Finite Group Databasebeta

← #14853479

Subgroups — #14853479

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077001C211yesmaximal, characteristic, complemented
2C4×#66993C211yesmaximal, characteristic
3#13070177C212yesmaximal, complemented
4#13069849C212yesmaximal
5#13069311C212yesmaximal, complemented
6#13069310C212yesmaximal, complemented
7#13068627C211yesmaximal, characteristic, complemented
8#13068626C211yesmaximal, characteristic, complemented
9#13068623C211yesmaximal, characteristic, complemented
10#13068471C211yesmaximal, characteristic, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66993C2211yescharacteristic
14C2×C4×C22⋊D11—22no—
15C2×C4×D44C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102C2212yes—
18C11×#382C2211yescharacteristic
19#10622834C2211yescharacteristic
20C2×#66896C2212yes—
21C2×#66885C2212yes—
22C2×#66879C2212yes—
23#10622601C2211yescharacteristic
24#10622598C2212yes—
25#10622589C2211yescharacteristic
26#10622586C2212yes—
27C2×#66873C2212yes—
28#10622570—22no—
29#10622549C2211yescharacteristic
30C42×Dic11C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622268—22no—
33#10622267—22no—
34C11×#340C2212yes—
35#10622189C2212yes—
36#10622188C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11—21no—
41C22×C22⋊D11—22no—
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C22×C8×C11C2312yes—
45C4×D4×C11—22no—
46C4×D4×C11—22no—
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11—22no—
52#66993—22no—
53#66993—22no—
54C4×C22⋊D11—48no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11D412yes—
63C2×C4×Dic11D412yes—
64C2×C4×Dic11C2311yescharacteristic
65C2×C4×Dic11C2311yescharacteristic
66C22×C11⋊C8C2312yes—
67C4×D44—22no—
68C4×D44—22no—
69C11×C4⋊C8—22no—
70C11×#102—42no—
71C11×#95—21no—
72C11×#95—21no—
73#66896—24no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78#66885—24no—
79#66879—42no—
80#66873—42no—
81C4⋊(C11⋊C8)—22no—
82#29127—111nomaximal, Sylow
83C24×C11—21no—
84C23×D11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11#4112yes—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—44no—
94C22×C4×C11—42no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C2×C22⋊D11—28no—
99C2×C22⋊D11—44no—
100C2×C22⋊D11—44no—
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D412yes—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44#4112yes—
111C2×C4×D11—44no—
112C2×C4×D11—42no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C22⋊C4—42no—
121C42×C11#4112yes—
122C42×C11#4112yes—
123C22⋊Dic11—44no—
124(C2×D11)⋊C4—44no—
125(C2×D11)⋊C4—42no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—44no—
131Dic11⋊C4—44no—
132Dic11⋊C4—44no—
133C4×Dic11—24no—
134C4×Dic11—21no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—21no—
138C4×Dic11—42no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142#2864—111no—
143C4×#127—111no—
144#2099—112no—
145#2041—112no—
146#1936—112no—
147#1936—112no—
148#1804—111no—
149#1804—111no—
150#1804—111no—
151#1804D1111yescharacteristic, complemented
152#1767—111no—
153C23×C11—22no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11C22×D411yescharacteristic
159C22×D11—22no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—42no—
163C22×D11—42no—
164D4×C11—22no—
165D4×C11—22no—
166D4×C11—41no—
167D4×C11—41no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—84no—
176C2×C4×C11#12412yes—
177C2×C4×C11#12412yes—
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11H(5,𝔽2)11yescharacteristic
183C2×C4×C112−1+411yescharacteristic
184C22⋊D11—416no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—42no—
191C2×Dic11—41no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11AGL(1,ℤ/8)14yes—
196D44—22no—
197D44—22no—
198D44—41no—
199D44—41no—
200C4×D11—84no—
201C8×C11—42no—
202C11⋊C8—42no—
203C2×#127—111no—
204C2×C4×D4—111no—
205C2×C4×D4—222no—
206C2×C4×D4C2×D1111yescharacteristic
207C2×C4⋊C8—111no—
208C2×C4⋊C8C2×D1111yescharacteristic
209C2×#102—112no—
210C2×#102—112no—
211C2×#102—112no—
212C2×#102C2×D1112yes—
213C2×#97—112no—
214#390—111no—
215#390—111no—
216#390—222no—
217#389—112no—
218#389—112no—
219#387—222no—
220#387—222no—
221#384—111no—
222#382—111no—
223#382C2×D1111yescharacteristic
224C43—111no—
225#340—112no—
226#340—112no—
227#340—112no—
228#340C2×D1112yes—
229#336—112no—
230C22×C11—42no—
231C22×C11—44no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—82no—
235C22×C11#52511yescharacteristic
236C22×C11C2×#12411yescharacteristic
