Finite Group Databasebeta

← #26233207

Subgroups — #26233207

Order 12032.

1212 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689175C211yesmaximal, characteristic, complemented
2C2×#15689085C211yesmaximal, characteristic
3C4×C22⋊C4×D47C211yesmaximal, characteristic
4#20244003C211yesmaximal, characteristic, complemented
5#20243997C211yesmaximal, characteristic, complemented
6#20243991C211yesmaximal, characteristic, complemented
7#20243572C211yesmaximal, characteristic, complemented
8#20243569C211yesmaximal, characteristic, complemented
9#20243455C211yesmaximal, characteristic, complemented
10#20243367C211yesmaximal, characteristic, complemented
11#20243297C211yesmaximal, characteristic
12#20243173C211yesmaximal, characteristic, complemented
13#20243170C211yesmaximal, characteristic, complemented
14#20243151C211yesmaximal, characteristic, complemented
15C47×#1924C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C2×C22⋊C4×D47C411yescharacteristic
20C2×C22⋊C4×D47C411yescharacteristic
21C2×C42×D47C2211yescharacteristic
22C2×C42×D47C2211yescharacteristic
23#15689175—24no—
24C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
25C2×Dic47⋊C8C2211yescharacteristic, complemented
26C2×Dic47⋊C8C2211yescharacteristic, complemented
27#15689085—24no—
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×(C2×D47)⋊C8C2211yescharacteristic
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×#13093935C2211yescharacteristic, complemented
37C2×C8×Dic47C2211yescharacteristic, complemented
38C2×C8×Dic47C2211yescharacteristic, complemented
39C22⋊C4×Dic47C411yescharacteristic
40C22⋊C4×Dic47C411yescharacteristic
41C4×(C2×D47)⋊C4C2211yescharacteristic
42C4×(C2×D47)⋊C4C2211yescharacteristic
43C4×C22⋊Dic47C2211yescharacteristic
44#15688970C411yescharacteristic
45#15688970C411yescharacteristic
46#95×D47C411yescharacteristic
47#95×D47C411yescharacteristic
48#15688878C2211yescharacteristic, complemented
49#15688878C2211yescharacteristic, complemented
50#15688877C2211yescharacteristic, complemented
51#15688877C2211yescharacteristic, complemented
52#15688877C2211yescharacteristic, complemented
53#15688877C2211yescharacteristic, complemented
54C2×C4⋊C8×C47C2211yescharacteristic, complemented
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×C22⋊C8×C47C2211yescharacteristic
57C2×#97×C47C2211yescharacteristic, complemented
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#336C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C24×D47C2×C411yescharacteristic
62C23×Dic47C2×C411yescharacteristic
63C22×C4×D47—22no—
64C22×C4×D47—22no—
65C22×C4×D47—22no—
66C22×C4×D47—22no—
67C22×C4×D47—41no—
68C22×C4×D47—41no—
69C22×C4×D47C2×C411yescharacteristic
70C22×C4×D47C2×C411yescharacteristic
71C22×C4×D47C2×C411yescharacteristic
72C22×C4×D47C2×C411yescharacteristic
73C22×C4×D47C2×C411yescharacteristic
74C22×C4×D47C2×C411yescharacteristic
75C22×C4×D47C2311yescharacteristic
76C22×C4×D47C2311yescharacteristic
77C2×#10625324—22no—
78C2×#10625324—22no—
79C2×#10625324—22no—
80C2×#10625324—22no—
81C2×#10625324—41no—
82C2×#10625324—41no—
83C22×C47⋊C8C2311yescharacteristic
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87C2×C22⋊Dic47C2×C411yescharacteristic
88C2×C22⋊Dic47C2×C411yescharacteristic
89C2×(C2×D47)⋊C4C2×C411yescharacteristic
90C2×(C2×D47)⋊C4C2×C411yescharacteristic
91C2×(C2×D47)⋊C4C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C22⋊C4×D47—24no—
