Finite Group Databasebeta

← #14812757

Subgroups — #14812757

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073652C211yesmaximal, characteristic
2#13071573C211yesmaximal, characteristic
3#13070157C212yesmaximal
4#13069993C212yesmaximal
5#13069380C211yesmaximal, characteristic
6#13069378C212yesmaximal
7#13069332C211yesmaximal, characteristic
8#13069197C212yesmaximal
9#13068772C211yesmaximal, characteristic
10C4×#66899C211yesmaximal, characteristic
11C11×#1803C211yesmaximal, characteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66943—21no—
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×#103C2212yes—
16C11×#384C2211yescharacteristic
17#10622843C2212yes—
18C2×#66899C2211yescharacteristic
19C2×#66899C2211yescharacteristic
20C2×#66881C2212yes—
21C2×Dic11⋊C8C2212yes—
22#10622598C2212yes—
23#10622597—22no—
24#10622594—22no—
25#10622589C2212yes—
26C4⋊C4×Dic11C2212yes—
27#10622586—21no—
28C2×#66872C2212yes—
29C2×#66872C2212yes—
30#10622549—21no—
31#10622548C2211yescharacteristic
32C4×C4⋊Dic11—21no—
33C4×C4⋊Dic11C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36C11×#340C2212yes—
37#10622189C2212yes—
38#10622188C2212yes—
39#10622167C2211yescharacteristic
40#10622167C2211yescharacteristic
41C22×Q8×C11C2311yescharacteristic
42C22×C8×C11C2312yes—
43C4×Q8×C11—22no—
44C4×Q8×C11Q814yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11D411yescharacteristic
56C2×C4⋊Dic11D411yescharacteristic
57C2×C4⋊Dic11C2311yescharacteristic
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2312yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11—21no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11C2312yes—
65C22×C11⋊C8C2311yescharacteristic
66C22×C11⋊C8C2311yescharacteristic
67#66943—44no—
68C11×C4⋊C8—22no—
69C11×#103—42no—
70#66899—22no—
71#66899—22no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95D412yes—
78#66881—42no—
79Dic11⋊C8—24no—
80#66872—24no—
81#66872—42no—
82C4×C11⋊C8—22no—
83#26088—111nomaximal, Sylow
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11C2×Q812yes—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—21no—
99C22×Dic11C2×D412yes—
100C22×Dic11C2×D412yes—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4—81no—
110C11×C4⋊C4C2×Q812yes—
111C42×C11—24no—
112C42×C11C2×Q812yes—
113C42×C11#4112yes—
114C4⋊Dic11—22no—
115C4⋊Dic11—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—44no—
122C4⋊Dic11—42no—
123C4⋊Dic11—81no—
124C4⋊Dic11SD1614yes—
125Dic11⋊C4—44no—
126Dic11⋊C4—82no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129C4×Dic11—42no—
130C4×Dic11—82no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8#4112yes—
136C2×C11⋊C8#4112yes—
137#2552—111no—
138#2355—111no—
139#2096—112no—
140#2066—112no—
141#1948—111no—
142#1948—112no—
143#1939—111no—
144#1919—112no—
145#1844—111no—
146#1803D1111yescharacteristic
147C4×#103—111no—
148C23×C11C22×D411yescharacteristic
149Q8×C11—22no—
150Q8×C11—22no—
151Q8×C11—41no—
152Q8×C11—41no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11C22⋊Q812yes—
165C2×C4×C11C22⋊Q812yes—
166C2×C4×C11C2×SD1612yes—
167C2×C4×C11#13712yes—
168C2×C4×C11C22×Q811yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×C4×C11H(5,𝔽2)11yescharacteristic
173C2×C4×C112−1+411yescharacteristic
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11C2×SD1614yes—
189C8×C11—42no—
190C11⋊C8—22no—
191C11⋊C8—22no—
192C2×#125—221no—
193C2×C4×Q8C2×D1111yescharacteristic
194C2×#106—112no—
195C2×#106—112no—
196C2×#106—112no—
197C2×C4⋊C8—112no—
198C2×C4⋊C8C2×D1111yescharacteristic
199C2×#103—111no—
200C2×#103—111no—
201C2×#103C2×D1112yes—
202C2×C4×C8—111no—
203#398—222no—
204#391—112no—
205#389—112no—
206#389—221no—
207#387—222no—
208#384—112no—
209#384—111no—
210#384C2×D1111yescharacteristic
211#382—221no—
212C4×C4⋊C4—111no—
213C4×C4⋊C4—112no—
214C4×C4⋊C4—111no—
215C4×C4⋊C4—221no—
216#340—112no—
217#340—111no—
218#340—111no—
219#340C2×D1112yes—
220#336—112no—
221C22×C11C2×C22⋊Q811yescharacteristic
222C22×C11#54711yescharacteristic
