Finite Group Databasebeta

← C47×#22400 #26062098

Subgroups — C47×#22400 #26062098

Order 12032.

1582 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#525C211yesmaximal, characteristic
2C2×C47×#436C211yesmaximal, characteristic, complemented
3C2×C47×#435C211yesmaximal, characteristic, complemented
4C2×C47×#408C211yesmaximal, characteristic, complemented
5C2×C47×#407C211yesmaximal, characteristic, complemented
6C47×#1955C211yesmaximal, characteristic, complemented
7C47×#1954C211yesmaximal, characteristic, complemented
8C47×#1870C211yesmaximal, characteristic, complemented
9C47×#1870C211yesmaximal, characteristic, complemented
10C47×#1870C211yesmaximal, characteristic, complemented
11C47×#1869C211yesmaximal, characteristic, complemented
12C47×#1798C211yesmaximal, characteristic, complemented
13C47×#1780C211yesmaximal, characteristic, complemented
14C47×#1779C211yesmaximal, characteristic, complemented
15C47×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C24×C4×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic, complemented
21C23×C8×C47C2211yescharacteristic, complemented
22C47×#525—24no—
23C47×#525—24no—
24C2×#123×C47C411yescharacteristic
25C2×#123×C47C411yescharacteristic
26C2×C22⋊Q8×C47C411yescharacteristic
27C2×C22⋊Q8×C47C411yescharacteristic
28C2×#121×C47C411yescharacteristic
29C2×#121×C47C411yescharacteristic
30C2×#120×C47C411yescharacteristic
31C2×#120×C47C411yescharacteristic
32C2×C4×D4×C47C2211yescharacteristic
33C2×C4×D4×C47C2211yescharacteristic
34C2×C4×D4×C47C2211yescharacteristic
35C2×C4×D4×C47C2211yescharacteristic
36C2×#117×C47C2211yescharacteristic
37C47×#436—24no—
38C47×#435—24no—
39C2×C4⋊C8×C47C2211yescharacteristic, complemented
40C2×C4⋊C8×C47C2211yescharacteristic, complemented
41C47×#408—24no—
42C47×#407—24no—
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C2×C22⋊C8×C47C2211yescharacteristic
49C2×C22⋊C8×C47C2211yescharacteristic
50C2×C22⋊C8×C47C2211yescharacteristic
51C2×C22⋊C8×C47C2211yescharacteristic
52C2×C22⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic, complemented
54C2×C22⋊C8×C47C2211yescharacteristic, complemented
55C2×C22⋊C8×C47C2211yescharacteristic, complemented
56C2×C22⋊C8×C47C2211yescharacteristic, complemented
57C2×C22⋊C8×C47C2211yescharacteristic, complemented
58C2×C22⋊C8×C47C2211yescharacteristic, complemented
59C2×#97×C47C2211yescharacteristic, complemented
60C2×C4×C8×C47C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C47×#336C2211yescharacteristic, complemented
64C47×#336C2211yescharacteristic, complemented
65C25×C47C2×C411yescharacteristic
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—41no—
71C2×#41×C47—41no—
72C22×Q8×C47C2×C411yescharacteristic
73C22×D4×C47C2×C411yescharacteristic
74C22×D4×C47C2×C411yescharacteristic
75C22×D4×C47C2×C411yescharacteristic
76C22×D4×C47C2×C411yescharacteristic
77C22×D4×C47C2×C411yescharacteristic
78C22×D4×C47C2×C411yescharacteristic
79C22×D4×C47C2×C411yescharacteristic
80C23×C4×C47—22no—
81C23×C4×C47—22no—
82C23×C4×C47—22no—
83C23×C4×C47—22no—
84C23×C4×C47—41no—
85C23×C4×C47—41no—
86C23×C4×C47C2×C411yescharacteristic
