Finite Group Databasebeta

← #14772067

Subgroups — #14772067

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622765C211yesmaximal, characteristic
2C2×D8×Dic11C211yesmaximal, characteristic
3#13071521C212yesmaximal, complemented
4#13069354C211yesmaximal, characteristic, complemented
5#13069352C211yesmaximal, characteristic, complemented
6#13068863C212yesmaximal, complemented
7#13068861C212yesmaximal, complemented
8#13068777C211yesmaximal, characteristic, complemented
9#13068624C212yesmaximal, complemented
10#13068484C211yesmaximal, characteristic, complemented
11C2×C11×#442C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C2×D4×Dic11C2212yes—
15C2×D4×Dic11C2212yes—
16C11×#442—24no—
17C2×C11×#106C2211yescharacteristic
18C2×C11×#102C2212yes—
19C2×C11×#97C2211yescharacteristic
20C2×#66896C2212yes—
21C2×#66896C2212yes—
22#10622823—22no—
23C2×C11⋊#95—22no—
24#10622765—24no—
25D8×Dic11C418yescomplemented
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622590C2212yes—
32#10622586C2212yes—
33C2×#66871C2212yes—
34#10622559—22no—
35#10622555—22no—
36C4×Dic11⋊C4C2211yescharacteristic
37#10622541C2212yes—
38#10622189C2212yes—
39#10622188C2211yescharacteristic
40#10622167C2212yes—
41#10622162C2211yescharacteristic
42C22×D4×C11C2312yes—
43C23×C4×C11—22no—
44C23×Dic11—22no—
45C23×Dic11—22no—
46C2×C11×D8C2×C414yes—
47C2×C11×D8D414yes—
48C2×C11×D8Q814yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×D4×C11—24no—
52C4×D4×C11—42no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58D4×Dic11—24no—
59D4×Dic11—24no—
60D4×Dic11—42no—
61D4×Dic11C2×C418yescomplemented
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2312yes—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4D412yes—
67C2×C4×Dic11C2311yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C11×#106—22no—
72C11×#102—24no—
73C11×#97—22no—
74#66896—24no—
75#66896C2×C418yescomplemented
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D412yes—
81#66882C2×C414yescomplemented
82#66881—22no—
83#66879—22no—
84Dic11⋊C8—22no—
85C8×Dic11C2×C414yescomplemented
86#66871—42no—
87#22672—111nomaximal, Sylow
88C24×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11C22×C414yes—
93C2×D4×C11C2×D414yes—
94C2×D4×C11C2×Q814yes—
95C22×C4×C11—22no—
96C22×C4×C11—44no—
97C22×C4×C11—44no—
98C22×C4×C11—82no—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—28no—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—44no—
105C22×Dic11—44no—
106C22×Dic11—82no—
107C22×Dic11—82no—
108C22×Dic11—82no—
109C22×Dic11C2×D412yes—
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C11×D8C4⋊C4116yescomplemented
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11C22×C412yes—
117C2×C8×C11C2×D412yes—
118C2×C8×C11C2×Q812yes—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C22⋊C4—44no—
122C42×C11—21no—
123C42×C11—21no—
124C22⋊Dic11—28no—
125C22⋊Dic11—44no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11C22×C414yes—
130Dic11⋊C4—42no—
131Dic11⋊C4—82no—
132Dic11⋊C4—82no—
133C4×Dic11—21no—
134C4×Dic11—21no—
135C4×Dic11C22×C412yes—
136C4×Dic11#4112yes—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8C22×C412yes—
143C2×#442—111no—
144C2×#442D1111yescharacteristic
145C2×C4×D8—111no—
146#2349—112no—
147#1943—111no—
148#1943—111no—
149#1862—112no—
150#1862—112no—
151#1846—111no—
152#1804—112no—
153#1770—111no—
154C23×C11—24no—
155C23×C11—24no—
156C23×C11—24no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11C22×D411yescharacteristic
162D4×C11—24no—
163D4×C11—24no—
164D4×C11—24no—
165D4×C11C2×C4⋊C418yes—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—88no—
173C2×C4×C11C23×C411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×Q811yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×C4×C11H(5,𝔽2)11yescharacteristic
178C2×C4×C112−1+411yescharacteristic
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—24no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—88no—
191C2×Dic11—88no—
192C2×Dic11C4×D412yes—
193C2×Dic11C4×D412yes—
194C8×C11—41no—
195C8×C11C2×C4⋊C414yes—
196C11⋊C8—22no—
197C11⋊C8—41no—
198C22×D8C2×D1111yescharacteristic
199C2×C4×D4—112no—
200C2×C4×D4—112no—
201C2×C4×D4C2×D1112yes—
202#442—24no—
203#442—224no—
204C4×D8—118no—
205C2×#107—111no—
206C2×#107—112no—
207C2×#106—111no—
208C2×#106C2×D1111yescharacteristic
209C2×C4⋊C8—111no—
210C2×#102—112no—
211C2×#102—112no—
212C2×#102C2×D1112yes—
213C2×#97—111no—
214C2×#97C2×D1111yescharacteristic
215C2×C4×C8—111no—
216#389—112no—
217#389—112no—
218#385—222no—
219#385—222no—
220#382—112no—
221#380—222no—
222C4×C4⋊C4—111no—
223C2×#95—222no—
224#340—112no—
225#340—112no—
226#336—111no—
227#336—111no—
228C22×C11—28no—
229C22×C11—44no—
