Finite Group Databasebeta

← #14926910

Subgroups — #14926910

Order 2816.

1816 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076999C211yesmaximal, characteristic, complemented
2#13076975C211yesmaximal, characteristic, complemented
3#13076966C211yesmaximal, characteristic, complemented
4#13076956C211yesmaximal, characteristic, complemented
5#13074809C212yesmaximal, complemented
6#13074798C212yesmaximal, complemented
7#13074008C212yesmaximal, complemented
8#13073701C212yesmaximal, complemented
9#13073146C211yesmaximal, characteristic, complemented
10#13073090C211yesmaximal, characteristic, complemented
11#13073045C211yesmaximal, characteristic, complemented
12#13072754C212yesmaximal, complemented
13#13072453C211yesmaximal, characteristic, complemented
14#13072431C212yesmaximal
15#13072319C211yesmaximal, characteristic, complemented
16#13072143C211yesmaximal, characteristic, complemented
17#13072067C211yesmaximal, characteristic
18#13071347C212yesmaximal, complemented
19#13071242C212yesmaximal
20#13071144C211yesmaximal, characteristic, complemented
21C2×#10622598C211yesmaximal, characteristic, complemented
22C4×D4×Dic11C211yesmaximal, characteristic
23C11×#2487C211yesmaximal, characteristic
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C2×D4×Dic11C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C2×#66977C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×#66942C2212yes—
35C2×#66941C2211yescharacteristic
36C2×#66940C2211yescharacteristic
37C2×#66931C2212yes—
38C2×#66931C2212yes—
39C11×#400C2212yes—
40C11×#399C2212yes—
41C11×#389C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#386C2212yes—
44C11×#385C2212yes—
45C11×#380C2211yescharacteristic
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48#10622833C2212yes—
49#10622825C2211yescharacteristic
50#10622823C2212yes—
51#10622823C2212yes—
52C4×C22⋊Dic11C2211yescharacteristic
53C4×C22⋊Dic11C2211yescharacteristic
54C2×C11⋊#95C2212yes—
55#10622598C2211yescharacteristic
56#10622598C2211yescharacteristic
57#10622598C2212yes—
58#10622598C2211yescharacteristic
59#10622598C2212yes—
60#10622598C2211yescharacteristic
61#10622598C2211yescharacteristic
62#10622597C2212yes—
63#10622597C2212yes—
64#10622596C2212yes—
65#10622594C2212yes—
66#10622593C2212yes—
67#10622593C2212yes—
68#10622591C2212yes—
69#10622589C2211yescharacteristic
70#10622589C2211yescharacteristic
71#10622589C2211yescharacteristic
72C4⋊C4×Dic11C2211yescharacteristic
73C4⋊C4×Dic11C2211yescharacteristic
74C4⋊C4×Dic11C2211yescharacteristic
75#10622587C2211yescharacteristic
76#10622587C2211yescharacteristic
77#10622587C2212yes—
78#10622587C2211yescharacteristic
79#10622586C2211yescharacteristic
80#10622586C2212yes—
81#10622586C2211yescharacteristic
82#10622585C2212yes—
83#10622563C2212yes—
84#10622562C2212yes—
85#10622561C2212yes—
86#10622561C2212yes—
87#10622559C2212yes—
88#10622559C2212yes—
89#10622558C2212yes—
90#10622557C2212yes—
91#10622556C2212yes—
92#10622555C2212yes—
93#10622555C2212yes—
94C22⋊C4×Dic11C2211yescharacteristic
95C22⋊C4×Dic11C2212yes—
96C22⋊C4×Dic11C2211yescharacteristic
97C22⋊C4×Dic11C2211yescharacteristic
