Finite Group Databasebeta

← #14720243

Subgroups — #14720243

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67037C211yesmaximal, characteristic
2#13077730C211yesmaximal, characteristic, complemented
3#13077580C211yesmaximal, characteristic, complemented
4#13067059C211yesmaximal, characteristic, complemented
5#13067057C211yesmaximal, characteristic, complemented
6#13067053C211yesmaximal, characteristic, complemented
7#13067052C211yesmaximal, characteristic, complemented
8#13067051C211yesmaximal, characteristic, complemented
9#13067047C211yesmaximal, characteristic, complemented
10#13067039C211yesmaximal, characteristic, complemented
11#13067005C211yesmaximal, characteristic, complemented
12#13067000C211yesmaximal, characteristic, complemented
13#13066995C211yesmaximal, characteristic, complemented
14D11×D4⋊C8C211yesmaximal, characteristic, complemented
15C11×#1486C211yesmaximal, characteristic, complemented
16C2×#67037C411yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18#10623329C411yescharacteristic
19C2×C4×C22⋊D11—21no—
20C2×C4×C22⋊D11—21no—
21#10623077—21no—
22#10623077C411yescharacteristic
23#10623077C411yescharacteristic
24#10623076—21no—
25#10623076C411yescharacteristic
26#10623076C411yescharacteristic
27C4×D4×D11—21no—
28C4×D4×D11C2211yescharacteristic
29C4×D4×D11C2211yescharacteristic
30C4×#4341—21no—
31C4×#4341C2211yescharacteristic
32C4×#4341C2211yescharacteristic
33#10623035C411yescharacteristic
34#10623035C411yescharacteristic
35#10623017—21no—
36#10623017—21no—
37C4×#4339C2211yescharacteristic
38C4×#4339C2211yescharacteristic
39C11×#431C2211yescharacteristic, complemented
40C11×#423C2211yescharacteristic, complemented
41#10622741—21no—
42#10622740—21no—
43#10622539C2211yescharacteristic, complemented
44C4×#4318C2211yescharacteristic, complemented
45#10622450C2211yescharacteristic, complemented
46#10622449—21no—
47#10622449—21no—
48#10622448C2211yescharacteristic, complemented
49#10622446C2211yescharacteristic, complemented
50D11×C4⋊C8C2211yescharacteristic, complemented
51#10622441—21no—
52#10622441—21no—
53#10622342—21no—
54#10622341—21no—
55C4×#4313C2211yescharacteristic, complemented
56#10622298C2211yescharacteristic, complemented
57#10622298C2211yescharacteristic, complemented
58C4×C8×D11C2211yescharacteristic, complemented
59C11×D4⋊C8C2211yescharacteristic, complemented
60C11×D4⋊C8C2211yescharacteristic, complemented
61C11×D4⋊C8C2211yescharacteristic, complemented
62C11×D4⋊C8C2211yescharacteristic, complemented
63D4⋊(C11⋊C8)C2211yescharacteristic, complemented
64D4⋊(C11⋊C8)C2211yescharacteristic, complemented
65D4⋊(C11⋊C8)C2211yescharacteristic, complemented
66D4⋊(C11⋊C8)C2211yescharacteristic, complemented
67#10622122C2211yescharacteristic, complemented
68#10622122C2211yescharacteristic, complemented
