Finite Group Databasebeta

← #14926328

Subgroups — #14926328

Order 2816.

4046 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2#13076903C214yesmaximal, complemented
3#13074421C214yesmaximal, complemented
4#13072277C2116yesmaximal, complemented
5#13071230C211yesmaximal, characteristic, complemented
6#13071228C212yesmaximal, complemented
7C2×#10622860C212yesmaximal
8C23×C11×C22⋊C4C211yesmaximal, characteristic
9C26×C11C2211yescharacteristic
10C24×C4×C11C2212yes—
11C22×C11×C22⋊C4—28no—
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2218yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2218yes—
19C2×#66977C2214yescomplemented
20C2×#66977C2218yescomplemented
21#10623014—28no—
22C2×#66931C2218yescomplemented
23#10622860C2218yes—
24#10622860C2214yes—
25#10622860C2214yes—
26#10622825C2214yescomplemented
27#10622825C2218yescomplemented
28#10622823C2218yescomplemented
29#10622823C22116yescomplemented
30#10622563C2218yescomplemented
31#10622562C2218yescomplemented
32#10622561C22116yescomplemented
33#10622560C2218yescomplemented
34#10622559C2218yescomplemented
35#10622555C2218yescomplemented
36C25×C11—24no—
37C25×C11—24no—
38C25×C11—48no—
39C25×C11Q818yescomplemented
40C25×C11C2311yescharacteristic
41C25×C11C2314yes—
42C25×C11C2311yescharacteristic
43C25×C11C2311yescharacteristic
44C23×C4×C11—28no—
45C23×C4×C11—48no—
46C23×C4×C11C2318yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×Dic11C2314yes—
50C23×Dic11C2314yes—
51C22×Dic22C2314yescomplemented
52C2×C11×C22⋊C4—24no—
53C2×C11×C22⋊C4—28no—
54C2×C11×C22⋊C4—232no—
55C2×C11×C22⋊C4D418yes—
56C2×C11×C22⋊C4C2314yes—
57C2×C11×C22⋊C4C2318yes—
58C2×C11×C22⋊C4C2314yes—
59C2×C22⋊Dic11—28no—
60C2×C22⋊Dic11—28no—
61C2×C22⋊Dic11—416no—
62C2×C22⋊Dic11C2314yes—
63C2×C22⋊Dic11C2314yes—
64C2×C22⋊Dic11C23116yes—
65C2×C22⋊Dic11C2314yes—
66C2×C22⋊Dic11C2314yes—
67C2×C22⋊Dic11C23116yes—
68C2×C4⋊Dic11C2314yescomplemented
69C2×C4⋊Dic11C2318yescomplemented
70#66977—216no—
71#66977—416no—
72C2×Dic11⋊C4C2318yescomplemented
73C2×Dic11⋊C4C23116yescomplemented
74#66931—232no—
75C11⋊#95C23116yescomplemented
76C11⋊#95C2318yescomplemented
77#34982—111nomaximal, Sylow
78C24×C11—22no—
79C24×C11—22no—
80C24×C11—28no—
81C24×C11—232no—
82C24×C11—28no—
83C24×C11—22no—
84C24×C11—28no—
85C24×C11—22no—
86C24×C11—216no—
87C24×C11—432no—
88C24×C11—44no—
89C24×C11—48no—
90C24×C11—44no—
91C24×C11—432no—
92C24×C11—432no—
93C24×C11C2×D414yes—
94C24×C11C2×Q814yes—
95C24×C11C2×Q8116yes—
96C24×C11C2×Q814yes—
97C24×C11C2×Q814yes—
98C24×C11#4114yes—
99C24×C11C2412yes—
100C24×C11C2411yescharacteristic
