Finite Group Databasebeta

← C2×#20246710 #26383828

Subgroups — C2×#20246710 #26383828

Order 12032.

7822 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D47C211yesmaximal, characteristic
2C22×#13094009C211yesmaximal, characteristic, complemented
3C22×#13094006C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#20246710C2116yesmaximal, direct product factor
6C2×#15689039C211yesmaximal, characteristic, complemented
7C2×#15689038C211yesmaximal, characteristic, complemented
8C2×#15689037C211yesmaximal, characteristic, complemented
9C2×#15689001C211yesmaximal, characteristic, complemented
10C2×#15688999C211yesmaximal, characteristic, complemented
11C2×#15688997C211yesmaximal, characteristic, complemented
12C2×#15688994C211yesmaximal, characteristic, complemented
13C2×#15688978C211yesmaximal, characteristic, complemented
14C2×#15688978C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic, complemented
16C2×C47×#394C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C25×D47C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C22⋊D47C2211yescharacteristic
22C22×D4×D47—28no—
23C22×D4×D47—28no—
24C22×D4×D47—28no—
25C22×D4×D47C2218yes—
26C23×C4×D47C2211yescharacteristic
27C23×C4×D47C2211yescharacteristic, complemented
28C23×C4×D47C2211yescharacteristic, complemented
29C2×#13094009—28no—
30C2×#13094009C2218yescomplemented
31C2×#13094006—28no—
32C2×#13094006C2218yescomplemented
33C22×C4⋊Dic47C2211yescharacteristic, complemented
34C22×Dic47⋊C4C2211yescharacteristic, complemented
35C22×Dic47⋊C4C2211yescharacteristic, complemented
36C22×C22⋊Dic47C2211yescharacteristic, complemented
37C22×C22⋊Dic47C2211yescharacteristic, complemented
38C22×C22⋊Dic47C2211yescharacteristic, complemented
39C22×C22⋊Dic47C2211yescharacteristic, complemented
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
48C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
50C2×C22⋊C4×D47—28no—
51C2×C22⋊C4×D47C2218yescomplemented
52#15689039C2218yescomplemented
53#15689038C2218yescomplemented
54#15689037C2218yescomplemented
55#15689001C2218yescomplemented
56#15688999C2218yescomplemented
57#15688997C2218yescomplemented
58#15688994C2218yescomplemented
59#15688978C2218yescomplemented
60#15688978C2218yescomplemented
61#15688978C2218yescomplemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C2×C47⋊#95C2211yescharacteristic, complemented
64C2×C47⋊#95C2211yescharacteristic, complemented
65C23×D4×C47C2211yescharacteristic
66C22×C4⋊C4×C47C2211yescharacteristic, complemented
67C22×C22⋊C4×C47C2211yescharacteristic, complemented
68C22×C22⋊C4×C47C2211yescharacteristic, complemented
69C22×C22⋊C4×C47C2211yescharacteristic, complemented
70C22×C22⋊C4×C47C2211yescharacteristic, complemented
71C47×#394C2218yescomplemented
72C2×#95×C47C2211yescharacteristic, complemented
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—24no—
76C24×D47—24no—
77C24×D47—24no—
78C24×D47—24no—
79C24×D47—24no—
80C24×D47—24no—
81C24×D47—24no—
82C24×D47—42no—
83C24×D47—42no—
84C24×D47—42no—
85C24×D47—42no—
86C24×D47D418yes—
87C24×D47C2311yescharacteristic
88C24×D47C2314yes—
89C24×D47C2314yes—
90C24×D47C2311yescharacteristic
91C24×D47C2311yescharacteristic
92C22×D188—24no—
93C22×D188—24no—
94C22×D188D418yes—
95C22×D188C2314yes—
96C22×C22⋊D47—24no—