230C22×C11—44no—
231C22×C11—44no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—44no—
235C22×C11C2×C4×D411yescharacteristic
236C22×C11D4211yescharacteristic
237C22×C11D4×Q811yescharacteristic
238C22×C11#57512yes—
239C22×C11#57612yes—
240C4×C11—42no—
241C4×C11—82no—
242C4×C11C22×C4⋊C411yescharacteristic
243C4×C11#52011yescharacteristic
244C4×C11#54711yescharacteristic
245C4×C11#55411yescharacteristic
246Dic11—22no—
247Dic11—22no—
248Dic11—44no—
249Dic11—42no—
250Dic11—82no—
251C22×D4C22×D1112yes—
252C23×C4—22no—
253C23×C4—222no—
254C23×C4—222no—
255C2×D8Dic2214yes—
256C2×D8C4×D1114yes—
257C2×D8C22⋊D1114yes—
258C22×C8—111no—
259C22×C8—111no—
260C22×C8C22×D1111yescharacteristic
261C22×C8C22×D1111yescharacteristic
262C4×D4—24no—
263C4×D4—42no—
264C4×D4—118no—
265C4×D4—224no—
266C4×D4—224no—
267C4×D4—442no—
268C2×C4⋊C4—112no—
269C2×C4⋊C4—112no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4C22×D1112yes—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—222no—
276C2×C22⋊C4—222no—
277C2×C42—111no—
278C2×C42—111no—
279C2×C42C22×D1111yescharacteristic
280#107—114no—
281#107—442no—
282#106—22no—
283#106—222no—
284C4⋊C8—222no—
285#102—24no—
286#102—118no—
287#102—224no—
288#97—22no—
289#97—222no—
290C4×C8—114no—
291#95—112no—
292#95—222no—
293#95—222no—
294#95—222no—
295#95—222no—
296C2×C11—48no—
297C2×C11D4×C4⋊C411yescharacteristic
298C2×C11#294311yescharacteristic
299C2×C11#294811yescharacteristic
300C2×C11#327312yes—
301C2×C11#338912yes—
302C24—22no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4C2×Dic2214yes—
307C2×D4C2×C4×D1114yes—
308C2×D4C2×C22⋊D1114yes—
309C22×C4—22no—
310C22×C4—44no—
311C22×C4—44no—
312C22×C4—82no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—112no—
316C22×C4—228no—
317C22×C4—222no—
318C22×C4—222no—
319C22×C4—444no—
320C22×C4—444no—
321C22×C4—882no—
322C22×C4—882no—
323C22×C4—882no—
324C22×C4D4×D1112yes—
325C22×C4C23×D1111yescharacteristic
326D8Dic11⋊C4116yescomplemented
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—112no—
331C2×C8—221no—
332C2×C8—221no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8C2×Dic2212yes—
337C2×C8C2×C4×D1112yes—
338C2×C8C2×C22⋊D1112yes—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—114no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—442no—
346C4⋊C4—882no—
347C4⋊C4—882no—
348C22⋊C4—44no—
349C22⋊C4—228no—
350C22⋊C4—444no—
351C42—21no—
352C42—21no—
353C42—112no—
354C42—112no—
355C42—221no—
356C42—221no—
357C11#2267211yescharacteristic, complemented, Sylow
358C23—24no—
359C23—24no—
360C23—24no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23C2×D4×D1111yescharacteristic
366D4—24no—
367D4—24no—
368D4—24no—
369D4C2×Dic11⋊C418yes—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—88no—
377C2×C4—112no—
378C2×C4—112no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—222no—
383C2×C4—224no—
384C2×C4—222no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—888no—
391C2×C4—888no—
392C2×C4C22×Dic2211yescharacteristic
393C2×C4C22×C4×D1111yescharacteristic
394C2×C4#6703711yescharacteristic
395C2×C4#41×D1111yescharacteristic
396C2×C4#6704311yescharacteristic
397C2×C4C22×C22⋊D1111yescharacteristic
398C8—41no—
399C8—222no—
400C8—441no—
401C8C2×Dic11⋊C414yes—
402C22—28no—
403C22—44no—
404C22—44no—
405C22—44no—
406C22—44no—
407C22—44no—
408C22—44no—
409C22D4×Dic2211yescharacteristic
410C22C4×D4×D1111yescharacteristic
411C22#1062330412yes—
412C22#1062330512yes—
413C22D4×C22⋊D1111yescharacteristic
414C4—42no—
415C4—82no—
416C4—222no—
417C4—222no—
418C4—442no—
419C4—444no—
420C4—882no—
421C4#1062307011yescharacteristic
422C4#1062307711yescharacteristic
423C4C22×Dic11⋊C411yescharacteristic
424C4#1062335511yescharacteristic
425C2—48no—
426C2D4×Dic11⋊C411yescharacteristic
427C2#1307741311yescharacteristic
428C2#1307746511yescharacteristic
429C2#1308022112yes—
430C2#1308157512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
cosocleC22×C4×C11C24
hypercenterC2×#442D11
hypocenterC11#22672
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
3. #13071521C2semidirect
4. #13069354C2semidirect
5. #13069352C2semidirect
6. #13068863C2semidirect
7. #13068861C2semidirect
8. #13068777C2semidirect
9. #13068624C2semidirect
10. #13068484C2semidirect
25. D8×Dic11C4semidirect
61. D4×Dic11C2×C4semidirect
75. #66896C2×C4semidirect
81. #66882C2×C4semidirect
85. C8×Dic11C2×C4semidirect
112. C11×D8C4⋊C4semidirect
326. D8Dic11⋊C4semidirect
357. C11#22672semidirect

Maximal subgroups

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

subgroupindex
C2×#106227652
C2×D8×Dic112
#130715212
#130693542
#130693522
#130688632
#130688612
#130687772
#130686242
#130684842
C2×C11×#4422
#2267211