Finite Group Databasebeta

← #14758178

Subgroups — #14758178

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67003C211yesmaximal, characteristic
2#13077268C211yesmaximal, characteristic, complemented
3#13077267C211yesmaximal, characteristic, complemented
4#13069501C212yesmaximal
5#13069363C212yesmaximal, complemented
6#13069328C212yesmaximal, complemented
7#13069324C212yesmaximal, complemented
8C4×#66886C211yesmaximal, characteristic, complemented
9#13068427C211yesmaximal, characteristic, complemented
10#13068303C211yesmaximal, characteristic, complemented
11C11×#1759C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C2×C11×#104C2212yes—
16C4×C11×M16C2211yescharacteristic
17C11×#376C2211yescharacteristic
18#10622847C2212yes—
19#10622846C2211yescharacteristic
20#10622742C2212yes—
21C2×#66886C2212yes—
22#10622732C2212yes—
23C4×#4326C412yescomplemented
24C4×#4325C412yescomplemented
25C4×#4324C412yescomplemented
26C4×#4323C412yescomplemented
27#10622615C2211yescharacteristic
28#10622613—22no—
29#10622612C2212yes—
30#10622611C2211yescharacteristic
31C2×#66869C2212yes—
32#10622539—22no—
33C4×#4318C2211yescharacteristic
34C2×#66867C2212yes—
35C2×#66867C2211yescharacteristic
36C2×C4×C11⋊C8C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622318—22no—
39#10622303—22no—
40C11×#339C2212yes—
41#10622196C2212yes—
42#10622161C2212yes—
43C2×C11×#41C2311yescharacteristic
44C2×#4339C2311yescharacteristic
45C2×C11×M16C2312yes—
46C4×Q8×C11C2×C412yes—
47C4×D4×C11—22no—
48C4×D4×C11C2×C412yes—
49C11×#117—21no—
50C11×#117C2311yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54#67003—24no—
55C2×#4326C2×C411yescharacteristic
56C2×#4325C2×C411yescharacteristic
57C2×#4324C2×C411yescharacteristic
58C2×#4323C2×C411yescharacteristic
59C4×C22⋊D11—22no—
60#66979C2311yescharacteristic
61C2×#4318C2312yes—
62C22×C11⋊C8C2311yescharacteristic
63C22×C11⋊C8C2312yes—
64C22×C11⋊C8C2311yescharacteristic
65C4×D44C2×C412yes—
66#66925—21no—
67C42×D11—21no—
68C4×Dic22C2×C412yes—
69C11×#104—24no—
70C11×#97—21no—
71C4×C8×C11—21no—
72C11×#95—22no—
73#66899C2×C412yes—
74#66896C2×C412yes—
75C22⋊(C11⋊C8)—24no—
76#66886—24no—
77(C2×D11)⋊C8—24no—
78Dic11⋊C8—24no—
79#66874C2×C412yes—
80#66873C2×C412yes—
81#66872C2×C412yes—
82#66871C2×C412yes—
83#66869—24no—
84C4⋊(C11⋊C8)—24no—
85#66867—21no—
86#66867—24no—
87#66867D412yes—
88#66867D412yes—
89C4×C11⋊C8—21no—
90C4×C11⋊C8—24no—
91C4×C11⋊C8C2×C412yes—
92C4×C11⋊C8C2×C412yes—
93#21294—111nomaximal, Sylow
94C11×#41—22no—
95C11×#41—22no—
96C2×Q8×C11C22×C411yescharacteristic
97C2×D4×C11—21no—
98C2×D4×C11C22×C411yescharacteristic
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11#4112yes—
103C22×C4×C11C2411yescharacteristic
104C2×C22⋊D11—21no—
105#4339—22no—
106#4339—22no—
107C2×D44C22×C411yescharacteristic
108C2×C4×D11—22no—
109C2×C4×D11—21no—
110C2×Dic22C22×C411yescharacteristic
111C11×M16—22no—
112C11×M16—22no—
113C2×C8×C11—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4C22×C412yes—
116C11×C22⋊C4—21no—
117C11×C22⋊C4—22no—
118C42×C11—22no—
119C42×C11—21no—
