Finite Group Databasebeta

← #28606060

Subgroups — #28606060

Order 15104.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432754C211yesmaximal, characteristic, complemented
2#21432545C211yesmaximal, characteristic
3#21424809C211yesmaximal, characteristic, complemented
4#21424802C211yesmaximal, characteristic, complemented
5#21424746C211yesmaximal, characteristic, complemented
6#21424746C211yesmaximal, characteristic, complemented
7#21424373C211yesmaximal, characteristic, complemented
8#21424373C211yesmaximal, characteristic, complemented
9#21424195C211yesmaximal, characteristic, complemented
10#21424138C211yesmaximal, characteristic, complemented
11#21424040C211yesmaximal, characteristic
12#21423943C211yesmaximal, characteristic, complemented
13#21423936C211yesmaximal, characteristic, complemented
14#21423877C211yesmaximal, characteristic, complemented
15C59×#2896C211yesmaximal, characteristic
16C2×#14273734C2211yescharacteristic
17C2×#14273734C2211yescharacteristic
18#16837463—21no—
19#16837463—21no—
20#16837459—21no—
21#16837455—21no—
22C2×#14273663C2211yescharacteristic, complemented
23C2×#14273663C2211yescharacteristic, complemented
24#16837429C2211yescharacteristic, complemented
25#16837429C2211yescharacteristic, complemented
26C2×#14273654C2211yescharacteristic
27C2×#14273654C2211yescharacteristic
28C2×#14273654C2211yescharacteristic
29C2×#14273654C2211yescharacteristic
30#16837369—21no—
31#16837369—21no—
32#16837369C2211yescharacteristic
33#16837369C2211yescharacteristic
34#16837366—21no—
35#16837366C2211yescharacteristic
36#16837366C2211yescharacteristic
37C2×C22⋊(C59⋊C8)—21no—
38C2×C22⋊(C59⋊C8)C2211yescharacteristic
39#16837358C2211yescharacteristic, complemented
40#16837358C2211yescharacteristic, complemented
41C2×#14273637C2211yescharacteristic, complemented
42C2×C8×Dic59C2211yescharacteristic, complemented
43C4×C22⋊Dic59C2211yescharacteristic
44#16837167C2211yescharacteristic, complemented
45#16837167C2211yescharacteristic, complemented
46#16837161C2211yescharacteristic, complemented
47#16837161C2211yescharacteristic, complemented
48#16837161C2211yescharacteristic, complemented
49#16837161C2211yescharacteristic, complemented
50#16837156C2211yescharacteristic, complemented
51#16837156C2211yescharacteristic, complemented
52C22×#41×C59C2211yescharacteristic
53C22×M16×C59C2211yescharacteristic
54C2×#117×C59C2211yescharacteristic
55C59×#419C411yescharacteristic, complemented
56C59×#419C411yescharacteristic, complemented
57C59×#418C411yescharacteristic, complemented
58C59×#418C411yescharacteristic, complemented
59C59×#417C411yescharacteristic, complemented
60C59×#417C411yescharacteristic, complemented
61C59×#417C411yescharacteristic, complemented
62C59×#417C411yescharacteristic, complemented
63C59×#416C2211yescharacteristic
64C59×#416C2211yescharacteristic
65C59×#416C2211yescharacteristic
66C59×#416C2211yescharacteristic
67#14273734—22no—
68#14273734—22no—
69#14273734—41no—
70#14273734—41no—
71C2×#11745664—21no—
72C2×#11745664—21no—
73C2×#11745664C2311yescharacteristic
74C2×#11745664C2311yescharacteristic
