Finite Group Databasebeta

← #14811865

Subgroups — #14811865

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073651C211yesmaximal, characteristic, complemented
2#13071563C211yesmaximal, characteristic
3#13069989C212yesmaximal
4#13069763C212yesmaximal
5#13069571C212yesmaximal, complemented
6#13069380C211yesmaximal, characteristic, complemented
7#13069195C212yesmaximal, complemented
8#13068744C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic
10C4×#66885C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C2×#66945—21no—
13C2×C4×D44C2211yescharacteristic
14C2×#66923C2212yes—
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C4⋊C8C2212yes—
17C2×C4×C8×C11C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19C2×#66885C2211yescharacteristic
20C2×#66885C2211yescharacteristic
21C2×#66885C2212yes—
22C2×#66881C2212yes—
23#10622600—21no—
24#10622589—21no—
25#10622586—21no—
26#10622552C2212yes—
27#10622548C2211yescharacteristic
28#10622548C2211yescharacteristic
29C4×C4⋊Dic11C2212yes—
30C4×C4⋊Dic11C2211yescharacteristic
31#10622541C2212yes—
32#10622283—22no—
33#10622270—22no—
34C11×#336C2212yes—
35#10622189C2211yescharacteristic
36#10622189C2212yes—
37#10622189C2212yes—
38#10622189C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2212yes—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2312yes—
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⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—21no—
67#66945—44no—
68C4×D44—22no—
69C4×D44Q814yes—
70#66923—24no—
71#66923—42no—
72C11×C4⋊C8—22no—
73C11×C4⋊C8—42no—
74C4×C8×C11—22no—
75C11×#95D412yes—
76C11⋊#95—21no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79#66885—22no—
80#66885—22no—
81#66885—42no—
82#66881—24no—
83#26021—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—22no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
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—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—42no—
130C4⋊Dic11—42no—
131C4⋊Dic11—81no—
132C4⋊Dic11—81no—
133C4⋊Dic11C2×Q812yes—
134C4⋊Dic11#4112yes—
135C4⋊Dic11#4112yes—
136Dic11⋊C4—44no—
137Dic11⋊C4—44no—
138Dic11⋊C4—82no—
139C4×Dic11—44no—
140C4×Dic11—42no—
141#2552—111no—
142#2354—111no—
143#2065—112no—
144#2025—112no—
145#1989—112no—
146#1948—111no—
147#1939D1111yescharacteristic, complemented
148#1919—112no—
149#1834—111no—
150#1802—111no—
151C4×#102—111no—
152C23×C11C22×D411yescharacteristic
153C22×D11—22no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11C22⋊Q812yes—
169C2×C4×C11C22⋊Q812yes—
170C2×C4×C11#13512yes—
171C2×C4×C11AGL(1,ℤ/8)12yes—
172C2×C4×C11C22×Q811yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C11H(5,𝔽2)11yescharacteristic
177C2×C4×C112−1+411yescharacteristic
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193D44—22no—
194D44—22no—
195D44—41no—
196D44—41no—
197C4×D11—48no—
198C8×C11—42no—
199C8×C11—41no—
200C8×C11—41no—
201C2×#125—112no—
202C2×C4×D4—111no—
203C2×#117—221no—
204C2×#106—112no—
205C2×C4⋊C8C2×D1111yescharacteristic
206C2×C4⋊C8C2×D1112yes—
207C2×#102—111no—
208C2×#102—111no—
209C2×#102—112no—
210C2×C4×C8C2×D1111yescharacteristic
211#398—222no—
212#390—112no—
213#389—112no—
214#389—221no—
215#388—222no—
216#384—111no—
217#384—111no—
218#384—221no—
219#380—221no—
220C4×C4⋊C4—112no—
221C4×C4⋊C4—111no—
222C4×C4⋊C4C2×D1111yescharacteristic
223#340—112no—
224#340—112no—
225#340—112no—
226#340—111no—
227#340—112no—
228#340—111no—
229#336C2×D1112yes—
230C22×C11C2×C22⋊Q811yescharacteristic
231C22×C11#54611yescharacteristic
232C22×C11#54811yescharacteristic
233C22×C11C2×#13511yescharacteristic
234C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
235C22×C11#57711yescharacteristic
236C22×C11#57711yescharacteristic
237C2×D11—42no—
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—81no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C4×C11—22no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11#47814yes—