94C22⋊C4×D47—24no—
95C2×C4×Dic47C2×C411yescharacteristic
96C2×C4×Dic47C2×C411yescharacteristic
97C2×C4×Dic47C2×C411yescharacteristic
98C2×C4×Dic47C2×C411yescharacteristic
99C2×C4×Dic47C2311yescharacteristic
100C2×C4×Dic47C2311yescharacteristic
101C42×D47—22no—
102C42×D47—22no—
103C42×D47—41no—
104C42×D47—41no—
105C4⋊(C47⋊C8)—22no—
106Dic47⋊C8—41no—
107Dic47⋊C8—41no—
108C22⋊(C47⋊C8)—22no—
109C22⋊(C47⋊C8)—41no—
110(C2×D47)⋊C8—22no—
111(C2×D47)⋊C8—22no—
112(C2×D47)⋊C8—22no—
113(C2×D47)⋊C8—22no—
114(C2×D47)⋊C8—22no—
115(C2×D47)⋊C8D414yes—
116#13093935—41no—
117C8×Dic47—22no—
118C8×Dic47—22no—
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C47⋊#95C2×C411yescharacteristic
122C47⋊#95C2×C411yescharacteristic
123C47⋊#95C2×C411yescharacteristic
124C47⋊#95C2×C411yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C2×C22⋊C4×C47C2×C411yescharacteristic
131C2×C22⋊C4×C47C2×C411yescharacteristic
132C2×C42×C47C2311yescharacteristic
133C2×C42×C47C2311yescharacteristic
134C4⋊C8×C47—22no—
135C22⋊C8×C47—22no—
136C22⋊C8×C47—41no—
137#97×C47—41no—
138#95×C47C2×C411yescharacteristic
139#95×C47C2×C411yescharacteristic
140C24×C47C22×C411yescharacteristic
141C23×D47—22no—
142C23×D47—22no—
143C23×D47—22no—
144C23×D47—22no—
145C23×D47—22no—
146C23×D47—41no—
147C23×D47—41no—
148C23×D47C22×C411yescharacteristic
149C23×D47C22×C411yescharacteristic
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×C47C22×C411yescharacteristic
157C22×C4×C47C22×C411yescharacteristic
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C22×C411yescharacteristic
160C22×C4×C47C22×C411yescharacteristic
161C22×C4×C47C2411yescharacteristic
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—41no—
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C22×Dic47C22×C411yescharacteristic
171C2×C4×D47—22no—
172C2×C4×D47—22no—
173C2×C4×D47—21no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—22no—
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—22no—
185C2×C4×D47—22no—
186C2×C4×D47—22no—
187C2×C4×D47—22no—
188C2×C4×D47—22no—
189C2×C4×D47—22no—
190C2×C4×D47—44no—
191C2×C4×D47—44no—
192C2×C4×D47—44no—
193C2×C4×D47—44no—
194C2×C4×D47—41no—
195C2×C4×D47—41no—
196C2×C4×D47—41no—
197C2×C4×D47—41no—
198C2×C4×D47—41no—
199C2×C4×D47—41no—
200C2×C4×D47M1614yescomplemented
201C2×C4×D47C2×D412yes—
202C2×C4×D47#4112yes—
203C2×C4×D47#4112yes—
204C2×C4×D47#4112yes—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47C2×D412yes—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C42×C47—21no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47—21no—
223C22⋊Dic47—22no—
224C22⋊Dic47M1614yescomplemented
225(C2×D47)⋊C4—22no—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4—22no—
229C4×Dic47—21no—
230C4×Dic47—21no—
231C4×Dic47—21no—
232C4×Dic47—21no—
233C4×Dic47—22no—
234C4×Dic47—22no—
235C4×Dic47—41no—
236C4×Dic47—41no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8—21no—
244C2×C47⋊C8—21no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8C2×D412yes—
249#10625324—44no—
250#10625324—44no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47C2×M1612yes—
258C23×C47C23×C411yescharacteristic
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—28no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
267C22×D47—21no—
268C22×D47—21no—
269C22×D47—21no—
270C22×D47—44no—
271C22×D47—44no—
272C22×D47—44no—
273C22×D47—44no—
