Finite Group Databasebeta

← #28497114

Subgroups — #28497114

Order 15104.

842 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837164C211yesmaximal, characteristic
2C2×#16837164C211yesmaximal, characteristic
3C2×#16837164C211yesmaximal, characteristic
4C2×#16837164C211yesmaximal, characteristic
5C2×#16837157C211yesmaximal, characteristic
6#21422326C211yesmaximal, characteristic
7C2×C59×#389C211yesmaximal, characteristic
8C23×C59⋊C8C2211yescharacteristic
9C23×C59⋊C8C2211yescharacteristic
10C22×C4⋊Dic59C2211yescharacteristic
11C22×C4⋊Dic59C2211yescharacteristic
12C2×C59⋊#95—21no—
13C2×C59⋊#95—21no—
14#16837164—22no—
15#16837164—22no—
16#16837164—22no—
17#16837164C414yescomplemented
18#16837157—22no—
19C22×C4⋊C4×C59—21no—
20C22×C4⋊C4×C59C2211yescharacteristic
21C22×C4⋊C4×C59C2211yescharacteristic
22C22×C42×C59C2211yescharacteristic
23C59×#389—22no—
24C59×#389—22no—
25C2×#95×C59—21no—
26C23×Dic59—21no—
27C23×Dic59—21no—
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30C22×C59⋊C8—21no—
31C22×C59⋊C8—21no—
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34C22×C59⋊C8—21no—
35C22×C59⋊C8—21no—
36C22×C59⋊C8—21no—
37C22×C59⋊C8—21no—
38C22×C59⋊C8—21no—
39C22×C59⋊C8—21no—
40C22×C59⋊C8C2×C412yes—
41C22×C59⋊C8D412yes—
42C2×C4⋊Dic59—21no—
43C2×C4⋊Dic59—21no—
44C2×C4⋊Dic59—21no—
45C2×C4⋊Dic59—21no—
46C2×C4⋊Dic59—21no—
47C2×C4⋊Dic59—21no—
48C2×C4⋊Dic59—21no—
49C2×C4⋊Dic59—21no—
50C2×C4⋊Dic59—21no—
51C2×C4⋊Dic59—21no—
52C2×C4⋊Dic59C2×C412yes—
53C2×C4⋊Dic59Q812yes—
54C59⋊#95—42no—
55C59⋊#95—42no—
56C23×C4×C59—21no—
57C23×C4×C59—21no—
58C23×C4×C59D411yescharacteristic
59C23×C4×C59D411yescharacteristic
60C23×C4×C59C2311yescharacteristic
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59—21no—
63C2×C4⋊C4×C59—21no—
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59—21no—
66C2×C4⋊C4×C59—21no—
67C2×C4⋊C4×C59—21no—
68C2×C4⋊C4×C59—24no—
69C2×C4⋊C4×C59—21no—
70C2×C4⋊C4×C59—42no—
71C2×C4⋊C4×C59—42no—
72C2×C4⋊C4×C59C2×C412yes—
73C2×C4⋊C4×C59D412yes—
74C2×C4⋊C4×C59D412yes—
75C2×C4⋊C4×C59Q812yes—
76C2×C42×C59—21no—
77C2×C42×C59—21no—
78C2×C42×C59—21no—
79C2×C42×C59—21no—
80C2×C42×C59—21no—
81C2×C42×C59—21no—
82#95×C59—24no—
83C24×C59C2×D411yescharacteristic
84C22×C4×C59—22no—
85C22×C4×C59—21no—
86C22×C4×C59—22no—
87C22×C4×C59—21no—
88C22×C4×C59—21no—
89C22×C4×C59—21no—
90C22×C4×C59—22no—
91C22×C4×C59—21no—
92C22×C4×C59—21no—
93C22×C4×C59—21no—
94C22×C4×C59—21no—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—21no—
98C22×C4×C59—21no—
99C22×C4×C59—22no—
100C22×C4×C59—41no—
101C22×C4×C59—41no—
102C22×C4×C59—41no—
103C22×C4×C59—41no—
104C22×C4×C59—41no—
105C22×C4×C59—41no—
106C22×C4×C59—41no—
107C22×C4×C59—41no—
108C22×C4×C59—41no—
109C22×C4×C59—41no—
110C22×C4×C59SD1612yes—
111C22×C4×C59Q1612yes—
112C22×C4×C59C22×C411yescharacteristic
113C22×C4×C59C2×D411yescharacteristic
114C22×C4×C59C2×D411yescharacteristic
115C22×C4×C59C2×D411yescharacteristic
116C22×C4×C59C2×Q811yescharacteristic
117C22×C4×C59C2×Q811yescharacteristic
118C22×C4×C59#4111yescharacteristic
119C22×C4×C59#4111yescharacteristic
120C22×C4×C59#4111yescharacteristic
121C22×C4×C59#4111yescharacteristic
122C22×C4×C59#4111yescharacteristic
123C22×C4×C59#4111yescharacteristic
