Finite Group Databasebeta

← #14925315

Subgroups — #14925315

Order 2816.

1870 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073956C212yesmaximal, complemented
2#13073933C212yesmaximal, complemented
3#13073923C212yesmaximal, complemented
4#13073900C212yesmaximal, complemented
5#13073218C211yesmaximal, characteristic, complemented
6#13073150C211yesmaximal, characteristic, complemented
7#13072953C211yesmaximal, characteristic, complemented
8#13072489C211yesmaximal, characteristic, complemented
9#13072405C211yesmaximal, characteristic, complemented
10#13072193C211yesmaximal, characteristic
11#13072110C211yesmaximal, characteristic
12#13071915C212yesmaximal, complemented
13#13071874C212yesmaximal, complemented
14#13071175C211yesmaximal, characteristic, complemented
15#13071155C211yesmaximal, characteristic, complemented
16#13071144C211yesmaximal, characteristic, complemented
17#13071122C211yesmaximal, characteristic
18#13071087C211yesmaximal, characteristic, complemented
19#13071058C212yesmaximal, complemented
20#13071013C212yesmaximal, complemented
21C4×#66946C211yesmaximal, characteristic, complemented
22C4×#66930C211yesmaximal, characteristic, complemented
23C11×#2495C211yesmaximal, characteristic, complemented
24C2×#66983C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×#66946C2211yescharacteristic
28C2×#66946C2211yescharacteristic
29C2×#66943C2211yescharacteristic
30C2×#66940C2211yescharacteristic
31C2×(C22⋊D11)⋊C4C2212yes—
32C2×#66930C2211yescharacteristic
33C2×#66930C2211yescharacteristic
34C2×#66928C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×C42×D11C2212yes—
37C11×#400C2212yes—
38C11×#397C2212yes—
39C11×#389C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#388C2212yes—
42C11×#383C2212yes—
43C11×#382C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C11×#380C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4C2211yescharacteristic
48C4×C22⋊Dic11C2211yescharacteristic
49#10622607C2212yes—
50#10622606C2212yes—
51#10622605C2212yes—
52#10622602C2212yes—
53#10622601C2211yescharacteristic
54#10622601C2211yescharacteristic
55#10622598C2211yescharacteristic
56#10622591C2212yes—
57#10622591C2212yes—
58#10622590C2211yescharacteristic
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2211yescharacteristic
61C4⋊C4×Dic11C2211yescharacteristic
62C4⋊C4×Dic11C2212yes—
63C4⋊C4×Dic11C2211yescharacteristic
64#10622587C2211yescharacteristic
65#10622587C2211yescharacteristic
66#10622587C2211yescharacteristic
67#10622586C2211yescharacteristic
68#10622586C2211yescharacteristic
69#10622574C2212yes—
70#10622572C2212yes—
71#10622571C2212yes—
72#10622569C2212yes—
73#10622569C2212yes—
74#10622565C2212yes—
75#10622564C2212yes—
76#10622559C2212yes—
77C22⋊C4×Dic11C2212yes—
78C22⋊C4×Dic11C2211yescharacteristic
79C22⋊C4×Dic11C2211yescharacteristic
80C4×(C2×D11)⋊C4C2212yes—
81#10622550C2212yes—
82#10622546C2212yes—
83C4×Dic11⋊C4C2211yescharacteristic
84C4×Dic11⋊C4C2211yescharacteristic
85C42×Dic11C2211yescharacteristic
86C42×Dic11C2211yescharacteristic
87#10622542C2211yescharacteristic
88#10622541C2211yescharacteristic
89#10622288C2212yes—
90#10622288C2212yes—
91#10622287C2212yes—
92#10622282C2212yes—
93#10622282C2212yes—
