Finite Group Databasebeta

← C2×#20246407 #26375810

Subgroups — C2×#20246407 #26375810

Order 12032.

4782 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093997C211yesmaximal, characteristic
2C22×#13093986C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
6#20246407C2116yesmaximal, direct product factor
7C2×#15689023C211yesmaximal, characteristic, complemented
8C2×#15689018C211yesmaximal, characteristic, complemented
9C2×#15689016C211yesmaximal, characteristic, complemented
10C2×#15689013C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15688999C211yesmaximal, characteristic, complemented
13C2×#15688997C211yesmaximal, characteristic, complemented
14C2×#15688974C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic
24C2×#13093997C4116yescomplemented
25C2×#13093997C2218yes—
26C2×#13093986—28no—
27C2×#13093986C2218yescomplemented
28C2×C4×C22⋊D47—28no—
29C2×C4×C22⋊D47—28no—
30C2×C4×C22⋊D47C2218yescomplemented
31C2×C4×C22⋊D47C2218yescomplemented
32C22×C4⋊Dic47C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C2×C4⋊C4×D47—28no—
38C2×C4⋊C4×D47C2218yescomplemented
39C22×C22⋊Dic47C2211yescharacteristic
40C22×C22⋊Dic47C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C22×C4×Dic47C2211yescharacteristic
48C22×C4×Dic47C2211yescharacteristic
49C22×C4×Dic47C2211yescharacteristic
50C22×C4×Dic47C2211yescharacteristic
51#15689023C2218yescomplemented
52#15689018C2218yescomplemented
53#15689016C2218yescomplemented
54#15689013C2218yescomplemented
55#15689001C2218yescomplemented
56#15688999C2218yescomplemented
57#15688997C2218yescomplemented
58#15688974C2218yescomplemented
59#15688970C2218yescomplemented
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C2×C47⋊#95C2211yescharacteristic
64C24×C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C22×C4⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C47×#385C2218yescomplemented
70C2×#95×C47C2211yescharacteristic
71C2×#95×C47C2211yescharacteristic
72C24×D47C2311yescharacteristic
73C24×D47C2311yescharacteristic
74C22×D188—24no—
75C22×D188—24no—
76C22×D188C2×C418yescomplemented
77C22×D188C2314yes—
78C22×C22⋊D47—24no—
79C22×C22⋊D47—24no—
80C22×C22⋊D47—24no—
81C22×C22⋊D47—24no—
82C22×C22⋊D47C2×C418yescomplemented
83C22×C22⋊D47C2×C418yescomplemented
84C22×C22⋊D47C2314yes—
85C22×C22⋊D47C2314yes—
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C23×Dic47C2311yescharacteristic
92C22×C4×D47—24no—
93C22×C4×D47—24no—
94C22×C4×D47—24no—
95C22×C4×D47—24no—
96C22×C4×D47—24no—
97C22×C4×D47—24no—
98C22×C4×D47—24no—
99C22×C4×D47—24no—
100C22×C4×D47—42no—
101C22×C4×D47—42no—
102C22×C4×D47—42no—
103C22×C4×D47C2×C418yescomplemented
104C22×C4×D47C2314yes—
105C22×C4×D47C2314yes—
106C22×C4×D47C2314yes—
107C22×C4×D47C2314yes—
108#13093997C2×C4164yescomplemented
