Finite Group Databasebeta

← #14959829

Subgroups — #14959829

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077007C212yesmaximal, complemented
2#13077004C212yesmaximal, complemented
3#13077002C211yesmaximal, characteristic, complemented
4#13076998C211yesmaximal, characteristic, complemented
5#13076987C211yesmaximal, characteristic, complemented
6#13076954C211yesmaximal, characteristic, complemented
7#13076946C211yesmaximal, characteristic
8#13076936C212yesmaximal, complemented
9#13076928C212yesmaximal, complemented
10#13076925C211yesmaximal, characteristic, complemented
11#13076916C211yesmaximal, characteristic
12#13071175C211yesmaximal, characteristic, complemented
13#126×Dic11C212yesmaximal, complemented
14#13071163C211yesmaximal, characteristic, complemented
15#13071146C211yesmaximal, characteristic, complemented
16#13071143C212yesmaximal, complemented
17#13071132C211yesmaximal, characteristic
18#13071110C212yesmaximal, complemented
19#13071087C211yesmaximal, characteristic, complemented
20#13071078C211yesmaximal, characteristic, complemented
21#13071058C212yesmaximal, complemented
22C43×D11C211yesmaximal, characteristic, complemented
23C11×#2860C211yesmaximal, characteristic, complemented
24C2×C11×#126C2212yes—
25C2×#66991C2211yescharacteristic
26C2×#66989C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C2×#66950C2211yescharacteristic
29C2×#66943C2211yescharacteristic
30C2×#66940C2211yescharacteristic
31C2×#66936C2212yes—
32C2×(C22⋊D11)⋊C4C2212yes—
33C2×#66930C2212yes—
34C2×C42×D11C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C42×D11C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×C42×D11C2211yescharacteristic
40C2×C42×D11C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#388C2212yes—
48C11×#388C2212yes—
49C11×#388C2212yes—
50C43×C11C2211yescharacteristic
51#10622834C2211yescharacteristic
52#10622602C2212yes—
53#10622602C2212yes—
54#10622602C2212yes—
55#10622600C2211yescharacteristic
56#10622600C2211yescharacteristic
57#10622598C2211yescharacteristic
58#10622594C2212yes—
59#10622594C2212yes—
60#10622594C2212yes—
61#10622591C2212yes—
62#10622591C2212yes—
63#10622591C2212yes—
64#10622590C2211yescharacteristic
65#10622590C2211yescharacteristic
66C4⋊C4×Dic11C2212yes—
67C4⋊C4×Dic11C2211yescharacteristic
68C4⋊C4×Dic11C2212yes—
69C4⋊C4×Dic11C2211yescharacteristic
70C4⋊C4×Dic11C2212yes—
71#10622587C2211yescharacteristic
72#10622586C2211yescharacteristic
73#10622569C2212yes—
74#10622569C2212yes—
75#10622569C2212yes—
76#10622569C2212yes—
77#10622564C2212yes—
78#10622564C2212yes—
79#10622564C2212yes—
80#10622564C2212yes—
81#10622564C2212yes—
82#10622558C2212yes—
83#10622558C2212yes—
84#10622558C2212yes—
85#10622557C2212yes—
86#10622557C2212yes—
87#10622557C2212yes—
88#10622557C2212yes—
89#10622557C2212yes—
90C22⋊C4×Dic11C2212yes—
91C22⋊C4×Dic11C2212yes—
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2212yes—
94#10622550C2212yes—
95#10622546C2212yes—
96#10622546C2212yes—
97#10622546C2212yes—
98C42×Dic11C2211yescharacteristic
99C42×Dic11C2211yescharacteristic
100C42×Dic11C2211yescharacteristic
101C42×Dic11C2211yescharacteristic
102C42×Dic11C2211yescharacteristic
103C42×Dic11C2211yescharacteristic
104C42×Dic11C2211yescharacteristic
105#10622542C2211yescharacteristic
106#10622542C2211yescharacteristic
107#10622542C2211yescharacteristic
108#10622541C2211yescharacteristic
109#10622541C2211yescharacteristic
110#10622541C2211yescharacteristic
111#10622281C2212yes—
112#10622279C2212yes—
113#10622277C2212yes—
114#10622268C2212yes—
115#10622268C2212yes—
116#10622267C2212yes—
117#10622266C2212yes—
