Finite Group Databasebeta

← #14725173

Subgroups — #14725173

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078651C211yesmaximal, characteristic
2#13077718C211yesmaximal, characteristic
3#13077706C211yesmaximal, characteristic
4#13067522C211yesmaximal, characteristic, complemented
5#13067510C211yesmaximal, characteristic, complemented
6#13067490C211yesmaximal, characteristic, complemented
7#13067484C211yesmaximal, characteristic, complemented
8#13067469C211yesmaximal, characteristic, complemented
9#13067463C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11#13067420C211yesmaximal, characteristic, complemented
12#13067397C211yesmaximal, characteristic
13#13067012C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic
15C11×#1497C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622704C411yescharacteristic
21#10622704C411yescharacteristic
22#10622703C411yescharacteristic
23#10622703C411yescharacteristic
24#10622663C411yescharacteristic
25#10622663C411yescharacteristic
26#10622657C411yescharacteristic
27#10622657C411yescharacteristic
28C4×#4326C2211yescharacteristic
29C4×#4326C2211yescharacteristic
30C4×#4326C2211yescharacteristic
31C4×#4326C2211yescharacteristic
32#10622637—21no—
33#10622637C2211yescharacteristic
34#10622637C2211yescharacteristic
35Q8×C11⋊C8—21no—
36Q8×C11⋊C8C2211yescharacteristic
37Q8×C11⋊C8C2211yescharacteristic
38#10622613—21no—
39#10622613—21no—
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622444C2211yescharacteristic
44#10622444C2211yescharacteristic
45#10622443C2211yescharacteristic
46#10622443C2211yescharacteristic
47#10622332—21no—
48#10622331—21no—
49#10622314—21no—
50#10622314—21no—
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×Q8⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622094C2211yescharacteristic
60#10622094C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Dic22C2×C411yescharacteristic
68C11×C4⋊Q8C2×C411yescharacteristic
69C11×C4⋊Q8C2×C411yescharacteristic
70C11×#125—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8C2×C411yescharacteristic
73C11×C22⋊Q8C2×C411yescharacteristic
74C4×Q8×C11—21no—
75C4×Q8×C11C2311yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C11×#117—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4326C2×C411yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C4×Dic22—21no—
87C4×Dic22—21no—
88C4×Dic22C2×C411yescharacteristic
89C4×Dic22C2×C411yescharacteristic
90C4×Dic22C2311yescharacteristic
91C4×Dic22C2311yescharacteristic
92C11×C4⋊C8—21no—
93C11×C4⋊C8C2311yescharacteristic
94C11×C4⋊C8C2311yescharacteristic
95C11×C22⋊C8—21no—
96C11×C22⋊C8—21no—
97C11×#97—21no—
98C4×C8×C11C2311yescharacteristic
99C4×C8×C11C2311yescharacteristic
100#66899C2×C411yescharacteristic
101#66899C2×C411yescharacteristic
102#66899C2×C411yescharacteristic
103#66899C2×C411yescharacteristic
104C22⋊(C11⋊C8)—21no—
105C22⋊(C11⋊C8)C2×C411yescharacteristic
106C22⋊(C11⋊C8)C2×C411yescharacteristic
107C22⋊(C11⋊C8)D411yescharacteristic
108C22⋊(C11⋊C8)D411yescharacteristic
109#66879—21no—
110#66879—21no—
111Dic11⋊C8—21no—
112Dic11⋊C8—21no—
113Dic11⋊C8—21no—
114Dic11⋊C8—21no—
115C8×Dic11—21no—
116C8×Dic11—21no—
117#66874C2×C411yescharacteristic
118#66874C2×C411yescharacteristic
119#66874C2×C411yescharacteristic
120#66874C2×C411yescharacteristic
121#66871C2×C411yescharacteristic
122#66871C2×C411yescharacteristic
123#66871C2×C411yescharacteristic
124#66871C2×C411yescharacteristic
125C4⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)C2×C411yescharacteristic
