Finite Group Databasebeta

← C2×#20251647 #26422697

Subgroups — C2×#20251647 #26422697

Order 12032.

2110 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251647C2116yesmaximal, direct product factor
2C2×#15689064C211yesmaximal, characteristic, complemented
3C2×#15689060C211yesmaximal, characteristic
4C2×#15689057C211yesmaximal, characteristic, complemented
5C2×#15689056C211yesmaximal, characteristic, complemented
6C2×#15689056C211yesmaximal, characteristic, complemented
7C2×#15689055C211yesmaximal, characteristic, complemented
8C2×#15689047C211yesmaximal, characteristic
9C2×#15689045C211yesmaximal, characteristic
10C2×#15689044C211yesmaximal, characteristic, complemented
11C2×#15689044C211yesmaximal, characteristic, complemented
12C2×#15689036C211yesmaximal, characteristic
13C2×#15688985C211yesmaximal, characteristic
14C2×#15688982C211yesmaximal, characteristic
15C2×#15688980C211yesmaximal, characteristic
16C2×C47×#400C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36#15689064C2218yescomplemented
37#15689060C2218yes—
38#15689057C2218yescomplemented
39#15689056C2218yescomplemented
40#15689056C2218yescomplemented
41#15689055C2218yescomplemented
42#15689047C2218yes—
43#15689045C2218yes—
44#15689044C2218yescomplemented
45#15689044C2218yescomplemented
46#15689036C2218yes—
47#15688985C2218yes—
48#15688982C2218yes—
49#15688980C2218yes—
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C22×C4⋊C4×C47C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C47×#400C2218yescomplemented
62C2×#95×C47C2211yescharacteristic
63C2×#95×C47C2211yescharacteristic
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C24×D47C2311yescharacteristic
68C22×Dic94—42no—
69C22×Dic94—42no—
70C22×Dic94—42no—
71C22×Dic94C2314yes—
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C22×C4×D47—42no—
80C22×C4×D47—42no—
81C22×C4×D47Q818yescomplemented
82C22×C4×D47C2314yes—
83C2×C4⋊Dic47—42no—
84C2×C4⋊Dic47—42no—
85C2×C4⋊Dic47—42no—
86C2×C4⋊Dic47—42no—
87C2×C4⋊Dic47—42no—
88C2×C4⋊Dic47C2314yes—
89C2×C4⋊Dic47C2314yes—
90C2×C4⋊Dic47C2314yes—
91C2×C4⋊Dic47C2314yes—
92C2×C4⋊Dic47C2314yes—
93C2×Dic47⋊C4—42no—
94C2×Dic47⋊C4—42no—
95C2×Dic47⋊C4—42no—
96C2×Dic47⋊C4—42no—
97C2×Dic47⋊C4—42no—
98C2×Dic47⋊C4—42no—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×(C2×D47)⋊C4—42no—
106C2×(C2×D47)⋊C4—42no—
107C2×(C2×D47)⋊C4—42no—
108C2×(C2×D47)⋊C4—42no—
109C2×(C2×D47)⋊C4—42no—
110C2×(C2×D47)⋊C4—42no—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47—42no—
134C2×C4⋊C4×C47—42no—
135C2×C4⋊C4×C47C2314yes—
136C2×C4⋊C4×C47C2314yes—
137#95×C47C2314yes—
138#95×C47C2314yes—
139#95×C47C2314yes—
140#95×C47C2314yes—
141#95×C47C2314yes—
142C24×C47C2411yescharacteristic
143C23×D47—22no—
144C23×D47—22no—
145C23×D47—22no—
146C23×D47—22no—
147C23×D47—22no—
148C23×D47—22no—
149C23×D47C2×Q814yes—
150C23×D47C2412yes—
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×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47C2×Q814yes—
172C22×C4×C47C2412yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2412yes—
177C22×C4×C47C2412yes—
178C22×C4×C47C2412yes—
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×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47C2×Q814yes—