69#10622121C2211yescharacteristic, complemented
70#10622121C2211yescharacteristic, complemented
71#10622097C2211yescharacteristic, complemented
72#10622097C2211yescharacteristic, complemented
73#10622094C2211yescharacteristic, complemented
74#10622094C2211yescharacteristic, complemented
75C22×D4×C11C2×C411yescharacteristic
76C23×C4×C11—21no—
77C22×C22⋊D11—21no—
78C22×C22⋊D11—21no—
79#67037—24no—
80#67037—24no—
81C2×#4341—21no—
82C2×#4341C2×C411yescharacteristic
83C2×#4341C2×C411yescharacteristic
84C2×D4×D11—21no—
85C2×D4×D11C2×C411yescharacteristic
86C2×D4×D11C2×C411yescharacteristic
87C2×#4339C2×C411yescharacteristic
88C2×#4339C2×C411yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C2×C11×M16—21no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11C2×C411yescharacteristic
95C4×D4×C11C2×C411yescharacteristic
96C4×D4×C11C2311yescharacteristic
97C4×D4×C11C2311yescharacteristic
98C2×C11×C4⋊C4C2×C411yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103D4×Dic11—21no—
104D4×Dic11—21no—
105D4×Dic11C2×C411yescharacteristic
106D4×Dic11C2×C411yescharacteristic
107D4×Dic11C2×C411yescharacteristic
108D4×Dic11C2×C411yescharacteristic
109C4×C22⋊D11—21no—
110C4×C22⋊D11—21no—
111C4×C22⋊D11—21no—
112C4×C22⋊D11—21no—
113C4×C22⋊D11—21no—
114C4×C22⋊D11—21no—
115C4×C22⋊D11—21no—
116C4×C22⋊D11—21no—
117C4×C22⋊D11—21no—
118C4×C22⋊D11—21no—
119C4×C22⋊D11—21no—
120C4×C22⋊D11—21no—
121C4×C22⋊D11—21no—
122C4×C22⋊D11—21no—
123C4×C22⋊D11D411yescharacteristic
124C4×C22⋊D11D411yescharacteristic
125C4×C22⋊D11D411yescharacteristic
126C4×C22⋊D11D411yescharacteristic
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129#66979C2×C411yescharacteristic
130#66979C2×C411yescharacteristic
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×#4318—21no—
136C2×#4313—21no—
137C2×#4313—21no—
138C2×C8×D11—21no—
139C2×C8×D11—21no—
140#66946—21no—
141#66946C2×C411yescharacteristic
142#66946C2×C411yescharacteristic
143#66945—21no—
144#66945C2×C411yescharacteristic
145#66945C2×C411yescharacteristic
146C4⋊C4×D11—21no—
147C4⋊C4×D11C2×C411yescharacteristic
148C4⋊C4×D11C2×C411yescharacteristic
149#66940—21no—
150#66940C2×C411yescharacteristic
151#66940C2×C411yescharacteristic
152(C22⋊D11)⋊C4—21no—
153(C22⋊D11)⋊C4—21no—
154(C22⋊D11)⋊C4—21no—
155(C22⋊D11)⋊C4—21no—
156(C22⋊D11)⋊C4—21no—
157(C22⋊D11)⋊C4—21no—
158(C22⋊D11)⋊C4—21no—
159(C22⋊D11)⋊C4—21no—
160C22⋊C4×D11—21no—
161C22⋊C4×D11—21no—
162C22⋊C4×D11—21no—
163C22⋊C4×D11—21no—
164#66930—21no—
165#66930—21no—
166#66930—21no—
167#66930—21no—
168C4×D44C2×C411yescharacteristic
169C4×D44D411yescharacteristic
170C4×D44D411yescharacteristic
171C4×D44C2311yescharacteristic
172#66925—21no—
173#66925C2×C411yescharacteristic
174#66925C2×C411yescharacteristic
175C42×D11—21no—
176C42×D11C2311yescharacteristic
177C42×D11C2311yescharacteristic
