Finite Group Databasebeta

← #26388534

Subgroups — #26388534

Order 12032.

3270 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689591C211yesmaximal, characteristic, complemented
2C2×C4×D4×D47C211yesmaximal, characteristic, complemented
3#20248956C211yesmaximal, characteristic, complemented
4#20248954C211yesmaximal, characteristic, complemented
5#20248948C211yesmaximal, characteristic, complemented
6#20248745C212yesmaximal, complemented
7#20248288C212yesmaximal, complemented
8#20247700C211yesmaximal, characteristic, complemented
9#20247698C211yesmaximal, characteristic, complemented
10#20247660C212yesmaximal, complemented
11#20246739C211yesmaximal, characteristic, complemented
12#20246737C211yesmaximal, characteristic, complemented
13#20246705C212yesmaximal, complemented
14#20246677C211yesmaximal, characteristic, complemented
15#20246676C211yesmaximal, characteristic, complemented
16#20246668C211yesmaximal, characteristic, complemented
17#20246666C211yesmaximal, characteristic, complemented
18#20245900C212yesmaximal, complemented
19#20245898C212yesmaximal, complemented
20#20245893C212yesmaximal, complemented
21#20245889C212yesmaximal, complemented
22#20245785C211yesmaximal, characteristic, complemented
23C47×#2598C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic
25C22×D4×D47C2211yescharacteristic
26C23×C4×D47C2212yes—
27C2×#13093997C2212yes—
28C2×#13093996C2212yes—
29C2×#13093994C2212yes—
30C2×#13093992C2212yes—
31#15689591—28no—
32C2×#13093989C2211yescharacteristic, complemented
33C2×#13093989C2211yescharacteristic, complemented
34C2×C4×D188C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×D4×Dic47C2212yescomplemented
37C2×#13093986C2211yescharacteristic
38C2×#13093986C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×#13093986C2212yescomplemented
41C2×C4×C22⋊D47C2212yes—
42C2×(C22⋊D47)⋊C4C2212yes—
43C2×(C22⋊D47)⋊C4C2211yescharacteristic
44C2×(C22⋊D47)⋊C4C2211yescharacteristic
45C2×(C22⋊D47)⋊C4C2211yescharacteristic, complemented
46C2×(C22⋊D47)⋊C4C2211yescharacteristic, complemented
47C2×(C22⋊D47)⋊C4C2212yescomplemented
48C2×(C22⋊D47)⋊C4C2212yescomplemented
49C4×D4×D47—28no—
50C2×#13093981C2211yescharacteristic
51C2×#13093981C2211yescharacteristic, complemented
52C2×C4⋊C4×D47C2211yescharacteristic
53C2×C22⋊C4×D47C2212yes—
54C22×C4×Dic47C2211yescharacteristic, complemented
55C2×C42×D47C2211yescharacteristic
56C2×C42×D47C2211yescharacteristic, complemented
57#15689063C2211yescharacteristic, complemented
58#15689062C2211yescharacteristic, complemented
59#15689061C2211yescharacteristic, complemented
60#15689060C2211yescharacteristic, complemented
61#15689059C2212yescomplemented
62#15689059C2211yescharacteristic, complemented
63#15689058C2212yescomplemented
64#15689058C2211yescharacteristic, complemented
65#15689052C2212yescomplemented
66#15689051C2212yescomplemented
67#15689041C2211yescharacteristic
68#15689040C2211yescharacteristic
69#15689037C2211yescharacteristic
70#15689036C2212yescomplemented
71#15689035C2212yescomplemented
72#15689033C2211yescharacteristic
73#15689032C2211yescharacteristic
74#15689032C2212yescomplemented
75#15689031C2211yescharacteristic
76#15689031C2212yescomplemented
77#15689023C2212yes—
78#15689023C2212yes—
79#15689020C2212yescomplemented
80#15689018C2212yescomplemented
81#15689015C2212yescomplemented
82#15689014C2212yescomplemented
83#15689011C2212yescomplemented
84#15689002C2212yescomplemented