200C22×Dic47C2412yes—
201C22×Dic47C2412yes—
202C22×Dic47C2412yes—
203C22×Dic47C2412yes—
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C2×C4×D47—416no—
208C2×C4×D47—44no—
209C2×C4×D47—44no—
210C2×C4×D47C2×Q8116yescomplemented
211C2×Dic94—44no—
212C2×Dic94—44no—
213C2×Dic94—44no—
214C2×Dic94—416no—
215C4⋊C4×C47—44no—
216C4⋊C4×C47—44no—
217(C2×D47)⋊C4—44no—
218(C2×D47)⋊C4—44no—
219(C2×D47)⋊C4—44no—
220(C2×D47)⋊C4—44no—
221(C2×D47)⋊C4—44no—
222(C2×D47)⋊C4—44no—
223C4⋊Dic47—44no—
224C4⋊Dic47—44no—
225C4⋊Dic47—44no—
226C4⋊Dic47—44no—
227C4⋊Dic47—44no—
228Dic47⋊C4—44no—
229Dic47⋊C4—44no—
230Dic47⋊C4—44no—
231Dic47⋊C4—44no—
232Dic47⋊C4—44no—
233Dic47⋊C4—44no—
234C23×C47C22×Q812yes—
235C23×C47H(5,𝔽2)12yes—
236C23×C47H(5,𝔽2)12yes—
237C23×C47H(5,𝔽2)12yes—
238C23×C47H(5,𝔽2)12yes—
239C23×C472−1+412yes—
240C23×C472−1+412yes—
241C23×C47C2511yescharacteristic
242C22×D47—28no—
243C22×D47—28no—
244C22×D47—28no—
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—44no—
252C22×D47—44no—
253C22×D47—44no—
254C22×D47—44no—
255C22×D47C22×Q814yes—
256C2×C4×C47—28no—
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—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—44no—
278C2×C4×C47—44no—
279C2×C4×C47—44no—
280C2×C4×C47—44no—
281C2×C4×C47—44no—
282C2×C4×C47—44no—
283C2×C4×C47C22×Q814yes—
284C2×Dic47—28no—
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—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—44no—
306C2×Dic47—44no—
307C2×Dic47—44no—
308C2×Dic47—44no—
309C2×Dic47—44no—
310C2×Dic47—44no—
311C2×Dic47C22×Q814yes—
312C4×D47—416no—
313Dic94—416no—
314C2×#2841—471nomaximal, Sylow
315C22×C47#54314yes—
316C22×C47#54414yes—
317C22×C47#54414yes—
318C22×C47#56014yes—
319C22×C47#56214yes—
320C22×C47#56214yes—
321C22×C47#56314yes—
322C22×C47C23×Q811yescharacteristic
323C22×C47C2×H(5,𝔽2)11yescharacteristic
324C22×C47C2×H(5,𝔽2)11yescharacteristic
325C22×C47C2×H(5,𝔽2)11yescharacteristic
326C22×C47C2×H(5,𝔽2)11yescharacteristic
327C22×C47C2×2−1+411yescharacteristic
328C22×C47C2×2−1+411yescharacteristic
329C2×D47—24no—
330C2×D47—24no—
331C2×D47—24no—
332C2×D47—416no—
333C2×D47—42no—
334C2×D47—42no—
335C2×D47—42no—
336C2×D47—42no—
337C4×C47—24no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47—42no—
342C4×C47—42no—
343C4×C47—42no—
344Dic47—24no—
345Dic47—42no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
350Dic47—42no—
351#2841—4716no—
352C2×#400—471no—
353C2×#400D4711yescharacteristic, complemented
354C2×#399—471no—
355C2×#398—471no—
356C2×#398—471no—
357C2×#398—471no—
358C2×#398—471no—
359C2×#396—471no—
360C2×#396—471no—
361C2×#395—471no—
362C2×#395—471no—
363C2×#393—471no—
364C2×#381—471no—
365C2×#380—471no—
366C2×#380—471no—
367C2×C47#284118yescomplemented
368C2×C47C2×#54311yescharacteristic
369C2×C47C2×#54411yescharacteristic
370C2×C47C2×#54411yescharacteristic
371C2×C47C2×#56011yescharacteristic
372C2×C47C2×#56211yescharacteristic
373C2×C47C2×#56211yescharacteristic
374C2×C47C2×#56311yescharacteristic
375D47—44no—
376C23×Q8—471no—
377C24×C4—471no—
378C22×C4⋊C4—471no—
379C22×C4⋊C4—471no—
380C22×C4⋊C4—471no—
381C22×C4⋊C4—471no—
382C22×C4⋊C4—471no—
383C22×C4⋊C4—471no—
384C22×C4⋊C4—471no—
