Finite Group Databasebeta

← #26216204

Subgroups — #26216204

Order 12032.

1350 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625350C211yesmaximal, characteristic
2C2×#15689179C211yesmaximal, characteristic, complemented
3C2×#15689175C211yesmaximal, characteristic, complemented
4#20243458C212yesmaximal, complemented
5#20243368C211yesmaximal, characteristic, complemented
6#20243365C211yesmaximal, characteristic, complemented
7#20243365C211yesmaximal, characteristic, complemented
8#20243299C212yesmaximal
9#20243156C212yesmaximal, complemented
10#20243153C212yesmaximal, complemented
11C47×#1797C211yesmaximal, characteristic, complemented
12C22×#10625350C2211yescharacteristic
13C4×#10625350—24no—
14C4×#10625350—24no—
15C2×C4×Dic94C411yescharacteristic
16C2×C4×Dic94C411yescharacteristic
17C2×C4×D188C411yescharacteristic
18C2×C4×D188C411yescharacteristic
19C2×C4×C22⋊D47C411yescharacteristic
20C2×C4×C22⋊D47C411yescharacteristic
21C2×C4×C22⋊D47C411yescharacteristic
22C2×C4×C22⋊D47C411yescharacteristic
23C2×#13093983C2211yescharacteristic
24C2×#13093981C2211yescharacteristic
25C2×#13093981C2211yescharacteristic
26C2×C42×D47C2211yescharacteristic
27C2×C42×D47C2211yescharacteristic
28#15689179—24no—
29#15689175—24no—
30C2×C4⋊(C47⋊C8)C2211yescharacteristic
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2212yes—
33C2×(C2×D47)⋊C8C2212yes—
34C2×(C2×D47)⋊C8C2212yes—
35C2×(C2×D47)⋊C8C2212yes—
36C2×(C2×D47)⋊C8C2212yes—
37C2×#13093934C2212yes—
38C2×C8×Dic47C2212yes—
39#15688878C2212yes—
40#15688877C2212yes—
41#15688877C2212yes—
42C22×C42×C47C2211yescharacteristic
43C2×C4⋊C8×C47C2211yescharacteristic
44C2×C4⋊C8×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2212yes—
46C47×#336C2212yes—
47C2×#10625350—22no—
48C2×#10625350—22no—
49C2×#10625350—22no—
50C2×#10625350—22no—
51C2×#10625350—22no—
52C2×#10625350—22no—
53C22×Dic94C2×C411yescharacteristic
54C22×D188C2×C411yescharacteristic
55C22×C22⋊D47C2×C411yescharacteristic
56C22×C22⋊D47C2×C411yescharacteristic
57C22×C4×D47C2×C411yescharacteristic
58C22×C4×D47C2×C411yescharacteristic
59C22×C4×D47C2×C411yescharacteristic
60C22×C4×D47C2×C411yescharacteristic
61C22×C4×D47C2311yescharacteristic
62C22×C4×D47C2311yescharacteristic
63C22×C47⋊C8C2312yes—
64C22×C47⋊C8C2312yes—
65C4×Dic94—24no—
66C4×Dic94—24no—
67C4×D188—24no—
68C4×D188—24no—
69C4×C22⋊D47—24no—
70C4×C22⋊D47—24no—
71C4×C22⋊D47—24no—
72C4×C22⋊D47—24no—
73#13093983—22no—
74#13093983—22no—
75#13093981—22no—
76#13093981—22no—
77#13093981—22no—
78#13093981—22no—
79C2×C4⋊Dic47C2×C411yescharacteristic
80C2×C4⋊Dic47C2×C411yescharacteristic
81C2×Dic47⋊C4C2×C411yescharacteristic
82C2×Dic47⋊C4C2×C411yescharacteristic
83C2×Dic47⋊C4C2×C411yescharacteristic
84C2×Dic47⋊C4C2×C411yescharacteristic
85C2×C22⋊Dic47C2×C411yescharacteristic
86C2×C22⋊Dic47C2×C411yescharacteristic
87C2×(C2×D47)⋊C4C2×C411yescharacteristic
88C2×(C2×D47)⋊C4C2×C411yescharacteristic
89C2×(C2×D47)⋊C4C2×C411yescharacteristic
90C2×(C2×D47)⋊C4C2×C411yescharacteristic
91C2×C4×Dic47C2×C411yescharacteristic
92C2×C4×Dic47C2×C411yescharacteristic
