Finite Group Databasebeta

← #26379225

Subgroups — #26379225

Order 12032.

2010 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094014C211yesmaximal, characteristic
2#20246572C212yesmaximal, complemented
3#20246570C212yesmaximal, complemented
4#20246485C212yesmaximal, complemented
5#20246479C212yesmaximal, complemented
6#20246266C211yesmaximal, characteristic
7#20246260C211yesmaximal, characteristic
8#20246258C211yesmaximal, characteristic
9#20246258C211yesmaximal, characteristic
10#20246257C211yesmaximal, characteristic
11#20246252C211yesmaximal, characteristic
12#20246252C211yesmaximal, characteristic
13#20246190C212yesmaximal, complemented
14#20246187C212yesmaximal, complemented
15#20246126C212yesmaximal, complemented
16#20246124C212yesmaximal, complemented
17#20246005C211yesmaximal, characteristic
18#20246004C211yesmaximal, characteristic
19#20245989C211yesmaximal, characteristic
20#20245988C211yesmaximal, characteristic
21#20245791C211yesmaximal, characteristic
22#20245779C211yesmaximal, characteristic
23C47×#2344C211yesmaximal, characteristic
24C2×#13094014C4116yescomplemented
25C2×#13094014C2211yescharacteristic
26C2×#13094014C2211yescharacteristic
27C2×#13094014C2211yescharacteristic
28C2×#13094014C2211yescharacteristic
29C2×#13094014C2211yescharacteristic
30C2×#13094014C2211yescharacteristic
31C2×#13094014C2211yescharacteristic
32C2×#13094014C2211yescharacteristic
33C2×#13093983C2211yescharacteristic
34C2×#13093983C2211yescharacteristic
35C2×#13093980C2211yescharacteristic
36C2×#13093980C2211yescharacteristic
37C22×C4⋊Dic47C2211yescharacteristic
38C22×Dic47⋊C4C2211yescharacteristic
39C22×Dic47⋊C4C2211yescharacteristic
40C22×Dic47⋊C4C2211yescharacteristic
41C22×Dic47⋊C4C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689022C2212yes—
44#15689021C2212yes—
45#15689021C2212yes—
46#15689020C2212yes—
47#15689020C2212yes—
48#15689020C2212yes—
49#15689020C2212yes—
50#15689020C2212yes—
51#15689019C2212yes—
52#15689019C2212yes—
53#15689018C2212yes—
54#15689018C2212yes—
55#15689018C2212yes—
56#15689018C2212yes—
57#15689018C2212yes—
58#15689010C2212yes—
59#15689010C2212yes—
60#15689010C2212yes—
61#15689009C2212yes—
62#15689009C2212yes—
63#15689008C2212yes—
64#15689008C2212yes—
65#15689007C2212yes—
66#15689007C2212yes—
67#15689007C2212yes—
68#15689007C2212yes—
69#15689007C2212yes—
70#15689006C2212yes—
71#15689006C2212yes—
72#15689005C2212yes—
73#15689005C2212yes—
74#15689005C2212yes—
75#15689005C2212yes—
76#15689005C2212yes—
77#15689004C2212yes—
78#15689004C2212yes—