109#13093986—232no—
110C4×C22⋊D47—232no—
111C4×C22⋊D47—232no—
112C2×C4⋊Dic47—24no—
113C2×C4⋊Dic47C2314yes—
114C2×Dic47⋊C4—24no—
115C2×Dic47⋊C4—24no—
116C2×Dic47⋊C4C2×C418yescomplemented
117C2×Dic47⋊C4D418yescomplemented
118C2×Dic47⋊C4C2314yes—
119C2×Dic47⋊C4C2314yes—
120C2×Dic47⋊C4C2314yes—
121C2×Dic47⋊C4C2314yes—
122C4⋊C4×D47—232no—
123C2×C22⋊Dic47—24no—
124C2×C22⋊Dic47—24no—
125C2×C22⋊Dic47C2314yes—
126C2×C22⋊Dic47C2314yes—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—24no—
129C2×(C2×D47)⋊C4—24no—
130C2×(C2×D47)⋊C4—42no—
131C2×(C2×D47)⋊C4C2×C418yescomplemented
132C2×(C2×D47)⋊C4D418yescomplemented
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×C4×Dic47—24no—
140C2×C4×Dic47—24no—
141C2×C4×Dic47—24no—
142C2×C4×Dic47—24no—
143C2×C4×Dic47C2314yes—
144C2×C4×Dic47C2314yes—
145C2×C4×Dic47C2314yes—
146C2×C4×Dic47C2314yes—
147C47⋊#95C2314yes—
148C47⋊#95C2314yes—
149C47⋊#95C2314yes—
150C47⋊#95C2314yes—
151C25×C47C2311yescharacteristic
152C23×C4×C47—24no—
153C23×C4×C47—24no—
154C23×C4×C47—42no—
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2314yes—
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C23×C4×C47C2311yescharacteristic
162C2×C4⋊C4×C47—24no—
163C2×C4⋊C4×C47—24no—
164C2×C4⋊C4×C47C2314yes—
165C2×C4⋊C4×C47C2314yes—
166C2×C22⋊C4×C47—42no—
167C2×C22⋊C4×C47C2×C418yescomplemented
168C2×C22⋊C4×C47C2314yes—
169C2×C22⋊C4×C47C2314yes—
170#95×C47C2314yes—
171#95×C47C2314yes—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47C22×C414yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47C22×C414yes—
192C23×D47C22×C414yes—
193C23×D47C2×D414yes—
194C23×D47#4114yes—
195C23×D47C2412yes—
196C23×D47C2412yes—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—28no—
212C22×C4×C47—28no—
213C22×C4×C47—44no—
214C22×C4×C47—416no—
215C22×C4×C47C22×C414yes—
216C22×C4×C47C22×C414yes—
217C22×C4×C47C2×D414yes—
218C22×C4×C47C2×D414yes—
219C22×C4×C47C2412yes—
220C22×C4×C47C2412yes—
221C22×C4×C47C2412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2412yes—
224C22×C4×C47C2412yes—
225C2×C22⋊D47—232no—
226C2×C22⋊D47—28no—
227C2×C22⋊D47—28no—
228C2×C22⋊D47—232no—
229C2×C22⋊D47—28no—
230C2×C22⋊D47—28no—
231C2×C22⋊D47C22×C4116yescomplemented
232C2×C22⋊D47C22×C4116yescomplemented
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47C22×C414yes—
246C22×Dic47C22×C414yes—
247C22×Dic47C2×D414yes—
248C22×Dic47C2×D414yes—
249C22×Dic47C2×D414yes—
250C22×Dic47#4114yes—
251C22×Dic47C2412yes—
252C22×Dic47C2412yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C2×D188—232no—
258C2×D188—28no—
259C2×D188—28no—
260C2×D188C22×C4116yescomplemented
261C2×C4×D47—232no—
262C2×C4×D47—28no—
263C2×C4×D47—28no—
264C2×C4×D47—28no—
265C2×C4×D47—28no—
266C2×C4×D47—28no—
267C2×C4×D47—28no—
268C2×C4×D47—28no—
269C2×C4×D47—28no—
