Finite Group Databasebeta

← C2×C47×#2650 #26074281

Subgroups — C2×C47×#2650 #26074281

Order 12032.

2026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2650C2116yesmaximal, direct product factor
2C2×C47×#400C211yesmaximal, characteristic, complemented
3C2×C47×#400C211yesmaximal, characteristic, complemented
4C2×C47×#400C211yesmaximal, characteristic, complemented
5C2×C47×#397C211yesmaximal, characteristic
6C2×C47×#397C211yesmaximal, characteristic
7C2×C47×#396C211yesmaximal, characteristic
8C2×C47×#395C211yesmaximal, characteristic, complemented
9C2×C47×#393C211yesmaximal, characteristic
10C2×C47×#391C211yesmaximal, characteristic, complemented
11C2×C47×#388C211yesmaximal, characteristic
12C2×C47×#388C211yesmaximal, characteristic
13C2×C47×#388C211yesmaximal, characteristic
14C2×C47×#387C211yesmaximal, characteristic, complemented
15C2×C47×#387C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
17C23×Q8×C47C2211yescharacteristic
18C22×C4⋊C4×C47C2211yescharacteristic
19C22×C4⋊C4×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C4⋊C4×C47C2211yescharacteristic
22C22×C4⋊C4×C47C2211yescharacteristic
23C22×C4⋊C4×C47C2211yescharacteristic
24C22×C4⋊C4×C47C2211yescharacteristic
25C22×C4⋊C4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2211yescharacteristic
28C22×C22⋊C4×C47C2211yescharacteristic
29C22×C22⋊C4×C47C2211yescharacteristic
30C22×C22⋊C4×C47C2211yescharacteristic
31C22×C22⋊C4×C47C2211yescharacteristic
32C22×C22⋊C4×C47C2211yescharacteristic
33C22×C42×C47C2211yescharacteristic
34C22×C42×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C47×#400C2218yescomplemented
37C47×#400C2218yescomplemented
38C47×#400C2218yescomplemented
39C47×#397C2218yes—
40C47×#397C2218yes—
41C47×#396C2218yes—
42C47×#395C2218yescomplemented
43C47×#393C2218yes—
44C47×#391C2218yescomplemented
45C47×#388C2218yes—
46C47×#388C2218yes—
47C47×#388C2218yes—
48C47×#387C2218yescomplemented
49C47×#387C2218yescomplemented
50C4×C4⋊C4×C47C2218yescomplemented
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C2×#95×C47C2211yescharacteristic
59C2×#95×C47C2211yescharacteristic
60C2×#95×C47C2211yescharacteristic
61C2×#95×C47C2211yescharacteristic
62C2×#95×C47C2211yescharacteristic
63C2×#95×C47C2211yescharacteristic
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C25×C47C2311yescharacteristic
68C22×Q8×C47—24no—
69C22×Q8×C47—42no—
70C22×Q8×C47—42no—
71C22×Q8×C47C2314yes—
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C23×C4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47—24no—
87C2×C4⋊C4×C47—24no—
88C2×C4⋊C4×C47—24no—
89C2×C4⋊C4×C47—24no—
90C2×C4⋊C4×C47—42no—
91C2×C4⋊C4×C47—42no—
92C2×C4⋊C4×C47—42no—
93C2×C4⋊C4×C47—42no—
94C2×C4⋊C4×C47C2314yes—
95C2×C4⋊C4×C47C2314yes—
96C2×C4⋊C4×C47C2314yes—
97C2×C4⋊C4×C47C2314yes—
98C2×C4⋊C4×C47C2314yes—
99C2×C4⋊C4×C47C2314yes—
100C2×C4⋊C4×C47C2314yes—
101C2×C4⋊C4×C47C2314yes—
102C2×C22⋊C4×C47—24no—
