Finite Group Databasebeta

← #14657673

Subgroups — #14657673

Order 2816.

446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079531C211yesmaximal, characteristic
2#13069455C211yesmaximal, characteristic, complemented
3#13067407C211yesmaximal, characteristic, complemented
4#13067285C211yesmaximal, characteristic, complemented
5#13067033C211yesmaximal, characteristic, complemented
6#13066505C211yesmaximal, characteristic, complemented
7C11×#1560C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66887—22no—
13#10622701—21no—
14#10622686—21no—
15#10622649—22no—
16#10622628—21no—
17#10622628—21no—
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21C11×#333—21no—
22C11×#331—21no—
23D4⋊(C11⋊C8)—22no—
24#10622123—22no—
25#10622118—21no—
26#10622117—21no—
27C2×C11×#41—21no—
28C22×D44—21no—
29C22×D44—21no—
30C22×D44D412yes—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×#127D411yescharacteristic
35C11×#124—21no—
36C11×#121—21no—
37C11×#121—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4323—22no—
42C2×#4323—22no—
43C2×#4318—21no—
44#66927—21no—
45#66927—21no—
46#66927—21no—
47#66927—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54#66887—44no—
55#66873—22no—
56#66873—22no—
57C4⋊(C11⋊C8)D411yescharacteristic
58C4⋊(C11⋊C8)D411yescharacteristic
59C4⋊(C11⋊C8)D412yes—
60#66867—21no—
61C4×C11⋊C8—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10488—111nomaximal, Sylow
65C23×D11—22no—
66C11×#41—82no—
67C2×Q8×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C2×D44—22no—
77C2×D44—22no—
78C2×D44—42no—
79C2×D44—42no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—81no—
85C2×D44—81no—
86C2×D44—82no—
87C11×M16—42no—
88C11×M16—81no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99#4323—82no—
100#4323—82no—
101#4318—22no—
102#4318—41no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—41no—
107#3205—111no—
108#1965—111no—
109#1574—111no—
110#1560D1111yescharacteristic, complemented
111#1545—111no—
112#1484—111no—
113#1299—111no—
114C23×C11—41no—
115C23×C11#12311yescharacteristic
116C22×D11—42no—
117C22×D11—44no—
118C22×D11—82no—
119C22×D11—82no—
120Q8×C11—81no—
121D4×C11—41no—
122D4×C11—41no—
123D4×C11—41no—
124D4×C11—41no—
125D4×C11—81no—
126D4×C11—82no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—82no—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12311yescharacteristic
139C2×C4×C11#12411yescharacteristic
140D44—42no—
141D44—42no—
142D44—82no—
143D44—82no—
144D44—82no—
145D44—81no—
146D44—81no—
147D44—82no—
148C8×C11—81no—
149C8×C11—81no—
150C11⋊C8—42no—
151C11⋊C8—41no—
152C11⋊C8—41no—
153C11⋊C8—42no—
154#532C2×D1111yescharacteristic
155C2×#127—111no—
156#493—221no—
157#486—221no—
158#459—221no—
159#459—221no—
160#447—222no—
161#431—111no—
162#431—111no—
163#423C2×D1111yescharacteristic
164#423C2×D1111yescharacteristic
165C2×#100—222no—
166C4×M16—111no—
167#335—221no—
168#334—221no—
169#333—21no—
170#331—21no—
171#331—222no—
172D4⋊C8—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11#39411yescharacteristic
180C2×D11—82no—
181C2×D11—82no—
182C2×D11—82no—
183C2×D11—164no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—81no—
188C4×C11#45311yescharacteristic
189C4×C11#45511yescharacteristic
190C4×C11#47111yescharacteristic
191C4×C11#47211yescharacteristic
192C4×C11#47212yes—
193C2×#41—21no—
194C22×D4—112no—
195C22×D4—221no—
196C22×D4—221no—
197C2×D8—222no—
198C2×D8—222no—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16—221no—
202C4⋊Q8C22⋊D1111yescharacteristic
203#127—221no—
204#127—221no—
205#127—221no—
206#127—221no—
207#127C22⋊D1111yescharacteristic
208#124—21no—
209#121—21no—
210#121—21no—
211C4×D4—21no—
212C4×D4—21no—
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—112no—
219C4⋊C8—111no—
220C4⋊C8—111no—
221#102—222no—
222#102—222no—
223#100—444no—
224C22⋊C8—221no—
225C22⋊C8—221no—
226#97—221no—
227C4×C8—221no—
228C4×C8—221no—
229C4×C8—221no—
230C2×C11—41no—
231C2×C11—161no—
232C2×C11#203711yescharacteristic
233C2×C11#204511yescharacteristic
234C2×C11#205111yescharacteristic
235D11—162no—
236C24—222no—
237#41—82no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—41no—
243C2×D4—222no—
244C2×D4—222no—
245C2×D4—442no—
246C2×D4—442no—
247C2×D4—441no—
248C2×D4—441no—
249C2×D4—441no—
250C2×D4—441no—
251C2×D4—881no—
252C2×D4—881no—
253C2×D4—882no—
254C22×C4—41no—
255C22×C4#433911yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4#434111yescharacteristic
258D8—882no—
259D8—882no—
260M16—42no—
261M16—81no—
262M16—222no—
263M16—441no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—222no—
267C2×C8—221no—
268C2×C8—221no—
269C2×C8—441no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42#433911yescharacteristic
275C42D4×D1111yescharacteristic
276C42D4×D1111yescharacteristic
277C42C2×C22⋊D1111yescharacteristic
278C11#1048811yescharacteristic, complemented, Sylow
279C23—41no—
280C23—444no—
281C23—442no—
282C23—882no—
283C23—882no—
284C23#6693611yescharacteristic
285Q8—81no—
286D4—41no—
287D4—41no—
288D4—41no—
289D4—41no—
290D4—81no—
291D4—82no—
292D4—442no—
293D4—442no—
294D4—882no—
295D4—882no—
296D4—882no—
297D4—881no—
298D4—881no—
299D4—882no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4#6693711yescharacteristic
308C2×C4#6693711yescharacteristic
309C2×C4#6693811yescharacteristic
310C2×C4#6698211yescharacteristic
311C2×C4#6699011yescharacteristic
312C2×C4#6699211yescharacteristic
313C8—81no—
314C8—81no—
315C8—442no—
316C8—441no—
317C8—441no—
318C8—442no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—882no—
326C22—882no—
327C22—882no—
328C22—1764no—
329C22#1062257211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4#1062236212yes—
335C4#1062281111yescharacteristic
336C4#1062281211yescharacteristic
337C4#1062281511yescharacteristic
338C4#1062281611yescharacteristic
339C2—41no—
340C2—161no—
341C2—1762no—
342C2#1306982411yescharacteristic
343C2#1306987011yescharacteristic
344C2#1306990611yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1560C2
socleC22×C11#394
prime radical#13079531C2
hypercenter#1560D11
hypocenterC11#10488
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1560

Complements

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

NH ≅ G/Ntype
2. #13069455C2semidirect
3. #13067407C2semidirect
4. #13067285C2semidirect
5. #13067033C2semidirect
6. #13066505C2semidirect
7. C11×#1560C2semidirect
110. #1560D11semidirect
278. C11#10488semidirect

Maximal subgroups

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

subgroupindex
#130795312
#130694552
#130674072
#130672852
#130670332
#130665052
C11×#15602
#1048811