Finite Group Databasebeta

← C2×#20246364 #26375764

Subgroups — C2×#20246364 #26375764

Order 12032.

5942 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093994C211yesmaximal, characteristic
2C22×#13093986C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
4C23×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
6#20246364C2116yesmaximal, direct product factor
7C2×#15689024C211yesmaximal, characteristic, complemented
8C2×#15689013C211yesmaximal, characteristic, complemented
9C2×#15689012C211yesmaximal, characteristic, complemented
10C2×#15689001C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15689000C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C24×Dic47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic
24C23×C4×D47C2211yescharacteristic, complemented
25C2×#13093994C4116yescomplemented
26C2×#13093994C2218yes—
27C2×#13093986—28no—
28C2×#13093986C2218yescomplemented
29C2×C4×C22⋊D47—28no—
30C2×C4×C22⋊D47C2218yescomplemented
31C22×Dic47⋊C4C2211yescharacteristic, complemented
32C22×C22⋊Dic47C2211yescharacteristic
33C22×(C2×D47)⋊C4—28no—
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)⋊C4C2218yescomplemented
43C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
46C2×C22⋊C4×D47—28no—
47C2×C22⋊C4×D47C2218yescomplemented
48C22×C4×Dic47C2211yescharacteristic, complemented
49C22×C4×Dic47C2211yescharacteristic, complemented
50C22×C4×Dic47C2211yescharacteristic, complemented
51#15689024C2218yescomplemented
52#15689013C2218yescomplemented
53#15689012C2218yescomplemented
54#15689001C2218yescomplemented
55#15689001C2218yescomplemented
56#15689000C2218yescomplemented
57#15688994C2218yescomplemented
58C22⋊C4×Dic47C2218yescomplemented
59#15688970C2218yescomplemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C2×C47⋊#95C2211yescharacteristic, complemented
64C24×C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic, complemented
66C22×C4⋊C4×C47C2211yescharacteristic, complemented
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C47×#385C2218yescomplemented
70C2×#95×C47C2211yescharacteristic, complemented
71C2×#95×C47C2211yescharacteristic, complemented
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—24no—
76C24×D47—42no—
77C24×D47—42no—
78C24×D47C2×C418yescomplemented
79C24×D47C2311yescharacteristic
80C24×D47C2311yescharacteristic
81C24×D47C2314yes—
82C24×D47C2311yescharacteristic
83C22×D188—24no—
84C22×D188—24no—
85C22×D188—42no—
86C22×D188—42no—
87C22×D188C2×C418yescomplemented
88C22×D188C2×C418yescomplemented
89C22×D188C2314yes—
90C22×D188C2314yes—
91C22×C22⋊D47—24no—
92C22×C22⋊D47—24no—
93C22×C22⋊D47C2×C418yescomplemented
94C22×C22⋊D47C2314yes—
95C23×Dic47—24no—
96C23×Dic47—24no—
97C23×Dic47—42no—
98C23×Dic47C2311yescharacteristic
99C23×Dic47C2314yes—
100C23×Dic47C2311yescharacteristic
101C23×Dic47C2311yescharacteristic
102C23×Dic47C2311yescharacteristic
103C23×Dic47C2311yescharacteristic
104C22×C4×D47—24no—
105C22×C4×D47—24no—
106C22×C4×D47—24no—
107C22×C4×D47—24no—
108C22×C4×D47—24no—
