Finite Group Databasebeta

← C4×#15689782 #26376101

Subgroups — C4×#15689782 #26376101

Order 12032.

3232 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689782C211yesmaximal, characteristic
2C2×C4×#10625350C211yesmaximal, characteristic, complemented
3C22×C4×Dic94C211yesmaximal, characteristic, complemented
4#20246460C212yesmaximal, complemented
5#20246457C211yesmaximal, characteristic, complemented
6#20246416C212yesmaximal, complemented
7#20246413C211yesmaximal, characteristic, complemented
8#20246405C212yesmaximal, complemented
9#20246402C211yesmaximal, characteristic, complemented
10#20246317C211yesmaximal, characteristic, complemented
11#20246311C212yesmaximal, complemented
12#20246308C211yesmaximal, characteristic, complemented
13#20246228C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic94C211yesmaximal, characteristic, complemented
15C4×#13094012C211yesmaximal, characteristic, complemented
16C4×#13094010C212yesmaximal, complemented
17C4×#13094003C211yesmaximal, characteristic, complemented
18C4×#13094002C212yesmaximal, complemented
19C4×#13093998C211yesmaximal, characteristic, complemented
20C4×#13093996C212yesmaximal, complemented
21C42×Dic94C211yesmaximal, characteristic, complemented
22C4×(C22⋊D47)⋊C4C212yesmaximal, complemented
23C42×D4×C47C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic
25C23×Dic94C2211yescharacteristic
26#15689782C4116yesdirect product factor
27C2×#13094012C2211yescharacteristic
28C2×#13094010C2212yes—
29C2×#13094003C2211yescharacteristic
30C2×#13094002C2212yes—
31C2×#13093998C2211yescharacteristic
32C2×#13093996C2212yes—
33C4×#10625350—28no—
34C2×C4×Dic94—28no—
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×Dic94C2211yescharacteristic
38C2×C4×Dic94C2212yes—
39C2×C4×Dic94C2212yes—
40C2×C4×Dic94C2211yescharacteristic
41C2×C4×Dic94C2211yescharacteristic
42C2×C4×Dic94C2211yescharacteristic
43C2×C4×Dic94C2211yescharacteristic
44C2×C4×D188C2211yescharacteristic
45C2×C4×D188C2211yescharacteristic
46C2×C4×C22⋊D47C2212yes—
47C2×C4×C22⋊D47C2212yes—
48C2×C4×C22⋊D47C2212yes—
49C2×(C22⋊D47)⋊C4C2212yes—
50C2×(C22⋊D47)⋊C4C2212yes—
51C2×#13093983C2211yescharacteristic
52C2×#13093981C2212yes—
53C22×C4⋊Dic47C2211yescharacteristic
54C22×Dic47⋊C4C2212yes—
55C22×C4×Dic47C2212yes—
56C2×C42×D47C2212yes—
57#15689029C2211yescharacteristic
58#15689029C2211yescharacteristic
59#15689027C2212yes—
60#15689027C2212yes—
61#15689025C2211yescharacteristic
62#15689025C2211yescharacteristic
63#15689023C2212yes—
64#15689023C2212yes—
65#15689021C2211yescharacteristic
66#15689021C2211yescharacteristic
67#15689018C2212yes—
68#15689018C2212yes—
69#15689017C2212yes—
70#15689016C2212yes—
71#15689015C2212yes—
72#15689014C2212yes—
73#15689014C2212yes—
74#15689014C2212yes—
75#15689013C2212yes—
76#15689012C2212yes—
77#15689011C2212yes—
78#15689009C2212yes—
79#15689007C2212yes—
80#15689005C2212yes—
81#15689003C2212yes—
82#15689002C2212yes—
83#15689000C2212yes—
84#15688997C2212yes—
85#15688996C2212yes—
86#15688994C2212yes—
87#15688989C2211yescharacteristic
88#15688987C2212yes—
89#15688983C2211yescharacteristic
90#15688983C2211yescharacteristic
91#15688982C2212yes—
92#15688981C2212yes—
93C4×Dic47⋊C4C2212yes—
94C4×Dic47⋊C4C2212yes—
95C4×Dic47⋊C4C2212yes—
