Finite Group Databasebeta

← #26375896

Subgroups — #26375896

Order 12032.

3298 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689670C211yesmaximal, characteristic
2C2×C4×#10625350C211yesmaximal, characteristic, complemented
3C2×#15689591C211yesmaximal, characteristic, complemented
4#20246462C212yesmaximal, complemented
5#20246456C212yesmaximal, complemented
6#20246451C212yesmaximal, complemented
7#20246443C212yesmaximal, complemented
8#20246437C212yesmaximal, complemented
9#20246434C212yesmaximal, complemented
10#20246407C212yesmaximal, complemented
11#20246401C212yesmaximal, complemented
12#20245874C211yesmaximal, characteristic, complemented
13#20245874C211yesmaximal, characteristic, complemented
14#20245851C211yesmaximal, characteristic, complemented
15#20245847C211yesmaximal, characteristic, complemented
16#20245833C211yesmaximal, characteristic, complemented
17#20245832C211yesmaximal, characteristic, complemented
18#20245829C211yesmaximal, characteristic, complemented
19C42×C22⋊D47C211yesmaximal, characteristic, complemented
20C4×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
21#20245727C211yesmaximal, characteristic, complemented
22C4×C4⋊C4×D47C211yesmaximal, characteristic, complemented
23C47×#2290C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic
25C22×#10625350C2211yescharacteristic
26#15689670C4116yescomplemented
27C2×#13094023C2211yescharacteristic
28C2×#13094020C2211yescharacteristic
29C2×#13094010C2211yescharacteristic
30C2×#13094010C2211yescharacteristic
31C2×#13093999C2211yescharacteristic
32C2×#13093997C2211yescharacteristic
33C2×#13093997C2211yescharacteristic
34C2×#13093995C2211yescharacteristic
35C4×#10625350—28no—
36#15689591—28no—
37C2×C4×Dic94C2212yes—
38C2×#13093989C2212yes—
39C2×C4×D188C2212yes—
40C2×C4×D188C2211yescharacteristic
41C2×#13093986C2212yes—
42C2×C4×C22⋊D47C2212yes—
43C2×C4×C22⋊D47C2212yes—
44C2×C4×C22⋊D47C2212yes—
45C2×C4×C22⋊D47C2211yescharacteristic
46C2×C4×C22⋊D47C2211yescharacteristic
47C2×(C22⋊D47)⋊C4C2212yes—
48C2×(C22⋊D47)⋊C4C2212yes—
49C2×(C22⋊D47)⋊C4C2212yes—
50C2×#13093983C2211yescharacteristic
51C2×#13093981C2211yescharacteristic
52C2×#13093981C2211yescharacteristic
53C2×#13093981C2211yescharacteristic
54C2×#13093981C2211yescharacteristic
55C2×C4⋊C4×D47C2212yes—
56C22×C4×Dic47C2211yescharacteristic
57C2×C42×D47C2211yescharacteristic
58C2×C42×D47C2211yescharacteristic
59C2×C42×D47C2211yescharacteristic
60C2×C42×D47C2211yescharacteristic
61C2×C42×D47C2211yescharacteristic
62#15689027C2212yes—
63#15689027C2212yes—
64#15689023C2212yes—
65#15689023C2212yes—
66#15689023C2212yes—
67#15689023C2212yes—
68#15689020C2212yes—
69#15689018C2212yes—
70#15689017C2212yes—
71#15689016C2212yes—
72#15689015C2212yes—
73#15689015C2212yes—
74#15689013C2212yes—
75#15689013C2212yes—
76#15689011C2212yes—
77#15689009C2212yes—
78#15689008C2212yes—
79#15689006C2212yes—
80#15689003C2212yes—
81#15689001C2212yes—
82#15689001C2212yes—
83#15689001C2212yes—
84#15689001C2212yes—
85#15688999C2212yes—
86#15688999C2212yes—
87#15688998C2212yes—
88#15688997C2212yes—
89#15688994C2212yes—
90C4⋊C4×Dic47C2212yes—
91C4×Dic47⋊C4C2211yescharacteristic
92C4×Dic47⋊C4C2212yes—
93C4×Dic47⋊C4C2211yescharacteristic
94C4×C4⋊Dic47C2211yescharacteristic