103C2×C22⋊C4×C47—24no—
104C2×C22⋊C4×C47—24no—
105C2×C22⋊C4×C47—42no—
106C2×C22⋊C4×C47—42no—
107C2×C22⋊C4×C47—42no—
108C2×C22⋊C4×C47—42no—
109C2×C22⋊C4×C47C2314yes—
110C2×C22⋊C4×C47C2314yes—
111C2×C22⋊C4×C47C2314yes—
112C2×C22⋊C4×C47C2314yes—
113C2×C22⋊C4×C47C2314yes—
114C2×C22⋊C4×C47C2314yes—
115C2×C22⋊C4×C47C2314yes—
116C2×C42×C47—24no—
117C2×C42×C47—42no—
118C2×C42×C47—42no—
119C2×C42×C47C2314yes—
120C2×C42×C47C2314yes—
121C2×C42×C47C2314yes—
122#95×C47C2314yes—
123#95×C47C2314yes—
124#95×C47C2314yes—
125#95×C47C2314yes—
126#95×C47C2314yes—
127#95×C47C2314yes—
128#95×C47C2314yes—
129#95×C47C2314yes—
130#95×C47C2314yes—
131#95×C47C2314yes—
132#95×C47C2314yes—
133#95×C47C2314yes—
134#95×C47C2314yes—
135#95×C47C2314yes—
136#95×C47C2314yes—
137#95×C47C2314yes—
138C24×C47—22no—
139C24×C47—22no—
140C24×C47—22no—
141C24×C47—22no—
142C24×C47—22no—
143C24×C47—22no—
144C24×C47—22no—
145C24×C47C2412yes—
146C24×C47C2411yescharacteristic
147C2×Q8×C47—28no—
148C2×Q8×C47—44no—
149C2×Q8×C47—44no—
150C2×Q8×C47—416no—
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×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
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#4114yes—
191C22×C4×C47#4114yes—
192C22×C4×C47#4114yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2412yes—
206C22×C4×C47C2412yes—
207C4⋊C4×C47—28no—
208C4⋊C4×C47—28no—
209C4⋊C4×C47—28no—
210C4⋊C4×C47—28no—
211C4⋊C4×C47—44no—
212C4⋊C4×C47—44no—
213C4⋊C4×C47—44no—
214C4⋊C4×C47—44no—
215C22⋊C4×C47—28no—
216C22⋊C4×C47—28no—
217C22⋊C4×C47—28no—
218C22⋊C4×C47—44no—
219C22⋊C4×C47—44no—
220C22⋊C4×C47—44no—
221C22⋊C4×C47—44no—
222C42×C47—28no—
223C42×C47—44no—
224C42×C47—44no—
225C23×C47—22no—
226C23×C47—22no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—44no—
233C23×C47—44no—
234C23×C47—44no—
235C23×C47—44no—
236C23×C47—44no—
237C23×C47—44no—
238C23×C47—44no—
239C23×C47C2×#4112yes—
240C23×C47C2×#4112yes—
241C23×C47C2×#4112yes—
242C23×C47H(5,𝔽2)12yes—
243C23×C47H(5,𝔽2)12yes—
244C23×C472−1+412yes—
245C23×C472−1+412yes—
246C23×C47C2511yescharacteristic
247Q8×C47—416no—
248C2×C4×C47—28no—
249C2×C4×C47—28no—
250C2×C4×C47—28no—
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—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—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—44no—
291C2×C4×C47—44no—
292C2×C4×C47—44no—
293C2×C4×C47—44no—
294C2×C4×C47—44no—
295C2×C4×C47—44no—
296C2×C4×C47—44no—
297C2×C4×C47—44no—
298C2×C4×C47—44no—
299C2×C4×C47—44no—
300C2×C4×C47—44no—
301C2×C4×C47C2×#4114yes—
302C2×C4×C47C2×#4114yes—
303C2×C4×C47C2×#4114yes—
304C2×#2650C4711yesmaximal, characteristic, direct product factor, Sylow
305C22×C47—42no—
306C22×C47—42no—
307C22×C47—42no—
308C22×C47—42no—
309C22×C47—42no—
310C22×C47—42no—
311C22×C47—42no—
312C22×C47—88no—
313C22×C47#52914yes—
314C22×C47#53814yes—
315C22×C47#53914yes—
316C22×C47#54114yes—
317C22×C47#54214yes—
318C22×C47#54214yes—
