Finite Group Databasebeta

← C2×#20247268 #26383778

Subgroups — C2×#20247268 #26383778

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×#13094008C211yesmaximal, characteristic, complemented
2C22×#13094006C211yesmaximal, characteristic, complemented
3C22×C4×D188C211yesmaximal, characteristic, complemented
4C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
5#20247268C2116yesmaximal, direct product factor
6C2×#15689060C211yesmaximal, characteristic, complemented
7C2×#15689040C211yesmaximal, characteristic, complemented
8C2×#15689039C211yesmaximal, characteristic, complemented
9C2×#15689032C211yesmaximal, characteristic
10C2×#15689022C211yesmaximal, characteristic, complemented
11C2×#15689021C211yesmaximal, characteristic, complemented
12C2×#15689015C211yesmaximal, characteristic, complemented
13C2×#15688998C211yesmaximal, characteristic, complemented
14C2×#15688997C211yesmaximal, characteristic, complemented
15C2×#15688997C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C24×Dic47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13094008—28no—
24C2×#13094008C2218yescomplemented
25C2×#13094006—28no—
26C2×#13094006C2218yescomplemented
27C2×C4×D188—28no—
28C2×C4×D188C2218yescomplemented
29C2×(C22⋊D47)⋊C4—28no—
30C2×(C22⋊D47)⋊C4C2218yescomplemented
31C22×C4⋊Dic47C2211yescharacteristic
32C22×C4⋊Dic47C2211yescharacteristic
33C22×C4⋊Dic47C2211yescharacteristic
34C22×C4⋊Dic47C2211yescharacteristic
35C22×C4⋊Dic47C2211yescharacteristic
36C22×C4⋊Dic47C2211yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38C22×Dic47⋊C4C2211yescharacteristic
39C22×C22⋊Dic47C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
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×(C2×D47)⋊C4C2211yescharacteristic
48C22×C4×Dic47C2211yescharacteristic
49#15689060C2218yescomplemented
50#15689040C2218yescomplemented
51#15689039C2218yescomplemented
52#15689032C2218yes—
53#15689022C2218yescomplemented
54#15689021C2218yescomplemented
55#15689015C2218yescomplemented
56#15688998C2218yescomplemented
57#15688997C2218yescomplemented
58#15688997C2218yescomplemented
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C42×C47C2211yescharacteristic
68C47×#388C2218yescomplemented
69C2×#95×C47C2211yescharacteristic
70C2×#95×C47C2211yescharacteristic
71C24×D47C2311yescharacteristic
72C24×D47C2311yescharacteristic
73C22×D188—24no—
74C22×D188—24no—
75C22×D188—24no—
76C22×D188C2314yes—
77C22×C22⋊D47—24no—
78C22×C22⋊D47—24no—
79C22×C22⋊D47—24no—
80C22×C22⋊D47—24no—
81C22×C22⋊D47—24no—
82C22×C22⋊D47—42no—
83C22×C22⋊D47C2314yes—
84C22×C22⋊D47C2314yes—
85C23×Dic47—24no—
86C23×Dic47—24no—
87C23×Dic47—42no—
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C23×Dic47C2311yescharacteristic
92C23×Dic47C2314yes—
93C23×Dic47C2311yescharacteristic
94C23×Dic47C2311yescharacteristic
95C22×C4×D47—24no—
96C22×C4×D47—24no—
97C22×C4×D47—24no—
98C22×C4×D47—24no—
99C22×C4×D47—42no—
100C22×C4×D47—42no—
101C22×C4×D47C2314yes—
102C22×C4×D47C2314yes—
103#13094008—232no—
104#13094006—232no—
105C4×D188—232no—
106(C22⋊D47)⋊C4—232no—
107C2×C4⋊Dic47—24no—
108C2×C4⋊Dic47—24no—
109C2×C4⋊Dic47—24no—
110C2×C4⋊Dic47—24no—
111C2×C4⋊Dic47—24no—
