Finite Group Databasebeta

← #14655157

Subgroups — #14655157

Order 2816.

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

normal subgroups only

This group has 590 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#13079603C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic, complemented
3#13067333C211yesmaximal, characteristic, complemented
4#13067214C211yesmaximal, characteristic, complemented
5#13067123C211yesmaximal, characteristic, complemented
6#13066509C211yesmaximal, characteristic, complemented
7C11×#2658C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#124—21no—
11C2×C11×#124C2211yescharacteristic
12#10623008C2211yescharacteristic
13C11×#399—22no—
14C11×#399—22no—
15C11×#376C2211yescharacteristic
16#10622840—21no—
17#10622830—21no—
18#10622706—21no—
19#10622702—22no—
20#10622701—21no—
21#10622671—21no—
22#10622670—22no—
23#10622668—21no—
24#10622579—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622185—22no—
29#10622178—22no—
30#10622089—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C2×#4339—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—44no—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C11×#124—21no—
44C11×#124—44no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D412yes—
48C2×C11×C22⋊C4—24no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4325—22no—
54C2×#4323—22no—
55#66983—21no—
56#66983—21no—
57C2×#4318—21no—
58#66928—21no—
59#66927D411yescharacteristic
60C4×D44—21no—
61C4×D44—21no—
62#66922D411yescharacteristic
63C11×#95—21no—
64C11×#95D412yes—
65#66899—22no—
66#66896—22no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66874—24no—
70#66873—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73#66867—21no—
74#66867—21no—
75#66867D412yes—
76C4×C11⋊C8—21no—
77#10094—111nomaximal, Sylow
78C24×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—42no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96#4339—44no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×Dic22—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—48no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—48no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—24no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117#4325—82no—
118#4323—82no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123#4318—42no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127#3213—111no—
128#3141—111no—
129#2658D1111yescharacteristic, complemented
130#1556—111no—
131#1527—111no—
132#1505—111no—
133#1300—111no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—41no—
137C23×C11—42no—
138C23×C11#12011yescharacteristic
139C22×D11—41no—
140Q8×C11—42no—
141Q8×C11—81no—
142Q8×C11—82no—
143Q8×C11—82no—
144D4×C11—42no—
145D4×C11—81no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C22⋊D11—82no—
164C2×Dic11—41no—
165D44—42no—
166D44—42no—
167D44—81no—
168C4×D11—82no—
169Dic22—42no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173#532—111no—
174C2×C4⋊Q8—21no—
175C2×C4⋊Q8C2×D1111yescharacteristic
176C2×#124—21no—
177C2×#124C2×D1111yescharacteristic
178#496—221no—
179#489—222no—
180#489—221no—
181#487—221no—
182#486—221no—
183#463—222no—
184#448—221no—
185#447—221no—
186#432—111no—
187#432—111no—
188#417—222no—
189C4×M16—111no—
190#399—22no—
191#399—22no—
192#376C2×D1111yescharacteristic
193#332—222no—
194#329—222no—
195#327—222no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—84no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#39211yescharacteristic
203C22×C11#45412yes—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—44no—
213C4×C11—81no—
214C4×C11—82no—
215C4×C11#45312yes—
216Dic11—81no—
217C2×#41—221no—
218C22×Q8—21no—
219C22×Q8C22⋊D1111yescharacteristic
220C22×D4C22⋊D1111yescharacteristic
221C2×SD16—222no—
222C2×D8—222no—
223C2×M16—221no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—44no—
229C4⋊Q8—111no—
230#127—111no—
231#124—21no—
232#124—21no—
233#124—21no—
234#124—21no—
235#124—44no—
236#124—221no—
237#121—221no—
238#121—221no—
239C4×D4—221no—
240C4×D4—221no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C22⋊D1112yes—
244C2×C22⋊C4—24no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C42—21no—
248C2×C42C22×D1111yescharacteristic
249C4⋊C8—112no—
250C4⋊C8—221no—
251#103—224no—
252#103—222no—
253#102—224no—
254#102—222no—
255C22⋊C8—221no—
256C22⋊C8—221no—
257#97—112no—
258#97—221no—
259#97—221no—
260C4×C8—221no—
261#95—21no—
262#95C22⋊D1112yes—
263C2×C11—22no—
264C2×C11—161no—
265C2×C11#200211yescharacteristic
266C2×C11#200311yescharacteristic
267C2×C11#200911yescharacteristic
268D11—161no—
269C24—21no—
270#41—444no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—42no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—221no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—42no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—441no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—441no—
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293SD16—882no—
294D8—882no—
295M16—442no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8—441no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—48no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C22⋊C4—48no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—441no—
312C22⋊C4—441no—
313C42—24no—
314C42D4×D1111yescharacteristic
315C42D4×D1111yescharacteristic
316C42D4×D1111yescharacteristic
317C42#434111yescharacteristic
318C11#1009411yescharacteristic, complemented, Sylow
319C23—42no—
320C23—42no—
321C23—41no—
322C23—42no—
323C23—441no—
324C23#6700611yescharacteristic
325Q8—42no—
326Q8—81no—
327Q8—82no—
328Q8—82no—
329Q8—442no—
330D4—42no—
331D4—81no—
332D4—442no—
333D4—442no—
334D4—881no—
335D4—882no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—441no—
348C2×C4—882no—
349C2×C4#6699011yescharacteristic
350C2×C4#6699011yescharacteristic
351C2×C4#6699111yescharacteristic
352C2×C4#6699211yescharacteristic
353C2×C4#6699211yescharacteristic
354C2×C4#6699311yescharacteristic
355C8—442no—
356C8—442no—
357C8—881no—
358C22—21no—
359C22—21no—
360C22—84no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22#1062283611yescharacteristic
368C22#1062285812yes—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—44no—
375C4—81no—
376C4—82no—
377C4—881no—
378C4#1062269012yes—
379C2—22no—
380C2—161no—
381C2—1761no—
382C2#1306963111yescharacteristic
383C2#1306963611yescharacteristic
384C2#1306967611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2658C2
socleC22×C11#392
prime radical#13079603C2
hypercenter#2658D11
hypocenterC11#10094
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2658

Complements

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

NH ≅ G/Ntype
2. #13079012C2semidirect
3. #13067333C2semidirect
4. #13067214C2semidirect
5. #13067123C2semidirect
6. #13066509C2semidirect
7. C11×#2658C2semidirect
129. #2658D11semidirect
318. C11#10094semidirect

Maximal subgroups

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

subgroupindex
#130796032
#130790122
#130673332
#130672142
#130671232
#130665092
C11×#26582
#1009411