Finite Group Databasebeta

← #28496503

Subgroups — #28496503

Order 15104.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273649C211yesmaximal, characteristic
2C22×#14273649C211yesmaximal, characteristic
3C2×#16837304C211yesmaximal, characteristic
4C2×#16837165C211yesmaximal, characteristic, complemented
5C2×#16837165C211yesmaximal, characteristic, complemented
6#21422326C211yesmaximal, characteristic, complemented
7C2×C59×#336C211yesmaximal, characteristic, complemented
8C23×D236C2211yescharacteristic
9C22×C4⋊Dic59C2211yescharacteristic
10C22×C4⋊Dic59C2211yescharacteristic
11C22×C4⋊Dic59C2211yescharacteristic
12C22×(C2×D59)⋊C4—21no—
13C22×(C2×D59)⋊C4—21no—
14C2×#14273649—22no—
15C2×#14273649—22no—
16C2×#14273649—22no—
17C2×#14273649—22no—
18C2×#14273649—22no—
19C2×#14273649C414yescomplemented
20#16837304—22no—
21#16837304—22no—
22C2×C59⋊#95—21no—
23C2×C59⋊#95—21no—
24#16837165—22no—
25#16837165—22no—
26C23×C8×C59C2211yescharacteristic
27C23×C8×C59C2211yescharacteristic
28C22×C42×C59C2211yescharacteristic
29C59×#336—22no—
30C24×D59—21no—
31C22×D236—21no—
32C22×D236—21no—
33C22×D236—21no—
34C22×D236—21no—
35C22×D236—21no—
36C22×D236—21no—
37C22×D236—21no—
38C22×D236—21no—
39C22×D236—21no—
40C22×D236—21no—
41C22×D236—21no—
42C22×D236C2×C412yes—
43C22×D236D412yes—
44C22×D236D412yes—
45C23×Dic59—21no—
46C23×Dic59—21no—
47C23×Dic59—21no—
48C2×C4⋊Dic59—21no—
49C2×C4⋊Dic59—21no—
50C2×C4⋊Dic59—21no—
51C2×C4⋊Dic59—21no—
52C2×C4⋊Dic59—21no—
53C2×C4⋊Dic59—21no—
54C2×C4⋊Dic59—21no—
55C2×C4⋊Dic59—21no—
56C2×C4⋊Dic59—21no—
57C2×C4⋊Dic59—21no—
58C2×C4⋊Dic59—21no—
59C2×C4⋊Dic59—21no—
60C2×C4⋊Dic59—21no—
61C2×C4⋊Dic59—21no—
62C2×C4⋊Dic59—21no—
63C2×C4⋊Dic59C2×C412yes—
64C2×C4⋊Dic59D412yes—
65C2×C4⋊Dic59D412yes—
66C2×(C2×D59)⋊C4—24no—
67C2×(C2×D59)⋊C4—24no—
68C2×(C2×D59)⋊C4—42no—
69C2×(C2×D59)⋊C4—42no—
70C2×(C2×D59)⋊C4—42no—
71C2×(C2×D59)⋊C4—42no—
72#14273649—28no—
73#14273649—28no—
74C59⋊#95—42no—
75C59⋊#95—42no—
76C23×C4×C59D411yescharacteristic
77C23×C4×C59D411yescharacteristic
78C23×C4×C59C2311yescharacteristic
79C22×C8×C59—21no—
80C22×C8×C59—21no—
81C22×C8×C59—21no—
82C22×C8×C59—21no—
83C22×C8×C59—21no—
84C22×C8×C59—21no—
85C22×C8×C59—21no—
86C22×C8×C59—21no—
87C22×C8×C59—21no—
88C22×C8×C59—21no—
89C22×C8×C59—21no—
90C22×C8×C59—21no—
91C22×C8×C59C2×C412yes—
92C22×C8×C59D412yes—
93C2×C42×C59—21no—
94C2×C42×C59—21no—
95C2×C42×C59—21no—
96C2×C42×C59—21no—
97C2×C42×C59—21no—
98C2×C42×C59—21no—
99C24×C59C2×D411yescharacteristic
100C23×D59—22no—
101C23×D59—22no—
102C23×D59—22no—
103C23×D59—41no—
104C23×D59—41no—
105C23×D59—41no—
106C23×D59—41no—
107C23×D59—41no—
108C23×D59—41no—
109C23×D59—41no—
110C23×D59—41no—
111C23×D59—41no—
112C23×D59—41no—
113C23×D59—41no—
