Finite Group Databasebeta

← #26124152

Subgroups — #26124152

Order 12032.

1186 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D47)⋊C8C211yesmaximal, characteristic
2C2×#15688980C211yesmaximal, characteristic
3C2×#15688980C211yesmaximal, characteristic
4C2×#15688886C211yesmaximal, characteristic, complemented
5C2×#15688885C211yesmaximal, characteristic, complemented
6C2×#15688885C211yesmaximal, characteristic, complemented
7C2×C47×#340C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C23×C47⋊C8C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C4⋊Dic47C2211yescharacteristic
12C22×(C2×D47)⋊C4—21no—
13C22×(C2×D47)⋊C4—21no—
14C2×(C2×D47)⋊C8—22no—
15C2×(C2×D47)⋊C8—22no—
16C2×(C2×D47)⋊C8—22no—
17#15688980—22no—
18#15688980—22no—
19#15688980—22no—
20#15688980C414yescomplemented
21C2×C47⋊#95—21no—
22C2×C47⋊#95—21no—
23#15688886—22no—
24#15688885—22no—
25#15688885—22no—
26C23×C8×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C22×C4⋊C4×C47C2211yescharacteristic
29C47×#340—22no—
30C24×D47D411yescharacteristic
31C23×Dic47—21no—
32C23×Dic47—21no—
33C23×Dic47D411yescharacteristic
34C22×C4×D47—21no—
35C22×C4×D47—21no—
36C22×C4×D47—21no—
37C22×C4×D47—21no—
38C22×C4×D47—21no—
39C22×C4×D47—21no—
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47—21no—
46C22×C4×D47C2×C412yes—
47C22×C4×D47D412yes—
48C22×C47⋊C8—21no—
49C22×C47⋊C8—21no—
50C22×C47⋊C8—21no—
51C22×C47⋊C8—21no—
52C22×C47⋊C8—21no—
53C22×C47⋊C8—21no—
54C22×C47⋊C8D412yes—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47—21no—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47—21no—
59C2×C4⋊Dic47—21no—
60C2×C4⋊Dic47—21no—
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2×C412yes—
66C2×C4⋊Dic47D412yes—
67C2×(C2×D47)⋊C4—24no—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—42no—
70C2×(C2×D47)⋊C4—42no—
71C2×(C2×D47)⋊C4—42no—
72C2×(C2×D47)⋊C4—42no—
73(C2×D47)⋊C8—28no—
74C47⋊#95—24no—
75C47⋊#95—24no—
76C23×C4×C47—21no—
77C23×C4×C47—21no—
78C23×C4×C47C2311yescharacteristic
79C22×C8×C47—21no—
80C22×C8×C47—21no—
81C22×C8×C47—21no—
82C22×C8×C47—21no—
83C22×C8×C47—21no—
84C22×C8×C47—21no—
85C22×C8×C47D412yes—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47C2×C412yes—
97C2×C4⋊C4×C47D412yes—
98C24×C47C2×D411yescharacteristic
99C23×D47—21no—
100C23×D47—21no—
101C23×D47—21no—
102C23×D47—21no—
103C23×D47—21no—
104C23×D47—21no—
105C23×D47—21no—
106C23×D47—21no—
107C23×D47—21no—
108C23×D47—21no—
109C23×D47—21no—
110C23×D47—21no—
111C23×D47C22⋊C412yes—
112C23×D47SD1612yes—
113C23×D47Q1612yes—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—41no—
117C22×C4×C47—41no—
118C22×C4×C47—41no—
119C22×C4×C47—41no—
120C22×C4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47—41no—
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C22×C4×C47—41no—
127C22×C4×C47—41no—
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47#4111yescharacteristic
135C22×C4×C47#4111yescharacteristic
136C22×C4×C47#4111yescharacteristic
137C22×C4×C47#4111yescharacteristic
138C22×C4×C47#4111yescharacteristic
139C22×C4×C47#4111yescharacteristic
140C22×C4×C47#4111yescharacteristic
141C22×C4×C47#4111yescharacteristic
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—41no—
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×Dic47—41no—
160C22×Dic47—41no—
161C22×Dic47—41no—
162C22×Dic47C22⋊C412yes—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—22no—
173C2×C4×D47—22no—
174C2×C4×D47—22no—
175C2×C4×D47—41no—
176C2×C4×D47—41no—
177C2×C4×D47—41no—
178C2×C4×D47—41no—
179C2×C4×D47—41no—
180C2×C4×D47—41no—
181C2×C4×D47—41no—
