Finite Group Databasebeta

← #26375037

Subgroups — #26375037

Order 12032.

3134 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689632C211yesmaximal, characteristic
2C2×#15689591C211yesmaximal, characteristic, complemented
3C2×#117×D47C211yesmaximal, characteristic, complemented
4#20246076C212yesmaximal, complemented
5#20246074C212yesmaximal, complemented
6#20246065C212yesmaximal, complemented
7#20246063C212yesmaximal, complemented
8#20246058C212yesmaximal, complemented
9#20246052C212yesmaximal, complemented
10#20246047C212yesmaximal, complemented
11#20246041C212yesmaximal, complemented
12#20245874C211yesmaximal, characteristic, complemented
13#20245868C211yesmaximal, characteristic, complemented
14#20245852C211yesmaximal, characteristic, complemented
15#20245847C211yesmaximal, characteristic, complemented
16#20245847C211yesmaximal, characteristic, complemented
17#20245834C211yesmaximal, characteristic, complemented
18#20245833C211yesmaximal, characteristic, complemented
19#20245829C211yesmaximal, characteristic, complemented
20#20245827C211yesmaximal, characteristic, complemented
21#20245769C211yesmaximal, characteristic, complemented
22C4×#13093981C211yesmaximal, characteristic, complemented
23C47×#2293C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26#15689632C4116yescomplemented
27C2×#13094009C2211yescharacteristic
28C2×#13094006C2211yescharacteristic
29C2×#13094002C2211yescharacteristic
30C2×#13094001C2211yescharacteristic
31C2×#13093997C2211yescharacteristic
32C2×#13093996C2211yescharacteristic
33C2×#13093994C2211yescharacteristic
34C2×#13093992C2211yescharacteristic
35#15689591—28no—
36C2×#13093989C2212yescomplemented
37C2×C4×D188C2211yescharacteristic
38C2×#13093986C2212yes—
39C2×C4×C22⋊D47C2211yescharacteristic
40C2×C4×C22⋊D47C2211yescharacteristic
41C2×(C22⋊D47)⋊C4C2212yes—
42C2×(C22⋊D47)⋊C4C2212yescomplemented
43C2×#13093983C2211yescharacteristic
44C2×#13093982C2212yes—
45C2×#13093981C2211yescharacteristic
46C2×#13093981C2211yescharacteristic
47C2×#13093981C2211yescharacteristic
48C2×#13093981C2211yescharacteristic
49C2×#13093981C2211yescharacteristic
50C2×#13093981C2211yescharacteristic, complemented
51C2×#13093980C2212yes—
52#117×D47—28no—
53C2×C4⋊C4×D47C2212yes—
54C2×C22⋊C4×D47C2212yes—
55C22×C4×Dic47C2211yescharacteristic, complemented
56C2×C42×D47C2211yescharacteristic
57C2×C42×D47C2211yescharacteristic
58C2×C42×D47C2211yescharacteristic, complemented
59#15689027C2212yescomplemented
60#15689025C2212yes—
61#15689023C2212yes—
62#15689023C2212yes—
63#15689023C2212yescomplemented
64#15689021C2212yescomplemented
65#15689020C2212yescomplemented
66#15689018C2212yescomplemented
67#15689018C2212yescomplemented
68#15689018C2212yescomplemented
69#15689017C2212yes—
70#15689017C2212yes—
71#15689017C2212yescomplemented
72#15689016C2212yes—
73#15689014C2212yes—
74#15689014C2212yescomplemented
75#15689013C2212yes—
76#15689013C2212yes—
77#15689013C2212yescomplemented
78#15689012C2212yes—
79#15689010C2212yescomplemented
80#15689009C2212yescomplemented
81#15689006C2212yescomplemented
82#15689005C2212yescomplemented
83#15689003C2212yes—
84#15689001C2212yes—
85#15689001C2212yes—
86#15689000C2212yes—
87#15688999C2212yes—
88#15688999C2212yes—
89#15688998C2212yescomplemented
90#15688997C2212yes—
91#15688997C2212yescomplemented
92#15688995C2212yescomplemented
