Finite Group Databasebeta

← #26388535

Subgroups — #26388535

Order 12032.

3270 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625352C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3#20248953C212yesmaximal, complemented
4#20248951C212yesmaximal, complemented
5#20248745C212yesmaximal, complemented
6#20248288C212yesmaximal, complemented
7#20247704C211yesmaximal, characteristic, complemented
8#20247702C211yesmaximal, characteristic, complemented
9#20247661C211yesmaximal, characteristic, complemented
10#20247659C211yesmaximal, characteristic, complemented
11#20246743C211yesmaximal, characteristic, complemented
12#20246741C211yesmaximal, characteristic, complemented
13#20246706C211yesmaximal, characteristic, complemented
14#20246704C211yesmaximal, characteristic, complemented
15#20246675C212yesmaximal, complemented
16#20246667C212yesmaximal, complemented
17C4×#13093997C212yesmaximal, complemented
18C4×#13093996C212yesmaximal, complemented
19C4×#13093994C211yesmaximal, characteristic, complemented
20C4×#13093993C211yesmaximal, characteristic, complemented
21C4×#13093992C211yesmaximal, characteristic, complemented
22#20245782C211yesmaximal, characteristic, complemented
23C4×#120×C47C211yesmaximal, characteristic, complemented
24C22×#10625352C2211yescharacteristic
25C23×C22⋊D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C2×#13093997C2212yes—
28C2×#13093996C2212yes—
29C2×#13093994C2211yescharacteristic
30C2×#13093993C2211yescharacteristic
31C2×#13093992C2211yescharacteristic
32C4×#10625352—28no—
33C2×C4×Dic94C2211yescharacteristic, complemented
34C2×#13093989C2211yescharacteristic, complemented
35C2×C4×D188C2212yescomplemented
36C2×D4×Dic47C2211yescharacteristic
37C2×C4×C22⋊D47—28no—
38C2×C4×C22⋊D47C2212yes—
39C2×C4×C22⋊D47C2212yes—
40C2×C4×C22⋊D47C2212yes—
41C2×C4×C22⋊D47C2212yes—
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×C4×C22⋊D47C2211yescharacteristic, complemented
44C2×C4×C22⋊D47C2212yescomplemented
45C2×C4×C22⋊D47C2212yescomplemented
46C2×(C22⋊D47)⋊C4C2211yescharacteristic
47C2×(C22⋊D47)⋊C4C2211yescharacteristic, complemented
48C2×#13093982C2211yescharacteristic, complemented
49C2×#13093980C2211yescharacteristic
50C2×#13093980C2211yescharacteristic, complemented
51C22×Dic47⋊C4C2211yescharacteristic
52C22×C22⋊Dic47C2211yescharacteristic
53C22×(C2×D47)⋊C4C2211yescharacteristic
54C22×C4×Dic47C2211yescharacteristic
55C22×C4×Dic47C2211yescharacteristic, complemented
56C2×C42×D47C2211yescharacteristic, complemented
57#15689065C2212yescomplemented
58#15689064C2212yescomplemented
59#15689059C2212yescomplemented
60#15689059C2212yescomplemented
61#15689058C2212yescomplemented
62#15689058C2212yescomplemented
63#15689052C2212yescomplemented
64#15689051C2212yescomplemented
65#15689039C2212yes—
66#15689038C2212yes—
67#15689036C2212yescomplemented
68#15689035C2212yescomplemented
69#15689032C2212yes—
70#15689032C2212yescomplemented
71#15689031C2212yes—
72#15689031C2212yescomplemented
73#15689023C2212yes—
74#15689023C2212yes—
75#15689020C2212yescomplemented
76#15689018C2212yescomplemented
77#15689017C2212yescomplemented
78#15689016C2212yescomplemented
79#15689013C2212yescomplemented
80#15689012C2212yescomplemented
81#15689003C2211yescharacteristic
82#15689003C2212yescomplemented
83#15689002C2211yescharacteristic
84#15689002C2212yescomplemented
85#15689001C2212yescomplemented
86#15689001C2212yescomplemented
87#15689000C2211yescharacteristic
88#15689000C2212yescomplemented