96C4×Dic47⋊C4C2212yes—
97C4×C4⋊Dic47C2211yescharacteristic
98C4×C4⋊Dic47C2211yescharacteristic
99C4×C4⋊Dic47C2211yescharacteristic
100#15688974C2212yes—
101#15688974C2212yes—
102C22⋊C4×Dic47C2212yes—
103C22⋊C4×Dic47C2212yes—
104C4×(C2×D47)⋊C4C2212yes—
105C4×(C2×D47)⋊C4C2212yes—
106C4×(C2×D47)⋊C4C2212yes—
107C4×C22⋊Dic47C2212yes—
108#15688970C2212yes—
109#15688970C2212yes—
110C42×Dic47C2212yes—
111C2×C4×D4×C47C2211yescharacteristic
112C2×C4×D4×C47C2211yescharacteristic
113C2×C4×D4×C47C2211yescharacteristic
114C22×C42×C47C2211yescharacteristic
115C22×C42×C47C2211yescharacteristic
116C4×C4⋊C4×C47C2211yescharacteristic
117C4×C4⋊C4×C47C2211yescharacteristic
118C4×C4⋊C4×C47C2211yescharacteristic
119C4×C22⋊C4×C47C2211yescharacteristic
120C4×C22⋊C4×C47C2211yescharacteristic
121C4×C22⋊C4×C47C2211yescharacteristic
122C4×C22⋊C4×C47C2211yescharacteristic
123C4×C22⋊C4×C47C2211yescharacteristic
124C4×C22⋊C4×C47C2211yescharacteristic
125C43×C47C2211yescharacteristic
126C2×#10625350—24no—
127C2×#10625350—24no—
128C2×#10625350C2×C418yescomplemented
129C22×Dic94—24no—
130C22×Dic94—24no—
131C22×Dic94C2×C418yescomplemented
132C22×Dic94C2312yes—
133C22×Dic94C2311yescharacteristic
134C22×Dic94C2311yescharacteristic
135C22×D188C2311yescharacteristic
136C22×C22⋊D47C2312yes—
137C22×C22⋊D47C2312yes—
138C23×Dic47C2312yes—
139C23×Dic47C2312yes—
140C22×C4×D47C2312yes—
141C22×C4×D47C2312yes—
142C22×C4×D47C2312yes—
143#13094012C2×C418yescomplemented
144#13094010C2×C4116yescomplemented
145#13094003C2×C418yescomplemented
146#13094002C2×C4116yescomplemented
147#13093998C2×C418yescomplemented
148#13093996C2×C4116yescomplemented
149C4×Dic94—24no—
150C4×Dic94—24no—
151C4×Dic94—24no—
152C4×Dic94—24no—
153C4×Dic94—24no—
154C4×Dic94—28no—
155C4×Dic94—28no—
156C4×Dic94C2×C418yescomplemented
157C4×Dic94D418yescomplemented
158C4×D188—24no—
159C4×D188—24no—
160C4×C22⋊D47—28no—
161C4×C22⋊D47—28no—
162C4×C22⋊D47—28no—
163(C22⋊D47)⋊C4—28no—
164(C22⋊D47)⋊C4C2×C4116yescomplemented
165#13093983—24no—
166#13093981—28no—
167C2×C4⋊Dic47—24no—
168C2×C4⋊Dic47C2311yescharacteristic
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2312yes—
172C2×C4⋊Dic47C2311yescharacteristic
173C2×C4⋊Dic47C2311yescharacteristic
174C2×Dic47⋊C4—28no—
175C2×Dic47⋊C4C2312yes—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×C22⋊Dic47C2312yes—
186C2×C22⋊Dic47C2312yes—
187C2×C22⋊Dic47C2312yes—
188C2×C22⋊Dic47C2312yes—
189C2×(C2×D47)⋊C4C2312yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×C4×Dic47—28no—
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2312yes—
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2312yes—
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2312yes—
208C2×C4×Dic47C2312yes—
209C2×C4×Dic47C2312yes—
210C42×D47—28no—
211C47⋊#95C2312yes—
212C47⋊#95C2312yes—
213C47⋊#95C2312yes—
214C47⋊#95C2312yes—
215C47⋊#95C2312yes—
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C22×D4×C47C2311yescharacteristic
225C23×C4×C47C2311yescharacteristic
226C23×C4×C47C2311yescharacteristic
227C23×C4×C47C2311yescharacteristic
228C23×C4×C47C2311yescharacteristic
229C23×C4×C47C2311yescharacteristic
230C23×C4×C47C2311yescharacteristic
231C4×D4×C47—24no—
232C4×D4×C47—24no—
233C4×D4×C47C2×C418yescomplemented
