Finite Group Databasebeta

← C2×#20249198 #26382622

Subgroups — C2×#20249198 #26382622

Order 12032.

4142 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094002C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D47C211yesmaximal, characteristic
3#20249198C2116yesmaximal, direct product factor
4C2×#15689059C211yesmaximal, characteristic, complemented
5C2×#15689058C211yesmaximal, characteristic, complemented
6C2×#15689046C211yesmaximal, characteristic, complemented
7C2×#15689045C211yesmaximal, characteristic, complemented
8C2×#15689045C211yesmaximal, characteristic, complemented
9C2×#15689036C211yesmaximal, characteristic, complemented
10C2×#15689035C211yesmaximal, characteristic, complemented
11C2×#15688997C211yesmaximal, characteristic, complemented
12C2×#15688994C211yesmaximal, characteristic, complemented
13C2×#15688980C211yesmaximal, characteristic, complemented
14C2×#15688978C211yesmaximal, characteristic
15C2×#15688978C211yesmaximal, characteristic
16C2×C47×#396C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×Dic94C2211yescharacteristic, complemented
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094002—28no—
22C2×#13094002C2218yescomplemented
23C22×C4⋊Dic47C2211yescharacteristic, complemented
24C22×C4⋊Dic47C2211yescharacteristic, complemented
25C22×Dic47⋊C4C2211yescharacteristic, complemented
26C22×Dic47⋊C4C2211yescharacteristic, complemented
27C22×Dic47⋊C4C2211yescharacteristic, complemented
28C22×Dic47⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C2×C22⋊C4×D47—28no—
43C2×C22⋊C4×D47C2218yes—
44#15689059C2218yescomplemented
45#15689058C2218yescomplemented
46#15689046C2218yescomplemented
47#15689045C2218yescomplemented
48#15689045C2218yescomplemented
49#15689036C2218yescomplemented
50#15689035C2218yescomplemented
51#15688997C2218yescomplemented
52#15688994C2218yescomplemented
53#15688980C2218yescomplemented
54#15688978C2218yes—
55#15688978C2218yes—
56C2×C47⋊#95C2211yescharacteristic, complemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C22×C4⋊C4×C47C2211yescharacteristic, complemented
62C22×C4⋊C4×C47C2211yescharacteristic, complemented
63C22×C4⋊C4×C47C2211yescharacteristic, complemented
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#396C2218yescomplemented
68C2×#95×C47C2211yescharacteristic, complemented
69C24×D47—24no—
70C24×D47—24no—
71C24×D47—42no—
72C24×D47—42no—
73C24×D47—42no—
74C24×D47—42no—
75C24×D47Q818yescomplemented
76C24×D47C2311yescharacteristic
77C24×D47C2311yescharacteristic
78C24×D47C2314yes—
79C22×Dic94—24no—
80C22×Dic94—42no—
81C22×Dic94—42no—
82C22×Dic94C2314yescomplemented
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C22×C4×D47—24no—
90C22×C4×D47—42no—
91C22×C4×D47—42no—
92C22×C4×D47—42no—
93C22×C4×D47—42no—
94C22×C4×D47D418yes—
95C22×C4×D47C2314yes—
96C22×C4×D47C2314yes—
97#13094002—232no—
98C2×C4⋊Dic47—42no—
99C2×C4⋊Dic47—42no—
100C2×C4⋊Dic47C2314yescomplemented
101C2×C4⋊Dic47C2314yescomplemented
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—42no—
105C2×Dic47⋊C4—42no—
106C2×Dic47⋊C4C2314yescomplemented
107C2×Dic47⋊C4C2314yescomplemented
108C2×Dic47⋊C4C2314yescomplemented