89#15688999C2212yescomplemented
90#15688999C2212yescomplemented
91#15688998C2211yescharacteristic
92#15688997C2212yescomplemented
93#15688996C2211yescharacteristic
94#15688996C2212yescomplemented
95#15688995C2211yescharacteristic
96#15688994C2212yescomplemented
97#15688990C2212yescomplemented
98#15688987C2212yescomplemented
99#15688984C2211yescharacteristic
100#15688984C2211yescharacteristic
101#15688982C2212yescomplemented
102#15688981C2211yescharacteristic
103#15688981C2211yescharacteristic
104#15688981C2212yescomplemented
105#15688979C2211yescharacteristic
106#15688978C2211yescharacteristic
107#15688978C2211yescharacteristic
108C4×Dic47⋊C4C2212yescomplemented
109C4×(C2×D47)⋊C4C2212yescomplemented
110C4×(C2×D47)⋊C4C2212yescomplemented
111C4×C22⋊Dic47C2211yescharacteristic
112C4×C22⋊Dic47C2212yescomplemented
113#15688969C2212yescomplemented
114C24×C4×C47C2211yescharacteristic
115C2×#120×C47C2211yescharacteristic
116C2×C4×D4×C47C2211yescharacteristic
117C2×C4×D4×C47C2212yescomplemented
118C47×#386C2211yescharacteristic
119C47×#386C2212yescomplemented
120C47×#385C2211yescharacteristic
121C47×#385C2212yescomplemented
122C47×#379C2211yescharacteristic
123C4×C22⋊C4×C47C2211yescharacteristic
124C4×C22⋊C4×C47C2212yescomplemented
125C24×D47C2311yescharacteristic
126C2×#10625352—24no—
127C2×#10625352—24no—
128C2×#10625352—24no—
129C22×Dic94C2311yescharacteristic
130C22×D188C2312yes—
131C22×C22⋊D47—28no—
132C22×C22⋊D47—24no—
133C22×C22⋊D47C2312yes—
134C22×C22⋊D47C2311yescharacteristic
135C22×C22⋊D47C2312yes—
136C22×C22⋊D47C2312yes—
137C22×C22⋊D47C2311yescharacteristic
138C22×C22⋊D47C2312yes—
139C23×Dic47C2311yescharacteristic
140C23×Dic47C2311yescharacteristic
141C23×Dic47C2311yescharacteristic
142C23×Dic47C2311yescharacteristic
143C23×Dic47C2311yescharacteristic
144C22×C4×D47—24no—
145C22×C4×D47—44no—
146C22×C4×D47C2312yes—
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2312yes—
151#13093997—28no—
152#13093996—28no—
153#13093994—24no—
154#13093993—24no—
155#13093992—24no—
156C4×Dic94—24no—
157#13093989—24no—
158C4×D188—44no—
159D4×Dic47—24no—
160C4×C22⋊D47—24no—
161C4×C22⋊D47—28no—
162C4×C22⋊D47—28no—
163C4×C22⋊D47—28no—
164C4×C22⋊D47—28no—
165C4×C22⋊D47—24no—
166C4×C22⋊D47—44no—
167C4×C22⋊D47—44no—
168(C22⋊D47)⋊C4—24no—
169(C22⋊D47)⋊C4—24no—
170#13093982—24no—
171#13093980—24no—
172#13093980—24no—
173C2×C4⋊Dic47C2311yescharacteristic
174C2×C4⋊Dic47C2312yes—
175C2×Dic47⋊C4—24no—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2311yescharacteristic
180C2×Dic47⋊C4C2311yescharacteristic
181C2×Dic47⋊C4C2311yescharacteristic
182C2×Dic47⋊C4C2311yescharacteristic
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×C22⋊Dic47—24no—
187C2×C22⋊Dic47C2311yescharacteristic
188C2×C22⋊Dic47C2311yescharacteristic
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2311yescharacteristic
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2311yescharacteristic
194C2×C22⋊Dic47C2312yes—
195C2×C22⋊Dic47C2312yes—
196C2×C22⋊Dic47C2312yes—
197C2×(C2×D47)⋊C4—24no—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2311yescharacteristic
204C2×(C2×D47)⋊C4C2311yescharacteristic
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2312yes—
207C2×(C2×D47)⋊C4C2312yes—
208C2×(C2×D47)⋊C4C2312yes—
209C2×(C2×D47)⋊C4C2312yes—
210C2×C4×Dic47—24no—
211C2×C4×Dic47D418yescomplemented
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2311yescharacteristic
215C2×C4×Dic47C2311yescharacteristic
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2311yescharacteristic