79#15689004C2212yes—
80#15688992C2212yes—
81#15688990C2212yes—
82#15688988C2212yes—
83#15688987C2212yes—
84#15688986C2211yescharacteristic
85#15688986C2211yescharacteristic
86#15688984C2211yescharacteristic
87#15688984C2211yescharacteristic
88#15688983C2211yescharacteristic
89#15688981C2211yescharacteristic
90#15688981C2211yescharacteristic
91#15688981C2211yescharacteristic
92#15688981C2211yescharacteristic
93#15688981C2211yescharacteristic
94#15688981C2211yescharacteristic
95#15688981C2211yescharacteristic
96#15688981C2211yescharacteristic
97C4⋊C4×Dic47C2212yes—
98C4×Dic47⋊C4C2212yes—
99C4×Dic47⋊C4C2212yes—
100C4×Dic47⋊C4C2212yes—
101C4×Dic47⋊C4C2212yes—
102C4×Dic47⋊C4C2212yes—
103#15688974C2212yes—
104#15688974C2212yes—
105#15688974C2212yes—
106#15688974C2212yes—
107C22⋊C4×Dic47C2211yescharacteristic
108C22⋊C4×Dic47C2211yescharacteristic
109C22⋊C4×Dic47C2211yescharacteristic
110C22⋊C4×Dic47C2211yescharacteristic
111C4×C22⋊Dic47C2211yescharacteristic
112#15688968C2212yes—
113C2×#117×C47C2211yescharacteristic
114C2×#117×C47C2211yescharacteristic
115C22×C4⋊C4×C47C2211yescharacteristic
116C47×#389C2212yes—
117C47×#387C2212yes—
118C47×#387C2212yes—
119C47×#381C2211yescharacteristic
120C47×#381C2211yescharacteristic
121C47×#380C2211yescharacteristic
122C4×C4⋊C4×C47C2212yes—
123C4×C22⋊C4×C47C2211yescharacteristic
124C23×Dic47C2311yescharacteristic
125C23×Dic47C2311yescharacteristic
126C23×Dic47C2311yescharacteristic
127C23×Dic47C2311yescharacteristic
128#13094014C2×C418yes—
129#13094014C2×C418yes—
130#13094014C2×C418yes—
131#13094014C2×C418yes—
132#13094014C2×C418yes—
133#13094014C2×C418yes—
134#13094014C2×C418yes—
135#13094014C2×C418yes—
136#13093983—42no—
137#13093983—42no—
138#13093980—42no—
139#13093980—42no—
140C2×C4⋊Dic47C2×C418yes—
141C2×C4⋊Dic47C2312yes—
142C2×C4⋊Dic47C2312yes—
143C2×C4⋊Dic47C2312yes—
144C2×C4⋊Dic47C2311yescharacteristic
145C2×C4⋊Dic47C2311yescharacteristic
146C2×C4⋊Dic47C2311yescharacteristic
147C2×C4⋊Dic47C2311yescharacteristic
148C2×Dic47⋊C4C2×C418yes—
149C2×Dic47⋊C4C2×C418yes—
150C2×Dic47⋊C4C2×C418yes—
151C2×Dic47⋊C4C2×C418yes—
152C2×Dic47⋊C4C2312yes—
153C2×Dic47⋊C4C2312yes—
154C2×Dic47⋊C4C2312yes—
155C2×Dic47⋊C4C2312yes—
156C2×Dic47⋊C4C2312yes—
157C2×Dic47⋊C4C2312yes—
158C2×Dic47⋊C4C2312yes—
159C2×Dic47⋊C4C2312yes—
160C2×Dic47⋊C4C2312yes—
161C2×Dic47⋊C4C2312yes—
162C2×Dic47⋊C4C2311yescharacteristic
163C2×Dic47⋊C4C2311yescharacteristic
164C2×Dic47⋊C4C2311yescharacteristic
165C2×Dic47⋊C4C2311yescharacteristic
166C2×Dic47⋊C4C2311yescharacteristic
