Finite Group Databasebeta

← #14723367

Subgroups — #14723367

Order 2816.

660 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
2C4×#66995C211yesmaximal, characteristic
3#13067494C212yesmaximal, complemented
4#13067487C212yesmaximal, complemented
5#13067466C212yesmaximal, complemented
6#13067459C212yesmaximal, complemented
7#13067366C211yesmaximal, characteristic, complemented
8#13067011C211yesmaximal, characteristic, complemented
9#13067001C211yesmaximal, characteristic
10#13066905C211yesmaximal, characteristic, complemented
11C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66995C411yescharacteristic
14C4×#4339C2211yescharacteristic
15C8×Q8×C11—21no—
16C8×Q8×C11—21no—
17C8×Q8×C11C2212yes—
18C8×Q8×C11C2212yes—
19C2×C11×C4⋊C8—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C4×C8×C11—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622838C411yescharacteristic
24#10622724—21no—
25#10622724—21no—
26#10622643C412yes—
27C4×#4326C2212yes—
28#10622639C412yes—
29C4×#4325C2212yes—
30#10622579C411yescharacteristic
31#10622577C411yescharacteristic
32#10622538C2211yescharacteristic
33#10622538C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622301C2211yescharacteristic
36#10622301C2211yescharacteristic
37C4×#4313—21no—
38#10622298—21no—
39#10622292C2211yescharacteristic
40#10622292C2211yescharacteristic
41Q8⋊(C11⋊C8)C2212yes—
42Q8⋊(C11⋊C8)C2212yes—
43#10622122C2212yes—
44#10622121C2212yes—
45#10622118C2212yes—
46#10622117C2212yes—
47#10622093C2212yes—
48#10622092C2212yes—
49C22×Q8×C11C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C22×C8×C11—21no—
52C22×C8×C11D411yescharacteristic
53C22×C8×C11D411yescharacteristic
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11C2×C412yes—
57C4×Q8×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326C2×C412yes—
63#66995—24no—
64C2×#4325C2×C412yes—
65C4×C22⋊D11—21no—
66C4×C22⋊D11—21no—
67#66979C2×C411yescharacteristic
68C2×#4318C2×C411yescharacteristic
69C2×#4318C2×C411yescharacteristic
70C2×#4313—21no—
71C2×#4313—21no—
72C4×D44C2×C411yescharacteristic
73C4×D44C2311yescharacteristic
74#66925—21no—
75C42×D11—21no—
76C4×Dic22C2×C411yescharacteristic
77C4×Dic22C2311yescharacteristic
78C11×C4⋊C8—22no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—21no—
81C11×C4⋊C8C2312yes—
82C4×C8×C11—22no—
83C4×C8×C11—22no—
84C4×C8×C11D411yescharacteristic
85C4×C8×C11D411yescharacteristic
86C4×C8×C11C2311yescharacteristic
87C4×C8×C11C2311yescharacteristic
88#66899C2×C412yes—
89#66899C2×C412yes—
90C22⋊(C11⋊C8)—21no—
91C22⋊(C11⋊C8)—21no—
92(C2×D11)⋊C8—21no—
93(C2×D11)⋊C8—21no—
94#66879—21no—
95#66879—21no—
96Dic11⋊C8—21no—
97Dic11⋊C8—21no—
98#66874C2×C412yes—
99#66873C2×C412yes—
100#66872C2×C412yes—
101#66871C2×C412yes—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4⋊(C11⋊C8)C2311yescharacteristic
105#66867C2×C412yes—
106C4×C11⋊C8—21no—
107C4×C11⋊C8C2312yes—
108C4×C11⋊C8C2312yes—
109#17870—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11M1614yescomplemented
113C2×Q8×C11C22×C412yes—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C2×C22⋊D11—21no—
120#4339—22no—
121#4339—22no—
122C2×D44C22×C411yescharacteristic
123C2×C4×D11—21no—
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×Dic22C22×C411yescharacteristic
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—41no—
130C2×C8×C11—42no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C22×C412yes—
139C42×C11—22no—
