Finite Group Databasebeta

← #26375676

Subgroups — #26375676

Order 12032.

3562 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2C22×#13093981C211yesmaximal, characteristic, complemented
3C2×#117×D47C211yesmaximal, characteristic, complemented
4#20246334C212yesmaximal, complemented
5#20246315C212yesmaximal, complemented
6#20246312C212yesmaximal, complemented
7#20246286C212yesmaximal, complemented
8#20246254C212yesmaximal, complemented
9#20246235C212yesmaximal, complemented
10#20246232C212yesmaximal, complemented
11#20246206C212yesmaximal
12#20245851C211yesmaximal, characteristic, complemented
13#20245847C211yesmaximal, characteristic, complemented
14#20245833C211yesmaximal, characteristic, complemented
15#20245832C211yesmaximal, characteristic, complemented
16#20245829C211yesmaximal, characteristic, complemented
17#20245792C211yesmaximal, characteristic, complemented
18#20245769C211yesmaximal, characteristic, complemented
19#20245769C211yesmaximal, characteristic, complemented
20C42×C22⋊D47C211yesmaximal, characteristic, complemented
21C4×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
22#20245727C211yesmaximal, characteristic, complemented
23C47×#2290C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C2×D4×Dic47C2211yescharacteristic
29C2×#13093986C2211yescharacteristic
30C2×C4×C22⋊D47C2212yes—
31C2×C4×C22⋊D47C2211yescharacteristic
32C2×C4×C22⋊D47C2211yescharacteristic
33C2×(C22⋊D47)⋊C4C2212yes—
34C2×(C22⋊D47)⋊C4C2211yescharacteristic
35C2×(C22⋊D47)⋊C4C2211yescharacteristic
36C4×D4×D47C4116yescomplemented
37C2×#13093983C2211yescharacteristic, complemented
38C2×#13093982C2212yes—
39C2×#13093981—28no—
40C2×#13093981C2211yescharacteristic
41C2×#13093981C2211yescharacteristic
42C2×#13093981C2211yescharacteristic
43C2×#13093981C2212yes—
44C2×#13093981C2211yescharacteristic
45C2×#13093981C2212yescomplemented
46C2×#13093981C2211yescharacteristic, complemented
47C2×#13093981C2211yescharacteristic, complemented
48C2×#13093980C2212yescomplemented
49#117×D47—28no—
50C22×Dic47⋊C4C2212yescomplemented
51C2×C4⋊C4×D47C2211yescharacteristic
52C2×C4⋊C4×D47C2212yescomplemented
53C22×(C2×D47)⋊C4C2212yes—
54C2×C22⋊C4×D47C2212yes—
55C2×C22⋊C4×D47C2211yescharacteristic
56C2×C22⋊C4×D47C2211yescharacteristic
57C22×C4×Dic47C2211yescharacteristic, complemented
58C2×C42×D47C2211yescharacteristic
59C2×C42×D47C2211yescharacteristic, complemented
60C2×C42×D47C2211yescharacteristic, complemented
61#15689023C2212yes—
62#15689023C2212yes—
63#15689020C2212yescomplemented
64#15689018C2212yescomplemented
65#15689017C2212yescomplemented
66#15689016C2212yescomplemented
67#15689015C2212yescomplemented
68#15689015C2212yescomplemented
69#15689013C2212yescomplemented
70#15689013C2212yescomplemented
71#15689011C2212yescomplemented
72#15689009C2212yescomplemented
73#15689008C2212yescomplemented
74#15689006C2212yescomplemented
75#15689003C2212yes—
76#15689001C2212yes—
77#15689001C2212yes—
78#15688998C2212yescomplemented
79#15688997C2212yescomplemented
80#15688994C2212yescomplemented
81#15688992C2212yescomplemented
82#15688987C2212yescomplemented
83#15688985C2212yes—
84#15688985C2212yes—
85#15688982C2212yes—
86#15688982C2212yescomplemented
87#15688982C2212yescomplemented
88#15688981C2212yescomplemented
89#15688981C2212yescomplemented
90#15688980C2212yes—
91#15688978C2212yes—
92#15688978C2212yes—
93C4×Dic47⋊C4C2211yescharacteristic, complemented
94C4×Dic47⋊C4C2211yescharacteristic, complemented
95C4×Dic47⋊C4C2212yescomplemented
