Finite Group Databasebeta

← #14770253

Subgroups — #14770253

Order 2816.

1262 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082176C211yesmaximal, characteristic
2M16×C22⋊D11C211yesmaximal, characteristic, complemented
3C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13069591C211yesmaximal, characteristic, complemented
5#13069558C211yesmaximal, characteristic, complemented
6#13069060C211yesmaximal, characteristic, complemented
7#13069056C211yesmaximal, characteristic, complemented
8#13068915C211yesmaximal, characteristic, complemented
9#13068716C211yesmaximal, characteristic, complemented
10#13068714C211yesmaximal, characteristic, complemented
11#13068634C211yesmaximal, characteristic, complemented
12#104×Dic11C211yesmaximal, characteristic, complemented
13C2×#10622193C211yesmaximal, characteristic, complemented
14D11×#339C211yesmaximal, characteristic, complemented
15C11×#1871C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C11×#525C2211yescharacteristic
18#10623359C2211yescharacteristic
19#41×Dic11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×M16×D11C2211yescharacteristic
24#10623189—21no—
25#10623181—21no—
26#10623173C411yescharacteristic, complemented
27#10623172C411yescharacteristic, complemented
28#10623170C411yescharacteristic, complemented
29#10623166C411yescharacteristic, complemented
30#10623149C411yescharacteristic, complemented
31#10623147C411yescharacteristic, complemented
32#10623145C411yescharacteristic, complemented
33#10623142C411yescharacteristic, complemented
34#10623122—21no—
35#10623118—21no—
36#10623088—21no—
37#10623069—21no—
38#10623069—21no—
39C4×#4341—21no—
40D11×#117C2211yescharacteristic
41#10623048C2211yescharacteristic
42C2×(C22⋊D11)⋊C4—21no—
43C2×C42×D11C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C4×C11×C22⋊C4C2211yescharacteristic
47C2×#66901C2211yescharacteristic
48C2×#66901C2211yescharacteristic
49#10622820C2211yescharacteristic
50#10622741—21no—
51#10622740—21no—
52#10622739C2211yescharacteristic
53#10622731C2211yescharacteristic
54M16×Dic11C2211yescharacteristic
55#10622724—21no—
56C8×C22⋊D11—21no—
57C22⋊C4×Dic11—21no—
58C4×(C2×D11)⋊C4C2211yescharacteristic
59C4×Dic11⋊C4C2211yescharacteristic
60C42×Dic11C2211yescharacteristic
61#10622279—21no—
62#10622262—21no—
63C11×#339C2211yescharacteristic
64C11×#339C2211yescharacteristic
65#10622193C2211yescharacteristic
66#10622193C2211yescharacteristic
67#10622193C2211yescharacteristic
68#10622193C2211yescharacteristic
69#10622170C2211yescharacteristic
70#10622170C2211yescharacteristic
71#10622161C2211yescharacteristic
72#10622161C2211yescharacteristic
73#10622161C2211yescharacteristic
74#10622161C2211yescharacteristic
75C2×C11×#41C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11D411yescharacteristic
78C23×Dic11—21no—
79C2×#4341—21no—
80C22×C4×D11—21no—
81C22×C4×D11C2311yescharacteristic
82C2×C11×M16—21no—
83C2×C11×M16—22no—
84C2×C11×M16—41no—
85C2×C11×M16C2311yescharacteristic
