Finite Group Databasebeta

← #14724093

Subgroups — #14724093

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078677C211yesmaximal, characteristic
2#13077582C211yesmaximal, characteristic, complemented
3#13077329C211yesmaximal, characteristic, complemented
4#13067531C212yesmaximal, complemented
5#13067520C212yesmaximal, complemented
6#13067454C212yesmaximal, complemented
7#13067447C212yesmaximal, complemented
8#13067405C211yesmaximal, characteristic, complemented
9#13067056C211yesmaximal, characteristic, complemented
10#13067034C211yesmaximal, characteristic, complemented
11C11×#1451C211yesmaximal, characteristic, complemented
12C2×#66954—21no—
13#10623008C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622724—21no—
19#10622724—21no—
20#10622723—21no—
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622463C411yescharacteristic
24#10622461C411yescharacteristic
25#10622456C411yescharacteristic
26#10622455C411yescharacteristic
27#10622350C412yes—
28#10622347C412yes—
29C4×D88C2212yes—
30C4×#4314C2212yes—
31#10622301—21no—
32#10622301C2212yes—
33#10622301C2211yescharacteristic
34#10622301C2211yescharacteristic
35C4×#4313—21no—
36C8×D44—21no—
37C8×D44C2212yes—
38#10622298—21no—
39#10622292C2211yescharacteristic
40#10622292C2211yescharacteristic
41C11×#322C2212yes—
42C11×#322C2212yes—
43#10622097C2212yes—
44#10622097C2212yes—
45#10622097C2212yes—
46#10622096C2212yes—
47#10622095C2212yes—
48#10622094C2212yes—
49C2×#4339—21no—
50C2×#4339C2×C411yescharacteristic
51C2×C11×M16—21no—
52C22×C8×C11D411yescharacteristic
53C22×C8×C11D411yescharacteristic
54C2×C42×C11C2311yescharacteristic
55#66983—21no—
56#66983C2×C412yes—
57C4×C22⋊D11—21no—
58C4×C22⋊D11—21no—
59#66979C2×C411yescharacteristic
60C2×#4318—21no—
61C2×D88C2×C412yes—
62C2×#4314C2×C412yes—
63#66954—44no—
64C2×#4313—21no—
65C2×#4313—21no—
66C2×#4313—22no—
67C2×C8×D11—22no—
68#66928—21no—
69#66927C2×C411yescharacteristic
70C4×D44—21no—
71C4×D44C2×C411yescharacteristic
72C4×D44C2311yescharacteristic
73C4×D44C2312yes—
74#66925—21no—
75C42×D11—21no—
76#66922C2×C411yescharacteristic
77C4×Dic22C2×C411yescharacteristic
78C4×Dic22C2311yescharacteristic
79C11×C4⋊C8C2×C411yescharacteristic
80C11×C4⋊C8C2×C411yescharacteristic
81C11×C22⋊C8C2×C412yes—
82C11×#97—21no—
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2312yes—
86C4×C8×C11C2312yes—
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C22⋊(C11⋊C8)—21no—
90#66885C2×C412yes—
91#66885C2×C412yes—
92#66885C2×C412yes—
93(C2×D11)⋊C8—22no—
94(C2×D11)⋊C8—22no—
95(C2×D11)⋊C8—21no—
96(C2×D11)⋊C8—21no—
97#66882C2×C412yes—
98#66881C2×C412yes—
99#66880C2×C412yes—
100#66879—21no—
101#66879—21no—
102Dic11⋊C8—21no—
103Dic11⋊C8—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4×C11⋊C8—21no—
109#17940—111nomaximal, Sylow
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—21no—
114C2×C22⋊D11—22no—
115#4339—41no—
116#4339—41no—
117#4339—42no—
118#4339—42no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44C22×C411yescharacteristic
122C2×D44C22×C412yes—
123C2×C4×D11—21no—
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×C4×D11—22no—
127C2×Dic22—21no—
128C2×Dic22C22×C411yescharacteristic
129C11×M16—42no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—41no—
133C2×C8×C11C22×C412yes—
134C2×C8×C11C22×C412yes—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C42×C11C22×C411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11#4111yescharacteristic
142C42×C11C2411yescharacteristic
143C22⋊Dic11—21no—
144(C2×D11)⋊C4—21no—
