Finite Group Databasebeta

← #14780303

Subgroups — #14780303

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66989C211yesmaximal, characteristic
2#13069554C212yesmaximal, complemented
3#13069232C212yesmaximal, complemented
4#13069226C212yesmaximal, complemented
5#13068914C211yesmaximal, characteristic
6#13068799C212yesmaximal, complemented
7#13068798C212yesmaximal, complemented
8#13068731C212yesmaximal, complemented
9C11×#1870C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66989C411yescharacteristic
13C22×#4318C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C2×C11×C22⋊C8C2211yescharacteristic
16C2×C11×C22⋊C8C2212yes—
17#10622834C411yescharacteristic
18C4×C22⋊Dic11C2212yes—
19C4×C22⋊Dic11C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×#66879C2212yes—
23C2×Dic11⋊C8C2212yes—
24C2×Dic11⋊C8C2212yes—
25C2×Dic11⋊C8C2212yes—
26#10622590C411yescharacteristic
27#10622587C411yescharacteristic
28#10622558C412yes—
29#10622558C412yes—
30C42×Dic11C2211yescharacteristic
31C11×#336C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2212yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×Dic22C2×C411yescharacteristic
41C2×C11×M16—41no—
42C2×C11×M16—42no—
43C22×C8×C11C2312yes—
44C22×C8×C11C2312yes—
45C4×D4×C11—41no—
46C4×D4×C11—41no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4C2×C411yescharacteristic
49C2×C11×C22⋊C4C2×C411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11C2×C412yes—
52C2×C22⋊Dic11C2×C412yes—
53C2×C22⋊Dic11C2×C412yes—
54C2×C22⋊Dic11C2×C412yes—
55#66989—24no—
56C2×C4⋊Dic11C2×C411yescharacteristic
57C2×Dic11⋊C4C2×C412yes—
58C2×C4×Dic11C2×C412yes—
59C2×C4×Dic11C2×C411yescharacteristic
60C2×C4×Dic11C2×C411yescharacteristic
61C2×C4×Dic11C2312yes—
62C2×C4×Dic11C2312yes—
63C2×#4318—41no—
64C2×#4318—42no—
65C22×C11⋊C8C2312yes—
66C22×C11⋊C8C2312yes—
67C4×Dic22—41no—
68C4×Dic22—41no—
69C11×C22⋊C8—42no—
70C11×C22⋊C8—41no—
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73C11⋊#95C2×C412yes—
74C11⋊#95C2×C412yes—
75C22⋊(C11⋊C8)—42no—
76C22⋊(C11⋊C8)—41no—
77#66879—42no—
78Dic11⋊C8—42no—
79Dic11⋊C8—42no—
80Dic11⋊C8—42no—
81#23353—111nomaximal, Sylow
82C24×C11C22×C411yescharacteristic
83C24×C11C22×C411yescharacteristic
84C2×D4×C11—22no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C412yes—
103C22×Dic11C22×C412yes—
104C2×Dic22—22no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C11×M16—44no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11—21no—
118C42×C11—21no—
119C22⋊Dic11—24no—
120C22⋊Dic11—24no—
121C22⋊Dic11—42no—
122C22⋊Dic11—42no—
123C4⋊Dic11—41no—
124Dic11⋊C4—42no—
125C4×Dic11—22no—
126C4×Dic11—22no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129C4×Dic11—41no—
130C4×Dic11—42no—
131C4×Dic11M1614yescomplemented
132#4318—44no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C4×#124—111no—
140#1985—112no—
141#1924—112no—
142#1924—112no—
143#1870—111no—
144#1870D1111yescharacteristic
145#1851—112no—
146#1851—112no—
147#1831—112no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11C23×C411yescharacteristic
159D4×C11—44no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11C2×M1612yes—
175C2×C4×C11H(5,𝔽2)12yes—
176C2×C4×C11H(5,𝔽2)11yescharacteristic
177C2×C4×C11H(5,𝔽2)11yescharacteristic
178C2×C4×C112−1+412yes—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11C2×M1614yes—
191Dic22—44no—
192C8×C11—42no—
193C8×C11—42no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C22×M16—111no—
197C22×M16C2×D1111yescharacteristic
198C2×#124—111no—
199C2×C4×Q8—111no—
200C2×C4×D4C2×D1111yescharacteristic
201C2×C4⋊C8—112no—
202C2×C4⋊C8—112no—
203C2×C4⋊C8—112no—
204C2×C22⋊C8—112no—
205C2×C22⋊C8—111no—
206C2×C22⋊C8C2×D1112yes—
207C2×C22⋊C8C2×D1111yescharacteristic
208C2×#97—112no—
209#391—111no—
210#390—111no—
211#388—112no—
212#388—112no—
213#382—111no—
214C4×C22⋊C4—112no—
215C4×C22⋊C4—112no—
216C43—111no—
217#336—112no—
218#336—112no—
219#336—112no—
220#336—112no—
221#336—112no—
