Finite Group Databasebeta

← #14756933

Subgroups — #14756933

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071259C211yesmaximal, characteristic
2#13070981C211yesmaximal, characteristic, complemented
3#13069245C212yesmaximal
4#13069203C212yesmaximal, complemented
5#13068973C212yesmaximal
6#13068886C212yesmaximal, complemented
7C4×#66881C211yesmaximal, characteristic, complemented
8#13068446C211yesmaximal, characteristic, complemented
9#13068441C211yesmaximal, characteristic
10#13068367C211yesmaximal, characteristic, complemented
11C2×C4×C11×SD16C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C4×C11×SD16C418yescomplemented
17C2×C11×#106C2211yescharacteristic
18C2×C11×#103C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C2×#66899C2212yes—
22#10622834C2212yes—
23C2×#66896C2212yes—
24#10622825—21no—
25#10622824—21no—
26C2×#66881C2212yes—
27#10622598C2212yes—
28C4⋊C4×Dic11—22no—
29C4⋊C4×Dic11C2212yes—
30#10622564—22no—
31C4×C4⋊Dic11—21no—
32C4×C4⋊Dic11C2211yescharacteristic
33C4×C4⋊Dic11C2211yescharacteristic
34#10622545—21no—
35#10622545C2211yescharacteristic
36C2×#66867C2211yescharacteristic
37#10622189C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C2×C11×SD16—24no—
46C2×C11×SD16C2×C414yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C4×Q8×C11—22no—
50C4×Q8×C11C2×C414yes—
51C4×D4×C11—22no—
52C4×D4×C11C2×C414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61Q8×Dic11—24no—
62Q8×Dic11—24no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2312yes—
73C11×#106C2×C414yes—
74C11×#103C2×C414yes—
75C11×#102C2×C414yes—
76C4×C8×C11C2×C414yes—
77#66899—24no—
78#66896—24no—
79C11⋊#95—21no—
80C11⋊#95—21no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95D411yescharacteristic
84C11⋊#95D411yescharacteristic
85C11⋊#95D412yes—
86#66881—24no—
87#66867—22no—
88#21131—111nomaximal, Sylow
89C24×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—21no—
92C2×Q8×C11C22×C412yes—
93C2×Q8×C11#4114yes—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11C22×C412yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—24no—
102C22×C4×C11—82no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11C2×D412yes—
109C22×Dic11C2×D412yes—
110C11×SD16—28no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11C22×C412yes—
114C2×C8×C11C22×C412yes—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4C22×C412yes—
119C11×C4⋊C4C22×C412yes—
120C11×C22⋊C4—24no—
121C42×C11—24no—
122C42×C11C22×C412yes—
123C42×C11#4112yes—
124C22⋊Dic11—82no—
125C22⋊Dic11—82no—
126C4⋊Dic11—28no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—82no—
131C4⋊Dic11#4114yes—
132C4×Dic11—28no—
133C4×Dic11—22no—
134C4×Dic11—22no—
135C4×Dic11—81no—
136C4×Dic11—81no—
137C4×Dic11—82no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C4×SD16D1111yescharacteristic
142#2319—111no—
143#2276—111no—
144#1926—112no—
145#1920—112no—
146#1880—112no—
147#1865—112no—
148C4×#106—111no—
149#1763—111no—
150#1762—111no—
151#1746—111no—
152C23×C11—22no—
153C23×C11—42no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11C22×D411yescharacteristic
158Q8×C11—22no—
159Q8×C11—24no—
160Q8×C11#11714yes—
161D4×C11—22no—
162D4×C11—22no—
163D4×C11—42no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—84no—
175C2×C4×C11C4×D412yes—
176C2×C4×C11C4×D412yes—
177C2×C4×C11C23×C411yescharacteristic
178C2×C4×C11C2×#4112yes—
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11C2×#4112yes—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—24no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C8×C11—22no—
194C8×C11—22no—
195C11⋊C8—42no—
196C22×SD16C2×D1111yescharacteristic
197C2×C4×Q8—112no—
198C2×C4×Q8C2×D1111yescharacteristic
199C2×C4×D4C2×D1111yescharacteristic
200C4×SD16Dic1118yescomplemented
201C2×#106—112no—
202C2×#106C2×D1111yescharacteristic
203C2×#103—112no—
204C2×#103C2×D1111yescharacteristic
205C2×#102—112no—
206C2×#102C2×D1111yescharacteristic
207C2×#97—111no—
208C2×C4×C8C2×D1111yescharacteristic
209#390—112no—
210#389—112no—
211#388—222no—
212#381—221no—
213#380—221no—
214C4×C4⋊C4—112no—
215C4×C4⋊C4—111no—
216C4×C4⋊C4—111no—
217C4×C4⋊C4—221no—
218C4×C4⋊C4—222no—
219#376—111no—
220#376—221no—
221#340—112no—
222#340—112no—
223#340—112no—
