Finite Group Databasebeta

← #26233195

Subgroups — #26233195

Order 12032.

1280 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
2C22×(C2×D47)⋊C8C211yesmaximal, characteristic
3C4×C22⋊C4×D47C211yesmaximal, characteristic
4#20243995C211yesmaximal, characteristic, complemented
5#20243995C211yesmaximal, characteristic, complemented
6#20243993C211yesmaximal, characteristic, complemented
7#20243993C211yesmaximal, characteristic, complemented
8#20243568C211yesmaximal, characteristic, complemented
9#20243455C211yesmaximal, characteristic, complemented
10#20243365C211yesmaximal, characteristic, complemented
11#20243297C211yesmaximal, characteristic
12#20243162C211yesmaximal, characteristic, complemented
13C8×C22⋊Dic47C211yesmaximal, characteristic, complemented
14#20243145C211yesmaximal, characteristic, complemented
15C47×#1850C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×C22⋊C4×D47C411yescharacteristic
19C2×C22⋊C4×D47C411yescharacteristic
20C2×C42×D47C2211yescharacteristic
21C2×C42×D47C2211yescharacteristic
22#15689175—24no—
23C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
24C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×(C2×D47)⋊C8—24no—
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
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×C8×Dic47C2211yescharacteristic, complemented
36C2×C8×Dic47C2211yescharacteristic, 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
54C23×C8×C47C2211yescharacteristic
55C2×C4⋊C8×C47C2211yescharacteristic, complemented
56C2×C4⋊C8×C47C2211yescharacteristic, complemented
57C2×C22⋊C8×C47C2211yescharacteristic
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
77C22×C47⋊C8—22no—
78C22×C47⋊C8—22no—
79C22×C47⋊C8—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×D47C818yescomplemented
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—
102C4⋊(C47⋊C8)—22no—
103C4⋊(C47⋊C8)—41no—
104C22⋊(C47⋊C8)—22no—
105(C2×D47)⋊C8—22no—
106(C2×D47)⋊C8—22no—
107(C2×D47)⋊C8—22no—
108(C2×D47)⋊C8—22no—
109(C2×D47)⋊C8—22no—
110(C2×D47)⋊C8—41no—
111(C2×D47)⋊C8—41no—
112(C2×D47)⋊C8D414yes—
113C8×Dic47—22no—
114C8×Dic47—22no—
115C8×Dic47—41no—
116C8×Dic47—41no—
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C47⋊#95C2×C411yescharacteristic
122C47⋊#95C2×C411yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C22×C8×C47—22no—
125C22×C8×C47—22no—
126C22×C8×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
135C4⋊C8×C47—22no—
136C4⋊C8×C47—41no—
137C22⋊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—41no—
146C23×D47—41no—
147C23×D47C2×C814yes—
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—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—22no—
189C2×C4×D47—22no—
190C2×C4×D47—22no—
191C2×C4×D47—44no—
192C2×C4×D47—44no—
193C2×C4×D47—44no—
194C2×C4×D47—44no—
195C2×C4×D47—41no—
196C2×C4×D47—41no—
197C2×C4×D47—41no—
198C2×C4×D47—41no—
199C2×C4×D47—41no—
200C2×C4×D47—41no—
201C2×C4×D47C2×C814yescomplemented
202C2×C4×D47C2×C814yescomplemented
203C2×C4×D47C2×D412yes—
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×C47—44no—
217C2×C8×C47C2×D412yes—
218C22⋊C4×C47—22no—
219C22⋊C4×C47C2×C814yes—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47—21no—
223C42×C47—21no—
224C22⋊Dic47C2×C814yes—
225C22⋊Dic47M1614yes—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4C2×C814yescomplemented
229(C2×D47)⋊C4C2×C814yescomplemented
230C4×Dic47—21no—
231C4×Dic47—21no—
232C4×Dic47—21no—
233C4×Dic47—21no—
234C4×Dic47—22no—
235C4×Dic47—22no—
236C4×Dic47—41no—
237C4×Dic47—41no—
