Finite Group Databasebeta

← #14656748

Subgroups — #14656748

Order 2816.

684 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 115 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#13068551C212yesmaximal
3#13066495C212yesmaximal
4#13066459C211yesmaximal, characteristic
5C11×#1446C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C2×#66977—21no—
8C2×C11×#95—21no—
9C2×C11×#95—21no—
10C2×C11×#95C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12C2×#66899—22no—
13C2×#66899—22no—
14#10622825—21no—
15#10622825C2212yes—
16C2×C22⋊(C11⋊C8)C2212yes—
17#10622274—22no—
18#10622269—22no—
19C22×Q8×C11—21no—
20C22×Q8×C11—22no—
21C22×Q8×C11—22no—
22C22×Q8×C11—42no—
23C22×Q8×C11—42no—
24C22×Q8×C11Q812yescomplemented
25C23×C4×C11—21no—
26C23×C4×C11—21no—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C22×Dic22—21no—
31C2×C22⋊Dic11—22no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D412yes—
36C2×C4⋊Dic11D412yes—
37#66977—42no—
38#66977—42no—
39C2×Dic11⋊C4—22no—
40C22×C11⋊C8—22no—
41C11×#95—22no—
42C11×#95—22no—
43C11×#95—42no—
44C11×#95—42no—
45#66899—44no—
46#66899—44no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—22no—
51#10341—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—24no—
54C2×Q8×C11—24no—
55C2×Q8×C11—24no—
56C2×Q8×C11—44no—
57C2×Q8×C11—42no—
58C2×Q8×C11—42no—
59C2×Q8×C11—44no—
60C2×Q8×C11—48no—
61C2×Q8×C11—42no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11SD1612yes—
87C22×C4×C11Q1612yes—
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×Q811yescharacteristic
90C22×C4×C11#4112yes—
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—22no—
93C22×Dic11—22no—
94C2×Dic22—42no—
95C2×Dic22—81no—
96C2×Dic22—81no—
97C22⋊Dic11—42no—
98C22⋊Dic11—42no—
99C4⋊Dic11—42no—
100C4⋊Dic11—42no—
101C4⋊Dic11—42no—
102C4⋊Dic11—81no—
103C4⋊Dic11—81no—
104Dic11⋊C4—44no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—42no—
107C2×C11⋊C8—42no—
108#2659—111no—
109#1787—112no—
110#1446D1111yescharacteristic
111#1294—112no—
112#1280—111no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11#12011yescharacteristic
118C23×C11C22⋊Q811yescharacteristic
119C23×C11#12411yescharacteristic
120C23×C11C2×SD1611yescharacteristic
121C23×C11C2×Q1611yescharacteristic
122C23×C11AGL(1,ℤ/8)11yescharacteristic
123C23×C11#13711yescharacteristic
124Q8×C11—28no—
125Q8×C11—44no—
126Q8×C11—44no—
127Q8×C11—44no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—24no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11C22⋊Q812yes—
158C2×C4×C11#12412yes—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165Dic22—84no—
166C11⋊C8—82no—
167C23×Q8C2×D1111yescharacteristic
168C2×C22⋊Q8—221no—
169C2×#103—222no—
170C2×#103—222no—
171C2×C22⋊C8—112no—
172#398—222no—
173#395—222no—
174#380—112no—
175#380—221no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95C2×D1111yescharacteristic
179C2×#95C2×D1111yescharacteristic
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—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#39311yescharacteristic
193C22×C11#45011yescharacteristic
194C22×C11#45111yescharacteristic
195C22×C11#45511yescharacteristic
196C22×C11#45611yescharacteristic
197C22×C11B(4,𝔽2)11yescharacteristic
198C22×C11B(4,𝔽2)11yescharacteristic
199C22×C11#47511yescharacteristic
200C22×C11#47711yescharacteristic
201C22×C11#48711yescharacteristic
202C22×C11#48911yescharacteristic
203C4×C11—22no—