85#15689002C2212yescomplemented
86#15689001C2212yes—
87#15689001C2212yescomplemented
88#15689001C2212yescomplemented
89#15688999C2212yes—
90#15688999C2212yescomplemented
91#15688999C2212yescomplemented
92#15688997C2212yes—
93#15688997C2212yescomplemented
94#15688996C2212yescomplemented
95#15688994C2212yes—
96#15688994C2212yescomplemented
97#15688991C2211yescharacteristic, complemented
98#15688987C2212yescomplemented
99#15688985C2212yes—
100#15688982C2211yescharacteristic
101#15688982C2211yescharacteristic
102#15688982C2212yescomplemented
103#15688981C2212yescomplemented
104#15688978C2212yes—
105#15688978C2212yes—
106#15688974C2212yescomplemented
107C22⋊C4×Dic47C2212yescomplemented
108C22⋊C4×Dic47C2212yescomplemented
109#15688970C2212yes—
110#15688970C2212yescomplemented
111#15688970C2212yescomplemented
112#15688968C2211yescharacteristic, complemented
113#15688968C2211yescharacteristic, complemented
114C2×C4×D4×C47C2211yescharacteristic
115C2×#117×C47C2211yescharacteristic, complemented
116C47×#400C2211yescharacteristic, complemented
117C47×#399C2211yescharacteristic, complemented
118C47×#394C2211yescharacteristic
119C47×#392C2211yescharacteristic
120C47×#388C2212yescomplemented
121C47×#386C2212yescomplemented
122C47×#386C2212yescomplemented
123C47×#385C2212yescomplemented
124C47×#383C2211yescharacteristic, complemented
125C24×D47C2312yes—
126C2×#10625350—24no—
127C2×#10625350—24no—
128C2×#10625350—24no—
129C22×Dic94C2311yescharacteristic
130C22×D188C2311yescharacteristic
131C22×D188C2312yes—
132C22×D188C2311yescharacteristic
133C22×C22⋊D47C2311yescharacteristic
134C22×C22⋊D47C2312yes—
135C22×C22⋊D47C2312yes—
136C22×C22⋊D47C2311yescharacteristic
137C22×C22⋊D47C2312yes—
138C2×D4×D47—28no—
139C2×D4×D47—24no—
140C23×Dic47C2312yes—
141C23×Dic47C2311yescharacteristic
142C23×Dic47C2311yescharacteristic
143C22×C4×D47—28no—
144C22×C4×D47—44no—
145C22×C4×D47—44no—
146C22×C4×D47C2312yes—
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2311yescharacteristic
151C22×C4×D47C2311yescharacteristic
152C22×C4×D47C2311yescharacteristic
153C22×C4×D47C2312yes—
154C22×C4×D47C2312yes—
155#13093997—28no—
156#13093996—28no—
157#13093994—28no—
158#13093992—28no—
159#13093989—24no—
160#13093989—24no—
161C4×D188—24no—
162D4×Dic47—24no—
163D4×Dic47—44no—
164#13093986—24no—
165#13093986—24no—
166#13093986—24no—
167#13093986—44no—
168C4×C22⋊D47—28no—
169(C22⋊D47)⋊C4—24no—
170(C22⋊D47)⋊C4—24no—
171(C22⋊D47)⋊C4—28no—
172(C22⋊D47)⋊C4—24no—
173(C22⋊D47)⋊C4—24no—
174(C22⋊D47)⋊C4—44no—
175(C22⋊D47)⋊C4—44no—
176#13093981—24no—
177#13093981—24no—
178C2×C4⋊Dic47C2311yescharacteristic
179C2×C4⋊Dic47C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2311yescharacteristic
184C2×Dic47⋊C4C2311yescharacteristic
185C2×Dic47⋊C4C2311yescharacteristic
186C2×Dic47⋊C4C2311yescharacteristic
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2312yes—
189C4⋊C4×D47—24no—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2312yes—
194C2×C22⋊Dic47C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2311yescharacteristic
203C2×(C2×D47)⋊C4C2311yescharacteristic
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2311yescharacteristic
206C2×(C2×D47)⋊C4C2312yes—
207C2×(C2×D47)⋊C4C2312yes—
208C2×(C2×D47)⋊C4C2312yes—
209C2×(C2×D47)⋊C4C2312yes—
210C2×(C2×D47)⋊C4C2312yes—
211C22⋊C4×D47—28no—
212C2×C4×Dic47—24no—
213C2×C4×Dic47C2312yes—
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2311yescharacteristic
