Finite Group Databasebeta

← #14654329

Subgroups — #14654329

Order 2816.

1020 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 119 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×#10622831C212yesmaximal
2#13074730C211yesmaximal, characteristic, complemented
3C2×#10622090C212yesmaximal, complemented
4#13066459C211yesmaximal, characteristic, complemented
5C11×#1438C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C22×C11×C22⋊C4—22no—
8C22×#4324—22no—
9C2×#66977C2212yes—
10C2×C11×#95C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12#10622831—24no—
13#10622831—24no—
14C2×#66896—22no—
15#10622825—22no—
16C2×C22⋊(C11⋊C8)C2212yes—
17#10622274—22no—
18#10622269—22no—
19#10622090—24no—
20C25×C11—21no—
21C22×D4×C11—22no—
22C22×D4×C11—22no—
23C22×D4×C11—21no—
24C22×D4×C11—44no—
25C22×D4×C11D412yes—
26C23×C4×C11—21no—
27C23×C4×C11D412yes—
28C23×C4×C11C2311yescharacteristic
29C22×Dic22D412yes—
30C2×C11×C22⋊C4—44no—
31C2×C11×C22⋊C4—44no—
32C2×C11×C22⋊C4—44no—
33C2×C22⋊Dic11—22no—
34C2×#4324—28no—
35C2×#4324—48no—
36C2×C4⋊Dic11—22no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11D412yes—
39#66977—22no—
40#66977—22no—
41#66977—22no—
42#66977—22no—
43C2×Dic11⋊C4—22no—
44C22×C11⋊C8—22no—
45C11×#95—22no—
46C11×#95—22no—
47#66896—28no—
48C11⋊#95—24no—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)D414yes—
51#9966—111nomaximal, Sylow
52C24×C11—24no—
53C24×C11—22no—
54C24×C11—42no—
55C24×C11—42no—
56C24×C11—42no—
57C24×C11—41no—
58C24×C11—41no—
59C24×C11—42no—
60C24×C11—42no—
61C24×C11C2×D411yescharacteristic
62C2×D4×C11—28no—
63C2×D4×C11—24no—
64C2×D4×C11—44no—
65C2×D4×C11—44no—
66C2×D4×C11—48no—
67C2×D4×C11—44no—
68C2×D4×C11—42no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—42no—
79C22×C4×C11SD1614yescomplemented
80C22×C4×C11C2×D412yes—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—22no—
86C2×Dic22—22no—
87C2×Dic22—22no—
88C2×Dic22—44no—
89C11×C22⋊C4—416no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92#4324—416no—
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—82no—
96C4⋊Dic11—82no—
97Dic11⋊C4—42no—
98Dic11⋊C4—42no—
99C2×C11⋊C8—24no—
100C2×C11⋊C8—44no—
101C2×#450—112no—
102#2659—111no—
103C2×#328—112no—
104#1438D1111yescharacteristic
105#1280—111no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—22no—
109C23×C11—24no—
110C23×C11—44no—
111C23×C11—44no—
112C23×C11—42no—
113C23×C11—44no—
114C23×C11—44no—
115C23×C11—44no—
116C23×C11—44no—
117C23×C11—42no—
118C23×C11—44no—
119C23×C11—44no—
120C23×C11—82no—
121C23×C11—82no—
122C23×C11—82no—
123C23×C11—82no—
124C23×C11—82no—
125C23×C11—82no—
126C23×C11—81no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11—81no—
130C23×C11#12011yescharacteristic
131C23×C11#12111yescharacteristic
132C23×C11#12711yescharacteristic
133C23×C11C2×SD1612yes—
134C23×C11#13712yes—
135D4×C11—28no—
136D4×C11—44no—
137D4×C11—48no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11—82no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11#12012yes—
153C2×C4×C11#12112yes—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—44no—
159Dic22—44no—
160Dic22—82no—
161C11⋊C8—44no—
162C23×D4C2×D1111yescharacteristic
163C22×SD16—222no—
164C2×C22⋊Q8—112no—
165C22×C22⋊C4—22no—
166#450—224no—
167#450—224no—
168C2×#102—222no—
169C2×C22⋊C8—112no—
170#398—222no—
171#395—222no—
172#380—222no—
173C2×#95C2×D1111yescharacteristic
174C2×#95C2×D1111yescharacteristic
175#328—224no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—48no—
185C22×C11—44no—
186C22×C11—84no—
187C22×C11—84no—
188C22×C11—84no—
189C22×C11—84no—
190C22×C11—84no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11#39211yescharacteristic
194C22×C11#44812yes—