97C22×C22⋊D47—24no—
98C22×C22⋊D47—24no—
99C22×C22⋊D47—24no—
100C22×C22⋊D47—24no—
101C22×C22⋊D47D418yes—
102C22×C22⋊D47C2314yes—
103C22×C22⋊D47C2314yes—
104C2×D4×D47—2128no—
105C2×D4×D47—232no—
106C2×D4×D47—232no—
107C2×D4×D47—232no—
108C23×Dic47C2311yescharacteristic
109C23×Dic47C2311yescharacteristic
110C23×Dic47C2311yescharacteristic
111C23×Dic47C2311yescharacteristic
112C23×Dic47C2311yescharacteristic
113C22×C4×D47—24no—
114C22×C4×D47—24no—
115C22×C4×D47—24no—
116C22×C4×D47—24no—
117C22×C4×D47—24no—
118C22×C4×D47—24no—
119C22×C4×D47—24no—
120C22×C4×D47—42no—
121C22×C4×D47—42no—
122C22×C4×D47C2314yes—
123C22×C4×D47C2314yescomplemented
124C22×C4×D47C2314yescomplemented
125#13094009—232no—
126#13094006—232no—
127C2×C4⋊Dic47—24no—
128C2×C4⋊Dic47C2314yescomplemented
129C2×Dic47⋊C4—24no—
130C2×Dic47⋊C4—24no—
131C2×Dic47⋊C4C2314yescomplemented
132C2×Dic47⋊C4C2314yescomplemented
133C2×C22⋊Dic47—24no—
134C2×C22⋊Dic47—24no—
135C2×C22⋊Dic47—42no—
136C2×C22⋊Dic47—42no—
137C2×C22⋊Dic47C2314yescomplemented
138C2×C22⋊Dic47C2314yescomplemented
139C2×C22⋊Dic47C2314yescomplemented
140C2×C22⋊Dic47C2314yescomplemented
141C2×(C2×D47)⋊C4—24no—
142C2×(C2×D47)⋊C4—24no—
143C2×(C2×D47)⋊C4—24no—
144C2×(C2×D47)⋊C4—24no—
145C2×(C2×D47)⋊C4—24no—
146C2×(C2×D47)⋊C4—24no—
147C2×(C2×D47)⋊C4—24no—
148C2×(C2×D47)⋊C4—24no—
149C2×(C2×D47)⋊C4—42no—
150C2×(C2×D47)⋊C4—42no—
151C2×(C2×D47)⋊C4C2314yes—
152C2×(C2×D47)⋊C4C2314yes—
153C2×(C2×D47)⋊C4C2314yes—
154C2×(C2×D47)⋊C4C2314yes—
155C2×(C2×D47)⋊C4C2314yescomplemented
156C2×(C2×D47)⋊C4C2314yescomplemented
157C2×(C2×D47)⋊C4C2314yescomplemented
158C2×(C2×D47)⋊C4C2314yescomplemented
159C2×(C2×D47)⋊C4C2314yescomplemented
160C2×(C2×D47)⋊C4C2314yescomplemented
161C22⋊C4×D47—232no—
162C47⋊#95C2314yescomplemented
163C47⋊#95C2314yescomplemented
164C47⋊#95C2314yescomplemented
165C25×C47C2311yescharacteristic
166C25×C47C2311yescharacteristic
167C22×D4×C47—24no—
168C22×D4×C47—24no—
169C22×D4×C47—24no—
170C22×D4×C47C2314yes—
171C23×C4×C47C2311yescharacteristic
172C23×C4×C47C2311yescharacteristic
173C23×C4×C47C2311yescharacteristic
174C23×C4×C47C2311yescharacteristic
175C23×C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47—24no—
177C2×C4⋊C4×C47C2314yescomplemented
178C2×C22⋊C4×C47—24no—
179C2×C22⋊C4×C47—24no—
180C2×C22⋊C4×C47—42no—
181C2×C22⋊C4×C47—42no—
182C2×C22⋊C4×C47C2314yescomplemented
183C2×C22⋊C4×C47C2314yescomplemented
184C2×C22⋊C4×C47C2314yescomplemented
185C2×C22⋊C4×C47C2314yescomplemented
186#95×C47C2314yescomplemented
187C24×C47—22no—
188C24×C47—22no—
189C24×C47—22no—
190C24×C47—22no—
191C24×C47—22no—
192C24×C47—22no—
193C24×C47—22no—
194C24×C47—22no—
195C24×C47—22no—
196C24×C47—22no—
197C24×C47—22no—
198C24×C47—22no—
199C24×C47C2×D414yes—
200C24×C47C2×D414yes—
201C24×C47C2412yes—
202C24×C47C2412yes—
203C24×C47C2411yescharacteristic
204C23×D47—22no—
205C23×D47—22no—
206C23×D47—22no—
207C23×D47—22no—
208C23×D47—22no—
209C23×D47—22no—
210C23×D47—22no—
211C23×D47—22no—
212C23×D47—232no—
213C23×D47—28no—
214C23×D47—22no—
215C23×D47—22no—
216C23×D47—22no—
217C23×D47—22no—
218C23×D47—22no—
219C23×D47—22no—
220C23×D47—232no—
221C23×D47—232no—
222C23×D47—28no—
223C23×D47—28no—
224C23×D47—28no—
225C23×D47—28no—
226C23×D47—28no—
227C23×D47—28no—
228C23×D47—28no—