93#15688994C2212yes—
94#15688994C2212yescomplemented
95#15688985C2212yes—
96#15688982C2212yes—
97#15688981C2212yes—
98#15688978C2212yes—
99C4×Dic47⋊C4C2212yescomplemented
100C4×Dic47⋊C4C2212yescomplemented
101C4×Dic47⋊C4C2211yescharacteristic, complemented
102C4×Dic47⋊C4C2211yescharacteristic, complemented
103C4×C4⋊Dic47C2211yescharacteristic, complemented
104C4×(C2×D47)⋊C4C2211yescharacteristic
105C4×(C2×D47)⋊C4C2211yescharacteristic
106C4×(C2×D47)⋊C4C2212yes—
107C4×(C2×D47)⋊C4C2212yes—
108C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
109C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
110C4×C22⋊Dic47C2211yescharacteristic
111C4×C22⋊Dic47C2211yescharacteristic, complemented
112#15688969C2211yescharacteristic, complemented
113#15688969C2211yescharacteristic, complemented
114C42×Dic47C2211yescharacteristic, complemented
115C2×C4×D4×C47C2211yescharacteristic
116C2×#117×C47C2211yescharacteristic
117C2×#117×C47C2211yescharacteristic, complemented
118C47×#390C2212yes—
119C47×#389C2212yescomplemented
120C47×#388C2212yes—
121C47×#388C2212yescomplemented
122C4×C4⋊C4×C47C2211yescharacteristic, complemented
123C4×C22⋊C4×C47C2211yescharacteristic
124C4×C22⋊C4×C47C2211yescharacteristic, complemented
125C43×C47C2211yescharacteristic, complemented
126C24×D47C2311yescharacteristic
127C2×#10625350—24no—
128C2×#10625350—24no—
129C2×#10625350C2×C418yes—
130C22×Dic94C2311yescharacteristic
131C22×D188C2311yescharacteristic
132C22×D188C2311yescharacteristic
133C22×C22⋊D47C2311yescharacteristic
134C22×C22⋊D47C2311yescharacteristic
135C22×C22⋊D47C2311yescharacteristic
136C22×C22⋊D47C2311yescharacteristic
137C23×Dic47C2311yescharacteristic
138C23×Dic47C2312yes—
139C22×C4×D47—24no—
140C22×C4×D47—24no—
141C22×C4×D47C2×C418yescomplemented
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2312yes—
147C22×C4×D47C2312yes—
148C22×C4×D47C2312yes—
149C22×C4×D47C2311yescharacteristic
150#13094009C2×C418yescomplemented
151#13094006C2×C418yescomplemented
152#13094002C2×C418yescomplemented
153#13094001C2×C418yescomplemented
154#13093997C2×C418yescomplemented
155#13093996C2×C418yescomplemented
156#13093994C2×C418yescomplemented
157#13093992C2×C418yescomplemented
158#13093989—28no—
159C4×D188C2×C418yescomplemented
160#13093986—28no—
161C4×C22⋊D47C2×C418yescomplemented
162C4×C22⋊D47C2×C418yescomplemented
163(C22⋊D47)⋊C4—28no—
164(C22⋊D47)⋊C4—28no—
165#13093983—24no—
166#13093982—28no—
167#13093981—24no—
168#13093981—24no—
169#13093981—24no—
170#13093981—24no—
171#13093981—24no—
172#13093981C2×C418yescomplemented
173#13093980—28no—
174C2×C4⋊Dic47C2312yes—
175C2×C4⋊Dic47C2312yes—
176C2×C4⋊Dic47C2311yescharacteristic
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2311yescharacteristic
185C2×Dic47⋊C4C2311yescharacteristic
186C2×Dic47⋊C4C2311yescharacteristic
187C2×Dic47⋊C4C2311yescharacteristic
188C4⋊C4×D47—28no—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2311yescharacteristic
193C2×C22⋊Dic47C2311yescharacteristic
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
208C2×(C2×D47)⋊C4C2311yescharacteristic
209C22⋊C4×D47—28no—
210C2×C4×Dic47—24no—
211C2×C4×Dic47C2311yescharacteristic
212C2×C4×Dic47C2311yescharacteristic
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2312yes—
217C2×C4×Dic47C2312yes—
218C2×C4×Dic47C2312yes—
219C2×C4×Dic47C2311yescharacteristic
220C2×C4×Dic47C2311yescharacteristic
