Finite Group Databasebeta

← #26376132

Subgroups — #26376132

Order 12032.

3420 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689791C211yesmaximal, characteristic
2C2×#15689591C211yesmaximal, characteristic, complemented
3C2×C4×#10625352C211yesmaximal, characteristic, complemented
4#20246451C212yesmaximal, complemented
5#20246450C211yesmaximal, characteristic, complemented
6#20246428C211yesmaximal, characteristic, complemented
7#20246427C212yesmaximal, complemented
8#20246423C212yesmaximal, complemented
9#20246338C211yesmaximal, characteristic, complemented
10#20246334C212yesmaximal, complemented
11#20246302C211yesmaximal, characteristic, complemented
12#20246228C211yesmaximal, characteristic, complemented
13#20246227C211yesmaximal, characteristic, complemented
14#20245952C212yesmaximal, complemented
15#20245952C211yesmaximal, characteristic, complemented
16#121×Dic47C211yesmaximal, characteristic, complemented
17#20245900C212yesmaximal, complemented
18#20245898C212yesmaximal, complemented
19#20245896C211yesmaximal, characteristic, complemented
20C4×#13093989C211yesmaximal, characteristic, complemented
21C4×(C22⋊D47)⋊C4C212yesmaximal, complemented
22C4×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
23C47×#2363C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic
25C22×#10625352C2211yescharacteristic
26#15689791C4116yescomplemented
27C2×#13094020C2211yescharacteristic
28C2×#13094020C2212yes—
29C2×#13093999C2211yescharacteristic
30C2×#13093997C2212yes—
31C2×#13093996C2212yes—
32#15689591—28no—
33C4×#10625352—28no—
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×#13093989C2211yescharacteristic
38C2×#13093989C2211yescharacteristic
39C2×D4×Dic47C2211yescharacteristic
40C2×D4×Dic47C2212yes—
41C2×#13093986C2211yescharacteristic
42C2×#13093986C2211yescharacteristic
43C2×#13093986C2212yes—
44C2×C4×C22⋊D47C2212yes—
45C2×C4×C22⋊D47C2212yes—
46C2×C4×C22⋊D47C2211yescharacteristic
47C2×(C22⋊D47)⋊C4C2212yes—
48C2×(C22⋊D47)⋊C4C2212yes—
49C2×(C22⋊D47)⋊C4C2212yes—
50C2×(C22⋊D47)⋊C4C2211yescharacteristic
51C2×(C22⋊D47)⋊C4C2211yescharacteristic
52C2×(C22⋊D47)⋊C4C2212yes—
53C2×(C22⋊D47)⋊C4C2212yes—
54C2×(C22⋊D47)⋊C4C2212yes—
55C2×#13093982C2211yescharacteristic
56C2×#13093981C2212yes—
57C2×#13093980C2212yes—
58C22×C4×Dic47C2212yes—
59C22×C4×Dic47C2211yescharacteristic
60C2×C42×D47C2211yescharacteristic
61C2×C42×D47C2212yes—
62#15689026C2211yescharacteristic
63#15689025C2211yescharacteristic
64#15689025C2212yes—
65#15689025C2211yescharacteristic
66#15689023C2212yes—
67#15689023C2212yes—
68#15689023C2212yes—
69#15689023C2212yes—
70#15689023C2212yes—
71#15689023C2212yes—
72#15689023C2212yes—
73#15689023C2212yes—
74#15689022C2211yescharacteristic
75#15689020C2212yes—
76#15689018C2212yes—
77#15689016C2212yes—
78#15689015C2212yes—
79#15689014C2212yes—
80#15689013C2212yes—
81#15689011C2212yes—
82#15689003C2212yes—
83#15689002C2212yes—
84#15689001C2212yes—
85#15689001C2212yes—
86#15688999C2212yes—
87#15688992C2212yes—
88#15688992C2211yescharacteristic
89#15688983C2211yescharacteristic
90#15688982C2212yes—
91#15688981C2212yes—
92#15688980C2211yescharacteristic
93C4⋊C4×Dic47C2211yescharacteristic
94C4⋊C4×Dic47C2211yescharacteristic
95C4×Dic47⋊C4C2211yescharacteristic
96C4×Dic47⋊C4C2212yes—
97C4×Dic47⋊C4C2212yes—
98#15688974C2212yes—
99#15688974C2211yescharacteristic
100#15688974C2212yes—
101#15688974C2212yes—