229C23×D47—28no—
230C23×D47—416no—
231C23×D47—44no—
232C23×D47—44no—
233C23×D47—44no—
234C23×D47—44no—
235C23×D47—416no—
236C23×D47—416no—
237C23×D47—416no—
238C23×D47—416no—
239C23×D47—416no—
240C23×D47—416no—
241C23×D47—416no—
242C23×D47—416no—
243C23×D47—416no—
244C23×D47—416no—
245C23×D47C2×D414yes—
246C23×D47C2×D4116yes—
247C23×D47C2×D414yes—
248C23×D47C2×D414yes—
249C23×D47C2×D414yes—
250C23×D47C2×D414yes—
251C23×D47#4114yes—
252C23×D47#4114yes—
253C23×D47C2412yes—
254C23×D47C2412yes—
255C23×D47C2412yes—
256C2×D4×C47—232no—
257C2×D4×C47—28no—
258C2×D4×C47—28no—
259C2×D4×C47—28no—
260C22×C4×C47—22no—
261C22×C4×C47—22no—
262C22×C4×C47—22no—
263C22×C4×C47—22no—
264C22×C4×C47—22no—
265C22×C4×C47—22no—
266C22×C4×C47—22no—
267C22×C4×C47—22no—
268C22×C4×C47—22no—
269C22×C4×C47—22no—
270C22×C4×C47—22no—
271C22×C4×C47—22no—
272C22×C4×C47—22no—
273C22×C4×C47—22no—
274C22×C4×C47C2×D414yes—
275C22×C4×C47C2412yes—
276C22×C4×C47C2412yes—
277C22×C4×C47C2412yes—
278C22×C4×C47C2412yes—
279C22×C4×C47C2412yes—
280C2×C22⋊D47—232no—
281C2×C22⋊D47—28no—
282C2×C22⋊D47—232no—
283C2×C22⋊D47—28no—
284C2×C22⋊D47—28no—
285C2×C22⋊D47—28no—
286C2×C22⋊D47—28no—
287C2×C22⋊D47C2×D4116yes—
288C22×Dic47—22no—
289C22×Dic47—22no—
290C22×Dic47—22no—
291C22×Dic47—22no—
292C22×Dic47—22no—
293C22×Dic47—22no—
294C22×Dic47—22no—
295C22×Dic47—22no—
296C22×Dic47—22no—
297C22×Dic47—22no—
298C22×Dic47—22no—
299C22×Dic47—22no—
300C22×Dic47—22no—
301C22×Dic47—22no—
302C22×Dic47C2×D414yes—
303C22×Dic47C2412yes—
304C22×Dic47C2412yes—
305C22×Dic47C2412yes—
306C22×Dic47C2412yes—
307C22×Dic47C2412yes—
308D4×D47—2256no—
309C2×D188—232no—
310C2×D188—28no—
311C2×D188—28no—
312C2×D188C2×D4116yes—
313C2×C4×D47—232no—
314C2×C4×D47—28no—
315C2×C4×D47—28no—
316C2×C4×D47—28no—
317C2×C4×D47—28no—
318C2×C4×D47—28no—
319C2×C4×D47—28no—
320C2×C4×D47—28no—
321C2×C4×D47—44no—
322C2×C4×D47—44no—
323C2×C4×D47—416no—
324C2×C4×D47—416no—
325C4⋊C4×C47—28no—
326C22⋊C4×C47—28no—
327C22⋊C4×C47—28no—
328C22⋊C4×C47—44no—
329C22⋊C4×C47—44no—
330C22⋊Dic47—28no—
331C22⋊Dic47—28no—
332C22⋊Dic47—44no—
333C22⋊Dic47—44no—
334(C2×D47)⋊C4—28no—
335(C2×D47)⋊C4—28no—
336(C2×D47)⋊C4—28no—
337(C2×D47)⋊C4—28no—
338(C2×D47)⋊C4—28no—
339(C2×D47)⋊C4—28no—
340(C2×D47)⋊C4—28no—
341(C2×D47)⋊C4—28no—
342(C2×D47)⋊C4—44no—
343(C2×D47)⋊C4—44no—
344C4⋊Dic47—28no—
345Dic47⋊C4—28no—
346Dic47⋊C4—28no—
347C23×C47—28no—
348C23×C47—28no—
349C23×C47—28no—
350C23×C47—28no—
351C23×C47—28no—
352C23×C47—28no—
353C23×C47—22no—
354C23×C47—22no—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—22no—
359C23×C47—22no—
360C23×C47—22no—
361C23×C47—22no—
362C23×C47—22no—
363C23×C47—22no—
364C23×C47—22no—
365C23×C47—44no—
366C23×C47—44no—
367C23×C47—44no—
368C23×C47—44no—
369C23×C47—44no—
370C23×C47—44no—
371C23×C47—44no—
372C23×C47—44no—
373C23×C47C22×D414yes—
374C23×C47C22×D414yes—
375C23×C47C22×D412yes—
376C23×C47C22×D412yes—
377C23×C47C22×D412yes—
378C23×C47C2×#4112yes—
379C23×C47C2×#4112yes—
380C23×C47H(5,𝔽2)12yes—
381C23×C47H(5,𝔽2)12yes—
382C23×C47C2511yescharacteristic
383C22×D47—28no—
384C22×D47—28no—
385C22×D47—28no—
386C22×D47—28no—
387C22×D47—28no—
388C22×D47—28no—
389C22×D47—28no—
390C22×D47—28no—
391C22×D47—28no—
392C22×D47—28no—
393C22×D47—28no—
394C22×D47—28no—
395C22×D47—22no—
