Finite Group Databasebeta

← #26226300

Subgroups — #26226300

Order 12032.

1122 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊C4×D47C211yesmaximal, characteristic
2#20243997C211yesmaximal, characteristic, complemented
3#20243996C211yesmaximal, characteristic, complemented
4#20243995C211yesmaximal, characteristic, complemented
5#20243994C211yesmaximal, characteristic, complemented
6#20243993C211yesmaximal, characteristic, complemented
7#20243992C211yesmaximal, characteristic, complemented
8#20243991C211yesmaximal, characteristic, complemented
9#20243367C211yesmaximal, characteristic, complemented
10#20243365C211yesmaximal, characteristic, complemented
11#20243297C211yesmaximal, characteristic
12#20243297C211yesmaximal, characteristic
13C4×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
14#20243145C211yesmaximal, characteristic, complemented
15C47×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C2×C22⋊C4×D47C411yescharacteristic
18C2×C22⋊C4×D47C411yescharacteristic
19C2×C42×D47C2211yescharacteristic
20C2×C42×D47C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
22C2×Dic47⋊C8C2211yescharacteristic, complemented
23C2×Dic47⋊C8C2211yescharacteristic, complemented
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×(C2×D47)⋊C8C2211yescharacteristic
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×C4×C47⋊C8C2211yescharacteristic, complemented
35C2×C8×Dic47C2211yescharacteristic, complemented
36C2×C8×Dic47C2211yescharacteristic, complemented
37C22⋊C4×Dic47C411yescharacteristic
38C22⋊C4×Dic47C411yescharacteristic
39C4×(C2×D47)⋊C4C2211yescharacteristic
40C4×(C2×D47)⋊C4C2211yescharacteristic
41C4×C22⋊Dic47C2211yescharacteristic
42#15688970C411yescharacteristic
43#15688970C411yescharacteristic
44#95×D47C411yescharacteristic
45#95×D47C411yescharacteristic
46#15688878C2211yescharacteristic, complemented
47#15688878C2211yescharacteristic, complemented
48#15688877C2211yescharacteristic, complemented
49#15688877C2211yescharacteristic, complemented
50#15688877C2211yescharacteristic, complemented
51#15688877C2211yescharacteristic, complemented
52C2×C4⋊C8×C47C2211yescharacteristic, complemented
53C2×C22⋊C8×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic, complemented
56C4×C22⋊C4×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic, complemented
58C47×#336C2211yescharacteristic, complemented
59C24×D47C2×C411yescharacteristic
60C23×Dic47C2×C411yescharacteristic
61C22×C4×D47—22no—
62C22×C4×D47—22no—
63C22×C4×D47—41no—
64C22×C4×D47—41no—
65C22×C4×D47—41no—
66C22×C4×D47—41no—
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2×C411yescharacteristic
69C22×C4×D47C2×C411yescharacteristic
70C22×C4×D47C2×C411yescharacteristic
71C22×C4×D47C2×C411yescharacteristic
72C22×C4×D47C2×C411yescharacteristic
73C22×C4×D47C2311yescharacteristic
74C22×C4×D47C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C2×C22⋊Dic47C2×C411yescharacteristic
80C2×C22⋊Dic47C2×C411yescharacteristic
81C2×(C2×D47)⋊C4C2×C411yescharacteristic
82C2×(C2×D47)⋊C4C2×C411yescharacteristic
83C2×(C2×D47)⋊C4C2×C411yescharacteristic
84C2×(C2×D47)⋊C4C2×C411yescharacteristic
85C22⋊C4×D47—24no—
86C22⋊C4×D47C818yescomplemented
87C2×C4×Dic47C2×C411yescharacteristic
88C2×C4×Dic47C2×C411yescharacteristic
89C2×C4×Dic47C2×C411yescharacteristic
90C2×C4×Dic47C2×C411yescharacteristic
91C2×C4×Dic47C2311yescharacteristic
