Finite Group Databasebeta

← #26233287

Subgroups — #26233287

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×#15689085C211yesmaximal, characteristic
2#20245767C211yesmaximal, characteristic
3#20244001C211yesmaximal, characteristic, complemented
4#20244000C211yesmaximal, characteristic, complemented
5#20243994C211yesmaximal, characteristic, complemented
6#20243993C211yesmaximal, characteristic, complemented
7#20243569C211yesmaximal, characteristic, complemented
8#20243569C211yesmaximal, characteristic, complemented
9#20243459C211yesmaximal, characteristic, complemented
10#20243370C211yesmaximal, characteristic, complemented
11#20243297C211yesmaximal, characteristic
12#20243173C211yesmaximal, characteristic, complemented
13#20243171C211yesmaximal, characteristic, complemented
14#20243156C211yesmaximal, characteristic, complemented
15C2×C47×#433C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20C2×Dic47⋊C8C2211yescharacteristic, complemented
21C2×Dic47⋊C8C2211yescharacteristic, complemented
22#15689085—24no—
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×(C2×D47)⋊C8C2211yescharacteristic
26C2×(C2×D47)⋊C8C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
29C2×(C2×D47)⋊C8C2211yescharacteristic
30C2×(C2×D47)⋊C8C2211yescharacteristic
31C2×#13093934C2211yescharacteristic, complemented
32C2×C8×Dic47C2211yescharacteristic, complemented
33#15688984C411yescharacteristic
34#15688984C411yescharacteristic
35#15688980C411yescharacteristic
36#15688980C411yescharacteristic
37#15688980C411yescharacteristic
38#15688980C411yescharacteristic
39#15688978C411yescharacteristic
40#15688978C411yescharacteristic
41C4×(C2×D47)⋊C4C2211yescharacteristic
42C4×(C2×D47)⋊C4C2211yescharacteristic
43C4×(C2×D47)⋊C4C2211yescharacteristic
44C4×(C2×D47)⋊C4C2211yescharacteristic
45#15688878C2211yescharacteristic, complemented
46#15688878C2211yescharacteristic, complemented
47#15688878C2211yescharacteristic, complemented
48#15688878C2211yescharacteristic, complemented
49#15688877C2211yescharacteristic, complemented
50#15688877C2211yescharacteristic, complemented
51#15688877C2211yescharacteristic, complemented
52#15688877C2211yescharacteristic, complemented
53C2×#117×C47C2211yescharacteristic
54C47×#433—24no—
55C2×C4⋊C8×C47C2211yescharacteristic, complemented
56C2×C4⋊C8×C47C2211yescharacteristic, complemented
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic, complemented
60C2×C4×C8×C47C2211yescharacteristic, 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×D47C2311yescharacteristic
72C22×C4×D47C2311yescharacteristic
73C2×#10625324—22no—
74C2×#10625324—22no—
75C2×#10625324—22no—
76C2×#10625324—22no—
77C2×#10625324—41no—
78C2×#10625324—41no—
79C22×C47⋊C8C2311yescharacteristic
80C22×C47⋊C8C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83#13093983—41no—
84#13093983—41no—
85C2×C4⋊Dic47C2×C411yescharacteristic
86C2×C4⋊Dic47C2×C411yescharacteristic
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
93C2×(C2×D47)⋊C4C2×C411yescharacteristic
94C2×(C2×D47)⋊C4C2×C411yescharacteristic
95C2×(C2×D47)⋊C4C2×C411yescharacteristic
96C2×(C2×D47)⋊C4C2×C411yescharacteristic
97C2×C4×Dic47C2311yescharacteristic
98C2×C4×Dic47C2311yescharacteristic
99Dic47⋊C8—41no—
100Dic47⋊C8—41no—
101C22⋊(C47⋊C8)—22no—
102C22⋊(C47⋊C8)—22no—
103(C2×D47)⋊C8—22no—
104(C2×D47)⋊C8—22no—
105(C2×D47)⋊C8—22no—
106(C2×D47)⋊C8—22no—
107(C2×D47)⋊C8—41no—
108(C2×D47)⋊C8—41no—
109#13093934—41no—
110C8×Dic47—41no—
111C47⋊#95C2×C411yescharacteristic
112C47⋊#95C2×C411yescharacteristic
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
124#117×C47—22no—
125#117×C47—22no—
126C2×C4⋊C4×C47C2×C411yescharacteristic
127C2×C4⋊C4×C47C2×C411yescharacteristic