221C2×C4×Dic47C2312yes—
222C42×D47—24no—
223C42×D47—24no—
224C42×D47D418yescomplemented
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C47⋊#95C2312yes—
237C47⋊#95C2312yes—
238C22×D4×C47C2311yescharacteristic
239C23×C4×C47C2311yescharacteristic
240C23×C4×C47C2311yescharacteristic
241C4×D4×C47C2×C418yescomplemented
242#117×C47—24no—
243#117×C47—24no—
244C2×C4⋊C4×C47C2312yes—
245C2×C4⋊C4×C47C2312yes—
246C2×C4⋊C4×C47C2312yes—
247C2×C4⋊C4×C47C2311yescharacteristic
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2312yes—
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2312yes—
252C2×C22⋊C4×C47C2311yescharacteristic
253C2×C22⋊C4×C47C2311yescharacteristic
254C2×C42×C47C2311yescharacteristic
255C2×C42×C47C2311yescharacteristic
256C2×C42×C47C2311yescharacteristic
257C2×C42×C47C2312yes—
258C2×C42×C47C2312yes—
259C2×C42×C47C2311yescharacteristic
260C2×C42×C47C2311yescharacteristic
261#95×C47C2312yes—
262#95×C47C2312yes—
263#95×C47C2312yes—
264C24×C47C2411yescharacteristic
265C24×C47C2411yescharacteristic
266C23×D47—22no—
267C23×D47—22no—
268C23×D47—42no—
269C23×D47—42no—
270C23×D47C22×C414yes—
271C23×D47C2411yescharacteristic
272C23×D47C2411yescharacteristic
273C23×D47C2411yescharacteristic
274C2×D4×C47—42no—
275C2×D4×C47C22×C414yes—
276C22×C4×C47—22no—
277C22×C4×C47—22no—
278C22×C4×C47—22no—
279C22×C4×C47—22no—
280C22×C4×C47C22×C414yes—
281C22×C4×C47C22×C414yes—
282C22×C4×C47C2412yes—
283C22×C4×C47C2412yes—
284C22×C4×C47C2412yes—
285C22×C4×C47C2411yescharacteristic
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2412yes—
290C22×C4×C47C2411yescharacteristic
291C2×C22⋊D47—22no—
292C2×C22⋊D47—22no—
293C2×C22⋊D47—22no—
294C2×C22⋊D47—22no—
295C2×C22⋊D47—42no—
296C2×C22⋊D47—42no—
297C2×C22⋊D47C22×C414yes—
298C2×C22⋊D47C22×C414yes—
299C2×C22⋊D47C22×C414yes—
300C2×C22⋊D47C22×C414yes—
301C22×Dic47—22no—
302C22×Dic47—22no—
303C22×Dic47—24no—
304C22×Dic47—42no—
305C22×Dic47—42no—
306C22×Dic47C22×C414yes—
307C22×Dic47C2412yes—
308C22×Dic47C2412yes—
309C22×Dic47C2412yes—
310C22×Dic47C2411yescharacteristic
311C22×Dic47C2411yescharacteristic
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2412yes—
315C22×Dic47C2411yescharacteristic
316#10625350—232no—
317C2×D188—22no—
318C2×D188—22no—
319C2×D188—42no—
320C2×D188C22×C414yes—
321C2×D188C22×C414yes—
322C2×C4×D47—22no—
323C2×C4×D47—22no—
324C2×C4×D47—22no—
325C2×C4×D47—22no—
326C2×C4×D47—22no—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—22no—
330C2×C4×D47—232no—
331C2×C4×D47—24no—
332C2×C4×D47—24no—
333C2×C4×D47—42no—
334C2×C4×D47—42no—
335C2×C4×D47—42no—
336C2×C4×D47—42no—
337C2×C4×D47—42no—
338C2×C4×D47—42no—
339C2×C4×D47C22×C414yes—
340C2×C4×D47C22×C414yes—
341C2×C4×D47C22×C414yes—
342C2×C4×D47C22×C414yes—
343C2×C4×D47C22×C414yes—
344C2×C4×D47C2×D418yes—
345C2×C4×D47C2×D414yes—
346C2×C4×D47#4114yes—
347C2×Dic94—22no—
348C2×Dic94—22no—
349C2×Dic94C22×C414yes—
350C4⋊C4×C47—24no—
351C4⋊C4×C47—24no—
352C4⋊C4×C47—42no—
353C4⋊C4×C47C22×C414yes—
354C22⋊C4×C47—24no—
355C22⋊C4×C47—24no—
356C22⋊C4×C47—42no—
357C22⋊C4×C47—42no—
358C22⋊C4×C47C22×C414yes—
359C22⋊C4×C47C22×C414yes—
360C42×C47—22no—
361C42×C47—22no—
362C42×C47—22no—
363C42×C47—42no—
364C42×C47—42no—
365C42×C47C22×C414yes—
366C42×C47C2×D414yes—
367C22⋊Dic47—24no—
368C22⋊Dic47—42no—
369C22⋊Dic47—42no—
370C22⋊Dic47C22×C414yes—
371C22⋊Dic47C22×C414yes—