120C42×C11—22no—
121C42×C11C22×C412yes—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4114yes—
125C22⋊Dic11—21no—
126#4326—22no—
127#4325—22no—
128#4324—22no—
129#4323—22no—
130(C2×D11)⋊C4—22no—
131C4⋊Dic11C22×C412yes—
132Dic11⋊C4—22no—
133C4×Dic11—22no—
134C4×Dic11—21no—
135#4318—22no—
136#4318—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8C22×C412yes—
142C2×C11⋊C8C22×C411yescharacteristic
143C2×C11⋊C8C22×C411yescharacteristic
144C2×C11⋊C8C2×D414yes—
145C2×C11⋊C8#4114yes—
146C4×#135—111no—
147#2923—111no—
148#2923—111no—
149#1974—112no—
150#1945—112no—
151#1938—112no—
152#1938—112no—
153C4×#108—111no—
154#1759—111no—
155#1759D1111yescharacteristic, complemented
156#1726—111no—
157C23×C11—21no—
158C23×C11C2×#4111yescharacteristic
159C22×D11—21no—
160Q8×C11—21no—
161Q8×C11—21no—
162D4×C11—21no—
163D4×C11—21no—
164D4×C11—42no—
165C2×C4×C11—22no—
166C2×C4×C11—21no—
167C2×C4×C11—24no—
168C2×C4×C11—42no—
169C2×C4×C11—44no—
170C2×C4×C11—42no—
171C2×C4×C11—82no—
172C2×C4×C11C4×D412yes—
173C2×C4×C11C4×D412yes—
174C2×C4×C11C23×C411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C2×#4112yes—
177C2×C4×C11C2×#4112yes—
178C22⋊D11—42no—
179C2×Dic11—21no—
180C2×Dic11—22no—
181D44—21no—
182D44—21no—
183C4×D11—42no—
184C4×D11—82no—
185Dic22—21no—
186Dic22—21no—
187C8×C11—42no—
188C11⋊C8—22no—
189C11⋊C8—24no—
190C11⋊C8—42no—
191C11⋊C8#11712yes—
192C11⋊C8#11712yes—
193C2×#135—111no—
194C4×#41—111no—
195C4×#41C2×D1111yescharacteristic
196C4×Q16—112no—
197C4×SD16—112no—
198C4×SD16—112no—
199C4×D8—112no—
200#433—222no—
201#433—222no—
202#432—222no—
203#432—222no—
204C2×#108—112no—
205#427—111no—
206#424—112no—
207#424—112no—
208C2×#104—112no—
209C2×#104C2×D1112yes—
210#416—111no—
211#416—111no—
212#408—112no—
213#408—112no—
214C4×M16—111no—
215C4×M16C2×D1111yescharacteristic
216C2×#97—111no—
217C2×#97—112no—
218C2×C4×C8—111no—
219C2×C4×C8—112no—
220#376C2×D1111yescharacteristic
221#341—112no—
222#339—112no—
223#339C2×D1112yes—
224C22×C11—22no—
225C22×C11—42no—
226C22×C11—41no—
227C22×C11C2×C4×D411yescharacteristic
228C22×C11#52912yes—
229C2×D11—42no—
230C2×D11—41no—
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—44no—
234C4×C11—42no—
235C4×C11—41no—
236C4×C11C2×#11711yescharacteristic
237C4×C11C4×#4111yescharacteristic
238C4×C11#53212yes—
239Dic11—42no—
240Dic11—41no—
241C2×#41—111no—
242C2×#41C22×D1111yescharacteristic
243#135—224no—
244C2×Q16—111no—
245C2×SD16—111no—
246C2×SD16—111no—
247C2×D8—111no—
248C2×M16—112no—
249C2×M16C22×D1112yes—
250C22×C8—111no—
251C22×C8—111no—
252C22×C8—112no—
253C4×Q8—112no—
254C4×Q8C4×D1112yes—
255C4×D4—22no—
256C4×D4—112no—
257C4×D4—222no—
258C4×D4C4×D1112yes—
259#117—21no—
260#117—111no—
261#117—221no—
262#117C22×D1111yescharacteristic
263C2×C42—21no—
264C2×C42—221no—
265C2×C42C22×D1112yes—
266C2×C42C22×D1111yescharacteristic
267#108—224no—
268#107—112no—
269#106—112no—
270C4⋊C8—224no—
271C4⋊C8—224no—
272#104—24no—
273#104—224no—
274#103—112no—
275#103—112no—
276#102—112no—
277#102—112no—
278C22⋊C8—224no—
279C22⋊C8—224no—