270C2×C4×D47—44no—
271C2×C4×D47—44no—
272C2×C4×D47—44no—
273C2×C4×D47—416no—
274C2×C4×D47—416no—
275C2×C4×D47—416no—
276C2×C4×D47C22×C4116yescomplemented
277C4⋊C4×C47—28no—
278C4⋊C4×C47—28no—
279C22⋊C4×C47—44no—
280C22⋊C4×C47C22×C4116yescomplemented
281C22⋊Dic47—28no—
282C22⋊Dic47—28no—
283(C2×D47)⋊C4—28no—
284(C2×D47)⋊C4—28no—
285(C2×D47)⋊C4—28no—
286(C2×D47)⋊C4—44no—
287(C2×D47)⋊C4C22×C4116yescomplemented
288(C2×D47)⋊C4C2×D4116yescomplemented
289C4⋊Dic47—28no—
290Dic47⋊C4—28no—
291Dic47⋊C4—28no—
292Dic47⋊C4C22×C4116yescomplemented
293Dic47⋊C4C2×D4116yescomplemented
294C4×Dic47—28no—
295C4×Dic47—28no—
296C4×Dic47—28no—
297C4×Dic47—28no—
298C23×C47—28no—
299C23×C47—28no—
300C23×C47—28no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—44no—
308C23×C47—44no—
309C23×C47—44no—
310C23×C47—44no—
311C23×C47C23×C414yes—
312C23×C47C23×C412yes—
313C23×C47C22×D412yes—
314C23×C47C22×D412yes—
315C23×C47C2×#4112yes—
316C23×C47C2×#4112yes—
317C23×C47H(5,𝔽2)12yes—
318C23×C472−1+412yes—
319C23×C47C2511yescharacteristic
320C22×D47—28no—
321C22×D47—28no—
322C22×D47—28no—
323C22×D47—28no—
324C22×D47—28no—
325C22×D47—28no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—28no—
331C22×D47—28no—
332C22×D47—28no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—44no—
340C22×D47—44no—
341C22×D47—44no—
342C22×D47—44no—
343C22×D47C4×D4116yescomplemented
344C22×D47C23×C414yes—
345C22×D47C23×C414yes—
346C22×D47C22×D414yes—
347C22×D47C2×#4114yes—
348C2×C4×C47—28no—
349C2×C4×C47—28no—
350C2×C4×C47—28no—
351C2×C4×C47—28no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—416no—
367C2×C4×C47—44no—
368C2×C4×C47—44no—
369C2×C4×C47C23×C414yes—
370C2×C4×C47C23×C414yes—
371C2×C4×C47C22×D414yes—
372C2×C4×C47C22×D414yes—
373C22⋊D47—232no—
374C22⋊D47—232no—
375C2×Dic47—28no—
376C2×Dic47—28no—
377C2×Dic47—28no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—44no—
391C2×Dic47—44no—
392C2×Dic47C4×D4116yescomplemented
393C2×Dic47C23×C414yes—
394C2×Dic47C23×C414yes—
395C2×Dic47C22×D414yes—
396C2×Dic47C22×D414yes—
397C2×Dic47C22×D414yes—
398C2×Dic47C2×#4114yes—
399D188—232no—
400C4×D47—232no—
401C4×D47—416no—
402C4×D47—416no—
403C4×D47—416no—
404C2×#2361—471nomaximal, Sylow
405C22×C47—24no—
406C22×C47—24no—
407C22×C47—24no—
408C22×C47—416no—
409C22×C47—42no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—42no—
413C22×C47C2×C4×D414yes—
414C22×C47C2×C4×D414yes—
415C22×C47#52014yes—
416C22×C47D4214yes—
417C22×C47#54714yes—
418C22×C47#54814yes—
419C22×C47#55314yes—
420C22×C47C24×C411yescharacteristic
421C22×C47C23×D411yescharacteristic
422C22×C47C23×D411yescharacteristic
423C22×C47C22×#4111yescharacteristic
424C22×C47C22×#4111yescharacteristic
425C22×C47C2×H(5,𝔽2)11yescharacteristic
426C22×C47C2×2−1+411yescharacteristic
427C2×D47—232no—