274C22×D47—44no—
275C22×D47—44no—
276C22×D47#11712yes—
277C22×D47C4×D412yes—
278C22×D47C2×M1612yes—
279C22×D47#13112yes—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
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—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47C2×M1612yes—
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47C2×#4111yescharacteristic
303C2×C4×C47H(5,𝔽2)11yescharacteristic
304C2×C4×C47H(5,𝔽2)11yescharacteristic
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—21no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—44no—
319C2×Dic47#11712yes—
320C2×Dic47C4×D412yes—
321C2×Dic47C2×M1612yes—
322C2×Dic47C2×M1612yes—
323C2×Dic47C2×M1612yes—
324C4×D47—28no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—22no—
329C4×D47—22no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—22no—
333C4×D47—44no—
334C4×D47—44no—
335C4×D47—44no—
336C4×D47—44no—
337C4×D47—44no—
338C8×C47—22no—
339C8×C47—41no—
340C8×C47—41no—
341C8×C47—41no—
342C47⋊C8—22no—
343C47⋊C8—41no—
344C47⋊C8—41no—
345C47⋊C8—41no—
346#22553—471nomaximal, Sylow
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47C2×#11711yescharacteristic
355C22×C47C2×C4×D411yescharacteristic
356C22×C47#51811yescharacteristic
357C22×C47C22×M1611yescharacteristic
358C22×C47C22×M1611yescharacteristic
359C22×C47C2×#13111yescharacteristic
360C22×C47#56811yescharacteristic
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—22no—
370C2×D47—416no—
371C2×D47—41no—
372C2×D47—41no—
373C2×D47—41no—
374C2×D47—41no—
375C2×D47#43514yes—
376C4×C47—22no—
377C4×C47—41no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—41no—
381C4×C47#54611yescharacteristic
382C4×C47#54611yescharacteristic
383C4×C47#55111yescharacteristic
384C4×C47#55111yescharacteristic
385Dic47—22no—
386Dic47—22no—
387Dic47—22no—
388Dic47—22no—
389Dic47—22no—
390Dic47—41no—
391C2×#431—471no—
392C2×#407—471no—
393C2×C4×C22⋊C4—471no—
394#1924—471no—
395#1924D4711yescharacteristic, complemented
396#1923—471no—
397#1923—471no—
398#1851—471no—
399#1851—471no—
400#1817—471no—
401#1797—471no—
402#1779—471no—
403#1753—471no—
404#1753—471no—
405#1749—471no—
406C2×C47—42no—
407C2×C47#234211yescharacteristic
408C2×C47#292011yescharacteristic
409C2×C47#292411yescharacteristic
410C2×C47C2×#43511yescharacteristic
411C2×C47D4×M1611yescharacteristic
412C2×C47#297411yescharacteristic
413C2×C47#297511yescharacteristic
414D47—24no—
415D47—42no—
416C24×C4—471no—
417C22×M16—471no—
418C22×M16—471no—
419C22×C22⋊C4—471no—
420C22×C22⋊C4—471no—
421C22×C42—471no—
422C22×C42—471no—
423#431—944no—
424C2×C4⋊C8—471no—
425C2×C4⋊C8—471no—
426C2×C4⋊C8—471no—
427C2×C4⋊C8C2×D4711yescharacteristic, complemented
428#407—944no—
429C2×C22⋊C8—471no—
430C2×C22⋊C8—471no—
431C2×C22⋊C8—471no—
432C2×C22⋊C8—471no—
433C2×C22⋊C8—471no—
434C2×C22⋊C8—471no—
435C2×C22⋊C8—471no—
436C2×C22⋊C8—471no—
437C2×C22⋊C8C2×D4711yescharacteristic
438C2×C22⋊C8C2×D4711yescharacteristic
439C2×#97—471no—
440C2×#97C2×D4711yescharacteristic, complemented
441C2×C4×C8—471no—
442C2×C4×C8—471no—
443C4×C22⋊C4—471no—
444C4×C22⋊C4—471no—
445C4×C22⋊C4—471no—
446C4×C22⋊C4—471no—
447C4×C22⋊C4—471no—
448C4×C22⋊C4—471no—
449C4×C22⋊C4—471no—
450C4×C22⋊C4C2×D4711yescharacteristic
451C2×#95—471no—
452C2×#95—471no—
453#336—471no—
454#336—471no—
455#336—471no—
456#336—471no—
457#336—471no—
458#336—471no—
459#336C2×D4711yescharacteristic, complemented
