Finite Group Databasebeta

← #14657449

Subgroups — #14657449

Order 2816.

460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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#13078076C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic, complemented
3#13067374C211yesmaximal, characteristic, complemented
4#13067067C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic, complemented
6#13066491C211yesmaximal, characteristic, complemented
7C11×#1547C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#67002—21no—
10C2×C4×D44C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622845—21no—
14C2×#66887—21no—
15#10622696—21no—
16#10622685—21no—
17#10622670—22no—
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×#332—21no—
22C11×#331—21no—
23#10622192—21no—
24D4⋊(C11⋊C8)—21no—
25D4⋊(C11⋊C8)—21no—
26#10622121—21no—
27#10622121—21no—
28#10622117—22no—
29C2×C11×#41—21no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C2×C11×M16—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C42×C11C2311yescharacteristic
42#67002—42no—
43#67002—42no—
44C2×#4325—22no—
45C2×#4323—22no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×#4318—21no—
49C2×#4318—21no—
50C22×C11⋊C8—21no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59#66899—22no—
60#66896—22no—
61#66887—42no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66C4×C11⋊C8—21no—
67C4×C11⋊C8D411yescharacteristic
68C4×C11⋊C8D411yescharacteristic
69#10456—111nomaximal, Sylow
70C23×D11—21no—
71C11×#41—41no—
72C11×#41—41no—
73C11×#41—41no—
74C11×#41—41no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44D812yes—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—81no—
94C2×C4×D11—81no—
95C11×M16—41no—
96C11×M16—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—81no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108#4325—44no—
109#4323—44no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114#4318—41no—
115#4318—41no—
116#4318—41no—
117#4318—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—41no—
123#3036—111no—
124#1800—111no—
125#1567—111no—
126#1547D1111yescharacteristic, complemented
127#1492—111no—
128C2×D4⋊C8—111no—
129#1292—111no—
130C23×C11—41no—
131C23×C11#12311yescharacteristic
132C22×D11—22no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—81no—
136C22×D11—81no—
137Q8×C11—41no—
138Q8×C11—41no—
139D4×C11—41no—
140D4×C11—41no—
141D4×C11—41no—
142D4×C11—41no—
143D4×C11—81no—
144D4×C11—81no—
145D4×C11—81no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12311yescharacteristic
157C2×C4×C11#12411yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C2×Dic11—41no—
163C2×Dic11—81no—
164D44—22no—
165D44—22no—
166D44—41no—
167D44—41no—
168C4×D11—82no—
169C4×D11—81no—
170C4×D11—81no—
171C8×C11—81no—
172C8×C11—81no—
173C11⋊C8—22no—
174C11⋊C8—41no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C2×AGL(1,ℤ/8)—221no—
178#532C2×D1111yescharacteristic
179C2×C4×D4—111no—
180#463—222no—
181#461—221no—
182#459—221no—
183#423—111no—
184#423—111no—
185#423C2×D1111yescharacteristic
186C2×C4⋊C8C2×D1111yescharacteristic
187#417—221no—
188C2×#100—221no—
189C2×C4×C8—111no—
190#343—221no—
191#335—222no—
192#332—21no—
193#331—21no—
194D4⋊C8—221no—
195D4⋊C8—221no—
196D4⋊C8—221no—
197D4⋊C8—221no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#39411yescharacteristic
204C22×C11#48011yescharacteristic
205C22×C11#48211yescharacteristic
206C2×D11—42no—
207C2×D11—82no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—82no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—81no—
215C4×C11#44711yescharacteristic
216C4×C11#45211yescharacteristic
217C4×C11#46611yescharacteristic
218C4×C11#46811yescharacteristic
219C4×C11#47111yescharacteristic
220C4×C11#47211yescharacteristic
