Finite Group Databasebeta

← C2×#20248448 #26386355

Subgroups — C2×#20248448 #26386355

Order 12032.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094018C211yesmaximal, characteristic, complemented
2C22×#13094007C211yesmaximal, characteristic, complemented
3#20248448C2116yesmaximal, direct product factor
4C2×#15689057C211yesmaximal, characteristic, complemented
5C2×#15689046C211yesmaximal, characteristic, complemented
6C2×#15689041C211yesmaximal, characteristic, complemented
7C2×#15689032C211yesmaximal, characteristic
8C2×#15689025C211yesmaximal, characteristic, complemented
9C2×#15689023C211yesmaximal, characteristic, complemented
10C2×#15689023C211yesmaximal, characteristic, complemented
11C2×#15689014C211yesmaximal, characteristic, complemented
12C2×#15689012C211yesmaximal, characteristic, complemented
13C2×#15689012C211yesmaximal, characteristic, complemented
14C2×#15689002C211yesmaximal, characteristic, complemented
15C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C2×#13094018—28no—
21C2×#13094018C2218yescomplemented
22C2×#13094007—28no—
23C2×#13094007C2218yescomplemented
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
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
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45#15689057C2218yescomplemented
46#15689046C2218yescomplemented
47#15689041C2218yescomplemented
48#15689032C2218yes—
49#15689025C2218yescomplemented
50#15689023C2218yescomplemented
51#15689023C2218yescomplemented
52#15689014C2218yescomplemented
53#15689012C2218yescomplemented
54#15689012C2218yescomplemented
55#15689002C2218yescomplemented
56C4×Dic47⋊C4C2218yescomplemented
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C24×C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C42×C47C2211yescharacteristic
65C22×C42×C47C2211yescharacteristic
66C4×C22⋊C4×C47C2218yescomplemented
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C24×D47C2311yescharacteristic
71C22×D188—24no—
72C22×D188—42no—
73C22×D188—42no—
74C22×D188C2314yes—
75C22×C22⋊D47—24no—
76C22×C22⋊D47—24no—
77C22×C22⋊D47—24no—
78C22×C22⋊D47—24no—
79C22×C22⋊D47—42no—
80C22×C22⋊D47—42no—
81C22×C22⋊D47C2314yes—
82C22×C22⋊D47C2314yes—
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89#13094018—232no—
90#13094007—232no—
91C2×C4⋊Dic47—42no—
92C2×C4⋊Dic47C2314yes—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—24no—
95C2×Dic47⋊C4—24no—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—42no—
98C2×Dic47⋊C4D418yescomplemented
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×C22⋊Dic47—24no—
106C2×C22⋊Dic47—42no—
107C2×C22⋊Dic47C2314yes—
108C2×C22⋊Dic47C2314yes—
109C2×(C2×D47)⋊C4—24no—
110C2×(C2×D47)⋊C4—24no—
111C2×(C2×D47)⋊C4—24no—
112C2×(C2×D47)⋊C4—24no—
113C2×(C2×D47)⋊C4—24no—
114C2×(C2×D47)⋊C4—24no—
115C2×(C2×D47)⋊C4—24no—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—42no—
118C2×(C2×D47)⋊C4—42no—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×C4×Dic47—24no—
130C2×C4×Dic47—42no—
131C2×C4×Dic47C2314yes—
132C2×C4×Dic47C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C25×C47C2311yescharacteristic
138C23×C4×C47—24no—
139C23×C4×C47—24no—
140C23×C4×C47—42no—
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2314yes—
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C2×C22⋊C4×C47—24no—
149C2×C22⋊C4×C47—24no—
150C2×C22⋊C4×C47C2314yes—