109C22×C4×D47—24no—
110C22×C4×D47—42no—
111C22×C4×D47—42no—
112C22×C4×D47—42no—
113C22×C4×D47C2314yes—
114C22×C4×D47C2314yes—
115C22×C4×D47C2314yescomplemented
116#13093994C2×C4164yescomplemented
117#13093986—232no—
118C4×C22⋊D47—232no—
119C2×Dic47⋊C4—24no—
120C2×Dic47⋊C4C2314yescomplemented
121C2×C22⋊Dic47D418yescomplemented
122C2×C22⋊Dic47C2314yes—
123C2×(C2×D47)⋊C4—24no—
124C2×(C2×D47)⋊C4—24no—
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—232no—
131C2×(C2×D47)⋊C4—42no—
132C2×(C2×D47)⋊C4C2×C418yescomplemented
133C2×(C2×D47)⋊C4C2×C418yescomplemented
134C2×(C2×D47)⋊C4D418yescomplemented
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×(C2×D47)⋊C4C2314yes—
142C2×(C2×D47)⋊C4C2314yes—
143C2×(C2×D47)⋊C4C2314yescomplemented
144C2×(C2×D47)⋊C4C2314yescomplemented
145C2×(C2×D47)⋊C4C2314yescomplemented
146C22⋊C4×D47—232no—
147C2×C4×Dic47—24no—
148C2×C4×Dic47—24no—
149C2×C4×Dic47—42no—
150C2×C4×Dic47C2314yescomplemented
151C2×C4×Dic47C2314yescomplemented
152C2×C4×Dic47C2314yescomplemented
153C47⋊#95C2314yescomplemented
154C47⋊#95C2314yescomplemented
155C47⋊#95C2314yescomplemented
156C47⋊#95C2314yescomplemented
157C25×C47C2311yescharacteristic
158C23×C4×C47—24no—
159C23×C4×C47—24no—
160C23×C4×C47—42no—
161C23×C4×C47C2311yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C23×C4×C47C2314yes—
165C23×C4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C23×C4×C47C2311yescharacteristic
168C2×C4⋊C4×C47—24no—
169C2×C4⋊C4×C47—42no—
170C2×C4⋊C4×C47C2314yescomplemented
171C2×C4⋊C4×C47C2314yescomplemented
172C2×C22⋊C4×C47—24no—
173C2×C22⋊C4×C47C2×C418yescomplemented
174C2×C22⋊C4×C47C2314yes—
175C2×C22⋊C4×C47C2314yes—
176#95×C47C2314yescomplemented
177#95×C47C2314yescomplemented
178C24×C47—22no—
179C24×C47—22no—
180C24×C47—22no—
181C24×C47—22no—
182C24×C47C22×C414yes—
183C24×C47C2×D414yes—
184C24×C47#4114yes—
185C24×C47C2412yes—
186C24×C47C2411yescharacteristic
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—232no—
192C23×D47—28no—
193C23×D47—22no—
194C23×D47—22no—
195C23×D47—22no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—28no—
200C23×D47—22no—
201C23×D47—22no—
202C23×D47—22no—
203C23×D47—22no—
204C23×D47—22no—
205C23×D47—22no—
206C23×D47—232no—
207C23×D47—28no—
208C23×D47—28no—
209C23×D47—416no—
210C23×D47—44no—
211C23×D47—44no—
212C23×D47—416no—
213C23×D47—416no—
214C23×D47—416no—
215C23×D47—416no—
216C23×D47C22×C414yes—
217C23×D47C22×C414yes—
218C23×D47C22×C414yes—
219C23×D47C22×C4116yescomplemented
220C23×D47C2×D414yes—
221C23×D47#4114yes—
222C23×D47C2412yes—
223C23×D47C2412yes—
224C23×D47C2412yes—
225C22×C4×C47—22no—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—22no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—22no—
235C22×C4×C47—22no—
236C22×C4×C47—28no—
237C22×C4×C47—22no—
238C22×C4×C47—22no—
239C22×C4×C47—22no—
240C22×C4×C47—22no—
241C22×C4×C47—28no—
242C22×C4×C47—44no—
243C22×C4×C47—416no—
244C22×C4×C47C22×C414yes—
245C22×C4×C47C22×C414yes—
246C22×C4×C47C2×D414yes—
247C22×C4×C47C2412yes—
248C22×C4×C47C2412yes—
