Finite Group Databasebeta

← #26226920

Subgroups — #26226920

Order 12032.

930 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Dic47C211yesmaximal, characteristic
2#20243997C211yesmaximal, characteristic, complemented
3#20243991C211yesmaximal, characteristic, complemented
4#20243946C211yesmaximal, characteristic, complemented
5#20243944C211yesmaximal, characteristic, complemented
6#20243681C211yesmaximal, characteristic
7#20243566C211yesmaximal, characteristic, complemented
8#20243565C211yesmaximal, characteristic, complemented
9#20243530C211yesmaximal, characteristic, complemented
10#20243503C211yesmaximal, characteristic, complemented
11#20243454C211yesmaximal, characteristic, complemented
12#20243366C211yesmaximal, characteristic, complemented
13C22⋊C8×Dic47C211yesmaximal, characteristic, complemented
14C2×#15688877C211yesmaximal, characteristic, complemented
15C47×#1869C211yesmaximal, characteristic
16C23×C47⋊C8C2211yescharacteristic
17C2×D4×Dic47C411yescharacteristic
18C2×D4×Dic47C411yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21C2×Dic47⋊C8C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×C8×Dic47C2211yescharacteristic
29C2×C8×Dic47C2211yescharacteristic
30C4⋊C4×Dic47C411yescharacteristic
31C4⋊C4×Dic47C411yescharacteristic
32C4×C4⋊Dic47C2211yescharacteristic
33C22⋊C4×Dic47C411yescharacteristic
34C22⋊C4×Dic47C411yescharacteristic
35C22⋊C4×Dic47C411yescharacteristic
36C22⋊C4×Dic47C411yescharacteristic
37C4×C22⋊Dic47C2211yescharacteristic
38C4×C22⋊Dic47C2211yescharacteristic
39C42×Dic47C2211yescharacteristic
40#15688878C2211yescharacteristic
41#15688878C2211yescharacteristic
42#15688877C2211yescharacteristic
43#15688877C2211yescharacteristic
44#15688877C2211yescharacteristic
45#15688877C2211yescharacteristic
46#15688877C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C23×C8×C47C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×C22⋊C8×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C23×Dic47C2×C411yescharacteristic
60C23×Dic47C2×C411yescharacteristic
61C23×Dic47C2×C411yescharacteristic
62C23×Dic47C2×C411yescharacteristic
63C22×C47⋊C8—22no—
64C22×C47⋊C8—41no—
65C22×C47⋊C8—41no—
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70D4×Dic47—24no—
71D4×Dic47C818yescomplemented
72C2×C4⋊Dic47C2×C411yescharacteristic
73C2×C4⋊Dic47C2×C411yescharacteristic
74C2×C22⋊Dic47C2×C411yescharacteristic
75C2×C22⋊Dic47C2×C411yescharacteristic
76C2×C22⋊Dic47C2×C411yescharacteristic
77C2×C22⋊Dic47C2×C411yescharacteristic
78C2×C4×Dic47—41no—
79C2×C4×Dic47—41no—
80C2×C4×Dic47—41no—
81C2×C4×Dic47—41no—
82C2×C4×Dic47C2×C411yescharacteristic
83C2×C4×Dic47C2×C411yescharacteristic
84C2×C4×Dic47C2×C411yescharacteristic
85C2×C4×Dic47C2×C411yescharacteristic
86C2×C4×Dic47C2×C411yescharacteristic
87C2×C4×Dic47C2×C411yescharacteristic
88C2×C4×Dic47C2×C411yescharacteristic
89C2×C4×Dic47C2×C411yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91C2×C4×Dic47C2311yescharacteristic