151C2×C22⋊C4×C47C2314yes—
152C2×C42×C47—24no—
153C2×C42×C47—42no—
154C2×C42×C47C2314yes—
155C2×C42×C47C2314yes—
156#95×C47C2314yes—
157#95×C47C2314yes—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47#4114yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
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×D47C2412yes—
182C23×D47C2412yes—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—28no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—28no—
200C22×C4×C47—44no—
201C22×C4×C47—416no—
202C22×C4×C47C2×D414yes—
203C22×C4×C47#4114yes—
204C22×C4×C47#4114yes—
205C22×C4×C47C2412yes—
206C22×C4×C47C2412yes—
207C22×C4×C47C2412yes—
208C22×C4×C47C2412yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2412yes—
211C2×C22⋊D47—28no—
212C2×C22⋊D47—28no—
213C2×C22⋊D47—28no—
214C2×C22⋊D47—28no—
215C2×C22⋊D47—44no—
216C2×C22⋊D47—44no—
217C2×C22⋊D47—416no—
218C2×C22⋊D47—416no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
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×Dic47C2×D414yes—
235C22×Dic47C2×D414yes—
236C22×Dic47#4114yes—
237C22×Dic47C2412yes—
238C22×Dic47C2412yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C2×D188—28no—
244C2×D188—44no—
245C2×D188—44no—
246C2×D188—416no—
247C22⋊C4×C47—28no—
248C22⋊C4×C47—28no—
249C42×C47—28no—
250C42×C47—44no—
251C22⋊Dic47—28no—
252C22⋊Dic47—44no—
253(C2×D47)⋊C4—28no—
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—28no—
256(C2×D47)⋊C4—28no—
257(C2×D47)⋊C4—28no—
258(C2×D47)⋊C4—28no—
259(C2×D47)⋊C4—28no—
260(C2×D47)⋊C4—28no—
261(C2×D47)⋊C4—44no—
262(C2×D47)⋊C4—44no—
263C4⋊Dic47—44no—
264Dic47⋊C4—28no—
265Dic47⋊C4—28no—
266Dic47⋊C4—28no—
267Dic47⋊C4—28no—
268Dic47⋊C4—44no—
269Dic47⋊C4C2×D4116yescomplemented
270C4×Dic47—28no—
271C4×Dic47—44no—
272C23×C47—28no—
273C23×C47—28no—
274C23×C47—28no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—44no—
282C23×C47—44no—
283C23×C47—44no—
284C23×C47—44no—
285C23×C47C22×D412yes—
286C23×C47C2×#4112yes—
287C23×C47C2×#4114yes—
288C23×C47C2×#4112yes—
289C23×C47C2×#4112yes—
290C23×C47C2×#4112yes—
291C23×C47H(5,𝔽2)12yes—
292C23×C47H(5,𝔽2)12yes—
293C23×C47C2511yescharacteristic
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—44no—
309C22×D47—44no—
310C22×D47—44no—
311C22×D47—44no—
312C22×D47—44no—
313C22×D47—44no—
314C22×D47—44no—
315C22×D47—44no—
316C22×D47—44no—
317C22×D47—44no—
318C22×D47—44no—
319C22×D47—44no—
320C22×D47—44no—
321C22×D47—44no—
322C2×C4×C47—28no—
323C2×C4×C47—28no—
324C2×C4×C47—28no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—416no—
341C2×C4×C47—44no—
342C2×C4×C47—44no—
343C2×C4×C47—44no—
344C2×C4×C47C22×D414yes—
345C2×C4×C47C2×#4114yes—
346C2×C4×C47C2×#4114yes—
347C22⋊D47—416no—
348C22⋊D47—416no—
349C2×Dic47—28no—
350C2×Dic47—28no—
351C2×Dic47—28no—
352C2×Dic47—22no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—22no—
357C2×Dic47—22no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—22no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—44no—
368C2×Dic47—44no—
369C2×Dic47—44no—
370C2×Dic47C22×D414yes—
371C2×Dic47C22×D414yes—
372C2×Dic47C2×#4114yes—
373D188—416no—
374C2×#2554—471nomaximal, Sylow
375C22×C47—24no—
376C22×C47—24no—
377C22×C47—24no—
378C22×C47—42no—
379C22×C47—42no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—416no—
383C22×C47#52914yes—
384C22×C47#53214yes—
385C22×C47#53814yes—
386C22×C47#54614yes—
387C22×C47#55014yes—