460#336C2×D4711yescharacteristic, complemented
461C47#2255311yescharacteristic, complemented, Sylow
462C25—471no—
463C23×C4—471no—
464C23×C4—471no—
465C23×C4—471no—
466C23×C4—471no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—942no—
473C23×C4—942no—
474C23×C4—942no—
475C23×C4—942no—
476C23×C4—1881no—
477C23×C4—1881no—
478C23×C4C22×D4711yescharacteristic
479C2×M16—942no—
480C2×M16—942no—
481C2×M16—942no—
482C2×M16—942no—
483C2×M16—1881no—
484C2×M16—1881no—
485C22×C8—471no—
486C22×C8—471no—
487C22×C8—471no—
488C22×C8—471no—
489C22×C8C22×D4711yescharacteristic
490C22×C8C22×D4711yescharacteristic
491C22×C8C22×D4711yescharacteristic
492C22×C8C22×D4711yescharacteristic
493C2×C22⋊C4—471no—
494C2×C22⋊C4—471no—
495C2×C22⋊C4—471no—
496C2×C22⋊C4—471no—
497C2×C22⋊C4—471no—
498C2×C22⋊C4—471no—
499C2×C22⋊C4—944no—
500C2×C22⋊C4—944no—
501C2×C22⋊C4C4×D4711yescharacteristic
502C2×C22⋊C4C4×D4711yescharacteristic
503C2×C42—471no—
504C2×C42—471no—
505C2×C42—471no—
506C2×C42—471no—
507C2×C42—471no—
508C2×C42—471no—
509C2×C42—942no—
510C2×C42—942no—
511C2×C42—1881no—
512C2×C42—1881no—
513C2×C42C22×D4711yescharacteristic
514C2×C42C22×D4711yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—942no—
517C4⋊C8—1881no—
518C4⋊C8—1881no—
519C22⋊C8—22no—
520C22⋊C8—41no—
521C22⋊C8—474no—
522C22⋊C8—942no—
523C22⋊C8—942no—
524C22⋊C8—942no—
525C22⋊C8—942no—
526C22⋊C8—942no—
527C22⋊C8—942no—
528C22⋊C8—1881no—
529#97—41no—
530#97—1881no—
531C4×C8—942no—
532C4×C8—942no—
533#95—471no—
534#95—471no—
535#95—471no—
536#95—471no—
537#95—471no—
538#95—471no—
539#95C4×D4711yescharacteristic
540#95C4×D4711yescharacteristic
541C24—471no—
542C24—471no—
543C24—942no—
544C24—942no—
545C24—942no—
546C24—942no—
547C24—942no—
548C24—1881no—
549C24—1881no—
550C24C2×C4×D4711yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—471no—
558C22×C4—471no—
559C22×C4—471no—
560C22×C4—471no—
561C22×C4—471no—
562C22×C4—474no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—472no—
567C22×C4—471no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—1881no—
590C22×C4—1881no—
591C22×C4—1881no—
592C22×C4—1881no—
593C22×C4—1881no—
594C22×C4—1881no—
595C22×C4—1884no—
596C22×C4—1884no—
597C22×C4—1884no—
598C22×C4—1884no—
599C22×C4—1881no—
600C22×C4C2×C4×D4711yescharacteristic
601C22×C4C2×C4×D4711yescharacteristic
602C22×C4C2×C4×D4711yescharacteristic
603C22×C4C2×C4×D4711yescharacteristic
604C22×C4C2×C4×D4711yescharacteristic
605C22×C4C23×D4711yescharacteristic
606M16—1884no—
607M16—1884no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—472no—
620C2×C8—941no—
621C2×C8—941no—
622C2×C8—941no—
623C2×C8—941no—
624C2×C8—941no—
625C2×C8—941no—
626C2×C8—941no—
627C2×C8—941no—
628C2×C8—941no—
629C2×C8—941no—
630C2×C8—941no—
631C2×C8D4×D4712yes—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—474no—
635C22⋊C4—942no—
636C22⋊C4—942no—
637C22⋊C4—942no—
638C22⋊C4—942no—
639C22⋊C4—942no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—942no—
645C42—942no—
646C42—941no—
647C42—941no—
648C42—941no—
649C42—941no—
650C42—1881no—
651C42—1881no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—472no—
659C23—472no—
660C23—472no—
661C23—472no—
662C23—948no—
663C23—941no—
664C23—941no—
665C23—941no—
666C23—941no—
667C23—941no—
668C23—941no—
669C23—941no—
670C23—941no—
671C23—941no—
672C23—941no—
673C23—1884no—
674C23—1884no—
675C23—1884no—
676C23—1884no—
