Finite Group Databasebeta

← #15638653

Subgroups — #15638653

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic, complemented
2#13080781C214yesmaximal, complemented
3#13080661C214yesmaximal, complemented
4#13080182C214yesmaximal, complemented
5#13080122C214yesmaximal, complemented
6#13079640C212yesmaximal, complemented
7#13079442C212yesmaximal, complemented
8#13079388C211yesmaximal, characteristic, complemented
9#13079373C211yesmaximal, characteristic, complemented
10#13078783C212yesmaximal, complemented
11#13077849C212yesmaximal, complemented
12C2×#10622663C211yesmaximal, characteristic, complemented
13C2×#10622653C211yesmaximal, characteristic, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C11×#3505C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C23×Dic22C2211yescharacteristic, complemented
18C11×#553—22no—
19C11×#553C2212yes—
20C11×#552C2212yes—
21C11×#551—22no—
22C11×#548C2212yes—
23C11×#546C2212yes—
24C11×#539—21no—
25C11×#538—21no—
26C11×#534—21no—
27C11×#529C2212yes—
28C11×#525C2212yes—
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C11×#518—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×#67004C2214yescomplemented
34C22×#4326C2212yescomplemented
35C2×D4×Dic11—21no—
36C22×#4324C2212yescomplemented
37C2×#66977C2211yescharacteristic
38C2×#66977C2211yescharacteristic, complemented
39D4×Dic22—22no—
40D4×Dic22—22no—
41D4×Dic22C2214yes—
42D4×Dic22C2214yescomplemented
43C2×#66941—21no—
44C2×#66931—21no—
45C2×#66931—21no—
46C2×#66922C2211yescharacteristic, complemented
47C2×C4×Dic22C2211yescharacteristic, complemented
48#10622852C2214yescomplemented
49#10622841C2212yescomplemented
50#10622831C2212yescomplemented
51#10622820C2212yescomplemented
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622682C2214yescomplemented
55#10622676C2214yescomplemented
56#10622673C2214yescomplemented
57#10622667C2214yescomplemented
58#10622665C2214yescomplemented
59#10622664C2214yescomplemented
60#10622663C2214yescomplemented
61#10622663C2212yescomplemented
62#10622663C2212yescomplemented
63#10622663C2214yescomplemented
64#10622663C2212yescomplemented
65#10622657C2212yescomplemented
66#10622655C2214yescomplemented
67#10622654C2214yescomplemented
68#10622653C2212yes—
69#10622653C2212yes—
70#10622653C2212yes—
71#10622653C2214yescomplemented
72#10622653C2214yescomplemented
73#10622647C2212yes—
74#10622644C2214yescomplemented
75#10622643C2214yescomplemented
76#10622632C2214yescomplemented
77#10622631C2214yescomplemented
78#10622624C2214yes—
79#10622624C2214yescomplemented
80#10622617C2214yescomplemented
81#10622609C2214yescomplemented
82#10622584C2212yescomplemented
83#10622583C2212yescomplemented
84C2×#66874C2212yescomplemented
85C2×#66874C2212yescomplemented
86#10622539C2212yescomplemented
87C2×C11×#41C2312yes—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11D411yescharacteristic
91C22×D4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×Dic11—21no—
95C23×Dic11—21no—
96C22×Dic22—21no—
97C22×Dic22—21no—
98C22×Dic22—21no—
99C22×Dic22—21no—
100C22×Dic22—22no—
101C22×Dic22—44no—
102C22×Dic22—44no—
