Finite Group Databasebeta

← #14724074

Subgroups — #14724074

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078696C211yesmaximal, characteristic
2#13077585C211yesmaximal, characteristic
3C2×#10622637C211yesmaximal, characteristic, complemented
4#13067522C212yesmaximal, complemented
5#13067521C212yesmaximal, complemented
6#13067469C212yesmaximal, complemented
7#13067455C212yesmaximal, complemented
8#13067402C211yesmaximal, characteristic, complemented
9#13067030C211yesmaximal, characteristic
10#13066903C211yesmaximal, characteristic, complemented
11C11×#1491C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13#10623010C2211yescharacteristic
14C11×#432C2211yescharacteristic
15C4×C11×M16C2211yescharacteristic
16#10622841C411yescharacteristic
17#10622840C411yescharacteristic
18C4×#4326C2212yes—
19#10622641C412yes—
20C4×#4325C2212yes—
21#10622637—21no—
22#10622637—21no—
23#10622637C2212yes—
24#10622637C2212yes—
25#10622635C412yes—
26#10622584C411yescharacteristic
27#10622580C411yescharacteristic
28#10622538C2211yescharacteristic
29C2×C4⋊(C11⋊C8)—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×#66867—21no—
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622451C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622343—21no—
38(C22⋊D11)⋊C8—21no—
39#10622322—21no—
40#10622321—21no—
41C11×Q8⋊C8C2212yes—
42C11×Q8⋊C8C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45#10622097C2212yes—
46#10622094C2212yes—
47#10622092C2212yes—
48#10622092C2212yes—
49C22×Q8×C11C2×C411yescharacteristic
50C2×C11×M16—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11C2×C412yes—
54C4×Q8×C11C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4326C2×C412yes—
60C2×#4325C2×C412yes—
61#66983C2×C411yescharacteristic
62#66982—21no—
63C4×C22⋊D11—21no—
64#66977C2×C411yescharacteristic
65C22×C11⋊C8—21no—
66C22×C11⋊C8D411yescharacteristic
67C22×C11⋊C8D411yescharacteristic
68C2×#4313—21no—
69C2×C8×D11—21no—
70#66929—21no—
71#66928C2×C411yescharacteristic
72C4×D44C2311yescharacteristic
73#66925—21no—
74#66923C2×C411yescharacteristic
75C4×Dic22C2311yescharacteristic
76C11×C4⋊C8C2311yescharacteristic
77C11×C4⋊C8C2311yescharacteristic
78C11×C22⋊C8—21no—
79C11×#97—21no—
80C11×#97—21no—
81C4×C8×C11C2312yes—
82#66899C2×C412yes—
83#66899C2×C412yes—
84C22⋊(C11⋊C8)C2×C411yescharacteristic
85C22⋊(C11⋊C8)C2×C411yescharacteristic
86(C2×D11)⋊C8—21no—
87(C2×D11)⋊C8—21no—
88#66879—21no—
89Dic11⋊C8—21no—
90Dic11⋊C8—21no—
91C8×Dic11—21no—
92#66874C2×C412yes—
93#66873C2×C412yes—
94#66872C2×C412yes—
95#66871C2×C412yes—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)—22no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)C2×C412yes—
100C4⋊(C11⋊C8)C2312yes—
101#66867—22no—
102#66867—22no—
103C4×C11⋊C8D411yescharacteristic
104C4×C11⋊C8D411yescharacteristic
105C4×C11⋊C8C2312yes—
106C4×C11⋊C8C2311yescharacteristic
107C4×C11⋊C8C2311yescharacteristic
108#17939—111nomaximal, Sylow
109C2×Q8×C11—21no—
110C2×Q8×C11—42no—
111C2×Q8×C11C22×C412yes—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×C22⋊D11—21no—
118C2×D44C22×C411yescharacteristic
119C2×C4×D11—21no—
120C2×Dic22C22×C411yescharacteristic
