Finite Group Databasebeta

← #28525267

Subgroups — #28525267

Order 15104.

1822 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273726C211yesmaximal, characteristic
2C2×#16837322C212yesmaximal
3C2×#16837300C211yesmaximal, characteristic
4C2×C4×Dic59⋊C4C211yesmaximal, characteristic
5#21422366C212yesmaximal
6#21422359C212yesmaximal
7#21422347C212yesmaximal
8#21422325C211yesmaximal, characteristic
9#21422325C211yesmaximal, characteristic
10#21422325C211yesmaximal, characteristic
11C2×C59×#389C211yesmaximal, characteristic
12C23×Dic118C2212yes—
13C2×#14273726—24no—
14C2×#14273726—24no—
15C2×#14273726—24no—
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2212yes—
19C22×Dic59⋊C4C2212yes—
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×C4×Dic59C2211yescharacteristic
23C22×C4×Dic59C2211yescharacteristic
24#16837322—28no—
25#16837300—24no—
26C4×Dic59⋊C4—24no—
27C2×C59⋊#95C2211yescharacteristic
28C2×C59⋊#95C2211yescharacteristic
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2212yes—
35C2×C59⋊#95C2212yes—
36C22×C4⋊C4×C59C2212yes—
37C22×C4⋊C4×C59C2211yescharacteristic
38C22×C4⋊C4×C59C2211yescharacteristic
39C22×C42×C59C2211yescharacteristic
40C59×#389—24no—
41C2×#95×C59C2212yes—
42C22×Dic118—24no—
43C22×Dic118—24no—
44C22×Dic118—24no—
45C22×Dic118—24no—
46C22×Dic118—24no—
47C22×Dic118—42no—
48C22×Dic118—42no—
49C23×Dic59C2312yes—
50C23×Dic59C2311yescharacteristic
51C23×Dic59C2312yes—
52C23×Dic59C2311yescharacteristic
53C23×Dic59C2311yescharacteristic
54C23×Dic59C2311yescharacteristic
55#14273726—232no—
56C2×C4⋊Dic59—22no—
57C2×C4⋊Dic59—22no—
58C2×C4⋊Dic59—22no—
59C2×C4⋊Dic59—22no—
60C2×C4⋊Dic59D414yes—
61C2×C4⋊Dic59Q814yescomplemented
62C2×Dic59⋊C4—24no—
63C2×Dic59⋊C4—24no—
64C2×Dic59⋊C4—24no—
65C2×Dic59⋊C4—22no—
66C2×Dic59⋊C4—22no—
67C2×Dic59⋊C4—22no—
68C2×Dic59⋊C4—22no—
69C2×Dic59⋊C4—24no—
70C2×Dic59⋊C4—24no—
71C2×Dic59⋊C4—42no—
72C2×Dic59⋊C4D414yes—
73C2×Dic59⋊C4Q814yescomplemented
74C2×C4×Dic59—22no—
75C2×C4×Dic59—22no—
76C2×C4×Dic59—22no—
77C2×C4×Dic59—22no—
78C2×C4×Dic59D414yes—
79C2×C4×Dic59Q814yescomplemented
80C59⋊#95—22no—
81C59⋊#95—22no—
82C59⋊#95—24no—
83C59⋊#95—24no—
84C59⋊#95—24no—
85C59⋊#95—24no—
86C59⋊#95—24no—
87C59⋊#95—42no—
88C59⋊#95—42no—
89C23×C4×C59C2312yes—
90C23×C4×C59C2311yescharacteristic
91C23×C4×C59C2311yescharacteristic
92C23×C4×C59C2312yes—
93C23×C4×C59C2311yescharacteristic
94C2×C4⋊C4×C59—22no—
95C2×C4⋊C4×C59—22no—
96C2×C4⋊C4×C59—22no—
97C2×C4⋊C4×C59—22no—
98C2×C4⋊C4×C59—24no—
99C2×C4⋊C4×C59—24no—
100C2×C4⋊C4×C59—42no—
101C2×C4⋊C4×C59D414yes—
102C2×C4⋊C4×C59Q814yescomplemented
103C2×C42×C59—22no—
104C2×C42×C59—22no—
105C2×C42×C59—22no—
106#95×C59—24no—
107C24×C59C2411yescharacteristic
108C22×C4×C59—21no—
109C22×C4×C59—22no—
110C22×C4×C59—21no—
111C22×C4×C59—21no—
112C22×C4×C59—21no—
113C22×C4×C59—21no—
114C22×C4×C59—21no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—22no—