98C22⋊C4×Dic11C2211yescharacteristic
99C4×C4⋊Dic11C2211yescharacteristic
100C42×Dic11C2211yescharacteristic
101#10622542C2211yescharacteristic
102#10622541C2211yescharacteristic
103#10622274C2212yes—
104#10622272C2212yes—
105#10622270C2212yes—
106#10622270C2212yes—
107#10622269C2212yes—
108#10622269C2212yes—
109#10622267C2212yes—
110#10622267C2212yes—
111#10622266C2212yes—
112#10622266C2212yes—
113#10622266C2212yes—
114#10622265C2212yes—
115#10622265C2212yes—
116#10622265C2212yes—
117#10622264C2212yes—
118#10622263C2212yes—
119#10622262C2212yes—
120#10622260C2212yes—
121#10622260C2212yes—
122#10622259C2212yes—
123C22×D4×C11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C23×Dic11C2311yescharacteristic
128C23×Dic11C2311yescharacteristic
129C23×Dic11C2312yes—
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C22×Dic22C2311yescharacteristic
133C22×Dic22C2312yes—
134C4×D4×C11—24no—
135C2×C11×C4⋊C4—24no—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2311yescharacteristic
146C2×C11×C22⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C42×C11C2311yescharacteristic
150C2×C22⋊Dic11C2312yes—
151C2×C22⋊Dic11C2311yescharacteristic
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2311yescharacteristic
155C2×C22⋊Dic11C2311yescharacteristic
156C2×C22⋊Dic11C2311yescharacteristic
157D4×Dic11—24no—
158D4×Dic11Q818yescomplemented
159C2×C4⋊Dic11—44no—
160C2×C4⋊Dic11—42no—
161C2×C4⋊Dic11C2312yes—
162C2×C4⋊Dic11C2312yes—
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2311yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2311yescharacteristic
172#66977—24no—
173#66977—42no—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×C4×Dic11—42no—
188C2×C4×Dic11—42no—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203#66942—44no—
204#66941—42no—
205#66940—42no—
206#66931—28no—
207#66931—44no—
208C11×#95C2312yes—
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11⋊#95C2312yes—
214C11⋊#95C2312yes—
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2311yescharacteristic
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237#35017—111nomaximal, Sylow
238C24×C11C2411yescharacteristic
239C24×C11C2411yescharacteristic
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11C2×Q814yes—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—24no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—42no—
250C22×C4×C11—42no—
251C22×C4×C11#4114yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—24no—
266C22×Dic11—41no—
267C22×Dic11—41no—
268C22×Dic11—41no—
269C22×Dic11—41no—
270C22×Dic11—41no—
271C22×Dic11—41no—
272C22×Dic11—42no—
273C22×Dic11—42no—
274C22×Dic11C2×Q814yes—
275C22×Dic11C2×Q814yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2411yescharacteristic
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2411yescharacteristic
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2411yescharacteristic
286C22×Dic11C2411yescharacteristic
287C22×Dic11C2411yescharacteristic
288C2×Dic22—24no—
289C2×Dic22—22no—
290C2×Dic22—22no—
291C2×Dic22—22no—
292C2×Dic22—42no—
293C2×Dic22—42no—