224#336—112no—
225#336—112no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11C2×C4×D411yescharacteristic
232C22×C11#52512yes—
233C22×C11#57712yes—
234C22×C11#57711yescharacteristic
235C22×C11#57711yescharacteristic
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—24no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11C2×#11711yescharacteristic
242C4×C11C4×#4111yescharacteristic
243C4×C11#52912yes—
244Dic11—42no—
245Dic11—44no—
246Dic11—42no—
247Dic11—82no—
248C22×Q8C22×D1111yescharacteristic
249C22×D4C22×D1111yescharacteristic
250C23×C4—21no—
251C2×SD16—24no—
252C2×SD16C2×Dic1114yes—
253C22×C8—112no—
254C22×C8C22×D1111yescharacteristic
255C22×C8C22×D1111yescharacteristic
256C4×Q8—22no—
257C4×Q8—224no—
258C4×Q8—224no—
259C4×Q8C2×Dic1114yes—
260C4×D4—22no—
261C4×D4C2×Dic1114yes—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4C22×D1111yescharacteristic
268C2×C4⋊C4C22×D1111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C42—21no—
273C2×C42—112no—
274C2×C42—222no—
275C2×C42—222no—
276C2×C42—221no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279#106—224no—
280#106C2×Dic1114yes—
281#103—224no—
282#103C2×Dic1114yes—
283#102—224no—
284#102C2×Dic1114yes—
285#97—222no—
286C4×C8C2×Dic1114yes—
287#95—111no—
288#95—111no—
289#95—112no—
290#95—222no—
291#95—222no—
292#95—221no—
293#95—221no—
294C2×C11—82no—
295C2×C11#229011yescharacteristic
296C2×C11#294911yescharacteristic
297C2×C11#295211yescharacteristic
298C2×C11#312512yes—
299C2×C11#312612yes—
300C24—21no—
301C2×Q8—21no—
302C2×Q8—22no—
303C2×Q8#433914yes—
304C2×Q8C22×Dic1112yes—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4C22×Dic1112yes—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—24no—
313C22×C4—82no—
314C22×C4—112no—
315C22×C4—112no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4D4×D1111yescharacteristic
319C22×C4D4×D1111yescharacteristic
320C22×C4C23×D1111yescharacteristic
321SD16—28no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8C22×Dic1112yes—
328C2×C8C22×Dic1112yes—
329C4⋊C4—24no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—114no—
333C4⋊C4—228no—
334C4⋊C4—222no—
335C4⋊C4—222no—
336C4⋊C4—222no—
337C4⋊C4—882no—
338C4⋊C4C22×Dic1112yes—
339C4⋊C4C22×Dic1112yes—
340C22⋊C4—24no—
341C22⋊C4—882no—
342C22⋊C4—882no—
343C42—24no—
344C42—228no—
345C42—222no—
346C42—222no—
347C42—881no—
348C42—881no—
349C42—882no—
350C42#434112yes—
351C42C22×Dic1112yes—
352C11#2113111yescharacteristic, complemented, Sylow
353C23—22no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23C2×D4×D1111yescharacteristic
359Q8—24no—
360Q8—22no—
361Q8#6697914yes—
362D4—22no—
363D4—22no—
364D4—42no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—84no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—224no—
382C2×C4—222no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4D4×Dic1112yes—
389C2×C4D4×Dic1112yes—
390C2×C4C2×#433912yes—
391C2×C4C2×#434111yescharacteristic
392C2×C4#41×D1112yes—
393C2×C4C23×Dic1111yescharacteristic
394C8—22no—
395C8—22no—
396C8—442no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—82no—
401C22—82no—
402C22#1062307812yes—
403C22#1062329312yes—
404C22#1062330111yescharacteristic
405C22#1062330111yescharacteristic
406C22C2×D4×Dic1111yescharacteristic
407C4—24no—
408C4—22no—
409C4—22no—
410C4—42no—
411C4—42no—
412C4—442no—
413C4—444no—
414C4—442no—
415C4—882no—
416C4#1062306912yes—
417C4C2×#6697911yescharacteristic
418C4#41×Dic1111yescharacteristic
419C2—82no—
420C2#1307106111yescharacteristic
421C2#1307747611yescharacteristic
422C2#1307750011yescharacteristic
423C2#1307889912yes—
424C2#1307890412yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×C4×SD16D11
hypocenterC11#21131
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. #13070981C2semidirect
4. #13069203C2semidirect
6. #13068886C2semidirect
7. C4×#66881C2semidirect
8. #13068446C2semidirect
10. #13068367C2semidirect
16. C4×C11×SD16C4semidirect
200. C4×SD16Dic11semidirect
352. C11#21131semidirect

Maximal subgroups

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

subgroupindex
#130712592
#130709812
#130692452
#130692032
#130689732
#130688862
C4×#668812
#130684462
#130684412
#130683672
C2×C4×C11×SD162
#2113111