Finite Group Databasebeta

← #14758036

Subgroups — #14758036

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4314C211yesmaximal, characteristic
2#13071268C211yesmaximal, characteristic, complemented
3#13071260C211yesmaximal, characteristic
4#13069470C212yesmaximal
5#13069344C212yesmaximal, complemented
6#13069313C212yesmaximal
7#13069306C212yesmaximal, complemented
8C4×#66881C211yesmaximal, characteristic, complemented
9#13068447C211yesmaximal, characteristic, complemented
10#13068442C211yesmaximal, characteristic
11C11×#1726C211yesmaximal, characteristic, complemented
12C22×#4314C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C2×C11×#97C2212yes—
16C2×C11×#97C2211yescharacteristic
17C2×C4×C8×C11C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C11×#376C2211yescharacteristic
20C2×#66885C2212yes—
21C2×#66885C2211yescharacteristic
22C2×#66881C2212yes—
23C2×#66881C2211yescharacteristic
24C2×#66880C2212yes—
25C2×#66880C2211yescharacteristic
26#10622552C2212yes—
27C4×C4⋊Dic11C2211yescharacteristic
28C4×C4⋊Dic11C2211yescharacteristic
29#10622542C2212yes—
30#10622541C2212yes—
31#10622541C2212yes—
32C4×#4314C418yescomplemented
33#10622282—22no—
34#10622280—21no—
35#10622277—21no—
36#10622265—22no—
37#10622264—21no—
38#10622263—21no—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C22×Dic22C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C22×C8×C11C2312yes—
47C22×C8×C11C2311yescharacteristic
48C2×C42×C11C2312yes—
49C2×C42×C11C2311yescharacteristic
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×C4⋊Dic11C2312yes—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2311yescharacteristic
56C2×C4⋊Dic11C2311yescharacteristic
57C2×Dic11⋊C4—21no—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—21no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11—21no—
63C2×#4314—24no—
64C2×#4314C2×C414yes—
65C4×D44—22no—
66C4×D44C2×C414yes—
67C4×Dic22—22no—
68C4×Dic22C2×C414yes—
69C11×#97—24no—
70C11×#97—22no—
71C4×C8×C11—24no—
72C4×C8×C11C2×C414yes—
73C11×#95D411yescharacteristic
74C11×#95D411yescharacteristic
75C11×#95D412yes—
76C11⋊#95—21no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95—21no—
81C11⋊#95—22no—
82#66885—24no—
83#66885C2×C414yes—
84#66881—24no—
85#66881C2×C414yes—
86#66880—24no—
87#66880C2×C414yes—
88#21280—111nomaximal, Sylow
89C23×D11—21no—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—22no—
99C22×Dic11—22no—
100C2×D44—21no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44C22×C412yes—
104C2×C4×D11—24no—
105C2×C4×D11—82no—
106C2×Dic22—22no—
107C2×Dic22—22no—
108C2×Dic22—21no—
109C2×Dic22C22×C412yes—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11C22×C412yes—
114C2×C8×C11C22×C412yes—
115C2×C8×C11#4114yes—
116C2×C8×C11#4114yes—
117C42×C11—22no—
118C42×C11—22no—
119C42×C11C22×C412yes—
120C42×C11#4112yes—
121(C2×D11)⋊C4—24no—
122(C2×D11)⋊C4—82no—
123(C2×D11)⋊C4—82no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11C22×C412yes—
131C4⋊Dic11C22×C412yes—
132Dic11⋊C4—24no—
133Dic11⋊C4—82no—
134Dic11⋊C4—82no—
135C4×Dic11—24no—
136C4×Dic11—81no—
137C4×Dic11—81no—
138#4314—28no—
139C2×C4×SD16—111no—
140#2320—111no—
141#2319—111no—
142#1968—112no—
143#1941—112no—
144#1936—112no—
145#1935—112no—
146C4×#106—111no—
147#1763—111no—
148#1762—111no—
149#1726D1111yescharacteristic, complemented
150C23×C11C22×D411yescharacteristic
151C22×D11—22no—
152C22×D11—42no—
153C22×D11—41no—
154C22×D11—42no—
155C22×D11—41no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11C4×D412yes—
166C2×C4×C11C4×D412yes—
167C2×C4×C11C23×C411yescharacteristic
168C2×C4×C11C2×#4112yes—
169C2×C4×C11C2×#4112yes—
170C2×C4×C11C2×#4111yescharacteristic
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184D44—22no—
185D44—22no—
186D44—42no—
187C4×D11—84no—
188Dic22—22no—
189Dic22—22no—
190Dic22—42no—
191C8×C11—22no—
192C8×C11—24no—
193C8×C11#11714yes—
194C22×SD16—111no—
195C2×C4×Q8—111no—
196C2×C4×D4—111no—
197C4×SD16—118no—
198C2×#106—111no—
199C2×#106—112no—
200C2×#103—111no—
201C2×#103—112no—
202C2×#102—111no—
203C2×#102—112no—
204C2×#97C2×D1112yes—
205C2×#97C2×D1111yescharacteristic
206C2×C4×C8C2×D1112yes—
207C2×C4×C8C2×D1111yescharacteristic
208#391—112no—
209#390—112no—
210#389—112no—
211#389—112no—
212#388—222no—
213#387—222no—