221Dic11—81no—
222C2×#41—21no—
223C22×D4—111no—
224C23×C4—221no—
225AGL(1,ℤ/8)—442no—
226AGL(1,ℤ/8)—442no—
227C2×SD16—222no—
228C2×D8—222no—
229C2×M16—21no—
230C2×M16—221no—
231C2×M16—221no—
232C22×C8—21no—
233C22×C8—221no—
234C4⋊Q8C22⋊D1111yescharacteristic
235#127C22⋊D1111yescharacteristic
236#124—21no—
237#121—21no—
238#121—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—221no—
242C4×D4—221no—
243C4×D4—221no—
244C4×D4—221no—
245C2×C4⋊C4—111no—
246C2×C22⋊C4—221no—
247C2×C42C22×D1111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255C4⋊C8—221no—
256#103—222no—
257#102—222no—
258#100—442no—
259C4×C8—111no—
260C4×C8—111no—
261C4×C8—221no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11—161no—
265C2×C11#203311yescharacteristic
266C2×C11#205011yescharacteristic
267C2×C11#205111yescharacteristic
268D11—82no—
269C24—221no—
270#41—41no—
271#41—41no—
272#41—41no—
273#41—41no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—112no—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4—221no—
285C22×C4—41no—
286C22×C4—221no—
287C22×C4—441no—
288C22×C4—441no—
289C22×C4—881no—
290C22×C4—881no—
291C22×C4#433911yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4#434111yescharacteristic
294SD16—444no—
295D8—444no—
296M16—41no—
297M16—41no—
298M16—441no—
299M16—441no—
300M16—441no—
301M16—441no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—81no—
305C2×C8—221no—
306C2×C8—221no—
307C2×C8—222no—
308C2×C8—442no—
309C2×C8—441no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C42#433911yescharacteristic
319C42D4×D1111yescharacteristic
320C42D4×D1111yescharacteristic
321C42C2×C22⋊D1111yescharacteristic
322C11#1045611yescharacteristic, complemented, Sylow
323C23—41no—
324C23—222no—
325C23—441no—
326C23—441no—
327C23—881no—
328C23—881no—
329C23#6693611yescharacteristic
330Q8—41no—
331Q8—41no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—81no—
337D4—81no—
338D4—81no—
339D4—222no—
340D4—222no—
341D4—441no—
342D4—441no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—441no—
350C2×C4—882no—
351C2×C4—881no—
352C2×C4—881no—
353C2×C4—881no—
354C2×C4#6693711yescharacteristic
355C2×C4#6693711yescharacteristic
356C2×C4#6693811yescharacteristic
357C2×C4D8×D1111yescharacteristic
358C2×C4#6696411yescharacteristic
359C2×C4#6696811yescharacteristic
360C2×C4#6696911yescharacteristic
361C2×C4#6698211yescharacteristic
362C2×C4#6699011yescharacteristic
363C2×C4#6699211yescharacteristic
364C8—81no—
365C8—81no—
366C8—222no—
367C8—441no—
368C8—442no—
369C8—881no—
370C22—21no—
371C22—21no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—442no—
376C22—882no—
377C22—882no—
378C22—881no—
379C22—881no—
380C22#1062238711yescharacteristic
381C22#1062239211yescharacteristic
382C22#1062257211yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—81no—
387C4—881no—
388C4#1062238811yescharacteristic
389C4#1062239311yescharacteristic
390C4#1062276911yescharacteristic
391C4#1062278611yescharacteristic
392C4#1062281211yescharacteristic
393C4#1062281611yescharacteristic
394C2—21no—
395C2—21no—
396C2—161no—
397C2—882no—
398C2#1306979611yescharacteristic
399C2#1306990111yescharacteristic
400C2#1306990611yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1547C2
socleC22×C11#394
prime radical#13078076C2
hypercenter#1547D11
hypocenterC11#10456
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
2. #13068605C2semidirect
3. #13067374C2semidirect
4. #13067067C2semidirect
5. C2×#10622121C2semidirect
6. #13066491C2semidirect
7. C11×#1547C2semidirect
126. #1547D11semidirect
322. C11#10456semidirect

Maximal subgroups

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

subgroupindex
#130780762
#130686052
#130673742
#130670672
C2×#106221212
#130664912
C11×#15472
#1045611