114C23×D59—41no—
115C22×C4×C59—21no—
116C22×C4×C59—21no—
117C22×C4×C59—21no—
118C22×C4×C59—21no—
119C22×C4×C59—21no—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59—21no—
126C22×C4×C59—21no—
127C22×C4×C59D812yes—
128C22×C4×C59SD1612yes—
129C22×C4×C59C22×C411yescharacteristic
130C22×C4×C59C2×D411yescharacteristic
131C22×C4×C59C2×D411yescharacteristic
132C22×C4×C59C2×D411yescharacteristic
133C22×C4×C59C2×D411yescharacteristic
134C22×C4×C59C2×D411yescharacteristic
135C22×C4×C59#4111yescharacteristic
136C22×C4×C59#4111yescharacteristic
137C22×C4×C59#4111yescharacteristic
138C22×C4×C59#4111yescharacteristic
139C22×C4×C59#4111yescharacteristic
140C22×C4×C59#4111yescharacteristic
141C22×C4×C59#4111yescharacteristic
142C22×C4×C59#4111yescharacteristic
143C22×Dic59—22no—
144C22×Dic59—22no—
145C22×Dic59—22no—
146C22×Dic59—41no—
147C22×Dic59—41no—
148C22×Dic59—41no—
149C22×Dic59—41no—
150C22×Dic59—41no—
151C22×Dic59—41no—
152C22×Dic59—41no—
153C22×Dic59—41no—
154C22×Dic59—41no—
155C22×Dic59—41no—
156C22×Dic59—41no—
157C22×Dic59—41no—
158C22×Dic59—41no—
159C22×Dic59—41no—
160C22×Dic59—41no—
161C22×Dic59—41no—
162C22×Dic59—41no—
163C22×Dic59—41no—
164C2×D236—22no—
165C2×D236—22no—
166C2×D236—22no—
167C2×D236—22no—
168C2×D236—22no—
169C2×D236—22no—
170C2×D236—22no—
171C2×D236—22no—
172C2×D236—22no—
173C2×D236—22no—
174C2×D236—22no—
175C2×D236—22no—
176C2×D236—22no—
177C2×D236—22no—
178C2×D236—22no—
179C2×D236—41no—
180C2×D236—41no—
181C2×D236—41no—
182C2×D236—41no—
183C2×D236—41no—
184C2×D236—41no—
185C2×D236—41no—
186C2×D236—41no—
187C2×D236—41no—
188C2×D236—41no—
189C2×D236—41no—
190C2×D236—41no—
191C2×D236C22⋊C414yes—
192C2×C8×C59—22no—
193C2×C8×C59—22no—
194C2×C8×C59—22no—
195C2×C8×C59—22no—
196C2×C8×C59—22no—
197C2×C8×C59—22no—
198C2×C8×C59—41no—
199C2×C8×C59—41no—
200C2×C8×C59—41no—
201C2×C8×C59—41no—
202C2×C8×C59—41no—
203C2×C8×C59—41no—
204C2×C8×C59—41no—
205C2×C8×C59—41no—
206C42×C59—41no—
207C42×C59—41no—
208C42×C59—41no—
209C42×C59—41no—
210(C2×D59)⋊C4—48no—
211(C2×D59)⋊C4—48no—
212C4⋊Dic59—22no—
213C4⋊Dic59—22no—
214C4⋊Dic59—22no—
215C4⋊Dic59—22no—
216C4⋊Dic59—22no—
217C4⋊Dic59—22no—
218C4⋊Dic59—41no—
219C4⋊Dic59—41no—
220C4⋊Dic59—41no—
221C4⋊Dic59—41no—
222C4⋊Dic59—41no—
223C4⋊Dic59—41no—
224C23×C59C4×D411yescharacteristic
225C23×C59#12011yescharacteristic
226C23×C59#12111yescharacteristic
227C23×C59#12111yescharacteristic
228C23×C59#12111yescharacteristic
229C23×C59#12311yescharacteristic
230C23×C59#12411yescharacteristic
231C23×C59C2×D811yescharacteristic
232C23×C59C2×SD1611yescharacteristic
233C23×C59#13511yescharacteristic
234C23×C59#13511yescharacteristic
235C23×C59AGL(1,ℤ/8)11yescharacteristic
236C23×C59AGL(1,ℤ/8)11yescharacteristic