112C2×C4⋊Dic47—42no—
113C2×C4⋊Dic47C2314yes—
114C2×C4⋊Dic47C2314yes—
115C2×C4⋊Dic47C2314yes—
116C2×C4⋊Dic47C2314yes—
117C2×C4⋊Dic47C2314yes—
118C2×C4⋊Dic47C2314yes—
119C2×Dic47⋊C4—24no—
120C2×Dic47⋊C4—24no—
121C2×Dic47⋊C4C2314yes—
122C2×Dic47⋊C4C2314yes—
123C2×C22⋊Dic47—24no—
124C2×C22⋊Dic47C2314yes—
125C2×(C2×D47)⋊C4—24no—
126C2×(C2×D47)⋊C4—24no—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—24no—
129C2×(C2×D47)⋊C4—24no—
130C2×(C2×D47)⋊C4—24no—
131C2×(C2×D47)⋊C4—42no—
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×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C2×C4×Dic47—24no—
142C2×C4×Dic47C2314yes—
143C47⋊#95C2314yes—
144C47⋊#95C2314yes—
145C47⋊#95C2314yes—
146C47⋊#95C2314yes—
147C25×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C2×C4⋊C4×C47—24no—
155C2×C4⋊C4×C47C2314yes—
156C2×C22⋊C4×C47—24no—
157C2×C22⋊C4×C47—24no—
158C2×C22⋊C4×C47D418yescomplemented
159C2×C22⋊C4×C47C2314yes—
160C2×C22⋊C4×C47C2314yes—
161C2×C22⋊C4×C47C2314yes—
162C2×C42×C47—24no—
163C2×C42×C47C2314yes—
164#95×C47C2314yes—
165#95×C47C2314yes—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47—22no—
171C24×C47—22no—
172C24×C47C2×D414yes—
173C24×C47C2412yes—
174C24×C47C2411yescharacteristic
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47C2×D414yes—
188C23×D47#4114yes—
189C23×D47C2412yes—
190C23×D47C2412yes—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
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—22no—
204C22×C4×C47—22no—
205C22×C4×C47C2×D414yes—
206C22×C4×C47C2×D414yes—
207C22×C4×C47C2×D414yes—
208C22×C4×C47#4114yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C2×C22⋊D47—232no—
216C2×C22⋊D47—28no—
217C2×C22⋊D47—28no—
218C2×C22⋊D47—28no—
219C2×C22⋊D47—28no—
220C2×C22⋊D47—28no—
221C2×C22⋊D47—44no—
222C2×C22⋊D47—416no—
223C22×Dic47—22no—
224C22×Dic47—22no—
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—28no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—28no—
241C22×Dic47—44no—
242C22×Dic47—416no—
243C22×Dic47C2×D414yes—
244C22×Dic47#4114yes—
245C22×Dic47C2412yes—
246C22×Dic47C2412yes—
247C22×Dic47C2412yes—
248C22×Dic47C2412yes—
249C22×Dic47C2412yes—
250C22×Dic47C2412yes—
251C2×D188—232no—
252C2×D188—28no—
253C2×D188—28no—
254C2×D188—28no—
255C2×C4×D47—28no—
256C2×C4×D47—28no—
257C2×C4×D47—28no—
258C2×C4×D47—28no—
259C2×C4×D47—44no—
260C2×C4×D47—44no—
261C2×C4×D47—416no—
262C2×C4×D47—416no—
263C4⋊C4×C47—28no—
264C22⋊C4×C47—28no—
265C22⋊C4×C47—28no—
266C22⋊C4×C47C2×D4116yescomplemented
267C42×C47—28no—
268C22⋊Dic47—28no—
269(C2×D47)⋊C4—28no—
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—44no—
276(C2×D47)⋊C4C2×D4116yescomplemented
277C4⋊Dic47—28no—
278C4⋊Dic47—28no—
279C4⋊Dic47—28no—
280C4⋊Dic47—28no—
281C4⋊Dic47—28no—
282C4⋊Dic47—44no—
283Dic47⋊C4—28no—
284Dic47⋊C4—28no—
285C4×Dic47—28no—
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×D414yes—
301C23×C47C22×D412yes—
302C23×C47C2×#4112yes—
303C23×C47C2×#4112yes—
304C23×C47C2×#4112yes—
305C23×C47H(5,𝔽2)12yes—
306C23×C472−1+412yes—
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—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—44no—
327C22×D47—44no—
328C22×D47—44no—
329C22×D47—44no—