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2311yescharacteristic
220C2×C4×Dic47C2311yescharacteristic
221C2×C4×Dic47C2311yescharacteristic
222C2×C4×Dic47C2311yescharacteristic
223C42×D47—24no—
224C42×D47D418yescomplemented
225C47⋊#95C2311yescharacteristic
226C47⋊#95C2311yescharacteristic
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C47⋊#95C2312yes—
237C22×D4×C47C2311yescharacteristic
238C22×D4×C47C2312yes—
239C23×C4×C47C2311yescharacteristic
240C23×C4×C47C2312yes—
241C4×D4×C47—24no—
242#117×C47—24no—
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2311yescharacteristic
246C2×C4⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2311yescharacteristic
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2312yes—
253C2×C22⋊C4×C47C2312yes—
254C2×C42×C47C2311yescharacteristic
255C2×C42×C47C2311yescharacteristic
256#95×C47C2311yescharacteristic
257#95×C47C2311yescharacteristic
258#95×C47C2312yes—
259#95×C47C2312yes—
260#95×C47C2312yes—
261#95×C47C2312yes—
262C24×C47C2412yes—
263C24×C47C2411yescharacteristic
264C23×D47—24no—
265C23×D47—24no—
266C23×D47—24no—
267C23×D47—24no—
268C23×D47—24no—
269C23×D47—42no—
270C23×D47—42no—
271C23×D47C2412yes—
272C23×D47C2411yescharacteristic
273C23×D47C2411yescharacteristic
274C2×D4×C47—24no—
275C2×D4×C47—24no—
276C2×D4×C47—24no—
277C2×D4×C47—22no—
278C2×D4×C47—42no—
279C22×C4×C47—22no—
280C22×C4×C47—22no—
281C22×C4×C47—22no—
282C22×C4×C47—24no—
283C22×C4×C47—42no—
284C22×C4×C47—42no—
285C22×C4×C47C2411yescharacteristic
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2412yes—
288C22×C4×C47C2412yes—
289C22×C4×C47C2412yes—
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2411yescharacteristic
293C22×C4×C47C2411yescharacteristic
294C2×C22⋊D47—22no—
295C2×C22⋊D47—22no—
296C2×C22⋊D47—22no—
297C2×C22⋊D47—22no—
298C2×C22⋊D47—24no—
299C2×C22⋊D47—24no—
300C2×C22⋊D47—24no—
301C2×C22⋊D47—24no—
302C2×C22⋊D47—22no—
303C2×C22⋊D47—24no—
304C2×C22⋊D47—24no—
305C2×C22⋊D47—42no—
306C2×C22⋊D47—42no—
307C2×C22⋊D47#4114yes—
308C2×C22⋊D47#4118yescomplemented
309C22×Dic47—22no—
310C22×Dic47—22no—
311C22×Dic47—24no—
312C22×Dic47—24no—
313C22×Dic47—24no—
314C22×Dic47—24no—
315C22×Dic47—24no—
316C22×Dic47C2412yes—
317C22×Dic47C2412yes—
318C22×Dic47C2411yescharacteristic
319C22×Dic47C2412yes—
320C22×Dic47C2411yescharacteristic
321C22×Dic47C2411yescharacteristic
322C22×Dic47C2411yescharacteristic
323C22×Dic47C2411yescharacteristic
324C22×Dic47C2411yescharacteristic
325D4×D47—232no—
326#10625350—232no—
327C2×D188—22no—
328C2×D188—24no—
329C2×D188—22no—
330C2×D188—22no—
331C2×D188—24no—
332C2×D188—24no—
333C2×D188—42no—
334C2×D188#4114yes—
335C2×C4×D47—22no—
336C2×C4×D47—22no—
337C2×C4×D47—22no—
338C2×C4×D47—22no—
339C2×C4×D47—24no—
340C2×C4×D47—22no—
341C2×C4×D47—24no—
342C2×C4×D47—24no—
343C2×C4×D47—24no—
344C2×C4×D47—22no—
345C2×C4×D47—22no—
346C2×C4×D47—24no—
347C2×C4×D47—24no—
348C2×C4×D47—24no—
349C2×C4×D47—24no—
350C2×C4×D47—24no—
351C2×C4×D47—432no—
352C2×C4×D47—42no—
353C2×C4×D47—42no—
354C2×C4×D47—42no—
355C2×C4×D47—42no—
356C2×C4×D47C2×D414yes—
357C2×C4×D47C2×D414yes—
358C2×C4×D47C2×D414yes—
359C2×Dic94—22no—
360C2×Dic94—22no—
361C2×Dic94—22no—
362C4⋊C4×C47—22no—
363C4⋊C4×C47—22no—
364C4⋊C4×C47—22no—
365C4⋊C4×C47—42no—
366C22⋊C4×C47—24no—
367C22⋊C4×C47—22no—
368C22⋊C4×C47—22no—
369C22⋊C4×C47—24no—
370C22⋊C4×C47—24no—
371C22⋊C4×C47—42no—
372C22⋊C4×C47—42no—
373C42×C47—22no—
374C42×C47C2×D414yes—
375C22⋊Dic47—24no—
