Finite Group Databasebeta

← #14758174

Subgroups — #14758174

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#13077265C211yesmaximal, characteristic, complemented
3#13069503C212yesmaximal
4#13069361C212yesmaximal, complemented
5#13069330C212yesmaximal, complemented
6#13069326C212yesmaximal, complemented
7C4×#66886C211yesmaximal, characteristic, complemented
8#13068429C211yesmaximal, characteristic, complemented
9#13068426C211yesmaximal, characteristic, complemented
10#13068304C211yesmaximal, characteristic, complemented
11C11×#2923C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#433—22no—
16C11×#432—22no—
17C11×#424C2212yes—
18C11×#408C2212yes—
19C4×C11×M16C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C2×#66901C2212yes—
22#10622846C2211yescharacteristic
23C2×#66889C2212yes—
24C2×#66886C2212yes—
25#10622723C2212yes—
26#10622715C2212yes—
27C2×#66879C2212yes—
28C2×C8×Dic11C2212yes—
29C4×#4326C412yescomplemented
30C4×#4325C412yescomplemented
31C4×#4324C412yescomplemented
32C4×#4323C412yescomplemented
33#10622615C2211yescharacteristic
34#10622611C2211yescharacteristic
35#10622545C2211yescharacteristic
36C4×#4318C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622322—22no—
39#10622318—22no—
40#10622196C2212yes—
41#10622193C2212yes—
42#10622170C2212yes—
43C2×C11×#41C2311yescharacteristic
44C2×#4339C2311yescharacteristic
45C2×C11×M16C2312yes—
46C22×C8×C11C2312yes—
47C4×Q8×C11C2×C412yes—
48C4×D4×C11—22no—
49C4×D4×C11C2×C412yes—
50C11×#117—21no—
51C11×#117C2311yescharacteristic
52C2×C42×C11—21no—
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×C4×Dic11C2312yes—
62C2×#4318C2312yes—
63C22×C11⋊C8C2311yescharacteristic
64C22×C11⋊C8C2311yescharacteristic
65C4×D44C2×C412yes—
66#66925—21no—
67C42×D11—21no—
68C4×Dic22C2×C412yes—
69C11×C4⋊C8—24no—
70C11×C22⋊C8—24no—
71C11×#97—21no—
72C11×#97D412yes—
73C11×#97D412yes—
74C4×C8×C11—21no—
75#66901—24no—
76#66899C2×C412yes—
77#66896C2×C412yes—
78C11⋊#95—22no—
79#66889—24no—
80#66886—24no—
81(C2×D11)⋊C8—24no—
82#66879—24no—
83Dic11⋊C8—24no—
84C8×Dic11—24no—
85#66874C2×C412yes—
86#66873C2×C412yes—
87#66872C2×C412yes—
88#66871C2×C412yes—
89#66867—21no—
90C4×C11⋊C8—21no—
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—21no—
100C22×C4×C11—22no—
101C22×C4×C11#4112yes—
102C22×C4×C11C2411yescharacteristic
103C2×C22⋊D11—21no—
104C22×Dic11—22no—
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—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11C2×D414yes—
117C11×C4⋊C4—22no—
118C11×C4⋊C4C22×C412yes—
119C11×C22⋊C4—21no—
120C11×C22⋊C4—22no—
121C42×C11—22no—
122C42×C11—21no—
123C42×C11C22×C412yes—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C22⋊Dic11—21no—
127#4326—22no—
128#4325—22no—
129#4324—22no—
130#4323—22no—
131(C2×D11)⋊C4—22no—
132C4⋊Dic11C22×C412yes—
133Dic11⋊C4—22no—
134C4×Dic11—22no—
135C4×Dic11—21no—
136C4×Dic11—22no—
137C4×Dic11#4114yes—
138#4318—22no—
139#4318—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8C22×C412yes—
143C2×C11⋊C8C22×C411yescharacteristic
144C2×C11⋊C8C22×C411yescharacteristic
145C2×C11⋊C8#4114yes—
146C4×#135—111no—
147#2923—111no—
148#2923D1111yescharacteristic, complemented
149#1974—112no—
150#1945—112no—
151#1938—112no—
152#1938—112no—
153C4×#108—111no—
154#1759—111no—
155#1759—111no—
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—42no—
168C2×C4×C11—42no—
169C2×C4×C11—82no—
170C2×C4×C11C4×D412yes—
171C2×C4×C11C4×D412yes—
172C2×C4×C11C23×C411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4112yes—
175C2×C4×C11C2×#4112yes—
176C22⋊D11—42no—
177C2×Dic11—21no—
178C2×Dic11—22no—
179C2×Dic11—24no—
180C2×Dic11—44no—
181D44—21no—
182D44—21no—
183C4×D11—42no—
184C4×D11—82no—
