Finite Group Databasebeta

← C2×#20248408 #26387462

Subgroups — C2×#20248408 #26387462

Order 12032.

2574 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094023C211yesmaximal, characteristic
2C22×#13094014C211yesmaximal, characteristic
3#20248408C2116yesmaximal, direct product factor
4C2×#15689056C211yesmaximal, characteristic
5C2×#15689053C211yesmaximal, characteristic
6C2×#15689043C211yesmaximal, characteristic
7C2×#15689043C211yesmaximal, characteristic
8C2×#15689029C211yesmaximal, characteristic
9C2×#15689027C211yesmaximal, characteristic
10C2×#15689020C211yesmaximal, characteristic
11C2×#15689018C211yesmaximal, characteristic
12C2×#15689018C211yesmaximal, characteristic
13C2×#15688987C211yesmaximal, characteristic
14C2×C4×Dic47⋊C4C211yesmaximal, characteristic
15C2×#15688974C211yesmaximal, characteristic
16C2×C47×#389C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C2×#13094023—28no—
20C2×#13094023C2218yes—
21C2×#13094014—28no—
22C2×#13094014C2218yes—
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39#15689056C2218yes—
40#15689053C2218yes—
41#15689043C2218yes—
42#15689043C2218yes—
43#15689029C2218yes—
44#15689027C2218yes—
45#15689020C2218yes—
46#15689018C2218yes—
47#15689018C2218yes—
48#15688987C2218yes—
49C4×Dic47⋊C4C2218yes—
50#15688974C2218yes—
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C42×C47C2211yescharacteristic
66C47×#389C2218yes—
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C22×Dic94—24no—
70C22×Dic94—24no—
71C22×Dic94—24no—
72C22×Dic94—24no—
73C22×Dic94—42no—
74C22×Dic94—42no—
75C22×Dic94C2314yes—
76C22×Dic94C2314yes—
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85#13094023—232no—
86#13094014—232no—
87C2×C4⋊Dic47—24no—
88C2×C4⋊Dic47—24no—
89C2×C4⋊Dic47C2314yes—
90C2×C4⋊Dic47C2314yes—
91C2×Dic47⋊C4—24no—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—24no—
95C2×Dic47⋊C4—24no—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—24no—
98C2×Dic47⋊C4—42no—
99C2×Dic47⋊C4D418yes—
100C2×Dic47⋊C4Q818yescomplemented
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×C4×Dic47—24no—
112C2×C4×Dic47—24no—
113C2×C4×Dic47—42no—
114C2×C4×Dic47Q818yescomplemented
115C2×C4×Dic47C2314yes—
116C2×C4×Dic47C2314yes—
117C2×C4×Dic47C2314yes—
118C2×C4×Dic47C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47—24no—
137C2×C4⋊C4×C47—24no—
138C2×C4⋊C4×C47—24no—
139C2×C4⋊C4×C47—42no—
140C2×C4⋊C4×C47C2314yes—
141C2×C4⋊C4×C47C2314yes—
142C2×C4⋊C4×C47C2314yes—
143C2×C4⋊C4×C47C2314yes—
144C2×C42×C47—42no—
145C2×C42×C47C2314yes—
146#95×C47C2314yes—
147#95×C47C2314yes—
148C24×C47C2411yescharacteristic
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47C2×D414yes—
167C22×C4×C47C2×Q814yes—
168C22×C4×C47C2×Q814yes—
169C22×C4×C47#4114yes—
170C22×C4×C47C2412yes—
171C22×C4×C47C2412yes—
172C22×C4×C47C2412yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2412yes—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47C2×D414yes—
195C22×Dic47C2×D414yes—
196C22×Dic47C2×Q814yes—
197C22×Dic47C2×Q814yes—
198C22×Dic47C2×Q814yes—