121C11×M16—42no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4C22×C412yes—
129C42×C11—22no—
130C42×C11—22no—
131C42×C11C22×C411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134C42×C11C2411yescharacteristic
135C22⋊Dic11—21no—
136#4326—42no—
137#4325—42no—
138(C2×D11)⋊C4—21no—
139(C2×D11)⋊C4—21no—
140(C2×D11)⋊C4—21no—
141(C2×D11)⋊C4—21no—
142C4⋊Dic11C22×C411yescharacteristic
143C4⋊Dic11C22×C411yescharacteristic
144Dic11⋊C4—21no—
145Dic11⋊C4—21no—
146Dic11⋊C4—21no—
147Dic11⋊C4—21no—
148C4×Dic11—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—42no—
153C2×C11⋊C8C22×C412yes—
154C2×C11⋊C8C22×C412yes—
155C2×C11⋊C8C2×D411yescharacteristic
156C2×C11⋊C8C2×D411yescharacteristic
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159#4313—42no—
160C8×D11—42no—
161#3108—111no—
162#2966—111no—
163C2×#446—111no—
164#1593—112no—
165#1592—112no—
166#1584—112no—
167#1582—112no—
168#1573—111no—
169#1491D1111yescharacteristic, complemented
170#1483—111no—
171#1451—111no—
172C23×C11C4×D411yescharacteristic
173C22×D11—21no—
174Q8×C11—22no—
175Q8×C11—22no—
176Q8×C11—42no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11C4×D411yescharacteristic
187C2×C4×C11C4×D411yescharacteristic
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C22⋊D11—42no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195D44—22no—
196C4×D11—41no—
197C4×D11—41no—
198Dic22—22no—
199C8×C11—42no—
200C8×C11—41no—
201C8×C11—41no—
202C11⋊C8—22no—
203C11⋊C8—22no—
204C11⋊C8—21no—
205C11⋊C8—21no—
206C11⋊C8—21no—
207C11⋊C8—42no—
208C11⋊C8#13712yes—
209#529—111no—
210C2×C4×Q8C2×D1111yescharacteristic
211#483—111no—
212#480—111no—
213#479—112no—
214#464—112no—
215#451—111no—
216#448—111no—
217#446—112no—
218#446—112no—
219#446—111no—
220#446—221no—
221#446—221no—
222C8×Q8—111no—
223C4×Q16—112no—
224C4×SD16—112no—
225#436—111no—
226#435—221no—
227C8×D4—111no—
228C8×D4—221no—
229#433—221no—
230#432C2×D1111yescharacteristic
231#431—111no—
232C2×C4⋊C8—111no—
233C2×C4⋊C8—221no—
234#405—221no—
235C4×M16C2×D1111yescharacteristic
236C2×#97—221no—
237C2×C4×C8—111no—
238#335—112no—
239#334—112no—
240Q8⋊C8—112no—
241Q8⋊C8C2×D1112yes—
242Q8⋊C8C2×D1112yes—
243D4⋊C8—112no—
244#322—112no—
245#322—112no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11#44412yes—
249C22×C11C2×C4×D411yescharacteristic
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11#56812yes—
260C4×C11C2×#13711yescharacteristic
261C4×C11#57511yescharacteristic
262Dic11—41no—
263Dic11—41no—
264Dic11—41no—
265C22×Q8C4×D1111yescharacteristic
266C2×Q16—112no—
267C2×SD16—112no—
268C2×M16—21no—
269C2×M16—221no—
270C22×C8—111no—
271C22×C8—111no—
272C22×C8—221no—
273C22×C8—221no—
274#126—221no—
275#125—111no—
276#124—111no—
277#123—221no—
278C22⋊Q8—111no—
279#121—111no—
280C4×Q8—21no—
281C4×Q8—21no—
282C4×Q8—111no—
283C4×Q8C4×D1112yes—
284C4×Q8C22×D1112yes—
285C4×D4—111no—
286C4×D4—221no—
287#117—221no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4C4×D1111yescharacteristic
290C2×C42—21no—
291C2×C42C22×D1111yescharacteristic
292#107—112no—
293#106—112no—
294C4⋊C8—112no—
295C4⋊C8—112no—
296C4⋊C8—222no—
297C4⋊C8—222no—
298C4⋊C8—221no—
299C4⋊C8—221no—
300C4⋊C8—221no—
301C4⋊C8C22×D1111yescharacteristic
