Finite Group Databasebeta

← #26388146

Subgroups — #26388146

Order 12032.

3578 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689632C212yesmaximal, complemented
2C2×#15689591C211yesmaximal, characteristic, complemented
3C2×C4×D4×D47C211yesmaximal, characteristic, complemented
4#20248305C212yesmaximal, complemented
5#20248300C212yesmaximal, complemented
6#20248294C211yesmaximal, characteristic, complemented
7#20248292C211yesmaximal, characteristic, complemented
8#20248286C211yesmaximal, characteristic, complemented
9#20248284C211yesmaximal, characteristic, complemented
10#20248279C212yesmaximal, complemented
11#20248273C212yesmaximal, complemented
12#20247691C211yesmaximal, characteristic, complemented
13#20247689C211yesmaximal, characteristic, complemented
14#20246739C211yesmaximal, characteristic, complemented
15#20246737C211yesmaximal, characteristic, complemented
16#20246628C211yesmaximal, characteristic, complemented
17#20246626C211yesmaximal, characteristic, complemented
18#20246624C211yesmaximal, characteristic, complemented
19C4×#13093997C212yesmaximal, complemented
20C4×#13093996C212yesmaximal, complemented
21#20245792C211yesmaximal, characteristic, complemented
22#20245769C212yesmaximal, complemented
23C47×#2392C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic
25C22×D4×D47C2211yescharacteristic
26C23×C4×D47C2212yes—
27#15689632—216no—
28C2×#13094009C2212yes—
29C2×#13094006C2212yes—
30C2×#13094002C2212yescomplemented
31C2×#13094001C2212yescomplemented
32C2×#13093997C2212yes—
33C2×#13093997C2212yescomplemented
34C2×#13093996C2212yes—
35C2×#13093996C2212yescomplemented
36C2×#13093994C2212yes—
37C2×#13093992C2212yes—
38#15689591—28no—
39C2×#13093989C2211yescharacteristic, complemented
40C2×#13093989C2211yescharacteristic, complemented
41C2×C4×D188C2211yescharacteristic
42C2×C4×D188C2212yescomplemented
43C2×D4×Dic47C2211yescharacteristic
44C2×#13093986C2211yescharacteristic
45C2×#13093986C2211yescharacteristic
46C2×#13093986C2211yescharacteristic
47C2×C4×C22⋊D47C2212yes—
48C2×C4×C22⋊D47C2212yescomplemented
49C2×C4×C22⋊D47C2212yescomplemented
50C2×(C22⋊D47)⋊C4C2212yes—
51C2×(C22⋊D47)⋊C4C2211yescharacteristic
52C2×(C22⋊D47)⋊C4C2211yescharacteristic
53C2×(C22⋊D47)⋊C4C2211yescharacteristic, complemented
54C2×(C22⋊D47)⋊C4C2211yescharacteristic, complemented
55C4×D4×D47—28no—
56C2×#13093981C2211yescharacteristic
57C2×#13093981C2212yes—
58C2×#13093981C2211yescharacteristic, complemented
59C2×C4⋊C4×D47C2211yescharacteristic
60C2×C22⋊C4×D47C2212yes—
61C22×C4×Dic47C2211yescharacteristic, complemented
62C2×C42×D47C2211yescharacteristic
63C2×C42×D47C2211yescharacteristic, complemented
64#15689055C2211yescharacteristic, complemented
65#15689054C2211yescharacteristic, complemented
66#15689053C2211yescharacteristic, complemented
67#15689050C2211yescharacteristic, complemented
68#15689049C2211yescharacteristic, complemented
69#15689048C2211yescharacteristic, complemented
70#15689046C2212yescomplemented
71#15689045C2212yescomplemented
72#15689045C2212yescomplemented
73#15689041C2211yescharacteristic
74#15689040C2211yescharacteristic
75#15689040C2212yescomplemented
76#15689039C2212yescomplemented
77#15689039C2212yescomplemented
78#15689037C2211yescharacteristic
79#15689033C2211yescharacteristic
80#15689032C2211yescharacteristic
81#15689031C2211yescharacteristic
82#15689023C2212yes—
83#15689023C2212yes—
84#15689020C2212yescomplemented
85#15689018C2212yescomplemented
86#15689017C2212yescomplemented
87#15689016C2212yescomplemented
88#15689013C2212yescomplemented
89#15689012C2212yescomplemented
90#15689003C2212yescomplemented
91#15689001C2212yescomplemented