249C22×C4×C47C2412yes—
250C22×C4×C47C2412yes—
251C22×C4×C47C2412yes—
252C22×C4×C47C2412yes—
253C2×C22⋊D47—232no—
254C2×C22⋊D47—28no—
255C2×C22⋊D47—28no—
256C2×C22⋊D47C22×C4116yescomplemented
257C22×Dic47—22no—
258C22×Dic47—22no—
259C22×Dic47—22no—
260C22×Dic47—22no—
261C22×Dic47—22no—
262C22×Dic47—22no—
263C22×Dic47—22no—
264C22×Dic47—22no—
265C22×Dic47—22no—
266C22×Dic47—28no—
267C22×Dic47—22no—
268C22×Dic47—22no—
269C22×Dic47—28no—
270C22×Dic47—44no—
271C22×Dic47—416no—
272C22×Dic47C22×C414yes—
273C22×Dic47C2×D414yes—
274C22×Dic47C2×D414yes—
275C22×Dic47C2×D414yes—
276C22×Dic47C2412yes—
277C22×Dic47C2412yes—
278C22×Dic47C2412yes—
279C22×Dic47C2412yes—
280C22×Dic47C2412yes—
281C2×D188—232no—
282C2×D188—28no—
283C2×D188—28no—
284C2×D188—416no—
285C2×D188—44no—
286C2×D188—44no—
287C2×D188C22×C4116yescomplemented
288C2×D188C22×C4116yescomplemented
289C2×C4×D47—28no—
290C2×C4×D47—28no—
291C2×C4×D47—28no—
292C2×C4×D47—28no—
293C2×C4×D47—28no—
294C2×C4×D47—28no—
295C2×C4×D47—44no—
296C2×C4×D47—44no—
297C2×C4×D47—44no—
298C2×C4×D47—416no—
299C2×C4×D47—416no—
300C2×C4×D47—416no—
301C4⋊C4×C47—28no—
302C4⋊C4×C47—44no—
303C22⋊C4×C47—28no—
304C22⋊C4×C47C22×C4116yescomplemented
305C22⋊Dic47C2×D4116yescomplemented
306(C2×D47)⋊C4—28no—
307(C2×D47)⋊C4—28no—
308(C2×D47)⋊C4—28no—
309(C2×D47)⋊C4—28no—
310(C2×D47)⋊C4—28no—
311(C2×D47)⋊C4—28no—
312(C2×D47)⋊C4—28no—
313(C2×D47)⋊C4—44no—
314(C2×D47)⋊C4C22×C4116yescomplemented
315(C2×D47)⋊C4C22×C4116yescomplemented
316(C2×D47)⋊C4C2×D4116yescomplemented
317Dic47⋊C4—28no—
318C4×Dic47—28no—
319C4×Dic47—28no—
320C4×Dic47—44no—
321C23×C47—28no—
322C23×C47—28no—
323C23×C47—28no—
324C23×C47—28no—
325C23×C47—28no—
326C23×C47—28no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47C4×D4116yescomplemented
332C23×C47C23×C414yes—
333C23×C47C23×C412yes—
334C23×C47C22×D414yes—
335C23×C47C22×D412yes—
336C23×C47C22×D412yes—
337C23×C47C2×#4112yes—
338C23×C47C2×#4114yes—
339C23×C47C2×#4112yes—
340C23×C47H(5,𝔽2)12yes—
341C23×C47H(5,𝔽2)12yes—
342C23×C47C2511yescharacteristic
343C22×D47—28no—
344C22×D47—28no—
345C22×D47—28no—
346C22×D47—28no—
347C22×D47—28no—
348C22×D47—28no—
349C22×D47—22no—
350C22×D47—22no—
351C22×D47—22no—
352C22×D47—22no—
353C22×D47—28no—
354C22×D47—28no—
355C22×D47—28no—
356C22×D47—28no—
357C22×D47—232no—
358C22×D47—28no—
359C22×D47—28no—
360C22×D47—22no—
361C22×D47—22no—
362C22×D47—22no—
363C22×D47—22no—
364C22×D47—22no—
365C22×D47—22no—
366C22×D47—22no—
367C22×D47—22no—
368C22×D47—22no—
369C22×D47—22no—
370C22×D47—22no—
371C22×D47—22no—
372C22×D47—232no—
373C22×D47—416no—
374C22×D47—4128no—
375C22×D47—416no—
376C22×D47—416no—
377C22×D47—416no—
378C22×D47—416no—
379C22×D47—44no—
380C22×D47—44no—
381C22×D47—44no—
382C22×D47—44no—
383C22×D47—44no—
384C22×D47—44no—
385C22×D47—44no—
386C22×D47—44no—
387C22×D47C4×D4116yescomplemented
388C22×D47C23×C414yes—
389C22×D47C23×C414yes—
390C22×D47C23×C414yes—
391C22×D47C22×D414yes—
392C22×D47C2×#4114yes—
393C2×C4×C47—28no—
394C2×C4×C47—28no—
395C2×C4×C47—28no—