376C22⋊Dic47—24no—
377C22⋊Dic47—24no—
378C22⋊Dic47—42no—
379C22⋊Dic47—42no—
380(C2×D47)⋊C4—22no—
381(C2×D47)⋊C4—22no—
382(C2×D47)⋊C4—24no—
383(C2×D47)⋊C4—24no—
384(C2×D47)⋊C4—24no—
385(C2×D47)⋊C4—24no—
386(C2×D47)⋊C4—24no—
387(C2×D47)⋊C4—22no—
388(C2×D47)⋊C4—22no—
389(C2×D47)⋊C4—24no—
390(C2×D47)⋊C4—24no—
391(C2×D47)⋊C4—24no—
392(C2×D47)⋊C4—42no—
393(C2×D47)⋊C4—42no—
394(C2×D47)⋊C4—42no—
395(C2×D47)⋊C4—42no—
396C4⋊Dic47—22no—
397C4⋊Dic47—42no—
398Dic47⋊C4—22no—
399Dic47⋊C4—22no—
400Dic47⋊C4—24no—
401Dic47⋊C4—22no—
402Dic47⋊C4—22no—
403Dic47⋊C4—24no—
404Dic47⋊C4—24no—
405Dic47⋊C4—42no—
406Dic47⋊C4—42no—
407C4×Dic47—22no—
408C4×Dic47—22no—
409C4×Dic47—22no—
410C4×Dic47—22no—
411C4×Dic47—22no—
412C4×Dic47—24no—
413C4×Dic47—24no—
414C4×Dic47C2×D414yes—
415C4×Dic47C2×D414yes—
416C4×Dic47C2×D414yes—
417C23×C47—22no—
418C23×C47—21no—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—22no—
422C23×C47—21no—
423C23×C47—22no—
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—22no—
427C23×C47C2×#4114yes—
428C23×C47C2×#4112yes—
429C23×C47C2511yescharacteristic
430C22×D47—22no—
431C22×D47—22no—
432C22×D47—216no—
433C22×D47—21no—
434C22×D47—22no—
435C22×D47—22no—
436C22×D47—22no—
437C22×D47—21no—
438C22×D47—22no—
439C22×D47—22no—
440C22×D47—22no—
441C22×D47—22no—
442C22×D47—22no—
443C22×D47—48no—
444C22×D47—48no—
445C22×D47—48no—
446C22×D47—48no—
447C22×D47—48no—
448C22×D47—48no—
449C22×D47C22×D412yes—
450C22×D47C2×#4114yes—
451C22×D47C2×#4112yes—
452C22×D47C2×#4112yes—
453C22×D47C2×#4112yes—
454D4×C47—28no—
455D4×C47—48no—
456C2×C4×C47—28no—
457C2×C4×C47—21no—
458C2×C4×C47—21no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—21no—
464C2×C4×C47—21no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—48no—
477C2×C4×C47C22×D412yes—
478C2×C4×C47C22×D412yes—
479C2×C4×C47C22×D412yes—
480C2×C4×C47C2×#4112yes—
481C22⋊D47—28no—
482C22⋊D47—28no—
483C22⋊D47—216no—
484C22⋊D47—48no—
485C22⋊D47—48no—
486C2×Dic47—21no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47—22no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—44no—
504C2×Dic47—48no—
505C2×Dic47—44no—
506C2×Dic47C22×D412yes—
507C2×Dic47C22×D412yes—
508C2×Dic47C22×D412yes—
509C2×Dic47C2×#4112yes—
510C2×Dic47C2×#4114yes—
511C2×Dic47H(5,𝔽2)14yes—
512D188—28no—
513D188—28no—
514D188—48no—
515C4×D47—28no—
516C4×D47—28no—
517C4×D47—28no—
518C4×D47—28no—
519C4×D47—48no—
520C4×D47—48no—
521C4×D47—44no—
522C4×D47—44no—
523C4×D47—48no—
524Dic94—28no—
525#34963—471nomaximal, Sylow
526C22×C47—22no—
527C22×C47—24no—
528C22×C47—24no—
529C22×C47—24no—
530C22×C47—24no—
531C22×C47—41no—
532C22×C47—42no—
533C22×C47—42no—
534C22×C47—41no—
535C22×C47—42no—
536C22×C47—42no—
537C22×C47—42no—
538C22×C47C23×D411yescharacteristic
539C22×C47C22×#4111yescharacteristic
540C22×C47C22×#4111yescharacteristic
541C22×C47C22×#4112yes—
542C22×C47C2×H(5,𝔽2)12yes—
543C2×D47—22no—
544C2×D47—22no—
545C2×D47—24no—
546C2×D47—24no—
547C2×D47—22no—
548C2×D47—24no—
549C2×D47—24no—
550C2×D47—24no—
551C2×D47—24no—
552C2×D47—432no—
553C2×D47—41no—
554C2×D47—42no—
555C2×D47—42no—
556C2×D47—41no—
557C2×D47—42no—
558C2×D47—42no—
559C2×D47—42no—
560C2×D47#52514yes—
561C4×C47—22no—
562C4×C47—22no—
563C4×C47—22no—
564C4×C47—22no—
565C4×C47—41no—
566C4×C47—42no—
567C4×C47—41no—
568C4×C47—42no—
569C4×C47—42no—
570Dic47—22no—
571Dic47—22no—
572Dic47—41no—
573Dic47—42no—
574Dic47—41no—
575Dic47—42no—
576Dic47—42no—
577Dic47#52514yes—
578Dic47#53514yes—
