Finite Group Databasebeta

← #14812743

Subgroups — #14812743

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073855C211yesmaximal, characteristic, complemented
2#13071563C211yesmaximal, characteristic
3#13070136C212yesmaximal
4#13070003C212yesmaximal
5#13069386C212yesmaximal, complemented
6#13069380C211yesmaximal, characteristic, complemented
7#13069209C212yesmaximal, complemented
8#13068776C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic
10C4×#66885C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C2×#66945—21no—
13C2×C4×D44C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2212yes—
16C2×C4×C8×C11C2211yescharacteristic
17C4×C11×C4⋊C4C2211yescharacteristic
18C2×#66885C2211yescharacteristic
19C2×#66885C2211yescharacteristic
20C2×#66885C2212yes—
21C2×#66882C2212yes—
22C2×#66882C2212yes—
23C2×#66881C2212yes—
24#10622600—21no—
25#10622590—21no—
26#10622586—21no—
27#10622552C2212yes—
28#10622549C2212yes—
29#10622548C2211yescharacteristic
30#10622548C2211yescharacteristic
31C4×C4⋊Dic11C2211yescharacteristic
32C4×C4⋊Dic11C2212yes—
33#10622541C2212yes—
34#10622283—22no—
35#10622273—22no—
36C11×#336C2212yes—
37#10622189C2212yes—
38#10622189C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C22×C8×C11C2312yes—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11C2312yes—
49C2×C42×C11C2311yescharacteristic
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11C2311yescharacteristic
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—21no—
65#66945—44no—
66C4×D44—22no—
67C4×D44Q814yes—
68C11×C4⋊C8—24no—
69C11×C4⋊C8—22no—
70C4×C8×C11—22no—
71C11×#95D412yes—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77#66885—22no—
78#66885—22no—
79#66885—42no—
80#66882—24no—
81#66882—42no—
82#66881—42no—
83#26087—111nomaximal, Sylow
84C23×D11—21no—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2411yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44C2×Q812yes—
101C2×C4×D11—24no—
102C2×C4×D11—42no—
103C2×C4×D11—42no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—21no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11#4112yes—
112C2×C8×C11#4112yes—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11C2×Q812yes—
118C42×C11#4112yes—
119(C2×D11)⋊C4—24no—
120(C2×D11)⋊C4—44no—
121(C2×D11)⋊C4—82no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—21no—
131C4⋊Dic11—42no—
132C4⋊Dic11—42no—
133C4⋊Dic11—81no—
134C4⋊Dic11—81no—
135C4⋊Dic11C2×Q812yes—
136Dic11⋊C4—82no—
137C4×Dic11—44no—
138C4×Dic11—42no—
139#2571—111no—
140#2354—111no—
141#2092—112no—
142#2067—112no—
143#1949—112no—
144#1948—111no—
145#1939D1111yescharacteristic, complemented
146#1921—112no—
147#1845—111no—
148#1802—111no—
149C4×#102—111no—
150C23×C11C22×D411yescharacteristic
151C22×D11—22no—
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11C22⋊Q812yes—
167C2×C4×C11C22⋊Q812yes—
168C2×C4×C11#13512yes—
169C2×C4×C11AGL(1,ℤ/8)12yes—
170C2×C4×C11C22×Q811yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C2×C4×C11H(5,𝔽2)11yescharacteristic
175C2×C4×C112−1+411yescharacteristic
176C2×Dic11—22no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—41no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—41no—
191D44—22no—
192D44—22no—
193D44—41no—
194D44—41no—
195C4×D11—48no—
196C8×C11—22no—
197C8×C11—22no—
198C8×C11—42no—
199C2×C4×D4—111no—
200C2×#117—221no—
201C2×#107—112no—
202C2×#107—112no—
203C2×#106—112no—
204C2×C4⋊C8C2×D1111yescharacteristic
205C2×C4⋊C8C2×D1112yes—
206C2×#102—111no—
207C2×#102—111no—
208C2×#102—112no—
209C2×C4×C8C2×D1111yescharacteristic
210#400—222no—
211#390—112no—
212#389—112no—
213#389—221no—
214#388—222no—
215#384—111no—
216#384—111no—
217#382—112no—
218#382—221no—
219#380—221no—
220C4×C4⋊C4—111no—
221C4×C4⋊C4—112no—
222C4×C4⋊C4C2×D1111yescharacteristic
223#340—112no—
224#340—112no—
225#340—111no—
226#340—111no—
227#336C2×D1112yes—
228C22×C11C2×C22⋊Q811yescharacteristic
229C22×C11#54711yescharacteristic
230C22×C11#55011yescharacteristic
231C22×C11C2×#13511yescharacteristic
232C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C22×C11#57611yescharacteristic
234C22×C11#57811yescharacteristic
235C2×D11—42no—
236C2×D11—42no—
237C2×D11—42no—
238C2×D11—81no—
239C2×D11—81no—
240C2×D11—81no—