75C2×#11745664C2311yescharacteristic
76C2×#11745664C2311yescharacteristic
77C22×C59⋊C8—21no—
78C22×C59⋊C8—21no—
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81C2×C22⋊Dic59—21no—
82C2×C4×Dic59C2311yescharacteristic
83C2×C4×Dic59C2311yescharacteristic
84#14273663—41no—
85#14273663—41no—
86C4⋊(C59⋊C8)—21no—
87C4⋊(C59⋊C8)—21no—
88C4⋊(C59⋊C8)—21no—
89C4⋊(C59⋊C8)—21no—
90#14273654—22no—
91#14273654—22no—
92#14273654—41no—
93#14273654—41no—
94C22⋊(C59⋊C8)—21no—
95C22⋊(C59⋊C8)—21no—
96C22⋊(C59⋊C8)—21no—
97C22⋊(C59⋊C8)—21no—
98C22⋊(C59⋊C8)—21no—
99C22⋊(C59⋊C8)—21no—
100C22⋊(C59⋊C8)—21no—
101C22⋊(C59⋊C8)—21no—
102C22⋊(C59⋊C8)D411yescharacteristic
103C22⋊(C59⋊C8)D411yescharacteristic
104C22⋊(C59⋊C8)D411yescharacteristic
105C22⋊(C59⋊C8)D411yescharacteristic
106#14273638—21no—
107#14273638—21no—
108#14273637—41no—
109C4×C59⋊C8—21no—
110C4×C59⋊C8—21no—
111C8×Dic59—41no—
112C59⋊#95—21no—
113C2×#41×C59—21no—
114C2×#41×C59—21no—
115C2×#41×C59—22no—
116C2×#41×C59—22no—
117C2×#41×C59—41no—
118C2×#41×C59—41no—
119C2×#41×C59C2×C411yescharacteristic
120C2×#41×C59C2×C411yescharacteristic
121C2×#41×C59C2311yescharacteristic
122C2×#41×C59C2311yescharacteristic
123C22×Q8×C59C2×C411yescharacteristic
124C22×D4×C59—21no—
125C22×D4×C59C2×C411yescharacteristic
126C23×C4×C59—21no—
127C23×C4×C59C2311yescharacteristic
128C2×M16×C59—41no—
129C2×M16×C59—41no—
130C2×M16×C59C2×C411yescharacteristic
131C2×M16×C59C2×C411yescharacteristic
132C2×M16×C59C2×C411yescharacteristic
133C2×M16×C59C2×C411yescharacteristic
134C22×C8×C59C2311yescharacteristic
135C22×C8×C59C2311yescharacteristic
136#117×C59—21no—
137#117×C59—21no—
138#117×C59C2×C411yescharacteristic
139#117×C59C2×C411yescharacteristic
140#117×C59C2311yescharacteristic
141#117×C59C2311yescharacteristic
142C2×C4⋊C4×C59C2×C411yescharacteristic
143C2×C4⋊C4×C59C2×C411yescharacteristic
144C2×C22⋊C4×C59—21no—
145C2×C42×C59—21no—
146#103×C59C2×C411yescharacteristic
147#103×C59C2×C411yescharacteristic
148#103×C59C2×C411yescharacteristic
149#103×C59C2×C411yescharacteristic
150#103×C59C2×C411yescharacteristic
151#103×C59C2×C411yescharacteristic
152#103×C59C2×C411yescharacteristic
153#103×C59C2×C411yescharacteristic
154#102×C59C2×C411yescharacteristic
155#102×C59C2×C411yescharacteristic
156#102×C59C2×C411yescharacteristic
157#102×C59C2×C411yescharacteristic
158#102×C59C2×C411yescharacteristic
159#102×C59C2×C411yescharacteristic
160#102×C59C2×C411yescharacteristic
161#102×C59C2×C411yescharacteristic
162C24×C59—21no—
163C24×C59#4111yescharacteristic
164#41×C59—21no—
165#41×C59—21no—
166#41×C59—22no—
167#41×C59—22no—
168#41×C59—21no—
169#41×C59—21no—
170#41×C59—21no—
171#41×C59—21no—
172#41×C59—42no—
173#41×C59—42no—
174#41×C59—41no—
175#41×C59—41no—
176#41×C59—42no—
177#41×C59—42no—
178#41×C59#4112yes—
179#41×C59#4112yes—
180C2×Q8×C59—21no—
181C2×Q8×C59—22no—
182C2×Q8×C59—41no—
183C2×Q8×C59C22×C411yescharacteristic
184C2×Q8×C59C22×C411yescharacteristic
185C2×D4×C59—21no—
186C2×D4×C59—22no—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—41no—
192C2×D4×C59—42no—
193C2×D4×C59—42no—
194C2×D4×C59C22×C411yescharacteristic