372(C2×D47)⋊C4—24no—
373(C2×D47)⋊C4—24no—
374(C2×D47)⋊C4—24no—
375(C2×D47)⋊C4—24no—
376(C2×D47)⋊C4—24no—
377(C2×D47)⋊C4—42no—
378(C2×D47)⋊C4—42no—
379(C2×D47)⋊C4—42no—
380(C2×D47)⋊C4—42no—
381(C2×D47)⋊C4C22×C414yes—
382(C2×D47)⋊C4C22×C414yes—
383(C2×D47)⋊C4C22×C414yes—
384(C2×D47)⋊C4C22×C414yes—
385(C2×D47)⋊C4C22×C414yes—
386(C2×D47)⋊C4C22×C414yes—
387C4⋊Dic47—24no—
388C4⋊Dic47—42no—
389C4⋊Dic47C22×C414yes—
390Dic47⋊C4—24no—
391Dic47⋊C4—24no—
392Dic47⋊C4—24no—
393Dic47⋊C4—24no—
394Dic47⋊C4—24no—
395Dic47⋊C4—42no—
396Dic47⋊C4—42no—
397Dic47⋊C4C22×C414yes—
398Dic47⋊C4C22×C414yes—
399Dic47⋊C4C22×C414yes—
400Dic47⋊C4C22×C414yes—
401C4×Dic47—22no—
402C4×Dic47—22no—
403C4×Dic47—22no—
404C4×Dic47—24no—
405C4×Dic47—24no—
406C4×Dic47—24no—
407C4×Dic47—42no—
408C4×Dic47—42no—
409C4×Dic47C22×C414yes—
410C4×Dic47C2×D414yes—
411C4×Dic47C2×D418yes—
412C23×C47—21no—
413C23×C47—21no—
414C23×C47—21no—
415C23×C47—21no—
416C23×C47—22no—
417C23×C47—22no—
418C23×C47—22no—
419C23×C47—22no—
420C23×C47C23×C412yes—
421C23×C47C23×C412yes—
422C23×C47C2511yescharacteristic
423C22×D47—22no—
424C22×D47—22no—
425C22×D47—21no—
426C22×D47—21no—
427C22×D47—21no—
428C22×D47—21no—
429C22×D47—22no—
430C22×D47—22no—
431C22×D47—22no—
432C22×D47—22no—
433C22×D47—28no—
434C22×D47—44no—
435C22×D47—44no—
436C22×D47—48no—
437C22×D47—48no—
438C22×D47C23×C412yes—
439C22×D47C23×C412yes—
440C22×D47C23×C412yes—
441C22×D47C22×D412yes—
442C22×D47C2×#4112yes—
443D4×C47—44no—
444C2×C4×C47—21no—
445C2×C4×C47—21no—
446C2×C4×C47—21no—
447C2×C4×C47—21no—
448C2×C4×C47—22no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—28no—
453C2×C4×C47—28no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—22no—
457C2×C4×C47—22no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47C23×C412yes—
464C2×C4×C47C23×C412yes—
465C2×C4×C47C23×C412yes—
466C2×C4×C47C23×C412yes—
467C2×C4×C47C23×C412yes—
468C2×C4×C47C22×D414yes—
469C2×C4×C47C22×D412yes—
470C2×C4×C47C2×#4112yes—
471C22⋊D47—28no—
472C22⋊D47—28no—
473C22⋊D47—44no—
474C22⋊D47—44no—
475C2×Dic47—21no—
476C2×Dic47—21no—
477C2×Dic47—21no—
478C2×Dic47—21no—
479C2×Dic47—22no—
480C2×Dic47—22no—
481C2×Dic47—22no—
482C2×Dic47—22no—
483C2×Dic47—28no—
484C2×Dic47—22no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—48no—
494C2×Dic47C23×C412yes—
495C2×Dic47C23×C412yes—
496C2×Dic47C23×C412yes—
497C2×Dic47C23×C412yes—
498C2×Dic47C23×C412yes—
499C2×Dic47C22×D414yes—
500C2×Dic47C22×D412yes—
501C2×Dic47C2×#4112yes—
502D188—28no—
503D188—44no—
504C4×D47—28no—
505C4×D47—28no—
506C4×D47—28no—
507C4×D47—28no—
508C4×D47—48no—
509C4×D47—48no—
510C4×D47—48no—
511C4×D47C4×D4116yes—
512Dic94—28no—
513#34065—471nomaximal, Sylow
514C22×C47—22no—
515C22×C47—22no—
516C22×C47—22no—
517C22×C47—22no—
518C22×C47—22no—
519C22×C47—22no—
520C22×C47—42no—
521C22×C47—42no—
522C22×C47—42no—
523C22×C47—42no—
524C22×C47C24×C411yescharacteristic
525C22×C47C23×D411yescharacteristic
526C22×C47C22×#4111yescharacteristic
527C22×C47#58512yes—
528C22×C47#58512yes—
529C2×D47—22no—
530C2×D47—22no—
531C2×D47—24no—
532C2×D47—24no—
533C2×D47—22no—
534C2×D47—22no—
535C2×D47—22no—
536C2×D47—22no—
537C2×D47—22no—
538C2×D47—22no—
539C2×D47—416no—
540C2×D47—42no—
541C2×D47—42no—
542C2×D47—42no—
543C2×D47—42no—
544C2×D47C2×C4×D414yes—
545C4×C47—22no—
546C4×C47—22no—
547C4×C47—22no—
548C4×C47—22no—
549C4×C47—24no—
550C4×C47—42no—