220C2×C4×Dic47C2311yescharacteristic
221C2×C4×Dic47C2311yescharacteristic
222C42×D47—24no—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C25×C47C2311yescharacteristic
237C22×D4×C47C2312yes—
238C22×D4×C47C2311yescharacteristic
239C23×C4×C47—24no—
240C23×C4×C47—44no—
241C23×C4×C47C2312yes—
242C23×C4×C47C2311yescharacteristic
243C23×C4×C47C2311yescharacteristic
244C23×C4×C47C2311yescharacteristic
245C23×C4×C47C2312yes—
246#120×C47—24no—
247C4×D4×C47—24no—
248C4×D4×C47—44no—
249C2×C4⋊C4×C47C2311yescharacteristic
250C2×C4⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2311yescharacteristic
253C2×C22⋊C4×C47C2311yescharacteristic
254C2×C22⋊C4×C47C2311yescharacteristic
255C2×C22⋊C4×C47C2312yes—
256C2×C22⋊C4×C47C2312yes—
257C2×C22⋊C4×C47C2312yes—
258C2×C22⋊C4×C47C2312yes—
259C2×C42×C47C2312yes—
260C2×C42×C47C2311yescharacteristic
261#95×C47C2312yes—
262#95×C47C2312yes—
263#95×C47C2312yes—
264C24×C47—22no—
265C24×C47—24no—
266C24×C47—22no—
267C24×C47—22no—
268C24×C47—42no—
269C24×C47C2412yes—
270C24×C47C2411yescharacteristic
271C24×C47C2411yescharacteristic
272C23×D47—22no—
273C23×D47—24no—
274C23×D47—22no—
275C23×D47—22no—
276C23×D47—42no—
277C23×D47C2412yes—
278C23×D47C2411yescharacteristic
279C2×D4×C47—22no—
280C2×D4×C47—22no—
281C2×D4×C47—24no—
282C2×D4×C47—24no—
283C2×D4×C47—42no—
284C2×D4×C47#4114yes—
285C22×C4×C47—24no—
286C22×C4×C47—22no—
287C22×C4×C47—22no—
288C22×C4×C47—24no—
289C22×C4×C47—24no—
290C22×C4×C47—24no—
291C22×C4×C47—24no—
292C22×C4×C47—24no—
293C22×C4×C47—42no—
294C22×C4×C47—42no—
295C22×C4×C47—42no—
296C22×C4×C47—416no—
297C22×C4×C47C2×D414yes—
298C22×C4×C47C2412yes—
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2412yes—
301C22×C4×C47C2411yescharacteristic
302C22×C4×C47C2412yes—
303C22×C4×C47C2411yescharacteristic
304C22×C4×C47C2411yescharacteristic
305C22×C4×C47C2411yescharacteristic
306C2×C22⋊D47—232no—
307C2×C22⋊D47—22no—
308C2×C22⋊D47—24no—
309C2×C22⋊D47—22no—
310C2×C22⋊D47—22no—
311C2×C22⋊D47—24no—
312C2×C22⋊D47—22no—
313C2×C22⋊D47—24no—
314C2×C22⋊D47—24no—
315C2×C22⋊D47—24no—
316C2×C22⋊D47—24no—
317C2×C22⋊D47—22no—
318C2×C22⋊D47—24no—
319C2×C22⋊D47—24no—
320C2×C22⋊D47—24no—
321C2×C22⋊D47—42no—
322C2×C22⋊D47—42no—
323C2×C22⋊D47#4114yes—
324C2×C22⋊D47#4118yescomplemented
325C22×Dic47—22no—
326C22×Dic47—22no—
327C22×Dic47—22no—
328C22×Dic47—22no—
329C22×Dic47—24no—
330C22×Dic47—22no—
331C22×Dic47—22no—
332C22×Dic47—22no—
333C22×Dic47—24no—
334C22×Dic47—42no—
335C22×Dic47C2×D414yes—
336C22×Dic47C2×D414yes—
337C22×Dic47C2412yes—
338C22×Dic47C2412yes—
339C22×Dic47C2411yescharacteristic
340C22×Dic47C2412yes—
341C22×Dic47C2411yescharacteristic
342C22×Dic47C2411yescharacteristic
343C22×Dic47C2411yescharacteristic
344C22×Dic47C2411yescharacteristic
345C22×Dic47C2411yescharacteristic
346C22×Dic47C2411yescharacteristic
347#10625352—232no—
348C2×D188—24no—
349C2×D188—24no—
350C2×D188—42no—
351C2×C4×D47—22no—
352C2×C4×D47—22no—
353C2×C4×D47—22no—
354C2×C4×D47—22no—
355C2×C4×D47—24no—
356C2×C4×D47—24no—
357C2×C4×D47—24no—
358C2×C4×D47—24no—
359C2×C4×D47—24no—
360C2×C4×D47—22no—
361C2×C4×D47—24no—
362C2×C4×D47—42no—
363C2×C4×D47—42no—
364C2×C4×D47—416no—
365C2×Dic94—22no—
366C2×Dic94—22no—
367C2×Dic94—22no—
368C4⋊C4×C47—22no—
369C4⋊C4×C47—42no—
370C22⋊C4×C47—22no—
371C22⋊C4×C47—22no—
372C22⋊C4×C47—22no—
373C22⋊C4×C47—24no—
374C22⋊C4×C47—22no—
375C22⋊C4×C47—24no—
376C22⋊C4×C47—42no—
377C22⋊C4×C47—42no—
378C42×C47—22no—
379C42×C47—24no—
