Finite Group Databasebeta

← #14758030

Subgroups — #14758030

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×#4325C211yesmaximal, characteristic
2#13071260C211yesmaximal, characteristic
3#13069473C212yesmaximal
4#13069341C212yesmaximal, complemented
5#13069312C212yesmaximal
6#13069309C212yesmaximal, complemented
7C4×#66872C211yesmaximal, characteristic, complemented
8#13068446C211yesmaximal, characteristic, complemented
9#13068444C211yesmaximal, characteristic
10#13068303C211yesmaximal, characteristic, complemented
11C11×#2320C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4325C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C11×#391C2212yes—
16C11×#389C2212yes—
17C11×#387—22no—
18C11×#383—21no—
19C11×#382—21no—
20C4×C11×C4⋊C4C2211yescharacteristic
21C11×#376C2211yescharacteristic
22C2×#66899C2212yes—
23C2×#66899C2211yescharacteristic
24C4×#4325C418yescomplemented
25C2×#66873C2212yes—
26C2×#66873C2211yescharacteristic
27C2×#66872C2212yes—
28C2×#66872C2211yescharacteristic
29#10622552C2212yes—
30C4×C4⋊Dic11C2211yescharacteristic
31#10622541C2212yes—
32C2×#66867C2212yes—
33C2×#66867C2211yescharacteristic
34C2×C4×C11⋊C8C2212yes—
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622282—22no—
37#10622280—21no—
38#10622277—21no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C4×Q8×C11—22no—
46C4×Q8×C11C2×C414yes—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2312yes—
54C2×C42×C11C2311yescharacteristic
55C2×#4325—24no—
56C2×#4325C2×C414yes—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—21no—
64C22×C11⋊C8C2311yescharacteristic
65C22×C11⋊C8C2312yes—
66C22×C11⋊C8C2311yescharacteristic
67C4×D44—22no—
68C4×D44C2×C414yes—
69C11×#95—21no—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95D411yescharacteristic
74C11×#95D411yescharacteristic
75C11×#95D412yes—
76#66899—24no—
77#66899C2×C414yes—
78C11⋊#95—21no—
79C11⋊#95—22no—
80#66873—24no—
81#66873C2×C414yes—
82#66872—24no—
83#66872C2×C414yes—
84#66867—22no—
85#66867—24no—
86C4×C11⋊C8—24no—
87C4×C11⋊C8C2×C414yes—
88#21280—111nomaximal, Sylow
89C23×D11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C22×C412yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—22no—
104C2×D44—21no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44C22×C412yes—
108C2×C4×D11—24no—
109C2×C4×D11—82no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—82no—
115C11×C4⋊C4C22×C412yes—
116C42×C11—24no—
117C42×C11—22no—
118C42×C11—22no—
119C42×C11—81no—
120C42×C11C22×C412yes—
121C42×C11#4112yes—
122#4325—28no—
123(C2×D11)⋊C4—24no—
124(C2×D11)⋊C4—82no—
125(C2×D11)⋊C4—82no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11C22×C412yes—
130Dic11⋊C4—82no—
131C4×Dic11—81no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8C22×C412yes—
136C2×C11⋊C8C22×C412yes—
137C2×C11⋊C8#4114yes—
138C2×C11⋊C8#4114yes—
139C2×C4×SD16—111no—
140#2320D1111yescharacteristic, complemented
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#1726—111no—
150C23×C11C22×D411yescharacteristic
151C22×D11—22no—
152C22×D11—42no—
153C22×D11—41no—
154C22×D11—42no—
155C22×D11—41no—
156Q8×C11—22no—
157Q8×C11—22no—
158Q8×C11—42no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—22no—
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×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C4×D412yes—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C23×C411yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11C2×#4112yes—
181C2×C4×C11C2×#4112yes—
182C2×Dic11—22no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187D44—22no—
188D44—22no—
189D44—42no—
190C4×D11—84no—
191C11⋊C8—22no—
192C11⋊C8—24no—
193C11⋊C8#11714yes—
194C22×SD16—111no—
195C2×C4×Q8C2×D1111yescharacteristic
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×#97—112no—
205C2×#97—111no—
206C2×C4×C8—111no—
207C2×C4×C8—112no—
208#391C2×D1112yes—
209#390—112no—
210#389—112no—