93C2×C4×Dic47C2×C411yescharacteristic
94C2×C4×Dic47C2×C411yescharacteristic
95C2×C4×Dic47C2311yescharacteristic
96C2×C4×Dic47C2311yescharacteristic
97C42×D47—22no—
98C42×D47—22no—
99C42×D47D414yes—
100C42×D47D414yes—
101C4⋊(C47⋊C8)—22no—
102C4⋊(C47⋊C8)—22no—
103C22⋊(C47⋊C8)—24no—
104(C2×D47)⋊C8—24no—
105(C2×D47)⋊C8—24no—
106(C2×D47)⋊C8—24no—
107(C2×D47)⋊C8—24no—
108#13093934—24no—
109C8×Dic47—24no—
110C23×C4×C47C2×C411yescharacteristic
111C23×C4×C47C2×C411yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C22×C8×C47C2312yes—
114C22×C8×C47C2312yes—
115C2×C42×C47—22no—
116C2×C42×C47—22no—
117C2×C42×C47C2×C411yescharacteristic
118C2×C42×C47C2×C411yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121C4⋊C8×C47—22no—
122C4⋊C8×C47—22no—
123C22⋊C8×C47—24no—
124C24×C47C22×C411yescharacteristic
125C23×D47C22×C411yescharacteristic
126C23×D47C22×C411yescharacteristic
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—41no—
136C22×C4×C47—41no—
137C22×C4×C47C22×C411yescharacteristic
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C22×C411yescharacteristic
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47#4112yes—
143C22×C4×C47#4112yes—
144C22×C4×C47C2411yescharacteristic
145C2×C22⋊D47—22no—
146C2×C22⋊D47—22no—
147C2×C22⋊D47—22no—
148C2×C22⋊D47—22no—
149C2×C22⋊D47—22no—
150C2×C22⋊D47—22no—
151C22×Dic47C22×C411yescharacteristic
152C22×Dic47C22×C411yescharacteristic
153C22×Dic47C22×C411yescharacteristic
154C22×Dic47C22×C411yescharacteristic
155C22×Dic47C22×C411yescharacteristic
156C22×Dic47C22×C411yescharacteristic
157#10625350—28no—
158#10625350—28no—
159#10625350—28no—
160#10625350—28no—
161C2×D188—22no—
162C2×D188—22no—
163C2×D188—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—21no—
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—21no—
174C2×C4×D47—22no—
175C2×C4×D47—22no—
176C2×C4×D47—22no—
177C2×C4×D47—22no—
178C2×C4×D47—41no—
179C2×C4×D47—41no—
180C2×C4×D47—41no—
181C2×C4×D47—41no—
182C2×C4×D47C22⋊C414yes—
183C2×C4×D47C22⋊C414yes—
184C2×C4×D47C2×D412yes—
185C2×C4×D47C2×D412yes—
186C2×C4×D47#4112yes—
187C2×C4×D47#4112yes—
188C2×Dic94—22no—
189C2×Dic94—22no—
190C2×Dic94—22no—
191C2×C8×C47—22no—
192C2×C8×C47—22no—
193C2×C8×C47—22no—
194C2×C8×C47—22no—
195C2×C8×C47—22no—
196C2×C8×C47—22no—
197C42×C47—22no—
198C42×C47—22no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47C2×D412yes—
202C42×C47C2×D412yes—
203C22⋊Dic47—22no—
204C22⋊Dic47—22no—
205(C2×D47)⋊C4—22no—
206(C2×D47)⋊C4—22no—
207(C2×D47)⋊C4—22no—
208(C2×D47)⋊C4—22no—
209C4⋊Dic47—22no—
210C4⋊Dic47—22no—
211Dic47⋊C4—22no—
212Dic47⋊C4—22no—
213Dic47⋊C4—22no—
214Dic47⋊C4—22no—
215C4×Dic47—22no—
216C4×Dic47—22no—
217C4×Dic47—21no—
218C4×Dic47—21no—
219C4×Dic47C22⋊C414yes—
220C4×Dic47C22⋊C414yes—
221C4×Dic47C2×D412yes—
222C4×Dic47C2×D412yes—
223C2×C47⋊C8—22no—
224C2×C47⋊C8—22no—
225C2×C47⋊C8—22no—
226C2×C47⋊C8—22no—
227C2×C47⋊C8—22no—
228C2×C47⋊C8—22no—
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×D47—21no—
244C22×D47—21no—
245C22×D47—21no—
246C22×D47—21no—
247C22×D47—21no—
248C22×D47—21no—