234C2×C4⋊C4×C47C2311yescharacteristic
235C2×C4⋊C4×C47C2311yescharacteristic
236C2×C4⋊C4×C47C2311yescharacteristic
237C2×C22⋊C4×C47C2311yescharacteristic
238C2×C22⋊C4×C47C2311yescharacteristic
239C2×C22⋊C4×C47C2311yescharacteristic
240C2×C22⋊C4×C47C2311yescharacteristic
241C2×C22⋊C4×C47C2311yescharacteristic
242C2×C22⋊C4×C47C2311yescharacteristic
243C2×C42×C47—24no—
244C2×C42×C47—24no—
245C2×C42×C47C2311yescharacteristic
246C2×C42×C47C2311yescharacteristic
247C2×C42×C47C2311yescharacteristic
248C2×C42×C47C2311yescharacteristic
249C2×C42×C47C2311yescharacteristic
250C2×C42×C47C2311yescharacteristic
251C2×C42×C47C2311yescharacteristic
252C2×C42×C47C2311yescharacteristic
253C2×C42×C47C2311yescharacteristic
254C2×C42×C47C2311yescharacteristic
255C2×C42×C47C2311yescharacteristic
256C2×C42×C47C2311yescharacteristic
257C2×C42×C47C2311yescharacteristic
258#95×C47C2311yescharacteristic
259#95×C47C2311yescharacteristic
260#95×C47C2311yescharacteristic
261#95×C47C2311yescharacteristic
262#95×C47C2311yescharacteristic
263#95×C47C2311yescharacteristic
264C24×C47C2411yescharacteristic
265C24×C47C2411yescharacteristic
266C23×D47C2412yes—
267C2×D4×C47—22no—
268C2×D4×C47—22no—
269C2×D4×C47C22×C414yes—
270C22×C4×C47—22no—
271C22×C4×C47—22no—
272C22×C4×C47—22no—
273C22×C4×C47—22no—
274C22×C4×C47—22no—
275C22×C4×C47—22no—
276C22×C4×C47—22no—
277C22×C4×C47—22no—
278C22×C4×C47—22no—
279C22×C4×C47—22no—
280C22×C4×C47—22no—
281C22×C4×C47—22no—
282C22×C4×C47—22no—
283C22×C4×C47—41no—
284C22×C4×C47—41no—
285C22×C4×C47C22×C414yes—
286C22×C4×C47C22×C414yes—
287C22×C4×C47#4114yescomplemented
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2411yescharacteristic
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2411yescharacteristic
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2411yescharacteristic
296C22×C4×C47C2411yescharacteristic
297C22×C4×C47C2411yescharacteristic
298C22×C4×C47C2411yescharacteristic
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2411yescharacteristic
301C2×C22⋊D47—24no—
302C2×C22⋊D47—24no—
303C2×C22⋊D47—24no—
304C2×C22⋊D47—24no—
305C2×C22⋊D47C22×C418yes—
306C2×C22⋊D47C22×C418yes—
307C22×Dic47—24no—
308C22×Dic47—24no—
309C22×Dic47—24no—
310C22×Dic47—24no—
311C22×Dic47—42no—
312C22×Dic47C22×C418yes—
313C22×Dic47C2412yes—
314C22×Dic47C2412yes—
315C22×Dic47C2412yes—
316C22×Dic47C2412yes—
317C22×Dic47C2412yes—
318C22×Dic47C2412yes—
319C22×Dic47C2412yes—
320#10625350—232no—
321C2×D188—22no—
322C2×D188—22no—
323C2×D188C22×C414yes—
324C2×C4×D47—24no—
325C2×C4×D47—24no—
326C2×C4×D47—24no—
327C2×C4×D47—24no—
328C2×C4×D47—24no—
329C2×C4×D47—24no—
330C2×C4×D47—24no—
331C2×C4×D47—42no—
332C2×C4×D47C22×C418yes—
333C2×Dic94—22no—
334C2×Dic94—22no—
335C2×Dic94—24no—
336C2×Dic94—24no—
337C2×Dic94—232no—
338C2×Dic94C22×C418yes—
339C2×Dic94C22×C414yes—
340C2×Dic94C22×C414yes—
341C2×Dic94C2×D414yes—
342C2×Dic94#4114yes—
343C4⋊C4×C47—22no—
344C4⋊C4×C47—22no—
345C4⋊C4×C47C22×C414yes—
346C22⋊C4×C47—22no—
347C22⋊C4×C47—22no—
348C22⋊C4×C47—22no—
349C22⋊C4×C47C22×C414yes—
350C22⋊C4×C47C22×C414yes—
351C22⋊C4×C47#4114yescomplemented
352C42×C47—22no—
353C42×C47—22no—
354C42×C47—22no—
355C42×C47—22no—
356C42×C47—22no—
357C42×C47—22no—
358C42×C47—22no—
359C42×C47—22no—
360C42×C47—22no—
361C42×C47—22no—