140C42×C11—22no—
141C42×C11C22×C411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144C42×C11C2411yescharacteristic
145C22⋊Dic11—21no—
146#4326—24no—
147#4325—24no—
148(C2×D11)⋊C4—21no—
149(C2×D11)⋊C4—21no—
150C4⋊Dic11C22×C411yescharacteristic
151C4⋊Dic11C22×C411yescharacteristic
152Dic11⋊C4—21no—
153Dic11⋊C4—21no—
154C4×Dic11—21no—
155C4×Dic11—21no—
156C4×Dic11—21no—
157#4318—22no—
158#4318—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8C22×C412yes—
163C2×C11⋊C8C22×C412yes—
164#4313—42no—
165#4313—42no—
166#2965—111no—
167C2×C8×Q8D1111yescharacteristic, complemented
168C4×#137—111no—
169#1588—112no—
170#1587—112no—
171#1584—112no—
172#1583—112no—
173#1565—111no—
174#1479—111no—
175#1477—111no—
176#1451—111no—
177C23×C11C4×D411yescharacteristic
178C22×D11—21no—
179Q8×C11—22no—
180Q8×C11—24no—
181Q8×C11C2×M1614yes—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11C4×D411yescharacteristic
190C2×C4×C11C4×D411yescharacteristic
191C2×C4×C11C4×D411yescharacteristic
192C2×C4×C11C2×M1612yes—
193C2×C4×C11#13112yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C22⋊D11—42no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201D44—21no—
202D44—21no—
203C4×D11—42no—
204C4×D11—41no—
205C4×D11—41no—
206C4×D11—42no—
207Dic22—21no—
208Dic22—21no—
209C8×C11—21no—
210C8×C11—21no—
211C8×C11—21no—
212C8×C11—42no—
213C8×C11#13712yescomplemented
214C11⋊C8—22no—
215C11⋊C8—22no—
216C11⋊C8—42no—
217C11⋊C8—41no—
218C11⋊C8—41no—
219C2×#137—111no—
220C4×#41—111no—
221C2×C4×Q8C2×D1111yescharacteristic
222#446—111no—
223#446—111no—
224C8×Q8—21no—
225C8×Q8—21no—
226C8×Q8C2×D1112yes—
227C8×Q8C2×D1112yes—
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—111no—
238#431—221no—
239#428—111no—
240C2×C4⋊C8—21no—
241C2×C4⋊C8C2×D1111yescharacteristic
242#419—111no—
243#417—111no—
244C4×M16—111no—
245C4×M16—221no—
246C2×C4×C8—21no—
247C2×C4×C8C2×D1111yescharacteristic
248#335—112no—
249#334—112no—
250Q8⋊C8—112no—
251Q8⋊C8—112no—
252Q8⋊C8—112no—
253D4⋊C8—112no—
254#322—112no—
255#322—112no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11#43512yes—
259C22×C11C2×C4×D411yescharacteristic
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C4×C11—24no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11#43512yes—
269C4×C11C22×M1611yescharacteristic
270C4×C11C2×#13111yescharacteristic
271C4×C11C2×#13711yescharacteristic
272C4×C11#57511yescharacteristic
273Dic11—41no—
274Dic11—41no—
275Dic11—41no—
276C2×#41—111no—
277C22×Q8C4×D1111yescharacteristic
278#137—224no—
279C2×Q16—112no—
280C2×SD16—112no—
281C2×M16—111no—
282C2×M16—111no—
283C2×M16—221no—
284C2×M16—221no—
285C22×C8—21no—
286C22×C8C22⋊D1111yescharacteristic
287C22×C8C22⋊D1111yescharacteristic
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—111no—
291C4×Q8—111no—
292C4×Q8C4×D1112yes—
293C4×Q8C22×D1112yes—
294C4×D4—111no—
295C4×D4—111no—
296C4×D4—221no—
297C4×D4—221no—
298#117—111no—
299#117—221no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4C4×D1111yescharacteristic
302C2×C42—21no—
303C2×C42—221no—
304C2×C42C22×D1111yescharacteristic
305#107—112no—
306#106—112no—
307C4⋊C8—22no—
308C4⋊C8—22no—
309C4⋊C8—21no—
310C4⋊C8—111no—
311C4⋊C8—111no—
312C4⋊C8—221no—
313C4⋊C8—221no—
314C4⋊C8—221no—
315C4⋊C8C22×D1112yes—
316#103—112no—
317#103—112no—
318#103—112no—
319#102—112no—
320C22⋊C8—221no—
321C22⋊C8—221no—
322C22⋊C8—221no—
323C22⋊C8—221no—
324#97—112no—
325#97—221no—
326#97—221no—
327C4×C8—22no—