241C2×D11—81no—
242C4×C11—22no—
243C4×C11—42no—
244C4×C11—42no—
245C4×C11#47814yes—
246C4×C11#53311yescharacteristic
247C4×C11#54411yescharacteristic
248C4×C11#55211yescharacteristic
249C4×C11#55311yescharacteristic
250Dic11—42no—
251Dic11—81no—
252Dic11—81no—
253Dic11—82no—
254Dic11—82no—
255C22×D4—111no—
256C23×C4—221no—
257C22×C8C22×D1112yes—
258C22×C8C22×D1111yescharacteristic
259C22×C8C22×D1111yescharacteristic
260C4×D4—114no—
261C4×D4—222no—
262#117—444no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—112no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4D4411yescharacteristic
274C2×C4⋊C4D4411yescharacteristic
275C2×C22⋊C4—221no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—222no—
278C2×C42—222no—
279C2×C42—221no—
280C2×C42C22×D1112yes—
281C2×C42C22×D1111yescharacteristic
282#107—224no—
283#107—442no—
284#106—442no—
285C4⋊C8—24no—
286C4⋊C8—22no—
287#102—222no—
288#102—222no—
289#102—442no—
290C4×C8—22no—
291#95—222no—
292#95—221no—
293#95—222no—
294#95—222no—
295#95—222no—
296#95D4412yes—
297C2×C11#244111yescharacteristic
298C2×C11C2×#47811yescharacteristic
299C2×C11#308311yescharacteristic
300C2×C11#334111yescharacteristic
301C2×C11#335311yescharacteristic
302C2×C11#339311yescharacteristic
303C2×C11#339911yescharacteristic
304D11—82no—
305C24—221no—
306C2×D4—112no—
307C2×D4—221no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—221no—
312C22×C4—221no—
313C22×C4—224no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4C2×D4412yes—
321C22×C4C2×D4412yes—
322C22×C4C2×D4411yescharacteristic
323C22×C4C2×D4411yescharacteristic
324C22×C4C23×D1111yescharacteristic
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8#434112yes—
333C2×C8#434312yes—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—112no—
337C4⋊C4—221no—
338C4⋊C4—221no—
339C4⋊C4—221no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C4⋊C4—221no—
344C4⋊C4—222no—
345C4⋊C4—221no—
346C4⋊C4—442no—
347C4⋊C4—442no—
348C4⋊C4—882no—
349C4⋊C4—881no—
350C4⋊C4—881no—
351C22⋊C4—224no—
352C22⋊C4—444no—
353C22⋊C4—882no—
354C42—22no—
355C42—22no—
356C42—444no—
357C42—442no—
358C42#434112yes—
359C42Q8×D1112yes—
360C11#2608711yescharacteristic, complemented, Sylow
361C23—222no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23C22×D4411yescharacteristic
369D4—222no—
370D4—222no—
371D4—441no—
372D4—441no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—222no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—448no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4#6695012yes—
398C2×C4#6695012yes—
399C2×C4#6695712yes—
400C2×C4#6696112yes—
401C2×C4C2×#434111yescharacteristic
402C2×C4C2×#434111yescharacteristic
403C2×C4C2×Q8×D1111yescharacteristic
404C2×C4C2×#434311yescharacteristic
405C2×C4#6704211yescharacteristic
406C2×C4#6704311yescharacteristic
407C8—22no—
408C8—22no—
409C8—42no—
410C22—442no—
411C22—442no—
412C22—442no—
413C22—881no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22C2×#6695011yescharacteristic
418C22#1062308611yescharacteristic
419C22#1062310811yescharacteristic
420C22C2×#6695711yescharacteristic
421C22C2×#6696111yescharacteristic
422C22#1062328311yescharacteristic
423C22#1062328411yescharacteristic
424C4—22no—
425C4—42no—
426C4—42no—
427C4—442no—
428C4—881no—
429C4—882no—
430C4—882no—
431C4—881no—
432C4#1062246014yes—
433C4#1062314911yescharacteristic
434C4#1062317311yescharacteristic
435C4#1062322011yescharacteristic
436C4#1062325911yescharacteristic
437C2—882no—
438C2#1307232711yescharacteristic
439C2C2×#1062246011yescharacteristic
440C2#1307846911yescharacteristic
441C2#1308103911yescharacteristic
442C2#1308120111yescharacteristic
443C2#1308160511yescharacteristic
444C2#1308166011yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#26087
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. #13073855C2semidirect
5. #13069386C2semidirect
6. #13069380C2semidirect
7. #13069209C2semidirect
8. #13068776C2semidirect
11. C11×#1939C2semidirect
145. #1939D11semidirect
360. C11#26087semidirect

Maximal subgroups

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

subgroupindex
#130738552
#130715632
#130701362
#130700032
#130693862
#130693802
#130692092
#130687762
#130686172
C4×#668852
C11×#19392
#2608711