118#10622266C2212yes—
119#10622265C2212yes—
120#10622265C2212yes—
121#10622262C2212yes—
122#10622261C2212yes—
123C22×D4×C11C2311yescharacteristic
124C22×C22⋊D11C2312yes—
125C23×Dic11C2312yes—
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×Dic22C2311yescharacteristic
134C11×#126—28no—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160#66991—24no—
161#66989—24no—
162D4×Dic11—24no—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×C4⋊Dic11C2312yes—
167C2×C4⋊Dic11C2312yes—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×C4×Dic11C2311yescharacteristic
179C2×C4×Dic11C2311yescharacteristic
180C2×C4×Dic11C2311yescharacteristic
181C2×C4×Dic11C2311yescharacteristic
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
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202#66950—24no—
203#66943—24no—
204#66940—24no—
205#66936—28no—
206(C22⋊D11)⋊C4—28no—
207#66930—28no—
208C42×D11—24no—
209C42×D11—24no—
210C42×D11—24no—
211C42×D11—24no—
212C42×D11—24no—
213C42×D11—24no—
214C42×D11—24no—
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11×#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
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—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239#36638—111nomaximal, Sylow
240C24×C11C2412yes—
241C23×D11C2411yescharacteristic
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—24no—
258C22×Dic11—24no—
259C22×Dic11—24no—
260C22×Dic11—24no—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2411yescharacteristic
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2411yescharacteristic
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2411yescharacteristic
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11—22no—
276C2×C4×D11—22no—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—22no—
280C2×C4×D11—22no—
281C2×C4×D11—22no—
282C2×C4×D11—22no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—22no—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11#4114yes—
291C2×C4×D11#4114yes—
292C2×C4×D11#4114yes—
293C2×Dic22—22no—
294C2×Dic22—22no—
295C2×Dic22—22no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—24no—
300C11×C4⋊C4—24no—
301C11×C4⋊C4—24no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—24no—
304C11×C22⋊C4—24no—
305C11×C22⋊C4—24no—
306C11×C22⋊C4—24no—
307C11×C22⋊C4—24no—
308C42×C11—22no—
309C42×C11—22no—
310C42×C11—22no—
311C42×C11—22no—
312C42×C11—22no—
313C42×C11—22no—
314C42×C11#4114yes—
315C22⋊Dic11—24no—
316C22⋊Dic11—24no—
317C22⋊Dic11—24no—
318C22⋊Dic11—24no—
319C22⋊Dic11—24no—
320C22⋊Dic11—24no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—24no—
324C4⋊Dic11—24no—
325C4⋊Dic11—24no—
326C4⋊Dic11—24no—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—22no—
330Dic11⋊C4—24no—
331Dic11⋊C4—24no—
332Dic11⋊C4—24no—
333Dic11⋊C4—24no—
334Dic11⋊C4—24no—
335Dic11⋊C4—24no—
336C4×Dic11—22no—
337C4×Dic11—22no—
338C4×Dic11—22no—
339C4×Dic11—22no—
340C4×Dic11—22no—
341C4×Dic11—22no—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11—22no—
346C4×Dic11—22no—
347C4×Dic11—22no—
348C4×Dic11—24no—
349C4×Dic11—24no—
350C4×Dic11—24no—
351C4×Dic11—22no—
352C4×Dic11—22no—
353C4×Dic11—22no—
354C4×Dic11—22no—
355C4×Dic11—22no—
356C4×Dic11—22no—
357C4×Dic11#4114yes—
358C4×Dic11#4114yes—
359C4×Dic11#4114yes—
360#2866—112no—
361#2865—112no—
362#2864—111no—
363#2863—111no—
364#2861—111no—
365#2860D1111yescharacteristic, complemented
366#2855—111no—
367#2854—111no—
368#2853—112no—
369#2852—112no—
370#2851—111no—
371#2850—111no—
372C4×#125—111no—
373C4×#126—112no—
374C4×#124—111no—
375C4×C22⋊Q8—111no—
376C4×#123—112no—