214#383—221no—
215#382—221no—
216#381—221no—
217#380—221no—
218C4×C4⋊C4—111no—
219C4×C4⋊C4—111no—
220#376C2×D1111yescharacteristic
221#340—112no—
222#340—112no—
223#340—112no—
224C22×C11C2×C4×D411yescharacteristic
225C22×C11#53212yes—
226C22×C11#57711yescharacteristic
227C22×C11#57712yes—
228C22×C11#57711yescharacteristic
229C2×D11—42no—
230C2×D11—42no—
231C2×D11—42no—
232C2×D11—82no—
233C2×D11—82no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—42no—
237C4×C11—42no—
238C4×C11C2×#11711yescharacteristic
239C4×C11C4×#4111yescharacteristic
240C4×C11#52912yes—
241Dic11—42no—
242Dic11—42no—
243Dic11—42no—
244Dic11—82no—
245Dic11—82no—
246C22×Q8—111no—
247C22×D4—111no—
248C23×C4—221no—
249C2×SD16—114no—
250C2×SD16—224no—
251C22×C8C22×D1111yescharacteristic
252C22×C8C22×D1112yes—
253C22×C8C22×D1111yescharacteristic
254C4×Q8—114no—
255C4×Q8—222no—
256C4×D4—114no—
257C4×D4—222no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—222no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—222no—
267C2×C22⋊C4—222no—
268C2×C42—221no—
269C2×C42—221no—
270C2×C42—221no—
271C2×C42C22×D1112yes—
272C2×C42C22×D1111yescharacteristic
273#106—114no—
274#106—224no—
275#103—114no—
276#103—224no—
277#102—114no—
278#102—224no—
279#97—24no—
280#97—22no—
281C4×C8—24no—
282C4×C8C4×D1114yes—
283#95—221no—
284#95—221no—
285#95—222no—
286#95—222no—
287#95—222no—
288#95—222no—
289#95D4411yescharacteristic
290#95D4411yescharacteristic
291#95D4412yes—
292C2×C11#229311yescharacteristic
293C2×C11#294911yescharacteristic
294C2×C11#295211yescharacteristic
295C2×C11#317312yes—
296C2×C11#317412yes—
297D11—82no—
298C24—221no—
299C2×Q8—112no—
300C2×Q8—221no—
301C2×Q8—222no—
302C2×Q8—222no—
303C2×D4—112no—
304C2×D4—222no—
305C2×D4—222no—
306C2×D4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—224no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—882no—
314C22×C4C2×D4412yes—
315C22×C4C2×D4412yes—
316C22×C4C2×D4411yescharacteristic
317C22×C4C2×D4411yescharacteristic
318C22×C4C23×D1111yescharacteristic
319SD16—228no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8C2×C4×D1112yes—
324C2×C8C2×C4×D1112yes—
325C2×C8#433914yes—
326C2×C8#433914yes—
327C4⋊C4—112no—
328C4⋊C4—112no—
329C4⋊C4—224no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C4⋊C4—222no—
335C4⋊C4—222no—
336C4⋊C4—882no—
337C4⋊C4—882no—
338C22⋊C4—224no—
339C22⋊C4—882no—
340C22⋊C4—882no—
341C42—22no—
342C42—22no—
343C42—224no—
344C42—881no—
345C42—881no—
346C42C2×C4×D1112yes—
347C42#433912yes—
348C11#2128011yescharacteristic, complemented, Sylow
349C23—222no—
350C23—442no—
351C23—441no—
352C23—442no—
353C23—441no—
354C23C22×D4411yescharacteristic
355Q8—222no—
356Q8—222no—
357Q8—442no—
358D4—222no—
359D4—222no—
360D4—442no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—442no—
374C2×C4—441no—
375C2×C4—442no—
376C2×C4—441no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—884no—
384C2×C4C4×D4412yes—
385C2×C4C4×D4412yes—
386C2×C4C22×C4×D1111yescharacteristic
387C2×C4C2×#433912yes—
388C2×C4C2×#433912yes—
389C2×C4C2×#433911yescharacteristic
390C8—22no—
391C8—24no—
392C8#6692514yes—
393C22—442no—
394C22—442no—
395C22—442no—
396C22—882no—
397C22—882no—
398C22C2×C4×D4411yescharacteristic
399C22#1062300812yes—
400C22#1062328211yescharacteristic
401C22#1062328212yes—
402C22#1062328211yescharacteristic
403C4—22no—
404C4—22no—
405C4—42no—
406C4—42no—
407C4—442no—
408C4—442no—
409C4—442no—
410C4—882no—
411C4—882no—
412C4C2×#6692511yescharacteristic
413C4C4×#433911yescharacteristic
414C4#1062301012yes—
415C2—882no—
416C2#1307108011yescharacteristic
417C2#1307747711yescharacteristic
418C2#1307750111yescharacteristic
419C2#1307923312yes—
420C2#1307924412yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1726C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1726D11
hypocenterC11#21280
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #13071268C2semidirect
5. #13069344C2semidirect
7. #13069306C2semidirect
8. C4×#66881C2semidirect
9. #13068447C2semidirect
11. C11×#1726C2semidirect
32. C4×#4314C4semidirect
149. #1726D11semidirect
348. C11#21280semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43142
#130712682
#130712602
#130694702
#130693442
#130693132
#130693062
C4×#668812
#130684472
#130684422
C11×#17262
#2128011