Finite Group Databasebeta

← #14685105

Subgroups — #14685105

Order 2816.

2842 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622833C212yesmaximal
3C2×#10622824C211yesmaximal, characteristic, complemented
4#13066853C214yesmaximal, complemented
5#13066848C214yesmaximal, complemented
6#13066838C212yesmaximal, complemented
7C22×C11×#123C211yesmaximal, characteristic
8C23×D4×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C24×Dic11C2212yes—
11C2×C11×#123—24no—
12C2×C11×#123—24no—
13C2×C11×#123C418yescomplemented
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2214yes—
19C22×C4×Dic11—24no—
20C22×C4×Dic11—28no—
21C22×C4×Dic11C2214yes—
22#10622833—28no—
23#10622824—24no—
24C2×C11⋊#95C2218yes—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C25×C11C2311yescharacteristic
28C25×C11C2311yescharacteristic
29C22×D4×C11—24no—
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—24no—
33C22×D4×C11C2×C414yes—
34C23×C4×C11—24no—
35C23×C4×C11—24no—
36C23×C4×C11C2×C414yes—
37C23×C4×C11D414yes—
38C23×C4×C11D414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×Dic11—24no—
43C23×Dic11—24no—
44C23×Dic11—216no—
45C23×Dic11D418yes—
46C23×Dic11C2314yes—
47C23×Dic11C2314yes—
48C11×#123—232no—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4C2×C418yescomplemented
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4C2×C414yes—
57C2×C11×C22⋊C4C2×C418yescomplemented
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—28no—
62C2×C22⋊Dic11—216no—
63C2×C4×Dic11—232no—
64C2×C4×Dic11—28no—
65C2×C4×Dic11—216no—
66C11⋊#95—28no—
67C11⋊#95—28no—
68C11⋊#95—216no—
69#14706—111nomaximal, Sylow
70C24×C11—28no—
71C24×C11—22no—
72C24×C11—21no—
73C24×C11—21no—
74C24×C11—28no—
75C24×C11—22no—
76C24×C11C22×C412yes—
77C24×C11C22×C412yes—
78C24×C11C2×D412yes—
79C24×C11C2×D412yes—
80C24×C11C2×D414yes—
81C24×C11#4114yes—
82C24×C11C2411yescharacteristic
83C2×D4×C11—28no—
84C2×D4×C11—216no—
85C2×D4×C11—44no—
86C2×D4×C11—48no—
87C2×D4×C11—44no—
88C22×C4×C11—216no—
89C22×C4×C11—28no—
90C22×C4×C11—216no—
91C22×C4×C11—28no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—28no—
100C22×C4×C11—22no—
101C22×C4×C11C22⋊C4116yescomplemented
102C22×C4×C11C22×C414yes—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C22×C414yes—
105C22×C4×C11C2×D414yes—
106C22×C4×C11C2×D414yes—
107C22×Dic11—232no—
108C22×Dic11—232no—
109C22×Dic11—232no—
110C22×Dic11—216no—
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11—24no—
114C22×Dic11—24no—
115C22×Dic11—28no—
116C22×Dic11—28no—
117C22×Dic11—24no—
118C22×Dic11—28no—
119C22×Dic11C2×D418yes—
120C22×Dic11#41116yes—
121C11×C4⋊C4—216no—
122C11×C22⋊C4—28no—
123C11×C22⋊C4—216no—
124C22⋊Dic11—416no—
125C22⋊Dic11—48no—
126C4×Dic11—232no—
127C22×#123D1111yescharacteristic
128C23×C42—111no—
129C2×#386—112no—
130C2×#381—111no—
131#1437—114no—
132#1436—114no—
133C22⋊#95—112no—
134C23×C11—28no—
135C23×C11—28no—
136C23×C11—28no—
137C23×C11—28no—
138C23×C11—216no—
139C23×C11—28no—
140C23×C11—22no—
141C23×C11—24no—
142C23×C11—28no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—44no—
146C23×C11—41no—
147C23×C11—44no—
148C23×C11—44no—