109C2×Dic47⋊C4C2314yescomplemented
110C2×C22⋊Dic47—24no—
111C2×C22⋊Dic47—42no—
112C2×C22⋊Dic47—42no—
113C2×C22⋊Dic47C2314yes—
114C2×C22⋊Dic47C2314yes—
115C2×C22⋊Dic47C2314yes—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4—24no—
120C2×(C2×D47)⋊C4—24no—
121C2×(C2×D47)⋊C4—24no—
122C2×(C2×D47)⋊C4—42no—
123C2×(C2×D47)⋊C4—42no—
124C2×(C2×D47)⋊C4—42no—
125C2×(C2×D47)⋊C4—42no—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C22⋊C4×D47—232no—
137C47⋊#95C2314yescomplemented
138C47⋊#95C2314yescomplemented
139C47⋊#95C2314yescomplemented
140C47⋊#95C2314yescomplemented
141C47⋊#95C2314yescomplemented
142C25×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C2×C4⋊C4×C47—24no—
150C2×C4⋊C4×C47—42no—
151C2×C4⋊C4×C47—42no—
152C2×C4⋊C4×C47C2314yescomplemented
153C2×C4⋊C4×C47C2314yescomplemented
154C2×C4⋊C4×C47C2314yescomplemented
155C2×C22⋊C4×C47—24no—
156C2×C22⋊C4×C47—42no—
157C2×C22⋊C4×C47—42no—
158C2×C22⋊C4×C47C2314yes—
159C2×C22⋊C4×C47C2314yes—
160C2×C22⋊C4×C47C2314yes—
161#95×C47C2314yescomplemented
162C24×C47—22no—
163C24×C47—22no—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47C2×Q814yes—
169C24×C47C2412yes—
170C24×C47C2411yescharacteristic
171C23×D47—22no—
172C23×D47—22no—
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—232no—
182C23×D47—28no—
183C23×D47—28no—
184C23×D47—416no—
185C23×D47—416no—
186C23×D47—44no—
187C23×D47—44no—
188C23×D47—44no—
189C23×D47—44no—
190C23×D47—416no—
191C23×D47—416no—
192C23×D47—416no—
193C23×D47—416no—
194C23×D47C2×D414yes—
195C23×D47C2×Q814yes—
196C23×D47C2×Q814yes—
197C23×D47C2×Q8116yescomplemented
198C23×D47#4114yes—
199C23×D47C2412yes—
200C23×D47C2412yes—
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—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47C2×D414yes—
219C22×C4×C47C2412yes—
220C22×C4×C47C2412yes—
221C22×C4×C47C2412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2412yes—
224C22×C4×C47C2412yes—
225C22×Dic47—22no—
226C22×Dic47—22no—
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—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47C2×D414yes—
243C22×Dic47C2412yes—
244C22×Dic47C2412yes—
245C22×Dic47C2412yes—
246C22×Dic47C2412yes—
247C22×Dic47C2412yes—
248C22×Dic47C2412yes—
249C2×C4×D47—28no—
250C2×C4×D47—416no—
251C2×C4×D47—44no—
252C2×C4×D47—44no—
253C2×C4×D47—44no—
254C2×C4×D47—44no—
255C2×C4×D47—416no—
256C2×C4×D47C2×D4116yes—
257C2×Dic94—28no—
258C2×Dic94—44no—
259C2×Dic94—44no—
260C2×Dic94—416no—
261C4⋊C4×C47—28no—
262C4⋊C4×C47—44no—
263C4⋊C4×C47—44no—
264C22⋊C4×C47—28no—
265C22⋊C4×C47—44no—
266C22⋊C4×C47—44no—
267C22⋊Dic47—28no—
268C22⋊Dic47—44no—
269C22⋊Dic47—44no—
270(C2×D47)⋊C4—28no—
271(C2×D47)⋊C4—28no—
272(C2×D47)⋊C4—28no—
273(C2×D47)⋊C4—28no—
274(C2×D47)⋊C4—28no—
275(C2×D47)⋊C4—28no—
276(C2×D47)⋊C4—44no—
277(C2×D47)⋊C4—44no—
278(C2×D47)⋊C4—44no—
279(C2×D47)⋊C4—44no—
280C4⋊Dic47—44no—
281C4⋊Dic47—44no—
282Dic47⋊C4—28no—
283Dic47⋊C4—28no—
284Dic47⋊C4—44no—
285Dic47⋊C4—44no—
286C23×C47—28no—
287C23×C47—28no—
288C23×C47—28no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—44no—
296C23×C47—44no—
297C23×C47—44no—
298C23×C47—44no—
299C23×C47C22×D412yes—
300C23×C47C22×Q814yes—
