Finite Group Databasebeta

← #14725169

Subgroups — #14725169

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#13077718C211yesmaximal, characteristic
2#13077705C211yesmaximal, characteristic
3#13067525C211yesmaximal, characteristic, complemented
4#13067513C211yesmaximal, characteristic, complemented
5#13067488C211yesmaximal, characteristic, complemented
6#13067488C211yesmaximal, characteristic, complemented
7#13067467C211yesmaximal, characteristic, complemented
8#13067467C211yesmaximal, characteristic, complemented
9#13067435C211yesmaximal, characteristic, complemented
10Q16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067396C211yesmaximal, characteristic
12#13067089C211yesmaximal, characteristic
13#13067011C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic
15C11×#3104C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#484C411yescharacteristic
19C11×#484C411yescharacteristic
20C11×#477C411yescharacteristic
21C11×#477C411yescharacteristic
22C11×#462C411yescharacteristic
23C11×#462C411yescharacteristic
24C11×#451C411yescharacteristic
25C11×#451C411yescharacteristic
26C4×C11×Q16C2211yescharacteristic
27C4×C11×Q16C2211yescharacteristic
28C4×C11×Q16C2211yescharacteristic
29C4×C11×Q16C2211yescharacteristic
30C11×#431C2211yescharacteristic
31#10622637—21no—
32#10622637—21no—
33#10622637—21no—
34#10622637C2211yescharacteristic
35#10622637C2211yescharacteristic
36#10622637C2211yescharacteristic
37#10622637C2211yescharacteristic
38Q8×C11⋊C8—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic
42Q8×C11⋊C8C2211yescharacteristic
43#10622613—21no—
44#10622613—21no—
45#10622539—21no—
46#10622539C2211yescharacteristic
47#10622538—21no—
48#10622538C2211yescharacteristic
49#10622538C2211yescharacteristic
50#10622538C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57Q8⋊(C11⋊C8)C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59#10622096C2211yescharacteristic
60#10622096C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C2×C11×Q16C2×C411yescharacteristic
71C2×C11×Q16C2×C411yescharacteristic
72C11×C4⋊Q8C2×C411yescharacteristic
73C11×C4⋊Q8C2×C411yescharacteristic
74C11×#125—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8C2×C411yescharacteristic
77C11×C22⋊Q8C2×C411yescharacteristic
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11C2×C411yescharacteristic
82C4×Q8×C11C2×C411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×Q8×C11C2311yescharacteristic
85C4×Q8×C11C2311yescharacteristic
86C4×Q8×C11C2311yescharacteristic
87C11×#117—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C11×#107C2×C411yescharacteristic
93C11×#107C2×C411yescharacteristic
94C11×#107C2×C411yescharacteristic
95C11×#107C2×C411yescharacteristic
96C11×C4⋊C8C2×C411yescharacteristic
97C11×C4⋊C8C2×C411yescharacteristic
98C11×#103C2×C411yescharacteristic
99C11×#103C2×C411yescharacteristic
100C11×#103C2×C411yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×C22⋊C8C2×C411yescharacteristic
107C11×C22⋊C8C2×C411yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)D411yescharacteristic
114C22⋊(C11⋊C8)D411yescharacteristic
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)—21no—
117C4⋊(C11⋊C8)—21no—
118C4⋊(C11⋊C8)—21no—
119C4⋊(C11⋊C8)—21no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)—21no—
123C4⋊(C11⋊C8)—21no—
124C4⋊(C11⋊C8)D411yescharacteristic
125C4⋊(C11⋊C8)D411yescharacteristic
126C4⋊(C11⋊C8)C2311yescharacteristic
127C4⋊(C11⋊C8)C2311yescharacteristic
128C4⋊(C11⋊C8)C2311yescharacteristic
129C4⋊(C11⋊C8)C2311yescharacteristic
130#66867—21no—
131#66867—21no—
132#66867—21no—
133#66867—21no—
134#66867—21no—
135C4×C11⋊C8—21no—
136C4×C11⋊C8—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×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C2×Q8×C11C22×C411yescharacteristic
150C2×Q8×C11C22×C411yescharacteristic
151C2×Q8×C11C22×C411yescharacteristic
152C2×Q8×C11C22×C411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C11×Q16—22no—
159C11×Q16—22no—
160C11×Q16—41no—
161C11×Q16—41no—
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11C22×C411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11#4111yescharacteristic
193C42×C11C2411yescharacteristic
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204#3104D1111yescharacteristic
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#1497—111no—
217#1479—111no—
218#1454—111no—
219C23×C11C4×D411yescharacteristic
220Q8×C11—21no—
221Q8×C11—21no—
222Q8×C11—21no—
223Q8×C11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—42no—
228Q8×C11—42no—
229Q8×C11#13112yes—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C8×C11—21no—
252C8×C11—21no—
253C8×C11—21no—
254C8×C11—21no—
255C11⋊C8—21no—
256C11⋊C8—21no—
257C11⋊C8—21no—
258C11⋊C8—21no—
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265#533C2×D1111yescharacteristic
266C2×C4×Q8C2×D1111yescharacteristic
267#484Dic1111yescharacteristic
268#484Dic1111yescharacteristic
269#477Dic1111yescharacteristic
270#477Dic1111yescharacteristic
271#462Dic1111yescharacteristic