96C4×C4⋊Dic47C2211yescharacteristic, complemented
97#15688974C2212yescomplemented
98#15688974C2212yescomplemented
99#15688974C2212yescomplemented
100C22⋊C4×Dic47C2212yescomplemented
101C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
102C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
103C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
104C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
105C4×(C2×D47)⋊C4C2212yescomplemented
106C4×C22⋊Dic47C2211yescharacteristic, complemented
107C4×C22⋊Dic47C2211yescharacteristic, complemented
108C4×C22⋊Dic47C2212yescomplemented
109#15688970C2212yes—
110#15688970C2212yes—
111#15688970C2212yescomplemented
112#15688969C2211yescharacteristic, complemented
113C42×Dic47C2211yescharacteristic, complemented
114C42×Dic47C2211yescharacteristic, complemented
115C2×C4×D4×C47C2211yescharacteristic
116C2×#117×C47C2211yescharacteristic, complemented
117C22×C42×C47C2211yescharacteristic, complemented
118C47×#388C2212yescomplemented
119C47×#387C2212yescomplemented
120C47×#386C2212yes—
121C47×#385C2212yescomplemented
122C4×C4⋊C4×C47C2211yescharacteristic, complemented
123C4×C22⋊C4×C47C2211yescharacteristic, complemented
124C4×C22⋊C4×C47C2211yescharacteristic, complemented
125C47×#376C2211yescharacteristic, complemented
126C24×D47C2311yescharacteristic
127C24×D47C2311yescharacteristic
128C22×D188C2311yescharacteristic
129C22×C22⋊D47C2311yescharacteristic
130C22×C22⋊D47C2311yescharacteristic
131C2×D4×D47—28no—
132C2×D4×D47C2×C418yes—
133C23×Dic47C2312yes—
134C23×Dic47C2311yescharacteristic
135C23×Dic47C2311yescharacteristic
136C22×C4×D47—24no—
137C22×C4×D47—24no—
138C22×C4×D47—24no—
139C22×C4×D47—24no—
140C22×C4×D47C2×C418yescomplemented
141C22×C4×D47C2×C418yescomplemented
142C22×C4×D47C2312yes—
143C22×C4×D47C2312yes—
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2311yescharacteristic
151C22×C4×D47C2311yescharacteristic
152C22×C4×D47C2311yescharacteristic
153C4×D188C2×C418yescomplemented
154D4×Dic47C2×C418yescomplemented
155#13093986C2×C418yescomplemented
156C4×C22⋊D47—28no—
157C4×C22⋊D47C2×C418yes—
158C4×C22⋊D47C2×C418yescomplemented
159(C22⋊D47)⋊C4—28no—
160(C22⋊D47)⋊C4C2×C418yes—
161(C22⋊D47)⋊C4C2×C418yescomplemented
162#13093983—24no—
163#13093982—28no—
164#13093981—24no—
165#13093981—24no—
166#13093981—24no—
167#13093981—24no—
168#13093981—28no—
169#13093981—28no—
170#13093981—24no—
171#13093981D418yescomplemented
172#13093980—28no—
173C2×C4⋊Dic47C2312yes—
174C2×C4⋊Dic47C2312yes—
175C2×C4⋊Dic47C2311yescharacteristic
176C2×Dic47⋊C4—28no—
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⋊C4C2312yes—
187C4⋊C4×D47—28no—
188C4⋊C4×D47C2×C418yescomplemented
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2311yescharacteristic
193C2×C22⋊Dic47C2311yescharacteristic
194C2×(C2×D47)⋊C4—28no—
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)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2311yescharacteristic
205C2×(C2×D47)⋊C4C2311yescharacteristic
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C2×(C2×D47)⋊C4C2311yescharacteristic
208C2×(C2×D47)⋊C4C2312yes—
209C22⋊C4×D47—28no—
210C22⋊C4×D47C2×C418yescomplemented
211C22⋊C4×D47C2×C418yescomplemented
212C2×C4×Dic47—24no—
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2312yes—
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2312yes—
220C2×C4×Dic47C2312yes—
221C2×C4×Dic47C2312yes—
222C2×C4×Dic47C2312yes—
223C2×C4×Dic47C2311yescharacteristic
224C2×C4×Dic47C2311yescharacteristic