167C2×Dic47⋊C4C2311yescharacteristic
168C2×Dic47⋊C4C2311yescharacteristic
169C2×Dic47⋊C4C2311yescharacteristic
170C2×Dic47⋊C4C2311yescharacteristic
171C2×Dic47⋊C4C2311yescharacteristic
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×Dic47⋊C4C2311yescharacteristic
176C2×Dic47⋊C4C2311yescharacteristic
177C2×Dic47⋊C4C2311yescharacteristic
178C2×C22⋊Dic47C2311yescharacteristic
179C2×C22⋊Dic47C2311yescharacteristic
180C2×C22⋊Dic47C2311yescharacteristic
181C2×C22⋊Dic47C2311yescharacteristic
182C2×C4×Dic47C2×C418yes—
183C2×C4×Dic47C2312yes—
184C2×C4×Dic47C2312yes—
185C2×C4×Dic47C2312yes—
186C2×C4×Dic47C2312yes—
187C2×C4×Dic47C2312yes—
188C2×C4×Dic47C2312yes—
189C2×C4×Dic47C2312yes—
190C2×C4×Dic47C2312yes—
191C2×C4×Dic47C2312yes—
192C2×C4×Dic47C2311yescharacteristic
193C2×C4×Dic47C2311yescharacteristic
194C2×C4×Dic47C2311yescharacteristic
195C2×C4×Dic47C2311yescharacteristic
196C47⋊#95C2312yes—
197C47⋊#95C2312yes—
198C47⋊#95C2312yes—
199C47⋊#95C2312yes—
200C47⋊#95C2312yes—
201C47⋊#95C2312yes—
202C47⋊#95C2312yes—
203C47⋊#95C2312yes—
204C47⋊#95C2312yes—
205C47⋊#95C2312yes—
206C47⋊#95C2312yes—
207C47⋊#95C2312yes—
208C47⋊#95C2312yes—
209C47⋊#95C2312yes—
210C47⋊#95C2312yes—
211C47⋊#95C2312yes—
212C47⋊#95C2312yes—
213C47⋊#95C2312yes—
214C47⋊#95C2312yes—
215C47⋊#95C2312yes—
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C23×C4×C47C2311yescharacteristic
219C23×C4×C47C2311yescharacteristic
220C23×C4×C47C2311yescharacteristic
221#117×C47—42no—
222#117×C47—42no—
223C2×C4⋊C4×C47C2×C418yes—
224C2×C4⋊C4×C47C2312yes—
225C2×C4⋊C4×C47C2312yes—
226C2×C4⋊C4×C47C2312yes—
227C2×C4⋊C4×C47C2311yescharacteristic
228C2×C4⋊C4×C47C2311yescharacteristic
229C2×C4⋊C4×C47C2311yescharacteristic
230C2×C4⋊C4×C47C2311yescharacteristic
231C2×C22⋊C4×C47C2311yescharacteristic
232C2×C22⋊C4×C47C2311yescharacteristic
233C2×C22⋊C4×C47C2311yescharacteristic
234C2×C22⋊C4×C47C2311yescharacteristic
235C2×C42×C47C2312yes—
236C2×C42×C47C2312yes—
237C2×C42×C47C2312yes—
238#95×C47C2312yes—
239#95×C47C2312yes—
240#95×C47C2312yes—
241#95×C47C2312yes—
242#95×C47C2312yes—
243#95×C47C2312yes—
244C24×C47C2411yescharacteristic
245C22×C4×C47—22no—
246C22×C4×C47—22no—
247C22×C4×C47—22no—
248C22×C4×C47—22no—
249C22×C4×C47—42no—
250C22×C4×C47C22×C414yes—
251C22×C4×C47C22×C414yes—
252C22×C4×C47C22×C414yes—
253C22×C4×C47C2412yes—
254C22×C4×C47C2412yes—
255C22×C4×C47C2412yes—
256C22×C4×C47C2412yes—
257C22×C4×C47C2411yescharacteristic
258C22×C4×C47C2411yescharacteristic
259C22×C4×C47C2411yescharacteristic
260C22×C4×C47C2411yescharacteristic