92#15689000C2212yescomplemented
93#15688999C2212yescomplemented
94#15688992C2212yescomplemented
95#15688987C2211yescharacteristic, complemented
96#15688987C2211yescharacteristic, complemented
97#15688985C2212yes—
98#15688985C2212yes—
99#15688982C2211yescharacteristic
100#15688982C2211yescharacteristic
101#15688982C2212yescomplemented
102#15688982C2212yescomplemented
103#15688982C2212yescomplemented
104#15688981C2212yescomplemented
105#15688981C2212yescomplemented
106#15688981C2212yescomplemented
107#15688980C2212yes—
108#15688978C2212yes—
109#15688978C2212yes—
110C4×Dic47⋊C4C2212yescomplemented
111C4×C4⋊Dic47C2211yescharacteristic, complemented
112C4×(C2×D47)⋊C4C2212yescomplemented
113C4×(C2×D47)⋊C4C2212yescomplemented
114C4×C22⋊Dic47C2212yescomplemented
115C2×C4×D4×C47C2211yescharacteristic
116C2×C4×D4×C47C2212yescomplemented
117C2×#117×C47C2211yescharacteristic, complemented
118C47×#398C2211yescharacteristic, complemented
119C47×#397C2211yescharacteristic, complemented
120C47×#396C2212yescomplemented
121C47×#394C2211yescharacteristic
122C47×#394C2212yescomplemented
123C47×#392C2211yescharacteristic
124C4×C4⋊C4×C47C2211yescharacteristic, complemented
125C4×C22⋊C4×C47C2212yescomplemented
126C24×D47C2312yes—
127C2×#10625350—24no—
128C2×#10625350—24no—
129C2×#10625350D418yescomplemented
130C22×Dic94C2311yescharacteristic
131C22×D188C2311yescharacteristic
132C22×D188C2312yes—
133C22×D188C2311yescharacteristic
134C22×C22⋊D47C2312yes—
135C22×C22⋊D47C2312yes—
136C22×C22⋊D47C2311yescharacteristic
137C22×C22⋊D47C2311yescharacteristic
138C22×C22⋊D47C2312yes—
139C2×D4×D47—28no—
140C2×D4×D47—24no—
141C23×Dic47C2311yescharacteristic
142C23×Dic47C2312yes—
143C23×Dic47C2311yescharacteristic
144C22×C4×D47—28no—
145C22×C4×D47—28no—
146C22×C4×D47—28no—
147C22×C4×D47C2312yes—
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2312yes—
150C22×C4×D47C2312yes—
151C22×C4×D47C2311yescharacteristic
152C22×C4×D47C2311yescharacteristic
153C22×C4×D47C2311yescharacteristic
154C22×C4×D47C2311yescharacteristic
155C22×C4×D47C2311yescharacteristic
156#13094009—28no—
157#13094006—28no—
158#13094002—28no—
159#13094001—28no—
160#13093997—28no—
161#13093997—28no—
162#13093996—28no—
163#13093996—28no—
164#13093994—28no—
165#13093992—28no—
166#13093989—24no—
167#13093989—24no—
168C4×D188—28no—
169C4×D188—24no—
170D4×Dic47—24no—
171#13093986—24no—
172#13093986—24no—
173#13093986—24no—
174C4×C22⋊D47—28no—
175C4×C22⋊D47—28no—
176C4×C22⋊D47—28no—
177(C22⋊D47)⋊C4—24no—
178(C22⋊D47)⋊C4—24no—
179(C22⋊D47)⋊C4—28no—
180(C22⋊D47)⋊C4—24no—
181(C22⋊D47)⋊C4—24no—
182#13093981—24no—
183#13093981—28no—
184#13093981—24no—
185C2×C4⋊Dic47C2312yes—
186C2×C4⋊Dic47C2311yescharacteristic
187C2×C4⋊Dic47C2312yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2312yes—
190C2×Dic47⋊C4C2311yescharacteristic
191C2×Dic47⋊C4C2311yescharacteristic
192C2×Dic47⋊C4C2312yes—
193C2×Dic47⋊C4C2312yes—
194C2×Dic47⋊C4C2312yes—
195C2×Dic47⋊C4C2312yes—
196C2×Dic47⋊C4C2312yes—
197C2×Dic47⋊C4C2311yescharacteristic
198C2×Dic47⋊C4C2311yescharacteristic
199C4⋊C4×D47—24no—
200C2×C22⋊Dic47C2312yes—
201C2×C22⋊Dic47C2312yes—
202C2×C22⋊Dic47C2312yes—
203C2×C22⋊Dic47C2312yes—
204C2×C22⋊Dic47C2312yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2312yes—
207C2×(C2×D47)⋊C4C2311yescharacteristic
208C2×(C2×D47)⋊C4C2311yescharacteristic
209C2×(C2×D47)⋊C4C2312yes—
210C2×(C2×D47)⋊C4C2312yes—
211C2×(C2×D47)⋊C4C2312yes—
212C2×(C2×D47)⋊C4C2312yes—
213C2×(C2×D47)⋊C4C2312yes—
214C2×(C2×D47)⋊C4C2312yes—
215C2×(C2×D47)⋊C4C2312yes—
216C2×(C2×D47)⋊C4C2311yescharacteristic
217C2×(C2×D47)⋊C4C2311yescharacteristic
218C2×(C2×D47)⋊C4C2312yes—
219C2×(C2×D47)⋊C4C2312yes—
220C2×(C2×D47)⋊C4C2312yes—