86C2×C11×M16C2311yescharacteristic
87C22×C8×C11—21no—
88C11×#123—21no—
89C11×C22⋊Q8C2×C411yescharacteristic, complemented
90C11×C22⋊Q8C2×C411yescharacteristic, complemented
91C11×#121C2×C411yescharacteristic, complemented
92C11×#121C2×C411yescharacteristic, complemented
93C11×#120—21no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C11×#117C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11D411yescharacteristic
102#66999C2×C411yescharacteristic, complemented
103#66999C2×C411yescharacteristic, complemented
104Q8×Dic11C2×C411yescharacteristic, complemented
105Q8×Dic11C2×C411yescharacteristic, complemented
106#66992—21no—
107#66992—21no—
108#66991—21no—
109#66991C2×C411yescharacteristic, complemented
110#66991C2×C411yescharacteristic, complemented
111#66990—21no—
112#66989—21no—
113#66988—21no—
114#66988—21no—
115#66988—21no—
116D4×Dic11—21no—
117D4×Dic11—21no—
118D4×Dic11—21no—
119D4×Dic11C2×C411yescharacteristic, complemented
120D4×Dic11C2×C411yescharacteristic, complemented
121C4×C22⋊D11—21no—
122C4×C22⋊D11—21no—
123C4×C22⋊D11C2×C411yescharacteristic
124C4×C22⋊D11C2×C411yescharacteristic
125C4×C22⋊D11C2×C411yescharacteristic
126C4×C22⋊D11C2×C411yescharacteristic
127C4×C22⋊D11D411yescharacteristic
128C4×C22⋊D11D411yescharacteristic
129C4×C22⋊D11D411yescharacteristic
130C4×C22⋊D11D411yescharacteristic
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4D411yescharacteristic
133#66979—21no—
134#66979—21no—
135#66979—21no—
136#66979C2×C411yescharacteristic, complemented
137#66979C2×C411yescharacteristic, complemented
138#66979C2311yescharacteristic
139#66979C2311yescharacteristic
140C2×C4⋊Dic11C2×C411yescharacteristic, complemented
141C2×C4⋊Dic11C2×C411yescharacteristic, complemented
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4D411yescharacteristic
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—21no—
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—41no—
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154C2×C4×Dic11C2311yescharacteristic
155C2×#4318C2311yescharacteristic
156C2×#4318C2311yescharacteristic
157M16×D11—22no—
158M16×D11—41no—
159C2×#4313—21no—
160C2×C8×D11—21no—
161#66951—21no—
162#66951—21no—
163#66950—21no—
164#66945—21no—
165#66945C2×C411yescharacteristic, complemented
166#66945C2×C411yescharacteristic, complemented
167C4⋊C4×D11C2×C411yescharacteristic, complemented
168C4⋊C4×D11C2×C411yescharacteristic, complemented
169#66943—21no—
170#66943C2×C411yescharacteristic, complemented
171#66943C2×C411yescharacteristic, complemented
172#66942—21no—
173#66942—21no—
174#66941C2×C411yescharacteristic, complemented
175#66941C2×C411yescharacteristic, complemented
176#66940—21no—
177#66939—21no—
178#66939—21no—
179#66938—21no—
180#66938—21no—
181#66936—21no—
182#66936—21no—
183(C22⋊D11)⋊C4—28no—
184(C22⋊D11)⋊C4—21no—
185(C22⋊D11)⋊C4—21no—
186C22⋊C4×D11—21no—
187#66932—21no—
188#66932—21no—
189#66932—21no—
190#66932—21no—
191#66931—21no—