128C2×C22⋊C4×C47C2×C411yescharacteristic
129C2×C22⋊C4×C47C2×C411yescharacteristic
130C2×C42×C47C2311yescharacteristic
131C2×C42×C47C2311yescharacteristic
132C4⋊C8×C47—22no—
133C4⋊C8×C47—22no—
134C22⋊C8×C47—22no—
135C22⋊C8×C47D414yes—
136#97×C47—22no—
137C4×C8×C47—22no—
138C24×C47C22×C411yescharacteristic
139C23×D47—22no—
140C23×D47—22no—
141C23×D47—22no—
142C23×D47—41no—
143C23×D47—41no—
144C23×D47—41no—
145C23×D47—41no—
146C23×D47C22×C411yescharacteristic
147C23×D47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C2×D412yes—
158C22×C4×C47#4112yes—
159C22×C4×C47C2411yescharacteristic
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—41no—
163C22×Dic47C22×C411yescharacteristic
164C22×Dic47C22×C411yescharacteristic
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C2×C4×D47—21no—
170C2×C4×D47—21no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—22no—
174C2×C4×D47—22no—
175C2×C4×D47—22no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—22no—
183C2×C4×D47—44no—
184C2×C4×D47—44no—
185C2×C4×D47—44no—
186C2×C4×D47—44no—
187C2×C4×D47—41no—
188C2×C4×D47—41no—
189C2×C4×D47#4112yes—
190C2×C4×D47#4112yes—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47C2×D412yes—
202C2×C8×C47C2×D412yes—
203C4⋊C4×C47—22no—
204C4⋊C4×C47—22no—
205C22⋊C4×C47—22no—
206C22⋊C4×C47—22no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C22⋊Dic47—41no—
212C22⋊Dic47—41no—
213(C2×D47)⋊C4—22no—
214(C2×D47)⋊C4—22no—
215(C2×D47)⋊C4—41no—
216(C2×D47)⋊C4—41no—
217(C2×D47)⋊C4—41no—
218(C2×D47)⋊C4—41no—
219(C2×D47)⋊C4—41no—
220(C2×D47)⋊C4—41no—
221C4⋊Dic47—41no—
222C4⋊Dic47—41no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226C4×Dic47—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—
239#10625324—44no—
240#10625324—44no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47C4×D412yes—
248C23×C47C23×C411yescharacteristic
249C22×D47—21no—
250C22×D47—21no—
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—44no—
262C22×D47—44no—
263C22×D47—44no—
264C22×D47—44no—
265C22×D47—44no—
266C22×D47—44no—
267C22×D47—44no—
268C22×D47#11712yes—
269C22×D47#13112yes—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
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—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47C4×D412yes—
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47H(5,𝔽2)11yescharacteristic
294C2×C4×C47H(5,𝔽2)11yescharacteristic
295C2×Dic47—21no—
296C2×Dic47—21no—
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—21no—
312C2×Dic47—44no—
313C2×Dic47#11712yes—
314C4×D47—22no—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—22no—
318C4×D47—44no—
319C4×D47—44no—
320C4×D47—41no—
321C4×D47—41no—
322C4×D47—41no—
323C4×D47—41no—
324C8×C47—22no—
325C8×C47—22no—
326C8×C47—41no—
327C8×C47—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—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47C2×#11711yescharacteristic
341C22×C47C2×C4×D411yescharacteristic
342C22×C47#51811yescharacteristic
343C22×C47C2×#13111yescharacteristic
344C22×C47#56811yescharacteristic
345C22×C47#56811yescharacteristic
346C22×C47#56811yescharacteristic
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—416no—
354C2×D47—41no—
355C2×D47—41no—
356C2×D47—41no—
357C2×D47—41no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C2×D47—41no—
362C4×C47—22no—
363C4×C47—41no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47—41no—
367C4×C47#54611yescharacteristic
368C4×C47#54611yescharacteristic
369C4×C47#55111yescharacteristic
370C4×C47#55111yescharacteristic
371Dic47—22no—
372Dic47—41no—
373Dic47—41no—
374Dic47—41no—
375Dic47—41no—
376Dic47—41no—
377C2×#433D4711yescharacteristic, complemented
378C2×#407—471no—