272#462Dic1111yescharacteristic
273#451Dic1111yescharacteristic
274#451Dic1111yescharacteristic
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×Q16C2×D1111yescharacteristic
288C4×Q16C2×D1111yescharacteristic
289C4×Q16C2×D1111yescharacteristic
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—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⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
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—22no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11C2×#13111yescharacteristic
333C4×C11#56811yescharacteristic
334C4×C11#57811yescharacteristic
335C4×C11#57811yescharacteristic
336C22×Q8C2×Dic1111yescharacteristic
337C2×Q16C2×Dic1111yescharacteristic
338C2×Q16C2×Dic1111yescharacteristic
339C2×Q16C2×Dic1111yescharacteristic
340C2×Q16C2×Dic1111yescharacteristic
341C4⋊Q8C2×Dic1111yescharacteristic
342C4⋊Q8C2×Dic1111yescharacteristic
343#125—21no—
344C22⋊Q8—21no—
345C22⋊Q8C2×Dic1111yescharacteristic
346C22⋊Q8C2×Dic1111yescharacteristic
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8C2×Dic1111yescharacteristic
351C4×Q8C2×Dic1111yescharacteristic
352C4×Q8C22×D1111yescharacteristic
353C4×Q8C22×D1111yescharacteristic
354C4×Q8C22×D1111yescharacteristic
355C4×Q8C22×D1111yescharacteristic
356#117—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C2×Dic1111yescharacteristic
359C2×C42—21no—
360C2×C42C22×D1111yescharacteristic
361#107C2×Dic1111yescharacteristic
362#107C2×Dic1111yescharacteristic
363#107C2×Dic1111yescharacteristic
364#107C2×Dic1111yescharacteristic
365C4⋊C8—111no—
366C4⋊C8—111no—
367C4⋊C8—111no—
368C4⋊C8—111no—
369C4⋊C8—111no—
370C4⋊C8—111no—
371C4⋊C8—221no—
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⋊C8C2×Dic1111yescharacteristic
381C4⋊C8C2×Dic1111yescharacteristic
382#103C2×Dic1111yescharacteristic
383#103C2×Dic1111yescharacteristic
384#103C2×Dic1111yescharacteristic
385#103C2×Dic1111yescharacteristic
386#103C2×Dic1111yescharacteristic
387#103C2×Dic1111yescharacteristic
388#103C2×Dic1111yescharacteristic
389#103C2×Dic1111yescharacteristic
390C22⋊C8—111no—
391C22⋊C8—111no—
392C22⋊C8—221no—
393C22⋊C8—221no—
394C22⋊C8—221no—
395C22⋊C8C2×Dic1111yescharacteristic
396C22⋊C8C2×Dic1111yescharacteristic
397#97—221no—
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—21no—
419C2×Q8—22no—
420C2×Q8—41no—
421C2×Q8C22×Dic1111yescharacteristic
422C2×Q8C22×Dic1111yescharacteristic
423C2×Q8C22×Dic1111yescharacteristic
424C2×Q8C22×Dic1111yescharacteristic
425C22×C4—21no—
426C22×C4—21no—
427C22×C4D4×D1111yescharacteristic
428C22×C4#434111yescharacteristic
429C22×C4C22×Dic1111yescharacteristic
430Q16—22no—
431Q16—22no—
432Q16—41no—
433Q16—41no—
434C2×C8—111no—
435C2×C8—111no—
436C2×C8—111no—
437C2×C8—111no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8C22×Dic1111yescharacteristic
445C2×C8C22×Dic1111yescharacteristic
446C2×C8C22×Dic1111yescharacteristic
447C2×C8C22×Dic1111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4C22×Dic1111yescharacteristic
461C4⋊C4C22×Dic1111yescharacteristic
462C4⋊C4C22×Dic1111yescharacteristic
463C4⋊C4C22×Dic1111yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42D4×D1111yescharacteristic
473C42#434111yescharacteristic
474C42C22×Dic1111yescharacteristic
475C42C23×D1111yescharacteristic
476C11#1803211yescharacteristic, complemented, Sylow
477C23D4×Dic1111yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—42no—
486Q8—42no—
487Q8#6700112yes—
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—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4D4×Dic1111yescharacteristic
504C2×C4D4×Dic1111yescharacteristic
505C2×C4D4×Dic1111yescharacteristic
506C2×C4C2×D4×D1111yescharacteristic
507C2×C4C2×#434111yescharacteristic
508C2×C4C23×Dic1111yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—221no—
514C8—221no—
515C8—221no—
516C8—221no—
517C8—441no—
518C8—441no—
519C8—441no—
520C8—441no—
521C8—441no—
522C8—441no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×D4×Dic1111yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—22no—
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4#1062329711yescharacteristic
540C4#1062329711yescharacteristic
541C4C2×#6700111yescharacteristic
542C4#1062335011yescharacteristic
543C2—41no—
544C2#1307734311yescharacteristic
545C2#1307748411yescharacteristic
546C2#1307751911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3104C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#3104D11
hypocenterC11#18032
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #13067525C2semidirect
4. #13067513C2semidirect
5. #13067488C2semidirect
6. #13067488C2semidirect
7. #13067467C2semidirect
8. #13067467C2semidirect
9. #13067435C2semidirect
10. Q16×C11⋊C8C2semidirect
476. C11#18032semidirect

Maximal subgroups

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

subgroupindex
#130777182
#130777052
#130675252
#130675132
#130674882
#130674672
#130674352
Q16×C11⋊C82
#130673962
#130670892
#130670112
#130669162
C11×#31042
#1803211