192#66931—21no—
193#66931—21no—
194#66931—21no—
195#66930—21no—
196#66930—21no—
197#66930—21no—
198#66925—21no—
199C42×D11—21no—
200C42×D11—22no—
201C42×D11—41no—
202C4×Dic22—21no—
203C4×Dic22—21no—
204C11×#104—22no—
205C11×#104—41no—
206C11×#95—21no—
207#66901—22no—
208#66901—41no—
209C11⋊#95—21no—
210C11⋊#95—21no—
211C22⋊(C11⋊C8)—21no—
212C22⋊(C11⋊C8)—21no—
213(C2×D11)⋊C8—21no—
214(C2×D11)⋊C8—21no—
215#66879—21no—
216Dic11⋊C8—21no—
217Dic11⋊C8—21no—
218C8×Dic11—21no—
219#22505—111nomaximal, Sylow
220C24×C11C2×D411yescharacteristic
221C23×D11C2×D411yescharacteristic
222C11×#41—21no—
223C11×#41—21no—
224C11×#41—21no—
225C11×#41—21no—
226C2×Q8×C11C22×C411yescharacteristic
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11C22×C411yescharacteristic
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11C22×C411yescharacteristic
239C22×C4×C11C22×C411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2411yescharacteristic
244C2×C22⋊D11—24no—
245C2×C22⋊D11—21no—
246C2×C22⋊D11—21no—
247C2×C22⋊D11C22⋊C411yescharacteristic
248C2×C22⋊D11C22⋊C411yescharacteristic
249C2×C22⋊D11C22⋊C411yescharacteristic
250C2×C22⋊D11C22⋊C411yescharacteristic
251C22×Dic11—24no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—42no—
259C22×Dic11—42no—
260C22×Dic11C2×D411yescharacteristic
261C22×Dic11C2×D411yescharacteristic
262C22×Dic11C2×D411yescharacteristic
263#4341—44no—
264C2×C4×D11—24no—
265C2×C4×D11—21no—
266C2×C4×D11—21no—
267C2×C4×D11—21no—
268C2×C4×D11—21no—
269C2×C4×D11—21no—
270C2×C4×D11—21no—
271C2×C4×D11—42no—
272C2×C4×D11—42no—
273C2×C4×D11C22×C411yescharacteristic
274C2×C4×D11C22×C411yescharacteristic
275C2×C4×D11C2×D411yescharacteristic
276C2×C4×D11C2×D411yescharacteristic
277C2×Dic22—21no—
278C2×Dic22—21no—
279C11×M16—21no—
280C11×M16—21no—
281C11×M16—21no—
282C11×M16—42no—
283C11×M16#4112yescomplemented
284C2×C8×C11—21no—
285C2×C8×C11—21no—
286C2×C8×C11—42no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4C22×C411yescharacteristic
290C11×C4⋊C4C22×C411yescharacteristic
291C11×C22⋊C4—24no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—21no—
295C11×C22⋊C4—21no—
296C11×C22⋊C4—21no—
297C42×C11—21no—
298C42×C11—21no—
299C42×C11—21no—
300C42×C11—21no—
301C42×C11—21no—
302C22⋊Dic11—21no—
303C22⋊Dic11—21no—
304C22⋊Dic11—21no—
305C22⋊Dic11—21no—
306C22⋊Dic11—21no—
307C22⋊Dic11—21no—
308C22⋊Dic11—21no—
309C22⋊Dic11—21no—
310C22⋊Dic11C22⋊C411yescharacteristic
311C22⋊Dic11C22⋊C411yescharacteristic
312C22⋊Dic11C22⋊C411yescharacteristic
313C22⋊Dic11C22⋊C411yescharacteristic
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—21no—
316(C2×D11)⋊C4—21no—
317(C2×D11)⋊C4—21no—
318(C2×D11)⋊C4—21no—
319(C2×D11)⋊C4C22⋊C411yescharacteristic
320(C2×D11)⋊C4C22⋊C411yescharacteristic
321(C2×D11)⋊C4C22⋊C411yescharacteristic
322(C2×D11)⋊C4C22⋊C411yescharacteristic
323C4⋊Dic11—21no—
324C4⋊Dic11—21no—
325C4⋊Dic11—21no—
326C4⋊Dic11—21no—
327C4⋊Dic11—21no—
328C4⋊Dic11—21no—
329C4⋊Dic11C22×C411yescharacteristic