388C22×C47#55114yes—
389C22×C47#55314yes—
390C22×C47C23×D411yescharacteristic
391C22×C47C22×#4111yescharacteristic
392C22×C47C22×#4111yescharacteristic
393C22×C47C22×#4111yescharacteristic
394C22×C47C22×#4111yescharacteristic
395C22×C47C2×H(5,𝔽2)11yescharacteristic
396C22×C47C2×H(5,𝔽2)11yescharacteristic
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—42no—
403C2×D47—42no—
404C2×D47—42no—
405C2×D47—42no—
406C2×D47—42no—
407C2×D47—42no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—88no—
412C2×D47—88no—
413C4×C47—24no—
414C4×C47—24no—
415C4×C47—24no—
416C4×C47—42no—
417C4×C47—42no—
418C4×C47—42no—
419Dic47—24no—
420Dic47—24no—
421Dic47—24no—
422Dic47—42no—
423Dic47—42no—
424Dic47—42no—
425C22×#126—471no—
426C22×#123—471no—
427#2554—4716no—
428C2×#398—471no—
429C2×#396—471no—
430C2×#394—471no—
431C2×#392—471no—
432C2×#390—471no—
433C2×#390—471no—
434C2×#390—471no—
435C2×#388—471no—
436C2×#388—471no—
437C2×#388—471no—
438C2×#386—471no—
439C2×C4×C4⋊C4—471no—
440C2×C4×C22⋊C4D4711yescharacteristic, complemented
441C2×C47—44no—
442C2×C47#255418yescomplemented
443C2×C47C2×#52911yescharacteristic
444C2×C47C2×#53211yescharacteristic
445C2×C47C2×#53811yescharacteristic
446C2×C47C2×#54611yescharacteristic
447C2×C47C2×#55011yescharacteristic
448C2×C47C2×#55111yescharacteristic
449C2×C47C2×#55311yescharacteristic
450D47—82no—
451D47—82no—
452C23×D4—471no—
453C23×D4—471no—
454C23×D4—471no—
455C24×C4C2×D4711yescharacteristic
456C2×#126—478no—
457C2×#126—948no—
458C2×#123—478no—
459C2×#123—948no—
460C22×C4⋊C4—471no—
461C22×C4⋊C4—471no—
462C22×C4⋊C4—471no—
463C22×C4⋊C4—471no—
464C22×C4⋊C4—471no—
465C22×C4⋊C4—471no—
466C22×C4⋊C4—471no—
467C22×C22⋊C4—471no—
468C22×C22⋊C4—471no—
469C22×C22⋊C4—471no—
470C22×C22⋊C4—471no—
471C22×C22⋊C4—471no—
472C22×C22⋊C4—471no—
473C22×C22⋊C4—471no—
474C22×C22⋊C4—471no—
475C22×C22⋊C4—471no—
476C22×C22⋊C4—471no—
477C22×C22⋊C4—471no—
478C22×C22⋊C4—471no—
479C22×C22⋊C4C2×D4711yescharacteristic
480C22×C22⋊C4C2×D4711yescharacteristic
481C22×C42—471no—
482C22×C42—471no—
483C22×C42C2×D4711yescharacteristic
484C22×C42C2×D4711yescharacteristic
485#398—478no—
486#396—478no—
487#394—478no—
488#392—478no—
489#390—478no—
490#390—478no—
491#390—478no—
492#388—478no—
493#388—478no—
494#388—478no—
495#386—478no—
496C4×C4⋊C4—478no—
497C4×C22⋊C4C2×D4718yescomplemented
498C2×#95—471no—
499C2×#95—471no—
500C2×#95—471no—
501C2×#95—471no—
502C2×#95C2×D4711yescharacteristic
503C2×#95C2×D4711yescharacteristic
504C47C2×#255411yescharacteristic, complemented, Sylow
505C25—471no—
506C25—471no—
507C25C22×D4711yescharacteristic
508C22×D4—474no—
509C22×D4—474no—
510C22×D4—474no—
511C22×D4—944no—
512C22×D4—944no—
513C22×D4—944no—
514C22×D4—944no—
515C22×D4—944no—
516C22×D4—1882no—
517C22×D4—1882no—
518C22×D4—1882no—
519C22×D4—1882no—
520C23×C4—24no—
521C23×C4—24no—
522C23×C4—42no—
523C23×C4—471no—
524C23×C4—471no—
525C23×C4—471no—
526C23×C4—471no—
527C23×C4—471no—
528C23×C4—471no—
529C23×C4C22×D4711yescharacteristic
530C23×C4C22×D4711yescharacteristic
531C23×C4C22×D4711yescharacteristic
532C23×C4C22×D4714yes—
533C23×C4C22×D4711yescharacteristic
534C23×C4C22×D4711yescharacteristic
535C23×C4C22×D4711yescharacteristic
536#126—9432no—
537#123—9432no—
538C2×C4⋊C4—478no—
539C2×C4⋊C4—474no—
540C2×C4⋊C4—474no—
541C2×C4⋊C4—474no—
542C2×C4⋊C4—474no—
543C2×C4⋊C4—474no—
544C2×C4⋊C4—474no—
