Finite Group Databasebeta

← #26376589

Subgroups — #26376589

Order 12032.

3246 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689633C211yesmaximal, characteristic
2C2×#15689602C211yesmaximal, characteristic, complemented
3C2×#117×D47C211yesmaximal, characteristic, complemented
4#20246383C212yesmaximal, complemented
5#20246379C212yesmaximal, complemented
6#20246371C212yesmaximal, complemented
7#20246369C212yesmaximal, complemented
8#20246336C212yesmaximal, complemented
9#20246316C212yesmaximal, complemented
10#20246315C212yesmaximal, complemented
11#20246286C212yesmaximal, complemented
12#20246083C211yesmaximal, characteristic, complemented
13#20246070C211yesmaximal, characteristic, complemented
14#20246066C211yesmaximal, characteristic, complemented
15#20246010C211yesmaximal, characteristic, complemented
16#20245978C211yesmaximal, characteristic, complemented
17C4×#13094004C211yesmaximal, characteristic, complemented
18#20245918C211yesmaximal, characteristic, complemented
19#20245904C211yesmaximal, characteristic, complemented
20C4×#13093995C211yesmaximal, characteristic, complemented
21#380×D47C211yesmaximal, characteristic, complemented
22#20245742C211yesmaximal, characteristic, complemented
23C47×#2324C211yesmaximal, characteristic, complemented
24C22×#10625352C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26#15689633C4116yescomplemented
27C2×#13094006C2212yes—
28C2×#13094004C2211yescharacteristic
29C2×#13094003C2211yescharacteristic
30C2×#13093995C2211yescharacteristic
31C2×#13093992C2212yes—
32#15689602—28no—
33C2×C4×Dic94C2211yescharacteristic, complemented
34C2×#13093989C2211yescharacteristic, complemented
35C2×D4×Dic47C2212yes—
36C2×D4×Dic47C2211yescharacteristic, complemented
37C2×C4×C22⋊D47C2212yes—
38C2×C4×C22⋊D47C2212yes—
39C2×(C22⋊D47)⋊C4C2212yes—
40C2×(C22⋊D47)⋊C4C2212yes—
41C2×(C22⋊D47)⋊C4C2212yes—
42C2×#13093983C2211yescharacteristic
43C2×#13093982C2211yescharacteristic
44C2×#13093982C2211yescharacteristic
45C2×#13093982C2211yescharacteristic
46C2×#13093981C2211yescharacteristic
47C2×#13093981C2211yescharacteristic
48C2×#13093980C2211yescharacteristic
49C2×#13093980C2211yescharacteristic
50C2×#13093980C2212yescomplemented
51#117×D47—28no—
52C22×Dic47⋊C4C2212yescomplemented
53C2×C4⋊C4×D47C2211yescharacteristic
54C2×C4⋊C4×D47C2211yescharacteristic
55C2×C4⋊C4×D47C2211yescharacteristic
56C2×C4⋊C4×D47C2211yescharacteristic
57C2×C22⋊C4×D47C2211yescharacteristic
58C2×C22⋊C4×D47C2211yescharacteristic
59C2×C22⋊C4×D47C2212yes—
60C2×C42×D47C2211yescharacteristic
61C2×C42×D47C2211yescharacteristic
62#15689029C2211yescharacteristic, complemented
63#15689028C2211yescharacteristic, complemented
64#15689026C2212yes—
65#15689026C2211yescharacteristic, complemented
66#15689022C2211yescharacteristic, complemented
67#15689021C2211yescharacteristic, complemented
68#15689020C2212yescomplemented
69#15689019C2211yescharacteristic, complemented
70#15689018C2212yescomplemented
71#15689017C2212yes—
72#15689017C2212yes—
73#15689017C2212yescomplemented
74#15689016C2212yescomplemented
75#15689011C2212yes—
76#15689011C2212yes—
77#15689011C2212yescomplemented
78#15689010C2212yescomplemented
79#15689008C2212yescomplemented
80#15689006C2212yescomplemented
81#15689004C2212yescomplemented
82#15689003C2212yes—
83#15688999C2212yes—
84#15688999C2212yes—
85#15688999C2212yes—
86#15688999C2212yes—
87#15688998C2212yescomplemented
88#15688997C2212yes—
89#15688997C2212yes—
90#15688994C2212yes—
91#15688994C2212yes—
92#15688992C2212yescomplemented
93#15688987C2212yescomplemented
94#15688983C2211yescharacteristic
