Finite Group Databasebeta

← #14756934

Subgroups — #14756934

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
1C2×C4×#4324C211yesmaximal, characteristic
2#13071259C211yesmaximal, characteristic
3#13070980C211yesmaximal, characteristic, complemented
4#13069246C212yesmaximal
5#13069204C212yesmaximal, complemented
6#13068968C212yesmaximal
7#13068885C212yesmaximal, complemented
8C4×#66872C211yesmaximal, characteristic, complemented
9#13068447C211yesmaximal, characteristic, complemented
10#13068369C211yesmaximal, characteristic, complemented
11C11×#1762C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4324C2211yescharacteristic
14C2×#66940C2212yes—
15C2×C4×Dic22C2211yescharacteristic
16C2×C11×#102C2212yes—
17C2×C11×#97C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19#10622834C2212yes—
20C2×#66896C2211yescharacteristic
21#10622825—21no—
22#10622824—21no—
23C2×#66880C2212yes—
24C4×#4324C418yescomplemented
25#10622598C2212yes—
26C4⋊C4×Dic11C2212yes—
27C2×#66874C2211yescharacteristic
28C2×#66872C2212yes—
29C2×#66872C2211yescharacteristic
30#10622564—22no—
31C4×C4⋊Dic11C2211yescharacteristic
32#10622545C2211yescharacteristic
33C4×Dic11⋊C4—22no—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622262—21no—
36#10622261—21no—
37C11×#340C2212yes—
38#10622189C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C22×Dic22C2311yescharacteristic
45C22×C8×C11C2312yes—
46C4×D4×C11—22no—
47C4×D4×C11C2×C414yes—
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C22⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×#4324—24no—
56C2×#4324C2×C414yes—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×Dic11⋊C4—21no—
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11—21no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11C2312yes—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69#66940—24no—
70#66940—24no—
71C4×Dic22—22no—
72C4×Dic22C2×C414yes—
73C11×#102—24no—
74C11×#97—22no—
75C11×#95—21no—
76#66896C2×C414yes—
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D411yescharacteristic
81C11⋊#95D411yescharacteristic
82C11⋊#95D412yes—
83#66880—24no—
84#66874C2×C414yes—
85#66872—24no—
86#66872C2×C414yes—
87C4×C11⋊C8C2×C414yes—
88#21131—111nomaximal, Sylow
89C24×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11C22×C412yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11C2×D412yes—
105C22×Dic11C2×D412yes—
106C2×Dic22—21no—
107C2×Dic22—22no—
108C2×Dic22C22×C412yes—
109C2×Dic22#4114yes—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4C22×C412yes—
116C11×C4⋊C4#4114yes—
117C11×C22⋊C4—24no—
118C42×C11—81no—
119C42×C11C22×C412yes—
120C42×C11#4112yes—
121C22⋊Dic11—82no—
122C22⋊Dic11—82no—
123#4324—28no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—82no—
128C4⋊Dic11C22×C412yes—
129Dic11⋊C4—28no—
130Dic11⋊C4—24no—
131C4×Dic11—28no—
132C4×Dic11—24no—
133C4×Dic11—22no—
134C4×Dic11—22no—
135C4×Dic11—81no—
136C4×Dic11—82no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8C22×C412yes—
140C2×C11⋊C8C22×C412yes—
141C2×C4×SD16—111no—
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#1762D1111yescharacteristic
151#1746—111no—
152C23×C11—22no—
153C23×C11—42no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11C22×D411yescharacteristic
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—42no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—84no—
170C2×C4×C11C4×D412yes—
171C2×C4×C11C4×D412yes—
172C2×C4×C11C23×C411yescharacteristic
173C2×C4×C11C2×#4112yes—
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11C2×#4112yes—
176C2×Dic11—22no—
177C2×Dic11—24no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190Dic22—22no—
191Dic22—24no—
192Dic22#11714yes—
193C8×C11—42no—
194C11⋊C8—22no—
195C11⋊C8—22no—
196C22×SD16—111no—
197C2×C4×Q8—112no—
198C2×C4×Q8—111no—
199C2×C4×D4C2×D1111yescharacteristic
200C4×SD16—118no—
201C2×#106—111no—
202C2×#106—112no—
203C2×#103—111no—
204C2×#103—112no—
205C2×#102—111no—
206C2×#102C2×D1112yes—
207C2×#97C2×D1111yescharacteristic
208C2×C4×C8—111no—
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—221no—