178C4×Dic22C2×C411yescharacteristic
179C4×Dic22D411yescharacteristic
180C4×Dic22D411yescharacteristic
181C4×Dic22C2311yescharacteristic
182C11×C4⋊C8—21no—
183C11×C4⋊C8—21no—
184C11×C4⋊C8C2311yescharacteristic
185C11×C4⋊C8C2311yescharacteristic
186C11×C22⋊C8—21no—
187C4×C8×C11C2311yescharacteristic
188C4×C8×C11C2311yescharacteristic
189C22⋊(C11⋊C8)—21no—
190(C2×D11)⋊C8—21no—
191(C2×D11)⋊C8—21no—
192(C2×D11)⋊C8—21no—
193(C2×D11)⋊C8—21no—
194#66879—21no—
195#66879—21no—
196Dic11⋊C8—21no—
197Dic11⋊C8—21no—
198Dic11⋊C8—21no—
199Dic11⋊C8—21no—
200C8×Dic11—21no—
201C8×Dic11—21no—
202C4⋊(C11⋊C8)C2311yescharacteristic
203C4⋊(C11⋊C8)C2311yescharacteristic
204#66867—21no—
205#66867—21no—
206C4×C11⋊C8C2311yescharacteristic
207C4×C11⋊C8C2311yescharacteristic
208#17453—111nomaximal, Sylow
209C24×C11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C2×D4×C11—22no—
213C2×D4×C11—22no—
214C2×D4×C11—21no—
215C2×D4×C11C22×C411yescharacteristic
216C2×D4×C11C22×C411yescharacteristic
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—81no—
223C22×C4×C11—81no—
224C22×C4×C11C22×C411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—21no—
230C2×C22⋊D11—21no—
231C2×C22⋊D11—21no—
232C2×C22⋊D11—21no—
233C2×C22⋊D11—21no—
234C2×C22⋊D11C22⋊C411yescharacteristic
235C2×C22⋊D11C22⋊C411yescharacteristic
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242#4341—28no—
243#4341—22no—
244#4341—22no—
245#4341—22no—
246#4341M1614yescomplemented
247D4×D11—28no—
248D4×D11—22no—
249D4×D11—22no—
250D4×D11—22no—
251D4×D11M1614yescomplemented
252#4339—22no—
253#4339—22no—
254#4339—22no—
255#4339—22no—
256C2×D44C22⋊C411yescharacteristic
257C2×D44C22×C411yescharacteristic
258C2×C4×D11—21no—
259C2×C4×D11—21no—
260C2×C4×D11—21no—
261C2×C4×D11—21no—
262C2×C4×D11—21no—
263C2×C4×D11—21no—
264C2×C4×D11—21no—
265C2×C4×D11—81no—
266C2×C4×D11—81no—
267C2×C4×D11—81no—
268C2×C4×D11—81no—
269C2×C4×D11C22×C411yescharacteristic
270C2×C4×D11C22×C411yescharacteristic
271C2×C4×D11C2×D411yescharacteristic
272C2×C4×D11C2×D411yescharacteristic
273C2×C4×D11C2×D411yescharacteristic
274C2×C4×D11C2×D411yescharacteristic
275C2×Dic22C22⋊C411yescharacteristic
276C2×Dic22C22×C411yescharacteristic
277C11×M16—81no—
278C2×C8×C11—21no—
279C2×C8×C11—21no—
280C2×C8×C11—21no—
281C2×C8×C11—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4C22×C411yescharacteristic
284C11×C4⋊C4C22×C411yescharacteristic
285C11×C22⋊C4—21no—
286C11×C22⋊C4—21no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C42×C11C22×C411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2411yescharacteristic
293C22⋊Dic11—21no—
294C22⋊Dic11—21no—
295C22⋊Dic11—21no—
296C22⋊Dic11—21no—
297C22⋊Dic11—21no—
298C22⋊Dic11C22⋊C411yescharacteristic
299C22⋊Dic11C22⋊C411yescharacteristic
300(C2×D11)⋊C4—21no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—21no—