124C22×C4×C59#4111yescharacteristic
125C22×C4×C59#4111yescharacteristic
126C22×Dic59—22no—
127C22×Dic59—22no—
128C22×Dic59—41no—
129C22×Dic59—41no—
130C22×Dic59—41no—
131C22×Dic59—41no—
132C22×Dic59—41no—
133C22×Dic59—41no—
134C22×Dic59—41no—
135C22×Dic59—41no—
136C22×Dic59—41no—
137C22×Dic59—41no—
138C22×Dic59—41no—
139C22×Dic59—41no—
140C4⋊C4×C59—22no—
141C4⋊C4×C59—22no—
142C4⋊C4×C59—22no—
143C4⋊C4×C59—22no—
144C4⋊C4×C59—22no—
145C4⋊C4×C59—48no—
146C4⋊C4×C59—41no—
147C4⋊C4×C59—41no—
148C4⋊C4×C59C4⋊C414yes—
149C42×C59—41no—
150C42×C59—41no—
151C42×C59—41no—
152C42×C59—41no—
153C4⋊Dic59—22no—
154C4⋊Dic59—22no—
155C4⋊Dic59—22no—
156C4⋊Dic59—22no—
157C4⋊Dic59—41no—
158C4⋊Dic59—41no—
159C4⋊Dic59—41no—
160C4⋊Dic59—41no—
161C2×C59⋊C8—22no—
162C2×C59⋊C8—22no—
163C2×C59⋊C8—22no—
164C2×C59⋊C8—22no—
165C2×C59⋊C8—22no—
166C2×C59⋊C8—22no—
167C2×C59⋊C8—41no—
168C2×C59⋊C8—41no—
169C2×C59⋊C8—41no—
170C2×C59⋊C8—41no—
171C2×C59⋊C8—41no—
172C2×C59⋊C8—41no—
173C2×C59⋊C8—41no—
174C2×C59⋊C8—41no—
175C23×C59C4×D411yescharacteristic
176C23×C59#12011yescharacteristic
177C23×C59#12111yescharacteristic
178C23×C59C22⋊Q811yescharacteristic
179C23×C59C22⋊Q811yescharacteristic
180C23×C59#12311yescharacteristic
181C23×C59#12411yescharacteristic
182C23×C59C2×SD1611yescharacteristic
183C23×C59C2×Q1611yescharacteristic
184C23×C59#13511yescharacteristic
185C23×C59#13511yescharacteristic
186C23×C59AGL(1,ℤ/8)11yescharacteristic
187C23×C59AGL(1,ℤ/8)11yescharacteristic
188C23×C59AGL(1,ℤ/8)11yescharacteristic
189C23×C59#13711yescharacteristic
190C2×C4×C59—24no—
191C2×C4×C59—22no—
192C2×C4×C59—22no—
193C2×C4×C59—22no—
194C2×C4×C59—22no—
195C2×C4×C59—22no—
196C2×C4×C59—22no—
197C2×C4×C59—41no—
198C2×C4×C59—41no—
199C2×C4×C59—42no—
200C2×C4×C59—42no—
201C2×C4×C59—41no—
202C2×C4×C59—41no—
203C2×C4×C59—42no—
204C2×C4×C59—42no—
205C2×C4×C59—41no—
206C2×C4×C59—41no—
207C2×C4×C59—42no—
208C2×C4×C59—42no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—42no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59—81no—
215C2×C4×C59—81no—
216C2×C4×C59—81no—
217C2×C4×C59—81no—
218C2×C4×C59C2×C4⋊C411yescharacteristic
219C2×C4×C59#11711yescharacteristic
220C2×C4×C59#11711yescharacteristic
221C2×C4×C59C4×D411yescharacteristic
222C2×C4×C59C4×D411yescharacteristic
223C2×C4×C59C4×Q811yescharacteristic
224C2×C4×C59#12111yescharacteristic
225C2×C4×C59#12111yescharacteristic
226C2×C4×C59C22⋊Q811yescharacteristic
227C2×C4×C59C22⋊Q811yescharacteristic
228C2×C4×C59C22⋊Q811yescharacteristic
229C2×C4×C59#12311yescharacteristic
230C2×C4×C59#12311yescharacteristic
231C2×C4×C59#12311yescharacteristic
232C2×C4×C59#12311yescharacteristic
233C2×C4×C59#12411yescharacteristic
234C2×C4×C59#12411yescharacteristic
235C2×C4×C59#12411yescharacteristic
236C2×C4×C59#12511yescharacteristic
237C2×C4×C59#12511yescharacteristic
238C2×C4×C59#12511yescharacteristic
239C2×C4×C59#12511yescharacteristic
240C2×C4×C59#12511yescharacteristic
241C2×C4×C59#12611yescharacteristic
242C2×C4×C59#12611yescharacteristic
243C2×C4×C59#12611yescharacteristic
244C2×C4×C59#12611yescharacteristic
245C2×C4×C59C4⋊Q811yescharacteristic
246C2×Dic59—42no—
247C2×Dic59—42no—
248C2×Dic59—42no—
249C2×Dic59—42no—
250C2×Dic59—42no—
251C2×Dic59—42no—
252C2×Dic59—81no—
