Finite Group Databasebeta

← C2×#20247267 #26383774

Subgroups — C2×#20247267 #26383774

Order 12032.

3894 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094005C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4#20247267C2116yesmaximal, direct product factor
5C2×#15689058C211yesmaximal, characteristic, complemented
6C2×#15689039C211yesmaximal, characteristic, complemented
7C2×#15689038C211yesmaximal, characteristic, complemented
8C2×#15689031C211yesmaximal, characteristic
9C2×#15689019C211yesmaximal, characteristic, complemented
10C2×#15689018C211yesmaximal, characteristic, complemented
11C2×#15689016C211yesmaximal, characteristic, complemented
12C2×#15689011C211yesmaximal, characteristic, complemented
13C2×#15688996C211yesmaximal, characteristic, complemented
14C2×#15688995C211yesmaximal, characteristic, complemented
15C2×#15688994C211yesmaximal, characteristic, complemented
16C22×#123×C47C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094005—28no—
22C2×#13094005C2218yescomplemented
23C2×C4×C22⋊D47—28no—
24C2×C4×C22⋊D47C2218yescomplemented
25C2×(C22⋊D47)⋊C4—28no—
26C2×(C22⋊D47)⋊C4C2218yescomplemented
27C22×C4⋊Dic47C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×C22⋊Dic47C2211yescharacteristic
37C22×C22⋊Dic47C2211yescharacteristic
38C22×C22⋊Dic47C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45#15689058C2218yescomplemented
46#15689039C2218yescomplemented
47#15689038C2218yescomplemented
48#15689031C2218yes—
49#15689019C2218yescomplemented
50#15689018C2218yescomplemented
51#15689016C2218yescomplemented
52#15689011C2218yescomplemented
53#15688996C2218yescomplemented
54#15688995C2218yescomplemented
55#15688994C2218yescomplemented
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C23×D4×C47C2211yescharacteristic
63C24×C4×C47C2211yescharacteristic
64C2×#123×C47—28no—
65C2×#123×C47C2218yescomplemented
66C22×C4⋊C4×C47C2211yescharacteristic
67C22×C4⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C22×C22⋊C4×C47C2211yescharacteristic
70C22×C22⋊C4×C47C2211yescharacteristic
71C24×D47C2311yescharacteristic
72C22×C22⋊D47—24no—
73C22×C22⋊D47—24no—
74C22×C22⋊D47—24no—
75C22×C22⋊D47—24no—
76C22×C22⋊D47—24no—
77C22×C22⋊D47—24no—
78C22×C22⋊D47C2314yes—
79C22×C22⋊D47C2314yes—
80C23×Dic47—24no—
81C23×Dic47—24no—
82C23×Dic47—42no—
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2314yes—
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47—42no—
94C22×C4×D47C2314yes—
95#13094005—232no—
96C4×C22⋊D47—232no—
97(C22⋊D47)⋊C4—232no—
98C2×C4⋊Dic47—24no—
99C2×C4⋊Dic47C2314yes—
100C2×Dic47⋊C4—24no—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—24no—
105C2×Dic47⋊C4—42no—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×C22⋊Dic47—24no—
113C2×C22⋊Dic47—24no—
114C2×C22⋊Dic47—24no—
115C2×C22⋊Dic47—24no—
116C2×C22⋊Dic47D418yescomplemented
117C2×C22⋊Dic47C2314yes—
