Finite Group Databasebeta

← #26376626

Subgroups — #26376626

Order 12032.

3642 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D47C211yesmaximal, characteristic
2C2×#15689595C212yesmaximal, complemented
3#20246437C212yesmaximal, complemented
4#20246434C212yesmaximal, complemented
5#20246407C212yesmaximal, complemented
6#20246401C212yesmaximal, complemented
7#20246254C212yesmaximal, complemented
8#20246235C212yesmaximal, complemented
9#20246232C212yesmaximal, complemented
10#20246206C212yesmaximal, complemented
11#20246093C211yesmaximal, characteristic, complemented
12#20246091C211yesmaximal, characteristic, complemented
13#20246088C211yesmaximal, characteristic, complemented
14#20245962C212yesmaximal, complemented
15#20245898C212yesmaximal, complemented
16C4×#13093996C212yesmaximal, complemented
17#380×D47C211yesmaximal, characteristic, complemented
18C2×#15688970C211yesmaximal, characteristic, complemented
19C47×#2325C211yesmaximal, characteristic, complemented
20C22×D4×D47C2212yes—
21C22×D4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13093999C2211yescharacteristic
24C2×#13093998C2211yescharacteristic
25C2×#13093997C2212yes—
26C2×#13093996C2212yes—
27C2×#13093995C2211yescharacteristic
28#121×D47C4116yescomplemented
29#15689595—216no—
30C2×C4×D188C2212yescomplemented
31C2×D4×Dic47C2212yescomplemented
32C2×#13093986C2212yescomplemented
33C2×C4×C22⋊D47C2212yescomplemented
34C2×C4×C22⋊D47C2212yescomplemented
35C2×C4×C22⋊D47C2212yescomplemented
36C2×(C22⋊D47)⋊C4C2212yescomplemented
37C2×(C22⋊D47)⋊C4C2212yescomplemented
38C2×(C22⋊D47)⋊C4C2212yescomplemented
39C2×#13093982C2212yes—
40C2×#13093981C2212yes—
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic, complemented
43C2×C4⋊C4×D47C2211yescharacteristic, complemented
44C22×(C2×D47)⋊C4C2212yes—
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C2×C22⋊C4×D47C2212yes—
48C2×C22⋊C4×D47C2212yes—
49C2×C22⋊C4×D47C2212yes—
50C22×C4×Dic47C2211yescharacteristic, complemented
51C22×C4×Dic47C2211yescharacteristic, complemented
52#15689023C2212yescomplemented
53#15689023C2212yescomplemented
54#15689020C2212yescomplemented
55#15689018C2212yescomplemented
56#15689017C2212yescomplemented
57#15689016C2212yescomplemented
58#15689015C2212yescomplemented
59#15689015C2212yescomplemented
60#15689013C2212yescomplemented
61#15689013C2212yescomplemented
62#15689011C2212yescomplemented
63#15689009C2212yescomplemented
64#15689008C2212yescomplemented
65#15689006C2212yescomplemented
66#15689003C2212yescomplemented
67#15689003C2212yescomplemented
68#15689002C2212yescomplemented
69#15689001C2212yescomplemented
70#15689001C2212yescomplemented
71#15689001C2212yescomplemented
72#15689001C2212yescomplemented
73#15689000C2212yescomplemented
74#15688999C2212yescomplemented
75#15688999C2212yescomplemented
76#15688998C2212yescomplemented
77#15688997C2212yescomplemented
78#15688994C2212yescomplemented
79#15688985C2212yes—
80#15688985C2212yes—
81#15688983C2211yescharacteristic, complemented
82#15688982C2212yes—
83#15688981C2212yescomplemented
84#15688980C2211yescharacteristic
85#15688980C2211yescharacteristic
86#15688978C2212yes—
87#15688978C2212yes—
88C4×Dic47⋊C4C2212yescomplemented
89#15688974C2212yescomplemented
90C22⋊C4×Dic47C2212yescomplemented
91C4×(C2×D47)⋊C4C2212yescomplemented
92C4×C22⋊Dic47C2212yescomplemented
93#15688970C2212yes—
94#15688970C2212yes—
95#15688970C2212yescomplemented
96#15688970C2212yescomplemented