253C2×Dic59—81no—
254C2×Dic59—81no—
255C2×Dic59—81no—
256C2×Dic59—81no—
257C2×Dic59—81no—
258C2×Dic59—81no—
259C2×Dic59—81no—
260C59⋊C8—42no—
261C59⋊C8—42no—
262#11293—591nomaximal, Sylow
263C22×C59#38511yescharacteristic
264C22×C59#38711yescharacteristic
265C22×C59#38811yescharacteristic
266C22×C59#39311yescharacteristic
267C22×C59#39411yescharacteristic
268C22×C59#39811yescharacteristic
269C22×C59#40011yescharacteristic
270C22×C59C4×SD1611yescharacteristic
271C22×C59C4×Q1611yescharacteristic
272C22×C59#44011yescharacteristic
273C22×C59#44211yescharacteristic
274C22×C59#44911yescharacteristic
275C22×C59#44911yescharacteristic
276C22×C59#45011yescharacteristic
277C22×C59#45111yescharacteristic
278C22×C59#46511yescharacteristic
279C22×C59#46711yescharacteristic
280C22×C59#46811yescharacteristic
281C22×C59#46911yescharacteristic
282C22×C59#47511yescharacteristic
283C22×C59#47611yescharacteristic
284C22×C59#47711yescharacteristic
285C22×C59#47711yescharacteristic
286C22×C59#47811yescharacteristic
287C22×C59#47811yescharacteristic
288C22×C59#47811yescharacteristic
289C22×C59#47911yescharacteristic
290C22×C59#48111yescharacteristic
291C22×C59#48211yescharacteristic
292C22×C59#48411yescharacteristic
293C22×C59#48511yescharacteristic
294C22×C59#48711yescharacteristic
295C22×C59#48811yescharacteristic
296C22×C59#48911yescharacteristic
297C22×C59#49011yescharacteristic
298C4×C59—44no—
299C4×C59—42no—
300C4×C59—42no—
301C4×C59—82no—
302C4×C59#38211yescharacteristic
303C4×C59#38711yescharacteristic
304C4×C59#38811yescharacteristic
305C4×C59#38911yescharacteristic
306C4×C59#39711yescharacteristic
307C4×C59#39811yescharacteristic
308C4×C59#40011yescharacteristic
309C4×C59#40011yescharacteristic
310Dic59—82no—
311Dic59—82no—
312C2×#389D5911yescharacteristic
313C2×#340—591no—
314C2×#340—591no—
315C2×#340—591no—
316C2×#340—591no—
317C2×#336—591no—
318C4⋊#95—591no—
319C2×C59#144211yescharacteristic
320C2×C59#186311yescharacteristic
321C2×C59#186411yescharacteristic
322C2×C59#191911yescharacteristic
323C2×C59#192111yescharacteristic
324C2×C59#193311yescharacteristic
325C2×C59#193611yescharacteristic
326C2×C59#202411yescharacteristic
327C2×C59#202511yescharacteristic
328C2×C59#203411yescharacteristic
329C2×C59#203611yescharacteristic
330C2×C59#208711yescharacteristic
331C2×C59#208811yescharacteristic
332C2×C59#210011yescharacteristic
333C2×C59#210111yescharacteristic
334C23×C8—591no—
335C23×C8—591no—
336C22×C4⋊C4—21no—
337C22×C4⋊C4—591no—
338C22×C4⋊C4—591no—
339C22×C4⋊C4C2×D5911yescharacteristic
340C22×C4⋊C4C2×D5911yescharacteristic
341C22×C42C2×D5911yescharacteristic
342#389—22no—
343#389—22no—
344C2×#95—21no—
345C2×#95—1181no—
346C2×#95—1181no—
347#340—594no—
348#340—1182no—
349#340—1182no—
350#340—1182no—
351#336—1182no—
352C59#1129311yescharacteristic, complemented, Sylow
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—1181no—
356C23×C4—1181no—
357C23×C4C22⋊D5911yescharacteristic
358C23×C4C22⋊D5911yescharacteristic
359C23×C4C22×D5911yescharacteristic
360C22×C8—592no—
361C22×C8—592no—
362C22×C8—1181no—
363C22×C8—1181no—
364C22×C8—1181no—
365C22×C8—1181no—
366C22×C8—1181no—
367C22×C8—1181no—
368C22×C8—1181no—
369C22×C8—1181no—
370C22×C8—1181no—