221C22⋊C4×D47—28no—
222C2×C4×Dic47—24no—
223C2×C4×Dic47C2311yescharacteristic
224C2×C4×Dic47C2312yes—
225C2×C4×Dic47C2311yescharacteristic
226C2×C4×Dic47C2311yescharacteristic
227C2×C4×Dic47C2311yescharacteristic
228C2×C4×Dic47C2311yescharacteristic
229C2×C4×Dic47C2311yescharacteristic
230C2×C4×Dic47C2311yescharacteristic
231C2×C4×Dic47C2311yescharacteristic
232C42×D47—24no—
233C42×D47D418yescomplemented
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C47⋊#95C2312yes—
237C47⋊#95C2312yes—
238C47⋊#95C2312yes—
239C47⋊#95C2312yes—
240C47⋊#95C2311yescharacteristic
241C47⋊#95C2311yescharacteristic
242C47⋊#95C2312yes—
243C47⋊#95C2312yes—
244C22×D4×C47C2311yescharacteristic
245C22×D4×C47C2312yes—
246C23×C4×C47C2312yes—
247C23×C4×C47C2311yescharacteristic
248C4×D4×C47—28no—
249C4×D4×C47—24no—
250#117×C47—24no—
251C2×C4⋊C4×C47C2312yes—
252C2×C4⋊C4×C47C2311yescharacteristic
253C2×C4⋊C4×C47C2311yescharacteristic
254C2×C4⋊C4×C47C2311yescharacteristic
255C2×C4⋊C4×C47C2312yes—
256C2×C22⋊C4×C47C2312yes—
257C2×C22⋊C4×C47C2312yes—
258C2×C22⋊C4×C47C2312yes—
259C2×C22⋊C4×C47C2311yescharacteristic
260C2×C22⋊C4×C47C2311yescharacteristic
261C2×C22⋊C4×C47C2312yes—
262C2×C22⋊C4×C47C2312yes—
263C2×C42×C47C2311yescharacteristic
264C2×C42×C47C2312yes—
265C2×C42×C47C2311yescharacteristic
266#95×C47C2311yescharacteristic
267#95×C47C2311yescharacteristic
268#95×C47C2312yes—
269#95×C47C2312yes—
270C24×C47C2411yescharacteristic
271C24×C47C2412yes—
272C23×D47—24no—
273C23×D47—24no—
274C23×D47—24no—
275C23×D47—24no—
276C23×D47—24no—
277C23×D47—42no—
278C23×D47—42no—
279C23×D47C2411yescharacteristic
280C23×D47C2412yes—
281C23×D47C2411yescharacteristic
282C2×D4×C47—24no—
283C2×D4×C47—24no—
284C2×D4×C47—24no—
285C2×D4×C47—22no—
286C2×D4×C47—42no—
287C22×C4×C47—22no—
288C22×C4×C47—22no—
289C22×C4×C47—24no—
290C22×C4×C47—24no—
291C22×C4×C47—24no—
292C22×C4×C47C2×D414yescomplemented
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2412yes—
296C22×C4×C47C2412yes—
297C22×C4×C47C2412yes—
298C22×C4×C47C2411yescharacteristic
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2411yescharacteristic
301C22×C4×C47C2411yescharacteristic
302C2×C22⋊D47—22no—
303C2×C22⋊D47—22no—
304C2×C22⋊D47—24no—
305C2×C22⋊D47—24no—
306C2×C22⋊D47—24no—
307C2×C22⋊D47—24no—
308C2×C22⋊D47—22no—
309C2×C22⋊D47—24no—
310C2×C22⋊D47—24no—
311C2×C22⋊D47—22no—
312C2×C22⋊D47—42no—
313C2×C22⋊D47—42no—
314C2×C22⋊D47C2×D414yes—
315C2×C22⋊D47C2×D414yescomplemented
316C2×C22⋊D47#4118yescomplemented
317C22×Dic47—22no—
318C22×Dic47—22no—
319C22×Dic47—24no—
320C22×Dic47—24no—
321C22×Dic47—24no—
322C22×Dic47—24no—
323C22×Dic47—42no—
324C22×Dic47C2411yescharacteristic
325C22×Dic47C2411yescharacteristic
326C22×Dic47C2412yes—
327C22×Dic47C2412yes—
328C22×Dic47C2412yes—
329C22×Dic47C2411yescharacteristic
330C22×Dic47C2411yescharacteristic
331C22×Dic47C2411yescharacteristic
332C22×Dic47C2411yescharacteristic
333D4×D47—232no—
334#10625350—232no—
335C2×D188—22no—
336C2×D188—24no—
337C2×D188—22no—
338C2×D188—22no—
339C2×D188—24no—
340C2×D188—24no—
341C2×D188—42no—
342C2×D188C2×D414yes—
343C2×C4×D47—22no—
344C2×C4×D47—22no—
345C2×C4×D47—24no—
346C2×C4×D47—24no—
347C2×C4×D47—24no—
348C2×C4×D47—24no—
349C2×C4×D47—24no—
350C2×C4×D47—24no—
351C2×C4×D47—24no—
352C2×C4×D47—22no—
353C2×C4×D47—22no—
354C2×C4×D47—24no—
355C2×C4×D47—24no—
356C2×C4×D47—24no—
357C2×C4×D47—24no—
358C2×C4×D47—42no—
359C2×C4×D47—42no—
360C2×C4×D47—432no—
361C2×C4×D47C2×D414yes—
362C2×C4×D47C2×D414yes—
363C2×C4×D47C2×D414yes—
364C2×C4×D47C2×D414yes—
365C2×C4×D47C2×D414yescomplemented
366C2×C4×D47#4114yes—
367C2×Dic94—22no—
368C2×Dic94—22no—
369C2×Dic94C2×D414yescomplemented