305(C2×D11)⋊C4—21no—
306(C2×D11)⋊C4C22⋊C411yescharacteristic
307(C2×D11)⋊C4C22⋊C411yescharacteristic
308(C2×D11)⋊C4C22⋊C411yescharacteristic
309(C2×D11)⋊C4C22⋊C411yescharacteristic
310C4⋊Dic11C22⋊C411yescharacteristic
311C4⋊Dic11C22⋊C411yescharacteristic
312C4⋊Dic11C22×C411yescharacteristic
313C4⋊Dic11C22×C411yescharacteristic
314Dic11⋊C4—21no—
315Dic11⋊C4—21no—
316Dic11⋊C4—21no—
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320Dic11⋊C4C22⋊C411yescharacteristic
321Dic11⋊C4C22⋊C411yescharacteristic
322Dic11⋊C4C22⋊C411yescharacteristic
323Dic11⋊C4C22⋊C411yescharacteristic
324C4×Dic11—21no—
325C4×Dic11—21no—
326C4×Dic11—21no—
327C4×Dic11—21no—
328C4×Dic11—21no—
329C4×Dic11—21no—
330C4×Dic11—21no—
331C4×Dic11C22×C411yescharacteristic
332C4×Dic11C22×C411yescharacteristic
333C4×Dic11C2×D411yescharacteristic
334C4×Dic11C2×D411yescharacteristic
335C4×Dic11C2×D411yescharacteristic
336C4×Dic11C2×D411yescharacteristic
337#4318—42no—
338C2×C11⋊C8—21no—
339C2×C11⋊C8—21no—
340C2×C11⋊C8—21no—
341C2×C11⋊C8—21no—
342#4313—42no—
343#4313—81no—
344C8×D11—42no—
345C8×D11—81no—
346C4×H(5,𝔽2)—111no—
347#2989—111no—
348#2965—111no—
349#1490—111no—
350#1490—111no—
351#1489—111no—
352#1489—111no—
353#1488—111no—
354#1488—111no—
355#1486—111no—
356#1486D1111yescharacteristic, complemented
357#1478—111no—
358#1477—111no—
359#1476—111no—
360C2×D4⋊C8—111no—
361C23×C11—24no—
362C23×C11—21no—
363C23×C11—21no—
364C23×C11—81no—
365C23×C11—81no—
366C23×C11C2×C22⋊C411yescharacteristic
367C22×D11—21no—
368C22×D11—24no—
369C22×D11—24no—
370C22×D11—81no—
371C22×D11—81no—
372C22×D11—81no—
373C22×D11—81no—
374C22×D11C2×C22⋊C411yescharacteristic
375C22×D11C2×C22⋊C411yescharacteristic
376D4×C11—24no—
377D4×C11—21no—
378D4×C11—21no—
379D4×C11C2×M1612yes—
380D4×C11C2×M1612yes—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—81no—
393C2×C4×C11—81no—
394C2×C4×C11—81no—
395C2×C4×C11C2×C22⋊C411yescharacteristic
396C2×C4×C11C2×C22⋊C411yescharacteristic
397C2×C4×C11C2×C22⋊C411yescharacteristic
398C2×C4×C11C23×C411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C22⋊D11—24no—
402C22⋊D11—24no—
403C22⋊D11—24no—
404C22⋊D11—22no—
405C22⋊D11—24no—
406C22⋊D11—22no—
407C22⋊D11—24no—
408C2×Dic11—24no—
409C2×Dic11—21no—
410C2×Dic11—24no—
411C2×Dic11—21no—
412C2×Dic11—21no—
413C2×Dic11—81no—
414C2×Dic11—81no—
415C2×Dic11—81no—
416C2×Dic11—81no—
417C2×Dic11C2×C22⋊C411yescharacteristic
418C2×Dic11C2×C22⋊C411yescharacteristic
419C2×Dic11C2×C22⋊C411yescharacteristic
420C2×Dic11C2×C22⋊C411yescharacteristic
421C2×Dic11C2×C22⋊C411yescharacteristic
422C2×Dic11C2×C22⋊C411yescharacteristic
423D44—22no—
424D44—21no—
425D44C2×M1612yes—
426C4×D11—24no—
427C4×D11—21no—
428C4×D11—21no—
429C4×D11—21no—
430C4×D11—21no—
431C4×D11—21no—
432C4×D11—21no—
433C4×D11—41no—
