Finite Group Databasebeta

← #14658113

Subgroups — #14658113

Order 2816.

500 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 79 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#13079364C211yesmaximal, characteristic
2#13069080C211yesmaximal, characteristic, complemented
3#13069077C211yesmaximal, characteristic, complemented
4#13068801C211yesmaximal, characteristic, complemented
5#13067131C211yesmaximal, characteristic, complemented
6#13066492C211yesmaximal, characteristic, complemented
7C11×#1507C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C22×#4318C2211yescharacteristic
11C11×#407C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622830—21no—
14C2×#66897—21no—
15#10622820C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66887—21no—
18#10622651—21no—
19#10622651—21no—
20#10622649—21no—
21#10622646—21no—
22#10622580—21no—
23C2×C4⋊(C11⋊C8)—21no—
24C11×#327—21no—
25C11×#327—21no—
26#10622192—21no—
27#10622168—21no—
28#10622162—21no—
29#10622089—21no—
30#10622089—21no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C22×D44D411yescharacteristic
36C2×C11×M16—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#121—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C42×C11—21no—
45C2×#4323—21no—
46C2×#4323—21no—
47#66983—21no—
48#66983—21no—
49#66983—21no—
50#66983—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×C4⋊Dic11D411yescharacteristic
53C2×#4318—21no—
54C2×#4318—21no—
55C2×#4318—21no—
56C2×#4318—42no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8D411yescharacteristic
59C22×C11⋊C8D411yescharacteristic
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#95D411yescharacteristic
63C11×#95D411yescharacteristic
64#66897—42no—
65#66896—21no—
66#66896—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66887—42no—
72#66873—21no—
73#66873—21no—
74#66871—21no—
75#66871—21no—
76C4⋊(C11⋊C8)—42no—
77#10557—111nomaximal, Sylow
78C24×C11—21no—
79C24×C11#4111yescharacteristic
80C23×D11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—81no—
88C2×D4×C11—81no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C2×C22⋊D11—81no—
103C2×C22⋊D11—81no—
104C22×Dic11—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—41no—
108C2×D44—41no—
109C11×M16—41no—
110C11×M16—41no—
111C2×C8×C11—41no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11—41no—
118C42×C11—41no—
119#4323—81no—
120#4323—81no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125#4318—22no—
126#4318—22no—
127#4318—41no—
128#4318—41no—
129#4318—41no—
130#4318—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139#3186—111no—
140#1900—111no—
141#1900—111no—
142#1851—111no—
143#1507—111no—
144#1507D1111yescharacteristic, complemented
145#1293—111no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—41no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11#12111yescharacteristic
155C23×C11#12311yescharacteristic
156C23×C11#12311yescharacteristic
157C22×D11—41no—
158C22×D11—42no—
159C22×D11—81no—
160C22×D11—81no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—81no—
164D4×C11—82no—
165D4×C11—81no—
166D4×C11—81no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—81no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12411yescharacteristic
188C22⋊D11—82no—
189C22⋊D11—81no—
190C22⋊D11—81no—
191C2×Dic11—41no—
192C2×Dic11—81no—
193D44—41no—
194D44—41no—
195D44—81no—
196C8×C11—81no—
197C11⋊C8—42no—
198C11⋊C8—41no—
199C11⋊C8—41no—
200C11⋊C8—81no—
201C22×M16—111no—
202C2×#121—111no—
203C2×#121C2×D1111yescharacteristic
204#480—221no—
205#480—221no—
206#466—221no—
207#466—221no—
208#447—221no—
209#447—221no—
210C2×C4⋊C8—221no—
211C2×#100—221no—
212C2×#100—221no—
213#407—111no—
214#407C2×D1111yescharacteristic
215C2×C22⋊C8—111no—
216C4×C22⋊C4C2×D1111yescharacteristic
217#343—221no—
218#343—221no—
219#336—221no—
220#327—21no—
221#327—21no—
222#327—221no—
223#327—221no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—162no—
238C22×C11#39411yescharacteristic
239C22×C11#47211yescharacteristic
240C22×C11#47211yescharacteristic