377C4×#121—111no—
378#2298—112no—
379#2295—111no—
380#2293—111no—
381#2290—112no—
382C2×C43—111no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11C2511yescharacteristic
391C22×D11—21no—
392C22×D11—21no—
393C22×D11—21no—
394C22×D11—21no—
395C22×D11C2×#4112yes—
396C22×D11C2×#4112yes—
397C22×D11C2×#4112yes—
398D4×C11—44no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11C2×#4112yes—
421C2×C4×C11C2×#4112yes—
422C2×C4×C11C2×#4112yes—
423C2×C4×C11C2×#4112yes—
424C2×C4×C11C2×#4112yes—
425C2×C4×C11C2×#4112yes—
426C2×C4×C11C2×#4112yes—
427C2×C4×C11C2×#4112yes—
428C2×C4×C11C2×#4112yes—
429C22⋊D11—48no—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—21no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—21no—
439C2×Dic11—21no—
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—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—48no—
455C2×Dic11C2×#4112yes—
456C2×Dic11C2×#4112yes—
457C2×Dic11C2×#4112yes—
458C2×Dic11C2×#4112yes—
459C2×Dic11C2×#4112yes—
460C2×Dic11C2×#4112yes—
461C2×Dic11C2×#4112yes—
462C2×Dic11C2×#4112yes—
463C2×Dic11C2×#4112yes—
464C4×D11—28no—
465C4×D11—28no—
466C4×D11—28no—
467C4×D11—28no—
468C4×D11—28no—
469C4×D11—28no—
470C4×D11—28no—
471Dic22—44no—
472C2×#126C2×D1112yes—
473C2×#125—111no—
474C2×#124—111no—
475C2×#123—112no—
476C2×C22⋊Q8—111no—
477C2×#121—111no—
478C2×C4×Q8—111no—
479C2×C4×D4—111no—
480C2×C4×D4—112no—
481C2×#117—112no—
482C22×C42—111no—
483C22×C42—111no—
484C22×C42—111no—
485C22×C42—111no—
486C22×C42—111no—
487C22×C42—111no—
488C22×C42—111no—
489#391—111no—
490#391—111no—
491#391—111no—
492#391—111no—
493#390—111no—
494#390C2×D1111yescharacteristic
495#390C2×D1111yescharacteristic
496#390C2×D1111yescharacteristic
497#389—111no—
498#389—111no—
499#389—111no—
500#389—111no—
501#389—111no—
502#389C2×D1111yescharacteristic
503#389C2×D1111yescharacteristic
504#389C2×D1111yescharacteristic
505#388—112no—
506#388—112no—
507#388—112no—
508#388—112no—
509#388—112no—
510#388—112no—
511#388—112no—
512#388—112no—
513#388—112no—
514#388—112no—
515#388—112no—
516#388—112no—
517#388—112no—
518#388C2×D1112yes—
519#388C2×D1112yes—
520#388C2×D1112yes—
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#387—112no—
531#387—112no—
532#387—112no—
533#387—112no—
534#387—112no—
535#387—112no—
536#387—112no—
537#386—112no—
538#386—112no—
539#386—112no—
540#386—112no—
541#385—112no—
542#385—112no—
543#385—112no—
544#385—112no—
545#383—112no—
546#382—111no—
547#382—111no—
548#381—112no—
549#380—111no—
550#380—111no—
551C4×C4⋊C4—112no—
552C4×C4⋊C4—112no—
553C4×C4⋊C4—112no—
554C4×C4⋊C4—111no—
555C4×C4⋊C4—111no—
556C4×C4⋊C4—112no—
557C4×C22⋊C4—112no—
558C4×C22⋊C4—112no—
559C4×C22⋊C4—112no—
560C4×C22⋊C4—112no—
561C4×C22⋊C4—112no—
562#376—112no—
563C43—111no—
564C43—111no—
565C43—111no—
566C43—111no—
567C43—111no—
568C43—111no—
569C43—111no—
570C43C2×D1111yescharacteristic
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11C22×#4111yescharacteristic
579C22×C11C22×#4111yescharacteristic
580C22×C11C22×#4111yescharacteristic
581C22×C11C22×#4111yescharacteristic
582C22×C11C22×#4111yescharacteristic
583C22×C11C22×#4111yescharacteristic
584C22×C11C22×#4111yescharacteristic
585C2×D11—22no—
586C2×D11—22no—
587C2×D11—22no—
588C2×D11—22no—
589C2×D11—22no—
590C2×D11—22no—
591C2×D11#52914yes—
592C4×C11—22no—
593C4×C11—22no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—22no—
597C4×C11—22no—
598C4×C11—42no—
599C4×C11—42no—
600C4×C11—42no—
601C4×C11#52914yes—
602Dic11—22no—
603Dic11—22no—
604Dic11—22no—
605Dic11—22no—
606Dic11—22no—
607Dic11—22no—
608Dic11—42no—
609Dic11—42no—
610Dic11—42no—