223C22×C11#55011yescharacteristic
224C22×C11C22×SD1611yescharacteristic
225C22×C11C2×#13711yescharacteristic
226C22×C11#57711yescharacteristic
227C22×C11#57711yescharacteristic
228C4×C11—22no—
229C4×C11—42no—
230C4×C11—42no—
231C4×C11—82no—
232C4×C11#47514yes—
233C4×C11#53311yescharacteristic
234C4×C11#54411yescharacteristic
235C4×C11#55211yescharacteristic
236C4×C11#55311yescharacteristic
237Dic11—24no—
238Dic11—42no—
239Dic11—81no—
240Dic11—81no—
241Dic11—82no—
242C22×Q8C22×D1111yescharacteristic
243C22×C8—111no—
244C22×C8—111no—
245C22×C8C22×D1112yes—
246#125—444no—
247C4×Q8—22no—
248C4×Q8Dic2214yes—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4C22×D1112yes—
263C2×C4⋊C4C22×D1111yescharacteristic
264C2×C42—21no—
265C2×C42—112no—
266C2×C42—221no—
267C2×C42—222no—
268C2×C42C22×D1111yescharacteristic
269#106—224no—
270#106—442no—
271#106—442no—
272C4⋊C8—22no—
273C4⋊C8—224no—
274#103—42no—
275#103—222no—
276#103—222no—
277C4×C8—222no—
278#95—112no—
279#95—222no—
280#95—222no—
281#95—222no—
282#95—222no—
283#95—221no—
284C2×C11#244111yescharacteristic
285C2×C11C2×#47511yescharacteristic
286C2×C11#308411yescharacteristic
287C2×C11#333511yescharacteristic
288C2×C11#335611yescharacteristic
289C2×C11#339211yescharacteristic
290C2×C11#340011yescharacteristic
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8C2×Dic2212yes—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—112no—
301C22×C4—112no—
302C22×C4—221no—
303C22×C4—222no—
304C22×C4—221no—
305C22×C4D4×D1111yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4C23×D1111yescharacteristic
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—112no—
312C2×C8—112no—
313C2×C8—221no—
314C2×C8—221no—
315C2×C8—221no—
316C2×C8—221no—
317C4⋊C4—24no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—42no—
322C4⋊C4—81no—
323C4⋊C4—114no—
324C4⋊C4—222no—
325C4⋊C4—222no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—222no—
331C4⋊C4—444no—
332C4⋊C4—444no—
333C4⋊C4—442no—
334C4⋊C4—881no—
335C4⋊C4—882no—
336C4⋊C4C2×Dic2212yes—
337C42—24no—
338C42—222no—
339C42—222no—
340C42—442no—
341C42—882no—
342C42C2×Dic2212yes—
343C42#434112yes—
344C11#2608811yescharacteristic, complemented, Sylow
345C23C2×D4×D1111yescharacteristic
346Q8—22no—
347Q8—22no—
348Q8—41no—
349Q8—41no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—114no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—442no—
370C2×C4—441no—
371C2×C4—442no—
372C2×C4—441no—
373C2×C4—442no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4#6693112yes—
377C2×C4#6693112yes—
378C2×C4SD16×D1112yes—
379C2×C4#6697112yes—
380C2×C4C22×Dic2211yescharacteristic
381C2×C4C2×#434111yescharacteristic
382C2×C4#6703711yescharacteristic
383C2×C4#6704011yescharacteristic
384C2×C4#41×D1111yescharacteristic
385C2×C4#41×D1111yescharacteristic
386C8—42no—
387C8—222no—
388C8—222no—
389C22C2×#6693111yescharacteristic
390C22#1062313011yescharacteristic
391C22#1062316211yescharacteristic
392C22C2×SD16×D1111yescharacteristic
393C22C2×#6697111yescharacteristic
394C22#1062330611yescharacteristic
395C22#1062330911yescharacteristic
396C4—22no—
397C4—42no—
398C4—42no—
399C4—82no—
400C4—224no—
401C4—442no—
402C4—882no—
403C4—881no—
404C4—881no—
405C4#1062240414yes—
406C4#1062303111yescharacteristic
407C4#1062304811yescharacteristic
408C4#1062314511yescharacteristic
409C4#1062317011yescharacteristic
410C2#1307233011yescharacteristic
411C2C2×#1062240411yescharacteristic
412C2#1307848211yescharacteristic
413C2#1308097611yescharacteristic
414C2#1308123411yescharacteristic
415C2#1308159611yescharacteristic
416C2#1308167311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socle, prime radicalC23×C11C22×D4
hypercenter#1803D11
hypocenterC11#26088
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
344. C11#26088semidirect

Maximal subgroups

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

subgroupindex
#130736522
#130715732
#130701572
#130699932
#130693802
#130693782
#130693322
#130691972
#130687722
C4×#668992
C11×#18032
#2608811