95#15688982C2212yes—
96#15688981C2212yes—
97#15688981C2212yescomplemented
98#15688981C2212yescomplemented
99#15688980C2211yescharacteristic
100#15688980C2211yescharacteristic
101C4⋊C4×Dic47C2211yescharacteristic, complemented
102C4⋊C4×Dic47C2212yescomplemented
103C4⋊C4×Dic47C2211yescharacteristic, complemented
104C4×Dic47⋊C4C2212yescomplemented
105C4×C4⋊Dic47C2211yescharacteristic, complemented
106C4×C4⋊Dic47C2212yescomplemented
107#15688974C2212yescomplemented
108C22⋊C4×Dic47C2212yescomplemented
109C4×(C2×D47)⋊C4C2212yes—
110C4×(C2×D47)⋊C4C2212yes—
111C4×C22⋊Dic47C2212yescomplemented
112#15688970C2212yes—
113#15688970C2212yes—
114#95×D47C2212yes—
115C2×#121×C47C2211yescharacteristic
116C2×C4×D4×C47C2211yescharacteristic, complemented
117C2×#117×C47C2211yescharacteristic
118C47×#390C2212yes—
119C47×#390C2211yescharacteristic, complemented
120C47×#389C2211yescharacteristic, complemented
121C47×#388C2212yescomplemented
122C47×#386C2212yes—
123C47×#385C2212yescomplemented
124C47×#380C2211yescharacteristic
125C4×C4⋊C4×C47C2211yescharacteristic, complemented
126C24×D47C2311yescharacteristic
127C2×#10625352—24no—
128C2×#10625352—24no—
129C2×#10625352C2×C418yescomplemented
130C22×Dic94C2311yescharacteristic
131C22×C22⋊D47C2312yes—
132C22×C22⋊D47C2312yes—
133C23×Dic47C2311yescharacteristic
134C23×Dic47C2312yes—
135C23×Dic47C2312yes—
136C22×C4×D47—24no—
137C22×C4×D47—24no—
138C22×C4×D47C2×C418yescomplemented
139C22×C4×D47C2311yescharacteristic
140C22×C4×D47C2311yescharacteristic
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2312yes—
147C22×C4×D47C2312yes—
148C22×C4×D47C2311yescharacteristic
149#13094006C2×C4116yescomplemented
150#13094004C2×C418yescomplemented
151#13094003C2×C418yescomplemented
152#13093995C2×C418yescomplemented
153#13093992C2×C4116yescomplemented
154C4×Dic94—24no—
155#13093989—24no—
156D4×Dic47—24no—
157D4×Dic47C2×C4116yescomplemented
158C4×C22⋊D47—28no—
159C4×C22⋊D47—44no—
160(C22⋊D47)⋊C4—28no—
161(C22⋊D47)⋊C4—44no—
162(C22⋊D47)⋊C4C2×C4116yescomplemented
163#13093983—24no—
164#13093982—24no—
165#13093982—24no—
166#13093982C2×C418yescomplemented
167#13093981—24no—
168#13093981D418yescomplemented
169#13093980—24no—
170#13093980—24no—
171#13093980—28no—
172C2×C4⋊Dic47C2311yescharacteristic
173C2×C4⋊Dic47C2311yescharacteristic
174C2×C4⋊Dic47C2311yescharacteristic
175C2×C4⋊Dic47C2311yescharacteristic
176C2×C4⋊Dic47C2312yes—
177C2×C4⋊Dic47C2312yes—
178C2×C4⋊Dic47C2311yescharacteristic
179C2×Dic47⋊C4—28no—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2311yescharacteristic
183C2×Dic47⋊C4C2311yescharacteristic
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2311yescharacteristic
190C2×Dic47⋊C4C2311yescharacteristic
191C4⋊C4×D47—24no—
192C4⋊C4×D47—24no—
193C4⋊C4×D47—24no—
194C4⋊C4×D47—24no—
195C2×C22⋊Dic47C2312yes—
196C2×C22⋊Dic47C2311yescharacteristic
197C2×C22⋊Dic47C2311yescharacteristic
198C2×C22⋊Dic47C2312yes—
199C2×C22⋊Dic47C2312yes—
200C2×C22⋊Dic47C2312yes—
201C2×C22⋊Dic47C2312yes—
202C2×C22⋊Dic47C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2311yescharacteristic
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C2×(C2×D47)⋊C4C2312yes—
208C2×(C2×D47)⋊C4C2312yes—
209C2×(C2×D47)⋊C4C2311yescharacteristic
210C2×(C2×D47)⋊C4C2311yescharacteristic
211C22⋊C4×D47—24no—
212C22⋊C4×D47—24no—
213C22⋊C4×D47—44no—
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2311yescharacteristic
216C2×C4×Dic47C2312yes—
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2311yescharacteristic
220C2×C4×Dic47C2311yescharacteristic
221C2×C4×Dic47C2312yes—
222C2×C4×Dic47C2312yes—
223C2×C4×Dic47C2312yes—