545C2×C4⋊C4—474no—
546C2×C4⋊C4—944no—
547C2×C4⋊C4—944no—
548C2×C4⋊C4—944no—
549C2×C4⋊C4—944no—
550C2×C4⋊C4—1882no—
551C2×C4⋊C4—1882no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—474no—
555C2×C22⋊C4—474no—
556C2×C22⋊C4—474no—
557C2×C22⋊C4—474no—
558C2×C22⋊C4—474no—
559C2×C22⋊C4—474no—
560C2×C22⋊C4—474no—
561C2×C22⋊C4—474no—
562C2×C22⋊C4—474no—
563C2×C22⋊C4—474no—
564C2×C22⋊C4—474no—
565C2×C22⋊C4—474no—
566C2×C22⋊C4—944no—
567C2×C22⋊C4—944no—
568C2×C22⋊C4—944no—
569C2×C22⋊C4—944no—
570C2×C22⋊C4—944no—
571C2×C22⋊C4—944no—
572C2×C22⋊C4—944no—
573C2×C22⋊C4—944no—
574C2×C22⋊C4—944no—
575C2×C22⋊C4—1882no—
576C2×C22⋊C4—1882no—
577C2×C22⋊C4—1882no—
578C2×C22⋊C4C22×D4714yes—
579C2×C22⋊C4C22×D4714yes—
580C2×C42—24no—
581C2×C42—42no—
582C2×C42—474no—
583C2×C42—474no—
584C2×C42—944no—
585C2×C42—1882no—
586C2×C42C22×D4714yes—
587C2×C42C22×D4714yes—
588#95—474no—
589#95—474no—
590#95—474no—
591#95—474no—
592#95C22×D4714yes—
593#95C22×D4714yes—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—472no—
601C24—472no—
602C24—942no—
603C24—942no—
604C24—942no—
605C24—942no—
606C24—942no—
607C24—942no—
608C24—942no—
609C24—942no—
610C24—942no—
611C24—942no—
612C24—942no—
613C24—942no—
614C24—942no—
615C24—942no—
616C24#1062535014yes—
617C24C23×D4712yes—
618C24C23×D4711yescharacteristic
619C2×D4—948no—
620C2×D4—948no—
621C2×D4—948no—
622C2×D4—948no—
623C2×D4—948no—
624C2×D4—1884no—
625C2×D4—1884no—
626C2×D4—18816no—
627C2×D4—1884no—
628C2×D4—1884no—
629C2×D4—18816no—
630C2×D4—18816no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—28no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—28no—
648C22×C4—44no—
649C22×C4—416no—
650C22×C4—474no—
651C22×C4—474no—
652C22×C4—474no—
653C22×C4—472no—
654C22×C4—472no—
655C22×C4—472no—
656C22×C4—472no—
657C22×C4—472no—
658C22×C4—472no—
659C22×C4—942no—
660C22×C4—942no—
661C22×C4—942no—
662C22×C4—942no—
663C22×C4—942no—
664C22×C4—942no—
665C22×C4—942no—
666C22×C4—942no—
667C22×C4—942no—
668C22×C4—942no—
669C22×C4—942no—
670C22×C4—942no—
671C22×C4—942no—
672C22×C4—942no—
673C22×C4—942no—
674C22×C4#1062535014yes—
675C22×C4#1062535014yes—
676C22×C4D4×D4714yes—
677C22×C4C23×D4712yes—
678C22×C4C23×D4712yes—
679C22×C4C23×D4712yes—
680C22×C4C23×D4712yes—
681C22×C4C23×D4712yes—
682C22×C4C23×D4712yes—
683C4⋊C4—4716no—
684C4⋊C4—948no—
685C4⋊C4—948no—
686C4⋊C4—948no—
687C4⋊C4—948no—
688C4⋊C4—1884no—
689C4⋊C4—1884no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—948no—
693C22⋊C4—948no—
694C22⋊C4—948no—
695C22⋊C4—948no—
696C22⋊C4—948no—
697C22⋊C4—948no—
698C22⋊C4—948no—
699C22⋊C4—948no—
700C22⋊C4—948no—
701C22⋊C4—1884no—
702C22⋊C4—1884no—
703C22⋊C4—1884no—
704C42—28no—
705C42—44no—
706C42—948no—
707C42—1884no—
708C23—28no—
709C23—28no—
710C23—28no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—942no—
722C23—942no—
723C23—942no—
724C23—942no—
725C23—942no—
726C23—942no—
727C23—942no—
728C23—942no—
729C23—942no—
730C23—942no—
731C23—942no—
732C23—942no—
733C23—942no—
734C23—942no—
735C23—1884no—
736C23—1884no—
737C23—1884no—
738C23—1884no—
739C23—1884no—
740C23—1884no—
741C23—1884no—
742C23—1884no—
743C23—1884no—
744C23—1884no—
745C23—1884no—
746C23—1884no—
747C23—1884no—
748C23—1884no—
749C23C2×D4×D4712yes—
750C23#41×D4712yes—
751C23C2×#1062535014yes—
752C23C2×#1062535012yes—
753C23C2×#1062535012yes—
754C23C2×#1062535012yes—
755C23#1309406912yes—