225C2×C4×Dic47C2311yescharacteristic
226C2×C4×Dic47C2311yescharacteristic
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×D47—24no—
270C23×D47—22no—
271C23×D47—22no—
272C23×D47—22no—
273C23×D47—22no—
274C23×D47—24no—
275C23×D47—42no—
276C23×D47—42no—
277C23×D47C22×C414yes—
278C23×D47C22×C414yes—
279C23×D47C2411yescharacteristic
280C23×D47C2411yescharacteristic
281C23×D47C2411yescharacteristic
282C2×D4×C47—24no—
283C2×D4×C47C22×C414yes—
284C22×C4×C47—22no—
285C22×C4×C47—22no—
286C22×C4×C47—22no—
287C22×C4×C47—22no—
288C22×C4×C47—24no—
289C22×C4×C47—24no—
290C22×C4×C47—42no—
291C22×C4×C47C22×C414yes—
292C22×C4×C47C22×C414yes—
293C22×C4×C47C2412yes—
294C22×C4×C47C2412yes—
295C22×C4×C47C2412yes—
296C22×C4×C47C2411yescharacteristic
297C22×C4×C47C2411yescharacteristic
298C22×C4×C47C2411yescharacteristic
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2412yes—
301C22×C4×C47C2411yescharacteristic
302C2×C22⋊D47—24no—
303C2×C22⋊D47C22×C414yes—
304C2×C22⋊D47C22×C414yes—
305C2×C22⋊D47#4118yes—
306C22×Dic47—22no—
307C22×Dic47—22no—
308C22×Dic47—22no—
309C22×Dic47—22no—
310C22×Dic47—24no—
311C22×Dic47—24no—
312C22×Dic47—42no—
313C22×Dic47C22×C414yes—
314C22×Dic47C22×C414yes—
315C22×Dic47C2412yes—
316C22×Dic47C2412yes—
317C22×Dic47C2412yes—
318C22×Dic47C2411yescharacteristic
319C22×Dic47C2411yescharacteristic
320C22×Dic47C2411yescharacteristic
321C22×Dic47C2412yes—
322C22×Dic47C2411yescharacteristic
323C22×Dic47C2411yescharacteristic
324D4×D47—232no—
325C2×D188—24no—
326C2×D188C22×C414yes—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—22no—
330C2×C4×D47—22no—
331C2×C4×D47—22no—
332C2×C4×D47—22no—
333C2×C4×D47—22no—
334C2×C4×D47—22no—
335C2×C4×D47—22no—
336C2×C4×D47—22no—
337C2×C4×D47—22no—
338C2×C4×D47—22no—
339C2×C4×D47—24no—
340C2×C4×D47—232no—
341C2×C4×D47—232no—
342C2×C4×D47—24no—
343C2×C4×D47—24no—
344C2×C4×D47—24no—
345C2×C4×D47—24no—
346C2×C4×D47—42no—
347C2×C4×D47—42no—
348C2×C4×D47—42no—
349C2×C4×D47C22×C414yes—
350C2×C4×D47C22×C414yes—
351C2×C4×D47C22×C414yes—
352C2×C4×D47C22×C414yes—
353C2×C4×D47C22×C414yes—
354C2×C4×D47C22×C414yes—
355C2×C4×D47C22×C414yes—
356C2×C4×D47C22×C414yes—
357C2×C4×D47C22×C414yes—
358C2×C4×D47C2×D414yes—
359C2×C4×D47#4114yes—
360C4⋊C4×C47—24no—
361C4⋊C4×C47—42no—
362C4⋊C4×C47C22×C414yes—
363C22⋊C4×C47—24no—
364C22⋊C4×C47—24no—
365C22⋊C4×C47—42no—
366C22⋊C4×C47C22×C414yes—
367C22⋊C4×C47C22×C414yes—
368C42×C47—24no—
369C42×C47—22no—
370C42×C47—22no—
371C42×C47—22no—
372C42×C47C22×C414yes—
373C42×C47C2×D414yescomplemented
374C22⋊Dic47—24no—
375C22⋊Dic47—24no—
376C22⋊Dic47—42no—
377C22⋊Dic47C22×C414yes—
378C22⋊Dic47C22×C414yes—
379(C2×D47)⋊C4—24no—
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—24no—
386(C2×D47)⋊C4—42no—
387(C2×D47)⋊C4—42no—
388(C2×D47)⋊C4C22×C414yes—
389(C2×D47)⋊C4C22×C414yes—
390(C2×D47)⋊C4C22×C414yes—
391(C2×D47)⋊C4C22×C414yes—
392(C2×D47)⋊C4C2×D418yes—
393C4⋊Dic47—24no—
394C4⋊Dic47—42no—
395C4⋊Dic47C22×C414yes—
396Dic47⋊C4—24no—
397Dic47⋊C4—24no—
398Dic47⋊C4—24no—
399Dic47⋊C4—24no—
400Dic47⋊C4—24no—
401Dic47⋊C4—24no—
402Dic47⋊C4—24no—
403Dic47⋊C4C22×C414yes—
404Dic47⋊C4C22×C414yes—
405Dic47⋊C4C2×D418yescomplemented
406C4×Dic47—24no—
407C4×Dic47—22no—
408C4×Dic47—22no—
409C4×Dic47—22no—
410C4×Dic47—24no—
411C4×Dic47—24no—
412C4×Dic47—24no—
413C4×Dic47—24no—
414C4×Dic47—42no—
415C4×Dic47—42no—
416C4×Dic47C22×C414yes—
417C4×Dic47C22×C414yes—
418C4×Dic47C22×C414yes—
419C4×Dic47C2×D414yescomplemented
420C23×C47—21no—
421C23×C47—21no—
422C23×C47—22no—
423C23×C47—21no—
