Finite Group Databasebeta

← #14648210

Subgroups — #14648210

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071680C211yesmaximal, characteristic
2#13069421C211yesmaximal, characteristic
3#13069377C211yesmaximal, characteristic, complemented
4C2×#10622123C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic, complemented
6#13066455C211yesmaximal, characteristic, complemented
7C11×#1948C211yesmaximal, characteristic, complemented
8C2×#66946—21no—
9C2×#66927C2211yescharacteristic
10C2×C4×D44—21no—
11C2×C11×#106—21no—
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15#10622601—21no—
16C2×#66873—22no—
17C2×#66872—21no—
18#10622552—21no—
19C4×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622278—22no—
23C11×#340—21no—
24#10622167—21no—
25#10622123C414yescomplemented
26C22×D44—21no—
27C22×D44—21no—
28C22×D44D412yes—
29C22×C4×D11—22no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38C2×(C2×D11)⋊C4—22no—
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4—22no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4×Dic11—21no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46#66946—42no—
47#66946—42no—
48#66927—21no—
49#66927—21no—
50#66927C2×C412yes—
51#66927Q812yes—
52C4×D44—42no—
53C4×D44—42no—
54C11×#106—42no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8C2×C412yescomplemented
57C11×#95—21no—
58C11⋊#95—21no—
59#66873—44no—
60#66872—42no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)C2×C412yescomplemented
63C4×C11⋊C8—21no—
64C4×C11⋊C8—21no—
65#8924—111nomaximal, Sylow
66C23×D11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—42no—
81C2×D44—42no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44C4⋊C414yes—
91C2×C4×D11—44no—
92C2×C4×D11—44no—
93C2×C4×D11—82no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4SD1612yes—
106C42×C11—41no—
107C42×C11—41no—
108C42×C11C22×C411yescharacteristic
109C42×C11C2×Q811yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11#4111yescharacteristic
112(C2×D11)⋊C4—44no—
113(C2×D11)⋊C4—44no—
114(C2×D11)⋊C4—82no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11SD1612yes—
119C4×Dic11—41no—
120C4×Dic11—41no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127#2366—111no—
128#1957—111no—
129#1948—111no—
130#1948D1111yescharacteristic, complemented
131C2×#331—111no—
132#1279—111no—
133#1279—111no—
134C23×C11#12011yescharacteristic
135C22×D11—24no—
136C22×D11—42no—
137C22×D11—42no—
138C22×D11—42no—
139C22×D11—42no—
140C22×D11—42no—
141C22×D11—42no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11C2×C4⋊C411yescharacteristic
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C22⋊Q811yescharacteristic
157C2×C4×C11C22⋊Q811yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11C2×SD1611yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×Dic11—22no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173D44—44no—
174D44—42no—
175D44—42no—
176D44—42no—
177D44—42no—
178D44—42no—
179D44—42no—
180D44—42no—
181D44—42no—
182D44—82no—
183C4×D11—88no—
184C8×C11—42no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C2×#127—111no—
188C2×C4×D4—221no—
189C2×C4×D4—221no—
190C2×#106—21no—
191C2×#106—221no—
192C2×C4⋊C8—111no—
193C2×C4⋊C8C2×D1111yescharacteristic
194C2×#102—222no—
195C2×C4×C8—111no—
196#390—221no—
197#390—221no—
198#386—222no—
199#384C2×D1111yescharacteristic
200C4×C4⋊C4—111no—
201C4×C4⋊C4C2×D1111yescharacteristic
202#340—21no—
203#340—221no—
204#331—114no—
205C22×C11#38511yescharacteristic
206C22×C11#44911yescharacteristic
207C22×C11#44911yescharacteristic
208C22×C11#45011yescharacteristic
209C22×C11#45011yescharacteristic
210C22×C11#45311yescharacteristic
211C22×C11#45511yescharacteristic
212C2×D11—44no—
213C2×D11—44no—
214C2×D11—44no—
215C2×D11—82no—
216C2×D11—82no—
217C2×D11—82no—
218C2×D11—82no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—42no—
222C4×C11—81no—
223C4×C11—161no—
224C4×C11C4×SD1611yescharacteristic
225C4×C11C4×SD1611yescharacteristic
226C4×C11#44211yescharacteristic
227C4×C11#44211yescharacteristic
228C4×C11#47611yescharacteristic
229C4×C11#47611yescharacteristic
230C4×C11#47811yescharacteristic
231C4×C11#47811yescharacteristic
232Dic11—42no—
233Dic11—81no—