97#15688970C2212yescomplemented
98C2×C47⋊#95C2211yescharacteristic, complemented
99#95×D47C2212yescomplemented
100C2×#121×C47C2211yescharacteristic
101C2×C4×D4×C47C2212yescomplemented
102C47×#388C2212yescomplemented
103C47×#387C2212yescomplemented
104C47×#386C2212yescomplemented
105C47×#386C2212yescomplemented
106C47×#385C2212yescomplemented
107C47×#380C2211yescharacteristic, complemented
108C2×#95×C47C2211yescharacteristic, complemented
109C24×D47C2312yes—
110C24×D47C2311yescharacteristic
111C22×D188C2312yes—
112C22×D188C2311yescharacteristic
113C22×C22⋊D47C2312yes—
114C22×C22⋊D47C2312yes—
115C22×C22⋊D47C2312yes—
116C2×D4×D47—28no—
117C2×D4×D47—28no—
118C2×D4×D47—42no—
119C2×D4×D47—42no—
120C2×D4×D47C2×C4116yescomplemented
121C2×D4×D47C2×C418yescomplemented
122C23×Dic47C2311yescharacteristic
123C23×Dic47C2311yescharacteristic
124C23×Dic47C2312yes—
125C23×Dic47C2311yescharacteristic
126C22×C4×D47—42no—
127C22×C4×D47—42no—
128C22×C4×D47C2×C418yescomplemented
129C22×C4×D47C2311yescharacteristic
130C22×C4×D47C2311yescharacteristic
131C22×C4×D47C2312yes—
132C22×C4×D47C2312yes—
133C22×C4×D47C2312yes—
134C22×C4×D47C2312yes—
135C22×C4×D47C2312yes—
136C22×C4×D47C2311yescharacteristic
137C22×C4×D47C2311yescharacteristic
138#13093999C2×C418yescomplemented
139#13093998C2×C418yescomplemented
140#13093997C2×C4116yescomplemented
141#13093996C2×C4116yescomplemented
142#13093995C2×C418yescomplemented
143C4×D188—28no—
144D4×Dic47—28no—
145#13093986—28no—
146C4×C22⋊D47—28no—
147C4×C22⋊D47—28no—
148C4×C22⋊D47—44no—
149(C22⋊D47)⋊C4—28no—
150(C22⋊D47)⋊C4—28no—
151(C22⋊D47)⋊C4—44no—
152#13093982—28no—
153#13093981—28no—
154C2×C4⋊Dic47C2312yes—
155C2×C4⋊Dic47C2311yescharacteristic
156C2×C4⋊Dic47C2311yescharacteristic
157C2×C4⋊Dic47C2311yescharacteristic
158C2×Dic47⋊C4C2312yes—
159C2×Dic47⋊C4C2312yes—
160C2×Dic47⋊C4C2312yes—
161C2×Dic47⋊C4C2312yes—
162C2×Dic47⋊C4C2312yes—
163C4⋊C4×D47—42no—
164C4⋊C4×D47—42no—
165C4⋊C4×D47C2×C418yescomplemented
166C2×C22⋊Dic47C2312yes—
167C2×C22⋊Dic47C2312yes—
168C2×C22⋊Dic47C2312yes—
169C2×C22⋊Dic47C2312yes—
170C2×C22⋊Dic47C2312yes—
171C2×(C2×D47)⋊C4—24no—
172C2×(C2×D47)⋊C4—28no—
173C2×(C2×D47)⋊C4D418yescomplemented
174C2×(C2×D47)⋊C4C2312yes—
175C2×(C2×D47)⋊C4C2312yes—
176C2×(C2×D47)⋊C4C2312yes—
177C2×(C2×D47)⋊C4C2312yes—
178C2×(C2×D47)⋊C4C2312yes—
179C2×(C2×D47)⋊C4C2312yes—
180C2×(C2×D47)⋊C4C2312yes—
181C2×(C2×D47)⋊C4C2312yes—
182C2×(C2×D47)⋊C4C2312yes—
183C2×(C2×D47)⋊C4C2312yes—
184C2×(C2×D47)⋊C4C2312yes—
185C2×(C2×D47)⋊C4C2312yes—
186C2×(C2×D47)⋊C4C2312yes—
187C2×(C2×D47)⋊C4C2312yes—
188C22⋊C4×D47—28no—
189C22⋊C4×D47—28no—
190C22⋊C4×D47C2×C4116yescomplemented
191C2×C4×Dic47—42no—
192C2×C4×Dic47—42no—
193C2×C4×Dic47C2312yes—
194C2×C4×Dic47C2312yes—
195C2×C4×Dic47C2312yes—
196C2×C4×Dic47C2312yes—
197C2×C4×Dic47C2312yes—
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2312yes—
200C47⋊#95C2312yes—
201C47⋊#95C2312yes—
202C47⋊#95C2312yes—
203C47⋊#95C2312yes—
204C47⋊#95C2312yes—
205C47⋊#95C2312yes—
206C47⋊#95C2312yes—
207C47⋊#95C2312yes—
208C47⋊#95C2312yes—
209C47⋊#95C2312yes—
210C47⋊#95C2312yes—
211C22×D4×C47C2312yes—
212C22×D4×C47C2311yescharacteristic
213C23×C4×C47C2312yes—
214C23×C4×C47C2311yescharacteristic
215C23×C4×C47C2311yescharacteristic
216C23×C4×C47C2311yescharacteristic
217#121×C47C2×C418yescomplemented
218C4×D4×C47—28no—
219C2×C4⋊C4×C47C2312yes—
220C2×C4⋊C4×C47C2311yescharacteristic
221C2×C4⋊C4×C47C2311yescharacteristic