579C2×C4×#41—471no—
580C22×C4×D4—471no—
581#2598—471no—
582#2598—471no—
583#2598—471no—
584#2598D4711yescharacteristic, complemented
585#2580—472no—
586#2535—472no—
587#2487—471no—
588#2487—471no—
589#2482—472no—
590#2408—471no—
591#2408—471no—
592#2404—472no—
593#2398—471no—
594#2398—471no—
595#2397—471no—
596#2397—471no—
597C4×#121—472no—
598C4×#121—472no—
599C4×#120—472no—
600C4×#120—472no—
601#2283—471no—
602C2×C47—44no—
603C2×C47—42no—
604C2×C47C2×#52511yescharacteristic
605C2×C47C2×#52511yescharacteristic
606C2×C47C2×#53511yescharacteristic
607C2×C47#348112yes—
608C2×C47#348112yes—
609D47—24no—
610D47—42no—
611D47—44no—
612C22×#41—471no—
613C23×D4—471no—
614C24×C4—472no—
615C2×#121—472no—
616C2×#121—472no—
617C2×#120—472no—
618C2×#120—472no—
619C4×#41—948no—
620C2×C4×Q8—471no—
621C2×C4×Q8—471no—
622C2×C4×D4—471no—
623C2×C4×D4—472no—
624C2×C4×D4—472no—
625C2×C4×D4—471no—
626C2×C4×D4—471no—
627C2×C4×D4—471no—
628C2×C4×D4—472no—
629C2×C4×D4—471no—
630C2×C4×D4—472no—
631C2×C4×D4—471no—
632C2×C4×D4—471no—
633C2×C4×D4—471no—
634C2×C4×D4—472no—
635C2×C4×D4—472no—
636C2×C4×D4—471no—
637C2×C4×D4—948no—
638C2×C4×D4C2×D4711yescharacteristic
639C2×#117—471no—
640C2×#117—471no—
641C2×#117C2×D4711yescharacteristic, complemented
642C22×C4⋊C4—471no—
643C22×C22⋊C4—472no—
644C22×C42—471no—
645C22×C42—471no—
646C22×C42—471no—
647#400—471no—
648#400—471no—
649#400—471no—
650#400C2×D4711yescharacteristic, complemented
651#399—472no—
652#399—471no—
653#399—472no—
654#399—471no—
655#399—471no—
656#399C2×D4711yescharacteristic, complemented
657#397—472no—
658#397—472no—
659#394—471no—
660#394—471no—
661#394—471no—
662#394C2×D4711yescharacteristic
663#393—472no—
664#393—472no—
665#392—471no—
666#392—472no—
667#392—471no—
668#392—472no—
669#392—471no—
670#392C2×D4711yescharacteristic
671#390—472no—
672#390—472no—
673#389—472no—
674#389—472no—
675#388—472no—
676#388—472no—
677#388—472no—
678#388C2×D4712yescomplemented
679#386—472no—
680#386—472no—
681#386—472no—
682#386—472no—
683#386—472no—
684#386—472no—
685#386—472no—
686#386—472no—
687#386C2×D4712yescomplemented
688#386C2×D4712yescomplemented
689#385—472no—
690#385—472no—
691#385—472no—
692#385—472no—
693#385—472no—
694#385C2×D4712yescomplemented
695#383—471no—
696#383C2×D4711yescharacteristic, complemented
697#382—472no—
698#381—472no—
699#380—472no—
700#380—471no—
701#380—471no—
702#380—472no—
703#379—472no—
704#379—472no—
705C4×C4⋊C4—472no—
706C4×C22⋊C4—472no—
707C4×C22⋊C4—472no—
708C4×C22⋊C4—472no—
709C4×C22⋊C4—472no—
710C4×C22⋊C4—472no—
711#376—471no—
712#376—471no—
713C47#3496311yescharacteristic, complemented, Sylow
714C25—472no—
715C2×#41—944no—
716C2×#41—944no—
717C2×#41—944no—
718C22×Q8—471no—
719C22×D4—471no—
720C22×D4—472no—
721C22×D4—471no—
722C22×D4—472no—
723C22×D4—472no—
724C22×D4—471no—
725C22×D4—471no—
726C22×D4—472no—
727C22×D4—944no—
728C22×D4—948no—
729C22×D4C22×D4711yescharacteristic
730C22×D4C22×D4712yes—
731C23×C4—471no—
732C23×C4—471no—
733C23×C4—471no—
734C23×C4—471no—
735C23×C4—472no—
736C23×C4—471no—
737C23×C4—471no—
738C23×C4—471no—
739C23×C4—472no—
740C23×C4—471no—
741C23×C4—472no—
742C23×C4—472no—
743C23×C4—948no—
744C23×C4—1884no—
745C23×C4—1884no—
746C23×C4C22×D4711yescharacteristic
747C23×C4C22×D4712yes—
748#121—948no—
749#121—948no—
750#120—948no—
751#120—948no—
752C4×Q8—944no—
753C4×Q8—944no—
754C4×D4—24no—
755C4×D4—948no—
756C4×D4—944no—
757C4×D4—944no—
758C4×D4—944no—
759C4×D4—948no—