370C4⋊C4×C47—22no—
371C4⋊C4×C47—22no—
372C4⋊C4×C47—22no—
373C4⋊C4×C47—24no—
374C4⋊C4×C47—42no—
375C22⋊C4×C47—24no—
376C22⋊C4×C47—24no—
377C22⋊C4×C47—22no—
378C22⋊C4×C47—22no—
379C22⋊C4×C47—24no—
380C22⋊C4×C47—24no—
381C22⋊C4×C47—42no—
382C42×C47—22no—
383C42×C47—24no—
384C42×C47C2×D414yes—
385C22⋊Dic47—24no—
386C22⋊Dic47—24no—
387C22⋊Dic47—24no—
388C22⋊Dic47—24no—
389C22⋊Dic47—42no—
390(C2×D47)⋊C4—22no—
391(C2×D47)⋊C4—22no—
392(C2×D47)⋊C4—24no—
393(C2×D47)⋊C4—24no—
394(C2×D47)⋊C4—24no—
395(C2×D47)⋊C4—24no—
396(C2×D47)⋊C4—24no—
397(C2×D47)⋊C4—24no—
398(C2×D47)⋊C4—24no—
399(C2×D47)⋊C4—22no—
400(C2×D47)⋊C4—22no—
401(C2×D47)⋊C4—24no—
402(C2×D47)⋊C4—24no—
403(C2×D47)⋊C4—24no—
404(C2×D47)⋊C4—42no—
405(C2×D47)⋊C4—42no—
406C4⋊Dic47—22no—
407C4⋊Dic47—24no—
408C4⋊Dic47—42no—
409Dic47⋊C4—22no—
410Dic47⋊C4—22no—
411Dic47⋊C4—24no—
412Dic47⋊C4—24no—
413Dic47⋊C4—22no—
414Dic47⋊C4—22no—
415Dic47⋊C4—24no—
416Dic47⋊C4—24no—
417Dic47⋊C4—24no—
418Dic47⋊C4—24no—
419Dic47⋊C4—24no—
420C4×Dic47—22no—
421C4×Dic47—24no—
422C4×Dic47—22no—
423C4×Dic47—22no—
424C4×Dic47—22no—
425C4×Dic47—22no—
426C4×Dic47C2×D414yes—
427C4×Dic47C2×D414yes—
428C4×Dic47C2×D414yes—
429C23×C47—22no—
430C23×C47—22no—
431C23×C47—21no—
432C23×C47—22no—
433C23×C47—22no—
434C23×C47—21no—
435C23×C47—22no—
436C23×C47—22no—
437C23×C47—22no—
438C23×C47—22no—
439C23×C47C22×D412yes—
440C23×C47C2×#4114yes—
441C23×C47C2511yescharacteristic
442C22×D47—22no—
443C22×D47—22no—
444C22×D47—216no—
445C22×D47—21no—
446C22×D47—22no—
447C22×D47—22no—
448C22×D47—22no—
449C22×D47—21no—
450C22×D47—22no—
451C22×D47—22no—
452C22×D47—22no—
453C22×D47—22no—
454C22×D47—22no—
455C22×D47—48no—
456C22×D47—48no—
457C22×D47—48no—
458C22×D47—48no—
459C22×D47—48no—
460C22×D47—48no—
461C22×D47C22×D412yes—
462C22×D47C22×D412yes—
463C22×D47C22×D412yes—
464C22×D47C2×#4114yes—
465C22×D47C2×#4112yes—
466D4×C47—28no—
467D4×C47—48no—
468C2×C4×C47—21no—
469C2×C4×C47—21no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—28no—
473C2×C4×C47—21no—
474C2×C4×C47—21no—
475C2×C4×C47—22no—
476C2×C4×C47—22no—
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
481C2×C4×C47—22no—
482C2×C4×C47—22no—
483C2×C4×C47—22no—
484C2×C4×C47—22no—
485C2×C4×C47—22no—
486C2×C4×C47—48no—
487C2×C4×C47C22×D412yes—
488C2×C4×C47C22×D412yes—
489C2×C4×C47C22×D412yes—
490C2×C4×C47C22×D412yes—
491C2×C4×C47C22×D412yes—
492C2×C4×C47C2×#4112yes—
493C22⋊D47—28no—
494C22⋊D47—28no—
495C22⋊D47—216no—
496C22⋊D47—48no—
497C22⋊D47—48no—
498C2×Dic47—21no—
499C2×Dic47—21no—
500C2×Dic47—22no—
501C2×Dic47—21no—
502C2×Dic47—21no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—22no—
506C2×Dic47—22no—
507C2×Dic47—22no—
508C2×Dic47—22no—
509C2×Dic47—22no—
510C2×Dic47—22no—
511C2×Dic47—22no—
512C2×Dic47—22no—
513C2×Dic47—22no—
514C2×Dic47—44no—
515C2×Dic47—48no—
516C2×Dic47—44no—
517C2×Dic47C22×D412yes—
518C2×Dic47C22×D412yes—
519C2×Dic47C22×D412yes—
520C2×Dic47C22×D412yes—
521C2×Dic47C22×D412yes—
522C2×Dic47C2×#4112yes—
523C2×Dic47C2×#4114yes—
524D188—28no—
525D188—28no—
526D188—48no—
527C4×D47—28no—
528C4×D47—28no—
529C4×D47—44no—
530C4×D47—44no—
531C4×D47—48no—
532C4×D47—48no—
533C4×D47—48no—
534C4×D47—44no—
535C4×D47#121116yescomplemented
536Dic94—28no—
537#34935—471nomaximal, Sylow
538C22×C47—22no—
539C22×C47—24no—
540C22×C47—24no—
541C22×C47—24no—
542C22×C47—24no—
543C22×C47—42no—
544C22×C47—41no—
545C22×C47—41no—
546C22×C47—42no—
547C22×C47—42no—
548C22×C47—42no—
549C22×C47—42no—
550C22×C47C23×D411yescharacteristic
551C22×C47C23×D411yescharacteristic
552C22×C47C22×#4111yescharacteristic
553C22×C47C22×#4112yes—
554C22×C47#58512yes—
555C2×D47—22no—
556C2×D47—22no—
557C2×D47—24no—
558C2×D47—24no—
559C2×D47—22no—
