Finite Group Databasebeta

← #14759630

Subgroups — #14759630

Order 2816.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623276C211yesmaximal, characteristic, complemented
2#13077832C211yesmaximal, characteristic
3C2×#10622758C211yesmaximal, characteristic, complemented
4C2×#10622757C211yesmaximal, characteristic, complemented
5#13068946C211yesmaximal, characteristic, complemented
6#13068946C211yesmaximal, characteristic, complemented
7#13068919C211yesmaximal, characteristic, complemented
8#13068890C211yesmaximal, characteristic, complemented
9#13068890C211yesmaximal, characteristic, complemented
10#13068820C211yesmaximal, characteristic, complemented
11#13068559C211yesmaximal, characteristic, complemented
12#13068462C211yesmaximal, characteristic, complemented
13#13068455C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C11×#2930C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic, complemented
18C22×C11×M16C2211yescharacteristic
19C11×#525C2211yescharacteristic
20C2×#67003C2211yescharacteristic
21C2×#67003C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10623276—24no—
24#10623276—24no—
25C2×#66960—21no—
26C2×#66960—21no—
27C2×M16×D11—21no—
28C2×M16×D11—21no—
29C2×#66954C2211yescharacteristic
30C2×#66954C2211yescharacteristic
31C2×#66954C2211yescharacteristic
32C2×#66954C2211yescharacteristic
33C11×#436—21no—
34C11×#436—21no—
35C11×#435—21no—
36C11×#435—21no—
37C11×#424C2211yescharacteristic, complemented
38C11×#408C2211yescharacteristic, complemented
39C11×#407C2211yescharacteristic
40C11×#405C2211yescharacteristic, complemented
41C2×#66901C2211yescharacteristic, complemented
42C2×#66901C2211yescharacteristic, complemented
43C4×C22⋊Dic11C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622758—24no—
46#10622757—24no—
47C2×#66889C2211yescharacteristic
48C2×#66889C2211yescharacteristic
49C2×#66889C2211yescharacteristic
50C2×#66889C2211yescharacteristic
51C2×#66886C2211yescharacteristic, complemented
52C2×#66886C2211yescharacteristic, complemented
53C2×#66879C2211yescharacteristic, complemented
54C2×C8×Dic11C2211yescharacteristic, complemented
55#10622663C411yescharacteristic, complemented
56#10622660C411yescharacteristic, complemented
57#10622660C411yescharacteristic, complemented
58#10622659C411yescharacteristic, complemented
59#10622653C411yescharacteristic, complemented
60#10622650C411yescharacteristic, complemented
61#10622650C411yescharacteristic, complemented
62#10622649C411yescharacteristic, complemented
63#10622615C2211yescharacteristic
64#10622615C2211yescharacteristic
65#10622196C2211yescharacteristic, complemented
66#10622196C2211yescharacteristic, complemented
67#10622188C2211yescharacteristic, complemented
68#10622188C2211yescharacteristic, complemented
69#10622170C2211yescharacteristic, complemented
70#10622170C2211yescharacteristic, complemented
71C2×C11×#41C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—21no—
74C2×#4339—21no—
75C2×#4339—21no—
76C2×#4339—22no—
77C2×#4339—22no—
78C2×#4339—22no—
79C2×#4339—22no—
80C2×#4339C2×C411yescharacteristic
81C2×#4339C2×C411yescharacteristic
82C2×#4339C2311yescharacteristic
83C2×#4339C2311yescharacteristic
84C22×D44C2×C411yescharacteristic
85C22×C4×D11—21no—
86C22×Dic22C2×C411yescharacteristic
87C11×#131—22no—
88C11×#131—22no—
