Finite Group Databasebeta

← #14724362

Subgroups — #14724362

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079212C211yesmaximal, characteristic
2#13077592C211yesmaximal, characteristic, complemented
3#13077327C211yesmaximal, characteristic, complemented
4#13067527C212yesmaximal, complemented
5#13067521C212yesmaximal, complemented
6#13067413C212yesmaximal, complemented
7#13067408C212yesmaximal, complemented
8#13067381C211yesmaximal, characteristic, complemented
9#13067086C211yesmaximal, characteristic, complemented
10#13066897C211yesmaximal, characteristic, complemented
11C11×#1495C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13C2×#66960—21no—
14#10623008C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17#10622742—21no—
18#10622680C411yescharacteristic
19#10622678C411yescharacteristic
20#10622671C411yescharacteristic
21#10622668C411yescharacteristic
22#10622662C412yes—
23#10622652C412yes—
24C4×#4325C2212yes—
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4323C2212yes—
28#10622625C2211yescharacteristic
29#10622624—21no—
30D4×C11⋊C8—21no—
31D4×C11⋊C8C2211yescharacteristic
32#10622613—21no—
33#10622610—21no—
34#10622539C2211yescharacteristic
35C4×#4318C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622451—21no—
38#10622451C2212yes—
39#10622447—21no—
40#10622447C2212yes—
41C11×Q8⋊C8C2212yes—
42C11×D4⋊C8C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45#10622097C2212yes—
46#10622097C2212yes—
47#10622092C2212yes—
48C8×C11⋊C8C2212yes—
49C2×#4339—21no—
50C2×C11×M16—21no—
51C11×#126—21no—
52C11×#125C2×C411yescharacteristic
53C11×#124C2×C411yescharacteristic
54C11×#123—21no—
55C11×C22⋊Q8C2×C411yescharacteristic
56C11×#121C2×C411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4325C2×C412yes—
63C2×#4323C2×C412yes—
64#66983—21no—
65#66983C2×C412yes—
66C2×#4318—21no—
67C2×#4318C2×C412yes—
68C22×C11⋊C8—21no—
69C22×C11⋊C8D411yescharacteristic
70C22×C11⋊C8D411yescharacteristic
71#66960—44no—
72C2×#4313—22no—
73C2×C8×D11—22no—
74#66928—21no—
75#66927C2×C411yescharacteristic
76C4×D44—21no—
77C4×D44C2312yes—
78#66922C2×C411yescharacteristic
79C11×C4⋊C8—21no—
80C11×C4⋊C8—21no—
81C11×C4⋊C8C2312yes—
82C11×C22⋊C8—21no—
83C4×C8×C11C2312yes—
84#66899C2×C412yes—
85#66896C2×C412yes—
86C22⋊(C11⋊C8)—21no—
87C22⋊(C11⋊C8)—21no—
88C22⋊(C11⋊C8)—21no—
89(C2×D11)⋊C8—22no—
90(C2×D11)⋊C8—22no—
91#66873C2×C412yes—
92#66873C2×C412yes—
93#66872C2×C412yes—
94#66871C2×C412yes—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99#66867—21no—
100#66867—21no—
101#66867C2×C411yescharacteristic
102#66867C2×C411yescharacteristic
103C4×C11⋊C8—21no—
104C4×C11⋊C8D411yescharacteristic
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8C2312yes—
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#17964—111nomaximal, Sylow
110C2×Q8×C11C22×C411yescharacteristic
111C2×D4×C11—21no—
112C2×D4×C11C22×C411yescharacteristic
113C22×C4×C11—21no—
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×C22⋊D11—22no—
118#4339—42no—
119#4339—42no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44C22×C412yes—
123C2×C4×D11—22no—
124C2×Dic22—21no—
125C11×M16—42no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4C22×C411yescharacteristic
133C11×C4⋊C4C22×C411yescharacteristic
134C11×C22⋊C4—21no—
135C11×C22⋊C4—21no—