87C23×C4×C47C2×C411yescharacteristic
88C23×C4×C47C2×C411yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2311yescharacteristic
94C2×M16×C47—22no—
95C2×M16×C47—22no—
96C2×M16×C47—22no—
97C2×M16×C47—22no—
98C2×M16×C47—22no—
99C2×M16×C47—22no—
100C2×M16×C47—41no—
101C2×M16×C47—41no—
102C2×M16×C47—41no—
103C22×C8×C47—22no—
104C22×C8×C47—22no—
105C22×C8×C47—41no—
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C22×C8×C47C2311yescharacteristic
109C22×C8×C47C2311yescharacteristic
110C22×C8×C47C2311yescharacteristic
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114#123×C47—24no—
115#123×C47—24no—
116C22⋊Q8×C47—24no—
117C22⋊Q8×C47—24no—
118#121×C47—24no—
119#121×C47—24no—
120#120×C47—24no—
121#120×C47—24no—
122C4×D4×C47—22no—
123C4×D4×C47—22no—
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128C4×D4×C47D414yes—
129C4×D4×C47D414yes—
130#117×C47—22no—
131#117×C47—22no—
132C2×C4⋊C4×C47C2×C411yescharacteristic
133C2×C4⋊C4×C47C2×C411yescharacteristic
134C2×C4⋊C4×C47C2×C411yescharacteristic
135C2×C4⋊C4×C47C2×C411yescharacteristic
136C2×C4⋊C4×C47C2×C411yescharacteristic
137C2×C4⋊C4×C47C2×C411yescharacteristic
138C2×C22⋊C4×C47C2×C411yescharacteristic
139C2×C22⋊C4×C47C2×C411yescharacteristic
140C2×C22⋊C4×C47C2×C411yescharacteristic
141C2×C22⋊C4×C47C2×C411yescharacteristic
142C2×C22⋊C4×C47C2×C411yescharacteristic
143C2×C22⋊C4×C47C2×C411yescharacteristic
144C2×C22⋊C4×C47C2×C411yescharacteristic
145C2×C22⋊C4×C47C2×C411yescharacteristic
146C2×C22⋊C4×C47C2×C411yescharacteristic
147C2×C22⋊C4×C47C2×C411yescharacteristic
148C2×C42×C47C2311yescharacteristic
149C2×C42×C47C2311yescharacteristic
150C4⋊C8×C47—22no—
151C4⋊C8×C47—22no—
152C22⋊C8×C47—22no—
153C22⋊C8×C47—22no—
154C22⋊C8×C47—22no—
155C22⋊C8×C47—22no—
156C22⋊C8×C47—22no—
157C22⋊C8×C47—22no—
158C22⋊C8×C47—22no—
159C22⋊C8×C47—22no—
160C22⋊C8×C47—22no—
161C22⋊C8×C47—22no—
162C22⋊C8×C47—22no—
163C22⋊C8×C47—41no—
164C22⋊C8×C47—41no—
165C22⋊C8×C47—41no—
166C22⋊C8×C47—41no—
167C22⋊C8×C47D414yescomplemented
168#97×C47—22no—
169C4×C8×C47—22no—
170C24×C47—22no—
171C24×C47—22no—
172C24×C47—22no—
173C24×C47—41no—
174C24×C47—41no—
175C24×C47—41no—
176C24×C47—41no—
177C24×C47C22×C411yescharacteristic
178C24×C47C22×C411yescharacteristic
179C24×C47C22×C411yescharacteristic
180C24×C47C22×C411yescharacteristic
181C24×C47C22×C411yescharacteristic
182#41×C47—44no—
183#41×C47—44no—
184#41×C47—44no—
185#41×C47—44no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—41no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47—41no—
201C2×D4×C47—41no—
202C2×D4×C47—41no—
203C2×D4×C47—41no—
204C2×D4×C47—41no—
205C2×D4×C47—41no—
206C2×D4×C47—41no—
207C2×D4×C47—41no—
208C2×D4×C47—41no—
209C2×D4×C47C22⋊C414yes—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47—22no—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—41no—
241C22×C4×C47—41no—
242C22×C4×C47—41no—
243C22×C4×C47—44no—
244C22×C4×C47—44no—
245C22×C4×C47—44no—
246C22×C4×C47—44no—
247C22×C4×C47C22×C411yescharacteristic
248C22×C4×C47C22×C411yescharacteristic
249C22×C4×C47C22×C411yescharacteristic
250C22×C4×C47C22×C411yescharacteristic