424C23×C47—21no—
425C23×C47—22no—
426C23×C47—22no—
427C23×C47C23×C412yes—
428C23×C47C23×C412yes—
429C23×C47C2×#4114yes—
430C23×C47C2511yescharacteristic
431C22×D47—21no—
432C22×D47—21no—
433C22×D47—22no—
434C22×D47—22no—
435C22×D47—22no—
436C22×D47—28no—
437C22×D47—21no—
438C22×D47—21no—
439C22×D47—22no—
440C22×D47—22no—
441C22×D47—28no—
442C22×D47—28no—
443C22×D47—28no—
444C22×D47—44no—
445C22×D47—44no—
446C22×D47—48no—
447C22×D47—48no—
448C22×D47—48no—
449C22×D47—48no—
450C22×D47C23×C412yes—
451C22×D47C23×C412yes—
452C22×D47C23×C412yes—
453C22×D47C22×D412yes—
454C22×D47C2×#4114yes—
455C22×D47C2×#4112yes—
456D4×C47—28no—
457C2×C4×C47—21no—
458C2×C4×C47—21no—
459C2×C4×C47—22no—
460C2×C4×C47—21no—
461C2×C4×C47—21no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—28no—
466C2×C4×C47—28no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—48no—
477C2×C4×C47C23×C412yes—
478C2×C4×C47C23×C412yes—
479C2×C4×C47C23×C412yes—
480C2×C4×C47C23×C412yes—
481C2×C4×C47C23×C412yes—
482C2×C4×C47C22×D414yes—
483C2×C4×C47C22×D412yes—
484C2×C4×C47C2×#4112yes—
485C22⋊D47—28no—
486C22⋊D47#117116yescomplemented
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—22no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—28no—
495C2×Dic47—28no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47—22no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—48no—
506C2×Dic47C23×C412yes—
507C2×Dic47C23×C412yes—
508C2×Dic47C23×C412yes—
509C2×Dic47C23×C412yes—
510C2×Dic47C23×C412yes—
511C2×Dic47C22×D414yes—
512C2×Dic47C22×D412yes—
513C2×Dic47C2×#4114yes—
514C2×Dic47C2×#4112yes—
515D188—28no—
516C4×D47—28no—
517C4×D47—28no—
518C4×D47—28no—
519C4×D47—28no—
520C4×D47—28no—
521C4×D47—28no—
522C4×D47—28no—
523C4×D47—44no—
524C4×D47—48no—
525C4×D47—48no—
526C4×D47C4×D4116yescomplemented
527D4×#117—471nomaximal, Sylow
528C22×C47—22no—
529C22×C47—22no—
530C22×C47—24no—
531C22×C47—24no—
532C22×C47—22no—
533C22×C47—22no—
534C22×C47—22no—
535C22×C47—42no—
536C22×C47—42no—
537C22×C47C2×#11714yescomplemented
538C22×C47C24×C411yescharacteristic
539C22×C47C23×D411yescharacteristic
540C22×C47C22×#4112yes—
541C22×C47C22×#4111yescharacteristic
542C22×C47#58512yes—
543C2×D47—22no—
544C2×D47—22no—
545C2×D47—22no—
546C2×D47—22no—
547C2×D47—24no—
548C2×D47—24no—
549C2×D47—24no—
550C2×D47—24no—
551C2×D47—22no—
552C2×D47—22no—
553C2×D47—22no—
554C2×D47—416no—
555C2×D47—416no—
556C2×D47—42no—
557C2×D47—42no—
558C2×D47C2×#11714yescomplemented
559C2×D47C2×C4×D414yes—
560C4×C47—22no—
561C4×C47—22no—
562C4×C47—22no—
563C4×C47—22no—
564C4×C47—24no—
565C4×C47—42no—
566C4×C47—42no—
567C4×C47—42no—
568C4×C47C2×C4×D414yes—
569Dic47—22no—
570Dic47—22no—
571Dic47—22no—
572Dic47—24no—
573Dic47—42no—
574Dic47—42no—
575Dic47—42no—
576Dic47C2×#11714yescomplemented
577Dic47C2×C4×D414yes—
578C22×C4×D4—471no—
579C22×#117—471no—
580C22×#117—471no—
581#2354—472no—
582#2352—472no—
583#2352—472no—
584D4×C4⋊C4—472no—
585#2344—472no—
586#2342—472no—
587#2342—472no—
588D4×C22⋊C4—472no—
589#2293—471no—
590#2293—471no—
591#2290—471no—
592#2290—471no—
593#2290—471no—
594#2290D4711yescharacteristic, complemented
595#2285—471no—
596#2280—471no—
597#2280—471no—
598C42×D4—471no—
599C42×D4—471no—
600C4×#117—471no—
601C2×C47—24no—
602C2×C47—42no—
603C2×C47C22×#11711yescharacteristic
604C2×C47C22×C4×D411yescharacteristic
605C2×C47#342811yescharacteristic
606C2×C47D4×#4112yes—
607C2×C47#347512yes—
608D47—24no—
609D47—24no—
610D47—42no—
611C23×D4—471no—
612C24×C4—471no—
613C24×C4—471no—