319C22×C47#54214yes—
320C22×C47C22×#4111yescharacteristic
321C22×C47C22×#4111yescharacteristic
322C22×C47C22×#4111yescharacteristic
323C22×C47C2×H(5,𝔽2)11yescharacteristic
324C22×C47C2×H(5,𝔽2)11yescharacteristic
325C22×C47C2×2−1+411yescharacteristic
326C22×C47C2×2−1+411yescharacteristic
327C4×C47—24no—
328C4×C47—24no—
329C4×C47—24no—
330C4×C47—42no—
331C4×C47—42no—
332C4×C47—42no—
333C4×C47—42no—
334C4×C47—42no—
335C4×C47—42no—
336C4×C47—42no—
337C4×C47—42no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47—42no—
341#2650C2×C47116yesdirect product factor
342C2×#400C2×C4711yescharacteristic, complemented
343C2×#400C2×C4711yescharacteristic, complemented
344C2×#400C2×C4711yescharacteristic, complemented
345C2×#397C2×C4711yescharacteristic
346C2×#397C2×C4711yescharacteristic
347C2×#396C2×C4711yescharacteristic
348C2×#395C2×C4711yescharacteristic, complemented
349C2×#393C2×C4711yescharacteristic
350C2×#391C2×C4711yescharacteristic, complemented
351C2×#388C2×C4711yescharacteristic
352C2×#388C2×C4711yescharacteristic
353C2×#388C2×C4711yescharacteristic
354C2×#387C2×C4711yescharacteristic, complemented
355C2×#387C2×C4711yescharacteristic, complemented
356C2×C4×C4⋊C4C2×C4711yescharacteristic, complemented
357C2×C47—82no—
358C2×C47#265018yesdirect product factor
359C2×C47C2×#52911yescharacteristic
360C2×C47C2×#53811yescharacteristic
361C2×C47C2×#53911yescharacteristic
362C2×C47C2×#54111yescharacteristic
363C2×C47C2×#54211yescharacteristic
364C2×C47C2×#54211yescharacteristic
365C2×C47C2×#54211yescharacteristic
366C23×Q8C22×C4711yescharacteristic
367C22×C4⋊C4C22×C4711yescharacteristic
368C22×C4⋊C4C22×C4711yescharacteristic
369C22×C4⋊C4C22×C4711yescharacteristic
370C22×C4⋊C4C22×C4711yescharacteristic
371C22×C4⋊C4C22×C4711yescharacteristic
372C22×C4⋊C4C22×C4711yescharacteristic
373C22×C4⋊C4C22×C4711yescharacteristic
374C22×C4⋊C4C22×C4711yescharacteristic
375C22×C22⋊C4C22×C4711yescharacteristic
376C22×C22⋊C4C22×C4711yescharacteristic
377C22×C22⋊C4C22×C4711yescharacteristic
378C22×C22⋊C4C22×C4711yescharacteristic
379C22×C22⋊C4C22×C4711yescharacteristic
380C22×C22⋊C4C22×C4711yescharacteristic
381C22×C22⋊C4C22×C4711yescharacteristic
382C22×C42C22×C4711yescharacteristic
383C22×C42C22×C4711yescharacteristic
384C22×C42C22×C4711yescharacteristic
385#400C22×C4718yescomplemented
386#400C22×C4718yescomplemented
387#400C22×C4718yescomplemented
388#397C22×C4718yes—
389#397C22×C4718yes—
390#396C22×C4718yes—
391#395C22×C4718yescomplemented
392#393C22×C4718yes—
393#391C22×C4718yescomplemented
394#388C22×C4718yes—
395#388C22×C4718yes—
396#388C22×C4718yes—
397#387C22×C4718yescomplemented
398#387C22×C4718yescomplemented
399C4×C4⋊C4C22×C4718yescomplemented
400C2×#95C22×C4711yescharacteristic
401C2×#95C22×C4711yescharacteristic
402C2×#95C22×C4711yescharacteristic
403C2×#95C22×C4711yescharacteristic
404C2×#95C22×C4711yescharacteristic
405C2×#95C22×C4711yescharacteristic