222C2×C4⋊C4×C47C2311yescharacteristic
223C2×C22⋊C4×C47C2312yes—
224C2×C22⋊C4×C47C2312yes—
225C2×C22⋊C4×C47C2312yes—
226C2×C22⋊C4×C47C2312yes—
227C2×C22⋊C4×C47C2312yes—
228C2×C42×C47C2312yes—
229#95×C47C2312yes—
230#95×C47C2312yes—
231#95×C47C2312yes—
232#95×C47C2312yes—
233#95×C47C2312yes—
234C24×C47C2412yes—
235C24×C47C2411yescharacteristic
236C23×D47—24no—
237C23×D47—24no—
238C23×D47—41no—
239C23×D47—41no—
240C23×D47—41no—
241C23×D47—41no—
242C23×D47—42no—
243C23×D47—42no—
244C23×D47—42no—
245C23×D47—42no—
246C23×D47C22×C418yes—
247C23×D47C22×C414yes—
248C23×D47C2×D414yes—
249C23×D47#4114yes—
250C23×D47C2412yes—
251C23×D47C2411yescharacteristic
252C23×D47C2411yescharacteristic
253C2×D4×C47—24no—
254C2×D4×C47—24no—
255C2×D4×C47—41no—
256C2×D4×C47—41no—
257C2×D4×C47C22×C418yes—
258C2×D4×C47C22×C414yes—
259C22×C4×C47—22no—
260C22×C4×C47—24no—
261C22×C4×C47—41no—
262C22×C4×C47—41no—
263C22×C4×C47—41no—
264C22×C4×C47—41no—
265C22×C4×C47—41no—
266C22×C4×C47—41no—
267C22×C4×C47—42no—
268C22×C4×C47—42no—
269C22×C4×C47C22×C414yes—
270C22×C4×C47C2×D414yescomplemented
271C22×C4×C47C2412yes—
272C22×C4×C47C2412yes—
273C22×C4×C47C2412yes—
274C22×C4×C47C2412yes—
275C22×C4×C47C2411yescharacteristic
276C22×C4×C47C2411yescharacteristic
277C22×C4×C47C2412yes—
278C2×C22⋊D47—24no—
279C2×C22⋊D47—24no—
280C2×C22⋊D47—24no—
281C2×C22⋊D47—24no—
282C2×C22⋊D47—24no—
283C2×C22⋊D47—24no—
284C2×C22⋊D47C22×C418yes—
285C2×C22⋊D47C22×C418yes—
286C2×C22⋊D47C22×C418yes—
287C22×Dic47—22no—
288C22×Dic47—22no—
289C22×Dic47—22no—
290C22×Dic47—24no—
291C22×Dic47—41no—
292C22×Dic47—41no—
293C22×Dic47—41no—
294C22×Dic47—41no—
295C22×Dic47—42no—
296C22×Dic47—42no—
297C22×Dic47C22×C414yes—
298C22×Dic47C2×D414yescomplemented
299C22×Dic47C2412yes—
300C22×Dic47C2412yes—
301C22×Dic47C2412yes—
302C22×Dic47C2411yescharacteristic
303C22×Dic47C2412yes—
304C22×Dic47C2412yes—
305C22×Dic47C2411yescharacteristic
306D4×D47—264no—
307D4×D47—416no—
308C2×D188—24no—
309C2×D188—24no—
310C2×D188—41no—
311C2×D188—41no—
312C2×D188C22×C418yes—
313C2×D188C22×C414yes—
314C2×C4×D47—24no—
315C2×C4×D47—24no—
316C2×C4×D47—22no—
317C2×C4×D47—22no—
318C2×C4×D47—22no—
319C2×C4×D47—22no—
320C2×C4×D47—24no—
321C2×C4×D47—24no—
322C2×C4×D47—24no—
323C2×C4×D47—24no—
324C2×C4×D47—416no—
325C2×C4×D47—41no—
326C2×C4×D47—41no—
327C2×C4×D47—41no—
328C2×C4×D47—41no—
329C2×C4×D47—42no—
330C2×C4×D47—42no—
331C2×C4×D47—42no—
332C2×C4×D47—42no—
333C2×C4×D47—42no—
334C2×C4×D47—42no—
335C2×C4×D47—42no—
336C2×C4×D47—42no—
337C2×C4×D47C22×C418yes—
338C2×C4×D47C22×C414yes—
339C2×C4×D47C22×C414yes—
340C2×C4×D47C22×C414yes—
341C2×C4×D47C22×C414yes—
342C4⋊C4×C47—24no—
343C4⋊C4×C47—41no—
344C4⋊C4×C47—41no—
345C4⋊C4×C47C22×C414yes—
346C22⋊C4×C47—24no—
347C22⋊C4×C47—24no—
348C22⋊C4×C47—42no—
349C22⋊C4×C47—42no—
350C22⋊C4×C47C22×C418yes—
351C42×C47—24no—
352C22⋊Dic47—24no—
353C22⋊Dic47—24no—
354C22⋊Dic47—42no—
355C22⋊Dic47—42no—
356C22⋊Dic47C22×C418yes—
357(C2×D47)⋊C4—24no—
358(C2×D47)⋊C4—24no—
359(C2×D47)⋊C4—24no—
360(C2×D47)⋊C4—24no—
361(C2×D47)⋊C4—24no—
362(C2×D47)⋊C4—24no—
363(C2×D47)⋊C4—42no—
364(C2×D47)⋊C4—42no—
365(C2×D47)⋊C4—42no—
366(C2×D47)⋊C4—42no—
367(C2×D47)⋊C4C22×C418yes—
368(C2×D47)⋊C4C22×C418yes—
369(C2×D47)⋊C4C2×D418yes—
370(C2×D47)⋊C4C2×D418yescomplemented
371C4⋊Dic47—24no—
372C4⋊Dic47—41no—
373C4⋊Dic47—41no—
374C4⋊Dic47C22×C414yes—
375Dic47⋊C4—24no—
376Dic47⋊C4—24no—
377Dic47⋊C4—24no—
378Dic47⋊C4—24no—
379Dic47⋊C4C22×C418yes—
380C4×Dic47—24no—