614C2×C4×D4—471no—
615C2×C4×D4—471no—
616C2×C4×D4—471no—
617C2×C4×D4—4716no—
618C2×C4×D4—472no—
619C2×C4×D4—471no—
620C2×C4×D4—471no—
621C2×C4×D4—471no—
622C2×C4×D4—472no—
623C2×C4×D4—471no—
624C2×C4×D4C2×D4711yescharacteristic
625C2×#117—471no—
626C2×#117—472no—
627C2×#117—472no—
628C2×#117—471no—
629C2×#117—472no—
630C2×#117—472no—
631C2×#117—471no—
632C2×#117—471no—
633C2×#117—471no—
634C2×#117—471no—
635C2×#117—471no—
636C2×#117—948no—
637C2×#117—948no—
638C2×#117C2×D4711yescharacteristic, complemented
639C22×C4⋊C4—471no—
640C22×C4⋊C4—472no—
641C22×C4⋊C4—472no—
642C22×C22⋊C4—471no—
643C22×C22⋊C4—471no—
644C22×C22⋊C4—472no—
645C22×C22⋊C4—472no—
646C22×C42—471no—
647C22×C42—471no—
648C22×C42—471no—
649C22×C42—471no—
650C22×C42C2×D4711yescharacteristic, complemented
651#390—472no—
652#390—472no—
653#389—472no—
654#389—472no—
655#388—472no—
656#388—472no—
657#388—472no—
658#388—472no—
659#388—472no—
660#388—472no—
661#388—472no—
662#388C2×D4712yescomplemented
663#387—472no—
664#387—472no—
665#387—472no—
666#387C2×D4712yescomplemented
667#386—472no—
668#386—472no—
669#386—472no—
670#386C2×D4712yes—
671#385—472no—
672#385—472no—
673#385—472no—
674#385C2×D4712yescomplemented
675#384—472no—
676#382—472no—
677#381—472no—
678#381—472no—
679#380—472no—
680#380—472no—
681#380—472no—
682#380—472no—
683#380—472no—
684#380—472no—
685#379—472no—
686#379—472no—
687C4×C4⋊C4—471no—
688C4×C4⋊C4—472no—
689C4×C4⋊C4—471no—
690C4×C4⋊C4—471no—
691C4×C4⋊C4—472no—
692C4×C4⋊C4—472no—
693C4×C4⋊C4—472no—
694C4×C4⋊C4C2×D4711yescharacteristic, complemented
695C4×C22⋊C4—472no—
696C4×C22⋊C4—471no—
697C4×C22⋊C4—471no—
698C4×C22⋊C4—472no—
699C4×C22⋊C4—472no—
700C4×C22⋊C4—471no—
701C4×C22⋊C4—471no—
702C4×C22⋊C4—471no—
703C4×C22⋊C4—471no—
704C4×C22⋊C4—472no—
705C4×C22⋊C4—472no—
706C4×C22⋊C4—472no—
707C4×C22⋊C4C2×D4711yescharacteristic, complemented
708C4×C22⋊C4C2×D4711yescharacteristic, complemented
709#376—471no—
710#376C2×D4711yescharacteristic, complemented
711C43—471no—
712C43—471no—
713C47D4×#11711yescharacteristic, complemented, Sylow
714C25—471no—
715C25—471no—
716C22×D4—471no—
717C22×D4—471no—
718C22×D4—478no—
719C22×D4—471no—
720C22×D4—948no—
721C22×D4C22×D4711yescharacteristic
722C23×C4—471no—
723C23×C4—471no—
724C23×C4—471no—
725C23×C4—478no—
726C23×C4—478no—
727C23×C4—471no—
728C23×C4—471no—
729C23×C4—471no—
730C23×C4—471no—
731C23×C4—471no—
732C23×C4—471no—
733C23×C4—471no—
734C23×C4—471no—
735C23×C4—472no—
736C23×C4—472no—
737C23×C4—472no—
738C23×C4—944no—
739C23×C4—944no—
740C23×C4—944no—
741C23×C4—944no—
742C23×C4C22×D4712yes—
743C23×C4C22×D4711yescharacteristic
744C23×C4C22×D4711yescharacteristic
745C4×D4—478no—
746C4×D4—478no—
747C4×D4—478no—
748C4×D4—478no—
749C4×D4—478no—
750C4×D4—478no—
751C4×D4—478no—
752C4×D4—948no—
753C4×D4—948no—
754C4×D4C4×D4718yescomplemented
755#117—24no—
756#117—478no—
757#117—944no—
758#117—948no—
759#117—948no—
760#117—944no—
761#117—944no—
762#117—944no—
763#117—944no—
764#117—948no—
765#117—948no—
766#117—944no—
767C2×C4⋊C4—472no—
768C2×C4⋊C4—471no—
769C2×C4⋊C4—471no—
770C2×C4⋊C4—471no—
771C2×C4⋊C4—478no—
772C2×C4⋊C4—472no—
773C2×C4⋊C4—472no—
774C2×C4⋊C4—472no—
775C2×C4⋊C4—472no—
776C2×C4⋊C4—472no—
777C2×C4⋊C4—472no—
778C2×C4⋊C4—472no—
779C2×C4⋊C4—472no—
780C2×C4⋊C4—472no—
781C2×C4⋊C4—948no—
782C2×C4⋊C4—948no—
783C2×C4⋊C4C22×D4712yes—
784C2×C4⋊C4C22×D4712yes—
785C2×C4⋊C4C22×D4711yescharacteristic
786C2×C22⋊C4—471no—
787C2×C22⋊C4—471no—
788C2×C22⋊C4—472no—
789C2×C22⋊C4—471no—