385C22×C4⋊C4—471no—
386C22×C4⋊C4—471no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4—471no—
389C22×C4⋊C4C2×D4711yescharacteristic
390C22×C4⋊C4C2×D4711yescharacteristic
391C22×C22⋊C4—471no—
392C22×C22⋊C4—471no—
393C22×C22⋊C4—471no—
394C22×C22⋊C4—471no—
395C22×C22⋊C4—471no—
396C22×C22⋊C4—471no—
397#400—478no—
398#400C2×D4718yescomplemented
399#399—478no—
400#398—478no—
401#398—478no—
402#398—478no—
403#398—478no—
404#396—478no—
405#396—478no—
406#395—478no—
407#395—478no—
408#393—478no—
409#381—478no—
410#380—478no—
411#380—478no—
412C2×#95—471no—
413C2×#95—471no—
414C2×#95—471no—
415C2×#95—471no—
416C2×#95—471no—
417C2×#95—471no—
418C2×#95—471no—
419C2×#95—471no—
420C2×#95—471no—
421C2×#95C2×D4711yescharacteristic
422C2×#95C2×D4711yescharacteristic
423C2×#95C2×D4711yescharacteristic
424C2×#95C2×D4711yescharacteristic
425C2×#95C2×D4711yescharacteristic
426C47C2×#284111yescharacteristic, complemented, Sylow
427C25—471no—
428C22×Q8—474no—
429C22×Q8—1882no—
430C22×Q8—1882no—
431C22×Q8—1882no—
432C23×C4—471no—
433C23×C4—478no—
434C23×C4—474no—
435C23×C4—471no—
436C23×C4—471no—
437C23×C4—471no—
438C23×C4—471no—
439C23×C4—471no—
440C23×C4—471no—
441C23×C4—1882no—
442C23×C4—1882no—
443C23×C4C22×D4711yescharacteristic
444C23×C4C22×D4711yescharacteristic
445C23×C4C22×D4711yescharacteristic
446C23×C4C22×D4711yescharacteristic
447C23×C4C22×D4711yescharacteristic
448C23×C4C22×D4711yescharacteristic
449C23×C4C22×D4711yescharacteristic
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
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—474no—
459C2×C4⋊C4—474no—
460C2×C4⋊C4—474no—
461C2×C4⋊C4—474no—
462C2×C4⋊C4—474no—
463C2×C4⋊C4—1882no—
464C2×C4⋊C4—1882no—
465C2×C4⋊C4—1882no—
466C2×C4⋊C4—1882no—
467C2×C4⋊C4—1882no—
468C2×C4⋊C4—1882no—
469C2×C4⋊C4—1882no—
470C2×C4⋊C4—1882no—
471C2×C4⋊C4—1882no—
472C2×C4⋊C4—1882no—
473C2×C4⋊C4—1882no—
474C2×C4⋊C4C22×D4714yes—
475C2×C4⋊C4C22×D4714yes—
476C2×C22⋊C4—474no—
477C2×C22⋊C4—474no—
478C2×C22⋊C4—474no—
479C2×C22⋊C4—474no—
480C2×C22⋊C4—474no—
481C2×C22⋊C4—474no—
482C2×C22⋊C4—1882no—
483C2×C22⋊C4—1882no—
484C2×C22⋊C4—1882no—
485C2×C22⋊C4—1882no—
486C2×C22⋊C4—1882no—
487C2×C22⋊C4—1882no—
488#95—474no—
489#95—474no—
490#95—474no—
491#95—474no—
492#95—474no—
493#95—474no—
494#95—474no—
495#95—474no—
496#95—474no—
497#95C22×D4714yes—
498#95C22×D4714yes—
499#95C22×D4714yes—
500#95C22×D4714yes—
501#95C22×D4714yes—
502C24—474no—
503C24—472no—
504C24—942no—
505C24—942no—
506C24—942no—
507C24—942no—
508C24—942no—
509C24—942no—
510C24C23×D4711yescharacteristic
511C2×Q8—1884no—
512C2×Q8—1884no—
513C2×Q8—1884no—
514C2×Q8—18816no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—474no—
536C22×C4—472no—
537C22×C4—4716no—
538C22×C4—472no—
539C22×C4—472no—
540C22×C4—472no—
541C22×C4—472no—
542C22×C4—472no—
543C22×C4—472no—
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—942no—
553C22×C4—942no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—942no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—18816no—
565C22×C4—1884no—
566C22×C4—1884no—
567C22×C4Q8×D4714yes—
568C22×C4C23×D4712yes—
569C22×C4C23×D4712yes—
570C22×C4C23×D4712yes—
571C22×C4C23×D4712yes—
572C22×C4C23×D4712yes—
573C22×C4C23×D4712yes—