428C2×D47—24no—
429C2×D47—24no—
430C2×D47—24no—
431C2×D47—24no—
432C2×D47—24no—
433C2×D47—24no—
434C2×D47—24no—
435C2×D47—24no—
436C2×D47—24no—
437C2×D47—416no—
438C2×D47—42no—
439C2×D47—42no—
440C2×D47—42no—
441C2×D47—42no—
442C2×D47C2×C4×D418yescomplemented
443C4×C47—24no—
444C4×C47—24no—
445C4×C47—24no—
446C4×C47—24no—
447C4×C47—42no—
448C4×C47—42no—
449Dic47—24no—
450Dic47—24no—
451Dic47—24no—
452Dic47—42no—
453Dic47—42no—
454Dic47C2×C4×D418yescomplemented
455C22×#121—471no—
456C22×C4×D4—471no—
457C22×C4×D4—471no—
458C22×C4×D4—471no—
459C23×C4⋊C4—471no—
460#2361—4716no—
461C2×#390—471no—
462C2×#389—471no—
463C2×#388—471no—
464C2×#388—471no—
465C2×#386—471no—
466C2×#386—471no—
467C2×#385—471no—
468C2×#385D4711yescharacteristic, complemented
469C2×C4×C4⋊C4—471no—
470C2×C4×C22⋊C4—471no—
471C2×C47—44no—
472C2×C47#236118yescomplemented
473C2×C47C22×C4×D411yescharacteristic
474C2×C47C22×C4×D411yescharacteristic
475C2×C47C2×#52011yescharacteristic
476C2×C47C2×D4211yescharacteristic
477C2×C47C2×#54711yescharacteristic
478C2×C47C2×#54811yescharacteristic
479C2×C47C2×#55311yescharacteristic
480D47—28no—
481D47—44no—
482C23×D4—471no—
483C23×D4—471no—
484C23×D4—471no—
485C24×C4—471no—
486C24×C4—471no—
487C24×C4—471no—
488C24×C4—471no—
489C24×C4C2×D4711yescharacteristic
490C2×#121—4716no—
491C2×#121—478no—
492C2×C4×D4—478no—
493C2×C4×D4—478no—
494C2×C4×D4—478no—
495C2×C4×D4—948no—
496C2×C4×D4—948no—
497C2×C4×D4—948no—
498C22×C4⋊C4—471no—
499C22×C4⋊C4—471no—
500C22×C4⋊C4—471no—
501C22×C4⋊C4—471no—
502C22×C4⋊C4—471no—
503C22×C4⋊C4—478no—
504C22×C4⋊C4—948no—
505C22×C4⋊C4C2×D4711yescharacteristic
506C22×C4⋊C4C2×D4711yescharacteristic
507C22×C22⋊C4—471no—
508C22×C22⋊C4—471no—
509C22×C22⋊C4—471no—
510C22×C22⋊C4—471no—
511C22×C22⋊C4—471no—
512C22×C22⋊C4—471no—
513C22×C22⋊C4—471no—
514C22×C22⋊C4—471no—
515C22×C22⋊C4C2×D4711yescharacteristic
516C22×C22⋊C4C2×D4711yescharacteristic
517C22×C42—471no—
518C22×C42—471no—
519C22×C42—471no—
520C22×C42—471no—
521#390—478no—
522#389—478no—
523#388—478no—
524#388—478no—
525#386—478no—
526#386—478no—
527#385—478no—
528#385C2×D4718yescomplemented
529C4×C4⋊C4—478no—
530C4×C22⋊C4—478no—
531C2×#95—471no—
532C2×#95—471no—
533C2×#95—471no—
534C2×#95—471no—
535C2×#95C2×D4711yescharacteristic
536C2×#95C2×D4711yescharacteristic
537C47C2×#236111yescharacteristic, complemented, Sylow
538C25—471no—
539C25—471no—
540C25C22×D4711yescharacteristic
541C22×D4—478no—
542C22×D4—478no—
543C22×D4—474no—
544C22×D4—474no—
545C22×D4—478no—
546C22×D4—474no—
547C22×D4—944no—
548C22×D4—944no—
549C22×D4—944no—
550C22×D4—944no—
551C22×D4—944no—
552C22×D4—944no—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—42no—
556C23×C4—471no—
557C23×C4—471no—
558C23×C4—471no—
559C23×C4—471no—
560C23×C4—478no—