380C22⋊Dic47—22no—
381C22⋊Dic47—22no—
382C22⋊Dic47—22no—
383C22⋊Dic47—24no—
384C22⋊Dic47—24no—
385C22⋊Dic47—24no—
386C22⋊Dic47—22no—
387C22⋊Dic47—24no—
388C22⋊Dic47—42no—
389C22⋊Dic47—42no—
390(C2×D47)⋊C4—24no—
391(C2×D47)⋊C4—24no—
392(C2×D47)⋊C4—22no—
393(C2×D47)⋊C4—24no—
394(C2×D47)⋊C4—24no—
395(C2×D47)⋊C4—24no—
396(C2×D47)⋊C4—22no—
397(C2×D47)⋊C4—24no—
398(C2×D47)⋊C4—42no—
399(C2×D47)⋊C4—42no—
400(C2×D47)⋊C4—42no—
401(C2×D47)⋊C4—42no—
402C4⋊Dic47—22no—
403C4⋊Dic47—42no—
404Dic47⋊C4—22no—
405Dic47⋊C4—24no—
406Dic47⋊C4—24no—
407Dic47⋊C4—22no—
408Dic47⋊C4—22no—
409Dic47⋊C4—22no—
410Dic47⋊C4—24no—
411Dic47⋊C4—24no—
412Dic47⋊C4—42no—
413Dic47⋊C4—42no—
414C4×Dic47—22no—
415C4×Dic47—24no—
416C4×Dic47—22no—
417C4×Dic47—22no—
418C4×Dic47—22no—
419C4×Dic47—22no—
420C4×Dic47C2×D414yes—
421C4×Dic47C2×D414yes—
422C4×Dic47C2×D414yes—
423C4×Dic47C2×D414yes—
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—28no—
427C23×C47—22no—
428C23×C47—21no—
429C23×C47—22no—
430C23×C47—22no—
431C23×C47—21no—
432C23×C47—22no—
433C23×C47—22no—
434C23×C47—22no—
435C23×C47—22no—
436C23×C47—22no—
437C23×C47—48no—
438C23×C47—48no—
439C23×C47—44no—
440C23×C47—44no—
441C23×C47C22×D412yes—
442C23×C47C2×#4114yes—
443C23×C47C2×#4112yes—
444C23×C47C2×#4112yes—
445C23×C47C2×#4112yes—
446C23×C47C2511yescharacteristic
447C22×D47—28no—
448C22×D47—21no—
449C22×D47—22no—
450C22×D47—22no—
451C22×D47—22no—
452C22×D47—22no—
453C22×D47—21no—
454C22×D47—22no—
455C22×D47—22no—
456C22×D47—22no—
457C22×D47—22no—
458C22×D47—48no—
459C22×D47—48no—
460C22×D47—44no—
461C22×D47—44no—
462C22×D47C2×#4114yes—
463C22×D47C2×#4112yes—
464D4×C47—28no—
465D4×C47—48no—
466C2×C4×C47—21no—
467C2×C4×C47—21no—
468C2×C4×C47—22no—
469C2×C4×C47—28no—
470C2×C4×C47—21no—
471C2×C4×C47—21no—
472C2×C4×C47—22no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—22no—
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
481C2×C4×C47—22no—
482C2×C4×C47—22no—
483C2×C4×C47—48no—
484C2×C4×C47—44no—
485C2×C4×C47—44no—
486C2×C4×C47—48no—
487C2×C4×C47C22×D412yes—
488C2×C4×C47C22×D412yes—
489C2×C4×C47C2×#4112yes—
490C2×C4×C47H(5,𝔽2)14yes—
491C22⋊D47—28no—
492C22⋊D47—216no—
493C22⋊D47—28no—
494C22⋊D47—216no—
495C22⋊D47—48no—
496C22⋊D47—48no—
497C2×Dic47—28no—
498C2×Dic47—28no—
499C2×Dic47—21no—
500C2×Dic47—21no—
501C2×Dic47—21no—
502C2×Dic47—21no—
503C2×Dic47—21no—
504C2×Dic47—21no—
505C2×Dic47—22no—
506C2×Dic47—28no—
507C2×Dic47—21no—
508C2×Dic47—21no—
509C2×Dic47—22no—
510C2×Dic47—22no—
511C2×Dic47—22no—
512C2×Dic47—22no—
513C2×Dic47—22no—
514C2×Dic47—22no—
515C2×Dic47—22no—
516C2×Dic47—22no—
517C2×Dic47—22no—
518C2×Dic47—22no—
519C2×Dic47—22no—
520C2×Dic47—44no—
521C2×Dic47—44no—
522C2×Dic47C22×D412yes—
523C2×Dic47C22×D412yes—
524C2×Dic47C22×D412yes—
525C2×Dic47C22×D412yes—
526C2×Dic47C2×#4112yes—
527C2×Dic47C2×#4114yes—
528D188—48no—
529C4×D47—28no—
530C4×D47—48no—
531C4×D47—44no—
532C4×D47—48no—
533C4×D47—44no—
534Dic94—28no—
535#34963—471nomaximal, Sylow
536C22×C47—22no—
537C22×C47—22no—
538C22×C47—24no—
539C22×C47—24no—
540C22×C47—22no—
541C22×C47—24no—
542C22×C47—24no—
543C22×C47—24no—
544C22×C47—24no—
545C22×C47—416no—
546C22×C47—41no—
547C22×C47—42no—
548C22×C47—42no—
549C22×C47—41no—
550C22×C47—42no—
551C22×C47—42no—
552C22×C47—42no—
553C22×C47#52514yes—
554C22×C47C23×D411yescharacteristic
555C22×C47C22×#4112yes—
556C22×C47C22×#4111yescharacteristic
557C22×C47C22×#4111yescharacteristic
558C22×C47C2×H(5,𝔽2)12yes—
559C2×D47—22no—
560C2×D47—24no—
561C2×D47—24no—
562C2×D47—24no—