396C22×D47—22no—
397C22×D47—22no—
398C22×D47—22no—
399C22×D47—22no—
400C22×D47—22no—
401C22×D47—22no—
402C22×D47—22no—
403C22×D47—232no—
404C22×D47—28no—
405C22×D47—28no—
406C22×D47—28no—
407C22×D47—22no—
408C22×D47—22no—
409C22×D47—22no—
410C22×D47—22no—
411C22×D47—22no—
412C22×D47—22no—
413C22×D47—232no—
414C22×D47—232no—
415C22×D47—416no—
416C22×D47—4128no—
417C22×D47—416no—
418C22×D47—416no—
419C22×D47—416no—
420C22×D47—416no—
421C22×D47—416no—
422C22×D47—416no—
423C22×D47—416no—
424C22×D47—416no—
425C22×D47—4128no—
426C22×D47—416no—
427C22×D47—44no—
428C22×D47—44no—
429C22×D47—44no—
430C22×D47—44no—
431C22×D47—416no—
432C22×D47#120116yes—
433C22×D47#123116yescomplemented
434C22×D47C22×D414yes—
435C22×D47C22×D414yes—
436C22×D47C22×D414yes—
437C22×D47C22×D414yes—
438C22×D47C22×D414yes—
439C22×D47C2×#4114yes—
440C22×D47C2×#4114yes—
441D4×C47—232no—
442C2×C4×C47—28no—
443C2×C4×C47—22no—
444C2×C4×C47—22no—
445C2×C4×C47—22no—
446C2×C4×C47—22no—
447C2×C4×C47—22no—
448C2×C4×C47—22no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—22no—
457C2×C4×C47—44no—
458C2×C4×C47—44no—
459C2×C4×C47—44no—
460C2×C4×C47—44no—
461C2×C4×C47C22×D414yes—
462C22⋊D47—232no—
463C22⋊D47—232no—
464C2×Dic47—28no—
465C2×Dic47—22no—
466C2×Dic47—22no—
467C2×Dic47—22no—
468C2×Dic47—22no—
469C2×Dic47—22no—
470C2×Dic47—22no—
471C2×Dic47—22no—
472C2×Dic47—22no—
473C2×Dic47—22no—
474C2×Dic47—22no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—22no—
478C2×Dic47—22no—
479C2×Dic47—44no—
480C2×Dic47—44no—
481C2×Dic47—44no—
482C2×Dic47—44no—
483C2×Dic47C22×D414yes—
484D188—232no—
485C4×D47—232no—
486C4×D47—416no—
487C4×D47—416no—
488C2×#2405—471nomaximal, Sylow
489C22×C47—24no—
490C22×C47—24no—
491C22×C47—24no—
492C22×C47—24no—
493C22×C47—24no—
494C22×C47—24no—
495C22×C47—416no—
496C22×C47—416no—
497C22×C47—42no—
498C22×C47—42no—
499C22×C47—42no—
500C22×C47—42no—
501C22×C47—42no—
502C22×C47—42no—
503C22×C47—42no—
504C22×C47—42no—
505C22×C47C2×#12014yes—
506C22×C47C2×#12314yes—
507C22×C47#53414yes—
508C22×C47#54614yes—
509C22×C47#54614yes—
510C22×C47#54614yes—
511C22×C47#54614yes—
512C22×C47C23×D411yescharacteristic
513C22×C47C23×D411yescharacteristic
514C22×C47C23×D411yescharacteristic
515C22×C47C22×#4111yescharacteristic
516C22×C47C22×#4111yescharacteristic
517C22×C47C2×H(5,𝔽2)11yescharacteristic
518C22×C47C2×H(5,𝔽2)11yescharacteristic
519C2×D47—232no—
520C2×D47—232no—
521C2×D47—24no—
522C2×D47—24no—
523C2×D47—24no—
524C2×D47—24no—
525C2×D47—24no—
526C2×D47—24no—
527C2×D47—24no—
528C2×D47—24no—
529C2×D47—24no—
530C2×D47—24no—
531C2×D47—24no—
532C2×D47—24no—
533C2×D47—24no—
534C2×D47—24no—
535C2×D47—24no—
536C2×D47—464no—
537C2×D47—464no—
538C2×D47—416no—
539C2×D47—42no—
540C2×D47—42no—
541C2×D47—42no—
542C2×D47—42no—
543C2×D47C2×#12018yes—
544C2×D47C2×#12318yescomplemented
545C4×C47—24no—
546C4×C47—42no—
547C4×C47—42no—
548C4×C47—42no—
549C4×C47—42no—
550Dic47—24no—
551Dic47—42no—
552Dic47—42no—
553Dic47—42no—
554Dic47—42no—
555C24×D4—471no—
556C22×#123—471no—
557C22×#123—471no—
558C23×C22⋊C4—471no—
559#2405—4716no—
560C2×#394—471no—
561C2×#394—471no—
562C2×#394—471no—
563C2×#394D4711yescharacteristic, complemented
564C2×#386—471no—
565C2×#386—471no—
566C2×#385—471no—
567C2×#385—471no—
568C2×#379—471no—