101C24×C11C2412yes—
102C24×C11C2412yes—
103C22×C4×C11—24no—
104C22×C4×C11—216no—
105C22×C4×C11—216no—
106C22×C4×C11—44no—
107C22×C4×C11—48no—
108C22×C4×C11—44no—
109C22×C4×C11—432no—
110C22×C4×C11C2×D418yes—
111C22×C4×C11C2414yes—
112C22×C4×C11C2414yes—
113C22×Dic11—28no—
114C22×Dic11—28no—
115C22×Dic11—48no—
116C22×Dic11—48no—
117C22×Dic11C2418yes—
118C22×Dic11C2418yes—
119C2×Dic22—28no—
120C2×Dic22—48no—
121C11×C22⋊C4—28no—
122C11×C22⋊C4—216no—
123C11×C22⋊C4C2×D4116yes—
124C22⋊Dic11—28no—
125C22⋊Dic11—28no—
126C22⋊Dic11—28no—
127C22⋊Dic11—28no—
128C22⋊Dic11—232no—
129C22⋊Dic11—416no—
130C4⋊Dic11—28no—
131C4⋊Dic11—48no—
132Dic11⋊C4—216no—
133Dic11⋊C4—416no—
134C2×#543—111no—
135C23×C22⋊C4D1111yescharacteristic
136#2848—114no—
137#2626—114no—
138#2437—1116no—
139#2315—112no—
140#2315—111no—
141C2×#379—112no—
142C23×C11—216no—
143C23×C11—216no—
144C23×C11—28no—
145C23×C11—216no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—28no—
149C23×C11—24no—
150C23×C11—24no—
151C23×C11—232no—
152C23×C11—28no—
153C23×C11—232no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—28no—
157C23×C11—48no—
158C23×C11—48no—
159C23×C11—416no—
160C23×C11—48no—
161C23×C11—48no—
162C23×C11—432no—
163C23×C11—432no—
164C23×C11—4128no—
165C23×C11—48no—
166C23×C11—48no—
167C23×C11C22⋊Q8116yescomplemented
168C23×C11C22×D412yes—
169C23×C11C22×D414yes—
170C23×C11C22×Q814yes—
171C23×C11C22×Q812yes—
172C23×C11C22×Q814yes—
173C23×C11C22×Q814yes—
174C23×C11C2×#4112yes—
175C23×C11C2×#4114yes—
176C23×C11H(5,𝔽2)18yes—
177C23×C11C2511yescharacteristic
178C2×C4×C11—28no—
179C2×C4×C11—24no—
180C2×C4×C11—28no—
181C2×C4×C11—48no—
182C2×C4×C11—432no—
183C2×C4×C11—48no—
184C2×C4×C11C22×D418yes—
185C2×Dic11—28no—
186C2×Dic11—28no—
187C2×Dic11—216no—
188C2×Dic11—216no—
189C2×Dic11—88no—
190C2×Dic11—88no—
191Dic22—88no—
192C26C2×D1111yescharacteristic
193C24×C4C2×D1112yes—
194#543—228no—
195C2×C22⋊Q8—114no—
196C2×C22⋊Q8—118no—
197C2×C22⋊Q8—118no—
198C22×C22⋊C4—28no—
199C22×C22⋊C4—112no—
200C22×C22⋊C4—112no—
201C22×C22⋊C4—118no—
202C22×C22⋊C4C2×D1111yescharacteristic
203C22×C22⋊C4C2×D1112yes—
204C22×C22⋊C4C2×D1118yes—
205C22×C22⋊C4C2×D1111yescharacteristic
206#399—118no—
207#396—1116no—
208#393—118no—
209#385—118no—
210#385—1116no—
211#385—118no—
212#385—118no—
213#380—114no—
214#380—118no—
215#380—118no—
216#379—114no—
217#379—114no—
218#379—118no—
219C22×C11—232no—
220C22×C11—24no—
221C22×C11—24no—
222C22×C11—24no—
223C22×C11—28no—
224C22×C11—24no—
225C22×C11—28no—
226C22×C11—28no—
227C22×C11—24no—
228C22×C11—28no—
229C22×C11—28no—