130C4⋊(C11⋊C8)C2×C411yescharacteristic
131C4⋊(C11⋊C8)D411yescharacteristic
132C4⋊(C11⋊C8)D411yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135#66867—21no—
136#66867—21no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18032—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×Dic22—22no—
154C2×Dic22—21no—
155C2×Dic22—41no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11C22×C411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11#4111yescharacteristic
178C42×C11C2411yescharacteristic
179#4326—22no—
180#4326—22no—
181#4326—41no—
182#4326—41no—
183C4⋊Dic11—21no—
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8C22×C411yescharacteristic
197C2×C11⋊C8C22×C411yescharacteristic
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204#3104—111no—
205#2986—111no—
206#2984—111no—
207#1593—111no—
208#1591—111no—
209#1587—111no—
210#1587—111no—
211#1584—111no—
212#1584—111no—
213#1579—111no—
214C8×Q16—111no—
215#1572—111no—
216#1497D1111yescharacteristic
217#1479—111no—
218#1454—111no—
219C23×C11C4×D411yescharacteristic
220Q8×C11—21no—
221Q8×C11—21no—
222Q8×C11—21no—
223Q8×C11—21no—
224Q8×C11—42no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246Dic22—21no—
247Dic22—21no—
248Dic22—21no—
249Dic22—42no—
250Dic22#13112yes—
251C8×C11—41no—
252C8×C11—41no—
253C8×C11—41no—
254C8×C11—41no—
255C11⋊C8—21no—
256C11⋊C8—21no—
257C11⋊C8—21no—
258C11⋊C8—21no—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265#533C2×D1111yescharacteristic
266C2×C4×Q8—111no—
267#484—111no—
268#484—111no—
269#477—111no—
270#477—111no—
271#462—111no—
272#462—111no—
273#451—111no—
274#451—111no—
275#446—111no—
276#446—111no—
277#446—111no—
278#446—111no—
279#446—221no—
280#446—221no—
281#446—221no—
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—221no—
287C4×Q16—111no—
288C4×Q16—111no—
289C4×Q16—111no—
290C4×Q16—111no—
291#433—221no—
292#433—221no—
293#432—221no—
294#432C2×D1111yescharacteristic
295#431—111no—
296#431—111no—
297#431—111no—
298#431—221no—
299#431C2×D1111yescharacteristic
300#335—111no—
301#335—111no—
302#334—111no—
303#334—111no—
304Q8⋊C8—111no—
305Q8⋊C8—111no—
306Q8⋊C8—111no—
307Q8⋊C8—111no—
308Q8⋊C8C2×D1111yescharacteristic
309Q8⋊C8C2×D1111yescharacteristic
310Q8⋊C8C2×D1111yescharacteristic
311Q8⋊C8C2×D1111yescharacteristic
312#322—111no—
313#322—111no—
314#322—111no—
315C82—111no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11C2×C4×D411yescharacteristic
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11C2×#13111yescharacteristic
329C4×C11#56811yescharacteristic
330C4×C11#57811yescharacteristic
331C4×C11#57811yescharacteristic
332Dic11—22no—
333Dic11—41no—
334Dic11—41no—
335Dic11—41no—
336C22×Q8—111no—
337C2×Q16—111no—
338C2×Q16—111no—
339C2×Q16—111no—
340C2×Q16—111no—
341C4⋊Q8C4×D1111yescharacteristic
342C4⋊Q8C4×D1111yescharacteristic
343#125—21no—
344C22⋊Q8—21no—
345C22⋊Q8C4×D1111yescharacteristic
346C22⋊Q8C4×D1111yescharacteristic
347C4×Q8—21no—
348C4×Q8—111no—
349C4×Q8—111no—
350C4×Q8—111no—
351C4×Q8—111no—
352C4×Q8—221no—
353C4×Q8—221no—
354C4×Q8C22×D1111yescharacteristic
355C4×Q8C22×D1111yescharacteristic
356#117—21no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—221no—
359C2×C42—221no—
360C2×C42C22×D1111yescharacteristic
361#107—111no—
362#107—111no—
363#107—111no—
364#107—111no—
365C4⋊C8—21no—
366C4⋊C8—111no—
367C4⋊C8—111no—
368C4⋊C8—111no—
369C4⋊C8—111no—
370C4⋊C8—111no—
371C4⋊C8—111no—
372C4⋊C8—221no—
373C4⋊C8—221no—
374C4⋊C8—221no—
375C4⋊C8—221no—
376C4⋊C8—221no—
377C4⋊C8—221no—
