Finite Group Databasebeta

← #15638487

Subgroups — #15638487

Order 2816.

2370 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082373C211yesmaximal, characteristic
2C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
3#13080477C214yesmaximal, complemented
4#13080474C214yesmaximal, complemented
5SD16×C22⋊D11C214yesmaximal, complemented
6#13080305C214yesmaximal, complemented
7#13079539C212yesmaximal, complemented
8#13079374C211yesmaximal, characteristic, complemented
9#13079373C211yesmaximal, characteristic, complemented
10#13079371C212yesmaximal, complemented
11#13078642C212yesmaximal, complemented
12C2×#10622840C211yesmaximal, characteristic, complemented
13D11×#448C212yesmaximal, complemented
14#13077638C211yesmaximal, characteristic, complemented
15C2×C11×#448C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic, complemented
17C22×Q8×D11C2211yescharacteristic, complemented
18C2×#67037—21no—
19C22×C11×SD16C2212yescomplemented
20C2×C11×#121C2211yescharacteristic
21Q8×C22⋊D11—22no—
22Q8×C22⋊D11—22no—
23Q8×C22⋊D11C2214yescomplemented
24Q8×C22⋊D11C2214yescomplemented
25C2×#66999—21no—
26C2×#66999C2211yescharacteristic, complemented
27C2×Q8×Dic11C2211yescharacteristic, complemented
28C2×#66997—21no—
29C2×#66997C2211yescharacteristic, complemented
30C22×#4325C2212yescomplemented
31#10623335—21no—
32D4×C22⋊D11C2212yes—
33C2×#66983C2211yescharacteristic
34C2×C4×C22⋊D11—21no—
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×#66977—21no—
37C2×#66977C2211yescharacteristic, complemented
38C2×SD16×D11C2214yescomplemented
39#10623142C2212yes—
40#10623141—22no—
41#10623140C2212yes—
42#10623136—21no—
43D11×#121C2212yes—
44#10623128—21no—
45#10623127C2212yes—
46#10623038C2212yes—
47#10623021—22no—
48C11×#448C2212yescomplemented
49C11×#448C2212yescomplemented
50C11×#448C2214yescomplemented
51C2×C11×#103C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53#10622840C2212yescomplemented
54#10622840C2212yescomplemented
55#10622840C2214yescomplemented
56C2×#66899C2212yescomplemented
57#10622831C2212yescomplemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622788C2214yescomplemented
60#10622784C2214yescomplemented
61#10622783C2214yescomplemented
62#10622782C2214yescomplemented
63#10622776C2214yescomplemented
64#10622775C2214yescomplemented
65SD16×Dic11C2214yescomplemented
66#10622727C2214yescomplemented
67C8×C22⋊D11C2214yescomplemented
68#10622654C2214yescomplemented
69#10622653C2212yescomplemented
70#10622647C2212yescomplemented
71#10622584C2212yescomplemented
72#10622431C2214yescomplemented
73#10622420C2214yescomplemented
74#10622419C2214yescomplemented
75#10622418C2214yescomplemented
76D11×#103C2214yescomplemented
77#10622405C2214yescomplemented
78#10622404C2214yescomplemented
79#10622401C2214yescomplemented
80#10622351C2212yescomplemented
81#10622348C2212yescomplemented
82#10622344C2212yescomplemented
83(C22⋊D11)⋊C8C2214yescomplemented
84D11×C22⋊C8C2212yescomplemented
85#10622334C2212yescomplemented
86#10622331C2212yescomplemented
87C22×Q8×C11—21no—
88C22×Q8×C11—21no—