102#15688974C2211yescharacteristic
103C22⋊C4×Dic47C2211yescharacteristic
104C22⋊C4×Dic47C2212yes—
105C22⋊C4×Dic47C2211yescharacteristic
106C22⋊C4×Dic47C2212yes—
107C4×(C2×D47)⋊C4C2212yes—
108C4×(C2×D47)⋊C4C2211yescharacteristic
109#15688970C2212yes—
110#15688970C2211yescharacteristic
111#15688970C2211yescharacteristic
112#15688970C2212yes—
113C42×Dic47C2211yescharacteristic
114C42×Dic47C2212yes—
115C2×#121×C47C2211yescharacteristic
116C2×C4×D4×C47C2211yescharacteristic
117C2×#117×C47C2211yescharacteristic
118C47×#390C2212yes—
119C47×#390C2211yescharacteristic
120C47×#389C2211yescharacteristic
121C47×#388C2212yes—
122C47×#386C2212yes—
123C4×C4⋊C4×C47C2211yescharacteristic
124C4×C22⋊C4×C47C2212yes—
125C4×C22⋊C4×C47C2211yescharacteristic
126C2×#10625350—24no—
127C2×#10625350—24no—
128C2×#10625350C2×C418yescomplemented
129C2×#10625352—24no—
130C2×#10625352—24no—
131C2×#10625352C2×C418yescomplemented
132C22×Dic94C2311yescharacteristic
133C22×D188C2311yescharacteristic
134C22×D188C2312yes—
135C22×C22⋊D47C2311yescharacteristic
136C22×C22⋊D47C2312yes—
137C22×C22⋊D47C2312yes—
138C22×C22⋊D47C2312yes—
139C22×C22⋊D47C2312yes—
140C23×Dic47C2311yescharacteristic
141C23×Dic47C2312yes—
142C23×Dic47C2311yescharacteristic
143C23×Dic47C2312yes—
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2312yes—
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2312yes—
148C22×C4×D47C2312yes—
149C22×C4×D47C2311yescharacteristic
150#13094020C2×C4116yescomplemented
151#13094020C2×C418yescomplemented
152#13093999C2×C418yescomplemented
153#13093997C2×C4116yescomplemented
154#13093996C2×C4116yescomplemented
155C4×Dic94—24no—
156C4×Dic94—24no—
157#13093989—24no—
158#13093989C2×C418yescomplemented
159#13093989D418yescomplemented
160D4×Dic47—24no—
161D4×Dic47—44no—
162#13093986—24no—
163#13093986—24no—
164#13093986—44no—
165C4×C22⋊D47—28no—
166C4×C22⋊D47—28no—
167C4×C22⋊D47C2×C418yescomplemented
168(C22⋊D47)⋊C4—28no—
169(C22⋊D47)⋊C4—24no—
170(C22⋊D47)⋊C4—28no—
171(C22⋊D47)⋊C4—28no—
172(C22⋊D47)⋊C4—28no—
173(C22⋊D47)⋊C4—24no—
174(C22⋊D47)⋊C4—44no—
175(C22⋊D47)⋊C4C2×C4116yescomplemented
176#13093982—24no—
177#13093981—28no—
178#13093980—28no—
179C2×C4⋊Dic47C2311yescharacteristic
180C2×C4⋊Dic47C2311yescharacteristic
181C2×C4⋊Dic47C2312yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2311yescharacteristic
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2311yescharacteristic
189C2×Dic47⋊C4C2312yes—
190C2×Dic47⋊C4C2312yes—
191C2×Dic47⋊C4C2311yescharacteristic
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2312yes—
194C2×C22⋊Dic47C2312yes—
195C2×C22⋊Dic47C2312yes—
196C2×C22⋊Dic47C2311yescharacteristic
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2311yescharacteristic
199C2×(C2×D47)⋊C4C2311yescharacteristic
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2312yes—
207C2×(C2×D47)⋊C4C2311yescharacteristic
208C2×(C2×D47)⋊C4C2312yes—
209C2×C4×Dic47—28no—
210C2×C4×Dic47—24no—
211C2×C4×Dic47C2311yescharacteristic
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2312yes—
214C2×C4×Dic47C2311yescharacteristic
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2312yes—
220C2×C4×Dic47C2312yes—
221C2×C4×Dic47C2311yescharacteristic
222C2×C4×Dic47C2311yescharacteristic
223C2×C4×Dic47C2312yes—
224C2×C4×Dic47C2311yescharacteristic
225C2×C4×Dic47C2312yes—
226C2×C4×Dic47C2311yescharacteristic
227C2×C4×Dic47C2312yes—
228C2×C4×Dic47C2311yescharacteristic
