Finite Group Databasebeta

← #14724356

Subgroups — #14724356

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#13079211C211yesmaximal, characteristic
2#13077585C211yesmaximal, characteristic, complemented
3#13077327C211yesmaximal, characteristic, complemented
4#13067529C212yesmaximal, complemented
5#13067517C212yesmaximal, complemented
6#13067415C212yesmaximal, complemented
7#13067410C212yesmaximal, complemented
8#13067084C211yesmaximal, characteristic, complemented
9#13067079C211yesmaximal, characteristic, complemented
10M16×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#1569C211yesmaximal, characteristic, complemented
12C2×#66960—21no—
13#10623010C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C4×C11×M16C2211yescharacteristic
18#10622748C412yes—
19#10622747C412yes—
20#10622742—21no—
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622451—21no—
24#10622451C2211yescharacteristic
25#10622451C2212yes—
26#10622447—21no—
27#10622447C2212yes—
28#10622447C2211yescharacteristic
29#10622444C2211yescharacteristic
30#10622443C2211yescharacteristic
31#10622343—21no—
32(C22⋊D11)⋊C8—21no—
33#10622327C411yescharacteristic
34#10622326C411yescharacteristic
35#10622325C411yescharacteristic
36#10622322—21no—
37#10622321—21no—
38#10622315C411yescharacteristic
39C4×D88C2212yes—
40C4×#4314C2212yes—
41C11×#335C2212yes—
42C11×#334C2212yes—
43#10622122C2212yes—
44#10622121C2212yes—
45#10622121C2212yes—
46#10622121C2212yes—
47#10622093C2212yes—
48C8×C11⋊C8C2212yes—
49C2×#4339—21no—
50C2×C11×M16—21no—
51C2×C11×M16C2×C412yes—
52C2×C42×C11C2311yescharacteristic
53#66983—21no—
54#66983C2×C412yes—
55#66983C2×C411yescharacteristic
56#66982—21no—
57C4×C22⋊D11—21no—
58#66977C2×C411yescharacteristic
59C22×C11⋊C8D411yescharacteristic
60C22×C11⋊C8D411yescharacteristic
61#66960—44no—
62C2×D88C2×C412yes—
63C2×#4314C2×C412yes—
64C2×#4313—22no—
65C2×#4313—21no—
66C2×C8×D11—22no—
67C2×C8×D11—21no—
68#66929—21no—
69#66928—21no—
70#66928C2×C411yescharacteristic
71#66927C2×C411yescharacteristic
72C4×D44—21no—
73C4×D44C2312yes—
74C4×D44C2311yescharacteristic
75#66925—21no—
76#66923C2×C411yescharacteristic
77#66922C2×C411yescharacteristic
78C4×Dic22C2311yescharacteristic
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2311yescharacteristic
81C11×C4⋊C8C2312yes—
82C11×C4⋊C8C2311yescharacteristic
83C11×C22⋊C8—21no—
84C11×#97—21no—
85C11×#97C2×C411yescharacteristic
86C11×#97C2×C411yescharacteristic
87C4×C8×C11C2312yes—
88C22⋊(C11⋊C8)—21no—
89#66885C2×C412yes—
90#66885C2×C412yes—
91#66885C2×C412yes—
92(C2×D11)⋊C8—22no—
93(C2×D11)⋊C8—22no—
94(C2×D11)⋊C8—21no—
95(C2×D11)⋊C8—21no—
96#66882C2×C412yes—
97#66881C2×C412yes—
98#66880C2×C412yes—
99#66879—21no—
100Dic11⋊C8—21no—
101Dic11⋊C8—21no—
102C8×Dic11—21no—
103C4⋊(C11⋊C8)—21no—
104C4×C11⋊C8D411yescharacteristic
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8C2312yes—
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#17964—111nomaximal, Sylow
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—21no—
114C2×C22⋊D11—22no—
115#4339—42no—
116#4339—42no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44C22×C412yes—
120C2×D44C22×C411yescharacteristic
121C2×C4×D11—21no—
122C2×C4×D11—22no—
123C2×Dic22—21no—
124C2×Dic22C22×C411yescharacteristic
125C11×M16—24no—
126C11×M16—42no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C22×C412yes—