328C4×C8—22no—
329C4×C8—112no—
330C4×C8—112no—
331C4×C8—221no—
332C4×C8C22⋊D1111yescharacteristic
333C4×C8C22⋊D1111yescharacteristic
334C4×C8C22×D1111yescharacteristic
335C4×C8C22×D1111yescharacteristic
336C2×C11—22no—
337C2×C11C2×#43511yescharacteristic
338C2×C11C4×#13711yescharacteristic
339C2×C11#295511yescharacteristic
340D11—81no—
341#41—222no—
342#41—222no—
343C2×Q8—22no—
344C2×Q8—21no—
345C2×Q8—111no—
346C2×Q8#431314yescomplemented
347C2×Q8C2×C4×D1112yes—
348C2×D4—111no—
349C2×D4—221no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4C2×C4×D1111yescharacteristic
356C22×C4#433911yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358Q16—224no—
359SD16—224no—
360M16—222no—
361M16—222no—
362M16—442no—
363M16—442no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—41no—
367C2×C8—42no—
368C2×C8—112no—
369C2×C8—112no—
370C2×C8—222no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8C2×C22⋊D1111yescharacteristic
374C2×C8C2×C22⋊D1111yescharacteristic
375C2×C8C2×C22⋊D1111yescharacteristic
376C2×C8C2×C22⋊D1111yescharacteristic
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—111no—
381C4⋊C4—111no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4C2×C4×D1112yes—
385C22⋊C4—221no—
386C22⋊C4—221no—
387C22⋊C4—221no—
388C42—22no—
389C42—22no—
390C42—221no—
391C42—221no—
392C42—221no—
393C42C2×C4×D1111yescharacteristic
394C42#433911yescharacteristic
395C42C2×C22⋊D1111yescharacteristic
396C42C23×D1111yescharacteristic
397C11#1787011yescharacteristic, complemented, Sylow
398C23—221no—
399C23C4×C22⋊D1111yescharacteristic
400Q8—24no—
401Q8—22no—
402Q8—221no—
403Q8—221no—
404Q8C2×#431314yes—
405D4—221no—
406D4—221no—
407D4—442no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4C2×#431312yes—
423C2×C4#6695412yes—
424C2×C4C4×C22⋊D1111yescharacteristic
425C2×C4C4×C22⋊D1111yescharacteristic
426C2×C4C4×C22⋊D1111yescharacteristic
427C2×C4C22×C4×D1111yescharacteristic
428C2×C4C2×#433911yescharacteristic
429C2×C4C22×C22⋊D1111yescharacteristic
430C8—21no—
431C8—21no—
432C8—21no—
433C8—42no—
434C8—222no—
435C8—222no—
436C8—442no—
437C8—441no—
438C8—441no—
439C8#6699512yescomplemented
440C22—21no—
441C22—21no—
442C22—441no—
443C22—441no—
444C22—441no—
445C22#1062272412yes—
446C22C2×C4×C22⋊D1111yescharacteristic
447C4—21no—
448C4—21no—
449C4—24no—
450C4—21no—
451C4—42no—
452C4—441no—
453C4—441no—
454C4—441no—
455C4#1062272412yes—
456C4C22×#431311yescharacteristic
457C4C2×#6695411yescharacteristic
458C4C2×#6699511yescharacteristic
459C4#1062335311yescharacteristic
460C2—22no—
461C2—881no—
462C2C2×#1062272411yescharacteristic
463C2C4×#6699511yescharacteristic
464C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C8×Q8×C11C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenterC2×C8×Q8D11
hypocenterC11#17870
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
3. #13067494C2semidirect
4. #13067487C2semidirect
5. #13067466C2semidirect
6. #13067459C2semidirect
7. #13067366C2semidirect
8. #13067011C2semidirect
10. #13066905C2semidirect
11. C2×C8×Q8×C11C2semidirect
112. C2×Q8×C11M16semidirect
167. C2×C8×Q8D11semidirect
213. C8×C11#137semidirect
346. C2×Q8#4313semidirect
397. C11#17870semidirect
439. C8#66995semidirect

Maximal subgroups

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

subgroupindex
#130775822
C4×#669952
#130674942
#130674872
#130674662
#130674592
#130673662
#130670112
#130670012
#130669052
C2×C8×Q8×C112
#1787011