103C22×Dic22C2311yescharacteristic
104C22×Dic22C2312yes—
105C22×Dic22C2314yes—
106C22×Dic22C2312yes—
107C22×Dic22C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C11×#126—22no—
110C11×#126—22no—
111C11×#126—22no—
112C11×#125—22no—
113C11×#125C2312yes—
114C11×#124—22no—
115C11×#124C2312yes—
116C11×#123—22no—
117C11×#123—22no—
118C11×#123—22no—
119C11×#123—22no—
120C11×#123—22no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8C2312yes—
125C11×C22⋊Q8C2312yes—
126C11×C22⋊Q8C2312yes—
127C11×#121—22no—
128C11×#121—22no—
129C11×#121—21no—
130C11×#121—21no—
131C11×#121—22no—
132C11×#121C2312yes—
133C11×#121C2312yes—
134C11×#121C2312yes—
135C11×#120—22no—
136C11×#120—22no—
137C4×Q8×C11C2312yes—
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—22no—
141C4×D4×C11—22no—
142C4×D4×C11—22no—
143C4×D4×C11D412yes—
144C4×D4×C11D412yes—
145C4×D4×C11C2312yes—
146C4×D4×C11C2312yes—
147C4×D4×C11C2312yes—
148C11×#117—22no—
149C11×#117—22no—
150C11×#117C2312yes—
151C2×C11×C4⋊C4—21no—
152C2×C11×C4⋊C4D411yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C22⋊C4—21no—
156C2×C11×C22⋊C4—21no—
157C2×C11×C22⋊C4—22no—
158C2×C11×C22⋊C4D411yescharacteristic
159C2×C11×C22⋊C4D411yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C22⋊Dic11—21no—
162C2×C22⋊Dic11—21no—
163#67004—48no—
164C2×#4326—44no—
165C2×#4326C2314yes—
166C2×#4326C2314yes—
167C2×#4326C2314yes—
168D4×Dic11—24no—
169D4×Dic11—24no—
170C2×#4324—44no—
171C2×#4324C2314yes—
172C2×#4324C2314yes—
173C2×#4324C2314yes—
174C2×C4⋊Dic11—21no—
175C2×C4⋊Dic11—21no—
176C2×C4⋊Dic11C2311yescharacteristic
177#66977—21no—
178#66977—21no—
179#66977—22no—
180#66977C2312yes—
181#66977C2312yes—
182#66977C2314yes—
183C2×Dic11⋊C4—21no—
184C2×Dic11⋊C4—21no—
185C2×Dic11⋊C4—21no—
186C2×C4×Dic11—21no—
187C2×#4318C2314yes—
188C22×C11⋊C8C2312yes—
189C22×C11⋊C8C2312yes—
190#66941—24no—
191#66941—24no—
192#66931—24no—
193#66931—24no—
194#66931—24no—
195#66931—24no—
196#66922—22no—
197#66922C2314yes—
198C4×Dic22—22no—
199C4×Dic22C2314yes—
200#66899C2314yes—
201#66896C2314yes—
202C22⋊(C11⋊C8)C2312yes—
203C22⋊(C11⋊C8)C2312yes—
204C22⋊(C11⋊C8)C2312yes—
205C22⋊(C11⋊C8)C2312yes—
206C22⋊(C11⋊C8)C2314yes—
207#66874C2314yes—
208#66874C2314yes—
209#66874C2314yes—
210#66874C2314yes—
211#66874C2314yes—
212#66874C2314yes—
213#66872C2314yes—
214#66871C2314yes—
215C4⋊(C11⋊C8)C2314yes—
216#66867C2314yes—
217#61574—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C11×#41—44no—
222C2×Q8×C11—21no—
223C2×Q8×C11—42no—
224C2×Q8×C11C2412yes—
225C2×D4×C11—24no—
226C2×D4×C11—22no—
227C2×D4×C11—22no—
228C2×D4×C11—22no—
229C2×D4×C11—22no—
230C2×D4×C11—21no—
231C2×D4×C11—42no—
232C2×D4×C11—44no—
233C2×D4×C11C2×D412yes—
234C2×D4×C11C2×D412yes—
235C2×D4×C11C2412yes—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11—42no—
242C22×C4×C11—42no—
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2412yes—
254C22×Dic11—21no—
255C22×Dic11—24no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—44no—
262C22×Dic11—44no—
263C2×Dic22—24no—
264C2×Dic22—24no—
265C2×Dic22—24no—
266C2×Dic22—28no—
267C2×Dic22—21no—