251C22×C4×C47C22×C411yescharacteristic
252C22×C4×C47C22×C411yescharacteristic
253C22×C4×C47C22×C411yescharacteristic
254C22×C4×C47C22×C411yescharacteristic
255C22×C4×C47C22×C411yescharacteristic
256C22×C4×C47C2×D412yes—
257C22×C4×C47C2×D412yes—
258C22×C4×C47C2×D412yes—
259C22×C4×C47C2×D412yes—
260C22×C4×C47C2×D412yes—
261C22×C4×C47#4112yes—
262C22×C4×C47C2411yescharacteristic
263M16×C47—44no—
264M16×C47—44no—
265M16×C47—44no—
266C2×C8×C47—21no—
267C2×C8×C47—21no—
268C2×C8×C47—21no—
269C2×C8×C47—21no—
270C2×C8×C47—21no—
271C2×C8×C47—21no—
272C2×C8×C47—21no—
273C2×C8×C47—21no—
274C2×C8×C47—21no—
275C2×C8×C47—21no—
276C2×C8×C47—21no—
277C2×C8×C47—21no—
278C2×C8×C47—21no—
279C2×C8×C47—21no—
280C2×C8×C47—21no—
281C2×C8×C47—21no—
282C2×C8×C47—21no—
283C2×C8×C47—21no—
284C2×C8×C47—21no—
285C2×C8×C47—21no—
286C2×C8×C47—21no—
287C2×C8×C47—21no—
288C2×C8×C47—44no—
289C2×C8×C47C2×D412yes—
290C2×C8×C47C2×D412yes—
291C4⋊C4×C47—22no—
292C4⋊C4×C47—22no—
293C4⋊C4×C47—22no—
294C4⋊C4×C47—22no—
295C4⋊C4×C47—22no—
296C4⋊C4×C47C22⋊C414yes—
297C22⋊C4×C47—22no—
298C22⋊C4×C47—22no—
299C22⋊C4×C47—22no—
300C22⋊C4×C47—22no—
301C22⋊C4×C47—22no—
302C22⋊C4×C47—22no—
303C22⋊C4×C47—22no—
304C22⋊C4×C47—22no—
305C22⋊C4×C47C22⋊C414yes—
306C22⋊C4×C47C22⋊C414yes—
307C42×C47—21no—
308C42×C47—21no—
309C42×C47C2×D412yes—
310C42×C47C2×D412yes—
311C23×C47—21no—
312C23×C47—21no—
313C23×C47—21no—
314C23×C47—21no—
315C23×C47—21no—
316C23×C47—21no—
317C23×C47—21no—
318C23×C47—21no—
319C23×C47—21no—
320C23×C47—21no—
321C23×C47—21no—
322C23×C47—21no—
323C23×C47—21no—
324C23×C47—21no—
325C23×C47—21no—
326C23×C47—21no—
327C23×C47—21no—
328C23×C47—21no—
329C23×C47—21no—
330C23×C47—21no—
331C23×C47—21no—
332C23×C47—21no—
333C23×C47—21no—
334C23×C47—21no—
335C23×C47—21no—
336C23×C47—21no—
337C23×C47—21no—
338C23×C47—21no—
339C23×C47—21no—
340C23×C47—21no—
341C23×C47—21no—
342C23×C47—44no—
343C23×C47—44no—
344C23×C47—44no—
345C23×C47—44no—
346C23×C47—44no—
347C23×C47—44no—
348C23×C47—44no—
349C23×C47C2×C22⋊C412yes—
350C23×C47C2×C22⋊C412yes—
351C23×C47C4×D412yes—
352C23×C47#13112yes—
353C23×C47C23×C411yescharacteristic
354Q8×C47—44no—
355D4×C47—44no—
356D4×C47—44no—
357D4×C47—44no—
358D4×C47—44no—
359D4×C47—44no—
360D4×C47—44no—
361D4×C47—44no—
362C2×C4×C47—21no—
363C2×C4×C47—21no—
364C2×C4×C47—21no—
365C2×C4×C47—21no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—21no—
370C2×C4×C47—21no—
371C2×C4×C47—21no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—21no—
385C2×C4×C47—21no—
386C2×C4×C47—21no—
387C2×C4×C47—21no—
388C2×C4×C47—21no—
389C2×C4×C47—21no—
390C2×C4×C47—21no—
391C2×C4×C47—21no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—21no—
395C2×C4×C47—21no—
396C2×C4×C47—44no—
397C2×C4×C47—44no—
398C2×C4×C47—44no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—41no—
405C2×C4×C47—41no—
406C2×C4×C47—41no—
407C2×C4×C47C2×C22⋊C412yes—
408C2×C4×C47C2×C22⋊C412yes—
409C2×C4×C47C2×C22⋊C412yes—
410C2×C4×C47C2×C22⋊C412yes—
411C2×C4×C47C4×D412yes—
412C2×C4×C47C22×D411yescharacteristic
413C2×C4×C47C22×D411yescharacteristic
414C2×C4×C47C22×D411yescharacteristic