248C4×C11#53311yescharacteristic
249C4×C11#54411yescharacteristic
250C4×C11#55511yescharacteristic
251C4×C11#55611yescharacteristic
252Dic11—42no—
253Dic11—42no—
254Dic11—42no—
255Dic11—82no—
256Dic11—82no—
257C22×D4—111no—
258C23×C4—221no—
259C22×C8C22×D1111yescharacteristic
260C22×C8C22×D1112yes—
261C22×C8C22×D1111yescharacteristic
262#125—224no—
263#125—442no—
264C4×D4—114no—
265C4×D4—222no—
266#117—444no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4D4411yescharacteristic
280C2×C4⋊C4D4411yescharacteristic
281C2×C22⋊C4—221no—
282C2×C22⋊C4—222no—
283C2×C22⋊C4—222no—
284C2×C42—222no—
285C2×C42—221no—
286C2×C42C22×D1112yes—
287C2×C42C22×D1111yescharacteristic
288#106—224no—
289C4⋊C8—22no—
290C4⋊C8—42no—
291#102—222no—
292#102—222no—
293#102—442no—
294C4×C8—22no—
295#95—222no—
296#95—221no—
297#95—222no—
298#95D4412yes—
299C2×C11#243911yescharacteristic
300C2×C11C2×#47811yescharacteristic
301C2×C11#308411yescharacteristic
302C2×C11#330311yescharacteristic
303C2×C11#333211yescharacteristic
304C2×C11#336011yescharacteristic
305C2×C11#336811yescharacteristic
306D11—82no—
307C24—221no—
308C2×D4—112no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—224no—
318C22×C4—222no—
319C22×C4—222no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4C2×D4412yes—
323C22×C4C2×D4412yes—
324C22×C4C2×D4411yescharacteristic
325C22×C4C2×D4411yescharacteristic
326C22×C4C23×D1111yescharacteristic
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—112no—
339C4⋊C4—112no—
340C4⋊C4—112no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—221no—
344C4⋊C4—222no—
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—444no—
349C4⋊C4—444no—
350C4⋊C4—442no—
351C4⋊C4—442no—
352C4⋊C4—882no—
353C4⋊C4—881no—
354C4⋊C4—881no—
355C22⋊C4—224no—
356C22⋊C4—444no—
357C22⋊C4—882no—
358C42—22no—
359C42—22no—
360C42—444no—
361C42—442no—
362C42#434112yes—
363C42Q8×D1112yes—
364C11#2602111yescharacteristic, complemented, Sylow
365C23—222no—
366C23—441no—
367C23—441no—
368C23—441no—
369C23—441no—
370C23—441no—
371C23—441no—
372C23C22×D4411yescharacteristic
373D4—222no—
374D4—222no—
375D4—441no—
376D4—441no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—448no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4#6695012yes—
402C2×C4#6695012yes—
403C2×C4#6695712yes—
404C2×C4#6696112yes—
405C2×C4C2×#434111yescharacteristic
406C2×C4#6703711yescharacteristic
407C2×C4C2×Q8×D1111yescharacteristic
408C2×C4#6704011yescharacteristic
409C2×C4#41×D1111yescharacteristic
410C2×C4#41×D1111yescharacteristic
411C8—41no—
412C8—42no—
413C8—41no—
414C22—442no—
415C22—442no—
416C22—442no—
417C22—881no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22C2×#6695011yescharacteristic
422C22#1062308511yescharacteristic
423C22#1062310711yescharacteristic
424C22C2×#6695711yescharacteristic
425C22C2×#6696111yescharacteristic
426C22#1062328211yescharacteristic
427C22#1062328211yescharacteristic
428C4—22no—
429C4—42no—
430C4—42no—
431C4—442no—
432C4—442no—
433C4—442no—
434C4—882no—
435C4—882no—
436C4#1062246014yes—
437C4#1062314711yescharacteristic
438C4#1062317211yescharacteristic
439C4#1062321911yescharacteristic
440C4#1062326011yescharacteristic
441C2—882no—
442C2#1307230511yescharacteristic
443C2C2×#1062246011yescharacteristic
444C2#1307848011yescharacteristic
445C2#1308054511yescharacteristic
446C2#1308094411yescharacteristic
447C2#1308126711yescharacteristic
448C2#1308134711yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#26021
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. #13073651C2semidirect
5. #13069571C2semidirect
6. #13069380C2semidirect
7. #13069195C2semidirect
8. #13068744C2semidirect
11. C11×#1939C2semidirect
147. #1939D11semidirect
364. C11#26021semidirect

Maximal subgroups

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

subgroupindex
#130736512
#130715632
#130699892
#130697632
#130695712
#130693802
#130691952
#130687442
#130686172
C4×#668852
C11×#19392
#2602111