124C22×C4×C59—21no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—22no—
132C22×C4×C59C2×D412yes—
133C22×C4×C59C2×D414yes—
134C22×C4×C59C2×D412yes—
135C22×C4×C59C2×D412yes—
136C22×C4×C59C2×D412yes—
137C22×C4×C59C2×Q814yes—
138C22×C4×C59C2×Q812yes—
139C22×C4×C59C2×Q812yes—
140C22×C4×C59C2×Q812yes—
141C22×C4×C59C2×Q812yes—
142C22×C4×C59#4112yes—
143C22×Dic59—21no—
144C22×Dic59—21no—
145C22×Dic59—21no—
146C22×Dic59—21no—
147C22×Dic59—21no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C22×Dic59—21no—
151C22×Dic59—21no—
152C22×Dic59—21no—
153C22×Dic59—21no—
154C22×Dic59—21no—
155C22×Dic59—21no—
156C22×Dic59—22no—
157C22×Dic59—22no—
158C22×Dic59—22no—
159C22×Dic59—22no—
160C22×Dic59—22no—
161C22×Dic59—22no—
162C22×Dic59—21no—
163C22×Dic59—22no—
164C22×Dic59—22no—
165C22×Dic59—21no—
166C22×Dic59—21no—
167C22×Dic59—22no—
168C22×Dic59—22no—
169C22×Dic59—22no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—22no—
173C22×Dic59C2×D414yes—
174C22×Dic59C2×D412yes—
175C22×Dic59C2×D412yes—
176C22×Dic59C2×D412yes—
177C22×Dic59C2×D412yes—
178C22×Dic59C2×Q812yes—
179C22×Dic59C2×Q814yes—
180C22×Dic59C2×Q812yes—
181C22×Dic59C2×Q812yes—
182C22×Dic59C2×Q812yes—
183C22×Dic59#4112yes—
184C22×Dic59#4112yes—
185C2×Dic118—216no—
186C2×Dic118—48no—
187C2×Dic118—48no—
188C2×Dic118—48no—
189C2×Dic118—48no—
190C2×Dic118—48no—
191C2×Dic118—48no—
192C4⋊C4×C59—28no—
193C4⋊C4×C59—28no—
194C4⋊C4×C59—48no—
195C42×C59—44no—
196C4⋊Dic59—28no—
197C4⋊Dic59—28no—
198Dic59⋊C4—216no—
199Dic59⋊C4—28no—
200Dic59⋊C4—28no—
201Dic59⋊C4—48no—
202C4×Dic59—28no—
203C4×Dic59—28no—
204C23×C59C22×D411yescharacteristic
205C23×C59C22×D411yescharacteristic
206C23×C59C22×D411yescharacteristic
207C23×C59C22×D411yescharacteristic
208C23×C59C22×Q811yescharacteristic
209C23×C59C22×Q811yescharacteristic
210C23×C59C22×Q811yescharacteristic
211C23×C59C22×Q811yescharacteristic
212C23×C59C2×#4111yescharacteristic
213C23×C59C2×#4111yescharacteristic
214C23×C59C2×#4111yescharacteristic
215C23×C59H(5,𝔽2)11yescharacteristic
216C23×C59H(5,𝔽2)11yescharacteristic
217C23×C592−1+411yescharacteristic
218C23×C592−1+411yescharacteristic
219C2×C4×C59—24no—
220C2×C4×C59—22no—
221C2×C4×C59—22no—
222C2×C4×C59—24no—
223C2×C4×C59—22no—
224C2×C4×C59—22no—
225C2×C4×C59—24no—
226C2×C4×C59—24no—
227C2×C4×C59—22no—
228C2×C4×C59—22no—
229C2×C4×C59—24no—
230C2×C4×C59—24no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—42no—
234C2×C4×C59—42no—
235C2×C4×C59—42no—
236C2×C4×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59—42no—
239C2×C4×C59—42no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—41no—
243C2×C4×C59—41no—
244C2×C4×C59—41no—
245C2×C4×C59—42no—
246C2×C4×C59—41no—
247C2×C4×C59#12014yes—
248C2×C4×C59C22⋊Q814yes—
249C2×C4×C59C22⋊Q814yes—
250C2×C4×C59C22⋊Q814yes—
251C2×C4×C59C4⋊Q814yes—
252C2×C4×C59C4⋊Q814yes—
253C2×C4×C59C4⋊Q814yes—
254C2×Dic59—22no—
255C2×Dic59—22no—
256C2×Dic59—22no—