132C42×C11C22×C411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11#4111yescharacteristic
135C42×C11C2411yescharacteristic
136C22⋊Dic11—21no—
137(C2×D11)⋊C4—21no—
138(C2×D11)⋊C4—21no—
139(C2×D11)⋊C4—22no—
140(C2×D11)⋊C4—21no—
141(C2×D11)⋊C4—22no—
142(C2×D11)⋊C4—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11C22×C412yes—
145C4⋊Dic11C22×C411yescharacteristic
146C4⋊Dic11C22×C411yescharacteristic
147Dic11⋊C4—21no—
148Dic11⋊C4—21no—
149Dic11⋊C4—21no—
150Dic11⋊C4—21no—
151C4×Dic11—21no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8C2×D411yescharacteristic
156C2×C11⋊C8C2×D411yescharacteristic
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159D88—24no—
160#4314—24no—
161#4313—42no—
162#4313—44no—
163C8×D11—42no—
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#1569D1111yescharacteristic, complemented
173#1496—111no—
174#1495—111no—
175C8×M16—111no—
176C23×C11C4×D411yescharacteristic
177C22×D11—21no—
178C22×D11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—41no—
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11C4×D411yescharacteristic
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11C23×C411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C22⋊D11—44no—
190C22⋊D11—42no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—22no—
195D44—22no—
196D44—22no—
197D44—22no—
198D44—42no—
199D44—42no—
200C4×D11—42no—
201C4×D11—41no—
202C4×D11—41no—
203C4×D11—42no—
204Dic22—22no—
205Dic22—42no—
206C8×C11—22no—
207C8×C11—42no—
208C8×C11—41no—
209C8×C11—41no—
210C8×C11#13114yescomplemented
211C11⋊C8—21no—
212C11⋊C8—21no—
213C11⋊C8—21no—
214C11⋊C8—42no—
215C11⋊C8AGL(1,ℤ/8)12yes—
216C2×#131—221no—
217#532—111no—
218#529—111no—
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—112no—
230#436—111no—
231#436—221no—
232#435—221no—
233C8×D4—111no—
234C8×D4—112no—
235C8×D4—221no—
236C8×D4—221no—
237#433—221no—
238#432C2×D1111yescharacteristic
239#431—111no—
240#423C2×D1111yescharacteristic
241#408—221no—
242#405—221no—
243C4×M16C2×D1111yescharacteristic
244C2×C4×C8—111no—
245#335C2×D1112yes—
246#334C2×D1112yes—
247Q8⋊C8—112no—
248D4⋊C8—112no—
249D4⋊C8—112no—
250D4⋊C8—112no—
251#322—112no—
252C82—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11C2×C4×D411yescharacteristic
257C2×D11—41no—
258C2×D11—42no—
259C2×D11—41no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—41no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11C2×#13112yes—
268C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C11#57511yescharacteristic
270Dic11—41no—
271Dic11—42no—
272Dic11—41no—
273Dic11—41no—
274C2×#41—221no—
275C2×SD16—112no—
276C2×D8—112no—
277#131—444no—
278C2×M16—21no—
279C2×M16—222no—
280C2×M16—221no—
281C2×M16C4×D1112yes—
282C22×C8—111no—
283C22×C8—111no—
284C22×C8—222no—
285C22×C8—221no—
286C4⋊Q8—111no—
287#127—111no—
288#126—221no—
289#125—111no—
290#124—111no—
291#124—221no—
292#123—221no—
293C22⋊Q8—111no—
294#121—111no—
295#121—112no—
296#121—221no—
297C4×Q8—111no—
298C4×D4—111no—
299C4×D4—112no—
300C4×D4—221no—
301C4×D4—221no—
302#117—221no—
303C2×C42C22×D1111yescharacteristic
304#107—112no—
305#106—112no—
306C4⋊C8—21no—
307C4⋊C8—221no—
308C4⋊C8—221no—
309C4⋊C8—221no—
310C4⋊C8C22×D1111yescharacteristic
311C4⋊C8C22×D1111yescharacteristic
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—21no—