563C2×D47—24no—
564C2×D47—416no—
565C2×D47—41no—
566C2×D47—42no—
567C2×D47—42no—
568C2×D47—41no—
569C2×D47—42no—
570C2×D47—42no—
571C2×D47—42no—
572C4×C47—22no—
573C4×C47—22no—
574C4×C47—41no—
575C4×C47—41no—
576C4×C47—42no—
577C4×C47—42no—
578C4×C47—42no—
579C4×C47#53514yes—
580Dic47—22no—
581Dic47—22no—
582Dic47—22no—
583Dic47—22no—
584Dic47—41no—
585Dic47—42no—
586Dic47—41no—
587Dic47—42no—
588Dic47—42no—
589Dic47#52514yes—
590C2×C4×#41—471no—
591C22×C4×D4—471no—
592#2598—472no—
593#2598—472no—
594#2580—472no—
595#2535—472no—
596#2487—471no—
597#2487—471no—
598#2482—471no—
599#2482—471no—
600#2408—471no—
601#2408—471no—
602#2404—471no—
603#2404—471no—
604#2398—472no—
605#2397—472no—
606C4×#121—472no—
607C4×#121—472no—
608C4×#120—471no—
609C4×#120—471no—
610C4×#120—471no—
611C4×#120D4711yescharacteristic, complemented
612#2283—471no—
613C2×C47—24no—
614C2×C47—42no—
615C2×C47—44no—
616C2×C47C2×#52511yescharacteristic
617C2×C47C2×#52511yescharacteristic
618C2×C47C2×#53511yescharacteristic
619C2×C47#348112yes—
620C2×C47#348112yes—
621D47—42no—
622D47—44no—
623C22×#41—471no—
624C23×D4—471no—
625C24×C4—471no—
626C24×C4C2×D4711yescharacteristic
627C2×#121—472no—
628C2×#121—472no—
629C2×#120—471no—
630C2×#120—471no—
631C2×#120—471no—
632C2×#120C2×D4711yescharacteristic
633C4×#41—948no—
634C2×C4×Q8—471no—
635C2×C4×Q8—471no—
636C2×C4×D4—471no—
637C2×C4×D4—472no—
638C2×C4×D4—472no—
639C2×C4×D4—471no—
640C2×C4×D4—472no—
641C2×C4×D4—472no—
642C2×C4×D4—471no—
643C2×C4×D4—472no—
644C2×C4×D4—472no—
645C2×C4×D4—471no—
646C2×C4×D4—471no—
647C2×C4×D4—472no—
648C2×C4×D4—948no—
649C2×C4×D4C2×D4711yescharacteristic
650C2×C4×D4C2×D4712yescomplemented
651C2×#117—471no—
652C2×#117—471no—
653C2×#117—471no—
654C22×C4⋊C4—471no—
655C22×C22⋊C4—471no—
656C22×C22⋊C4—471no—
657C22×C42—471no—
658C22×C42—471no—
659C22×C42—471no—
660#400—472no—
661#400—472no—
662#399—472no—
663#399—472no—
664#399—472no—
665#399—472no—
666#397—472no—
667#397—472no—
668#394—472no—
669#394—472no—
670#393—472no—
671#393—472no—
672#392—472no—
673#392—472no—
674#392—472no—
675#392—472no—
676#390—472no—
677#390—472no—
678#389—472no—
679#389—472no—
680#388—472no—
681#388—472no—
682#388—472no—
683#388—472no—
684#386—472no—
685#386—471no—
686#386—472no—
687#386—471no—
688#386—472no—
689#386—472no—
690#386—472no—
691#386—471no—
692#386—472no—
693#386—472no—
694#386C2×D4711yescharacteristic
695#386C2×D4712yescomplemented
696#385—472no—
697#385—471no—
698#385—472no—
699#385—471no—
700#385—471no—
701#385—472no—
702#385C2×D4711yescharacteristic
703#385C2×D4712yescomplemented
704#383—472no—
705#382—472no—
706#381—471no—
707#381—471no—
708#380—471no—
709#380—471no—
710#380—472no—
711#380—472no—
712#379—471no—
713#379—471no—
714#379—471no—
715#379C2×D4711yescharacteristic
716C4×C4⋊C4—472no—
717C4×C22⋊C4—471no—
718C4×C22⋊C4—472no—
719C4×C22⋊C4—472no—
720C4×C22⋊C4—472no—
721C4×C22⋊C4C2×D4711yescharacteristic
722C4×C22⋊C4C2×D4712yescomplemented
723#376—472no—
724C47#3496311yescharacteristic, complemented, Sylow
725C25—471no—
726C25C22×D4711yescharacteristic
727C2×#41—944no—
728C2×#41—944no—
729C2×#41—944no—
730C22×Q8—471no—
731C22×D4—471no—
732C22×D4—472no—
733C22×D4—472no—
734C22×D4—471no—
735C22×D4—472no—
736C22×D4—472no—
737C22×D4—472no—
738C22×D4—944no—
739C22×D4—948no—
740C22×D4C22×D4712yes—
741C22×D4C22×D4711yescharacteristic
742C23×C4—24no—
743C23×C4—44no—
744C23×C4—471no—
745C23×C4—471no—
746C23×C4—471no—
747C23×C4—471no—
748C23×C4—471no—
749C23×C4—471no—
