Finite Group Databasebeta

← #14650734

Subgroups — #14650734

Order 2816.

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

normal subgroups only

This group has 464 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#13079430C211yesmaximal, characteristic
2#13077676C211yesmaximal, characteristic, complemented
3#13067173C211yesmaximal, characteristic, complemented
4#13067145C211yesmaximal, characteristic, complemented
5#13066525C211yesmaximal, characteristic, complemented
6#13066493C211yesmaximal, characteristic, complemented
7C11×#1471C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9#10623322C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12#10622831C411yescharacteristic, complemented
13#10622830C411yescharacteristic, complemented
14#10622824C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622741—21no—
18#10622740—21no—
19#10622655—21no—
20#10622652—21no—
21#10622650—21no—
22#10622648—21no—
23#10622584C411yescharacteristic, complemented
24#10622580C411yescharacteristic, complemented
25#10622342—21no—
26#10622341—21no—
27#10622340—21no—
28#10622333—21no—
29C11×#323—21no—
30C11×#323—21no—
31#10622175—21no—
32#10622175—21no—
33#10622108—21no—
34#10622105—21no—
35C22×D4×C11—21no—
36C22×D4×C11C2×C411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C2×#4339D411yescharacteristic
39C2×C11×M16—21no—
40C22×C8×C11—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4—21no—
47#67006—21no—
48C2×C22⋊Dic11—21no—
49C2×#4324—21no—
50C2×#4323—21no—
51#66983C2×C411yescharacteristic
52#66983D411yescharacteristic
53#66982—21no—
54C4×C22⋊D11—21no—
55C4×C22⋊D11—21no—
56#66979D411yescharacteristic
57#66977C2×C411yescharacteristic
58#66977D411yescharacteristic
59C2×#4318—21no—
60C2×#4318—21no—
61C2×#4313—21no—
62C2×C8×D11—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8D411yescharacteristic
67C11×C22⋊C8D411yescharacteristic
68#66896—21no—
69#66896—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)C2×C411yescharacteristic
75C22⋊(C11⋊C8)C2×C411yescharacteristic
76C22⋊(C11⋊C8)D411yescharacteristic
77C22⋊(C11⋊C8)D411yescharacteristic
78(C2×D11)⋊C8—21no—
79(C2×D11)⋊C8—21no—
80#66879—21no—
81Dic11⋊C8—21no—
82Dic11⋊C8—21no—
83C8×Dic11—21no—
84#66874—21no—
85#66873—21no—
86#66872—21no—
87#66871—21no—
88#9332—111nomaximal, Sylow
89C24×C11—21no—
90C24×C11#4111yescharacteristic
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—81no—
96C2×D4×C11—82no—
97C22×C4×C11—21no—
98C22×C4×C11—81no—
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C2×C22⋊D11—21no—
106C2×C22⋊D11—21no—
107C2×C22⋊D11—21no—
108C22×Dic11—41no—
109#4339—81no—
110C2×D44C22⋊C411yescharacteristic
111C2×C4×D11—21no—
112C2×Dic22C22⋊C411yescharacteristic
113C11×M16—81no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—41no—
117C2×C8×C11—81no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C22⋊Dic11—21no—
123C22⋊Dic11—21no—
124C22⋊Dic11—21no—
125C22⋊Dic11—81no—
126#4324—81no—
127#4323—81no—
128(C2×D11)⋊C4—21no—
129(C2×D11)⋊C4—21no—
130C4⋊Dic11C22⋊C411yescharacteristic
131C4⋊Dic11C22⋊C411yescharacteristic
132Dic11⋊C4—21no—
133Dic11⋊C4—21no—
134C4×Dic11—21no—
135#4318—81no—
136#4318—81no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141#4313—81no—
142C8×D11—81no—
143#3194—111no—
144#2978—111no—
145#1516—111no—
146#1510—111no—
147#1471D1111yescharacteristic, complemented
148#1306—111no—
149#1293—111no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—42no—
154C23×C11—41no—
155C23×C11—81no—
156C23×C11—81no—
157C23×C11C4×D411yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11#12311yescharacteristic
160C22×D11—21no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—81no—
164D4×C11—82no—
165D4×C11—82no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—81no—
174C2×C4×C11C2×C22⋊C411yescharacteristic
175C2×C4×C11C4×D411yescharacteristic
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C22⋊D11—81no—
179C22⋊D11—81no—
180C22⋊D11—81no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186C2×Dic11—81no—
187D44—41no—
188C4×D11—41no—
189C4×D11—41no—
190Dic22—41no—
191C8×C11—41no—
192C8×C11—41no—
193C8×C11—81no—
194C11⋊C8—41no—
195C11⋊C8—41no—
196C11⋊C8—41no—
197C11⋊C8—41no—
198#525—111no—
199C2×#121C2×D1111yescharacteristic
200#483—111no—
201#482—221no—
202#480—111no—
203#469—221no—
204#468—221no—
205#450—111no—
206#449—221no—
207#447—111no—
208#436—221no—
209#436—221no—
210#435—221no—
211#435—221no—
212#433—221no—