790C2×C22⋊C4—471no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—471no—
793C2×C22⋊C4—478no—
794C2×C22⋊C4—478no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—472no—
797C2×C22⋊C4—472no—
798C2×C22⋊C4—472no—
799C2×C22⋊C4—472no—
800C2×C22⋊C4—472no—
801C2×C22⋊C4—472no—
802C2×C22⋊C4—472no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—472no—
806C2×C22⋊C4—472no—
807C2×C22⋊C4—948no—
808C2×C22⋊C4—948no—
809C2×C22⋊C4C22×D4712yes—
810C2×C22⋊C4C22×D4712yes—
811C2×C22⋊C4C22×D4712yes—
812C2×C22⋊C4C22×D4711yescharacteristic
813C2×C22⋊C4C22×D4711yescharacteristic
814C2×C42—24no—
815C2×C42—471no—
816C2×C42—471no—
817C2×C42—471no—
818C2×C42—471no—
819C2×C42—478no—
820C2×C42—472no—
821C2×C42—472no—
822C2×C42—472no—
823C2×C42—472no—
824C2×C42—472no—
825C2×C42—471no—
826C2×C42—471no—
827C2×C42—471no—
828C2×C42—472no—
829C2×C42—472no—
830C2×C42—944no—
831C2×C42—944no—
832C2×C42—944no—
833C2×C42C22×D4712yes—
834C2×C42C22×D4711yescharacteristic
835C2×C42C22×D4711yescharacteristic
836C2×C42C22×D4711yescharacteristic
837C2×C42C22×D4711yescharacteristic
838C2×C42C22×D4711yescharacteristic
839#95—472no—
840#95—472no—
841#95—472no—
842#95—472no—
843#95—472no—
844#95—472no—
845#95—472no—
846#95—472no—
847#95—472no—
848#95—472no—
849#95—472no—
850#95C22×D4712yes—
851#95C22×D4712yes—
852#95C22×D4712yes—
853#95C22×D4712yes—
854#95C22×D4712yes—
855C24—471no—
856C24—471no—
857C24—471no—
858C24—474no—
859C24—474no—
860C24—942no—
861C24—942no—
862C24—942no—
863C24—942no—
864C24—944no—
865C24—944no—
866C24—1882no—
867C24—1882no—
868C24C23×D4711yescharacteristic
869C24C23×D4711yescharacteristic
870C2×D4—24no—
871C2×D4—474no—
872C2×D4—478no—
873C2×D4—474no—
874C2×D4—474no—
875C2×D4—944no—
876C2×D4—944no—
877C2×D4—9432no—
878C2×D4C2×C4×D4714yes—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—471no—
887C22×C4—471no—
888C22×C4—474no—
889C22×C4—474no—
890C22×C4—474no—
891C22×C4—474no—
892C22×C4—474no—
893C22×C4—471no—
894C22×C4—471no—
895C22×C4—471no—
896C22×C4—472no—
897C22×C4—474no—
898C22×C4—474no—
899C22×C4—474no—
900C22×C4—474no—
901C22×C4—474no—
902C22×C4—474no—
903C22×C4—474no—
904C22×C4—474no—
905C22×C4—472no—
906C22×C4—472no—
907C22×C4—472no—
908C22×C4—942no—
909C22×C4—942no—
910C22×C4—942no—
911C22×C4—942no—
912C22×C4—9432no—
913C22×C4—9432no—
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—942no—
923C22×C4—942no—
924C22×C4—942no—
925C22×C4—942no—
926C22×C4—944no—
927C22×C4—942no—
928C22×C4—942no—
929C22×C4—942no—
930C22×C4—942no—
931C22×C4—944no—
932C22×C4—944no—
933C22×C4—1882no—
934C22×C4—1882no—
935C22×C4—1882no—
936C22×C4—1882no—
937C22×C4C2×C4×D4714yes—
938C22×C4C2×C4×D4714yes—
939C22×C4C23×D4712yes—
940C22×C4C23×D4712yes—
941C22×C4C23×D4712yes—
942C22×C4C23×D4711yescharacteristic
943C22×C4C23×D4711yescharacteristic
944C22×C4C23×D4711yescharacteristic
945C22×C4C23×D4711yescharacteristic
946C22×C4C23×D4712yes—
947C22×C4C23×D4711yescharacteristic
948C4⋊C4—24no—
949C4⋊C4—42no—
950C4⋊C4—474no—
951C4⋊C4—474no—
952C4⋊C4—474no—
953C4⋊C4—478no—
954C4⋊C4—944no—
955C4⋊C4—944no—
956C4⋊C4—944no—
957C4⋊C4—944no—
958C4⋊C4—944no—
959C4⋊C4—944no—
960C4⋊C4—944no—
961C4⋊C4—944no—
962C4⋊C4—1882no—
963C4⋊C4C2×C4×D4714yes—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—42no—
967C22⋊C4—474no—
968C22⋊C4—474no—
969C22⋊C4—474no—
970C22⋊C4—474no—
971C22⋊C4—474no—
972C22⋊C4—474no—
973C22⋊C4—478no—
974C22⋊C4—944no—
975C22⋊C4—944no—
976C22⋊C4—944no—
977C22⋊C4—944no—
978C22⋊C4—944no—
979C22⋊C4—944no—
980C22⋊C4—944no—
981C22⋊C4—944no—
