Finite Group Databasebeta

← #14723108

Subgroups — #14723108

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077741C211yesmaximal, characteristic
2#13077583C211yesmaximal, characteristic
3#13067402C211yesmaximal, characteristic, complemented
4#13067399C211yesmaximal, characteristic, complemented
5#13067397C211yesmaximal, characteristic, complemented
6#13067394C211yesmaximal, characteristic, complemented
7#13067392C211yesmaximal, characteristic, complemented
8#13067390C211yesmaximal, characteristic, complemented
9#13067384C211yesmaximal, characteristic, complemented
10#13067381C211yesmaximal, characteristic, complemented
11#13067377C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067366C211yesmaximal, characteristic, complemented
14C2×#10622117C211yesmaximal, characteristic, complemented
15C11×#2990C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17C11×#446—21no—
18C11×#435—21no—
19C11×#435—21no—
20C8×D4×C11—21no—
21C11×#432C2211yescharacteristic
22C11×#432C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27#10622637—21no—
28#10622637C411yescharacteristic
29#10622637C411yescharacteristic
30#10622625C411yescharacteristic
31#10622625C411yescharacteristic
32#10622624—21no—
33#10622624—21no—
34#10622624C411yescharacteristic
35#10622624C411yescharacteristic
36#10622624C411yescharacteristic
37#10622624C411yescharacteristic
38D4×C11⋊C8—21no—
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44#10622538C2211yescharacteristic
45#10622537C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49C4×#4318C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622118C2211yescharacteristic
52#10622118C2211yescharacteristic
53#10622118C2211yescharacteristic
54#10622118C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622117C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41Q811yescharacteristic
68C2×C11×M16—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C4×Q8×C11C2×C411yescharacteristic
72C4×Q8×C11D411yescharacteristic
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2×C411yescharacteristic
75C4×D4×C11C2×C411yescharacteristic
76C4×D4×C11D411yescharacteristic
77C4×D4×C11D411yescharacteristic
78C4×D4×C11D411yescharacteristic
79C11×#117Q811yescharacteristic
80C11×#117Q811yescharacteristic
81C11×#117Q811yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×#4318—21no—
86C2×#4318C2×C411yescharacteristic
87C2×#4318C2×C411yescharacteristic
88C2×#4318C2×C411yescharacteristic
89C2×#4318C2×C411yescharacteristic
90C22×C11⋊C8—21no—
91C22×C11⋊C8—21no—
92C22×C11⋊C8C2×C411yescharacteristic
93C22×C11⋊C8C2×C411yescharacteristic
94C11×C4⋊C8—21no—
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C22⋊C8—21no—
102C11×C22⋊C8—21no—
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C11×#97—21no—
106C4×C8×C11—21no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)C2×C411yescharacteristic
111C22⋊(C11⋊C8)C2×C411yescharacteristic
112C22⋊(C11⋊C8)C2×C411yescharacteristic
113C22⋊(C11⋊C8)C2×C411yescharacteristic
114C22⋊(C11⋊C8)C2×C411yescharacteristic
115C22⋊(C11⋊C8)C2×C411yescharacteristic
116C4⋊(C11⋊C8)—21no—
117C4⋊(C11⋊C8)—21no—
118C4⋊(C11⋊C8)—21no—
119C4⋊(C11⋊C8)C2×C411yescharacteristic
120C4⋊(C11⋊C8)C2×C411yescharacteristic
121C4⋊(C11⋊C8)C2×C411yescharacteristic
122C4⋊(C11⋊C8)C2×C411yescharacteristic
123C4⋊(C11⋊C8)C2×C411yescharacteristic
124C4⋊(C11⋊C8)C2×C411yescharacteristic
125C4⋊(C11⋊C8)C2311yescharacteristic
126C4⋊(C11⋊C8)C2311yescharacteristic
127C4⋊(C11⋊C8)C2311yescharacteristic
128C4⋊(C11⋊C8)C2311yescharacteristic
129#66867—21no—
130#66867—21no—
131#66867C2×C411yescharacteristic
132#66867C2×C411yescharacteristic
133#66867C2×C411yescharacteristic
134#66867C2×C411yescharacteristic
135C4×C11⋊C8—21no—
136C4×C11⋊C8C2×C411yescharacteristic
137C4×C11⋊C8C2×C411yescharacteristic
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2311yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142#17840—111nomaximal, Sylow
143C11×#41—42no—
144C2×Q8×C11C4⋊C411yescharacteristic
145C2×D4×C11C4⋊C411yescharacteristic
146C2×D4×C11C4⋊C411yescharacteristic
147C2×D4×C11C4⋊C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×Q811yescharacteristic
