Finite Group Databasebeta

← #26375851

Subgroups — #26375851

Order 12032.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689632C211yesmaximal, characteristic
2C2×C4×#10625350C211yesmaximal, characteristic, complemented
3C2×#117×D47C211yesmaximal, characteristic, complemented
4#20246429C212yesmaximal, complemented
5#20246418C212yesmaximal, complemented
6#20246407C212yesmaximal, complemented
7#20246396C212yesmaximal, complemented
8#20246387C212yesmaximal, complemented
9#20246383C212yesmaximal, complemented
10#20246371C212yesmaximal, complemented
11#20246366C212yesmaximal, complemented
12#20245874C211yesmaximal, characteristic, complemented
13#20245868C211yesmaximal, characteristic, complemented
14#20245853C211yesmaximal, characteristic, complemented
15#20245847C211yesmaximal, characteristic, complemented
16#20245834C211yesmaximal, characteristic, complemented
17#20245834C211yesmaximal, characteristic, complemented
18#20245832C211yesmaximal, characteristic, complemented
19C42×C22⋊D47C211yesmaximal, characteristic, complemented
20C4×#13093986C211yesmaximal, characteristic, complemented
21#20245727C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D47C211yesmaximal, characteristic, complemented
23C47×#2290C211yesmaximal, 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
35C4×#10625350—28no—
36C2×C4×Dic94C2212yescomplemented
37C2×C4×D188C2212yes—
38C2×C4×D188C2211yescharacteristic
39C2×#13093986C2212yes—
40C2×C4×C22⋊D47C2212yes—
41C2×C4×C22⋊D47C2212yes—
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×C4×C22⋊D47C2211yescharacteristic
44C2×C4×C22⋊D47C2212yescomplemented
45C2×#13093983C2211yescharacteristic
46C2×#13093983C2211yescharacteristic, complemented
47C2×#13093982C2212yes—
48C2×#13093981C2211yescharacteristic
49C2×#13093981C2211yescharacteristic
50C2×#13093981C2211yescharacteristic
51C2×#13093981C2211yescharacteristic, complemented
52C2×#13093980C2212yes—
53#117×D47—28no—
54C2×C4⋊C4×D47C2212yes—
55C2×C22⋊C4×D47C2212yes—
56C2×C22⋊C4×D47C2212yes—
57C2×C42×D47C2211yescharacteristic
58C2×C42×D47C2211yescharacteristic
59C2×C42×D47C2211yescharacteristic
60C2×C42×D47C2211yescharacteristic
61C2×C42×D47C2211yescharacteristic, complemented
62#15689027C2212yescomplemented
63#15689026C2212yes—
64#15689023C2212yes—
65#15689023C2212yescomplemented
66#15689022C2212yescomplemented
67#15689020C2212yescomplemented
68#15689018C2212yescomplemented
69#15689018C2212yescomplemented
70#15689017C2212yes—
71#15689017C2212yes—
72#15689017C2212yescomplemented
73#15689016C2212yes—
74#15689016C2212yescomplemented
75#15689015C2212yescomplemented
76#15689013C2212yescomplemented
77#15689010C2212yescomplemented
78#15689010C2212yescomplemented
79#15689008C2212yescomplemented
80#15689001C2212yes—
81#15689001C2212yes—
82#15688999C2212yes—
83#15688999C2212yes—
84#15688999C2212yes—
85#15688997C2212yes—
86#15688997C2212yes—
87#15688997C2212yes—
88#15688997C2212yescomplemented
89#15688994C2212yes—
90C4⋊C4×Dic47C2212yescomplemented
91C4×Dic47⋊C4C2211yescharacteristic, complemented
92C4×Dic47⋊C4C2211yescharacteristic, complemented
93C4×Dic47⋊C4C2212yescomplemented
94C4×C4⋊Dic47C2211yescharacteristic, complemented
95#15688974C2212yescomplemented