396C2×C4×C47—22no—
397C2×C4×C47—22no—
398C2×C4×C47—22no—
399C2×C4×C47—22no—
400C2×C4×C47—22no—
401C2×C4×C47—22no—
402C2×C4×C47—22no—
403C2×C4×C47—22no—
404C2×C4×C47—22no—
405C2×C4×C47—22no—
406C2×C4×C47—22no—
407C2×C4×C47—22no—
408C2×C4×C47—22no—
409C2×C4×C47—22no—
410C2×C4×C47—22no—
411C2×C4×C47—416no—
412C2×C4×C47—44no—
413C2×C4×C47—44no—
414C2×C4×C47—44no—
415C2×C4×C47C23×C414yes—
416C2×C4×C47C23×C414yes—
417C2×C4×C47C22×D414yes—
418C22⋊D47—232no—
419C2×Dic47—28no—
420C2×Dic47—28no—
421C2×Dic47—28no—
422C2×Dic47—28no—
423C2×Dic47—22no—
424C2×Dic47—22no—
425C2×Dic47—22no—
426C2×Dic47—22no—
427C2×Dic47—22no—
428C2×Dic47—22no—
429C2×Dic47—22no—
430C2×Dic47—22no—
431C2×Dic47—22no—
432C2×Dic47—22no—
433C2×Dic47—22no—
434C2×Dic47—416no—
435C2×Dic47—44no—
436C2×Dic47C23×C414yes—
437C2×Dic47C22×D414yes—
438C2×Dic47C22×D414yes—
439C2×Dic47C22×D414yes—
440D188—232no—
441D188—416no—
442C4×D47—416no—
443C4×D47—416no—
444C4×D47—416no—
445C2×#2358—471nomaximal, Sylow
446C22×C47—232no—
447C22×C47—24no—
448C22×C47—24no—
449C22×C47—24no—
450C22×C47—24no—
451C22×C47—24no—
452C22×C47—24no—
453C22×C47C2×C4×D414yes—
454C22×C47C2×C4×D414yes—
455C22×C47C2×C4×D418yescomplemented
456C22×C47#51814yes—
457C22×C47D4214yes—
458C22×C47#54614yes—
459C22×C47#54614yes—
460C22×C47#55114yes—
461C22×C47C24×C411yescharacteristic
462C22×C47C23×D411yescharacteristic
463C22×C47C23×D411yescharacteristic
464C22×C47C22×#4111yescharacteristic
465C22×C47C22×#4111yescharacteristic
466C22×C47C2×H(5,𝔽2)11yescharacteristic
467C22×C47C2×H(5,𝔽2)11yescharacteristic
468C2×D47—232no—
469C2×D47—24no—
470C2×D47—24no—
471C2×D47—24no—
472C2×D47—24no—
473C2×D47—24no—
474C2×D47—24no—
475C2×D47—24no—
476C2×D47—24no—
477C2×D47—24no—
478C2×D47—24no—
479C2×D47—24no—
480C2×D47—24no—
481C2×D47—464no—
482C2×D47—416no—
483C2×D47—416no—
484C2×D47—42no—
485C2×D47—42no—
486C2×D47—42no—
487C2×D47—42no—
488C2×D47—42no—
489C2×D47—42no—
490C2×D47—42no—
491C2×D47—42no—
492C2×D47C2×C4×D418yescomplemented
493C4×C47—24no—
494C4×C47—24no—
495C4×C47—24no—
496C4×C47—42no—
497C4×C47—42no—
498C4×C47—42no—
499Dic47—24no—
500Dic47—24no—
501Dic47—24no—
502Dic47—24no—
503Dic47—42no—
504C22×#120—471no—
505C22×C4×D4—471no—
506C22×C4×D4—471no—
507C23×C22⋊C4—471no—
508C23×C22⋊C4—471no—
509#2358—4716no—
510C2×#390—471no—
511C2×#388—471no—
512C2×#388—471no—
513C2×#386—471no—
514C2×#386—471no—
515C2×#386—471no—
516C2×#385—471no—
517C2×#385D4711yescharacteristic, complemented
518C2×C4×C22⋊C4—471no—
519C2×C4×C22⋊C4—471no—
520C2×C47—28no—
521C2×C47#235818yescomplemented
522C2×C47C22×C4×D411yescharacteristic
523C2×C47C22×C4×D411yescharacteristic
524C2×C47C2×#51811yescharacteristic
525C2×C47C2×D4211yescharacteristic
526C2×C47C2×#54611yescharacteristic
527C2×C47C2×#54611yescharacteristic
528C2×C47C2×#55111yescharacteristic
529D47—28no—
530D47—44no—
531D47—44no—
532C26—471no—
533C23×D4—471no—
534C23×D4—471no—
535C23×D4—471no—
536C24×C4—471no—
537C24×C4—471no—
538C24×C4—471no—
539C24×C4—471no—
540C24×C4C2×D4711yescharacteristic