95#15688974C2212yes—
96#15688974C2212yes—
97#15688974C2212yes—
98#15688974C2212yes—
99C22⋊C4×Dic47C2212yes—
100C4×(C2×D47)⋊C4C2211yescharacteristic
101C4×(C2×D47)⋊C4C2211yescharacteristic
102C4×(C2×D47)⋊C4C2211yescharacteristic
103C4×(C2×D47)⋊C4C2211yescharacteristic
104C4×(C2×D47)⋊C4C2212yes—
105C4×C22⋊Dic47C2211yescharacteristic
106C4×C22⋊Dic47C2211yescharacteristic
107C4×C22⋊Dic47C2212yes—
108#15688970C2212yes—
109#15688970C2212yes—
110#15688970C2212yes—
111#15688969C2211yescharacteristic
112#95×D47C2212yes—
113C42×Dic47C2211yescharacteristic
114C42×Dic47C2211yescharacteristic
115C2×C4×D4×C47C2211yescharacteristic
116C2×#117×C47C2211yescharacteristic
117C22×C42×C47C2211yescharacteristic
118C47×#388C2212yes—
119C47×#387C2212yes—
120C47×#386C2212yes—
121C47×#385C2212yes—
122C4×C4⋊C4×C47C2211yescharacteristic
123C4×C22⋊C4×C47C2211yescharacteristic
124C4×C22⋊C4×C47C2211yescharacteristic
125C47×#376C2211yescharacteristic
126C2×#10625350—24no—
127C2×#10625350—24no—
128C2×#10625350—24no—
129C2×#10625350—24no—
130C2×#10625350C2×C418yescomplemented
131C2×#10625350C2×C418yescomplemented
132C22×Dic94C2311yescharacteristic
133C22×Dic94C2311yescharacteristic
134C22×D188C2311yescharacteristic
135C22×D188C2311yescharacteristic
136C22×D188C2311yescharacteristic
137C22×C22⋊D47C2311yescharacteristic
138C22×C22⋊D47C2311yescharacteristic
139C22×C22⋊D47C2311yescharacteristic
140C22×C22⋊D47C2311yescharacteristic
141C22×C22⋊D47C2311yescharacteristic
142C22×C22⋊D47C2311yescharacteristic
143C23×Dic47C2312yes—
144C22×C4×D47C2312yes—
145C22×C4×D47C2312yes—
146C22×C4×D47C2312yes—
147C22×C4×D47C2312yes—
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2311yescharacteristic
151C22×C4×D47C2311yescharacteristic
152C22×C4×D47C2311yescharacteristic
153#13094023C2×C418yescomplemented
154#13094020C2×C418yescomplemented
155#13094010C2×C418yescomplemented
156#13094010C2×C418yescomplemented
157#13093999C2×C418yescomplemented
158#13093997C2×C418yescomplemented
159#13093997C2×C418yescomplemented
160#13093995C2×C418yescomplemented
161C4×Dic94—28no—
162#13093989—28no—
163C4×D188—28no—
164C4×D188C2×C418yescomplemented
165#13093986—28no—
166C4×C22⋊D47—28no—
167C4×C22⋊D47—28no—
168C4×C22⋊D47—28no—
169C4×C22⋊D47C2×C418yescomplemented
170C4×C22⋊D47C2×C418yescomplemented
171(C22⋊D47)⋊C4—28no—
172(C22⋊D47)⋊C4—28no—
173(C22⋊D47)⋊C4—28no—
174#13093983—24no—
175#13093981—24no—
176#13093981—24no—
177#13093981—24no—
178#13093981D418yescomplemented
179C2×C4⋊Dic47C2312yes—
180C2×C4⋊Dic47C2312yes—
181C2×C4⋊Dic47C2311yescharacteristic
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2311yescharacteristic
187C2×Dic47⋊C4C2311yescharacteristic
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2312yes—
190C4⋊C4×D47—28no—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2312yes—
194C2×C22⋊Dic47C2311yescharacteristic
195C2×C22⋊Dic47C2311yescharacteristic
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C2×(C2×D47)⋊C4C2312yes—
208C2×C4×Dic47—24no—
209C2×C4×Dic47C2311yescharacteristic
210C2×C4×Dic47C2312yes—
211C2×C4×Dic47C2312yes—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2311yescharacteristic
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2312yes—
