Finite Group Databasebeta

← #26233286

Subgroups — #26233286

Order 12032.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689184C211yesmaximal, characteristic, complemented
2C2×#15689087C211yesmaximal, characteristic
3#20244003C211yesmaximal, characteristic, complemented
4#20244003C211yesmaximal, characteristic, complemented
5#20243996C211yesmaximal, characteristic, complemented
6#20243996C211yesmaximal, characteristic, complemented
7#20243573C211yesmaximal, characteristic, complemented
8#20243573C211yesmaximal, characteristic, complemented
9#20243459C211yesmaximal, characteristic, complemented
10#20243372C211yesmaximal, characteristic, complemented
11#20243298C211yesmaximal, characteristic
12#20243172C211yesmaximal, characteristic, complemented
13#20243172C211yesmaximal, characteristic, complemented
14#20243154C211yesmaximal, characteristic, complemented
15C47×#2280C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18#15689184—24no—
19C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
20C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
21C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
22C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
23#15689087—24no—
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×#13093935C2211yescharacteristic, complemented
35C2×#13093935C2211yescharacteristic, complemented
36C2×C4×C47⋊C8C2211yescharacteristic, complemented
37C2×C4×C47⋊C8C2211yescharacteristic, complemented
38#15688878C2211yescharacteristic, complemented
39#15688878C2211yescharacteristic, complemented
40#15688878C2211yescharacteristic, complemented
41#15688878C2211yescharacteristic, complemented
42#15688878C2211yescharacteristic, complemented
43#15688878C2211yescharacteristic, complemented
44#15688878C2211yescharacteristic, complemented
45#15688878C2211yescharacteristic, complemented
46C24×C4×C47C2211yescharacteristic
47C2×#117×C47C2211yescharacteristic
48C2×#117×C47C2211yescharacteristic
49C47×#381C411yescharacteristic
50C47×#381C411yescharacteristic
51C47×#380C411yescharacteristic
52C47×#380C411yescharacteristic
53C47×#380C411yescharacteristic
54C47×#380C411yescharacteristic
55C47×#379C411yescharacteristic
56C47×#379C411yescharacteristic
57C4×C22⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C4×C22⋊C4×C47C2211yescharacteristic
60C4×C22⋊C4×C47C2211yescharacteristic
61C2×#10625329—22no—
62C2×#10625329—22no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329—41no—
66C2×#10625329—41no—
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C4⋊(C47⋊C8)—22no—
76C4⋊(C47⋊C8)—22no—
77C4⋊(C47⋊C8)—41no—
78C4⋊(C47⋊C8)—41no—
79C22⋊(C47⋊C8)—22no—
80C22⋊(C47⋊C8)—22no—
81C22⋊(C47⋊C8)—22no—
82C22⋊(C47⋊C8)—22no—
83C22⋊(C47⋊C8)—22no—
84C22⋊(C47⋊C8)—22no—
85C22⋊(C47⋊C8)—22no—
86C22⋊(C47⋊C8)—41no—
87C22⋊(C47⋊C8)—41no—
88C22⋊(C47⋊C8)D414yes—
89#13093935—22no—
90#13093935—41no—
91C4×C47⋊C8—22no—
92C4×C47⋊C8—41no—
93C25×C47C2×C411yescharacteristic
94C23×C4×C47—22no—
95C23×C4×C47—22no—
96C23×C4×C47—22no—
97C23×C4×C47—22no—
98C23×C4×C47—41no—
99C23×C4×C47—41no—
100C23×C4×C47C2×C411yescharacteristic
101C23×C4×C47C2×C411yescharacteristic
102C23×C4×C47C2×C411yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106#117×C47—22no—
107#117×C47—22no—
108#117×C47—41no—
109#117×C47—41no—
110C2×C4⋊C4×C47C2×C411yescharacteristic
111C2×C4⋊C4×C47C2×C411yescharacteristic
112C2×C4⋊C4×C47C2×C411yescharacteristic
113C2×C4⋊C4×C47C2×C411yescharacteristic
114C2×C22⋊C4×C47C2×C411yescharacteristic
115C2×C22⋊C4×C47C2×C411yescharacteristic
116C2×C22⋊C4×C47C2×C411yescharacteristic
117C2×C22⋊C4×C47C2×C411yescharacteristic
118C2×C22⋊C4×C47C2×C411yescharacteristic