378C4⋊C8—221no—
379C4⋊C8—221no—
380C4⋊C8C22×D1111yescharacteristic
381C4⋊C8C22×D1111yescharacteristic
382#103—111no—
383#103—111no—
384#103—111no—
385#103—111no—
386#103—111no—
387#103—111no—
388#103—111no—
389#103—111no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—111no—
393C22⋊C8—111no—
394C22⋊C8—111no—
395C22⋊C8—111no—
396C22⋊C8—221no—
397#97—21no—
398#97—221no—
399#97—221no—
400#97—221no—
401#97—221no—
402C4×C8—111no—
403C4×C8—111no—
404C4×C8—111no—
405C4×C8—111no—
406C4×C8—221no—
407C4×C8—221no—
408C4×C8—221no—
409C4×C8—221no—
410C4×C8—221no—
411C4×C8C22×D1111yescharacteristic
412C4×C8C22×D1111yescharacteristic
413C2×C11—41no—
414C2×C11#293311yescharacteristic
415C2×C11#295011yescharacteristic
416C2×C11#295511yescharacteristic
417C2×Q8—21no—
418C2×Q8—111no—
419C2×Q8—111no—
420C2×Q8—222no—
421C2×Q8—221no—
422C2×Q8—441no—
423C2×Q8C2×C4×D1111yescharacteristic
424C2×Q8C2×C4×D1111yescharacteristic
425C22×C4—221no—
426C22×C4—221no—
427C22×C4C2×C4×D1111yescharacteristic
428C22×C4D4×D1111yescharacteristic
429C22×C4#434111yescharacteristic
430Q16—222no—
431Q16—222no—
432Q16—441no—
433Q16—441no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—111no—
439C2×C8—111no—
440C2×C8—111no—
441C2×C8—111no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—111no—
446C2×C8—221no—
447C2×C8—221no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—111no—
456C4⋊C4—111no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4C2×C4×D1111yescharacteristic
463C4⋊C4C2×C4×D1111yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—21no—
466C42—21no—
467C42—21no—
468C42—221no—
469C42—221no—
470C42—221no—
471C42—221no—
472C42C2×C4×D1111yescharacteristic
473C42D4×D1111yescharacteristic
474C42#434111yescharacteristic
475C42C23×D1111yescharacteristic
476C11#1803211yescharacteristic, complemented, Sylow
477C23(C22⋊D11)⋊C411yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—42no—
483Q8—112no—
484Q8—221no—
485Q8—221no—
486Q8—221no—
487Q8—442no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4(C22⋊D11)⋊C411yescharacteristic
504C2×C4(C22⋊D11)⋊C411yescharacteristic
505C2×C4(C22⋊D11)⋊C411yescharacteristic
506C2×C4C22×C4×D1111yescharacteristic
507C2×C4C2×D4×D1111yescharacteristic
508C2×C4C2×#434111yescharacteristic
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—221no—
514C8—221no—
515C8—221no—
516C8—221no—
517C8—221no—
518C8—221no—
519C8—221no—
520C8—221no—
521C8—441no—
522C8—441no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×(C22⋊D11)⋊C411yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—222no—
536C4—441no—
537C4—441no—
538C4—441no—
539C4D11×#13111yescharacteristic
540C4#1062328111yescharacteristic
541C4#1062331011yescharacteristic
542C4#1062331011yescharacteristic
543C2—41no—
544C2#1307734611yescharacteristic
545C2#1307748011yescharacteristic
546C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1497C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#1497D11
hypocenterC11#18032
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
4. #13067522C2semidirect
5. #13067510C2semidirect
6. #13067490C2semidirect
7. #13067484C2semidirect
8. #13067469C2semidirect
9. #13067463C2semidirect
10. #13067432C2semidirect
11. #13067420C2semidirect
476. C11#18032semidirect

Maximal subgroups

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

subgroupindex
#130786512
#130777182
#130777062
#130675222
#130675102
#130674902
#130674842
#130674692
#130674632
#130674322
#130674202
#130673972
#130670122
#130669162
C11×#14972
#1803211