551C4×C47—42no—
552C4×C47—42no—
553C4×C47C2×C4×D414yes—
554Dic47—22no—
555Dic47—22no—
556Dic47—22no—
557Dic47—22no—
558Dic47—24no—
559Dic47—42no—
560Dic47—42no—
561Dic47—42no—
562Dic47C2×C4×D414yes—
563C2×#525—471no—
564C2×C4×#41—471no—
565C22×#117—471no—
566#2324—472no—
567#2324—472no—
568#2323—472no—
569#2323—472no—
570#2322—472no—
571#2322—472no—
572#2321—472no—
573#2321—472no—
574#2297—471no—
575#2296—471no—
576#2293—471no—
577#2293—471no—
578#2293—471no—
579#2293D4711yescharacteristic, complemented
580#2290—471no—
581#2290—471no—
582#2290—471no—
583#2290—471no—
584#2280—471no—
585C4×#117—471no—
586C2×C47—42no—
587C2×C47—42no—
588C2×C47C22×C4×D411yescharacteristic
589C2×C47#342811yescharacteristic
590C2×C47#342811yescharacteristic
591C2×C47#344912yes—
592C2×C47#345512yes—
593D47—24no—
594D47—42no—
595D47—42no—
596C22×#41—471no—
597C24×C4—471no—
598#525—4716no—
599C2×#123—471no—
600C2×#123—471no—
601C2×C22⋊Q8—471no—
602C2×C22⋊Q8—471no—
603C2×#121—471no—
604C2×#121—471no—
605C2×#120—471no—
606C2×#120—471no—
607C4×#41—948no—
608C2×C4×Q8—472no—
609C2×C4×D4—471no—
610C2×C4×D4—471no—
611C2×C4×D4—472no—
612C2×C4×D4—472no—
613C2×C4×D4—472no—
614C2×C4×D4—471no—
615C2×C4×D4C2×D4711yescharacteristic
616C2×#117—471no—
617C2×#117—472no—
618C2×#117—472no—
619C2×#117—471no—
620C2×#117—471no—
621C2×#117—471no—
622C2×#117—471no—
623C2×#117—471no—
624C2×#117—471no—
625C2×#117—948no—
626C2×#117C2×D4711yescharacteristic
627C2×#117C2×D4711yescharacteristic, complemented
628C22×C4⋊C4—472no—
629C22×C22⋊C4—472no—
630C22×C42—471no—
631C22×C42—471no—
632C22×C42—471no—
633C22×C42—471no—
634#391—472no—
635#390—472no—
636#390—472no—
637#390—472no—
638#390—472no—
639#390C2×D4712yes—
640#389—472no—
641#389—472no—
642#389—472no—
643#389—472no—
644#389—472no—
645#389C2×D4712yescomplemented
646#388—472no—
647#388—472no—
648#388—472no—
649#388—472no—
650#388—472no—
651#388—472no—
652#388—472no—
653#388—472no—
654#388—472no—
655#388—472no—
656#388C2×D4712yes—
657#388C2×D4712yescomplemented
658#387—472no—
659#387—472no—
660#387—472no—
661#387—472no—
662#386—472no—
663#386—472no—
664#386—472no—
665#386—472no—
666#386—472no—
667#386—472no—
668#385—472no—
669#385—472no—
670#385—472no—
671#385—472no—
672#385—472no—
673#385—472no—
674#381—472no—
675#380—472no—
676#380—472no—
677#379—472no—
678C4×C4⋊C4—471no—
679C4×C4⋊C4—472no—
680C4×C4⋊C4—472no—
681C4×C4⋊C4—471no—
682C4×C4⋊C4—471no—
683C4×C4⋊C4C2×D4711yescharacteristic, complemented
684C4×C22⋊C4—471no—
685C4×C22⋊C4—471no—
686C4×C22⋊C4—472no—
687C4×C22⋊C4—472no—
688C4×C22⋊C4—471no—
689C4×C22⋊C4—471no—
690C4×C22⋊C4—471no—
691C4×C22⋊C4—471no—
692C4×C22⋊C4C2×D4711yescharacteristic
693C4×C22⋊C4C2×D4711yescharacteristic, complemented
694#376—471no—
695#376—471no—
696C43—471no—
697C43C2×D4711yescharacteristic, complemented
698C47#3406511yescharacteristic, complemented, Sylow
699C25—471no—
700C2×#41—478no—
701C2×#41—944no—
702C2×#41—944no—
703C22×Q8—471no—
704C22×D4—471no—
705C22×D4—471no—
706C22×D4—471no—
707C22×D4—471no—
708C22×D4—471no—
709C22×D4—471no—
710C22×D4C22×D4711yescharacteristic
711C23×C4—471no—
712C23×C4—471no—
713C23×C4—478no—
714C23×C4—471no—
715C23×C4—471no—
716C23×C4—471no—
717C23×C4—471no—
718C23×C4—472no—
719C23×C4—472no—
720C23×C4—472no—
721C23×C4—472no—
722C23×C4—944no—
723C23×C4—944no—
724C23×C4C22×D4711yescharacteristic
725C23×C4C22×D4711yescharacteristic