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—162no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—42no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11B(4,𝔽2)11yescharacteristic
252C4×C11#45811yescharacteristic
253Dic11—81no—
254C22×D4—21no—
255C22×D4—111no—
256C22×D4—221no—
257C22×D4D4411yescharacteristic
258C23×C4C22×D1111yescharacteristic
259C2×D8—221no—
260C2×D8—221no—
261C2×M16—21no—
262C2×M16—221no—
263C2×M16—221no—
264C2×M16—221no—
265C2×M16—442no—
266C22×C8—111no—
267C22×C8—111no—
268C22×C8—221no—
269#121—21no—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—221no—
274#121—221no—
275#121—221no—
276#121—221no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4D4411yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—221no—
282C2×C42—21no—
283#107—221no—
284#107—221no—
285C4⋊C8—442no—
286#102—221no—
287#102—221no—
288#102—221no—
289#102—221no—
290#100—442no—
291#100—442no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—221no—
295C22⋊C8—221no—
296C22⋊C8—221no—
297C22⋊C8—221no—
298#95C22⋊D1111yescharacteristic
299#95C22⋊D1111yescharacteristic
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—41no—
303C2×C11—41no—
304C2×C11—161no—
305C2×C11#204411yescharacteristic
306C2×C11#204511yescharacteristic
307C2×C11#205011yescharacteristic
308D11—161no—
309C24—21no—
310C24—221no—
311C24#434111yescharacteristic
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—81no—
319C2×D4—81no—
320C2×D4—221no—
321C2×D4—221no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4—881no—
327C2×D4—881no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—221no—
334C22×C4C2×D4411yescharacteristic
335C22×C4#433911yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4D4×D1111yescharacteristic
338C22×C4#434111yescharacteristic
339C22×C4C2×C22⋊D1111yescharacteristic
340D8—881no—
341D8—881no—
342M16—41no—
343M16—41no—
344M16—222no—
345M16—222no—
346M16—441no—
347M16—441no—
348M16—441no—
349M16—441no—
350C2×C8—41no—
351C2×C8—222no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8—441no—
355C2×C8—441no—
356C2×C8—441no—
357C2×C8—441no—
358C2×C8—441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C22⋊C4—42no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C42—41no—
369C42—41no—
370C11#1055711yescharacteristic, complemented, Sylow
371C23—21no—
372C23—21no—
373C23—41no—
374C23—41no—
375C23—42no—
376C23—41no—
377C23—81no—
378C23—81no—
379C23—442no—
380C23—441no—
381C23—881no—
382C23—881no—
383C23#6693611yescharacteristic
384C23#6693911yescharacteristic
385C23#6699211yescharacteristic
386D4—41no—
387D4—41no—
388D4—81no—
389D4—82no—
390D4—81no—
391D4—81no—
392D4—441no—
393D4—441no—
394D4—881no—
395D4—882no—
396D4—881no—
397D4—881no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—81no—
415C2×C4—441no—
416C2×C4—881no—
417C2×C4#6693511yescharacteristic
418C2×C4#6693811yescharacteristic
419C2×C4#6698311yescharacteristic
420C2×C4#6699111yescharacteristic
421C8—81no—
422C8—442no—
423C8—441no—
424C8—441no—
425C8—881no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—162no—
440C22—881no—
441C22—881no—
442C22—881no—
443C22—1762no—
444C22#1062257411yescharacteristic
445C22#1062281211yescharacteristic
446C22#1062281211yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—42no—
451C4—81no—
452C4—81no—
453C4—881no—
454C4#1062235411yescharacteristic
455C4#1062235511yescharacteristic
456C2—21no—
457C2—21no—
458C2—41no—
459C2—41no—
460C2—161no—
461C2—1761no—
462C2#1306986611yescharacteristic
463C2#1306987111yescharacteristic
464C2#1306990211yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1507C2
socleC22×C11#394
prime radical#13079364C2
hypercenter#1507D11
hypocenterC11#10557
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #13069080C2semidirect
3. #13069077C2semidirect
4. #13068801C2semidirect
5. #13067131C2semidirect
6. #13066492C2semidirect
7. C11×#1507C2semidirect
144. #1507D11semidirect
370. C11#10557semidirect

Maximal subgroups

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

subgroupindex
#130793642
#130690802
#130690772
#130688012
#130671312
#130664922
C11×#15072
#1055711