415C2×C4×C47C2×#4111yescharacteristic
416C2×C4×C47H(5,𝔽2)11yescharacteristic
417C2×C4×C47H(5,𝔽2)11yescharacteristic
418C8×C47—22no—
419C8×C47—22no—
420C8×C47—41no—
421C8×C47—41no—
422C8×C47—41no—
423C8×C47—41no—
424C8×C47—41no—
425C8×C47—41no—
426#22400C4711yesmaximal, characteristic, direct product factor, Sylow
427C22×C47—22no—
428C22×C47—22no—
429C22×C47—22no—
430C22×C47—22no—
431C22×C47—22no—
432C22×C47—22no—
433C22×C47—22no—
434C22×C47—22no—
435C22×C47—22no—
436C22×C47—22no—
437C22×C47—22no—
438C22×C47—22no—
439C22×C47—416no—
440C22×C47—41no—
441C22×C47—41no—
442C22×C47—41no—
443C22×C47—41no—
444C22×C47—41no—
445C22×C47—41no—
446C22×C47—41no—
447C22×C47—41no—
448C22×C47—41no—
449C22×C47—41no—
450C22×C47—41no—
451C22×C47—41no—
452C22×C47—41no—
453C22×C47—41no—
454C22×C47—41no—
455C22×C47—41no—
456C22×C47—41no—
457C22×C47—41no—
458C22×C47—41no—
459C22×C47—41no—
460C22×C47—41no—
461C22×C47—41no—
462C22×C47—41no—
463C22×C47C22×C22⋊C411yescharacteristic
464C22×C47C2×C4×D411yescharacteristic
465C22×C47#51811yescharacteristic
466C22×C47C2×#13111yescharacteristic
467C22×C47#56811yescharacteristic
468C22×C47#56811yescharacteristic
469C22×C47#56811yescharacteristic
470C4×C47—22no—
471C4×C47—22no—
472C4×C47—22no—
473C4×C47—22no—
474C4×C47—22no—
475C4×C47—41no—
476C4×C47—41no—
477C4×C47—41no—
478C4×C47—41no—
479C4×C47D4211yescharacteristic
480C4×C47D4211yescharacteristic
481C4×C47#54611yescharacteristic
482C4×C47#54611yescharacteristic
483C2×#525C2×C4711yescharacteristic
484C2×#436C2×C4711yescharacteristic, complemented
485C2×#435C2×C4711yescharacteristic, complemented
486C2×#408C2×C4711yescharacteristic, complemented
487C2×#407C2×C4711yescharacteristic, complemented
488#1955C2×C4711yescharacteristic, complemented
489#1954C2×C4711yescharacteristic, complemented
490#1870C2×C4711yescharacteristic, complemented
491#1870C2×C4711yescharacteristic, complemented
492#1870C2×C4711yescharacteristic, complemented
493#1869C2×C4711yescharacteristic, complemented
494#1798C2×C4711yescharacteristic, complemented
495#1780C2×C4711yescharacteristic, complemented
496#1779C2×C4711yescharacteristic, complemented
497#1750C2×C4711yescharacteristic, complemented
498C2×C47—42no—
499C2×C47—42no—
500C2×C47—42no—
501C2×C47—42no—
502C2×C47—81no—
503C2×C47D4×C22⋊C411yescharacteristic
504C2×C47#287911yescharacteristic
505C2×C47#288011yescharacteristic
506C2×C47#293011yescharacteristic
507C2×C47#293311yescharacteristic
508C2×C47#297611yescharacteristic
509C2×C47#297811yescharacteristic
510C22×#41C22×C4711yescharacteristic
511C24×C4C22×C4711yescharacteristic
512C22×M16C22×C4711yescharacteristic
513C22×M16C22×C4711yescharacteristic
514C22×M16C22×C4711yescharacteristic, complemented
515C23×C8C22×C4711yescharacteristic, complemented
516#525—24no—
517#525—24no—
518C2×#123C4×C4711yescharacteristic
519C2×#123C4×C4711yescharacteristic
520C2×C22⋊Q8C4×C4711yescharacteristic
521C2×C22⋊Q8C4×C4711yescharacteristic
522C2×#121C4×C4711yescharacteristic
523C2×#121C4×C4711yescharacteristic
524C2×#120C4×C4711yescharacteristic
525C2×#120C4×C4711yescharacteristic