92C2×C4×Dic47C2311yescharacteristic
93C2×C4×Dic47C2311yescharacteristic
94Dic47⋊C8—41no—
95Dic47⋊C8—41no—
96Dic47⋊C8—41no—
97Dic47⋊C8—41no—
98C22⋊(C47⋊C8)—22no—
99C22⋊(C47⋊C8)—41no—
100C22⋊(C47⋊C8)—41no—
101C8×Dic47—41no—
102C8×Dic47—41no—
103C47⋊#95C2×C411yescharacteristic
104C47⋊#95C2×C411yescharacteristic
105C47⋊#95C2×C411yescharacteristic
106C47⋊#95C2×C411yescharacteristic
107C47⋊#95C2×C411yescharacteristic
108C47⋊#95C2×C411yescharacteristic
109C22×D4×C47C2×C411yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C23×C4×C47C2311yescharacteristic
112C22×C8×C47—22no—
113C22×C8×C47—41no—
114C22×C8×C47—41no—
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118C22×C8×C47C2311yescharacteristic
119C4×D4×C47—22no—
120C4×D4×C47—22no—
121C2×C4⋊C4×C47C2×C411yescharacteristic
122C2×C22⋊C4×C47C2×C411yescharacteristic
123C2×C22⋊C4×C47C2×C411yescharacteristic
124C2×C42×C47C2311yescharacteristic
125C22⋊C8×C47—22no—
126C22⋊C8×C47—41no—
127C22⋊C8×C47—41no—
128C24×C47C22×C411yescharacteristic
129C24×C47C22×C411yescharacteristic
130C2×D4×C47—22no—
131C2×D4×C47—22no—
132C2×D4×C47C2×C814yes—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C22×C411yescharacteristic
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47#4112yes—
148C22×C4×C47#4112yes—
149C22×C4×C47C2411yescharacteristic
150C22×Dic47—22no—
151C22×Dic47—41no—
152C22×Dic47—41no—
153C22×Dic47—41no—
154C22×Dic47—41no—
155C22×Dic47—41no—
156C22×Dic47—41no—
157C22×Dic47—41no—
158C22×Dic47—41no—
159C22×Dic47C2×C814yes—
160C22×Dic47C2×C814yescomplemented
161C22×Dic47M1614yes—
162C22×Dic47C22×C411yescharacteristic
163C22×Dic47C22×C411yescharacteristic
164C22×Dic47C22×C411yescharacteristic
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—44no—
183C4⋊C4×C47—22no—
184C22⋊C4×C47—22no—
185C22⋊C4×C47—22no—
186C42×C47—21no—
187C42×C47—21no—
188C22⋊Dic47—22no—
189C22⋊Dic47—22no—
190C22⋊Dic47C2×C814yes—
191C22⋊Dic47C2×C814yescomplemented
192C4⋊Dic47—22no—
193C4⋊Dic47C2×C814yescomplemented
194C4×Dic47—21no—
195C4×Dic47—21no—
196C4×Dic47—21no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47—21no—
200C4×Dic47—21no—
201C4×Dic47—21no—
202C4×Dic47—22no—
203C4×Dic47—41no—
204C4×Dic47—41no—
205C4×Dic47—41no—
206C4×Dic47—41no—
207C4×Dic47—41no—
208C4×Dic47—41no—
209C4×Dic47C2×C814yescomplemented
210C2×C47⋊C8—21no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8—21no—
214C2×C47⋊C8—21no—
215C2×C47⋊C8—21no—
216C2×C47⋊C8—21no—
217C2×C47⋊C8—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—44no—
223C23×C47—21no—
224C23×C47—21no—
225C23×C47—21no—
226C23×C47—21no—
227C23×C47—21no—
228C23×C47—21no—
229C23×C47—21no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47#11712yes—
234C23×C47C22×C812yes—
235C23×C47C22×C812yes—
236C23×C47C2×M1612yes—
237C23×C47C23×C411yescharacteristic
238D4×C47—28no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—22no—
244C2×C4×C47—22no—
245C2×C4×C47—22no—
