Finite Group Databasebeta

← #26235304

Subgroups — #26235304

Order 12032.

984 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689174C211yesmaximal, characteristic, complemented
2C2×#15689146C211yesmaximal, characteristic, complemented
3C4×(C22⋊D47)⋊C4C211yesmaximal, characteristic
4#20244001C211yesmaximal, characteristic, complemented
5#20243999C211yesmaximal, characteristic, complemented
6#20243945C211yesmaximal, characteristic, complemented
7#20243943C211yesmaximal, characteristic, complemented
8#20243685C211yesmaximal, characteristic
9#20243683C211yesmaximal, characteristic
10#20243503C211yesmaximal, characteristic, complemented
11#20243367C211yesmaximal, characteristic, complemented
12#20243366C211yesmaximal, characteristic, complemented
13#20243242C211yesmaximal, characteristic, complemented
14#20243172C211yesmaximal, characteristic, complemented
15C47×#1753C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C2×C4×C22⋊D47C2211yescharacteristic
18C2×(C22⋊D47)⋊C4C411yescharacteristic
19C2×(C22⋊D47)⋊C4C411yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21C2×C42×D47C2211yescharacteristic
22#15689174—24no—
23#15689146—24no—
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×Dic47⋊C8C2211yescharacteristic
28C2×Dic47⋊C8C2211yescharacteristic
29C2×Dic47⋊C8C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×#13093935C2211yescharacteristic
36C2×C4×C47⋊C8C2211yescharacteristic
37C4×Dic47⋊C4C2211yescharacteristic
38#15688974C411yescharacteristic
39#15688974C411yescharacteristic
40C22⋊C4×Dic47C411yescharacteristic
41C22⋊C4×Dic47C411yescharacteristic
42C4×(C2×D47)⋊C4C2211yescharacteristic
43#15688970C411yescharacteristic
44#15688970C411yescharacteristic
45C42×Dic47C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C22×M16×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×#97×C47C2211yescharacteristic
57C2×C4×C8×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×C22⋊D47C2×C411yescharacteristic
62C23×Dic47C2×C411yescharacteristic
63C23×Dic47C2×C411yescharacteristic
64C22×C4×D47C2×C411yescharacteristic
65C22×C4×D47C2×C411yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C2×#10625329—22no—
68C2×#10625329—22no—
69C2×#10625329—41no—
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C4×C22⋊D47—22no—
75C4×C22⋊D47—22no—
76(C22⋊D47)⋊C4—24no—
77(C22⋊D47)⋊C4—24no—
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×C22⋊Dic47C2×C411yescharacteristic
82C2×(C2×D47)⋊C4C2×C411yescharacteristic
83C2×(C2×D47)⋊C4C2×C411yescharacteristic
84C2×(C2×D47)⋊C4C2×C411yescharacteristic
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47C2×C411yescharacteristic
88C2×C4×Dic47C2×C411yescharacteristic
89C2×C4×Dic47C2×C411yescharacteristic
90C2×C4×Dic47C2×C411yescharacteristic
91C2×C4×Dic47C2×C411yescharacteristic
92C2×C4×Dic47C2×C411yescharacteristic
93C2×C4×Dic47C2×C411yescharacteristic
94C2×C4×Dic47C2×C411yescharacteristic
95C2×C4×Dic47C2311yescharacteristic
96C2×C4×Dic47C2311yescharacteristic