89C2×C11×M16—22no—
90C2×C11×M16—22no—
91C2×C11×M16—21no—
92C2×C11×M16D411yescharacteristic
93C2×C11×M16D411yescharacteristic
94C2×C11×M16D411yescharacteristic
95C2×C11×M16D411yescharacteristic
96C2×C11×M16C2311yescharacteristic
97C2×C11×M16C2311yescharacteristic
98C22×C8×C11—21no—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×#123—21no—
102C11×C22⋊Q8C2×C411yescharacteristic
103C11×C22⋊Q8C2×C411yescharacteristic
104C11×#121C2×C411yescharacteristic
105C11×#121C2×C411yescharacteristic
106C11×#120—21no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C11×#117C2311yescharacteristic
110C2×C22⋊Dic11—21no—
111#67003—22no—
112#67003—22no—
113#67003—22no—
114#67003—22no—
115C2×#4326C2×C411yescharacteristic
116C2×#4326C2×C411yescharacteristic
117C2×#4325C2×C411yescharacteristic
118C2×#4325C2×C411yescharacteristic
119C2×#4324C2×C411yescharacteristic
120C2×#4324C2×C411yescharacteristic
121C2×#4323C2×C411yescharacteristic
122C2×#4323C2×C411yescharacteristic
123C2×C4×Dic11C2311yescharacteristic
124C2×C4×Dic11C2311yescharacteristic
125C2×#4318—21no—
126C2×#4318—22no—
127C2×#4318—22no—
128C2×#4318C2311yescharacteristic
129C2×#4318C2311yescharacteristic
130C22×C11⋊C8—21no—
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133#66960—28no—
134#66960—28no—
135M16×D11—28no—
136M16×D11—28no—
137#66954—22no—
138#66954—22no—
139#66954—22no—
140#66954—22no—
141#66954—22no—
142#66954—22no—
143#66954D414yescomplemented
144#66954D414yescomplemented
145C2×#4313—21no—
146C2×#4313—21no—
147C2×#4313—21no—
148C2×#4313—21no—
149C2×C8×D11—21no—
150C2×C8×D11—21no—
151C2×C8×D11—21no—
152C2×C8×D11—21no—
153C11×C4⋊C8—21no—
154C11×C4⋊C8—21no—
155C11×C22⋊C8—21no—
156C11×C22⋊C8—21no—
157C11×C22⋊C8—21no—
158C11×C22⋊C8—21no—
159C11×#97—21no—
160C4×C8×C11—21no—
161#66901—22no—
162#66901—22no—
163C11⋊#95—21no—
164C22⋊(C11⋊C8)C2×C411yescharacteristic
165C22⋊(C11⋊C8)C2×C411yescharacteristic
166C22⋊(C11⋊C8)C2×C411yescharacteristic
167C22⋊(C11⋊C8)C2×C411yescharacteristic
168#66889—22no—
169#66889—22no—
170#66889—22no—
171#66889—22no—
172#66886—22no—
173#66886—22no—
174#66879—22no—
175C8×Dic11—22no—
176#66874C2×C411yescharacteristic
177#66874C2×C411yescharacteristic
178#66874C2×C411yescharacteristic
179#66874C2×C411yescharacteristic
180#66873C2×C411yescharacteristic
181#66873C2×C411yescharacteristic
182#66873C2×C411yescharacteristic
183#66873C2×C411yescharacteristic
184#21468—111nomaximal, Sylow
185C24×C11#4111yescharacteristic
186C23×D11—21no—
187C11×#41—21no—
188C11×#41—21no—
189C11×#41—21no—
190C11×#41—21no—
191C2×Q8×C11C22×C411yescharacteristic
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11C22×C411yescharacteristic
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11#4111yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—21no—
210C2×C22⋊D11—21no—
211C2×C22⋊D11—21no—
212C2×C22⋊D11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216#4339—24no—
217#4339—24no—
218#4339—24no—
219#4339—24no—
220#4339—22no—
221#4339—22no—
222#4339—22no—
223#4339—22no—
224#4339—21no—
225#4339—21no—
226#4339—21no—
227#4339—21no—
228#4339C2×D412yes—
229#4339C2×D412yes—
230#4339#4112yes—
231#4339#4112yes—
232C2×D44—22no—
233C2×D44—22no—
234C2×D44—21no—
235C2×D44C22×C411yescharacteristic
236C2×D44C22×C411yescharacteristic