574C22×C4C23×D4712yes—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—1884no—
578C4⋊C4—1884no—
579C4⋊C4—1884no—
580C4⋊C4—1884no—
581C4⋊C4—1884no—
582C4⋊C4—1884no—
583C4⋊C4—1884no—
584C4⋊C4—1884no—
585C4⋊C4—1884no—
586C4⋊C4—1884no—
587C4⋊C4—1884no—
588C22⋊C4—1884no—
589C22⋊C4—1884no—
590C22⋊C4—1884no—
591C22⋊C4—1884no—
592C22⋊C4—1884no—
593C22⋊C4—1884no—
594C23—474no—
595C23—948no—
596C23—948no—
597C23—948no—
598C23—942no—
599C23—942no—
600C23—942no—
601C23—942no—
602C23—942no—
603C23—942no—
604C23—1884no—
605C23—1884no—
606C23—1884no—
607C23—1884no—
608C23C2×Q8×D4712yes—
609C23#1309406912yes—
610C23#1309407012yes—
611C23#1309407012yes—
612C23#1309407012yes—
613C23#1309407112yes—
614C23#1309407112yes—
615C23C24×D4711yescharacteristic
616Q8—18816no—
617C2×C4—28no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—474no—
645C2×C4—948no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—18816no—
667C2×C4—1884no—
668C2×C4—1884no—
669C2×C4—1884no—
670C2×C4—1884no—
671C2×C4—1884no—
672C2×C4—1884no—
673C2×C4C2×Q8×D4714yes—
674C22—944no—
675C22—944no—
676C22—944no—
677C22—1882no—
678C22—1882no—
679C22—1882no—
680C22—1882no—
681C22—18816no—
682C22#1568974814yes—
683C22#1568975314yes—
684C22#1568975314yes—
685C22#1568986414yes—
686C22#1568986714yes—
687C22#1568987014yes—
688C22#1568987514yes—
689C22C22×Q8×D4711yescharacteristic
690C22C2×#1309406911yescharacteristic
691C22C2×#1309407011yescharacteristic
692C22C2×#1309407011yescharacteristic
693C22C2×#1309407011yescharacteristic
694C22C2×#1309407111yescharacteristic
695C22C2×#1309407111yescharacteristic
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—944no—
704C4—1882no—
705C4—1882no—
706C4—1882no—
707C4—1882no—
708C4—1882no—
709C4—1882no—
710C2—1884no—
711C2#2025164718yesdirect product factor
712C2C2×#1568974811yescharacteristic
713C2C2×#1568975311yescharacteristic
714C2C2×#1568975311yescharacteristic
715C2C2×#1568986411yescharacteristic
716C2C2×#1568986711yescharacteristic
717C2C2×#1568987011yescharacteristic
718C2C2×#1568987511yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#400C2
socleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#400D47
hypocenterC47C2×#2841
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #20251647C2direct (N × H)
2. C2×#15689064C2semidirect
4. C2×#15689057C2semidirect
5. C2×#15689056C2semidirect
6. C2×#15689056C2semidirect
7. C2×#15689055C2semidirect
10. C2×#15689044C2semidirect
11. C2×#15689044C2semidirect
16. C2×C47×#400C2semidirect
36. #15689064C22semidirect
38. #15689057C22semidirect
39. #15689056C22semidirect
40. #15689056C22semidirect
41. #15689055C22semidirect
44. #15689044C22semidirect
45. #15689044C22semidirect
61. C47×#400C22semidirect
81. C22×C4×D47Q8semidirect
210. C2×C4×D47C2×Q8semidirect
353. C2×#400D47semidirect
367. C2×C47#2841semidirect
398. #400C2×D47semidirect
426. C47C2×#2841semidirect
711. C2#20251647direct (N × H)

Maximal subgroups

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

subgroupindex
#202516472
C2×#156890642
C2×#156890602
C2×#156890572
C2×#156890562
C2×#156890552
C2×#156890472
C2×#156890452
C2×#156890442
C2×#156890362
C2×#156889852
C2×#156889822
C2×#156889802
C2×C47×#4002
C2×#284147