362C42×C47—41no—
363C42×C47C22×C414yes—
364C42×C47C2×D414yes—
365C22⋊Dic47—24no—
366C22⋊Dic47—24no—
367C22⋊Dic47—42no—
368C22⋊Dic47C22×C418yes—
369(C2×D47)⋊C4—24no—
370(C2×D47)⋊C4—24no—
371(C2×D47)⋊C4—24no—
372(C2×D47)⋊C4—24no—
373(C2×D47)⋊C4—42no—
374(C2×D47)⋊C4—42no—
375(C2×D47)⋊C4C22×C418yes—
376(C2×D47)⋊C4C22×C418yes—
377(C2×D47)⋊C4C22×C418yes—
378C4⋊Dic47—22no—
379C4⋊Dic47—22no—
380C4⋊Dic47—22no—
381C4⋊Dic47—24no—
382C4⋊Dic47C22×C414yes—
383C4⋊Dic47C2×D414yes—
384Dic47⋊C4—24no—
385Dic47⋊C4—24no—
386Dic47⋊C4—24no—
387Dic47⋊C4—24no—
388Dic47⋊C4—24no—
389Dic47⋊C4—24no—
390Dic47⋊C4—24no—
391Dic47⋊C4C22×C418yes—
392Dic47⋊C4C22×C418yes—
393Dic47⋊C4C2×D418yes—
394C4×Dic47—24no—
395C4×Dic47—24no—
396C4×Dic47—24no—
397C4×Dic47—24no—
398C4×Dic47—24no—
399C4×Dic47—24no—
400C4×Dic47—24no—
401C4×Dic47—24no—
402C4×Dic47—42no—
403C4×Dic47C22×C418yes—
404C4×Dic47C2×D418yes—
405C23×C47—21no—
406C23×C47—21no—
407C23×C47—21no—
408C23×C47—21no—
409C23×C47—21no—
410C23×C47—21no—
411C23×C47—21no—
412C23×C47—21no—
413C23×C47—21no—
414C23×C47—21no—
415C23×C47C23×C412yes—
416C23×C47C23×C412yes—
417C23×C47C2×#4112yes—
418C23×C47C2×#4112yes—
419C23×C47C2511yescharacteristic
420C22×D47—22no—
421C22×D47—22no—
422C22×D47—22no—
423C22×D47—22no—
424C22×D47—22no—
425C22×D47—22no—
426C22×D47C23×C414yes—
427D4×C47—28no—
428C2×C4×C47—21no—
429C2×C4×C47—21no—
430C2×C4×C47—21no—
431C2×C4×C47—21no—
432C2×C4×C47—21no—
433C2×C4×C47—21no—
434C2×C4×C47—21no—
435C2×C4×C47—21no—
436C2×C4×C47—21no—
437C2×C4×C47—21no—
438C2×C4×C47—21no—
439C2×C4×C47—21no—
440C2×C4×C47—21no—
441C2×C4×C47—21no—
442C2×C4×C47—21no—
443C2×C4×C47—21no—
444C2×C4×C47—28no—
445C2×C4×C47—28no—
446C2×C4×C47—28no—
447C2×C4×C47—21no—
448C2×C4×C47—21no—
449C2×C4×C47—21no—
450C2×C4×C47—21no—
451C2×C4×C47—21no—
452C2×C4×C47—21no—
453C2×C4×C47—21no—
454C2×C4×C47—21no—
455C2×C4×C47—21no—
456C2×C4×C47—44no—
457C2×C4×C47—44no—
458C2×C4×C47—44no—
459C2×C4×C47C23×C412yes—
460C2×C4×C47C23×C412yes—
461C2×C4×C47C23×C412yes—
462C2×C4×C47C23×C412yes—
463C2×C4×C47C23×C412yes—
464C2×C4×C47C22×D412yes—
465C2×C4×C47C22×D412yes—
466C2×C4×C47C22×D412yes—
467C2×C4×C47C2×#4112yes—
468C2×C4×C47C2×#4112yes—
469C2×C4×C47C2×#4112yes—
470C2×C4×C47C2×#4112yes—
471C2×C4×C47C2×#4112yes—
472C2×C4×C472−1+412yes—
473C22⋊D47—216no—
474C22⋊D47—216no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—22no—
478C2×Dic47—22no—
479C2×Dic47—22no—
480C2×Dic47—22no—
481C2×Dic47—216no—
482C2×Dic47—22no—
483C2×Dic47—22no—
484C2×Dic47—22no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—48no—
492C2×Dic47C23×C414yes—
493C2×Dic47C23×C414yes—
494C2×Dic47C23×C414yes—
495C2×Dic47C22×D414yes—
496C2×Dic47C22×D414yes—
497C2×Dic47C2×#4114yes—
498D188—28no—
499C4×D47—216no—
500C4×D47—48no—
501C4×D47—48no—
502Dic94—28no—
503Dic94—216no—
504Dic94C4×D4116yescomplemented
505C4×#548—471nomaximal, Sylow
506C22×C47—22no—
507C22×C47—22no—
508C22×C47—22no—
509C22×C47—22no—
510C22×C47—22no—
511C22×C47—22no—
512C22×C47—22no—
513C22×C47—22no—
514C22×C47—22no—
515C22×C47—41no—
516C22×C47—41no—
517C22×C47—41no—
518C22×C47—41no—
519C22×C47C4×#4114yescomplemented
520C22×C47C24×C411yescharacteristic
521C22×C47C23×D411yescharacteristic
522C22×C47C22×#4111yescharacteristic
523C22×C47C22×#4111yescharacteristic