155C22×C4×C11C2×Q811yescharacteristic
156C22×C4×C11C2×Q811yescharacteristic
157C11×M16—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—81no—
163C2×C8×C11—81no—
164C11×C4⋊C4C4⋊C411yescharacteristic
165C11×C4⋊C4C4⋊C411yescharacteristic
166C11×C4⋊C4C4⋊C411yescharacteristic
167C11×C4⋊C4C4⋊C411yescharacteristic
168C11×C4⋊C4C4⋊C411yescharacteristic
169C11×C4⋊C4C4⋊C411yescharacteristic
170C11×C22⋊C4C4⋊C411yescharacteristic
171C11×C22⋊C4C4⋊C411yescharacteristic
172C11×C22⋊C4C4⋊C411yescharacteristic
173C11×C22⋊C4C4⋊C411yescharacteristic
174C11×C22⋊C4C4⋊C411yescharacteristic
175C11×C22⋊C4C4⋊C411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C42×C11C22×C411yescharacteristic
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×Q811yescharacteristic
183C42×C11C2×Q811yescharacteristic
184C42×C11C2×Q811yescharacteristic
185C42×C11C2411yescharacteristic
186#4318—22no—
187#4318—22no—
188#4318—41no—
189#4318—41no—
190#4318—81no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—81no—
198C2×C11⋊C8—81no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207#2990—111no—
208#2990D1111yescharacteristic
209#2965—111no—
210#1573—111no—
211#1573—111no—
212#1572—111no—
213#1572—111no—
214#1571—111no—
215#1571—111no—
216#1569—111no—
217#1569—111no—
218#1568—111no—
219#1565—111no—
220#1565—111no—
221C2×#335—111no—
222C23×C11C2×C4⋊C411yescharacteristic
223C23×C11C2×C4⋊C411yescharacteristic
224C23×C11C2×C4⋊C411yescharacteristic
225Q8×C11—41no—
226D4×C11—22no—
227D4×C11—22no—
228D4×C11—41no—
229C2×C4×C11—22no—
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—41no—
244C2×C4×C11C2×C4⋊C411yescharacteristic
245C2×C4×C11C2×C4⋊C411yescharacteristic
246C2×C4×C11C2×C4⋊C411yescharacteristic
247C2×C4×C11C2×C4⋊C411yescharacteristic
248C2×C4×C11C2×C4⋊C411yescharacteristic
249C2×C4×C11C2×C4⋊C411yescharacteristic
250C2×C4×C11C2×C4⋊C411yescharacteristic
251C2×C4×C11C2×C4⋊C411yescharacteristic
252C2×C4×C11C2×C4⋊C411yescharacteristic
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×Q811yescharacteristic
256C8×C11—41no—
257C8×C11—41no—
258C8×C11—41no—
259C8×C11—41no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8#13112yes—
272C4×#41C2×D1111yescharacteristic
273#446—21no—
274#446—111no—
275#446—111no—
276#446—221no—
277#436—111no—
278#436—111no—
279#435—21no—
280#435—21no—
281#435—111no—
282#435—111no—
283#435—111no—
284#435—111no—
285#435—221no—
286#435—221no—
287C8×D4—21no—
288C8×D4—221no—
289#432—111no—
290#432—111no—
291#432C2×D1111yescharacteristic
292#432C2×D1111yescharacteristic
293#431—111no—
294#431—111no—
295#431—111no—
296#431—111no—
297#431C2×D1111yescharacteristic
298#423—111no—
299#423C2×D1111yescharacteristic
300C2×C4⋊C8—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8C2×D1111yescharacteristic
303C2×C4⋊C8C2×D1111yescharacteristic
304C4×M16—111no—
305C4×M16—111no—
306C2×C4×C8—111no—
307#335—111no—
308#335—111no—
309#335—111no—
310#335—111no—
311#335—111no—
312#335—111no—
313#335—111no—
314#335—111no—
315#335—111no—
316#335—111no—
317#334—111no—
318#334—111no—
319#334—111no—
320#334—111no—
321#334—111no—
322#334—111no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11#43012yes—
332C22×C11C22×C4⋊C411yescharacteristic
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11C2×#13111yescharacteristic
344C4×C11#56811yescharacteristic
345C4×C11#57611yescharacteristic
346C4×C11#57811yescharacteristic
347C2×#41Dic2211yescharacteristic
348C2×M16—21no—
349C2×M16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C2×M16—111no—
353C2×M16—221no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—221no—
359C22×C8—221no—
360C4×Q8C4×D1111yescharacteristic
361C4×Q8C22⋊D1111yescharacteristic
362C4×D4C4×D1111yescharacteristic
363C4×D4C4×D1111yescharacteristic
364C4×D4C4×D1111yescharacteristic
365C4×D4C22⋊D1111yescharacteristic
366C4×D4C22⋊D1111yescharacteristic
367C4×D4C22⋊D1111yescharacteristic
368#117Dic2211yescharacteristic
369#117Dic2211yescharacteristic
370#117Dic2211yescharacteristic
371C2×C42C22×D1111yescharacteristic
372C2×C42C22×D1111yescharacteristic
373C2×C42C22×D1111yescharacteristic
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C22×D1111yescharacteristic