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⋊C8—21no—
249C2×C47⋊C8—44no—
250C2×C47⋊C8C2×D412yes—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47#11712yes—
256C23×C47C22×C812yes—
257C23×C47C2×M1612yes—
258C23×C47C23×C411yescharacteristic
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
267C22×D47—21no—
268C22×D47—21no—
269C22×D47—28no—
270C22×D47—28no—
271C22×D47—44no—
272C22×D47—44no—
273C22×D47—44no—
274C22×D47—44no—
275C22×D47—44no—
276C22×D47C4×D412yes—
277C22×D47C22×C812yes—
278C22×D47C22×C812yes—
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×C47C22×C812yes—
298C2×C4×C47C22×C812yes—
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×Dic47C4×D412yes—
320C2×Dic47C22×C812yes—
321C2×Dic47C22×C812yes—
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#22552—471nomaximal, Sylow
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—22no—
353C22×C47#43114yescomplemented
354C22×C47C2×#11711yescharacteristic
355C22×C47C2×C4×D411yescharacteristic
356C22×C47#51811yescharacteristic
357C22×C47C23×C811yescharacteristic
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×D47C8×D414yes—
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—22no—
389Dic47—22no—
390Dic47—41no—
391C2×#431—471no—
392C22×C22⋊C8—471no—
393C2×C4×C22⋊C4—471no—
394#1923—471no—
395#1923—471no—
396#1923—471no—
397#1923—471no—
398#1850—471no—
399#1850D4711yescharacteristic, complemented
400#1817—471no—
401#1797—471no—
402#1779—471no—
403C8×C22⋊C4—471no—
404C8×C22⋊C4—471no—
405C4×C22⋊C8—471no—
406C2×C47—24no—
407C2×C47#234211yescharacteristic
408C2×C47C2×#43111yescharacteristic
409C2×C47#292411yescharacteristic
410C2×C47C2×C8×D411yescharacteristic
411C2×C47D4×M1611yescharacteristic
412C2×C47#297211yescharacteristic
413C2×C47#297411yescharacteristic
414D47—24no—
415D47—42no—
416C24×C4—471no—
417C23×C8—471no—
418C23×C8C2×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⋊C8C2×D4711yescharacteristic, complemented
427C2×C4⋊C8C2×D4711yescharacteristic, complemented
428C2×C22⋊C8—471no—
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—944no—
438C2×C22⋊C8C2×D4711yescharacteristic
439C2×C4×C8—471no—
440C2×C4×C8—471no—
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#2255211yescharacteristic, 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
479C22×C8—22no—
480C22×C8—22no—
481C22×C8—41no—
482C22×C8—471no—
483C22×C8—471no—
484C22×C8—471no—
485C22×C8—471no—
486C22×C8—942no—
487C22×C8—942no—
488C22×C8—1881no—
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—478no—
498C2×C22⋊C4—471no—
499C2×C22⋊C4—471no—
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—41no—
517C4⋊C8—942no—
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—
529C4×C8—942no—
530C4×C8—942no—
531C4×C8—1881no—
532C4×C8—1881no—
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—474no—
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—471no—
559C22×C4—471no—
560C22×C4—474no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—474no—
564C22×C4—471no—
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—942no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—941no—
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#1062535212yes—
604C22×C4#1062535412yes—
605C22×C4C23×D4711yescharacteristic
606C2×C8—21no—
607C2×C8—21no—
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—44no—
618C2×C8—472no—
619C2×C8—941no—
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—1884no—
631C2×C8D4×D4712yes—
632C22⋊C4—22no—
633C22⋊C4—474no—
634C22⋊C4—474no—
635C22⋊C4—474no—
636C22⋊C4—474no—