199C22×Dic47C2×Q814yes—
200C22×Dic47#4114yes—
201C22×Dic47C2412yes—
202C22×Dic47C2412yes—
203C22×Dic47C2412yes—
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C2×Dic94—28no—
210C2×Dic94—28no—
211C2×Dic94—28no—
212C2×Dic94—28no—
213C2×Dic94—44no—
214C2×Dic94—44no—
215C2×Dic94—416no—
216C2×Dic94—416no—
217C4⋊C4×C47—28no—
218C4⋊C4×C47—28no—
219C4⋊C4×C47—28no—
220C4⋊C4×C47—44no—
221C42×C47—44no—
222C4⋊Dic47—28no—
223C4⋊Dic47—28no—
224Dic47⋊C4—28no—
225Dic47⋊C4—28no—
226Dic47⋊C4—28no—
227Dic47⋊C4—28no—
228Dic47⋊C4—28no—
229Dic47⋊C4—28no—
230Dic47⋊C4—28no—
231Dic47⋊C4—44no—
232Dic47⋊C4C2×D4116yes—
233Dic47⋊C4C2×Q8116yescomplemented
234C4×Dic47—28no—
235C4×Dic47—28no—
236C4×Dic47—44no—
237C4×Dic47C2×Q8116yescomplemented
238C23×C47C22×D412yes—
239C23×C47C22×Q812yes—
240C23×C47C22×Q812yes—
241C23×C47C2×#4112yes—
242C23×C47C2×#4112yes—
243C23×C47H(5,𝔽2)12yes—
244C23×C472−1+412yes—
245C23×C47C2511yescharacteristic
246C2×C4×C47—28no—
247C2×C4×C47—28no—
248C2×C4×C47—28no—
249C2×C4×C47—28no—
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—44no—
268C2×C4×C47—44no—
269C2×C4×C47—44no—
270C2×C4×C47C22×D414yes—
271C2×C4×C47C22×Q814yes—
272C2×C4×C47C22×Q814yes—
273C2×C4×C47C2×#4114yes—
274C2×Dic47—28no—
275C2×Dic47—28no—
276C2×Dic47—28no—
277C2×Dic47—28no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—22no—
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—44no—
296C2×Dic47—44no—
297C2×Dic47—44no—
298C2×Dic47C4⋊Q8116yes—
299C2×Dic47C22×D414yes—
300C2×Dic47C22×D414yes—
301C2×Dic47C22×Q814yes—
302C2×Dic47C22×Q814yes—
303C2×Dic47C22×Q814yes—
304C2×Dic47C22×Q814yes—
305C2×Dic47C2×#4114yes—
306Dic94—416no—
307Dic94—416no—
308C2×#2550—471nomaximal, Sylow
309C22×C47C2×C4⋊Q814yes—
310C22×C47#53314yes—
311C22×C47#54414yes—
312C22×C47#54614yes—
313C22×C47#54814yes—
314C22×C47#55414yes—
315C22×C47#55714yes—
316C22×C47C23×D411yescharacteristic
317C22×C47C23×Q811yescharacteristic
318C22×C47C23×Q811yescharacteristic
319C22×C47C22×#4111yescharacteristic
320C22×C47C22×#4111yescharacteristic
321C22×C47C2×H(5,𝔽2)11yescharacteristic
322C22×C47C2×2−1+411yescharacteristic
323C4×C47—24no—
324C4×C47—24no—
325C4×C47—24no—
326C4×C47—24no—
327C4×C47—42no—
328C4×C47—42no—
329C4×C47—42no—
330Dic47—24no—
331Dic47—24no—
332Dic47—24no—
333Dic47—24no—
334Dic47—42no—
335Dic47—42no—
336Dic47—42no—
337Dic47C2×C4⋊Q818yes—
338C22×C4⋊Q8—471no—
339C22×#125—471no—
340#2550—4716no—
341C2×#398—471no—
342C2×#398—471no—
343C2×#395—471no—
344C2×#395—471no—
345C2×#391—471no—
346C2×#391—471no—
347C2×#389—471no—
348C2×#389—471no—
349C2×#389—471no—
350C2×#389D4711yescharacteristic
351C2×#382—471no—
352C2×C4×C4⋊C4—471no—
353C2×C4×C4⋊C4—471no—
354C2×C47#255018yescomplemented
355C2×C47C22×C4⋊Q811yescharacteristic
356C2×C47C2×#53311yescharacteristic
357C2×C47C2×#54411yescharacteristic
358C2×C47C2×#54611yescharacteristic
359C2×C47C2×#54811yescharacteristic
360C2×C47C2×#55411yescharacteristic
361C2×C47C2×#55711yescharacteristic
362C23×Q8—471no—
363C23×Q8—471no—
364C2×C4⋊Q8—478no—
365C2×C4⋊Q8—948no—
366C2×#125—478no—
367C2×#125—948no—
