Finite Group Databasebeta

← #26233202

Subgroups — #26233202

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×#15689174C211yesmaximal, characteristic, complemented
2C2×#15689086C211yesmaximal, characteristic
3C4×C22⋊C4×D47C211yesmaximal, characteristic
4#20244001C211yesmaximal, characteristic, complemented
5#20243999C211yesmaximal, characteristic, complemented
6#20243994C211yesmaximal, characteristic, complemented
7#20243992C211yesmaximal, characteristic, complemented
8#20243571C211yesmaximal, characteristic, complemented
9#20243570C211yesmaximal, characteristic, complemented
10#20243455C211yesmaximal, characteristic, complemented
11#20243367C211yesmaximal, characteristic, complemented
12#20243297C211yesmaximal, characteristic
13#20243172C211yesmaximal, characteristic, complemented
14#20243151C211yesmaximal, characteristic, complemented
15C47×#1753C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C2×C22⋊C4×D47C411yescharacteristic
19C2×C22⋊C4×D47C411yescharacteristic
20C2×C42×D47C2211yescharacteristic
21C2×C42×D47C2211yescharacteristic
22#15689174—24no—
23C2×Dic47⋊C8C2211yescharacteristic, complemented
24C2×Dic47⋊C8C2211yescharacteristic, complemented
25C2×Dic47⋊C8C2211yescharacteristic, complemented
26C2×Dic47⋊C8C2211yescharacteristic, complemented
27#15689086—24no—
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×(C2×D47)⋊C8C2211yescharacteristic
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×(C2×D47)⋊C8C2211yescharacteristic
37C2×#13093935C2211yescharacteristic, complemented
38C2×C4×C47⋊C8C2211yescharacteristic, 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
54C22×M16×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×#97×C47C2211yescharacteristic, complemented
57C2×C4×C8×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×#10625329—22no—
78C2×#10625329—22no—
79C2×#10625329—41no—
80C22×C47⋊C8C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84C2×C22⋊Dic47C2×C411yescharacteristic
85C2×C22⋊Dic47C2×C411yescharacteristic
86C2×(C2×D47)⋊C4C2×C411yescharacteristic
87C2×(C2×D47)⋊C4C2×C411yescharacteristic
88C2×(C2×D47)⋊C4C2×C411yescharacteristic
89C2×(C2×D47)⋊C4C2×C411yescharacteristic
90C22⋊C4×D47—24no—
91C22⋊C4×D47—24no—
92C2×C4×Dic47C2×C411yescharacteristic
93C2×C4×Dic47C2×C411yescharacteristic
94C2×C4×Dic47C2×C411yescharacteristic
95C2×C4×Dic47C2×C411yescharacteristic
96C2×C4×Dic47C2311yescharacteristic
97C2×C4×Dic47C2311yescharacteristic
98C42×D47—22no—
99C42×D47—22no—
100C42×D47—41no—
101C42×D47—41no—
102Dic47⋊C8—22no—
103Dic47⋊C8—22no—
104Dic47⋊C8—41no—
105Dic47⋊C8—41no—
106C22⋊(C47⋊C8)—22no—
107(C2×D47)⋊C8—22no—
108(C2×D47)⋊C8—22no—
109(C2×D47)⋊C8—22no—
110(C2×D47)⋊C8—22no—
111(C2×D47)⋊C8—22no—
112(C2×D47)⋊C8—41no—
113(C2×D47)⋊C8—41no—
114(C2×D47)⋊C8D414yes—
115#13093935—41no—
116C4×C47⋊C8—22no—
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C47⋊#95C2×C411yescharacteristic
122C47⋊#95C2×C411yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C2×M16×C47—22no—
125C2×M16×C47—22no—
126C2×M16×C47—41no—
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C2×C22⋊C4×C47C2×C411yescharacteristic
132C2×C22⋊C4×C47C2×C411yescharacteristic
133C2×C42×C47C2311yescharacteristic
134C2×C42×C47C2311yescharacteristic
135C22⋊C8×C47—22no—
136#97×C47—41no—
137C4×C8×C47—22no—
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×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C22×C411yescharacteristic
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47#4112yes—