229C2×C4×Dic47C2311yescharacteristic
230C42×D47—24no—
231C42×D47—28no—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2311yescharacteristic
235C47⋊#95C2311yescharacteristic
236C47⋊#95C2311yescharacteristic
237C47⋊#95C2311yescharacteristic
238C47⋊#95C2312yes—
239C47⋊#95C2312yes—
240C47⋊#95C2312yes—
241C22×D4×C47C2311yescharacteristic
242C22×D4×C47C2312yes—
243C23×C4×C47C2312yes—
244C23×C4×C47C2311yescharacteristic
245#121×C47C2×C418yescomplemented
246C4×D4×C47—24no—
247#117×C47—24no—
248C2×C4⋊C4×C47C2311yescharacteristic
249C2×C4⋊C4×C47C2312yes—
250C2×C4⋊C4×C47C2311yescharacteristic
251C2×C4⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2311yescharacteristic
253C2×C22⋊C4×C47C2311yescharacteristic
254C2×C22⋊C4×C47C2312yes—
255C2×C22⋊C4×C47C2312yes—
256C2×C22⋊C4×C47C2312yes—
257C2×C22⋊C4×C47C2312yes—
258C2×C22⋊C4×C47C2312yes—
259C2×C42×C47C2311yescharacteristic
260C2×C42×C47C2312yes—
261C2×C42×C47C2311yescharacteristic
262C2×C42×C47C2312yes—
263#95×C47C2311yescharacteristic
264#95×C47C2311yescharacteristic
265#95×C47C2312yes—
266#95×C47C2312yes—
267C24×C47C2412yes—
268C24×C47C2411yescharacteristic
269C23×D47C2412yes—
270C23×D47C2411yescharacteristic
271C2×D4×C47—22no—
272C2×D4×C47—22no—
273C2×D4×C47—42no—
274C2×D4×C47—42no—
275C2×D4×C47C22×C414yes—
276C2×D4×C47C22×C418yes—
277C22×C4×C47—22no—
278C22×C4×C47—22no—
279C22×C4×C47—24no—
280C22×C4×C47—24no—
281C22×C4×C47—42no—
282C22×C4×C47C22×C414yes—
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2412yes—
285C22×C4×C47C2411yescharacteristic
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2412yes—
288C22×C4×C47C2412yes—
289C22×C4×C47C2411yescharacteristic
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C2×C22⋊D47—24no—
293C2×C22⋊D47—24no—
294C2×C22⋊D47—22no—
295C2×C22⋊D47—22no—
296C2×C22⋊D47—24no—
297C2×C22⋊D47—24no—
298C2×C22⋊D47—24no—
299C2×C22⋊D47—24no—
300C2×C22⋊D47—42no—
301C2×C22⋊D47—42no—
302C2×C22⋊D47C22×C418yes—
303C2×C22⋊D47C22×C414yes—
304C2×C22⋊D47C22×C418yes—
305C2×C22⋊D47C22×C418yes—
306C2×C22⋊D47C22×C418yes—
307C22×Dic47—24no—
308C22×Dic47—24no—
309C22×Dic47—22no—
310C22×Dic47—22no—
311C22×Dic47—24no—
312C22×Dic47—22no—
313C22×Dic47—22no—
314C22×Dic47—24no—
315C22×Dic47—24no—
316C22×Dic47—22no—
317C22×Dic47—41no—
318C22×Dic47C22×C418yes—
319C22×Dic47C2412yes—
320C22×Dic47C2411yescharacteristic
321C22×Dic47C2412yes—
322C22×Dic47C2411yescharacteristic
323C22×Dic47C2411yescharacteristic
324C22×Dic47C2411yescharacteristic
325C22×Dic47C2411yescharacteristic
326C22×Dic47C2412yes—
327C22×Dic47C2411yescharacteristic
328C22×Dic47C2411yescharacteristic
329#10625352—232no—
330#10625350—232no—
331C2×D188—22no—
332C2×D188—22no—
333C2×D188—42no—
334C2×D188—42no—
335C2×D188C22×C414yes—
336C2×D188C22×C418yes—
337C2×C4×D47—22no—
338C2×C4×D47—22no—
339C2×C4×D47—24no—
340C2×C4×D47—24no—
341C2×C4×D47—24no—
342C2×C4×D47—22no—
343C2×C4×D47—22no—
344C2×C4×D47—24no—
345C2×C4×D47—22no—
346C2×C4×D47—22no—
347C2×C4×D47—24no—
348C2×C4×D47—24no—
349C2×C4×D47—24no—
350C2×C4×D47—22no—
351C2×C4×D47—41no—
352C2×C4×D47—42no—
353C2×C4×D47C22×C418yes—
354C2×C4×D47C22×C414yes—
355C2×Dic94C22×C414yes—
356C2×Dic94C2×D414yes—
357C2×Dic94#4114yes—
358C4⋊C4×C47—22no—
359C4⋊C4×C47—42no—
360C4⋊C4×C47C22×C414yes—
361C4⋊C4×C47C2×D414yes—
362C22⋊C4×C47—24no—
363C22⋊C4×C47—24no—
364C22⋊C4×C47—22no—
365C22⋊C4×C47—22no—
366C22⋊C4×C47—24no—
367C22⋊C4×C47—42no—
368C22⋊C4×C47C22×C418yes—