96#15688974C2212yescomplemented
97C22⋊C4×Dic47C2212yes—
98C4×(C2×D47)⋊C4C2211yescharacteristic
99C4×(C2×D47)⋊C4C2212yes—
100C4×(C2×D47)⋊C4C2211yescharacteristic
101C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
102C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
103C4×C22⋊Dic47C2211yescharacteristic
104C4×C22⋊Dic47C2211yescharacteristic, complemented
105C4×C22⋊Dic47C2212yescomplemented
106#15688970C2212yes—
107#15688970C2212yes—
108#15688970C2212yes—
109#15688970C2212yes—
110#15688970C2212yescomplemented
111#15688969C2211yescharacteristic, complemented
112#95×D47C2212yes—
113C42×Dic47C2211yescharacteristic, complemented
114C42×Dic47C2211yescharacteristic, complemented
115C2×C4×D4×C47C2211yescharacteristic
116C2×#117×C47C2211yescharacteristic
117C22×C42×C47C2211yescharacteristic, complemented
118C47×#388C2212yes—
119C47×#387C2212yescomplemented
120C47×#386C2212yes—
121C47×#385C2212yescomplemented
122C4×C4⋊C4×C47C2211yescharacteristic, complemented
123C4×C22⋊C4×C47C2211yescharacteristic
124C4×C22⋊C4×C47C2211yescharacteristic, complemented
125C47×#376C2211yescharacteristic, complemented
126C24×D47C2311yescharacteristic
127C2×#10625350—24no—
128C2×#10625350—24no—
129C2×#10625350C2×C418yescomplemented
130C22×Dic94C2311yescharacteristic
131C22×D188C2311yescharacteristic
132C22×D188C2311yescharacteristic
133C22×C22⋊D47C2311yescharacteristic
134C22×C22⋊D47C2311yescharacteristic
135C22×C22⋊D47C2311yescharacteristic
136C22×C22⋊D47C2311yescharacteristic
137C23×Dic47C2311yescharacteristic
138C22×C4×D47—24no—
139C22×C4×D47—24no—
140C22×C4×D47C2×C418yescomplemented
141C22×C4×D47C2312yes—
142C22×C4×D47C2312yes—
143C22×C4×D47C2312yes—
144C22×C4×D47C2312yes—
145C22×C4×D47C2312yes—
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2311yescharacteristic
151#13094009C2×C418yescomplemented
152#13094006C2×C418yescomplemented
153#13094002C2×C418yescomplemented
154#13094001C2×C418yescomplemented
155#13093997C2×C418yescomplemented
156#13093996C2×C418yescomplemented
157#13093994C2×C418yescomplemented
158#13093992C2×C418yescomplemented
159C4×Dic94—28no—
160C4×D188—28no—
161C4×D188C2×C418yescomplemented
162#13093986—28no—
163C4×C22⋊D47—28no—
164C4×C22⋊D47—28no—
165C4×C22⋊D47—28no—
166C4×C22⋊D47C2×C418yescomplemented
167C4×C22⋊D47C2×C418yescomplemented
168#13093983—24no—
169#13093983—24no—
170#13093982—28no—
171#13093981—24no—
172#13093981—24no—
173#13093981C2×C418yescomplemented
174#13093981D418yescomplemented
175#13093980—28no—
176C2×C4⋊Dic47C2312yes—
177C2×C4⋊Dic47C2312yes—
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2311yescharacteristic
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2311yescharacteristic
185C2×Dic47⋊C4C2311yescharacteristic
186C2×Dic47⋊C4C2311yescharacteristic
187C2×Dic47⋊C4C2311yescharacteristic
188C2×Dic47⋊C4C2312yes—
189C4⋊C4×D47—28no—
190C2×C22⋊Dic47C2312yes—
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)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2311yescharacteristic
203C2×(C2×D47)⋊C4C2311yescharacteristic
204C2×(C2×D47)⋊C4C2311yescharacteristic
205C2×(C2×D47)⋊C4C2311yescharacteristic
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C2×(C2×D47)⋊C4C2312yes—
208C2×(C2×D47)⋊C4C2312yes—
209C22⋊C4×D47—28no—