94#10622282C2212yes—
95#10622281C2212yes—
96#10622280C2212yes—
97#10622280C2212yes—
98#10622279C2212yes—
99#10622279C2212yes—
100#10622279C2212yes—
101#10622279C2212yes—
102#10622279C2212yes—
103#10622277C2212yes—
104#10622277C2212yes—
105C11⋊#401C2212yes—
106#10622273C2212yes—
107#10622272C2212yes—
108#10622271C2212yes—
109#10622270C2212yes—
110#10622268C2212yes—
111#10622266C2212yes—
112#10622265C2212yes—
113#10622265C2212yes—
114#10622263C2212yes—
115#10622263C2212yes—
116#10622262C2212yes—
117#10622262C2211yescharacteristic
118#10622262C2212yes—
119#10622262C2211yescharacteristic
120#10622261C2211yescharacteristic
121#10622261C2211yescharacteristic
122#10622261C2212yes—
123C23×C4×C11C2311yescharacteristic
124C22×C22⋊D11C2312yes—
125C23×Dic11C2311yescharacteristic
126C23×Dic11C2311yescharacteristic
127C22×D44C2311yescharacteristic
128C22×C4×D11C2312yes—
129C22×C4×D11C2312yes—
130C22×C4×D11C2312yes—
131C22×Dic22C2311yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C22⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4C2311yescharacteristic
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C42×C11C2312yes—
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2311yescharacteristic
145C2×C22⋊Dic11C2311yescharacteristic
146C2×C22⋊Dic11C2311yescharacteristic
147C2×C22⋊Dic11C2312yes—
148#66983—24no—
149C2×(C2×D11)⋊C4C2312yes—
150C2×(C2×D11)⋊C4C2312yes—
151C2×(C2×D11)⋊C4C2312yes—
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2312yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×C4⋊Dic11C2312yes—
160C2×C4⋊Dic11C2311yescharacteristic
161C2×C4⋊Dic11C2312yes—
162C2×C4⋊Dic11C2311yescharacteristic
163#66977—24no—
164C2×Dic11⋊C4C2311yescharacteristic
165C2×Dic11⋊C4C2311yescharacteristic
166C2×Dic11⋊C4C2311yescharacteristic
167C2×Dic11⋊C4C2311yescharacteristic
168C2×Dic11⋊C4C2312yes—
169C2×Dic11⋊C4C2312yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×C4×Dic11—24no—
175C2×C4×Dic11C2312yes—
176C2×C4×Dic11C2312yes—
177C2×C4×Dic11C2311yescharacteristic
178C2×C4×Dic11C2311yescharacteristic
179C2×C4×Dic11C2311yescharacteristic
180C2×C4×Dic11C2312yes—
181C2×C4×Dic11C2312yes—
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193#66946—24no—
194#66946—24no—
195#66943—24no—
196#66940—24no—
197(C22⋊D11)⋊C4—28no—
198#66930—24no—
199#66930—24no—
200#66928—24no—
201C4×D44—24no—
202C42×D11—28no—
203C11×#95C2311yescharacteristic
204C11×#95C2311yescharacteristic
205C11×#95C2312yes—
206C11×#95C2312yes—
207C11×#95C2312yes—
208C11×#95C2312yes—
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11⋊#95C2311yescharacteristic
213C11⋊#95C2311yescharacteristic
214C11⋊#95C2311yescharacteristic
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2311yescharacteristic
219C11⋊#95C2311yescharacteristic
220C11⋊#95C2311yescharacteristic
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235#34913—111nomaximal, Sylow
236C24×C11C2411yescharacteristic
237C23×D11C2412yes—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2411yescharacteristic
244C22×C4×C11C2411yescharacteristic
245C22×C4×C11C2412yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—24no—
252C2×C22⋊D11—24no—
253C2×C22⋊D11—42no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—41no—
