Finite Group Databasebeta

← #14723020

Subgroups — #14723020

Order 2816.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077578C211yesmaximal, characteristic
2#13077277C211yesmaximal, characteristic
3#13077181C211yesmaximal, characteristic
4#13067404C211yesmaximal, characteristic, complemented
5#13067403C211yesmaximal, characteristic, complemented
6#13067400C211yesmaximal, characteristic, complemented
7#13067399C211yesmaximal, characteristic, complemented
8#13067389C211yesmaximal, characteristic, complemented
9#13067385C211yesmaximal, characteristic, complemented
10#13067383C211yesmaximal, characteristic, complemented
11#13067382C211yesmaximal, characteristic, complemented
12#13067373C211yesmaximal, characteristic, complemented
13#13067365C211yesmaximal, characteristic, complemented
14D11×#334C211yesmaximal, characteristic, complemented
15C11×#1565C211yesmaximal, characteristic, complemented
16C2×#66954—21no—
17C4×#4339C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21#10622741C411yescharacteristic
22#10622741C411yescharacteristic
23#10622740C411yescharacteristic
24#10622740C411yescharacteristic
25#10622715—21no—
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29#10622452—21no—
30#10622452—21no—
31#10622450C2211yescharacteristic
32#10622450C2211yescharacteristic
33#10622450C2211yescharacteristic
34#10622448C2211yescharacteristic
35#10622446C2211yescharacteristic
36D11×C4⋊C8C2211yescharacteristic
37D11×C4⋊C8C2211yescharacteristic
38D11×C4⋊C8C2211yescharacteristic
39#10622340—21no—
40#10622333—21no—
41#10622319C411yescharacteristic
42#10622319C411yescharacteristic
43#10622314C411yescharacteristic
44#10622314C411yescharacteristic
45#10622303—21no—
46#10622302—21no—
47C4×#4313C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622118C2211yescharacteristic
58#10622118C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×#4339D411yescharacteristic
68C2×C11×M16C2×C411yescharacteristic
69C2×C11×M16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C4×C22⋊D11C2×C411yescharacteristic
73C4×C22⋊D11C2×C411yescharacteristic
74C4×C22⋊D11Q811yescharacteristic
75C4×C22⋊D11Q811yescharacteristic
76#66979D411yescharacteristic
77C2×#4318—21no—
78#66954—44no—
79C2×#4313—21no—
80C2×#4313—21no—
81C2×#4313—21no—
82C2×#4313C2×C411yescharacteristic
83C2×#4313C2×C411yescharacteristic
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11C2×C411yescharacteristic
88C2×C8×D11C2×C411yescharacteristic
89C4×D44C2×C411yescharacteristic
90C4×D44Q811yescharacteristic
91#66925D411yescharacteristic
92#66925D411yescharacteristic
93C42×D11C2311yescharacteristic
94C42×D11C2311yescharacteristic
95C4×Dic22C2×C411yescharacteristic
96C4×Dic22Q811yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C11×#97C2×C411yescharacteristic
104C11×#97C2×C411yescharacteristic
105C4×C8×C11—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)C2×C411yescharacteristic
110C22⋊(C11⋊C8)C2×C411yescharacteristic
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8C2×C411yescharacteristic
114(C2×D11)⋊C8C2×C411yescharacteristic
115(C2×D11)⋊C8C2×C411yescharacteristic
116(C2×D11)⋊C8C2×C411yescharacteristic
117#66879—21no—
118#66879C2×C411yescharacteristic
119#66879C2×C411yescharacteristic
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8C2×C411yescharacteristic
127Dic11⋊C8C2×C411yescharacteristic
128Dic11⋊C8C2×C411yescharacteristic
129Dic11⋊C8C2×C411yescharacteristic
130C8×Dic11—21no—
131C8×Dic11C2×C411yescharacteristic
132C8×Dic11C2×C411yescharacteristic
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)C2×C411yescharacteristic
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143#17830—111nomaximal, Sylow
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×Q811yescharacteristic
147C2×C22⋊D11C4⋊C411yescharacteristic
148C2×C22⋊D11C4⋊C411yescharacteristic
149#4339—22no—
150#4339—22no—
151C2×D44C4⋊C411yescharacteristic
152C2×C4×D11C22×C411yescharacteristic
153C2×C4×D11C22×C411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×C4×D11C2×D411yescharacteristic
156C2×C4×D11C2×Q811yescharacteristic