195C2×D4×C59C22×C411yescharacteristic
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—42no—
208C22×C4×C59—42no—
209C22×C4×C59C22×C411yescharacteristic
210C22×C4×C59C22×C411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59#4111yescharacteristic
214C22×C4×C59C2411yescharacteristic
215C22×Dic59—21no—
216C22×Dic59—21no—
217M16×C59—41no—
218M16×C59—41no—
219M16×C59—41no—
220M16×C59—41no—
221C2×C8×C59—21no—
222C2×C8×C59—21no—
223C2×C8×C59—21no—
224C2×C8×C59—21no—
225C2×C8×C59C22×C411yescharacteristic
226C2×C8×C59C22×C411yescharacteristic
227C2×C8×C59C22×C411yescharacteristic
228C2×C8×C59C22×C411yescharacteristic
229C4⋊C4×C59—21no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59C22×C411yescharacteristic
232C4⋊C4×C59C22×C411yescharacteristic
233C4⋊C4×C59C22×C411yescharacteristic
234C4⋊C4×C59C22×C411yescharacteristic
235C22⋊C4×C59—21no—
236C22⋊C4×C59—21no—
237C22⋊C4×C59—21no—
238C22⋊C4×C59—21no—
239C42×C59—21no—
240C42×C59—21no—
241C42×C59—21no—
242C42×C59—21no—
243C22⋊Dic59—42no—
244C4×Dic59—21no—
245C4×Dic59—21no—
246C4×Dic59—21no—
247C4×Dic59—21no—
248#11745664—21no—
249#11745664—21no—
250#11745664—21no—
251#11745664—21no—
252#11745664—21no—
253#11745664—21no—
254#11745664—21no—
255#11745664—21no—
256#11745664—42no—
257#11745664—42no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—21no—
260C2×C59⋊C8—21no—
261C2×C59⋊C8—21no—
262C2×C59⋊C8—21no—
263C2×C59⋊C8—21no—
264C2×C59⋊C8—21no—
265C2×C59⋊C8—21no—
266C2×C59⋊C8—42no—
267C2×C59⋊C8—42no—
268C2×C59⋊C8C2×D411yescharacteristic
269C2×C59⋊C8C2×D411yescharacteristic
270C2×C59⋊C8C2×D411yescharacteristic
271C2×C59⋊C8C2×D411yescharacteristic
272C23×C59—21no—
273C23×C59—21no—
274C23×C59—21no—
275C23×C59—21no—
276C23×C59—41no—
277C23×C59—41no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59—81no—
281C23×C59C4×D411yescharacteristic
282C23×C59C4×D411yescharacteristic
283C23×C59C2×#4111yescharacteristic
284Q8×C59—21no—
285Q8×C59—21no—
286Q8×C59—21no—
287Q8×C59—42no—
288Q8×C59#11712yes—
289D4×C59—22no—
290D4×C59—22no—
291D4×C59—21no—
292D4×C59—21no—
293D4×C59—21no—
294D4×C59—42no—
295D4×C59—42no—
296D4×C59—42no—
297D4×C59—41no—
298D4×C59—41no—
299D4×C59#11712yes—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—21no—
310C2×C4×C59—21no—
311C2×C4×C59—21no—
312C2×C4×C59—21no—
313C2×C4×C59—21no—
314C2×C4×C59—21no—
315C2×C4×C59—21no—
316C2×C4×C59—21no—
317C2×C4×C59—21no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—42no—
321C2×C4×C59—42no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—81no—
325C2×C4×C59C4×D411yescharacteristic
326C2×C4×C59C4×D411yescharacteristic
327C2×C4×C59C23×C411yescharacteristic
328C2×C4×C59C22×D411yescharacteristic
329C2×C4×C59C2×#4111yescharacteristic
330C2×C4×C59C2×#4111yescharacteristic
331C2×C4×C59H(5,𝔽2)11yescharacteristic
332C2×C4×C59H(5,𝔽2)11yescharacteristic
333C2×Dic59—22no—
334C2×Dic59—41no—
335C2×Dic59—41no—
336C2×Dic59—41no—
337C2×Dic59—41no—
338C2×Dic59—41no—
339C8×C59—21no—
340C8×C59—21no—
341C8×C59—21no—
342C8×C59—21no—
343C59⋊C8—21no—
344C59⋊C8—21no—
345C59⋊C8—21no—
346C59⋊C8—21no—
347C59⋊C8—41no—