89C22×Q8×C11—21no—
90C22×Q8×C11—44no—
91C22×Q8×C11C2311yescharacteristic
92C22×Q8×C11C2312yes—
93C22×Q8×C11C2312yes—
94C22×Q8×C11C2311yescharacteristic
95C22×D4×C11—21no—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—21no—
100C22×C22⋊D11—22no—
101C22×C22⋊D11D411yescharacteristic
102C2×Q8×D11—22no—
103C2×Q8×D11—44no—
104C2×Q8×D11C2314yes—
105#67037—48no—
106C2×#4341—22no—
107C2×#4341—22no—
108C2×D4×D11—22no—
109C2×D4×D11—22no—
110C2×D4×D11C2312yes—
111C2×#4339—22no—
112C22×D44C2311yescharacteristic
113C22×C4×D11—21no—
114C22×C4×D11C2311yescharacteristic
115C22×Dic22—21no—
116C22×Dic22C2311yescharacteristic
117C2×C11×SD16—44no—
118C2×C11×SD16C2314yes—
119C2×C11×SD16C2314yes—
120C22×C8×C11C2312yes—
121C11×#121—21no—
122C11×#121—21no—
123C11×#121C2312yes—
124C11×#121C2312yes—
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C22⋊C4—21no—
127#67006—22no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11D411yescharacteristic
130#66999—22no—
131#66999—24no—
132#66999—24no—
133#66999C2314yes—
134Q8×Dic11—22no—
135Q8×Dic11C2314yes—
136#66997—24no—
137#66997—24no—
138#66997—22no—
139#66997C2314yes—
140C2×#4325—44no—
141C2×#4325C2314yes—
142C2×#4325C2314yes—
143#66993C2312yes—
144#66992—22no—
145#66992—22no—
146#66992—22no—
147#66991C2312yes—
148#66990—22no—
149#66990—22no—
150#66988—22no—
151D4×Dic11C2312yes—
152C2×#4324C2314yes—
153#66983—21no—
154#66983—21no—
155#66983C2312yes—
156#66983C2312yes—
157#66982—22no—
158C4×C22⋊D11—24no—
159C4×C22⋊D11—24no—
160C4×C22⋊D11D412yes—
161C4×C22⋊D11D412yes—
162C4×C22⋊D11C2312yes—
163C4×C22⋊D11C2312yes—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4D411yescharacteristic
167C2×C4⋊Dic11—21no—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170#66977—21no—
171#66977—21no—
172#66977—24no—
173#66977—24no—
174#66977C2312yes—
175#66977C2312yes—
176C2×Dic11⋊C4—21no—
177C2×Dic11⋊C4—21no—
178C2×Dic11⋊C4—21no—
179C2×Dic11⋊C4—21no—
180C2×Dic11⋊C4D411yescharacteristic
181C2×C4×Dic11—21no—
182C2×C4×Dic11C2311yescharacteristic
183C22×C11⋊C8C2312yes—
184SD16×D11—48no—
185C2×#4314C2314yes—
186C2×C8×D11C2314yes—
187#66949—22no—
188#66948C2312yes—
189#66947—22no—
190#66946C2312yes—
191C4⋊C4×D11C2312yes—
192#66941C2312yes—
193#66938—22no—
194#66937—22no—
195#66937—22no—
196#66936—22no—
197#66935—22no—
198(C22⋊D11)⋊C4—22no—
199C22⋊C4×D11—22no—
200#66931—22no—
201C11×#103C2314yes—
202C11×#103C2314yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yes—
205#66899C2314yes—
206#66899C2314yes—
207#66896C2314yes—
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yes—
210#66885C2314yes—
211(C2×D11)⋊C8C2314yes—
212#66881C2314yes—
213#66880C2314yes—
214Dic11⋊C8C2314yes—
215C8×Dic11C2314yes—
216#66874C2314yes—
217#66872C2314yes—
218#61562—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C23×D11—22no—
223C23×D11C2×D411yescharacteristic
224C2×Q8×C11—24no—
225C2×Q8×C11—21no—
226C2×Q8×C11—22no—
227C2×Q8×C11—22no—
228C2×Q8×C11—21no—
229C2×Q8×C11—24no—
230C2×Q8×C11—24no—
231C2×Q8×C11—42no—
232C2×Q8×C11—42no—
233C2×Q8×C11—42no—
234C2×Q8×C11—44no—
235C2×Q8×C11—44no—