149C23×C11—48no—
150C23×C11—44no—
151C23×C11C2×C22⋊C414yes—
152C23×C11C4×D418yes—
153C23×C11#12014yes—
154C23×C11#12118yes—
155C23×C11#12314yes—
156C23×C11C23×C411yescharacteristic
157C23×C11C22×D412yes—
158C23×C11C22×D411yescharacteristic
159C23×C11C22×D411yescharacteristic
160C23×C11C2×#4112yes—
161C23×C11C2×#4118yes—
162D4×C11—416no—
163C2×C4×C11—28no—
164C2×C4×C11—24no—
165C2×C4×C11—28no—
166C2×C4×C11—24no—
167C2×C4×C11—232no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—28no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11C2×C22⋊C418yes—
178C2×Dic11—264no—
179C2×Dic11—28no—
180C2×Dic11—28no—
181C2×Dic11—216no—
182C2×Dic11—216no—
183C2×Dic11—44no—
184C2×Dic11—44no—
185C2×Dic11—44no—
186C2×Dic11—48no—
187C2×Dic11—48no—
188C2×Dic11#123116yescomplemented
189C23×D4C2×D1111yescharacteristic
190C24×C4—112no—
191C24×C4C2×D1111yescharacteristic
192C2×#123—24no—
193C2×#123—24no—
194C2×#123Dic1118yescomplemented
195C22×C4⋊C4C2×D1112yes—
196C22×C22⋊C4—112no—
197C22×C22⋊C4—114no—
198C22×C22⋊C4C2×D1111yescharacteristic
199C22×C22⋊C4C2×D1112yes—
200C22×C42—114no—
201C22×C42—228no—
202C22×C42—224no—
203#386—228no—
204#381—224no—
205C2×#95—118no—
206C2×#95—114no—
207C2×#95—114no—
208C22×C11—28no—
209C22×C11—28no—
210C22×C11—216no—
211C22×C11—28no—
212C22×C11—216no—
213C22×C11—42no—
214C22×C11—44no—
215C22×C11—48no—
216C22×C11—82no—
217C22×C11—82no—
218C22×C11—84no—
219C22×C11#38618yes—
220C22×C11C22×C22⋊C411yescharacteristic
221C22×C11C2×C4×D412yes—
222C22×C11C4×#4114yes—
223C22×C11C2×#12011yescharacteristic
224C22×C11C2×#12112yes—
225C22×C11C2×#12311yescharacteristic
226C22×C11C2×#12314yes—
227C22×C11#52514yes—
228C22×C11#52514yes—
229C22×C11#52918yes—
230C22×C11#53214yes—
231C4×C11—28no—
232C4×C11—42no—
233C4×C11—44no—
234Dic11—216no—
235Dic11—84no—
236C25C22×D1111yescharacteristic
237C25C22×D1111yescharacteristic
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4C2×Dic1114yes—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—114no—
246C23×C4—118no—
247C23×C4—114no—
248C23×C4—2216no—
249C23×C4—224no—
250C23×C4—224no—
251C23×C4C2×Dic1114yes—
252C23×C4C22⋊D1114yes—
253C23×C4C22⋊D1114yes—
254C23×C4C22×D1112yes—
255C23×C4C22×D1111yescharacteristic
256C23×C4C22×D1112yes—
257#123—232no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4C2×Dic1118yescomplemented
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—24no—
264C2×C22⋊C4—24no—
265C2×C22⋊C4—228no—
266C2×C22⋊C4—2216no—
267C2×C22⋊C4—224no—
268C2×C22⋊C4—224no—
269C2×C22⋊C4—224no—
270C2×C22⋊C4C2×Dic1114yes—
271C2×C22⋊C4C2×Dic1118yescomplemented
272C2×C42—2216no—
273C2×C42—2232no—
274C2×C42—228no—
275#95—2216no—
276#95—228no—
277#95—228no—
278C2×C11—28no—
279C2×C11—82no—
280C2×C11C2×#38611yescharacteristic
281C2×C11#229712yes—
282C2×C11C4×#12314yes—
283C2×C11#284912yes—
284C2×C11#285312yes—
285C2×C11#285414yes—
286C24—28no—
287C24—22no—
288C24—22no—
289C24—28no—
290C24—21no—
291C24—21no—
292C24D4×D1114yes—
293C24#434114yes—
294C24C22×Dic1112yes—
295C24C22×Dic1112yes—
296C24C2×C22⋊D1112yes—
297C24C2×C22⋊D1112yes—
298C24C23×D1111yescharacteristic
299C2×D4—216no—