406C2×#95C22×C4711yescharacteristic
407C2×#95C22×C4711yescharacteristic
408C2×#95C22×C4711yescharacteristic
409C2×#95C22×C4711yescharacteristic
410C2×#95C22×C4711yescharacteristic
411C2×#95C22×C4711yescharacteristic
412C2×#95C22×C4711yescharacteristic
413C2×#95C22×C4711yescharacteristic
414C2×#95C22×C4711yescharacteristic
415C2×#95C22×C4711yescharacteristic
416C47C2×#265011yescharacteristic, direct product factor, Sylow
417C25C23×C4711yescharacteristic
418C22×Q8—24no—
419C22×Q8—42no—
420C22×Q8—42no—
421C22×Q8C23×C4714yes—
422C23×C4C23×C4711yescharacteristic
423C23×C4C23×C4711yescharacteristic
424C23×C4C23×C4711yescharacteristic
425C23×C4C23×C4711yescharacteristic
426C23×C4C23×C4711yescharacteristic
427C23×C4C23×C4711yescharacteristic
428C23×C4C23×C4711yescharacteristic
429C23×C4C23×C4711yescharacteristic
430C23×C4C23×C4711yescharacteristic
431C23×C4C23×C4711yescharacteristic
432C23×C4C23×C4711yescharacteristic
433C23×C4C23×C4711yescharacteristic
434C23×C4C23×C4711yescharacteristic
435C23×C4C23×C4711yescharacteristic
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4C23×C4714yes—
445C2×C4⋊C4C23×C4714yes—
446C2×C4⋊C4C23×C4714yes—
447C2×C4⋊C4C23×C4714yes—
448C2×C4⋊C4C23×C4714yes—
449C2×C4⋊C4C23×C4714yes—
450C2×C4⋊C4C23×C4714yes—
451C2×C4⋊C4C23×C4714yes—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4C23×C4714yes—
460C2×C22⋊C4C23×C4714yes—
461C2×C22⋊C4C23×C4714yes—
462C2×C22⋊C4C23×C4714yes—
463C2×C22⋊C4C23×C4714yes—
464C2×C22⋊C4C23×C4714yes—
465C2×C22⋊C4C23×C4714yes—
466C2×C42—24no—
467C2×C42—42no—
468C2×C42—42no—
469C2×C42C23×C4714yes—
470C2×C42C23×C4714yes—
471C2×C42C23×C4714yes—
472#95C23×C4714yes—
473#95C23×C4714yes—
474#95C23×C4714yes—
475#95C23×C4714yes—
476#95C23×C4714yes—
477#95C23×C4714yes—
478#95C23×C4714yes—
479#95C23×C4714yes—
480#95C23×C4714yes—
481#95C23×C4714yes—
482#95C23×C4714yes—
483#95C23×C4714yes—
484#95C23×C4714yes—
485#95C23×C4714yes—
486#95C23×C4714yes—
487#95C23×C4714yes—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24C24×C4712yes—
496C24C24×C4711yescharacteristic
497C2×Q8—28no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—416no—
501C22×C4—22no—
502C22×C4—22no—
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—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—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4#41×C4714yes—
541C22×C4#41×C4714yes—
542C22×C4#41×C4714yes—
543C22×C4C24×C4712yes—
544C22×C4C24×C4712yes—
545C22×C4C24×C4712yes—
546C22×C4C24×C4712yes—
547C22×C4C24×C4712yes—
548C22×C4C24×C4712yes—
549C22×C4C24×C4712yes—
550C22×C4C24×C4712yes—
551C22×C4C24×C4712yes—
552C22×C4C24×C4712yes—
553C22×C4C24×C4712yes—
554C22×C4C24×C4712yes—
555C22×C4C24×C4712yes—
556C22×C4C24×C4712yes—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C22⋊C4—28no—
566C22⋊C4—28no—
567C22⋊C4—28no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4—44no—
571C22⋊C4—44no—
572C42—28no—