118C2×C22⋊Dic47C2314yes—
119C2×C22⋊Dic47C2314yes—
120C2×C22⋊Dic47C2314yes—
121C2×C22⋊Dic47C2314yes—
122C2×(C2×D47)⋊C4—24no—
123C2×(C2×D47)⋊C4—24no—
124C2×(C2×D47)⋊C4—24no—
125C2×(C2×D47)⋊C4—42no—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×C4×Dic47—24no—
131C2×C4×Dic47—24no—
132C2×C4×Dic47C2314yes—
133C2×C4×Dic47C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C47⋊#95C2314yes—
140C25×C47C2311yescharacteristic
141C25×C47C2311yescharacteristic
142C22×D4×C47—24no—
143C22×D4×C47—24no—
144C22×D4×C47—42no—
145C22×D4×C47C2314yes—
146C23×C4×C47—24no—
147C23×C4×C47—24no—
148C23×C4×C47—42no—
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2314yes—
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155#123×C47—232no—
156C2×C4⋊C4×C47—24no—
157C2×C4⋊C4×C47—24no—
158C2×C4⋊C4×C47C2314yes—
159C2×C4⋊C4×C47C2314yes—
160C2×C22⋊C4×C47—24no—
161C2×C22⋊C4×C47—24no—
162C2×C22⋊C4×C47D418yescomplemented
163C2×C22⋊C4×C47C2314yes—
164C2×C22⋊C4×C47C2314yes—
165C2×C22⋊C4×C47C2314yes—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47—22no—
171C24×C47—22no—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47C2×D414yes—
179C24×C47C2×D414yes—
180C24×C47C2412yes—
181C24×C47C2412yes—
182C24×C47C2411yescharacteristic
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47#4114yes—
190C23×D47C2412yes—
191C2×D4×C47—28no—
192C2×D4×C47—28no—
193C2×D4×C47—44no—
194C2×D4×C47—416no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
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—28no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—28no—
210C22×C4×C47—44no—
211C22×C4×C47—416no—
212C22×C4×C47C2×D414yes—
213C22×C4×C47C2×D414yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2412yes—
219C2×C22⋊D47—232no—
220C2×C22⋊D47—232no—
221C2×C22⋊D47—28no—
222C2×C22⋊D47—28no—
223C2×C22⋊D47—28no—
224C2×C22⋊D47—28no—
225C2×C22⋊D47—28no—
226C2×C22⋊D47—28no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—22no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—28no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—28no—
246C22×Dic47—44no—
247C22×Dic47—416no—
248C22×Dic47C2×D414yes—
249C22×Dic47C2×D414yes—
250C22×Dic47#4114yes—
251C22×Dic47#4114yes—
252C22×Dic47C2412yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C22×Dic47C2412yes—
258C22×Dic47C2412yes—
259C2×C4×D47—28no—
260C2×C4×D47—28no—
261C2×C4×D47—44no—
262C2×C4×D47—416no—
263C4⋊C4×C47—28no—
264C4⋊C4×C47—28no—
265C22⋊C4×C47—28no—
266C22⋊C4×C47—28no—
267C22⋊C4×C47C2×D4116yescomplemented
268C22⋊Dic47—28no—
269C22⋊Dic47—28no—
270C22⋊Dic47—28no—
271C22⋊Dic47—28no—
272C22⋊Dic47C2×D4116yescomplemented
273(C2×D47)⋊C4—28no—
274(C2×D47)⋊C4—28no—
275(C2×D47)⋊C4—28no—
276(C2×D47)⋊C4—44no—
277C4⋊Dic47—28no—
278Dic47⋊C4—28no—
279Dic47⋊C4—28no—
280Dic47⋊C4—28no—
281Dic47⋊C4—28no—
282Dic47⋊C4—28no—
283Dic47⋊C4—44no—
284C4×Dic47—28no—
285C4×Dic47—28no—
286C23×C47—28no—