637C22⋊C4—942no—
638C22⋊C4—942no—
639C22⋊C4C8×D4714yes—
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—472no—
657C23—472no—
658C23—472no—
659C23—472no—
660C23—948no—
661C23—941no—
662C23—941no—
663C23—941no—
664C23—941no—
665C23—941no—
666C23—941no—
667C23—941no—
668C23—941no—
669C23—941no—
670C23—941no—
671C23—948no—
672C23—1884no—
673C23—1884no—
674C23—1884no—
675C23—1884no—
676C23—1884no—
677C23#1309398212yes—
678C23C2×C8×D4712yes—
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—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—472no—
701C2×C4—472no—
702C2×C4—948no—
703C2×C4—941no—
704C2×C4—941no—
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—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
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#1309398212yes—
731C2×C4C2×C8×D4712yes—
732C2×C4C2×C8×D4712yes—
733C2×C4C2×D4×D4711yescharacteristic
734C2×C4#41×D4711yescharacteristic
735C2×C4C2×#1062535211yescharacteristic
736C2×C4C2×#1062535411yescharacteristic
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—22no—
751C22—22no—
752C22—22no—
753C22—474no—
754C22—942no—
755C22—942no—
756C22—942no—
757C22—942no—
758C22—942no—
759C22—942no—
760C22—942no—
761C22—942no—
762C22—942no—
763C22—18816no—
764C22—1881no—
765C22—1881no—
766C22—1881no—
767C22—1881no—
768C22#1568917514yescomplemented
769C22C2×#1309398211yescharacteristic
770C22C4×D4×D4711yescharacteristic
771C22#1568959511yescharacteristic
772C22C22×C8×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—942no—
785C4—942no—
786C4—1881no—
787C4#1568976011yescharacteristic
788C4#1568976411yescharacteristic
789C4#1568979611yescharacteristic
790C4#1568980011yescharacteristic
791C2—24no—
792C2—944no—
793C2—1882no—
794C2#2024623511yescharacteristic
795C2C2×#1568917511yescharacteristic
796C2#2025204511yescharacteristic
797C2C8×D4×D4711yescharacteristic
798C2#2025212111yescharacteristic
799C2#2025240911yescharacteristic
800C2#2025241811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC47×#1850C2
socleC23×C47C23×C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1850D47
hypocenterC47#22552
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#15689175C2semidirect
4. #20243995C2semidirect
5. #20243995C2semidirect
6. #20243993C2semidirect
7. #20243993C2semidirect
8. #20243568C2semidirect
9. #20243455C2semidirect
10. #20243365C2semidirect
12. #20243162C2semidirect
13. C8×C22⋊Dic47C2semidirect
14. #20243145C2semidirect
15. C47×#1850C2semidirect
23. C2×C4⋊(C47⋊C8)C22semidirect
24. C2×C4⋊(C47⋊C8)C22semidirect
35. C2×C8×Dic47C22semidirect
36. C2×C8×Dic47C22semidirect
37. C2×C8×Dic47C22semidirect
38. C2×C8×Dic47C22semidirect
48. #15688878C22semidirect
49. #15688878C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
52. #15688877C22semidirect
53. #15688877C22semidirect
55. C2×C4⋊C8×C47C22semidirect
56. C2×C4⋊C8×C47C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
91. C22⋊C4×D47C8semidirect
201. C2×C4×D47C2×C8semidirect
202. C2×C4×D47C2×C8semidirect
228. (C2×D47)⋊C4C2×C8semidirect
229. (C2×D47)⋊C4C2×C8semidirect
353. C22×C47#431semidirect
399. #1850D47semidirect
426. C2×C4⋊C8C2×D47semidirect
427. C2×C4⋊C8C2×D47semidirect
459. #336C2×D47semidirect
460. #336C2×D47semidirect
461. C47#22552semidirect
768. C22#15689175semidirect

Maximal subgroups

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

subgroupindex
C2×#156891752
C22×(C2×D47)⋊C82
C4×C22⋊C4×D472
#202439952
#202439932
#202435682
#202434552
#202433652
#202432972
#202431622
C8×C22⋊Dic472
#202431452
C47×#18502
#2255247