294C11×C4⋊C4—24no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4—42no—
301C11×C4⋊C4—42no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4—42no—
306C11×C22⋊C4—42no—
307C42×C11—22no—
308C22⋊Dic11—22no—
309C22⋊Dic11—24no—
310C22⋊Dic11—42no—
311C22⋊Dic11—42no—
312C22⋊Dic11C2×Q814yes—
313C22⋊Dic11C2×Q814yes—
314C22⋊Dic11#4114yes—
315C4⋊Dic11—24no—
316C4⋊Dic11—22no—
317C4⋊Dic11—24no—
318C4⋊Dic11—24no—
319C4⋊Dic11—22no—
320C4⋊Dic11—22no—
321C4⋊Dic11—22no—
322C4⋊Dic11—42no—
323C4⋊Dic11—42no—
324C4⋊Dic11—42no—
325C4⋊Dic11C2×Q814yes—
326Dic11⋊C4—24no—
327Dic11⋊C4—24no—
328Dic11⋊C4—24no—
329Dic11⋊C4—24no—
330Dic11⋊C4—42no—
331Dic11⋊C4—42no—
332Dic11⋊C4—42no—
333Dic11⋊C4—42no—
334Dic11⋊C4—42no—
335Dic11⋊C4—42no—
336Dic11⋊C4—42no—
337Dic11⋊C4—42no—
338Dic11⋊C4—42no—
339C4×Dic11—22no—
340C4×Dic11—22no—
341C4×Dic11—22no—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11—42no—
346C4×Dic11—41no—
347C4×Dic11—41no—
348C4×Dic11—41no—
349C4×Dic11—41no—
350C4×Dic11—42no—
351C4×Dic11—41no—
352C4×Dic11C2×Q814yes—
353#2863—111no—
354#2859—111no—
355#2857—111no—
356#2855—111no—
357#2667—112no—
358#2666—112no—
359#2585—112no—
360#2556—112no—
361#2507—111no—
362#2502—111no—
363#2497—111no—
364#2487D1111yescharacteristic
365#2473—112no—
366#2451—111no—
367#2449—112no—
368#2440—111no—
369#2423—111no—
370#2417—111no—
371#2329—112no—
372#2318—112no—
373C4×C22⋊Q8—111no—
374C2×#389—111no—
375C42×D4—111no—
376C23×C11—21no—
377C23×C11—21no—
378C23×C11—21no—
379C23×C11—21no—
380C23×C11—21no—
381C23×C11—21no—
382C23×C11—21no—
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11C22×Q812yes—
387C23×C11C22×Q812yes—
388C23×C11C2×#4112yes—
389C23×C11C2×#4112yes—
390C23×C11C2511yescharacteristic
391D4×C11—28no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—28no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—21no—
411C2×C4×C11—22no—
412C2×C4×C11—21no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—48no—
416C2×C4×C11—44no—
417C2×C4×C11C22×Q812yes—
418C2×C4×C11C2×#4112yes—
419C2×C4×C11C2×#4112yes—
420C2×C4×C11H(5,𝔽2)12yes—
421C2×C4×C112−1+412yes—
422C2×Dic11—21no—
423C2×Dic11—21no—
424C2×Dic11—21no—
425C2×Dic11—21no—
426C2×Dic11—21no—
427C2×Dic11—21no—
428C2×Dic11—21no—
429C2×Dic11—21no—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—21no—
435C2×Dic11—21no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—21no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—44no—
452C2×Dic11—44no—
453C2×Dic11—44no—
454C2×Dic11—44no—
455C2×Dic11—84no—
456C2×Dic11C22×Q812yes—
457C2×Dic11C22×Q812yes—
458C2×Dic11C22×Q812yes—
459C2×Dic11C22×Q812yes—
460C2×Dic11C2×#4112yes—
461C2×Dic11C2×#4112yes—
462C2×Dic11H(5,𝔽2)12yes—
463Dic22—44no—
464Dic22—84no—
465C2×C4⋊Q8—111no—
466C2×#125—112no—
467C2×C22⋊Q8—111no—
468C2×C22⋊Q8—111no—
469C2×C22⋊Q8—112no—
470C2×C22⋊Q8—112no—
471C2×C4×Q8—111no—
472C2×C4×D4—111no—
473C2×C4×D4—111no—
474C2×C4×D4C2×D1111yescharacteristic
475C22×C4⋊C4—111no—
476C22×C4⋊C4—112no—
477C22×C4⋊C4C2×D1111yescharacteristic
478C22×C42—111no—
479C22×C42—111no—
480#400—112no—
481#400C2×D1112yes—
482#399—112no—
483#399C2×D1112yes—
484#398—112no—
485#398—112no—
486#398—112no—