371C22×C8—1181no—
372C22×C8—1181no—
373C22×C8—1181no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—592no—
386C2×C4⋊C4—592no—
387C2×C4⋊C4—1181no—
388C2×C4⋊C4—1181no—
389C2×C4⋊C4—1181no—
390C2×C4⋊C4—1181no—
391C2×C4⋊C4—1181no—
392C2×C4⋊C4—1181no—
393C2×C4⋊C4—1181no—
394C2×C4⋊C4—1181no—
395C2×C4⋊C4—1181no—
396C2×C4⋊C4—1181no—
397C2×C4⋊C4Dic11812yes—
398C2×C4⋊C4C4×D5912yes—
399C2×C4⋊C4C22⋊D5912yes—
400C2×C4⋊C4C22⋊D5912yes—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407#95—24no—
408#95—2362no—
409#95—2362no—
410C24C2×C22⋊D5911yescharacteristic
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—1182no—
438C22×C4—1182no—
439C22×C4—2361no—
440C22×C4—2361no—
441C22×C4—2361no—
442C22×C4—2361no—
443C22×C4—2361no—
444C22×C4—2361no—
445C22×C4—2361no—
446C22×C4—2361no—
447C22×C4—2361no—
448C22×C4—2361no—
449C22×C4—2361no—
450C22×C4—2361no—
451C22×C4#1174567012yes—
452C22×C4#1174567212yes—
453C22×C4C2×Dic11811yescharacteristic
454C22×C4C2×C4×D5911yescharacteristic
455C22×C4#1174568511yescharacteristic
456C22×C4#1174568511yescharacteristic
457C22×C4D4×D5911yescharacteristic
458C22×C4#1174568711yescharacteristic
459C22×C4#1174568711yescharacteristic
460C22×C4#1174568711yescharacteristic
461C22×C4Q8×D5911yescharacteristic
462C22×C4#1174568911yescharacteristic
463C22×C4#1174568911yescharacteristic
464C22×C4#1174568911yescharacteristic
465C22×C4C2×C22⋊D5911yescharacteristic
466C22×C4C2×C22⋊D5911yescharacteristic
467C2×C8—1182no—
468C2×C8—1182no—
469C2×C8—1182no—
470C2×C8—1182no—
471C2×C8—1182no—
472C2×C8—1182no—
473C2×C8—2361no—
474C2×C8—2361no—
475C2×C8—2361no—
476C2×C8—2361no—
477C2×C8—2361no—
478C2×C8—2361no—
479C2×C8—2361no—
480C2×C8—2361no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—48no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—1182no—
490C4⋊C4—1182no—
491C4⋊C4—1182no—
492C4⋊C4—1182no—
493C4⋊C4—2361no—
494C4⋊C4—2361no—
495C4⋊C4—2361no—
496C4⋊C4—2361no—
497C4⋊C4Dic59⋊C414yes—
498C42—41no—
499C42—41no—
500C42—41no—
501C42—41no—
502C23C4×C22⋊D5911yescharacteristic
503C23#1427369611yescharacteristic
504C23#1427369911yescharacteristic
505C23#1427370311yescharacteristic
506C23#1427370611yescharacteristic
507C23#1427370811yescharacteristic
508C23#1427371611yescharacteristic
509C23C2×#1174567011yescharacteristic
510C23C2×#1174567211yescharacteristic
511C23#1427374711yescharacteristic
512C23#1427374711yescharacteristic
513C23#1427375211yescharacteristic
514C23#1427375211yescharacteristic
515C23#1427375311yescharacteristic
516C23#1427375811yescharacteristic
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—4721no—
546C2×C4—4721no—
547C2×C4—4721no—
548C2×C4—4721no—
549C2×C4—4721no—
550C2×C4—4721no—
551C2×C4—4721no—
552C2×C4—4721no—
553C2×C4—2362no—
554C2×C4—2362no—
555C2×C4—2362no—
556C2×C4—2362no—
557C2×C4—2362no—
558C2×C4—2362no—
559C2×C4C2×Dic59⋊C411yescharacteristic
560C2×C4#1427368511yescharacteristic
561C2×C4#1427368511yescharacteristic
562C2×C4C4×C22⋊D5911yescharacteristic
563C2×C4#1427368911yescharacteristic
564C2×C4#1427369211yescharacteristic
565C2×C4#1427369811yescharacteristic
566C2×C4#1427369911yescharacteristic
567C2×C4#1427370311yescharacteristic
568C2×C4#1427370311yescharacteristic
569C2×C4#1427370611yescharacteristic