541C2×#120—4716no—
542C2×#120—478no—
543C2×C4×D4—478no—
544C2×C4×D4—478no—
545C2×C4×D4—948no—
546C2×C4×D4—948no—
547C22×C4⋊C4—471no—
548C22×C4⋊C4C2×D4711yescharacteristic, complemented
549C22×C4⋊C4C2×D4711yescharacteristic, complemented
550C22×C22⋊C4—471no—
551C22×C22⋊C4—471no—
552C22×C22⋊C4—471no—
553C22×C22⋊C4—471no—
554C22×C22⋊C4—478no—
555C22×C22⋊C4—471no—
556C22×C22⋊C4—471no—
557C22×C22⋊C4—471no—
558C22×C22⋊C4—471no—
559C22×C22⋊C4—471no—
560C22×C22⋊C4—471no—
561C22×C22⋊C4—471no—
562C22×C22⋊C4—471no—
563C22×C22⋊C4—478no—
564C22×C22⋊C4—948no—
565C22×C22⋊C4—948no—
566C22×C22⋊C4C2×D4711yescharacteristic
567C22×C22⋊C4C2×D4711yescharacteristic
568C22×C42—471no—
569C22×C42—471no—
570C22×C42—471no—
571#390—478no—
572#388—478no—
573#388—478no—
574#386—478no—
575#386—478no—
576#386—478no—
577#385—478no—
578#385C2×D4718yescomplemented
579C4×C22⋊C4—478no—
580C4×C22⋊C4—478no—
581C2×#95—471no—
582C2×#95—471no—
583C2×#95—471no—
584C2×#95—471no—
585C2×#95C2×D4711yescharacteristic, complemented
586C2×#95C2×D4711yescharacteristic, complemented
587C47C2×#235811yescharacteristic, complemented, Sylow
588C25—471no—
589C25—471no—
590C25—471no—
591C25—478no—
592C25—474no—
593C25—944no—
594C25—944no—
595C25—944no—
596C25—944no—
597C25—1882no—
598C25—1882no—
599C25C22×D4711yescharacteristic
600C22×D4—478no—
601C22×D4—474no—
602C22×D4—478no—
603C22×D4—478no—
604C22×D4—474no—
605C22×D4—474no—
606C22×D4—944no—
607C22×D4—944no—
608C22×D4—944no—
609C22×D4—944no—
610C22×D4—1882no—
611C22×D4—1882no—
612C23×C4—24no—
613C23×C4—24no—
614C23×C4—42no—
615C23×C4—471no—
616C23×C4—471no—
617C23×C4—471no—
618C23×C4—471no—
619C23×C4—471no—
620C23×C4—474no—
621C23×C4—474no—
622C23×C4—474no—
623C23×C4—474no—
624C23×C4—944no—
625C23×C4—944no—
626C23×C4—944no—
627C23×C4—944no—
628C23×C4—944no—
629C23×C4—944no—
630C23×C4—944no—
631C23×C4—944no—
632C23×C4—1882no—
633C23×C4—1882no—
634C23×C4—1882no—
635C23×C4—1882no—
636C23×C4C22×D4711yescharacteristic
637C23×C4C22×D4711yescharacteristic
638C23×C4C22×D4711yescharacteristic
639C23×C4C22×D4714yes—
640C23×C4C22×D4711yescharacteristic
641C23×C4C22×D4711yescharacteristic
642C23×C4C22×D4711yescharacteristic
643#120—4764no—
644C4×D4—9432no—
645C4×D4—9432no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—42no—
648C2×C4⋊C4—474no—
649C2×C4⋊C4—944no—
650C2×C4⋊C4C22×D4714yescomplemented
651C2×C4⋊C4C22×D4714yescomplemented
652C2×C22⋊C4—24no—
653C2×C22⋊C4—478no—
654C2×C22⋊C4—474no—
655C2×C22⋊C4—478no—
656C2×C22⋊C4—478no—
657C2×C22⋊C4—478no—
658C2×C22⋊C4—474no—
659C2×C22⋊C4—474no—
660C2×C22⋊C4—474no—
661C2×C22⋊C4—474no—
662C2×C22⋊C4—474no—
663C2×C22⋊C4—474no—
664C2×C22⋊C4—474no—
665C2×C22⋊C4—474no—
666C2×C22⋊C4—474no—
667C2×C22⋊C4—474no—
668C2×C22⋊C4—474no—
669C2×C22⋊C4—9432no—
670C2×C22⋊C4—9432no—
671C2×C22⋊C4—944no—
672C2×C22⋊C4—944no—
673C2×C22⋊C4—944no—
674C2×C22⋊C4—944no—
675C2×C22⋊C4—944no—
676C2×C22⋊C4—944no—
677C2×C22⋊C4—944no—
678C2×C22⋊C4—1882no—
679C2×C22⋊C4C4×D4718yescomplemented
680C2×C22⋊C4C22×D4714yes—
681C2×C22⋊C4C22×D4714yes—