487#398—112no—
488#398—112no—
489#398—112no—
490#398—112no—
491#398—112no—
492#396—112no—
493#396—112no—
494#395—112no—
495#395—112no—
496#391—112no—
497#391—111no—
498#391—111no—
499#391—111no—
500#391—111no—
501#391—112no—
502#389—112no—
503#389—112no—
504#389—112no—
505#389—111no—
506#389—111no—
507#389—111no—
508#389—111no—
509#389—111no—
510#389—112no—
511#389—111no—
512#389—111no—
513#389—111no—
514#389—112no—
515#389—112no—
516#389C2×D1111yescharacteristic
517#389C2×D1111yescharacteristic
518#388—112no—
519#388—112no—
520#387—112no—
521#387—112no—
522#387—112no—
523#387—112no—
524#387—112no—
525#387—112no—
526#387—112no—
527#387—112no—
528#387—112no—
529#387—112no—
530#386—112no—
531#386C2×D1112yes—
532#385—112no—
533#385—112no—
534#385—112no—
535#385—112no—
536#385—112no—
537#385C2×D1112yes—
538#384—111no—
539#384—111no—
540#384—111no—
541#383—112no—
542#382—112no—
543#381—112no—
544#380—111no—
545#380—112no—
546#380—112no—
547#380C2×D1111yescharacteristic
548#380C2×D1111yescharacteristic
549#380C2×D1111yescharacteristic
550C4×C4⋊C4—111no—
551C4×C4⋊C4—111no—
552C4×C4⋊C4—111no—
553C4×C4⋊C4—111no—
554C4×C4⋊C4—112no—
555C4×C22⋊C4—111no—
556C4×C22⋊C4—111no—
557C4×C22⋊C4—112no—
558C4×C22⋊C4—111no—
559C4×C22⋊C4—111no—
560C4×C22⋊C4—111no—
561C4×C22⋊C4—111no—
562C2×#95—112no—
563C43—111no—
564C22×C11—22no—
565C22×C11—22no—
566C22×C11—22no—
567C22×C11—22no—
568C22×C11—22no—
569C22×C11—22no—
570C22×C11—22no—
571C22×C11—22no—
572C22×C11—22no—
573C22×C11—41no—
574C22×C11—41no—
575C22×C11—41no—
576C22×C11—41no—
577C22×C11#53314yes—
578C22×C11C23×Q811yescharacteristic
579C22×C11C22×#4111yescharacteristic
580C22×C11C22×#4111yescharacteristic
581C22×C11C2×H(5,𝔽2)11yescharacteristic
582C22×C11C2×H(5,𝔽2)11yescharacteristic
583C22×C11C2×2−1+411yescharacteristic
584C22×C11#58511yescharacteristic
585C4×C11—22no—
586C4×C11—22no—
587C4×C11—41no—
588C4×C11—41no—
589C4×C11—42no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11#53914yes—
594Dic11—22no—
595Dic11—22no—
596Dic11—22no—
597Dic11—22no—
598Dic11—22no—
599Dic11—22no—
600Dic11—22no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11—41no—
605Dic11—42no—
606C22×Q8—111no—
607C22×Q8—112no—
608C22×D4C22×D1111yescharacteristic
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—112no—
614C23×C4C22×D1111yescharacteristic
615C23×C4C22×D1111yescharacteristic
616C23×C4C22×D1112yes—
617C4⋊Q8—442no—
618#125—444no—
619C22⋊Q8—228no—
620C22⋊Q8—224no—
621C22⋊Q8—444no—
622C22⋊Q8—442no—
623C4×Q8—442no—
624C4×D4—24no—
625C4×D4—118no—
626C4×D4—224no—
627C2×C4⋊C4—24no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—112no—
637C2×C4⋊C4—112no—
638C2×C4⋊C4—112no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—442no—
653C2×C4⋊C4—444no—
654C2×C4⋊C4C22×D1111yescharacteristic
655C2×C4⋊C4C22×D1111yescharacteristic
656C2×C4⋊C4C22×D1112yes—
657C2×C4⋊C4C22×D1111yescharacteristic
658C2×C4⋊C4C22×D1111yescharacteristic
659C2×C4⋊C4C22×D1111yescharacteristic
660C2×C4⋊C4C22×D1112yes—
661C2×C4⋊C4C22×D1112yes—
662C2×C22⋊C4—111no—
663C2×C22⋊C4—111no—
664C2×C22⋊C4—111no—