301C23×C47C22×Q812yes—
302C23×C47C2×#4112yes—
303C23×C47H(5,𝔽2)12yes—
304C23×C47H(5,𝔽2)12yes—
305C23×C47H(5,𝔽2)12yes—
306C23×C47H(5,𝔽2)12yes—
307C23×C47C2511yescharacteristic
308C22×D47—28no—
309C22×D47—28no—
310C22×D47—28no—
311C22×D47—28no—
312C22×D47—28no—
313C22×D47—28no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—28no—
319C22×D47—28no—
320C22×D47—28no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—232no—
328C22×D47—416no—
329C22×D47—416no—
330C22×D47—4128no—
331C22×D47—416no—
332C22×D47—416no—
333C22×D47—416no—
334C22×D47—416no—
335C22×D47—44no—
336C22×D47—44no—
337C22×D47—44no—
338C22×D47—44no—
339C22×D47C22⋊Q8116yes—
340C22×D47C22×D414yes—
341C22×D47C22×Q814yes—
342C22×D47C22×Q814yes—
343C22×D47C2×#4114yes—
344C2×C4×C47—28no—
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—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—44no—
363C2×C4×C47—44no—
364C2×C4×C47—44no—
365C2×C4×C47—44no—
366C2×C4×C47—44no—
367C2×C4×C47C22×D414yes—
368C2×Dic47—28no—
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—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—44no—
387C2×Dic47—44no—
388C2×Dic47—44no—
389C2×Dic47—44no—
390C2×Dic47—44no—
391C2×Dic47C22×D414yes—
392C4×D47—416no—
393C4×D47—416no—
394Dic94—416no—
395C2×#2626—471nomaximal, Sylow
396C22×C47—24no—
397C22×C47—24no—
398C22×C47—24no—
399C22×C47—416no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—42no—
404C22×C47C2×C22⋊Q814yes—
405C22×C47#53414yes—
406C22×C47#53514yes—
407C22×C47#53814yes—
408C22×C47#53814yes—
409C22×C47#54314yes—
410C22×C47#54314yes—
411C22×C47C23×D411yescharacteristic
412C22×C47C23×Q811yescharacteristic
413C22×C47C22×#4111yescharacteristic
414C22×C47C2×H(5,𝔽2)11yescharacteristic
415C22×C47C2×H(5,𝔽2)11yescharacteristic
416C22×C47C2×H(5,𝔽2)11yescharacteristic
417C22×C47C2×H(5,𝔽2)11yescharacteristic
418C2×D47—232no—
419C2×D47—24no—
420C2×D47—24no—
421C2×D47—24no—
422C2×D47—24no—
423C2×D47—24no—
424C2×D47—24no—
425C2×D47—24no—
426C2×D47—24no—
427C2×D47—24no—
428C2×D47—464no—
429C2×D47—416no—
430C2×D47—42no—
431C2×D47—42no—
432C2×D47—42no—
433C2×D47—42no—
434C2×D47C2×C22⋊Q818yes—
435C4×C47—24no—
436C4×C47—42no—
437C4×C47—42no—
438C4×C47—42no—
439C4×C47—42no—
440C4×C47—42no—
441Dic47—24no—
442Dic47—42no—
443Dic47—42no—
444Dic47—42no—
445Dic47—42no—
446Dic47—42no—
447C22×C22⋊Q8—471no—
448C23×C22⋊C4—471no—
449#2626—4716no—
450C2×#399—471no—
451C2×#399—471no—
452C2×#396—471no—
453C2×#396—471no—
454C2×#396—471no—
455C2×#396D4711yescharacteristic, complemented
456C2×#393—471no—
457C2×#393—471no—
458C2×#385—471no—
459C2×#385—471no—
460C2×#380—471no—
461C2×#379—471no—
462C2×#379—471no—
463C2×C47—44no—
464C2×C47#262618yescomplemented
465C2×C47C22×C22⋊Q811yescharacteristic
466C2×C47C2×#53411yescharacteristic
467C2×C47C2×#53511yescharacteristic
468C2×C47C2×#53811yescharacteristic
469C2×C47C2×#53811yescharacteristic
470C2×C47C2×#54311yescharacteristic
471C2×C47C2×#54311yescharacteristic
472D47—28no—
473D47—44no—
474C26—471no—
475C23×Q8—471no—
476C24×C4—471no—
477C24×C4—471no—
478C2×C22⋊Q8—478no—
479C2×C22⋊Q8—948no—
480C22×C4⋊C4—471no—
481C22×C4⋊C4—471no—
482C22×C4⋊C4—471no—