217C4×C4⋊C4—222no—
218C4×C4⋊C4C2×D1111yescharacteristic
219#376—111no—
220#376—221no—
221#340—112no—
222#340—112no—
223#340C2×D1112yes—
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#57711yescharacteristic
234C22×C11#57712yes—
235C22×C11#57711yescharacteristic
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—44no—
239C4×C11—42no—
240C4×C11C2×#11711yescharacteristic
241C4×C11C4×#4111yescharacteristic
242C4×C11#52912yes—
243Dic11—24no—
244Dic11—42no—
245Dic11—42no—
246Dic11—42no—
247Dic11—82no—
248C22×Q8—111no—
249C22×D4C22×D1111yescharacteristic
250C23×C4—21no—
251C2×SD16—114no—
252C2×SD16—224no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8C22×D1112yes—
256C4×Q8—114no—
257C4×Q8—224no—
258C4×Q8—224no—
259C4×Q8—222no—
260C4×D4—22no—
261C4×D4C4×D1114yes—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4C22×D1111yescharacteristic
268C2×C4⋊C4C22×D1112yes—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C42—21no—
273C2×C42—112no—
274C2×C42—222no—
275C2×C42—221no—
276C2×C42—222no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279#106—114no—
280#106—224no—
281#103—114no—
282#103—224no—
283#102—24no—
284#102—114no—
285#97—22no—
286C4×C8—114no—
287#95—21no—
288#95—111no—
289#95—111no—
290#95—112no—
291#95—222no—
292#95—222no—
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—112no—
302C2×Q8—114no—
303C2×Q8—222no—
304C2×Q8—221no—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4C2×C4×D1112yes—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—24no—
312C22×C4—82no—
313C22×C4—112no—
314C22×C4—112no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—222no—
318C22×C4D4×D1111yescharacteristic
319C22×C4D4×D1111yescharacteristic
320C22×C4C23×D1111yescharacteristic
321SD16—228no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—112no—
326C2×C8—112no—
327C2×C8—222no—
328C2×C8—222no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—112no—
332C4⋊C4—228no—
333C4⋊C4—224no—
334C4⋊C4—221no—
335C4⋊C4—222no—
336C4⋊C4—222no—
337C4⋊C4—882no—
338C4⋊C4C2×C4×D1112yes—
339C4⋊C4#433914yes—
340C22⋊C4—24no—
341C22⋊C4—882no—
342C22⋊C4—882no—
343C42—81no—
344C42—228no—
345C42—224no—
346C42—222no—
347C42—222no—
348C42—881no—
349C42—882no—
350C42C2×C4×D1112yes—
351C42#434112yes—
352C11#2113111yescharacteristic, complemented, Sylow
353C23—22no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23C2×D4×D1111yescharacteristic
359Q8—114no—
360Q8—222no—
361Q8—224no—
362D4—22no—
363D4—22no—
364D4—42no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—84no—
374C2×C4—222no—
375C2×C4—224no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—222no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4(C22⋊D11)⋊C412yes—
389C2×C4(C22⋊D11)⋊C412yes—
390C2×C4C22×C4×D1111yescharacteristic
391C2×C4C2×#433912yes—
392C2×C4C2×#434111yescharacteristic
393C2×C4#41×D1112yes—
394C8—42no—
395C8—222no—
396C8—222no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—82no—
401C22—82no—
402C22C2×(C22⋊D11)⋊C411yescharacteristic
403C22#1062307812yes—
404C22#1062330611yescharacteristic
405C22#1062330612yes—
406C22#1062330911yescharacteristic
407C4—22no—
408C4—22no—
409C4—44no—
410C4—42no—
411C4—224no—
412C4—442no—
413C4—442no—
414C4—442no—
415C4—882no—
416C4C4×#433911yescharacteristic
417C4D11×#11711yescharacteristic
418C4#1062308812yes—
419C2—82no—
420C2#1307106211yescharacteristic
421C2#1307747811yescharacteristic
422C2#1307749511yescharacteristic
423C2#1307889712yes—
424C2#1307890612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1762C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1762D11
hypocenterC11#21131
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. #13070980C2semidirect
5. #13069204C2semidirect
7. #13068885C2semidirect
8. C4×#66872C2semidirect
9. #13068447C2semidirect
10. #13068369C2semidirect
24. C4×#4324C4semidirect
352. C11#21131semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43242
#130712592
#130709802
#130692462
#130692042
#130689682
#130688852
C4×#668722
#130684472
#130683692
C11×#17622
#2113111