569C2×#379—471no—
570C2×#379—471no—
571C2×C47—44no—
572C2×C47—44no—
573C2×C47#240518yescomplemented
574C2×C47C22×#12011yescharacteristic
575C2×C47C22×#12311yescharacteristic
576C2×C47C2×#53411yescharacteristic
577C2×C47C2×#54611yescharacteristic
578C2×C47C2×#54611yescharacteristic
579C2×C47C2×#54611yescharacteristic
580C2×C47C2×#54611yescharacteristic
581D47—28no—
582D47—28no—
583D47—44no—
584C26—471no—
585C26—471no—
586C23×D4—471no—
587C23×D4—471no—
588C23×D4—478no—
589C23×D4—471no—
590C23×D4—948no—
591C23×D4—948no—
592C23×D4—948no—
593C23×D4C2×D4711yescharacteristic
594C24×C4—471no—
595C24×C4—471no—
596C24×C4—471no—
597C2×#123—478no—
598C2×#123—478no—
599C2×#123—948no—
600C2×#123—948no—
601C22×C4⋊C4—471no—
602C22×C4⋊C4—471no—
603C22×C4⋊C4—471no—
604C22×C4⋊C4C2×D4711yescharacteristic, complemented
605C22×C22⋊C4—471no—
606C22×C22⋊C4—471no—
607C22×C22⋊C4—471no—
608C22×C22⋊C4—471no—
609C22×C22⋊C4—471no—
610C22×C22⋊C4—471no—
611C22×C22⋊C4—471no—
612C22×C22⋊C4—471no—
613C22×C22⋊C4—471no—
614C22×C22⋊C4—471no—
615C22×C22⋊C4—471no—
616C22×C22⋊C4—471no—
617C22×C22⋊C4—471no—
618C22×C22⋊C4—471no—
619C22×C22⋊C4—478no—
620C22×C22⋊C4—948no—
621C22×C22⋊C4C2×D4711yescharacteristic, complemented
622C22×C22⋊C4C2×D4711yescharacteristic, complemented
623C22×C22⋊C4C2×D4711yescharacteristic, complemented
624C22×C22⋊C4C2×D4711yescharacteristic, complemented
625#394—478no—
626#394—478no—
627#394—478no—
628#394C2×D4718yescomplemented
629#386—478no—
630#386—478no—
631#385—478no—
632#385—478no—
633#379—478no—
634#379—478no—
635#379—478no—
636C2×#95—471no—
637C2×#95—471no—
638C2×#95—471no—
639C2×#95C2×D4711yescharacteristic, complemented
640C47C2×#240511yescharacteristic, complemented, Sylow
641C25—471no—
642C25—471no—
643C25—471no—
644C25—478no—
645C25—474no—
646C25—474no—
647C25—944no—
648C25—944no—
649C25—944no—
650C25—944no—
651C25—944no—
652C25—944no—
653C25—944no—
654C25—944no—
655C25—944no—
656C25—1882no—
657C25—1882no—
658C25—1882no—
659C25—1882no—
660C25C22×D4711yescharacteristic
661C25C22×D4711yescharacteristic
662C22×D4—24no—
663C22×D4—24no—
664C22×D4—24no—
665C22×D4—478no—
666C22×D4—474no—
667C22×D4—474no—
668C22×D4—478no—
669C22×D4—474no—
670C22×D4—944no—
671C22×D4—944no—
672C22×D4—944no—
673C22×D4—9432no—
674C22×D4—9432no—
675C22×D4—9432no—
676C22×D4—94128no—
677C22×D4—944no—
678C22×D4—944no—
679C22×D4—944no—
680C22×D4—944no—
681C22×D4C22×D4714yes—
682C23×C4—471no—
683C23×C4—471no—
684C23×C4—471no—
685C23×C4—471no—
686C23×C4—471no—
687C23×C4—474no—
688C23×C4—474no—
689C23×C4—474no—
690C23×C4—944no—
691C23×C4—944no—
692C23×C4—944no—
693C23×C4—944no—
694C23×C4—944no—
695C23×C4—944no—
696C23×C4—944no—
697C23×C4—1882no—
698C23×C4—1882no—
699C23×C4C22×D4711yescharacteristic
700C23×C4C22×D4711yescharacteristic
701C23×C4C22×D4711yescharacteristic
702C23×C4C22×D4711yescharacteristic
703C23×C4C22×D4711yescharacteristic
704#123—9432no—
705#123—9432no—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—474no—
708C2×C4⋊C4—474no—
709C2×C4⋊C4—474no—
710C2×C4⋊C4—944no—
711C2×C4⋊C4—944no—
712C2×C4⋊C4—944no—
713C2×C4⋊C4C22×D4714yescomplemented
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—42no—
717C2×C22⋊C4—42no—
718C2×C22⋊C4—474no—
719C2×C22⋊C4—474no—
720C2×C22⋊C4—474no—
721C2×C22⋊C4—474no—