330C4⋊Dic11C22×C411yescharacteristic
331C4⋊Dic11C22×C411yescharacteristic
332C4⋊Dic11C22×C411yescharacteristic
333Dic11⋊C4—24no—
334Dic11⋊C4—21no—
335Dic11⋊C4—21no—
336Dic11⋊C4—21no—
337Dic11⋊C4—21no—
338Dic11⋊C4—21no—
339Dic11⋊C4—21no—
340Dic11⋊C4—21no—
341Dic11⋊C4—21no—
342Dic11⋊C4C22⋊C411yescharacteristic
343Dic11⋊C4C22⋊C411yescharacteristic
344Dic11⋊C4C22⋊C411yescharacteristic
345Dic11⋊C4C22⋊C411yescharacteristic
346C4×Dic11—24no—
347C4×Dic11—21no—
348C4×Dic11—21no—
349C4×Dic11—21no—
350C4×Dic11—21no—
351C4×Dic11—21no—
352C4×Dic11—21no—
353C4×Dic11—21no—
354C4×Dic11—21no—
355C4×Dic11—21no—
356C4×Dic11—21no—
357C4×Dic11—21no—
358C4×Dic11—42no—
359C4×Dic11—42no—
360C4×Dic11—42no—
361C4×Dic11C22×C411yescharacteristic
362C4×Dic11C22×C411yescharacteristic
363C4×Dic11C2×D411yescharacteristic
364C4×Dic11C2×D411yescharacteristic
365C4×Dic11#4112yescomplemented
366#4318—21no—
367#4318—21no—
368#4318—21no—
369#4318—21no—
370C2×C11⋊C8—21no—
371C2×C11⋊C8—21no—
372#4313—42no—
373C8×D11—42no—
374#3475—111no—
375D4×M16—111no—
376C42×D4—111no—
377#1994—111no—
378#1986—111no—
379#1896—111no—
380#1896—111no—
381#1871—111no—
382#1871D1111yescharacteristic, complemented
383#1826—111no—
384#1826—111no—
385#1806—111no—
386C4×#104—111no—
387C2×#339—111no—
388C2×#339—111no—
389C23×C11—21no—
390C23×C11—21no—
391C23×C11—22no—
392C23×C11—21no—
393C23×C11—41no—
394C23×C11C2×C22⋊C411yescharacteristic
395C23×C11C2×C22⋊C411yescharacteristic
396C23×C11C22×D411yescharacteristic
397C22×D11—21no—
398C22×D11—21no—
399C22×D11—22no—
400C22×D11—41no—
401C22×D11C2×C22⋊C411yescharacteristic
402C22×D11C2×C22⋊C411yescharacteristic
403Q8×C11—21no—
404Q8×C11—21no—
405D4×C11—21no—
406D4×C11—21no—
407D4×C11—41no—
408D4×C11—41no—
409D4×C11—42no—
410D4×C11—81no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11C2×C22⋊C411yescharacteristic
433C2×C4×C11C2×C22⋊C411yescharacteristic
434C2×C4×C11C23×C411yescharacteristic
435C2×C4×C11C22×D411yescharacteristic
436C2×C4×C11C2×#4111yescharacteristic
437C2×C4×C11C2×#4111yescharacteristic
438C2×C4×C11H(5,𝔽2)11yescharacteristic
439C2×C4×C112−1+411yescharacteristic
440C22⋊D11—22no—
441C22⋊D11—22no—
442C22⋊D11—22no—
443C22⋊D11—42no—
444C22⋊D11—81no—
445C22⋊D11#10414yescomplemented
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—21no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—21no—
454C2×Dic11—21no—
455C2×Dic11—21no—
456C2×Dic11—21no—
457C2×Dic11—41no—
458C2×Dic11—48no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—42no—
462C2×Dic11—42no—
463C2×Dic11—81no—
464C2×Dic11—81no—
465C2×Dic11C2×C22⋊C411yescharacteristic
466C2×Dic11C2×C22⋊C411yescharacteristic
467C2×Dic11C2×C22⋊C411yescharacteristic
468C2×Dic11C2×C22⋊C411yescharacteristic
469C2×Dic11C2×C22⋊C411yescharacteristic
470C2×Dic11C2×C22⋊C411yescharacteristic
471C4×D11—21no—
472C4×D11—21no—
473C4×D11—21no—
474C4×D11—21no—
475C4×D11—21no—
476C4×D11—21no—
477C4×D11—21no—
478C4×D11—21no—
479C4×D11—48no—
480C4×D11—42no—