236C2×Q8×C11—44no—
237C2×Q8×C11C2412yes—
238C2×Q8×C11C2412yes—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—21no—
242C2×D4×C11—42no—
243C2×D4×C11—44no—
244C2×D4×C11C2412yes—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—21no—
250C22×C4×C11—42no—
251C22×C4×C11—44no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C2×C22⋊D11—22no—
259C2×C22⋊D11—22no—
260C2×C22⋊D11—22no—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—22no—
263C2×C22⋊D11—22no—
264C2×C22⋊D11—48no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11SD1618yescomplemented
267C2×C22⋊D11C2×D412yes—
268C2×C22⋊D11C2×D412yes—
269C22×Dic11—22no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11C2×D411yescharacteristic
274C22×Dic11C2×D411yescharacteristic
275C22×Dic11C2×D411yescharacteristic
276Q8×D11—28no—
277Q8×D11—44no—
278Q8×D11—48no—
279#4341—48no—
280#4341—48no—
281D4×D11—44no—
282D4×D11—48no—
283D4×D11—48no—
284#4339—48no—
285C2×D44—22no—
286C2×D44—21no—
287C2×D44—42no—
288C2×D44C2412yes—
289C2×C4×D11—22no—
290C2×C4×D11—22no—
291C2×C4×D11—24no—
292C2×C4×D11—42no—
293C2×C4×D11—44no—
294C2×C4×D11C2×D412yes—
295C2×C4×D11C2412yes—
296C2×Dic22—22no—
297C2×Dic22—24no—
298C2×Dic22—21no—
299C2×Dic22—42no—
300C2×Dic22—44no—
301C2×Dic22C2412yes—
302C11×SD16—28no—
303C11×SD16—44no—
304C2×C8×C11—42no—
305C2×C8×C11C2414yes—
306C11×C4⋊C4—21no—
307C11×C4⋊C4C2412yes—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C22⋊Dic11—22no—
311C22⋊Dic11—22no—
312C22⋊Dic11—22no—
313C22⋊Dic11—22no—
314C22⋊Dic11C2×D412yes—
315C22⋊Dic11C2×D412yes—
316#4325—28no—
317#4325—44no—
318#4324—44no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4C2×D412yes—
325(C2×D11)⋊C4C2×D412yes—
326C4⋊Dic11—24no—
327C4⋊Dic11—21no—
328C4⋊Dic11—21no—
329C4⋊Dic11C2412yes—
330C4⋊Dic11C2412yes—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—24no—
334Dic11⋊C4—24no—
335Dic11⋊C4—24no—
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4C2×D412yes—
339Dic11⋊C4C2×D412yes—
340C4×Dic11—24no—
341C4×Dic11C2×D412yes—
342C4×Dic11C2412yes—
343C2×C11⋊C8—42no—
344C2×C11⋊C8C2414yes—
345#4314—44no—
346C8×D11—44no—
347#3496—111no—
348C2×D4×Q8—111no—
349#3298—114no—
350#3298—114no—
351D4×SD16—114no—
352D4×SD16—114no—
353#3206—112no—
354#3187—112no—
355#3187—111no—
356#3187—111no—
357#3103—112no—
358C2×#448—112no—
359C2×#448—111no—
360C2×#448D1111yescharacteristic, complemented
361#2972—111no—
362C23×C11—22no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—42no—
366C23×C11—81no—
367C23×C11—81no—
368C23×C11C2×SD1614yescomplemented
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C22×D11—22no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—42no—
376C22×D11—44no—
377C22×D11—82no—
378C22×D11—82no—
379C22×D11—81no—
380C22×D11—81no—
381C22×D11C2×SD1614yescomplemented
382C22×D11C22×D412yes—
383Q8×C11—24no—
384Q8×C11—22no—
385Q8×C11—22no—
386Q8×C11—22no—
387Q8×C11—44no—
388Q8×C11—44no—
389Q8×C11—42no—
390Q8×C11H(5,𝔽2)14yescomplemented
391D4×C11—24no—
392D4×C11—44no—
393D4×C11—44no—
394D4×C11—81no—
395C2×C4×C11—24no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—44no—