92C2×C4×Dic47C2311yescharacteristic
93C42×D47—41no—
94C42×D47—41no—
95C42×D47—41no—
96C42×D47—41no—
97C4⋊(C47⋊C8)—41no—
98Dic47⋊C8—41no—
99Dic47⋊C8—41no—
100C22⋊(C47⋊C8)—41no—
101C22⋊(C47⋊C8)—41no—
102(C2×D47)⋊C8—22no—
103(C2×D47)⋊C8—22no—
104(C2×D47)⋊C8—22no—
105(C2×D47)⋊C8—22no—
106(C2×D47)⋊C8—41no—
107(C2×D47)⋊C8—41no—
108(C2×D47)⋊C8—41no—
109(C2×D47)⋊C8—41no—
110C4×C47⋊C8—41no—
111C8×Dic47—41no—
112C8×Dic47—41no—
113C47⋊#95C2×C411yescharacteristic
114C47⋊#95C2×C411yescharacteristic
115C47⋊#95C2×C411yescharacteristic
116C47⋊#95C2×C411yescharacteristic
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C23×C4×C47C2311yescharacteristic
120C22×C8×C47C2311yescharacteristic
121C22×C8×C47C2311yescharacteristic
122C22×C8×C47C2311yescharacteristic
123C22×C8×C47C2311yescharacteristic
124C2×C22⋊C4×C47C2×C411yescharacteristic
125C2×C22⋊C4×C47C2×C411yescharacteristic
126C2×C42×C47C2311yescharacteristic
127C2×C42×C47C2311yescharacteristic
128C4⋊C8×C47—41no—
129C22⋊C8×C47—41no—
130C22⋊C8×C47—41no—
131C4×C8×C47—41no—
132#95×C47C2×C411yescharacteristic
133#95×C47C2×C411yescharacteristic
134C24×C47C22×C411yescharacteristic
135C23×D47—22no—
136C23×D47—22no—
137C23×D47—41no—
138C23×D47—41no—
139C23×D47—41no—
140C23×D47—41no—
141C23×D47C2×C814yes—
142C23×D47C22×C411yescharacteristic
143C23×D47C22×C411yescharacteristic
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C2411yescharacteristic
156C22×Dic47—22no—
157C22×Dic47—41no—
158C22×Dic47—41no—
159C22×Dic47C22×C411yescharacteristic
160C22×Dic47C22×C411yescharacteristic
161C22×Dic47C22×C411yescharacteristic
162C22×Dic47C22×C411yescharacteristic
163C22×Dic47C22×C411yescharacteristic
164C22×Dic47C22×C411yescharacteristic
165C2×C4×D47—21no—
166C2×C4×D47—21no—
167C2×C4×D47—21no—
168C2×C4×D47—21no—
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—21no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—22no—
178C2×C4×D47—44no—
179C2×C4×D47—44no—
180C2×C4×D47—44no—
181C2×C4×D47—44no—
182C2×C4×D47—41no—
183C2×C4×D47—41no—
184C2×C4×D47—41no—
185C2×C4×D47—41no—
186C2×C4×D47—41no—
187C2×C4×D47—41no—
188C2×C4×D47—41no—
189C2×C4×D47—41no—
190C2×C4×D47—41no—
191C2×C4×D47—41no—
192C2×C4×D47—41no—
193C2×C4×D47—41no—
194C2×C4×D47C2×C814yes—
195C2×C4×D47C2×C814yes—
196C2×C4×D47M1614yes—
197C2×C4×D47#4112yes—
198C2×C4×D47#4112yes—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C22⋊C4×C47—22no—
212C22⋊C4×C47C2×C814yes—
213C42×C47—21no—
214C42×C47—21no—
215C42×C47—21no—
216C42×C47—21no—
217C22⋊Dic47—22no—
218C22⋊Dic47C2×C814yes—
219(C2×D47)⋊C4—22no—
220(C2×D47)⋊C4—22no—
221(C2×D47)⋊C4C2×C814yes—
222(C2×D47)⋊C4C2×C814yes—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226C4×Dic47—21no—
227C4×Dic47—41no—
228C4×Dic47—41no—
229C4×Dic47—41no—
230C4×Dic47—41no—
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⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47C22×C812yes—
250C23×C47C23×C411yescharacteristic
251C22×D47—21no—
252C22×D47—21no—
253C22×D47—21no—
254C22×D47—21no—
255C22×D47—21no—
256C22×D47—21no—
257C22×D47—21no—
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—28no—
262C22×D47—44no—
263C22×D47—44no—
264C22×D47—44no—
265C22×D47—44no—
266C22×D47—44no—
267C22×D47—44no—
268C22×D47#11712yes—
269C22×D47C22×C812yes—
270C22×D47C22×C812yes—
271C22×D47C2×M1612yes—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47C22×C812yes—