261C22×C4×C47C2411yescharacteristic
262C22×C4×C47C2411yescharacteristic
263C22×Dic47—22no—
264C22×Dic47—22no—
265C22×Dic47—24no—
266C22×Dic47—42no—
267C22×Dic47—42no—
268C22×Dic47C22×C414yes—
269C22×Dic47C22×C414yes—
270C22×Dic47C22×C414yes—
271C22×Dic47C22×C414yes—
272C22×Dic47C2412yes—
273C22×Dic47C2412yes—
274C22×Dic47C2412yes—
275C22×Dic47C2412yes—
276C22×Dic47C2411yescharacteristic
277C22×Dic47C2411yescharacteristic
278C22×Dic47C2411yescharacteristic
279C22×Dic47C2411yescharacteristic
280C22×Dic47C2411yescharacteristic
281C22×Dic47C2411yescharacteristic
282C22×Dic47C2411yescharacteristic
283C22×Dic47C2411yescharacteristic
284C4⋊C4×C47—42no—
285C4⋊C4×C47—42no—
286C4⋊C4×C47—42no—
287C4⋊C4×C47C22×C414yes—
288C4⋊C4×C47C22×C414yes—
289C4⋊C4×C47C22×C414yes—
290C4⋊C4×C47C22×C414yes—
291C22⋊C4×C47—22no—
292C22⋊C4×C47—22no—
293C22⋊C4×C47—22no—
294C22⋊C4×C47—22no—
295C42×C47—42no—
296C42×C47—42no—
297C42×C47—42no—
298C22⋊Dic47—22no—
299C22⋊Dic47—22no—
300C22⋊Dic47—22no—
301C22⋊Dic47—22no—
302C4⋊Dic47—42no—
303C4⋊Dic47—42no—
304C4⋊Dic47—42no—
305C4⋊Dic47C22×C414yes—
306C4⋊Dic47C22×C414yes—
307C4⋊Dic47C22×C414yes—
308C4⋊Dic47C22×C414yes—
309Dic47⋊C4—24no—
310Dic47⋊C4—24no—
311Dic47⋊C4—42no—
312Dic47⋊C4—42no—
313Dic47⋊C4—42no—
314Dic47⋊C4—42no—
315Dic47⋊C4—42no—
316Dic47⋊C4—42no—
317Dic47⋊C4—42no—
318Dic47⋊C4—42no—
319Dic47⋊C4C22×C414yes—
320Dic47⋊C4C22×C414yes—
321Dic47⋊C4C22×C414yes—
322Dic47⋊C4C22×C414yes—
323Dic47⋊C4C22×C414yes—
324Dic47⋊C4C22×C414yes—
325Dic47⋊C4C22×C414yes—
326Dic47⋊C4C22×C414yes—
327Dic47⋊C4C22×C414yes—
328Dic47⋊C4C22×C414yes—
329Dic47⋊C4C22×C414yes—
330Dic47⋊C4C22×C414yes—
331Dic47⋊C4C22×C414yes—
332Dic47⋊C4C22×C414yes—
333Dic47⋊C4C22×C414yes—
334Dic47⋊C4C22×C414yes—
335C4×Dic47—24no—
336C4×Dic47—24no—
337C4×Dic47—42no—
338C4×Dic47—42no—
339C4×Dic47—42no—
340C4×Dic47—42no—
341C4×Dic47—42no—
342C4×Dic47—42no—
343C4×Dic47—42no—
344C4×Dic47C22×C414yes—
345C4×Dic47C22×C414yes—
346C4×Dic47C22×C414yes—
347C4×Dic47C22×C414yes—
348C23×C47—22no—
349C23×C47—22no—
350C23×C47C23×C412yes—
351C23×C47H(5,𝔽2)12yes—
352C23×C472−1+412yes—
353C23×C47C2511yescharacteristic
354C2×C4×C47—28no—
355C2×C4×C47—28no—
356C2×C4×C47—21no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—21no—
360C2×C4×C47—21no—
361C2×C4×C47—21no—
362C2×C4×C47—21no—
363C2×C4×C47—21no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—44no—
379C2×C4×C47C23×C412yes—
380C2×C4×C47C23×C412yes—
381C2×C4×C47C23×C412yes—
382C2×C4×C47C23×C412yes—
383C2×C4×C47C23×C412yes—
384C2×C4×C47C23×C412yes—