97C2×C4×Dic47C2311yescharacteristic
98C42×D47—22no—
99C42×D47—22no—
100Dic47⋊C8—22no—
101Dic47⋊C8—22no—
102Dic47⋊C8—22no—
103Dic47⋊C8—22no—
104Dic47⋊C8—22no—
105Dic47⋊C8D414yescomplemented
106C22⋊(C47⋊C8)—22no—
107(C2×D47)⋊C8—22no—
108(C2×D47)⋊C8—22no—
109(C2×D47)⋊C8—41no—
110(C2×D47)⋊C8—41no—
111#13093935—41no—
112C4×C47⋊C8—22no—
113C47⋊#95C2×C411yescharacteristic
114C47⋊#95C2×C411yescharacteristic
115C47⋊#95C2×C411yescharacteristic
116C47⋊#95C2×C411yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C2×M16×C47—22no—
119C2×M16×C47—22no—
120C2×M16×C47—41no—
121C22×C8×C47C2311yescharacteristic
122C22×C8×C47C2311yescharacteristic
123C22×C8×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125C2×C22⋊C4×C47C2×C411yescharacteristic
126C2×C22⋊C4×C47C2×C411yescharacteristic
127C2×C42×C47C2311yescharacteristic
128C2×C42×C47C2311yescharacteristic
129C22⋊C8×C47—22no—
130#97×C47—41no—
131C4×C8×C47—22no—
132#95×C47C2×C411yescharacteristic
133#95×C47C2×C411yescharacteristic
134C24×C47C22×C411yescharacteristic
135C23×D47C22×C411yescharacteristic
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47#4112yes—
146C22×C4×C47#4112yes—
147C22×C4×C47C2411yescharacteristic
148C2×C22⋊D47—22no—
149C2×C22⋊D47—22no—
150C2×C22⋊D47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—41no—
157C22×Dic47C22×C411yescharacteristic
158C22×Dic47C22×C411yescharacteristic
159C22×Dic47C22×C411yescharacteristic
160C22×Dic47C22×C411yescharacteristic
161C22×Dic47C22×C411yescharacteristic
162C22×Dic47C22×C411yescharacteristic
163C22×Dic47C22×C411yescharacteristic
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—21no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×C4×D47—21no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—22no—
174C2×C4×D47—41no—
175C2×C4×D47M1614yescomplemented
176M16×C47—44no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47C2×D412yes—
189C22⋊C4×C47—22no—
190C22⋊C4×C47—22no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C22⋊Dic47—22no—
196(C2×D47)⋊C4—22no—
197(C2×D47)⋊C4—22no—
198(C2×D47)⋊C4—22no—
199Dic47⋊C4—22no—
200Dic47⋊C4—22no—
201Dic47⋊C4M1614yescomplemented
202C4×Dic47—21no—
203C4×Dic47—21no—
204C4×Dic47—21no—
205C4×Dic47—21no—
206C4×Dic47—22no—
207C4×Dic47—22no—
208C4×Dic47—22no—
209C4×Dic47—22no—
210C4×Dic47—22no—
211C4×Dic47—22no—
212C4×Dic47—22no—
213C4×Dic47—41no—
214C4×Dic47C2×D412yes—
215C4×Dic47#4112yes—
216#10625329—44no—
217C2×C47⋊C8—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8C2×D412yes—
229C23×C47—21no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47#11712yes—
236C23×C47C23×C411yescharacteristic
237C22×D47—21no—
238C22×D47—21no—
239C22×D47—21no—
240C22×D47—21no—
241C22×D47—21no—
242C22×D47—21no—
243C22×D47C2×M1612yes—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47#11712yes—
261C2×C4×C47C2×M1612yes—
262C2×C4×C47C2×M1612yes—
263C2×C4×C47C22×D411yescharacteristic
264C2×C4×C47C2×#4111yescharacteristic
265C2×C4×C47C2×#4111yescharacteristic
266C2×C4×C47C2×#4111yescharacteristic