434C4×D11—41no—
435C4×D11—41no—
436C4×D11—41no—
437C4×D11—81no—
438C4×D11—81no—
439C4×D11—81no—
440C4×D11—81no—
441C4×D11—81no—
442C4×D11C2×M1612yes—
443C4×D11C2×M1612yes—
444Dic22—21no—
445Dic22—22no—
446Dic22C2×M1612yes—
447C8×C11—41no—
448C8×C11—41no—
449C8×C11—41no—
450C8×C11—41no—
451C11⋊C8—22no—
452C11⋊C8—41no—
453C11⋊C8—41no—
454C11⋊C8—41no—
455C2×H(5,𝔽2)—111no—
456#520—111no—
457#520—111no—
458#520—111no—
459#520—111no—
460#520—221no—
461#518—111no—
462#518—111no—
463#518—111no—
464#518—221no—
465#518—221no—
466#518—221no—
467C4×#41—111no—
468C4×#41—111no—
469C4×#41—111no—
470C4×#41—111no—
471C4×#41—221no—
472C2×C4×D4—111no—
473C2×C4×D4—111no—
474C2×C4×D4—221no—
475C2×C4×D4—221no—
476C2×C4×D4—221no—
477C2×C4×D4C2×D1111yescharacteristic
478#446—221no—
479#446—221no—
480#436—221no—
481#436—221no—
482#435—221no—
483#435—221no—
484#435—221no—
485#435—221no—
486#432—111no—
487#432—111no—
488#431—111no—
489#431—111no—
490#431—111no—
491#431C2×D1111yescharacteristic, complemented
492#423—111no—
493#423C2×D1111yescharacteristic, complemented
494C2×C4⋊C8—111no—
495C4×M16—111no—
496C4×M16—111no—
497C2×C4×C8—111no—
498Q8⋊C8—111no—
499Q8⋊C8—111no—
500Q8⋊C8—111no—
501Q8⋊C8—111no—
502D4⋊C8—111no—
503D4⋊C8—111no—
504D4⋊C8—111no—
505D4⋊C8—111no—
506D4⋊C8—111no—
507D4⋊C8—111no—
508D4⋊C8—111no—
509D4⋊C8—111no—
510D4⋊C8C2×D1111yescharacteristic, complemented
511D4⋊C8C2×D1111yescharacteristic, complemented
512D4⋊C8C2×D1111yescharacteristic, complemented
513D4⋊C8C2×D1111yescharacteristic, complemented
514C22×C11—21no—
515C22×C11—22no—
516C22×C11—22no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—41no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11—41no—
523C22×C11—84no—
524C22×C11C22×C22⋊C411yescharacteristic
525C2×D11—21no—
526C2×D11—21no—
527C2×D11—22no—
528C2×D11—21no—
529C2×D11—21no—
530C2×D11—21no—
531C2×D11—41no—
532C2×D11—41no—
533C2×D11—84no—
534C2×D11—84no—
535C2×D11#40712yes—
536C4×C11—21no—
537C4×C11—21no—
538C4×C11—21no—
539C4×C11—21no—
540C4×C11—41no—
541C4×C11—41no—
542C4×C11C22×M1611yescharacteristic
543C4×C11C22×M1611yescharacteristic
544C4×C11#57611yescharacteristic
545C4×C11#57711yescharacteristic
546Dic11—21no—
547Dic11—22no—
548Dic11—21no—
549Dic11—21no—
550Dic11—21no—
551Dic11—21no—
552Dic11—41no—
553Dic11—41no—
554Dic11#40712yes—
555H(5,𝔽2)—224no—
556H(5,𝔽2)—224no—
557C2×#41—111no—
558C2×#41—111no—
559C2×#41—111no—
560C2×#41—111no—
561C2×#41—221no—
562C22×D4—111no—
563C22×D4—111no—
564C22×D4—221no—
565C22×D4—221no—
566C22×D4—221no—
567C22×D4C4×D1111yescharacteristic
568C23×C4—21no—
569C23×C4—221no—
570C23×C4—221no—
571C2×M16—21no—
572C2×M16—221no—
573C2×M16—221no—
574C2×M16—221no—
575C22×C8—221no—
576C22×C8—221no—
577C4×Q8—111no—
578C4×Q8—111no—
579C4×Q8—111no—
580C4×Q8—111no—
581C4×Q8—111no—
582C4×Q8—111no—