119C2×C22⋊C4×C47C2×C411yescharacteristic
120C2×C22⋊C4×C47C2×C411yescharacteristic
121C2×C22⋊C4×C47C2×C411yescharacteristic
122C2×C22⋊C4×C47C2×C411yescharacteristic
123C2×C22⋊C4×C47C2×C411yescharacteristic
124C2×C22⋊C4×C47C2×C411yescharacteristic
125C2×C22⋊C4×C47C2×C411yescharacteristic
126C2×C42×C47C2311yescharacteristic
127C2×C42×C47C2311yescharacteristic
128C2×C42×C47C2311yescharacteristic
129C2×C42×C47C2311yescharacteristic
130#95×C47C2×C411yescharacteristic
131#95×C47C2×C411yescharacteristic
132#95×C47C2×C411yescharacteristic
133#95×C47C2×C411yescharacteristic
134#95×C47C2×C411yescharacteristic
135#95×C47C2×C411yescharacteristic
136#95×C47C2×C411yescharacteristic
137#95×C47C2×C411yescharacteristic
138C24×C47—22no—
139C24×C47—22no—
140C24×C47—22no—
141C24×C47—41no—
142C24×C47—41no—
143C24×C47—41no—
144C24×C47—41no—
145C24×C47C22×C411yescharacteristic
146C24×C47C22×C411yescharacteristic
147C24×C47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
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—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—41no—
169C22×C4×C47—41no—
170C22×C4×C47—41no—
171C22×C4×C47—44no—
172C22×C4×C47—44no—
173C22×C4×C47—44no—
174C22×C4×C47—44no—
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C22×C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C22×C411yescharacteristic
185C22×C4×C47C22×C411yescharacteristic
186C22×C4×C47C2×D412yes—
187C22×C4×C47#4112yes—
188C22×C4×C47#4112yes—
189C22×C4×C47#4112yes—
190C22×C4×C47C2411yescharacteristic
191C4⋊C4×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—41no—
194C4⋊C4×C47—41no—
195C22⋊C4×C47—22no—
196C22⋊C4×C47—22no—
197C22⋊C4×C47—22no—
198C22⋊C4×C47—22no—
199C22⋊C4×C47—41no—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C22⋊C4×C47—41no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C22⋊C4×C47—41no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47—21no—
212C42×C47—21no—
213C42×C47—21no—
214C42×C47—21no—
215#10625329—44no—
216#10625329—44no—
217C2×C47⋊C8—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8C2×D412yes—
240C2×C47⋊C8C2×D412yes—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—44no—
260C23×C47—44no—
261C23×C47—44no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47#11712yes—
267C23×C47C4×D412yes—
268C23×C47#13112yes—
269C23×C47C23×C411yescharacteristic
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
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—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47—44no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47#11712yes—
317C2×C4×C47C4×D412yes—
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4111yescharacteristic
320C2×C4×C47C2×#4111yescharacteristic
321C2×C4×C47C2×#4111yescharacteristic
322C2×C4×C47H(5,𝔽2)11yescharacteristic
323C2×C4×C47H(5,𝔽2)11yescharacteristic
324C47⋊C8—22no—
325C47⋊C8—22no—
326C47⋊C8—41no—
327C47⋊C8—41no—
328C47⋊C8—41no—
329C47⋊C8—41no—
330C47⋊C8—41no—
331C47⋊C8—41no—
332#22559—471nomaximal, Sylow
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—416no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47C2×#11711yescharacteristic
356C22×C47C2×C4×D411yescharacteristic
357C22×C47#51811yescharacteristic
358C22×C47C2×#13111yescharacteristic
359C22×C47#56811yescharacteristic
360C22×C47#56811yescharacteristic
361C22×C47#56811yescharacteristic
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47—41no—
367C4×C47—41no—
368C4×C47—41no—
369C4×C47—41no—
370C4×C47—41no—
371C4×C47—41no—
372C4×C47—41no—
373C4×C47#54611yescharacteristic
374C4×C47#54611yescharacteristic
375C4×C47#55111yescharacteristic
376C4×C47#55111yescharacteristic