726#123—478no—
727#123—478no—
728C22⋊Q8—478no—
729C22⋊Q8—478no—
730#121—478no—
731#121—478no—
732#120—478no—
733#120—478no—
734C4×Q8—948no—
735C4×D4—478no—
736C4×D4—478no—
737C4×D4—478no—
738C4×D4—948no—
739C4×D4—948no—
740C4×D4—948no—
741C4×D4C4×D4718yescomplemented
742#117—24no—
743#117—24no—
744#117—478no—
745#117—944no—
746#117—944no—
747#117—944no—
748#117—948no—
749#117—948no—
750#117—944no—
751#117—944no—
752#117—944no—
753C2×C4⋊C4—471no—
754C2×C4⋊C4—471no—
755C2×C4⋊C4—471no—
756C2×C4⋊C4—471no—
757C2×C4⋊C4—471no—
758C2×C4⋊C4—472no—
759C2×C4⋊C4—472no—
760C2×C4⋊C4—472no—
761C2×C4⋊C4—472no—
762C2×C4⋊C4—472no—
763C2×C4⋊C4—472no—
764C2×C4⋊C4—472no—
765C2×C4⋊C4—472no—
766C2×C4⋊C4—472no—
767C2×C4⋊C4—948no—
768C2×C4⋊C4C22×D4712yes—
769C2×C4⋊C4C22×D4712yes—
770C2×C4⋊C4C22×D4712yes—
771C2×C4⋊C4C22×D4711yescharacteristic
772C2×C22⋊C4—471no—
773C2×C22⋊C4—471no—
774C2×C22⋊C4—471no—
775C2×C22⋊C4—471no—
776C2×C22⋊C4—471no—
777C2×C22⋊C4—471no—
778C2×C22⋊C4—471no—
779C2×C22⋊C4—471no—
780C2×C22⋊C4—472no—
781C2×C22⋊C4—472no—
782C2×C22⋊C4—472no—
783C2×C22⋊C4—472no—
784C2×C22⋊C4—472no—
785C2×C22⋊C4—472no—
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—948no—
793C2×C22⋊C4C22×D4712yes—
794C2×C22⋊C4C22×D4712yes—
795C2×C22⋊C4C22×D4712yes—
796C2×C22⋊C4C22×D4712yes—
797C2×C22⋊C4C22×D4711yescharacteristic
798C2×C22⋊C4C22×D4711yescharacteristic
799C2×C42—472no—
800C2×C42—471no—
801C2×C42—471no—
802C2×C42—478no—
803C2×C42—472no—
804C2×C42—472no—
805C2×C42—472no—
806C2×C42—471no—
807C2×C42—471no—
808C2×C42—471no—
809C2×C42—472no—
810C2×C42—472no—
811C2×C42—944no—
812C2×C42—944no—
813C2×C42—944no—
814C2×C42C22×D4711yescharacteristic
815C2×C42C22×D4711yescharacteristic
816C2×C42C22×D4711yescharacteristic
817C2×C42C22×D4712yes—
818C2×C42C22×D4712yes—
819C2×C42C22×D4711yescharacteristic
820C2×C42C22×D4711yescharacteristic
821#95—472no—
822#95—472no—
823#95—472no—
824#95—472no—
825#95—472no—
826#95—472no—
827#95—472no—
828#95—472no—
829#95—472no—
830#95—472no—
831#95—472no—
832#95—472no—
833#95—472no—
834#95C22×D4712yes—
835#95C22×D4712yes—
836#95C22×D4712yes—
837C24—471no—
838C24—471no—
839C24—471no—
840C24—474no—
841C24—942no—
842C24—942no—
843C24—1882no—
844C24—1882no—
845C24C23×D4711yescharacteristic
846C24C23×D4711yescharacteristic
847#41—9432no—
848C2×Q8—474no—
849C2×Q8—942no—
850C2×Q8—942no—
851C2×D4—42no—
852C2×D4—474no—
853C2×D4—474no—
854C2×D4—474no—
855C2×D4—474no—
856C2×D4—474no—
857C2×D4—474no—
858C2×D4—942no—
859C2×D4—942no—
860C2×D4—942no—
861C2×D4—942no—
862C2×D4—942no—
863C2×D4—942no—
864C2×D4—1882no—
865C2×D4—1882no—
866C2×D4—1882no—
867C2×D4C2×C4×D4714yes—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—471no—
873C22×C4—474no—
874C22×C4—474no—
875C22×C4—474no—
876C22×C4—474no—
877C22×C4—472no—
878C22×C4—471no—
879C22×C4—471no—
880C22×C4—471no—
881C22×C4—471no—
882C22×C4—474no—
883C22×C4—474no—
884C22×C4—474no—
885C22×C4—474no—
886C22×C4—478no—
887C22×C4—472no—
888C22×C4—472no—
889C22×C4—472no—
890C22×C4—942no—
891C22×C4—942no—
892C22×C4—9432no—
893C22×C4—944no—
894C22×C4—942no—
895C22×C4—942no—
896C22×C4—944no—
897C22×C4—942no—
898C22×C4—942no—
899C22×C4—944no—
900C22×C4—942no—
901C22×C4—942no—
902C22×C4—942no—
903C22×C4—942no—
904C22×C4—1882no—
905C22×C4—1882no—
906C22×C4—1882no—
907C22×C4—1882no—
908C22×C4—1882no—
909C22×C4—1882no—
910C22×C4—1882no—