750C23×C4—471no—
751C23×C4—471no—
752C23×C4—472no—
753C23×C4—472no—
754C23×C4—944no—
755C23×C4—1884no—
756C23×C4C22×D4711yescharacteristic
757C23×C4C22×D4712yes—
758C23×C4C22×D4711yescharacteristic
759C23×C4C22×D4711yescharacteristic
760C23×C4C22×D4712yes—
761#121—948no—
762#121—948no—
763#120—24no—
764#120—944no—
765#120—944no—
766#120—944no—
767C4×Q8—944no—
768C4×Q8—944no—
769C4×D4—24no—
770C4×D4—44no—
771C4×D4—944no—
772C4×D4—948no—
773C4×D4—948no—
774C4×D4—948no—
775C4×D4—948no—
776C4×D4—944no—
777C4×D4—944no—
778C4×D4—944no—
779C4×D4—944no—
780C4×D4—1884no—
781C4×D4—1884no—
782C4×D4—1884no—
783#117—944no—
784#117—944no—
785#117—944no—
786C2×C4⋊C4—472no—
787C2×C4⋊C4—472no—
788C2×C4⋊C4—471no—
789C2×C4⋊C4—471no—
790C2×C4⋊C4—471no—
791C2×C4⋊C4—471no—
792C2×C4⋊C4—471no—
793C2×C4⋊C4—472no—
794C2×C4⋊C4—472no—
795C2×C4⋊C4—472no—
796C2×C4⋊C4—472no—
797C2×C4⋊C4—472no—
798C2×C4⋊C4—944no—
799C2×C4⋊C4C22×D4711yescharacteristic
800C2×C4⋊C4C22×D4712yes—
801C2×C22⋊C4—472no—
802C2×C22⋊C4—472no—
803C2×C22⋊C4—471no—
804C2×C22⋊C4—471no—
805C2×C22⋊C4—471no—
806C2×C22⋊C4—471no—
807C2×C22⋊C4—472no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—472no—
810C2×C22⋊C4—472no—
811C2×C22⋊C4—471no—
812C2×C22⋊C4—471no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4—472no—
817C2×C22⋊C4—472no—
818C2×C22⋊C4—472no—
819C2×C22⋊C4—472no—
820C2×C22⋊C4—472no—
821C2×C22⋊C4—472no—
822C2×C22⋊C4—472no—
823C2×C22⋊C4—944no—
824C2×C22⋊C4—944no—
825C2×C22⋊C4C22×D4711yescharacteristic
826C2×C22⋊C4C22×D4711yescharacteristic
827C2×C22⋊C4C22×D4711yescharacteristic
828C2×C22⋊C4C22×D4711yescharacteristic
829C2×C22⋊C4C22×D4712yes—
830C2×C22⋊C4C22×D4712yes—
831C2×C22⋊C4C22×D4712yes—
832C2×C22⋊C4C22×D4712yes—
833C2×C42—478no—
834C2×C42—471no—
835C2×C42—471no—
836C2×C42—471no—
837C2×C42—471no—
838C2×C42—471no—
839C2×C42—471no—
840C2×C42—471no—
841C2×C42—471no—
842C2×C42—472no—
843C2×C42—471no—
844C2×C42—944no—
845C2×C42—944no—
846C2×C42C22×D4712yes—
847C2×C42C22×D4711yescharacteristic
848#95—472no—
849#95—472no—
850#95—472no—
851#95—472no—
852#95—472no—
853#95—472no—
854#95—472no—
855#95—472no—
856#95—472no—
857#95—472no—
858#95—472no—
859#95—472no—
860#95—472no—
861#95C22×D4712yes—
862#95C22×D4712yes—
863#95C22×D4712yes—
864C24—22no—
865C24—24no—
866C24—22no—
867C24—22no—
868C24—42no—
869C24—472no—
870C24—471no—
871C24—944no—
872C24—942no—
873C24—942no—
874C24—942no—
875C24—1882no—
876C24C23×D4712yes—
877C24C23×D4711yescharacteristic
878C24C23×D4711yescharacteristic
879#41—9432no—
880C2×Q8—942no—
881C2×Q8—942no—
882C2×Q8—942no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—42no—
888C2×D4—474no—
889C2×D4—478no—
890C2×D4—944no—
891C2×D4—944no—
892C2×D4—944no—
893C2×D4—944no—
894C2×D4—942no—
895C2×D4—944no—
896C2×D4—944no—
897C2×D4—942no—
898C2×D4—9432no—
899C2×D4—942no—
900C2×D4—944no—
901C2×D4—942no—
902C2×D4—942no—
903C2×D4—944no—
904C2×D4—944no—
905C2×D4—944no—
906C2×D4—944no—
907C2×D4—1882no—
908C2×D4—1882no—
909C2×D4—1882no—
910C2×D4#1062535014yes—
911C22×C4—24no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—416no—
923C22×C4—471no—
924C22×C4—474no—
925C22×C4—474no—
926C22×C4—471no—
927C22×C4—471no—
928C22×C4—471no—
929C22×C4—471no—
930C22×C4—472no—
931C22×C4—472no—
932C22×C4—471no—
933C22×C4—472no—
934C22×C4—471no—
935C22×C4—942no—
936C22×C4—942no—
937C22×C4—944no—
938C22×C4—942no—
939C22×C4—942no—
940C22×C4—944no—
941C22×C4—942no—
942C22×C4—942no—
943C22×C4—944no—
944C22×C4—942no—
945C22×C4—942no—
946C22×C4—942no—