611Dic11—42no—
612Dic11#52914yes—
613C22×Q8—111no—
614C22×D4—112no—
615C22×D4C22×D1111yescharacteristic
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—112no—
620C23×C4—111no—
621C23×C4—111no—
622C23×C4—111no—
623C23×C4—111no—
624#126—28no—
625#125—224no—
626#124—224no—
627#123—228no—
628C22⋊Q8—224no—
629#121—224no—
630C4×Q8—224no—
631C4×D4—224no—
632C4×D4—228no—
633#117—228no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—112no—
638C2×C4⋊C4—112no—
639C2×C4⋊C4—111no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—111no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4C22×D1111yescharacteristic
647C2×C4⋊C4C22×D1111yescharacteristic
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1112yes—
650C2×C4⋊C4C22×D1112yes—
651C2×C4⋊C4C22×D1112yes—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—112no—
661C2×C22⋊C4C22×D1112yes—
662C2×C22⋊C4C22×D1112yes—
663C2×C22⋊C4C22×D1112yes—
664C2×C22⋊C4C22×D1112yes—
665C2×C22⋊C4C22×D1112yes—
666C2×C22⋊C4C22×D1112yes—
667C2×C42—111no—
668C2×C42—111no—
669C2×C42—111no—
670C2×C42—112no—
671C2×C42—112no—
672C2×C42—112no—
673C2×C42—111no—
674C2×C42—111no—
675C2×C42—111no—
676C2×C42—111no—
677C2×C42—111no—
678C2×C42—111no—
679C2×C42—111no—
680C2×C42—111no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—111no—
684C2×C42—111no—
685C2×C42—111no—
686C2×C42—111no—
687C2×C42—111no—
688C2×C42—111no—
689C2×C42—111no—
690C2×C42—111no—
691C2×C42—224no—
692C2×C42—224no—
693C2×C42—224no—
694C2×C42—224no—
695C2×C42—224no—
696C2×C42—224no—
697C2×C42—224no—
698C2×C42C22×D1111yescharacteristic
699C2×C42C22×D1111yescharacteristic
700C2×C42C22×D1111yescharacteristic
701C2×C42C22×D1111yescharacteristic
702C2×C42C22×D1111yescharacteristic
703C2×C42C22×D1111yescharacteristic
704C2×C42C22×D1111yescharacteristic
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#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95C22×D1112yes—
727#95C22×D1112yes—
728#95C22×D1112yes—
729C2×C11—82no—
730C2×C11C2×#52911yescharacteristic
731C2×C11C2×#52911yescharacteristic
732C2×C11C2×#52911yescharacteristic
733C2×C11#344411yescharacteristic
734C2×C11#344411yescharacteristic
735C2×C11#344411yescharacteristic
736C2×C11#344411yescharacteristic
737D11—24no—
738C24—111no—
739C24C23×D1112yes—
740C2×Q8—222no—
741C2×Q8—222no—
742C2×Q8—222no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—224no—
747C2×D4—224no—
748C2×D4—224no—
749C22×C4—111no—
750C22×C4—111no—
751C22×C4—111no—
752C22×C4—111no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—111no—
756C22×C4—114no—
757C22×C4—114no—
758C22×C4—114no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—222no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—224no—
776C22×C4—224no—
777C22×C4—224no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—222no—
783C22×C4—222no—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1111yescharacteristic
788C22×C4C23×D1111yescharacteristic
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791C22×C4C23×D1111yescharacteristic
792C22×C4C23×D1111yescharacteristic
793C22×C4C23×D1111yescharacteristic
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—224no—
801C4⋊C4—224no—
802C4⋊C4—224no—
803C4⋊C4—224no—
804C4⋊C4—224no—
805C4⋊C4—224no—
806C4⋊C4—224no—
807C4⋊C4—224no—
808C4⋊C4—222no—
809C4⋊C4—222no—
810C4⋊C4—224no—
811C4⋊C4—222no—
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—24no—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—224no—
819C22⋊C4—224no—
820C22⋊C4—224no—
821C22⋊C4—224no—
822C22⋊C4—224no—
823C22⋊C4—224no—
824C22⋊C4—224no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C42—22no—