911C22×C4—1882no—
912C22×C4C2×C4×D4714yes—
913C22×C4C2×C4×D4714yes—
914C22×C4C23×D4712yes—
915C22×C4C23×D4712yes—
916C22×C4C23×D4712yes—
917C22×C4C23×D4711yescharacteristic
918C22×C4C23×D4711yescharacteristic
919C22×C4C23×D4711yescharacteristic
920C22×C4C23×D4711yescharacteristic
921C22×C4C23×D4712yes—
922C22×C4C23×D4711yescharacteristic
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—42no—
926C4⋊C4—474no—
927C4⋊C4—474no—
928C4⋊C4—474no—
929C4⋊C4—474no—
930C4⋊C4—474no—
931C4⋊C4—944no—
932C4⋊C4—944no—
933C4⋊C4—944no—
934C4⋊C4—944no—
935C4⋊C4—944no—
936C4⋊C4—944no—
937C4⋊C4—1882no—
938C4⋊C4—1882no—
939C4⋊C4—1882no—
940C4⋊C4C2×C4×D4714yes—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—474no—
946C22⋊C4—474no—
947C22⋊C4—474no—
948C22⋊C4—474no—
949C22⋊C4—474no—
950C22⋊C4—474no—
951C22⋊C4—474no—
952C22⋊C4—474no—
953C22⋊C4—944no—
954C22⋊C4—944no—
955C22⋊C4—944no—
956C22⋊C4—944no—
957C22⋊C4—944no—
958C22⋊C4—944no—
959C22⋊C4—1882no—
960C22⋊C4—1882no—
961C22⋊C4—1882no—
962C22⋊C4—1882no—
963C22⋊C4—1882no—
964C22⋊C4—1882no—
965C22⋊C4C2×C4×D4714yes—
966C22⋊C4C2×C4×D4714yes—
967C42—22no—
968C42—22no—
969C42—22no—
970C42—42no—
971C42—42no—
972C42—474no—
973C42—474no—
974C42—478no—
975C42—944no—
976C42—944no—
977C42—944no—
978C42—942no—
979C42—942no—
980C42—942no—
981C42—1882no—
982C42—1882no—
983C42C2×C4×D4714yes—
984C42D4×D4714yes—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—472no—
994C23—472no—
995C23—472no—
996C23—472no—
997C23—472no—
998C23—948no—
999C23—942no—
1000C23—942no—
1001C23—941no—
1002C23—941no—
1003C23—941no—
1004C23—941no—
1005C23—942no—
1006C23—942no—
1007C23—942no—
1008C23—942no—
1009C23—1884no—
1010C23—1884no—
1011C23—1888no—
1012C23—1888no—
1013C23C22×C4×D4712yes—
1014C23C22×C4×D4712yes—
1015C23C24×D4711yescharacteristic
1016Q8—948no—
1017D4—44no—
1018D4—948no—
1019D4—948no—
1020D4—948no—
1021D4—1884no—
1022D4—1884no—
1023D4—1884no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—28no—
1033C2×C4—28no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—472no—
1044C2×C4—472no—
1045C2×C4—472no—
1046C2×C4—4716no—
1047C2×C4—472no—
1048C2×C4—472no—
1049C2×C4—472no—
1050C2×C4—472no—
1051C2×C4—474no—
1052C2×C4—948no—
1053C2×C4—948no—
1054C2×C4—948no—
1055C2×C4—941no—
1056C2×C4—941no—
1057C2×C4—941no—
1058C2×C4—941no—
1059C2×C4—942no—
1060C2×C4—942no—
1061C2×C4—942no—
1062C2×C4—942no—
1063C2×C4—948no—
1064C2×C4—948no—
1065C2×C4—942no—
1066C2×C4—942no—
1067C2×C4—942no—
1068C2×C4—942no—
1069C2×C4—942no—
1070C2×C4—942no—
1071C2×C4—942no—
1072C2×C4—942no—
1073C2×C4—942no—
1074C2×C4—1888no—
1075C2×C4—1888no—
1076C2×C4—1888no—
1077C2×C4—1888no—
1078C2×C4C22×C4×D4712yes—
1079C2×C4C22×C4×D4712yes—
1080C2×C4C22×C4×D4712yes—
1081C2×C4C22×C4×D4712yes—
1082C2×C4C22×C4×D4712yes—
1083C2×C4C2×D4×D4714yes—
1084C2×C4C2×D4×D4712yes—
1085C2×C4#41×D4712yes—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—474no—
1097C22—944no—
1098C22—942no—
1099C22—942no—
1100C22—944no—
1101C22—942no—
1102C22—942no—
1103C22—942no—
1104C22—942no—
1105C22—942no—
1106C22—942no—
1107C22—18816no—
1108C22—1882no—
1109C22—1882no—
1110C22—1882no—
1111C22—1882no—
1112C22C23×C4×D4711yescharacteristic
1113C22C22×D4×D4711yescharacteristic
1114C22C2×#41×D4711yescharacteristic
1115C22#1568995912yes—
1116C22#1568995912yes—
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—24no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—474no—