369C42×C47—24no—
370C42×C47—22no—
371C42×C47—22no—
372C42×C47—42no—
373C22⋊Dic47—24no—
374C22⋊Dic47—24no—
375C22⋊Dic47—42no—
376C22⋊Dic47—42no—
377C22⋊Dic47C22×C414yes—
378(C2×D47)⋊C4—24no—
379(C2×D47)⋊C4—24no—
380(C2×D47)⋊C4—22no—
381(C2×D47)⋊C4—24no—
382(C2×D47)⋊C4—24no—
383(C2×D47)⋊C4—24no—
384(C2×D47)⋊C4—22no—
385(C2×D47)⋊C4—42no—
386(C2×D47)⋊C4—42no—
387(C2×D47)⋊C4—42no—
388(C2×D47)⋊C4C22×C418yes—
389(C2×D47)⋊C4C22×C414yes—
390C4⋊Dic47—22no—
391C4⋊Dic47—22no—
392C4⋊Dic47—42no—
393Dic47⋊C4—24no—
394Dic47⋊C4—24no—
395Dic47⋊C4—24no—
396Dic47⋊C4—22no—
397Dic47⋊C4—24no—
398Dic47⋊C4—42no—
399Dic47⋊C4C22×C414yes—
400Dic47⋊C4C22×C418yes—
401Dic47⋊C4C2×D418yes—
402Dic47⋊C4#4114yescomplemented
403C4×Dic47—24no—
404C4×Dic47—22no—
405C4×Dic47—22no—
406C4×Dic47—22no—
407C4×Dic47—22no—
408C4×Dic47—24no—
409C4×Dic47—22no—
410C4×Dic47—24no—
411C4×Dic47—22no—
412C4×Dic47—24no—
413C4×Dic47—24no—
414C4×Dic47—22no—
415C4×Dic47—24no—
416C4×Dic47—41no—
417C4×Dic47C22×C418yes—
418C4×Dic47C22×C414yes—
419C4×Dic47C2×D418yes—
420C4×Dic47C2×D414yes—
421C4×Dic47#4114yescomplemented
422C23×C47—22no—
423C23×C47—21no—
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—21no—
427C23×C47—21no—
428C23×C47—22no—
429C23×C47—21no—
430C23×C47—21no—
431C23×C47—22no—
432C23×C47—21no—
433C23×C47—22no—
434C23×C47C23×C412yes—
435C23×C47C23×C414yes—
436C23×C47C2511yescharacteristic
437C22×D47—22no—
438C22×D47—21no—
439C22×D47—22no—
440C22×D47—21no—
441C22×D47—22no—
442C22×D47—21no—
443C22×D47—22no—
444C22×D47—21no—
445C22×D47—21no—
446C22×D47—22no—
447C22×D47—21no—
448C22×D47—22no—
449C22×D47C23×C414yes—
450C22×D47C23×C412yes—
451D4×C47—28no—
452D4×C47—48no—
453C2×C4×C47—21no—
454C2×C4×C47—21no—
455C2×C4×C47—21no—
456C2×C4×C47—22no—
457C2×C4×C47—21no—
458C2×C4×C47—22no—
459C2×C4×C47—21no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—21no—
463C2×C4×C47—28no—
464C2×C4×C47—21no—
465C2×C4×C47—22no—
466C2×C4×C47—21no—
467C2×C4×C47—21no—
468C2×C4×C47—21no—
469C2×C4×C47—22no—
470C2×C4×C47—21no—
471C2×C4×C47—22no—
472C2×C4×C47—21no—
473C2×C4×C47—48no—
474C2×C4×C47C23×C414yes—
475C2×C4×C47C23×C412yes—
476C2×C4×C47C23×C412yes—
477C2×C4×C47C22×D414yes—
478C2×C4×C47C22×D412yes—
479C2×C4×C47C2×#4112yes—
480C2×C4×C47C2×#4112yes—
481C2×C4×C47C2×#4112yes—
482C22⋊D47—216no—
483C22⋊D47—216no—
484C22⋊D47—28no—
485C22⋊D47—216no—
486C22⋊D47—48no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—21no—
493C2×Dic47—21no—
494C2×Dic47—21no—
495C2×Dic47—216no—
496C2×Dic47—21no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47—21no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—22no—
504C2×Dic47—21no—
505C2×Dic47—44no—
506C2×Dic47—44no—
507C2×Dic47—48no—
508C2×Dic47C23×C412yes—
509C2×Dic47C23×C412yes—
510C2×Dic47C23×C414yes—
511C2×Dic47C23×C412yes—
512C2×Dic47C22×D412yes—
513C2×Dic47C22×D414yes—
514C2×Dic47C22×D412yes—
515C2×Dic47C2×#4112yes—
516C2×Dic47C2×#4114yes—
517C2×Dic47C2×#4112yes—
518C2×Dic47C2×#4112yes—
519C2×Dic47C2×#4112yes—
520C2×Dic47H(5,𝔽2)12yes—
521D188—28no—
522D188—48no—
523C4×D47—28no—
524C4×D47—216no—
525C4×D47—48no—
526C4×D47—44no—
527C4×D47—44no—
528C4×D47—48no—
529Dic94C4×D4116yescomplemented
530C4×#550—471nomaximal, Sylow
531C22×C47—24no—
532C22×C47—22no—
533C22×C47—24no—
534C22×C47—22no—
535C22×C47—24no—
536C22×C47—22no—
537C22×C47—42no—
538C22×C47—41no—
539C22×C47—41no—
540C22×C47—42no—
541C22×C47—42no—
542C22×C47—41no—