483C22×C4⋊C4—471no—
484C22×C4⋊C4—471no—
485C22×C4⋊C4—471no—
486C22×C4⋊C4C2×D4711yescharacteristic, complemented
487C22×C4⋊C4C2×D4711yescharacteristic, complemented
488C22×C4⋊C4C2×D4711yescharacteristic, complemented
489C22×C22⋊C4—471no—
490C22×C22⋊C4—471no—
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⋊C4—471no—
501C22×C22⋊C4—471no—
502C22×C22⋊C4—478no—
503C22×C22⋊C4—948no—
504C22×C22⋊C4C2×D4711yescharacteristic
505C22×C22⋊C4C2×D4711yescharacteristic
506C22×C22⋊C4C2×D4711yescharacteristic
507#399—478no—
508#399—478no—
509#396—478no—
510#396—478no—
511#396—478no—
512#396C2×D4718yescomplemented
513#393—478no—
514#393—478no—
515#385—478no—
516#385—478no—
517#380—478no—
518#379—478no—
519#379—478no—
520C2×#95—471no—
521C2×#95—471no—
522C2×#95—471no—
523C2×#95—471no—
524C2×#95—471no—
525C2×#95C2×D4711yescharacteristic, complemented
526C47C2×#262611yescharacteristic, complemented, Sylow
527C25—471no—
528C25—471no—
529C25—478no—
530C25—474no—
531C25—944no—
532C25—944no—
533C25—1882no—
534C25—1882no—
535C25—1882no—
536C25—1882no—
537C25C22×D4711yescharacteristic
538C22×Q8—474no—
539C22×Q8—944no—
540C22×Q8—1882no—
541C22×Q8—1882no—
542C23×C4—471no—
543C23×C4—478no—
544C23×C4—474no—
545C23×C4—471no—
546C23×C4—471no—
547C23×C4—471no—
548C23×C4—471no—
549C23×C4—471no—
550C23×C4—474no—
551C23×C4—944no—
552C23×C4—1882no—
553C23×C4—1882no—
554C23×C4—1882no—
555C23×C4—1882no—
556C23×C4C22×D4711yescharacteristic
557C23×C4C22×D4711yescharacteristic
558C23×C4C22×D4711yescharacteristic
559C23×C4C22×D4711yescharacteristic
560C23×C4C22×D4711yescharacteristic
561C23×C4C22×D4711yescharacteristic
562C22⋊Q8—9432no—
563C2×C4⋊C4—24no—
564C2×C4⋊C4—42no—
565C2×C4⋊C4—42no—
566C2×C4⋊C4—474no—
567C2×C4⋊C4—474no—
568C2×C4⋊C4—474no—
569C2×C4⋊C4—474no—
570C2×C4⋊C4—474no—
571C2×C4⋊C4—474no—
572C2×C4⋊C4—944no—
573C2×C4⋊C4—944no—
574C2×C4⋊C4—1882no—
575C2×C4⋊C4—1882no—
576C2×C4⋊C4—1882no—
577C2×C4⋊C4—1882no—
578C2×C4⋊C4C22×D4714yescomplemented
579C2×C4⋊C4C22×D4714yescomplemented
580C2×C4⋊C4C22×D4714yescomplemented
581C2×C22⋊C4—24no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—474no—
585C2×C22⋊C4—474no—
586C2×C22⋊C4—474no—
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—474no—
597C2×C22⋊C4—9432no—
598C2×C22⋊C4—944no—
599C2×C22⋊C4—944no—
600C2×C22⋊C4—944no—
601C2×C22⋊C4—944no—
602C2×C22⋊C4—944no—
603C2×C22⋊C4—944no—
604C2×C22⋊C4—944no—
605C2×C22⋊C4—1882no—
606C2×C22⋊C4—1882no—
607C2×C22⋊C4—1882no—
608C2×C22⋊C4—1882no—
609C2×C22⋊C4—1882no—
610C2×C22⋊C4—1882no—
611C2×C22⋊C4C22×D4714yes—
612C2×C22⋊C4C22×D4714yes—
613C2×C22⋊C4C22×D4714yes—
614#95—474no—
615#95—474no—
616#95—474no—
617#95—474no—
618#95—474no—
619#95C22×D4714yescomplemented
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—474no—
627C24—474no—
628C24—474no—
629C24—472no—
630C24—474no—
631C24—472no—
632C24—4716no—
633C24—948no—
634C24—9432no—
635C24—948no—
636C24—942no—
637C24—942no—
638C24—942no—
639C24—942no—
640C24—942no—
641C24—942no—
642C24—942no—
643C24—942no—
644C24—942no—
645C24—942no—
646C24—18816no—
647C24—18816no—
648C24—1884no—
649C24—1884no—
650C24—1884no—
651C24—1884no—
652C24—18816no—
653C24—18816no—
654C24—18816no—