583C4×Q8—221no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—111no—
587C4×D4—111no—
588C4×D4—111no—
589C4×D4—111no—
590C4×D4—111no—
591C4×D4—111no—
592C4×D4—111no—
593C4×D4—111no—
594C4×D4—111no—
595C4×D4—111no—
596C4×D4—111no—
597C4×D4—111no—
598C4×D4—111no—
599C4×D4—111no—
600C4×D4—221no—
601C4×D4—221no—
602C4×D4—221no—
603C4×D4—221no—
604C4×D4—221no—
605C4×D4—221no—
606C4×D4—221no—
607C4×D4—221no—
608C4×D4—221no—
609C4×D4—221no—
610C4×D4—221no—
611C4×D4—221no—
612C4×D4—221no—
613C4×D4—221no—
614C4×D4—221no—
615C4×D4—221no—
616C4×D4—221no—
617C4×D4—221no—
618C4×D4—221no—
619C4×D4—221no—
620C4×D4—221no—
621C4×D4—221no—
622C4×D4—221no—
623C4×D4—221no—
624C4×D4—221no—
625C4×D4C4×D1111yescharacteristic
626C4×D4C4×D1111yescharacteristic
627C4×D4C22×D1111yescharacteristic
628C4×D4C22×D1111yescharacteristic
629#117—111no—
630#117—111no—
631#117—111no—
632#117—111no—
633#117—111no—
634#117—111no—
635#117—221no—
636#117—221no—
637#117—221no—
638#117—221no—
639#117—221no—
640#117—221no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—221no—
644C2×C4⋊C4—221no—
645C2×C4⋊C4—221no—
646C2×C4⋊C4C4×D1111yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—221no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4—221no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C22⋊C4—221no—
655C2×C22⋊C4—221no—
656C2×C42—111no—
657C2×C42—111no—
658C2×C42—221no—
659C2×C42—221no—
660C2×C42—221no—
661C2×C42C22×D1111yescharacteristic
662C4⋊C8—21no—
663C4⋊C8—21no—
664C4⋊C8—111no—
665C4⋊C8—111no—
666C4⋊C8—221no—
667C4⋊C8—221no—
668C4⋊C8—221no—
669C4⋊C8—221no—
670C4⋊C8C22×D1111yescharacteristic
671C4⋊C8C22×D1111yescharacteristic
672C22⋊C8—21no—
673C22⋊C8—221no—
674C22⋊C8—221no—
675C22⋊C8—221no—
676C22⋊C8—221no—
677C22⋊C8—221no—
678#97—221no—
679#97—221no—
680#97—221no—
681#97—221no—
682C4×C8—111no—
683C4×C8—111no—
684C4×C8—221no—
685C4×C8—221no—
686C4×C8C22×D1111yescharacteristic
687C4×C8C22×D1111yescharacteristic
688C2×C11—42no—
689C2×C11—42no—
690C2×C11—41no—
691C2×C11C2×#40711yescharacteristic
692C2×C11#289711yescharacteristic
693C2×C11#290111yescharacteristic
694D11—22no—
695D11—41no—
696D11—42no—
697C24—21no—
698C24—221no—
699C24—221no—
700#41—114no—
701#41—222no—
702#41—222no—
703#41—222no—
704#41—222no—
705#41—222no—
706#41—222no—
707#41—228no—
708#41—222no—
709C2×Q8—111no—
710C2×Q8—111no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—21no—
714C2×D4—114no—
715C2×D4—111no—
716C2×D4—111no—
717C2×D4—111no—
718C2×D4—111no—
719C2×D4—222no—
720C2×D4—221no—
721C2×D4—221no—
722C2×D4—222no—
723C2×D4—228no—
724C2×D4—221no—
725C2×D4—221no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—221no—
729C2×D4—222no—
730C2×D4C2×C4×D1111yescharacteristic
731C2×D4C2×C4×D1111yescharacteristic
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—81no—