258C22×Dic11—41no—
259C22×Dic11#4114yes—
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2411yescharacteristic
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2411yescharacteristic
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2412yes—
270C22×Dic11C2411yescharacteristic
271C2×D44—22no—
272C2×D44—22no—
273C2×D44#4114yes—
274C2×C4×D11—24no—
275C2×C4×D11—24no—
276C2×C4×D11—24no—
277C2×C4×D11—24no—
278C2×C4×D11—24no—
279C2×C4×D11—24no—
280C2×C4×D11—24no—
281C2×C4×D11—42no—
282C2×C4×D11—42no—
283C2×Dic22—22no—
284C2×Dic22—22no—
285C2×Dic22—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—42no—
291C11×C4⋊C4—42no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—42no—
296C42×C11—24no—
297C42×C11—22no—
298C42×C11—22no—
299C22⋊Dic11—22no—
300C22⋊Dic11—24no—
301C22⋊Dic11—22no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—42no—
310(C2×D11)⋊C4—42no—
311(C2×D11)⋊C4—42no—
312C4⋊Dic11—24no—
313C4⋊Dic11—22no—
314C4⋊Dic11—42no—
315C4⋊Dic11#4114yes—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—24no—
320Dic11⋊C4—24no—
321Dic11⋊C4—24no—
322Dic11⋊C4—24no—
323Dic11⋊C4—22no—
324Dic11⋊C4—42no—
325Dic11⋊C4—42no—
326C4×Dic11—24no—
327C4×Dic11—24no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11—22no—
331C4×Dic11—24no—
332C4×Dic11—24no—
333C4×Dic11—22no—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11—22no—
337C4×Dic11—22no—
338C4×Dic11—41no—
339C4×Dic11—41no—
340C4×Dic11—41no—
341C4×Dic11—41no—
342C4×Dic11#4114yes—
343C4×Dic11#4114yes—
344#2578—112no—
345#2577—112no—
346#2576—112no—
347#2575—112no—
348#2514—111no—
349#2508—111no—
350#2495D1111yescharacteristic, complemented
351#2489—111no—
352#2454—111no—
353#2447—111no—
354#2427—111no—
355#2420—111no—
356#2401—112no—
357#2395—112no—
358C4×#125—111no—
359C4×#124—111no—
360C4×C22⋊Q8—111no—
361C4×#121—111no—
362#2295—111no—
363#2290—112no—
364#2283—112no—
365C42×D4—111no—
366C4×#117—111no—
367C23×C11—21no—
368C23×C11—21no—
369C23×C11—21no—
370C23×C11—21no—
371C23×C11—21no—
372C23×C11—21no—
373C23×C11C2×#4112yes—
374C23×C11C2511yescharacteristic
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11C2×#4114yes—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—21no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—44no—
409C2×C4×C11C2×#4112yes—
410C2×C4×C11C2×#4112yes—
411C2×C4×C11C2×#4112yes—
412C2×C4×C11C2×#4112yes—
413C22⋊D11—48no—
414C2×Dic11—22no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—21no—
418C2×Dic11—21no—
419C2×Dic11—21no—
420C2×Dic11—21no—
421C2×Dic11—22no—
422C2×Dic11—28no—
423C2×Dic11—21no—
424C2×Dic11—21no—
425C2×Dic11—21no—
426C2×Dic11—21no—
427C2×Dic11—21no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—21no—
439C2×Dic11—22no—
440C2×Dic11—21no—
441C2×Dic11—44no—
442C2×Dic11C2×#4112yes—
443C2×Dic11C2×#4112yes—
444C2×Dic11C2×#4112yes—
445C2×Dic11C2×#4114yes—
446C2×Dic11C2×#4112yes—
447C2×Dic11C2×#4112yes—
448C2×Dic11C2×#4112yes—
449D44—28no—
450C4×D11—48no—
451C4×D11—48no—
452C4×D11—48no—
453Dic22—44no—
454C2×#125—111no—
455C2×#124—111no—
456C2×C22⋊Q8—111no—
457C2×#121—111no—
458C2×C4×Q8—111no—
459C2×C4×D4—111no—
460C2×C4×D4—111no—
461C2×C4×D4—112no—
462C2×C4×D4—111no—
463C2×#117—111no—
464C2×#117—111no—