377C2×#433—471no—
378C2×#407—471no—
379#2280D4711yescharacteristic
380#1924—471no—
381#1924—471no—
382#1923—471no—
383#1923—471no—
384#1851—471no—
385#1851—471no—
386#1818—471no—
387#1798—471no—
388#1779—471no—
389#1753—471no—
390#1753—471no—
391#1750—471no—
392C2×C47—42no—
393C2×C47—42no—
394C2×C47—42no—
395C2×C47#234211yescharacteristic
396C2×C47#292111yescharacteristic
397C2×C47#292411yescharacteristic
398C2×C47#293011yescharacteristic
399C2×C47#293311yescharacteristic
400C2×C47#297611yescharacteristic
401C2×C47#297811yescharacteristic
402C24×C4C2×D4711yescharacteristic
403C22×M16—471no—
404C22×M16—471no—
405C2×#117C2×D4711yescharacteristic
406C2×#117C2×D4711yescharacteristic
407#433—944no—
408C2×C4⋊C8—471no—
409C2×C4⋊C8—471no—
410C2×C4⋊C8—471no—
411C2×C4⋊C8—471no—
412#407—944no—
413C2×C22⋊C8—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×C22⋊C8—471no—
417C2×C22⋊C8—471no—
418C2×C22⋊C8—471no—
419C2×C22⋊C8—471no—
420C2×C22⋊C8—471no—
421C2×C22⋊C8—471no—
422C2×C22⋊C8—471no—
423C2×#97—471no—
424C2×#97—471no—
425C2×C4×C8—471no—
426C2×C4×C8—471no—
427#381Dic4711yescharacteristic
428#381Dic4711yescharacteristic
429#380Dic4711yescharacteristic
430#380Dic4711yescharacteristic
431#380Dic4711yescharacteristic
432#380Dic4711yescharacteristic
433#379Dic4711yescharacteristic
434#379Dic4711yescharacteristic
435C4×C22⋊C4C2×D4711yescharacteristic
436C4×C22⋊C4C2×D4711yescharacteristic
437C4×C22⋊C4C2×D4711yescharacteristic
438C4×C22⋊C4C2×D4711yescharacteristic
439#336—471no—
440#336—471no—
441#336—471no—
442#336—471no—
443#336—471no—
444#336—471no—
445#336—471no—
446#336—471no—
447C47#2255911yescharacteristic, complemented, Sylow
448C25C2×Dic4711yescharacteristic
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4C2×Dic4711yescharacteristic
456C23×C4C2×Dic4711yescharacteristic
457C23×C4C2×Dic4711yescharacteristic
458C23×C4C22×D4711yescharacteristic
459C23×C4C22×D4711yescharacteristic
460C23×C4C22×D4711yescharacteristic
461C2×M16—942no—
462C2×M16—942no—
463C2×M16—942no—
464C2×M16—942no—
465C2×M16—1881no—
466C2×M16—1881no—
467C22×C8—471no—
468C22×C8—471no—
469C22×C8—471no—
470C22×C8—471no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8—471no—
474C22×C8—471no—
475#117—22no—
476#117—22no—
477#117—41no—
478#117—41no—
479C2×C4⋊C4C2×Dic4711yescharacteristic
480C2×C4⋊C4C2×Dic4711yescharacteristic
481C2×C4⋊C4C2×Dic4711yescharacteristic
482C2×C4⋊C4C2×Dic4711yescharacteristic
483C2×C22⋊C4C2×Dic4711yescharacteristic
484C2×C22⋊C4C2×Dic4711yescharacteristic
485C2×C22⋊C4C2×Dic4711yescharacteristic
486C2×C22⋊C4C2×Dic4711yescharacteristic
487C2×C22⋊C4C2×Dic4711yescharacteristic
488C2×C22⋊C4C2×Dic4711yescharacteristic
489C2×C22⋊C4C2×Dic4711yescharacteristic
490C2×C22⋊C4C2×Dic4711yescharacteristic
491C2×C22⋊C4C2×Dic4711yescharacteristic
492C2×C22⋊C4C2×Dic4711yescharacteristic
493C2×C22⋊C4C2×Dic4711yescharacteristic
494C2×C22⋊C4C2×Dic4711yescharacteristic
495C2×C42C22×D4711yescharacteristic
496C2×C42C22×D4711yescharacteristic
497C2×C42C22×D4711yescharacteristic
498C2×C42C22×D4711yescharacteristic
499C4⋊C8—942no—
500C4⋊C8—942no—
501C4⋊C8—1881no—
502C4⋊C8—1881no—
503C22⋊C8—474no—
504C22⋊C8—942no—
505C22⋊C8—942no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508C22⋊C8—942no—
509C22⋊C8—942no—
510C22⋊C8—942no—
511C22⋊C8—1881no—
512C22⋊C8—1881no—
513#97—942no—
514#97—1881no—
515C4×C8—942no—
516C4×C8—1881no—
517#95C2×Dic4711yescharacteristic
518#95C2×Dic4711yescharacteristic
519#95C2×Dic4711yescharacteristic
520#95C2×Dic4711yescharacteristic
521#95C2×Dic4711yescharacteristic
522#95C2×Dic4711yescharacteristic
523#95C2×Dic4711yescharacteristic