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×C8×C47—22no—
192C2×C8×C47—22no—
193C2×C8×C47—22no—
194C2×C8×C47—41no—
195C2×C8×C47—41no—
196C2×C8×C47—41no—
197C2×C8×C47—41no—
198C4⋊C4×C47—22no—
199C4⋊C4×C47—22no—
200C4⋊C4×C47—22no—
201C4⋊C4×C47—22no—
202C4⋊C4×C47—41no—
203C4⋊C4×C47—41no—
204C4⋊C4×C47—41no—
205C4⋊C4×C47—41no—
206(C2×D47)⋊C4—48no—
207(C2×D47)⋊C4—48no—
208C4⋊Dic47—22no—
209C4⋊Dic47—22no—
210C4⋊Dic47—22no—
211C4⋊Dic47—22no—
212C4⋊Dic47—41no—
213C4⋊Dic47—41no—
214C4⋊Dic47—41no—
215C4⋊Dic47—41no—
216C2×C47⋊C8—22no—
217C2×C47⋊C8—22no—
218C2×C47⋊C8—22no—
219C2×C47⋊C8—41no—
220C2×C47⋊C8—41no—
221C2×C47⋊C8—41no—
222C2×C47⋊C8—41no—
223C23×C47C2×C22⋊C411yescharacteristic
224C23×C47#12011yescharacteristic
225C23×C47#12111yescharacteristic
226C23×C47#12111yescharacteristic
227C23×C47#12311yescharacteristic
228C23×C47#12311yescharacteristic
229C23×C47#12311yescharacteristic
230C23×C47C2×SD1611yescharacteristic
231C23×C47C2×Q1611yescharacteristic
232C23×C47#13511yescharacteristic
233C23×C47#13511yescharacteristic
234C23×C47AGL(1,ℤ/8)11yescharacteristic
235C23×C47AGL(1,ℤ/8)11yescharacteristic
236C23×C47AGL(1,ℤ/8)11yescharacteristic
237C23×C47#13711yescharacteristic
238C22×D47—22no—
239C22×D47—22no—
240C22×D47—22no—
241C22×D47—22no—
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—22no—
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—22no—
255C22×D47—22no—
256C22×D47—41no—
257C22×D47—41no—
258C22×D47—41no—
259C22×D47—41no—
260C22×D47—41no—
261C22×D47—41no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—41no—
265C22×D47—41no—
266C22×D47—41no—
267C22×D47—41no—
268C22×D47—41no—
269C22×D47—41no—
270C22×D47—41no—
271C22×D47—41no—
272C22×D47#10314yes—
273C2×C4×C47—42no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—81no—
280C2×C4×C47—81no—
281C2×C4×C47—81no—
282C2×C4×C47—81no—
283C2×C4×C47—81no—
284C2×C4×C47—81no—
285C2×C4×C47—81no—
286C2×C4×C47—81no—
287C2×C4×C47#11711yescharacteristic
288C2×C4×C47#11711yescharacteristic
289C2×C4×C47C4×D411yescharacteristic
290C2×C4×C47C4×D411yescharacteristic
291C2×C4×C47C4×D411yescharacteristic
292C2×C4×C47C4×D411yescharacteristic
293C2×C4×C47#12011yescharacteristic
294C2×C4×C47#12111yescharacteristic
295C2×C4×C47#12111yescharacteristic
296C2×C4×C47#12111yescharacteristic
297C2×C4×C47#12111yescharacteristic
298C2×C4×C47#12111yescharacteristic
299C2×C4×C47#12111yescharacteristic
300C2×C4×C47#12311yescharacteristic
301C2×C4×C47#12311yescharacteristic
302C2×C4×C47#12311yescharacteristic
303C2×C4×C47#12311yescharacteristic
304C2×C4×C47#12311yescharacteristic
305C2×C4×C47#12311yescharacteristic
306C2×C4×C47#12311yescharacteristic
307C2×C4×C47#12411yescharacteristic
308C2×C4×C47#12411yescharacteristic
309C2×C4×C47#12411yescharacteristic
310C2×C4×C47#12411yescharacteristic
311C2×C4×C47#12611yescharacteristic
312C2×C4×C47#12611yescharacteristic
313C2×C4×C47#12611yescharacteristic
314C2×C4×C47#12611yescharacteristic
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—81no—
329C2×Dic47—81no—
330C2×Dic47—81no—
331C2×Dic47—81no—
332C2×Dic47—81no—
333C2×Dic47—81no—
334C2×Dic47—81no—
335C2×Dic47—81no—
336C4×D47—42no—
337C4×D47—42no—
338C4×D47—42no—
339C4×D47—42no—
340C4×D47—42no—
341C4×D47—42no—
342C4×D47—42no—
343C4×D47—42no—
344C8×C47—42no—
345C47⋊C8—42no—
346#11200—471nomaximal, Sylow
347C22×C47#38111yescharacteristic
348C22×C47#38611yescharacteristic
349C22×C47#38611yescharacteristic
350C22×C47#39411yescharacteristic
351C22×C47#39411yescharacteristic
352C22×C47#39711yescharacteristic
353C22×C47#39711yescharacteristic