465C22×C42—111no—
466C22×C42—112no—
467#401—112no—
468#400—112no—
469#400—112no—
470#400—112no—
471#400C2×D1112yes—
472#399—112no—
473#398—112no—
474#397—112no—
475#397—112no—
476#397—112no—
477#397—112no—
478#397—112no—
479#397C2×D1112yes—
480#396—112no—
481#394—112no—
482#394—112no—
483#391—111no—
484#391—111no—
485#391—111no—
486#391—111no—
487#390—111no—
488#390—111no—
489#389—111no—
490#389—111no—
491#389—111no—
492#389—111no—
493#389C2×D1111yescharacteristic
494#389C2×D1111yescharacteristic
495#388—112no—
496#388—112no—
497#388—112no—
498#388—112no—
499#388C2×D1112yes—
500#387—112no—
501#387—112no—
502#387—112no—
503#387—112no—
504#387—112no—
505#387—112no—
506#387—112no—
507#386—112no—
508#386—112no—
509#386—112no—
510#385—112no—
511#385—112no—
512#385—112no—
513#383—112no—
514#383C2×D1112yes—
515#382—111no—
516#382—112no—
517#382—112no—
518#382C2×D1111yescharacteristic
519#381—112no—
520#381—112no—
521#380—112no—
522#380—112no—
523#380C2×D1111yescharacteristic
524#380C2×D1111yescharacteristic
525C4×C4⋊C4—112no—
526C4×C4⋊C4—111no—
527C4×C4⋊C4—111no—
528C4×C4⋊C4—112no—
529C4×C4⋊C4—111no—
530C4×C4⋊C4—111no—
531C4×C4⋊C4—111no—
532C4×C4⋊C4—112no—
533C4×C4⋊C4—111no—
534C4×C4⋊C4—111no—
535C4×C4⋊C4—112no—
536C4×C4⋊C4C2×D1111yescharacteristic
537C4×C22⋊C4—111no—
538C4×C22⋊C4—111no—
539C4×C22⋊C4—111no—
540C4×C22⋊C4—112no—
541C4×C22⋊C4—112no—
542C4×C22⋊C4—112no—
543C4×C22⋊C4—112no—
544C4×C22⋊C4—112no—
545C4×C22⋊C4—112no—
546C4×C22⋊C4—112no—
547C4×C22⋊C4C2×D1111yescharacteristic
548#376—111no—
549#376—111no—
550#376—112no—
551C43—111no—
552C43—111no—
553C22×C11—22no—
554C22×C11—22no—
555C22×C11—22no—
556C22×C11—41no—
557C22×C11—41no—
558C22×C11—41no—
559C22×C11—41no—
560C22×C11C22×#4111yescharacteristic
561C22×C11C22×#4111yescharacteristic
562C22×C11C22×#4111yescharacteristic
563C22×C11C22×#4111yescharacteristic
564C22×C11C22×#4111yescharacteristic
565C22×C11#58511yescharacteristic
566C22×C11#58511yescharacteristic
567C2×D11—24no—
568C2×D11—24no—
569C2×D11—24no—
570C2×D11—42no—
571C2×D11—42no—
572C2×D11—42no—
573C2×D11—42no—
574C4×C11—22no—
575C4×C11—41no—
576C4×C11—42no—
577C4×C11—42no—
578C4×C11—41no—
579C4×C11—41no—
580C4×C11—42no—
581C4×C11—41no—
582C4×C11—42no—
583C4×C11#52914yes—
584Dic11—22no—
585Dic11—22no—
586Dic11—22no—
587Dic11—24no—
588Dic11—42no—
589Dic11—41no—
590Dic11—41no—
591Dic11—41no—
592Dic11—42no—
593Dic11—41no—
594Dic11#52914yes—
595C22×Q8—111no—
596C22×D4—112no—
597C22×D4—111no—
598C23×C4—111no—
599C23×C4—111no—
600C23×C4—112no—
601C23×C4—112no—
602C23×C4—112no—
603C23×C4C22×D1111yescharacteristic
604#125—224no—
605#124—224no—
606C22⋊Q8—224no—
607#121—224no—
608C4×Q8—224no—
609C4×D4—224no—
610C4×D4—224no—
611C4×D4—228no—
612C4×D4—224no—
613#117—224no—
614#117—224no—
615C2×C4⋊C4—111no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—111no—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—111no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4C22×D1111yescharacteristic
630C2×C4⋊C4C22×D1111yescharacteristic
631C2×C4⋊C4C22×D1111yescharacteristic
632C2×C4⋊C4C22×D1111yescharacteristic
633C2×C4⋊C4C22×D1112yes—
634C2×C4⋊C4C22×D1112yes—
635C2×C22⋊C4—111no—
636C2×C22⋊C4—111no—
637C2×C22⋊C4—112no—