222#336C2×D1112yes—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11#51811yescharacteristic
234C22×C11#52012yes—
235C22×C11C22×M1611yescharacteristic
236C22×C11#56811yescharacteristic
237C22×C11#56812yes—
238C4×C11—22no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—41no—
242C4×C11H(3,𝔽4)11yescharacteristic
243C4×C11#56212yes—
244C4×C11#56311yescharacteristic
245Dic11—24no—
246Dic11—42no—
247Dic11—42no—
248Dic11—42no—
249C22×Q8—111no—
250C22×D4C4×D1111yescharacteristic
251C23×C4C22×D1111yescharacteristic
252C23×C4C22×D1111yescharacteristic
253C2×M16—42no—
254C2×M16—41no—
255C2×M16—442no—
256C2×M16—441no—
257C22×C8—112no—
258C22×C8—112no—
259C22×C8C22×D1112yes—
260C22×C8C22×D1112yes—
261#124—224no—
262C4×Q8—441no—
263C4×Q8—441no—
264C4×D4—41no—
265C4×D4—41no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4C4×D1111yescharacteristic
269C2×C22⋊C4—112no—
270C2×C22⋊C4—112no—
271C2×C22⋊C4—112no—
272C2×C22⋊C4—112no—
273C2×C22⋊C4C4×D1111yescharacteristic
274C2×C22⋊C4C4×D1111yescharacteristic
275C2×C42—111no—
276C2×C42—112no—
277C2×C42—112no—
278C2×C42—112no—
279C2×C42—111no—
280C2×C42C22×D1111yescharacteristic
281C4⋊C8—442no—
282C4⋊C8—442no—
283C4⋊C8—442no—
284C22⋊C8—41no—
285C22⋊C8—42no—
286C22⋊C8—441no—
287C22⋊C8—442no—
288#97—442no—
289#95—112no—
290#95—112no—
291#95—112no—
292#95—112no—
293C2×C11—81no—
294C2×C11—81no—
295C2×C11#237911yescharacteristic
296C2×C11#297511yescharacteristic
297C2×C11#298011yescharacteristic
298C2×C11#298912yes—
299C2×C11#299512yes—
300C24C2×C4×D1111yescharacteristic
301C24C2×C4×D1111yescharacteristic
302C2×Q8—222no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×D4—22no—
306C2×D4—41no—
307C2×D4—41no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—112no—
317C22×C4—112no—
318C22×C4—112no—
319C22×C4—112no—
320C22×C4C2×C4×D1111yescharacteristic
321C22×C4C2×C4×D1111yescharacteristic
322C22×C4C2×C4×D1111yescharacteristic
323C22×C4C2×C4×D1111yescharacteristic
324C22×C4C23×D1111yescharacteristic
325M16—44no—
326M16—444no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—222no—
339C4⋊C4—41no—
340C4⋊C4—442no—
341C4⋊C4—441no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—224no—
345C22⋊C4—224no—
346C22⋊C4—442no—
347C22⋊C4—442no—
348C42—21no—
349C42—21no—
350C42—114no—
351C42—222no—
352C42—222no—
353C42—222no—
354C42—222no—
355C42—441no—
356C42—442no—
357C11#2335311yescharacteristic, complemented, Sylow
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23C22×C4×D1111yescharacteristic
369Q8—444no—
370D4—44no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—114no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4M16×D1112yes—
398C2×C4#6703712yes—
399C2×C4#6703711yescharacteristic
400C2×C4#6703711yescharacteristic
401C2×C4#6704312yes—
402C8—42no—
403C8—42no—
404C8—442no—
405C8—442no—
406C22—42no—
407C22—42no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—42no—
415C22—42no—
416C22#1062301711yescharacteristic
417C22#1062307712yes—
418C22C2×M16×D1111yescharacteristic
419C22#1062327611yescharacteristic
420C22#1062328112yes—
421C4—22no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—224no—
426C4—442no—
427C4—442no—
428C4—442no—
429C4#1062312511yescharacteristic
430C4#1062315212yes—
431C4#1062318211yescharacteristic
432C2—81no—
433C2—81no—
434C2#1307178611yescharacteristic
435C2#1307765511yescharacteristic
436C2#1307768511yescharacteristic
437C2#1307773112yes—
438C2#1307778212yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#23353
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #13069554C2semidirect
3. #13069232C2semidirect
4. #13069226C2semidirect
6. #13068799C2semidirect
7. #13068798C2semidirect
8. #13068731C2semidirect
131. C4×Dic11M16semidirect
357. C11#23353semidirect

Maximal subgroups

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

subgroupindex
C4×#669892
#130695542
#130692322
#130692262
#130689142
#130687992
#130687982
#130687312
C11×#18702
#2335311