300C2×D4—28no—
301C2×D4—44no—
302C2×D4—44no—
303C2×D4—48no—
304C22×C4—216no—
305C22×C4—28no—
306C22×C4—28no—
307C22×C4—216no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—28no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—118no—
318C22×C4—1116no—
319C22×C4—2232no—
320C22×C4—2232no—
321C22×C4—2232no—
322C22×C4—2216no—
323C22×C4—224no—
324C22×C4—228no—
325C22×C4—224no—
326C22×C4—224no—
327C22×C4—224no—
328C22×C4—228no—
329C22×C4—228no—
330C22×C4—224no—
331C22×C4C22⋊Dic11116yescomplemented
332C22×C4C22×Dic1114yes—
333C22×C4C22×Dic1112yes—
334C22×C4C22×Dic1114yes—
335C22×C4C2×C22⋊D1114yes—
336C22×C4C2×C22⋊D1114yes—
337C4⋊C4—216no—
338C22⋊C4—28no—
339C22⋊C4—216no—
340C22⋊C4—4416no—
341C22⋊C4—448no—
342C42—2232no—
343C11#1470611yescharacteristic, complemented, Sylow
344C23—28no—
345C23—28no—
346C23—28no—
347C23—216no—
348C23—28no—
349C23—28no—
350C23—24no—
351C23—28no—
352C23—22no—
353C23—41no—
354C23—41no—
355C23—42no—
356C23—44no—
357C23—44no—
358C23—48no—
359C23—44no—
360C23—44no—
361C23D4×Dic1118yes—
362C23#6698814yes—
363C23#6699014yes—
364C23#6699218yes—
365C23C2×C22⋊Dic1114yes—
366C23C2×D4×D1112yes—
367C23C2×#434112yes—
368C23#41×D1118yes—
369C23C23×Dic1111yescharacteristic
370C23C22×C22⋊D1111yescharacteristic
371C23C22×C22⋊D1111yescharacteristic
372D4—416no—
373C2×C4—28no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—28no—
377C2×C4—232no—
378C2×C4—24no—
379C2×C4—28no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—1116no—
388C2×C4—2264no—
389C2×C4—228no—
390C2×C4—2216no—
391C2×C4—228no—
392C2×C4—2216no—
393C2×C4—444no—
394C2×C4—448no—
395C2×C4—448no—
396C2×C4—444no—
397C2×C4—444no—
398C2×C4C2×C22⋊Dic1118yes—
399C22—28no—
400C22—216no—
401C22—28no—
402C22—28no—
403C22—216no—
404C22—44no—
405C22—48no—
406C22—42no—
407C22—82no—
408C22—82no—
409C22—84no—
410C22#1062283318yes—
411C22#1062318018yes—
412C22D11×#12314yes—
413C22#1062318714yes—
414C22C2×D4×Dic1112yes—
415C22C2×#6698811yescharacteristic
416C22C2×#6699011yescharacteristic
417C22C2×#6699212yes—
418C22#41×Dic1114yes—
419C22#1062335914yes—
420C22#1062336314yes—
421C22C22×C22⋊Dic1111yescharacteristic
422C4—28no—
423C4—44no—
424C4—42no—
425C4—2216no—
426C4—884no—
427C2—28no—
428C2—82no—
429C2C2×#1062283311yescharacteristic
430C2#1307110712yes—
431C2#123×Dic1114yes—
432C2#1307690512yes—
433C2#1307693512yes—
434C2#1307694514yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#123C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#123D11
hypocenterC11#14706
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C23×C4×Dic11C2semidirect
3. C2×#10622824C2semidirect
4. #13066853C2semidirect
5. #13066848C2semidirect
6. #13066838C2semidirect
13. C2×C11×#123C4semidirect
51. C2×C11×C4⋊C4C2×C4semidirect
57. C2×C11×C22⋊C4C2×C4semidirect
101. C22×C4×C11C22⋊C4semidirect
188. C2×Dic11#123semidirect
194. C2×#123Dic11semidirect
260. C2×C4⋊C4C2×Dic11semidirect
271. C2×C22⋊C4C2×Dic11semidirect
331. C22×C4C22⋊Dic11semidirect
343. C11#14706semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic112
C2×#106228332
C2×#106228242
#130668532
#130668482
#130668382
C22×C11×#1232
#1470611