638C2×C22⋊C4—112no—
639C2×C22⋊C4—112no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—112no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4—112no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4—112no—
648C2×C22⋊C4C22×D1111yescharacteristic
649C2×C22⋊C4C22×D1111yescharacteristic
650C2×C22⋊C4C22×D1112yes—
651C2×C22⋊C4C22×D1112yes—
652C2×C42—111no—
653C2×C42—111no—
654C2×C42—111no—
655C2×C42—111no—
656C2×C42—111no—
657C2×C42—111no—
658C2×C42—112no—
659C2×C42—112no—
660C2×C42—111no—
661C2×C42—111no—
662C2×C42—112no—
663C2×C42—112no—
664C2×C42—111no—
665C2×C42—111no—
666C2×C42—111no—
667C2×C42—111no—
668C2×C42—111no—
669C2×C42—111no—
670C2×C42—228no—
671C2×C42—224no—
672C2×C42C22×D1111yescharacteristic
673C2×C42C22×D1111yescharacteristic
674C2×C42C22×D1112yes—
675#95—111no—
676#95—111no—
677#95—111no—
678#95—111no—
679#95—111no—
680#95—111no—
681#95—112no—
682#95—112no—
683#95—112no—
684#95—112no—
685#95—112no—
686#95—112no—
687#95—112no—
688#95—112no—
689#95—112no—
690#95—112no—
691#95—112no—
692#95—112no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95C22×D1111yescharacteristic
699#95C22×D1111yescharacteristic
700#95C22×D1112yes—
701#95C22×D1112yes—
702#95C22×D1112yes—
703#95C22×D1112yes—
704#95C22×D1112yes—
705#95C22×D1112yes—
706#95C22×D1112yes—
707C2×C11—42no—
708C2×C11C2×#52911yescharacteristic
709C2×C11C2×#52911yescharacteristic
710C2×C11#345511yescharacteristic
711C2×C11#347511yescharacteristic
712C2×C11#347511yescharacteristic
713C2×C11#347511yescharacteristic
714C2×C11#348011yescharacteristic
715D11—44no—
716C24—112no—
717C24C23×D1111yescharacteristic
718C2×Q8—222no—
719C2×Q8—222no—
720C2×Q8—222no—
721C2×D4—114no—
722C2×D4—224no—
723C2×D4—224no—
724C2×D4—222no—
725C2×D4—222no—
726C2×D4—442no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—111no—
731C22×C4—114no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—112no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—111no—
740C22×C4—111no—
741C22×C4—111no—
742C22×C4—224no—
743C22×C4—224no—
744C22×C4—224no—
745C22×C4—224no—
746C22×C4—224no—
747C22×C4—224no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—224no—
752C22×C4—442no—
753C22×C4—442no—
754C22×C4—441no—
755C22×C4—441no—
756C22×C4C23×D1112yes—
757C22×C4C23×D1112yes—
758C22×C4C23×D1111yescharacteristic
759C22×C4C23×D1111yescharacteristic
760C22×C4C23×D1112yes—
761C22×C4C23×D1111yescharacteristic
762C22×C4C23×D1112yes—
763C22×C4C23×D1111yescharacteristic
764C22×C4C23×D1111yescharacteristic
765C22×C4C23×D1111yescharacteristic
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—42no—
771C4⋊C4—42no—
772C4⋊C4—114no—
773C4⋊C4—222no—
774C4⋊C4—222no—
775C4⋊C4—222no—
776C4⋊C4—224no—
777C4⋊C4—224no—
778C4⋊C4—224no—
779C4⋊C4—224no—
780C4⋊C4—224no—
781C4⋊C4—222no—
782C4⋊C4—222no—
783C4⋊C4—442no—
784C4⋊C4—442no—
785C4⋊C4—442no—
786C22⋊C4—22no—
787C22⋊C4—24no—
788C22⋊C4—22no—
789C22⋊C4—42no—
790C22⋊C4—224no—
791C22⋊C4—224no—
792C22⋊C4—224no—
793C22⋊C4—224no—
794C22⋊C4—224no—
795C22⋊C4—224no—
796C22⋊C4—224no—
797C22⋊C4—222no—
798C22⋊C4—224no—
799C22⋊C4—222no—
800C22⋊C4—442no—
801C22⋊C4—442no—
802C22⋊C4—442no—
803C42—24no—
804C42—22no—
805C42—22no—
806C42—114no—
807C42—114no—
808C42—224no—
809C42—224no—