756C23#1309407012yes—
757C23C24×D4711yescharacteristic
758D4—18816no—
759D4—18816no—
760D4—18816no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—416no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—474no—
784C2×C4—474no—
785C2×C4—474no—
786C2×C4—948no—
787C2×C4—948no—
788C2×C4—948no—
789C2×C4—942no—
790C2×C4—942no—
791C2×C4—942no—
792C2×C4—942no—
793C2×C4—942no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—942no—
797C2×C4—942no—
798C2×C4—942no—
799C2×C4—942no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—1884no—
805C2×C4—1884no—
806C2×C4—1884no—
807C2×C4C2×D4×D4714yes—
808C2×C4C2×#1062535014yes—
809C2×C4C2×#1062535014yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—416no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—3768no—
819C22—3768no—
820C22—1882no—
821C22—1882no—
822C22—1882no—
823C22—1882no—
824C22—1882no—
825C22—1882no—
826C22—1882no—
827C22—1882no—
828C22—1882no—
829C22—1882no—
830C22—1882no—
831C22—1882no—
832C22—1882no—
833C22—1882no—
834C22#1568965714yes—
835C22#1568967014yes—
836C22#1568970614yes—
837C22#1568976314yes—
838C22#1568979414yes—
839C22#1568979714yes—
840C22#1568982214yes—
841C22C22×D4×D4711yescharacteristic
842C22C2×#41×D4711yescharacteristic
843C22C22×#1062535011yescharacteristic
844C22C22×#1062535011yescharacteristic
845C22C22×#1062535011yescharacteristic
846C22C2×#1309406911yescharacteristic
847C22C2×#1309407011yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—944no—
855C4—944no—
856C4—944no—
857C4—1882no—
858C4—1882no—
859C4—1882no—
860C2—44no—
861C2—3762no—
862C2—3762no—
863C2#2024844818yesdirect product factor
864C2C2×#1568965711yescharacteristic
865C2C2×#1568967011yescharacteristic
866C2C2×#1568970611yescharacteristic
867C2C2×#1568976311yescharacteristic
868C2C2×#1568979411yescharacteristic
869C2C2×#1568979711yescharacteristic
870C2C2×#1568982211yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C4×C22⋊C4×C47C2
socleC24×C47C24
prime radicalC2×#15689032C2
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C2×#2554
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#13094018C2semidirect
2. C22×#13094007C2semidirect
3. #20248448C2direct (N × H)
4. C2×#15689057C2semidirect
5. C2×#15689046C2semidirect
6. C2×#15689041C2semidirect
8. C2×#15689025C2semidirect
9. C2×#15689023C2semidirect
10. C2×#15689023C2semidirect
11. C2×#15689014C2semidirect
12. C2×#15689012C2semidirect
13. C2×#15689012C2semidirect
14. C2×#15689002C2semidirect
15. C2×C4×Dic47⋊C4C2semidirect
16. C2×C4×C22⋊C4×C47C2semidirect
21. C2×#13094018C22semidirect
23. C2×#13094007C22semidirect
45. #15689057C22semidirect
46. #15689046C22semidirect
47. #15689041C22semidirect
49. #15689025C22semidirect
50. #15689023C22semidirect
51. #15689023C22semidirect
52. #15689014C22semidirect
53. #15689012C22semidirect
54. #15689012C22semidirect
55. #15689002C22semidirect
56. C4×Dic47⋊C4C22semidirect
66. C4×C22⋊C4×C47C22semidirect
98. C2×Dic47⋊C4D4semidirect
269. Dic47⋊C4C2×D4semidirect
440. C2×C4×C22⋊C4D47semidirect
442. C2×C47#2554semidirect
497. C4×C22⋊C4C2×D47semidirect
504. C47C2×#2554semidirect
863. C2#20248448direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940182
C22×#130940072
#202484482
C2×#156890572
C2×#156890462
C2×#156890412
C2×#156890322
C2×#156890252
C2×#156890232
C2×#156890142
C2×#156890122
C2×#156890022
C2×C4×Dic47⋊C42
C2×C4×C22⋊C4×C472
C2×#255447