760C4×D4—944no—
761C4×D4—944no—
762C4×D4—944no—
763C4×D4—944no—
764C4×D4—944no—
765C4×D4—944no—
766C4×D4—1884no—
767C4×D4—1884no—
768C4×D4—1884no—
769C4×D4—1884no—
770#117—24no—
771#117—944no—
772#117—944no—
773C2×C4⋊C4—472no—
774C2×C4⋊C4—471no—
775C2×C4⋊C4—471no—
776C2×C4⋊C4—471no—
777C2×C4⋊C4—471no—
778C2×C4⋊C4—471no—
779C2×C4⋊C4—472no—
780C2×C4⋊C4—472no—
781C2×C4⋊C4—472no—
782C2×C4⋊C4—472no—
783C2×C4⋊C4—472no—
784C2×C4⋊C4—944no—
785C2×C4⋊C4C22×D4711yescharacteristic
786C2×C4⋊C4C22×D4711yescharacteristic
787C2×C4⋊C4C22×D4711yescharacteristic
788C2×C4⋊C4C22×D4712yes—
789C2×C22⋊C4—472no—
790C2×C22⋊C4—472no—
791C2×C22⋊C4—472no—
792C2×C22⋊C4—472no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—471no—
795C2×C22⋊C4—471no—
796C2×C22⋊C4—471no—
797C2×C22⋊C4—471no—
798C2×C22⋊C4—472no—
799C2×C22⋊C4—472no—
800C2×C22⋊C4—472no—
801C2×C22⋊C4—472no—
802C2×C22⋊C4—472no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—472no—
806C2×C22⋊C4—472no—
807C2×C22⋊C4—472no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—472no—
810C2×C22⋊C4—948no—
811C2×C22⋊C4C22×D4712yes—
812C2×C22⋊C4C22×D4711yescharacteristic
813C2×C22⋊C4C22×D4711yescharacteristic
814C2×C22⋊C4C22×D4712yes—
815C2×C22⋊C4C22×D4712yes—
816C2×C22⋊C4C22×D4712yes—
817C2×C22⋊C4C22×D4712yes—
818C2×C42—471no—
819C2×C42—471no—
820C2×C42—471no—
821C2×C42—478no—
822C2×C42—471no—
823C2×C42—472no—
824C2×C42—472no—
825C2×C42—471no—
826C2×C42—471no—
827C2×C42—471no—
828C2×C42—471no—
829C2×C42—944no—
830C2×C42—944no—
831C2×C42C22×D4711yescharacteristic
832C2×C42C22×D4711yescharacteristic
833#95—471no—
834#95—471no—
835#95—472no—
836#95—472no—
837#95—472no—
838#95—472no—
839#95—472no—
840#95—472no—
841#95—472no—
842#95—472no—
843#95—472no—
844#95—472no—
845#95C22×D4711yescharacteristic
846#95C22×D4711yescharacteristic
847#95C22×D4712yes—
848#95C22×D4712yes—
849#95C22×D4712yes—
850#95C22×D4712yes—
851C24—471no—
852C24—472no—
853C24—471no—
854C24—944no—
855C24—944no—
856C24—944no—
857C24—944no—
858C24—944no—
859C24—1882no—
860C24—1882no—
861C24C23×D4712yes—
862C24C23×D4711yescharacteristic
863#41—9432no—
864C2×Q8—942no—
865C2×Q8—942no—
866C2×Q8—942no—
867C2×D4—24no—
868C2×D4—24no—
869C2×D4—24no—
870C2×D4—22no—
871C2×D4—42no—
872C2×D4—474no—
873C2×D4—478no—
874C2×D4—474no—
875C2×D4—942no—
876C2×D4—944no—
877C2×D4—942no—
878C2×D4—944no—
879C2×D4—944no—
880C2×D4—944no—
881C2×D4—942no—
882C2×D4—944no—
883C2×D4—9432no—
884C2×D4—942no—
885C2×D4—942no—
886C2×D4—942no—
887C2×D4—942no—
888C2×D4—944no—
889C2×D4—944no—
890C2×D4—944no—
891C2×D4—944no—
892C2×D4—942no—
893C2×D4—1882no—
894C2×D4—1882no—
895C2×D4—1882no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—24no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—471no—
903C22×C4—471no—
904C22×C4—471no—
905C22×C4—471no—
906C22×C4—474no—
907C22×C4—474no—
908C22×C4—474no—
909C22×C4—472no—
910C22×C4—472no—
911C22×C4—471no—
912C22×C4—472no—
913C22×C4—471no—
914C22×C4—944no—
915C22×C4—944no—
916C22×C4—942no—
917C22×C4—942no—
918C22×C4—942no—
919C22×C4—944no—
920C22×C4—944no—
921C22×C4—944no—
922C22×C4—944no—
923C22×C4—944no—
924C22×C4—942no—
925C22×C4—942no—
926C22×C4—942no—
927C22×C4—944no—
928C22×C4—942no—
929C22×C4—942no—
930C22×C4—944no—
931C22×C4—944no—
932C22×C4—944no—
933C22×C4—944no—
934C22×C4—944no—
935C22×C4—942no—
936C22×C4—944no—
937C22×C4—1882no—
938C22×C4—1882no—
939C22×C4—1882no—
940C22×C4—1882no—
941C22×C4—18832no—
942C22×C4C23×D4712yes—