249C22×D47C2×C22⋊C412yes—
250C22×D47#11712yes—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—44no—
266C2×C4×C47—44no—
267C2×C4×C47C2×C22⋊C412yes—
268C2×C4×C47C2×C22⋊C412yes—
269C2×C4×C47#11712yes—
270C2×C4×C47#13112yes—
271C2×C4×C47#13112yes—
272C2×C4×C47C22×D411yescharacteristic
273C2×C4×C47C22×D411yescharacteristic
274C2×C4×C47C2×#4111yescharacteristic
275C2×C4×C47C2×#4111yescharacteristic
276C2×C4×C47C2×#4111yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C22⋊D47—28no—
279C22⋊D47—28no—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—21no—
286C2×Dic47—21no—
287C2×Dic47—21no—
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47C2×C22⋊C412yes—
295C2×Dic47C2×C22⋊C412yes—
296C2×Dic47C2×C22⋊C412yes—
297C2×Dic47#11712yes—
298D188—28no—
299C4×D47—22no—
300C4×D47—22no—
301C4×D47—22no—
302C4×D47—22no—
303C4×D47—22no—
304C4×D47—22no—
305C4×D47—22no—
306C4×D47—22no—
307C4×D47—28no—
308C4×D47—44no—
309C4×D47—44no—
310C4×D47—44no—
311Dic94—28no—
312C8×C47—42no—
313C8×C47—42no—
314C47⋊C8—42no—
315C47⋊C8—42no—
316#20721—471nomaximal, Sylow
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47C22×C22⋊C411yescharacteristic
325C22×C47C2×#11711yescharacteristic
326C22×C47C2×#11711yescharacteristic
327C22×C47C2×#13111yescharacteristic
328C22×C47C2×#13111yescharacteristic
329C22×C47#56811yescharacteristic
330C22×C47#56811yescharacteristic
331C2×D47—22no—
332C2×D47—22no—
333C2×D47—22no—
334C2×D47—22no—
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—41no—
338C2×D47—41no—
339C2×D47—41no—
340C2×D47—41no—
341C2×D47—41no—
342C2×D47—41no—
343C2×D47—41no—
344C2×D47—41no—
345C4×C47—22no—
346C4×C47—22no—
347C4×C47—41no—
348C4×C47—41no—
349C4×C47#40814yes—
350C4×C47#52511yescharacteristic
351C4×C47#52511yescharacteristic
352C4×C47#52511yescharacteristic
353C4×C47#52511yescharacteristic
354Dic47—22no—
355Dic47—22no—
356Dic47—22no—
357Dic47—22no—
358Dic47—41no—
359Dic47—41no—
360C2×C4×#41—471no—
361C2×#432—471no—
362C2×#431—471no—
363#1818—472no—
364#1797—471no—
365#1797—471no—
366#1797—471no—
367#1797D4711yescharacteristic, complemented
368#1780—472no—
369#1750—472no—
370#1750—472no—
371C2×C47—42no—
372C2×C47#228011yescharacteristic
373C2×C47C2×#40811yescharacteristic
374C2×C47#287911yescharacteristic
375C2×C47#292511yescharacteristic
376C2×C47#292511yescharacteristic
377C2×C47#292511yescharacteristic
378C2×C47#292511yescharacteristic
379D47—42no—
380D47—42no—
381C22×#41—471no—
382C4×#41—944no—
383C4×#41—944no—
384C2×C4×Q8—471no—
385C2×C4×Q8—471no—
386C2×C4×D4—471no—
387C2×C4×D4—471no—
388C2×C4×D4—471no—
389C2×C4×D4—471no—
390C2×C4×D4—471no—
391C2×C4×D4—471no—
392C2×#117—471no—
393C2×#117—471no—
394C2×#117—471no—
395C22×C42—471no—
396C22×C42—471no—
397C22×C42C2×D4711yescharacteristic
398#432—944no—
399#431—944no—
400C2×C4⋊C8—471no—
401C2×C4⋊C8—471no—
402C2×C4⋊C8C2×D4711yescharacteristic
403C2×C4⋊C8C2×D4711yescharacteristic
404C2×C22⋊C8—472no—
405C2×C22⋊C8—472no—
406C2×C22⋊C8—472no—
407C2×C22⋊C8—472no—
408C2×C22⋊C8—472no—
409C2×C22⋊C8C2×D4712yes—
410C2×#97—472no—
411C2×C4×C8—472no—