210C22⋊C4×D47—28no—
211C2×C4×Dic47C2311yescharacteristic
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2312yes—
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2312yes—
217C2×C4×Dic47C2312yes—
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2311yescharacteristic
220C2×C4×Dic47C2312yes—
221C2×C4×Dic47C2312yes—
222C2×C4×Dic47C2312yes—
223C2×C4×Dic47C2311yescharacteristic
224C2×C4×Dic47C2311yescharacteristic
225C42×D47—24no—
226C42×D47—24no—
227C42×D47—24no—
228C42×D47—24no—
229C42×D47—24no—
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—22no—
270C23×D47—24no—
271C23×D47—22no—
272C23×D47—42no—
273C23×D47C22×C414yes—
274C23×D47C2411yescharacteristic
275C23×D47C2411yescharacteristic
276C23×D47C2411yescharacteristic
277C2×D4×C47—42no—
278C2×D4×C47C22×C414yes—
279C22×C4×C47—22no—
280C22×C4×C47—22no—
281C22×C4×C47—22no—
282C22×C4×C47—22no—
283C22×C4×C47—24no—
284C22×C4×C47—24no—
285C22×C4×C47—42no—
286C22×C4×C47C22×C414yes—
287C22×C4×C47C22×C414yes—
288C22×C4×C47C2412yes—
289C22×C4×C47C2412yes—
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2411yescharacteristic
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2412yes—
295C22×C4×C47C2412yes—
296C22×C4×C47C2411yescharacteristic
297C2×C22⋊D47—22no—
298C2×C22⋊D47—24no—
299C2×C22⋊D47—22no—
300C2×C22⋊D47—22no—
301C2×C22⋊D47—22no—
302C2×C22⋊D47—42no—
303C2×C22⋊D47C22×C414yes—
304C2×C22⋊D47C22×C414yes—
305C2×C22⋊D47C22×C414yes—
306C2×C22⋊D47C22×C414yes—
307C22×Dic47—22no—
308C22×Dic47—22no—
309C22×Dic47C22×C414yes—
310C22×Dic47C2412yes—
311C22×Dic47C2412yes—
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2411yescharacteristic
316C22×Dic47C2412yes—
317C22×Dic47C2412yes—
318C22×Dic47C2411yescharacteristic
319#10625350—232no—
320C2×D188—22no—
321C2×D188—24no—
322C2×D188—22no—
323C2×D188C22×C414yes—
324C2×D188C22×C414yes—
325C2×C4×D47—22no—
326C2×C4×D47—22no—
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—232no—
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—24no—
344C2×C4×D47—42no—
345C2×C4×D47—42no—
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×D47C2×D414yes—
355C2×C4×D47#4114yes—
356C2×Dic94—22no—
357C2×Dic94—22no—
358C2×Dic94C22×C414yes—
359C4⋊C4×C47—24no—
360C4⋊C4×C47—24no—
361C4⋊C4×C47C22×C414yes—
362C22⋊C4×C47—24no—
363C22⋊C4×C47—24no—
364C22⋊C4×C47—42no—
365C22⋊C4×C47C22×C414yes—
366C22⋊C4×C47C22×C414yes—
367C42×C47—22no—
368C42×C47—24no—
369C42×C47—22no—
370C42×C47—22no—
371C42×C47C22×C414yes—
372C42×C47C2×D414yes—
373C22⋊Dic47—24no—
374C22⋊Dic47—24no—
375C22⋊Dic47—24no—
376C22⋊Dic47—24no—
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—42no—
384(C2×D47)⋊C4C22×C414yes—
385(C2×D47)⋊C4C22×C414yes—
386(C2×D47)⋊C4C22×C414yes—
387(C2×D47)⋊C4C22×C414yes—
388(C2×D47)⋊C4C22×C414yes—
389(C2×D47)⋊C4C22×C414yes—
390(C2×D47)⋊C4C2×D418yes—
391(C2×D47)⋊C4#4118yescomplemented
392C4⋊Dic47—24no—
393C4⋊Dic47—24no—
394C4⋊Dic47—42no—
395C4⋊Dic47C22×C414yes—
396Dic47⋊C4—24no—
397Dic47⋊C4—24no—
398Dic47⋊C4—24no—
399Dic47⋊C4—42no—
400Dic47⋊C4C22×C414yes—
401Dic47⋊C4C22×C414yes—
402Dic47⋊C4C22×C414yes—
403Dic47⋊C4C22×C414yes—
404Dic47⋊C4C2×D418yes—
405C4×Dic47—24no—
406C4×Dic47—22no—
407C4×Dic47—22no—
408C4×Dic47—22no—
409C4×Dic47—24no—
410C4×Dic47—24no—