287C23×C47—28no—
288C23×C47—28no—
289C23×C47—28no—
290C23×C47—28no—
291C23×C47—28no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—44no—
305C23×C47—44no—
306C23×C47—44no—
307C23×C47—44no—
308C23×C47—44no—
309C23×C47—44no—
310C23×C47—44no—
311C23×C47—44no—
312C23×C47C22×D414yes—
313C23×C47C22×D412yes—
314C23×C47C22×D414yes—
315C23×C47C22×D412yes—
316C23×C47C2×#4112yes—
317C23×C47C2×#4112yes—
318C23×C47C2×#4112yes—
319C23×C47H(5,𝔽2)12yes—
320C23×C472−1+412yes—
321C23×C47C2511yescharacteristic
322C22×D47—28no—
323C22×D47—28no—
324C22×D47—28no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—44no—
332C22×D47—44no—
333C22×D47—44no—
334C22×D47—44no—
335C22×D47C2×#4114yes—
336D4×C47—416no—
337C2×C4×C47—28no—
338C2×C4×C47—28no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—416no—
353C2×C4×C47—44no—
354C2×C4×C47—44no—
355C2×C4×C47—44no—
356C2×C4×C47C22×D414yes—
357C2×C4×C47C22×D414yes—
358C22⋊D47—232no—
359C22⋊D47—232no—
360C2×Dic47—28no—
361C2×Dic47—28no—
362C2×Dic47—28no—
363C2×Dic47—28no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—416no—
382C2×Dic47—44no—
383C2×Dic47—44no—
384C2×Dic47—44no—
385C2×Dic47C22×D414yes—
386C2×Dic47C22×D414yes—
387C2×Dic47C2×#4114yes—
388C2×Dic47C2×#4114yes—
389C4×D47—416no—
390C2×#2455—471nomaximal, Sylow
391C22×C47—24no—
392C22×C47—24no—
393C22×C47—24no—
394C22×C47—24no—
395C22×C47—24no—
396C22×C47—24no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—416no—
404C22×C47—416no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47#52514yes—
408C22×C47#52514yes—
409C22×C47#53914yes—
410C22×C47D4214yes—
411C22×C47#54714yes—
412C22×C47#54714yes—
413C22×C47#55914yes—
414C22×C47C23×D411yescharacteristic
415C22×C47C23×D411yescharacteristic
416C22×C47C22×#4111yescharacteristic
417C22×C47C22×#4111yescharacteristic
418C22×C47C22×#4111yescharacteristic
419C22×C47C2×H(5,𝔽2)11yescharacteristic
420C22×C47C2×2−1+411yescharacteristic
421C2×D47—24no—
422C2×D47—24no—
423C2×D47—24no—
424C2×D47—42no—
425C2×D47—42no—
426C2×D47—42no—
427C2×D47—416no—
428C2×D47—42no—
429C4×C47—24no—
430C4×C47—24no—
431C4×C47—42no—
432C4×C47—42no—
433C4×C47—42no—
434Dic47—24no—
435Dic47—24no—
436Dic47—24no—
437Dic47—24no—
438Dic47—42no—
439Dic47—42no—
440Dic47—42no—
441C22×#123—471no—
442C22×#123D4711yescharacteristic, complemented
443C22×C4×D4—471no—
444C22×C4×D4—471no—
445#2455—4716no—
446C2×#399—471no—
447C2×#394—471no—
448C2×#394—471no—
449C2×#392—471no—
450C2×#389—471no—
451C2×#389—471no—
452C2×#388—471no—
453C2×#388—471no—
454C2×#385—471no—
455C2×#385—471no—
456C2×#385—471no—
457C2×C47—44no—
458C2×C47—44no—
459C2×C47#245518yescomplemented
460C2×C47C2×#52511yescharacteristic
461C2×C47C2×#52511yescharacteristic
462C2×C47C2×#53911yescharacteristic
463C2×C47C2×D4211yescharacteristic
464C2×C47C2×#54711yescharacteristic
465C2×C47C2×#54711yescharacteristic
466C2×C47C2×#55911yescharacteristic