677C23—1884no—
678C23—1884no—
679C23M16×D4712yes—
680C23C22×C4×D4711yescharacteristic
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—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—472no—
700C2×C4—472no—
701C2×C4—472no—
702C2×C4—472no—
703C2×C4—472no—
704C2×C4—948no—
705C2×C4—941no—
706C2×C4—941no—
707C2×C4—941no—
708C2×C4—941no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—941no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—941no—
724C2×C4—941no—
725C2×C4—941no—
726C2×C4—1884no—
727C2×C4—1884no—
728C2×C4—1884no—
729C2×C4—1884no—
730C2×C4—1884no—
731C2×C4—1884no—
732C2×C4M16×D4712yes—
733C2×C4C2×D4×D4711yescharacteristic
734C2×C4#41×D4711yescharacteristic
735C2×C4#41×D4711yescharacteristic
736C2×C4#41×D4711yescharacteristic
737C2×C4#1309406911yescharacteristic
738C2×C4#1309407011yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—942no—
744C8—1881no—
745C8—1881no—
746C8—1881no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—474no—
755C22—942no—
756C22—942no—
757C22—942no—
758C22—942no—
759C22—942no—
760C22—942no—
761C22—942no—
762C22—942no—
763C22—942no—
764C22—18816no—
765C22—1881no—
766C22—1881no—
767C22—1881no—
768C22—1881no—
769C22#117×D4711yescharacteristic
770C22C4×D4×D4711yescharacteristic
771C22#1568959511yescharacteristic
772C22C2×M16×D4711yescharacteristic
773C22C2×M16×D4711yescharacteristic
774C22#131×D4711yescharacteristic
775C22#1568988811yescharacteristic
776C4—22no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—942no—
782C4—942no—
783C4—942no—
784C4—942no—
785C4—942no—
786C4—1881no—
787C4#1568976211yescharacteristic
788C4#1568976611yescharacteristic
789C4#1568979811yescharacteristic
790C4#1568980111yescharacteristic
791C2—42no—
792C2—944no—
793C2—1882no—
794C2#2024623611yescharacteristic
795C2#2025201811yescharacteristic
796C2#2025204411yescharacteristic
797C2#435×D4711yescharacteristic
798C2#2025212111yescharacteristic
799C2#2025241811yescharacteristic
800C2#2025242611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1924C2
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1924D47
hypocenterC47#22553
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#15689175C2semidirect
4. #20244003C2semidirect
5. #20243997C2semidirect
6. #20243991C2semidirect
7. #20243572C2semidirect
8. #20243569C2semidirect
9. #20243455C2semidirect
10. #20243367C2semidirect
12. #20243173C2semidirect
13. #20243170C2semidirect
14. #20243151C2semidirect
15. C47×#1924C2semidirect
24. C2×C4⋊(C47⋊C8)C22semidirect
25. C2×Dic47⋊C8C22semidirect
26. C2×Dic47⋊C8C22semidirect
36. C2×#13093935C22semidirect
37. C2×C8×Dic47C22semidirect
38. C2×C8×Dic47C22semidirect
48. #15688878C22semidirect
49. #15688878C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
52. #15688877C22semidirect
53. #15688877C22semidirect
54. C2×C4⋊C8×C47C22semidirect
57. C2×#97×C47C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
200. C2×C4×D47M16semidirect
224. C22⋊Dic47M16semidirect
395. #1924D47semidirect
427. C2×C4⋊C8C2×D47semidirect
440. C2×#97C2×D47semidirect
459. #336C2×D47semidirect
460. #336C2×D47semidirect
461. C47#22553semidirect

Maximal subgroups

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

subgroupindex
C2×#156891752
C2×#156890852
C4×C22⋊C4×D472
#202440032
#202439972
#202439912
#202435722
#202435692
#202434552
#202433672
#202432972
#202431732
#202431702
#202431512
C47×#19242
#2255347