Finite Group Databasebeta

← #14769933

Subgroups — #14769933

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic
2M16×D44C212yesmaximal, complemented
3#13069605C212yesmaximal, complemented
4#13069076C214yesmaximal, complemented
5#13068695C212yesmaximal, complemented
6#13068608C211yesmaximal, characteristic, complemented
7D11×#343C212yesmaximal, complemented
8C4×C11×#100C211yesmaximal, characteristic, complemented
9C22×#4339C412yes—
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66991C2212yes—
12C2×#66977C412yes—
13C2×M16×D11C2214yes—
14#10623082—22no—
15#10623082—22no—
16#10623082—24no—
17C2×C4⋊C4×D11C2212yes—
18C2×#66936C414yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×#100C2212yes—
22C4×C11×M16C2212yes—
23C2×#66897C2212yes—
24#10622739C2214yes—
25#10622537C2212yes—
26#10622319—24no—
27#10622301—22no—
28C8×D44—22no—
29C11×#343C2211yescharacteristic
30C11×#343C2211yescharacteristic
31#10622192C2214yes—
32#10622192C2214yes—
33#10622168C2212yes—
34C22×D4×C11C2311yescharacteristic
35C23×C4×C11C2×C412yes—
36C22×C22⋊D11C2×C414yes—
37C2×#4339—24no—
38C2×#4339—22no—
39C2×#4339—22no—
40C2×#4339—48no—
41C22×D44C2×C411yescharacteristic
42C22×C4×D11C2×C414yes—
43C22×C4×D11C2312yes—
44C22×Dic22C2×C412yes—
45C2×C11×M16C2312yes—
46C2×C11×M16C2312yes—
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C22⋊C4C2×C412yes—
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11C2×C414yes—
53#66991—24no—
54#66991—24no—
55C2×(C2×D11)⋊C4C2×C412yes—
56C2×C4⋊Dic11C2×C412yes—
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×C4⋊Dic11C2312yes—
59#66977—24no—
60#66977—24no—
61C2×Dic11⋊C4C2×C414yes—
62C2×#4318C2314yes—
63M16×D11—28no—
64M16×D11—44no—
65C2×#4313—24no—
66C2×C8×D11—24no—
67C4⋊C4×D11—24no—
68C4⋊C4×D11—24no—
69#66936—28no—
70#66936—28no—
71C4×D44D412yes—
72C4×D44D412yes—
73C4×D44D414yes—
74#66922—22no—
75#66922—22no—
76C11×#100—24no—
77C11×#97—22no—
78C4×C8×C11—22no—
79#66897—42no—
80(C2×D11)⋊C8—24no—
81(C2×D11)⋊C8—24no—
82C4⋊(C11⋊C8)—22no—
83C4⋊(C11⋊C8)—22no—
84#22479—111nomaximal, Sylow
85C24×C11C22×C412yes—
86C23×D11C22×C412yes—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—44no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C2×C22⋊D11—24no—
99C2×C22⋊D11—24no—
100C2×C22⋊D11—48no—
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C414yes—
103#4339—416no—
104#4339—48no—
105#4339—48no—
106C2×D44—24no—
107C2×D44C22⋊C412yes—
108C2×D44C22⋊C411yescharacteristic
109C2×D44C22⋊C411yescharacteristic
110C2×C4×D11—24no—
111C2×C4×D11—24no—
112C2×C4×D11—24no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—48no—
116C2×C4×D11C2×D414yes—
117C2×C4×D11C2×D414yes—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—44no—
121C11×M16—22no—
122C11×M16—22no—
123C11×M16—22no—
124C11×M16#4114yescomplemented
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C11×C4⋊C4—22no—
128C11×C22⋊C4—24no—
129C42×C11C2×D412yes—
130C42×C11C2×D412yes—
131C22⋊Dic11—28no—
132(C2×D11)⋊C4C22⋊C414yes—
133(C2×D11)⋊C4C22⋊C414yes—
134C4⋊Dic11—24no—
135C4⋊Dic11—24no—
136C4⋊Dic11C22⋊C412yes—
137C4⋊Dic11C22⋊C412yes—
138Dic11⋊C4—28no—
139#4318—24no—
140#4318—24no—
141C2×C11⋊C8—24no—