224C2×C4×Dic47C2312yes—
225C2×C4×Dic47C2311yescharacteristic
226C42×D47—24no—
227C42×D47—24no—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C47⋊#95C2312yes—
237C47⋊#95C2312yes—
238C47⋊#95C2312yes—
239C47⋊#95C2312yes—
240C47⋊#95C2312yes—
241C22×D4×C47C2311yescharacteristic
242C22×D4×C47C2312yes—
243C23×C4×C47C2311yescharacteristic
244C23×C4×C47C2312yes—
245#121×C47C2×C418yescomplemented
246C4×D4×C47—24no—
247#117×C47—24no—
248C2×C4⋊C4×C47C2311yescharacteristic
249C2×C4⋊C4×C47C2311yescharacteristic
250C2×C4⋊C4×C47C2311yescharacteristic
251C2×C4⋊C4×C47C2311yescharacteristic
252C2×C4⋊C4×C47C2312yes—
253C2×C4⋊C4×C47C2311yescharacteristic
254C2×C22⋊C4×C47C2312yes—
255C2×C22⋊C4×C47C2311yescharacteristic
256C2×C22⋊C4×C47C2311yescharacteristic
257C2×C22⋊C4×C47C2312yes—
258C2×C22⋊C4×C47C2312yes—
259C2×C22⋊C4×C47C2312yes—
260C2×C22⋊C4×C47C2312yes—
261C2×C42×C47C2311yescharacteristic
262C2×C42×C47C2312yes—
263C2×C42×C47C2311yescharacteristic
264#95×C47C2312yes—
265#95×C47C2312yes—
266#95×C47C2312yes—
267C24×C47C2411yescharacteristic
268C24×C47C2412yes—
269C23×D47—22no—
270C23×D47—22no—
271C23×D47—22no—
272C23×D47—22no—
273C23×D47—41no—
274C23×D47—41no—
275C23×D47C22×C414yes—
276C23×D47C2411yescharacteristic
277C23×D47C2411yescharacteristic
278C2×D4×C47—22no—
279C2×D4×C47—22no—
280C2×D4×C47—42no—
281C2×D4×C47—42no—
282C2×D4×C47C22×C414yes—
283C2×D4×C47C22×C418yes—
284C22×C4×C47—22no—
285C22×C4×C47—22no—
286C22×C4×C47—24no—
287C22×C4×C47—42no—
288C22×C4×C47—42no—
289C22×C4×C47C22×C414yes—
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2412yes—
293C22×C4×C47C2412yes—
294C22×C4×C47C2412yes—
295C22×C4×C47C2411yescharacteristic
296C22×C4×C47C2411yescharacteristic
297C22×C4×C47C2411yescharacteristic
298C22×C4×C47C2411yescharacteristic
299C2×C22⋊D47—24no—
300C2×C22⋊D47—24no—
301C2×C22⋊D47—24no—
302C2×C22⋊D47—24no—
303C2×C22⋊D47C22×C418yes—
304C2×C22⋊D47C22×C418yes—
305C22×Dic47—24no—
306C22×Dic47—22no—
307C22×Dic47—22no—
308C22×Dic47—24no—
309C22×Dic47—24no—
310C22×Dic47—42no—
311C22×Dic47—42no—
312C22×Dic47C22×C418yes—
313C22×Dic47C22×C414yes—
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2412yes—
316C22×Dic47C2412yes—
317C22×Dic47C2411yescharacteristic
318C22×Dic47C2411yescharacteristic
319C22×Dic47C2412yes—
320C22×Dic47C2412yes—
321C22×Dic47C2411yescharacteristic
322C22×Dic47C2411yescharacteristic
323C22×Dic47C2411yescharacteristic
324#10625352—232no—
325C2×C4×D47—22no—
326C2×C4×D47—22no—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—22no—
330C2×C4×D47—22no—
331C2×C4×D47—232no—
332C2×C4×D47—22no—
333C2×C4×D47—22no—
334C2×C4×D47—22no—
335C2×C4×D47—22no—
336C2×C4×D47—22no—
337C2×C4×D47—22no—
338C2×C4×D47—22no—
339C2×C4×D47—22no—
340C2×C4×D47—24no—
341C2×C4×D47—24no—
342C2×C4×D47—41no—
343C2×C4×D47—41no—
344C2×C4×D47—41no—
345C2×C4×D47—41no—
346C2×C4×D47—42no—
347C2×C4×D47—42no—
348C2×C4×D47—42no—
349C2×C4×D47—42no—
350C2×C4×D47C22×C414yes—
351C2×C4×D47C22×C414yes—
352C2×C4×D47C22×C414yes—
353C2×C4×D47C22×C414yes—
354C2×C4×D47C2×D414yes—
355C2×C4×D47#4114yes—
356C2×Dic94—22no—
357C2×Dic94—22no—
358C2×Dic94C22×C414yes—
359C4⋊C4×C47—22no—
360C4⋊C4×C47—22no—
361C4⋊C4×C47—22no—
362C4⋊C4×C47—22no—
363C4⋊C4×C47—42no—
364C4⋊C4×C47C22×C414yes—
365C22⋊C4×C47—22no—
366C22⋊C4×C47—22no—
367C22⋊C4×C47—24no—
368C22⋊C4×C47—42no—
369C22⋊C4×C47—42no—
370C22⋊C4×C47—42no—
371C22⋊C4×C47C22×C418yes—
372C42×C47—22no—
373C42×C47—42no—
374C42×C47C2×D414yes—
375C22⋊Dic47—22no—
376C22⋊Dic47—22no—
377C22⋊Dic47—24no—
378C22⋊Dic47—42no—
379C22⋊Dic47—42no—
380C22⋊Dic47—42no—
381C22⋊Dic47C22×C418yes—
382C22⋊Dic47C22×C418yes—