411C4×Dic47—24no—
412C4×Dic47—24no—
413C4×Dic47—24no—
414C4×Dic47—24no—
415C4×Dic47—42no—
416C4×Dic47—42no—
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—21no—
431C22×D47—21no—
432C22×D47—22no—
433C22×D47—22no—
434C22×D47—22no—
435C22×D47—21no—
436C22×D47—22no—
437C22×D47—21no—
438C22×D47—22no—
439C22×D47—28no—
440C22×D47—28no—
441C22×D47—44no—
442C22×D47—48no—
443C22×D47—48no—
444C22×D47C23×C412yes—
445C22×D47C23×C412yes—
446C22×D47C23×C412yes—
447C22×D47C22×D412yes—
448C22×D47C2×#4112yes—
449C22×D47C2×#4114yes—
450D4×C47—44no—
451C2×C4×C47—22no—
452C2×C4×C47—21no—
453C2×C4×C47—21no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—21no—
457C2×C4×C47—21no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—28no—
462C2×C4×C47—28no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—48no—
470C2×C4×C47C23×C412yes—
471C2×C4×C47C23×C412yes—
472C2×C4×C47C23×C412yes—
473C2×C4×C47C23×C412yes—
474C2×C4×C47C23×C412yes—
475C2×C4×C47C22×D414yes—
476C2×C4×C47C22×D412yes—
477C2×C4×C47C2×#4114yes—
478C2×C4×C47C2×#4112yes—
479C22⋊D47—28no—
480C22⋊D47—28no—
481C22⋊D47—28no—
482C22⋊D47—44no—
483C2×Dic47—21no—
484C2×Dic47—21no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—22no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—28no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47C23×C412yes—
501C2×Dic47C23×C412yes—
502C2×Dic47C23×C412yes—
503C2×Dic47C23×C412yes—
504C2×Dic47C23×C412yes—
505C2×Dic47C22×D414yes—
506C2×Dic47C22×D412yes—
507C2×Dic47C2×#4114yes—
508C2×Dic47C2×#4112yes—
509D188—28no—
510D188—28no—
511C4×D47—28no—
512C4×D47—28no—
513C4×D47—28no—
514C4×D47—28no—
515C4×D47—48no—
516C4×D47—48no—
517C4×D47—48no—
518C4×D47—48no—
519C4×D47—48no—
520C4×D47C4×D4116yescomplemented
521Dic94—28no—
522#34136—471nomaximal, Sylow
523C22×C47—22no—
524C22×C47—22no—
525C22×C47—22no—
526C22×C47—22no—
527C22×C47—22no—
528C22×C47—22no—
529C22×C47—42no—
530C22×C47—42no—
531C22×C47—42no—
532C22×C47—42no—
533C22×C47C24×C411yescharacteristic
534C22×C47C23×D411yescharacteristic
535C22×C47C22×#4111yescharacteristic
536C22×C47C22×#4112yes—
537C22×C47#58512yes—
538C2×D47—22no—
539C2×D47—22no—
540C2×D47—22no—
541C2×D47—22no—
542C2×D47—24no—
543C2×D47—24no—
544C2×D47—24no—
545C2×D47—24no—
546C2×D47—22no—
547C2×D47—22no—
548C2×D47—22no—
549C2×D47—416no—
550C2×D47—42no—
551C2×D47—42no—
552C2×D47C2×C4×D414yes—
553C2×D47C4×#4114yescomplemented
554C4×C47—22no—
555C4×C47—22no—
556C4×C47—22no—
557C4×C47—22no—
558C4×C47—24no—
559C4×C47—24no—
560C4×C47—42no—
561C4×C47—42no—
562C4×C47C2×C4×D414yes—
563Dic47—22no—
564Dic47—22no—
565Dic47—22no—
566Dic47—22no—
567Dic47—24no—
568Dic47—24no—
569Dic47—42no—
570Dic47—42no—
571Dic47C2×C4×D414yes—
572C2×#525—471no—
573C2×C4×#41—471no—
574C22×#117—471no—
575#2363—472no—
576#2362—472no—
577#2361—472no—
578#2360—472no—
579#2359—472no—
580#2359—472no—
581#2358—472no—
582#2358—472no—
583#2297—471no—
584#2296—471no—
585#2293—471no—
586#2293—471no—
587#2290—471no—
588#2290—471no—
589#2290—471no—
590#2290D4711yescharacteristic, complemented
591C42×D4—471no—
592C42×D4—471no—
593C4×#117—471no—
594C2×C4×C22⋊C4—471no—
595C2×C47—42no—
596C2×C47—42no—
597C2×C47C22×C4×D411yescharacteristic
598C2×C47C2×C4×#4111yescharacteristic