467D47—44no—
468C23×D4—471no—
469C23×D4—471no—
470C23×D4C2×D4711yescharacteristic
471C24×C4—471no—
472C24×C4—471no—
473C24×C4C2×D4711yescharacteristic
474C2×#123—28no—
475C2×#123—478no—
476C2×#123—948no—
477C2×#123C2×D4718yescomplemented
478C2×C4×D4—478no—
479C2×C4×D4—478no—
480C2×C4×D4—948no—
481C2×C4×D4—948no—
482C22×C4⋊C4—471no—
483C22×C4⋊C4—471no—
484C22×C4⋊C4—471no—
485C22×C4⋊C4—471no—
486C22×C4⋊C4—471no—
487C22×C4⋊C4—471no—
488C22×C4⋊C4—471no—
489C22×C4⋊C4C2×D4711yescharacteristic
490C22×C4⋊C4C2×D4711yescharacteristic
491C22×C22⋊C4—471no—
492C22×C22⋊C4—471no—
493C22×C22⋊C4—471no—
494C22×C22⋊C4—471no—
495C22×C22⋊C4—471no—
496C22×C22⋊C4—471no—
497C22×C22⋊C4—471no—
498C22×C22⋊C4—471no—
499C22×C22⋊C4—471no—
500C22×C22⋊C4C2×D4711yescharacteristic
501C22×C22⋊C4C2×D4711yescharacteristic
502C22×C22⋊C4C2×D4711yescharacteristic
503C22×C42—471no—
504C22×C42—471no—
505#399—478no—
506#394—478no—
507#394—478no—
508#392—478no—
509#389—478no—
510#389—478no—
511#388—478no—
512#388—478no—
513#385—478no—
514#385—478no—
515#385—478no—
516C2×#95—471no—
517C2×#95—471no—
518C2×#95—471no—
519C2×#95—471no—
520C2×#95—471no—
521C2×#95—471no—
522C47C2×#245511yescharacteristic, complemented, Sylow
523C25—471no—
524C25C22×D4711yescharacteristic
525C25C22×D4711yescharacteristic
526C22×D4—24no—
527C22×D4—24no—
528C22×D4—42no—
529C22×D4—474no—
530C22×D4—474no—
531C22×D4—944no—
532C22×D4—944no—
533C22×D4—944no—
534C22×D4—944no—
535C22×D4—944no—
536C22×D4—944no—
537C22×D4C22×D4714yes—
538C23×C4—24no—
539C23×C4—24no—
540C23×C4—42no—
541C23×C4—471no—
542C23×C4—471no—
543C23×C4—471no—
544C23×C4—471no—
545C23×C4—471no—
546C23×C4—471no—
547C23×C4—471no—
548C23×C4—474no—
549C23×C4—474no—
550C23×C4—944no—
551C23×C4—944no—
552C23×C4—944no—
553C23×C4—944no—
554C23×C4—1882no—
555C23×C4—1882no—
556C23×C4C22×D4711yescharacteristic
557C23×C4C22×D4711yescharacteristic
558C23×C4C22×D4711yescharacteristic
559C23×C4C22×D4714yes—
560C23×C4C22×D4711yescharacteristic
561C23×C4C22×D4711yescharacteristic
562#123—232no—
563#123—9432no—
564C4×D4—9432no—
565C4×D4—9432no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—474no—
569C2×C4⋊C4—474no—
570C2×C4⋊C4—474no—
571C2×C4⋊C4—474no—
572C2×C4⋊C4—474no—
573C2×C4⋊C4—474no—
574C2×C4⋊C4—474no—
575C2×C4⋊C4—944no—
576C2×C4⋊C4—944no—
577C2×C4⋊C4—944no—
578C2×C4⋊C4—944no—
579C2×C4⋊C4—944no—
580C2×C4⋊C4—944no—
581C2×C4⋊C4—1882no—
582C2×C4⋊C4C22×D4714yes—
583C2×C4⋊C4C22×D4714yes—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—478no—
587C2×C22⋊C4—474no—
588C2×C22⋊C4—474no—
589C2×C22⋊C4—474no—
590C2×C22⋊C4—474no—
591C2×C22⋊C4—474no—
592C2×C22⋊C4—474no—
593C2×C22⋊C4—474no—
594C2×C22⋊C4—474no—
595C2×C22⋊C4—474no—
596C2×C22⋊C4—944no—
597C2×C22⋊C4—944no—
598C2×C22⋊C4—944no—
599C2×C22⋊C4—944no—
600C2×C22⋊C4—944no—
601C2×C22⋊C4—944no—
602C2×C22⋊C4—944no—
603C2×C22⋊C4—1882no—
604C2×C22⋊C4C22⋊D4718yescomplemented