246C2×C4×C47—22no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47#11712yes—
258C2×C4×C47C22×C812yes—
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C47H(5,𝔽2)11yescharacteristic
262C2×C4×C47H(5,𝔽2)11yescharacteristic
263C2×C4×C47H(5,𝔽2)11yescharacteristic
264C2×C4×C472−1+411yescharacteristic
265C2×Dic47—21no—
266C2×Dic47—21no—
267C2×Dic47—21no—
268C2×Dic47—21no—
269C2×Dic47—21no—
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—44no—
284C2×Dic47—44no—
285C2×Dic47—44no—
286C2×Dic47—44no—
287C2×Dic47C22×C812yes—
288C2×Dic47C22×C812yes—
289C2×Dic47C22×C812yes—
290C2×Dic47C22×C812yes—
291C2×Dic47C2×M1612yes—
292C2×Dic47C2×M1612yes—
293C8×C47—41no—
294C8×C47—41no—
295C8×C47—41no—
296C8×C47—41no—
297C47⋊C8—41no—
298C47⋊C8—41no—
299C47⋊C8—41no—
300C47⋊C8—41no—
301#21996—471nomaximal, Sylow
302C22×C47—22no—
303C22×C47—22no—
304C22×C47—22no—
305C22×C47—22no—
306C22×C47—22no—
307C22×C47—22no—
308C22×C47—22no—
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—41no—
312C22×C47—41no—
313C22×C47—41no—
314C22×C47—41no—
315C22×C47#43114yes—
316C22×C47C2×#11711yescharacteristic
317C22×C47#51811yescharacteristic
318C22×C47#52011yescharacteristic
319C22×C47C23×C811yescharacteristic
320C22×C47C22×M1611yescharacteristic
321C22×C47#56811yescharacteristic
322C22×C47#56811yescharacteristic
323C4×C47—22no—
324C4×C47—22no—
325C4×C47—41no—
326C4×C47—41no—
327C4×C47#53811yescharacteristic
328C4×C47#53811yescharacteristic
329C4×C47#53911yescharacteristic
330C4×C47#53911yescharacteristic
331Dic47—22no—
332Dic47—22no—
333Dic47—22no—
334Dic47—22no—
335Dic47—22no—
336Dic47—22no—
337Dic47—41no—
338Dic47—41no—
339C42×D4—471no—
340#1923—471no—
341#1923—471no—
342#1916—471no—
343#1916—471no—
344#1869—471no—
345#1869D4711yescharacteristic
346#1850—471no—
347#1850—471no—
348#1839—471no—
349#1831—471no—
350#1817—471no—
351#1797—471no—
352C4×C22⋊C8—471no—
353C2×#336—471no—
354C2×C47—24no—
355C2×C47—42no—
356C2×C47#231811yescharacteristic
357C2×C47C2×#43111yescharacteristic
358C2×C47#292311yescharacteristic
359C2×C47#297211yescharacteristic
360C2×C47#297311yescharacteristic
361C2×C47#298811yescharacteristic
362C2×C47#298911yescharacteristic
363C23×C8—471no—
364C23×C8C2×D4711yescharacteristic
365C2×C4×D4—471no—
366C2×C4×D4—471no—
367C2×C4×D4C2×D4711yescharacteristic
368C22×C42—471no—
369C22×C42—471no—
370C2×C4⋊C8—471no—
371C2×C4⋊C8—471no—
372C2×C4⋊C8—471no—
373C2×C4⋊C8—471no—
374C2×C22⋊C8—471no—
375C2×C22⋊C8—471no—
376C2×C22⋊C8—471no—
377C2×C22⋊C8C2×D4711yescharacteristic
378C2×C22⋊C8C2×D4711yescharacteristic
379C2×C22⋊C8C2×D4711yescharacteristic
380C2×C4×C8—471no—
381C2×C4×C8—471no—
382C4×C4⋊C4—471no—
383C4×C4⋊C4—471no—
384C4×C4⋊C4—471no—
385C4×C22⋊C4—471no—
386C4×C22⋊C4—471no—
387C4×C22⋊C4—471no—
388C4×C22⋊C4—471no—
389C4×C22⋊C4—471no—
390C4×C22⋊C4—471no—
391C43—471no—
392#336—471no—
393#336—471no—
394#336—471no—
395#336—471no—
396#336—471no—
397#336—471no—
398#336—471no—
399#336—471no—