524C22×C47C22×#4111yescharacteristic
525C22×C47C2×2−1+411yescharacteristic
526C22×C47#58511yescharacteristic
527C2×D47—24no—
528C2×D47—24no—
529C2×D47—24no—
530C2×D47—42no—
531C2×D47—42no—
532C2×D47—42no—
533C2×D47—42no—
534C4×C47—22no—
535C4×C47—22no—
536C4×C47—22no—
537C4×C47—22no—
538C4×C47—22no—
539C4×C47—22no—
540C4×C47—22no—
541C4×C47—22no—
542C4×C47—41no—
543C4×C47—41no—
544C4×C47—41no—
545C4×C47C2×C4×D414yes—
546C4×C47#54814yescomplemented
547Dic47—24no—
548Dic47—24no—
549Dic47—24no—
550Dic47—42no—
551Dic47—42no—
552Dic47—42no—
553Dic47C2×C4×D418yes—
554C2×#548—471no—
555C2×C4×#41—471no—
556C22×C4×Q8—471no—
557#2367—471no—
558#2367—472no—
559#2362—472no—
560#2362—471no—
561#2361—471no—
562#2361—472no—
563#2352—472no—
564#2352—471no—
565#2351—471no—
566#2341—471no—
567Q8×C22⋊C4—471no—
568C4×#124—472no—
569C4×#124—471no—
570C4×C22⋊Q8—471no—
571C4×C22⋊Q8—472no—
572C4×#121—471no—
573C4×#121—472no—
574C42×Q8—471no—
575C42×D4—472no—
576C42×D4D4711yescharacteristic, complemented
577C2×C47—24no—
578C2×C47—42no—
579C2×C47C22×C4×D411yescharacteristic
580C2×C47C2×C4×#4111yescharacteristic
581C2×C47C4×2−1+411yescharacteristic
582C2×C47C2×#54811yescharacteristic
583C2×C47D4×#4111yescharacteristic
584C2×C47#348011yescharacteristic
585C2×C47#348211yescharacteristic
586D47—44no—
587C22×#41—471no—
588C23×Q8—471no—
589#548—4716no—
590C2×#124—472no—
591C2×#124—471no—
592C2×C22⋊Q8—471no—
593C2×C22⋊Q8—472no—
594C2×#121—472no—
595C2×#121—471no—
596C4×#41—948no—
597C2×C4×Q8—471no—
598C2×C4×Q8—471no—
599C2×C4×Q8—471no—
600C2×C4×Q8—471no—
601C2×C4×Q8—471no—
602C2×C4×Q8—471no—
603C2×C4×Q8—472no—
604C2×C4×Q8—472no—
605C2×C4×Q8—471no—
606C2×C4×Q8—948no—
607C2×C4×D4—472no—
608C2×C4×D4—472no—
609C2×C4×D4—472no—
610C2×C4×D4—472no—
611C2×C4×D4—472no—
612C2×C4×D4—471no—
613C2×C4×D4—471no—
614C2×C4×D4C2×D4711yescharacteristic
615C2×C4×D4C2×D4711yescharacteristic
616C2×C4×D4C2×D4711yescharacteristic
617C2×#117—471no—
618C2×#117—472no—
619C22×C4⋊C4—472no—
620C22×C4⋊C4—471no—
621C22×C42—472no—
622C22×C42—472no—
623C22×C42C2×D4711yescharacteristic
624C22×C42C2×D4711yescharacteristic
625#391—471no—
626#391—471no—
627#391—472no—
628#391—472no—
629#390—472no—
630#390—472no—
631#390—471no—
632#390—471no—
633#389—472no—
634#389—472no—
635#389—471no—
636#389—471no—
637#388—472no—
638#388—472no—
639#388—472no—
640#388—472no—
641#388—472no—
642#388—472no—
643#388—472no—
644#388—472no—
645#388—472no—
646#387—472no—
647#387—472no—
648#387—472no—
649#386—472no—
650#386—472no—
651#386—472no—
652#385—472no—
653#385—472no—
654#385—472no—
655#382—471no—
656#382—472no—
657#380—471no—
658#380—471no—
659#380—472no—
660#380—472no—
661C4×C4⋊C4—471no—
662C4×C4⋊C4—471no—
663C4×C4⋊C4—471no—
664C4×C4⋊C4—472no—
665C4×C4⋊C4—472no—
666C4×C4⋊C4—472no—
667C4×C4⋊C4—472no—
668C4×C4⋊C4—472no—
669C4×C4⋊C4—472no—
670C4×C4⋊C4C2×D4711yescharacteristic
671C4×C4⋊C4C2×D4711yescharacteristic
672C4×C4⋊C4C2×D4711yescharacteristic
673C4×C22⋊C4—472no—
674C4×C22⋊C4—472no—
675C4×C22⋊C4—472no—
676C4×C22⋊C4—472no—
677C4×C22⋊C4—472no—
678C4×C22⋊C4—472no—
679C4×C22⋊C4—472no—
680C4×C22⋊C4—472no—
681C4×C22⋊C4C2×D4711yescharacteristic
682C4×C22⋊C4C2×D4711yescharacteristic
683C4×C22⋊C4C2×D4711yescharacteristic
684C4×C22⋊C4C2×D4711yescharacteristic
