C11⋊C8—22no—
83#18210—111nomaximal, Sylow
84C24×C11—21no—
85C24×C11C2×D412yes—
86C23×D11—24no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—42no—
91C2×D4×C11—44no—
92C2×D4×C11—44no—
93C2×D4×C11—82no—
94C2×D4×C11D814yescomplemented
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—82no—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—28no—
108C2×C22⋊D11—24no—
109C2×C22⋊D11—48no—
110C2×C22⋊D11—48no—
111C22×Dic11—24no—
112#4341—416no—
113D4×D11—416no—
114#4339—44no—
115#4339—44no—
116C2×D44—24no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—84no—
120C2×D44C2×D414yes—
121C2×C4×D11—24no—
122C2×Dic22—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—42no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—44no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—82no—
131C42×C11C2×D412yes—
132C42×C11C2×D412yes—
133#4323—48no—
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—
141#3496—111no—
142#3100—112no—
143#2535D1111yescharacteristic, complemented
144#1607—114no—
145#1595—114no—
146#1517—112no—
147#1460—111no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11C2×D814yes—
160C23×C11C22×D411yescharacteristic
161C22×D11—24no—
162C22×D11—48no—
163C22×D11—84no—
164C22×D11—84no—
165D4×C11—24no—
166D4×C11—28no—
167D4×C11—42no—
168D4×C11—88no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—44no—
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—41no—
180C2×C4×C11—82no—
181C2×C4×C11—84no—
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12012yes—
185C2×C4×C11C2×D812yes—
186C2×C4×C11AGL(1,ℤ/8)12yes—
187C2×C4×C11C22×D412yes—
188C22⋊D11—416no—
189C22⋊D11—44no—
190C22⋊D11—44no—
191C2×Dic11—24no—
192C2×Dic11—48no—
193D44—44no—
194D44—44no—
195D44—44no—
196D44—84no—
197C4×D11—48no—
198Dic22—44no—
199C11⋊C8—44no—
200C2×H(5,𝔽2)—221no—
201#547—222no—
202#546—224no—
203D42—222no—
204#537—221no—
205#534—114no—
206#532—112no—
207C2×#121—21no—
208C2×#121—222no—
209C2×C4×D4C2×D1111yescharacteristic
210C2×C4×D4C2×D1111yescharacteristic, complemented
211#480—114no—
212#474—222no—
213#459—222no—
214#447—114no—
215C4×D8—224no—
216#431—112no—
217#397C2×D1112yescomplemented
218#392C2×D1112yescomplemented
219#386—22no—
220#382C2×D1111yescharacteristic, complemented
221#380—21no—
222#327—118no—
223#323—114no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—24no—
227C22×C11—44no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—82no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11C2×#12011yescharacteristic
239C22×C11C22×D811yescharacteristic
240C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
241C2×D11—44no—
242C2×D11—44no—
243C2×D11—44no—
244C2×D11—168no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—22no—
248C4×C11—42no—
249C4×C11—82no—
250C4×C11—81no—
251C4×C11#44714yes—
252Dic11—44no—
253H(5,𝔽2)—444no—
254H(5,𝔽2)—444no—
255C2×#41—224no—
256C2×#41—222no—
257C22×D4—22no—
258C22×D4—222no—
259C22×D4—224no—
260C22×D4—224no—
261C22×D4C22⋊D1111yescharacteristic
262C22×D4C22×D1111yescharacteristic
263C23×C4—21no—
264C23×C4C22⋊D1112yes—
265C2×D8—224no—
266C4⋊Q8—112no—
267#127—112no—
268#124—222no—
269#123—228no—
270C22⋊Q8—224no—
271#121—44no—
272#121—114no—
273#121—224no—
274#121—224no—
275#121—224no—
276#121—222no—
277#121—224no—
278#120—228no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—114no—
284C4×D4—222no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4C22⋊D1111yescharacteristic
288C2×C4⋊C4C22×D1111yescharacteristic
289C2×C22⋊C4—22no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—224no—
293C2×C22⋊C4C22×D1112yes—