381C4×Dic47—24no—
382C4×Dic47—24no—
383C4×Dic47—24no—
384C4×Dic47—24no—
385C4×Dic47—42no—
386C4×Dic47—42no—
387C23×C47—21no—
388C23×C47—21no—
389C23×C47—21no—
390C23×C47—21no—
391C23×C47—22no—
392C23×C47—22no—
393C23×C47—22no—
394C23×C47—22no—
395C23×C47—22no—
396C23×C47—22no—
397C23×C47C23×C414yes—
398C23×C47C23×C412yes—
399C23×C47C22×D412yes—
400C23×C47C2×#4112yes—
401C23×C47C2511yescharacteristic
402C22×D47—21no—
403C22×D47—21no—
404C22×D47—21no—
405C22×D47—21no—
406C22×D47—21no—
407C22×D47—21no—
408C22×D47—21no—
409C22×D47—21no—
410C22×D47—22no—
411C22×D47—22no—
412C22×D47—22no—
413C22×D47—22no—
414C22×D47—22no—
415C22×D47—22no—
416C22×D47—216no—
417C22×D47—44no—
418C22×D47—44no—
419C22×D47—44no—
420C22×D47—44no—
421C22×D47—44no—
422C22×D47—44no—
423C22×D47—48no—
424C22×D47—48no—
425C22×D47—84no—
426C22×D47—84no—
427C22×D47—84no—
428C22×D47—84no—
429C22×D47C4×D4116yescomplemented
430C22×D47C23×C414yes—
431C22×D47C23×C412yes—
432C22×D47C23×C412yes—
433C22×D47C22×D412yes—
434C22×D47C22×D412yes—
435C22×D47C2×#4112yes—
436C22×D47C2×#4112yes—
437D4×C47—216no—
438D4×C47—44no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—21no—
443C2×C4×C47—21no—
444C2×C4×C47—21no—
445C2×C4×C47—21no—
446C2×C4×C47—22no—
447C2×C4×C47—22no—
448C2×C4×C47—22no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—44no—
457C2×C4×C47—44no—
458C2×C4×C47—44no—
459C2×C4×C47—84no—
460C2×C4×C47C23×C414yes—
461C2×C4×C47C23×C412yes—
462C2×C4×C47C23×C412yes—
463C2×C4×C47C22×D414yes—
464C22⋊D47—216no—
465C22⋊D47—216no—
466C22⋊D47—216no—
467C2×Dic47—22no—
468C2×Dic47—22no—
469C2×Dic47—22no—
470C2×Dic47—21no—
471C2×Dic47—21no—
472C2×Dic47—22no—
473C2×Dic47—28no—
474C2×Dic47—22no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—22no—
478C2×Dic47—22no—
479C2×Dic47—22no—
480C2×Dic47—22no—
481C2×Dic47—22no—
482C2×Dic47—22no—
483C2×Dic47—44no—
484C2×Dic47—44no—
485C2×Dic47—84no—
486C2×Dic47C23×C414yes—
487C2×Dic47C23×C412yes—
488C2×Dic47C23×C412yes—
489C2×Dic47C22×D414yes—
490C2×Dic47H(5,𝔽2)12yes—
491C2×Dic47H(5,𝔽2)12yes—
492D188—216no—
493D188—44no—
494C4×D47—216no—
495C4×D47—28no—
496C4×D47—28no—
497C4×D47—44no—
498C4×D47—44no—
499C4×D47—84no—
500C4×D47—84no—
501C4×D47—84no—
502C4×D47—84no—
503#34205—471nomaximal, Sylow
504C22×C47—22no—
505C22×C47—22no—
506C22×C47—22no—
507C22×C47—22no—
508C22×C47—22no—
509C22×C47—22no—
510C22×C47—24no—
511C22×C47—24no—
512C22×C47—24no—
513C22×C47—42no—
514C22×C47—42no—
515C22×C47—42no—
516C22×C47—42no—
517C22×C47C2×C4×D414yes—
518C22×C47C24×C411yescharacteristic
519C22×C47C23×D411yescharacteristic
520C22×C47C22×#4111yescharacteristic
521C22×C47C2×H(5,𝔽2)11yescharacteristic
522C22×C47C2×H(5,𝔽2)11yescharacteristic
523C22×C47#58511yescharacteristic
524C22×C47#58511yescharacteristic
525C2×D47—22no—
526C2×D47—22no—
527C2×D47—22no—
528C2×D47—22no—
529C2×D47—22no—
530C2×D47—22no—
531C2×D47—22no—
532C2×D47—22no—
533C2×D47—22no—
534C2×D47—22no—
535C2×D47—22no—
536C2×D47—22no—
537C2×D47—24no—
538C2×D47—24no—
539C2×D47—24no—
540C2×D47—416no—
541C2×D47—42no—
542C2×D47—42no—
543C2×D47—42no—
544C2×D47—42no—
545C2×D47—816no—
546C2×D47C2×C4×D414yes—
547C2×D47C2×C4×D414yes—
548C4×C47—24no—
549C4×C47—22no—
550C4×C47—22no—
551C4×C47—24no—
552C4×C47—42no—
553C4×C47—42no—
554C4×C47—42no—
555Dic47—24no—
556Dic47—22no—
557Dic47—24no—
558Dic47—42no—
559Dic47—42no—
560Dic47—42no—
561Dic47#51814yescomplemented
562C22×#121—471no—
563C2×#518—472no—
564#2364—472no—
565#2364—472no—