560C2×D47—24no—
561C2×D47—24no—
562C2×D47—24no—
563C2×D47—24no—
564C2×D47—432no—
565C2×D47—42no—
566C2×D47—41no—
567C2×D47—41no—
568C2×D47—42no—
569C2×D47—42no—
570C2×D47—42no—
571C2×D47—42no—
572C2×D47C2×#12114yes—
573C4×C47—22no—
574C4×C47—22no—
575C4×C47—22no—
576C4×C47—42no—
577C4×C47—41no—
578C4×C47—41no—
579C4×C47—42no—
580C4×C47—42no—
581C4×C47C2×#12114yes—
582Dic47—22no—
583Dic47—22no—
584Dic47—42no—
585Dic47—41no—
586Dic47—41no—
587Dic47—42no—
588Dic47—42no—
589Dic47C2×#12114yes—
590Dic47#52514yescomplemented
591C2×#525—472no—
592C2×C4×#41—471no—
593C22×C4×D4—471no—
594#2538—472no—
595#2537—472no—
596#2536—471no—
597#2536—471no—
598#2535—471no—
599#2535—471no—
600#2534—472no—
601#2534—472no—
602#2486—471no—
603#2486—471no—
604#2408—471no—
605#2408—471no—
606#2392—471no—
607#2392—471no—
608#2392—471no—
609#2392D4711yescharacteristic, complemented
610C4×#121—472no—
611C4×#121—472no—
612#2285—471no—
613#2280—472no—
614C2×C47—44no—
615C2×C47—42no—
616C2×C47C22×#12111yescharacteristic
617C2×C47C2×#52511yescharacteristic
618C2×C47#344911yescharacteristic
619C2×C47D4×#4112yes—
620C2×C47#347512yes—
621D47—24no—
622D47—42no—
623D47—44no—
624C22×#41—471no—
625C23×D4—471no—
626C24×C4—472no—
627#525—9416no—
628C2×#123—472no—
629C2×#123—472no—
630C2×C22⋊Q8—472no—
631C2×C22⋊Q8—472no—
632C2×#121—472no—
633C2×#121—472no—
634C2×#121—472no—
635C2×#121—472no—
636C2×#120—472no—
637C2×#120—472no—
638C4×#41—948no—
639C2×C4×Q8—471no—
640C2×C4×Q8—471no—
641C2×C4×D4—471no—
642C2×C4×D4—472no—
643C2×C4×D4—472no—
644C2×C4×D4—472no—
645C2×C4×D4—471no—
646C2×C4×D4—471no—
647C2×C4×D4—471no—
648C2×C4×D4—472no—
649C2×C4×D4—471no—
650C2×C4×D4—471no—
651C2×C4×D4—471no—
652C2×C4×D4—471no—
653C2×C4×D4—471no—
654C2×C4×D4—472no—
655C2×C4×D4—948no—
656C2×C4×D4C2×D4711yescharacteristic
657C2×C4×D4C2×D4712yescomplemented
658C2×#117—471no—
659C2×#117—471no—
660C2×#117—472no—
661C2×#117C2×D4711yescharacteristic, complemented
662C22×C4⋊C4—471no—
663C22×C22⋊C4—472no—
664C22×C42—471no—
665C22×C42—471no—
666C22×C42—471no—
667#398—471no—
668#398—471no—
669#398—471no—
670#398C2×D4711yescharacteristic, complemented
671#397—471no—
672#397—471no—
673#397—471no—
674#397C2×D4711yescharacteristic, complemented
675#396—472no—
676#396—472no—
677#396—472no—
678#396C2×D4712yescomplemented
679#394—471no—
680#394—471no—
681#394—472no—
682#394—472no—
683#394—472no—
684#394—471no—
685#394C2×D4711yescharacteristic
686#394C2×D4712yescomplemented
687#392—471no—
688#392—471no—
689#392—471no—
690#392C2×D4711yescharacteristic
691#390—472no—
692#390—472no—
693#389—472no—
694#389—472no—
695#388—472no—
696#388—472no—
697#388—472no—
698#388—472no—
699#386—472no—
700#386—472no—
701#386—472no—
702#386—472no—
703#384—472no—
704#382—471no—
705#382—471no—
706#381—472no—
707#381—472no—
708#380—472no—
709#380—472no—
710#380—472no—
711#380—472no—
712#380—471no—
713#380—471no—
714#380—472no—
715#380—472no—
716#380—472no—
717#379—472no—
718#379—472no—
719C4×C4⋊C4—471no—
720C4×C4⋊C4—472no—
721C4×C4⋊C4C2×D4711yescharacteristic, complemented
722C4×C22⋊C4—472no—
723C4×C22⋊C4—472no—
724C4×C22⋊C4—472no—
725C4×C22⋊C4C2×D4712yescomplemented
726C47#3493511yescharacteristic, complemented, Sylow
727C25—472no—
728C2×#41—478no—
729C2×#41—944no—
730C2×#41—944no—
731C22×Q8—471no—
732C22×D4—471no—
733C22×D4—471no—
734C22×D4—472no—
735C22×D4—472no—
736C22×D4—472no—
737C22×D4—471no—
738C22×D4—471no—
739C22×D4—472no—
740C22×D4—944no—
741C22×D4—948no—
742C22×D4C22×D4711yescharacteristic
743C22×D4C22×D4712yes—
744C23×C4—471no—
745C23×C4—471no—
746C23×C4—471no—
747C23×C4—471no—
748C23×C4—471no—
749C23×C4—472no—
750C23×C4—471no—
751C23×C4—472no—
752C23×C4—471no—