204C4×C11—22no—
205C4×C11—42no—
206C4×C11—42no—
207C4×C11—44no—
208C4×C11—82no—
209Dic11—82no—
210Dic11—82no—
211C22×Q8—21no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—42no—
215C22×Q8—42no—
216C22×Q8—221no—
217C22×Q8Dic2212yescomplemented
218C23×C4—21no—
219C23×C4—21no—
220C23×C4C22⋊D1111yescharacteristic
221C23×C4C22⋊D1111yescharacteristic
222C23×C4C22×D1111yescharacteristic
223C22×C8—222no—
224C22⋊Q8—442no—
225C22⋊Q8—442no—
226C2×C4⋊C4—112no—
227C2×C4⋊C4—112no—
228C2×C4⋊C4—222no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C22⋊C4—222no—
233#103—444no—
234#103—444no—
235C22⋊C8—222no—
236C22⋊C8—222no—
237#95—22no—
238#95—22no—
239#95—42no—
240#95—42no—
241#95—222no—
242#95—222no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11#160111yescharacteristic
248C2×C11#160211yescharacteristic
249C2×C11#160411yescharacteristic
250C2×C11#160511yescharacteristic
251C2×C11#202411yescharacteristic
252C2×C11#202811yescharacteristic
253C2×C11#202911yescharacteristic
254C24C2×C22⋊D1111yescharacteristic
255C2×Q8—24no—
256C2×Q8—24no—
257C2×Q8—24no—
258C2×Q8—44no—
259C2×Q8—42no—
260C2×Q8—42no—
261C2×Q8—44no—
262C2×Q8—48no—
263C2×Q8—42no—
264C2×Q8—442no—
265C2×Q8—881no—
266C2×Q8—881no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—222no—
292C22×C4—222no—
293C22×C4#432512yes—
294C22×C4#432612yes—
295C22×C4C2×Dic2211yescharacteristic
296C22×C4#433911yescharacteristic
297C22×C4D4×D1112yes—
298C22×C4#434112yes—
299C2×C8—442no—
300C2×C8—442no—
301C2×C8—442no—
302C4⋊C4—442no—
303C4⋊C4—442no—
304C4⋊C4—444no—
305C4⋊C4—442no—
306C4⋊C4—881no—
307C4⋊C4—881no—
308C22⋊C4—442no—
309C22⋊C4—442no—
310C11#1034111yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23#6697711yescharacteristic
316C23#6698911yescharacteristic
317C23#6699011yescharacteristic
318C23C2×#432511yescharacteristic
319C23C2×#432611yescharacteristic
320C23#6700211yescharacteristic
321C23#6700411yescharacteristic
322Q8—28no—
323Q8—44no—
324Q8—44no—
325Q8—44no—
326Q8—884no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4#6693112yes—
363C2×C4#6693812yes—
364C8—882no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22#1062256011yescharacteristic
378C22#1062263311yescharacteristic
379C22#1062263411yescharacteristic
380C22#1062264511yescharacteristic
381C22#1062264511yescharacteristic
382C22#1062265911yescharacteristic
383C22#1062266311yescharacteristic
384C22#1062266811yescharacteristic
385C22#1062267411yescharacteristic
386C22#1062269411yescharacteristic
387C22#1062270811yescharacteristic
388C4—22no—
389C4—22no—
390C4—42no—
391C4—42no—
392C4—44no—
393C4—82no—
394C4—882no—
395C4—882no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2#1306756711yescharacteristic
401C2#1306757211yescharacteristic
402C2#1306758411yescharacteristic
403C2#1306758911yescharacteristic
404C2#1306975711yescharacteristic
405C2#1306977711yescharacteristic
406C2#1306978011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1446C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1446D11
hypocenterC11#10341
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1446

Complements

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

NH ≅ G/Ntype
24. C22×Q8×C11Q8semidirect
217. C22×Q8Dic22semidirect
310. C11#10341semidirect

Maximal subgroups

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

subgroupindex
#130747302
#130685512
#130664952
#130664592
C11×#14462
#1034111