302C4⋊C8C22×D1111yescharacteristic
303#103—112no—
304#103—112no—
305#103—112no—
306#102—112no—
307C22⋊C8—21no—
308C22⋊C8—111no—
309C22⋊C8—111no—
310C22⋊C8—221no—
311C22⋊C8—221no—
312#97—21no—
313#97—21no—
314#97—222no—
315#97—222no—
316#97—221no—
317C4×C8—111no—
318C4×C8—111no—
319C4×C8—112no—
320C4×C8—111no—
321C4×C8—111no—
322C4×C8—221no—
323C4×C8C22×D1112yes—
324C2×C11—22no—
325C2×C11#293011yescharacteristic
326C2×C11C4×#13711yescharacteristic
327C2×C11C2×#44411yescharacteristic
328D11—81no—
329C2×Q8—21no—
330C2×Q8—42no—
331C2×Q8—111no—
332C2×Q8C2×C4×D1112yes—
333C2×D4—111no—
334C2×D4—221no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—221no—
338C22×C4C2×C4×D1111yescharacteristic
339C22×C4D4×D1111yescharacteristic
340C22×C4#434111yescharacteristic
341Q16—442no—
342SD16—442no—
343M16—42no—
344M16—442no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—111no—
349C2×C8—112no—
350C2×C8—112no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—111no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—442no—
357C2×C8—441no—
358C2×C8—442no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—111no—
363C4⋊C4—111no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4C2×C4×D1112yes—
369C22⋊C4—221no—
370C22⋊C4—221no—
371C22⋊C4—221no—
372C22⋊C4—221no—
373C22⋊C4—221no—
374C42—22no—
375C42—22no—
376C42—221no—
377C42C2×C4×D1111yescharacteristic
378C42D4×D1111yescharacteristic
379C42#434111yescharacteristic
380C42C23×D1111yescharacteristic
381C11#1793911yescharacteristic, complemented, Sylow
382C23—221no—
383C23(C22⋊D11)⋊C411yescharacteristic
384Q8—22no—
385Q8—22no—
386Q8—42no—
387Q8—222no—
388D4—222no—
389D4—442no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4(C22⋊D11)⋊C411yescharacteristic
404C2×C4(C22⋊D11)⋊C411yescharacteristic
405C2×C4(C22⋊D11)⋊C411yescharacteristic
406C2×C4C22×C4×D1111yescharacteristic
407C2×C4C2×D4×D1111yescharacteristic
408C2×C4C2×#434111yescharacteristic
409C8—42no—
410C8—41no—
411C8—41no—
412C8—112no—
413C8—222no—
414C8—222no—
415C8—221no—
416C8—221no—
417C8—221no—
418C8—442no—
419C22—21no—
420C22—21no—
421C22—441no—
422C22—441no—
423C22—441no—
424C22#1062243612yes—
425C22C2×(C22⋊D11)⋊C411yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—42no—
431C4—42no—
432C4—441no—
433C4—441no—
434C4—441no—
435C4#1062327612yes—
436C4D11×#13711yescharacteristic
437C4#1062330811yescharacteristic
438C2—22no—
439C2—881no—
440C2#1307731511yescharacteristic
441C2#1307743111yescharacteristic
442C2C2×#1062243611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1491C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#1491D11
hypocenterC11#17939
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
3. C2×#10622637C2semidirect
4. #13067522C2semidirect
5. #13067521C2semidirect
6. #13067469C2semidirect
7. #13067455C2semidirect
8. #13067402C2semidirect
10. #13066903C2semidirect
11. C11×#1491C2semidirect
169. #1491D11semidirect
381. C11#17939semidirect

Maximal subgroups

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

subgroupindex
#130786962
#130775852
C2×#106226372
#130675222
#130675212
#130674692
#130674552
#130674022
#130670302
#130669032
C11×#14912
#1793911