Finite Group Databasebeta

← #14723573

Subgroups — #14723573

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077582C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3C4×#66962C211yesmaximal, characteristic
4#13067526C212yesmaximal, complemented
5#13067520C212yesmaximal, complemented
6#13067514C212yesmaximal, complemented
7#13067508C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067012C211yesmaximal, characteristic, complemented
10#13067004C211yesmaximal, characteristic
11C8×C11×M16C211yesmaximal, characteristic, complemented
12C2×#66962C411yescharacteristic
13C4×#4339C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622746C411yescharacteristic
19#10622734C411yescharacteristic
20#10622733C411yescharacteristic
21#10622724—21no—
22#10622724—21no—
23C2×#66879—21no—
24C2×Dic11⋊C8—21no—
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622329C412yes—
28#10622323C412yes—
29C4×Dic44C2212yes—
30C4×#4314C2212yes—
31#10622301C2211yescharacteristic
32#10622301C2211yescharacteristic
33C4×#4313—21no—
34#10622298—21no—
35#10622292—21no—
36#10622292—21no—
37#10622292C2212yes—
38#10622292C2211yescharacteristic
39#10622292C2212yes—
40#10622292C2211yescharacteristic
41C11×#322C2212yes—
42C82×C11C2212yes—
43#10622097C2212yes—
44#10622096C2212yes—
45#10622095C2212yes—
46#10622094C2212yes—
47#10622094C2212yes—
48#10622094C2212yes—
49C2×#4339C2×C411yescharacteristic
50C22×Dic22C2×C411yescharacteristic
51C2×C11×M16C2×C411yescharacteristic
52C2×C11×M16C2×C411yescharacteristic
53C22×C8×C11D411yescharacteristic
54C22×C8×C11D411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C4×C22⋊D11—21no—
57C4×C22⋊D11—21no—
58#66979C2×C411yescharacteristic
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×Dic11⋊C4—21no—
61C2×C4×Dic11—21no—
62C22×C11⋊C8—21no—
63#66962—24no—
64C2×Dic44C2×C412yes—
65C2×#4314C2×C412yes—
66C2×#4313—21no—
67C2×#4313—21no—
68C4×D44C2×C411yescharacteristic
69C4×D44C2311yescharacteristic
70#66925—21no—
71C42×D11—21no—
72C4×Dic22—21no—
73C4×Dic22—21no—
74C4×Dic22C2×C412yes—
75C4×Dic22C2×C411yescharacteristic
76C4×Dic22C2312yes—
77C4×Dic22C2311yescharacteristic
78C11×C4⋊C8—21no—
79C11×C22⋊C8—21no—
80C11×#97C2×C412yes—
81C4×C8×C11D411yescharacteristic
82C4×C8×C11D411yescharacteristic
83C4×C8×C11C2312yes—
84C4×C8×C11C2312yes—
85C4×C8×C11C2311yescharacteristic
86C4×C8×C11C2311yescharacteristic
87C22⋊(C11⋊C8)—21no—
88#66885C2×C412yes—
89(C2×D11)⋊C8—21no—
90(C2×D11)⋊C8—21no—
91#66882C2×C412yes—
92#66881C2×C412yes—
93#66880C2×C412yes—
94#66880C2×C412yes—
95#66880C2×C412yes—
96#66879—21no—
97#66879—21no—
98#66879—22no—
99#66879—22no—
100Dic11⋊C8—21no—
101Dic11⋊C8—21no—
102Dic11⋊C8—22no—
103Dic11⋊C8—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4×C11⋊C8—21no—
109#17892—111nomaximal, Sylow
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116#4339—22no—
117#4339—22no—
118C2×D44C22×C411yescharacteristic
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11—21no—
122C2×Dic22—21no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22C22×C412yes—
126C2×Dic22C22×C411yescharacteristic
127C11×M16—22no—
128C11×M16M1614yescomplemented
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—41no—
132C2×C8×C11C22×C412yes—
133C2×C8×C11C22×C412yes—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C42×C11C22×C411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11#4111yescharacteristic
141C42×C11C2411yescharacteristic