543C22×C47—42no—
544C22×C47—41no—
545C22×C47C24×C411yescharacteristic
546C22×C47C23×D411yescharacteristic
547C22×C47C22×#4111yescharacteristic
548C22×C47C22×#4111yescharacteristic
549C22×C47C22×#4111yescharacteristic
550C22×C47C2×H(5,𝔽2)11yescharacteristic
551C22×C47#58511yescharacteristic
552C2×D47—24no—
553C2×D47—22no—
554C2×D47—24no—
555C2×D47—22no—
556C2×D47—22no—
557C2×D47—24no—
558C2×D47—42no—
559C2×D47—41no—
560C2×D47—42no—
561C2×D47—41no—
562C2×D47—42no—
563C2×D47—41no—
564C2×D47—42no—
565C2×D47—41no—
566C4×C47—22no—
567C4×C47—24no—
568C4×C47—22no—
569C4×C47—24no—
570C4×C47—22no—
571C4×C47—41no—
572C4×C47—42no—
573C4×C47—41no—
574C4×C47C2×C4×D414yes—
575Dic47—22no—
576Dic47—22no—
577Dic47—22no—
578Dic47—22no—
579Dic47—41no—
580Dic47—42no—
581Dic47—42no—
582Dic47C2×C4×D418yes—
583Dic47C4×#4114yescomplemented
584Dic47#55014yescomplemented
585C2×#550—471no—
586C2×C4×#41—471no—
587C2×C4×#41—471no—
588#2366—472no—
589#2366—471no—
590#2363—472no—
591#2363—471no—
592#2363—472no—
593#2363D4711yescharacteristic, complemented
594#2354—472no—
595#2354—471no—
596Q8×C4⋊C4—471no—
597#2341—471no—
598#2341—471no—
599C4×#127—471no—
600C4×#127—472no—
601C4×#121—471no—
602C4×#121—472no—
603C4×#121—472no—
604C4×#121—471no—
605C42×Q8—471no—
606C42×D4—471no—
607C42×D4—472no—
608C2×C47—44no—
609C2×C47—42no—
610C2×C47C22×C4×D411yescharacteristic
611C2×C47C2×C4×#4111yescharacteristic
612C2×C47C4×H(5,𝔽2)11yescharacteristic
613C2×C47C2×#55011yescharacteristic
614C2×C47D4×#4111yescharacteristic
615C2×C47#348011yescharacteristic
616C2×C47#348311yescharacteristic
617D47—44no—
618D47—42no—
619C22×#41—471no—
620C22×#41—471no—
621#550—4716no—
622C2×#127—472no—
623C2×#127—471no—
624C2×#121—472no—
625C2×#121—471no—
626C2×#121—472no—
627C2×#121C2×D4711yescharacteristic
628C4×#41—948no—
629C4×#41—948no—
630C2×C4×Q8—471no—
631C2×C4×Q8—471no—
632C2×C4×Q8—471no—
633C2×C4×Q8—471no—
634C2×C4×Q8—471no—
635C2×C4×D4—471no—
636C2×C4×D4—471no—
637C2×C4×D4—472no—
638C2×C4×D4—472no—
639C2×C4×D4—472no—
640C2×C4×D4—471no—
641C2×C4×D4—471no—
642C2×C4×D4—472no—
643C2×C4×D4—472no—
644C2×C4×D4—471no—
645C2×C4×D4—472no—
646C2×C4×D4—472no—
647C2×C4×D4—472no—
648C2×C4×D4—472no—
649C2×C4×D4—471no—
650C2×C4×D4—472no—
651C2×C4×D4C2×D4711yescharacteristic
652C2×#117—471no—
653C2×#117—472no—
654C2×#117—472no—
655C2×#117C2×D4711yescharacteristic
656C22×C42—472no—
657C22×C42—471no—
658C22×C42—471no—
659C22×C42—472no—
660#390—471no—
661#390—472no—
662#390—472no—
663#390—472no—
664#390—472no—
665#390—472no—
666#390—472no—
667#390—472no—
668#390—472no—
669#390—471no—
670#390—472no—
671#390—471no—
672#390C2×D4711yescharacteristic
673#390C2×D4712yes—
674#389—472no—
675#389—471no—
676#389—472no—
677#389C2×D4711yescharacteristic
678#388—472no—
679#388—472no—
680#388—472no—
681#388—472no—
682#388—472no—
683#388C2×D4712yes—
684#386—472no—
685#386—472no—
686#386—472no—
687#386—472no—
688#386—472no—
689#386C2×D4712yes—
690#384—472no—
691#384—471no—
692#380—471no—
693#380—471no—
694#380—472no—
695#380—472no—
696C4×C4⋊C4—471no—
697C4×C4⋊C4—471no—
698C4×C4⋊C4—471no—
699C4×C4⋊C4—472no—
700C4×C4⋊C4—472no—
701C4×C4⋊C4—472no—
702C4×C4⋊C4—471no—
703C4×C4⋊C4—472no—
704C4×C4⋊C4—471no—
705C4×C4⋊C4—472no—
706C4×C4⋊C4C2×D4711yescharacteristic
707C4×C22⋊C4—472no—
708C4×C22⋊C4—471no—
709C4×C22⋊C4—471no—
710C4×C22⋊C4—472no—
711C4×C22⋊C4—471no—
712C4×C22⋊C4—472no—
713C4×C22⋊C4—472no—
714C4×C22⋊C4—471no—