481C4×D11—81no—
482Dic22—42no—
483Dic22—81no—
484C8×C11—22no—
485C8×C11—41no—
486C11⋊C8—41no—
487C11⋊C8—41no—
488C22×M16—111no—
489C22×M16C2×D1111yescharacteristic
490#556—111no—
491#555—111no—
492#554—111no—
493#553—111no—
494#553—111no—
495#552—111no—
496#552—111no—
497#552—221no—
498#551—221no—
499#551—221no—
500#547—111no—
501#546—221no—
502#533—111no—
503#529—221no—
504#529—221no—
505#529—221no—
506#525—111no—
507#525C2×D1111yescharacteristic
508C4×#41—111no—
509C4×#41—221no—
510C2×C4×D4—111no—
511C2×C4×D4—221no—
512C2×#117—111no—
513C2×#117—111no—
514C22×C42—111no—
515C22×C42—111no—
516#436—221no—
517#435—221no—
518#435—221no—
519C8×D4—221no—
520#423—111no—
521C2×#104—111no—
522C2×#104—111no—
523C2×#104C2×D1111yescharacteristic
524C2×#104C2×D1111yescharacteristic
525#407—111no—
526#407—111no—
527C4×M16—111no—
528C4×C4⋊C4—111no—
529C4×C4⋊C4—221no—
530C4×C22⋊C4—111no—
531C4×C22⋊C4—221no—
532C4×C22⋊C4—221no—
533C4×C22⋊C4C2×D1111yescharacteristic
534C43—111no—
535#339—111no—
536#339—111no—
537#339—111no—
538#339—111no—
539#339—111no—
540#339—111no—
541#339—111no—
542#339—111no—
543#339—111no—
544#339—111no—
545#339C2×D1111yescharacteristic
546#339C2×D1111yescharacteristic
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—21no—
550C22×C11—21no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—21no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—41no—
557C22×C11—41no—
558C22×C11—41no—
559C22×C11C2×#10412yes—
560C22×C11C22×C22⋊C411yescharacteristic
561C22×C11#54611yescharacteristic
562C22×C11#54711yescharacteristic
563C2×D11—21no—
564C2×D11—21no—
565C2×D11—21no—
566C2×D11—21no—
567C2×D11—21no—
568C2×D11—42no—
569C2×D11—42no—
570C2×D11C2×#10412yes—
571C4×C11—21no—
572C4×C11—21no—
573C4×C11—42no—
574C4×C11—42no—
575C4×C11—41no—
576C4×C11—41no—
577C4×C11—41no—
578C4×C11C4×#4111yescharacteristic
579C4×C11#52011yescharacteristic
580C4×C11#54611yescharacteristic
581C4×C11#54711yescharacteristic
582Dic11—24no—
583Dic11—21no—
584Dic11—21no—
585Dic11—21no—
586Dic11—21no—
587Dic11—21no—
588Dic11—42no—
589Dic11—41no—
590Dic11—41no—
591Dic11—41no—
592Dic11—41no—
593Dic11C2×#10412yes—
594C2×#41—221no—
595C2×#41C22×D1111yescharacteristic
596C22×D4—111no—
597C23×C4—111no—
598C23×C4—221no—
599C23×C4—221no—
600C23×C4C22×D1111yescharacteristic
601C2×M16—21no—
602C2×M16—22no—
603C2×M16—41no—
604C2×M16—111no—
605C2×M16—111no—
606C2×M16—221no—
607C2×M16—222no—
608C2×M16—441no—
609C2×M16C22×D1111yescharacteristic
610C2×M16C22×D1111yescharacteristic
611C22×C8—21no—
612C22×C8—221no—
613C4⋊Q8—111no—
614C4⋊Q8—111no—
615#126—221no—
616#126—221no—
617#126—221no—
618#126—221no—
619#126—221no—
620#126—221no—
621#125—111no—
622#125—111no—
623#125—221no—
624#125—221no—
625#125—221no—
626#124—221no—
627#124—221no—
628#124—221no—
629#123—21no—
630#123—221no—
631#123—221no—
632#123—221no—
633#123—221no—
634#123—221no—
635#123—221no—
636#123—221no—
637C22⋊Q8—111no—
638C22⋊Q8—111no—
639C22⋊Q8—221no—
640C22⋊Q8—221no—