412#336—472no—
413#336—472no—
414#336—472no—
415#336C2×D4712yes—
416C47#2072111yescharacteristic, complemented, Sylow
417C2×#41—942no—
418C2×#41—942no—
419C2×#41—942no—
420C2×#41—942no—
421C2×#41—942no—
422C2×#41—942no—
423C22×Q8—471no—
424C22×D4—471no—
425C22×D4—471no—
426C22×D4—471no—
427C23×C4—471no—
428C23×C4—471no—
429C23×C4—471no—
430C23×C4—471no—
431C23×C4—471no—
432C23×C4—471no—
433C23×C4C4×D4711yescharacteristic
434C23×C4C4×D4711yescharacteristic
435C23×C4C22×D4711yescharacteristic
436C22×C8—472no—
437C22×C8—472no—
438C22×C8C22×D4712yes—
439C22×C8C22×D4712yes—
440C4×Q8—944no—
441C4×Q8—944no—
442C4×D4—944no—
443C4×D4—944no—
444C4×D4—944no—
445C4×D4—944no—
446C4×D4—944no—
447C4×D4—944no—
448#117—942no—
449#117—942no—
450#117—942no—
451#117—942no—
452#117—942no—
453#117—942no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—471no—
459C2×C4⋊C4—471no—
460C2×C22⋊C4—471no—
461C2×C22⋊C4—471no—
462C2×C22⋊C4—471no—
463C2×C22⋊C4—471no—
464C2×C22⋊C4—471no—
465C2×C22⋊C4—471no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—471no—
469C2×C42—471no—
470C2×C42—471no—
471C2×C42—474no—
472C2×C42—474no—
473C2×C42—471no—
474C2×C42—471no—
475C2×C42—471no—
476C2×C42—942no—
477C2×C42—942no—
478C2×C42C4×D4711yescharacteristic
479C2×C42C4×D4711yescharacteristic
480C2×C42C22×D4711yescharacteristic
481C2×C42C22×D4711yescharacteristic
482C4⋊C8—22no—
483C4⋊C8—22no—
484C4⋊C8—942no—
485C4⋊C8—942no—
486C22⋊C8—24no—
487C22⋊C8—944no—
488C22⋊C8—944no—
489C22⋊C8—944no—
490C22⋊C8—944no—
491C22⋊C8—944no—
492#97—944no—
493C4×C8—944no—
494C24—471no—
495C24—471no—
496C24C2×C4×D4711yescharacteristic
497#41—948no—
498#41—948no—
499#41—948no—
500#41—948no—
501C2×Q8—942no—
502C2×Q8—942no—
503C2×Q8—942no—
504C2×D4—942no—
505C2×D4—942no—
506C2×D4—942no—
507C2×D4—942no—
508C2×D4—942no—
509C2×D4—942no—
510C2×D4—942no—
511C2×D4—942no—
512C2×D4—942no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—471no—
524C22×C4—471no—
525C22×C4—471no—
526C22×C4—471no—
527C22×C4—474no—
528C22×C4—472no—
529C22×C4—472no—
530C22×C4—472no—
531C22×C4—472no—
532C22×C4—474no—
533C22×C4—471no—
534C22×C4—471no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—941no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4—941no—
541C22×C4—941no—
542C22×C4—941no—
543C22×C4—941no—
544C22×C4—941no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—1881no—
550C22×C4—1881no—
551C22×C4—1881no—
552C22×C4—1881no—
553C22×C4C2×C4×D4711yescharacteristic
554C22×C4C2×C4×D4711yescharacteristic
555C22×C4C2×C4×D4711yescharacteristic
556C22×C4C2×C4×D4711yescharacteristic
557C22×C4C2×C4×D4711yescharacteristic
558C22×C4#1062535212yes—
559C22×C4#1062535412yes—
560C22×C4C23×D4711yescharacteristic
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—942no—
568C2×C8—942no—
569C2×C8—942no—
570C2×C8—942no—
571C2×C8—942no—
572C2×C8—942no—
573C4⋊C4—942no—
574C4⋊C4—942no—
575C4⋊C4—942no—
576C4⋊C4—942no—
577C4⋊C4—942no—
578C4⋊C4—942no—
579C22⋊C4—942no—
580C22⋊C4—942no—
581C22⋊C4—942no—
582C22⋊C4—942no—
583C22⋊C4—942no—
584C22⋊C4—942no—
585C42—22no—
586C42—22no—