566#2361—472no—
567#2361—472no—
568#2344—472no—
569#2342—472no—
570#2342—472no—
571D4×C22⋊C4—472no—
572#2325—471no—
573#2325—471no—
574#2325—471no—
575#2325D4711yescharacteristic, complemented
576#2308—472no—
577C4×#121—472no—
578C4×#121—472no—
579C2×#380—471no—
580C2×C4×C22⋊C4—471no—
581C2×C47—24no—
582C2×C47—44no—
583C2×C47C22×C4×D411yescharacteristic
584C2×C47C2×#51811yescharacteristic
585C2×C47#342811yescharacteristic
586C2×C47#349611yescharacteristic
587C2×C47#349611yescharacteristic
588C2×C47#350511yescharacteristic
589C2×C47#350511yescharacteristic
590D47—24no—
591D47—24no—
592D47—44no—
593C23×D4—472no—
594C23×D4—471no—
595C24×C4—471no—
596C2×#121—471no—
597C2×#121—472no—
598C2×#121—471no—
599C2×#121—4716no—
600C2×#121—471no—
601C2×#121—472no—
602C2×#121C2×D4711yescharacteristic
603#518—9416no—
604C2×C4×D4—472no—
605C2×C4×D4—472no—
606C2×C4×D4—472no—
607C2×C4×D4—472no—
608C2×C4×D4—472no—
609C2×C4×D4—472no—
610C2×C4×D4—472no—
611C2×C4×D4—472no—
612C2×C4×D4—472no—
613C2×C4×D4C2×D4712yescomplemented
614C2×#117—472no—
615C2×#117—472no—
616C22×C4⋊C4—471no—
617C22×C4⋊C4—471no—
618C22×C4⋊C4—471no—
619C22×C22⋊C4—471no—
620C22×C22⋊C4—472no—
621C22×C22⋊C4—471no—
622C22×C22⋊C4—472no—
623C22×C22⋊C4—472no—
624C22×C22⋊C4—472no—
625C22×C42—471no—
626C22×C42—471no—
627#390—472no—
628#390—472no—
629#389—472no—
630#389—472no—
631#388—472no—
632#388—472no—
633#388—472no—
634#388—472no—
635#388—472no—
636#388—472no—
637#388—472no—
638#388C2×D4712yescomplemented
639#387—472no—
640#387—472no—
641#387—472no—
642#387C2×D4712yescomplemented
643#386—472no—
644#386—472no—
645#386—472no—
646#386—472no—
647#386—472no—
648#386—472no—
649#386—472no—
650#386—472no—
651#386—472no—
652#386—472no—
653#386C2×D4712yescomplemented
654#386C2×D4712yescomplemented
655#385—472no—
656#385—472no—
657#385—472no—
658#385C2×D4712yescomplemented
659#381—472no—
660#381—472no—
661#380—471no—
662#380—471no—
663#380—471no—
664#380—472no—
665#380—472no—
666#380C2×D4711yescharacteristic, complemented
667#379—472no—
668#379—472no—
669C4×C4⋊C4—472no—
670C4×C4⋊C4—472no—
671C4×C22⋊C4—472no—
672C4×C22⋊C4—472no—
673C4×C22⋊C4—472no—
674C4×C22⋊C4—472no—
675C4×C22⋊C4—472no—
676C4×C22⋊C4—472no—
677C4×C22⋊C4—472no—
678C4×C22⋊C4—472no—
679C2×#95—471no—
680C2×#95—472no—
681C2×#95C2×D4711yescharacteristic, complemented
682C47#3420511yescharacteristic, complemented, Sylow
683C25—471no—
684C25—472no—
685C22×D4—472no—
686C22×D4—472no—
687C22×D4—472no—
688C22×D4—4716no—
689C22×D4—478no—
690C22×D4—472no—
691C22×D4—471no—
692C22×D4—948no—
693C22×D4—948no—
694C22×D4—1882no—
695C22×D4—1882no—
696C22×D4C22×D4712yes—
697C22×D4C22×D4711yescharacteristic
698C23×C4—471no—
699C23×C4—471no—
700C23×C4—472no—
701C23×C4—471no—
702C23×C4—471no—
703C23×C4—478no—
704C23×C4—471no—
705C23×C4—471no—
706C23×C4—472no—
707C23×C4—471no—
708C23×C4—472no—
709C23×C4—472no—
710C23×C4—472no—
711C23×C4—472no—
712C23×C4—1882no—
713C23×C4—1882no—
714C23×C4C22×D4712yes—
715C23×C4C22×D4711yescharacteristic
716C23×C4C22×D4711yescharacteristic
717C23×C4C22×D4711yescharacteristic
718#121—478no—
719#121—4716no—
720#121—478no—
721#121—478no—
722#121—4716no—
723#121C4×D4718yescomplemented
724C4×D4—28no—
725C4×D4—948no—
726C4×D4—948no—
727C4×D4—948no—
728C4×D4—948no—
729C4×D4—948no—
730C4×D4—948no—
731C4×D4—948no—
732C4×D4—1884no—
733C4×D4—1884no—
734#117—948no—
735#117—948no—
736C2×C4⋊C4—472no—
737C2×C4⋊C4—471no—
738C2×C4⋊C4—478no—
739C2×C4⋊C4—472no—
740C2×C4⋊C4—472no—