354C22×C47C2×#10311yescharacteristic
355C22×C47#41611yescharacteristic
356C22×C47#41711yescharacteristic
357C22×C47#41811yescharacteristic
358C22×C47#44911yescharacteristic
359C22×C47#44911yescharacteristic
360C22×C47#45011yescharacteristic
361C22×C47#45111yescharacteristic
362C22×C47#46511yescharacteristic
363C22×C47#46511yescharacteristic
364C22×C47#46711yescharacteristic
365C22×C47#46711yescharacteristic
366C22×C47#46811yescharacteristic
367C22×C47#46811yescharacteristic
368C22×C47#46911yescharacteristic
369C22×C47#46911yescharacteristic
370C22×C47#48111yescharacteristic
371C22×C47#48111yescharacteristic
372C22×C47#48211yescharacteristic
373C22×C47#48211yescharacteristic
374C22×C47#48211yescharacteristic
375C22×C47#48211yescharacteristic
376C22×C47#48311yescharacteristic
377C22×C47#48411yescharacteristic
378C22×C47#48411yescharacteristic
379C22×C47#48411yescharacteristic
380C22×C47#48511yescharacteristic
381C22×C47#48511yescharacteristic
382C2×D47—24no—
383C2×D47—24no—
384C2×D47—24no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C4×C47—82no—
398C4×C47—82no—
399C4×C47#38811yescharacteristic
400C4×C47#38811yescharacteristic
401C4×C47#38811yescharacteristic
402C4×C47#38811yescharacteristic
403C4×C47#39411yescharacteristic
404C4×C47#39411yescharacteristic
405C4×C47#39711yescharacteristic
406C4×C47#39711yescharacteristic
407Dic47—42no—
408Dic47—82no—
409Dic47—82no—
410C22×C22⋊C8—471no—
411C2×#380—471no—
412C2×#380—471no—
413C2×#340—471no—
414C2×#340—471no—
415C2×#340—471no—
416C2×#340D4711yescharacteristic, complemented
417C2×C47#144011yescharacteristic
418C2×C47#182411yescharacteristic
419C2×C47#182511yescharacteristic
420C2×C47#187211yescharacteristic
421C2×C47#187511yescharacteristic
422C2×C47#189211yescharacteristic
423C2×C47#189511yescharacteristic
424C2×C47#203411yescharacteristic
425C2×C47#203411yescharacteristic
426C2×C47#203611yescharacteristic
427C2×C47#203611yescharacteristic
428C2×C47#207611yescharacteristic
429C2×C47#207611yescharacteristic
430C2×C47#207711yescharacteristic
431C2×C47#207711yescharacteristic
432D47—44no—
433C24×C4—471no—
434C23×C8—471no—
435C23×C8C2×D4711yescharacteristic
436C22×C4⋊C4—471no—
437C22×C4⋊C4—471no—
438C22×C4⋊C4C2×D4711yescharacteristic
439C22×C4⋊C4C2×D4711yescharacteristic
440C22×C22⋊C4—941no—
441C22×C22⋊C4—941no—
442C2×C22⋊C8—942no—
443C2×C22⋊C8—942no—
444C2×C22⋊C8—942no—
445#380—474no—
446#380—942no—
447#380—942no—
448#380—942no—
449C2×#95—941no—
450C2×#95—941no—
451#340—22no—
452#340—942no—
453#340—942no—
454#340—942no—
455C47#1120011yescharacteristic, complemented, Sylow
456C25—471no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—471no—
460C23×C4—472no—
461C23×C4—472no—
462C23×C4—941no—
463C23×C4—941no—
464C23×C4—941no—
465C23×C4—941no—
466C23×C4—941no—
467C23×C4—941no—
468C23×C4—941no—
469C23×C4—941no—
470C23×C4—941no—
471C23×C4—941no—
472C23×C4—941no—
473C23×C4—941no—
474C23×C4—941no—
475C23×C4—941no—
476C23×C4C22×D4711yescharacteristic
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—472no—
484C22×C8—941no—
485C22×C8—941no—
486C22×C8—941no—
487C22×C8—941no—
488C22×C8—941no—
489C22×C8—941no—
490C22×C8C22⋊D4712yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—472no—
502C2×C4⋊C4—472no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4C4×D4712yes—
514C2×C4⋊C4D18812yes—
515C2×C22⋊C4—944no—
516C2×C22⋊C4—944no—
517C2×C22⋊C4—1882no—
518C2×C22⋊C4—1882no—
519C2×C22⋊C4—1882no—
520C2×C22⋊C4—1882no—
521C22⋊C8—948no—
522#95—944no—
523#95—944no—
524C24—472no—
525C24—472no—
526C24—472no—
527C24—941no—