237C23×C59AGL(1,ℤ/8)11yescharacteristic
238C23×C59#13711yescharacteristic
239C22×D59—24no—
240C22×D59—42no—
241C22×D59—42no—
242C22×D59—42no—
243C22×D59—42no—
244C22×D59—42no—
245C22×D59—42no—
246C22×D59—42no—
247C22×D59—42no—
248C22×D59—42no—
249C22×D59—42no—
250C22×D59—42no—
251C22×D59—42no—
252C22×D59—42no—
253C22×D59—42no—
254C22×D59—42no—
255C22×D59—42no—
256C22×D59—42no—
257C22×D59—42no—
258C22×D59—81no—
259C22×D59—81no—
260C22×D59—81no—
261C22×D59—81no—
262C22×D59—81no—
263C22×D59—81no—
264C22×D59—81no—
265C22×D59—81no—
266C22×D59—81no—
267C22×D59—81no—
268C22×D59—81no—
269C22×D59—81no—
270C22×D59—81no—
271C22×D59—81no—
272C22×D59—81no—
273C22×D59—81no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59C2×C22⋊C411yescharacteristic
289C2×C4×C59#11711yescharacteristic
290C2×C4×C59#11711yescharacteristic
291C2×C4×C59C4×D411yescharacteristic
292C2×C4×C59C4×D411yescharacteristic
293C2×C4×C59C4×D411yescharacteristic
294C2×C4×C59#12011yescharacteristic
295C2×C4×C59#12111yescharacteristic
296C2×C4×C59#12111yescharacteristic
297C2×C4×C59#12111yescharacteristic
298C2×C4×C59#12111yescharacteristic
299C2×C4×C59#12111yescharacteristic
300C2×C4×C59#12311yescharacteristic
301C2×C4×C59#12311yescharacteristic
302C2×C4×C59#12311yescharacteristic
303C2×C4×C59#12311yescharacteristic
304C2×C4×C59#12311yescharacteristic
305C2×C4×C59#12311yescharacteristic
306C2×C4×C59#12311yescharacteristic
307C2×C4×C59#12311yescharacteristic
308C2×C4×C59#12311yescharacteristic
309C2×C4×C59#12411yescharacteristic
310C2×C4×C59#12411yescharacteristic
311C2×C4×C59#12411yescharacteristic
312C2×C4×C59#12611yescharacteristic
313C2×C4×C59#12611yescharacteristic
314C2×C4×C59#12611yescharacteristic
315C2×C4×C59#12611yescharacteristic
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59—81no—
326C2×Dic59—81no—
327C2×Dic59—81no—
328C2×Dic59—81no—
329C2×Dic59—81no—
330C2×Dic59—81no—
331C2×Dic59—81no—
332C2×Dic59—81no—
333C2×Dic59—81no—
334C2×Dic59—81no—
335C2×Dic59—81no—
336C2×Dic59—81no—
337D236—24no—
338D236—24no—
339D236—42no—
340D236—42no—
341D236—42no—
342D236—42no—
343D236—42no—
344D236—42no—
345C8×C59—42no—
346C8×C59—42no—
347#11189—591nomaximal, Sylow
348C22×C59#38611yescharacteristic
349C22×C59#38811yescharacteristic
350C22×C59#38811yescharacteristic
351C22×C59#39411yescharacteristic
352C22×C59#39411yescharacteristic
353C22×C59#39411yescharacteristic
354C22×C59#39711yescharacteristic
355C22×C59C4×D811yescharacteristic
356C22×C59C4×SD1611yescharacteristic
357C22×C59#44011yescharacteristic
358C22×C59#44211yescharacteristic
359C22×C59#44711yescharacteristic
360C22×C59#44911yescharacteristic
361C22×C59#45011yescharacteristic
362C22×C59#45211yescharacteristic
363C22×C59#45911yescharacteristic