741C2×C4⋊C4—472no—
742C2×C4⋊C4—472no—
743C2×C4⋊C4—472no—
744C2×C4⋊C4—471no—
745C2×C4⋊C4—471no—
746C2×C4⋊C4—1882no—
747C2×C4⋊C4—1882no—
748C2×C4⋊C4C22×D4712yes—
749C2×C4⋊C4C22×D4711yescharacteristic
750C2×C4⋊C4C22×D4711yescharacteristic
751C2×C4⋊C4C22×D4711yescharacteristic
752C2×C22⋊C4—472no—
753C2×C22⋊C4—478no—
754C2×C22⋊C4—472no—
755C2×C22⋊C4—472no—
756C2×C22⋊C4—472no—
757C2×C22⋊C4—472no—
758C2×C22⋊C4—4716no—
759C2×C22⋊C4—472no—
760C2×C22⋊C4—472no—
761C2×C22⋊C4—472no—
762C2×C22⋊C4—472no—
763C2×C22⋊C4—472no—
764C2×C22⋊C4—472no—
765C2×C22⋊C4—472no—
766C2×C22⋊C4—472no—
767C2×C22⋊C4—472no—
768C2×C22⋊C4—472no—
769C2×C22⋊C4—472no—
770C2×C22⋊C4—472no—
771C2×C22⋊C4—472no—
772C2×C22⋊C4—472no—
773C2×C22⋊C4—948no—
774C2×C22⋊C4—948no—
775C2×C22⋊C4—948no—
776C2×C22⋊C4—944no—
777C2×C22⋊C4C22×D4712yes—
778C2×C22⋊C4C22×D4712yes—
779C2×C22⋊C4C22×D4712yes—
780C2×C22⋊C4C22×D4712yes—
781C2×C22⋊C4C22×D4712yes—
782C2×C42—472no—
783C2×C42—472no—
784C2×C42—472no—
785C2×C42—472no—
786C2×C42—472no—
787C2×C42—472no—
788C2×C42—472no—
789C2×C42—1882no—
790C2×C42—1882no—
791C2×C42C22×D4712yes—
792#95—472no—
793#95—472no—
794#95—472no—
795#95—472no—
796#95—472no—
797#95—472no—
798#95—472no—
799#95—472no—
800#95—472no—
801#95—472no—
802#95—472no—
803#95C22×D4712yes—
804#95C22×D4712yes—
805#95C22×D4712yes—
806#95C22×D4712yes—
807#95C22×D4712yes—
808C24—471no—
809C24—471no—
810C24—474no—
811C24—474no—
812C24—474no—
813C24—472no—
814C24—478no—
815C24—944no—
816C24—944no—
817C24—1882no—
818C24—1882no—
819C24—1882no—
820C24—1882no—
821C24—1881no—
822C24—1881no—
823C24—1881no—
824C24—1881no—
825C24C23×D4712yes—
826C24C23×D4711yescharacteristic
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—478no—
832C2×D4—478no—
833C2×D4—478no—
834C2×D4—478no—
835C2×D4—474no—
836C2×D4—944no—
837C2×D4—944no—
838C2×D4—944no—
839C2×D4—944no—
840C2×D4—9464no—
841C2×D4—944no—
842C2×D4—944no—
843C2×D4—944no—
844C2×D4—944no—
845C2×D4—1881no—
846C2×D4—1881no—
847C2×D4—18816no—
848C2×D4C2×C4×D4718yes—
849C2×D4C2×C4×D4714yes—
850C22×C4—22no—
851C22×C4—24no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—471no—
861C22×C4—474no—
862C22×C4—471no—
863C22×C4—472no—
864C22×C4—472no—
865C22×C4—474no—
866C22×C4—478no—
867C22×C4—474no—
868C22×C4—474no—
869C22×C4—474no—
870C22×C4—474no—
871C22×C4—472no—
872C22×C4—472no—
873C22×C4—472no—
874C22×C4—942no—
875C22×C4—942no—
876C22×C4—942no—
877C22×C4—942no—
878C22×C4—944no—
879C22×C4—944no—
880C22×C4—944no—
881C22×C4—944no—
882C22×C4—944no—
883C22×C4—942no—
884C22×C4—942no—
885C22×C4—944no—
886C22×C4—942no—
887C22×C4—944no—
888C22×C4—1882no—
889C22×C4—1882no—
890C22×C4—1882no—
891C22×C4—1882no—
892C22×C4—1882no—
893C22×C4—1882no—
894C22×C4—1882no—
895C22×C4—1882no—
896C22×C4—1881no—
897C22×C4—1881no—
898C22×C4—1881no—
899C22×C4—1881no—
900C22×C4—18816no—
901C22×C4—1882no—
902C22×C4—1882no—
903C22×C4—1881no—
904C22×C4—1881no—
905C22×C4—1881no—
906C22×C4—1881no—
907C22×C4C2×C4×D4714yes—
908C22×C4D4×D4714yescomplemented
909C22×C4C23×D4712yes—
910C22×C4C23×D4712yes—
911C22×C4C23×D4712yes—
912C22×C4C23×D4711yescharacteristic
913C22×C4C23×D4712yes—
914C22×C4C23×D4711yescharacteristic
915C22×C4C23×D4712yes—
916C4⋊C4—24no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—478no—
920C4⋊C4—474no—
921C4⋊C4—944no—
922C4⋊C4—944no—
923C4⋊C4—944no—
924C4⋊C4—944no—
925C4⋊C4—944no—
926C4⋊C4—1881no—
927C4⋊C4—1881no—
928C4⋊C4C2×C4×D4714yes—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—478no—
