Finite Group Databasebeta

← #14656755

Subgroups — #14656755

Order 2816.

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

normal subgroups only

This group has 544 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#13068704C212yesmaximal
2#13066885C211yesmaximal, characteristic
3#13066494C212yesmaximal
4#13066459C211yesmaximal, characteristic
5C11×#2659C211yesmaximal, characteristic
6C2×C11×C22⋊Q8—21no—
7C22×C4⋊Dic11C2211yescharacteristic
8C11×#398—22no—
9C11×#395—22no—
10C11×#380—21no—
11C11×#380C2212yes—
12C2×C11×#95C2211yescharacteristic
13C2×C11⋊#95—21no—
14C2×C11⋊#95—21no—
15C2×C11⋊#95C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2212yes—
17#10622167—22no—
18#10622167—22no—
19C22×Q8×C11—21no—
20C23×C4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C11×C22⋊Q8—42no—
26C11×C22⋊Q8—42no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D412yes—
32C2×C11×C4⋊C4D412yes—
33C2×C11×C22⋊C4—22no—
34C2×C4⋊Dic11—22no—
35C2×C4⋊Dic11—22no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11Q812yescomplemented
38C22×C11⋊C8—22no—
39C11×#95—22no—
40C11×#95—22no—
41C11×#95—22no—
42C11⋊#95—22no—
43C11⋊#95—42no—
44C11⋊#95—42no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)—22no—
47#10343—111nomaximal, Sylow
48C24×C11C2×D411yescharacteristic
49C2×Q8×C11—42no—
50C2×Q8×C11—81no—
51C2×Q8×C11—81no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
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×Q811yescharacteristic
68C22×C4×C11#4112yes—
69C22×C4×C11#4111yescharacteristic
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—41no—
73C22×Dic11—41no—
74C22×Dic11—41no—
75C22×Dic11—41no—
76C22×Dic11—41no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—44no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—81no—
89C11×C4⋊C4—81no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4—42no—
92C4⋊Dic11—24no—
93C4⋊Dic11—42no—
94C2×C11⋊C8—42no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—42no—
97#2659D1111yescharacteristic
98#1824—112no—
99#1445—111no—
100#1294—112no—
101#1280—111no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11#12011yescharacteristic
107C23×C11C22⋊Q811yescharacteristic
108C23×C11#12411yescharacteristic
109C23×C11C2×SD1611yescharacteristic
110C23×C11C2×Q1611yescharacteristic
111C23×C11AGL(1,ℤ/8)11yescharacteristic
112C23×C11#13711yescharacteristic
113Q8×C11—84no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11C22⋊Q812yes—
136C2×C4×C11#12412yes—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—81no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150C2×Dic11—81no—
151C11⋊C8—82no—
152C2×C22⋊Q8—21no—
153C22×C4⋊C4—111no—
154C2×C22⋊C8—112no—
155#398—22no—
156#395—22no—
157#380—21no—
158#380C2×D1112yes—
159C2×#95—111no—
160C2×#95—221no—
161C2×#95—221no—
162C2×#95C2×D1111yescharacteristic
163#340—222no—
164#340—222no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39311yescharacteristic
178C22×C11#45011yescharacteristic
179C22×C11#45111yescharacteristic
180C22×C11#45311yescharacteristic
181C22×C11#45411yescharacteristic
182C22×C11#45811yescharacteristic
183C22×C11#45811yescharacteristic
184C22×C11#47511yescharacteristic
185C22×C11#47711yescharacteristic
186C22×C11#48711yescharacteristic
187C22×C11#48911yescharacteristic
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—42no—
191C4×C11—42no—
192C4×C11—82no—
193C4×C11—82no—
194Dic11—82no—
195Dic11—82no—
196C22×Q8—21no—
197C23×C4—221no—
198C23×C4—221no—
199C23×C4C22⋊D1111yescharacteristic
200C23×C4C22⋊D1111yescharacteristic
201C23×C4C22×D1111yescharacteristic
202C22×C8—222no—
203C22⋊Q8—42no—
204C22⋊Q8—42no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—112no—
210C2×C4⋊C4—222no—
211C2×C4⋊C4—222no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4C22⋊D1112yes—
214C2×C4⋊C4C22⋊D1112yes—
215C2×C22⋊C4—22no—
216C22⋊C8—222no—
217C22⋊C8—222no—
218#95—22no—
219#95—22no—
220#95—22no—
221#95—222no—
222#95—442no—
223#95—442no—
224C2×C11—21no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11#161311yescharacteristic
229C2×C11#161411yescharacteristic
230C2×C11#161611yescharacteristic
231C2×C11#161711yescharacteristic
232C2×C11#202411yescharacteristic
233C2×C11#202711yescharacteristic
234C2×C11#203011yescharacteristic
235C24C2×C22⋊D1111yescharacteristic
236C2×Q8—42no—
237C2×Q8—81no—
238C2×Q8—81no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—222no—
252C22×C4—222no—
253C22×C4—441no—
254C22×C4—441no—
255C22×C4—441no—
256C22×C4—441no—
257C22×C4—441no—
258C22×C4—441no—
259C22×C4—441no—
260C22×C4—441no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4—441no—
265C22×C4#432412yes—
266C22×C4#432612yes—
267C22×C4Q8×D1111yescharacteristic
268C22×C4#434312yes—
269C22×C4#434311yescharacteristic
270C22×C4C2×C22⋊D1112yes—
271C2×C8—442no—
272C2×C8—442no—
273C2×C8—442no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—44no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C4⋊C4—224no—
281C4⋊C4—442no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C11#1034311yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#6698511yescharacteristic
290C23C2×#432411yescharacteristic
291C23#6699511yescharacteristic
292C23C2×#432611yescharacteristic
293C23#6699911yescharacteristic
294C23#6700011yescharacteristic
295C23#6700611yescharacteristic
296Q8—84no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4—881no—
328C2×C4—881no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4—881no—
332C2×C4#6699912yes—
333C2×C4#6700012yes—
334C8—882no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22#1062270211yescharacteristic
348C22#1062270411yescharacteristic
349C22#1062270611yescharacteristic
350C22#1062270711yescharacteristic
351C22#1062283111yescharacteristic
352C22#1062284111yescharacteristic
353C22#1062284411yescharacteristic
354C22#1062285411yescharacteristic
355C22#1062285611yescharacteristic
356C22#1062285611yescharacteristic
357C22#1062285811yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—42no—
362C4—82no—
363C4—82no—
364C4—882no—
365C4—882no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2#1306763611yescharacteristic
371C2#1306764111yescharacteristic
372C2#1306765311yescharacteristic
373C2#1306765811yescharacteristic
374C2#1306975411yescharacteristic
375C2#1306976911yescharacteristic
376C2#1306978211yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2659C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#2659D11
hypocenterC11#10343
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
37. C2×C4⋊Dic11Q8semidirect
284. C11#10343semidirect

Maximal subgroups

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

subgroupindex
#130687042
#130668852
#130664942
#130664592
C11×#26592
#1034311