142#4313—48no—
143C8×D11—48no—
144C2×#547—111no—
145D4×M16—112no—
146#1997—112no—
147#1900—114no—
148#1821—112no—
149#1800—111no—
150C4×#100D1111yescharacteristic, complemented
151C2×#343—112no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11C23×C411yescharacteristic
158C22×D11—22no—
159C22×D11—22no—
160C22×D11—24no—
161C22×D11—42no—
162C22×D11C2×C22⋊C412yes—
163C22×D11C2×C22⋊C412yes—
164D4×C11—42no—
165D4×C11—42no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—44no—
170C2×C4×C11—44no—
171C2×C4×C11—42no—
172C2×C4×C11C2×C22⋊C412yes—
173C2×C4×C11C2×C22⋊C411yescharacteristic
174C2×C4×C11C2×C22⋊C411yescharacteristic
175C2×C4×C11C22×D412yes—
176C2×C4×C11C2×#4112yes—
177C2×C4×C11H(5,𝔽2)11yescharacteristic
178C2×C4×C112−1+411yescharacteristic
179C22⋊D11—48no—
180C22⋊D11—48no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—24no—
184C2×Dic11—44no—
185C2×Dic11C2×C22⋊C414yes—
186D44—24no—
187D44—22no—
188D44#10014yescomplemented
189C4×D11—24no—
190C4×D11—24no—
191C4×D11—24no—
192C4×D11—24no—
193C4×D11—48no—
194C4×D11—48no—
195Dic22—44no—
196Dic22—44no—
197C8×C11—24no—
198C8×C11—42no—
199C11⋊C8—44no—
200C22×#41—112no—
201C22×M16—114no—
202#547—222no—
203#547—224no—
204#547—222no—
205C2×C4⋊Q8—111no—
206C2×#123—114no—
207C2×C22⋊Q8—112no—
208C2×#121—112no—
209C2×C4×D4—111no—
210C2×C4×D4C2×D1111yescharacteristic
211C22×C4⋊C4—112no—
212#436—222no—
213#435—224no—
214C8×D4—222no—
215#423—112no—
216C2×#100—112no—
217C2×#100C2×D1112yes—
218#407—114no—
219C4×M16C2×D1112yes—
220#343—114no—
221#343—114no—
222#343—112no—
223#343C2×D1111yescharacteristic
224#343C2×D1111yescharacteristic
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—82no—
231C22×C11—82no—
232C22×C11C22×C22⋊C411yescharacteristic
233C22×C11C4×#4111yescharacteristic
234C22×C11#52011yescharacteristic
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—22no—
239C2×D11—22no—
240C2×D11—44no—
241C2×D11—44no—
242C2×D11C2×#10014yes—
243C4×C11—21no—
244C4×C11—22no—
245C4×C11—42no—
246C4×C11C2×#10012yes—
247C4×C11#54612yes—
248C4×C11#54712yes—
249Dic11—24no—
250Dic11—44no—
251C2×#41—222no—
252C2×#41—224no—
253C2×#41—222no—
254C2×#41—448no—
255C22×Q8—112no—
256C22×D4—114no—
257C22×D4—111no—
258C22×D4C22×D1111yescharacteristic
259C23×C4—112no—
260C23×C4—114no—
261C23×C4C4×D1112yes—
262C2×M16—114no—
263C2×M16—224no—
264C2×M16—228no—
265C2×M16—444no—
266C2×M16C22×D1112yes—
267C2×M16C22×D1112yes—
268C22×C8—224no—
269C4⋊Q8—222no—
270C4⋊Q8—222no—
271#123—228no—
272#123—228no—
273C22⋊Q8—224no—
274C22⋊Q8—224no—
275#121—224no—
276#121—224no—
277C4×D4—22no—
278C4×D4—22no—
279C4×D4—112no—
280C4×D4—114no—
281C4×D4—112no—
282C2×C4⋊C4—111no—
283C2×C4⋊C4—114no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—224no—
287C2×C4⋊C4—224no—
288C2×C4⋊C4C22×D1111yescharacteristic
289C2×C22⋊C4—112no—
290C2×C22⋊C4—114no—
291C2×C22⋊C4C4×D1112yes—
292C2×C42C22×D1111yescharacteristic
293C4⋊C8—222no—
294C4⋊C8—222no—
295#100—24no—
296#100—442no—
297C22⋊C8—224no—
298C22⋊C8—224no—
299#97—22no—
300C4×C8—22no—
301C2×C11—21no—
302C2×C11—21no—
303C2×C11—82no—
304C2×C11#233911yescharacteristic
305C2×C11C22×#10011yescharacteristic
306C2×C11#288911yescharacteristic