570C2×C4#1427370811yescharacteristic
571C2×C4#1427371011yescharacteristic
572C2×C4#1427371211yescharacteristic
573C2×C4#1427371211yescharacteristic
574C2×C4#1427371411yescharacteristic
575C2×C4#1427371611yescharacteristic
576C2×C4#1427371611yescharacteristic
577C2×C4#1427371711yescharacteristic
578C2×C4#1427371711yescharacteristic
579C2×C4#1427371811yescharacteristic
580C2×C4#1427371811yescharacteristic
581C2×C4#1427371811yescharacteristic
582C2×C4#1427372211yescharacteristic
583C2×C4#1427372211yescharacteristic
584C2×C4#1427372211yescharacteristic
585C2×C4#1427372211yescharacteristic
586C2×C4#1427372611yescharacteristic
587C8—2362no—
588C8—2362no—
589C22#1683727511yescharacteristic
590C22#1683728311yescharacteristic
591C22#1683729211yescharacteristic
592C22#1683731311yescharacteristic
593C22#1683731611yescharacteristic
594C22#1683733511yescharacteristic
595C22#1683734111yescharacteristic
596C22C4×#1174567011yescharacteristic
597C22C4×#1174567211yescharacteristic
598C22#1683750011yescharacteristic
599C22#1683751211yescharacteristic
600C22#1683754711yescharacteristic
601C22#1683754711yescharacteristic
602C22#1683755311yescharacteristic
603C22#1683755811yescharacteristic
604C22#1683762911yescharacteristic
605C22#1683764111yescharacteristic
606C22#1683765011yescharacteristic
607C22#1683765311yescharacteristic
608C22#1683768411yescharacteristic
609C22#1683769211yescharacteristic
610C22#1683769411yescharacteristic
611C22#1683769711yescharacteristic
612C22#1683769911yescharacteristic
613C22#1683769911yescharacteristic
614C22#1683770211yescharacteristic
615C22#1683770911yescharacteristic
616C22#1683771811yescharacteristic
617C22#1683772311yescharacteristic
618C22#1683773511yescharacteristic
619C22#1683774011yescharacteristic
620C22#1683775411yescharacteristic
621C22#1683775911yescharacteristic
622C22#1683776411yescharacteristic
623C22#1683776811yescharacteristic
624C4—42no—
625C4—42no—
626C4—44no—
627C4—82no—
628C4—4722no—
629C4—4722no—
630C4#1683726711yescharacteristic
631C4#1683728311yescharacteristic
632C4#1683729211yescharacteristic
633C4#1683729811yescharacteristic
634C4#1683732811yescharacteristic
635C4#1683733511yescharacteristic
636C4#1683734011yescharacteristic
637C4#1683734111yescharacteristic
638C2#2142235511yescharacteristic
639C2#2142435011yescharacteristic
640C2#2142435711yescharacteristic
641C2#2142467111yescharacteristic
642C2#2142468511yescharacteristic
643C2#2142477111yescharacteristic
644C2#2142479211yescharacteristic
645C2#2142523411yescharacteristic
646C2#2142523911yescharacteristic
647C2#2142528211yescharacteristic
648C2#2142529611yescharacteristic
649C2#2142559211yescharacteristic
650C2#2142559711yescharacteristic
651C2#2142565911yescharacteristic
652C2#2142566411yescharacteristic
subgroupG/H
centerC24C2×C22⋊D59
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#389C2
socle, prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenterC2×#389D59
hypocenterC59#11293
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
17. #16837164C4semidirect
352. C59#11293semidirect

Maximal subgroups

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

subgroupindex
C2×#168371642
C2×#168371572
#214223262
C2×C59×#3892
#1129359