599C2×C47#342811yescharacteristic
600C2×C47D4×#4112yes—
601C2×C47#347512yes—
602D47—24no—
603D47—24no—
604D47—42no—
605C22×#41—471no—
606C24×C4—471no—
607#525—4716no—
608C2×#123—471no—
609C2×#123—471no—
610C2×C22⋊Q8—471no—
611C2×C22⋊Q8—471no—
612C2×#121—471no—
613C2×#121—471no—
614C2×#120—471no—
615C2×#120—471no—
616C4×#41—948no—
617C2×C4×Q8—472no—
618C2×C4×D4—471no—
619C2×C4×D4—471no—
620C2×C4×D4—472no—
621C2×C4×D4—472no—
622C2×C4×D4—472no—
623C2×C4×D4—472no—
624C2×C4×D4—471no—
625C2×C4×D4—472no—
626C2×C4×D4C2×D4711yescharacteristic
627C2×#117—471no—
628C2×#117—471no—
629C2×#117—472no—
630C2×#117—472no—
631C2×#117—471no—
632C2×#117—471no—
633C2×#117—471no—
634C2×#117—471no—
635C2×#117—948no—
636C2×#117C2×D4711yescharacteristic
637C22×C4⋊C4—472no—
638C22×C22⋊C4—472no—
639C22×C22⋊C4—472no—
640C22×C42—471no—
641C22×C42—471no—
642C22×C42—471no—
643C22×C42—471no—
644C22×C42—471no—
645C22×C42C2×D4711yescharacteristic, complemented
646#391—472no—
647#390—472no—
648#390—472no—
649#390—472no—
650#389—472no—
651#389—472no—
652#389—472no—
653#389—472no—
654#388—472no—
655#388—472no—
656#388—472no—
657#388—472no—
658#388—472no—
659#388—472no—
660#388—472no—
661#388C2×D4712yes—
662#387—472no—
663#387—472no—
664#387—472no—
665#387C2×D4712yescomplemented
666#386—472no—
667#386—472no—
668#386—472no—
669#386—472no—
670#386—472no—
671#386C2×D4712yes—
672#385—472no—
673#385—472no—
674#385—472no—
675#385—472no—
676#385—472no—
677#385C2×D4712yescomplemented
678C4×C4⋊C4—472no—
679C4×C4⋊C4—471no—
680C4×C4⋊C4—472no—
681C4×C4⋊C4—471no—
682C4×C4⋊C4—471no—
683C4×C4⋊C4—472no—
684C4×C4⋊C4—472no—
685C4×C4⋊C4C2×D4711yescharacteristic, complemented
686C4×C22⋊C4—471no—
687C4×C22⋊C4—472no—
688C4×C22⋊C4—471no—
689C4×C22⋊C4—472no—
690C4×C22⋊C4—472no—
691C4×C22⋊C4—471no—
692C4×C22⋊C4—471no—
693C4×C22⋊C4—471no—
694C4×C22⋊C4—471no—
695C4×C22⋊C4—472no—
696C4×C22⋊C4—472no—
697C4×C22⋊C4—472no—
698C4×C22⋊C4—472no—
699C4×C22⋊C4—472no—
700C4×C22⋊C4C2×D4711yescharacteristic
701C4×C22⋊C4C2×D4711yescharacteristic, complemented
702#376—471no—
703#376C2×D4711yescharacteristic, complemented
704C2×#95—472no—
705C43—471no—
706C43—471no—
707C47#3413611yescharacteristic, complemented, Sylow
708C25—471no—
709C2×#41—478no—
710C2×#41—944no—
711C2×#41—944no—
712C22×Q8—471no—
713C22×D4—471no—
714C22×D4—471no—
715C22×D4—471no—
716C22×D4—471no—
717C22×D4—471no—
718C22×D4—471no—
719C22×D4C22×D4711yescharacteristic
720C23×C4—471no—
721C23×C4—471no—
722C23×C4—478no—
723C23×C4—471no—
724C23×C4—471no—
725C23×C4—471no—
726C23×C4—471no—
727C23×C4—472no—
728C23×C4—472no—
729C23×C4—472no—
730C23×C4—472no—
731C23×C4—472no—
732C23×C4—944no—
733C23×C4—944no—
734C23×C4C22×D4712yes—
735C23×C4C22×D4711yescharacteristic
736C23×C4C22×D4711yescharacteristic
737#123—478no—
738#123—478no—
739C22⋊Q8—478no—
740C22⋊Q8—478no—
741#121—478no—
742#121—478no—
743#120—478no—
744#120—478no—
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×D4C4×D4718yescomplemented
755#117—24no—
756#117—478no—
757#117—478no—
758#117—944no—
759#117—944no—
760#117—944no—
761#117—948no—
762#117—948no—
763#117—944no—
764C2×C4⋊C4—472no—
765C2×C4⋊C4—471no—
766C2×C4⋊C4—471no—
767C2×C4⋊C4—471no—
768C2×C4⋊C4—471no—
769C2×C4⋊C4—471no—
770C2×C4⋊C4—472no—