573C42—44no—
574C42—44no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23—44no—
587C23—44no—
588C23—44no—
589C23C2×#41×C4712yes—
590C23C2×#41×C4712yes—
591C23C2×#41×C4712yes—
592C23H(5,𝔽2)×C4712yes—
593C23H(5,𝔽2)×C4712yes—
594C232−1+4×C4712yes—
595C232−1+4×C4712yes—
596C23C25×C4711yescharacteristic
597Q8—416no—
598C2×C4—28no—
599C2×C4—28no—
600C2×C4—28no—
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—22no—
616C2×C4—22no—
617C2×C4—22no—
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—22no—
639C2×C4—22no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4C2×#41×C4714yes—
652C2×C4C2×#41×C4714yes—
653C2×C4C2×#41×C4714yes—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—88no—
662C22C47×#52914yes—
663C22C47×#53814yes—
664C22C47×#53914yes—
665C22C47×#54114yes—
666C22C47×#54214yes—
667C22C47×#54214yes—
668C22C47×#54214yes—
669C22C22×#41×C4711yescharacteristic
670C22C22×#41×C4711yescharacteristic
671C22C22×#41×C4711yescharacteristic
672C22C2×H(5,𝔽2)×C4711yescharacteristic
673C22C2×H(5,𝔽2)×C4711yescharacteristic
674C22C2×2−1+4×C4711yescharacteristic
675C22C2×2−1+4×C4711yescharacteristic
676C4—24no—
677C4—24no—
678C4—24no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—42no—
690C2—82no—
691C2C47×#265018yesdirect product factor
692C2C2×C47×#52911yescharacteristic
693C2C2×C47×#53811yescharacteristic
694C2C2×C47×#53911yescharacteristic
695C2C2×C47×#54111yescharacteristic
696C2C2×C47×#54211yescharacteristic
697C2C2×C47×#54211yescharacteristic
698C2C2×C47×#54211yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC23C25×C47
prime radicalC25×C47C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2650C2direct (N × H)
2. C2×C47×#400C2semidirect
3. C2×C47×#400C2semidirect
4. C2×C47×#400C2semidirect
8. C2×C47×#395C2semidirect
10. C2×C47×#391C2semidirect
14. C2×C47×#387C2semidirect
15. C2×C47×#387C2semidirect
16. C2×C4×C4⋊C4×C47C2semidirect
36. C47×#400C22semidirect
37. C47×#400C22semidirect
38. C47×#400C22semidirect
42. C47×#395C22semidirect
44. C47×#391C22semidirect
48. C47×#387C22semidirect
49. C47×#387C22semidirect
50. C4×C4⋊C4×C47C22semidirect
304. C2×#2650C47direct (N × H)
341. #2650C2×C47direct (N × H)
342. C2×#400C2×C47semidirect
343. C2×#400C2×C47semidirect
344. C2×#400C2×C47semidirect
348. C2×#395C2×C47semidirect
350. C2×#391C2×C47semidirect
354. C2×#387C2×C47semidirect
355. C2×#387C2×C47semidirect
356. C2×C4×C4⋊C4C2×C47semidirect
358. C2×C47#2650direct (N × H)
385. #400C22×C47semidirect
386. #400C22×C47semidirect
387. #400C22×C47semidirect
391. #395C22×C47semidirect
393. #391C22×C47semidirect
397. #387C22×C47semidirect
398. #387C22×C47semidirect
399. C4×C4⋊C4C22×C47semidirect
416. C47C2×#2650direct (N × H)
691. C2C47×#2650direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#26502
C2×C47×#4002
C2×C47×#3972
C2×C47×#3962
C2×C47×#3952
C2×C47×#3932
C2×C47×#3912
C2×C47×#3882
C2×C47×#3872
C2×C4×C4⋊C4×C472
C2×#265047