641C22⋊Q8—221no—
642C22⋊Q8—221no—
643C22⋊Q8—221no—
644C22⋊Q8C4×D1111yescharacteristic, complemented
645C22⋊Q8C4×D1111yescharacteristic, complemented
646#121—111no—
647#121—111no—
648#121—221no—
649#121—221no—
650#121—221no—
651#121C4×D1111yescharacteristic, complemented
652#121C4×D1111yescharacteristic, complemented
653#120—21no—
654#120—221no—
655C4×Q8—111no—
656C4×Q8—111no—
657C4×Q8—221no—
658C4×Q8—221no—
659C4×Q8—221no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—111no—
663C4×D4—111no—
664C4×D4—111no—
665C4×D4—111no—
666C4×D4—111no—
667C4×D4—111no—
668C4×D4—111no—
669C4×D4—111no—
670C4×D4—111no—
671C4×D4—111no—
672C4×D4—221no—
673C4×D4—221no—
674C4×D4—228no—
675C4×D4—221no—
676C4×D4—221no—
677C4×D4—221no—
678C4×D4—221no—
679C4×D4—221no—
680#117—111no—
681#117—111no—
682#117—111no—
683#117—111no—
684#117—111no—
685#117—111no—
686#117—221no—
687#117—221no—
688#117—221no—
689#117—221no—
690#117—221no—
691#117—221no—
692#117—221no—
693#117—221no—
694#117C22×D1111yescharacteristic
695C2×C4⋊C4—111no—
696C2×C4⋊C4—111no—
697C2×C4⋊C4—111no—
698C2×C4⋊C4—111no—
699C2×C4⋊C4—111no—
700C2×C4⋊C4—221no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—111no—
703C2×C22⋊C4—111no—
704C2×C22⋊C4—221no—
705C2×C22⋊C4—221no—
706C2×C22⋊C4—221no—
707C2×C42—111no—
708C2×C42—111no—
709C2×C42—111no—
710C2×C42—222no—
711C2×C42—221no—
712C2×C42—221no—
713C2×C42—222no—
714C2×C42—221no—
715C2×C42—221no—
716C2×C42—221no—
717C2×C42—221no—
718C2×C42—221no—
719C2×C42—441no—
720C2×C42—441no—
721C2×C42C22×D1111yescharacteristic
722C2×C42C22×D1111yescharacteristic
723C4⋊C8—221no—
724C4⋊C8—221no—
725#104—22no—
726#104—41no—
727#104—222no—
728#104—441no—
729C22⋊C8—221no—
730C22⋊C8—221no—
731C22⋊C8—221no—
732C22⋊C8—221no—
733#97—221no—
734C4×C8—221no—
735#95—21no—
736#95—221no—
737#95—221no—
738C2×C11—21no—
739C2×C11—21no—
740C2×C11—22no—
741C2×C11—41no—
742C2×C11—81no—
743C2×C11#233911yescharacteristic
744C2×C11C22×#10411yescharacteristic
745C2×C11#290111yescharacteristic
746D11—22no—
747D11—41no—
748C24—111no—
749C24D4×D1111yescharacteristic
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—444no—
755C2×Q8—221no—
756C2×Q8—221no—
757C2×Q8C2×C4×D1111yescharacteristic
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—111no—
762C2×D4—111no—
763C2×D4—111no—
764C2×D4—111no—
765C2×D4—224no—
766C2×D4—221no—
767C2×D4—221no—
768C2×D4C2×C4×D1111yescharacteristic
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—111no—
777C22×C4—111no—
778C22×C4—111no—
779C22×C4—111no—
780C22×C4—111no—
781C22×C4—111no—
782C22×C4—111no—
783C22×C4—221no—
784C22×C4—224no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—224no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—442no—
798C22×C4—442no—
799C22×C4—442no—
800C22×C4—442no—
801C22×C4C2×C4×D1111yescharacteristic
802C22×C4C2×C4×D1111yescharacteristic
803C22×C4D4×D1111yescharacteristic
804C22×C4D4×D1111yescharacteristic
805C22×C4D4×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807M16—21no—