400#336—471no—
401#336—471no—
402#336—471no—
403#336—471no—
404#336C2×D4711yescharacteristic
405#336C2×D4711yescharacteristic
406C47#2199611yescharacteristic, complemented, Sylow
407C22×D4C4×D4711yescharacteristic
408C23×C4—471no—
409C23×C4—471no—
410C23×C4—471no—
411C23×C4—471no—
412C23×C4C22×D4711yescharacteristic
413C23×C4C22×D4711yescharacteristic
414C22×C8—22no—
415C22×C8—41no—
416C22×C8—41no—
417C22×C8—471no—
418C22×C8—471no—
419C22×C8—471no—
420C22×C8—471no—
421C22×C8—942no—
422C22×C8—1881no—
423C22×C8—1881no—
424C22×C8C22×D4711yescharacteristic
425C22×C8C22×D4711yescharacteristic
426C22×C8C22×D4711yescharacteristic
427C22×C8C22×D4711yescharacteristic
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—478no—
431C4×D4—944no—
432C2×C4⋊C4—471no—
433C2×C4⋊C4—471no—
434C2×C4⋊C4C4×D4711yescharacteristic
435C2×C22⋊C4—471no—
436C2×C22⋊C4—471no—
437C2×C22⋊C4—471no—
438C2×C22⋊C4—471no—
439C2×C22⋊C4C4×D4711yescharacteristic
440C2×C22⋊C4C4×D4711yescharacteristic
441C2×C42—471no—
442C2×C42—471no—
443C2×C42—471no—
444C2×C42—471no—
445C2×C42—471no—
446C2×C42—471no—
447C2×C42—471no—
448C2×C42—471no—
449C2×C42—471no—
450C2×C42—471no—
451C2×C42—471no—
452C2×C42—471no—
453C2×C42—1881no—
454C2×C42—1881no—
455C2×C42—1881no—
456C2×C42—1881no—
457C2×C42C22×D4711yescharacteristic
458C4⋊C8—1881no—
459C4⋊C8—1881no—
460C4⋊C8—1881no—
461C4⋊C8—1881no—
462C22⋊C8—22no—
463C22⋊C8—41no—
464C22⋊C8—41no—
465C22⋊C8—942no—
466C22⋊C8—1881no—
467C22⋊C8—1881no—
468C4×C8—1881no—
469C4×C8—1881no—
470#95—471no—
471#95—471no—
472#95—471no—
473#95—471no—
474#95—471no—
475#95—471no—
476C24C2×C4×D4711yescharacteristic
477C24C2×C4×D4711yescharacteristic
478C2×D4—22no—
479C2×D4—22no—
480C2×D4C8×D4714yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—471no—
492C22×C4—471no—
493C22×C4—471no—
494C22×C4—471no—
495C22×C4—471no—
496C22×C4—471no—
497C22×C4—474no—
498C22×C4—474no—
499C22×C4—474no—
500C22×C4—471no—
501C22×C4—471no—
502C22×C4—942no—
503C22×C4—1881no—
504C22×C4—1881no—
505C22×C4—1881no—
506C22×C4—1881no—
507C22×C4—1881no—
508C22×C4—1881no—
509C22×C4—1881no—
510C22×C4—1881no—
511C22×C4C2×C4×D4711yescharacteristic
512C22×C4C2×C4×D4711yescharacteristic
513C22×C4C2×C4×D4711yescharacteristic
514C22×C4C2×C4×D4711yescharacteristic
515C22×C4#1062535212yes—
516C22×C4#1062535212yes—
517C22×C4C23×D4711yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—44no—
531C2×C8—941no—
532C2×C8—941no—
533C2×C8—941no—
534C2×C8—941no—
535C2×C8—941no—
536C2×C8—941no—
537C2×C8—941no—
538C2×C8—941no—
539C2×C8—941no—
540C2×C8—941no—
541C2×C8—941no—
542C2×C8—941no—
543C2×C8—1884no—
544C4⋊C4—22no—
545C4⋊C4—474no—
546C4⋊C4—942no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—474no—
550C22⋊C4—474no—
551C22⋊C4—942no—
552C22⋊C4—942no—
553C42—21no—
554C42—21no—
555C42—474no—
556C42—942no—
557C42—941no—
558C42—941no—
559C42—941no—
560C42—941no—
561C42—941no—
562C42—941no—
563C42—941no—
564C42—941no—
565C42—1881no—