605C2×C22⋊C4C22×D4714yes—
606C2×C22⋊C4C22×D4714yes—
607C2×C22⋊C4C22×D4714yes—
608C2×C42—474no—
609C2×C42—474no—
610C2×C42—944no—
611C2×C42—944no—
612#95—474no—
613#95—474no—
614#95—474no—
615#95—474no—
616#95—474no—
617#95—474no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—474no—
631C24—472no—
632C24—942no—
633C24—942no—
634C24—942no—
635C24—942no—
636C24—942no—
637C24—942no—
638C24D4×D4714yes—
639C24C2×C22⋊D4714yes—
640C24C23×D4712yes—
641C24C23×D4712yes—
642C24C23×D4711yescharacteristic
643C2×D4—28no—
644C2×D4—28no—
645C2×D4—44no—
646C2×D4—416no—
647C2×D4—948no—
648C2×D4—948no—
649C2×D4—948no—
650C2×D4—948no—
651C2×D4—9432no—
652C2×D4—9432no—
653C2×D4—948no—
654C2×D4—948no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—28no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—44no—
671C22×C4—416no—
672C22×C4—474no—
673C22×C4—474no—
674C22×C4—474no—
675C22×C4—474no—
676C22×C4—472no—
677C22×C4—472no—
678C22×C4—472no—
679C22×C4—472no—
680C22×C4—472no—
681C22×C4—472no—
682C22×C4—472no—
683C22×C4—948no—
684C22×C4—948no—
685C22×C4—942no—
686C22×C4—942no—
687C22×C4—942no—
688C22×C4—942no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4—942no—
692C22×C4—942no—
693C22×C4—942no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4—948no—
697C22×C4—942no—
698C22×C4—942no—
699C22×C4—942no—
700C22×C4—942no—
701C22×C4—942no—
702C22×C4—942no—
703C22×C4—948no—
704C22×C4—1884no—
705C22×C4—18816no—
706C22×C4—1884no—
707C22×C4—18816no—
708C22×C4C2×C22⋊D4714yes—
709C22×C4C2×C22⋊D4714yes—
710C22×C4C23×D4712yes—
711C22×C4C23×D4712yes—
712C22×C4C23×D4712yes—
713C22×C4C23×D4712yes—
714C22×C4C23×D4712yes—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—948no—
718C4⋊C4—948no—
719C4⋊C4—948no—
720C4⋊C4—948no—
721C4⋊C4—948no—
722C4⋊C4—948no—
723C4⋊C4—1884no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—4716no—
727C22⋊C4—948no—
728C22⋊C4—948no—
729C22⋊C4—948no—
730C22⋊C4—948no—
731C22⋊C4—948no—
732C22⋊C4—948no—
733C22⋊C4—948no—
734C22⋊C4—1884no—
735C22⋊C4C2×C22⋊D47116yescomplemented
736C42—948no—
737C42—948no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—474no—
765C23—948no—
766C23—948no—
767C23—942no—
768C23—942no—
769C23—942no—
770C23—942no—
771C23—942no—
772C23—942no—
773C23—948no—
774C23—1884no—
775C23—1884no—
776C23—1884no—
777C23—1884no—
778C23C2×D4×D4714yes—
779C23C2×D4×D4712yes—
780C23C22×C22⋊D4714yes—
781C23C22×C22⋊D4712yes—
782C23#41×D4712yes—
783C23#41×D4712yes—
784C23#41×D4712yes—
785C23#1309406912yes—
786C23#1309407112yes—
787C23C24×D4711yescharacteristic
788D4—416no—
789D4—9432no—
790D4—9432no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—416no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—474no—
811C2×C4—474no—
812C2×C4—474no—
813C2×C4—474no—
814C2×C4—948no—
815C2×C4—948no—
816C2×C4—948no—
817C2×C4—948no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—942no—