753C23×C4—472no—
754C23×C4—472no—
755C23×C4—471no—
756C23×C4—948no—
757C23×C4—948no—
758C23×C4—948no—
759C23×C4C22×D4712yes—
760C23×C4C22×D4711yescharacteristic
761#123—948no—
762#123—948no—
763C22⋊Q8—948no—
764C22⋊Q8—948no—
765#121—948no—
766#121—948no—
767#121—948no—
768#121—948no—
769#120—948no—
770#120—948no—
771C4×Q8—944no—
772C4×Q8—944no—
773C4×D4—28no—
774C4×D4—24no—
775C4×D4—948no—
776C4×D4—948no—
777C4×D4—944no—
778C4×D4—944no—
779C4×D4—944no—
780C4×D4—948no—
781C4×D4—944no—
782C4×D4—944no—
783C4×D4—944no—
784C4×D4—944no—
785C4×D4—944no—
786C4×D4—948no—
787C4×D4—948no—
788C4×D4—944no—
789#117—24no—
790#117—944no—
791#117—948no—
792#117—944no—
793C2×C4⋊C4—472no—
794C2×C4⋊C4—471no—
795C2×C4⋊C4—471no—
796C2×C4⋊C4—471no—
797C2×C4⋊C4—471no—
798C2×C4⋊C4—471no—
799C2×C4⋊C4—472no—
800C2×C4⋊C4—472no—
801C2×C4⋊C4—472no—
802C2×C4⋊C4—472no—
803C2×C4⋊C4—472no—
804C2×C4⋊C4—472no—
805C2×C4⋊C4—472no—
806C2×C4⋊C4—472no—
807C2×C4⋊C4—944no—
808C2×C4⋊C4C22×D4711yescharacteristic
809C2×C4⋊C4C22×D4711yescharacteristic
810C2×C4⋊C4C22×D4711yescharacteristic
811C2×C4⋊C4C22×D4712yes—
812C2×C4⋊C4C22×D4712yes—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4—472no—
817C2×C22⋊C4—472no—
818C2×C22⋊C4—472no—
819C2×C22⋊C4—471no—
820C2×C22⋊C4—471no—
821C2×C22⋊C4—471no—
822C2×C22⋊C4—471no—
823C2×C22⋊C4—472no—
824C2×C22⋊C4—472no—
825C2×C22⋊C4—472no—
826C2×C22⋊C4—472no—
827C2×C22⋊C4—472no—
828C2×C22⋊C4—472no—
829C2×C22⋊C4—472no—
830C2×C22⋊C4—472no—
831C2×C22⋊C4—472no—
832C2×C22⋊C4—472no—
833C2×C22⋊C4—472no—
834C2×C22⋊C4—948no—
835C2×C22⋊C4C22×D4712yes—
836C2×C22⋊C4C22×D4711yescharacteristic
837C2×C22⋊C4C22×D4711yescharacteristic
838C2×C22⋊C4C22×D4712yes—
839C2×C22⋊C4C22×D4712yes—
840C2×C22⋊C4C22×D4712yes—
841C2×C22⋊C4C22×D4712yes—
842C2×C42—471no—
843C2×C42—471no—
844C2×C42—471no—
845C2×C42—478no—
846C2×C42—471no—
847C2×C42—471no—
848C2×C42—471no—
849C2×C42—471no—
850C2×C42—471no—
851C2×C42—472no—
852C2×C42—944no—
853C2×C42—944no—
854C2×C42C22×D4711yescharacteristic
855C2×C42C22×D4712yes—
856C2×C42C22×D4711yescharacteristic
857#95—472no—
858#95—472no—
859#95—472no—
860#95—472no—
861#95—472no—
862#95—472no—
863#95—472no—
864#95—472no—
865#95—471no—
866#95—471no—
867#95C22×D4712yes—
868#95C22×D4712yes—
869#95C22×D4711yescharacteristic
870#95C22×D4711yescharacteristic
871C24—471no—
872C24—472no—
873C24—471no—
874C24—944no—
875C24—944no—
876C24—944no—
877C24—944no—
878C24—944no—
879C24—1882no—
880C24—1882no—
881C24C23×D4711yescharacteristic
882C24C23×D4712yes—
883#41—9432no—
884C2×Q8—474no—
885C2×Q8—942no—
886C2×Q8—942no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—24no—
890C2×D4—22no—
891C2×D4—42no—
892C2×D4—474no—
893C2×D4—474no—
894C2×D4—478no—
895C2×D4—474no—
896C2×D4—942no—
897C2×D4—944no—
898C2×D4—942no—
899C2×D4—944no—
900C2×D4—944no—
901C2×D4—944no—
902C2×D4—942no—
903C2×D4—944no—
904C2×D4—942no—
905C2×D4—9432no—
906C2×D4—942no—
907C2×D4—942no—
908C2×D4—944no—
909C2×D4—944no—
910C2×D4—944no—
911C2×D4—944no—
912C2×D4—942no—
913C2×D4—1882no—
914C2×D4—1882no—
915C2×D4—1882no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—471no—
922C22×C4—471no—
923C22×C4—474no—
924C22×C4—474no—
925C22×C4—474no—
926C22×C4—471no—
927C22×C4—471no—
928C22×C4—474no—
929C22×C4—474no—
930C22×C4—474no—
931C22×C4—471no—
932C22×C4—471no—
933C22×C4—472no—
934C22×C4—472no—
935C22×C4—472no—
936C22×C4—944no—
937C22×C4—942no—
938C22×C4—942no—
939C22×C4—944no—
940C22×C4—944no—
941C22×C4—944no—
942C22×C4—944no—
943C22×C4—944no—
944C22×C4—944no—
945C22×C4—944no—
946C22×C4—942no—
947C22×C4—942no—
948C22×C4—944no—
949C22×C4—944no—
950C22×C4—944no—
951C22×C4—944no—
952C22×C4—942no—
953C22×C4—942no—
954C22×C4—944no—