383(C2×D47)⋊C4—22no—
384(C2×D47)⋊C4—22no—
385(C2×D47)⋊C4—24no—
386(C2×D47)⋊C4—24no—
387(C2×D47)⋊C4C22×C418yes—
388(C2×D47)⋊C4C22×C418yes—
389(C2×D47)⋊C4C2×D414yes—
390(C2×D47)⋊C4C2×D414yes—
391C4⋊Dic47—22no—
392C4⋊Dic47—22no—
393C4⋊Dic47—22no—
394C4⋊Dic47—22no—
395C4⋊Dic47—42no—
396C4⋊Dic47C22×C414yes—
397C4⋊Dic47C22×C418yes—
398Dic47⋊C4—24no—
399Dic47⋊C4—24no—
400Dic47⋊C4—22no—
401Dic47⋊C4—22no—
402Dic47⋊C4—24no—
403Dic47⋊C4—24no—
404Dic47⋊C4—42no—
405Dic47⋊C4—42no—
406Dic47⋊C4C22×C418yes—
407Dic47⋊C4C2×D414yes—
408Dic47⋊C4C2×D414yes—
409C4×Dic47—22no—
410C4×Dic47—22no—
411C4×Dic47—22no—
412C4×Dic47—24no—
413C4×Dic47—22no—
414C4×Dic47—22no—
415C4×Dic47—24no—
416C4×Dic47—42no—
417C4×Dic47—42no—
418C4×Dic47—42no—
419C4×Dic47C22×C418yes—
420C4×Dic47C2×D414yes—
421C23×C47—21no—
422C23×C47—22no—
423C23×C47—22no—
424C23×C47—21no—
425C23×C47—21no—
426C23×C47—22no—
427C23×C47—22no—
428C23×C47—21no—
429C23×C47—22no—
430C23×C47—22no—
431C23×C47—21no—
432C23×C47—21no—
433C23×C47C23×C412yes—
434C23×C47C23×C414yes—
435C23×C47C2511yescharacteristic
436C22×D47—21no—
437C22×D47—21no—
438C22×D47—21no—
439C22×D47—21no—
440C22×D47—21no—
441C22×D47—21no—
442C22×D47—21no—
443C22×D47—21no—
444C22×D47—28no—
445C22×D47—28no—
446C22×D47—44no—
447C22×D47—44no—
448C22×D47—44no—
449C22×D47—44no—
450C22×D47—44no—
451C22×D47C23×C412yes—
452C22×D47C23×C412yes—
453C22×D47C22×D412yes—
454C22×D47C2×#4112yes—
455C22×D47H(5,𝔽2)12yes—
456C22×D472−1+412yes—
457D4×C47—28no—
458D4×C47—48no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—21no—
462C2×C4×C47—21no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—21no—
466C2×C4×C47—21no—
467C2×C4×C47—28no—
468C2×C4×C47—22no—
469C2×C4×C47—21no—
470C2×C4×C47—21no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—21no—
474C2×C4×C47—22no—
475C2×C4×C47—21no—
476C2×C4×C47—22no—
477C2×C4×C47—21no—
478C2×C4×C47—21no—
479C2×C4×C47—22no—
480C2×C4×C47—84no—
481C2×C4×C47C23×C414yes—
482C2×C4×C47C23×C412yes—
483C2×C4×C47C23×C412yes—
484C2×C4×C47C22×D412yes—
485C2×C4×C47C22×D412yes—
486C2×C4×C47C22×D412yes—
487C2×C4×C47C2×#4112yes—
488C22⋊D47—216no—
489C22⋊D47—216no—
490C2×Dic47—21no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—21no—
494C2×Dic47—22no—
495C2×Dic47—21no—
496C2×Dic47—21no—
497C2×Dic47—22no—
498C2×Dic47—21no—
499C2×Dic47—21no—
500C2×Dic47—28no—
501C2×Dic47—216no—
502C2×Dic47—21no—
503C2×Dic47—21no—
504C2×Dic47—22no—
505C2×Dic47—22no—
506C2×Dic47—22no—
507C2×Dic47—21no—
508C2×Dic47—22no—
509C2×Dic47—21no—
510C2×Dic47—22no—
511C2×Dic47—21no—
512C2×Dic47—22no—
513C2×Dic47—21no—
514C2×Dic47—84no—
515C2×Dic47C23×C414yes—
516C2×Dic47C23×C414yes—
517C2×Dic47C23×C412yes—
518C2×Dic47C23×C412yes—
519C2×Dic47C22×D412yes—
520C2×Dic47C22×D412yes—
521C2×Dic47C22×D412yes—
522C2×Dic47C2×#4112yes—
523C4×D47—28no—
524C4×D47—28no—
525C4×D47—28no—
526C4×D47—44no—
527C4×D47—44no—
528C4×D47—44no—
529C4×D47—44no—
530C4×D47—84no—
531C4×D47—84no—
532C4×D47C4×D4116yescomplemented
533Dic94—28no—
534#34202—471nomaximal, Sylow
535C22×C47—24no—
536C22×C47—22no—
537C22×C47—24no—
538C22×C47—22no—
539C22×C47—22no—
540C22×C47—24no—
541C22×C47—42no—
542C22×C47—41no—
543C22×C47—41no—
544C22×C47—42no—
545C22×C47—41no—
546C22×C47—42no—
547C22×C47—41no—
548C22×C47—42no—
549C22×C47C24×C411yescharacteristic
550C22×C47C23×D411yescharacteristic
551C22×C47C22×#4111yescharacteristic
552C22×C47C2×H(5,𝔽2)11yescharacteristic
553C22×C47C2×2−1+411yescharacteristic
554C22×C47#58511yescharacteristic
555C22×C47#58511yescharacteristic
556C2×D47—22no—
557C2×D47—22no—
558C2×D47—22no—
559C2×D47—22no—
560C2×D47—22no—
