Finite Group Databasebeta

← #14725170

Subgroups — #14725170

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#13078653C211yesmaximal, characteristic
2#13077714C211yesmaximal, characteristic
3#13077704C211yesmaximal, characteristic
4#13067523C211yesmaximal, characteristic, complemented
5#13067512C211yesmaximal, characteristic, complemented
6#13067484C211yesmaximal, characteristic, complemented
7#13067484C211yesmaximal, characteristic, complemented
8#13067468C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10Q16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067395C211yesmaximal, characteristic
12#13067087C211yesmaximal, characteristic
13#13067009C211yesmaximal, characteristic
14#13066917C211yesmaximal, characteristic
15C11×#1584C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622799C411yescharacteristic
22#10622795C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4326C2211yescharacteristic
25Q8×C11⋊C8C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622497C411yescharacteristic
28#10622488C411yescharacteristic
29#10622453—21no—
30#10622448—21no—
31#10622448C2211yescharacteristic
32#10622446C2211yescharacteristic
33#10622444—21no—
34#10622444C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622443—21no—
37#10622422C411yescharacteristic
38#10622421C411yescharacteristic
39#10622407C411yescharacteristic
40#10622406C411yescharacteristic
41#10622322—21no—
42#10622314—21no—
43C4×Dic44C2211yescharacteristic
44#10622298—21no—
45#10622298C2211yescharacteristic
46#10622298C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622292—21no—
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71#66999C2×C411yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4326C2×C411yescharacteristic
76C2×Dic44C2×C411yescharacteristic
77#66950C2×C411yescharacteristic
78#66949—21no—
79C4⋊C4×D11—21no—
80C4⋊C4×D11C2×C411yescharacteristic
81#66942—21no—
82#66941C2×C411yescharacteristic
83#66940—21no—
84#66940C2×C411yescharacteristic
85#66925—21no—
86C42×D11—21no—
87C42×D11C2311yescharacteristic
88C4×Dic22—21no—
89C4×Dic22—21no—
90C4×Dic22C2311yescharacteristic
91C4×Dic22C2311yescharacteristic
92C11×#107C2×C411yescharacteristic
93C11×C4⋊C8—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8C2311yescharacteristic
96C11×C4⋊C8C2311yescharacteristic
97C11×#103C2×C411yescharacteristic
98C11×#103C2×C411yescharacteristic
99C11×#97—21no—
100C4×C8×C11—21no—
101C4×C8×C11C2311yescharacteristic
102C4×C8×C11C2311yescharacteristic
103C4×C8×C11C2311yescharacteristic
104#66899C2×C411yescharacteristic
105#66899C2×C411yescharacteristic
106(C2×D11)⋊C8—21no—
107(C2×D11)⋊C8—21no—
108(C2×D11)⋊C8—21no—
109(C2×D11)⋊C8C2×C411yescharacteristic
110(C2×D11)⋊C8C2×C411yescharacteristic
111(C2×D11)⋊C8D411yescharacteristic
112(C2×D11)⋊C8D411yescharacteristic
113#66882C2×C411yescharacteristic
114#66880C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66879—21no—
117#66879—21no—
118#66879—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8C2×C411yescharacteristic
126Dic11⋊C8C2×C411yescharacteristic
127Dic11⋊C8D411yescharacteristic
128Dic11⋊C8D411yescharacteristic
129C8×Dic11—21no—
130C8×Dic11—21no—
131#66874C2×C411yescharacteristic
132#66874C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18032—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147Q8×D11—22no—
148Q8×D11—41no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11C22×C411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11#4111yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C11×Q16—22no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C411yescharacteristic
169C11×C4⋊C4C22×C411yescharacteristic
170C42×C11—21no—
171C42×C11—21no—
172C42×C11C2411yescharacteristic
173#4326—22no—
174#4326—41no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22×C411yescharacteristic
180C4⋊Dic11C22×C411yescharacteristic
181Dic11⋊C4—21no—
182Dic11⋊C4—21no—
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11#4111yescharacteristic
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203Dic44—41no—
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#1584D1111yescharacteristic, complemented
213#1579—111no—
214C8×Q16—111no—
215#1572—111no—
216#1497—111no—
217#1479—111no—
218#1454—111no—
219C22×D11C4×D411yescharacteristic
220Q8×C11—21no—
221Q8×C11—21no—
222Q8×C11—21no—
223Q8×C11#13112yes—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11C4×D411yescharacteristic
236C2×Dic11C4×D411yescharacteristic
237C2×Dic11C4×D411yescharacteristic
238C4×D11—21no—
239C4×D11—21no—
240C4×D11—21no—
241C4×D11—21no—
242C4×D11—41no—
243C4×D11—42no—
244C4×D11—42no—
245Dic22—21no—
246Dic22—21no—
247Dic22—21no—
248Dic22—21no—
249Dic22—42no—
250Dic22—42no—
251C8×C11—21no—
252C8×C11—21no—
253C8×C11—21no—
254C8×C11—21no—
255C8×C11—41no—
256C8×C11—41no—
257C8×C11—41no—
258C11⋊C8—21no—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265#533—111no—
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—221no—
279#446—221no—
280#446—221no—
281#446C2×D1111yescharacteristic
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—111no—
285C8×Q8—221no—
286C8×Q8C2×D1111yescharacteristic