136C11×C22⋊C4—21no—
137C11×C22⋊C4—21no—
138C11×C22⋊C4—21no—
139C42×C11—21no—
140C42×C11C22×C411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144#4325—24no—
145#4323—24no—
146(C2×D11)⋊C4—22no—
147(C2×D11)⋊C4—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11C22×C412yes—
150#4318—24no—
151#4318—42no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—41no—
156C2×C11⋊C8—42no—
157C2×C11⋊C8C22×C412yes—
158C2×C11⋊C8C22×C412yes—
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163#4313—44no—
164C8×D11—44no—
165#3171—111no—
166#2966—111no—
167#2931—111no—
168#1594—112no—
169#1592—112no—
170C8×SD16—112no—
171C8×D8—112no—
172#1569—111no—
173#1496—111no—
174#1495D1111yescharacteristic, complemented
175C8×M16—111no—
176C23×C11—21no—
177C23×C11C4×D411yescharacteristic
178C22×D11—22no—
179Q8×C11—22no—
180D4×C11—22no—
181D4×C11—42no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11C4×D411yescharacteristic
192C2×C4×C11C4×D411yescharacteristic
193C2×C4×C11C4×D411yescharacteristic
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C22⋊D11—44no—
198C2×Dic11—22no—
199D44—22no—
200D44—22no—
201D44—42no—
202D44—42no—
203C4×D11—42no—
204C4×D11—42no—
205Dic22—42no—
206C8×C11—42no—
207C8×C11—42no—
208C11⋊C8—22no—
209C11⋊C8—21no—
210C11⋊C8—21no—
211C11⋊C8—21no—
212C11⋊C8—41no—
213C11⋊C8—41no—
214C11⋊C8#13114yescomplemented
215C11⋊C8AGL(1,ℤ/8)12yes—
216C2×#131—221no—
217#532—111no—
218#529C2×D1111yescharacteristic
219#501—111no—
220#496—111no—
221#490—111no—
222#489—111no—
223#469—112no—
224#468—112no—
225#446—111no—
226C8×Q8—111no—
227C4×SD16—112no—
228C4×D8—112no—
229#436—111no—
230#436—112no—
231#436—221no—
232#435—221no—
233C8×D4—111no—
234C8×D4—112no—
235C8×D4—221no—
236C8×D4—221no—
237#433—221no—
238#432—111no—
239#431C2×D1111yescharacteristic
240#423C2×D1111yescharacteristic
241#408—221no—
242#405—221no—
243C4×M16—111no—
244C2×C4×C8—111no—
245#335—112no—
246#334—112no—
247Q8⋊C8C2×D1112yes—
248D4⋊C8—112no—
249D4⋊C8—112no—
250D4⋊C8C2×D1112yes—
251#322—112no—
252C82—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11C2×C4×D411yescharacteristic
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—42no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—41no—
268C4×C11—41no—
269C4×C11—41no—
270C4×C11C2×#13112yes—
271C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C4×C11#57511yescharacteristic
273Dic11—42no—
274C2×#41—221no—
275C2×SD16—112no—
276C2×D8—112no—
277#131—444no—
278C2×M16—21no—
279C2×M16—112no—
280C2×M16—222no—
281C2×M16—221no—
282C22×C8—111no—
283C22×C8—111no—
284C22×C8—222no—
285C22×C8—221no—
286C4⋊Q8—111no—
287#127—111no—
288#126—21no—
289#125C4×D1111yescharacteristic
290#124—221no—
291#124C4×D1111yescharacteristic
292#123—21no—
293C22⋊Q8C4×D1111yescharacteristic
294#121—112no—
295#121—221no—
296#121C4×D1111yescharacteristic
297C4×Q8C22×D1111yescharacteristic
298C4×D4—21no—
299C4×D4—112no—
300C4×D4—221no—
301C4×D4C22×D1111yescharacteristic
302#117—21no—
303C2×C42C22×D1111yescharacteristic
304#107—112no—
305#106—112no—
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—111no—
309C4⋊C8—111no—
310C4⋊C8—221no—
311C4⋊C8—221no—
312C4⋊C8C22×D1112yes—
313#103—112no—
314#102—112no—
315#102—112no—
316#102—112no—
317C22⋊C8—21no—
318C22⋊C8—222no—
319C22⋊C8—222no—
320C22⋊C8—221no—
321C22⋊C8—221no—