157C2×C4×D11C2×Q811yescharacteristic
158C2×Dic22C4⋊C411yescharacteristic
159C11×M16—22no—
160C11×M16—41no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—42no—
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C42×C11C22×C411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2×Q811yescharacteristic
173C42×C11C2411yescharacteristic
174C22⋊Dic11C4⋊C411yescharacteristic
175C22⋊Dic11C4⋊C411yescharacteristic
176(C2×D11)⋊C4C4⋊C411yescharacteristic
177(C2×D11)⋊C4C4⋊C411yescharacteristic
178(C2×D11)⋊C4C4⋊C411yescharacteristic
179(C2×D11)⋊C4C4⋊C411yescharacteristic
180C4⋊Dic11C4⋊C411yescharacteristic
181C4⋊Dic11C4⋊C411yescharacteristic
182Dic11⋊C4C4⋊C411yescharacteristic
183Dic11⋊C4C4⋊C411yescharacteristic
184Dic11⋊C4C4⋊C411yescharacteristic
185Dic11⋊C4C4⋊C411yescharacteristic
186C4×Dic11C22×C411yescharacteristic
187C4×Dic11C22×C411yescharacteristic
188C4×Dic11C2×D411yescharacteristic
189C4×Dic11C2×D411yescharacteristic
190C4×Dic11C2×Q811yescharacteristic
191C4×Dic11C2×Q811yescharacteristic
192#4318—42no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C22×C411yescharacteristic
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201#4313—22no—
202#4313—41no—
203#4313—42no—
204#4313—42no—
205#4313—42no—
206C8×D11—22no—
207C8×D11—41no—
208C8×D11—42no—
209C8×D11—42no—
210C8×D11—42no—
211#2965—111no—
212#2925—111no—
213#2906—111no—
214#1574—111no—
215#1574—111no—
216#1573—111no—
217#1573—111no—
218#1571—111no—
219#1570—111no—
220#1569—111no—
221#1569—111no—
222#1567—111no—
223#1565—111no—
224#1565D1111yescharacteristic, complemented
225C2×#334—111no—
226C23×C11C2×C4⋊C411yescharacteristic
227C22×D11C2×C4⋊C411yescharacteristic
228C22×D11C2×C4⋊C411yescharacteristic
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11C2×C4⋊C411yescharacteristic
235C2×C4×C11C2×C4⋊C411yescharacteristic
236C2×C4×C11C2×C4⋊C411yescharacteristic
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×Q811yescharacteristic
240C22⋊D11—22no—
241C22⋊D11—22no—
242C2×Dic11C2×C4⋊C411yescharacteristic
243C2×Dic11C2×C4⋊C411yescharacteristic
244C2×Dic11C2×C4⋊C411yescharacteristic
245C2×Dic11C2×C4⋊C411yescharacteristic
246C2×Dic11C2×C4⋊C411yescharacteristic
247C2×Dic11C2×C4⋊C411yescharacteristic
248D44—22no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11AGL(1,ℤ/8)12yes—
258C4×D11#13712yes—
259Dic22—22no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11#13112yescomplemented
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C2×#131—221no—
277C4×#41—111no—
278#446—111no—
279#446—111no—
280#436—111no—
281#436—111no—
282#435—111no—
283#435—111no—
284#435—111no—
285#435—111no—
286#433—221no—
287#433—221no—
288#432—111no—
289#432—111no—
290#431—111no—
291#431—111no—
292#431—111no—
293#431—111no—
294#431C2×D1111yescharacteristic
295#424—221no—
296#424—221no—
297#424—221no—
298#423—111no—
299#423—111no—
300#423—111no—
301#423—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8—111no—
304C2×C4⋊C8—111no—
305C2×C4⋊C8C2×D1111yescharacteristic
306#408—221no—
307#405—221no—
308C4×M16—111no—
309C4×M16C2×D1111yescharacteristic
310C2×C4×C8—111no—
311#335—111no—
312#335—111no—
313#335—111no—
314#335—111no—
315#335—111no—
316#335—111no—
317#335C2×D1111yescharacteristic
318#335C2×D1111yescharacteristic
319#334—111no—
320#334—111no—
321#334—111no—
322#334—111no—
323#334—111no—
324#334—111no—
325#334C2×D1111yescharacteristic
326#334C2×D1111yescharacteristic
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11C22×C4⋊C411yescharacteristic
331C2×D11—21no—
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—21no—
336C2×D11#42812yes—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11C2×#13111yescharacteristic
342C4×C11#56811yescharacteristic
343C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
344C4×C11C2×#13711yescharacteristic
345Dic11—21no—
346Dic11—21no—
347Dic11—21no—
348Dic11—21no—
349Dic11—21no—
350Dic11#42812yes—
351C2×#41—111no—
352#131—444no—
353C2×M16—111no—
354C2×M16—111no—
355C2×M16—221no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16—221no—
359C2×M16C4×D1111yescharacteristic