230C22×C11—24no—
231C22×C11—28no—
232C22×C11—416no—
233C22×C11—464no—
234C22×C11—416no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11C2×C22⋊Q814yes—
238C22×C11C2×C22⋊Q818yes—
239C22×C11#54318yescomplemented
240C22×C11C23×D411yescharacteristic
241C22×C11C23×Q811yescharacteristic
242C22×C11C22×#4111yescharacteristic
243C22×C11C2×H(5,𝔽2)14yes—
244C4×C11—28no—
245C4×C11—44no—
246Dic11—48no—
247Dic11—48no—
248C25—24no—
249C25—24no—
250C25—48no—
251C25Dic2218yescomplemented
252C25C22×D1111yescharacteristic
253C25C22×D1114yes—
254C25C22×D1111yescharacteristic
255C25C22×D1111yescharacteristic
256C22×Q8—114no—
257C23×C4—28no—
258C23×C4—48no—
259C23×C4—114no—
260C23×C4—114no—
261C23×C4C22×D1118yes—
262C23×C4C22×D1112yes—
263C23×C4C22×D1112yes—
264C22⋊Q8—2216no—
265C22⋊Q8—2232no—
266C22⋊Q8—4416no—
267C2×C4⋊C4—114no—
268C2×C4⋊C4—118no—
269C2×C4⋊C4—118no—
270C2×C4⋊C4—1116no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—28no—
273C2×C22⋊C4—232no—
274C2×C22⋊C4—114no—
275C2×C22⋊C4—114no—
276C2×C22⋊C4—1116no—
277C2×C22⋊C4—114no—
278C2×C22⋊C4—114no—
279C2×C22⋊C4—1116no—
280C2×C22⋊C4—228no—
281C2×C22⋊C4—228no—
282C2×C22⋊C4—4416no—
283C2×C22⋊C4C22⋊D1118yes—
284C2×C22⋊C4C22×D1114yes—
285C2×C22⋊C4C22×D1118yes—
286C2×C22⋊C4C22×D1114yes—
287#95—1116no—
288#95—118no—
289C2×C11—24no—
290C2×C11—28no—
291C2×C11—28no—
292C2×C11—44no—
293C2×C11C22×C22⋊Q811yescharacteristic
294C2×C11C2×#54312yes—
295C2×C11#348412yes—
296C2×C11#349012yes—
297C24—22no—
298C24—28no—
299C24—22no—
300C24—232no—
301C24—28no—
302C24—22no—
303C24—216no—
304C24—28no—
305C24—22no—
306C24—44no—
307C24—48no—
308C24—44no—
309C24—432no—
310C24—432no—
311C24—432no—
312C24C2×Dic2214yes—
313C24C2×Dic22116yes—
314C24C2×Dic2214yes—
315C24C2×Dic2214yes—
316C24#433914yes—
317C24C2×C22⋊D1114yes—
318C24C23×D1112yes—
319C24C23×D1111yescharacteristic
320C24C23×D1112yes—
321C24C23×D1112yes—
322C2×Q8—228no—
323C2×Q8—448no—
324C22×C4—216no—
325C22×C4—24no—
326C22×C4—216no—
327C22×C4—44no—
328C22×C4—48no—
329C22×C4—44no—
330C22×C4—432no—
331C22×C4—118no—
332C22×C4—118no—
333C22×C4—228no—
334C22×C4—228no—
335C22×C4—448no—
336C22×C4—448no—
337C22×C4C2×C22⋊D1118yes—
338C22×C4C23×D1114yes—
339C22×C4C23×D1114yes—
340C4⋊C4—2216no—
341C4⋊C4—228no—
342C4⋊C4—4416no—
343C4⋊C4—448no—
344C22⋊C4—28no—
345C22⋊C4—216no—
346C22⋊C4—228no—
347C22⋊C4—228no—
348C22⋊C4—2232no—
349C22⋊C4—228no—
350C22⋊C4—228no—
351C22⋊C4—4416no—
352C22⋊C4C2×C22⋊D11116yes—
353C11#3498211yescharacteristic, complemented, Sylow
354C23—216no—
355C23—216no—
356C23—216no—
357C23—28no—
358C23—22no—
359C23—24no—