234C22×D4—112no—
235C22×D4—221no—
236C22×D4—221no—
237C23×C4—222no—
238C22×C8—21no—
239C22×C8—221no—
240C22×C8—221no—
241#127—112no—
242#127—112no—
243#127—221no—
244#127—221no—
245C4×D4—442no—
246C4×D4—442no—
247C4×D4—442no—
248C4×D4—442no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4C22⋊D1111yescharacteristic
255C2×C4⋊C4C22⋊D1111yescharacteristic
256C2×C22⋊C4—222no—
257C2×C22⋊C4—222no—
258C2×C22⋊C4—222no—
259C2×C42—21no—
260C2×C42—221no—
261C2×C42C22×D1111yescharacteristic
262#106—42no—
263#106—442no—
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8—221no—
267C4⋊C8C4×D1112yescomplemented
268#102—444no—
269C4×C8—221no—
270C4×C8—221no—
271#95—21no—
272#95—221no—
273C2×C11#162011yescharacteristic
274C2×C11#162911yescharacteristic
275C2×C11#164211yescharacteristic
276C2×C11#164211yescharacteristic
277C2×C11#185611yescharacteristic
278C2×C11#186411yescharacteristic
279C2×C11#186411yescharacteristic
280D11—84no—
281C24—222no—
282C2×D4—114no—
283C2×D4—222no—
284C2×D4—222no—
285C2×D4—222no—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—442no—
289C2×D4—442no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—444no—
304C22×C4—444no—
305C22×C4—882no—
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—441no—
315C2×C8—441no—
316C2×C8—441no—
317C2×C8—441no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—112no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4#432512yes—
331C22⋊C4—444no—
332C22⋊C4—444no—
333C22⋊C4—882no—
334C42—41no—
335C42—41no—
336C42—441no—
337C42—441no—
338C42C2×C4×D1111yescharacteristic
339C42#433911yescharacteristic
340C42Q8×D1111yescharacteristic
341C42#434311yescharacteristic
342C11#892411yescharacteristic, complemented, Sylow
343C23—224no—
344C23—442no—
345C23—442no—
346C23—442no—
347C23—442no—
348C23—442no—
349C23—442no—
350C23#6699011yescharacteristic
351D4—444no—
352D4—442no—
353D4—442no—
354D4—442no—
355D4—442no—
356D4—442no—
357D4—442no—
358D4—442no—
359D4—442no—
360D4—882no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—222no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—888no—
379C2×C4C4⋊C4×D1111yescharacteristic
380C2×C4#6694611yescharacteristic
381C2×C4#6694711yescharacteristic
382C2×C4#6694911yescharacteristic
383C2×C4SD16×D1111yescharacteristic
384C2×C4#6696711yescharacteristic
385C2×C4#6696711yescharacteristic
386C2×C4#6696911yescharacteristic
387C2×C4C4×C22⋊D1111yescharacteristic
388C2×C4#6698511yescharacteristic
389C2×C4C2×#432511yescharacteristic
390C2×C4#6699911yescharacteristic
391C2×C4#6700211yescharacteristic
392C2×C4#6700311yescharacteristic
393C8—42no—
394C8—442no—
395C8—442no—
396C22—444no—
397C22—444no—
398C22—444no—
399C22—882no—
400C22—882no—
401C22—882no—
402C22—882no—
403C22#1062260211yescharacteristic
404C22#1062265011yescharacteristic
405C22#1062265911yescharacteristic
406C22#1062278211yescharacteristic
407C22#1062278511yescharacteristic
408C22#1062281111yescharacteristic
409C22#1062281511yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—161no—
415C4—442no—
416C4—881no—
417C4#1062246511yescharacteristic
418C4#1062248211yescharacteristic
419C4#1062248311yescharacteristic
420C4#1062248411yescharacteristic
421C4#1062262711yescharacteristic
422C4C4×#432511yescharacteristic
423C4#1062267911yescharacteristic
424C4#1062269711yescharacteristic
425C2—884no—
426C2#1306767411yescharacteristic
427C2#1306773111yescharacteristic
428C2#1306781411yescharacteristic
429C2#1306781511yescharacteristic
430C2#1306882411yescharacteristic
431C2#1306887411yescharacteristic
432C2#1306887611yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1948C2
socleC23×C11#120
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1948D11
hypocenterC11#8924
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #13069377C2semidirect
5. #13066457C2semidirect
6. #13066455C2semidirect
7. C11×#1948C2semidirect
25. #10622123C4semidirect
56. C11×C4⋊C8C2×C4semidirect
62. C4⋊(C11⋊C8)C2×C4semidirect
130. #1948D11semidirect
267. C4⋊C8C4×D11semidirect
342. C11#8924semidirect

Maximal subgroups

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

subgroupindex
#130716802
#130694212
#130693772
C2×#106221232
#130664572
#130664552
C11×#19482
#892411