368C22×C4⋊C4—471no—
369C22×C4⋊C4—471no—
370C22×C4⋊C4—471no—
371C22×C4⋊C4—471no—
372C22×C4⋊C4—471no—
373C22×C4⋊C4—471no—
374C22×C4⋊C4—471no—
375C22×C4⋊C4—471no—
376C22×C4⋊C4—471no—
377C22×C4⋊C4—471no—
378C22×C4⋊C4—471no—
379C22×C4⋊C4—471no—
380C22×C4⋊C4C2×D4711yescharacteristic
381C22×C4⋊C4C2×D4711yescharacteristic
382C22×C4⋊C4C2×D4711yescharacteristic
383C22×C4⋊C4C2×D4711yescharacteristic
384C22×C42—471no—
385C22×C42—471no—
386C22×C42—471no—
387C22×C42—471no—
388C22×C42C2×D4711yescharacteristic
389#398—478no—
390#398—478no—
391#395—478no—
392#395—478no—
393#391—478no—
394#391—478no—
395#389—478no—
396#389—478no—
397#389—478no—
398#389C2×D4718yes—
399#382—478no—
400C4×C4⋊C4—478no—
401C4×C4⋊C4—478no—
402C2×#95—471no—
403C2×#95—471no—
404C2×#95—471no—
405C2×#95—471no—
406C2×#95—471no—
407C2×#95—471no—
408C2×#95—471no—
409C2×#95—471no—
410C2×#95—471no—
411C2×#95—471no—
412C2×#95C2×D4711yescharacteristic
413C2×#95C2×D4711yescharacteristic
414C47C2×#255011yescharacteristic, complemented, Sylow
415C22×Q8—474no—
416C22×Q8—474no—
417C22×Q8—944no—
418C22×Q8—944no—
419C22×Q8—944no—
420C22×Q8—944no—
421C22×Q8—1882no—
422C22×Q8—1882no—
423C23×C4—471no—
424C23×C4—471no—
425C23×C4—471no—
426C23×C4—471no—
427C23×C4—471no—
428C23×C4—471no—
429C23×C4—471no—
430C23×C4—471no—
431C23×C4C22×D4711yescharacteristic
432C23×C4C22×D4711yescharacteristic
433C23×C4C22×D4711yescharacteristic
434C23×C4C22×D4711yescharacteristic
435C23×C4C22×D4711yescharacteristic
436C23×C4C22×D4711yescharacteristic
437C23×C4C22×D4711yescharacteristic
438C4⋊Q8—9432no—
439#125—9432no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—478no—
445C2×C4⋊C4—478no—
446C2×C4⋊C4—474no—
447C2×C4⋊C4—474no—
448C2×C4⋊C4—474no—
449C2×C4⋊C4—474no—
450C2×C4⋊C4—474no—
451C2×C4⋊C4—474no—
452C2×C4⋊C4—474no—
453C2×C4⋊C4—474no—
454C2×C4⋊C4—474no—
455C2×C4⋊C4—474no—
456C2×C4⋊C4—474no—
457C2×C4⋊C4—474no—
458C2×C4⋊C4—944no—
459C2×C4⋊C4—944no—
460C2×C4⋊C4—944no—
461C2×C4⋊C4—944no—
462C2×C4⋊C4—944no—
463C2×C4⋊C4—944no—
464C2×C4⋊C4—944no—
465C2×C4⋊C4—944no—
466C2×C4⋊C4—944no—
467C2×C4⋊C4—1882no—
468C2×C4⋊C4C22×D4714yes—
469C2×C4⋊C4C22×D4714yes—
470C2×C4⋊C4C22×D4714yes—
471C2×C4⋊C4C22×D4714yes—
472C2×C42—42no—
473C2×C42—478no—
474C2×C42—474no—
475C2×C42—474no—
476C2×C42—474no—
477C2×C42—474no—
478C2×C42—944no—
479C2×C42—944no—
480C2×C42—1882no—
481C2×C42C22×D4714yes—
482#95—474no—
483#95—474no—
484#95—474no—
485#95—474no—
486#95—474no—
487#95—474no—
488#95—474no—
489#95—474no—
490#95—474no—
491#95—474no—
492#95C22×D4714yes—
493#95C22×D4714yes—
494C24C23×D4711yescharacteristic
495C2×Q8—948no—
496C2×Q8—948no—
497C2×Q8—948no—
498C2×Q8—948no—
499C2×Q8—1884no—
500C2×Q8—1884no—
501C2×Q8—18816no—
502C2×Q8—18816no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—474no—
521C22×C4—474no—
522C22×C4—474no—
523C22×C4—472no—
524C22×C4—474no—
525C22×C4—474no—
526C22×C4—474no—
527C22×C4—474no—
528C22×C4—472no—
529C22×C4—472no—
530C22×C4—472no—
531C22×C4—472no—
532C22×C4—472no—
533C22×C4—472no—
534C22×C4—472no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4#1062535014yes—