364C22×C59#45911yescharacteristic
365C22×C59#46011yescharacteristic
366C22×C59#46111yescharacteristic
367C22×C59#46311yescharacteristic
368C22×C59#46311yescharacteristic
369C22×C59#46311yescharacteristic
370C22×C59#46411yescharacteristic
371C22×C59#46511yescharacteristic
372C22×C59#46611yescharacteristic
373C22×C59#46811yescharacteristic
374C22×C59#46911yescharacteristic
375C22×C59#48011yescharacteristic
376C22×C59#48111yescharacteristic
377C22×C59#48211yescharacteristic
378C22×C59#48211yescharacteristic
379C22×C59#48611yescharacteristic
380C22×C59#48811yescharacteristic
381C22×C59#48911yescharacteristic
382C22×C59#49011yescharacteristic
383C2×D59—44no—
384C2×D59—44no—
385C2×D59—44no—
386C2×D59—82no—
387C2×D59—82no—
388C2×D59—82no—
389C2×D59—82no—
390C2×D59—82no—
391C2×D59—82no—
392C2×D59—82no—
393C2×D59—82no—
394C2×D59—82no—
395C2×D59—82no—
396C2×D59—82no—
397C2×D59—82no—
398C4×C59—42no—
399C4×C59—42no—
400C4×C59#38111yescharacteristic
401C4×C59#38611yescharacteristic
402C4×C59#38811yescharacteristic
403C4×C59#38811yescharacteristic
404C4×C59#39411yescharacteristic
405C4×C59#39711yescharacteristic
406C4×C59#39711yescharacteristic
407C4×C59#39711yescharacteristic
408Dic59—82no—
409Dic59—82no—
410Dic59—82no—
411C22×#102—591no—
412C22×#102—591no—
413C2×#390—591no—
414C2×#340—591no—
415C2×#340—591no—
416C2×#336D5911yescharacteristic, complemented
417C4⋊#95—591no—
418C2×C59#144011yescharacteristic
419C2×C59#187711yescharacteristic
420C2×C59#187911yescharacteristic
421C2×C59#192511yescharacteristic
422C2×C59#192611yescharacteristic
423C2×C59#193411yescharacteristic
424C2×C59#193611yescharacteristic
425C2×C59#203311yescharacteristic
426C2×C59#203411yescharacteristic
427C2×C59#204111yescharacteristic
428C2×C59#204211yescharacteristic
429C2×C59#205411yescharacteristic
430C2×C59#205511yescharacteristic
431C2×C59#207111yescharacteristic
432C2×C59#207311yescharacteristic
433D59—84no—
434C23×D4—591no—
435C23×C8C2×D5911yescharacteristic
436C23×C8C2×D5911yescharacteristic
437C22×C4⋊C4—591no—
438C22×C4⋊C4—591no—
439C22×C4⋊C4—591no—
440C22×C22⋊C4—1181no—
441C22×C22⋊C4—1181no—
442C22×C42C2×D5911yescharacteristic
443C2×#102—594no—
444C2×#102—1182no—
445C2×#102—1182no—
446C2×#102—1182no—
447C2×#102—1182no—
448C2×#102—1182no—
449#390—1182no—
450#390—1182no—
451C2×#95—1181no—
452C2×#95—1181no—
453#340—1182no—
454#340—1182no—
455#336—22no—
456C59#1118911yescharacteristic, complemented, Sylow
457C25—1181no—
458C22×D4—592no—
459C22×D4—592no—
460C22×D4—592no—
461C22×D4—1181no—
462C22×D4—1181no—
463C22×D4—1181no—
464C22×D4—1181no—
465C22×D4—1181no—
466C22×D4—1181no—
467C22×D4—1181no—
468C22×D4—1181no—
469C22×D4—1181no—
470C22×D4—1181no—
471C22×D4—1181no—
472C23×C4—1181no—
473C23×C4—1181no—