655C24—18816no—
656C24Q8×D4714yes—
657C24C23×D4712yes—
658C24C23×D4711yescharacteristic
659C2×Q8—948no—
660C2×Q8—1884no—
661C2×Q8—1884no—
662C2×Q8—18816no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—474no—
681C22×C4—472no—
682C22×C4—4716no—
683C22×C4—472no—
684C22×C4—472no—
685C22×C4—472no—
686C22×C4—472no—
687C22×C4—472no—
688C22×C4—948no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4—942no—
692C22×C4—942no—
693C22×C4—942no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4—942no—
697C22×C4—942no—
698C22×C4—942no—
699C22×C4—942no—
700C22×C4—942no—
701C22×C4—942no—
702C22×C4—942no—
703C22×C4—942no—
704C22×C4—942no—
705C22×C4—942no—
706C22×C4—18816no—
707C22×C4—1884no—
708C22×C4—1884no—
709C22×C4—1884no—
710C22×C4—1884no—
711C22×C4—18816no—
712C22×C4D4×D4714yes—
713C22×C4C23×D4712yes—
714C22×C4C23×D4712yes—
715C22×C4C23×D4712yes—
716C22×C4C23×D4712yes—
717C22×C4C23×D4712yes—
718C22×C4C23×D4712yes—
719C4⋊C4—28no—
720C4⋊C4—44no—
721C4⋊C4—44no—
722C4⋊C4—948no—
723C4⋊C4—948no—
724C4⋊C4—1884no—
725C4⋊C4—1884no—
726C4⋊C4—1884no—
727C4⋊C4—1884no—
728C22⋊C4—28no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—948no—
732C22⋊C4—948no—
733C22⋊C4—948no—
734C22⋊C4—948no—
735C22⋊C4—948no—
736C22⋊C4—948no—
737C22⋊C4—948no—
738C22⋊C4—1884no—
739C22⋊C4—1884no—
740C22⋊C4—1884no—
741C22⋊C4—1884no—
742C22⋊C4—1884no—
743C22⋊C4—1884no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—4716no—
758C23—474no—
759C23—474no—
760C23—474no—
761C23—474no—
762C23—9432no—
763C23—948no—
764C23—948no—
765C23—948no—
766C23—948no—
767C23—942no—
768C23—942no—
769C23—942no—
770C23—942no—
771C23—948no—
772C23—948no—
773C23—948no—
774C23—948no—
775C23—948no—
776C23—942no—
777C23—942no—
778C23—942no—
779C23—942no—
780C23—942no—
781C23—942no—
782C23—18816no—
783C23—18816no—
784C23—188128no—
785C23—18816no—
786C23—18816no—
787C23—18816no—
788C23—18816no—
789C23—1884no—
790C23—1884no—
791C23—1884no—
792C23—1884no—
793C23C2×D4×D4712yes—
794C23C2×Q8×D4714yes—
795C23C2×Q8×D4712yes—
796C23#41×D4712yes—
797C23#1309406912yes—
798C23#1309406912yes—
799C23#1309407012yes—
800C23#1309407012yes—
801C23C24×D4711yescharacteristic
802Q8—18816no—
803C2×C4—28no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—474no—
827C2×C4—948no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—942no—
832C2×C4—942no—
833C2×C4—942no—
834C2×C4—942no—
835C2×C4—942no—
836C2×C4—942no—
837C2×C4—942no—
838C2×C4—942no—
839C2×C4—942no—
840C2×C4—942no—
841C2×C4—942no—
842C2×C4—942no—
843C2×C4—942no—
844C2×C4—942no—
845C2×C4—18816no—
846C2×C4—18816no—
847C2×C4—1884no—
848C2×C4—1884no—
849C2×C4—1884no—
850C2×C4—1884no—
851C2×C4—1884no—
852C2×C4C2×D4×D4714yes—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—416no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—478no—
862C22—944no—
863C22—944no—
864C22—9432no—
865C22—944no—
866C22—944no—
867C22—944no—
868C22—944no—
869C22—944no—
870C22—944no—
871C22—944no—
872C22—18864no—
873C22—18816no—
874C22—1882no—
875C22—1882no—
876C22—1882no—
877C22—1882no—
878C22C22⋊Q8×D4714yes—
879C22#1568968114yes—
880C22#1568968914yes—
881C22#1568970514yes—
882C22#1568971214yes—