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—21no—
240C2×C4×D11—21no—
241C2×C4×D11—21no—
242C2×C4×D11—21no—
243C2×Dic22—22no—
244C2×Dic22—22no—
245C2×Dic22—21no—
246C2×Dic22C22×C411yescharacteristic
247C2×Dic22C22×C411yescharacteristic
248C11×M16—22no—
249C11×M16—22no—
250C11×M16—22no—
251C11×M16—22no—
252C11×M16—21no—
253C11×M16—21no—
254C11×M16—21no—
255C11×M16—21no—
256C11×M16—42no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—42no—
262C2×C8×C11C2×D412yes—
263C2×C8×C11C2×D412yes—
264C2×C8×C11C2×D411yescharacteristic
265C2×C8×C11C2×D411yescharacteristic
266C2×C8×C11C2×D411yescharacteristic
267C2×C8×C11C2×D411yescharacteristic
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4C22×C411yescharacteristic
271C11×C4⋊C4C22×C411yescharacteristic
272C11×C22⋊C4—21no—
273C11×C22⋊C4—21no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—21no—
276C11×C22⋊C4—21no—
277C42×C11—21no—
278C22⋊Dic11—42no—
279#4326—22no—
280#4326—22no—
281#4325—22no—
282#4325—22no—
283#4324—22no—
284#4324—22no—
285#4323—22no—
286#4323—22no—
287C4×Dic11—21no—
288C4×Dic11—21no—
289C4×Dic11—21no—
290C4×Dic11—21no—
291#4318—24no—
292#4318—21no—
293#4318—21no—
294#4318C2×D412yes—
295#4318C2×D412yes—
296C2×C11⋊C8—24no—
297C2×C11⋊C8—21no—
298C2×C11⋊C8—21no—
299C2×C11⋊C8—21no—
300C2×C11⋊C8—21no—
301C2×C11⋊C8—21no—
302C2×C11⋊C8—21no—
303C2×C11⋊C8C22×C411yescharacteristic
304C2×C11⋊C8C22×C411yescharacteristic
305C2×C11⋊C8C22×C411yescharacteristic
306C2×C11⋊C8C22×C411yescharacteristic
307#4313—24no—
308#4313—24no—
309#4313—24no—
310#4313—24no—
311C8×D11—24no—
312C8×D11—24no—
313C8×D11—24no—
314C8×D11—24no—
315C2×#568—111no—
316#3002—111no—
317C2×#444—111no—
318C2×#443—111no—
319#2930D1111yescharacteristic, complemented
320#1876—111no—
321#1876—111no—
322#1871—111no—
323#1866—111no—
324#1866—111no—
325#1855—111no—
326#1789—111no—
327#1765—111no—
328#1764—111no—
329#1753—111no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11C4×D411yescharacteristic
336C23×C11C4×D411yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C22×D11—21no—
339C22×D11—21no—
340C22×D11—24no—
341C22×D11—81no—
342C22×D11—81no—
343Q8×C11—21no—
344Q8×C11—21no—
345D4×C11—21no—
346D4×C11—21no—
347D4×C11—41no—
348D4×C11—41no—
349D4×C11—81no—
350D4×C11—81no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11C4×D411yescharacteristic
367C2×C4×C11C4×D411yescharacteristic
368C2×C4×C11C23×C411yescharacteristic
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C2×#4111yescharacteristic
373C2×C4×C11C2×#4111yescharacteristic
374C22⋊D11—24no—
375C22⋊D11—24no—
376C22⋊D11—22no—
377C22⋊D11—22no—
378C22⋊D11—22no—
379C22⋊D11—22no—
380C2×Dic11—24no—
381C2×Dic11—21no—
382C2×Dic11—21no—
383C2×Dic11—22no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389D44—24no—
390D44—21no—
391D44—21no—
392D44C4×D412yes—
393D44C4×D412yes—
394C4×D11—24no—
395C4×D11—24no—
396C4×D11—22no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—22no—
400Dic22—24no—
401Dic22—21no—
402Dic22—21no—
403Dic22C4×D412yes—
404Dic22C4×D412yes—
405C8×C11—21no—
406C8×C11—21no—
407C8×C11—41no—
408C8×C11—41no—
409C8×C11#12012yes—
410C8×C11#12012yes—
411C11⋊C8—21no—
412C11⋊C8—21no—
413C11⋊C8—21no—
414C11⋊C8—21no—
415C11⋊C8—22no—
416C11⋊C8—22no—
417C22×#41—111no—
418C2×#135—111no—
419C2×#135—111no—
420#568—224no—