715C4×C22⋊C4—472no—
716C4×C22⋊C4—471no—
717C4×C22⋊C4C2×D4711yescharacteristic
718C4×C22⋊C4C2×D4712yes—
719C43—472no—
720C43—471no—
721C47C4×#55011yescharacteristic, complemented, Sylow
722C2×#41—478no—
723C2×#41—478no—
724C2×#41—944no—
725C2×#41—944no—
726C2×#41—944no—
727C2×#41—944no—
728C22×Q8—471no—
729C22×D4—471no—
730C22×D4—472no—
731C22×D4—472no—
732C22×D4—472no—
733C22×D4—472no—
734C22×D4—471no—
735C22×D4—472no—
736C22×D4C22×D4711yescharacteristic
737C22×D4C22×D4712yes—
738C23×C4—472no—
739C23×C4—472no—
740C23×C4—471no—
741C23×C4—472no—
742C23×C4—471no—
743C23×C4—471no—
744C23×C4—472no—
745C23×C4—471no—
746C23×C4—472no—
747C23×C4—471no—
748C23×C4C22×D4712yes—
749C23×C4C22×D4711yescharacteristic
750#127—4716no—
751#127—478no—
752#121—4716no—
753#121—478no—
754#121—4716no—
755#121C4×D4718yescomplemented
756C4×Q8—478no—
757C4×Q8—478no—
758C4×Q8—944no—
759C4×Q8—944no—
760C4×Q8—944no—
761C4×D4—24no—
762C4×D4—478no—
763C4×D4—4716no—
764C4×D4—948no—
765C4×D4—948no—
766C4×D4—948no—
767C4×D4—944no—
768C4×D4—944no—
769C4×D4—944no—
770C4×D4—948no—
771C4×D4—944no—
772C4×D4—948no—
773C4×D4—948no—
774C4×D4—944no—
775C4×D4—1884no—
776C4×D4—1884no—
777C4×D4—1884no—
778#117—24no—
779#117—948no—
780#117—948no—
781#117—944no—
782C2×C4⋊C4—472no—
783C2×C4⋊C4—471no—
784C2×C4⋊C4—471no—
785C2×C4⋊C4—472no—
786C2×C4⋊C4—472no—
787C2×C4⋊C4—472no—
788C2×C4⋊C4—471no—
789C2×C4⋊C4—471no—
790C2×C4⋊C4—472no—
791C2×C4⋊C4—472no—
792C2×C4⋊C4—471no—
793C2×C4⋊C4—472no—
794C2×C4⋊C4—472no—
795C2×C4⋊C4C22×D4711yescharacteristic
796C2×C4⋊C4C22×D4712yes—
797C2×C4⋊C4C22×D4711yescharacteristic
798C2×C4⋊C4C22×D4711yescharacteristic
799C2×C22⋊C4—471no—
800C2×C22⋊C4—472no—
801C2×C22⋊C4—471no—
802C2×C22⋊C4—472no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—472no—
806C2×C22⋊C4—472no—
807C2×C22⋊C4—471no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—471no—
810C2×C22⋊C4—472no—
811C2×C22⋊C4—472no—
812C2×C22⋊C4—472no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4C22×D4712yes—
817C2×C22⋊C4C22×D4712yes—
818C2×C22⋊C4C22×D4711yescharacteristic
819C2×C22⋊C4C22×D4712yes—
820C2×C22⋊C4C22×D4711yescharacteristic
821C2×C22⋊C4C22×D4712yes—
822C2×C22⋊C4C22×D4712yes—
823C2×C42—471no—
824C2×C42—472no—
825C2×C42—471no—
826C2×C42—472no—
827C2×C42—471no—
828C2×C42—471no—
829C2×C42—471no—
830C2×C42—472no—
831C2×C42—471no—
832C2×C42—472no—
833C2×C42—472no—
834C2×C42—472no—
835C2×C42—471no—
836C2×C42—471no—
837C2×C42—472no—
838C2×C42—472no—
839C2×C42—471no—
840C2×C42—471no—
841C2×C42—471no—
842C2×C42—948no—
843C2×C42—944no—
844C2×C42—944no—
845C2×C42—948no—
846C2×C42C22×D4712yes—
847C2×C42C22×D4711yescharacteristic
848C2×C42C22×D4711yescharacteristic
849C2×C42C22×D4712yes—
850#95—471no—
851#95—472no—
852#95—471no—
853#95—472no—
854#95—471no—
855#95—472no—
856#95—471no—
857#95—472no—
858#95—472no—
859#95C22×D4711yescharacteristic
860#95C22×D4711yescharacteristic
861#95C22×D4712yes—
862#95C22×D4712yes—
863C24—471no—
864C24—472no—
865C24C23×D4711yescharacteristic
866C24C23×D4712yes—
867#41—9432no—
868#41—9432no—
869C2×Q8—474no—
870C2×Q8—474no—
871C2×Q8—474no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—474no—
877C2×D4—478no—
878C2×D4—478no—
879C2×D4—478no—
880C2×D4—478no—
881C2×D4—474no—
882C2×D4—478no—
883C2×D4—944no—
884C2×D4—944no—
885C2×D4—942no—
886C2×D4—944no—
887C2×D4—942no—
888C2×D4—944no—
889C2×D4—944no—
890C2×D4—944no—
891C2×D4—942no—