682C2×C42—474no—
683C2×C42—474no—
684C2×C42—474no—
685C2×C42—944no—
686C2×C42—944no—
687C2×C42—1882no—
688#95—474no—
689#95—474no—
690#95—474no—
691#95—474no—
692#95C22×D4714yescomplemented
693#95C22×D4714yescomplemented
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—474no—
699C24—474no—
700C24—474no—
701C24—472no—
702C24—474no—
703C24—474no—
704C24—472no—
705C24—472no—
706C24—4716no—
707C24—948no—
708C24—9432no—
709C24—948no—
710C24—942no—
711C24—942no—
712C24—942no—
713C24—942no—
714C24—9432no—
715C24—948no—
716C24—942no—
717C24—942no—
718C24—942no—
719C24—942no—
720C24—942no—
721C24—942no—
722C24—942no—
723C24—948no—
724C24—942no—
725C24—942no—
726C24—942no—
727C24—942no—
728C24—942no—
729C24—18816no—
730C24—1884no—
731C24—1884no—
732C24—18816no—
733C24—18816no—
734C24—18816no—
735C24—18816no—
736C24C2×C4×D4714yes—
737C24D4×D4714yes—
738C24#1062535414yes—
739C24C23×D4712yes—
740C24C23×D4711yescharacteristic
741C2×D4—4716no—
742C2×D4—4716no—
743C2×D4—4716no—
744C2×D4—948no—
745C2×D4—9432no—
746C2×D4—948no—
747C2×D4—9432no—
748C2×D4—948no—
749C2×D4—948no—
750C2×D4—18816no—
751C2×D4—1884no—
752C2×D4—1884no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—28no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—28no—
770C22×C4—44no—
771C22×C4—416no—
772C22×C4—474no—
773C22×C4—474no—
774C22×C4—474no—
775C22×C4—474no—
776C22×C4—472no—
777C22×C4—472no—
778C22×C4—472no—
779C22×C4—472no—
780C22×C4—472no—
781C22×C4—948no—
782C22×C4—948no—
783C22×C4—948no—
784C22×C4—948no—
785C22×C4—948no—
786C22×C4—948no—
787C22×C4—942no—
788C22×C4—942no—
789C22×C4—942no—
790C22×C4—942no—
791C22×C4—942no—
792C22×C4—942no—
793C22×C4—942no—
794C22×C4—942no—
795C22×C4—942no—
796C22×C4—948no—
797C22×C4—942no—
798C22×C4—942no—
799C22×C4—948no—
800C22×C4—1884no—
801C22×C4—1884no—
802C22×C4—1884no—
803C22×C4—18816no—
804C22×C4—18816no—
805C22×C4—18816no—
806C22×C4—1884no—
807C22×C4—18816no—
808C22×C4C2×C4×D4714yes—
809C22×C4C2×C4×D4714yes—
810C22×C4D4×D4714yes—
811C22×C4C23×D4712yes—
812C22×C4C23×D4712yes—
813C22×C4C23×D4712yes—
814C22×C4C23×D4712yes—
815C22×C4C23×D4712yes—
816C22×C4C23×D4712yes—
817C4⋊C4—28no—
818C4⋊C4—44no—
819C4⋊C4—948no—
820C22⋊C4—28no—
821C22⋊C4—4716no—
822C22⋊C4—4716no—
823C22⋊C4—4716no—
824C22⋊C4—4716no—
825C22⋊C4—948no—
826C22⋊C4—948no—
827C22⋊C4—948no—
828C22⋊C4—948no—
829C22⋊C4—948no—
830C22⋊C4—948no—
831C22⋊C4—948no—
832C22⋊C4—1884no—
833C22⋊C4C2×C4×D47116yescomplemented
834C42—948no—
835C42—948no—
836C42—1884no—
837C23—28no—
838C23—28no—
839C23—28no—
840C23—28no—
841C23—28no—
842C23—28no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—4716no—
848C23—474no—
849C23—474no—
850C23—474no—
851C23—474no—
852C23—474no—
853C23—9432no—
854C23—948no—
855C23—948no—
856C23—948no—
857C23—948no—
858C23—948no—
859C23—948no—
860C23—942no—
861C23—942no—
862C23—942no—
863C23—942no—
864C23—948no—
865C23—948no—
866C23—948no—
867C23—948no—
868C23—9432no—
869C23—948no—
870C23—948no—
871C23—942no—
872C23—942no—
873C23—942no—
874C23—942no—