324#97—221no—
325#97C4×D1111yescharacteristic
326#97C4×D1111yescharacteristic
327C4×C8—111no—
328C4×C8—111no—
329C4×C8—111no—
330C4×C8—111no—
331C4×C8—112no—
332C4×C8—221no—
333C4×C8C22×D1112yes—
334C2×C11—41no—
335C2×C11#293111yescharacteristic
336C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
337C2×C11#295511yescharacteristic
338D11—81no—
339D11—82no—
340#41—442no—
341#41—442no—
342C2×Q8—111no—
343C2×Q8—221no—
344C2×D4—111no—
345C2×D4—112no—
346C2×D4—221no—
347C2×D4—222no—
348C2×D4—221no—
349C2×D4—221no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4C2×C4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4#434311yescharacteristic
355SD16—224no—
356D8—224no—
357M16—24no—
358M16—42no—
359M16—444no—
360M16—442no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—22no—
364C2×C8—111no—
365C2×C8—111no—
366C2×C8—111no—
367C2×C8—111no—
368C2×C8—222no—
369C2×C8—222no—
370C2×C8—444no—
371C2×C8—442no—
372C2×C8—441no—
373C2×C8C2×C4×D1112yes—
374C2×C8C2×C4×D1112yes—
375C4⋊C4—111no—
376C4⋊C4—111no—
377C4⋊C4—112no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C22⋊C4—221no—
384C22⋊C4—221no—
385C22⋊C4—221no—
386C22⋊C4—222no—
387C22⋊C4—221no—
388C22⋊C4—222no—
389C22⋊C4—221no—
390C42—221no—
391C42C2×C4×D1111yescharacteristic
392C42D4×D1111yescharacteristic
393C42#434311yescharacteristic
394C42C23×D1111yescharacteristic
395C11#1796411yescharacteristic, complemented, Sylow
396C23—221no—
397C23—222no—
398C23#6694611yescharacteristic
399Q8—222no—
400Q8—442no—
401D4—222no—
402D4—222no—
403D4—222no—
404D4—442no—
405D4—442no—
406D4—444no—
407D4—442no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—222no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—442no—
420C2×C4#6694611yescharacteristic
421C2×C4#6694611yescharacteristic
422C2×C4#6694611yescharacteristic
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×D4×D1111yescharacteristic
425C2×C4C2×#434311yescharacteristic
426C8—22no—
427C8—42no—
428C8—41no—
429C8—41no—
430C8—112no—
431C8—221no—
432C8—221no—
433C8—221no—
434C8—442no—
435C8#6696014yescomplemented
436C22—21no—
437C22—21no—
438C22—21no—
439C22—442no—
440C22—441no—
441C22—441no—
442C22—442no—
443C22—442no—
444C22—441no—
445C22C2×#6694611yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—441no—
451C4—441no—
452C4—442no—
453C4—441no—
454C4C2×#6696012yes—
455C4D11×AGL(1,ℤ/8)11yescharacteristic
456C4#1062330811yescharacteristic
457C2—41no—
458C2—882no—
459C2—881no—
460C2#1307732711yescharacteristic
461C2#1307742311yescharacteristic
462C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1569C2
socleC22×C11C2×C4×D4
prime radical#13079211C2
cosocleC42×C11C24
hypercenter#1569D11
hypocenterC11#17964
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
2. #13077585C2semidirect
3. #13077327C2semidirect
4. #13067529C2semidirect
5. #13067517C2semidirect
6. #13067415C2semidirect
7. #13067410C2semidirect
8. #13067084C2semidirect
9. #13067079C2semidirect
10. M16×C11⋊C8C2semidirect
11. C11×#1569C2semidirect
172. #1569D11semidirect
210. C8×C11#131semidirect
395. C11#17964semidirect
435. C8#66960semidirect

Maximal subgroups

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

subgroupindex
#130792112
#130775852
#130773272
#130675292
#130675172
#130674152
#130674102
#130670842
#130670792
M16×C11⋊C82
C11×#15692
#1796411