287C4×Q16—111no—
288C4×Q16—111no—
289C4×Q16—111no—
290C4×Q16C2×D1111yescharacteristic
291#433—221no—
292#433—221no—
293#432—111no—
294#432—221no—
295#431—111no—
296#431—111no—
297#431—111no—
298#431—111no—
299#431—221no—
300#335—111no—
301#335C2×D1111yescharacteristic
302#334—111no—
303#334—111no—
304Q8⋊C8—111no—
305Q8⋊C8—111no—
306Q8⋊C8—111no—
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8C2×D1111yescharacteristic
311Q8⋊C8C2×D1111yescharacteristic
312#322—111no—
313#322—111no—
314#322C2×D1111yescharacteristic
315C82—111no—
316C22×C11C2×C4×D411yescharacteristic
317C2×D11—21no—
318C2×D11—21no—
319C2×D11—21no—
320C4×C11—22no—
321C4×C11—21no—
322C4×C11—41no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11C2×#13111yescharacteristic
326C4×C11#56811yescharacteristic
327C4×C11#57811yescharacteristic
328C4×C11#57811yescharacteristic
329Dic11—21no—
330Dic11—21no—
331Dic11—21no—
332Dic11—41no—
333Dic11—41no—
334Dic11—41no—
335Dic11—41no—
336C22×Q8—111no—
337C2×Q16—111no—
338C2×Q16—111no—
339C2×Q16—111no—
340C2×Q16C4×D1111yescharacteristic
341C4⋊Q8—111no—
342C4⋊Q8—111no—
343#125—221no—
344C22⋊Q8—111no—
345C22⋊Q8—111no—
346C22⋊Q8—221no—
347C4×Q8—111no—
348C4×Q8—111no—
349C4×Q8—111no—
350C4×Q8—111no—
351C4×Q8—221no—
352C4×Q8—221no—
353C4×Q8—221no—
354C4×Q8C22×D1111yescharacteristic
355C4×Q8C22×D1111yescharacteristic
356#117—221no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—221no—
359C2×C42—111no—
360C2×C42—221no—
361#107—111no—
362#107—111no—
363#107—111no—
364#107C4×D1111yescharacteristic
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—111no—
368C4⋊C8—111no—
369C4⋊C8—111no—
370C4⋊C8—111no—
371C4⋊C8—111no—
372C4⋊C8—111no—
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#103C4×D1111yescharacteristic
389#103C4×D1111yescharacteristic
390C22⋊C8—111no—
391C22⋊C8—111no—
392C22⋊C8—111no—
393C22⋊C8—111no—
394C22⋊C8—221no—
395C22⋊C8—221no—
396C22⋊C8—221no—
397#97—21no—
398#97—221no—
399#97—221no—
400#97—221no—
401#97—221no—
402C4×C8—21no—
403C4×C8—111no—
404C4×C8—111no—
405C4×C8—111no—
406C4×C8—221no—
407C4×C8—221no—
408C4×C8—221no—
409C4×C8—221no—
410C4×C8C22×D1111yescharacteristic
411C4×C8C22×D1111yescharacteristic
412C4×C8C22×D1111yescharacteristic
413C2×C11#293311yescharacteristic
414C2×C11#295011yescharacteristic
415C2×C11#295511yescharacteristic
416D11—41no—
417C2×Q8—111no—
418C2×Q8—111no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×Q8—222no—
422C2×Q8—441no—
423C2×Q8C2×C4×D1111yescharacteristic
424C2×Q8C2×C4×D1111yescharacteristic
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—221no—
429C22×C4—221no—
430Q16—22no—
431Q16—222no—
432Q16—441no—
433Q16—441no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—111no—
438C2×C8—111no—
439C2×C8—111no—
440C2×C8—111no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8C2×C4×D1111yescharacteristic
445C2×C8C2×C4×D1111yescharacteristic
446C2×C8D4×D1111yescharacteristic
447C2×C8D4×D1111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—111no—
451C4⋊C4—111no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
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—221no—
465C22⋊C4—221no—
466C42—21no—
467C42—21no—
468C42—111no—
469C42—111no—
470C42—111no—
471C42—221no—
472C42—221no—
473C42—221no—
474C42—221no—
475C42C23×D1111yescharacteristic
476C11#1803211yescharacteristic, complemented, Sylow
477C23—111no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—221no—
482Q8—221no—
483Q8—221no—
484Q8—221no—
485Q8—442no—
486Q8—442no—
487Q8#6696012yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—111no—
493C2×C4—111no—
494C2×C4—111no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—441no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4C22×C4×D1111yescharacteristic
507C2×C4C2×D4×D1111yescharacteristic
508C2×C4#41×D1111yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—221no—
517C8—221no—
518C8—221no—
519C8—221no—
520C8—441no—
521C8—441no—
522C8—441no—
523C22—221no—
524C22—221no—
525C22—221no—
526C22C4×D4×D1111yescharacteristic
527C4—21no—
528C4—22no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—221no—
533C4—221no—
534C4—221no—
535C4—441no—
536C4—441no—
537C4—441no—
538C4—441no—
539C4C2×#6696011yescharacteristic
540C4#1062328111yescharacteristic
541C4#1062329711yescharacteristic
542C4#1062330211yescharacteristic
543C2—441no—
544C2#1307734211yescharacteristic
545C2#1307747911yescharacteristic
546C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1584C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1584D11
hypocenterC11#18032
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #13067523C2semidirect
5. #13067512C2semidirect
6. #13067484C2semidirect
7. #13067484C2semidirect
8. #13067468C2semidirect
9. #13067433C2semidirect
10. Q16×C11⋊C8C2semidirect
15. C11×#1584C2semidirect
212. #1584D11semidirect
476. C11#18032semidirect

Maximal subgroups

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

subgroupindex
#130786532
#130777142
#130777042
#130675232
#130675122
#130674842
#130674682
#130674332
Q16×C11⋊C82
#130673952
#130670872
#130670092
#130669172
C11×#15842
#1803211