142C22⋊Dic11—21no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11C22×C411yescharacteristic
147C4⋊Dic11C22×C411yescharacteristic
148C4⋊Dic11C22×C412yes—
149Dic11⋊C4—22no—
150Dic11⋊C4—21no—
151Dic11⋊C4—22no—
152Dic11⋊C4—21no—
153C4×Dic11—22no—
154C4×Dic11—21no—
155C4×Dic11—21no—
156C4×Dic11—22no—
157C4×Dic11—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—42no—
162Dic44—24no—
163#4314—24no—
164#4313—42no—
165#4313—42no—
166#2965—111no—
167C2×#446—111no—
168C4×#137—111no—
169#1593—112no—
170#1592—112no—
171#1591—112no—
172#1590—112no—
173#1565—111no—
174#1479—111no—
175#1477—111no—
176C8×M16D1111yescharacteristic, complemented
177C23×C11C4×D411yescharacteristic
178C22×D11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—41no—
182C2×C4×C11C4×D411yescharacteristic
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11C4×D411yescharacteristic
185C2×C4×C11C2×M1612yes—
186C2×C4×C11#13112yes—
187C2×C4×C11C23×C411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C22⋊D11—42no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198D44—21no—
199D44—21no—
200C4×D11—42no—
201C4×D11—41no—
202C4×D11—41no—
203C4×D11—42no—
204Dic22—22no—
205Dic22—21no—
206Dic22—22no—
207Dic22—21no—
208Dic22—42no—
209C8×C11—22no—
210C8×C11—21no—
211C8×C11—21no—
212C8×C11—21no—
213C8×C11—42no—
214C8×C11C2×M1614yes—
215C8×C11#13712yescomplemented
216C11⋊C8—41no—
217C11⋊C8—41no—
218C11⋊C8—42no—
219C2×#137—111no—
220C4×#41—111no—
221C2×C4×Q8—111no—
222#446—112no—
223#446—111no—
224#446—112no—
225#446—111no—
226#446—221no—
227#446—221no—
228#441—112no—
229#440—112no—
230C4×Q16—112no—
231C4×SD16—112no—
232#436—111no—
233#436—111no—
234#435—221no—
235#435—221no—
236#431—111no—
237#431—221no—
238#431C2×D1111yescharacteristic
239#428—111no—
240C2×C4⋊C8—111no—
241C2×C4⋊C8—221no—
242#419—111no—
243#417—111no—
244C4×M16—221no—
245C4×M16C2×D1111yescharacteristic
246C2×#97—221no—
247C2×C4×C8C2×D1111yescharacteristic
248#335—112no—
249#334—112no—
250Q8⋊C8—112no—
251Q8⋊C8—112no—
252Q8⋊C8—112no—
253D4⋊C8—112no—
254#322C2×D1112yes—
255C82C2×D1112yes—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11#43612yes—
259C22×C11C2×C4×D411yescharacteristic
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11#43612yes—
267C4×C11C22×M1611yescharacteristic
268C4×C11C2×#13111yescharacteristic
269C4×C11C2×#13711yescharacteristic
270C4×C11#57511yescharacteristic
271Dic11—42no—
272Dic11—41no—
273Dic11—41no—
274Dic11—41no—
275Dic11—42no—
276C2×#41—111no—
277C22×Q8—111no—
278#137—224no—
279C2×Q16—112no—
280C2×SD16—112no—
281C2×M16—221no—
282C2×M16—221no—
283C2×M16C4×D1111yescharacteristic
284C2×M16C4×D1111yescharacteristic
285C22×C8—221no—
286C22×C8D4411yescharacteristic
287C22×C8D4411yescharacteristic
288C4×Q8—112no—
289C4×Q8—111no—
290C4×Q8—112no—
291C4×Q8—111no—
292C4×Q8—221no—
293C4×Q8—221no—
294C4×D4—111no—
295C4×D4—111no—
296C4×D4—221no—
297C4×D4—221no—
298#117—111no—
299#117—221no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—221no—
302C2×C42—221no—
303C2×C42—221no—
304C2×C42C22×D1111yescharacteristic
305#107—112no—
306#106—112no—
307C4⋊C8—21no—
308C4⋊C8—112no—
309C4⋊C8—111no—
310C4⋊C8—111no—
311C4⋊C8—222no—
312C4⋊C8—222no—
313C4⋊C8—221no—
314C4⋊C8—221no—
315C4⋊C8—221no—
316#103—112no—
317#103—112no—
318#103—112no—
319#102—112no—
320C22⋊C8—21no—
321C22⋊C8—221no—
322C22⋊C8—221no—
323C22⋊C8—221no—
324#97—222no—
325#97—222no—
326#97—221no—
327#97—221no—