722C2×C22⋊C4—474no—
723C2×C22⋊C4—474no—
724C2×C22⋊C4—474no—
725C2×C22⋊C4—474no—
726C2×C22⋊C4—474no—
727C2×C22⋊C4—474no—
728C2×C22⋊C4—474no—
729C2×C22⋊C4—474no—
730C2×C22⋊C4—474no—
731C2×C22⋊C4—474no—
732C2×C22⋊C4—9432no—
733C2×C22⋊C4—944no—
734C2×C22⋊C4—944no—
735C2×C22⋊C4—944no—
736C2×C22⋊C4—944no—
737C2×C22⋊C4—944no—
738C2×C22⋊C4—944no—
739C2×C22⋊C4—944no—
740C2×C22⋊C4—944no—
741C2×C22⋊C4—944no—
742C2×C22⋊C4—944no—
743C2×C22⋊C4—1882no—
744C2×C22⋊C4—1882no—
745C2×C22⋊C4—1882no—
746C2×C22⋊C4—1882no—
747C2×C22⋊C4C22×D4714yescomplemented
748C2×C22⋊C4C22×D4714yescomplemented
749C2×C22⋊C4C22×D4714yescomplemented
750C2×C22⋊C4C22×D4714yescomplemented
751#95—474no—
752#95—474no—
753#95—474no—
754#95C22×D4714yescomplemented
755C24—22no—
756C24—22no—
757C24—22no—
758C24—22no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—22no—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—474no—
768C24—474no—
769C24—474no—
770C24—474no—
771C24—474no—
772C24—474no—
773C24—472no—
774C24—472no—
775C24—474no—
776C24—472no—
777C24—4716no—
778C24—9432no—
779C24—948no—
780C24—948no—
781C24—948no—
782C24—948no—
783C24—9432no—
784C24—948no—
785C24—948no—
786C24—948no—
787C24—948no—
788C24—9432no—
789C24—942no—
790C24—942no—
791C24—942no—
792C24—942no—
793C24—942no—
794C24—942no—
795C24—942no—
796C24—942no—
797C24—948no—
798C24—942no—
799C24—942no—
800C24—942no—
801C24—942no—
802C24—942no—
803C24—942no—
804C24—18816no—
805C24—1884no—
806C24—1884no—
807C24—1884no—
808C24—1884no—
809C24—18816no—
810C24—18816no—
811C24—18816no—
812C24—18816no—
813C24—18816no—
814C24—18816no—
815C24—18816no—
816C24—18816no—
817C24—18816no—
818C24—18816no—
819C24D4×D4714yes—
820C24D4×D4714yes—
821C24C23×D4712yes—
822C24C23×D4712yes—
823C24C23×D4711yescharacteristic
824C2×D4—232no—
825C2×D4—28no—
826C2×D4—28no—
827C2×D4—28no—
828C2×D4—4716no—
829C2×D4—4716no—
830C2×D4—9432no—
831C2×D4—948no—
832C2×D4—948no—
833C2×D4—948no—
834C2×D4—94256no—
835C2×D4—9432no—
836C2×D4—948no—
837C2×D4—948no—
838C2×D4—948no—
839C2×D4—9432no—
840C2×D4—948no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—474no—
856C22×C4—472no—
857C22×C4—472no—
858C22×C4—472no—
859C22×C4—472no—
860C22×C4—472no—
861C22×C4—948no—
862C22×C4—948no—
863C22×C4—9432no—
864C22×C4—948no—
865C22×C4—948no—
866C22×C4—948no—
867C22×C4—948no—
868C22×C4—942no—
869C22×C4—942no—
870C22×C4—948no—
871C22×C4—942no—
872C22×C4—942no—
873C22×C4—942no—
874C22×C4—942no—
875C22×C4—942no—
876C22×C4—942no—
877C22×C4—942no—
878C22×C4—942no—
879C22×C4—942no—
880C22×C4—942no—
881C22×C4—942no—
882C22×C4—942no—
883C22×C4—1884no—
884C22×C4—1884no—
885C22×C4—18816no—
886C22×C4—18816no—
887C22×C4D4×D4714yes—
888C22×C4C23×D4712yes—
889C22×C4C23×D4712yes—
890C22×C4C23×D4712yes—
891C22×C4C23×D4712yes—
892C22×C4C23×D4712yes—
893C4⋊C4—28no—
894C4⋊C4—948no—
895C4⋊C4—948no—
896C4⋊C4—948no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—948no—
902C22⋊C4—948no—
903C22⋊C4—948no—
904C22⋊C4—948no—
905C22⋊C4—948no—
906C22⋊C4—948no—
907C22⋊C4—948no—
908C22⋊C4—948no—
909C22⋊C4—948no—
910C22⋊C4—948no—
911C22⋊C4—1884no—
912C22⋊C4—1884no—
913C22⋊C4—1884no—
914C22⋊C4—1884no—
915C23—28no—
916C23—28no—
917C23—28no—
918C23—28no—
919C23—28no—
920C23—28no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—44no—