685C4×C22⋊C4C2×D4711yescharacteristic
686C4×C22⋊C4C2×D4711yescharacteristic
687C43—472no—
688C43C2×D4711yescharacteristic
689C47C4×#54811yescharacteristic, complemented, Sylow
690C2×#41—478no—
691C2×#41—944no—
692C2×#41—944no—
693C22×Q8—478no—
694C22×Q8—471no—
695C22×Q8—472no—
696C22×Q8—471no—
697C22×Q8—944no—
698C22×Q8—944no—
699C22×D4—472no—
700C22×D4—472no—
701C22×D4—471no—
702C22×D4C22×D4711yescharacteristic
703C23×C4—472no—
704C23×C4—472no—
705C23×C4—472no—
706C23×C4—472no—
707C23×C4—472no—
708C23×C4C22×D4711yescharacteristic
709C23×C4C22×D4711yescharacteristic
710C23×C4C22×D4711yescharacteristic
711C23×C4C22×D4711yescharacteristic
712C23×C4C22×D4711yescharacteristic
713C23×C4C22×D4711yescharacteristic
714#124—4716no—
715#124—478no—
716C22⋊Q8—478no—
717C22⋊Q8—4716no—
718#121—4716no—
719#121—478no—
720C4×Q8—478no—
721C4×Q8—478no—
722C4×Q8—948no—
723C4×Q8—948no—
724C4×Q8—944no—
725C4×Q8—944no—
726C4×Q8—944no—
727C4×Q8—944no—
728C4×Q8—944no—
729C4×D4—24no—
730C4×D4—24no—
731C4×D4—4716no—
732C4×D4—944no—
733C4×D4—948no—
734C4×D4—948no—
735C4×D4—948no—
736C4×D4—948no—
737C4×D4—944no—
738C4×D4C4×D4718yescomplemented
739#117—948no—
740#117—944no—
741C2×C4⋊C4—472no—
742C2×C4⋊C4—471no—
743C2×C4⋊C4—472no—
744C2×C4⋊C4—472no—
745C2×C4⋊C4—471no—
746C2×C4⋊C4—472no—
747C2×C4⋊C4—472no—
748C2×C4⋊C4—472no—
749C2×C4⋊C4—471no—
750C2×C4⋊C4—472no—
751C2×C4⋊C4—472no—
752C2×C4⋊C4—471no—
753C2×C4⋊C4—472no—
754C2×C4⋊C4—472no—
755C2×C4⋊C4—472no—
756C2×C4⋊C4—471no—
757C2×C4⋊C4—948no—
758C2×C4⋊C4—944no—
759C2×C4⋊C4C22×D4711yescharacteristic
760C2×C4⋊C4C22×D4711yescharacteristic
761C2×C4⋊C4C22×D4711yescharacteristic
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—472no—
774C2×C22⋊C4—472no—
775C2×C22⋊C4C22×D4711yescharacteristic
776C2×C22⋊C4C22×D4711yescharacteristic
777C2×C22⋊C4C22×D4711yescharacteristic
778C2×C22⋊C4C22×D4711yescharacteristic
779C2×C22⋊C4C22×D4711yescharacteristic
780C2×C22⋊C4C22×D4711yescharacteristic
781C2×C42—24no—
782C2×C42—24no—
783C2×C42—472no—
784C2×C42—472no—
785C2×C42—472no—
786C2×C42—472no—
787C2×C42—472no—
788C2×C42—472no—
789C2×C42—472no—
790C2×C42—472no—
791C2×C42—472no—
792C2×C42—472no—
793C2×C42—472no—
794C2×C42—948no—
795C2×C42—948no—
796C2×C42C22×D4711yescharacteristic
797C2×C42C22×D4711yescharacteristic
798C2×C42C22×D4711yescharacteristic
799C2×C42C22×D4711yescharacteristic
800C2×C42C22×D4711yescharacteristic
801C2×C42C22×D4711yescharacteristic
802C2×C42C22×D4711yescharacteristic
803C2×C42C22×D4711yescharacteristic
804C2×C42C22×D4711yescharacteristic
805C2×C42C22×D4711yescharacteristic
806C2×C42C22×D4711yescharacteristic
807C2×C42C22×D4711yescharacteristic
808C2×C42C22×D4711yescharacteristic
809#95—472no—
810#95—472no—
811#95—472no—
812#95—472no—
813#95—472no—
814#95—472no—
815#95—472no—
816#95—472no—
817#95—472no—
818#95—472no—
819#95—472no—
820#95—472no—
821#95—472no—
822#95C22×D4711yescharacteristic
823#95C22×D4711yescharacteristic
824#95C22×D4711yescharacteristic
825#95C22×D4711yescharacteristic
826#95C22×D4711yescharacteristic
827#95C22×D4711yescharacteristic
828C24—472no—
829C24C23×D4711yescharacteristic
830C24C23×D4711yescharacteristic
831#41—9432no—
832C2×Q8—474no—
833C2×Q8—478no—
834C2×Q8—474no—
835C2×Q8—474no—
836C2×Q8—474no—