561C23×C4—474no—
562C23×C4—471no—
563C23×C4—471no—
564C23×C4—474no—
565C23×C4—474no—
566C23×C4—474no—
567C23×C4—944no—
568C23×C4—944no—
569C23×C4—944no—
570C23×C4—944no—
571C23×C4—944no—
572C23×C4—944no—
573C23×C4—944no—
574C23×C4—944no—
575C23×C4—1882no—
576C23×C4—1882no—
577C23×C4—1882no—
578C23×C4C22×D4711yescharacteristic
579C23×C4C22×D4711yescharacteristic
580C23×C4C22×D4714yes—
581C23×C4C22×D4711yescharacteristic
582C23×C4C22×D4711yescharacteristic
583C23×C4C22×D4711yescharacteristic
584C23×C4C22×D4711yescharacteristic
585#121—4764no—
586C4×D4—9432no—
587C4×D4—9432no—
588C4×D4—9432no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—478no—
592C2×C4⋊C4—478no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—474no—
595C2×C4⋊C4—474no—
596C2×C4⋊C4—474no—
597C2×C4⋊C4—474no—
598C2×C4⋊C4—9432no—
599C2×C4⋊C4—944no—
600C2×C4⋊C4—944no—
601C2×C4⋊C4—944no—
602C2×C4⋊C4C22×D4714yes—
603C2×C4⋊C4C22×D4714yes—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—478no—
606C2×C22⋊C4—478no—
607C2×C22⋊C4—474no—
608C2×C22⋊C4—474no—
609C2×C22⋊C4—474no—
610C2×C22⋊C4—474no—
611C2×C22⋊C4—474no—
612C2×C22⋊C4—474no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—944no—
616C2×C22⋊C4—944no—
617C2×C22⋊C4—944no—
618C2×C22⋊C4—944no—
619C2×C22⋊C4—944no—
620C2×C22⋊C4—1882no—
621C2×C22⋊C4C4×D4718yescomplemented
622C2×C22⋊C4C22×D4714yes—
623C2×C22⋊C4C22×D4714yes—
624C2×C42—474no—
625C2×C42—474no—
626C2×C42—474no—
627C2×C42—474no—
628C2×C42—944no—
629C2×C42—944no—
630C2×C42—944no—
631C2×C42—944no—
632#95—474no—
633#95—474no—
634#95—474no—
635#95—474no—
636#95C22×D4714yes—
637#95C22×D4714yes—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—474no—
645C24—474no—
646C24—474no—
647C24—472no—
648C24—474no—
649C24—472no—
650C24—942no—
651C24—942no—
652C24—942no—
653C24—942no—
654C24—942no—
655C24—942no—
656C24—942no—
657C24—942no—
658C24—942no—
659C24—942no—
660C24C2×C4×D4714yes—
661C24C23×D4712yes—
662C24C23×D4711yescharacteristic
663C2×D4—4716no—
664C2×D4—4716no—
665C2×D4—4716no—
666C2×D4—948no—
667C2×D4—9432no—
668C2×D4—948no—
669C2×D4—948no—
670C2×D4—9432no—
671C2×D4—948no—
672C2×D4—948no—
673C2×D4—9432no—
674C2×D4—948no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—44no—
692C22×C4—416no—
693C22×C4—474no—
694C22×C4—474no—
695C22×C4—474no—
696C22×C4—472no—
697C22×C4—474no—
698C22×C4—474no—
699C22×C4—474no—
700C22×C4—472no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—4716no—
704C22×C4—472no—
705C22×C4—472no—
706C22×C4—948no—
707C22×C4—9432no—
708C22×C4—948no—
709C22×C4—948no—
710C22×C4—948no—
711C22×C4—948no—
712C22×C4—948no—
713C22×C4—942no—
714C22×C4—942no—
715C22×C4—942no—
716C22×C4—942no—
717C22×C4—942no—
718C22×C4—942no—
719C22×C4—942no—
720C22×C4—942no—
721C22×C4—942no—
722C22×C4—942no—
723C22×C4—942no—