385C2×Dic47—28no—
386C2×Dic47—21no—
387C2×Dic47—21no—
388C2×Dic47—22no—
389C2×Dic47—21no—
390C2×Dic47—21no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—28no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—22no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—44no—
409C2×Dic47—44no—
410C2×Dic47C23×C412yes—
411C2×Dic47C23×C412yes—
412C2×Dic47C23×C412yes—
413C2×Dic47C23×C412yes—
414C2×Dic47C23×C412yes—
415C2×Dic47C23×C412yes—
416C2×Dic47C23×C412yes—
417C2×Dic47C23×C412yes—
418C2×Dic472−1+414yes—
419#34378—471nomaximal, Sylow
420C22×C47—22no—
421C22×C47—22no—
422C22×C47—24no—
423C22×C47—24no—
424C22×C47#52014yes—
425C22×C47C24×C411yescharacteristic
426C22×C47C2×H(5,𝔽2)11yescharacteristic
427C22×C47C2×2−1+412yes—
428C22×C47C2×2−1+411yescharacteristic
429C22×C47#58512yes—
430C4×C47—22no—
431C4×C47—22no—
432C4×C47—22no—
433C4×C47—22no—
434C4×C47—22no—
435C4×C47—22no—
436C4×C47—42no—
437C4×C47—42no—
438C4×C47—42no—
439C4×C47—42no—
440Dic47—22no—
441Dic47—22no—
442Dic47—22no—
443Dic47—22no—
444Dic47—22no—
445Dic47—22no—
446Dic47—22no—
447Dic47—42no—
448Dic47—42no—
449Dic47—42no—
450Dic47—42no—
451Dic47#51914yes—
452C22×#125—471no—
453#2382—472no—
454#2382—472no—
455#2370—472no—
456#2370—472no—
457#2345—471no—
458#2345—471no—
459#2344—471no—
460#2344—471no—
461#2344—471no—
462#2344—471no—
463#2344—471no—
464#2344D4711yescharacteristic
465#2336—472no—
466#2336—472no—
467#2330—472no—
468#2330—472no—
469#2316—471no—
470#2316—471no—
471#2313—471no—
472#2313—471no—
473#2285—471no—
474#2283—471no—
475C2×C47—24no—
476C2×C47C2×#51911yescharacteristic
477C2×C47C2×#52011yescharacteristic
478C2×C47#342811yescharacteristic
479C2×C47#355912yes—
480C2×C47#356312yes—
481C2×#125—4716no—
482C2×#125—471no—
483C2×#125—471no—
484C2×#125—471no—
485C2×#125—471no—
486C2×#125—471no—
487C2×#125—471no—
488C2×#125—471no—
489C2×#125—471no—
490C2×#117—471no—
491C2×#117—471no—
492C2×#117—471no—
493C2×#117—471no—
494C2×#117C2×D4711yescharacteristic
495C2×#117C2×D4711yescharacteristic
496C22×C4⋊C4—471no—
497C22×C4⋊C4—471no—
498C22×C4⋊C4—471no—
499C22×C4⋊C4—471no—
500C22×C4⋊C4—471no—
501C22×C4⋊C4C2×D4711yescharacteristic
502C22×C42—471no—
503#389—472no—
504#389—472no—
505#389—472no—
506#389—472no—
507#389—472no—
508#389—472no—
509#389—472no—
510#389—472no—
511#389—472no—
512#389—472no—
513#389—472no—
514#389—472no—
515#389—472no—
516#389—472no—
517#389—472no—
518#389C2×D4712yes—
519#387—472no—
520#387—472no—
521#387—472no—
522#387—472no—
523#387—472no—
524#387—472no—
525#387—472no—
526#387—472no—