883C22#1568974814yes—
884C22#1568974814yes—
885C22C22×D4×D4711yescharacteristic
886C22C22×Q8×D4711yescharacteristic
887C22C2×#41×D4711yescharacteristic
888C22C2×#1309406911yescharacteristic
889C22C2×#1309406911yescharacteristic
890C22C2×#1309407011yescharacteristic
891C22C2×#1309407011yescharacteristic
892C4—24no—
893C4—42no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—944no—
899C4—1882no—
900C4—1882no—
901C4—1882no—
902C4—1882no—
903C4—1882no—
904C2—44no—
905C2—948no—
906C2—1884no—
907C2#2024919818yesdirect product factor
908C2C2×C22⋊Q8×D4711yescharacteristic
909C2C2×#1568968111yescharacteristic
910C2C2×#1568968911yescharacteristic
911C2C2×#1568970511yescharacteristic
912C2C2×#1568971211yescharacteristic
913C2C2×#1568974811yescharacteristic
914C2C2×#1568974811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×#396D47
hypocenterC47C2×#2626
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13094002C2semidirect
3. #20249198C2direct (N × H)
4. C2×#15689059C2semidirect
5. C2×#15689058C2semidirect
6. C2×#15689046C2semidirect
7. C2×#15689045C2semidirect
8. C2×#15689045C2semidirect
9. C2×#15689036C2semidirect
10. C2×#15689035C2semidirect
11. C2×#15688997C2semidirect
12. C2×#15688994C2semidirect
13. C2×#15688980C2semidirect
16. C2×C47×#396C2semidirect
18. C23×Dic94C22semidirect
22. C2×#13094002C22semidirect
23. C22×C4⋊Dic47C22semidirect
24. C22×C4⋊Dic47C22semidirect
25. C22×Dic47⋊C4C22semidirect
26. C22×Dic47⋊C4C22semidirect
27. C22×Dic47⋊C4C22semidirect
28. C22×Dic47⋊C4C22semidirect
44. #15689059C22semidirect
45. #15689058C22semidirect
46. #15689046C22semidirect
47. #15689045C22semidirect
48. #15689045C22semidirect
49. #15689036C22semidirect
50. #15689035C22semidirect
51. #15688997C22semidirect
52. #15688994C22semidirect
53. #15688980C22semidirect
56. C2×C47⋊#95C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C22×C4⋊C4×C47C22semidirect
62. C22×C4⋊C4×C47C22semidirect
63. C22×C4⋊C4×C47C22semidirect
67. C47×#396C22semidirect
68. C2×#95×C47C22semidirect
75. C24×D47Q8semidirect
82. C22×Dic94C23semidirect
100. C2×C4⋊Dic47C23semidirect
101. C2×C4⋊Dic47C23semidirect
106. C2×Dic47⋊C4C23semidirect
107. C2×Dic47⋊C4C23semidirect
108. C2×Dic47⋊C4C23semidirect
109. C2×Dic47⋊C4C23semidirect
137. C47⋊#95C23semidirect
138. C47⋊#95C23semidirect
139. C47⋊#95C23semidirect
140. C47⋊#95C23semidirect
141. C47⋊#95C23semidirect
152. C2×C4⋊C4×C47C23semidirect
153. C2×C4⋊C4×C47C23semidirect
154. C2×C4⋊C4×C47C23semidirect
161. #95×C47C23semidirect
197. C23×D47C2×Q8semidirect
455. C2×#396D47semidirect
464. C2×C47#2626semidirect
486. C22×C4⋊C4C2×D47semidirect
487. C22×C4⋊C4C2×D47semidirect
488. C22×C4⋊C4C2×D47semidirect
512. #396C2×D47semidirect
525. C2×#95C2×D47semidirect
526. C47C2×#2626semidirect
578. C2×C4⋊C4C22×D47semidirect
579. C2×C4⋊C4C22×D47semidirect
580. C2×C4⋊C4C22×D47semidirect
619. #95C22×D47semidirect
907. C2#20249198direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940022
C22×C22⋊C4×D472
#202491982
C2×#156890592
C2×#156890582
C2×#156890462
C2×#156890452
C2×#156890362
C2×#156890352
C2×#156889972
C2×#156889942
C2×#156889802
C2×#156889782
C2×C47×#3962
C2×#262647