474C23×C4—1181no—
475C23×C4D23611yescharacteristic
476C23×C4D23611yescharacteristic
477C23×C4C22×D5911yescharacteristic
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8C4×D5912yes—
491C22×C8C22⋊D5912yes—
492C2×C4⋊C4—592no—
493C2×C4⋊C4—592no—
494C2×C4⋊C4—592no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C22⋊C4—1184no—
511C2×C22⋊C4—1184no—
512C2×C22⋊C4—2362no—
513C2×C22⋊C4—2362no—
514C2×C22⋊C4—2362no—
515C2×C22⋊C4—2362no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—21no—
522#102—1188no—
523#102—1188no—
524#95—2362no—
525#95—2362no—
526C24—1182no—
527C24—1182no—
528C24—1182no—
529C24—2361no—
530C24—2361no—
531C24—2361no—
532C24—2361no—
533C24—2361no—
534C24—2361no—
535C24—2361no—
536C24—2361no—
537C24—2361no—
538C24—2361no—
539C24—2361no—
540C24—2361no—
541C24C2×D23611yescharacteristic
542C2×D4—594no—
543C2×D4—1182no—
544C2×D4—1182no—
545C2×D4—1182no—
546C2×D4—1182no—
547C2×D4—1182no—
548C2×D4—1182no—
549C2×D4—1182no—
550C2×D4—1182no—
551C2×D4—1182no—
552C2×D4—1182no—
553C2×D4—1182no—
554C2×D4—1182no—
555C2×D4—1182no—
556C2×D4—1182no—
557C2×D4—1182no—
558C2×D4—2361no—
559C2×D4—2361no—
560C2×D4—2361no—
561C2×D4—2361no—
562C2×D4—2361no—
563C2×D4—2361no—
564C2×D4—2361no—
565C2×D4—2361no—
566C2×D4—2361no—
567C2×D4—2361no—
568C2×D4—2361no—
569C2×D4—2361no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—1182no—
583C22×C4—1182no—
584C22×C4—1182no—
585C22×C4—2361no—
586C22×C4—2361no—
587C22×C4—2361no—
588C22×C4—2361no—
589C22×C4—2361no—
590C22×C4—2361no—
591C22×C4—2361no—
592C22×C4—2361no—
593C22×C4—2361no—
594C22×C4—2361no—
595C22×C4—2361no—
596C22×C4—2361no—
597C22×C4—2361no—
598C22×C4—2361no—
599C22×C4—2361no—
600C22×C4—2361no—
601C22×C4—2361no—
602C22×C4—2361no—
603C22×C4#1174566012yes—
604C22×C4D47212yes—
605C22×C4C2×C4×D5911yescharacteristic
606C22×C4#1174568511yescharacteristic
607C22×C4#1174568511yescharacteristic
608C22×C4#1174568511yescharacteristic
609C22×C4#1174568511yescharacteristic
610C22×C4D4×D5911yescharacteristic
611C22×C4D4×D5911yescharacteristic
612C22×C4D4×D5911yescharacteristic
613C22×C4D4×D5911yescharacteristic
614C22×C4#1174568711yescharacteristic
615C22×C4#1174568711yescharacteristic
616C22×C4#1174568911yescharacteristic
617C22×C4#1174568911yescharacteristic
618C22×C4C2×C22⋊D5911yescharacteristic
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C4⋊C4—1182no—
634C4⋊C4—1182no—
635C4⋊C4—1182no—
636C4⋊C4—1182no—
637C4⋊C4—1182no—
638C4⋊C4—1182no—
639C4⋊C4—2361no—
640C4⋊C4—2361no—
641C4⋊C4—2361no—
642C4⋊C4—2361no—
643C4⋊C4—2361no—
644C4⋊C4—2361no—
645C22⋊C4—2368no—
646C22⋊C4—2368no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C23—1184no—
652C23—4721no—
653C23—4721no—
654C23—4721no—
655C23—4721no—