837C2×Q8—944no—
838C2×Q8—944no—
839C2×Q8—9432no—
840C2×Q8—942no—
841C2×Q8—942no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—478no—
845C2×D4—478no—
846C2×D4—474no—
847C2×D4—944no—
848C2×D4—944no—
849C2×D4—944no—
850C2×D4—944no—
851C2×D4—942no—
852C2×D4—942no—
853C2×D4C2×C4×D4714yes—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—472no—
870C22×C4—478no—
871C22×C4—472no—
872C22×C4—472no—
873C22×C4—472no—
874C22×C4—478no—
875C22×C4—472no—
876C22×C4—472no—
877C22×C4—472no—
878C22×C4—944no—
879C22×C4—944no—
880C22×C4—944no—
881C22×C4—944no—
882C22×C4—944no—
883C22×C4—944no—
884C22×C4—944no—
885C22×C4—944no—
886C22×C4—944no—
887C22×C4—944no—
888C22×C4—944no—
889C22×C4—1882no—
890C22×C4—1882no—
891C22×C4C2×C4×D4714yes—
892C22×C4C2×C4×D4714yes—
893C22×C4#1062535014yescomplemented
894C22×C4C23×D4711yescharacteristic
895C22×C4C23×D4711yescharacteristic
896C22×C4C23×D4711yescharacteristic
897C22×C4C23×D4711yescharacteristic
898C22×C4C23×D4711yescharacteristic
899C22×C4C23×D4711yescharacteristic
900C22×C4C23×D4711yescharacteristic
901C22×C4C23×D4711yescharacteristic
902C22×C4C23×D4711yescharacteristic
903C22×C4C23×D4711yescharacteristic
904C22×C4C23×D4711yescharacteristic
905C22×C4C23×D4711yescharacteristic
906C22×C4C23×D4711yescharacteristic
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—478no—
910C4⋊C4—478no—
911C4⋊C4—474no—
912C4⋊C4—478no—
913C4⋊C4—474no—
914C4⋊C4—944no—
915C4⋊C4—944no—
916C4⋊C4—944no—
917C4⋊C4—944no—
918C4⋊C4—944no—
919C4⋊C4—944no—
920C4⋊C4—942no—
921C4⋊C4—942no—
922C4⋊C4—942no—
923C4⋊C4—944no—
924C4⋊C4—944no—
925C4⋊C4C2×C4×D4714yes—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—478no—
930C22⋊C4—478no—
931C22⋊C4—478no—
932C22⋊C4—478no—
933C22⋊C4—944no—
934C22⋊C4—944no—
935C22⋊C4—944no—
936C22⋊C4—944no—
937C22⋊C4—944no—
938C22⋊C4—944no—
939C22⋊C4—1882no—
940C22⋊C4—1882no—
941C22⋊C4—1882no—
942C22⋊C4C2×C4×D4714yes—
943C22⋊C4C2×C4×D4714yes—
944C22⋊C4#1062535014yescomplemented
945C42—22no—
946C42—22no—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—22no—
955C42—41no—
956C42—478no—
957C42—478no—
958C42—944no—
959C42—944no—
960C42—944no—
961C42—944no—
962C42—944no—
963C42—944no—
964C42—944no—
965C42—944no—
966C42—1882no—
967C42C2×C4×D4714yes—
968C42D4×D4714yes—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—474no—
980C23—942no—
981C23—942no—
982C23—942no—
983C23—942no—
984C23—942no—
985C23—942no—
986C23C22×C4×D4712yes—
987C23C22×C4×D4712yes—
988C23C2×#1062535012yes—
989C23C2×#1062535012yes—
990C23C24×D4711yescharacteristic
991Q8—4716no—
992Q8—9416no—
993Q8—948no—
994D4—28no—
995D4—9416no—
996D4—9416no—
997D4—948no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—28no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—474no—
1030C2×C4—474no—
1031C2×C4—474no—
1032C2×C4—474no—
1033C2×C4—474no—
1034C2×C4—474no—
1035C2×C4—9416no—
1036C2×C4—9416no—
1037C2×C4—942no—
1038C2×C4—942no—
1039C2×C4—942no—
1040C2×C4—942no—
1041C2×C4—942no—
1042C2×C4—942no—
1043C2×C4—942no—
1044C2×C4—942no—
1045C2×C4—942no—
1046C2×C4—942no—
1047C2×C4—942no—
1048C2×C4—942no—
1049C2×C4—942no—
1050C2×C4—942no—
1051C2×C4—942no—
1052C2×C4—1888no—
1053C2×C4—1888no—
1054C2×C4—1888no—
1055C2×C4C22×C4×D4712yes—
1056C2×C4C22×C4×D4712yes—
1057C2×C4C22×C4×D4712yes—