527#387—472no—
528#387—472no—
529#387—472no—
530#387—472no—
531#387—472no—
532#387—472no—
533#387—472no—
534#387—472no—
535#387—472no—
536#387—472no—
537#387—472no—
538#387—472no—
539#387—472no—
540#387—472no—
541#387C2×D4712yes—
542#387C2×D4712yes—
543#384—472no—
544#383—472no—
545#382—472no—
546#382—472no—
547#381—471no—
548#381—471no—
549#381—471no—
550#381—471no—
551#381C2×D4711yescharacteristic
552#381C2×D4711yescharacteristic
553#380—471no—
554#380—471no—
555#380—471no—
556#380—471no—
557#380—471no—
558#380—471no—
559#380—471no—
560#380—471no—
561#380—471no—
562#380C2×D4711yescharacteristic
563C4×C4⋊C4—472no—
564C4×C4⋊C4—472no—
565C4×C4⋊C4—472no—
566C4×C4⋊C4—472no—
567C4×C4⋊C4—472no—
568C4×C4⋊C4—472no—
569C4×C4⋊C4—472no—
570C4×C4⋊C4—472no—
571C4×C4⋊C4—472no—
572C4×C4⋊C4—472no—
573C4×C4⋊C4C2×D4712yes—
574C4×C22⋊C4—471no—
575C4×C22⋊C4—471no—
576C4×C22⋊C4—471no—
577C4×C22⋊C4—471no—
578C4×C22⋊C4—471no—
579C4×C22⋊C4C2×D4711yescharacteristic
580#376—472no—
581C47#3437811yescharacteristic, complemented, Sylow
582C23×C4—471no—
583C23×C4—471no—
584C23×C4—471no—
585C23×C4—471no—
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588C23×C4C22×D4711yescharacteristic
589#125—478no—
590#125—478no—
591#125—478no—
592#125—478no—
593#125—478no—
594#125—478no—
595#125—478no—
596#125—478no—
597#117—42no—
598#117—42no—
599#117—1882no—
600#117—1882no—
601#117—1882no—
602#117—1882no—
603C2×C4⋊C4—478no—
604C2×C4⋊C4—478no—
605C2×C4⋊C4—478no—
606C2×C4⋊C4—478no—
607C2×C4⋊C4—478no—
608C2×C4⋊C4—471no—
609C2×C4⋊C4—471no—
610C2×C4⋊C4—471no—
611C2×C4⋊C4—471no—
612C2×C4⋊C4—471no—
613C2×C4⋊C4—471no—
614C2×C4⋊C4—471no—
615C2×C4⋊C4—471no—
616C2×C4⋊C4—471no—
617C2×C4⋊C4—471no—
618C2×C4⋊C4—471no—
619C2×C4⋊C4—471no—
620C2×C4⋊C4—471no—
621C2×C4⋊C4—471no—
622C2×C4⋊C4—471no—
623C2×C4⋊C4—471no—
624C2×C4⋊C4—471no—
625C2×C4⋊C4—471no—
626C2×C4⋊C4—471no—
627C2×C4⋊C4—471no—
628C2×C4⋊C4—472no—
629C2×C4⋊C4—472no—
630C2×C4⋊C4—472no—
631C2×C4⋊C4—472no—
632C2×C4⋊C4—472no—
633C2×C4⋊C4—472no—
634C2×C4⋊C4—472no—
635C2×C4⋊C4—472no—
636C2×C4⋊C4—472no—
637C2×C4⋊C4—472no—
638C2×C4⋊C4—472no—
639C2×C4⋊C4—472no—
640C2×C4⋊C4—472no—
641C2×C4⋊C4C4×D4718yes—
642C2×C4⋊C4C22×D4712yes—
643C2×C4⋊C4C22×D4712yes—
644C2×C4⋊C4C22×D4712yes—
645C2×C4⋊C4C22×D4711yescharacteristic
646C2×C4⋊C4C22×D4711yescharacteristic
647C2×C4⋊C4C22×D4711yescharacteristic
648C2×C4⋊C4C22×D4711yescharacteristic
649C2×C22⋊C4—471no—
650C2×C22⋊C4—471no—
651C2×C22⋊C4—471no—
652C2×C22⋊C4—471no—
653C2×C22⋊C4C22×D4711yescharacteristic
654C2×C22⋊C4C22×D4711yescharacteristic