553C22×C4D4×D4714yes—
554C22×C4Q8×D4714yes—
555C22×C4Q8×D4714yes—
556C22×C4C23×D4712yes—
557C22×C4C23×D4712yes—
558C22×C4C23×D4712yes—
559C22×C4C23×D4712yes—
560C22×C4C23×D4712yes—
561C22×C4C23×D4712yes—
562C22×C4C23×D4712yes—
563C4⋊C4—28no—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—44no—
567C4⋊C4—4716no—
568C4⋊C4—4716no—
569C4⋊C4—948no—
570C4⋊C4—948no—
571C4⋊C4—948no—
572C4⋊C4—948no—
573C4⋊C4—948no—
574C4⋊C4—948no—
575C4⋊C4—948no—
576C4⋊C4—948no—
577C4⋊C4—948no—
578C4⋊C4—1884no—
579C42—44no—
580C42—4716no—
581C42—948no—
582C42—948no—
583C42—1884no—
584C23C2×D4×D4712yes—
585C23C2×Q8×D4712yes—
586C23C2×Q8×D4712yes—
587C23#41×D4712yes—
588C23C2×#1062535012yes—
589C23#1309406912yes—
590C23#1309407112yes—
591C23C24×D4711yescharacteristic
592Q8—18816no—
593Q8—18816no—
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—28no—
597C2×C4—28no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—4716no—
619C2×C4—474no—
620C2×C4—474no—
621C2×C4—474no—
622C2×C4—474no—
623C2×C4—474no—
624C2×C4—474no—
625C2×C4—474no—
626C2×C4—948no—
627C2×C4—948no—
628C2×C4—948no—
629C2×C4—948no—
630C2×C4—942no—
631C2×C4—942no—
632C2×C4—942no—
633C2×C4—942no—
634C2×C4—942no—
635C2×C4—942no—
636C2×C4—942no—
637C2×C4—942no—
638C2×C4—942no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—1884no—
648C2×C4—1884no—
649C2×C4—1884no—
650C2×C4C2×D4×D4714yes—
651C2×C4C2×Q8×D4714yes—
652C2×C4C2×Q8×D4714yes—
653C2×C4C2×#1062535014yes—
654C22C4⋊Q8×D4714yes—
655C22#1568967714yes—
656C22#1568975214yes—
657C22#1568976214yes—
658C22#1568978214yes—
659C22#1568982814yes—
660C22#1568985014yes—
661C22C22×D4×D4711yescharacteristic
662C22C22×Q8×D4711yescharacteristic
663C22C22×Q8×D4711yescharacteristic
664C22C2×#41×D4711yescharacteristic
665C22C22×#1062535011yescharacteristic
666C22C2×#1309406911yescharacteristic
667C22C2×#1309407111yescharacteristic
668C4—24no—
669C4—24no—
670C4—24no—
671C4—24no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—478no—
676C4—944no—
677C4—944no—
678C4—944no—
679C4—944no—
680C4—1882no—
681C4—1882no—
682C4—1882no—
683C2#2024840818yesdirect product factor
684C2C2×C4⋊Q8×D4711yescharacteristic
685C2C2×#1568967711yescharacteristic
686C2C2×#1568975211yescharacteristic
687C2C2×#1568976211yescharacteristic
688C2C2×#1568978211yescharacteristic
689C2C2×#1568982811yescharacteristic
690C2C2×#1568985011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#389C2
socle, prime radicalC24×C47C24
hypercenterC2×#389D47
hypocenterC47C2×#2550
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #20248408C2direct (N × H)
100. C2×Dic47⋊C4Q8semidirect
114. C2×C4×Dic47Q8semidirect
233. Dic47⋊C4C2×Q8semidirect
237. C4×Dic47C2×Q8semidirect
354. C2×C47#2550semidirect
414. C47C2×#2550semidirect
683. C2#20248408direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940232
C22×#130940142
#202484082
C2×#156890562
C2×#156890532
C2×#156890432
C2×#156890292
C2×#156890272
C2×#156890202
C2×#156890182
C2×#156889872
C2×C4×Dic47⋊C42
C2×#156889742
C2×C47×#3892
C2×#255047