1058C2×C4C22×C4×D4712yes—
1059C2×C4C22×C4×D4712yes—
1060C2×C4C2×D4×D4712yes—
1061C2×C4C2×D4×D4712yes—
1062C2×C4C2×D4×D4712yes—
1063C2×C4#41×D4712yes—
1064C2×C4C2×#1062535012yes—
1065C2×C4C2×#1062535012yes—
1066C2×C4C2×#1062535012yes—
1067C2×C4C2×#1062535012yes—
1068C2×C4#1309407112yes—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—944no—
1083C22—944no—
1084C22—944no—
1085C22—1882no—
1086C22—1882no—
1087C22—1882no—
1088C22—1882no—
1089C22C4×#1062535014yescomplemented
1090C22C23×C4×D4711yescharacteristic
1091C22C22×D4×D4711yescharacteristic
1092C22C2×#41×D4711yescharacteristic
1093C22C22×#1062535011yescharacteristic
1094C22C22×#1062535011yescharacteristic
1095C22C2×#1309407111yescharacteristic
1096C22#1568995911yescharacteristic
1097C4—22no—
1098C4—22no—
1099C4—22no—
1100C4—22no—
1101C4—22no—
1102C4—22no—
1103C4—22no—
1104C4—22no—
1105C4—41no—
1106C4—41no—
1107C4—41no—
1108C4—478no—
1109C4—944no—
1110C4—944no—
1111C4—944no—
1112C4—1882no—
1113C4—1882no—
1114C4—1882no—
1115C4C4×D4×D4714yes—
1116C4#1568978214yesdirect product factor
1117C2—24no—
1118C2—42no—
1119C2—1884no—
1120C2C2×C4×D4×D4711yescharacteristic
1121C2C2×C4×#1062535011yescharacteristic
1122C2C4×#1309407111yescharacteristic
1123C2C2×#1568978211yescharacteristic
1124C2D4×#1062535011yescharacteristic
1125C2#2025698111yescharacteristic
1126C2#2025700311yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC42×D4×C47C2
socle, cosocleC23×C47C25
prime radicalC2×#15689782C2
hypercenterC42×D4D47
hypocenterC47C4×#548
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625350C2semidirect
3. C22×C4×Dic94C2semidirect
4. #20246460C2semidirect
5. #20246457C2semidirect
6. #20246416C2semidirect
7. #20246413C2semidirect
8. #20246405C2semidirect
9. #20246402C2semidirect
10. #20246317C2semidirect
11. #20246311C2semidirect
12. #20246308C2semidirect
13. #20246228C2semidirect
14. C22⋊C4×Dic94C2semidirect
15. C4×#13094012C2semidirect
16. C4×#13094010C2semidirect
17. C4×#13094003C2semidirect
18. C4×#13094002C2semidirect
19. C4×#13093998C2semidirect
20. C4×#13093996C2semidirect
21. C42×Dic94C2semidirect
22. C4×(C22⋊D47)⋊C4C2semidirect
23. C42×D4×C47C2semidirect
26. #15689782C4direct (N × H)
128. C2×#10625350C2×C4semidirect
131. C22×Dic94C2×C4semidirect
143. #13094012C2×C4semidirect
144. #13094010C2×C4semidirect
145. #13094003C2×C4semidirect
146. #13094002C2×C4semidirect
147. #13093998C2×C4semidirect
148. #13093996C2×C4semidirect
156. C4×Dic94C2×C4semidirect
157. C4×Dic94D4semidirect
164. (C22⋊D47)⋊C4C2×C4semidirect
233. C4×D4×C47C2×C4semidirect
287. C22×C4×C47#41semidirect
351. C22⋊C4×C47#41semidirect
504. Dic94C4×D4semidirect
519. C22×C47C4×#41semidirect
546. C4×C47#548semidirect
576. C42×D4D47semidirect
689. C47C4×#548semidirect
738. C4×D4C4×D47semidirect
893. C22×C4#10625350semidirect
944. C22⋊C4#10625350semidirect
1089. C22C4×#10625350semidirect
1116. C4#15689782direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897822
C2×C4×#106253502
C22×C4×Dic942
#202464602
#202464572
#202464162
#202464132
#202464052
#202464022
#202463172
#202463112
#202463082
#202462282
C22⋊C4×Dic942
C4×#130940122
C4×#130940102
C4×#130940032
C4×#130940022
C4×#130939982
C4×#130939962
C42×Dic942
C4×(C22⋊D47)⋊C42
C42×D4×C472
C4×#54847