892C2×D4—942no—
893C2×D4—1882no—
894C2×D4—1882no—
895C2×D4—1882no—
896C2×D4—1882no—
897C2×D4C2×C4×D4714yes—
898C2×D4C2×C4×D4718yes—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—42no—
904C22×C4—471no—
905C22×C4—471no—
906C22×C4—472no—
907C22×C4—478no—
908C22×C4—471no—
909C22×C4—471no—
910C22×C4—471no—
911C22×C4—471no—
912C22×C4—478no—
913C22×C4—474no—
914C22×C4—472no—
915C22×C4—472no—
916C22×C4—471no—
917C22×C4—944no—
918C22×C4—944no—
919C22×C4—942no—
920C22×C4—942no—
921C22×C4—944no—
922C22×C4—944no—
923C22×C4—944no—
924C22×C4—942no—
925C22×C4—944no—
926C22×C4—942no—
927C22×C4—944no—
928C22×C4—944no—
929C22×C4—942no—
930C22×C4—944no—
931C22×C4—942no—
932C22×C4—944no—
933C22×C4—942no—
934C22×C4—942no—
935C22×C4—944no—
936C22×C4—942no—
937C22×C4—942no—
938C22×C4—942no—
939C22×C4—944no—
940C22×C4—942no—
941C22×C4—1882no—
942C22×C4—1881no—
943C22×C4—1881no—
944C22×C4C2×C4×D4714yes—
945C22×C4C23×D4711yescharacteristic
946C22×C4C23×D4711yescharacteristic
947C22×C4C23×D4712yes—
948C22×C4C23×D4711yescharacteristic
949C22×C4C23×D4712yes—
950C22×C4C23×D4712yes—
951C22×C4C23×D4711yescharacteristic
952C22×C4C23×D4711yescharacteristic
953C22×C4C23×D4711yescharacteristic
954C4⋊C4—22no—
955C4⋊C4—42no—
956C4⋊C4—474no—
957C4⋊C4—478no—
958C4⋊C4—478no—
959C4⋊C4—474no—
960C4⋊C4—944no—
961C4⋊C4—944no—
962C4⋊C4—942no—
963C4⋊C4—944no—
964C4⋊C4—944no—
965C4⋊C4—942no—
966C4⋊C4—942no—
967C4⋊C4—1882no—
968C4⋊C4—1882no—
969C4⋊C4C2×C4×D4714yes—
970C4⋊C4D4×D4714yes—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—22no—
974C22⋊C4—24no—
975C22⋊C4—22no—
976C22⋊C4—42no—
977C22⋊C4—474no—
978C22⋊C4—474no—
979C22⋊C4—478no—
980C22⋊C4—944no—
981C22⋊C4—942no—
982C22⋊C4—944no—
983C22⋊C4—944no—
984C22⋊C4—944no—
985C22⋊C4—944no—
986C22⋊C4—944no—
987C22⋊C4—942no—
988C22⋊C4—944no—
989C22⋊C4—1882no—
990C22⋊C4—1882no—
991C22⋊C4—1882no—
992C22⋊C4—1882no—
993C22⋊C4—1882no—
994C22⋊C4C2×C4×D4718yes—
995C42—24no—
996C42—22no—
997C42—22no—
998C42—42no—
999C42—478no—
1000C42—474no—
1001C42—478no—
1002C42—474no—
1003C42—474no—
1004C42—942no—
1005C42—942no—
1006C42—942no—
1007C42—942no—
1008C42—944no—
1009C42—944no—
1010C42—944no—
1011C42—942no—
1012C42—944no—
1013C42—942no—
1014C42—944no—
1015C42—944no—
1016C42—942no—
1017C42—1881no—
1018C23—21no—
1019C23—22no—
1020C23—21no—
1021C23—22no—
1022C23—21no—
1023C23—22no—
1024C23—21no—
1025C23—22no—
1026C23—22no—
1027C23—21no—
1028C23—22no—
1029C23—21no—
1030C23—472no—
1031C23—474no—
1032C23—942no—
1033C23—941no—
1034C23—941no—
1035C23—942no—
1036C23—941no—
1037C23—942no—
1038C23—942no—
1039C23—941no—
1040C23—941no—
1041C23—942no—
1042C23—941no—
1043C23—942no—
1044C23C22×C4×D4712yes—
1045C23C22×C4×D4714yes—
1046C23C24×D4711yescharacteristic
1047Q8—4716no—
1048D4—28no—
1049D4—48no—
1050D4—948no—
1051D4—9416no—
1052D4—9416no—
1053D4—9416no—
1054D4—948no—
1055D4—1888no—
1056D4—1888no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—28no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—48no—
1078C2×C4—472no—
1079C2×C4—474no—
1080C2×C4—472no—
1081C2×C4—474no—
1082C2×C4—472no—
1083C2×C4—472no—
1084C2×C4—472no—
1085C2×C4—474no—
1086C2×C4—472no—
1087C2×C4—472no—
1088C2×C4—472no—
1089C2×C4—472no—
1090C2×C4—472no—
1091C2×C4—9416no—
1092C2×C4—9416no—
1093C2×C4—941no—
1094C2×C4—941no—
1095C2×C4—941no—
1096C2×C4—941no—
1097C2×C4—941no—
1098C2×C4—941no—
1099C2×C4—941no—
1100C2×C4—941no—
1101C2×C4—948no—
1102C2×C4—941no—