348C59⋊C8—41no—
349C59⋊C8—41no—
350C59⋊C8—41no—
351#22588—591nomaximal, Sylow
352C22×C59—21no—
353C22×C59—21no—
354C22×C59—21no—
355C22×C59—21no—
356C22×C59—22no—
357C22×C59—21no—
358C22×C59—21no—
359C22×C59—21no—
360C22×C59—21no—
361C22×C59—41no—
362C22×C59—41no—
363C22×C59—41no—
364C22×C59—41no—
365C22×C59—41no—
366C22×C59—81no—
367C22×C59—81no—
368C22×C59—84no—
369C22×C59C2×C4×D411yescharacteristic
370C22×C59#55111yescharacteristic
371C22×C59#55111yescharacteristic
372C4×C59—21no—
373C4×C59—21no—
374C4×C59—22no—
375C4×C59—41no—
376C4×C59—41no—
377C4×C59—41no—
378C4×C59—41no—
379C4×C59—41no—
380C4×C59C2×#11711yescharacteristic
381C4×C59#51811yescharacteristic
382C4×C59#54611yescharacteristic
383C4×C59#54611yescharacteristic
384Dic59—42no—
385Dic59—81no—
386#2924—591no—
387#2896D5911yescharacteristic
388#2880—591no—
389#1938—591no—
390#1937—591no—
391#1929—591no—
392#1929—591no—
393#1866—591no—
394#1866—591no—
395#1826—591no—
396#1811—591no—
397#1789—591no—
398#1765—591no—
399#1764—591no—
400#1753—591no—
401C2×C59—21no—
402C2×C59—21no—
403C2×C59—41no—
404C2×C59—41no—
405C2×C59—42no—
406C2×C59—81no—
407C2×C59#234211yescharacteristic
408C2×C59#295511yescharacteristic
409C2×C59#295611yescharacteristic
410C22×#41C2×D5911yescharacteristic
411C2×#131—591no—
412C2×#131—591no—
413C22×M16C2×D5911yescharacteristic
414C2×#117C2×D5911yescharacteristic
415#433—1181no—
416#433—1181no—
417#432—1181no—
418#431—1181no—
419C2×#108—591no—
420C2×#108—591no—
421#424—591no—
422#424—591no—
423C2×#104—591no—
424C2×#104—591no—
425C2×#104—591no—
426C2×#104—591no—
427#419Dic5911yescharacteristic, complemented
428#419Dic5911yescharacteristic, complemented
429#418Dic5911yescharacteristic, complemented
430#418Dic5911yescharacteristic, complemented
431#417Dic5911yescharacteristic, complemented
432#417Dic5911yescharacteristic, complemented
433#417Dic5911yescharacteristic, complemented
434#417Dic5911yescharacteristic, complemented
435#416C2×D5911yescharacteristic
436#416C2×D5911yescharacteristic
437#416C2×D5911yescharacteristic
438#416C2×D5911yescharacteristic
439#408—591no—
440#408—591no—
441#408—1181no—
442#408—1181no—
443#407—591no—
444#407—591no—
445#407—1181no—
446C2×C22⋊C8—591no—
447C2×C22⋊C8—1181no—
448#405—591no—
449#405—591no—
450C2×#97—591no—
451C2×C4×C8—591no—
452C4×C22⋊C4—591no—
453#341—591no—
454#341—591no—
455#339—591no—
456#339—591no—
457#339—591no—
458#339—591no—
459#336—591no—
460#336—591no—
461C59#2258811yescharacteristic, complemented, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×Dic5911yescharacteristic
469C2×#41C2×Dic5911yescharacteristic
470C2×#41C22×D5911yescharacteristic
471C2×#41C22×D5911yescharacteristic
472C22×Q8C2×Dic5911yescharacteristic
473C22×D4—21no—
474C22×D4C2×Dic5911yescharacteristic
475C23×C4—21no—
476C23×C4C22×D5911yescharacteristic
477#131—1182no—
478#131—1182no—
479#131—2361no—
480#131—2361no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—591no—
484C2×M16—591no—
485C2×M16—591no—
486C2×M16—591no—
487C2×M16—1181no—
488C2×M16—1181no—
489C2×M16C2×Dic5911yescharacteristic
490C2×M16C2×Dic5911yescharacteristic