391C4⋊C8C22×D1111yescharacteristic
392C4⋊C8C22×D1111yescharacteristic
393C4⋊C8C22×D1111yescharacteristic
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—111no—
398C22⋊C8—111no—
399C22⋊C8—111no—
400C22⋊C8—111no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406#97—21no—
407#97—21no—
408#97—111no—
409#97—111no—
410#97—111no—
411#97—111no—
412#97—221no—
413#97—221no—
414C4×C8—21no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—221no—
422C2×C11—22no—
423C2×C11—41no—
424C2×C11—41no—
425C2×C11#290611yescharacteristic
426C2×C11#291311yescharacteristic
427C2×C11C2×#43011yescharacteristic
428#41—42no—
429C2×Q8Dic11⋊C411yescharacteristic
430C2×D4Dic11⋊C411yescharacteristic
431C2×D4Dic11⋊C411yescharacteristic
432C2×D4Dic11⋊C411yescharacteristic
433C22×C4C2×Dic2211yescharacteristic
434C22×C4C2×Dic2211yescharacteristic
435C22×C4C2×Dic2211yescharacteristic
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442M16—81no—
443M16—222no—
444M16—222no—
445M16—441no—
446M16—441no—
447M16—881no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—81no—
453C2×C8—81no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—222no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—441no—
468C2×C8—881no—
469C2×C8—881no—
470C4⋊C4Dic11⋊C411yescharacteristic
471C4⋊C4Dic11⋊C411yescharacteristic
472C4⋊C4Dic11⋊C411yescharacteristic
473C4⋊C4Dic11⋊C411yescharacteristic
474C4⋊C4Dic11⋊C411yescharacteristic
475C4⋊C4Dic11⋊C411yescharacteristic
476C22⋊C4Dic11⋊C411yescharacteristic
477C22⋊C4Dic11⋊C411yescharacteristic
478C22⋊C4Dic11⋊C411yescharacteristic
479C22⋊C4Dic11⋊C411yescharacteristic
480C22⋊C4Dic11⋊C411yescharacteristic
481C22⋊C4Dic11⋊C411yescharacteristic
482C42C2×Dic2211yescharacteristic
483C42C2×Dic2211yescharacteristic
484C42C2×Dic2211yescharacteristic
485C42C2×C4×D1111yescharacteristic
486C42C2×C4×D1111yescharacteristic
487C42C2×C4×D1111yescharacteristic
488C42C2×C22⋊D1111yescharacteristic
489C42C2×C22⋊D1111yescharacteristic
490C42C2×C22⋊D1111yescharacteristic
491C42C23×D1111yescharacteristic
492C11#1784011yescharacteristic, complemented, Sylow
493C23C2×Dic11⋊C411yescharacteristic
494C23C2×Dic11⋊C411yescharacteristic
495C23C2×Dic11⋊C411yescharacteristic
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4C2×Dic11⋊C411yescharacteristic
516C2×C4C2×Dic11⋊C411yescharacteristic
517C2×C4C2×Dic11⋊C411yescharacteristic
518C2×C4C2×Dic11⋊C411yescharacteristic
519C2×C4C2×Dic11⋊C411yescharacteristic
520C2×C4C2×Dic11⋊C411yescharacteristic
521C2×C4C2×Dic11⋊C411yescharacteristic
522C2×C4C2×Dic11⋊C411yescharacteristic
523C2×C4C2×Dic11⋊C411yescharacteristic
524C2×C4C22×Dic2211yescharacteristic
525C2×C4C22×C4×D1111yescharacteristic
526C2×C4C22×C22⋊D1111yescharacteristic
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—112no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—221no—
537C8—221no—
538C8—221no—
539C8—441no—
540C8—441no—
541C8—441no—
542C8—441no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22#1062273712yes—
552C22C22×Dic11⋊C411yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4D11×#13111yescharacteristic
564C4#1062328111yescharacteristic
565C4#1062336611yescharacteristic
566C4#1062336911yescharacteristic
567C2—22no—
568C2—41no—
569C2—41no—
570C2#1307718211yescharacteristic
571C2#1307721411yescharacteristic
572C2C2×#1062273711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2990C2
socleC22×C11C22×C4⋊C4
prime radicalC2×C11×#41Q8
cosocleC42×C11C24
hypercenter#2990D11
hypocenterC11#17840
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
3. #13067402C2semidirect
4. #13067399C2semidirect
5. #13067397C2semidirect
6. #13067394C2semidirect
7. #13067392C2semidirect
8. #13067390C2semidirect
9. #13067384C2semidirect
10. #13067381C2semidirect
11. #13067377C2semidirect
12. #13067369C2semidirect
13. #13067366C2semidirect
14. C2×#10622117C2semidirect
492. C11#17840semidirect

Maximal subgroups

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

subgroupindex
#130777412
#130775832
#130674022
#130673992
#130673972
#130673942
#130673922
#130673902
#130673842
#130673812
#130673772
#130673692
#130673662
C2×#106221172
C11×#29902
#1784011