406C2×C4×C11—44no—
407C2×C4×C11—42no—
408C2×C4×C11—42no—
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C2511yescharacteristic
413C22⋊D11—44no—
414C22⋊D11—44no—
415C22⋊D11—44no—
416C22⋊D11—44no—
417C22⋊D11—82no—
418C22⋊D11—82no—
419C22⋊D11C2×SD1618yescomplemented
420C22⋊D11C2×SD1618yescomplemented
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—42no—
427C2×Dic11—42no—
428C2×Dic11—42no—
429C2×Dic11—44no—
430C2×Dic11C2×SD1614yescomplemented
431C2×Dic11C22×D412yes—
432C2×Dic11C22×D412yes—
433C2×Dic11C22×D412yes—
434D44—24no—
435D44—44no—
436D44—81no—
437C4×D11—24no—
438C4×D11—42no—
439C4×D11—48no—
440C4×D11—44no—
441C4×D11—44no—
442Dic22—24no—
443Dic22—48no—
444Dic22—42no—
445Dic22—44no—
446C8×C11—24no—
447C11⋊C8—24no—
448C2×H(5,𝔽2)—221no—
449C23×Q8—111no—
450C23×Q8C2×D1111yescharacteristic, complemented
451C22×SD16—112no—
452C22×SD16—114no—
453C22×SD16C2×D1112yescomplemented
454D4×Q8—114no—
455D4×Q8—114no—
456D4×Q8—222no—
457D4×Q8—222no—
458#547—112no—
459#547—112no—
460#546—222no—
461#546—222no—
462D42—112no—
463D42—112no—
464#537—221no—
465#534—221no—
466#534—221no—
467#532—112no—
468C2×C4⋊Q8—111no—
469C2×C4⋊Q8—221no—
470C2×C22⋊Q8—111no—
471C2×C22⋊Q8—111no—
472C2×C22⋊Q8—221no—
473C2×C22⋊Q8—221no—
474C2×#121—111no—
475C2×#121—112no—
476C2×#121C2×D1111yescharacteristic
477C2×C4×Q8—111no—
478C2×C4×D4—111no—
479C2×C4×D4—221no—
480#492—114no—
481#487—114no—
482#483—112no—
483#483—114no—
484#483—112no—
485#481—112no—
486#481—112no—
487#475—114no—
488#465—114no—
489#465—114no—
490#465—114no—
491#465—114no—
492#461—114no—
493#461—114no—
494#460—114no—
495#450—112no—
496#450—114no—
497#450—112no—
498#448—112no—
499#448—112no—
500#448—114no—
501#448—114no—
502#448—112no—
503#448—114no—
504#448—112no—
505#448C2×D1112yescomplemented
506#448C2×D1112yescomplemented
507#448C2×D1114yescomplemented
508C4×SD16—114no—
509C4×SD16—114no—
510C8×D4—114no—
511C8×D4—114no—
512#431—112no—
513C2×#103—112no—
514C2×#103—114no—
515C2×#103C2×D1112yescomplemented
516C2×C22⋊C8—111no—
517C2×C22⋊C8—112no—
518C2×C22⋊C8C2×D1111yescharacteristic, complemented
519C22×C11—21no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—21no—
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—44no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—162no—
530C22×C11C22×SD1612yes—
531C22×C11C22×SD1612yes—
532C22×C11C22×SD1612yes—
533C22×C11C23×D411yescharacteristic
534C2×D11—22no—
535C2×D11—22no—
536C2×D11—44no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—164no—
541C2×D11—162no—
542C2×D11C22×SD1614yes—
543C4×C11—24no—
544C4×C11—21no—
545C4×C11—21no—
546C4×C11—21no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11C2×H(5,𝔽2)12yes—
550Dic11—22no—
551Dic11—22no—
552Dic11—42no—
553Dic11—42no—
554Dic11—42no—
555Dic11C22×SD1614yes—
556H(5,𝔽2)—448no—
557C2×#41—222no—
558C2×#41—222no—
559C2×#41—222no—
560C22×Q8—21no—
561C22×Q8—21no—
562C22×Q8—21no—
563C22×Q8—44no—
564C22×Q8—114no—
565C22×Q8—111no—
566C22×Q8—221no—
567C22×Q8—222no—
568C22×Q8—444no—
569C22×Q8C22×D1111yescharacteristic
570C22×Q8C22×D1112yes—