655C2×C22⋊C4C22×D4711yescharacteristic
656C2×C22⋊C4C22×D4711yescharacteristic
657C2×C42—478no—
658C2×C42—471no—
659C2×C42—471no—
660C2×C42—471no—
661C2×C42—471no—
662C2×C42—472no—
663C2×C42—472no—
664C2×C42—472no—
665C2×C42—472no—
666C2×C42—472no—
667C2×C42—472no—
668C2×C42—472no—
669C2×C42—472no—
670C2×C42—472no—
671C2×C42C22×D4712yes—
672C2×C42C22×D4712yes—
673C2×C42C22×D4712yes—
674#95—472no—
675#95—472no—
676#95—472no—
677#95—472no—
678#95—472no—
679#95—472no—
680#95—472no—
681#95—472no—
682#95—472no—
683#95—472no—
684#95—472no—
685#95—472no—
686#95—472no—
687#95—472no—
688#95—472no—
689#95—472no—
690#95—472no—
691#95—472no—
692#95—472no—
693#95—472no—
694#95—472no—
695#95—472no—
696#95C22×D4712yes—
697#95C22×D4712yes—
698#95C22×D4712yes—
699#95C22×D4712yes—
700#95C22×D4712yes—
701#95C22×D4712yes—
702C24C23×D4711yescharacteristic
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—42no—
708C22×C4—471no—
709C22×C4—474no—
710C22×C4—474no—
711C22×C4—471no—
712C22×C4—471no—
713C22×C4—471no—
714C22×C4—471no—
715C22×C4—471no—
716C22×C4—471no—
717C22×C4—471no—
718C22×C4—474no—
719C22×C4—474no—
720C22×C4—472no—
721C22×C4—472no—
722C22×C4—472no—
723C22×C4—472no—
724C22×C4—944no—
725C22×C4—942no—
726C22×C4—942no—
727C22×C4—1882no—
728C22×C4—1882no—
729C22×C4C2×C4×D4714yes—
730C22×C4C2×C4×D4714yes—
731C22×C4C2×C4×D4714yes—
732C22×C4C23×D4712yes—
733C22×C4C23×D4712yes—
734C22×C4C23×D4712yes—
735C22×C4C23×D4712yes—
736C22×C4C23×D4711yescharacteristic
737C22×C4C23×D4711yescharacteristic
738C22×C4C23×D4711yescharacteristic
739C22×C4C23×D4711yescharacteristic
740C22×C4C23×D4711yescharacteristic
741C22×C4C23×D4711yescharacteristic
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—474no—
746C4⋊C4—474no—
747C4⋊C4—474no—
748C4⋊C4—474no—
749C4⋊C4—474no—
750C4⋊C4—474no—
751C4⋊C4—474no—
752C4⋊C4—474no—
753C4⋊C4—474no—
754C4⋊C4—474no—
755C4⋊C4—474no—
756C4⋊C4—474no—
757C4⋊C4—474no—
758C4⋊C4—474no—
759C4⋊C4—474no—
760C4⋊C4—474no—
761C4⋊C4—474no—
762C4⋊C4—474no—
763C4⋊C4—474no—
764C4⋊C4—474no—
765C4⋊C4—944no—
766C4⋊C4—944no—
767C4⋊C4—1882no—
768C4⋊C4—1882no—
769C4⋊C4—1882no—
770C4⋊C4—1882no—
771C4⋊C4—1882no—
772C4⋊C4—1882no—
773C4⋊C4—1882no—
774C4⋊C4—1882no—
775C4⋊C4—1882no—
776C4⋊C4—1882no—
777C4⋊C4—1882no—
778C4⋊C4C2×C4×D4714yes—
779C4⋊C4C2×C4×D4714yes—
780C4⋊C4C2×C4×D4714yes—
781C4⋊C4C2×C4×D4714yes—
782C22⋊C4—22no—
783C22⋊C4—22no—
784C22⋊C4—22no—
785C22⋊C4—22no—
786C22⋊C4—942no—
787C22⋊C4—942no—
788C22⋊C4—942no—
789C22⋊C4—942no—
790C42—42no—
791C42—42no—
792C42—42no—
793C42—474no—