875C23—942no—
876C23—942no—
877C23—942no—
878C23—942no—
879C23—942no—
880C23—942no—
881C23—942no—
882C23—942no—
883C23—18816no—
884C23—18816no—
885C23—18816no—
886C23—18816no—
887C23—188128no—
888C23—18816no—
889C23—1884no—
890C23—1884no—
891C23—1884no—
892C23—1884no—
893C23—1884no—
894C23—1884no—
895C23—1884no—
896C23—1884no—
897C23#13093986116yescomplemented
898C23C22×C4×D4714yes—
899C23C22×C4×D4712yes—
900C23C2×D4×D4714yes—
901C23C2×D4×D4712yes—
902C23C2×D4×D4712yes—
903C23#41×D4712yes—
904C23C2×#1062535414yes—
905C23C2×#1062535412yes—
906C23#1309406912yes—
907C23#1309407012yes—
908C23C24×D4711yescharacteristic
909D4—9432no—
910D4—9432no—
911D4—18816no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—416no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—474no—
935C2×C4—474no—
936C2×C4—474no—
937C2×C4—474no—
938C2×C4—948no—
939C2×C4—948no—
940C2×C4—948no—
941C2×C4—948no—
942C2×C4—942no—
943C2×C4—942no—
944C2×C4—942no—
945C2×C4—942no—
946C2×C4—942no—
947C2×C4—942no—
948C2×C4—942no—
949C2×C4—942no—
950C2×C4—942no—
951C2×C4—942no—
952C2×C4—942no—
953C2×C4—18816no—
954C2×C4—18816no—
955C2×C4—18816no—
956C2×C4—18816no—
957C2×C4—1884no—
958C2×C4C22×C4×D4714yes—
959C2×C4C22×C4×D4714yes—
960C2×C4C2×D4×D4714yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—232no—
967C22—24no—
968C22—478no—
969C22—944no—
970C22—944no—
971C22—944no—
972C22—944no—
973C22—944no—
974C22—9432no—
975C22—944no—
976C22—944no—
977C22—944no—
978C22—944no—
979C22—944no—
980C22—944no—
981C22—944no—
982C22—18864no—
983C22—1882no—
984C22—1882no—
985C22—1882no—
986C22—1882no—
987C22—1882no—
988C22—1882no—
989C22—18816no—
990C22—18816no—
991C22—1882no—
992C22—1882no—
993C22C4×D4×D4714yes—
994C22C2×#1309398614yes—
995C22C2×#1309398618yescomplemented
996C22#1568959514yes—
997C22#1568975514yes—
998C22#1568976414yes—
999C22#1568976514yes—
1000C22#1568980014yes—
1001C22C23×C4×D4711yescharacteristic
1002C22C22×D4×D4711yescharacteristic
1003C22C22×D4×D4711yescharacteristic
1004C22C2×#41×D4711yescharacteristic
1005C22C22×#1062535411yescharacteristic
1006C22C2×#1309406911yescharacteristic
1007C22C2×#1309407011yescharacteristic
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—944no—
1015C4—944no—
1016C4—944no—
1017C4—944no—
1018C4—1882no—
1019C2—28no—
1020C2—948no—
1021C2—1884no—
1022C2—1884no—
1023C2#2024636418yesdirect product factor
1024C2C2×C4×D4×D4711yescharacteristic
1025C2C22×#1309398611yescharacteristic
1026C2C2×#1568959511yescharacteristic
1027C2C2×#1568975511yescharacteristic
1028C2C2×#1568976411yescharacteristic
1029C2C2×#1568976511yescharacteristic
1030C2C2×#1568980011yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC22×#13093994C2
cosocleC23×C47C25
hypercenterC2×#385D47
hypocenterC47C2×#2358
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. C23×(C2×D47)⋊C4C2semidirect
5. C22×C22⋊C4×D47C2semidirect
6. #20246364C2direct (N × H)
7. C2×#15689024C2semidirect
8. C2×#15689013C2semidirect
9. C2×#15689012C2semidirect