665C2×C22⋊C4—111no—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4C22×D1111yescharacteristic
670C2×C22⋊C4C22×D1111yescharacteristic
671C2×C22⋊C4C22×D1112yes—
672C2×C22⋊C4C22×D1112yes—
673C2×C22⋊C4C22×D1112yes—
674C2×C42—111no—
675C2×C42—111no—
676C2×C42—111no—
677C2×C42—111no—
678C2×C42—111no—
679C2×C42—111no—
680C2×C42—111no—
681C2×C42—112no—
682C2×C42—111no—
683C2×C42—111no—
684C2×C42—112no—
685C2×C42—111no—
686C2×C42—111no—
687C2×C42—111no—
688C2×C42—442no—
689C2×C42—442no—
690C2×C42C22×D1111yescharacteristic
691#95—112no—
692#95—112no—
693#95—112no—
694#95—112no—
695#95—111no—
696#95—111no—
697#95—111no—
698#95—111no—
699#95—111no—
700#95—111no—
701#95—112no—
702#95—112no—
703#95—112no—
704#95—112no—
705#95—112no—
706#95—112no—
707#95—112no—
708#95—112no—
709#95—112no—
710#95—112no—
711#95—112no—
712#95—112no—
713#95—112no—
714#95—112no—
715#95C22×D1112yes—
716#95C22×D1112yes—
717#95C22×D1112yes—
718#95C22×D1112yes—
719#95C22×D1112yes—
720C2×C11—24no—
721C2×C11—42no—
722C2×C11C2×#53311yescharacteristic
723C2×C11C2×#53911yescharacteristic
724C2×C11#346011yescharacteristic
725C2×C11#350111yescharacteristic
726C2×C11#350311yescharacteristic
727C2×C11#351511yescharacteristic
728C2×C11#351911yescharacteristic
729C24C23×D1111yescharacteristic
730C24C23×D1111yescharacteristic
731C2×Q8—224no—
732C2×Q8—222no—
733C2×Q8—222no—
734C2×Q8—222no—
735C2×Q8—442no—
736C2×Q8—442no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4Q8×D1114yes—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—24no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—111no—
749C22×C4—111no—
750C22×C4—111no—
751C22×C4—111no—
752C22×C4—111no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—114no—
756C22×C4—114no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—111no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—224no—
767C22×C4—441no—
768C22×C4—441no—
769C22×C4—441no—
770C22×C4—441no—
771C22×C4—441no—
772C22×C4—441no—
773C22×C4—442no—
774C22×C4—442no—
775C22×C4#434114yes—
776C22×C4C23×D1112yes—
777C22×C4C23×D1111yescharacteristic
778C22×C4C23×D1112yes—
779C22×C4C23×D1112yes—
780C22×C4C23×D1111yescharacteristic
781C22×C4C23×D1112yes—
782C22×C4C23×D1111yescharacteristic
783C22×C4C23×D1111yescharacteristic
784C22×C4C23×D1111yescharacteristic
785C4⋊C4—24no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—114no—
794C4⋊C4—224no—
795C4⋊C4—224no—
796C4⋊C4—222no—
797C4⋊C4—224no—
798C4⋊C4—224no—
799C4⋊C4—224no—
800C4⋊C4—224no—
801C4⋊C4—224no—
802C4⋊C4—222no—
803C4⋊C4—222no—
804C4⋊C4—222no—
805C4⋊C4—442no—
806C4⋊C4—442no—
807C4⋊C4—442no—
808C4⋊C4—442no—
809C4⋊C4—442no—
810C4⋊C4—442no—
811C4⋊C4—442no—
812C4⋊C4—442no—
813C4⋊C4—442no—
814C4⋊C4—442no—
815C4⋊C4—442no—
816C4⋊C4—442no—
817C22⋊C4—22no—
818C22⋊C4—24no—
819C22⋊C4—22no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—114no—
823C22⋊C4—114no—
824C22⋊C4—114no—
825C22⋊C4—222no—
826C22⋊C4—224no—
827C22⋊C4—442no—
828C22⋊C4—442no—
829C42—22no—
830C42—114no—
831C42—222no—
832C42—222no—
833C42—222no—
834C42—222no—
835C42—222no—
836C42—222no—
837C42—441no—
838C42—441no—
839C42—441no—
840C42—441no—
841C42—442no—
842C42—442no—
843C42—441no—