217C2×C4×Dic47C2312yes—
218C2×C4×Dic47C2312yes—
219C2×C4×Dic47C2312yes—
220C2×C4×Dic47C2312yes—
221C2×C4×Dic47C2311yescharacteristic
222C2×C4×Dic47C2311yescharacteristic
223C2×C4×Dic47C2311yescharacteristic
224C2×C4×Dic47C2311yescharacteristic
225C42×D47—24no—
226C42×D47—24no—
227C42×D47—24no—
228C42×D47—24no—
229C42×D47C2×C418yescomplemented
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
242C23×C4×C47C2312yes—
243C23×C4×C47C2311yescharacteristic
244C23×C4×C47C2311yescharacteristic
245C4×D4×C47C2×C418yescomplemented
246#117×C47—24no—
247C2×C4⋊C4×C47C2312yes—
248C2×C4⋊C4×C47C2312yes—
249C2×C4⋊C4×C47C2311yescharacteristic
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2312yes—
252C2×C22⋊C4×C47C2312yes—
253C2×C22⋊C4×C47C2311yescharacteristic
254C2×C22⋊C4×C47C2311yescharacteristic
255C2×C42×C47—24no—
256C2×C42×C47C2311yescharacteristic
257C2×C42×C47C2311yescharacteristic
258C2×C42×C47C2312yes—
259C2×C42×C47C2311yescharacteristic
260C2×C42×C47C2311yescharacteristic
261C2×C42×C47C2311yescharacteristic
262#95×C47C2312yes—
263#95×C47C2312yes—
264#95×C47C2312yes—
265#95×C47C2312yes—
266#95×C47C2312yes—
267C24×C47C2411yescharacteristic
268C24×C47C2411yescharacteristic
269C23×D47C2411yescharacteristic
270C23×D47C2411yescharacteristic
271C23×D47C2411yescharacteristic
272C2×D4×C47—42no—
273C2×D4×C47C22×C414yes—
274C22×C4×C47—22no—
275C22×C4×C47—22no—
276C22×C4×C47—22no—
277C22×C4×C47—22no—
278C22×C4×C47—24no—
279C22×C4×C47—24no—
280C22×C4×C47—42no—
281C22×C4×C47C22×C414yes—
282C22×C4×C47C22×C414yes—
283C22×C4×C47C2412yes—
284C22×C4×C47C2412yes—
285C22×C4×C47C2411yescharacteristic
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2412yes—
290C22×C4×C47C2412yes—
291C22×C4×C47C2411yescharacteristic
292C2×C22⋊D47—22no—
293C2×C22⋊D47—22no—
294C2×C22⋊D47—22no—
295C2×C22⋊D47—22no—
296C2×C22⋊D47—22no—
297C2×C22⋊D47—22no—
298C2×C22⋊D47—24no—
299C2×C22⋊D47—24no—
300C2×C22⋊D47—22no—
301C2×C22⋊D47—22no—
302C2×C22⋊D47C22×C414yes—
303C2×C22⋊D47C22×C414yes—
304C2×C22⋊D47C22×C414yes—
305C2×C22⋊D47C22×C414yes—
306C2×C22⋊D47C22×C414yes—
307C2×C22⋊D47C22×C414yes—
308C22×Dic47—24no—
309C22×Dic47—24no—
310C22×Dic47—42no—
311C22×Dic47C2412yes—
312C22×Dic47C2412yes—
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2411yescharacteristic
316C22×Dic47C2412yes—
317C22×Dic47C2412yes—
318C22×Dic47C2411yescharacteristic
319C22×Dic47C2411yescharacteristic
320#10625350—232no—
321#10625350—232no—
322C2×D188—22no—
323C2×D188—22no—
324C2×D188—22no—
325C2×D188—22no—
326C2×D188—42no—
327C2×D188C22×C414yes—
328C2×D188C22×C414yes—
329C2×D188C22×C414yes—
330C2×C4×D47—22no—
331C2×C4×D47—22no—
332C2×C4×D47—22no—
333C2×C4×D47—22no—
334C2×C4×D47—24no—
335C2×C4×D47—24no—
336C2×C4×D47—24no—
337C2×C4×D47—24no—
338C2×C4×D47—24no—
339C2×C4×D47—24no—
340C2×C4×D47—24no—
341C2×C4×D47—24no—
342C2×C4×D47—24no—
343C2×C4×D47—42no—
344C2×C4×D47—42no—
345C2×C4×D47—42no—
346C2×C4×D47—42no—
347C2×C4×D47—42no—
348C2×C4×D47C22×C414yes—
349C2×C4×D47C22×C414yes—
350C2×C4×D47C22×C414yes—
351C2×C4×D47C22×C414yes—
352C2×C4×D47C22×C414yes—
353C2×C4×D47C2×D414yes—
354C2×C4×D47#4114yes—
355C2×Dic94—22no—
356C2×Dic94—22no—
357C2×Dic94—22no—
358C2×Dic94—22no—
359C2×Dic94C22×C414yes—
360C2×Dic94C22×C414yes—
361C4⋊C4×C47—24no—