10. C2×#15689001C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15689000C2semidirect
13. C2×#15688994C2semidirect
14. C2×C22⋊C4×Dic47C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#385C2semidirect
24. C23×C4×D47C22semidirect
25. C2×#13093994C4semidirect
28. C2×#13093986C22semidirect
30. C2×C4×C22⋊D47C22semidirect
31. C22×Dic47⋊C4C22semidirect
42. C22×(C2×D47)⋊C4C22semidirect
43. C22×(C2×D47)⋊C4C22semidirect
44. C22×(C2×D47)⋊C4C22semidirect
45. C22×(C2×D47)⋊C4C22semidirect
47. C2×C22⋊C4×D47C22semidirect
48. C22×C4×Dic47C22semidirect
49. C22×C4×Dic47C22semidirect
50. C22×C4×Dic47C22semidirect
51. #15689024C22semidirect
52. #15689013C22semidirect
53. #15689012C22semidirect
54. #15689001C22semidirect
55. #15689001C22semidirect
56. #15689000C22semidirect
57. #15688994C22semidirect
58. C22⋊C4×Dic47C22semidirect
59. #15688970C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C2×C47⋊#95C22semidirect
63. C2×C47⋊#95C22semidirect
65. C22×C4⋊C4×C47C22semidirect
66. C22×C4⋊C4×C47C22semidirect
69. C47×#385C22semidirect
70. C2×#95×C47C22semidirect
71. C2×#95×C47C22semidirect
78. C24×D47C2×C4semidirect
87. C22×D188C2×C4semidirect
88. C22×D188C2×C4semidirect
93. C22×C22⋊D47C2×C4semidirect
115. C22×C4×D47C23semidirect
116. #13093994C2×C4semidirect
120. C2×Dic47⋊C4C23semidirect
121. C2×C22⋊Dic47D4semidirect
132. C2×(C2×D47)⋊C4C2×C4semidirect
133. C2×(C2×D47)⋊C4C2×C4semidirect
134. C2×(C2×D47)⋊C4D4semidirect
143. C2×(C2×D47)⋊C4C23semidirect
144. C2×(C2×D47)⋊C4C23semidirect
145. C2×(C2×D47)⋊C4C23semidirect
150. C2×C4×Dic47C23semidirect
151. C2×C4×Dic47C23semidirect
152. C2×C4×Dic47C23semidirect
153. C47⋊#95C23semidirect
154. C47⋊#95C23semidirect
155. C47⋊#95C23semidirect
156. C47⋊#95C23semidirect
170. C2×C4⋊C4×C47C23semidirect
171. C2×C4⋊C4×C47C23semidirect
173. C2×C22⋊C4×C47C2×C4semidirect
176. #95×C47C23semidirect
177. #95×C47C23semidirect
219. C23×D47C22×C4semidirect
256. C2×C22⋊D47C22×C4semidirect
287. C2×D188C22×C4semidirect
288. C2×D188C22×C4semidirect
304. C22⋊C4×C47C22×C4semidirect
305. C22⋊Dic47C2×D4semidirect
314. (C2×D47)⋊C4C22×C4semidirect
315. (C2×D47)⋊C4C22×C4semidirect
316. (C2×D47)⋊C4C2×D4semidirect
331. C23×C47C4×D4semidirect
387. C22×D47C4×D4semidirect
455. C22×C47C2×C4×D4semidirect
492. C2×D47C2×C4×D4semidirect
517. C2×#385D47semidirect
521. C2×C47#2358semidirect
548. C22×C4⋊C4C2×D47semidirect
549. C22×C4⋊C4C2×D47semidirect
578. #385C2×D47semidirect
585. C2×#95C2×D47semidirect
586. C2×#95C2×D47semidirect
587. C47C2×#2358semidirect
650. C2×C4⋊C4C22×D47semidirect
651. C2×C4⋊C4C22×D47semidirect
679. C2×C22⋊C4C4×D47semidirect
692. #95C22×D47semidirect
693. #95C22×D47semidirect
833. C22⋊C4C2×C4×D47semidirect
897. C23#13093986semidirect
995. C22C2×#13093986semidirect
1023. C2#20246364direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939942
C22×#130939862
C22×C4×C22⋊D472
C23×(C2×D47)⋊C42
C22×C22⋊C4×D472
#202463642
C2×#156890242
C2×#156890132
C2×#156890122
C2×#156890012
C2×#156890002
C2×#156889942
C2×C22⋊C4×Dic472
C2×#156889702
C2×C47×#3852
C2×#235847