289C2×C4×C47C22×C812yes—
290C2×C4×C47C2×M1612yes—
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47H(5,𝔽2)11yescharacteristic
294C2×C4×C47H(5,𝔽2)11yescharacteristic
295C2×C4×C47H(5,𝔽2)11yescharacteristic
296C2×C4×C47H(5,𝔽2)11yescharacteristic
297C2×Dic47—21no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—44no—
312C2×Dic47#11712yes—
313C2×Dic47C22×C812yes—
314C2×Dic47C22×C812yes—
315C2×Dic47C2×M1612yes—
316C4×D47—22no—
317C4×D47—22no—
318C4×D47—22no—
319C4×D47—22no—
320C4×D47—44no—
321C4×D47—44no—
322C4×D47—44no—
323C4×D47—44no—
324C4×D47—44no—
325C4×D47—44no—
326C4×D47—41no—
327C4×D47—41no—
328C4×D47—41no—
329C4×D47—41no—
330C8×C47—41no—
331C8×C47—41no—
332C8×C47—41no—
333C8×C47—41no—
334C47⋊C8—41no—
335C47⋊C8—41no—
336C47⋊C8—41no—
337C47⋊C8—41no—
338#21902—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47C2×#11711yescharacteristic
347C22×C47#51811yescharacteristic
348C22×C47#51811yescharacteristic
349C22×C47C23×C811yescharacteristic
350C22×C47C22×M1611yescharacteristic
351C22×C47#56811yescharacteristic
352C22×C47#56811yescharacteristic
353C2×D47—22no—
354C2×D47—22no—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—22no—
358C2×D47—22no—
359C2×D47—22no—
360C2×D47—22no—
361C2×D47—22no—
362C2×D47—416no—
363C2×D47—41no—
364C2×D47—41no—
365C2×D47—41no—
366C2×D47—41no—
367C2×D47#43114yes—
368C4×C47—22no—
369C4×C47—22no—
370C4×C47—22no—
371C4×C47—41no—
372C4×C47—41no—
373C4×C47#53811yescharacteristic
374C4×C47#53811yescharacteristic
375C4×C47#53811yescharacteristic
376C4×C47#53811yescharacteristic
377Dic47—22no—
378Dic47—22no—
379Dic47—22no—
380Dic47—22no—
381Dic47—41no—
382Dic47—41no—
383C2×C4×C22⋊C4—471no—
384#1923—471no—
385#1923—471no—
386#1923—471no—
387#1923—471no—
388#1923—471no—
389#1923—471no—
390#1923—471no—
391#1923D4711yescharacteristic, complemented
392#1797—471no—
393#1797—471no—
394#1779—471no—
395#1779—471no—
396C4×C22⋊C8—471no—
397C4×C22⋊C8—471no—
398C2×C47—42no—
399C2×C47#231211yescharacteristic
400C2×C47C2×#43111yescharacteristic
401C2×C47#292111yescharacteristic
402C2×C47#297211yescharacteristic
403C2×C47#297211yescharacteristic
404C2×C47#297311yescharacteristic
405C2×C47#297511yescharacteristic
406D47—24no—
407D47—42no—
408C24×C4—471no—
409C22×C22⋊C4—471no—
410C22×C22⋊C4—471no—
411C22×C42—471no—
412C22×C42—471no—
413C2×C4⋊C8—471no—
414C2×C4⋊C8—471no—
415C2×C4⋊C8—471no—
416C2×C4⋊C8C2×D4711yescharacteristic, complemented
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×C22⋊C8—471no—
424C2×C22⋊C8—471no—
425C2×C22⋊C8—471no—
426C2×C22⋊C8—471no—
427C2×C22⋊C8C2×D4711yescharacteristic
428C2×C22⋊C8C2×D4711yescharacteristic
429C2×C4×C8—471no—
430C2×C4×C8—471no—
431C2×C4×C8—471no—
432C2×C4×C8C2×D4711yescharacteristic, complemented
433C4×C22⋊C4—471no—
434C4×C22⋊C4—471no—
435C4×C22⋊C4—471no—
436C4×C22⋊C4—471no—
437C4×C22⋊C4—471no—
438C4×C22⋊C4—471no—
439C4×C22⋊C4—471no—
440C4×C22⋊C4C2×D4711yescharacteristic
441C2×#95—471no—
442C2×#95—471no—
443#336—471no—
444#336—471no—
445#336—471no—
446#336—471no—
447#336—471no—
448#336—471no—
449#336C2×D4711yescharacteristic, complemented
450#336C2×D4711yescharacteristic, complemented
451C47#2190211yescharacteristic, complemented, Sylow
452C25—471no—
453C23×C4—471no—
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—471no—
457C23×C4—471no—
458C23×C4—471no—
459C23×C4—471no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—942no—