808M16—21no—
809M16—21no—
810M16—42no—
811M16—221no—
812M16—221no—
813M16—221no—
814M16—221no—
815M16—442no—
816M16#434112yescomplemented
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—42no—
820C2×C8—221no—
821C2×C8—221no—
822C2×C8—442no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—111no—
826C4⋊C4—111no—
827C4⋊C4—111no—
828C4⋊C4—111no—
829C4⋊C4—111no—
830C4⋊C4—111no—
831C4⋊C4—111no—
832C4⋊C4—111no—
833C4⋊C4—221no—
834C4⋊C4—221no—
835C4⋊C4—221no—
836C4⋊C4—221no—
837C4⋊C4—221no—
838C4⋊C4—221no—
839C4⋊C4—221no—
840C4⋊C4—221no—
841C4⋊C4—221no—
842C4⋊C4—221no—
843C4⋊C4—221no—
844C4⋊C4—221no—
845C4⋊C4—224no—
846C4⋊C4—221no—
847C4⋊C4—221no—
848C4⋊C4C2×C4×D1111yescharacteristic
849C4⋊C4C2×C4×D1111yescharacteristic
850C22⋊C4—24no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—111no—
857C22⋊C4—111no—
858C22⋊C4—111no—
859C22⋊C4—111no—
860C22⋊C4—111no—
861C22⋊C4—111no—
862C22⋊C4—111no—
863C22⋊C4—111no—
864C22⋊C4—221no—
865C22⋊C4—221no—
866C22⋊C4—221no—
867C22⋊C4—221no—
868C22⋊C4—224no—
869C22⋊C4—221no—
870C22⋊C4—221no—
871C22⋊C4—221no—
872C22⋊C4—221no—
873C22⋊C4—221no—
874C22⋊C4—221no—
875C22⋊C4—221no—
876C22⋊C4—221no—
877C42—21no—
878C42—21no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—111no—
883C42—111no—
884C42—111no—
885C42—111no—
886C42—112no—
887C42—221no—
888C42—221no—
889C42—221no—
890C42—221no—
891C42—224no—
892C42—221no—
893C42—221no—
894C42—221no—
895C42—221no—
896C42—221no—
897C42—221no—
898C42—221no—
899C42—442no—
900C42—442no—
901C42—442no—
902C11#2250511yescharacteristic, complemented, Sylow
903C23—21no—
904C23—21no—
905C23—22no—
906C23—21no—
907C23—41no—
908C23—111no—
909C23—111no—
910C23—222no—
911C23—221no—
912C23—221no—
913C23—441no—
914C23C22⋊C4×D1111yescharacteristic
915C23C22⋊C4×D1111yescharacteristic
916C23C2×D4×D1111yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—442no—
920Q8—881no—
921D4—21no—
922D4—21no—
923D4—41no—
924D4—41no—
925D4—42no—
926D4—81no—
927D4—114no—
928D4—222no—
929D4—222no—
930D4—222no—
931D4—442no—
932D4—881no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—111no—
955C2×C4—111no—
956C2×C4—111no—
957C2×C4—111no—
958C2×C4—111no—
959C2×C4—111no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—221no—
965C2×C4—221no—
966C2×C4—221no—
967C2×C4—221no—
968C2×C4—221no—
969C2×C4—221no—
970C2×C4—221no—
971C2×C4—221no—
972C2×C4—221no—
973C2×C4—221no—
974C2×C4—222no—
975C2×C4—221no—
976C2×C4—221no—
977C2×C4—221no—
978C2×C4—221no—
979C2×C4—448no—
980C2×C4—442no—
981C2×C4—442no—
982C2×C4—441no—
983C2×C4—448no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4—442no—
987C2×C4—881no—
988C2×C4—881no—
989C2×C4—881no—
990C2×C4C22⋊C4×D1111yescharacteristic
991C2×C4C22⋊C4×D1111yescharacteristic
992C2×C4C22×C4×D1111yescharacteristic
993C2×C4C2×D4×D1111yescharacteristic
994C2×C4C2×#434111yescharacteristic
995C2×C4#6703711yescharacteristic
996C2×C4#41×D1111yescharacteristic
997C2×C4#6704311yescharacteristic
