Finite Group Databasebeta

← #14655420

Subgroups — #14655420

Order 2816.

558 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079744C211yesmaximal, characteristic, complemented
2#13079603C211yesmaximal, characteristic
3#13067333C211yesmaximal, characteristic, complemented
4#13067226C211yesmaximal, characteristic, complemented
5#13066968C211yesmaximal, characteristic, complemented
6#13066515C211yesmaximal, characteristic, complemented
7C2×C11×#497C211yesmaximal, characteristic, complemented
8C22×C11×Q16—21no—
9C22×C11×SD16—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#124C2211yescharacteristic
12#10623008C2211yescharacteristic
13C11×#497—22no—
14C11×#497—22no—
15C2×C11×#97C2211yescharacteristic
16#10622840—21no—
17#10622830—21no—
18#10622701—21no—
19#10622697—22no—
20#10622692—21no—
21#10622671—21no—
22#10622670—22no—
23#10622668—21no—
24#10622581—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622185—22no—
29#10622163—22no—
30#10622102—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C2×#4339—21no—
35C2×C11×Q16—24no—
36C2×C11×Q16—44no—
37C2×C11×SD16—24no—
38C2×C11×SD16—44no—
39C22×C8×C11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8D412yes—
44C11×#124—21no—
45C11×#124—21no—
46C11×#124—21no—
47C11×#124—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4325—22no—
54C2×#4323—22no—
55#66983—21no—
56#66983—21no—
57#66928—21no—
58#66927D411yescharacteristic
59C4×D44—21no—
60C4×D44—21no—
61#66922D411yescharacteristic
62C11×#97—21no—
63C11×#97D412yes—
64#66899—22no—
65#66896—22no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66873—24no—
70#66872—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74#66867—21no—
75#66867—21no—
76C4×C11⋊C8—21no—
77#10132—111nomaximal, Sylow
78C24×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11—42no—
85C2×Q8×C11—41no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—42no—
89C22×C4×C11—21no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C2×C22⋊D11—41no—
95#4339—82no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C11×Q16—48no—
102C11×SD16—48no—
103C2×C8×C11—24no—
104C2×C8×C11—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117#4325—82no—
118#4323—82no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126#3227—111no—
127#3213—111no—
128C2×#497D1111yescharacteristic, complemented
129#1556—111no—
130#1530—111no—
131#1469—111no—
132#1302—111no—
133C23×C11—41no—
134C23×C11—42no—
135C23×C11—81no—
136C23×C11—81no—
137C23×C11#12111yescharacteristic
138C22×D11—41no—
139Q8×C11—42no—
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—42no—
143Q8×C11—82no—
144D4×C11—42no—
145D4×C11—42no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—82no—
152C2×C4×C11—81no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C22⋊D11—82no—
160C2×Dic11—41no—
161D44—42no—
162D44—42no—
163D44—81no—
164C4×D11—82no—
165Dic22—81no—
166C8×C11—24no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C22×Q16—21no—
171C22×SD16—21no—
172#532—111no—
173C2×C4⋊Q8C2×D1111yescharacteristic
174C2×#124C2×D1111yescharacteristic
175#498—221no—
176#497—22no—
177#497—22no—
178#496—221no—
179#489—221no—
180#486—221no—
181#481—222no—
182#476—222no—
183#463—222no—
184#448—221no—
185#447—221no—
186#432—111no—
187#432—111no—
188#431—111no—
189C2×#97C2×D1111yescharacteristic
190#332—222no—
191#329—222no—
192#323—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—162no—
199C22×C11#39211yescharacteristic
200C22×C11#47112yes—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11#45312yes—
212Dic11—81no—
213C2×#41—221no—
214C22×Q8—21no—
215C22×Q8C22⋊D1111yescharacteristic
216C22×D4C22⋊D1111yescharacteristic
217C2×Q16—24no—
218C2×Q16—44no—
219C2×SD16—24no—
220C2×SD16—44no—
221C2×SD16—222no—
222C2×D8—222no—
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—111no—
228C4⋊Q8C22⋊D1112yes—
229#127—111no—
230#124—21no—
231#124—21no—
232#124—21no—
233#124—21no—
234#124—221no—
235#121—221no—
236#121—221no—
237C4×D4—221no—
238C4×D4—221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C42C22×D1111yescharacteristic
244#106—224no—
245C4⋊C8—112no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248#103—222no—
249#102—224no—
250#102—222no—
251C22⋊C8—112no—
252C22⋊C8—221no—
253C22⋊C8—221no—
254#97—21no—
255#97—221no—
256#97—221no—
257#97C22⋊D1112yes—
258C4×C8—221no—
259C2×C11—22no—
260C2×C11—161no—
261C2×C11#200211yescharacteristic
262C2×C11#200911yescharacteristic
263C2×C11#201911yescharacteristic
264D11—161no—
265C24—21no—
266#41—882no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—22no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×Q8—221no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—42no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—441no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—441no—
285C22×C4D4×D1111yescharacteristic
286C22×C4#434111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—48no—
289SD16—48no—
290SD16—882no—
291D8—882no—
292C2×C8—24no—
293C2×C8—22no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—441no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C11#1013211yescharacteristic, complemented, Sylow
314C23—41no—
315C23—42no—
316C23—81no—
317C23—81no—
318C23—441no—
319C23#6699211yescharacteristic
320Q8—42no—
321Q8—42no—
322Q8—42no—
323Q8—42no—
324Q8—82no—
325Q8—881no—
326D4—42no—
327D4—42no—
328D4—442no—
329D4—442no—
330D4—881no—
331D4—882no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4—441no—
340C2×C4—882no—
341C2×C4#6699011yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699111yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4#6699311yescharacteristic
346C2×C4#6700611yescharacteristic
347C8—24no—
348C8—442no—
349C8—442no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—162no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22#1062281612yes—
361C22#1062283611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—81no—
369C4—881no—
370C4#1062269012yes—
371C2—22no—
372C2—161no—
373C2—1761no—
374C2#1306963111yescharacteristic
375C2#1306967411yescharacteristic
376C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#497C2
socleC22×C11#392
prime radical#13079603C2
hypercenterC2×#497D11
hypocenterC11#10132
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. #13079744C2semidirect
3. #13067333C2semidirect
4. #13067226C2semidirect
5. #13066968C2semidirect
6. #13066515C2semidirect
7. C2×C11×#497C2semidirect
128. C2×#497D11semidirect
313. C11#10132semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130796032
#130673332
#130672262
#130669682
#130665152
C2×C11×#4972
#1013211