379#2280—471no—
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#234211yescharacteristic
394C2×C47#292111yescharacteristic
395C2×C47#292411yescharacteristic
396C2×C47#293011yescharacteristic
397C2×C47#293311yescharacteristic
398C2×C47#297611yescharacteristic
399C2×C47#297811yescharacteristic
400D47—42no—
401D47—42no—
402C24×C4—471no—
403C22×M16—471no—
404C22×M16—471no—
405C2×#117—471no—
406C2×#117C2×D4711yescharacteristic
407#433—24no—
408C2×C4⋊C8—471no—
409C2×C4⋊C8—471no—
410C2×C4⋊C8C2×D4711yescharacteristic, complemented
411C2×C4⋊C8C2×D4711yescharacteristic, complemented
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⋊C8C2×D4711yescharacteristic
422C2×C22⋊C8C2×D4711yescharacteristic
423C2×#97—471no—
424C2×#97C2×D4711yescharacteristic, complemented
425C2×C4×C8—471no—
426C2×C4×C8C2×D4711yescharacteristic, complemented
427#381—471no—
428#381—471no—
429#380—471no—
430#380—471no—
431#380—471no—
432#380—471no—
433#379—471no—
434#379—471no—
435C4×C22⋊C4—471no—
436C4×C22⋊C4—471no—
437C4×C22⋊C4—471no—
438C4×C22⋊C4—471no—
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
448C25—471no—
449C23×C4—471no—
450C23×C4—471no—
451C23×C4—471no—
452C23×C4—471no—
453C23×C4—471no—
454C23×C4—942no—
455C23×C4—942no—
456C23×C4—942no—
457C23×C4—942no—
458C23×C4—1881no—
459C23×C4—1881no—
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×C8C22×D4711yescharacteristic
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475#117—22no—
476#117—22no—
477#117—1881no—
478#117—1881no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4C4×D4711yescharacteristic
482C2×C4⋊C4C4×D4711yescharacteristic
483C2×C22⋊C4—471no—
484C2×C22⋊C4—471no—
485C2×C22⋊C4—471no—
486C2×C22⋊C4—471no—
487C2×C22⋊C4—471no—
488C2×C22⋊C4—471no—
489C2×C22⋊C4—471no—
490C2×C22⋊C4—471no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4C4×D4711yescharacteristic
494C2×C22⋊C4C4×D4711yescharacteristic
495C2×C42—471no—
496C2×C42—471no—
497C2×C42C22×D4711yescharacteristic
498C2×C42C22×D4711yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—1881no—
502C4⋊C8—1881no—
503C22⋊C8—22no—
504C22⋊C8—942no—
505C22⋊C8—942no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508C22⋊C8—942no—
509C22⋊C8—942no—
510C22⋊C8—1881no—
511C22⋊C8—1881no—
512C22⋊C8C22⋊D4714yes—
513#97—22no—
514#97—1881no—
515C4×C8—22no—
516C4×C8—1881no—
517#95—471no—
518#95—471no—
519#95—471no—
520#95—471no—
521#95—471no—
522#95—471no—
523#95—471no—
524#95—471no—
525C24—471no—
526C24—471no—
527C24—942no—
528C24—942no—
529C24—942no—
530C24—1881no—
531C24—1881no—
532C24—1881no—
533C24—1881no—
534C24C2×C4×D4711yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—471no—
540C22×C4—472no—
541C22×C4—472no—
542C22×C4—471no—
543C22×C4—471no—
544C22×C4—471no—
545C22×C4—471no—
546C22×C4—471no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—941no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—1881no—
564C22×C4—1881no—
565C22×C4—1884no—
566C22×C4—1884no—
567C22×C4—1884no—
568C22×C4—1884no—
569C22×C4—1881no—
570C22×C4C2×C4×D4711yescharacteristic
571C22×C4C2×C4×D4711yescharacteristic
572C22×C4C2×C4×D4711yescharacteristic
573C22×C4C2×C4×D4711yescharacteristic
574C22×C4C2×C4×D4711yescharacteristic
575C22×C4#1062535012yes—
576C22×C4C2×C22⋊D4712yes—
577C22×C4C23×D4711yescharacteristic
578M16—1884no—
579M16—1884no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
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×C8C2×C22⋊D4712yes—
603C2×C8C2×C22⋊D4712yes—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—1881no—
607C4⋊C4—1881no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—942no—
611C22⋊C4—942no—
612C22⋊C4—1881no—
613C22⋊C4—1881no—
614C22⋊C4—1881no—
615C22⋊C4—1881no—