947C22×C4—942no—
948C22×C4—942no—
949C22×C4—942no—
950C22×C4—944no—
951C22×C4—944no—
952C22×C4—944no—
953C22×C4—944no—
954C22×C4—944no—
955C22×C4—1882no—
956C22×C4—1882no—
957C22×C4—18816no—
958C22×C4—1882no—
959C22×C4D4×D4714yes—
960C22×C4C23×D4712yes—
961C22×C4C23×D4712yes—
962C22×C4C23×D4711yescharacteristic
963C22×C4C23×D4712yes—
964C22×C4C23×D4711yescharacteristic
965C22×C4C23×D4711yescharacteristic
966C22×C4C23×D4711yescharacteristic
967C22×C4C23×D4711yescharacteristic
968C4⋊C4—22no—
969C4⋊C4—42no—
970C4⋊C4—944no—
971C4⋊C4—944no—
972C4⋊C4—942no—
973C4⋊C4—942no—
974C4⋊C4—942no—
975C4⋊C4—944no—
976C4⋊C4—944no—
977C4⋊C4—942no—
978C4⋊C4—942no—
979C4⋊C4—1882no—
980C4⋊C4—1882no—
981C4⋊C4—1882no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—24no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—944no—
991C22⋊C4—944no—
992C22⋊C4—942no—
993C22⋊C4—944no—
994C22⋊C4—944no—
995C22⋊C4—944no—
996C22⋊C4—944no—
997C22⋊C4—944no—
998C22⋊C4—942no—
999C22⋊C4—944no—
1000C22⋊C4—942no—
1001C22⋊C4—942no—
1002C22⋊C4—944no—
1003C22⋊C4—942no—
1004C22⋊C4—942no—
1005C22⋊C4—944no—
1006C22⋊C4—1882no—
1007C22⋊C4—1882no—
1008C22⋊C4—1882no—
1009C22⋊C4—1882no—
1010C22⋊C4—1882no—
1011C22⋊C4—1882no—
1012C42—22no—
1013C42—24no—
1014C42—474no—
1015C42—474no—
1016C42—474no—
1017C42—474no—
1018C42—942no—
1019C42—942no—
1020C42—942no—
1021C42—942no—
1022C42—942no—
1023C42—944no—
1024C23—22no—
1025C23—22no—
1026C23—28no—
1027C23—21no—
1028C23—22no—
1029C23—22no—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—48no—
1038C23—48no—
1039C23—44no—
1040C23—44no—
1041C23—474no—
1042C23—472no—
1043C23—948no—
1044C23—941no—
1045C23—942no—
1046C23—942no—
1047C23—942no—
1048C23—942no—
1049C23—942no—
1050C23—941no—
1051C23—942no—
1052C23—942no—
1053C23—942no—
1054C23—1888no—
1055C23—1888no—
1056C23—1884no—
1057C23—1884no—
1058C23C2×D4×D4712yes—
1059C23#41×D4714yes—
1060C23#41×D4712yes—
1061C23C2×#1062535012yes—
1062C23C2×#1062535012yes—
1063C23C24×D4711yescharacteristic
1064Q8—948no—
1065D4—28no—
1066D4—48no—
1067D4—9416no—
1068D4—9416no—
1069D4—948no—
1070D4—948no—
1071D4—1888no—
1072D4—1888no—
1073D4—1888no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—28no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—48no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—48no—
1095C2×C4—472no—
1096C2×C4—474no—
1097C2×C4—472no—
1098C2×C4—472no—
1099C2×C4—472no—
1100C2×C4—472no—
1101C2×C4—948no—
1102C2×C4—948no—
1103C2×C4—948no—
1104C2×C4—948no—
1105C2×C4—941no—
1106C2×C4—941no—
1107C2×C4—942no—
1108C2×C4—941no—
1109C2×C4—941no—
1110C2×C4—941no—
1111C2×C4—941no—
1112C2×C4—941no—
1113C2×C4—941no—
1114C2×C4—942no—
1115C2×C4—942no—
1116C2×C4—942no—
1117C2×C4—942no—
1118C2×C4—942no—
1119C2×C4—942no—
1120C2×C4—942no—
1121C2×C4—942no—
1122C2×C4—942no—
1123C2×C4—942no—
1124C2×C4—942no—
1125C2×C4—1888no—
1126C2×C4—1884no—
1127C2×C4—1884no—
1128C2×C4—1884no—
1129C2×C4—1884no—
1130C2×C4—1888no—
1131C2×C4C2×D4×D4712yes—
1132C2×C4C2×D4×D4712yes—
1133C2×C4C2×#1062535012yes—
1134C2×C4#1309406914yes—
1135C22—22no—
1136C22—22no—
1137C22—24no—
1138C22—24no—
1139C22—24no—
1140C22—22no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—416no—
1145C22—41no—
1146C22—42no—
1147C22—42no—
1148C22—41no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—944no—
1153C22—942no—
1154C22—944no—
1155C22—944no—
1156C22—944no—
1157C22—18816no—
1158C22—1881no—
1159C22—1882no—
1160C22—1882no—
1161C22—1881no—
1162C22—1882no—
1163C22—1882no—
1164C22—1882no—