943C22×C4C23×D4711yescharacteristic
944C22×C4C23×D4712yes—
945C22×C4C23×D4712yes—
946C22×C4C23×D4711yescharacteristic
947C22×C4C23×D4711yescharacteristic
948C22×C4C23×D4711yescharacteristic
949C22×C4C23×D4711yescharacteristic
950C22×C4C23×D4711yescharacteristic
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—42no—
955C4⋊C4—944no—
956C4⋊C4—942no—
957C4⋊C4—942no—
958C4⋊C4—944no—
959C4⋊C4—944no—
960C4⋊C4—942no—
961C4⋊C4—942no—
962C4⋊C4—942no—
963C4⋊C4—1882no—
964C4⋊C4—1882no—
965C4⋊C4—1882no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—24no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—944no—
974C22⋊C4—944no—
975C22⋊C4—942no—
976C22⋊C4—942no—
977C22⋊C4—944no—
978C22⋊C4—944no—
979C22⋊C4—944no—
980C22⋊C4—944no—
981C22⋊C4—944no—
982C22⋊C4—944no—
983C22⋊C4—944no—
984C22⋊C4—944no—
985C22⋊C4—942no—
986C22⋊C4—942no—
987C22⋊C4—944no—
988C22⋊C4—1882no—
989C22⋊C4—1882no—
990C22⋊C4—1882no—
991C22⋊C4—1882no—
992C22⋊C4—1882no—
993C22⋊C4—1882no—
994C42—22no—
995C42—474no—
996C42—474no—
997C42—474no—
998C42—942no—
999C42—942no—
1000C42—942no—
1001C42—942no—
1002C42—944no—
1003C42—944no—
1004C42—942no—
1005C42D4×D4714yes—
1006C23—21no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—21no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—472no—
1017C23—472no—
1018C23—472no—
1019C23—474no—
1020C23—472no—
1021C23—9416no—
1022C23—942no—
1023C23—942no—
1024C23—941no—
1025C23—942no—
1026C23—942no—
1027C23—942no—
1028C23—941no—
1029C23—942no—
1030C23—942no—
1031C23—942no—
1032C23—942no—
1033C23—942no—
1034C23—1888no—
1035C23—1888no—
1036C23—1888no—
1037C23—1888no—
1038C23—1888no—
1039C23—1888no—
1040C23#41×D4714yes—
1041C23#41×D4712yes—
1042C23C24×D4711yescharacteristic
1043Q8—948no—
1044D4—28no—
1045D4—48no—
1046D4—948no—
1047D4—948no—
1048D4—9416no—
1049D4—948no—
1050D4—948no—
1051D4—1888no—
1052D4—1888no—
1053D4—1888no—
1054C2×C4—28no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—48no—
1075C2×C4—472no—
1076C2×C4—472no—
1077C2×C4—474no—
1078C2×C4—474no—
1079C2×C4—472no—
1080C2×C4—472no—
1081C2×C4—948no—
1082C2×C4—948no—
1083C2×C4—948no—
1084C2×C4—948no—
1085C2×C4—941no—
1086C2×C4—941no—
1087C2×C4—941no—
1088C2×C4—941no—
1089C2×C4—941no—
1090C2×C4—941no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—942no—
1094C2×C4—942no—
1095C2×C4—942no—
1096C2×C4—942no—
1097C2×C4—942no—
1098C2×C4—942no—
1099C2×C4—942no—
1100C2×C4—942no—
1101C2×C4—942no—
1102C2×C4—1888no—
1103C2×C4—1884no—
1104C2×C4—1884no—
1105C2×C4—1888no—
1106C2×C4—1888no—
1107C2×C4—1884no—
1108C2×C4—1884no—
1109C2×C4—1888no—
1110C2×C4C2×D4×D4712yes—
1111C2×C4C2×D4×D4712yes—
1112C2×C4C2×D4×D4712yes—
1113C2×C4#41×D4712yes—
1114C22—22no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—41no—
1120C22—42no—
1121C22—42no—
1122C22—41no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—474no—
1127C22—942no—
1128C22—942no—
1129C22—944no—
1130C22—944no—
1131C22—942no—
1132C22—944no—
1133C22—944no—
1134C22—944no—
1135C22—944no—
1136C22—18832no—
1137C22—1881no—
1138C22—1882no—
1139C22—1882no—
1140C22—1881no—
1141C22—1882no—
1142C22—1882no—
1143C22—1882no—
1144C22C22×D4×D4711yescharacteristic
1145C22C2×#41×D4711yescharacteristic
1146C22C2×#41×D4712yes—
1147C22C2×#41×D4711yescharacteristic
1148C22H(5,𝔽2)×D4712yes—
1149C4—22no—
1150C4—22no—
1151C4—22no—
1152C4—22no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—42no—
1157C4—42no—
1158C4—474no—
1159C4—474no—
1160C4—942no—
1161C4—942no—