421#568—224no—
422C2×#131—111no—
423C2×#131—111no—
424C2×#131—111no—
425C2×#131—111no—
426C2×#131—221no—
427C2×#131—221no—
428C2×#131C2×D1111yescharacteristic, complemented
429C22×M16—111no—
430C22×M16—221no—
431C22×M16—221no—
432C22×M16C2×D1111yescharacteristic
433#525C2×D1111yescharacteristic
434#452—111no—
435#452—111no—
436#451—111no—
437#450—111no—
438#449—111no—
439#449—111no—
440#448—111no—
441#447—111no—
442#444—224no—
443#443—224no—
444#436—21no—
445#436—21no—
446#435—21no—
447#435—21no—
448C2×#108—111no—
449C2×#108—111no—
450#424C2×D1111yescharacteristic, complemented
451C2×#104—111no—
452C2×#104—111no—
453C2×#104—111no—
454C2×#104—111no—
455C2×#104—111no—
456C2×#104—111no—
457#416—111no—
458#416—111no—
459#408C2×D1111yescharacteristic, complemented
460#407C2×D1111yescharacteristic
461C2×C22⋊C8—111no—
462#405C2×D1111yescharacteristic, complemented
463C2×#97—111no—
464C2×C4×C8—111no—
465C4×C22⋊C4—111no—
466#341—111no—
467#341—111no—
468#339—111no—
469#339—111no—
470#336—111no—
471#336—111no—
472C22×C11—21no—
473C22×C11—21no—
474C22×C11—21no—
475C22×C11—21no—
476C22×C11—21no—
477C22×C11—21no—
478C22×C11—21no—
479C22×C11—21no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11C2×C4×D411yescharacteristic
486C22×C11#52511yescharacteristic
487C22×C11#52511yescharacteristic
488C2×D11—22no—
489C2×D11—22no—
490C2×D11—41no—
491C2×D11—41no—
492C2×D11—41no—
493C2×D11—41no—
494C2×D11—84no—
495C4×C11—21no—
496C4×C11—21no—
497C4×C11—41no—
498C4×C11—41no—
499C4×C11—41no—
500C4×C11C2×C4×D411yescharacteristic
501C4×C11C2×C4×D411yescharacteristic
502C4×C11C2×#12011yescharacteristic
503C4×C11#52511yescharacteristic
504Dic11—22no—
505Dic11—22no—
506Dic11—42no—
507Dic11—81no—
508C2×#41—111no—
509C2×#41—111no—
510C2×#41—111no—
511C2×#41—111no—
512C2×#41—222no—
513C2×#41—222no—
514C2×#41—222no—
515C2×#41—222no—
516C2×#41—221no—
517C2×#41—221no—
518C2×#41C22×D1111yescharacteristic
519C22×Q8—111no—
520C22×D4—111no—
521C22×D4—221no—
522C23×C4—221no—
523C23×C4C22×D1111yescharacteristic
524#135—222no—
525#135—222no—
526#135—222no—
527#135—222no—
528C2×Q16—111no—
529C2×Q16—111no—
530C2×SD16—111no—
531C2×SD16—111no—
532C2×SD16—111no—
533C2×SD16—111no—
534C2×D8—111no—
535C2×D8—111no—
536#131—22no—
537#131—22no—
538#131—114no—
539#131—114no—
540#131—222no—
541#131—222no—
542#131—222no—
543#131—222no—
544#131—228no—
545#131—228no—
546#131—222no—
547#131—222no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—21no—
551C2×M16—111no—
552C2×M16—111no—
553C2×M16—228no—
554C2×M16—228no—
555C2×M16—222no—
556C2×M16—222no—
557C2×M16—221no—
558C2×M16—221no—
559C2×M16—221no—
560C2×M16—221no—
561C2×M16—221no—
562C2×M16C22⋊D1111yescharacteristic
563C2×M16C22⋊D1111yescharacteristic
564C2×M16C22⋊D1111yescharacteristic
565C2×M16C22⋊D1111yescharacteristic
566C2×M16C22×D1111yescharacteristic
567C2×M16C22×D1111yescharacteristic
568C22×C8—21no—
569C22×C8—111no—
570C22×C8—111no—
571C22×C8—221no—
572C22×C8—221no—
573C22×C8—221no—
574C22×C8—221no—
575C22×C8—221no—
576C22×C8C22×D1111yescharacteristic
577C22×C8C22×D1111yescharacteristic
578#123—21no—
579C22⋊Q8C4×D1111yescharacteristic
580C22⋊Q8C4×D1111yescharacteristic
581#121C4×D1111yescharacteristic
582#121C4×D1111yescharacteristic
583#120—21no—
584C4×D4—21no—
585C4×D4—21no—