211#389C2×D1112yes—
212#388—222no—
213#387—22no—
214#383—21no—
215#382—21no—
216#381—221no—
217#380—221no—
218C4×C4⋊C4—111no—
219C4×C4⋊C4C2×D1111yescharacteristic
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×C11—42no—
239C4×C11—42no—
240C4×C11—82no—
241C4×C11C2×#11711yescharacteristic
242C4×C11C4×#4111yescharacteristic
243C4×C11#52912yes—
244Dic11—42no—
245Dic11—82no—
246C22×Q8C22×D1111yescharacteristic
247C22×D4—111no—
248C23×C4—221no—
249C2×SD16—114no—
250C2×SD16—224no—
251C22×C8—111no—
252C22×C8—111no—
253C22×C8—112no—
254C4×Q8—22no—
255C4×Q8C4×D1114yes—
256C4×D4—114no—
257C4×D4—222no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4C22×D1112yes—
264C2×C4⋊C4C22×D1111yescharacteristic
265C2×C22⋊C4—221no—
266C2×C22⋊C4—222no—
267C2×C22⋊C4—222no—
268C2×C42—21no—
269C2×C42—21no—
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—224no—
280#97—222no—
281C4×C8—114no—
282C4×C8—224no—
283#95—21no—
284#95—22no—
285#95—22no—
286#95—22no—
287#95—221no—
288#95—222no—
289#95C22⋊D1111yescharacteristic
290#95C22⋊D1111yescharacteristic
291#95C22⋊D1112yes—
292C2×C11#229311yescharacteristic
293C2×C11#294911yescharacteristic
294C2×C11#295211yescharacteristic
295C2×C11#317312yes—
296C2×C11#317412yes—
297D11—82no—
298C24—221no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8C2×C4×D1112yes—
303C2×D4—112no—
304C2×D4—221no—
305C2×D4—222no—
306C2×D4—222no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—221no—
311C22×C4—224no—
312C22×C4—222no—
313C22×C4—882no—
314C22×C4C2×C22⋊D1112yes—
315C22×C4C2×C22⋊D1112yes—
316C22×C4C2×C22⋊D1111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C23×D1111yescharacteristic
319SD16—228no—
320C2×C8—112no—
321C2×C8—114no—
322C2×C8—112no—
323C2×C8—114no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—222no—
327C4⋊C4—24no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—82no—
332C4⋊C4—112no—
333C4⋊C4—221no—
334C4⋊C4—222no—
335C4⋊C4—222no—
336C4⋊C4—882no—
337C4⋊C4C2×C4×D1112yes—
338C22⋊C4—224no—
339C22⋊C4—882no—
340C22⋊C4—882no—
341C42—24no—
342C42—22no—
343C42—22no—
344C42—81no—
345C42—881no—
346C42C2×C4×D1112yes—
347C42#433912yes—
348C11#2128011yescharacteristic, complemented, Sylow
349C23—222no—
350C23—442no—
351C23—441no—
352C23—441no—
353C23—442no—
354C23C22×C22⋊D1111yescharacteristic
355Q8—22no—
356Q8—22no—
357Q8—42no—
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—22no—
371C2×C4—22no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—222no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—884no—
384C2×C4C4×C22⋊D1112yes—
385C2×C4C4×C22⋊D1112yes—
386C2×C4C22×C4×D1111yescharacteristic
387C2×C4C2×#433911yescharacteristic
388C2×C4#41×D1112yes—
389C2×C4#41×D1112yes—
390C8—114no—
391C8—222no—
392C8—224no—
393C22—442no—
394C22—442no—
395C22—442no—
396C22—882no—
397C22—882no—
398C22C2×C4×C22⋊D1111yescharacteristic
399C22#1062336312yes—
400C22#1062336711yescharacteristic
401C22#1062336812yes—
402C22#1062336811yescharacteristic
403C4—22no—
404C4—22no—
405C4—42no—
406C4—42no—
407C4—42no—
408C4—42no—
409C4—82no—
410C4—442no—
411C4—882no—
412C4D11×#11711yescharacteristic
413C4#1062305311yescharacteristic
414C4#1062305912yes—
415C2—882no—
416C2#1307107511yescharacteristic
417C2#1307747511yescharacteristic
418C2#1307749711yescharacteristic
419C2#1307922712yes—
420C2#1307924512yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2320C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2320D11
hypocenterC11#21280
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
4. #13069341C2semidirect
6. #13069309C2semidirect
7. C4×#66872C2semidirect
8. #13068446C2semidirect
10. #13068303C2semidirect
11. C11×#2320C2semidirect
24. C4×#4325C4semidirect
140. #2320D11semidirect
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×#43252
#130712602
#130694732
#130693412
#130693122
#130693092
C4×#668722
#130684462
#130684442
#130683032
C11×#23202
#2128011