810C42—222no—
811C42—222no—
812C42—222no—
813C42—222no—
814C42—222no—
815C42—224no—
816C42—224no—
817C42—222no—
818C42—222no—
819C42—222no—
820C42—441no—
821C42—441no—
822C42—441no—
823C42—441no—
824C11#3491311yescharacteristic, complemented, Sylow
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—114no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23#41×D1112yes—
839C23C24×D1111yescharacteristic
840Q8—444no—
841D4—228no—
842D4—448no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—112no—
871C2×C4—112no—
872C2×C4—112no—
873C2×C4—112no—
874C2×C4—112no—
875C2×C4—114no—
876C2×C4—112no—
877C2×C4—228no—
878C2×C4—221no—
879C2×C4—222no—
880C2×C4—221no—
881C2×C4—221no—
882C2×C4—221no—
883C2×C4—221no—
884C2×C4—221no—
885C2×C4—222no—
886C2×C4—221no—
887C2×C4—221no—
888C2×C4—221no—
889C2×C4—221no—
890C2×C4—221no—
891C2×C4—221no—
892C2×C4—221no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—221no—
901C2×C4—221no—
902C2×C4—221no—
903C2×C4—222no—
904C2×C4—448no—
905C2×C4—448no—
906C2×C4—448no—
907C2×C4—444no—
908C2×C4#41×D1112yes—
909C2×C4#41×D1112yes—
910C2×C4#41×D1112yes—
911C2×C4#41×D1112yes—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—224no—
920C22—224no—
921C22—224no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22C2×#41×D1111yescharacteristic
927C22C2×#41×D1111yescharacteristic
928C22C2×#41×D1111yescharacteristic
929C22C2×#41×D1111yescharacteristic
930C22C2×#41×D1111yescharacteristic
931C22#1062345511yescharacteristic
932C22#1062345711yescharacteristic
933C4—22no—
934C4—42no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—42no—
941C4—42no—
942C4—114no—
943C4—222no—
944C4—222no—
945C4—224no—
946C4—222no—
947C4—442no—
948C4—442no—
949C4—441no—
950C4—441no—
951C4—441no—
952C4—441no—
953C4#1062323714yes—
954C2—42no—
955C2—444no—
956C2D11×#52911yescharacteristic
957C2C2×#1062323711yescharacteristic
958C2#1308200311yescharacteristic
959C2#1308217311yescharacteristic
960C2#1308218111yescharacteristic
961C2#1308218111yescharacteristic
962C2#1308221011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2495C2
prime radicalC2×#66983C22
hypercenter#2495D11
hypocenterC11#34913
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2495

Complements

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

NH ≅ G/Ntype
1. #13073956C2semidirect
2. #13073933C2semidirect
3. #13073923C2semidirect
4. #13073900C2semidirect
5. #13073218C2semidirect
6. #13073150C2semidirect
7. #13072953C2semidirect
8. #13072489C2semidirect
9. #13072405C2semidirect
12. #13071915C2semidirect
13. #13071874C2semidirect
14. #13071175C2semidirect
15. #13071155C2semidirect
16. #13071144C2semidirect
18. #13071087C2semidirect
19. #13071058C2semidirect
20. #13071013C2semidirect
21. C4×#66946C2semidirect
22. C4×#66930C2semidirect
23. C11×#2495C2semidirect
350. #2495D11semidirect
824. C11#34913semidirect

Maximal subgroups

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

subgroupindex
#130739562
#130739332
#130739232
#130739002
#130732182
#130731502
#130729532
#130724892
#130724052
#130721932
#130721102
#130719152
#130718742
#130711752
#130711552
#130711442
#130711222
#130710872
#130710582
#130710132
C4×#669462
C4×#669302
C11×#24952
#3491311