771C2×C4⋊C4—472no—
772C2×C4⋊C4—472no—
773C2×C4⋊C4—472no—
774C2×C4⋊C4—472no—
775C2×C4⋊C4—472no—
776C2×C4⋊C4—472no—
777C2×C4⋊C4—948no—
778C2×C4⋊C4C22×D4712yes—
779C2×C4⋊C4C22×D4712yes—
780C2×C4⋊C4C22×D4711yescharacteristic
781C2×C22⋊C4—471no—
782C2×C22⋊C4—471no—
783C2×C22⋊C4—472no—
784C2×C22⋊C4—472no—
785C2×C22⋊C4—471no—
786C2×C22⋊C4—471no—
787C2×C22⋊C4—471no—
788C2×C22⋊C4—471no—
789C2×C22⋊C4—471no—
790C2×C22⋊C4—471no—
791C2×C22⋊C4—472no—
792C2×C22⋊C4—472no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—472no—
797C2×C22⋊C4—472no—
798C2×C22⋊C4—472no—
799C2×C22⋊C4—472no—
800C2×C22⋊C4—948no—
801C2×C22⋊C4—948no—
802C2×C22⋊C4C22×D4712yes—
803C2×C22⋊C4C22×D4712yes—
804C2×C22⋊C4C22×D4712yes—
805C2×C22⋊C4C22×D4711yescharacteristic
806C2×C22⋊C4C22×D4711yescharacteristic
807C2×C42—24no—
808C2×C42—471no—
809C2×C42—471no—
810C2×C42—472no—
811C2×C42—472no—
812C2×C42—472no—
813C2×C42—472no—
814C2×C42—472no—
815C2×C42—472no—
816C2×C42—472no—
817C2×C42—471no—
818C2×C42—471no—
819C2×C42—471no—
820C2×C42—472no—
821C2×C42—472no—
822C2×C42—944no—
823C2×C42—944no—
824C2×C42—944no—
825C2×C42—944no—
826C2×C42—944no—
827C2×C42C22×D4712yes—
828C2×C42C22×D4711yescharacteristic
829C2×C42C22×D4711yescharacteristic
830C2×C42C22×D4711yescharacteristic
831C2×C42C22×D4711yescharacteristic
832C2×C42C22×D4711yescharacteristic
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#95—472no—
842#95—472no—
843#95—472no—
844#95C22×D4712yes—
845#95C22×D4712yes—
846#95C22×D4712yes—
847#95C22×D4712yes—
848#95C22×D4712yes—
849C24—471no—
850C24—471no—
851C24—471no—
852C24—474no—
853C24—942no—
854C24—944no—
855C24—942no—
856C24—1882no—
857C24C23×D4711yescharacteristic
858C24C23×D4711yescharacteristic
859#41—9432no—
860C2×Q8—474no—
861C2×Q8—942no—
862C2×Q8—942no—
863C2×D4—42no—
864C2×D4—474no—
865C2×D4—474no—
866C2×D4—474no—
867C2×D4—474no—
868C2×D4—474no—
869C2×D4—474no—
870C2×D4—942no—
871C2×D4—944no—
872C2×D4—942no—
873C2×D4—942no—
874C2×D4—942no—
875C2×D4—942no—
876C2×D4—944no—
877C2×D4—942no—
878C2×D4—1882no—
879C2×D4C2×C4×D4714yes—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—42no—
887C22×C4—471no—
888C22×C4—474no—
889C22×C4—474no—
890C22×C4—474no—
891C22×C4—474no—
892C22×C4—472no—
893C22×C4—471no—
894C22×C4—471no—
895C22×C4—471no—
896C22×C4—471no—
897C22×C4—472no—
898C22×C4—474no—
899C22×C4—474no—
900C22×C4—474no—
901C22×C4—474no—
902C22×C4—472no—
903C22×C4—472no—
904C22×C4—942no—
905C22×C4—942no—
906C22×C4—9432no—
907C22×C4—944no—
908C22×C4—944no—
909C22×C4—944no—
910C22×C4—942no—
911C22×C4—942no—
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—942no—
921C22×C4—942no—
922C22×C4—944no—
923C22×C4—944no—
924C22×C4—944no—
925C22×C4—1882no—
926C22×C4—1882no—
927C22×C4—1882no—
928C22×C4—1882no—
929C22×C4—1882no—
930C22×C4C2×C4×D4714yes—
931C22×C4C2×C4×D4714yes—
932C22×C4C23×D4712yes—
933C22×C4C23×D4712yes—
934C22×C4C23×D4711yescharacteristic
935C22×C4C23×D4711yescharacteristic
936C22×C4C23×D4711yescharacteristic
937C22×C4C23×D4711yescharacteristic
938C22×C4C23×D4712yes—
939C22×C4C23×D4712yes—
940C22×C4C23×D4711yescharacteristic
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—474no—
944C4⋊C4—474no—
945C4⋊C4—474no—
946C4⋊C4—474no—
947C4⋊C4—474no—