656C23—4721no—
657C23—4721no—
658C23—4721no—
659C23—4721no—
660C23—4721no—
661C23—4721no—
662C23—4721no—
663C23—4721no—
664C23—4721no—
665C23—4721no—
666C23—4721no—
667C23—4721no—
668C23—2362no—
669C23—2362no—
670C23—2362no—
671C23—2362no—
672C23—2362no—
673C23—2362no—
674C23—2362no—
675C23—2362no—
676C23—2362no—
677C23—2362no—
678C23—2362no—
679C23—2362no—
680C23—2362no—
681C23—2362no—
682C23—2362no—
683C23—2362no—
684C23—2362no—
685C23—2362no—
686C23C4×D23611yescharacteristic
687C23#1427369711yescharacteristic
688C23#1427370111yescharacteristic
689C23#1427370211yescharacteristic
690C23#1427370211yescharacteristic
691C23#1427371111yescharacteristic
692C23#1427371511yescharacteristic
693C23C2×D47211yescharacteristic
694C23C2×#1174566011yescharacteristic
695C23#1427374911yescharacteristic
696C23#1427374911yescharacteristic
697C23#1427375511yescharacteristic
698C23#1427375511yescharacteristic
699C23#1427375511yescharacteristic
700C23#1427376011yescharacteristic
701D4—1184no—
702D4—1184no—
703D4—2362no—
704D4—2362no—
705D4—2362no—
706D4—2362no—
707D4—2362no—
708D4—2362no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—4721no—
724C2×C4—4721no—
725C2×C4—4721no—
726C2×C4—4721no—
727C2×C4—4721no—
728C2×C4—4721no—
729C2×C4—4721no—
730C2×C4—4721no—
731C2×C4—4721no—
732C2×C4—4721no—
733C2×C4—4721no—
734C2×C4—4721no—
735C2×C4—2362no—
736C2×C4—2362no—
737C2×C4—2362no—
738C2×C4—2362no—
739C2×C4—2362no—
740C2×C4—2362no—
741C2×C4—2362no—
742C2×C4—2362no—
743C2×C4—2362no—
744C2×C4C22⋊C4×D5911yescharacteristic
745C2×C4#1427368411yescharacteristic
746C2×C4#1427368511yescharacteristic
747C2×C4(C22⋊D59)⋊C411yescharacteristic
748C2×C4C4×C22⋊D5911yescharacteristic
749C2×C4#1427368911yescharacteristic
750C2×C4#1427369511yescharacteristic
751C2×C4#1427369811yescharacteristic
752C2×C4#1427369911yescharacteristic
753C2×C4#1427370011yescharacteristic
754C2×C4#1427370011yescharacteristic
755C2×C4#1427370011yescharacteristic
756C2×C4#1427370911yescharacteristic
757C2×C4#1427370911yescharacteristic
758C2×C4#1427370911yescharacteristic
759C2×C4#1427371011yescharacteristic
760C2×C4#1427371211yescharacteristic
761C2×C4#1427371211yescharacteristic
762C2×C4#1427371211yescharacteristic
763C2×C4#1427371211yescharacteristic
764C2×C4#1427371211yescharacteristic
765C2×C4#1427371311yescharacteristic
766C2×C4#1427371311yescharacteristic
767C2×C4#1427371611yescharacteristic
768C2×C4#1427372111yescharacteristic
769C2×C4#1427372211yescharacteristic
770C2×C4#1427372211yescharacteristic
771C2×C4#1427372211yescharacteristic
772C8—42no—
773C8—42no—
774C22—4722no—
775C22—4722no—
776C22—4722no—
777C22—4722no—
778C22—4722no—
779C22—4722no—
780C22—4722no—
781C22—4722no—
782C22—4722no—
783C22—4722no—