526C2×C4×D4C22×C4711yescharacteristic
527C2×C4×D4C22×C4711yescharacteristic
528C2×C4×D4C22×C4711yescharacteristic
529C2×C4×D4C22×C4711yescharacteristic
530C2×#117C22×C4711yescharacteristic
531#436—24no—
532#435—24no—
533C2×C4⋊C8C22×C4711yescharacteristic, complemented
534C2×C4⋊C8C22×C4711yescharacteristic, complemented
535#408—24no—
536#407—24no—
537C2×C22⋊C8C22×C4711yescharacteristic
538C2×C22⋊C8C22×C4711yescharacteristic
539C2×C22⋊C8C22×C4711yescharacteristic
540C2×C22⋊C8C22×C4711yescharacteristic
541C2×C22⋊C8C22×C4711yescharacteristic
542C2×C22⋊C8C22×C4711yescharacteristic
543C2×C22⋊C8C22×C4711yescharacteristic
544C2×C22⋊C8C22×C4711yescharacteristic
545C2×C22⋊C8C22×C4711yescharacteristic
546C2×C22⋊C8C22×C4711yescharacteristic
547C2×C22⋊C8C22×C4711yescharacteristic, complemented
548C2×C22⋊C8C22×C4711yescharacteristic, complemented
549C2×C22⋊C8C22×C4711yescharacteristic, complemented
550C2×C22⋊C8C22×C4711yescharacteristic, complemented
551C2×C22⋊C8C22×C4711yescharacteristic, complemented
552C2×C22⋊C8C22×C4711yescharacteristic, complemented
553C2×#97C22×C4711yescharacteristic, complemented
554C2×C4×C8C22×C4711yescharacteristic, complemented
555#336C22×C4711yescharacteristic, complemented
556#336C22×C4711yescharacteristic, complemented
557#336C22×C4711yescharacteristic, complemented
558#336C22×C4711yescharacteristic, complemented
559C47#2240011yescharacteristic, direct product factor, Sylow
560C25C2×C4×C4711yescharacteristic
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—22no—
564C2×#41—22no—
565C2×#41—41no—
566C2×#41—41no—
567C22×Q8C2×C4×C4711yescharacteristic
568C22×D4C2×C4×C4711yescharacteristic
569C22×D4C2×C4×C4711yescharacteristic
570C22×D4C2×C4×C4711yescharacteristic
571C22×D4C2×C4×C4711yescharacteristic
572C22×D4C2×C4×C4711yescharacteristic
573C22×D4C2×C4×C4711yescharacteristic
574C22×D4C2×C4×C4711yescharacteristic
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—41no—
580C23×C4—41no—
581C23×C4C2×C4×C4711yescharacteristic
582C23×C4C2×C4×C4711yescharacteristic
583C23×C4C2×C4×C4711yescharacteristic
584C23×C4C23×C4711yescharacteristic
585C23×C4C23×C4711yescharacteristic
586C23×C4C23×C4711yescharacteristic
587C23×C4C23×C4711yescharacteristic
588C23×C4C23×C4711yescharacteristic
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C2×M16—22no—
593C2×M16—22no—
594C2×M16—22no—
595C2×M16—41no—
596C2×M16—41no—
597C2×M16—41no—
598C22×C8—22no—
599C22×C8—22no—
600C22×C8—41no—
601C22×C8C23×C4711yescharacteristic
602C22×C8C23×C4711yescharacteristic
603C22×C8C23×C4711yescharacteristic
604C22×C8C23×C4711yescharacteristic
605C22×C8C23×C4711yescharacteristic
606C22×C8C23×C4711yescharacteristic
607C22×C8C23×C4711yescharacteristic
608C22×C8C23×C4711yescharacteristic
609#123—24no—
610#123—24no—
611C22⋊Q8—24no—
612C22⋊Q8—24no—
613#121—24no—
614#121—24no—
615#120—24no—
616#120—24no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4D4×C4714yes—
624C4×D4D4×C4714yes—
625#117—22no—
626#117—22no—
627C2×C4⋊C4C2×C4×C4711yescharacteristic
628C2×C4⋊C4C2×C4×C4711yescharacteristic
629C2×C4⋊C4C2×C4×C4711yescharacteristic
630C2×C4⋊C4C2×C4×C4711yescharacteristic