267C2×C4×C47H(5,𝔽2)11yescharacteristic
268C2×C4×C472−1+411yescharacteristic
269C22⋊D47—28no—
270C2×Dic47—21no—
271C2×Dic47—21no—
272C2×Dic47—21no—
273C2×Dic47—21no—
274C2×Dic47—21no—
275C2×Dic47—21no—
276C2×Dic47—21no—
277C2×Dic47—21no—
278C2×Dic47—21no—
279C2×Dic47—21no—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—44no—
286C2×Dic47—44no—
287C2×Dic47C4×D412yes—
288C2×Dic47C4×D412yes—
289C2×Dic47C2×M1612yes—
290C2×Dic47C2×M1612yes—
291C2×Dic47C2×M1612yes—
292C2×Dic47#13112yes—
293C4×D47—28no—
294C4×D47—44no—
295C4×D47—41no—
296C4×D47—41no—
297C4×D47—41no—
298C4×D47—41no—
299C8×C47—22no—
300C8×C47—41no—
301C8×C47—41no—
302C8×C47—41no—
303C47⋊C8—22no—
304C47⋊C8—41no—
305C47⋊C8—41no—
306C47⋊C8—41no—
307#22749—471nomaximal, Sylow
308C22×C47—22no—
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—41no—
312C22×C47—41no—
313C22×C47—41no—
314C22×C47—41no—
315C22×C47C2×#11711yescharacteristic
316C22×C47C2×C4×D411yescharacteristic
317C22×C47#52011yescharacteristic
318C22×C47C22×M1611yescharacteristic
319C22×C47C22×M1611yescharacteristic
320C22×C47C2×#13111yescharacteristic
321C22×C47#56811yescharacteristic
322C2×D47—22no—
323C2×D47—22no—
324C2×D47—22no—
325C2×D47—41no—
326C2×D47—41no—
327C2×D47—41no—
328C2×D47—41no—
329C4×C47—22no—
330C4×C47—22no—
331C4×C47—22no—
332C4×C47—41no—
333C4×C47—41no—
334C4×C47#54611yescharacteristic
335C4×C47#54811yescharacteristic
336C4×C47#55211yescharacteristic
337C4×C47#55311yescharacteristic
338Dic47—22no—
339Dic47—22no—
340Dic47—22no—
341Dic47—41no—
342Dic47—41no—
343Dic47—41no—
344Dic47#43514yes—
345C2×#431—471no—
346C2×#423—471no—
347C42×D4—471no—
348#1924—471no—
349#1924—471no—
350#1916—471no—
351#1916—471no—
352#1870—471no—
353#1870—471no—
354#1831—471no—
355#1797—471no—
356#1797—471no—
357#1767—471no—
358#1753—471no—
359#1753D4711yescharacteristic, complemented
360C2×C47—42no—
361C2×C47#235211yescharacteristic
362C2×C47#292011yescharacteristic
363C2×C47#292511yescharacteristic
364C2×C47C2×#43511yescharacteristic
365C2×C47D4×M1611yescharacteristic
366C2×C47#298911yescharacteristic
367C2×C47#299111yescharacteristic
368D47—42no—
369C22×M16—471no—
370C22×M16C2×D4711yescharacteristic
371C2×C4×D4—471no—
372C2×C4×D4—471no—
373C2×C4×D4—471no—
374C22×C42—471no—
375C22×C42—471no—
376#431—944no—
377#423—944no—
378C2×C4⋊C8—471no—
379C2×C4⋊C8—471no—
380C2×C4⋊C8—471no—
381C2×C4⋊C8—471no—
382C2×C4⋊C8—471no—
383C2×C4⋊C8—471no—
384C2×C22⋊C8—471no—
385C2×C22⋊C8—471no—
386C2×C22⋊C8—471no—
387C2×C22⋊C8—471no—
388C2×C22⋊C8—471no—
389C2×C22⋊C8C2×D4711yescharacteristic
390C2×#97—471no—
391C2×#97C2×D4711yescharacteristic
392C2×C4×C8—471no—
393C2×C4×C8C2×D4711yescharacteristic
394C4×C4⋊C4—471no—
395C4×C4⋊C4—471no—
396C4×C4⋊C4—471no—
397C4×C22⋊C4—471no—
398C4×C22⋊C4—471no—
399C4×C22⋊C4—471no—
400C4×C22⋊C4—471no—
401C4×C22⋊C4—471no—
402C4×C22⋊C4C2×D4711yescharacteristic
403C43—471no—
404#336—471no—
405#336—471no—
406#336—471no—
407#336—471no—
408#336—471no—
409#336—471no—