463C23×C4—942no—
464C23×C4—1881no—
465C23×C4—1881no—
466C23×C4—1881no—
467C23×C4—1881no—
468C23×C4C22×D4711yescharacteristic
469C22×C8—471no—
470C22×C8—471no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4711yescharacteristic
477C2×C22⋊C4—471no—
478C2×C22⋊C4—471no—
479C2×C22⋊C4—471no—
480C2×C22⋊C4—478no—
481C2×C22⋊C4—471no—
482C2×C22⋊C4—471no—
483C2×C22⋊C4—471no—
484C2×C22⋊C4—944no—
485C2×C22⋊C4C4×D4711yescharacteristic
486C2×C22⋊C4C4×D4711yescharacteristic
487C2×C42—471no—
488C2×C42—471no—
489C2×C42—471no—
490C2×C42—471no—
491C2×C42—471no—
492C2×C42—471no—
493C2×C42—1881no—
494C2×C42—1881no—
495C2×C42—1881no—
496C2×C42—1881no—
497C2×C42C22×D4711yescharacteristic
498C2×C42C22×D4711yescharacteristic
499C4⋊C8—41no—
500C4⋊C8—1881no—
501C4⋊C8—1881no—
502C4⋊C8—1881no—
503C22⋊C8—41no—
504C22⋊C8—41no—
505C22⋊C8—942no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508C22⋊C8—942no—
509C22⋊C8—1881no—
510C22⋊C8—1881no—
511C22⋊C8—1881no—
512C22⋊C8—1881no—
513C22⋊C8—1881no—
514C22⋊C8—1881no—
515C4×C8—41no—
516C4×C8—1881no—
517C4×C8—1881no—
518C4×C8—1881no—
519#95—471no—
520#95—471no—
521#95—471no—
522#95—471no—
523#95—471no—
524#95—471no—
525#95C4×D4711yescharacteristic
526#95C4×D4711yescharacteristic
527C24—471no—
528C24—471no—
529C24—474no—
530C24—942no—
531C24—942no—
532C24—1881no—
533C24—1881no—
534C24—1881no—
535C24—1881no—
536C24C2×C4×D4711yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—471no—
544C22×C4—471no—
545C22×C4—471no—
546C22×C4—471no—
547C22×C4—472no—
548C22×C4—472no—
549C22×C4—474no—
550C22×C4—474no—
551C22×C4—474no—
552C22×C4—471no—
553C22×C4—471no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—942no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—1881no—
569C22×C4—1881no—
570C22×C4—1881no—
571C22×C4—1881no—
572C22×C4—1881no—
573C22×C4—1881no—
574C22×C4—1881no—
575C22×C4—1881no—
576C22×C4—1881no—
577C22×C4—1881no—
578C22×C4—1881no—
579C22×C4—1881no—
580C22×C4—1884no—
581C22×C4—1884no—
582C22×C4—1884no—
583C22×C4—1884no—
584C22×C4—1881no—
585C22×C4—1881no—
586C22×C4C2×C4×D4711yescharacteristic
587C22×C4C2×C4×D4711yescharacteristic
588C22×C4C2×C4×D4711yescharacteristic
589C22×C4C2×C4×D4711yescharacteristic
590C22×C4C2×C4×D4711yescharacteristic
591C22×C4C23×D4711yescharacteristic
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—941no—
605C2×C8—941no—
606C2×C8—941no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C2×C8—941no—
612C2×C8—941no—
613C2×C8—941no—
614C2×C8—941no—
615C2×C8—941no—
616C22⋊C4—22no—
617C22⋊C4—474no—
618C22⋊C4—474no—
619C22⋊C4—474no—
620C22⋊C4—942no—
621C22⋊C4—942no—
622C22⋊C4—942no—
623C22⋊C4C8×D4714yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—941no—
629C42—941no—
630C42—941no—
631C42—941no—
632C42—1881no—
633C42—1881no—
634C42—1881no—
635C42—1881no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—472no—
643C23—472no—
644C23—472no—
645C23—472no—
646C23—948no—
647C23—941no—
648C23—941no—
649C23—941no—
650C23—941no—
651C23—941no—
652C23—941no—
653C23—941no—
654C23—941no—
655C23—941no—
656C23—941no—
657C23—1884no—
658C23—1884no—
659C23—1884no—
660C23—1884no—
661C23—1884no—
662C23—1884no—
663C23C2×C8×D4712yes—
664C23C22×C4×D4711yescharacteristic
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
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—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—472no—