631C2×C4⋊C4C2×C4×C4711yescharacteristic
632C2×C4⋊C4C2×C4×C4711yescharacteristic
633C2×C22⋊C4C2×C4×C4711yescharacteristic
634C2×C22⋊C4C2×C4×C4711yescharacteristic
635C2×C22⋊C4C2×C4×C4711yescharacteristic
636C2×C22⋊C4C2×C4×C4711yescharacteristic
637C2×C22⋊C4C2×C4×C4711yescharacteristic
638C2×C22⋊C4C2×C4×C4711yescharacteristic
639C2×C22⋊C4C2×C4×C4711yescharacteristic
640C2×C22⋊C4C2×C4×C4711yescharacteristic
641C2×C22⋊C4C2×C4×C4711yescharacteristic
642C2×C22⋊C4C2×C4×C4711yescharacteristic
643C2×C42C23×C4711yescharacteristic
644C2×C42C23×C4711yescharacteristic
645C4⋊C8—22no—
646C4⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—22no—
650C22⋊C8—22no—
651C22⋊C8—22no—
652C22⋊C8—22no—
653C22⋊C8—22no—
654C22⋊C8—22no—
655C22⋊C8—22no—
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659C22⋊C8—41no—
660C22⋊C8—41no—
661C22⋊C8—41no—
662C22⋊C8D4×C4714yescomplemented
663#97—22no—
664C4×C8—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—41no—
669C24—41no—
670C24—41no—
671C24—41no—
672C24C22×C4×C4711yescharacteristic
673C24C22×C4×C4711yescharacteristic
674C24C22×C4×C4711yescharacteristic
675C24C22×C4×C4711yescharacteristic
676C24C22×C4×C4711yescharacteristic
677#41—44no—
678#41—44no—
679#41—44no—
680#41—44no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—41no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4C22⋊C4×C4714yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—41no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4C22×C4×C4711yescharacteristic
743C22×C4C22×C4×C4711yescharacteristic
744C22×C4C22×C4×C4711yescharacteristic
745C22×C4C22×C4×C4711yescharacteristic
746C22×C4C22×C4×C4711yescharacteristic
747C22×C4C22×C4×C4711yescharacteristic
748C22×C4C22×C4×C4711yescharacteristic
749C22×C4C22×C4×C4711yescharacteristic
750C22×C4C22×C4×C4711yescharacteristic
751C22×C4C2×D4×C4712yes—
752C22×C4C2×D4×C4712yes—
753C22×C4C2×D4×C4712yes—
754C22×C4C2×D4×C4712yes—
755C22×C4C2×D4×C4712yes—
756C22×C4#41×C4712yes—
757C22×C4C24×C4711yescharacteristic
758M16—44no—
759M16—44no—
760M16—44no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C4712yes—
785C2×C8C2×D4×C4712yes—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4C22⋊C4×C4714yes—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4C22⋊C4×C4714yes—
801C22⋊C4C22⋊C4×C4714yes—
802C42—21no—
803C42—21no—
804C42C2×D4×C4712yes—
805C42C2×D4×C4712yes—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—44no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23C2×C22⋊C4×C4712yes—
845C23C2×C22⋊C4×C4712yes—
846C23C4×D4×C4712yes—
847C23#131×C4712yes—
848C23C23×C4×C4711yescharacteristic
849Q8—44no—
850D4—44no—
851D4—44no—
852D4—44no—
853D4—44no—
854D4—44no—
855D4—44no—
856D4—44no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4C2×C22⋊C4×C4712yes—
903C2×C4C2×C22⋊C4×C4712yes—
904C2×C4C2×C22⋊C4×C4712yes—
905C2×C4C2×C22⋊C4×C4712yes—
906C2×C4C4×D4×C4712yes—
907C2×C4C22×D4×C4711yescharacteristic
908C2×C4C22×D4×C4711yescharacteristic
909C2×C4C22×D4×C4711yescharacteristic
910C2×C4C2×#41×C4711yescharacteristic
911C2×C4H(5,𝔽2)×C4711yescharacteristic
912C2×C4H(5,𝔽2)×C4711yescharacteristic