362C4⋊C4×C47—24no—
363C4⋊C4×C47C22×C414yes—
364C22⋊C4×C47—24no—
365C22⋊C4×C47—24no—
366C22⋊C4×C47—42no—
367C22⋊C4×C47C22×C414yes—
368C22⋊C4×C47C22×C414yes—
369C42×C47—22no—
370C42×C47—24no—
371C42×C47—22no—
372C42×C47—22no—
373C42×C47C22×C414yes—
374C42×C47C2×D414yes—
375C22⋊Dic47—24no—
376C22⋊Dic47—24no—
377C22⋊Dic47—42no—
378C22⋊Dic47C22×C414yes—
379C22⋊Dic47C22×C414yes—
380(C2×D47)⋊C4—24no—
381(C2×D47)⋊C4—24no—
382(C2×D47)⋊C4—24no—
383(C2×D47)⋊C4—24no—
384(C2×D47)⋊C4—24no—
385(C2×D47)⋊C4—42no—
386(C2×D47)⋊C4—42no—
387(C2×D47)⋊C4C22×C414yes—
388(C2×D47)⋊C4C22×C414yes—
389(C2×D47)⋊C4C22×C414yes—
390(C2×D47)⋊C4C22×C414yes—
391(C2×D47)⋊C4C2×D418yes—
392C4⋊Dic47—24no—
393C4⋊Dic47—24no—
394C4⋊Dic47C22×C414yes—
395Dic47⋊C4—24no—
396Dic47⋊C4—24no—
397Dic47⋊C4—24no—
398Dic47⋊C4—24no—
399Dic47⋊C4C22×C414yes—
400Dic47⋊C4C22×C414yes—
401Dic47⋊C4C2×D418yes—
402Dic47⋊C4#4118yescomplemented
403C4×Dic47—22no—
404C4×Dic47—22no—
405C4×Dic47—24no—
406C4×Dic47—22no—
407C4×Dic47—24no—
408C4×Dic47—24no—
409C4×Dic47—24no—
410C4×Dic47—24no—
411C4×Dic47—24no—
412C4×Dic47—24no—
413C4×Dic47—42no—
414C4×Dic47—42no—
415C4×Dic47C22×C414yes—
416C4×Dic47C22×C414yes—
417C4×Dic47C22×C414yes—
418C4×Dic47C2×D414yes—
419C23×C47—21no—
420C23×C47—21no—
421C23×C47—22no—
422C23×C47—22no—
423C23×C47—21no—
424C23×C47—21no—
425C23×C47—22no—
426C23×C47—22no—
427C23×C47C23×C412yes—
428C23×C47C23×C412yes—
429C23×C47C2511yescharacteristic
430C22×D47—22no—
431C22×D47—22no—
432C22×D47—21no—
433C22×D47—21no—
434C22×D47—22no—
435C22×D47—22no—
436C22×D47—21no—
437C22×D47—21no—
438C22×D47—22no—
439C22×D47—22no—
440C22×D47C23×C412yes—
441C22×D47C23×C412yes—
442C22×D47C23×C412yes—
443C22×D47C22×D412yes—
444C22×D47C2×#4112yes—
445D4×C47—44no—
446C2×C4×C47—22no—
447C2×C4×C47—21no—
448C2×C4×C47—21no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—21no—
452C2×C4×C47—21no—
453C2×C4×C47—22no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—28no—
457C2×C4×C47—28no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—48no—
465C2×C4×C47C23×C412yes—
466C2×C4×C47C23×C412yes—
467C2×C4×C47C23×C412yes—
468C2×C4×C47C23×C412yes—
469C2×C4×C47C23×C412yes—
470C2×C4×C47C22×D414yes—
471C2×C4×C47C22×D412yes—
472C2×C4×C47C2×#4114yes—
473C2×C4×C47C2×#4112yes—
474C22⋊D47—28no—
475C22⋊D47—28no—
476C22⋊D47—28no—
477C22⋊D47—28no—
478C22⋊D47—28no—
479C22⋊D47—28no—
480C2×Dic47—22no—
481C2×Dic47—21no—
482C2×Dic47—21no—
483C2×Dic47—22no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—22no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—48no—
496C2×Dic47C23×C412yes—
497C2×Dic47C23×C412yes—
498C2×Dic47C23×C412yes—
499C2×Dic47C23×C412yes—
500C2×Dic47C23×C412yes—
501C2×Dic47C22×D414yes—
502C2×Dic47C22×D412yes—
503C2×Dic47C2×#4114yes—
504C2×Dic47C2×#4112yes—
505C2×Dic47C2×#4114yes—
506D188—28no—
507D188—28no—
508D188—44no—
509C4×D47—28no—
510C4×D47—28no—
511C4×D47—28no—
512C4×D47—44no—
513C4×D47—48no—
514C4×D47—48no—
515C4×D47—48no—
516C4×D47—48no—
517C4×D47C4×D4116yescomplemented
518Dic94—28no—
519Dic94—28no—
520#34141—471nomaximal, Sylow
521C22×C47—22no—
522C22×C47—22no—
523C22×C47—22no—
524C22×C47—22no—
525C22×C47—22no—
526C22×C47—22no—
527C22×C47—42no—
528C22×C47—42no—
529C22×C47—42no—
530C22×C47—42no—