982C22⋊C4—944no—
983C22⋊C4—1882no—
984C22⋊C4—1882no—
985C22⋊C4—1882no—
986C22⋊C4C2×C4×D4714yes—
987C22⋊C4C2×C4×D4714yes—
988C42—24no—
989C42—22no—
990C42—22no—
991C42—22no—
992C42—474no—
993C42—474no—
994C42—474no—
995C42—474no—
996C42—944no—
997C42—944no—
998C42—944no—
999C42—944no—
1000C42—944no—
1001C42—942no—
1002C42—942no—
1003C42—942no—
1004C42—1882no—
1005C42—1882no—
1006C42C2×C4×D4714yes—
1007C42D4×D4714yescomplemented
1008C23—21no—
1009C23—21no—
1010C23—22no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23—22no—
1015C23—472no—
1016C23—472no—
1017C23—472no—
1018C23—472no—
1019C23—474no—
1020C23—472no—
1021C23—948no—
1022C23—948no—
1023C23—948no—
1024C23—941no—
1025C23—941no—
1026C23—942no—
1027C23—942no—
1028C23—942no—
1029C23—948no—
1030C23—941no—
1031C23—941no—
1032C23—942no—
1033C23—942no—
1034C23—1884no—
1035C23—1884no—
1036C23—1888no—
1037C23—1888no—
1038C23—1888no—
1039C23—1888no—
1040C23C22×C4×D4712yes—
1041C23C22×C4×D4712yes—
1042C23#41×D4714yes—
1043C23C24×D4711yescharacteristic
1044D4—28no—
1045D4—4716no—
1046D4—948no—
1047D4—948no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—28no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—48no—
1068C2×C4—472no—
1069C2×C4—472no—
1070C2×C4—472no—
1071C2×C4—474no—
1072C2×C4—472no—
1073C2×C4—4716no—
1074C2×C4—472no—
1075C2×C4—472no—
1076C2×C4—472no—
1077C2×C4—474no—
1078C2×C4—948no—
1079C2×C4—948no—
1080C2×C4—948no—
1081C2×C4—948no—
1082C2×C4—948no—
1083C2×C4—948no—
1084C2×C4—948no—
1085C2×C4—941no—
1086C2×C4—941no—
1087C2×C4—942no—
1088C2×C4—941no—
1089C2×C4—941no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—948no—
1093C2×C4—948no—
1094C2×C4—942no—
1095C2×C4—942no—
1096C2×C4—942no—
1097C2×C4—942no—
1098C2×C4—942no—
1099C2×C4—942no—
1100C2×C4—942no—
1101C2×C4—942no—
1102C2×C4—942no—
1103C2×C4—1884no—
1104C2×C4—1888no—
1105C2×C4—1888no—
1106C2×C4—1888no—
1107C2×C4C22×C4×D4712yes—
1108C2×C4C22×C4×D4712yes—
1109C2×C4C22×C4×D4712yes—
1110C2×C4C22×C4×D4712yes—
1111C2×C4C22×C4×D4712yes—
1112C2×C4C2×D4×D4714yes—
1113C2×C4C2×D4×D4712yes—
1114C2×C4#41×D4712yes—
1115C22—22no—
1116C22—22no—
1117C22—24no—
1118C22—24no—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—42no—
1123C22—42no—
1124C22—474no—
1125C22—474no—
1126C22—942no—
1127C22—942no—
1128C22—942no—
1129C22—942no—
1130C22—944no—
1131C22—944no—
1132C22—944no—
1133C22—944no—
1134C22—942no—
1135C22—942no—
1136C22—942no—
1137C22—18816no—
1138C22—18816no—
1139C22—1882no—
1140C22—1882no—
1141C22#117×D4714yescomplemented
1142C22C23×C4×D4711yescharacteristic
1143C22C22×D4×D4711yescharacteristic
1144C22C2×#41×D4712yes—
1145C22C2×#41×D4711yescharacteristic
1146C22#1568995912yes—
1147C4—22no—
1148C4—22no—
1149C4—22no—
1150C4—22no—
1151C4—24no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—474no—
1156C4—474no—
1157C4—942no—
1158C4—942no—
1159C4—942no—
1160C4—944no—
1161C4—1882no—
1162C4—1882no—
1163C4—1882no—
1164C4C4×D4×D4714yes—
1165C2—24no—
1166C2—42no—
1167C2—944no—
1168C2—944no—
1169C2—1882no—
1170C2C2×#117×D4711yescharacteristic
1171C2C2×C4×D4×D4711yescharacteristic
1172C2#2025658711yescharacteristic
1173C2#2025687112yes—
1174C2#2025694012yes—
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC47×#2290C2
socle, cosocleC23×C47C25
prime radicalC22×D4×D47C22
hypercenter#2290D47
hypocenterC47D4×#117
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. C22×#13093981C2semidirect
3. C2×#117×D47C2semidirect
4. #20246334C2semidirect
5. #20246315C2semidirect
6. #20246312C2semidirect