1165C22#1568963214yes—
1166C22C22×D4×D4711yescharacteristic
1167C22C2×#41×D4712yes—
1168C22C2×#41×D4711yescharacteristic
1169C22C22×#1062535011yescharacteristic
1170C22C2×#1309406912yes—
1171C4—22no—
1172C4—22no—
1173C4—41no—
1174C4—42no—
1175C4—41no—
1176C4—42no—
1177C4—42no—
1178C4—474no—
1179C4—942no—
1180C4—942no—
1181C4—942no—
1182C4—942no—
1183C4—1881no—
1184C4—1882no—
1185C4—1881no—
1186C4—1882no—
1187C4—1882no—
1188C4#1568968814yes—
1189C2—24no—
1190C2—44no—
1191C2—42no—
1192C2—1884no—
1193C2—1882no—
1194C2#525×D4711yescharacteristic
1195C2C2×#1568963211yescharacteristic
1196C2C2×#1568968811yescharacteristic
1197C2#2025699012yes—
1198C2#2025699212yes—
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC4×#120×C47C2
hypercenterC4×#120D47
hypocenterC47#34963
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×C4×#10625352C2semidirect
2. C22×C4×C22⋊D47C2semidirect
3. #20248953C2semidirect
4. #20248951C2semidirect
5. #20248745C2semidirect
6. #20248288C2semidirect
7. #20247704C2semidirect
8. #20247702C2semidirect
9. #20247661C2semidirect
10. #20247659C2semidirect
11. #20246743C2semidirect
12. #20246741C2semidirect
13. #20246706C2semidirect
14. #20246704C2semidirect
15. #20246675C2semidirect
16. #20246667C2semidirect
17. C4×#13093997C2semidirect
18. C4×#13093996C2semidirect
19. C4×#13093994C2semidirect
20. C4×#13093993C2semidirect
21. C4×#13093992C2semidirect
22. #20245782C2semidirect
23. C4×#120×C47C2semidirect
33. C2×C4×Dic94C22semidirect
34. C2×#13093989C22semidirect
35. C2×C4×D188C22semidirect
43. C2×C4×C22⋊D47C22semidirect
44. C2×C4×C22⋊D47C22semidirect
45. C2×C4×C22⋊D47C22semidirect
47. C2×(C22⋊D47)⋊C4C22semidirect
48. C2×#13093982C22semidirect
50. C2×#13093980C22semidirect
55. C22×C4×Dic47C22semidirect
56. C2×C42×D47C22semidirect
57. #15689065C22semidirect
58. #15689064C22semidirect
59. #15689059C22semidirect
60. #15689059C22semidirect
61. #15689058C22semidirect
62. #15689058C22semidirect
63. #15689052C22semidirect
64. #15689051C22semidirect
67. #15689036C22semidirect
68. #15689035C22semidirect
70. #15689032C22semidirect
72. #15689031C22semidirect
75. #15689020C22semidirect
76. #15689018C22semidirect
77. #15689017C22semidirect
78. #15689016C22semidirect
79. #15689013C22semidirect
80. #15689012C22semidirect
82. #15689003C22semidirect
84. #15689002C22semidirect
85. #15689001C22semidirect
86. #15689001C22semidirect
88. #15689000C22semidirect
89. #15688999C22semidirect
90. #15688999C22semidirect
92. #15688997C22semidirect
94. #15688996C22semidirect
96. #15688994C22semidirect
97. #15688990C22semidirect
98. #15688987C22semidirect
101. #15688982C22semidirect
104. #15688981C22semidirect
108. C4×Dic47⋊C4C22semidirect
109. C4×(C2×D47)⋊C4C22semidirect
110. C4×(C2×D47)⋊C4C22semidirect
112. C4×C22⋊Dic47C22semidirect
113. #15688969C22semidirect
117. C2×C4×D4×C47C22semidirect
119. C47×#386C22semidirect
121. C47×#385C22semidirect
124. C4×C22⋊C4×C47C22semidirect
211. C2×C4×Dic47D4semidirect
324. C2×C22⋊D47#41semidirect
611. C4×#120D47semidirect
650. C2×C4×D4C2×D47semidirect
695. #386C2×D47semidirect
703. #385C2×D47semidirect
722. C4×C22⋊C4C2×D47semidirect
724. C47#34963semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253522
C22×C4×C22⋊D472
#202489532
#202489512
#202487452
#202482882
#202477042
#202477022
#202476612
#202476592
#202467432
#202467412
#202467062
#202467042
#202466752
#202466672
C4×#130939972
C4×#130939962
C4×#130939942
C4×#130939932
C4×#130939922
#202457822
C4×#120×C472
#3496347