491C2×M16C2×Dic5911yescharacteristic
492C2×M16C2×Dic5911yescharacteristic
493C22×C8—591no—
494C22×C8—591no—
495C22×C8—1181no—
496C22×C8—1181no—
497C22×C8C22×D5911yescharacteristic
498C22×C8C22×D5911yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×Dic5911yescharacteristic
502#117C2×Dic5911yescharacteristic
503#117C22×D5911yescharacteristic
504#117C22×D5911yescharacteristic
505C2×C4⋊C4C2×Dic5911yescharacteristic
506C2×C4⋊C4C2×Dic5911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1181no—
509C2×C42—21no—
510C2×C42—591no—
511C2×C42—591no—
512#108—2361no—
513#108—2361no—
514C4⋊C8—1181no—
515C4⋊C8—1181no—
516C4⋊C8—1181no—
517C4⋊C8—1181no—
518#104—1182no—
519#104—1182no—
520#104—2361no—
521#104—2361no—
522#103C2×Dic5911yescharacteristic
523#103C2×Dic5911yescharacteristic
524#103C2×Dic5911yescharacteristic
525#103C2×Dic5911yescharacteristic
526#103C2×Dic5911yescharacteristic
527#103C2×Dic5911yescharacteristic
528#103C2×Dic5911yescharacteristic
529#103C2×Dic5911yescharacteristic
530#102C2×Dic5911yescharacteristic
531#102C2×Dic5911yescharacteristic
532#102C2×Dic5911yescharacteristic
533#102C2×Dic5911yescharacteristic
534#102C2×Dic5911yescharacteristic
535#102C2×Dic5911yescharacteristic
536#102C2×Dic5911yescharacteristic
537#102C2×Dic5911yescharacteristic
538C22⋊C8—591no—
539C22⋊C8—591no—
540C22⋊C8—591no—
541C22⋊C8—591no—
542C22⋊C8—1181no—
543C22⋊C8—1181no—
544C22⋊C8—1181no—
545C22⋊C8—1181no—
546C22⋊C8—1181no—
547C22⋊C8—1181no—
548C22⋊C8—1181no—
549C22⋊C8—1181no—
550#97—1181no—
551#97—1181no—
552#97—2361no—
553C4×C8—1181no—
554C4×C8—1181no—
555C4×C8—2361no—
556#95—1181no—
557C24—21no—
558C24#1174568711yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1174568512yes—
574#41#1174568512yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×Dic5911yescharacteristic
579C2×Q8C22×Dic5911yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×Dic5911yescharacteristic
590C2×D4C22×Dic5911yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1181no—
605C22×C4—1181no—
606C22×C4D4×D5911yescharacteristic
607C22×C4D4×D5911yescharacteristic
608C22×C4#1174568711yescharacteristic
609C22×C4C22×Dic5911yescharacteristic
610C22×C4C22×Dic5911yescharacteristic
611C22×C4C23×D5911yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—1181no—
617M16—1181no—
618M16—1181no—
619M16—1181no—
620M16—1181no—
621M16—1181no—
622M16—1181no—
623M16—1181no—
624M16—2362no—
625M16—2362no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—591no—
631C2×C8—591no—
632C2×C8—591no—
633C2×C8—591no—
634C2×C8—1181no—
635C2×C8—1181no—
636C2×C8—1181no—
637C2×C8—1181no—
638C2×C8—1181no—
639C2×C8—1181no—
640C2×C8—1181no—
641C2×C8—1181no—
642C2×C8—2362no—
643C2×C8—2362no—
644C2×C8C22×Dic5911yescharacteristic
645C2×C8C22×Dic5911yescharacteristic
646C2×C8C22×Dic5911yescharacteristic
647C2×C8C22×Dic5911yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×Dic5911yescharacteristic
651C4⋊C4C22×Dic5911yescharacteristic
652C4⋊C4C22×Dic5911yescharacteristic
653C4⋊C4C22×Dic5911yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—2362no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1181no—