328#97C4×D1112yes—
329C4×C8—221no—
330C4×C8D4411yescharacteristic
331C4×C8D4411yescharacteristic
332C4×C8C22×D1112yes—
333C4×C8C22×D1112yes—
334C4×C8C22×D1111yescharacteristic
335C4×C8C22×D1111yescharacteristic
336C2×C11—22no—
337C2×C11C2×#43611yescharacteristic
338C2×C11C4×#13711yescharacteristic
339C2×C11#295511yescharacteristic
340D11—81no—
341#41—222no—
342#41—222no—
343C2×Q8—112no—
344C2×Q8—111no—
345C2×Q8—221no—
346C2×Q8—222no—
347C2×Q8—222no—
348C2×D4—111no—
349C2×D4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4C2×C4×D1111yescharacteristic
356C22×C4C2×D4411yescharacteristic
357C22×C4#433911yescharacteristic
358Q16—224no—
359SD16—224no—
360M16—22no—
361M16—442no—
362M16—442no—
363M16#431314yescomplemented
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—41no—
367C2×C8—221no—
368C2×C8—221no—
369C2×C8—222no—
370C2×C8—442no—
371C2×C8C2×C4×D1112yes—
372C2×C8C2×C4×D1112yes—
373C2×C8C2×D4411yescharacteristic
374C2×C8C2×D4411yescharacteristic
375C2×C8C2×D4411yescharacteristic
376C2×C8C2×D4411yescharacteristic
377C4⋊C4—112no—
378C4⋊C4—111no—
379C4⋊C4—111no—
380C4⋊C4—221no—
381C4⋊C4—222no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C22⋊C4—221no—
386C22⋊C4—221no—
387C22⋊C4—221no—
388C42—221no—
389C42—221no—
390C42—222no—
391C42—221no—
392C42—222no—
393C42C2×C4×D1111yescharacteristic
394C42C2×D4411yescharacteristic
395C42#433911yescharacteristic
396C42C23×D1111yescharacteristic
397C11#1789211yescharacteristic, complemented, Sylow
398C23—221no—
399C23C4×D4411yescharacteristic
400Q8—222no—
401Q8—221no—
402Q8—222no—
403Q8—221no—
404Q8—442no—
405D4—221no—
406D4—221no—
407D4—442no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—222no—
414C2×C4—221no—
415C2×C4—222no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4C4×D4411yescharacteristic
423C2×C4C4×D4411yescharacteristic
424C2×C4C4×D4411yescharacteristic
425C2×C4C2×#431312yes—
426C2×C4#6695412yes—
427C2×C4C22×C4×D1111yescharacteristic
428C2×C4C22×D4411yescharacteristic
429C2×C4C2×#433911yescharacteristic
430C8—22no—
431C8—21no—
432C8—21no—
433C8—21no—
434C8—42no—
435C8—441no—
436C8—442no—
437C8—441no—
438C8C2×#431314yes—
439C8#6696212yescomplemented
440C22—21no—
441C22—21no—
442C22—441no—
443C22—441no—
444C22—441no—
445C22#1062230112yes—
446C22C2×C4×D4411yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—441no—
451C4—442no—
452C4—441no—
453C4—442no—
454C4—441no—
455C4#1062230112yes—
456C4C22×#431311yescharacteristic
457C4C2×#6695411yescharacteristic
458C4C2×#6696211yescharacteristic
459C4#1062327911yescharacteristic
460C2—22no—
461C2—881no—
462C2C2×#1062230111yescharacteristic
463C2C4×#6696211yescharacteristic
464C2#1307752011yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×M16C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenterC8×M16D11
hypocenterC11#17892
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
4. #13067526C2semidirect
5. #13067520C2semidirect
6. #13067514C2semidirect
7. #13067508C2semidirect
8. #13067368C2semidirect
9. #13067012C2semidirect
11. C8×C11×M16C2semidirect
128. C11×M16M16semidirect
176. C8×M16D11semidirect
215. C8×C11#137semidirect
363. M16#4313semidirect
397. C11#17892semidirect
439. C8#66962semidirect

Maximal subgroups

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

subgroupindex
#130775822
C2×#106222922
C4×#669622
#130675262
#130675202
#130675142
#130675082
#130673682
#130670122
#130670042
C8×C11×M162
#1789211