280#97—21no—
281#97—112no—
282#97—112no—
283#97—224no—
284#97—221no—
285C4×C8—21no—
286C4×C8—112no—
287C4×C8—112no—
288C4×C8—224no—
289C4×C8—221no—
290#95—22no—
291C2×C11—22no—
292C2×C11—81no—
293C2×C11#229311yescharacteristic
294C2×C11#295712yes—
295D11—81no—
296#41—22no—
297#41—22no—
298#41—222no—
299#41—222no—
300C2×Q8—111no—
301C2×Q8C2×C4×D1111yescharacteristic
302C2×D4—21no—
303C2×D4—111no—
304C2×D4—221no—
305C2×D4C2×C4×D1111yescharacteristic
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—221no—
310C22×C4—222no—
311C22×C4#434112yes—
312C22×C4C23×D1111yescharacteristic
313Q16—222no—
314SD16—222no—
315SD16—222no—
316D8—222no—
317M16—22no—
318M16—22no—
319M16—222no—
320M16—222no—
321C2×C8—22no—
322C2×C8—111no—
323C2×C8—111no—
324C2×C8—114no—
325C2×C8—112no—
326C2×C8—114no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C4⋊C4—22no—
332C4⋊C4—112no—
333C4⋊C4—222no—
334C4⋊C4C2×C4×D1112yes—
335C22⋊C4—21no—
336C22⋊C4—22no—
337C22⋊C4—221no—
338C22⋊C4—222no—
339C42—22no—
340C42—21no—
341C42—22no—
342C42—222no—
343C42—221no—
344C42C2×C4×D1112yes—
345C42#433914yes—
346C42D4×D1111yescharacteristic
347C42D4×D1111yescharacteristic
348C11#2129411yescharacteristic, complemented, Sylow
349C23—21no—
350C23—221no—
351C23C2×#434111yescharacteristic
352Q8—21no—
353Q8—21no—
354Q8—221no—
355Q8—221no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4—221no—
360D4—221no—
361D4—442no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—24no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—222no—
370C2×C4—221no—
371C2×C4—442no—
372C2×C4—882no—
373C2×C4(C22⋊D11)⋊C412yes—
374C2×C4(C22⋊D11)⋊C412yes—
375C2×C4C22×C4×D1111yescharacteristic
376C2×C4C2×#433912yes—
377C2×C4C2×D4×D1111yescharacteristic
378C2×C4#41×D1112yes—
379C8—42no—
380C8—112no—
381C8—112no—
382C8—222no—
383C8—224no—
384C8—442no—
385C22—22no—
386C22—42no—
387C22—41no—
388C22—442no—
389C22—441no—
390C22C2×(C22⋊D11)⋊C411yescharacteristic
391C22#1062306912yes—
392C4—22no—
393C4—22no—
394C4—44no—
395C4—42no—
396C4—41no—
397C4—442no—
398C4—441no—
399C4C4×#433911yescharacteristic
400C4D11×#11711yescharacteristic
401C4#1062307912yes—
402C2—22no—
403C2—81no—
404C2—881no—
405C2#1307107911yescharacteristic
406C2#1307752912yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1759C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C22
cosocleC22×C4×C11C24
hypercenter#1759D11
hypocenterC11#21294
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #13077268C2semidirect
3. #13077267C2semidirect
5. #13069363C2semidirect
6. #13069328C2semidirect
7. #13069324C2semidirect
8. C4×#66886C2semidirect
9. #13068427C2semidirect
10. #13068303C2semidirect
11. C11×#1759C2semidirect
23. C4×#4326C4semidirect
24. C4×#4325C4semidirect
25. C4×#4324C4semidirect
26. C4×#4323C4semidirect
155. #1759D11semidirect
348. C11#21294semidirect

Maximal subgroups

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

subgroupindex
C4×#670032
#130772682
#130772672
#130695012
#130693632
#130693282
#130693242
C4×#668862
#130684272
#130683032
C11×#17592
#2129411