784C22—4722no—
785C22—4722no—
786C22—2364no—
787C22—2364no—
788C22—2364no—
789C22#1683728011yescharacteristic
790C22#1683729311yescharacteristic
791C22#1683729411yescharacteristic
792C22#1683731811yescharacteristic
793C22#1683731911yescharacteristic
794C22#1683732011yescharacteristic
795C22#1683732911yescharacteristic
796C22C4×D47211yescharacteristic
797C22C4×#1174566011yescharacteristic
798C22#1683750411yescharacteristic
799C22#1683751511yescharacteristic
800C22#1683753811yescharacteristic
801C22#1683754911yescharacteristic
802C22#1683755511yescharacteristic
803C22#1683756611yescharacteristic
804C22#1683759811yescharacteristic
805C22#1683759811yescharacteristic
806C22#1683760311yescharacteristic
807C22#1683760811yescharacteristic
808C22#1683761811yescharacteristic
809C22#1683761811yescharacteristic
810C22#1683761811yescharacteristic
811C22#1683762511yescharacteristic
812C22#1683763111yescharacteristic
813C22#1683763811yescharacteristic
814C22#1683764811yescharacteristic
815C22#1683765511yescharacteristic
816C22#1683771611yescharacteristic
817C22#1683772111yescharacteristic
818C22#1683772711yescharacteristic
819C22#1683772711yescharacteristic
820C22#1683774911yescharacteristic
821C22#1683775711yescharacteristic
822C22#1683776211yescharacteristic
823C22#1683776711yescharacteristic
824C4—42no—
825C4—42no—
826C4—4722no—
827C4—4722no—
828C4—4722no—
829C4#1683726411yescharacteristic
830C4#1683727811yescharacteristic
831C4#1683729111yescharacteristic
832C4#1683729211yescharacteristic
833C4#1683731711yescharacteristic
834C4#1683732811yescharacteristic
835C4#1683733111yescharacteristic
836C4#1683733111yescharacteristic
837C2—4724no—
838C2#2142234411yescharacteristic
839C2#2142442911yescharacteristic
840C2#2142444311yescharacteristic
841C2#2142471711yescharacteristic
842C2#2142472411yescharacteristic
843C2#2142477911yescharacteristic
844C2#2142479311yescharacteristic
845C2#2142527911yescharacteristic
846C2#2142528611yescharacteristic
847C2#2142533111yescharacteristic
848C2#2142533811yescharacteristic
849C2#2142540711yescharacteristic
850C2#2142541411yescharacteristic
851C2#2142550111yescharacteristic
852C2#2142551111yescharacteristic
subgroupG/H
centerC24C2×D236
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#336C2
socleC24×C59C2×D4
prime radicalC23×D236C22
cosocleC23×C4×C59C23
hypercenterC2×#336D59
hypocenterC59#11189
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. C2×#16837165C2semidirect
5. C2×#16837165C2semidirect
6. #21422326C2semidirect
7. C2×C59×#336C2semidirect
19. C2×#14273649C4semidirect
416. C2×#336D59semidirect
456. C59#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#142736492
C2×#168373042
C2×#168371652
#214223262
C2×C59×#3362
#1118959