587C42—21no—
588C42—21no—
589C42—474no—
590C42—474no—
591C42—472no—
592C42—472no—
593C42—942no—
594C42—942no—
595C42—941no—
596C42—941no—
597C42D4×D4712yes—
598C42D4×D4712yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—472no—
606C23—472no—
607C23—941no—
608C23—941no—
609C23—941no—
610C23—941no—
611C23—941no—
612C23—941no—
613C23—941no—
614C23—941no—
615C23—941no—
616C23—941no—
617C23—941no—
618C23—941no—
619C23#1309398212yes—
620C23C22×C4×D4711yescharacteristic
621Q8—948no—
622D4—948no—
623D4—948no—
624D4—948no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—472no—
642C2×C4—472no—
643C2×C4—472no—
644C2×C4—472no—
645C2×C4—941no—
646C2×C4—941no—
647C2×C4—941no—
648C2×C4—941no—
649C2×C4—941no—
650C2×C4—941no—
651C2×C4—941no—
652C2×C4—941no—
653C2×C4—948no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—941no—
663C2×C4—941no—
664C2×C4—941no—
665C2×C4—941no—
666C2×C4—941no—
667C2×C4—941no—
668C2×C4—1884no—
669C2×C4—1884no—
670C2×C4—1884no—
671C2×C4C22⋊C4×D4712yes—
672C2×C4C22⋊C4×D4712yes—
673C2×C4#1309398212yes—
674C2×C4#1309403012yes—
675C2×C4#1309403212yes—
676C2×C4C2×D4×D4711yescharacteristic
677C2×C4C2×D4×D4711yescharacteristic
678C2×C4#41×D4711yescharacteristic
679C2×C4#41×D4711yescharacteristic
680C2×C4C2×#1062535211yescharacteristic
681C2×C4C2×#1062535411yescharacteristic
682C8—42no—
683C8—42no—
684C8—1882no—
685C8—1882no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—942no—
694C22—942no—
695C22—942no—
696C22—942no—
697C22—942no—
698C22—942no—
699C22—1881no—
700C22—1881no—
701C22—1881no—
702C22—1881no—
703C22—1881no—
704C22—1881no—
705C22—1881no—
706C22—1881no—
707C22C2×C22⋊C4×D4711yescharacteristic
708C22#117×D4711yescharacteristic
709C22C2×#1309398211yescharacteristic
710C22C2×#1309403011yescharacteristic
711C22C2×#1309403211yescharacteristic
712C22#1568988911yescharacteristic
713C22#1568988911yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—942no—
719C4—942no—
720C4—942no—
721C4—942no—
722C4—1881no—
723C4—1881no—
724C4#1568908814yes—
725C4#1568963311yescharacteristic
726C4#1568963311yescharacteristic
727C4#1568963611yescharacteristic
728C4#1568963611yescharacteristic
729C2—42no—
730C2—1882no—
731C2—1882no—
732C2#2024577011yescharacteristic
733C2C2×#1568908811yescharacteristic
734C2#2025183111yescharacteristic
735C2#2025204911yescharacteristic
736C2#2025205311yescharacteristic
737C2#2025205511yescharacteristic
738C2#2025205611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1797C2
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#1797D47
hypocenterC47#20721
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#15689179C2semidirect
3. C2×#15689175C2semidirect
4. #20243458C2semidirect
5. #20243368C2semidirect
6. #20243365C2semidirect
7. #20243365C2semidirect
9. #20243156C2semidirect
10. #20243153C2semidirect
11. C47×#1797C2semidirect
367. #1797D47semidirect
416. C47#20721semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253502
C2×#156891792
C2×#156891752
#202434582
#202433682
#202433652
#202432992
#202431562
#202431532
C47×#17972
#2072147