913C8—22no—
914C8—22no—
915C8—41no—
916C8—41no—
917C8—41no—
918C8—41no—
919C8—41no—
920C8—41no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—416no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22C22×C22⋊C4×C4711yescharacteristic
958C22C2×C4×D4×C4711yescharacteristic
959C22C47×#51811yescharacteristic
960C22C2×#131×C4711yescharacteristic
961C22C47×#56811yescharacteristic
962C22C47×#56811yescharacteristic
963C22C47×#56811yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—22no—
968C4—22no—
969C4—41no—
970C4—41no—
971C4—41no—
972C4—41no—
973C4D42×C4711yescharacteristic
974C4D42×C4711yescharacteristic
975C4C47×#54611yescharacteristic
976C4C47×#54611yescharacteristic
977C2—42no—
978C2—42no—
979C2—42no—
980C2—42no—
981C2—81no—
982C2D4×C22⋊C4×C4711yescharacteristic
983C2C47×#287911yescharacteristic
984C2C47×#288011yescharacteristic
985C2C47×#293011yescharacteristic
986C2C47×#293311yescharacteristic
987C2C47×#297611yescharacteristic
988C2C47×#297811yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC2×C47×#525C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#436C2semidirect
3. C2×C47×#435C2semidirect
4. C2×C47×#408C2semidirect
5. C2×C47×#407C2semidirect
6. C47×#1955C2semidirect
7. C47×#1954C2semidirect
8. C47×#1870C2semidirect
9. C47×#1870C2semidirect
10. C47×#1870C2semidirect
11. C47×#1869C2semidirect
12. C47×#1798C2semidirect
13. C47×#1780C2semidirect
14. C47×#1779C2semidirect
15. C47×#1750C2semidirect
20. C22×M16×C47C22semidirect
21. C23×C8×C47C22semidirect
39. C2×C4⋊C8×C47C22semidirect
40. C2×C4⋊C8×C47C22semidirect
53. C2×C22⋊C8×C47C22semidirect
54. C2×C22⋊C8×C47C22semidirect
55. C2×C22⋊C8×C47C22semidirect
56. C2×C22⋊C8×C47C22semidirect
57. C2×C22⋊C8×C47C22semidirect
58. C2×C22⋊C8×C47C22semidirect
59. C2×#97×C47C22semidirect
60. C2×C4×C8×C47C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
63. C47×#336C22semidirect
64. C47×#336C22semidirect
167. C22⋊C8×C47D4semidirect
426. #22400C47direct (N × H)
484. C2×#436C2×C47semidirect
485. C2×#435C2×C47semidirect
486. C2×#408C2×C47semidirect
487. C2×#407C2×C47semidirect
488. #1955C2×C47semidirect
489. #1954C2×C47semidirect
490. #1870C2×C47semidirect
491. #1870C2×C47semidirect
492. #1870C2×C47semidirect
493. #1869C2×C47semidirect
494. #1798C2×C47semidirect
495. #1780C2×C47semidirect
496. #1779C2×C47semidirect
497. #1750C2×C47semidirect
514. C22×M16C22×C47semidirect
515. C23×C8C22×C47semidirect
533. C2×C4⋊C8C22×C47semidirect
534. C2×C4⋊C8C22×C47semidirect
547. C2×C22⋊C8C22×C47semidirect
548. C2×C22⋊C8C22×C47semidirect
549. C2×C22⋊C8C22×C47semidirect
550. C2×C22⋊C8C22×C47semidirect
551. C2×C22⋊C8C22×C47semidirect
552. C2×C22⋊C8C22×C47semidirect
553. C2×#97C22×C47semidirect
554. C2×C4×C8C22×C47semidirect
555. #336C22×C47semidirect
556. #336C22×C47semidirect
557. #336C22×C47semidirect
558. #336C22×C47semidirect
559. C47#22400direct (N × H)
662. C22⋊C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5252
C2×C47×#4362
C2×C47×#4352
C2×C47×#4082
C2×C47×#4072
C47×#19552
C47×#19542
C47×#18702
C47×#18692
C47×#17982
C47×#17802
C47×#17792
C47×#17502
#2240047