561C2×D47—22no—
562C2×D47—22no—
563C2×D47—22no—
564C2×D47—22no—
565C2×D47—22no—
566C2×D47—22no—
567C2×D47—22no—
568C2×D47—416no—
569C2×D47C2×C4×D414yes—
570C2×D47#52014yescomplemented
571C4×C47—22no—
572C4×C47—24no—
573C4×C47—22no—
574C4×C47—22no—
575C4×C47—41no—
576C4×C47—42no—
577C4×C47—41no—
578C4×C47—42no—
579C4×C47C2×C4×D414yes—
580Dic47—24no—
581Dic47—22no—
582Dic47—24no—
583Dic47—22no—
584Dic47—22no—
585Dic47—41no—
586Dic47—42no—
587Dic47—41no—
588Dic47—42no—
589Dic47C2×C4×D414yes—
590C2×#525—471no—
591C2×#520—471no—
592C22×#117—471no—
593#2359—472no—
594#2359—472no—
595#2358—472no—
596#2358—472no—
597#2354—472no—
598#2352—472no—
599#2352—472no—
600D4×C4⋊C4—472no—
601#2324—471no—
602#2324D4711yescharacteristic, complemented
603#2323—471no—
604#2323—471no—
605#2317—471no—
606#2311—471no—
607C4×C22⋊Q8—471no—
608C4×C22⋊Q8—471no—
609C4×#121—471no—
610C4×#121—471no—
611C2×#380—471no—
612#2274—471no—
613C2×C47—42no—
614C2×C47—44no—
615C2×C47C22×C4×D411yescharacteristic
616C2×C47C2×#52011yescharacteristic
617C2×C47#342811yescharacteristic
618C2×C47#348811yescharacteristic
619C2×C47#348911yescharacteristic
620C2×C47#349411yescharacteristic
621C2×C47#349511yescharacteristic
622D47—24no—
623D47—24no—
624C22×#41—471no—
625C24×C4—471no—
626#525—4716no—
627C2×#123—472no—
628C2×C22⋊Q8—471no—
629C2×C22⋊Q8—471no—
630C2×#121—471no—
631C2×#121C2×D4711yescharacteristic
632C2×#120—472no—
633#520—948no—
634C2×C4×Q8—471no—
635C2×C4×Q8—471no—
636C2×C4×D4—472no—
637C2×C4×D4—471no—
638C2×C4×D4—472no—
639C2×C4×D4—472no—
640C2×C4×D4—472no—
641C2×C4×D4—472no—
642C2×C4×D4—472no—
643C2×C4×D4C2×D4711yescharacteristic, complemented
644C2×#117—471no—
645C2×#117—471no—
646C2×#117—471no—
647C2×#117—471no—
648C2×#117—471no—
649C2×#117—472no—
650C2×#117—471no—
651C2×#117—471no—
652C2×#117—471no—
653C2×#117—948no—
654C2×#117C2×D4711yescharacteristic
655C22×C4⋊C4—472no—
656C22×C4⋊C4—471no—
657C22×C4⋊C4—471no—
658C22×C4⋊C4—471no—
659C22×C4⋊C4—471no—
660C22×C22⋊C4—471no—
661C22×C22⋊C4—471no—
662C22×C22⋊C4—472no—
663C22×C42—471no—
664C22×C42—471no—
665#391—471no—
666#391—471no—
667#390—471no—
668#390—472no—
669#390C2×D4712yes—
670#390C2×D4711yescharacteristic, complemented
671#389—471no—
672#389—471no—
673#389—472no—
674#389—471no—
675#389—472no—
676#389C2×D4711yescharacteristic, complemented
677#388—472no—
678#388—472no—
679#388—472no—
680#388—472no—
681#388—472no—
682#388—472no—
683#388—472no—
684#388C2×D4712yescomplemented
685#387—472no—
686#387—472no—
687#387—472no—
688#387—472no—
689#386—472no—
690#386—472no—
691#386—472no—
692#386—472no—
693#386—472no—
694#386C2×D4712yes—
695#385—472no—
696#385—472no—
697#385—472no—
698#385—472no—
699#385—472no—
700#385C2×D4712yescomplemented
701#384—472no—
702#382—472no—
703#380—471no—
704#380—471no—
705#380—471no—
706#380—472no—
707#380—472no—
708#380—472no—
709#380—472no—
710#380C2×D4711yescharacteristic
711C4×C4⋊C4—471no—
712C4×C4⋊C4—471no—
713C4×C4⋊C4—472no—
714C4×C4⋊C4—471no—
715C4×C4⋊C4—472no—
716C4×C4⋊C4—472no—
717C4×C4⋊C4—472no—
718C4×C4⋊C4C2×D4711yescharacteristic, complemented
719C4×C22⋊C4—472no—
720C4×C22⋊C4—472no—
721C4×C22⋊C4—472no—
722C4×C22⋊C4—472no—
723C4×C22⋊C4—472no—
724C4×C22⋊C4—472no—
725C2×#95—472no—
726C47#3420211yescharacteristic, complemented, Sylow
727C25—471no—
728C2×#41—478no—
729C2×#41—944no—
730C2×#41—944no—
731C22×Q8—471no—
732C22×D4—472no—
733C22×D4—472no—
734C22×D4C22×D4711yescharacteristic
735C22×D4C22×D4712yes—
736C23×C4—471no—
737C23×C4—472no—
738C23×C4—471no—
739C23×C4—478no—
740C23×C4—471no—
741C23×C4—471no—
742C23×C4—471no—
743C23×C4—472no—
744C23×C4—471no—