160C22×C4×C47#4112yes—
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—22no—
178C2×C4×D47—22no—
179C2×C4×D47—22no—
180C2×C4×D47—22no—
181C2×C4×D47—22no—
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—22no—
191C2×C4×D47—22no—
192C2×C4×D47—44no—
193C2×C4×D47—44no—
194C2×C4×D47—44no—
195C2×C4×D47—44no—
196C2×C4×D47—41no—
197C2×C4×D47—41no—
198C2×C4×D47—41no—
199C2×C4×D47—41no—
200C2×C4×D47—41no—
201C2×C4×D47—41no—
202C2×C4×D47M1614yescomplemented
203C2×C4×D47C2×D412yes—
204C2×C4×D47#4112yes—
205M16×C47—44no—
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×C47—21no—
217C2×C8×C47C2×D412yes—
218C22⋊C4×C47—22no—
219C22⋊C4×C47—22no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47—21no—
223C42×C47—21no—
224C22⋊Dic47—22no—
225C22⋊Dic47—22no—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4—22no—
229(C2×D47)⋊C4M1614yescomplemented
230C4×Dic47—21no—
231C4×Dic47—21no—
232C4×Dic47—21no—
233C4×Dic47—21no—
234C4×Dic47—22no—
235C4×Dic47—22no—
236C4×Dic47—41no—
237C4×Dic47—41no—
238#10625329—44no—
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⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8C2×D412yes—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47#11712yes—
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×D47C4×D412yes—
277C22×D47C2×M1612yes—
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—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
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#11712yes—
297C2×C4×C47C2×M1612yes—
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—21no—
319C2×Dic47—21no—
320C2×Dic47—44no—
321C2×Dic47C4×D412yes—
322C2×Dic47C2×M1612yes—
323C2×Dic47C2×M1612yes—
324C4×D47—28no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—22no—
329C4×D47—44no—
330C4×D47—44no—
331C4×D47—44no—
332C4×D47—44no—
333C4×D47—44no—
334C4×D47—41no—
335C4×D47—41no—
336C4×D47—41no—
337C4×D47—41no—
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—22no—
378C4×C47—22no—
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—41no—
389Dic47—41no—
390Dic47—41no—
391C2×#431—471no—
392C2×#407—471no—
393C2×C4×C22⋊C4—471no—
394#1924—471no—
395#1924—471no—
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#1753D4711yescharacteristic, complemented
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×M16C2×D4711yescharacteristic
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⋊C8—471no—
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⋊C8—471no—
438C2×C22⋊C8C2×D4711yescharacteristic
439C2×#97—471no—
440C2×#97C2×D4711yescharacteristic, complemented
441C2×C4×C8—471no—
442C2×C4×C8C2×D4711yescharacteristic, complemented
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—22no—
480C2×M16—22no—
481C2×M16—41no—
482C2×M16—942no—
483C2×M16—942no—
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—942no—
516C4⋊C8—942no—
517C4⋊C8—1881no—
518C4⋊C8—1881no—
519C22⋊C8—22no—
520C22⋊C8—474no—
521C22⋊C8—942no—
522C22⋊C8—942no—
523C22⋊C8—942no—
524C22⋊C8—942no—
525C22⋊C8—942no—
526C22⋊C8—942no—
527C22⋊C8—1881no—
528C22⋊C8—1881no—
529#97—41no—
530#97—1881no—
531C4×C8—22no—
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—471no—
556C22×C4—471no—
557C22×C4—471no—
558C22×C4—474no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—471no—
562C22×C4—471no—
563C22×C4—471no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—941no—
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—1881no—