307D11—24no—
308D11—42no—
309C24—112no—
310C24C2×C4×D1112yes—
311#41—448no—
312#41—4416no—
313#41—448no—
314C2×Q8—222no—
315C2×Q8—222no—
316C2×Q8—444no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—111no—
322C2×D4—112no—
323C2×D4—111no—
324C2×D4—224no—
325C2×D4—224no—
326C2×D4—224no—
327C2×D4—448no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—44no—
331C22×C4—112no—
332C22×C4—114no—
333C22×C4—114no—
334C22×C4—114no—
335C22×C4—224no—
336C22×C4—224no—
337C22×C4—224no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—448no—
341C22×C4C2×C4×D1111yescharacteristic
342C22×C4C2×C4×D1112yes—
343C22×C4C2×C4×D1111yescharacteristic
344C22×C4C23×D1111yescharacteristic
345M16—22no—
346M16—22no—
347M16—22no—
348M16—224no—
349M16—224no—
350M16—448no—
351M16#433914yescomplemented
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—224no—
355C2×C8—448no—
356C4⋊C4—22no—
357C4⋊C4—112no—
358C4⋊C4—112no—
359C4⋊C4—228no—
360C4⋊C4—224no—
361C4⋊C4—224no—
362C22⋊C4—24no—
363C22⋊C4—114no—
364C22⋊C4—114no—
365C22⋊C4—228no—
366C42D4×D1112yes—
367C42D4×D1112yes—
368C11#2247911yescharacteristic, complemented, Sylow
369C23—22no—
370C23—22no—
371C23—22no—
372C23—42no—
373C23—42no—
374C23—112no—
375C23—112no—
376C23—224no—
377C23—222no—
378C23—222no—
379C23—442no—
380C23C22×C4×D1111yescharacteristic
381Q8—444no—
382Q8—444no—
383D4—42no—
384D4—42no—
385D4—114no—
386D4—224no—
387D4—222no—
388D4—448no—
389D4—448no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—114no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—224no—
400C2×C4—224no—
401C2×C4—224no—
402C2×C4—224no—
403C2×C4—224no—
404C2×C4—448no—
405C2×C4—448no—
406C2×C4—444no—
407C2×C4C22⋊C4×D1112yes—
408C2×C4C22⋊C4×D1111yescharacteristic
409C2×C4C22⋊C4×D1111yescharacteristic
410C2×C4C2×#433912yes—
411C2×C4C2×D4×D1112yes—
412C2×C4#6704211yescharacteristic
413C2×C4#6704311yescharacteristic
414C8—24no—
415C8—42no—
416C8—444no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—82no—
423C22—82no—
424C22—114no—
425C22—222no—
426C22—222no—
427C22—222no—
428C22—222no—
429C22—222no—
430C22—444no—
431C22—444no—
432C22C4×#433911yescharacteristic
433C22C2×C22⋊C4×D1111yescharacteristic
434C22#1062305411yescharacteristic
435C4—21no—
436C4—22no—
437C4—42no—
438C4—224no—
439C4—444no—
440C4D11×#10012yes—
441C4#1062308112yes—
442C4#1062308212yes—
443C2—21no—
444C2—21no—
445C2—82no—
446C2—224no—
447C2—442no—
448C2#1307144711yescharacteristic
449C2C2×D11×#10011yescharacteristic
450C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#100C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623082C2
cosocleC22×C4×C11C24
hypercenterC4×#100D11
hypocenterC11#22479
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. M16×D44C2semidirect
3. #13069605C2semidirect
4. #13069076C2semidirect
5. #13068695C2semidirect
6. #13068608C2semidirect
7. D11×#343C2semidirect
8. C4×C11×#100C2semidirect
124. C11×M16#41semidirect
150. C4×#100D11semidirect
188. D44#100semidirect
351. M16#4339semidirect
368. C11#22479semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
M16×D442
#130696052
#130690762
#130686952
#130686082
D11×#3432
C4×C11×#1002
#2247911