794C42—474no—
795C42—474no—
796C42—474no—
797C42—944no—
798C42—944no—
799C42—1882no—
800C42—1882no—
801C42—1882no—
802C42—1882no—
803C42—1882no—
804C42—1882no—
805C42—1882no—
806C23—22no—
807C23—22no—
808C23C22×C4×D4712yes—
809C23#1309406912yes—
810C23#1309407112yes—
811C23C24×D4711yescharacteristic
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—44no—
837C2×C4—472no—
838C2×C4—474no—
839C2×C4—472no—
840C2×C4—472no—
841C2×C4—472no—
842C2×C4—472no—
843C2×C4—472no—
844C2×C4—472no—
845C2×C4—472no—
846C2×C4—948no—
847C2×C4—948no—
848C2×C4—941no—
849C2×C4—941no—
850C2×C4—942no—
851C2×C4—941no—
852C2×C4—941no—
853C2×C4—942no—
854C2×C4—942no—
855C2×C4—942no—
856C2×C4—942no—
857C2×C4—942no—
858C2×C4—942no—
859C2×C4—942no—
860C2×C4—942no—
861C2×C4—942no—
862C2×C4—942no—
863C2×C4—942no—
864C2×C4—942no—
865C2×C4—942no—
866C2×C4—942no—
867C2×C4—942no—
868C2×C4—942no—
869C2×C4—1884no—
870C2×C4—1884no—
871C2×C4C22×C4×D4712yes—
872C2×C4C22×C4×D4712yes—
873C2×C4C22×C4×D4712yes—
874C2×C4C22×C4×D4712yes—
875C2×C4C22×C4×D4712yes—
876C2×C4C22×C4×D4712yes—
877C22—22no—
878C22—22no—
879C22—24no—
880C22—24no—
881C22#1568960214yes—
882C22C23×C4×D4711yescharacteristic
883C22C2×#1309406911yescharacteristic
884C222−1+4×D4712yes—
885C22C2×#1309407111yescharacteristic
886C22#1568995912yes—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—22no—
892C4—22no—
893C4—42no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—474no—
898C4—942no—
899C4—942no—
900C4—942no—
901C4—942no—
902C4—942no—
903C4—942no—
904C4—942no—
905C4—1882no—
906C4—1882no—
907C4—1882no—
908C4—1882no—
909C2—24no—
910C2#519×D4711yescharacteristic
911C2C2×#1568960211yescharacteristic
912C2#2025658911yescharacteristic
913C2#2025791312yes—
914C2#2025798512yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2344C2
socle, cosocleC23×C47C25
prime radicalC24×C47C24
hypercenter#2344D47
hypocenterC47#34378
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #20246572C2semidirect
3. #20246570C2semidirect
4. #20246485C2semidirect
5. #20246479C2semidirect
13. #20246190C2semidirect
14. #20246187C2semidirect
15. #20246126C2semidirect
16. #20246124C2semidirect
24. C2×#13094014C4semidirect
581. C47#34378semidirect

Maximal subgroups

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

subgroupindex
C22×#130940142
#202465722
#202465702
#202464852
#202464792
#202462662
#202462602
#202462582
#202462572
#202462522
#202461902
#202461872
#202461262
#202461242
#202460052
#202460042
#202459892
#202459882
#202457912
#202457792
C47×#23442
#3437847