724C22×C4—942no—
725C22×C4—948no—
726C22×C4—948no—
727C22×C4—1884no—
728C22×C4—1884no—
729C22×C4—1884no—
730C22×C4—18816no—
731C22×C4—18816no—
732C22×C4—18816no—
733C22×C4C2×C4×D4714yes—
734C22×C4C2×C4×D4714yes—
735C22×C4D4×D4714yes—
736C22×C4D4×D4714yes—
737C22×C4C23×D4712yes—
738C22×C4C23×D4712yes—
739C22×C4C23×D4712yes—
740C22×C4C23×D4712yes—
741C22×C4C23×D4712yes—
742C22×C4C23×D4712yes—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—4716no—
746C4⋊C4—4716no—
747C4⋊C4—948no—
748C4⋊C4—948no—
749C4⋊C4—948no—
750C22⋊C4—44no—
751C22⋊C4—4716no—
752C22⋊C4—4716no—
753C22⋊C4—948no—
754C22⋊C4—948no—
755C22⋊C4—948no—
756C22⋊C4—948no—
757C22⋊C4—948no—
758C22⋊C4—1884no—
759C22⋊C4C2×C4×D47116yescomplemented
760C42—948no—
761C42—948no—
762C42—948no—
763C42—948no—
764C23—28no—
765C23—28no—
766C23—28no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—4716no—
778C23—474no—
779C23—474no—
780C23—474no—
781C23—474no—
782C23—948no—
783C23—948no—
784C23—948no—
785C23—948no—
786C23—948no—
787C23—948no—
788C23—942no—
789C23—942no—
790C23—942no—
791C23—942no—
792C23—948no—
793C23—948no—
794C23—948no—
795C23—942no—
796C23—942no—
797C23—942no—
798C23—942no—
799C23—942no—
800C23—942no—
801C23—1884no—
802C23—1884no—
803C23—1884no—
804C23—1884no—
805C23C22×C4×D4714yes—
806C23C22×C4×D4712yes—
807C23C2×D4×D4712yes—
808C23C2×D4×D4712yes—
809C23#41×D4712yes—
810C23#41×D4712yes—
811C23#1309406912yes—
812C23#1309407212yes—
813C23C24×D4711yescharacteristic
814D4—9432no—
815D4—9432no—
816D4—9432no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—416no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—4716no—
839C2×C4—474no—
840C2×C4—474no—
841C2×C4—474no—
842C2×C4—474no—
843C2×C4—474no—
844C2×C4—474no—
845C2×C4—9432no—
846C2×C4—948no—
847C2×C4—948no—
848C2×C4—948no—
849C2×C4—942no—
850C2×C4—942no—
851C2×C4—942no—
852C2×C4—942no—
853C2×C4—942no—
854C2×C4—942no—
855C2×C4—942no—
856C2×C4—942no—
857C2×C4—942no—
858C2×C4—942no—
859C2×C4—942no—
860C2×C4—942no—
861C2×C4—18816no—
862C2×C4—18816no—
863C2×C4—18816no—
864C2×C4—1884no—
865C2×C4—1884no—
866C2×C4C22×C4×D4714yes—
867C2×C4C22×C4×D4714yes—
868C2×C4C2×D4×D4714yes—
869C2×C4C2×D4×D4714yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—416no—
877C22—42no—
878C22—478no—
879C22—944no—
880C22—944no—
881C22—944no—
882C22—944no—
883C22—944no—
884C22—9432no—
885C22—944no—
886C22—944no—
887C22—944no—
888C22—944no—
889C22—1882no—
890C22—1882no—
891C22—1882no—
892C22—18816no—
893C22—1882no—
894C22C4×D4×D4714yes—
895C22C4×D4×D4714yes—
896C22#1568960414yes—
897C22#1568975514yes—
898C22#1568977514yes—
899C22#1568978314yes—
900C22#1568981814yes—
901C22C23×C4×D4711yescharacteristic
902C22C22×D4×D4711yescharacteristic
903C22C22×D4×D4711yescharacteristic
904C22C2×#41×D4711yescharacteristic