524#95C2×Dic4711yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24C22×Dic4711yescharacteristic
533C24C22×Dic4711yescharacteristic
534C24C22×Dic4711yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4#1062535012yes—
563C22×C4#1062535012yes—
564C22×C4D4×D4712yes—
565C22×C4#1062535212yes—
566C22×C4C22×Dic4711yescharacteristic
567C22×C4C22×Dic4711yescharacteristic
568C22×C4C22×Dic4711yescharacteristic
569C22×C4C22×Dic4711yescharacteristic
570C22×C4C22×Dic4711yescharacteristic
571C22×C4C22×Dic4711yescharacteristic
572C22×C4C22×Dic4711yescharacteristic
573C22×C4C22×Dic4711yescharacteristic
574C22×C4C22×Dic4711yescharacteristic
575C22×C4C22×Dic4711yescharacteristic
576C22×C4C22×Dic4711yescharacteristic
577C22×C4C23×D4711yescharacteristic
578M16—1884no—
579M16—1884no—
580C2×C8—472no—
581C2×C8—472no—
582C2×C8—941no—
583C2×C8—941no—
584C2×C8—941no—
585C2×C8—941no—
586C2×C8—941no—
587C2×C8—941no—
588C2×C8—941no—
589C2×C8—941no—
590C2×C8—941no—
591C2×C8—941no—
592C2×C8—941no—
593C2×C8—941no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—941no—
601C2×C8—941no—
602C2×C8—941no—
603C2×C8—941no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#1309398312yes—
654C23D4×Dic4712yes—
655C23#1309403112yes—
656C23C23×Dic4711yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4#1309398312yes—
704C2×C4D4×Dic4712yes—
705C2×C4C2×D4×D4711yescharacteristic
706C2×C4C2×#1062535211yescharacteristic
707C2×C4C2×#1062535011yescharacteristic
708C2×C4C2×#1062535011yescharacteristic
709C2×C4#1309406911yescharacteristic
710C2×C4#1309406911yescharacteristic
711C8—942no—
712C8—942no—
713C8—1881no—
714C8—1881no—
715C8—1881no—
716C8—1881no—
717C8—1881no—
718C8—1881no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—416no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22C2×#1309398311yescharacteristic
742C22C2×D4×Dic4711yescharacteristic
743C22#1568959811yescharacteristic
744C22C2×#1309403111yescharacteristic
745C22#1568989011yescharacteristic
746C22#1568989011yescharacteristic
747C22#1568989011yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4#1568976311yescharacteristic
760C4#1568976311yescharacteristic
761C4#1568979911yescharacteristic
762C4#1568979911yescharacteristic
763C2—42no—
764C2—42no—
765C2—42no—
766C2#2024623711yescharacteristic
767C2#2025202611yescharacteristic
768C2#2025204611yescharacteristic
769C2#2025209211yescharacteristic
770C2#2025211511yescharacteristic
771C2#2025243611yescharacteristic
772C2#2025245011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#2280C2
prime radicalC25×C47C2×C4
cosocleC22×C4×C47C24
hypercenter#2280D47
hypocenterC47#22559
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. C2×#15689184C2semidirect
3. #20244003C2semidirect
4. #20244003C2semidirect
5. #20243996C2semidirect
6. #20243996C2semidirect
7. #20243573C2semidirect
8. #20243573C2semidirect
9. #20243459C2semidirect
10. #20243372C2semidirect
12. #20243172C2semidirect
13. #20243172C2semidirect
14. #20243154C2semidirect
19. C2×C4⋊(C47⋊C8)C22semidirect
20. C2×C4⋊(C47⋊C8)C22semidirect
21. C2×C4⋊(C47⋊C8)C22semidirect
22. C2×C4⋊(C47⋊C8)C22semidirect
34. C2×#13093935C22semidirect
35. C2×#13093935C22semidirect
36. C2×C4×C47⋊C8C22semidirect
37. C2×C4×C47⋊C8C22semidirect
38. #15688878C22semidirect
39. #15688878C22semidirect
40. #15688878C22semidirect
41. #15688878C22semidirect
42. #15688878C22semidirect
43. #15688878C22semidirect
44. #15688878C22semidirect
45. #15688878C22semidirect
447. C47#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#156891842
C2×#156890872
#202440032
#202439962
#202435732
#202434592
#202433722
#202432982
#202431722
#202431542
C47×#22802
#2255947