145(C2×D11)⋊C4—22no—
146(C2×D11)⋊C4—21no—
147(C2×D11)⋊C4—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11C22×C412yes—
150C4⋊Dic11C22×C411yescharacteristic
151C4⋊Dic11C22×C411yescharacteristic
152Dic11⋊C4—21no—
153Dic11⋊C4—21no—
154C4×Dic11—21no—
155C4×Dic11—21no—
156C4×Dic11—21no—
157#4318—42no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161D88—42no—
162#4314—42no—
163#4313—42no—
164#4313—44no—
165#4313—42no—
166C8×D11—44no—
167#3106—111no—
168#2965—111no—
169#2931—111no—
170#1594—112no—
171#1592—112no—
172#1582—112no—
173#1581—112no—
174#1574—111no—
175#1489—111no—
176#1484—111no—
177#1451D1111yescharacteristic, complemented
178C23×C11C4×D411yescharacteristic
179C22×D11—21no—
180C22×D11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11C4×D411yescharacteristic
187C2×C4×C11C4×D411yescharacteristic
188C2×C4×C11C4×D411yescharacteristic
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C22⋊D11—42no—
193C22⋊D11—44no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—22no—
198D44—22no—
199D44—21no—
200D44—22no—
201D44—21no—
202D44—42no—
203D44—42no—
204C4×D11—42no—
205C4×D11—42no—
206C4×D11—41no—
207C4×D11—41no—
208C4×D11—42no—
209C4×D11—42no—
210Dic22—21no—
211Dic22—21no—
212Dic22—42no—
213C8×C11—22no—
214C8×C11—22no—
215C8×C11—21no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—42no—
219C8×C11AGL(1,ℤ/8)12yes—
220C11⋊C8—42no—
221C11⋊C8—41no—
222C11⋊C8—41no—
223C2×#131—221no—
224#532—111no—
225C4×#41—111no—
226#482—112no—
227#477—111no—
228#476—111no—
229#460—111no—
230#459—111no—
231#449—112no—
232#446—111no—
233#446—111no—
234C4×SD16—112no—
235C4×D8—112no—
236#436—111no—
237#436—112no—
238#436—111no—
239#436—221no—
240#435—221no—
241#435—221no—
242C8×D4—112no—
243C8×D4—221no—
244#431—111no—
245#431—221no—
246#431C2×D1111yescharacteristic
247#423—111no—
248#408—221no—
249C4×M16—221no—
250C4×M16C2×D1111yescharacteristic
251C2×C4×C8C2×D1111yescharacteristic
252#335—112no—
253#334—112no—
254Q8⋊C8—112no—
255D4⋊C8—112no—
256D4⋊C8—112no—
257D4⋊C8—112no—
258#322C2×D1112yes—
259#322C2×D1112yes—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11C2×C4×D411yescharacteristic
264C2×D11—41no—
265C2×D11—42no—
266C2×D11—41no—
267C2×D11—42no—
268C2×D11—41no—
269C2×D11—42no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11#44412yes—
274C4×C11#56811yescharacteristic
275C4×C11#56811yescharacteristic
276C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C11#57511yescharacteristic
278Dic11—41no—
279Dic11—42no—
280Dic11—41no—
281Dic11—41no—
282C2×#41—111no—
283C2×#41—221no—
284C2×SD16—112no—
285C2×D8—112no—
286#131—444no—
287C2×M16—21no—
288C2×M16—221no—
289C2×M16—222no—
290C2×M16—221no—
291C2×M16—221no—
292C22×C8—222no—
293C22×C8D4411yescharacteristic
294C22×C8D4411yescharacteristic
295C4⋊Q8—111no—
296#127—111no—
297#124—221no—
298#121—112no—
299#121—221no—
300C4×Q8—111no—
301C4×Q8—111no—
302C4×D4—111no—
303C4×D4—111no—
304C4×D4—112no—
305C4×D4—221no—
306C4×D4—221no—
307C4×D4—221no—
308#117—111no—
309#117—221no—
310C2×C42—221no—
311C2×C42C22×D1111yescharacteristic
312#107—112no—
313#106—112no—
314C4⋊C8—111no—
315C4⋊C8—111no—
316C4⋊C8—112no—
317C4⋊C8—221no—
318C4⋊C8—221no—
319C4⋊C8—221no—
320C4⋊C8C4×D1111yescharacteristic
321C4⋊C8C4×D1111yescharacteristic
322#103—112no—
323#102—112no—
324#102—112no—
325#102—112no—
326C22⋊C8—221no—
327C22⋊C8—222no—
328C22⋊C8—222no—
329C22⋊C8—221no—
330C22⋊C8—221no—
331C22⋊C8C4×D1112yes—
332#97—21no—
333#97—221no—
334#97—221no—
335C4×C8—221no—
336C4×C8D4411yescharacteristic