330C22×D47—44no—
331C22×D47—44no—
332C22×D47—44no—
333C22×D47—44no—
334C22×D47C22×D414yes—
335C22×D47C2×#4114yes—
336C2×C4×C47—28no—
337C2×C4×C47—28no—
338C2×C4×C47—28no—
339C2×C4×C47—28no—
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—22no—
353C2×C4×C47—22no—
354C2×C4×C47—44no—
355C2×C4×C47—44no—
356C2×C4×C47C22×D414yes—
357C2×C4×C47C22×D414yes—
358C2×C4×C47C22×D414yes—
359C2×C4×C47C2×#4114yes—
360C22⋊D47—232no—
361C22⋊D47—416no—
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—416no—
381C2×Dic47—44no—
382C2×Dic47—44no—
383C2×Dic47—44no—
384C2×Dic47—44no—
385C2×Dic47C22×D414yes—
386C2×Dic47C2×#4114yes—
387D188—232no—
388C4×D47—416no—
389C4×D47—416no—
390C2×#2455—471nomaximal, Sylow
391C22×C47—24no—
392C22×C47—24no—
393C22×C47—24no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—416no—
398C22×C47—42no—
399C22×C47#52514yes—
400C22×C47#52514yes—
401C22×C47#53914yes—
402C22×C47D4214yes—
403C22×C47#54714yes—
404C22×C47#54714yes—
405C22×C47#55914yes—
406C22×C47C23×D411yescharacteristic
407C22×C47C23×D411yescharacteristic
408C22×C47C22×#4111yescharacteristic
409C22×C47C22×#4111yescharacteristic
410C22×C47C22×#4111yescharacteristic
411C22×C47C2×H(5,𝔽2)11yescharacteristic
412C22×C47C2×2−1+411yescharacteristic
413C2×D47—24no—
414C2×D47—24no—
415C2×D47—24no—
416C2×D47—24no—
417C2×D47—24no—
418C2×D47—24no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—42no—
424C2×D47—42no—
425C2×D47—416no—
426C2×D47—416no—
427C2×D47—42no—
428C2×D47—42no—
429C4×C47—24no—
430C4×C47—24no—
431C4×C47—24no—
432C4×C47—24no—
433C4×C47—42no—
434C4×C47—42no—
435Dic47—24no—
436Dic47—24no—
437Dic47—42no—
438Dic47—42no—
439Dic47—42no—
440Dic47—42no—
441C22×#123—471no—
442C22×#123—471no—
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×#388D4711yescharacteristic, complemented
454C2×#385—471no—
455C2×#385—471no—
456C2×#385—471no—
457C2×C47—44no—
458C2×C47#245518yescomplemented
459C2×C47C2×#52511yescharacteristic
460C2×C47C2×#52511yescharacteristic
461C2×C47C2×#53911yescharacteristic
462C2×C47C2×D4211yescharacteristic
463C2×C47C2×#54711yescharacteristic
464C2×C47C2×#54711yescharacteristic
465C2×C47C2×#55911yescharacteristic
466D47—44no—
467D47—44no—
468C23×D4—471no—
469C23×D4—471no—
470C23×D4—471no—
471C24×C4—471no—
472C24×C4—471no—
473C24×C4—471no—
474C2×#123—478no—
475C2×#123—478no—
476C2×#123—948no—
477C2×#123—948no—
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⋊C4—471no—
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×C42C2×D4711yescharacteristic
505#399—478no—
506#394—478no—
507#394—478no—
508#392—478no—
509#389—478no—
510#389—478no—
511#388—478no—
512#388C2×D4718yescomplemented
513#385—478no—
514#385—478no—
515#385—478no—
516C2×#95—471no—
517C2×#95—471no—
518C2×#95—471no—
519C2×#95—471no—
520C2×#95C2×D4711yescharacteristic
521C2×#95C2×D4711yescharacteristic
522C47C2×#245511yescharacteristic, complemented, Sylow
523C25—471no—
524C25—471no—
525C25C22×D4711yescharacteristic
526C22×D4—474no—
527C22×D4—474no—
528C22×D4—474no—
529C22×D4—944no—
530C22×D4—944no—
531C22×D4—944no—
532C22×D4—944no—
533C22×D4—944no—
534C22×D4—944no—
535C22×D4—944no—
536C22×D4—944no—
537C22×D4—1882no—
538C23×C4—471no—