237C22×C11#53711yescharacteristic
238C22×C11C2×AGL(1,ℤ/8)12yes—
239C22×C11#57512yes—
240C2×D11—42no—
241C2×D11—44no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—82no—
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—81no—
248C4×C11—82no—
249C4×C11#55211yescharacteristic
250C4×C11#55211yescharacteristic
251C4×C11#55311yescharacteristic
252C4×C11#55311yescharacteristic
253Dic11—24no—
254Dic11—42no—
255Dic11—82no—
256Dic11—81no—
257C22×D4—111no—
258C22×D4—222no—
259C22×D4C22×D1111yescharacteristic
260C23×C4—21no—
261C23×C4—221no—
262C22×C8—112no—
263C22×C8C22×D1112yes—
264#127—222no—
265#127—222no—
266C4×D4—22no—
267C4×D4—22no—
268C4×D4—222no—
269C4×D4—222no—
270C4×D4—448no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4C22×D1111yescharacteristic
277C2×C4⋊C4C22×D1112yes—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—222no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4—221no—
282C2×C42—112no—
283C2×C42—111no—
284C2×C42—111no—
285C2×C42—112no—
286C2×C42C22×D1111yescharacteristic
287C4⋊C8—22no—
288C4⋊C8—222no—
289#102—42no—
290#102—224no—
291#102—224no—
292#102—442no—
293#97—442no—
294#95—21no—
295#95—21no—
296#95—222no—
297#95—222no—
298#95—221no—
299#95—221no—
300C2×C11—82no—
301C2×C11#256211yescharacteristic
302C2×C11#311412yes—
303C2×C11#313511yescharacteristic
304C2×C11#313811yescharacteristic
305C2×C11#325112yes—
306D11—82no—
307C24—21no—
308C24—221no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—112no—
315C2×D4—228no—
316C2×D4—221no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—444no—
322C2×D4—444no—
323C2×D4#434312yes—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—44no—
327C22×C4—42no—
328C22×C4—112no—
329C22×C4—112no—
330C22×C4—222no—
331C22×C4—221no—
332C22×C4—444no—
333C22×C4—442no—
334C22×C4D4×D1111yescharacteristic
335C22×C4D4×D1111yescharacteristic
336C22×C4C23×D1111yescharacteristic
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—222no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—222no—
350C4⋊C4—222no—
351C4⋊C4—444no—
352C4⋊C4—444no—
353C4⋊C4—444no—
354C22⋊C4—42no—
355C22⋊C4—444no—
356C22⋊C4—444no—
357C22⋊C4—442no—
358C42—224no—
359C42—221no—
360C42—221no—
361C42—221no—
362C42—221no—
363C42—442no—
364C42#433912yes—
365C42#434112yes—
366C11#2912711yescharacteristic, complemented, Sylow
367C23—22no—
368C23—41no—
369C23—42no—
370C23—42no—
371C23—41no—
372C23—222no—
373C23—441no—
374C23—442no—
375C23—442no—
376C23—441no—
377C23C2×D4×D1111yescharacteristic
378D4—22no—
379D4—22no—
380D4—41no—
381D4—41no—
382D4—222no—
383D4—222no—
384D4—4416no—
385D4—441no—
386D4—441no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—84no—
395C2×C4—114no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—441no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—884no—
407C2×C4#6693812yes—
408C2×C4#6693812yes—
409C2×C4C2×#433911yescharacteristic
410C2×C4C2×#434111yescharacteristic
411C2×C4#6703711yescharacteristic
412C2×C4C2×#434311yescharacteristic
413C2×C4#41×D1111yescharacteristic
414C2×C4#6704311yescharacteristic
415C8—42no—
416C8—442no—
417C22—42no—
418C22—44no—
419C22—82no—
420C22—81no—
421C22—81no—
422C22—442no—
423C22—444no—
424C22—882no—
425C22—881no—
426C22—881no—
427C22C2×#6693811yescharacteristic
428C22#1062313911yescharacteristic
429C22#1062315811yescharacteristic
430C22#1062329912yes—
431C22D11×AGL(1,ℤ/8)12yes—
432C4—22no—
433C4—22no—
434C4—82no—
435C4—81no—
436C4—224no—
437C4—442no—
438C4—881no—
439C4—882no—
440C4#1062304511yescharacteristic
441C4#1062306011yescharacteristic
442C4#1062314511yescharacteristic
443C4#1062317311yescharacteristic
444C2—82no—
445C2—882no—
446C2#1307378111yescharacteristic
447C2#1307875912yes—
448C2#1307895911yescharacteristic
449C2#1307898811yescharacteristic
450C2#1307997512yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
hypercenter#1804D11
hypocenterC11#29127
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. #13077001C2semidirect
3. #13070177C2semidirect
5. #13069311C2semidirect
6. #13069310C2semidirect
7. #13068627C2semidirect
8. #13068626C2semidirect
9. #13068623C2semidirect
10. #13068471C2semidirect
11. C11×#1804C2semidirect
151. #1804D11semidirect
366. C11#29127semidirect

Maximal subgroups

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

subgroupindex
#130770012
C4×#669932
#130701772
#130698492
#130693112
#130693102
#130686272
#130686262
#130686232
#130684712
C11×#18042
#2912711