934C22⋊C4—478no—
935C22⋊C4—478no—
936C22⋊C4—478no—
937C22⋊C4—478no—
938C22⋊C4—944no—
939C22⋊C4—944no—
940C22⋊C4—944no—
941C22⋊C4—944no—
942C22⋊C4—944no—
943C22⋊C4—944no—
944C22⋊C4—944no—
945C22⋊C4—944no—
946C22⋊C4—1882no—
947C22⋊C4—1882no—
948C22⋊C4—1882no—
949C22⋊C4—1882no—
950C22⋊C4—1882no—
951C22⋊C4—1882no—
952C22⋊C4C2×C4×D4718yes—
953C42—24no—
954C42—944no—
955C42—944no—
956C42—944no—
957C42—944no—
958C42—944no—
959C42—1882no—
960C42—1882no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—472no—
972C23—472no—
973C23—472no—
974C23—472no—
975C23—472no—
976C23—472no—
977C23—4716no—
978C23—474no—
979C23—9416no—
980C23—941no—
981C23—941no—
982C23—941no—
983C23—941no—
984C23—941no—
985C23—941no—
986C23—941no—
987C23—941no—
988C23—942no—
989C23—942no—
990C23—942no—
991C23—942no—
992C23—942no—
993C23—942no—
994C23—3764no—
995C23—3764no—
996C23—3764no—
997C23—3764no—
998C23—1888no—
999C23—1888no—
1000C23—1884no—
1001C23—1884no—
1002C23—1884no—
1003C23—1884no—
1004C23—1884no—
1005C23—1884no—
1006C23C22×C4×D4714yes—
1007C23C22×C4×D4712yes—
1008C23C2×D4×D4712yes—
1009C23#41×D4712yes—
1010C23C24×D4711yescharacteristic
1011D4—216no—
1012D4—44no—
1013D4—9416no—
1014D4—9416no—
1015D4—9416no—
1016D4—9416no—
1017D4—1884no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—44no—
1038C2×C4—84no—
1039C2×C4—472no—
1040C2×C4—472no—
1041C2×C4—472no—
1042C2×C4—472no—
1043C2×C4—474no—
1044C2×C4—474no—
1045C2×C4—948no—
1046C2×C4—948no—
1047C2×C4—9416no—
1048C2×C4—948no—
1049C2×C4—942no—
1050C2×C4—942no—
1051C2×C4—942no—
1052C2×C4—941no—
1053C2×C4—941no—
1054C2×C4—942no—
1055C2×C4—942no—
1056C2×C4—942no—
1057C2×C4—942no—
1058C2×C4—942no—
1059C2×C4—942no—
1060C2×C4—942no—
1061C2×C4—942no—
1062C2×C4—942no—
1063C2×C4—942no—
1064C2×C4—3764no—
1065C2×C4—3764no—
1066C2×C4—3764no—
1067C2×C4—3764no—
1068C2×C4—3764no—
1069C2×C4—1884no—
1070C2×C4—1884no—
1071C2×C4—1884no—
1072C2×C4—1884no—
1073C2×C4C22×C4×D4712yes—
1074C2×C4C22×C4×D4714yes—
1075C2×C4C22×C4×D4712yes—
1076C2×C4C2×D4×D4714yes—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—24no—
1084C22—24no—
1085C22—24no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—474no—
1091C22—474no—
1092C22—942no—
1093C22—942no—
1094C22—942no—
1095C22—942no—
1096C22—942no—
1097C22—942no—
1098C22—942no—
1099C22—942no—
1100C22—942no—
1101C22—942no—
1102C22—942no—
1103C22—942no—
1104C22—944no—
1105C22—944no—
1106C22—944no—
1107C22—37616no—
1108C22—18816no—
1109C22—1882no—
1110C22—1882no—
1111C22—1882no—
1112C22—1882no—
1113C22C4×D4×D4714yes—
1114C22C23×C4×D4711yescharacteristic
1115C22C22×D4×D4711yescharacteristic
1116C22C2×#41×D4711yescharacteristic
1117C22H(5,𝔽2)×D4711yescharacteristic
1118C22H(5,𝔽2)×D4711yescharacteristic
1119C22#1568995811yescharacteristic
1120C22#1568996011yescharacteristic
1121C4—24no—
1122C4—22no—
1123C4—22no—
1124C4—24no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—474no—
1129C4—944no—
1130C4—942no—
1131C4—944no—
1132C4—1882no—
1133C4—1882no—
1134C4—1882no—
1135C2—24no—
1136C2—44no—
1137C2—944no—
1138C2—944no—
1139C2—1884no—
1140C2C2×C4×D4×D4711yescharacteristic
1141C2#518×D4711yescharacteristic
1142C2#2025658811yescharacteristic
1143C2#2025714911yescharacteristic
1144C2#2025715111yescharacteristic
1145C2#2025722011yescharacteristic
1146C2#2025722611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2325C2
socle, cosocleC23×C47C25
prime radicalC2×#121×D47C2
hypercenter#2325D47