360C23—24no—
361C23—28no—
362C23—22no—
363C23—232no—
364C23—232no—
365C23—28no—
366C23—22no—
367C23—28no—
368C23—22no—
369C23—48no—
370C23—416no—
371C23—48no—
372C23—48no—
373C23—48no—
374C23—432no—
375C23—432no—
376C23—4128no—
377C23—48no—
378C23—48no—
379C23#66977116yescomplemented
380C23C22×Dic2214yes—
381C23C22×Dic2214yes—
382C23C22×Dic2212yes—
383C23C22×Dic2214yes—
384C23C2×#433912yes—
385C23C2×#433914yes—
386C23#6703718yes—
387C23C22×C22⋊D1114yes—
388C23C22×C22⋊D1112yes—
389C23C24×D1111yescharacteristic
390Q8—888no—
391C2×C4—28no—
392C2×C4—28no—
393C2×C4—24no—
394C2×C4—48no—
395C2×C4—432no—
396C2×C4—48no—
397C2×C4—228no—
398C2×C4—2216no—
399C2×C4—2216no—
400C2×C4—228no—
401C2×C4—888no—
402C2×C4—888no—
403C2×C4C22×C22⋊D1118yes—
404C22—232no—
405C22—28no—
406C22—24no—
407C22—28no—
408C22—24no—
409C22—24no—
410C22—28no—
411C22—28no—
412C22—24no—
413C22—28no—
414C22—24no—
415C22—28no—
416C22—24no—
417C22—416no—
418C22—464no—
419C22—416no—
420C22—44no—
421C22—44no—
422C22#1062301418yescomplemented
423C22C2×#6697714yes—
424C22C2×#6697718yes—
425C22C23×Dic2211yescharacteristic
426C22C22×#433911yescharacteristic
427C22C2×#6703714yes—
428C22C23×C22⋊D1111yescharacteristic
429C4—28no—
430C4—44no—
431C4—448no—
432C4—448no—
433C2—28no—
434C2—24no—
435C2—28no—
436C2—44no—
437C2C22×#6697711yescharacteristic
438C2C2×#1062301412yes—
439C2#1308225112yes—
440C2#1308230512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC23×C11×C22⋊C4C2
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11#34982
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
2. #13076903C2semidirect
3. #13074421C2semidirect
4. #13072277C2semidirect
5. #13071230C2semidirect
6. #13071228C2semidirect
19. C2×#66977C22semidirect
20. C2×#66977C22semidirect
22. C2×#66931C22semidirect
26. #10622825C22semidirect
27. #10622825C22semidirect
28. #10622823C22semidirect
29. #10622823C22semidirect
30. #10622563C22semidirect
31. #10622562C22semidirect
32. #10622561C22semidirect
33. #10622560C22semidirect
34. #10622559C22semidirect
35. #10622555C22semidirect
39. C25×C11Q8semidirect
51. C22×Dic22C23semidirect
68. C2×C4⋊Dic11C23semidirect
69. C2×C4⋊Dic11C23semidirect
72. C2×Dic11⋊C4C23semidirect
73. C2×Dic11⋊C4C23semidirect
75. C11⋊#95C23semidirect
76. C11⋊#95C23semidirect
167. C23×C11C22⋊Q8semidirect
239. C22×C11#543semidirect
251. C25Dic22semidirect
353. C11#34982semidirect
379. C23#66977semidirect
422. C22#10623014semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130769032
#130744212
#130722772
#130712302
#130712282
C2×#106228602
C23×C11×C22⋊C42
#3498211