268C2×Dic22—21no—
269C2×Dic22—21no—
270C2×Dic22—24no—
271C2×Dic22—22no—
272C2×Dic22—22no—
273C2×Dic22—42no—
274C2×Dic22—42no—
275C2×Dic22—44no—
276C2×Dic22—42no—
277C2×Dic22—42no—
278C2×Dic22—44no—
279C2×Dic22—44no—
280C2×Dic22—48no—
281C2×Dic22—44no—
282C2×Dic22—44no—
283C2×Dic22C2412yes—
284C2×Dic22C2412yes—
285C2×Dic22C2412yes—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4C2×D412yes—
295C11×C4⋊C4C2×D412yes—
296C11×C4⋊C4C2412yes—
297C11×C4⋊C4C2412yes—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4—22no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4C2×D412yes—
309C11×C22⋊C4C2×D412yes—
310C11×C22⋊C4C2×D412yes—
311C11×C22⋊C4C2×D412yes—
312C42×C11—22no—
313C42×C11—22no—
314C42×C11C2×D412yes—
315C42×C11C2412yes—
316C22⋊Dic11—24no—
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319#4326—28no—
320#4326—44no—
321#4326—44no—
322#4324—28no—
323#4324—44no—
324#4324—44no—
325C4⋊Dic11—21no—
326C4⋊Dic11—24no—
327C4⋊Dic11—24no—
328C4⋊Dic11C2412yes—
329Dic11⋊C4—24no—
330Dic11⋊C4—24no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333C4×Dic11—24no—
334#4318—44no—
335C2×C11⋊C8—42no—
336C2×C11⋊C8—42no—
337C2×C11⋊C8C2414yes—
338C2×C11⋊C8C2414yes—
339#3505D1111yescharacteristic
340C2×D4×Q8—111no—
341#3320—114no—
342#3312—114no—
343#3270—114no—
344#3266—114no—
345#3218—112no—
346#3196—112no—
347#3189—111no—
348#3187—111no—
349#3117—112no—
350#3004—112no—
351C2×#451—111no—
352C2×#448—111no—
353#2973—111no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—42no—
361C23×C11—81no—
362C23×C11—81no—
363C23×C11#13714yescomplemented
364C23×C11C22×D412yes—
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368Q8×C11—24no—
369Q8×C11—81no—
370D4×C11—24no—
371D4×C11—24no—
372D4×C11—24no—
373D4×C11—44no—
374D4×C11—44no—
375D4×C11—81no—
376D4×C11—82no—
377D4×C11—82no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—24no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—42no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—42no—
393C2×C4×C11—82no—
394C2×C4×C11—82no—
395C2×C4×C11—81no—
396C2×C4×C11—81no—
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D412yes—
399C2×C4×C11C22×D412yes—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C2511yescharacteristic
404C2×Dic11—24no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—44no—
410C2×Dic11—44no—
411C2×Dic11—48no—
412C2×Dic11—42no—
413C2×Dic11—42no—
414C2×Dic11—42no—
415Dic22—24no—
416Dic22—22no—
417Dic22—22no—
418Dic22—24no—
419Dic22—22no—
420Dic22—48no—
421Dic22—44no—
422Dic22—44no—
423Dic22—42no—
424Dic22—42no—
425Dic22H(5,𝔽2)14yes—
426C11⋊C8—24no—
427C11⋊C8—24no—
428C23×Q8—111no—
429C23×Q8—111no—
430C2×#137—114no—
431C22×Q16—112no—
432C22×SD16—112no—
433#553—22no—
434#553C2×D1112yes—
435#552C2×D1112yes—
436#551—22no—
437D4×Q8—114no—
438D4×Q8—114no—
439D4×Q8—222no—
440D4×Q8—222no—
441#548C2×D1112yes—
442#546C2×D1112yes—
443#539—21no—
444#538—21no—
445#534—21no—
446C2×C4⋊Q8—111no—
447C2×C4⋊Q8—221no—
448#529C2×D1112yes—
449#525C2×D1112yes—
450C2×C22⋊Q8—111no—
451C2×C22⋊Q8—111no—
452C2×C22⋊Q8—221no—
453C2×C22⋊Q8—221no—
454C2×C22⋊Q8C2×D1111yescharacteristic