539C23×C4—471no—
540C23×C4—471no—
541C23×C4—471no—
542C23×C4—471no—
543C23×C4—471no—
544C23×C4—474no—
545C23×C4—474no—
546C23×C4—474no—
547C23×C4—944no—
548C23×C4—944no—
549C23×C4—944no—
550C23×C4—944no—
551C23×C4—944no—
552C23×C4—944no—
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
562#123—9432no—
563#123—9432no—
564C4×D4—9432no—
565C4×D4—9432no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—474no—
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—944no—
582C2×C4⋊C4—1882no—
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⋊C4D18818yescomplemented
605C2×C22⋊C4C22×D4714yes—
606C2×C22⋊C4C22×D4714yes—
607C2×C22⋊C4C22×D4714yes—
608C2×C42—24no—
609C2×C42—474no—
610C2×C42—944no—
611C2×C42C22×D4714yes—
612#95—474no—
613#95—474no—
614#95—474no—
615#95—474no—
616#95C22×D4714yes—
617#95C22×D4714yes—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—474no—
625C24—474no—
626C24—472no—
627C24—472no—
628C24—942no—
629C24—942no—
630C24—942no—
631C24—942no—
632C24—942no—
633C24—942no—
634C24—942no—
635C24—942no—
636C24—942no—
637C24—942no—
638C24—942no—
639C24—942no—
640C24C2×D18814yes—
641C24C23×D4712yes—
642C24C23×D4711yescharacteristic
643C2×D4—948no—
644C2×D4—948no—
645C2×D4—9432no—
646C2×D4—948no—
647C2×D4—948no—
648C2×D4—9432no—
649C2×D4—948no—
650C2×D4—948no—
651C2×D4—948no—
652C2×D4—948no—
653C2×D4—1884no—
654C2×D4—18816no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—474no—
670C22×C4—474no—
671C22×C4—472no—
672C22×C4—472no—
673C22×C4—472no—
674C22×C4—472no—
675C22×C4—472no—
676C22×C4—472no—
677C22×C4—948no—
678C22×C4—948no—
679C22×C4—948no—
680C22×C4—942no—
681C22×C4—942no—
682C22×C4—942no—
683C22×C4—942no—
684C22×C4—942no—
685C22×C4—942no—
686C22×C4—942no—
687C22×C4—942no—
688C22×C4—942no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4—948no—
692C22×C4—942no—
693C22×C4—942no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4—942no—
697C22×C4—948no—
698C22×C4—948no—
699C22×C4—1884no—
700C22×C4—1884no—
701C22×C4—18816no—
702C22×C4—18816no—
703C22×C4—1884no—
704C22×C4—18816no—
705C22×C4C2×D18814yes—
706C22×C4C2×D18814yes—
707C22×C4D4×D4714yes—
708C22×C4#1062535214yes—
709C22×C4C23×D4712yes—
710C22×C4C23×D4712yes—
711C22×C4C23×D4712yes—
712C22×C4C23×D4712yes—
713C22×C4C23×D4712yes—
714C22×C4C23×D4712yes—
715C4⋊C4—28no—
716C4⋊C4—948no—
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×D188116yescomplemented
736C42—28no—
737C42—948no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—474no—
752C23—474no—
753C23—948no—
754C23—948no—
755C23—948no—
756C23—948no—
757C23—948no—
758C23—942no—
759C23—942no—
760C23—942no—
761C23—942no—
762C23—942no—
763C23—942no—
764C23—942no—
765C23—942no—
766C23—942no—
767C23—942no—
768C23—942no—
769C23—942no—
770C23—948no—
771C23—1884no—
772C23—1884no—
773C23—1884no—
774C23—1884no—
775C23—1884no—
776C23—1884no—
777C23—1884no—
778C23—1884no—
779C23C2×D4×D4712yes—
780C23C22×D18814yes—
781C23C22×D18812yes—
782C23#41×D4712yes—
783C23#41×D4712yes—
784C23C2×#1062535212yes—
785C23#1309407012yes—
786C23#1309407112yes—
787C23C24×D4711yescharacteristic
788D4—9432no—
789D4—9432no—
790D4—18816no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