905C22C2×#41×D4711yescharacteristic
906C22C2×#1309406911yescharacteristic
907C22C2×#1309407211yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—42no—
914C4—478no—
915C4—944no—
916C4—944no—
917C4—944no—
918C4—1882no—
919C4—1882no—
920C2—44no—
921C2—948no—
922C2—1884no—
923C2#2024640718yesdirect product factor
924C2C2×C4×D4×D4711yescharacteristic
925C2C2×C4×D4×D4711yescharacteristic
926C2C2×#1568960411yescharacteristic
927C2C2×#1568975511yescharacteristic
928C2C2×#1568977511yescharacteristic
929C2C2×#1568978311yescharacteristic
930C2C2×#1568981811yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC22×#13093997C2
cosocleC23×C47C25
hypercenterC2×#385D47
hypocenterC47C2×#2361
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#13093986C2semidirect
3. C22×C4×C22⋊D47C2semidirect
4. C22×C4×C22⋊D47C2semidirect
5. C22×C4⋊C4×D47C2semidirect
6. #20246407C2direct (N × H)
7. C2×#15689023C2semidirect
8. C2×#15689018C2semidirect
9. C2×#15689016C2semidirect
10. C2×#15689013C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15688999C2semidirect
13. C2×#15688997C2semidirect
14. C2×#15688974C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#385C2semidirect
24. C2×#13093997C4semidirect
27. C2×#13093986C22semidirect
30. C2×C4×C22⋊D47C22semidirect
31. C2×C4×C22⋊D47C22semidirect
38. C2×C4⋊C4×D47C22semidirect
51. #15689023C22semidirect
52. #15689018C22semidirect
53. #15689016C22semidirect
54. #15689013C22semidirect
55. #15689001C22semidirect
56. #15688999C22semidirect
57. #15688997C22semidirect
58. #15688974C22semidirect
59. #15688970C22semidirect
69. C47×#385C22semidirect
76. C22×D188C2×C4semidirect
82. C22×C22⋊D47C2×C4semidirect
83. C22×C22⋊D47C2×C4semidirect
103. C22×C4×D47C2×C4semidirect
108. #13093997C2×C4semidirect
116. C2×Dic47⋊C4C2×C4semidirect
117. C2×Dic47⋊C4D4semidirect
131. C2×(C2×D47)⋊C4C2×C4semidirect
132. C2×(C2×D47)⋊C4D4semidirect
167. C2×C22⋊C4×C47C2×C4semidirect
231. C2×C22⋊D47C22×C4semidirect
232. C2×C22⋊D47C22×C4semidirect
260. C2×D188C22×C4semidirect
276. C2×C4×D47C22×C4semidirect
280. C22⋊C4×C47C22×C4semidirect
287. (C2×D47)⋊C4C22×C4semidirect
288. (C2×D47)⋊C4C2×D4semidirect
292. Dic47⋊C4C22×C4semidirect
293. Dic47⋊C4C2×D4semidirect
343. C22×D47C4×D4semidirect
392. C2×Dic47C4×D4semidirect
442. C2×D47C2×C4×D4semidirect
454. Dic47C2×C4×D4semidirect
468. C2×#385D47semidirect
472. C2×C47#2361semidirect
528. #385C2×D47semidirect
537. C47C2×#2361semidirect
621. C2×C22⋊C4C4×D47semidirect
759. C22⋊C4C2×C4×D47semidirect
923. C2#20246407direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939972
C22×#130939862
C22×C4×C22⋊D472
C22×C4⋊C4×D472
#202464072
C2×#156890232
C2×#156890182
C2×#156890162
C2×#156890132
C2×#156890012
C2×#156889992
C2×#156889972
C2×#156889742
C2×#156889702
C2×C47×#3852
C2×#236147