455C2×#121C2×D1111yescharacteristic
456#518—21no—
457C2×C4×Q8—111no—
458C2×C4×D4—221no—
459C2×C4×D4C2×D1111yescharacteristic
460#497—114no—
461#491—114no—
462#485—114no—
463#484—112no—
464#484—112no—
465#483—112no—
466#481—112no—
467#479—114no—
468#470—114no—
469#468—114no—
470#467—114no—
471#465—114no—
472#464—114no—
473#462—114no—
474#461—114no—
475#452—114no—
476#451—112no—
477#451—112no—
478#451—112no—
479#451—112no—
480#451—114no—
481#451—114no—
482#450—112no—
483#448—112no—
484#448—112no—
485#448—112no—
486#448—114no—
487#448—114no—
488#441—114no—
489#440—114no—
490#435—114no—
491#435—114no—
492#432—112no—
493#419—114no—
494C2×#103—112no—
495C2×#103—112no—
496#407—112no—
497C2×C22⋊C8—111no—
498C2×C22⋊C8—111no—
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—21no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—44no—
509C22×C11—44no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—162no—
514C22×C11C2×#13712yes—
515C22×C11C2×#13712yes—
516C22×C11C2×#13712yes—
517C22×C11C23×D411yescharacteristic
518C4×C11—22no—
519C4×C11—21no—
520C4×C11—22no—
521C4×C11—21no—
522C4×C11—21no—
523C4×C11—22no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527C4×C11C2×H(5,𝔽2)12yes—
528Dic11—24no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532C2×#41C22×D1112yes—
533C22×Q8—111no—
534C22×Q8—112no—
535C22×Q8—112no—
536C22×Q8—114no—
537C22×Q8—111no—
538C22×Q8—111no—
539C22×Q8—221no—
540C22×Q8—221no—
541C22×Q8—221no—
542C22×Q8—221no—
543C22×Q8—222no—
544C22×Q8—444no—
545C22×Q8—444no—
546C22×Q8C22×D1111yescharacteristic
547C22×D4—21no—
548C22×D4C22⋊D1111yescharacteristic
549C22×D4C22×D1111yescharacteristic
550C23×C4—221no—
551C23×C4—221no—
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554#137—448no—
555C2×Q16—114no—
556C2×Q16—114no—
557C2×Q16—114no—
558C2×Q16—444no—
559C2×SD16—114no—
560C2×SD16—114no—
561C2×SD16—114no—
562C2×SD16—444no—
563C2×M16—114no—
564C22×C8—112no—
565C22×C8—112no—
566C4⋊Q8—114no—
567C4⋊Q8—224no—
568C4⋊Q8—224no—
569C4⋊Q8—222no—
570#126—22no—
571#126—22no—
572#126—22no—
573#125—22no—
574#125C22×D1112yes—
575#124—22no—
576#124C22×D1112yes—
577#123—22no—
578#123—22no—
579#123—22no—
580#123—22no—
581#123—22no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8—22no—
585C22⋊Q8—112no—
586C22⋊Q8—112no—
587C22⋊Q8—114no—
588C22⋊Q8—221no—
589C22⋊Q8—221no—
590C22⋊Q8—222no—
591C22⋊Q8—224no—
592C22⋊Q8—224no—
593C22⋊Q8—224no—
594C22⋊Q8—224no—
595C22⋊Q8C22×D1112yes—
596C22⋊Q8C22×D1112yes—
597C22⋊Q8C22×D1112yes—
598#121—22no—
599#121—22no—
600#121—21no—
601#121—21no—
602#121—22no—
603#121C22×D1112yes—
604#121C22×D1112yes—
605#121C22×D1112yes—
606#120—22no—
607#120—22no—
608C4×Q8—114no—
609C4×Q8—222no—
610C4×Q8C22×D1112yes—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—224no—
617C4×D4—224no—
618C4×D4C22⋊D1112yes—
619C4×D4C22⋊D1112yes—
620C4×D4C22×D1112yes—
621C4×D4C22×D1112yes—
622C4×D4C22×D1112yes—
623#117—22no—
624#117—22no—
625#117C22×D1112yes—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—221no—
629C2×C4⋊C4—221no—
630C2×C4⋊C4—221no—
631C2×C4⋊C4—221no—
632C2×C4⋊C4—221no—