738C22×C4—81no—
739C22×C4—111no—
740C22×C4—111no—
741C22×C4—111no—
742C22×C4—111no—
743C22×C4—111no—
744C22×C4—111no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—881no—
759C22×C4—881no—
760C22×C4—881no—
761C22×C4—881no—
762C22×C4C2×C4×D1111yescharacteristic
763C22×C4D4×D1111yescharacteristic
764C22×C4D4×D1111yescharacteristic
765M16—81no—
766M16—442no—
767M16—442no—
768M16—881no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—221no—
774C2×C8—221no—
775C2×C8—221no—
776C2×C8—221no—
777C2×C8—442no—
778C2×C8—881no—
779C4⋊C4—21no—
780C4⋊C4—111no—
781C4⋊C4—111no—
782C4⋊C4—111no—
783C4⋊C4—111no—
784C4⋊C4—111no—
785C4⋊C4—111no—
786C4⋊C4—111no—
787C4⋊C4—111no—
788C4⋊C4—221no—
789C4⋊C4—221no—
790C4⋊C4—221no—
791C4⋊C4—221no—
792C4⋊C4—221no—
793C4⋊C4—221no—
794C4⋊C4C2×C4×D1111yescharacteristic
795C4⋊C4C2×C4×D1111yescharacteristic
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—111no—
801C22⋊C4—111no—
802C22⋊C4—111no—
803C22⋊C4—111no—
804C22⋊C4—111no—
805C22⋊C4—111no—
806C22⋊C4—221no—
807C22⋊C4—221no—
808C22⋊C4—221no—
809C22⋊C4—221no—
810C22⋊C4—221no—
811C22⋊C4—221no—
812C22⋊C4—221no—
813C22⋊C4—221no—
814C22⋊C4—221no—
815C22⋊C4—221no—
816C22⋊C4—221no—
817C42—111no—
818C42—111no—
819C42—111no—
820C42—111no—
821C42—111no—
822C42—111no—
823C42—221no—
824C42—221no—
825C42—221no—
826C42—221no—
827C42—221no—
828C42—221no—
829C42—221no—
830C42C2×C4×D1111yescharacteristic
831C42D4×D1111yescharacteristic
832C42D4×D1111yescharacteristic
833C42C23×D1111yescharacteristic
834C11#1745311yescharacteristic, complemented, Sylow
835C23—24no—
836C23—21no—
837C23—21no—
838C23—81no—
839C23—81no—
840C23—111no—
841C23—111no—
842C23—224no—
843C23—224no—
844C23—221no—
845C23—881no—
846C23—881no—
847C23—881no—
848C23—881no—
849C23C22⋊C4×D1111yescharacteristic
850Q8—112no—
851Q8—222no—
852Q8—221no—
853D4—24no—
854D4—21no—
855D4—21no—
856D4—112no—
857D4—222no—
858D4—222no—
859D4—224no—
860D4—222no—
861D4—224no—
862D4—224no—
863D4—224no—
864D4—224no—
865D4—221no—
866D4M16×D1112yes—
867D4M16×D1112yes—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—111no—
883C2×C4—112no—
884C2×C4—112no—
885C2×C4—111no—
886C2×C4—111no—
887C2×C4—111no—
888C2×C4—111no—
889C2×C4—111no—
890C2×C4—224no—
891C2×C4—224no—
892C2×C4—224no—
893C2×C4—221no—
894C2×C4—221no—
895C2×C4—221no—
896C2×C4—221no—
897C2×C4—221no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—221no—
901C2×C4—221no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—881no—
907C2×C4—881no—
908C2×C4—881no—
909C2×C4—881no—
910C2×C4—881no—
911C2×C4—881no—
912C2×C4—881no—
913C2×C4—881no—
914C2×C4—881no—
915C2×C4C22⋊C4×D1111yescharacteristic
916C2×C4C22⋊C4×D1111yescharacteristic
917C2×C4C22⋊C4×D1111yescharacteristic
918C2×C4C22×C4×D1111yescharacteristic
919C2×C4C2×D4×D1111yescharacteristic