682C2×C4—472no—
683C2×C4—472no—
684C2×C4—472no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—941no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—941no—
691C2×C4—941no—
692C2×C4—941no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—941no—
698C2×C4—941no—
699C2×C4—941no—
700C2×C4—941no—
701C2×C4—941no—
702C2×C4—941no—
703C2×C4—1884no—
704C2×C4—1884no—
705C2×C4—1884no—
706C2×C4—1884no—
707C2×C4—1884no—
708C2×C4—1884no—
709C2×C4—1884no—
710C2×C4—1881no—
711C2×C4—1881no—
712C2×C4—1881no—
713C2×C4—1881no—
714C2×C4C2×C8×D4712yes—
715C2×C4C2×C8×D4712yes—
716C2×C4M16×D4712yes—
717C2×C4#41×D4711yescharacteristic
718C2×C4#41×D4711yescharacteristic
719C2×C4#1309406911yescharacteristic
720C2×C4#1309406911yescharacteristic
721C2×C4#1309407011yescharacteristic
722C2×C4#1309407011yescharacteristic
723C8—41no—
724C8—41no—
725C8—41no—
726C8—41no—
727C8—1881no—
728C8—1881no—
729C8—1881no—
730C8—1881no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—474no—
739C22—942no—
740C22—942no—
741C22—942no—
742C22—942no—
743C22—942no—
744C22—942no—
745C22—942no—
746C22—942no—
747C22—942no—
748C22—18816no—
749C22—1881no—
750C22—1881no—
751C22—1881no—
752C22—1881no—
753C22#117×D4711yescharacteristic
754C22#1568959511yescharacteristic
755C22#1568959511yescharacteristic
756C22C22×C8×D4711yescharacteristic
757C22C2×M16×D4711yescharacteristic
758C22#1568988811yescharacteristic
759C22#1568988811yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—41no—
764C4—41no—
765C4—942no—
766C4—942no—
767C4—942no—
768C4—942no—
769C4—1881no—
770C4—1881no—
771C4#1568970511yescharacteristic
772C4#1568970711yescharacteristic
773C4#1568970911yescharacteristic
774C4#1568971211yescharacteristic
775C2—42no—
776C2—944no—
777C2—1882no—
778C2#2024598211yescharacteristic
779C2#431×D4711yescharacteristic
780C2#2025202211yescharacteristic
781C2#2025240911yescharacteristic
782C2#2025240911yescharacteristic
783C2#2025241311yescharacteristic
784C2#2025242611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC47×#1923C2
socleC23×C47C23×C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1923D47
hypocenterC47#21902
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #20243997C2semidirect
3. #20243996C2semidirect
4. #20243995C2semidirect
5. #20243994C2semidirect
6. #20243993C2semidirect
7. #20243992C2semidirect
8. #20243991C2semidirect
9. #20243367C2semidirect
10. #20243365C2semidirect
13. C4×(C2×D47)⋊C8C2semidirect
14. #20243145C2semidirect
15. C47×#1923C2semidirect
21. C2×C4⋊(C47⋊C8)C22semidirect
22. C2×Dic47⋊C8C22semidirect
23. C2×Dic47⋊C8C22semidirect
34. C2×C4×C47⋊C8C22semidirect
35. C2×C8×Dic47C22semidirect
36. C2×C8×Dic47C22semidirect
46. #15688878C22semidirect
47. #15688878C22semidirect
48. #15688877C22semidirect
49. #15688877C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
52. C2×C4⋊C8×C47C22semidirect
55. C2×C4×C8×C47C22semidirect
57. C47×#336C22semidirect
58. C47×#336C22semidirect
86. C22⋊C4×D47C8semidirect
391. #1923D47semidirect
416. C2×C4⋊C8C2×D47semidirect
432. C2×C4×C8C2×D47semidirect
449. #336C2×D47semidirect
450. #336C2×D47semidirect
451. C47#21902semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊C4×D472
#202439972
#202439962
#202439952
#202439942
#202439932
#202439922
#202439912
#202433672
#202433652
#202432972
C4×(C2×D47)⋊C82
#202431452
C47×#19232
#2190247