294C2×C42C22×D1111yescharacteristic
295#107—224no—
296C4⋊C8—222no—
297#102—224no—
298#102—224no—
299C22⋊C8—114no—
300C4×C8—222no—
301#95—22no—
302#95—21no—
303#95C22×D1112yes—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—44no—
307C2×C11—82no—
308C2×C11C2×#44711yescharacteristic
309C2×C11#301911yescharacteristic
310C2×C11#302511yescharacteristic
311D11—84no—
312C24—21no—
313C24—224no—
314C24C2×C22⋊D1112yes—
315#41—4416no—
316#41—444no—
317#41—444no—
318C2×Q8—222no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—42no—
323C2×D4—44no—
324C2×D4—44no—
325C2×D4—82no—
326C2×D4—114no—
327C2×D4—224no—
328C2×D4—228no—
329C2×D4—224no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—4416no—
333C2×D4—448no—
334C2×D4—448no—
335C2×D4—884no—
336C2×D4#432314yescomplemented
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—82no—
345C22×C4—224no—
346C22×C4—224no—
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351D8—448no—
352C2×C8—224no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—42no—
356C4⋊C4—114no—
357C4⋊C4—224no—
358C4⋊C4—222no—
359C22⋊C4—24no—
360C22⋊C4—44no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—82no—
364C22⋊C4—228no—
365C22⋊C4—224no—
366C22⋊C4—224no—
367C42D4×D1112yes—
368C42D4×D1112yes—
369C11#1821011yescharacteristic, complemented, Sylow
370C23—22no—
371C23—22no—
372C23—22no—
373C23—42no—
374C23—42no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—224no—
382C23—448no—
383C23—884no—
384C23—884no—
385C23C2×#432314yes—
386C23C22×C22⋊D1111yescharacteristic
387Q8—444no—
388D4—24no—
389D4—28no—
390D4—42no—
391D4—88no—
392D4—444no—
393D4—444no—
394D4—4416no—
395D4—444no—
396D4—444no—
397D4—444no—
398D4—884no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—82no—
411C2×C4—84no—
412C2×C4—224no—
413C2×C4—448no—
414C2×C4—448no—
415C2×C4C2×#432312yes—
416C2×C4#6699011yescharacteristic
417C2×C4#6699011yescharacteristic
418C2×C4#6699012yes—
419C2×C4#6700212yes—
420C2×C4C2×D4×D1112yes—
421C8—444no—
422C22—21no—
423C22—21no—
424C22—24no—
425C22—44no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—82no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22—444no—
437C22—444no—
438C22—444no—
439C22—1768no—
440C22C22×#432311yescharacteristic
441C22C2×#6699011yescharacteristic
442C22C2×#6700211yescharacteristic
443C4—21no—
444C4—21no—
445C4—22no—
446C4—42no—
447C4—82no—
448C4—81no—
449C4—444no—
450C4#1062264914yes—
451C2—21no—
452C2—21no—
453C2—44no—
454C2—82no—
455C2—884no—
456C2C2×#1062264911yescharacteristic
457C2#1307797211yescharacteristic
458C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2535C2
socleC22×C11C2×#120
hypercenter#2535D11
hypocenterC11#18210
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. #13082380C2semidirect
2. #13078616C2semidirect
3. #13067601C2semidirect
4. #13067533C2semidirect
5. #13067175C2semidirect
6. #13066937C2semidirect
7. C11×#2535C2semidirect
11. C2×C4×D4×C11C22semidirect
19. C11×#397C22semidirect
20. C11×#392C22semidirect
22. C11×#382C22semidirect
24. #10622830C22semidirect
28. #10622580C22semidirect
29. #10622538C22semidirect
30. #10622163C22semidirect
31. #10622089C22semidirect
70. #66927D4semidirect
72. C4×D44D4semidirect
73. #66922D4semidirect
94. C2×D4×C11D8semidirect
143. #2535D11semidirect
210. C2×C4×D4C2×D11semidirect
217. #397C2×D11semidirect
218. #392C2×D11semidirect
220. #382C2×D11semidirect
336. C2×D4#4323semidirect
369. C11#18210semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130786162
#130676012
#130675332
#130671752
#130669372
C11×#25352
#1821011