528C24—941no—
529C24—941no—
530C24—941no—
531C24—941no—
532C24—941no—
533C24—941no—
534C24—941no—
535C24—941no—
536C24—941no—
537C24—941no—
538C24—941no—
539C24D4×D4711yescharacteristic
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—472no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—1881no—
576C22×C4—1881no—
577C22×C4—1881no—
578C22×C4—1881no—
579C22×C4—1881no—
580C22×C4—1881no—
581C22×C4—1881no—
582C22×C4—1881no—
583C22×C4—1881no—
584C22×C4—1881no—
585C22×C4—1881no—
586C22×C4—1881no—
587C22×C4—1881no—
588C22×C4—1881no—
589C22×C4—1881no—
590C22×C4—1881no—
591C22×C4—1881no—
592C22×C4—1881no—
593C22×C4—1881no—
594C22×C4—1881no—
595C22×C4—1881no—
596C22×C4—1881no—
597C22×C4—1881no—
598C22×C4—1881no—
599C22×C4—1881no—
600C22×C4—1881no—
601C22×C4—1881no—
602C22×C4—1881no—
603C22×C4C2×C4×D4711yescharacteristic
604C22×C4C2×D18811yescharacteristic
605C22×C4#1062535011yescharacteristic
606C22×C4#1062535011yescharacteristic
607C22×C4#1062535011yescharacteristic
608C22×C4#1062535011yescharacteristic
609C22×C4D4×D4711yescharacteristic
610C22×C4D4×D4711yescharacteristic
611C22×C4D4×D4711yescharacteristic
612C22×C4#1062535211yescharacteristic
613C22×C4#1062535211yescharacteristic
614C22×C4#1062535411yescharacteristic
615C22×C4#1062535411yescharacteristic
616C22×C4C2×C22⋊D4711yescharacteristic
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—942no—
625C2×C8—942no—
626C2×C8—942no—
627C2×C8—1881no—
628C2×C8—1881no—
629C2×C8—1881no—
630C2×C8—1881no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—942no—
640C4⋊C4—942no—
641C4⋊C4—942no—
642C4⋊C4—942no—
643C4⋊C4—1881no—
644C4⋊C4—1881no—
645C4⋊C4—1881no—
646C4⋊C4—1881no—
647C22⋊C4—1888no—
648C22⋊C4—1888no—
649C23—474no—
650C23—942no—
651C23—942no—
652C23—942no—
653C23—942no—
654C23—942no—
655C23—942no—
656C23—942no—
657C23—942no—
658C23—942no—
659C23—942no—
660C23—942no—
661C23—942no—
662C23—942no—
663C23—942no—
664C23—942no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23—1881no—
669C23—1881no—
670C23—1881no—
671C23—1881no—
672C23—1881no—
673C23—1881no—
674C23—1881no—
675C23—1881no—
676C23—1881no—
677C23—1881no—
678C23—1881no—
679C23—1881no—
680C23—1881no—
681C23—1881no—
682C23—1881no—
683C23—1881no—
684C23C22⋊C4×D4711yescharacteristic
685C23#1309399411yescharacteristic
686C23#1309399511yescharacteristic
687C23#1309399711yescharacteristic
688C23#1309400611yescharacteristic
689C23#1309400911yescharacteristic
690C23#1309400911yescharacteristic
691C23SD16×D4711yescharacteristic
692C23Q16×D4711yescharacteristic
693C23#1309404511yescharacteristic
694C23#1309404711yescharacteristic
695C23#1309404811yescharacteristic
696C23#1309404811yescharacteristic
697C23#1309405111yescharacteristic
698C23#1309405311yescharacteristic
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—3761no—
717C2×C4—3761no—
718C2×C4—3761no—
719C2×C4—3761no—
720C2×C4—3761no—
721C2×C4—3761no—
722C2×C4—3761no—
723C2×C4—3761no—
724C2×C4—1882no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4—1882no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4—1881no—
731C2×C4—1881no—
732C2×C4—1881no—
733C2×C4—1881no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1882no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4—1882no—
742C2×C4#1309398111yescharacteristic
743C2×C4#1309398211yescharacteristic
744C2×C4(C22⋊D47)⋊C411yescharacteristic
745C2×C4C4×C22⋊D4711yescharacteristic
746C2×C4#1309398611yescharacteristic
747C2×C4C4×D18811yescharacteristic
748C2×C4#1309399211yescharacteristic
749C2×C4#1309399611yescharacteristic