745C23×C4—471no—
746C23×C4—471no—
747C23×C4—471no—
748C23×C4—472no—
749C23×C4—472no—
750C23×C4—944no—
751C23×C4—944no—
752C23×C4C22×D4711yescharacteristic
753C23×C4C22×D4712yes—
754#123—4716no—
755C22⋊Q8—478no—
756C22⋊Q8—478no—
757#121—478no—
758#121C4×D4718yescomplemented
759#120—4716no—
760C4×Q8—944no—
761C4×Q8—944no—
762C4×D4—24no—
763C4×D4—4716no—
764C4×D4—4716no—
765C4×D4—944no—
766C4×D4—948no—
767C4×D4—948no—
768C4×D4—1884no—
769C4×D4—1884no—
770#117—24no—
771#117—478no—
772#117—478no—
773#117—944no—
774#117—944no—
775#117—944no—
776#117—944no—
777#117—948no—
778#117—944no—
779#117—944no—
780C2×C4⋊C4—471no—
781C2×C4⋊C4—471no—
782C2×C4⋊C4—471no—
783C2×C4⋊C4—472no—
784C2×C4⋊C4—472no—
785C2×C4⋊C4—472no—
786C2×C4⋊C4—471no—
787C2×C4⋊C4—471no—
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—471no—
795C2×C4⋊C4—472no—
796C2×C4⋊C4—472no—
797C2×C4⋊C4—472no—
798C2×C4⋊C4—944no—
799C2×C4⋊C4—944no—
800C2×C4⋊C4—944no—
801C2×C4⋊C4—944no—
802C2×C4⋊C4—948no—
803C2×C4⋊C4C22×D4711yescharacteristic
804C2×C4⋊C4C22×D4711yescharacteristic
805C2×C4⋊C4C22×D4711yescharacteristic
806C2×C4⋊C4C22×D4711yescharacteristic
807C2×C4⋊C4C22×D4712yes—
808C2×C4⋊C4C22×D4711yescharacteristic
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—471no—
816C2×C22⋊C4—471no—
817C2×C22⋊C4—472no—
818C2×C22⋊C4—471no—
819C2×C22⋊C4—471no—
820C2×C22⋊C4—472no—
821C2×C22⋊C4—472no—
822C2×C22⋊C4—472no—
823C2×C22⋊C4—472no—
824C2×C22⋊C4—472no—
825C2×C22⋊C4—944no—
826C2×C22⋊C4—944no—
827C2×C22⋊C4—1884no—
828C2×C22⋊C4C22×D4711yescharacteristic
829C2×C22⋊C4C22×D4711yescharacteristic
830C2×C22⋊C4C22×D4712yes—
831C2×C22⋊C4C22×D4712yes—
832C2×C22⋊C4C22×D4712yes—
833C2×C22⋊C4C22×D4712yes—
834C2×C22⋊C4C22×D4712yes—
835C2×C42—471no—
836C2×C42—472no—
837C2×C42—471no—
838C2×C42—471no—
839C2×C42—471no—
840C2×C42—471no—
841C2×C42—471no—
842C2×C42—472no—
843C2×C42—472no—
844C2×C42—472no—
845C2×C42—472no—
846C2×C42—472no—
847C2×C42—944no—
848C2×C42—944no—
849C2×C42C22×D4711yescharacteristic
850C2×C42C22×D4712yes—
851C2×C42C22×D4711yescharacteristic
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#95—472no—
862#95—472no—
863#95—472no—
864#95—472no—
865#95C22×D4712yes—
866#95C22×D4712yes—
867#95C22×D4712yes—
868C24—471no—
869C24—471no—
870C24—474no—
871C24—942no—
872C24—942no—
873C24—942no—
874C24—942no—
875C24—1881no—
876C24—1881no—
877C24C23×D4711yescharacteristic
878C24C23×D4712yes—
879#41—9432no—
880C2×Q8—474no—
881C2×Q8—942no—
882C2×Q8—942no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—478no—
888C2×D4—478no—
889C2×D4—944no—
890C2×D4—944no—
891C2×D4—944no—
892C2×D4—944no—
893C2×D4C2×C4×D4714yes—
894C2×D4C2×C4×D4718yes—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—24no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—471no—
901C22×C4—474no—
902C22×C4—474no—
903C22×C4—474no—
904C22×C4—474no—
905C22×C4—478no—
906C22×C4—471no—
907C22×C4—472no—
908C22×C4—472no—
909C22×C4—471no—
910C22×C4—471no—
911C22×C4—474no—
912C22×C4—474no—
913C22×C4—474no—
914C22×C4—471no—
915C22×C4—472no—
916C22×C4—472no—
917C22×C4—471no—
918C22×C4—942no—
919C22×C4—942no—
920C22×C4—9432no—
921C22×C4—942no—
922C22×C4—942no—
923C22×C4—942no—
924C22×C4—942no—
925C22×C4—944no—
926C22×C4—944no—
927C22×C4—942no—
928C22×C4—942no—
929C22×C4—942no—
930C22×C4—942no—
931C22×C4—944no—
932C22×C4—942no—
933C22×C4—942no—
934C22×C4—944no—
935C22×C4—944no—
936C22×C4—942no—
937C22×C4—942no—
938C22×C4—942no—
939C22×C4—942no—
940C22×C4—1882no—
941C22×C4—1882no—
942C22×C4—1882no—
943C22×C4—1882no—
944C22×C4—1881no—
945C22×C4—1881no—
946C22×C4—1881no—
947C22×C4—1881no—
948C22×C4—1882no—