586#117C22×D1111yescharacteristic
587C2×C22⋊C4—221no—
588C2×C42—111no—
589C2×C42—111no—
590#108—222no—
591#108—222no—
592C4⋊C8—21no—
593C4⋊C8—21no—
594#104—222no—
595#104—222no—
596#104—222no—
597#104—222no—
598#104—222no—
599#104—222no—
600#103—111no—
601#103—111no—
602#103—111no—
603#103—111no—
604#102—111no—
605#102—111no—
606#102—111no—
607#102—111no—
608C22⋊C8—21no—
609C22⋊C8—21no—
610C22⋊C8—21no—
611C22⋊C8—21no—
612C22⋊C8—111no—
613C22⋊C8—111no—
614C22⋊C8—111no—
615C22⋊C8—111no—
616#97—21no—
617#97—222no—
618C4×C8—21no—
619C4×C8—222no—
620#95—221no—
621C2×C11—21no—
622C2×C11—21no—
623C2×C11—41no—
624C2×C11—41no—
625C2×C11—81no—
626C2×C11C4×#12011yescharacteristic
627C2×C11#295611yescharacteristic
628C2×C11#295711yescharacteristic
629D11—42no—
630D11—42no—
631C24—221no—
632C24#433911yescharacteristic
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—112no—
638#41—112no—
639#41—112no—
640#41—112no—
641#41—222no—
642#41—222no—
643#41—222no—
644#41—222no—
645#41—224no—
646#41—224no—
647#41—224no—
648#41—224no—
649#41—221no—
650#41—221no—
651#41—221no—
652#41—221no—
653C2×Q8—111no—
654C2×Q8—111no—
655C2×Q8—222no—
656C2×Q8—222no—
657C2×Q8—221no—
658C2×Q8C2×C4×D1111yescharacteristic
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—111no—
663C2×D4—111no—
664C2×D4—222no—
665C2×D4—222no—
666C2×D4—224no—
667C2×D4—224no—
668C2×D4—221no—
669C2×D4—221no—
670C2×D4—221no—
671C2×D4—221no—
672C2×D4—221no—
673C2×D4C2×C4×D1111yescharacteristic
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—224no—
680C22×C4—224no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4C2×C4×D1111yescharacteristic
689C22×C4C2×C4×D1111yescharacteristic
690C22×C4#433911yescharacteristic
691C22×C4C2×C22⋊D1111yescharacteristic
692C22×C4C2×C22⋊D1111yescharacteristic
693C22×C4C23×D1111yescharacteristic
694Q16—222no—
695Q16—222no—
696SD16—222no—
697SD16—222no—
698SD16—222no—
699SD16—222no—
700D8—222no—
701D8—222no—
702M16—22no—
703M16—22no—
704M16—22no—
705M16—22no—
706M16—21no—
707M16—21no—
708M16—21no—
709M16—21no—
710M16—42no—
711M16—112no—
712M16—112no—
713M16—224no—
714M16—224no—
715M16—224no—
716M16—221no—
717M16—221no—
718M16—224no—
719M16—224no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—42no—
725C2×C8—111no—
726C2×C8—111no—
727C2×C8—111no—
728C2×C8—111no—
729C2×C8—224no—
730C2×C8—224no—
731C2×C8—224no—
732C2×C8—221no—
733C2×C8—221no—
734C2×C8—221no—
735C2×C8—221no—
736C2×C8—221no—
737C2×C8—221no—
738C2×C8—224no—
739C2×C8—224no—
740C2×C8D4×D1112yes—
741C2×C8D4×D1112yes—
742C2×C8C2×C22⋊D1111yescharacteristic
743C2×C8C2×C22⋊D1111yescharacteristic
744C2×C8C2×C22⋊D1111yescharacteristic
745C2×C8C2×C22⋊D1111yescharacteristic
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4C2×C4×D1111yescharacteristic
749C4⋊C4C2×C4×D1111yescharacteristic
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—442no—
756C42—21no—
757C42—221no—
758C42—221no—
759C42—221no—
760C42—221no—
761C11#2146811yescharacteristic, complemented, Sylow
762C23—21no—
763C23—21no—
764C23—21no—
765C23—41no—
766C23—41no—
767C23—224no—
768C23—221no—
769C23—221no—
770C23—881no—
771C23—881no—
772C23C4×C22⋊D1111yescharacteristic
773C23C4×C22⋊D1111yescharacteristic
774C23C2×#433911yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—112no—
778Q8—112no—
779Q8—224no—