633C2×C4⋊C4C22⋊D1111yescharacteristic
634C2×C4⋊C4C22×D1111yescharacteristic
635C2×C4⋊C4C22×D1111yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—221no—
641C2×C22⋊C4C22⋊D1111yescharacteristic
642C2×C22⋊C4C22⋊D1111yescharacteristic
643C2×C42—221no—
644C2×C42C22×D1111yescharacteristic
645#107—114no—
646#106—114no—
647C4⋊C8—114no—
648#103—114no—
649#103—114no—
650#103—114no—
651#103—114no—
652#103—114no—
653#103—114no—
654#103—114no—
655#102—114no—
656C22⋊C8—112no—
657C22⋊C8—112no—
658C22⋊C8—112no—
659C22⋊C8—112no—
660C22⋊C8—114no—
661#97—114no—
662C2×C11—22no—
663C2×C11—22no—
664C2×C11—22no—
665C2×C11—42no—
666C2×C11—82no—
667C2×C11#348411yescharacteristic
668C2×C11C22×#13711yescharacteristic
669C2×C11#358611yescharacteristic
670C24—21no—
671C24C2×C22⋊D1111yescharacteristic
672C24C2×C22⋊D1111yescharacteristic
673#41—44no—
674C2×Q8—21no—
675C2×Q8—42no—
676C2×Q8—112no—
677C2×Q8—112no—
678C2×Q8—112no—
679C2×Q8—224no—
680C2×Q8—224no—
681C2×Q8—224no—
682C2×Q8—228no—
683C2×Q8—221no—
684C2×Q8—224no—
685C2×Q8—222no—
686C2×Q8—222no—
687C2×Q8—221no—
688C2×Q8—221no—
689C2×Q8—442no—
690C2×Q8—442no—
691C2×Q8—444no—
692C2×Q8—442no—
693C2×Q8—442no—
694C2×Q8—444no—
695C2×Q8—444no—
696C2×Q8—448no—
697C2×Q8—444no—
698C2×Q8—444no—
699C2×Q8C23×D1112yes—
700C2×D4—24no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—42no—
707C2×D4—44no—
708C2×D4C2×C22⋊D1112yes—
709C2×D4C2×C22⋊D1112yes—
710C2×D4C23×D1112yes—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—224no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—444no—
726C22×C4—444no—
727C22×C4C2×C22⋊D1111yescharacteristic
728C22×C4C2×C22⋊D1111yescharacteristic
729C22×C4C2×C22⋊D1111yescharacteristic
730C22×C4C2×C22⋊D1111yescharacteristic
731C22×C4C2×C22⋊D1111yescharacteristic
732C22×C4C2×C22⋊D1111yescharacteristic
733C22×C4C2×C22⋊D1112yes—
734C22×C4C23×D1111yescharacteristic
735C22×C4C23×D1111yescharacteristic
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1112yes—
738Q16—228no—
739Q16—444no—
740Q16—444no—
741SD16—228no—
742SD16—444no—
743SD16—444no—
744M16—444no—
745C2×C8—114no—
746C2×C8—114no—
747C2×C8—442no—
748C2×C8—442no—
749C4⋊C4—22no—
750C4⋊C4—22no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—112no—
758C4⋊C4—221no—
759C4⋊C4—224no—
760C4⋊C4—224no—
761C4⋊C4—224no—
762C4⋊C4—222no—
763C4⋊C4—222no—
764C4⋊C4—224no—
765C4⋊C4C2×C22⋊D1112yes—
766C4⋊C4C2×C22⋊D1112yes—
767C4⋊C4C23×D1112yes—
768C4⋊C4C23×D1112yes—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—224no—
780C22⋊C4—222no—
781C22⋊C4—222no—
782C22⋊C4C2×C22⋊D1112yes—
783C22⋊C4C2×C22⋊D1112yes—
784C22⋊C4C2×C22⋊D1112yes—
785C22⋊C4C2×C22⋊D1112yes—
786C42—22no—
787C42—22no—
788C42—224no—
789C42C2×C22⋊D1112yes—
790C42C23×D1112yes—
791C11#6157411yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—42no—
799C23—81no—
800C23—81no—
801C23#6700414yescomplemented
802C23C22×C22⋊D1112yes—
803C23C22×C22⋊D1111yescharacteristic
804C23C22×C22⋊D1111yescharacteristic
805C23C22×C22⋊D1111yescharacteristic
806Q8—24no—
807Q8—81no—
808Q8—114no—
809Q8—224no—
810Q8—222no—
811Q8—222no—
812Q8—224no—
813Q8—222no—
814Q8—448no—