322C22⋊C8—221no—
323#97—111no—
324#97—111no—
325#97—221no—
326#97—221no—
327C4×C8—111no—
328C4×C8—111no—
329C4×C8—111no—
330C4×C8—112no—
331C4×C8—111no—
332C4×C8—221no—
333C4×C8C22×D1112yes—
334C2×C11—41no—
335C2×C11—81no—
336C2×C11#293111yescharacteristic
337C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
338C2×C11#295511yescharacteristic
339D11—82no—
340#41—442no—
341#41—442no—
342C2×Q8—221no—
343C2×Q8C2×C4×D1111yescharacteristic
344C2×D4—21no—
345C2×D4—112no—
346C2×D4—222no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4C2×C4×D1111yescharacteristic
350C22×C4—21no—
351C22×C4—222no—
352C22×C4C2×C4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4#434111yescharacteristic
355SD16—224no—
356D8—224no—
357M16—42no—
358M16—224no—
359M16—444no—
360M16—442no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—112no—
364C2×C8—111no—
365C2×C8—112no—
366C2×C8—111no—
367C2×C8—111no—
368C2×C8—111no—
369C2×C8—222no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8—444no—
373C2×C8—442no—
374C2×C8—441no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—112no—
380C4⋊C4—221no—
381C4⋊C4C2×C4×D1111yescharacteristic
382C4⋊C4C2×C4×D1111yescharacteristic
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—222no—
389C22⋊C4—222no—
390C42—21no—
391C42C2×C4×D1111yescharacteristic
392C42D4×D1111yescharacteristic
393C42#434111yescharacteristic
394C42C23×D1111yescharacteristic
395C11#1796411yescharacteristic, complemented, Sylow
396C23—21no—
397C23—222no—
398C23(C22⋊D11)⋊C411yescharacteristic
399Q8—22no—
400Q8—442no—
401D4—22no—
402D4—42no—
403D4—222no—
404D4—222no—
405D4—442no—
406D4—442no—
407D4—444no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—222no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4(C22⋊D11)⋊C411yescharacteristic
421C2×C4(C22⋊D11)⋊C411yescharacteristic
422C2×C4(C22⋊D11)⋊C411yescharacteristic
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×D4×D1111yescharacteristic
425C2×C4C2×#434111yescharacteristic
426C8—42no—
427C8—42no—
428C8—114no—
429C8—112no—
430C8—222no—
431C8—221no—
432C8—221no—
433C8—221no—
434C8—441no—
435C8—441no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—442no—
443C22—442no—
444C22—442no—
445C22C2×(C22⋊D11)⋊C411yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—41no—
451C4—41no—
452C4—41no—
453C4—442no—
454C4D11×#13112yes—
455C4D11×AGL(1,ℤ/8)11yescharacteristic
456C4#1062330811yescharacteristic
457C2—41no—
458C2—81no—
459C2—882no—
460C2#1307732411yescharacteristic
461C2#1307742911yescharacteristic
462C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1495C2
socleC22×C11C2×C4×D4
prime radical#13079212C2
cosocleC42×C11C24
hypercenter#1495D11
hypocenterC11#17964
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #13077592C2semidirect
3. #13077327C2semidirect
4. #13067527C2semidirect
5. #13067521C2semidirect
6. #13067413C2semidirect
7. #13067408C2semidirect
8. #13067381C2semidirect
9. #13067086C2semidirect
10. #13066897C2semidirect
11. C11×#1495C2semidirect
174. #1495D11semidirect
214. C11⋊C8#131semidirect
395. C11#17964semidirect

Maximal subgroups

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

subgroupindex
#130792122
#130775922
#130773272
#130675272
#130675212
#130674132
#130674082
#130673812
#130670862
#130668972
C11×#14952
#1796411