hypocenterC47#34205
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2325

Complements

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

NH ≅ G/Ntype
2. C2×#15689595C2semidirect
3. #20246437C2semidirect
4. #20246434C2semidirect
5. #20246407C2semidirect
6. #20246401C2semidirect
7. #20246254C2semidirect
8. #20246235C2semidirect
9. #20246232C2semidirect
10. #20246206C2semidirect
11. #20246093C2semidirect
12. #20246091C2semidirect
13. #20246088C2semidirect
14. #20245962C2semidirect
15. #20245898C2semidirect
16. C4×#13093996C2semidirect
17. #380×D47C2semidirect
18. C2×#15688970C2semidirect
19. C47×#2325C2semidirect
28. #121×D47C4semidirect
30. C2×C4×D188C22semidirect
31. C2×D4×Dic47C22semidirect
32. C2×#13093986C22semidirect
33. C2×C4×C22⋊D47C22semidirect
34. C2×C4×C22⋊D47C22semidirect
35. C2×C4×C22⋊D47C22semidirect
36. C2×(C22⋊D47)⋊C4C22semidirect
37. C2×(C22⋊D47)⋊C4C22semidirect
38. C2×(C22⋊D47)⋊C4C22semidirect
42. C2×C4⋊C4×D47C22semidirect
43. C2×C4⋊C4×D47C22semidirect
50. C22×C4×Dic47C22semidirect
51. C22×C4×Dic47C22semidirect
52. #15689023C22semidirect
53. #15689023C22semidirect
54. #15689020C22semidirect
55. #15689018C22semidirect
56. #15689017C22semidirect
57. #15689016C22semidirect
58. #15689015C22semidirect
59. #15689015C22semidirect
60. #15689013C22semidirect
61. #15689013C22semidirect
62. #15689011C22semidirect
63. #15689009C22semidirect
64. #15689008C22semidirect
65. #15689006C22semidirect
66. #15689003C22semidirect
67. #15689003C22semidirect
68. #15689002C22semidirect
69. #15689001C22semidirect
70. #15689001C22semidirect
71. #15689001C22semidirect
72. #15689001C22semidirect
73. #15689000C22semidirect
74. #15688999C22semidirect
75. #15688999C22semidirect
76. #15688998C22semidirect
77. #15688997C22semidirect
78. #15688994C22semidirect
81. #15688983C22semidirect
83. #15688981C22semidirect
88. C4×Dic47⋊C4C22semidirect
89. #15688974C22semidirect
90. C22⋊C4×Dic47C22semidirect
91. C4×(C2×D47)⋊C4C22semidirect
92. C4×C22⋊Dic47C22semidirect
95. #15688970C22semidirect
96. #15688970C22semidirect
97. #15688970C22semidirect
98. C2×C47⋊#95C22semidirect
99. #95×D47C22semidirect
101. C2×C4×D4×C47C22semidirect
102. C47×#388C22semidirect
103. C47×#387C22semidirect
104. C47×#386C22semidirect
105. C47×#386C22semidirect
106. C47×#385C22semidirect
107. C47×#380C22semidirect
108. C2×#95×C47C22semidirect
120. C2×D4×D47C2×C4semidirect
121. C2×D4×D47C2×C4semidirect
128. C22×C4×D47C2×C4semidirect
138. #13093999C2×C4semidirect
139. #13093998C2×C4semidirect
140. #13093997C2×C4semidirect
141. #13093996C2×C4semidirect
142. #13093995C2×C4semidirect
165. C4⋊C4×D47C2×C4semidirect
173. C2×(C2×D47)⋊C4D4semidirect
190. C22⋊C4×D47C2×C4semidirect
217. #121×C47C2×C4semidirect
270. C22×C4×C47C2×D4semidirect
298. C22×Dic47C2×D4semidirect
370. (C2×D47)⋊C4C2×D4semidirect
429. C22×D47C4×D4semidirect
561. Dic47#518semidirect
575. #2325D47semidirect
613. C2×C4×D4C2×D47semidirect
638. #388C2×D47semidirect
642. #387C2×D47semidirect
653. #386C2×D47semidirect
654. #386C2×D47semidirect
658. #385C2×D47semidirect
666. #380C2×D47semidirect
681. C2×#95C2×D47semidirect
682. C47#34205semidirect
723. #121C4×D47semidirect
908. C22×C4D4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D472
C2×#156895952
#202464372
#202464342
#202464072
#202464012
#202462542
#202462352
#202462322
#202462062
#202460932
#202460912
#202460882
#202459622
#202458982
C4×#130939962
#380×D472
C2×#156889702
C47×#23252
#3420547