780Q8—221no—
781Q8—221no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—41no—
786D4—81no—
787D4—81no—
788D4—112no—
789D4—112no—
790D4—224no—
791D4—224no—
792D4—224no—
793D4—222no—
794D4—222no—
795D4—222no—
796D4—222no—
797D4—221no—
798D4—221no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—224no—
815C2×C4—224no—
816C2×C4—224no—
817C2×C4—221no—
818C2×C4—221no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—441no—
829C2×C4C4×C22⋊D1111yescharacteristic
830C2×C4C4×C22⋊D1111yescharacteristic
831C2×C4C22×C4×D1111yescharacteristic
832C2×C4C2×D4×D1111yescharacteristic
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4#41×D1111yescharacteristic
835C2×C4#41×D1111yescharacteristic
836C2×C4C22×C22⋊D1111yescharacteristic
837C8—21no—
838C8—21no—
839C8—41no—
840C8—41no—
841C8—222no—
842C8—222no—
843C8—221no—
844C8—221no—
845C8—221no—
846C8—221no—
847C8#6699012yes—
848C8#6699012yes—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—81no—
861C22—81no—
862C22—222no—
863C22—222no—
864C22—441no—
865C22—441no—
866C22—441no—
867C22—441no—
868C22—884no—
869C22#1062307811yescharacteristic
870C22#1062307811yescharacteristic
871C22C2×C4×C22⋊D1111yescharacteristic
872C4—21no—
873C4—21no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—222no—
878C4—222no—
879C4—442no—
880C4—881no—
881C4C4×D4×D1111yescharacteristic
882C4C4×D4×D1111yescharacteristic
883C4C2×#6699011yescharacteristic
884C4#1062335911yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—442no—
891C2—442no—
892C2C4×#6699011yescharacteristic
893C2#1307752311yescharacteristic
894C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2930C2
socleC22×C11C2×C4×D4
prime radical#13077832C2
cosocleC22×C4×C11C24
hypercenter#2930D11
hypocenterC11#21468
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

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

NH ≅ G/Ntype
1. C2×#10623276C2semidirect
3. C2×#10622758C2semidirect
4. C2×#10622757C2semidirect
5. #13068946C2semidirect
6. #13068946C2semidirect
7. #13068919C2semidirect
8. #13068890C2semidirect
9. #13068890C2semidirect
10. #13068820C2semidirect
11. #13068559C2semidirect
12. #13068462C2semidirect
13. #13068455C2semidirect
14. #13068397C2semidirect
15. C11×#2930C2semidirect
17. C2×C11×#131C22semidirect
37. C11×#424C22semidirect
38. C11×#408C22semidirect
40. C11×#405C22semidirect
41. C2×#66901C22semidirect
42. C2×#66901C22semidirect
51. C2×#66886C22semidirect
52. C2×#66886C22semidirect
53. C2×#66879C22semidirect
54. C2×C8×Dic11C22semidirect
55. #10622663C4semidirect
56. #10622660C4semidirect
57. #10622660C4semidirect
58. #10622659C4semidirect
59. #10622653C4semidirect
60. #10622650C4semidirect
61. #10622650C4semidirect
62. #10622649C4semidirect
65. #10622196C22semidirect
66. #10622196C22semidirect
67. #10622188C22semidirect
68. #10622188C22semidirect
69. #10622170C22semidirect
70. #10622170C22semidirect
143. #66954D4semidirect
144. #66954D4semidirect
319. #2930D11semidirect
428. C2×#131C2×D11semidirect
450. #424C2×D11semidirect
459. #408C2×D11semidirect
462. #405C2×D11semidirect
761. C11#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#106232762
#130778322
C2×#106227582
C2×#106227572
#130689462
#130689192
#130688902
#130688202
#130685592
#130684622
#130684552
#130683972
C11×#29302
#2146811