185Dic22—21no—
186Dic22—21no—
187C8×C11—24no—
188C8×C11—42no—
189C11⋊C8—22no—
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—22no—
201#433—222no—
202#432—22no—
203#432—222no—
204C2×#108—112no—
205#427—111no—
206#424—112no—
207#424C2×D1112yes—
208C2×#104—112no—
209C2×#104—112no—
210#416—111no—
211#416—111no—
212#408—112no—
213#408C2×D1112yes—
214C4×M16—111no—
215C4×M16C2×D1111yescharacteristic
216C2×#97—112no—
217C2×#97C2×D1111yescharacteristic
218C2×C4×C8—111no—
219C2×C4×C8—112no—
220#376—111no—
221#341—112no—
222#339—112no—
223#339—112no—
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—42no—
234C4×C11—41no—
235C4×C11C2×#11711yescharacteristic
236C4×C11C4×#4111yescharacteristic
237C4×C11#53212yes—
238Dic11—44no—
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×C8C22×D1112yes—
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—112no—
265C2×C42—221no—
266C2×C42C22×D1111yescharacteristic
267#108—224no—
268#107—112no—
269#106—112no—
270C4⋊C8—24no—
271C4⋊C8—224no—
272#104—224no—
273#104—224no—
274#103—112no—
275#103—112no—
276#102—112no—
277#102—112no—
278C22⋊C8—24no—
279C22⋊C8—224no—
280#97—21no—
281#97—224no—
282#97—221no—
283#97C22⋊D1112yes—
284#97C22⋊D1112yes—
285C4×C8—21no—
286C4×C8—112no—
287C4×C8—112no—
288C4×C8—224no—
289C4×C8—221no—
290#95—222no—
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—21no—
307C22×C4—22no—
308C22×C4—222no—
309C22×C4—221no—
310C22×C4—222no—
311C22×C4#433912yes—
312C22×C4C23×D1111yescharacteristic
313Q16—222no—
314SD16—222no—
315SD16—222no—
316D8—222no—
317M16—22no—
318M16—22no—
319M16—222no—
320M16—222no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—111no—
325C2×C8—111no—
326C2×C8—114no—
327C2×C8—112no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8C2×C22⋊D1114yes—
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—114no—
342C42—222no—
343C42—222no—
344C42—221no—
345C42C2×C4×D1112yes—
346C42C2×C22⋊D1111yescharacteristic
347C42C2×C22⋊D1111yescharacteristic
348C11#2129411yescharacteristic, complemented, Sylow
349C23—21no—
350C23—221no—
351C23C2×#433911yescharacteristic
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—42no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—224no—
368C2×C4—222no—
369C2×C4—221no—
370C2×C4—444no—
371C2×C4—442no—
372C2×C4—882no—
373C2×C4C4×C22⋊D1112yes—
374C2×C4C4×C22⋊D1112yes—
375C2×C4C22×C4×D1111yescharacteristic
376C2×C4#41×D1112yes—
377C2×C4#41×D1112yes—
378C2×C4C22×C22⋊D1111yescharacteristic
379C8—24no—
380C8—42no—
381C8—112no—
382C8—112no—
383C8—222no—
384C8—442no—
385C22—22no—
386C22—42no—
387C22—41no—
388C22—442no—
389C22—441no—
390C22#1062305912yes—
391C22C2×C4×C22⋊D1111yescharacteristic
392C4—22no—
393C4—22no—
394C4—42no—
395C4—41no—
396C4—444no—
397C4—442no—
398C4—441no—
399C4D11×#11711yescharacteristic
400C4#1062305311yescharacteristic
401C4#1062336312yes—
402C2—22no—
403C2—81no—
404C2—881no—
405C2#1307107511yescharacteristic
406C2#1307753112yes—
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2923C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C22
cosocleC22×C4×C11C24
hypercenter#2923D11
hypocenterC11#21294
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #13077265C2semidirect
4. #13069361C2semidirect
5. #13069330C2semidirect
6. #13069326C2semidirect
7. C4×#66886C2semidirect
8. #13068429C2semidirect
9. #13068426C2semidirect
10. #13068304C2semidirect
11. C11×#2923C2semidirect
29. C4×#4326C4semidirect
30. C4×#4325C4semidirect
31. C4×#4324C4semidirect
32. C4×#4323C4semidirect
148. #2923D11semidirect
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
#130772652
#130695032
#130693612
#130693302
#130693262
C4×#668862
#130684292
#130684262
#130683042
C11×#29232
#2129411