213#408—221no—
214#407—111no—
215#407—111no—
216#407C2×D1111yescharacteristic
217C2×C22⋊C8C2×D1111yescharacteristic
218#381—111no—
219#328—221no—
220#327—221no—
221#327—221no—
222#327—221no—
223#323—21no—
224#323—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—82no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—162no—
239C22×C11#38611yescharacteristic
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—81no—
248Dic11—41no—
249Dic11—41no—
250Dic11—41no—
251Dic11—161no—
252C2×#41—111no—
253C22×D4—21no—
254C22×D4C4×D1111yescharacteristic
255C23×C4C22×D1111yescharacteristic
256C2×SD16—221no—
257C2×D8—221no—
258C2×M16—21no—
259C2×M16—221no—
260C2×M16—221no—
261C2×M16—221no—
262C22×C8—21no—
263C22×C8—221no—
264#123—221no—
265C22⋊Q8—111no—
266C22⋊Q8—111no—
267#121—21no—
268#121—21no—
269#121—21no—
270#121—21no—
271#121—111no—
272#121—111no—
273#120—221no—
274C4×D4—221no—
275C4×D4—221no—
276#117—111no—
277C2×C4⋊C4C4×D1111yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—221no—
280#107—221no—
281#106—221no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284#103—221no—
285#102—221no—
286#102—221no—
287#102—221no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8—111no—
292C22⋊C8—111no—
293C22⋊C8—111no—
294C22⋊C8—111no—
295C22⋊C8—221no—
296C22⋊C8—221no—
297C22⋊C8—221no—
298C22⋊C8—221no—
299C22⋊C8C22⋊D1111yescharacteristic
300C22⋊C8C22⋊D1111yescharacteristic
301#97—221no—
302C4×C8—221no—
303#95—221no—
304#95—221no—
305C2×C11—41no—
306C2×C11—41no—
307C2×C11—41no—
308C2×C11—161no—
309C2×C11#188111yescharacteristic
310C2×C11#190311yescharacteristic
311C2×C11#191311yescharacteristic
312D11—81no—
313C24—21no—
314C24#433911yescharacteristic
315#41—881no—
316C2×Q8—111no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—81no—
322C2×D4—82no—
323C2×D4—111no—
324C2×D4—221no—
325C2×D4—221no—
326C2×D4—221no—
327C22×C4—21no—
328C22×C4—81no—
329C22×C4—221no—
330C22×C4—441no—
331C22×C4C2×C4×D1111yescharacteristic
332C22×C4D4×D1111yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4#434111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337SD16—881no—
338D8—881no—
339M16—81no—
340M16—881no—
341M16—881no—
342M16—881no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—41no—
346C2×C8—81no—
347C2×C8—221no—
348C2×C8—221no—
349C2×C8—221no—
350C2×C8—221no—
351C2×C8—881no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—111no—
355C4⋊C4—111no—
356C4⋊C4—221no—
357C4⋊C4—221no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—221no—
361C22⋊C4—221no—
362C22⋊C4—221no—
363C22⋊C4—221no—
364C22⋊C4—221no—
365C22⋊C4—881no—
366C42—221no—
367C11#933211yescharacteristic, complemented, Sylow
368C23—41no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23—41no—
373C23—81no—
374C23—81no—
375C23—221no—
376C23#6693611yescharacteristic
377C23#6693711yescharacteristic
378C23C4×C22⋊D1111yescharacteristic
379Q8—441no—
380D4—41no—
381D4—41no—
382D4—81no—
383D4—82no—
384D4—82no—
385D4—441no—
386D4—881no—
387D4—881no—
388D4—881no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—881no—
403C2×C4—881no—
404C2×C4—881no—
405C2×C4C22⋊C4×D1111yescharacteristic
406C2×C4(C22⋊D11)⋊C411yescharacteristic
407C2×C4#6699011yescharacteristic
408C2×C4#6699111yescharacteristic
409C8—41no—
410C8—41no—
411C8—81no—
412C8—441no—
413C8—441no—
414C8—441no—
415C8—441no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—82no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—162no—
430C22—441no—
431C22—441no—
432C22—441no—
433C22#1062256911yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—441no—
440C4—441no—
441C4—441no—
442C4—1761no—
443C2—41no—
444C2—41no—
445C2—41no—
446C2—161no—
447C2—881no—
448C2#1306898111yescharacteristic
449C2#1306909911yescharacteristic
450C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1471C2
socleC22×C11#386
prime radical#13079430C2
cosocleC23×C4×C11C23
hypercenter#1471D11
hypocenterC11#9332
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #13077676C2semidirect
3. #13067173C2semidirect
4. #13067145C2semidirect
5. #13066525C2semidirect
6. #13066493C2semidirect
7. C11×#1471C2semidirect
12. #10622831C4semidirect
13. #10622830C4semidirect
23. #10622584C4semidirect
24. #10622580C4semidirect
147. #1471D11semidirect
367. C11#9332semidirect

Maximal subgroups

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

subgroupindex
#130794302
#130776762
#130671732
#130671452
#130665252
#130664932
C11×#14712
#933211