360C2×M16C4×D1111yescharacteristic
361C22×C8—21no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8—221no—
365C22×C8—221no—
366C22×C8—221no—
367C4×Q8—111no—
368C4×Q8—111no—
369C4×D4—111no—
370C4×D4—111no—
371C4×D4—111no—
372C4×D4—111no—
373C4×D4—111no—
374C4×D4—111no—
375#117—111no—
376#117—111no—
377#117—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42C22×D1111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403C22⋊C8—21no—
404C22⋊C8—111no—
405C22⋊C8—111no—
406C22⋊C8—111no—
407C22⋊C8—111no—
408C22⋊C8—111no—
409C22⋊C8—111no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—111no—
414#97—111no—
415#97—221no—
416#97—221no—
417#97C4×D1111yescharacteristic
418#97C4×D1111yescharacteristic
419C4×C8—21no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11—41no—
428C2×C11#290611yescharacteristic
429C2×C11C2×#42811yescharacteristic
430C2×C11#291611yescharacteristic
431D11—22no—
432D11—41no—
433#41—222no—
434#41—222no—
435C2×Q8—111no—
436C2×D4—111no—
437C2×D4—111no—
438C2×D4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4D4×D1111yescharacteristic
447C22×C4Q8×D1111yescharacteristic
448M16—22no—
449M16—41no—
450M16—222no—
451M16—441no—
452M16—442no—
453M16—442no—
454M16—442no—
455M16—442no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—222no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—441no—
471C2×C8—442no—
472C2×C8—442no—
473C2×C8—442no—
474C2×C8C2×C4×D1111yescharacteristic
475C2×C8C2×C4×D1111yescharacteristic
476C2×C8C2×C4×D1111yescharacteristic
477C2×C8C2×C4×D1111yescharacteristic
478C4⋊C4—111no—
479C4⋊C4—111no—
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—111no—
483C4⋊C4—111no—
484C22⋊C4—111no—
485C22⋊C4—111no—
486C22⋊C4—111no—
487C22⋊C4—111no—
488C22⋊C4—111no—
489C22⋊C4—111no—
490C42—111no—
491C42—111no—
492C42—111no—
493C42—111no—
494C42—111no—
495C42—111no—
496C42C2×C4×D1111yescharacteristic
497C42D4×D1111yescharacteristic
498C42Q8×D1111yescharacteristic
499C42C23×D1111yescharacteristic
500C11#1783011yescharacteristic, complemented, Sylow
501C23—111no—
502C23—111no—
503C23C4⋊C4×D1111yescharacteristic
504Q8—222no—
505D4—222no—
506D4—222no—
507D4—222no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—111no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—111no—
517C2×C4—111no—
518C2×C4—111no—
519C2×C4—111no—
520C2×C4—111no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4C4⋊C4×D1111yescharacteristic
530C2×C4C4⋊C4×D1111yescharacteristic
531C2×C4C4⋊C4×D1111yescharacteristic
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4C2×Q8×D1111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8—441no—
550C8#6695412yescomplemented
551C22—21no—
552C22—21no—
553C22—21no—
554C22—112no—
555C22—221no—
556C22—221no—
557C22—221no—
558C22—221no—
559C22—221no—
560C22C2×C4⋊C4×D1111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—112no—
566C4—221no—
567C4—221no—
568C4—221no—
569C4—221no—
570C4—221no—
571C4C2×#6695411yescharacteristic
572C4#1062327611yescharacteristic
573C4D11×AGL(1,ℤ/8)11yescharacteristic
574C4D11×#13711yescharacteristic
575C2—41no—
576C2—222no—
577C2—441no—
578C2#1307718111yescharacteristic
579C2D11×#42811yescharacteristic
580C2#1307722611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1565C2
socleC22×C11C22×C4⋊C4
prime radicalC2×#4339D4
cosocleC42×C11C24
hypercenter#1565D11
hypocenterC11#17830
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
4. #13067404C2semidirect
5. #13067403C2semidirect
6. #13067400C2semidirect
7. #13067399C2semidirect
8. #13067389C2semidirect
9. #13067385C2semidirect
10. #13067383C2semidirect
11. #13067382C2semidirect
12. #13067373C2semidirect
13. #13067365C2semidirect
14. D11×#334C2semidirect
15. C11×#1565C2semidirect
224. #1565D11semidirect
267. C8×C11#131semidirect
500. C11#17830semidirect
550. C8#66954semidirect

Maximal subgroups

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

subgroupindex
#130775782
#130772772
#130771812
#130674042
#130674032
#130674002
#130673992
#130673892
#130673852
#130673832
#130673822
#130673732
#130673652
D11×#3342
C11×#15652
#1783011