Finite Group Databasebeta

← #14657123

Subgroups — #14657123

Order 2816.

576 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 117 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#13068924C212yesmaximal
2C2×#10622176C212yesmaximal
3#13066872C211yesmaximal, characteristic
4#13066459C211yesmaximal, characteristic
5C11×#2659C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2212yes—
7C22×C4⋊Dic11C2211yescharacteristic
8C11×#398—22no—
9C11×#395—22no—
10C11×#380—21no—
11C11×#380—21no—
12C2×C11×#95C2211yescharacteristic
13C2×#66899—22no—
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2212yes—
18#10622176—24no—
19#10622167—22no—
20C22×Q8×C11D412yes—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C23×Dic11—21no—
25C23×Dic11—21no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—22no—
29C11×C22⋊Q8—22no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D412yes—
36C2×C11×C22⋊C4—22no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11—42no—
39C22×C11⋊C8—22no—
40C11×#95—22no—
41C11×#95—22no—
42C11×#95—22no—
43#66899—44no—
44C11⋊#95—21no—
45C11⋊#95—42no—
46C11⋊#95—42no—
47C11⋊#95D412yes—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50#10407—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11SD1612yes—
69C22×C4×C11Q1612yes—
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4112yes—
73C22×C4×C11#4111yescharacteristic
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—
86C22×Dic11—41no—
87C22×Dic11—41no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—81no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—42no—
98C4⋊Dic11—24no—
99C4⋊Dic11—42no—
100C2×C11⋊C8—42no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—42no—
103#2659D1111yescharacteristic
104#1872—112no—
105C2×#328—112no—
106#1442—111no—
107#1280—111no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11#12011yescharacteristic
113C23×C11#12111yescharacteristic
114C23×C11#12411yescharacteristic
115C23×C11C2×SD1611yescharacteristic
116C23×C11C2×Q1611yescharacteristic
117C23×C11#13711yescharacteristic
118C23×C11#13711yescharacteristic
119Q8×C11—44no—
120Q8×C11—82no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11#12112yes—
143C2×C4×C11#12312yes—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—81no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C11⋊C8—82no—
159C2×C22⋊Q8C2×D1112yes—
160C22×C4⋊C4—111no—
161C2×#103—222no—
162C2×C22⋊C8—112no—
163#398—22no—
164#395—22no—
165#380—21no—
166#380—21no—
167C2×#95—111no—
168C2×#95—221no—
169C2×#95—221no—
170C2×#95C2×D1111yescharacteristic
171#340—222no—
172#328—224no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
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#39411yescharacteristic
186C22×C11#44811yescharacteristic
187C22×C11#45111yescharacteristic
188C22×C11#45411yescharacteristic
189C22×C11#45511yescharacteristic
190C22×C11B(4,𝔽2)11yescharacteristic
191C22×C11#45811yescharacteristic
192C22×C11#46111yescharacteristic
193C22×C11#46211yescharacteristic
194C22×C11#48711yescharacteristic
195C22×C11#49111yescharacteristic
196C4×C11—22no—
197C4×C11—22no—
198C4×C11—42no—
199C4×C11—42no—
200C4×C11—82no—
201C4×C11—82no—
202Dic11—82no—
203Dic11—82no—
204C22×Q8C22⋊D1112yes—
205C23×C4—221no—
206C23×C4—221no—
207C23×C4C22⋊D1111yescharacteristic
208C23×C4C22⋊D1111yescharacteristic
209C23×C4C22×D1111yescharacteristic
210C22×C8—222no—
211C22⋊Q8—22no—
212C22⋊Q8—22no—
213C22⋊Q8—22no—
214C22⋊Q8—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—442no—
222C2×C4⋊C4C22⋊D1112yes—
223C2×C22⋊C4—22no—
224#103—444no—
225C22⋊C8—222no—
226C22⋊C8—222no—
227#95—22no—
228#95—22no—
229#95—22no—
230#95—112no—
231#95—221no—
232#95—442no—
233#95—442no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11#159911yescharacteristic
239C2×C11#160211yescharacteristic
240C2×C11#160811yescharacteristic
241C2×C11#161711yescharacteristic
242C2×C11#204011yescharacteristic
243C2×C11#204311yescharacteristic
244C2×C11#204411yescharacteristic
245C24C2×C22⋊D1111yescharacteristic
246C2×Q8—22no—
247C2×Q8—22no—
248C2×Q8—42no—
249C2×Q8—42no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—222no—
263C22×C4—222no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4—441no—
267C22×C4—441no—
268C22×C4—441no—
269C22×C4—441no—
270C22×C4—441no—
271C22×C4—441no—
272C22×C4—441no—
273C22×C4—441no—
274C22×C4—441no—
275C22×C4—441no—
276C22×C4#432512yes—
277C22×C4#432612yes—
278C22×C4D4×D1111yescharacteristic
279C22×C4#434111yescharacteristic
280C22×C4#434112yes—
281C22×C4C2×C22⋊D1112yes—
282C2×C8—442no—
283C2×C8—442no—
284C2×C8—442no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—81no—
293C4⋊C4—224no—
294C4⋊C4—442no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C11#1040711yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#6698911yescharacteristic
303C23#6699111yescharacteristic
304C23C2×#432511yescharacteristic
305C23#6699511yescharacteristic
306C23#6699511yescharacteristic
307C23C2×#432611yescharacteristic
308C23#6700611yescharacteristic
309Q8—44no—
310Q8—82no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4#6698812yes—
347C2×C4#6699212yes—
348C8—882no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22#1062269411yescharacteristic
362C22#1062269511yescharacteristic
363C22#1062269611yescharacteristic
364C22#1062270311yescharacteristic
365C22#1062283511yescharacteristic
366C22#1062284011yescharacteristic
367C22#1062284111yescharacteristic
368C22#1062285511yescharacteristic
369C22#1062285611yescharacteristic
370C22#1062285711yescharacteristic
371C22#1062285811yescharacteristic
372C4—22no—
373C4—22no—
374C4—42no—
375C4—42no—
376C4—82no—
377C4—82no—
378C4—882no—
379C4—882no—
380C2—21no—
381C2—21no—
382C2—21no—
383C2—21no—
384C2#1306755611yescharacteristic
385C2#1306757311yescharacteristic
386C2#1306760711yescharacteristic
387C2#1306765811yescharacteristic
388C2#1306984211yescharacteristic
389C2#1306985911yescharacteristic
390C2#1306986411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2659C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#2659D11
hypocenterC11#10407
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2659

Complements

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

NH ≅ G/Ntype
297. C11#10407semidirect

Maximal subgroups

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

subgroupindex
#130689242
C2×#106221762
#130668722
#130664592
C11×#26592
#1040711