1103C2×C4—942no—
1104C2×C4—942no—
1105C2×C4—942no—
1106C2×C4—942no—
1107C2×C4—941no—
1108C2×C4—942no—
1109C2×C4—942no—
1110C2×C4—941no—
1111C2×C4—1884no—
1112C2×C4—1888no—
1113C2×C4—1884no—
1114C2×C4—1888no—
1115C2×C4—1884no—
1116C2×C4—1888no—
1117C2×C4—1884no—
1118C2×C4C22×C4×D4714yes—
1119C2×C4C22×C4×D4712yes—
1120C2×C4C22×C4×D4712yes—
1121C2×C4C2×D4×D4714yes—
1122C2×C4C2×D4×D4712yes—
1123C2×C4#41×D4712yes—
1124C2×C4#41×D4712yes—
1125C2×C4#41×D4712yes—
1126C22—22no—
1127C22—24no—
1128C22—22no—
1129C22—24no—
1130C22—22no—
1131C22—24no—
1132C22—41no—
1133C22—42no—
1134C22—42no—
1135C22—41no—
1136C22—41no—
1137C22—42no—
1138C22—41no—
1139C22—42no—
1140C22—944no—
1141C22—942no—
1142C22—942no—
1143C22—944no—
1144C22—942no—
1145C22—944no—
1146C22—1882no—
1147C22—1881no—
1148C22—1881no—
1149C22—1882no—
1150C22—1882no—
1151C22—1881no—
1152C22—1881no—
1153C22—1882no—
1154C22C23×C4×D4711yescharacteristic
1155C22C22×D4×D4711yescharacteristic
1156C22C2×#41×D4711yescharacteristic
1157C22C2×#41×D4711yescharacteristic
1158C22C2×#41×D4711yescharacteristic
1159C22H(5,𝔽2)×D4711yescharacteristic
1160C22#1568995811yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—22no—
1164C4—24no—
1165C4—22no—
1166C4—41no—
1167C4—42no—
1168C4—41no—
1169C4—478no—
1170C4—474no—
1171C4—474no—
1172C4—942no—
1173C4—942no—
1174C4—942no—
1175C4—942no—
1176C4—1881no—
1177C4—1882no—
1178C4—1882no—
1179C4C4×D4×D4714yes—
1180C2—42no—
1181C2—44no—
1182C2—1884no—
1183C2—1882no—
1184C2C2×C4×D4×D4711yescharacteristic
1185C2C4×#41×D4711yescharacteristic
1186C2#2025659211yescharacteristic
1187C2#550×D4711yescharacteristic
1188C2#2025687211yescharacteristic
1189C2#2025698211yescharacteristic
1190C2#2025701311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2363C2
socle, cosocleC23×C47C25
prime radicalC2×#15689791C2
hypercenter#2363D47
hypocenterC47C4×#550
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#15689591C2semidirect
3. C2×C4×#10625352C2semidirect
4. #20246451C2semidirect
5. #20246450C2semidirect
6. #20246428C2semidirect
7. #20246427C2semidirect
8. #20246423C2semidirect
9. #20246338C2semidirect
10. #20246334C2semidirect
11. #20246302C2semidirect
12. #20246228C2semidirect
13. #20246227C2semidirect
14. #20245952C2semidirect
15. #20245952C2semidirect
16. #121×Dic47C2semidirect
17. #20245900C2semidirect
18. #20245898C2semidirect
19. #20245896C2semidirect
20. C4×#13093989C2semidirect
21. C4×(C22⋊D47)⋊C4C2semidirect
22. C4×(C22⋊D47)⋊C4C2semidirect
23. C47×#2363C2semidirect
26. #15689791C4semidirect
128. C2×#10625350C2×C4semidirect
131. C2×#10625352C2×C4semidirect
150. #13094020C2×C4semidirect
151. #13094020C2×C4semidirect
152. #13093999C2×C4semidirect
153. #13093997C2×C4semidirect
154. #13093996C2×C4semidirect
158. #13093989C2×C4semidirect
159. #13093989D4semidirect
167. C4×C22⋊D47C2×C4semidirect
175. (C22⋊D47)⋊C4C2×C4semidirect
245. #121×C47C2×C4semidirect
402. Dic47⋊C4#41semidirect
421. C4×Dic47#41semidirect
529. Dic94C4×D4semidirect
583. Dic47C4×#41semidirect
584. Dic47#550semidirect
593. #2363D47semidirect
721. C47C4×#550semidirect
755. #121C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156897912
C2×#156895912
C2×C4×#106253522
#202464512
#202464502
#202464282
#202464272
#202464232
#202463382
#202463342
#202463022
#202462282
#202462272
#202459522
#121×Dic472
#202459002
#202458982
#202458962
C4×#130939892
C4×(C22⋊D47)⋊C42
C47×#23632
C4×#55047