815Q8—444no—
816Q8—444no—
817Q8—442no—
818Q8—442no—
819D4—24no—
820D4—24no—
821D4—24no—
822D4—44no—
823D4—44no—
824D4—81no—
825D4—82no—
826D4—82no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—82no—
843C2×C4—82no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—224no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—444no—
852C2×C4—444no—
853C2×C4—448no—
854C2×C4—442no—
855C2×C4—442no—
856C2×C4—442no—
857C2×C4C22×C22⋊D1112yes—
858C2×C4C22×C22⋊D1112yes—
859C2×C4C22×C22⋊D1112yes—
860C2×C4C22×C22⋊D1111yescharacteristic
861C2×C4C22×C22⋊D1111yescharacteristic
862C2×C4C22×C22⋊D1111yescharacteristic
863C2×C4C24×D1111yescharacteristic
864C8—224no—
865C8—224no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—162no—
881C22C2×#6700412yes—
882C22C2×#6700412yes—
883C22C2×#6700412yes—
884C22C23×C22⋊D1111yescharacteristic
885C4—22no—
886C4—21no—
887C4—22no—
888C4—21no—
889C4—21no—
890C4—22no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—224no—
895C4—442no—
896C4—442no—
897C4—442no—
898C4D11×H(5,𝔽2)12yes—
899C2—22no—
900C2—22no—
901C2—22no—
902C2—42no—
903C2—82no—
904C2#1308224711yescharacteristic
905C2C22×#6700411yescharacteristic
906C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3505C2
socleC22×C11C23×D4
hypercenter#3505D11
hypocenterC11#61574
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic22C2semidirect
2. #13080781C2semidirect
3. #13080661C2semidirect
4. #13080182C2semidirect
5. #13080122C2semidirect
6. #13079640C2semidirect
7. #13079442C2semidirect
8. #13079388C2semidirect
9. #13079373C2semidirect
10. #13078783C2semidirect
11. #13077849C2semidirect
12. C2×#10622663C2semidirect
13. C2×#10622653C2semidirect
14. #13077645C2semidirect
17. C23×Dic22C22semidirect
33. C2×#67004C22semidirect
34. C22×#4326C22semidirect
36. C22×#4324C22semidirect
38. C2×#66977C22semidirect
42. D4×Dic22C22semidirect
46. C2×#66922C22semidirect
47. C2×C4×Dic22C22semidirect
48. #10622852C22semidirect
49. #10622841C22semidirect
50. #10622831C22semidirect
51. #10622820C22semidirect
54. #10622682C22semidirect
55. #10622676C22semidirect
56. #10622673C22semidirect
57. #10622667C22semidirect
58. #10622665C22semidirect
59. #10622664C22semidirect
60. #10622663C22semidirect
61. #10622663C22semidirect
62. #10622663C22semidirect
63. #10622663C22semidirect
64. #10622663C22semidirect
65. #10622657C22semidirect
66. #10622655C22semidirect
67. #10622654C22semidirect
71. #10622653C22semidirect
72. #10622653C22semidirect
74. #10622644C22semidirect
75. #10622643C22semidirect
76. #10622632C22semidirect
77. #10622631C22semidirect
79. #10622624C22semidirect
80. #10622617C22semidirect
81. #10622609C22semidirect
82. #10622584C22semidirect
83. #10622583C22semidirect
84. C2×#66874C22semidirect
85. C2×#66874C22semidirect
86. #10622539C22semidirect
363. C23×C11#137semidirect
791. C11#61574semidirect
801. C23#67004semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
#130807812
#130806612
#130801822
#130801222
#130796402
#130794422
#130793882
#130793732
#130787832
#130778492
C2×#106226632
C2×#106226532
#130776452
C11×#35052
#6157411