531C22×C47C24×C411yescharacteristic
532C22×C47C23×D411yescharacteristic
533C22×C47C22×#4111yescharacteristic
534C22×C47C22×#4112yes—
535C22×C47#58512yes—
536C2×D47—22no—
537C2×D47—22no—
538C2×D47—24no—
539C2×D47—24no—
540C2×D47—22no—
541C2×D47—22no—
542C2×D47—22no—
543C2×D47—22no—
544C2×D47—22no—
545C2×D47—22no—
546C2×D47—42no—
547C2×D47—42no—
548C2×D47—42no—
549C2×D47—42no—
550C2×D47C2×C4×D414yes—
551C4×C47—22no—
552C4×C47—22no—
553C4×C47—22no—
554C4×C47—22no—
555C4×C47—24no—
556C4×C47—24no—
557C4×C47—42no—
558C4×C47—42no—
559C4×C47C2×C4×D414yes—
560Dic47—22no—
561Dic47—22no—
562Dic47—22no—
563Dic47—24no—
564Dic47—24no—
565Dic47—42no—
566Dic47—42no—
567Dic47C2×C4×D414yes—
568Dic47C4×#4114yescomplemented
569C2×#532—471no—
570C2×C4×#41—471no—
571C2×C4×#41—471no—
572#2367—472no—
573#2367—472no—
574#2366—472no—
575#2365—472no—
576#2364—472no—
577#2364—472no—
578#2361—472no—
579#2361—472no—
580#2297—471no—
581#2297—471no—
582#2293—471no—
583#2293—471no—
584#2290—471no—
585#2290—471no—
586#2290—471no—
587#2290D4711yescharacteristic, complemented
588C42×D4—471no—
589C42×D4—471no—
590C4×#117—471no—
591C2×C4×C4⋊C4—471no—
592C2×C47—42no—
593C2×C47—42no—
594C2×C47C22×C4×D411yescharacteristic
595C2×C47C2×C4×#4111yescharacteristic
596C2×C47#342811yescharacteristic
597C2×C47D4×#4112yes—
598C2×C47#348012yes—
599D47—24no—
600D47—42no—
601D47—42no—
602C22×#41—471no—
603C22×#41—471no—
604#532—4716no—
605C2×C4⋊Q8—471no—
606C2×#127—471no—
607C2×#124—471no—
608C2×#124—471no—
609C2×#121—471no—
610C2×#121—471no—
611C2×#121—471no—
612C2×#121—471no—
613C4×#41—948no—
614C4×#41—948no—
615C2×C4×Q8—472no—
616C2×C4×Q8—472no—
617C2×C4×D4—471no—
618C2×C4×D4—471no—
619C2×C4×D4—472no—
620C2×C4×D4—472no—
621C2×C4×D4—472no—
622C2×C4×D4—472no—
623C2×C4×D4—472no—
624C2×C4×D4—472no—
625C2×C4×D4—472no—
626C2×C4×D4—471no—
627C2×C4×D4—472no—
628C2×C4×D4C2×D4711yescharacteristic
629C2×#117—471no—
630C2×#117—471no—
631C2×#117—471no—
632C2×#117—471no—
633C2×#117—471no—
634C2×#117C2×D4711yescharacteristic
635C22×C4⋊C4—472no—
636C22×C42—471no—
637C22×C42—471no—
638C22×C42—471no—
639C22×C42—471no—
640C22×C42—471no—
641C22×C42—471no—
642C22×C42C2×D4711yescharacteristic
643#391—472no—
644#391—472no—
645#390—472no—
646#390—472no—
647#390—472no—
648#390—472no—
649#389—472no—
650#389—472no—
651#388—472no—
652#388—472no—
653#388—472no—
654#388—472no—
655#388—472no—
656#388—472no—
657#388—472no—
658#388C2×D4712yes—
659#387—472no—
660#387—472no—
661#387—472no—
662#387C2×D4712yes—
663#386—472no—
664#386—472no—
665#386—472no—
666#386—472no—
667#386—472no—
668#386—472no—
669#386—472no—
670#386C2×D4712yes—
671#385—472no—
672#385—472no—
673#385—472no—
674#385C2×D4712yes—
675C4×C4⋊C4—472no—
676C4×C4⋊C4—471no—
677C4×C4⋊C4—472no—
678C4×C4⋊C4—471no—
679C4×C4⋊C4—471no—
680C4×C4⋊C4—472no—
681C4×C4⋊C4—472no—
682C4×C4⋊C4—472no—
683C4×C4⋊C4—472no—
684C4×C4⋊C4C2×D4711yescharacteristic
685C4×C22⋊C4—472no—
686C4×C22⋊C4—471no—
687C4×C22⋊C4—471no—
688C4×C22⋊C4—472no—
689C4×C22⋊C4—472no—
690C4×C22⋊C4—471no—
691C4×C22⋊C4—471no—
692C4×C22⋊C4—471no—
693C4×C22⋊C4—471no—
694C4×C22⋊C4—472no—
695C4×C22⋊C4—472no—
696C4×C22⋊C4—472no—
697C4×C22⋊C4C2×D4711yescharacteristic
698C4×C22⋊C4C2×D4711yescharacteristic
699#376—471no—
700#376C2×D4711yescharacteristic