934C23—44no—
935C23—44no—
936C23—44no—
937C23—44no—
938C23—44no—
939C23—44no—
940C23—44no—
941C23—4716no—
942C23—4716no—
943C23—474no—
944C23—474no—
945C23—474no—
946C23—474no—
947C23—474no—
948C23—474no—
949C23—474no—
950C23—9432no—
951C23—9432no—
952C23—9432no—
953C23—948no—
954C23—948no—
955C23—948no—
956C23—948no—
957C23—948no—
958C23—948no—
959C23—948no—
960C23—948no—
961C23—948no—
962C23—948no—
963C23—948no—
964C23—948no—
965C23—942no—
966C23—942no—
967C23—942no—
968C23—942no—
969C23—942no—
970C23—942no—
971C23—942no—
972C23—942no—
973C23—948no—
974C23—948no—
975C23—948no—
976C23—942no—
977C23—942no—
978C23—942no—
979C23—942no—
980C23—942no—
981C23—942no—
982C23—18816no—
983C23—18816no—
984C23—18816no—
985C23—18816no—
986C23—18816no—
987C23—18816no—
988C23—18816no—
989C23—18816no—
990C23—18816no—
991C23—18816no—
992C23—188128no—
993C23—18816no—
994C23—188128no—
995C23—1884no—
996C23—1884no—
997C23—1884no—
998C23—1884no—
999C23C2×D4×D4714yes—
1000C23C2×D4×D4714yes—
1001C23C2×D4×D4712yes—
1002C23C2×D4×D4712yes—
1003C23C2×D4×D4712yes—
1004C23#41×D4712yes—
1005C23#41×D4712yes—
1006C23#1309406912yes—
1007C23#1309407012yes—
1008C23C24×D4711yescharacteristic
1009D4—232no—
1010D4—9432no—
1011D4—9432no—
1012D4—9432no—
1013C2×C4—28no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—44no—
1029C2×C4—44no—
1030C2×C4—44no—
1031C2×C4—44no—
1032C2×C4—474no—
1033C2×C4—9432no—
1034C2×C4—948no—
1035C2×C4—942no—
1036C2×C4—942no—
1037C2×C4—942no—
1038C2×C4—942no—
1039C2×C4—942no—
1040C2×C4—942no—
1041C2×C4—942no—
1042C2×C4—942no—
1043C2×C4—942no—
1044C2×C4—942no—
1045C2×C4—942no—
1046C2×C4—942no—
1047C2×C4—942no—
1048C2×C4—942no—
1049C2×C4—18816no—
1050C2×C4—18816no—
1051C2×C4—1884no—
1052C2×C4—1884no—
1053C2×C4—1884no—
1054C2×C4—1884no—
1055C2×C4C2×D4×D4714yes—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—416no—
1071C22—416no—
1072C22—478no—
1073C22—478no—
1074C22—944no—
1075C22—944no—
1076C22—944no—
1077C22—944no—
1078C22—944no—
1079C22—944no—
1080C22—944no—
1081C22—944no—
1082C22—944no—
1083C22—944no—
1084C22—944no—
1085C22—944no—
1086C22—9432no—
1087C22—9432no—
1088C22—944no—
1089C22—944no—
1090C22—944no—
1091C22—18864no—
1092C22—18864no—
1093C22—1882no—
1094C22—1882no—
1095C22—1882no—
1096C22—1882no—
1097C22—18816no—
1098C22#120×D4714yes—
1099C22#123×D4714yes—
1100C22#1568968114yes—
1101C22#1568976214yes—
1102C22#1568976514yes—
1103C22#1568976614yes—
1104C22#1568977014yes—
1105C22C22×D4×D4711yescharacteristic
1106C22C22×D4×D4711yescharacteristic
1107C22C22×D4×D4711yescharacteristic
1108C22C2×#41×D4711yescharacteristic
1109C22C2×#41×D4711yescharacteristic
1110C22C2×#1309406911yescharacteristic
1111C22C2×#1309407011yescharacteristic
1112C4—24no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—944no—
1118C4—1882no—
1119C4—1882no—
1120C4—1882no—
1121C4—1882no—
1122C2—44no—
1123C2—44no—
1124C2—948no—
1125C2—948no—
1126C2—1884no—
1127C2#2024671018yesdirect product factor
1128C2C2×#120×D4711yescharacteristic
1129C2C2×#123×D4711yescharacteristic
1130C2C2×#1568968111yescharacteristic
1131C2C2×#1568976211yescharacteristic
1132C2C2×#1568976511yescharacteristic
1133C2C2×#1568976611yescharacteristic
1134C2C2×#1568977011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#394C2