410#336—471no—
411#336—471no—
412#336C2×D4711yescharacteristic
413#336C2×D4711yescharacteristic
414C47#2274911yescharacteristic, complemented, Sylow
415C22×D4—471no—
416C23×C4—471no—
417C23×C4—471no—
418C23×C4—471no—
419C23×C4—471no—
420C23×C4—471no—
421C23×C4C22×D4711yescharacteristic
422C2×M16—22no—
423C2×M16—22no—
424C2×M16—41no—
425C2×M16—942no—
426C2×M16—942no—
427C2×M16—1881no—
428C22×C8—471no—
429C22×C8—471no—
430C22×C8—471no—
431C22×C8—471no—
432C22×C8C22×D4711yescharacteristic
433C22×C8C22×D4711yescharacteristic
434C22×C8C22×D4711yescharacteristic
435C22×C8C22×D4711yescharacteristic
436C4×D4—944no—
437C4×D4—944no—
438C4×D4—942no—
439C4×D4—942no—
440C2×C4⋊C4—471no—
441C2×C4⋊C4—471no—
442C2×C4⋊C4—471no—
443C2×C22⋊C4—471no—
444C2×C22⋊C4—471no—
445C2×C22⋊C4—471no—
446C2×C22⋊C4—471no—
447C2×C22⋊C4C4×D4711yescharacteristic
448C2×C22⋊C4C4×D4711yescharacteristic
449C2×C42—471no—
450C2×C42—471no—
451C2×C42—471no—
452C2×C42—471no—
453C2×C42—471no—
454C2×C42—471no—
455C2×C42—471no—
456C2×C42—471no—
457C2×C42—471no—
458C2×C42—471no—
459C2×C42—471no—
460C2×C42—942no—
461C2×C42—942no—
462C2×C42—942no—
463C2×C42—942no—
464C2×C42C22×D4711yescharacteristic
465C2×C42C22×D4711yescharacteristic
466C4⋊C8—474no—
467C4⋊C8—942no—
468C4⋊C8—942no—
469C4⋊C8—942no—
470C4⋊C8—942no—
471C4⋊C8—942no—
472C22⋊C8—22no—
473C22⋊C8—942no—
474C22⋊C8—942no—
475C22⋊C8—942no—
476C22⋊C8—1881no—
477C22⋊C8—1881no—
478#97—41no—
479#97—1881no—
480C4×C8—22no—
481C4×C8—942no—
482#95—471no—
483#95—471no—
484#95—471no—
485#95—471no—
486#95C4×D4711yescharacteristic
487#95C4×D4711yescharacteristic
488C24—471no—
489C24C2×C4×D4711yescharacteristic
490C2×D4—942no—
491C2×D4—942no—
492C2×D4—942no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—471no—
498C22×C4—471no—
499C22×C4—471no—
500C22×C4—471no—
501C22×C4—474no—
502C22×C4—471no—
503C22×C4—471no—
504C22×C4—471no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4—942no—
514C22×C4—941no—
515C22×C4—941no—
516C22×C4—941no—
517C22×C4—941no—
518C22×C4—941no—
519C22×C4—941no—
520C22×C4—1881no—
521C22×C4—1881no—
522C22×C4C2×C4×D4711yescharacteristic
523C22×C4C2×C4×D4711yescharacteristic
524C22×C4C2×C4×D4711yescharacteristic
525C22×C4C2×C4×D4711yescharacteristic
526C22×C4C2×C4×D4711yescharacteristic
527C22×C4#1062535012yes—
528C22×C4#1062535012yes—
529C22×C4C23×D4711yescharacteristic
530M16—44no—
531M16—1884no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—472no—
544C2×C8—941no—
545C2×C8—941no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—941no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8D4×D4712yes—
556C4⋊C4—474no—
557C4⋊C4—942no—
558C4⋊C4—942no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—942no—
562C22⋊C4—942no—
563C22⋊C4—942no—
564C22⋊C4—942no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—472no—
570C42—472no—
571C42—942no—
572C42—942no—
573C42—942no—
574C42—942no—
575C42—942no—
576C42—942no—
577C42—942no—
578C42—941no—
579C42—941no—
580C42—941no—
581C42—941no—