701C2×#95—472no—
702C43—471no—
703C43—471no—
704C47#3414111yescharacteristic, complemented, Sylow
705C2×#41—478no—
706C2×#41—478no—
707C2×#41—944no—
708C2×#41—944no—
709C2×#41—944no—
710C2×#41—944no—
711C22×Q8—471no—
712C22×Q8—471no—
713C22×D4—471no—
714C22×D4—471no—
715C22×D4—471no—
716C22×D4—471no—
717C22×D4—471no—
718C22×D4—471no—
719C22×D4—471no—
720C22×D4—471no—
721C22×D4—471no—
722C22×D4C22×D4711yescharacteristic
723C23×C4—471no—
724C23×C4—471no—
725C23×C4—471no—
726C23×C4—471no—
727C23×C4—471no—
728C23×C4—472no—
729C23×C4—472no—
730C23×C4—472no—
731C23×C4—472no—
732C23×C4—472no—
733C23×C4C22×D4712yes—
734C23×C4C22×D4711yescharacteristic
735C23×C4C22×D4711yescharacteristic
736C4⋊Q8—478no—
737#127—478no—
738#124—478no—
739#124—478no—
740#121—478no—
741#121—478no—
742#121—478no—
743#121—478no—
744C4×Q8—948no—
745C4×Q8—948no—
746C4×D4—478no—
747C4×D4—478no—
748C4×D4—478no—
749C4×D4—948no—
750C4×D4—948no—
751C4×D4—948no—
752C4×D4—948no—
753C4×D4—948no—
754C4×D4—948no—
755C4×D4—948no—
756C4×D4—948no—
757C4×D4C4×D4718yescomplemented
758#117—24no—
759#117—478no—
760#117—944no—
761#117—944no—
762#117—944no—
763#117—944no—
764C2×C4⋊C4—472no—
765C2×C4⋊C4—472no—
766C2×C4⋊C4—471no—
767C2×C4⋊C4—471no—
768C2×C4⋊C4—471no—
769C2×C4⋊C4—472no—
770C2×C4⋊C4—472no—
771C2×C4⋊C4—472no—
772C2×C4⋊C4—472no—
773C2×C4⋊C4—472no—
774C2×C4⋊C4—472no—
775C2×C4⋊C4—948no—
776C2×C4⋊C4C22×D4712yes—
777C2×C4⋊C4C22×D4712yes—
778C2×C4⋊C4C22×D4711yescharacteristic
779C2×C22⋊C4—471no—
780C2×C22⋊C4—471no—
781C2×C22⋊C4—472no—
782C2×C22⋊C4—471no—
783C2×C22⋊C4—471no—
784C2×C22⋊C4—471no—
785C2×C22⋊C4—471no—
786C2×C22⋊C4—472no—
787C2×C22⋊C4—472no—
788C2×C22⋊C4—472no—
789C2×C22⋊C4—472no—
790C2×C22⋊C4—472no—
791C2×C22⋊C4—472no—
792C2×C22⋊C4—472no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4C22×D4712yes—
797C2×C22⋊C4C22×D4712yes—
798C2×C22⋊C4C22×D4712yes—
799C2×C22⋊C4C22×D4711yescharacteristic
800C2×C22⋊C4C22×D4711yescharacteristic
801C2×C42—24no—
802C2×C42—471no—
803C2×C42—471no—
804C2×C42—471no—
805C2×C42—471no—
806C2×C42—478no—
807C2×C42—472no—
808C2×C42—472no—
809C2×C42—472no—
810C2×C42—472no—
811C2×C42—472no—
812C2×C42—472no—
813C2×C42—472no—
814C2×C42—471no—
815C2×C42—471no—
816C2×C42—471no—
817C2×C42—472no—
818C2×C42—472no—
819C2×C42—944no—
820C2×C42—944no—
821C2×C42—944no—
822C2×C42—944no—
823C2×C42—944no—
824C2×C42C22×D4712yes—
825C2×C42C22×D4711yescharacteristic
826C2×C42C22×D4711yescharacteristic
827C2×C42C22×D4711yescharacteristic
828C2×C42C22×D4711yescharacteristic
829C2×C42C22×D4711yescharacteristic
830#95—472no—
831#95—472no—
832#95—472no—
833#95—472no—
834#95—472no—
835#95—472no—
836#95—472no—
837#95—472no—
838#95—472no—
839#95—472no—
840#95—472no—
841#95C22×D4712yes—
842#95C22×D4712yes—
843#95C22×D4712yes—
844#95C22×D4712yes—
845#95C22×D4712yes—
846C24—471no—
847C24—471no—
848C24—471no—
849C24C23×D4711yescharacteristic
850C24C23×D4711yescharacteristic
851#41—9432no—
852#41—9432no—
853C2×Q8—474no—
854C2×Q8—474no—
855C2×Q8—942no—
856C2×Q8—942no—
857C2×Q8—942no—
858C2×Q8—942no—
859C2×D4—42no—
860C2×D4—474no—
861C2×D4—474no—
862C2×D4—474no—
863C2×D4—474no—
864C2×D4—474no—
865C2×D4—474no—
866C2×D4—474no—
867C2×D4—474no—
868C2×D4—474no—
869C2×D4—942no—