571C22×Q8C22×D1112yes—
572C22×Q8C22×D1111yescharacteristic
573C22×D4—21no—
574C22×D4—111no—
575C22×D4—112no—
576C22×D4—111no—
577C22×D4—222no—
578C22×D4—222no—
579C22×D4—222no—
580C22×D4—221no—
581C22×D4C22×D1111yescharacteristic
582C23×C4—21no—
583C23×C4—111no—
584C23×C4—221no—
585C23×C4C22×D1111yescharacteristic
586C2×SD16—44no—
587C2×SD16—114no—
588C2×SD16—114no—
589C2×SD16—114no—
590C2×SD16—114no—
591C2×SD16—448no—
592C2×SD16—444no—
593C2×SD16C22×D1114yes—
594C2×SD16C22×D1114yes—
595C22×C8—112no—
596C22×C8—114no—
597C22×C8C22×D1112yes—
598C4⋊Q8—112no—
599C4⋊Q8—114no—
600C4⋊Q8—222no—
601C4⋊Q8—224no—
602C4⋊Q8—224no—
603#127—112no—
604#124—222no—
605#123—222no—
606#123—222no—
607#123—222no—
608#123—222no—
609C22⋊Q8—114no—
610C22⋊Q8—112no—
611C22⋊Q8—112no—
612C22⋊Q8—222no—
613C22⋊Q8—224no—
614C22⋊Q8—224no—
615C22⋊Q8—224no—
616C22⋊Q8—224no—
617C22⋊Q8—222no—
618C22⋊Q8—222no—
619C22⋊Q8—221no—
620C22⋊Q8—221no—
621#121—21no—
622#121—21no—
623#121—112no—
624#121—112no—
625#121—112no—
626#121—112no—
627#121—222no—
628#121—222no—
629#121—222no—
630#121—222no—
631#121—222no—
632#121—221no—
633#121—221no—
634#121C22×D1112yes—
635#121C22×D1112yes—
636#120—222no—
637#120—222no—
638#120—222no—
639#120—222no—
640C4×Q8—114no—
641C4×Q8—222no—
642C4×D4—112no—
643C4×D4—112no—
644C4×D4—112no—
645C4×D4—112no—
646C4×D4—112no—
647C4×D4—112no—
648C4×D4—222no—
649C4×D4—224no—
650C4×D4—224no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—221no—
656C2×C4⋊C4—221no—
657C2×C4⋊C4—221no—
658C2×C4⋊C4—221no—
659C2×C4⋊C4—221no—
660C2×C4⋊C4C22×D1111yescharacteristic
661C2×C22⋊C4—21no—
662C2×C22⋊C4—111no—
663C2×C22⋊C4—111no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—221no—
666C2×C22⋊C4—221no—
667C2×C22⋊C4—221no—
668C2×C42—111no—
669C2×C42—221no—
670#106—114no—
671#106—114no—
672C4⋊C8—114no—
673#103—114no—
674#103—114no—
675#103—114no—
676#103—114no—
677#103C22×D1114yes—
678#103C22×D1114yes—
679#102—114no—
680#102—114no—
681C22⋊C8—112no—
682C22⋊C8—112no—
683C22⋊C8—114no—
684C22⋊C8C22×D1112yes—
685C22⋊C8C22×D1112yes—
686C4×C8—114no—
687C2×C11—22no—
688C2×C11—22no—
689C2×C11—22no—
690C2×C11—82no—
691C2×C11#348411yescharacteristic
692C2×C11C23×SD1611yescharacteristic
693C2×C11#358611yescharacteristic
694D11—24no—
695D11—82no—
696C24—21no—
697C24—111no—
698C24—222no—
699C24—221no—
700C24D4×D1111yescharacteristic
701#41—448no—
702#41—448no—
703#41—448no—
704C2×Q8—24no—
705C2×Q8—21no—
706C2×Q8—22no—
707C2×Q8—22no—
708C2×Q8—21no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—42no—
712C2×Q8—42no—
713C2×Q8—42no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—112no—
718C2×Q8—222no—
719C2×Q8—224no—
720C2×Q8—221no—
721C2×Q8—228no—
722C2×Q8—442no—
723C2×Q8—444no—
724C2×Q8—444no—
725C2×Q8—448no—
726C2×Q8C23×D1112yes—
727C2×Q8C23×D1112yes—
728C2×D4—22no—
729C2×D4—22no—
730C2×D4—21no—
731C2×D4—42no—
732C2×D4—44no—
733C2×D4—118no—
734C2×D4—112no—
735C2×D4—112no—
736C2×D4—112no—
737C2×D4—222no—
738C2×D4—222no—
739C2×D4—222no—
740C2×D4—222no—
741C2×D4—222no—
742C2×D4—222no—
743C2×D4—222no—
744C2×D4—221no—