337C4×C8D4411yescharacteristic
338C4×C8C22×D1112yes—
339C4×C8C22×D1112yes—
340C4×C8C22×D1111yescharacteristic
341C4×C8C22×D1111yescharacteristic
342C2×C11—41no—
343C2×C11#293011yescharacteristic
344C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
345C2×C11C2×#44411yescharacteristic
346D11—81no—
347D11—82no—
348#41—441no—
349#41—441no—
350#41—442no—
351#41—442no—
352C2×Q8—111no—
353C2×Q8—221no—
354C2×D4—111no—
355C2×D4—112no—
356C2×D4—221no—
357C2×D4—222no—
358C2×D4—221no—
359C2×D4—221no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—222no—
364C22×C4C2×C4×D1111yescharacteristic
365C22×C4C2×D4411yescharacteristic
366C22×C4#433911yescharacteristic
367SD16—442no—
368D8—442no—
369M16—42no—
370M16—444no—
371M16—442no—
372M16—442no—
373M16—442no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—41no—
377C2×C8—221no—
378C2×C8—221no—
379C2×C8—222no—
380C2×C8—444no—
381C2×C8C2×C4×D1112yes—
382C2×C8C2×C4×D1112yes—
383C2×C8C2×D4411yescharacteristic
384C2×C8C2×D4411yescharacteristic
385C2×C8C2×D4411yescharacteristic
386C2×C8C2×D4411yescharacteristic
387C4⋊C4—111no—
388C4⋊C4—111no—
389C4⋊C4—112no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C22⋊C4—221no—
394C22⋊C4—221no—
395C22⋊C4—222no—
396C22⋊C4—221no—
397C22⋊C4—222no—
398C42—221no—
399C42—221no—
400C42—221no—
401C42C2×C4×D1111yescharacteristic
402C42C2×D4411yescharacteristic
403C42#433911yescharacteristic
404C42C23×D1111yescharacteristic
405C11#1794011yescharacteristic, complemented, Sylow
406C23—221no—
407C23—222no—
408C23C4×D4411yescharacteristic
409Q8—221no—
410Q8—221no—
411Q8—442no—
412D4—221no—
413D4—222no—
414D4—222no—
415D4—221no—
416D4—442no—
417D4—442no—
418D4—444no—
419D4—442no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—222no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4C4×D4411yescharacteristic
436C2×C4C4×D4411yescharacteristic
437C2×C4C4×D4411yescharacteristic
438C2×C4C22×C4×D1111yescharacteristic
439C2×C4C22×D4411yescharacteristic
440C2×C4C2×#433911yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8—22no—
445C8—22no—
446C8—42no—
447C8—442no—
448C8—441no—
449C8—441no—
450C8#6696112yes—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—441no—
455C22—442no—
456C22—441no—
457C22—442no—
458C22—442no—
459C22—441no—
460C22C2×C4×D4411yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—441no—
465C4—441no—
466C4—442no—
467C4—441no—
468C4#1062233012yes—
469C4C2×#6696111yescharacteristic
470C4#1062327911yescharacteristic
471C4#1062328111yescharacteristic
472C4#1062328111yescharacteristic
473C2—41no—
474C2—881no—
475C2—882no—
476C2#1307732111yescharacteristic
477C2C4×#6696111yescharacteristic
478C2C2×#1062233011yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1451C2
socleC22×C11C2×C4×D4
prime radical#13078677C2
cosocleC42×C11C24
hypercenter#1451D11
hypocenterC11#17940
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #1451

Complements

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

NH ≅ G/Ntype
2. #13077582C2semidirect
3. #13077329C2semidirect
4. #13067531C2semidirect
5. #13067520C2semidirect
6. #13067454C2semidirect
7. #13067447C2semidirect
8. #13067405C2semidirect
9. #13067056C2semidirect
10. #13067034C2semidirect
11. C11×#1451C2semidirect
177. #1451D11semidirect
405. C11#17940semidirect

Maximal subgroups

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

subgroupindex
#130786772
#130775822
#130773292
#130675312
#130675202
#130674542
#130674472
#130674052
#130670562
#130670342
C11×#14512
#1794011