870C2×D4—942no—
871C2×D4—942no—
872C2×D4—942no—
873C2×D4—942no—
874C2×D4—942no—
875C2×D4—944no—
876C2×D4—944no—
877C2×D4—942no—
878C2×D4—942no—
879C2×D4—942no—
880C2×D4—942no—
881C2×D4—942no—
882C2×D4—942no—
883C2×D4—1882no—
884C2×D4C2×C4×D4714yes—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—42no—
892C22×C4—471no—
893C22×C4—471no—
894C22×C4—474no—
895C22×C4—474no—
896C22×C4—474no—
897C22×C4—471no—
898C22×C4—472no—
899C22×C4—471no—
900C22×C4—471no—
901C22×C4—472no—
902C22×C4—474no—
903C22×C4—474no—
904C22×C4—474no—
905C22×C4—474no—
906C22×C4—472no—
907C22×C4—472no—
908C22×C4—944no—
909C22×C4—944no—
910C22×C4—944no—
911C22×C4—944no—
912C22×C4—944no—
913C22×C4—944no—
914C22×C4—944no—
915C22×C4—944no—
916C22×C4—942no—
917C22×C4—942no—
918C22×C4—942no—
919C22×C4—942no—
920C22×C4—944no—
921C22×C4—944no—
922C22×C4—944no—
923C22×C4—1882no—
924C22×C4—1882no—
925C22×C4—1882no—
926C22×C4—1882no—
927C22×C4—1882no—
928C22×C4—1882no—
929C22×C4C2×C4×D4714yes—
930C22×C4C2×C4×D4714yes—
931C22×C4C23×D4712yes—
932C22×C4C23×D4712yes—
933C22×C4C23×D4711yescharacteristic
934C22×C4C23×D4711yescharacteristic
935C22×C4C23×D4711yescharacteristic
936C22×C4C23×D4711yescharacteristic
937C22×C4C23×D4712yes—
938C22×C4C23×D4712yes—
939C22×C4C23×D4711yescharacteristic
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—474no—
943C4⋊C4—474no—
944C4⋊C4—474no—
945C4⋊C4—478no—
946C4⋊C4—478no—
947C4⋊C4—944no—
948C4⋊C4—944no—
949C4⋊C4—944no—
950C4⋊C4—944no—
951C4⋊C4—944no—
952C4⋊C4—944no—
953C4⋊C4C2×C4×D4714yes—
954C22⋊C4—24no—
955C22⋊C4—24no—
956C22⋊C4—42no—
957C22⋊C4—474no—
958C22⋊C4—474no—
959C22⋊C4—474no—
960C22⋊C4—474no—
961C22⋊C4—474no—
962C22⋊C4—474no—
963C22⋊C4—478no—
964C22⋊C4—944no—
965C22⋊C4—944no—
966C22⋊C4—944no—
967C22⋊C4—944no—
968C22⋊C4—944no—
969C22⋊C4—944no—
970C22⋊C4—944no—
971C22⋊C4—1882no—
972C22⋊C4—1882no—
973C22⋊C4—1882no—
974C22⋊C4C2×C4×D4714yes—
975C22⋊C4C2×C4×D4714yes—
976C42—22no—
977C42—24no—
978C42—22no—
979C42—22no—
980C42—474no—
981C42—474no—
982C42—474no—
983C42—474no—
984C42—944no—
985C42—944no—
986C42—944no—
987C42—944no—
988C42—944no—
989C42—944no—
990C42—942no—
991C42—942no—
992C42—944no—
993C42—942no—
994C42—1882no—
995C42—1882no—
996C42C2×C4×D4714yes—
997C42D4×D4714yes—
998C23—21no—
999C23—21no—
1000C23—22no—
1001C23—22no—
1002C23—21no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—472no—
1007C23—472no—
1008C23—472no—
1009C23—472no—
1010C23—472no—
1011C23—942no—
1012C23—942no—
1013C23—941no—
1014C23—941no—
1015C23—942no—
1016C23—942no—
1017C23—941no—
1018C23—941no—
1019C23—942no—
1020C23—942no—
1021C23C22×C4×D4712yes—
1022C23C22×C4×D4712yes—
1023C23C24×D4711yescharacteristic
1024Q8—948no—
1025Q8—948no—
1026D4—44no—
1027D4—948no—
1028D4—948no—
1029D4—948no—
1030D4—948no—
1031D4—948no—
1032D4—948no—
1033D4—948no—
1034D4—948no—
1035D4—1884no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—28no—
1047C2×C4—28no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—48no—
1055C2×C4—472no—
1056C2×C4—472no—
1057C2×C4—472no—
1058C2×C4—474no—
1059C2×C4—472no—
1060C2×C4—4716no—
1061C2×C4—472no—
1062C2×C4—472no—
1063C2×C4—472no—
1064C2×C4—474no—
1065C2×C4—474no—
1066C2×C4—948no—
1067C2×C4—942no—
1068C2×C4—941no—
1069C2×C4—941no—
1070C2×C4—942no—