998C8—22no—
999C8—41no—
1000C8—441no—
1001C8—441no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—112no—
1015C22—221no—
1016C22—221no—
1017C22—221no—
1018C22—221no—
1019C22—221no—
1020C22—442no—
1021C22—442no—
1022C22D11×#10412yes—
1023C22C2×C22⋊C4×D1111yescharacteristic
1024C22#1062314111yescharacteristic
1025C22#1062314211yescharacteristic
1026C4—21no—
1027C4—21no—
1028C4—42no—
1029C4—42no—
1030C4—41no—
1031C4—41no—
1032C4—41no—
1033C4—112no—
1034C4—224no—
1035C4—221no—
1036C4—221no—
1037C4—221no—
1038C4—221no—
1039C4—221no—
1040C4—442no—
1041C4—441no—
1042C4—441no—
1043C4—441no—
1044C4—441no—
1045C4C4×#434111yescharacteristic
1046C4#1062307711yescharacteristic
1047C4#1062312211yescharacteristic
1048C4#1062318611yescharacteristic
1049C2—21no—
1050C2—21no—
1051C2—22no—
1052C2—41no—
1053C2—81no—
1054C2—222no—
1055C2—441no—
1056C2#1307144211yescharacteristic
1057C2C2×D11×#10411yescharacteristic
1058C2#1307716211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1871C2
socleC22×C11C22×C22⋊C4
prime radical#13082176C2
cosocleC22×C4×C11C24
hypercenter#1871D11
hypocenterC11#22505
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D11C2semidirect
3. C4×(C22⋊D11)⋊C4C2semidirect
4. #13069591C2semidirect
5. #13069558C2semidirect
6. #13069060C2semidirect
7. #13069056C2semidirect
8. #13068915C2semidirect
9. #13068716C2semidirect
10. #13068714C2semidirect
11. #13068634C2semidirect
12. #104×Dic11C2semidirect
13. C2×#10622193C2semidirect
14. D11×#339C2semidirect
15. C11×#1871C2semidirect
26. #10623173C4semidirect
27. #10623172C4semidirect
28. #10623170C4semidirect
29. #10623166C4semidirect
30. #10623149C4semidirect
31. #10623147C4semidirect
32. #10623145C4semidirect
33. #10623142C4semidirect
89. C11×C22⋊Q8C2×C4semidirect
90. C11×C22⋊Q8C2×C4semidirect
91. C11×#121C2×C4semidirect
92. C11×#121C2×C4semidirect
102. #66999C2×C4semidirect
103. #66999C2×C4semidirect
104. Q8×Dic11C2×C4semidirect
105. Q8×Dic11C2×C4semidirect
109. #66991C2×C4semidirect
110. #66991C2×C4semidirect
119. D4×Dic11C2×C4semidirect
120. D4×Dic11C2×C4semidirect
136. #66979C2×C4semidirect
137. #66979C2×C4semidirect
140. C2×C4⋊Dic11C2×C4semidirect
141. C2×C4⋊Dic11C2×C4semidirect
165. #66945C2×C4semidirect
166. #66945C2×C4semidirect
167. C4⋊C4×D11C2×C4semidirect
168. C4⋊C4×D11C2×C4semidirect
170. #66943C2×C4semidirect
171. #66943C2×C4semidirect
174. #66941C2×C4semidirect
175. #66941C2×C4semidirect
283. C11×M16#41semidirect
365. C4×Dic11#41semidirect
382. #1871D11semidirect
445. C22⋊D11#104semidirect
644. C22⋊Q8C4×D11semidirect
645. C22⋊Q8C4×D11semidirect
651. #121C4×D11semidirect
652. #121C4×D11semidirect
816. M16#4341semidirect
902. C11#22505semidirect

Maximal subgroups

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

subgroupindex
#130821762
M16×C22⋊D112
C4×(C22⋊D11)⋊C42
#130695912
#130695582
#130690602
#130690562
#130689152
#130687162
#130687142
#130686342
#104×Dic112
C2×#106221932
D11×#3392
C11×#18712
#2250511