948C4⋊C4—478no—
949C4⋊C4—944no—
950C4⋊C4—944no—
951C4⋊C4—944no—
952C4⋊C4—944no—
953C4⋊C4—944no—
954C4⋊C4—1882no—
955C4⋊C4—1882no—
956C4⋊C4C2×C4×D4714yes—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—42no—
960C22⋊C4—474no—
961C22⋊C4—474no—
962C22⋊C4—474no—
963C22⋊C4—474no—
964C22⋊C4—474no—
965C22⋊C4—474no—
966C22⋊C4—474no—
967C22⋊C4—474no—
968C22⋊C4—478no—
969C22⋊C4—478no—
970C22⋊C4—944no—
971C22⋊C4—944no—
972C22⋊C4—944no—
973C22⋊C4—944no—
974C22⋊C4—944no—
975C22⋊C4—944no—
976C22⋊C4—944no—
977C22⋊C4—944no—
978C22⋊C4—1882no—
979C22⋊C4C2×C4×D4714yes—
980C22⋊C4C2×C4×D4714yes—
981C42—22no—
982C42—24no—
983C42—22no—
984C42—22no—
985C42—474no—
986C42—474no—
987C42—944no—
988C42—944no—
989C42—944no—
990C42—944no—
991C42—944no—
992C42—944no—
993C42—944no—
994C42—942no—
995C42—942no—
996C42—942no—
997C42—1882no—
998C42—1882no—
999C42C2×C4×D4714yes—
1000C42D4×D4714yes—
1001C23—21no—
1002C23—21no—
1003C23—22no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—22no—
1009C23—472no—
1010C23—472no—
1011C23—472no—
1012C23—474no—
1013C23—472no—
1014C23—472no—
1015C23—948no—
1016C23—948no—
1017C23—941no—
1018C23—941no—
1019C23—942no—
1020C23—942no—
1021C23—942no—
1022C23—941no—
1023C23—942no—
1024C23—941no—
1025C23—942no—
1026C23—1884no—
1027C23—1888no—
1028C23—1888no—
1029C23C22×C4×D4712yes—
1030C23C22×C4×D4712yes—
1031C23C24×D4711yescharacteristic
1032Q8—948no—
1033D4—44no—
1034D4—948no—
1035D4—948no—
1036D4—948no—
1037D4—948no—
1038D4—948no—
1039D4—1884no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—28no—
1051C2×C4—28no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—48no—
1059C2×C4—472no—
1060C2×C4—472no—
1061C2×C4—472no—
1062C2×C4—4716no—
1063C2×C4—472no—
1064C2×C4—472no—
1065C2×C4—472no—
1066C2×C4—472no—
1067C2×C4—474no—
1068C2×C4—474no—
1069C2×C4—948no—
1070C2×C4—948no—
1071C2×C4—948no—
1072C2×C4—941no—
1073C2×C4—941no—
1074C2×C4—942no—
1075C2×C4—942no—
1076C2×C4—942no—
1077C2×C4—941no—
1078C2×C4—941no—
1079C2×C4—942no—
1080C2×C4—942no—
1081C2×C4—942no—
1082C2×C4—948no—
1083C2×C4—948no—
1084C2×C4—942no—
1085C2×C4—942no—
1086C2×C4—942no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—1888no—
1091C2×C4—1888no—
1092C2×C4—1888no—
1093C2×C4—1888no—
1094C2×C4—1888no—
1095C2×C4C22×C4×D4712yes—
1096C2×C4C22×C4×D4712yes—
1097C2×C4C22×C4×D4712yes—
1098C2×C4C22×C4×D4712yes—
1099C2×C4C22×C4×D4712yes—
1100C2×C4C2×D4×D4714yes—
1101C2×C4C2×D4×D4712yes—
1102C2×C4#41×D4714yes—
1103C2×C4#41×D4712yes—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—474no—
1115C22—474no—
1116C22—942no—
1117C22—942no—
1118C22—942no—
1119C22—942no—
1120C22—944no—
1121C22—944no—
1122C22—944no—
1123C22—944no—
1124C22—942no—
1125C22—942no—
1126C22—942no—
1127C22—18816no—
1128C22—1882no—
1129C22—1882no—
1130C22C23×C4×D4711yescharacteristic
1131C22C22×D4×D4711yescharacteristic
1132C22C2×#41×D4711yescharacteristic
1133C22C2×#41×D4712yes—
1134C22#1568995912yes—
1135C4—22no—
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—24no—
1140C4—24no—
1141C4—42no—
1142C4—42no—
1143C4—474no—
1144C4—942no—
1145C4—942no—
1146C4—942no—
1147C4—942no—
1148C4—944no—
1149C4—944no—
1150C4—1882no—
1151C4—1882no—
1152C4C4×D4×D4714yes—
1153C2—42no—
1154C2—42no—
1155C2—944no—