1071C2×C4—941no—
1072C2×C4—941no—
1073C2×C4—942no—
1074C2×C4—942no—
1075C2×C4—942no—
1076C2×C4—948no—
1077C2×C4—948no—
1078C2×C4—942no—
1079C2×C4—942no—
1080C2×C4—942no—
1081C2×C4—942no—
1082C2×C4—942no—
1083C2×C4—942no—
1084C2×C4—1884no—
1085C2×C4—1888no—
1086C2×C4—1888no—
1087C2×C4—1888no—
1088C2×C4—1888no—
1089C2×C4—1888no—
1090C2×C4C22×C4×D4712yes—
1091C2×C4C22×C4×D4712yes—
1092C2×C4C22×C4×D4712yes—
1093C2×C4C22×C4×D4712yes—
1094C2×C4C22×C4×D4712yes—
1095C2×C4C2×D4×D4714yes—
1096C2×C4C2×D4×D4712yes—
1097C2×C4#41×D4714yes—
1098C2×C4#41×D4712yes—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—474no—
1110C22—942no—
1111C22—942no—
1112C22—944no—
1113C22—944no—
1114C22—942no—
1115C22—942no—
1116C22—942no—
1117C22—942no—
1118C22—942no—
1119C22—942no—
1120C22—1882no—
1121C22—1882no—
1122C22—1882no—
1123C22—1882no—
1124C22C23×C4×D4711yescharacteristic
1125C22C22×D4×D4711yescharacteristic
1126C22C2×#41×D4711yescharacteristic
1127C22C2×#41×D4712yes—
1128C22#1568995912yes—
1129C4—22no—
1130C4—22no—
1131C4—22no—
1132C4—22no—
1133C4—24no—
1134C4—24no—
1135C4—42no—
1136C4—42no—
1137C4—474no—
1138C4—474no—
1139C4—942no—
1140C4—942no—
1141C4—942no—
1142C4—944no—
1143C4—944no—
1144C4—1882no—
1145C4—1882no—
1146C4C4×D4×D4714yes—
1147C2—42no—
1148C2—42no—
1149C2—944no—
1150C2—1882no—
1151C2—1882no—
1152C2C2×C4×D4×D4711yescharacteristic
1153C2C4×#41×D4711yescharacteristic
1154C2#2025658911yescharacteristic
1155C2#2025687112yes—
1156C2#2025697912yes—
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC47×#2290C2
socle, cosocleC23×C47C25
prime radicalC2×#15689670C2
hypercenter#2290D47
hypocenterC47#34141
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625350C2semidirect
3. C2×#15689591C2semidirect
4. #20246462C2semidirect
5. #20246456C2semidirect
6. #20246451C2semidirect
7. #20246443C2semidirect
8. #20246437C2semidirect
9. #20246434C2semidirect
10. #20246407C2semidirect
11. #20246401C2semidirect
12. #20245874C2semidirect
13. #20245874C2semidirect
14. #20245851C2semidirect
15. #20245847C2semidirect
16. #20245833C2semidirect
17. #20245832C2semidirect
18. #20245829C2semidirect
19. C42×C22⋊D47C2semidirect
20. C4×(C22⋊D47)⋊C4C2semidirect
21. #20245727C2semidirect
22. C4×C4⋊C4×D47C2semidirect
23. C47×#2290C2semidirect
26. #15689670C4semidirect
130. C2×#10625350C2×C4semidirect
131. C2×#10625350C2×C4semidirect
153. #13094023C2×C4semidirect
154. #13094020C2×C4semidirect
155. #13094010C2×C4semidirect
156. #13094010C2×C4semidirect
157. #13093999C2×C4semidirect
158. #13093997C2×C4semidirect
159. #13093997C2×C4semidirect
160. #13093995C2×C4semidirect
164. C4×D188C2×C4semidirect
169. C4×C22⋊D47C2×C4semidirect
170. C4×C22⋊D47C2×C4semidirect
178. #13093981D4semidirect
229. C42×D47C2×C4semidirect
245. C4×D4×C47C2×C4semidirect
402. Dic47⋊C4#41semidirect
517. C4×D47C4×D4semidirect
568. Dic47C4×#41semidirect
587. #2290D47semidirect
704. C47#34141semidirect
757. C4×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896702
C2×C4×#106253502
C2×#156895912
#202464622
#202464562
#202464512
#202464432
#202464372
#202464342
#202464072
#202464012
#202458742
#202458512
#202458472
#202458332
#202458322
#202458292
C42×C22⋊D472
C4×(C22⋊D47)⋊C42
#202457272
C4×C4⋊C4×D472
C47×#22902
#3414147