955C22×C4—944no—
956C22×C4—944no—
957C22×C4—1882no—
958C22×C4—1882no—
959C22×C4—18832no—
960C22×C4—1882no—
961C22×C4D4×D4714yescomplemented
962C22×C4C23×D4711yescharacteristic
963C22×C4C23×D4711yescharacteristic
964C22×C4C23×D4712yes—
965C22×C4C23×D4712yes—
966C22×C4C23×D4712yes—
967C22×C4C23×D4711yescharacteristic
968C22×C4C23×D4711yescharacteristic
969C22×C4C23×D4711yescharacteristic
970C22×C4C23×D4711yescharacteristic
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—24no—
975C4⋊C4—42no—
976C4⋊C4—944no—
977C4⋊C4—942no—
978C4⋊C4—942no—
979C4⋊C4—944no—
980C4⋊C4—944no—
981C4⋊C4—944no—
982C4⋊C4—944no—
983C4⋊C4—944no—
984C4⋊C4—944no—
985C4⋊C4—942no—
986C4⋊C4—942no—
987C4⋊C4—944no—
988C4⋊C4—942no—
989C4⋊C4—1882no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—24no—
996C22⋊C4—42no—
997C22⋊C4—944no—
998C22⋊C4—944no—
999C22⋊C4—942no—
1000C22⋊C4—942no—
1001C22⋊C4—944no—
1002C22⋊C4—944no—
1003C22⋊C4—944no—
1004C22⋊C4—944no—
1005C22⋊C4—944no—
1006C22⋊C4—944no—
1007C22⋊C4—944no—
1008C22⋊C4—944no—
1009C22⋊C4—944no—
1010C22⋊C4—944no—
1011C22⋊C4—944no—
1012C22⋊C4—942no—
1013C22⋊C4—942no—
1014C22⋊C4—944no—
1015C22⋊C4—1882no—
1016C22⋊C4—1882no—
1017C22⋊C4—1882no—
1018C42—22no—
1019C42—24no—
1020C42—474no—
1021C42—474no—
1022C42—474no—
1023C42—942no—
1024C42—942no—
1025C42—942no—
1026C42—942no—
1027C42—942no—
1028C42—944no—
1029C42D4×D4714yes—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—21no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—472no—
1041C23—472no—
1042C23—472no—
1043C23—472no—
1044C23—474no—
1045C23—9416no—
1046C23—942no—
1047C23—942no—
1048C23—941no—
1049C23—942no—
1050C23—942no—
1051C23—942no—
1052C23—941no—
1053C23—942no—
1054C23—942no—
1055C23—942no—
1056C23—942no—
1057C23—942no—
1058C23—1888no—
1059C23—1888no—
1060C23—1888no—
1061C23—1888no—
1062C23—1888no—
1063C23—1888no—
1064C23C2×D4×D4712yes—
1065C23#41×D4714yes—
1066C23C24×D4711yescharacteristic
1067Q8—948no—
1068D4—28no—
1069D4—48no—
1070D4—948no—
1071D4—948no—
1072D4—9416no—
1073D4—948no—
1074D4—948no—
1075D4—1888no—
1076D4—1888no—
1077D4—1888no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—28no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—48no—
1097C2×C4—472no—
1098C2×C4—472no—
1099C2×C4—472no—
1100C2×C4—474no—
1101C2×C4—472no—
1102C2×C4—4716no—
1103C2×C4—472no—
1104C2×C4—472no—
1105C2×C4—948no—
1106C2×C4—941no—
1107C2×C4—941no—
1108C2×C4—942no—
1109C2×C4—948no—
1110C2×C4—941no—
1111C2×C4—941no—
1112C2×C4—942no—
1113C2×C4—942no—
1114C2×C4—942no—
1115C2×C4—942no—
1116C2×C4—942no—
1117C2×C4—942no—
1118C2×C4—942no—
1119C2×C4—942no—
1120C2×C4—942no—
1121C2×C4—942no—
1122C2×C4—942no—
1123C2×C4—1884no—
1124C2×C4—1884no—
1125C2×C4—1888no—
1126C2×C4—1884no—
1127C2×C4—1888no—
1128C2×C4—1884no—
1129C2×C4—1888no—
1130C2×C4—1884no—
1131C2×C4—1888no—
1132C2×C4C2×D4×D4712yes—
1133C2×C4C2×D4×D4712yes—
1134C2×C4C2×D4×D4712yes—
1135C2×C4C2×D4×D4712yes—
1136C2×C4C2×D4×D4712yes—
1137C2×C4#41×D4712yes—
1138C22—22no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—42no—
1144C22—42no—
1145C22—41no—
1146C22—42no—
1147C22—42no—
1148C22—41no—
1149C22—42no—
1150C22—474no—
1151C22—944no—
1152C22—942no—
1153C22—944no—
1154C22—942no—
1155C22—942no—
1156C22—944no—
1157C22—944no—
1158C22—944no—
1159C22—944no—
1160C22—18832no—
1161C22—1882no—
1162C22—1882no—
1163C22—1881no—
1164C22—1882no—
1165C22—1882no—
1166C22—1881no—
1167C22—1882no—
1168C22C22×D4×D4711yescharacteristic
1169C22C22×D4×D4711yescharacteristic
1170C22C2×#41×D4711yescharacteristic
1171C22C2×#41×D4712yes—
1172C22#1568995912yes—
1173C4—22no—
1174C4—22no—
1175C4—22no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—41no—
1180C4—41no—