7. #20246286C2semidirect
8. #20246254C2semidirect
9. #20246235C2semidirect
10. #20246232C2semidirect
12. #20245851C2semidirect
13. #20245847C2semidirect
14. #20245833C2semidirect
15. #20245832C2semidirect
16. #20245829C2semidirect
17. #20245792C2semidirect
18. #20245769C2semidirect
19. #20245769C2semidirect
20. C42×C22⋊D47C2semidirect
21. C4×(C22⋊D47)⋊C4C2semidirect
22. #20245727C2semidirect
23. C47×#2290C2semidirect
36. C4×D4×D47C4semidirect
37. C2×#13093983C22semidirect
45. C2×#13093981C22semidirect
46. C2×#13093981C22semidirect
47. C2×#13093981C22semidirect
48. C2×#13093980C22semidirect
50. C22×Dic47⋊C4C22semidirect
52. C2×C4⋊C4×D47C22semidirect
57. C22×C4×Dic47C22semidirect
59. C2×C42×D47C22semidirect
60. C2×C42×D47C22semidirect
63. #15689020C22semidirect
64. #15689018C22semidirect
65. #15689017C22semidirect
66. #15689016C22semidirect
67. #15689015C22semidirect
68. #15689015C22semidirect
69. #15689013C22semidirect
70. #15689013C22semidirect
71. #15689011C22semidirect
72. #15689009C22semidirect
73. #15689008C22semidirect
74. #15689006C22semidirect
78. #15688998C22semidirect
79. #15688997C22semidirect
80. #15688994C22semidirect
81. #15688992C22semidirect
82. #15688987C22semidirect
86. #15688982C22semidirect
87. #15688982C22semidirect
88. #15688981C22semidirect
89. #15688981C22semidirect
93. C4×Dic47⋊C4C22semidirect
94. C4×Dic47⋊C4C22semidirect
95. C4×Dic47⋊C4C22semidirect
96. C4×C4⋊Dic47C22semidirect
97. #15688974C22semidirect
98. #15688974C22semidirect
99. #15688974C22semidirect
100. C22⋊C4×Dic47C22semidirect
101. C4×(C2×D47)⋊C4C22semidirect
102. C4×(C2×D47)⋊C4C22semidirect
103. C4×(C2×D47)⋊C4C22semidirect
104. C4×(C2×D47)⋊C4C22semidirect
105. C4×(C2×D47)⋊C4C22semidirect
106. C4×C22⋊Dic47C22semidirect
107. C4×C22⋊Dic47C22semidirect
108. C4×C22⋊Dic47C22semidirect
111. #15688970C22semidirect
112. #15688969C22semidirect
113. C42×Dic47C22semidirect
114. C42×Dic47C22semidirect
116. C2×#117×C47C22semidirect
117. C22×C42×C47C22semidirect
118. C47×#388C22semidirect
119. C47×#387C22semidirect
121. C47×#385C22semidirect
122. C4×C4⋊C4×C47C22semidirect
123. C4×C22⋊C4×C47C22semidirect
124. C4×C22⋊C4×C47C22semidirect
125. C47×#376C22semidirect
140. C22×C4×D47C2×C4semidirect
141. C22×C4×D47C2×C4semidirect
153. C4×D188C2×C4semidirect
154. D4×Dic47C2×C4semidirect
155. #13093986C2×C4semidirect
158. C4×C22⋊D47C2×C4semidirect
161. (C22⋊D47)⋊C4C2×C4semidirect
171. #13093981D4semidirect
188. C4⋊C4×D47C2×C4semidirect
210. C22⋊C4×D47C2×C4semidirect
211. C22⋊C4×D47C2×C4semidirect
229. C42×D47C2×C4semidirect
245. C4×D4×C47C2×C4semidirect
373. C42×C47C2×D4semidirect
405. Dic47⋊C4C2×D4semidirect
419. C4×Dic47C2×D4semidirect
486. C22⋊D47#117semidirect
526. C4×D47C4×D4semidirect
537. C22×C47C2×#117semidirect
558. C2×D47C2×#117semidirect
576. Dic47C2×#117semidirect
594. #2290D47semidirect
638. C2×#117C2×D47semidirect
650. C22×C42C2×D47semidirect
662. #388C2×D47semidirect
666. #387C2×D47semidirect
674. #385C2×D47semidirect
694. C4×C4⋊C4C2×D47semidirect
707. C4×C22⋊C4C2×D47semidirect
708. C4×C22⋊C4C2×D47semidirect
710. #376C2×D47semidirect
713. C47D4×#117semidirect
754. C4×D4C4×D47semidirect
1007. C42D4×D47semidirect
1141. C22#117×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
C22×#130939812
C2×#117×D472
#202463342
#202463152
#202463122
#202462862
#202462542
#202462352
#202462322
#202462062
#202458512
#202458472
#202458332
#202458322
#202458292
#202457922
#202457692
C42×C22⋊D472
C4×(C22⋊D47)⋊C42
#202457272
C47×#22902
D4×#11747