195C22×C11#45311yescharacteristic
196C22×C11#45411yescharacteristic
197C22×C11B(4,𝔽2)12yes—
198C22×C11#46112yes—
199C22×C11#49211yescharacteristic
200C22×C11#49711yescharacteristic
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—44no—
204C4×C11—82no—
205Dic11—82no—
206Dic11—82no—
207C25—21no—
208C22×Q8—112no—
209C22×D4—21no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—44no—
213C22×D4D4412yes—
214C23×C4—21no—
215C23×C4C22⋊D1112yes—
216C23×C4C22×D1111yescharacteristic
217C2×SD16—228no—
218C2×SD16—448no—
219C22×C8—222no—
220C22⋊Q8—222no—
221C22⋊Q8—222no—
222C22⋊Q8—222no—
223C22⋊Q8—222no—
224C2×C4⋊C4—112no—
225C2×C4⋊C4—222no—
226C2×C4⋊C4—222no—
227C2×C4⋊C4—222no—
228C2×C22⋊C4—44no—
229C2×C22⋊C4—44no—
230C2×C22⋊C4—44no—
231C2×C22⋊C4—222no—
232#102—228no—
233C22⋊C8—114no—
234C22⋊C8—222no—
235#95—22no—
236#95—22no—
237#95—224no—
238C2×C11—21no—
239C2×C11—22no—
240C2×C11—21no—
241C2×C11—84no—
242C2×C11#159612yes—
243C2×C11#159912yes—
244C2×C11#200611yescharacteristic
245C2×C11#201311yescharacteristic
246C2×C11#202111yescharacteristic
247C24—24no—
248C24—22no—
249C24—42no—
250C24—42no—
251C24—42no—
252C24—42no—
253C24—41no—
254C24—41no—
255C24—42no—
256C24C2×C22⋊D1111yescharacteristic
257C2×Q8—222no—
258C2×Q8—222no—
259C2×Q8—444no—
260C2×D4—28no—
261C2×D4—24no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4—48no—
265C2×D4—44no—
266C2×D4—42no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4#432414yescomplemented
280C22×C4C2×D4411yescharacteristic
281C22×C4#433911yescharacteristic
282C22×C4D4×D1112yes—
283C22×C4D4×D1112yes—
284SD16—4416no—
285C2×C8—224no—
286C2×C8—444no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—442no—
290C4⋊C4—442no—
291C4⋊C4—882no—
292C4⋊C4—882no—
293C22⋊C4—416no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C11#996611yescharacteristic, complemented, Sylow
297C23—22no—
298C23—21no—
299C23—21no—
300C23—24no—
301C23—44no—
302C23—44no—
303C23—42no—
304C23—44no—
305C23—44no—
306C23—44no—
307C23—44no—
308C23—42no—
309C23—44no—
310C23—44no—
311C23—82no—
312C23—82no—
313C23—82no—
314C23—82no—
315C23—82no—
316C23—82no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23#6698311yescharacteristic
322C23C2×#432412yes—
323C23#6699011yescharacteristic
324C23#6699311yescharacteristic
325C23#6700412yes—
326Q8—444no—
327Q8—882no—
328D4—28no—
329D4—44no—
330D4—48no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—444no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4#6693512yes—
351C2×C4#6693712yes—
352C8—444no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—48no—
362C22—44no—
363C22—84no—
364C22—84no—
365C22—84no—
366C22—84no—
367C22—84no—
368C22—82no—
369C22—82no—
370C22#1062257311yescharacteristic
371C22#1062263212yes—
372C22#1062264512yes—
373C22#1062265312yes—
374C22#1062267311yescharacteristic
375C22#1062267511yescharacteristic
376C22#1062268911yescharacteristic
377C22#1062269011yescharacteristic
378C4—22no—
379C4—22no—
380C4—44no—
381C4—82no—
382C4—882no—
383C4—882no—
384C2—21no—
385C2—22no—
386C2—21no—
387C2—84no—
388C2#1306753812yes—
389C2#1306755512yes—
390C2#1306965711yescharacteristic
391C2#1306969811yescharacteristic
392C2#1306974211yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1438C2
socleC23×C11#120
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#9966
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. #13074730C2semidirect
3. C2×#10622090C2semidirect
4. #13066459C2semidirect
79. C22×C4×C11SD16semidirect
279. C22×C4#4324semidirect
296. C11#9966semidirect

Maximal subgroups

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

subgroupindex
C2×#106228312
#130747302
C2×#106220902
#130664592
C11×#14382
#996611