566C42—1881no—
567C42—1881no—
568C42—1881no—
569C42—1881no—
570C42—1881no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23#1309398012yes—
582C23C2×C8×D4712yes—
583C23C2×C8×D4712yes—
584C23M16×D4712yes—
585C23C22×C4×D4711yescharacteristic
586D4—28no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—472no—
606C2×C4—472no—
607C2×C4—472no—
608C2×C4—472no—
609C2×C4—472no—
610C2×C4—472no—
611C2×C4—941no—
612C2×C4—941no—
613C2×C4—941no—
614C2×C4—941no—
615C2×C4—941no—
616C2×C4—941no—
617C2×C4—941no—
618C2×C4—941no—
619C2×C4—941no—
620C2×C4—941no—
621C2×C4—941no—
622C2×C4—941no—
623C2×C4—941no—
624C2×C4—941no—
625C2×C4—941no—
626C2×C4—941no—
627C2×C4—941no—
628C2×C4—941no—
629C2×C4—1884no—
630C2×C4—1884no—
631C2×C4—1884no—
632C2×C4—1884no—
633C2×C4#1309398012yes—
634C2×C4C2×C8×D4712yes—
635C2×C4C2×#1062535211yescharacteristic
636C2×C4C2×#1062535211yescharacteristic
637C2×C4#1309406911yescharacteristic
638C2×C4#1309406911yescharacteristic
639C2×C4#1309407011yescharacteristic
640C2×C4#1309407111yescharacteristic
641C8—41no—
642C8—41no—
643C8—41no—
644C8—41no—
645C8—1881no—
646C8—1881no—
647C8—1881no—
648C8—1881no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22#1568917314yes—
663C22C2×#1309398011yescharacteristic
664C22#1568959511yescharacteristic
665C22#1568960211yescharacteristic
666C22C22×C8×D4711yescharacteristic
667C22C2×M16×D4711yescharacteristic
668C22#1568988811yescharacteristic
669C22#1568988811yescharacteristic
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—942no—
675C4—942no—
676C4—942no—
677C4—942no—
678C4—942no—
679C4—942no—
680C4—1881no—
681C4—1881no—
682C4#1568970811yescharacteristic
683C4#1568971011yescharacteristic
684C4#1568971711yescharacteristic
685C4#1568971811yescharacteristic
686C2—24no—
687C2—42no—
688C2#2024601411yescharacteristic
689C2C2×#1568917311yescharacteristic
690C2#2025203511yescharacteristic
691C2#2025240911yescharacteristic
692C2#2025241311yescharacteristic
693C2#2025249511yescharacteristic
694C2#2025250011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC47×#1869C2
socleC23×C47C23×C4
prime radicalC22×D4×C47C2×C4
cosocleC22×C4×C47C24
hypercenter#1869D47
hypocenterC47#21996
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #20243997C2semidirect
3. #20243991C2semidirect
4. #20243946C2semidirect
5. #20243944C2semidirect
7. #20243566C2semidirect
8. #20243565C2semidirect
9. #20243530C2semidirect
10. #20243503C2semidirect
11. #20243454C2semidirect
12. #20243366C2semidirect
13. C22⋊C8×Dic47C2semidirect
14. C2×#15688877C2semidirect
71. D4×Dic47C8semidirect
160. C22×Dic47C2×C8semidirect
191. C22⋊Dic47C2×C8semidirect
193. C4⋊Dic47C2×C8semidirect
209. C4×Dic47C2×C8semidirect
406. C47#21996semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Dic472
#202439972
#202439912
#202439462
#202439442
#202436812
#202435662
#202435652
#202435302
#202435032
#202434542
#202433662
C22⋊C8×Dic472
C2×#156888772
C47×#18692
#2199647