832C2×C4—942no—
833C2×C4—942no—
834C2×C4—942no—
835C2×C4—18816no—
836C2×C4—18816no—
837C2×C4—1884no—
838C2×C4—1884no—
839C2×C4—1884no—
840C2×C4C22×C22⋊D4714yes—
841C2×C4C22×C22⋊D4714yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—944no—
859C22—944no—
860C22—944no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1882no—
865C22—18816no—
866C22#1568963014yes—
867C22#1568963114yes—
868C22#1568971614yes—
869C22D4×C22⋊D4714yes—
870C22#1568977114yes—
871C22#1568977214yes—
872C22#1568985714yes—
873C22C22×D4×D4711yescharacteristic
874C22C23×C22⋊D4711yescharacteristic
875C22C2×#41×D4711yescharacteristic
876C22C2×#41×D4711yescharacteristic
877C22C2×#41×D4711yescharacteristic
878C22C2×#1309406911yescharacteristic
879C22C2×#1309407111yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—944no—
886C4—944no—
887C4—944no—
888C4—944no—
889C4—1882no—
890C4—1882no—
891C4—1882no—
892C2—44no—
893C2—44no—
894C2—1884no—
895C2#2024726718yesdirect product factor
896C2C2×#1568963011yescharacteristic
897C2C2×#1568963111yescharacteristic
898C2C2×#1568971611yescharacteristic
899C2C2×D4×C22⋊D4711yescharacteristic
900C2C2×#1568977111yescharacteristic
901C2C2×#1568977211yescharacteristic
902C2C2×#1568985711yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×#123×C47C2
socleC24×C47C24
prime radicalC2×#15689031C2
hypercenterC22×#123D47
hypocenterC47C2×#2455
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#13094005C2semidirect
2. C22×C4×C22⋊D47C2semidirect
3. C22×(C22⋊D47)⋊C4C2semidirect
4. #20247267C2direct (N × H)
5. C2×#15689058C2semidirect
6. C2×#15689039C2semidirect
7. C2×#15689038C2semidirect
9. C2×#15689019C2semidirect
10. C2×#15689018C2semidirect
11. C2×#15689016C2semidirect
12. C2×#15689011C2semidirect
13. C2×#15688996C2semidirect
14. C2×#15688995C2semidirect
15. C2×#15688994C2semidirect
16. C22×#123×C47C2semidirect
22. C2×#13094005C22semidirect
24. C2×C4×C22⋊D47C22semidirect
26. C2×(C22⋊D47)⋊C4C22semidirect
45. #15689058C22semidirect
46. #15689039C22semidirect
47. #15689038C22semidirect
49. #15689019C22semidirect
50. #15689018C22semidirect
51. #15689016C22semidirect
52. #15689011C22semidirect
53. #15688996C22semidirect
54. #15688995C22semidirect
55. #15688994C22semidirect
65. C2×#123×C47C22semidirect
116. C2×C22⋊Dic47D4semidirect
162. C2×C22⋊C4×C47D4semidirect
267. C22⋊C4×C47C2×D4semidirect
272. C22⋊Dic47C2×D4semidirect
442. C22×#123D47semidirect
459. C2×C47#2455semidirect
477. C2×#123C2×D47semidirect
522. C47C2×#2455semidirect
604. C2×C22⋊C4C22⋊D47semidirect
735. C22⋊C4C2×C22⋊D47semidirect
895. C2#20247267direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940052
C22×C4×C22⋊D472
C22×(C22⋊D47)⋊C42
#202472672
C2×#156890582
C2×#156890392
C2×#156890382
C2×#156890312
C2×#156890192
C2×#156890182
C2×#156890162
C2×#156890112
C2×#156889962
C2×#156889952
C2×#156889942
C22×#123×C472
C2×#245547