588C22×C4—1881no—
589C22×C4—1881no—
590C22×C4—1881no—
591C22×C4—1881no—
592C22×C4—1881no—
593C22×C4—1884no—
594C22×C4—1884no—
595C22×C4—1884no—
596C22×C4—1884no—
597C22×C4—1881no—
598C22×C4C2×C4×D4711yescharacteristic
599C22×C4C2×C4×D4711yescharacteristic
600C22×C4C2×C4×D4711yescharacteristic
601C22×C4C2×C4×D4711yescharacteristic
602C22×C4C2×C4×D4711yescharacteristic
603C22×C4#1062535012yes—
604C22×C4#1062535012yes—
605C22×C4C23×D4711yescharacteristic
606M16—44no—
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—
679C23#1309398112yes—
680C23C22×C4×D4711yescharacteristic
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—472no—
698C2×C4—472no—
699C2×C4—472no—
700C2×C4—948no—
701C2×C4—941no—
702C2×C4—941no—
703C2×C4—941no—
704C2×C4—941no—
705C2×C4—941no—
706C2×C4—941no—
707C2×C4—942no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—941no—
715C2×C4—941no—
716C2×C4—941no—
717C2×C4—941no—
718C2×C4—941no—
719C2×C4—941no—
720C2×C4—1884no—
721C2×C4—1884no—
722C2×C4—1884no—
723C2×C4—1884no—
724C2×C4—1884no—
725C2×C4—1884no—
726C2×C4—1881no—
727C2×C4—1881no—
728C2×C4—1881no—
729C2×C4—1881no—
730C2×C4#1309398112yes—
731C2×C4M16×D4712yes—
732C2×C4M16×D4712yes—
733C2×C4C2×D4×D4711yescharacteristic
734C2×C4#41×D4711yescharacteristic
735C2×C4C2×#1062535011yescharacteristic
736C2×C4C2×#1062535011yescharacteristic
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—
769C22C2×#1309398111yescharacteristic
770C22C4×D4×D4711yescharacteristic
771C22#1568959511yescharacteristic
772C22C2×M16×D4711yescharacteristic
773C22C2×M16×D4711yescharacteristic
774C22#131×D4711yescharacteristic
775C22#1568988811yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—41no—
781C4—942no—
782C4—942no—
783C4—942no—
784C4—1881no—
785C4—1881no—
786C4—1881no—
787C4#1568976311yescharacteristic
788C4#1568976911yescharacteristic
789C4#1568979711yescharacteristic
790C4#1568980211yescharacteristic
791C2—42no—
792C2—944no—
793C2—1882no—
794C2#2024623111yescharacteristic
795C2#2025201911yescharacteristic
796C2#2025204311yescharacteristic
797C2#435×D4711yescharacteristic
798C2#2025212111yescharacteristic
799C2#2025242011yescharacteristic
800C2#2025242611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1753C2
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1753D47
hypocenterC47#22553
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#15689174C2semidirect
4. #20244001C2semidirect
5. #20243999C2semidirect
6. #20243994C2semidirect
7. #20243992C2semidirect
8. #20243571C2semidirect
9. #20243570C2semidirect
10. #20243455C2semidirect
11. #20243367C2semidirect
13. #20243172C2semidirect
14. #20243151C2semidirect
15. C47×#1753C2semidirect
23. C2×Dic47⋊C8C22semidirect
24. C2×Dic47⋊C8C22semidirect
25. C2×Dic47⋊C8C22semidirect
26. C2×Dic47⋊C8C22semidirect
37. C2×#13093935C22semidirect
38. C2×C4×C47⋊C8C22semidirect
48. #15688878C22semidirect
49. #15688878C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
52. #15688877C22semidirect
53. #15688877C22semidirect
56. C2×#97×C47C22semidirect
57. C2×C4×C8×C47C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
202. C2×C4×D47M16semidirect
229. (C2×D47)⋊C4M16semidirect
404. #1753D47semidirect
440. C2×#97C2×D47semidirect
442. C2×C4×C8C2×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×#156891742
C2×#156890862
C4×C22⋊C4×D472
#202440012
#202439992
#202439942
#202439922
#202435712
#202435702
#202434552
#202433672
#202432972
#202431722
#202431512
C47×#17532
#2255347