582C42—1881no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—472no—
590C23—941no—
591C23—941no—
592C23—941no—
593C23—941no—
594C23—941no—
595C23—941no—
596C23#1309398112yes—
597C23C22×C4×D4711yescharacteristic
598D4—948no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—472no—
616C2×C4—472no—
617C2×C4—472no—
618C2×C4—472no—
619C2×C4—472no—
620C2×C4—472no—
621C2×C4—948no—
622C2×C4—941no—
623C2×C4—941no—
624C2×C4—941no—
625C2×C4—941no—
626C2×C4—941no—
627C2×C4—941no—
628C2×C4—941no—
629C2×C4—941no—
630C2×C4—941no—
631C2×C4—941no—
632C2×C4—941no—
633C2×C4—941no—
634C2×C4—941no—
635C2×C4—941no—
636C2×C4—941no—
637C2×C4—1884no—
638C2×C4—1884no—
639C2×C4—1884no—
640C2×C4—1881no—
641C2×C4—1881no—
642C2×C4—1881no—
643C2×C4—1881no—
644C2×C4#1309398112yes—
645C2×C4M16×D4712yes—
646C2×C4M16×D4712yes—
647C2×C4C2×D4×D4711yescharacteristic
648C2×C4#41×D4711yescharacteristic
649C2×C4C2×#1062535011yescharacteristic
650C2×C4C2×#1062535011yescharacteristic
651C2×C4#1309406911yescharacteristic
652C2×C4#1309407111yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—942no—
658C8—1881no—
659C8—1881no—
660C8—1881no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—942no—
669C22—942no—
670C22—942no—
671C22—1881no—
672C22—1881no—
673C22—1881no—
674C22—1881no—
675C22C2×#1309398111yescharacteristic
676C22C4×D4×D4711yescharacteristic
677C22#1568960211yescharacteristic
678C22C2×M16×D4711yescharacteristic
679C22C2×M16×D4711yescharacteristic
680C22#131×D4711yescharacteristic
681C22#1568988811yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—41no—
686C4—41no—
687C4—474no—
688C4—942no—
689C4—942no—
690C4—942no—
691C4—1881no—
692C4—1881no—
693C4—1881no—
694C4#1568976311yescharacteristic
695C4#1568978211yescharacteristic
696C4#1568980611yescharacteristic
697C4#1568982211yescharacteristic
698C2—42no—
699C2—1882no—
700C2#2024631111yescharacteristic
701C2#2025201911yescharacteristic
702C2#2025205211yescharacteristic
703C2#435×D4711yescharacteristic
704C2#2025212111yescharacteristic
705C2#2025250311yescharacteristic
706C2#2025251611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1753C2
prime radicalC22×C22⋊D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1753D47
hypocenterC47#22749
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
2. C2×#15689146C2semidirect
4. #20244001C2semidirect
5. #20243999C2semidirect
6. #20243945C2semidirect
7. #20243943C2semidirect
10. #20243503C2semidirect
11. #20243367C2semidirect
12. #20243366C2semidirect
13. #20243242C2semidirect
14. #20243172C2semidirect
15. C47×#1753C2semidirect
105. Dic47⋊C8D4semidirect
175. C2×C4×D47M16semidirect
201. Dic47⋊C4M16semidirect
359. #1753D47semidirect
414. C47#22749semidirect

Maximal subgroups

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

subgroupindex
C2×#156891742
C2×#156891462
C4×(C22⋊D47)⋊C42
#202440012
#202439992
#202439452
#202439432
#202436852
#202436832
#202435032
#202433672
#202433662
#202432422
#202431722
C47×#17532
#2274947