Finite Group Databasebeta

← #14657122

Subgroups — #14657122

Order 2816.

620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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#13074730C211yesmaximal, characteristic
2#13068921C212yesmaximal
3C2×#10622105C212yesmaximal
4#13066880C211yesmaximal, characteristic
5C11×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic11C2211yescharacteristic
7C2×#66977C2212yes—
8C22×Dic11⋊C4—21no—
9C2×C11×C22⋊C8C2212yes—
10C2×C11×#95C2211yescharacteristic
11#10622825—21no—
12#10622825—21no—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2211yescharacteristic
15C2×#66880—22no—
16#10622274—22no—
17#10622269—22no—
18#10622189—22no—
19#10622105—24no—
20C23×C4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C22×Dic22D412yes—
26C22×C8×C11—22no—
27C2×C22⋊Dic11—22no—
28C2×C4⋊Dic11—22no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—42no—
34C2×C4⋊Dic11D412yes—
35#66977—22no—
36#66977—22no—
37#66977—22no—
38#66977—22no—
39C2×Dic11⋊C4—22no—
40C2×Dic11⋊C4—42no—
41C2×Dic11⋊C4—42no—
42C2×Dic11⋊C4—42no—
43C11×C22⋊C8—22no—
44C11×C22⋊C8—22no—
45C11×#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95—42no—
50C11⋊#95D412yes—
51#66880—44no—
52#10406—111nomaximal, Sylow
53C24×C11C2×D411yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11SD1612yes—
65C22×C4×C11Q1612yes—
66C22×C4×C11C2×D412yes—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4112yes—
69C22×C4×C11#4111yescharacteristic
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—22no—
73C22×Dic11—22no—
74C22×Dic11—22no—
75C22×Dic11—22no—
76C22×Dic11—41no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—41no—
85C22×Dic11—41no—
86C2×Dic22—22no—
87C2×Dic22—22no—
88C2×Dic22—42no—
89C2×Dic22—42no—
90C2×C8×C11—42no—
91C2×C8×C11—42no—
92C2×C8×C11—42no—
93C22⋊Dic11—42no—
94C22⋊Dic11—42no—
95C4⋊Dic11—24no—
96C4⋊Dic11—22no—
97C4⋊Dic11—22no—
98C4⋊Dic11—42no—
99C4⋊Dic11—81no—
100C4⋊Dic11—81no—
101C4⋊Dic11—81no—
102C4⋊Dic11—81no—
103Dic11⋊C4—48no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106#2659—111no—
107#1872—112no—
108C2×#328—112no—
109#1444—111no—
110#1280D1111yescharacteristic
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11#12011yescharacteristic
116C23×C11#12111yescharacteristic
117C23×C11#12411yescharacteristic
118C23×C11C2×SD1611yescharacteristic
119C23×C11C2×Q1611yescharacteristic
120C23×C11#13711yescharacteristic
121C23×C11#13711yescharacteristic
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11#12112yes—
138C2×C4×C11#12312yes—
139C2×Dic11—24no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159Dic22—44no—
160Dic22—82no—
161C8×C11—82no—
162C2×C22⋊Q8—112no—
163C22×C4⋊C4—111no—
164C22×C4⋊C4—221no—
165C2×#103—222no—
166C2×C22⋊C8C2×D1112yes—
167#398—222no—
168#395—222no—
169#380—221no—
170#380—221no—
171C2×#95—111no—
172C2×#95—221no—
173C2×#95C2×D1111yescharacteristic
174#340—222no—
175#328—224no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11#39411yescharacteristic
189C22×C11#44811yescharacteristic
190C22×C11#45111yescharacteristic
191C22×C11#45311yescharacteristic
192C22×C11#45611yescharacteristic
193C22×C11B(4,𝔽2)11yescharacteristic
194C22×C11#45811yescharacteristic
195C22×C11#46111yescharacteristic
196C22×C11#46211yescharacteristic
197C22×C11#48711yescharacteristic
198C22×C11#49111yescharacteristic
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—42no—
202C4×C11—42no—
203Dic11—44no—
204Dic11—82no—
205Dic11—82no—
206Dic11—82no—
207C22×Q8—112no—
208C23×C4—221no—
209C23×C4—221no—
210C23×C4D4411yescharacteristic
211C23×C4D4411yescharacteristic
212C23×C4C22×D1111yescharacteristic
213C22×C8—22no—
214C22⋊Q8—222no—
215C22⋊Q8—222no—
216C22⋊Q8—222no—
217C22⋊Q8—222no—
218C2×C4⋊C4—112no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—442no—
226C2×C4⋊C4—442no—
227C2×C4⋊C4—442no—
228C2×C4⋊C4—442no—
229C2×C22⋊C4—222no—
230#103—444no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233#95—22no—
234#95—112no—
235#95—222no—
236#95—222no—
237#95—221no—
238#95—442no—
239C2×C11—21no—
240C2×C11—21no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11#159611yescharacteristic
244C2×C11#160511yescharacteristic
245C2×C11#161111yescharacteristic
246C2×C11#161411yescharacteristic
247C2×C11#203911yescharacteristic
248C2×C11#204311yescharacteristic
249C2×C11#204411yescharacteristic
250C24C2×D4411yescharacteristic
251C2×Q8—222no—
252C2×Q8—222no—
253C2×Q8—442no—
254C2×Q8—442no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—222no—
266C22×C4—222no—
267C22×C4—222no—
268C22×C4—222no—
269C22×C4—222no—
270C22×C4—222no—
271C22×C4—441no—
272C22×C4—441no—
273C22×C4—441no—
274C22×C4—441no—
275C22×C4—441no—
276C22×C4—441no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4#431412yes—
282C22×C4Dic4412yes—
283C22×C4#433912yes—
284C22×C4D4×D1112yes—
285C22×C4D4×D1111yescharacteristic
286C22×C4#434311yescharacteristic
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C4⋊C4—224no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—442no—
294C4⋊C4—448no—
295C4⋊C4—442no—
296C4⋊C4—442no—
297C4⋊C4—881no—
298C4⋊C4—881no—
299C4⋊C4—881no—
300C4⋊C4—881no—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C11#1040611yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#6692811yescharacteristic
309C23#6693511yescharacteristic
310C23#6694811yescharacteristic
311C23C2×#431411yescharacteristic
312C23C2×Dic4411yescharacteristic
313C23#6696211yescharacteristic
314C23#6696211yescharacteristic
315Q8—444no—
316Q8—882no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—224no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—881no—
349C2×C4—881no—
350C2×C4—881no—
351C2×C4—881no—
352C2×C4#6693712yes—
353C2×C4#6694712yes—
354C8—82no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1062228511yescharacteristic
368C22#1062229411yescharacteristic
369C22#1062231611yescharacteristic
370C22#1062235111yescharacteristic
371C22#1062235211yescharacteristic
372C22#1062235411yescharacteristic
373C22#1062235511yescharacteristic
374C22#1062236011yescharacteristic
375C22#1062236511yescharacteristic
376C22#1062245411yescharacteristic
377C22#1062246211yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—444no—
383C4—882no—
384C4—882no—
385C4—882no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#1306754111yescharacteristic
391C2#1306759211yescharacteristic
392C2#1306762611yescharacteristic
393C2#1306764311yescharacteristic
394C2#1306984111yescharacteristic
395C2#1306986311yescharacteristic
396C2#1306986811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1280C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1280D11
hypocenterC11#10406
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
303. C11#10406semidirect

Maximal subgroups

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

subgroupindex
#130747302
#130689212
C2×#106221052
#130668802
C11×#12802
#1040611