1162C4—1881no—
1163C4—1882no—
1164C4—1881no—
1165C4—1882no—
1166C4—1882no—
1167C2—44no—
1168C2—42no—
1169C2—944no—
1170C2—1884no—
1171C2—1882no—
1172C2#525×D4711yescharacteristic
1173C2#525×D4711yescharacteristic
1174C2#535×D4711yescharacteristic
1175C2#2025699112yes—
1176C2#2025699512yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2598C2
hypercenter#2598D47
hypocenterC47#34963
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2598

Complements

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

NH ≅ G/Ntype
1. C2×#15689591C2semidirect
2. C2×C4×D4×D47C2semidirect
3. #20248956C2semidirect
4. #20248954C2semidirect
5. #20248948C2semidirect
6. #20248745C2semidirect
7. #20248288C2semidirect
8. #20247700C2semidirect
9. #20247698C2semidirect
10. #20247660C2semidirect
11. #20246739C2semidirect
12. #20246737C2semidirect
13. #20246705C2semidirect
14. #20246677C2semidirect
15. #20246676C2semidirect
16. #20246668C2semidirect
17. #20246666C2semidirect
18. #20245900C2semidirect
19. #20245898C2semidirect
20. #20245893C2semidirect
21. #20245889C2semidirect
22. #20245785C2semidirect
23. C47×#2598C2semidirect
32. C2×#13093989C22semidirect
33. C2×#13093989C22semidirect
36. C2×D4×Dic47C22semidirect
40. C2×#13093986C22semidirect
45. C2×(C22⋊D47)⋊C4C22semidirect
46. C2×(C22⋊D47)⋊C4C22semidirect
47. C2×(C22⋊D47)⋊C4C22semidirect
48. C2×(C22⋊D47)⋊C4C22semidirect
51. C2×#13093981C22semidirect
54. C22×C4×Dic47C22semidirect
56. C2×C42×D47C22semidirect
57. #15689063C22semidirect
58. #15689062C22semidirect
59. #15689061C22semidirect
60. #15689060C22semidirect
61. #15689059C22semidirect
62. #15689059C22semidirect
63. #15689058C22semidirect
64. #15689058C22semidirect
65. #15689052C22semidirect
66. #15689051C22semidirect
70. #15689036C22semidirect
71. #15689035C22semidirect
74. #15689032C22semidirect
76. #15689031C22semidirect
79. #15689020C22semidirect
80. #15689018C22semidirect
81. #15689015C22semidirect
82. #15689014C22semidirect
83. #15689011C22semidirect
84. #15689002C22semidirect
85. #15689002C22semidirect
87. #15689001C22semidirect
88. #15689001C22semidirect
90. #15688999C22semidirect
91. #15688999C22semidirect
93. #15688997C22semidirect
94. #15688996C22semidirect
96. #15688994C22semidirect
97. #15688991C22semidirect
98. #15688987C22semidirect
102. #15688982C22semidirect
103. #15688981C22semidirect
106. #15688974C22semidirect
107. C22⋊C4×Dic47C22semidirect
108. C22⋊C4×Dic47C22semidirect
110. #15688970C22semidirect
111. #15688970C22semidirect
112. #15688968C22semidirect
113. #15688968C22semidirect
115. C2×#117×C47C22semidirect
116. C47×#400C22semidirect
117. C47×#399C22semidirect
120. C47×#388C22semidirect
121. C47×#386C22semidirect
122. C47×#386C22semidirect
123. C47×#385C22semidirect
124. C47×#383C22semidirect
224. C42×D47D4semidirect
308. C2×C22⋊D47#41semidirect
584. #2598D47semidirect
641. C2×#117C2×D47semidirect
650. #400C2×D47semidirect
656. #399C2×D47semidirect
678. #388C2×D47semidirect
687. #386C2×D47semidirect
688. #386C2×D47semidirect
694. #385C2×D47semidirect
696. #383C2×D47semidirect
713. C47#34963semidirect

Maximal subgroups

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

subgroupindex
C2×#156895912
C2×C4×D4×D472
#202489562
#202489542
#202489482
#202487452
#202482882
#202477002
#202476982
#202476602
#202467392
#202467372
#202467052
#202466772
#202466762
#202466682
#202466662
#202459002
#202458982
#202458932
#202458892
#202457852
C47×#25982
#3496347