745C2×D4—442no—
746C2×D4—444no—
747C2×D4—448no—
748C2×D4—448no—
749C2×D4—448no—
750C2×D4—444no—
751C2×D4C23×D1112yes—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—42no—
758C22×C4—44no—
759C22×C4—111no—
760C22×C4—111no—
761C22×C4—111no—
762C22×C4—112no—
763C22×C4—112no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—224no—
767C22×C4—222no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—442no—
772C22×C4—444no—
773C22×C4D4×D1111yescharacteristic
774C22×C4D4×D1111yescharacteristic
775C22×C4D4×D1111yescharacteristic
776C22×C4C23×D1111yescharacteristic
777C22×C4C23×D1111yescharacteristic
778C22×C4C23×D1111yescharacteristic
779SD16—28no—
780SD16—44no—
781SD16—228no—
782SD16—444no—
783SD16—444no—
784SD16—444no—
785C2×C8—42no—
786C2×C8—114no—
787C2×C8—444no—
788C2×C8—442no—
789C2×C8C23×D1114yes—
790C4⋊C4—21no—
791C4⋊C4—112no—
792C4⋊C4—112no—
793C4⋊C4—112no—
794C4⋊C4—112no—
795C4⋊C4—222no—
796C4⋊C4—224no—
797C4⋊C4—224no—
798C4⋊C4—224no—
799C4⋊C4—224no—
800C4⋊C4—222no—
801C4⋊C4—221no—
802C4⋊C4—221no—
803C4⋊C4—222no—
804C4⋊C4—222no—
805C4⋊C4C23×D1112yes—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—112no—
809C22⋊C4—112no—
810C22⋊C4—112no—
811C22⋊C4—112no—
812C22⋊C4—222no—
813C22⋊C4—222no—
814C22⋊C4—224no—
815C22⋊C4—222no—
816C22⋊C4—222no—
817C22⋊C4—222no—
818C22⋊C4—222no—
819C22⋊C4—222no—
820C22⋊C4—222no—
821C42—112no—
822C42—112no—
823C42—224no—
824C11#6156211yescharacteristic, complemented, Sylow
825C23—22no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—81no—
830C23—81no—
831C23—112no—
832C23—114no—
833C23—222no—
834C23—441no—
835C23—441no—
836C23—444no—
837C23—442no—
838C23—881no—
839C23—881no—
840C23—882no—
841C23—882no—
842C23SD16×D1114yescomplemented
843C23C2×D4×D1111yescharacteristic
844C23C2×D4×D1111yescharacteristic
845C23C2×D4×D1111yescharacteristic
846Q8—24no—
847Q8—22no—
848Q8—22no—
849Q8—22no—
850Q8—44no—
851Q8—44no—
852Q8—42no—
853Q8—224no—
854Q8—448no—
855Q8—442no—
856Q8—444no—
857Q8#6703714yescomplemented
858D4—24no—
859D4—44no—
860D4—44no—
861D4—81no—
862D4—118no—
863D4—118no—
864D4—224no—
865D4—444no—
866D4—444no—
867D4—444no—
868D4—444no—
869D4—444no—
870D4—881no—
871D4—882no—
872D4—882no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—114no—
888C2×C4—112no—
889C2×C4—112no—
890C2×C4—112no—
891C2×C4—224no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—442no—
896C2×C4—448no—
897C2×C4—444no—
898C2×C4—444no—
899C2×C4—444no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—442no—
903C2×C4—442no—
904C2×C4—442no—
905C2×C4C2×D4×D1111yescharacteristic
906C2×C4C2×D4×D1111yescharacteristic
907C2×C4C2×D4×D1111yescharacteristic
908C2×C4C24×D1111yescharacteristic
909C8—24no—
910C8—224no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—44no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—114no—
922C22—162no—
923C22—222no—
924C22—222no—
925C22—444no—
926C22—442no—
927C22—442no—
928C22—442no—
929C22—1762no—
930C22—1764no—
931C22C2×SD16×D1112yes—
932C22C2×SD16×D1112yes—
933C22C2×SD16×D1112yes—
934C22C22×D4×D1111yescharacteristic