1156C2—944no—
1157C2—1882no—
1158C2C2×C4×D4×D4711yescharacteristic
1159C2C4×#41×D4711yescharacteristic
1160C2#2025658911yescharacteristic
1161C2#2025687112yes—
1162C2#2025694412yes—
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC47×#2290C2
socle, cosocleC23×C47C25
prime radicalC2×#15689632C2
hypercenter#2290D47
hypocenterC47#34136
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×#117×D47C2semidirect
4. #20246429C2semidirect
5. #20246418C2semidirect
6. #20246407C2semidirect
7. #20246396C2semidirect
8. #20246387C2semidirect
9. #20246383C2semidirect
10. #20246371C2semidirect
11. #20246366C2semidirect
12. #20245874C2semidirect
13. #20245868C2semidirect
14. #20245853C2semidirect
15. #20245847C2semidirect
16. #20245834C2semidirect
17. #20245834C2semidirect
18. #20245832C2semidirect
19. C42×C22⋊D47C2semidirect
20. C4×#13093986C2semidirect
21. #20245727C2semidirect
22. C4×C22⋊C4×D47C2semidirect
23. C47×#2290C2semidirect
26. #15689632C4semidirect
36. C2×C4×Dic94C22semidirect
44. C2×C4×C22⋊D47C22semidirect
46. C2×#13093983C22semidirect
51. C2×#13093981C22semidirect
61. C2×C42×D47C22semidirect
62. #15689027C22semidirect
65. #15689023C22semidirect
66. #15689022C22semidirect
67. #15689020C22semidirect
68. #15689018C22semidirect
69. #15689018C22semidirect
72. #15689017C22semidirect
74. #15689016C22semidirect
75. #15689015C22semidirect
76. #15689013C22semidirect
77. #15689010C22semidirect
78. #15689010C22semidirect
79. #15689008C22semidirect
88. #15688997C22semidirect
90. C4⋊C4×Dic47C22semidirect
91. C4×Dic47⋊C4C22semidirect
92. C4×Dic47⋊C4C22semidirect
93. C4×Dic47⋊C4C22semidirect
94. C4×C4⋊Dic47C22semidirect
95. #15688974C22semidirect
96. #15688974C22semidirect
101. C4×(C2×D47)⋊C4C22semidirect
102. C4×(C2×D47)⋊C4C22semidirect
104. C4×C22⋊Dic47C22semidirect
105. C4×C22⋊Dic47C22semidirect
110. #15688970C22semidirect
111. #15688969C22semidirect
113. C42×Dic47C22semidirect
114. C42×Dic47C22semidirect
117. C22×C42×C47C22semidirect
119. C47×#387C22semidirect
121. C47×#385C22semidirect
122. C4×C4⋊C4×C47C22semidirect
124. C4×C22⋊C4×C47C22semidirect
125. C47×#376C22semidirect
129. C2×#10625350C2×C4semidirect
140. C22×C4×D47C2×C4semidirect
151. #13094009C2×C4semidirect
152. #13094006C2×C4semidirect
153. #13094002C2×C4semidirect
154. #13094001C2×C4semidirect
155. #13093997C2×C4semidirect
156. #13093996C2×C4semidirect
157. #13093994C2×C4semidirect
158. #13093992C2×C4semidirect
161. C4×D188C2×C4semidirect
166. C4×C22⋊D47C2×C4semidirect
167. C4×C22⋊D47C2×C4semidirect
173. #13093981C2×C4semidirect
174. #13093981D4semidirect
245. C4×D4×C47C2×C4semidirect
391. (C2×D47)⋊C4#41semidirect
520. C4×D47C4×D4semidirect
553. C2×D47C4×#41semidirect
590. #2290D47semidirect
645. C22×C42C2×D47semidirect
665. #387C2×D47semidirect
677. #385C2×D47semidirect
685. C4×C4⋊C4C2×D47semidirect
701. C4×C22⋊C4C2×D47semidirect
703. #376C2×D47semidirect
707. C47#34136semidirect
754. 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×C4×#106253502
C2×#117×D472
#202464292
#202464182
#202464072
#202463962
#202463872
#202463832
#202463712
#202463662
#202458742
#202458682
#202458532
#202458472
#202458342
#202458322
C42×C22⋊D472
C4×#130939862
#202457272
C4×C22⋊C4×D472
C47×#22902
#3413647