949C22×C4—1882no—
950C22×C4C2×C4×D4714yes—
951C22×C4C23×D4711yescharacteristic
952C22×C4C23×D4712yes—
953C22×C4C23×D4712yes—
954C22×C4C23×D4711yescharacteristic
955C22×C4C23×D4712yes—
956C22×C4C23×D4711yescharacteristic
957C22×C4C23×D4711yescharacteristic
958C22×C4C23×D4711yescharacteristic
959C22×C4C23×D4711yescharacteristic
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—42no—
965C4⋊C4—478no—
966C4⋊C4—474no—
967C4⋊C4—478no—
968C4⋊C4—474no—
969C4⋊C4—474no—
970C4⋊C4—944no—
971C4⋊C4—944no—
972C4⋊C4—942no—
973C4⋊C4—942no—
974C4⋊C4—944no—
975C4⋊C4—942no—
976C4⋊C4—942no—
977C4⋊C4—944no—
978C4⋊C4—942no—
979C4⋊C4—942no—
980C4⋊C4—1882no—
981C4⋊C4—1882no—
982C4⋊C4—1882no—
983C4⋊C4C2×C4×D4714yes—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—24no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—478no—
991C22⋊C4—478no—
992C22⋊C4—478no—
993C22⋊C4—478no—
994C22⋊C4—474no—
995C22⋊C4—474no—
996C22⋊C4—942no—
997C22⋊C4—942no—
998C22⋊C4—944no—
999C22⋊C4—944no—
1000C22⋊C4—942no—
1001C22⋊C4—942no—
1002C22⋊C4—944no—
1003C22⋊C4—1882no—
1004C22⋊C4—1882no—
1005C22⋊C4—1882no—
1006C22⋊C4C2×C4×D4718yes—
1007C42—22no—
1008C42—42no—
1009C42—478no—
1010C42—474no—
1011C42—942no—
1012C42—942no—
1013C42—944no—
1014C42—942no—
1015C42—942no—
1016C42—942no—
1017C42—944no—
1018C42—1882no—
1019C42—1882no—
1020C42—1882no—
1021C42D4×D4714yes—
1022C23—21no—
1023C23—22no—
1024C23—21no—
1025C23—22no—
1026C23—21no—
1027C23—22no—
1028C23—22no—
1029C23—21no—
1030C23—22no—
1031C23—22no—
1032C23—21no—
1033C23—21no—
1034C23—472no—
1035C23—472no—
1036C23—472no—
1037C23—472no—
1038C23—472no—
1039C23—472no—
1040C23—948no—
1041C23—948no—
1042C23—941no—
1043C23—941no—
1044C23—941no—
1045C23—941no—
1046C23—941no—
1047C23—941no—
1048C23—941no—
1049C23—941no—
1050C23—1884no—
1051C23—1884no—
1052C23—1884no—
1053C23—1884no—
1054C23—1884no—
1055C23C22×C4×D4712yes—
1056C23C22×C4×D4714yes—
1057C23C24×D4711yescharacteristic
1058Q8—948no—
1059D4—28no—
1060D4—48no—
1061D4—9416no—
1062D4—9416no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—28no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—84no—
1085C2×C4—472no—
1086C2×C4—472no—
1087C2×C4—472no—
1088C2×C4—4716no—
1089C2×C4—474no—
1090C2×C4—472no—
1091C2×C4—474no—
1092C2×C4—472no—
1093C2×C4—472no—
1094C2×C4—948no—
1095C2×C4—948no—
1096C2×C4—948no—
1097C2×C4—9416no—
1098C2×C4—941no—
1099C2×C4—942no—
1100C2×C4—941no—
1101C2×C4—942no—
1102C2×C4—942no—
1103C2×C4—941no—
1104C2×C4—941no—
1105C2×C4—942no—
1106C2×C4—941no—
1107C2×C4—941no—
1108C2×C4—948no—
1109C2×C4—941no—
1110C2×C4—941no—
1111C2×C4—942no—
1112C2×C4—942no—
1113C2×C4—942no—
1114C2×C4—942no—
1115C2×C4—941no—
1116C2×C4—941no—
1117C2×C4—942no—
1118C2×C4—941no—
1119C2×C4—941no—
1120C2×C4—942no—
1121C2×C4—3764no—
1122C2×C4—3764no—
1123C2×C4—3764no—
1124C2×C4—1884no—
1125C2×C4—1884no—
1126C2×C4—1884no—
1127C2×C4—1884no—
1128C2×C4C22×C4×D4714yes—
1129C2×C4C22×C4×D4712yes—
1130C2×C4C22×C4×D4712yes—
1131C2×C4C2×D4×D4712yes—
1132C2×C4C2×D4×D4712yes—
1133C2×C4C2×D4×D4712yes—
1134C2×C4#41×D4712yes—
1135C22—22no—
1136C22—24no—
1137C22—24no—
1138C22—22no—
1139C22—22no—
1140C22—24no—
1141C22—42no—
1142C22—41no—
1143C22—41no—
1144C22—42no—
1145C22—41no—
1146C22—42no—
1147C22—41no—
1148C22—42no—
1149C22—474no—
1150C22—474no—
1151C22—942no—
1152C22—942no—
1153C22—942no—
1154C22—942no—
1155C22—942no—
1156C22—942no—
1157C22—942no—
1158C22—942no—
1159C22—942no—
1160C22—942no—
1161C22—942no—
1162C22—942no—
1163C22—18816no—
1164C22C23×C4×D4711yescharacteristic
1165C22C22×D4×D4711yescharacteristic
1166C22C2×#41×D4711yescharacteristic
1167C22H(5,𝔽2)×D4711yescharacteristic