935C4—24no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—42no—
940C4—42no—
941C4—114no—
942C4—222no—
943C4—222no—
944C4—442no—
945C4—442no—
946C4—442no—
947C4C2×#6703712yes—
948C2—22no—
949C2—22no—
950C2—22no—
951C2—82no—
952C2—224no—
953C2—882no—
954C2#1308224511yescharacteristic
955C2C22×SD16×D1111yescharacteristic
956C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#448C2
socleC22×C11C23×D4
prime radical#13082373C2
hypercenterC2×#448D11
hypocenterC11#61562
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C22⋊D11C2semidirect
3. #13080477C2semidirect
4. #13080474C2semidirect
5. SD16×C22⋊D11C2semidirect
6. #13080305C2semidirect
7. #13079539C2semidirect
8. #13079374C2semidirect
9. #13079373C2semidirect
10. #13079371C2semidirect
11. #13078642C2semidirect
12. C2×#10622840C2semidirect
13. D11×#448C2semidirect
14. #13077638C2semidirect
15. C2×C11×#448C2semidirect
16. C23×Q8×C11C22semidirect
17. C22×Q8×D11C22semidirect
19. C22×C11×SD16C22semidirect
23. Q8×C22⋊D11C22semidirect
24. Q8×C22⋊D11C22semidirect
26. C2×#66999C22semidirect
27. C2×Q8×Dic11C22semidirect
29. C2×#66997C22semidirect
30. C22×#4325C22semidirect
37. C2×#66977C22semidirect
38. C2×SD16×D11C22semidirect
48. C11×#448C22semidirect
49. C11×#448C22semidirect
50. C11×#448C22semidirect
51. C2×C11×#103C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. #10622840C22semidirect
54. #10622840C22semidirect
55. #10622840C22semidirect
56. C2×#66899C22semidirect
57. #10622831C22semidirect
58. C2×C22⋊(C11⋊C8)C22semidirect
59. #10622788C22semidirect
60. #10622784C22semidirect
61. #10622783C22semidirect
62. #10622782C22semidirect
63. #10622776C22semidirect
64. #10622775C22semidirect
65. SD16×Dic11C22semidirect
66. #10622727C22semidirect
67. C8×C22⋊D11C22semidirect
68. #10622654C22semidirect
69. #10622653C22semidirect
70. #10622647C22semidirect
71. #10622584C22semidirect
72. #10622431C22semidirect
73. #10622420C22semidirect
74. #10622419C22semidirect
75. #10622418C22semidirect
76. D11×#103C22semidirect
77. #10622405C22semidirect
78. #10622404C22semidirect
79. #10622401C22semidirect
80. #10622351C22semidirect
81. #10622348C22semidirect
82. #10622344C22semidirect
83. (C22⋊D11)⋊C8C22semidirect
84. D11×C22⋊C8C22semidirect
85. #10622334C22semidirect
86. #10622331C22semidirect
266. C2×C22⋊D11SD16semidirect
360. C2×#448D11semidirect
368. C23×C11C2×SD16semidirect
381. C22×D11C2×SD16semidirect
390. Q8×C11H(5,𝔽2)semidirect
419. C22⋊D11C2×SD16semidirect
420. C22⋊D11C2×SD16semidirect
430. C2×Dic11C2×SD16semidirect
450. C23×Q8C2×D11semidirect
453. C22×SD16C2×D11semidirect
505. #448C2×D11semidirect
506. #448C2×D11semidirect
507. #448C2×D11semidirect
515. C2×#103C2×D11semidirect
518. C2×C22⋊C8C2×D11semidirect
824. C11#61562semidirect
842. C23SD16×D11semidirect
857. Q8#67037semidirect

Maximal subgroups

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

subgroupindex
#130823732
C2×Q8×C22⋊D112
#130804772
#130804742
SD16×C22⋊D112
#130803052
#130795392
#130793742
#130793732
#130793712
#130786422
C2×#106228402
D11×#4482
#130776382
C2×C11×#4482
#6156211