920C2×C4C2×D4×D1111yescharacteristic
921C8—41no—
922C8—41no—
923C8—41no—
924C8—41no—
925C8—222no—
926C8—441no—
927C8—441no—
928C8—441no—
929C22—21no—
930C22—22no—
931C22—22no—
932C22—21no—
933C22—21no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—84no—
939C22—112no—
940C22—221no—
941C22—221no—
942C22—222no—
943C22—221no—
944C22—221no—
945C22—221no—
946C22—441no—
947C22—441no—
948C22—884no—
949C22—884no—
950C22C2×C22⋊C4×D1111yescharacteristic
951C4—21no—
952C4—21no—
953C4—21no—
954C4—21no—
955C4—41no—
956C4—41no—
957C4—112no—
958C4—221no—
959C4—222no—
960C4—221no—
961C4—221no—
962C4—221no—
963C4—221no—
964C4—441no—
965C4—441no—
966C4C2×M16×D1111yescharacteristic
967C4C2×M16×D1111yescharacteristic
968C4#1062328811yescharacteristic
969C4#1062329311yescharacteristic
970C2—41no—
971C2—42no—
972C2—42no—
973C2—222no—
974C2—441no—
975C2—442no—
976C2D11×#40711yescharacteristic
977C2#1307713711yescharacteristic
978C2#1307716211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1486C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#67037C4
cosocleC42×C11C24
hypercenter#1486D11
hypocenterC11#17453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13077730C2semidirect
3. #13077580C2semidirect
4. #13067059C2semidirect
5. #13067057C2semidirect
6. #13067053C2semidirect
7. #13067052C2semidirect
8. #13067051C2semidirect
9. #13067047C2semidirect
10. #13067039C2semidirect
11. #13067005C2semidirect
12. #13067000C2semidirect
13. #13066995C2semidirect
14. D11×D4⋊C8C2semidirect
15. C11×#1486C2semidirect
39. C11×#431C22semidirect
40. C11×#423C22semidirect
43. #10622539C22semidirect
44. C4×#4318C22semidirect
45. #10622450C22semidirect
48. #10622448C22semidirect
49. #10622446C22semidirect
50. D11×C4⋊C8C22semidirect
55. C4×#4313C22semidirect
56. #10622298C22semidirect
57. #10622298C22semidirect
58. C4×C8×D11C22semidirect
59. C11×D4⋊C8C22semidirect
60. C11×D4⋊C8C22semidirect
61. C11×D4⋊C8C22semidirect
62. C11×D4⋊C8C22semidirect
63. D4⋊(C11⋊C8)C22semidirect
64. D4⋊(C11⋊C8)C22semidirect
65. D4⋊(C11⋊C8)C22semidirect
66. D4⋊(C11⋊C8)C22semidirect
67. #10622122C22semidirect
68. #10622122C22semidirect
69. #10622121C22semidirect
70. #10622121C22semidirect
71. #10622097C22semidirect
72. #10622097C22semidirect
73. #10622094C22semidirect
74. #10622094C22semidirect
246. #4341M16semidirect
251. D4×D11M16semidirect
356. #1486D11semidirect
491. #431C2×D11semidirect
493. #423C2×D11semidirect
510. D4⋊C8C2×D11semidirect
511. D4⋊C8C2×D11semidirect
512. D4⋊C8C2×D11semidirect
513. D4⋊C8C2×D11semidirect
834. C11#17453semidirect

Maximal subgroups

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

subgroupindex
C4×#670372
#130777302
#130775802
#130670592
#130670572
#130670532
#130670522
#130670512
#130670472
#130670392
#130670052
#130670002
#130669952
D11×D4⋊C82
C11×#14862
#1745311