1168C222−1+4×D4711yescharacteristic
1169C22#1568995811yescharacteristic
1170C22#1568995811yescharacteristic
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—24no—
1175C4—42no—
1176C4—41no—
1177C4—41no—
1178C4—42no—
1179C4—474no—
1180C4—942no—
1181C4—942no—
1182C4—942no—
1183C4—944no—
1184C4—944no—
1185C4—1882no—
1186C4—1881no—
1187C4—1881no—
1188C4—1882no—
1189C4C4×D4×D4714yes—
1190C2—42no—
1191C2—44no—
1192C2—944no—
1193C2—944no—
1194C2C2×C4×D4×D4711yescharacteristic
1195C2#520×D4711yescharacteristic
1196C2#2025658611yescharacteristic
1197C2#2025705511yescharacteristic
1198C2#2025706311yescharacteristic
1199C2#2025711511yescharacteristic
1200C2#2025713811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2324C2
socle, cosocleC23×C47C25
prime radicalC2×#15689633C2
hypercenter#2324D47
hypocenterC47#34202
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×#15689602C2semidirect
3. C2×#117×D47C2semidirect
4. #20246383C2semidirect
5. #20246379C2semidirect
6. #20246371C2semidirect
7. #20246369C2semidirect
8. #20246336C2semidirect
9. #20246316C2semidirect
10. #20246315C2semidirect
11. #20246286C2semidirect
12. #20246083C2semidirect
13. #20246070C2semidirect
14. #20246066C2semidirect
15. #20246010C2semidirect
16. #20245978C2semidirect
17. C4×#13094004C2semidirect
18. #20245918C2semidirect
19. #20245904C2semidirect
20. C4×#13093995C2semidirect
21. #380×D47C2semidirect
22. #20245742C2semidirect
23. C47×#2324C2semidirect
26. #15689633C4semidirect
33. C2×C4×Dic94C22semidirect
34. C2×#13093989C22semidirect
36. C2×D4×Dic47C22semidirect
50. C2×#13093980C22semidirect
52. C22×Dic47⋊C4C22semidirect
62. #15689029C22semidirect
63. #15689028C22semidirect
65. #15689026C22semidirect
66. #15689022C22semidirect
67. #15689021C22semidirect
68. #15689020C22semidirect
69. #15689019C22semidirect
70. #15689018C22semidirect
73. #15689017C22semidirect
74. #15689016C22semidirect
77. #15689011C22semidirect
78. #15689010C22semidirect
79. #15689008C22semidirect
80. #15689006C22semidirect
81. #15689004C22semidirect
87. #15688998C22semidirect
92. #15688992C22semidirect
93. #15688987C22semidirect
97. #15688981C22semidirect
98. #15688981C22semidirect
101. C4⋊C4×Dic47C22semidirect
102. C4⋊C4×Dic47C22semidirect
103. C4⋊C4×Dic47C22semidirect
104. C4×Dic47⋊C4C22semidirect
105. C4×C4⋊Dic47C22semidirect
106. C4×C4⋊Dic47C22semidirect
107. #15688974C22semidirect
108. C22⋊C4×Dic47C22semidirect
111. C4×C22⋊Dic47C22semidirect
116. C2×C4×D4×C47C22semidirect
119. C47×#390C22semidirect
120. C47×#389C22semidirect
121. C47×#388C22semidirect
123. C47×#385C22semidirect
125. C4×C4⋊C4×C47C22semidirect
129. C2×#10625352C2×C4semidirect
138. C22×C4×D47C2×C4semidirect
149. #13094006C2×C4semidirect
150. #13094004C2×C4semidirect
151. #13094003C2×C4semidirect
152. #13093995C2×C4semidirect
153. #13093992C2×C4semidirect
157. D4×Dic47C2×C4semidirect
162. (C22⋊D47)⋊C4C2×C4semidirect
166. #13093982C2×C4semidirect
168. #13093981D4semidirect
245. #121×C47C2×C4semidirect
532. C4×D47C4×D4semidirect
570. C2×D47#520semidirect
602. #2324D47semidirect
643. C2×C4×D4C2×D47semidirect
670. #390C2×D47semidirect
676. #389C2×D47semidirect
684. #388C2×D47semidirect
700. #385C2×D47semidirect
718. C4×C4⋊C4C2×D47semidirect
726. C47#34202semidirect
758. #121C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896332
C2×#156896022
C2×#117×D472
#202463832
#202463792
#202463712
#202463692
#202463362
#202463162
#202463152
#202462862
#202460832
#202460702
#202460662
#202460102
#202459782
C4×#130940042
#202459182
#202459042
C4×#130939952
#380×D472
#202457422
C47×#23242
#3420247