1181C4—474no—
1182C4—474no—
1183C4—942no—
1184C4—942no—
1185C4—1882no—
1186C4—1882no—
1187C4—1882no—
1188C4—1881no—
1189C4—1881no—
1190C4#121×D4714yes—
1191C2—44no—
1192C2—42no—
1193C2—944no—
1194C2—1884no—
1195C2—1882no—
1196C2C2×#121×D4711yescharacteristic
1197C2#525×D4711yescharacteristic
1198C2#2025671511yescharacteristic
1199C2#2025687112yes—
1200C2#2025694012yes—
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC47×#2392C2
hypercenter#2392D47
hypocenterC47#34935
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. C2×#15689632C2semidirect
2. C2×#15689591C2semidirect
3. C2×C4×D4×D47C2semidirect
4. #20248305C2semidirect
5. #20248300C2semidirect
6. #20248294C2semidirect
7. #20248292C2semidirect
8. #20248286C2semidirect
9. #20248284C2semidirect
10. #20248279C2semidirect
11. #20248273C2semidirect
12. #20247691C2semidirect
13. #20247689C2semidirect
14. #20246739C2semidirect
15. #20246737C2semidirect
16. #20246628C2semidirect
17. #20246626C2semidirect
18. #20246624C2semidirect
19. C4×#13093997C2semidirect
20. C4×#13093996C2semidirect
21. #20245792C2semidirect
22. #20245769C2semidirect
23. C47×#2392C2semidirect
30. C2×#13094002C22semidirect
31. C2×#13094001C22semidirect
33. C2×#13093997C22semidirect
35. C2×#13093996C22semidirect
39. C2×#13093989C22semidirect
40. C2×#13093989C22semidirect
42. C2×C4×D188C22semidirect
48. C2×C4×C22⋊D47C22semidirect
49. C2×C4×C22⋊D47C22semidirect
53. C2×(C22⋊D47)⋊C4C22semidirect
54. C2×(C22⋊D47)⋊C4C22semidirect
58. C2×#13093981C22semidirect
61. C22×C4×Dic47C22semidirect
63. C2×C42×D47C22semidirect
64. #15689055C22semidirect
65. #15689054C22semidirect
66. #15689053C22semidirect
67. #15689050C22semidirect
68. #15689049C22semidirect
69. #15689048C22semidirect
70. #15689046C22semidirect
71. #15689045C22semidirect
72. #15689045C22semidirect
75. #15689040C22semidirect
76. #15689039C22semidirect
77. #15689039C22semidirect
84. #15689020C22semidirect
85. #15689018C22semidirect
86. #15689017C22semidirect
87. #15689016C22semidirect
88. #15689013C22semidirect
89. #15689012C22semidirect
90. #15689003C22semidirect
91. #15689001C22semidirect
92. #15689000C22semidirect
93. #15688999C22semidirect
94. #15688992C22semidirect
95. #15688987C22semidirect
96. #15688987C22semidirect
101. #15688982C22semidirect
102. #15688982C22semidirect
103. #15688982C22semidirect
104. #15688981C22semidirect
105. #15688981C22semidirect
106. #15688981C22semidirect
110. C4×Dic47⋊C4C22semidirect
111. C4×C4⋊Dic47C22semidirect
112. C4×(C2×D47)⋊C4C22semidirect
113. C4×(C2×D47)⋊C4C22semidirect
114. C4×C22⋊Dic47C22semidirect
116. C2×C4×D4×C47C22semidirect
117. C2×#117×C47C22semidirect
118. C47×#398C22semidirect
119. C47×#397C22semidirect
120. C47×#396C22semidirect
122. C47×#394C22semidirect
124. C4×C4⋊C4×C47C22semidirect
125. C4×C22⋊C4×C47C22semidirect
129. C2×#10625350D4semidirect
233. C42×D47D4semidirect
292. C22×C4×C47C2×D4semidirect
315. C2×C22⋊D47C2×D4semidirect
316. C2×C22⋊D47#41semidirect
365. C2×C4×D47C2×D4semidirect
369. C2×Dic94C2×D4semidirect
535. C4×D47#121semidirect
590. Dic47#525semidirect
609. #2392D47semidirect
657. C2×C4×D4C2×D47semidirect
661. C2×#117C2×D47semidirect
670. #398C2×D47semidirect
674. #397C2×D47semidirect
678. #396C2×D47semidirect
686. #394C2×D47semidirect
721. C4×C4⋊C4C2×D47semidirect
725. C4×C22⋊C4C2×D47semidirect
726. C47#34935semidirect
961. C22×C4D4×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×C4×D4×D472
#202483052
#202483002
#202482942
#202482922
#202482862
#202482842
#202482792
#202482732
#202476912
#202476892
#202467392
#202467372
#202466282
#202466262
#202466242
C4×#130939972
C4×#130939962
#202457922
#202457692
C47×#23922
#3493547