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—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—474no—
812C2×C4—474no—
813C2×C4—948no—
814C2×C4—948no—
815C2×C4—942no—
816C2×C4—942no—
817C2×C4—942no—
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—18816no—
832C2×C4—18816no—
833C2×C4—18816no—
834C2×C4—1884no—
835C2×C4—1884no—
836C2×C4—1884no—
837C2×C4—1884no—
838C2×C4C2×D4×D4714yes—
839C2×C4C22×D18814yes—
840C2×C4C22×D18814yes—
841C2×C4C2×#1062535214yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—416no—
850C22—944no—
851C22—944no—
852C22—944no—
853C22—944no—
854C22—944no—
855C22—944no—
856C22—1882no—
857C22—1882no—
858C22—1882no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—18816no—
865C22—18816no—
866C22#1568963314yes—
867C22#1568963514yes—
868C22#1568971414yes—
869C22D4×D18814yes—
870C22#1568977114yes—
871C22#1568977714yes—
872C22#1568985514yes—
873C22C22×D4×D4711yescharacteristic
874C22C23×D18811yescharacteristic
875C22C2×#41×D4711yescharacteristic
876C22C2×#41×D4711yescharacteristic
877C22C22×#1062535211yescharacteristic
878C22C2×#1309407011yescharacteristic
879C22C2×#1309407111yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—944no—
887C4—944no—
888C4—1882no—
889C4—1882no—
890C4—1882no—
891C4—1882no—
892C2—44no—
893C2—1884no—
894C2—1884no—
895C2#2024726818yesdirect product factor
896C2C2×#1568963311yescharacteristic
897C2C2×#1568963511yescharacteristic
898C2C2×#1568971411yescharacteristic
899C2C2×D4×D18811yescharacteristic
900C2C2×#1568977111yescharacteristic
901C2C2×#1568977711yescharacteristic
902C2C2×#1568985511yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC2×#15689032C2
hypercenterC2×#388D47
hypocenterC47C2×#2455
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13094008C2semidirect
2. C22×#13094006C2semidirect
3. C22×C4×D188C2semidirect
4. C22×(C22⋊D47)⋊C4C2semidirect
5. #20247268C2direct (N × H)
6. C2×#15689060C2semidirect
7. C2×#15689040C2semidirect
8. C2×#15689039C2semidirect
10. C2×#15689022C2semidirect
11. C2×#15689021C2semidirect
12. C2×#15689015C2semidirect
13. C2×#15688998C2semidirect
14. C2×#15688997C2semidirect
15. C2×#15688997C2semidirect
16. C2×C47×#388C2semidirect
24. C2×#13094008C22semidirect
26. C2×#13094006C22semidirect
28. C2×C4×D188C22semidirect
30. C2×(C22⋊D47)⋊C4C22semidirect
49. #15689060C22semidirect
50. #15689040C22semidirect
51. #15689039C22semidirect
53. #15689022C22semidirect
54. #15689021C22semidirect
55. #15689015C22semidirect
56. #15688998C22semidirect
57. #15688997C22semidirect
58. #15688997C22semidirect
68. C47×#388C22semidirect
132. C2×(C2×D47)⋊C4D4semidirect
158. C2×C22⋊C4×C47D4semidirect
266. C22⋊C4×C47C2×D4semidirect
276. (C2×D47)⋊C4C2×D4semidirect
453. C2×#388D47semidirect
458. C2×C47#2455semidirect
512. #388C2×D47semidirect
522. C47C2×#2455semidirect
604. C2×C22⋊C4D188semidirect
735. C22⋊C4C2×D188semidirect
895. C2#20247268direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940082
C22×#130940062
C22×C4×D1882
C22×(C22⋊D47)⋊C42
#202472682
C2×#156890602
C2×#156890402
C2×#156890392
C2×#156890322
C2×#156890222
C2×#156890212
C2×#156890152
C2×#156889982
C2×#156889972
C2×C47×#3882
C2×#245547