1126C4—942no—
1127C4—942no—
1128C4—942no—
1129C4—942no—
1130C4—944no—
1131C4—1882no—
1132C4—1882no—
1133C4—1882no—
1134C4C4×D4×D4714yes—
1135C2—42no—
1136C2—42no—
1137C2—944no—
1138C2—1882no—
1139C2—1882no—
1140C2C2×C4×D4×D4711yescharacteristic
1141C2#2025658711yescharacteristic
1142C2#2025658911yescharacteristic
1143C2#2025671512yes—
1144C2#2025677112yes—
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC47×#2293C2
socle, cosocleC23×C47C25
prime radicalC2×#15689632C2
hypercenter#2293D47
hypocenterC47#34065
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. C2×#15689591C2semidirect
3. C2×#117×D47C2semidirect
4. #20246076C2semidirect
5. #20246074C2semidirect
6. #20246065C2semidirect
7. #20246063C2semidirect
8. #20246058C2semidirect
9. #20246052C2semidirect
10. #20246047C2semidirect
11. #20246041C2semidirect
12. #20245874C2semidirect
13. #20245868C2semidirect
14. #20245852C2semidirect
15. #20245847C2semidirect
16. #20245847C2semidirect
17. #20245834C2semidirect
18. #20245833C2semidirect
19. #20245829C2semidirect
20. #20245827C2semidirect
21. #20245769C2semidirect
22. C4×#13093981C2semidirect
23. C47×#2293C2semidirect
26. #15689632C4semidirect
36. C2×#13093989C22semidirect
42. C2×(C22⋊D47)⋊C4C22semidirect
50. C2×#13093981C22semidirect
55. C22×C4×Dic47C22semidirect
58. C2×C42×D47C22semidirect
59. #15689027C22semidirect
63. #15689023C22semidirect
64. #15689021C22semidirect
65. #15689020C22semidirect
66. #15689018C22semidirect
67. #15689018C22semidirect
68. #15689018C22semidirect
71. #15689017C22semidirect
74. #15689014C22semidirect
77. #15689013C22semidirect
79. #15689010C22semidirect
80. #15689009C22semidirect
81. #15689006C22semidirect
82. #15689005C22semidirect
89. #15688998C22semidirect
91. #15688997C22semidirect
92. #15688995C22semidirect
94. #15688994C22semidirect
99. C4×Dic47⋊C4C22semidirect
100. C4×Dic47⋊C4C22semidirect
101. C4×Dic47⋊C4C22semidirect
102. C4×Dic47⋊C4C22semidirect
103. C4×C4⋊Dic47C22semidirect
108. C4×(C2×D47)⋊C4C22semidirect
109. C4×(C2×D47)⋊C4C22semidirect
111. C4×C22⋊Dic47C22semidirect
112. #15688969C22semidirect
113. #15688969C22semidirect
114. C42×Dic47C22semidirect
117. C2×#117×C47C22semidirect
119. C47×#389C22semidirect
121. C47×#388C22semidirect
122. C4×C4⋊C4×C47C22semidirect
124. C4×C22⋊C4×C47C22semidirect
125. C43×C47C22semidirect
141. C22×C4×D47C2×C4semidirect
150. #13094009C2×C4semidirect
151. #13094006C2×C4semidirect
152. #13094002C2×C4semidirect
153. #13094001C2×C4semidirect
154. #13093997C2×C4semidirect
155. #13093996C2×C4semidirect
156. #13093994C2×C4semidirect
157. #13093992C2×C4semidirect
159. C4×D188C2×C4semidirect
161. C4×C22⋊D47C2×C4semidirect
162. C4×C22⋊D47C2×C4semidirect
172. #13093981C2×C4semidirect
224. C42×D47D4semidirect
241. C4×D4×C47C2×C4semidirect
579. #2293D47semidirect
627. C2×#117C2×D47semidirect
645. #389C2×D47semidirect
657. #388C2×D47semidirect
683. C4×C4⋊C4C2×D47semidirect
693. C4×C22⋊C4C2×D47semidirect
697. C43C2×D47semidirect
698. C47#34065semidirect
741. C4×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896322
C2×#156895912
C2×#117×D472
#202460762
#202460742
#202460652
#202460632
#202460582
#202460522
#202460472
#202460412
#202458742
#202458682
#202458522
#202458472
#202458342
#202458332
#202458292
#202458272
#202457692
C4×#130939812
C47×#22932
#3406547