socleC24×C47C24
prime radicalC23×D4×D47C2
hypercenterC2×#394D47
hypocenterC47C2×#2405
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#13094009C2semidirect
3. C22×#13094006C2semidirect
4. C22×C22⋊C4×D47C2semidirect
5. #20246710C2direct (N × H)
6. C2×#15689039C2semidirect
7. C2×#15689038C2semidirect
8. C2×#15689037C2semidirect
9. C2×#15689001C2semidirect
10. C2×#15688999C2semidirect
11. C2×#15688997C2semidirect
12. C2×#15688994C2semidirect
13. C2×#15688978C2semidirect
14. C2×#15688978C2semidirect
15. C2×#15688978C2semidirect
16. C2×C47×#394C2semidirect
27. C23×C4×D47C22semidirect
28. C23×C4×D47C22semidirect
30. C2×#13094009C22semidirect
32. C2×#13094006C22semidirect
33. C22×C4⋊Dic47C22semidirect
34. C22×Dic47⋊C4C22semidirect
35. C22×Dic47⋊C4C22semidirect
36. C22×C22⋊Dic47C22semidirect
37. C22×C22⋊Dic47C22semidirect
38. C22×C22⋊Dic47C22semidirect
39. C22×C22⋊Dic47C22semidirect
44. C22×(C2×D47)⋊C4C22semidirect
45. C22×(C2×D47)⋊C4C22semidirect
46. C22×(C2×D47)⋊C4C22semidirect
47. C22×(C2×D47)⋊C4C22semidirect
48. C22×(C2×D47)⋊C4C22semidirect
49. C22×(C2×D47)⋊C4C22semidirect
51. C2×C22⋊C4×D47C22semidirect
52. #15689039C22semidirect
53. #15689038C22semidirect
54. #15689037C22semidirect
55. #15689001C22semidirect
56. #15688999C22semidirect
57. #15688997C22semidirect
58. #15688994C22semidirect
59. #15688978C22semidirect
60. #15688978C22semidirect
61. #15688978C22semidirect
62. C2×C47⋊#95C22semidirect
63. C2×C47⋊#95C22semidirect
64. C2×C47⋊#95C22semidirect
66. C22×C4⋊C4×C47C22semidirect
67. C22×C22⋊C4×C47C22semidirect
68. C22×C22⋊C4×C47C22semidirect
69. C22×C22⋊C4×C47C22semidirect
70. C22×C22⋊C4×C47C22semidirect
71. C47×#394C22semidirect
72. C2×#95×C47C22semidirect
123. C22×C4×D47C23semidirect
124. C22×C4×D47C23semidirect
128. C2×C4⋊Dic47C23semidirect
131. C2×Dic47⋊C4C23semidirect
132. C2×Dic47⋊C4C23semidirect
137. C2×C22⋊Dic47C23semidirect
138. C2×C22⋊Dic47C23semidirect
139. C2×C22⋊Dic47C23semidirect
140. C2×C22⋊Dic47C23semidirect
155. C2×(C2×D47)⋊C4C23semidirect
156. C2×(C2×D47)⋊C4C23semidirect
157. C2×(C2×D47)⋊C4C23semidirect
158. C2×(C2×D47)⋊C4C23semidirect
159. C2×(C2×D47)⋊C4C23semidirect
160. C2×(C2×D47)⋊C4C23semidirect
162. C47⋊#95C23semidirect
163. C47⋊#95C23semidirect
164. C47⋊#95C23semidirect
177. C2×C4⋊C4×C47C23semidirect
182. C2×C22⋊C4×C47C23semidirect
183. C2×C22⋊C4×C47C23semidirect
184. C2×C22⋊C4×C47C23semidirect
185. C2×C22⋊C4×C47C23semidirect
186. #95×C47C23semidirect
433. C22×D47#123semidirect
544. C2×D47C2×#123semidirect
563. C2×#394D47semidirect
573. C2×C47#2405semidirect
604. C22×C4⋊C4C2×D47semidirect
621. C22×C22⋊C4C2×D47semidirect
622. C22×C22⋊C4C2×D47semidirect
623. C22×C22⋊C4C2×D47semidirect
624. C22×C22⋊C4C2×D47semidirect
628. #394C2×D47semidirect
639. C2×#95C2×D47semidirect
640. C47C2×#2405semidirect
713. C2×C4⋊C4C22×D47semidirect
747. C2×C22⋊C4C22×D47semidirect
748. C2×C22⋊C4C22×D47semidirect
749. C2×C22⋊C4C22×D47semidirect
750. C2×C22⋊C4C22×D47semidirect
754. #95C22×D47semidirect
1127. C2#20246710direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4×D472
C22×#130940092
C22×#130940062
C22×C22⋊C4×D472
#202467102
C2×#156890392
C2×#156890382
C2×#156890372
C2×#156890012
C2×#156889992
C2×#156889972
C2×#156889942
C2×#156889782
C2×C47×#3942
C2×#240547