750C2×C4#1309399711yescharacteristic
751C2×C4#1309399711yescharacteristic
752C2×C4#1309399811yescharacteristic
753C2×C4#1309399911yescharacteristic
754C2×C4#1309399911yescharacteristic
755C2×C4#1309400611yescharacteristic
756C2×C4#1309400611yescharacteristic
757C2×C4#1309400711yescharacteristic
758C2×C4#1309400811yescharacteristic
759C2×C4#1309400911yescharacteristic
760C2×C4#1309400911yescharacteristic
761C2×C4#1309400911yescharacteristic
762C2×C4#1309401011yescharacteristic
763C2×C4#1309401011yescharacteristic
764C2×C4#1309401211yescharacteristic
765C2×C4#1309401311yescharacteristic
766C2×C4#1309401811yescharacteristic
767C2×C4#1309401911yescharacteristic
768C2×C4#1309401911yescharacteristic
769C2×C4#1309401911yescharacteristic
770C8—42no—
771C8—1882no—
772C22—944no—
773C22—944no—
774C22—944no—
775C22—1882no—
776C22—1882no—
777C22—1882no—
778C22—1882no—
779C22—1882no—
780C22—1882no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—1882no—
786C22—1882no—
787C22#1568898511yescharacteristic
788C22#1568899911yescharacteristic
789C22#1568900111yescharacteristic
790C22#1568903911yescharacteristic
791C22#1568904111yescharacteristic
792C22#1568904911yescharacteristic
793C22#1568905211yescharacteristic
794C22#103×D4711yescharacteristic
795C22#1568911811yescharacteristic
796C22#1568912111yescharacteristic
797C22#1568912611yescharacteristic
798C22#1568926911yescharacteristic
799C22#1568927111yescharacteristic
800C22#1568927511yescharacteristic
801C22#1568928011yescharacteristic
802C22#1568934911yescharacteristic
803C22#1568935511yescharacteristic
804C22#1568936111yescharacteristic
805C22#1568936311yescharacteristic
806C22#1568936611yescharacteristic
807C22#1568936811yescharacteristic
808C22#1568937311yescharacteristic
809C22#1568937511yescharacteristic
810C22#1568944011yescharacteristic
811C22#1568944311yescharacteristic
812C22#1568944611yescharacteristic
813C22#1568944911yescharacteristic
814C22#1568945011yescharacteristic
815C22#1568945011yescharacteristic
816C22#1568945511yescharacteristic
817C22#1568945711yescharacteristic
818C22#1568946011yescharacteristic
819C22#1568946011yescharacteristic
820C22#1568946311yescharacteristic
821C22#1568946711yescharacteristic
822C4—82no—
823C4—82no—
824C4—3762no—
825C4—3762no—
826C4—1882no—
827C4#1568901211yescharacteristic
828C4#1568901311yescharacteristic
829C4#1568901411yescharacteristic
830C4#1568901511yescharacteristic
831C4#1568903811yescharacteristic
832C4#1568904011yescharacteristic
833C4#1568905011yescharacteristic
834C4#1568905211yescharacteristic
835C2—1884no—
836C2#2024163611yescharacteristic
837C2#2024347711yescharacteristic
838C2#2024348211yescharacteristic
839C2#2024369411yescharacteristic
840C2#2024370911yescharacteristic
841C2#2024380811yescharacteristic
842C2#2024382311yescharacteristic
843C2#2024457611yescharacteristic
844C2#2024458011yescharacteristic
845C2#2024459011yescharacteristic
846C2#2024459411yescharacteristic
847C2#2024481711yescharacteristic
848C2#2024482011yescharacteristic
849C2#2024482211yescharacteristic
850C2#2024482711yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socleC24×C47C2×D4
prime radicalC24×D47D4
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#11200
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#15688886C2semidirect
5. C2×#15688885C2semidirect
6. C2×#15688885C2semidirect
7. C2×C47×#340C2semidirect
20. #15688980C4semidirect
416. C2×#340D47semidirect
455. C47#11200semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D47)⋊C82
C2×#156889802
C2×#156888862
C2×#156888852
C2×C47×#3402
#1120047