616C22⋊C4—1881no—
617C22⋊C4—1881no—
618C22⋊C4—1881no—
619C22⋊C4—1881no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—941no—
625C42—941no—
626C42—941no—
627C42—941no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—472no—
635C23—472no—
636C23—941no—
637C23—941no—
638C23—941no—
639C23—941no—
640C23—941no—
641C23—941no—
642C23—941no—
643C23—941no—
644C23—941no—
645C23—941no—
646C23—941no—
647C23—941no—
648C23—1884no—
649C23—1884no—
650C23—1884no—
651C23—1884no—
652C23—1884no—
653C23—1884no—
654C23—1884no—
655C23C4×C22⋊D4712yes—
656C23C22×C4×D4711yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
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—472no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—941no—
683C2×C4—941no—
684C2×C4—941no—
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—941no—
694C2×C4—941no—
695C2×C4—941no—
696C2×C4—941no—
697C2×C4—1884no—
698C2×C4—1884no—
699C2×C4—1884no—
700C2×C4—1881no—
701C2×C4—1881no—
702C2×C4—1881no—
703C2×C4—1881no—
704C2×C4C4×C22⋊D4712yes—
705C2×C4C22×C22⋊D4711yescharacteristic
706C2×C4#41×D4711yescharacteristic
707C2×C4#41×D4711yescharacteristic
708C2×C4C2×#1062535011yescharacteristic
709C2×C4#1309407011yescharacteristic
710C2×C4#1309407011yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—1881no—
716C8—1881no—
717C8—1881no—
718C8—1881no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—942no—
727C22—942no—
728C22—942no—
729C22—942no—
730C22—942no—
731C22—942no—
732C22—18816no—
733C22—1881no—
734C22—1881no—
735C22—1881no—
736C22—1881no—
737C22—1881no—
738C22—1881no—
739C22—1881no—
740C22—1881no—
741C22#117×D4711yescharacteristic
742C22C2×C4×C22⋊D4711yescharacteristic
743C22#1568959711yescharacteristic
744C22#131×D4711yescharacteristic
745C22#1568988811yescharacteristic
746C22#1568988811yescharacteristic
747C22#1568988811yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—942no—
754C4—1881no—
755C4—1881no—
756C4—1881no—
757C4—1881no—
758C4—1881no—
759C4#1568976111yescharacteristic
760C4#1568976111yescharacteristic
761C4#1568979711yescharacteristic
762C4#1568979711yescharacteristic
763C2—42no—
764C2—1882no—
765C2—1882no—
766C2#2024623811yescharacteristic
767C2#2025202211yescharacteristic
768C2#2025204411yescharacteristic
769C2#2025208911yescharacteristic
770C2#2025211011yescharacteristic
771C2#2025243411yescharacteristic
772C2#2025244911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#433C2
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenterC2×#433D47
hypocenterC47#22559
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #20244001C2semidirect
4. #20244000C2semidirect
5. #20243994C2semidirect
6. #20243993C2semidirect
7. #20243569C2semidirect
8. #20243569C2semidirect
9. #20243459C2semidirect
10. #20243370C2semidirect
12. #20243173C2semidirect
13. #20243171C2semidirect
14. #20243156C2semidirect
15. C2×C47×#433C2semidirect
20. C2×Dic47⋊C8C22semidirect
21. C2×Dic47⋊C8C22semidirect
31. C2×#13093934C22semidirect
32. C2×C8×Dic47C22semidirect
45. #15688878C22semidirect
46. #15688878C22semidirect
47. #15688878C22semidirect
48. #15688878C22semidirect
49. #15688877C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
52. #15688877C22semidirect
55. C2×C4⋊C8×C47C22semidirect
56. C2×C4⋊C8×C47C22semidirect
59. C2×#97×C47C22semidirect
60. C2×C4×C8×C47C22semidirect
377. C2×#433D47semidirect
410. C2×C4⋊C8C2×D47semidirect
411. C2×C4⋊C8C2×D47semidirect
424. C2×#97C2×D47semidirect
426. C2×C4×C8C2×D47semidirect
447. C47#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#156890852
#202457672
#202440012
#202440002
#202439942
#202439932
#202435692
#202434592
#202433702
#202432972
#202431732
#202431712
#202431562
C2×C47×#4332
#2255947