828C42—22no—
829C42—22no—
830C42—22no—
831C42—22no—
832C42—22no—
833C42—114no—
834C42—114no—
835C42—114no—
836C42—222no—
837C42—222no—
838C42—222no—
839C42—222no—
840C42—222no—
841C42—222no—
842C42—222no—
843C42—222no—
844C42—222no—
845C42—222no—
846C42—222no—
847C42—222no—
848C42—224no—
849C42—224no—
850C42—224no—
851C42—222no—
852C42—222no—
853C42—222no—
854C42—222no—
855C42—222no—
856C42—222no—
857C42#434114yes—
858C11#3663811yescharacteristic, complemented, Sylow
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—112no—
867C23—112no—
868C23—112no—
869C23—221no—
870C23—221no—
871C23—221no—
872C23—221no—
873C23C24×D1111yescharacteristic
874Q8—444no—
875D4—44no—
876D4—448no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—112no—
899C2×C4—112no—
900C2×C4—112no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—112no—
904C2×C4—112no—
905C2×C4—112no—
906C2×C4—112no—
907C2×C4—228no—
908C2×C4—228no—
909C2×C4—228no—
910C2×C4—228no—
911C2×C4—228no—
912C2×C4—228no—
913C2×C4—221no—
914C2×C4—221no—
915C2×C4—221no—
916C2×C4—221no—
917C2×C4—221no—
918C2×C4—221no—
919C2×C4—221no—
920C2×C4—221no—
921C2×C4—221no—
922C2×C4—221no—
923C2×C4—221no—
924C2×C4—221no—
925C2×C4—228no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—448no—
939C2×C4C2×#434112yes—
940C2×C4C2×#434112yes—
941C2×C4C2×#434112yes—
942C2×C4#41×D1112yes—
943C2×C4#41×D1112yes—
944C2×C4#41×D1112yes—
945C2×C4#41×D1112yes—
946C2×C4#41×D1112yes—
947C2×C4#41×D1112yes—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—114no—
956C22—222no—
957C22—222no—
958C22—222no—
959C22—222no—
960C22—222no—
961C22—222no—
962C22C22×#434111yescharacteristic
963C22C2×#41×D1111yescharacteristic
964C22C2×#41×D1111yescharacteristic
965C22C2×#41×D1111yescharacteristic
966C22C2×#41×D1111yescharacteristic
967C22C2×#41×D1111yescharacteristic
968C22C2×#41×D1111yescharacteristic
969C4—22no—
970C4—22no—
971C4—22no—
972C4—22no—
973C4—22no—
974C4—22no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—114no—
979C4—222no—
980C4—222no—
981C4—222no—
982C4—222no—
983C4—222no—
984C4—222no—
985C4—442no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4#1062323714yes—
990C2—82no—
991C2—224no—
992C2D11×#52911yescharacteristic
993C2D11×#52911yescharacteristic
994C2C2×#1062323711yescharacteristic
995C2#1308191011yescharacteristic
996C2#1308191111yescharacteristic
997C2#1308191111yescharacteristic
998C2#1308191111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2860C2
prime radicalC2×#66991C22
hypercenter#2860D11
hypocenterC11#36638
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2860

Complements

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

NH ≅ G/Ntype
1. #13077007C2semidirect
2. #13077004C2semidirect
3. #13077002C2semidirect
4. #13076998C2semidirect
5. #13076987C2semidirect
6. #13076954C2semidirect
8. #13076936C2semidirect
9. #13076928C2semidirect
10. #13076925C2semidirect
12. #13071175C2semidirect
13. #126×Dic11C2semidirect
14. #13071163C2semidirect
15. #13071146C2semidirect
16. #13071143C2semidirect
18. #13071110C2semidirect
19. #13071087C2semidirect
20. #13071078C2semidirect
21. #13071058C2semidirect
22. C43×D11C2semidirect
23. C11×#2860C2semidirect
365. #2860D11semidirect
858. C11#36638semidirect

Maximal subgroups

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

subgroupindex
#130770072
#130770042
#130770022
#130769982
#130769872
#130769542
#130769462
#130769362
#130769282
#130769252
#130769162
#130711752
#126×Dic112
#130711632
#130711462
#130711432
#130711322
#130711102
#130710872
#130710782
#130710582
C43×D112
C11×#28602
#3663811