844C11#3501711yescharacteristic, complemented, Sylow
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23C2×#434112yes—
856C23C2×Q8×D1112yes—
857C23C2×Q8×D1112yes—
858C23#41×D1112yes—
859C23C24×D1111yescharacteristic
860Q8—444no—
861Q8—884no—
862D4—28no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—28no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—48no—
887C2×C4—44no—
888C2×C4—112no—
889C2×C4—112no—
890C2×C4—112no—
891C2×C4—112no—
892C2×C4—112no—
893C2×C4—112no—
894C2×C4—112no—
895C2×C4—221no—
896C2×C4—221no—
897C2×C4—221no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—221no—
901C2×C4—221no—
902C2×C4—221no—
903C2×C4—221no—
904C2×C4—221no—
905C2×C4—221no—
906C2×C4—221no—
907C2×C4—221no—
908C2×C4—221no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—221no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—221no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—221no—
923C2×C4—222no—
924C2×C4—444no—
925C2×C4—444no—
926C2×C4—444no—
927C2×C4—444no—
928C2×C4—884no—
929C2×C4C2×#434112yes—
930C2×C4C2×#434112yes—
931C2×C4C2×Q8×D1112yes—
932C2×C4#6704212yes—
933C2×C4#6704312yes—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22#1062315314yes—
948C22C22×#434111yescharacteristic
949C22C22×Q8×D1111yescharacteristic
950C22C2×#41×D1111yescharacteristic
951C22C2×#6704211yescharacteristic
952C22C2×#6704311yescharacteristic
953C22D11×H(5,𝔽2)11yescharacteristic
954C22#1062345511yescharacteristic
955C4—22no—
956C4—22no—
957C4—42no—
958C4—41no—
959C4—42no—
960C4—42no—
961C4—41no—
962C4—42no—
963C4—222no—
964C4—222no—
965C4—222no—
966C4—222no—
967C4—222no—
968C4—222no—
969C4—222no—
970C4—441no—
971C4—442no—
972C4—442no—
973C4—442no—
974C4—442no—
975C4#1062319614yes—
976C2—24no—
977C2—42no—
978C2C2×#1062315311yescharacteristic
979C2C2×#1062319611yescharacteristic
980C2#1308202911yescharacteristic
981C2#1308241311yescharacteristic
982C2#1308243011yescharacteristic
983C2#1308258711yescharacteristic
984C2#1308264111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2487C2
prime radicalC22×D4×C11C23
hypercenter#2487D11
hypocenterC11#35017
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2487

Complements

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

NH ≅ G/Ntype
1. #13076999C2semidirect
2. #13076975C2semidirect
3. #13076966C2semidirect
4. #13076956C2semidirect
5. #13074809C2semidirect
6. #13074798C2semidirect
7. #13074008C2semidirect
8. #13073701C2semidirect
9. #13073146C2semidirect
10. #13073090C2semidirect
11. #13073045C2semidirect
12. #13072754C2semidirect
13. #13072453C2semidirect
15. #13072319C2semidirect
16. #13072143C2semidirect
18. #13071347C2semidirect
20. #13071144C2semidirect
21. C2×#10622598C2semidirect
158. D4×Dic11Q8semidirect
844. C11#35017semidirect

Maximal subgroups

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

subgroupindex
#130769992
#130769752
#130769662
#130769562
#130748092
#130747982
#130740082
#130737012
#130731462
#130730902
#130730452
#130727542
#130724532
#130724312
#130723192
#130721432
#130720672
#130713472
#130712422
#130711442
C2×#106225982
C4×D4×Dic112
C11×#24872
#3501711