664C42—1181no—
665C42—1181no—
666C42—1181no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23D4×Dic5911yescharacteristic
677C23D4×Dic5911yescharacteristic
678C23C2×#1174568711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1427368612yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1427368612yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—1182no—
721C2×C4—2361no—
722C2×C4—2361no—
723C2×C4—2361no—
724C2×C4—2361no—
725C2×C4—2361no—
726C2×C4D4×Dic5911yescharacteristic
727C2×C4D4×Dic5911yescharacteristic
728C2×C4C23×Dic5911yescharacteristic
729C2×C4C2×D4×D5911yescharacteristic
730C2×C4C2×#1174568511yescharacteristic
731C2×C4C2×#1174568511yescharacteristic
732C2×C4#1427377211yescharacteristic
733C2×C4#1427377211yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—1181no—
739C8—1181no—
740C8—1181no—
741C8—1181no—
742C8—2361no—
743C8—2361no—
744C8—2361no—
745C8—2361no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—22no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×D4×Dic5911yescharacteristic
764C22#1683807811yescharacteristic
765C22#1683807811yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—4721no—
775C4—2362no—
776C4C2×#1427368611yescharacteristic
777C4#1683787711yescharacteristic
778C4#1683804211yescharacteristic
779C4#1683804211yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2142694511yescharacteristic
787C2#2143299911yescharacteristic
788C2#2143300611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2896C2
socleC22×C59C2×C4×D4
prime radicalC22×#41×C59C22
cosocleC22×C4×C59C24
hypercenter#2896D59
hypocenterC59#22588
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #21432754C2semidirect
3. #21424809C2semidirect
4. #21424802C2semidirect
5. #21424746C2semidirect
6. #21424746C2semidirect
7. #21424373C2semidirect
8. #21424373C2semidirect
9. #21424195C2semidirect
10. #21424138C2semidirect
12. #21423943C2semidirect
13. #21423936C2semidirect
14. #21423877C2semidirect
22. C2×#14273663C22semidirect
23. C2×#14273663C22semidirect
24. #16837429C22semidirect
25. #16837429C22semidirect
39. #16837358C22semidirect
40. #16837358C22semidirect
41. C2×#14273637C22semidirect
42. C2×C8×Dic59C22semidirect
44. #16837167C22semidirect
45. #16837167C22semidirect
46. #16837161C22semidirect
47. #16837161C22semidirect
48. #16837161C22semidirect
49. #16837161C22semidirect
50. #16837156C22semidirect
51. #16837156C22semidirect
55. C59×#419C4semidirect
56. C59×#419C4semidirect
57. C59×#418C4semidirect
58. C59×#418C4semidirect
59. C59×#417C4semidirect
60. C59×#417C4semidirect
61. C59×#417C4semidirect
62. C59×#417C4semidirect
427. #419Dic59semidirect
428. #419Dic59semidirect
429. #418Dic59semidirect
430. #418Dic59semidirect
431. #417Dic59semidirect
432. #417Dic59semidirect
433. #417Dic59semidirect
434. #417Dic59semidirect
461. C59#22588semidirect

Maximal subgroups

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

subgroupindex
#214327542
#214325452
#214248092
#214248022
#214247462
#214243732
#214241952
#214241382
#214240402
#214239432
#214239362
#214238772
C59×#28962
#2258859