257C2×Dic59—22no—
258C2×Dic59—22no—
259C2×Dic59—22no—
260C2×Dic59—22no—
261C2×Dic59—22no—
262C2×Dic59—22no—
263C2×Dic59—22no—
264C2×Dic59—22no—
265C2×Dic59—22no—
266C2×Dic59—22no—
267C2×Dic59—22no—
268C2×Dic59—22no—
269C2×Dic59—22no—
270C2×Dic59—22no—
271C2×Dic59—22no—
272C2×Dic59—24no—
273C2×Dic59—22no—
274C2×Dic59—24no—
275C2×Dic59—22no—
276C2×Dic59—22no—
277C2×Dic59—24no—
278C2×Dic59—24no—
279C2×Dic59—24no—
280C2×Dic59—24no—
281C2×Dic59—42no—
282C2×Dic59—42no—
283C2×Dic59—42no—
284C2×Dic59—41no—
285C2×Dic59—41no—
286C2×Dic59—41no—
287C2×Dic59—41no—
288C2×Dic59—42no—
289C2×Dic59—42no—
290C2×Dic59—42no—
291C2×Dic59—42no—
292C2×Dic59—42no—
293C2×Dic59#12114yes—
294C2×Dic59C22⋊Q814yes—
295C2×Dic59C4⋊Q814yescomplemented
296Dic118—432no—
297#15128—591nomaximal, Sylow
298C22×C59C2×#12011yescharacteristic
299C22×C59C2×#12111yescharacteristic
300C22×C59C2×C22⋊Q811yescharacteristic
301C22×C59C2×C22⋊Q811yescharacteristic
302C22×C59C2×C22⋊Q811yescharacteristic
303C22×C59C2×C22⋊Q811yescharacteristic
304C22×C59C2×C4⋊Q811yescharacteristic
305C22×C59C2×C4⋊Q811yescharacteristic
306C22×C59C2×C4⋊Q811yescharacteristic
307C22×C59C2×C4⋊Q811yescharacteristic
308C22×C59#53211yescharacteristic
309C22×C59#53311yescharacteristic
310C22×C59#53311yescharacteristic
311C22×C59#53511yescharacteristic
312C22×C59#53611yescharacteristic
313C22×C59#54211yescharacteristic
314C22×C59#54211yescharacteristic
315C22×C59#54411yescharacteristic
316C22×C59#54411yescharacteristic
317C22×C59D4211yescharacteristic
318C22×C59D4211yescharacteristic
319C22×C59#54611yescharacteristic
320C22×C59#54611yescharacteristic
321C22×C59#54811yescharacteristic
322C22×C59#54811yescharacteristic
323C22×C59D4×Q811yescharacteristic
324C22×C59D4×Q811yescharacteristic
325C22×C59D4×Q811yescharacteristic
326C22×C59D4×Q811yescharacteristic
327C22×C59#55411yescharacteristic
328C22×C59#55411yescharacteristic
329C22×C59#55711yescharacteristic
330C22×C59#55711yescharacteristic
331C22×C59Q8211yescharacteristic
332C22×C59Q8211yescharacteristic
333C4×C59—44no—
334C4×C59—42no—
335C4×C59—42no—
336C4×C59—44no—
337C4×C59#39518yescomplemented
338Dic59—24no—
339Dic59—24no—
340Dic59—24no—
341Dic59—42no—
342Dic59—44no—
343Dic59—44no—
344C22×C4⋊Q8—591no—
345C2×#395—592no—
346C2×#389—591no—
347C2×#389D5911yescharacteristic
348C2×C4×C4⋊C4—591no—
349#1446—592no—
350#1444—592no—
351#1441—592no—
352C4⋊#95—591no—
353C4⋊#95—591no—
354C4⋊#95—591no—
355C2×C59C2×#39511yescharacteristic
356C2×C59#240811yescharacteristic
357C2×C59#240911yescharacteristic
358C2×C59#245111yescharacteristic
359C2×C59#245111yescharacteristic
360C2×C59#245211yescharacteristic
361C2×C59#245211yescharacteristic
362C2×C59#254611yescharacteristic
363C2×C59#255011yescharacteristic
364C2×C59#255011yescharacteristic
365C2×C59#255111yescharacteristic
366C2×C59#255111yescharacteristic
367C2×C59#256711yescharacteristic
368C2×C59#262811yescharacteristic
369C2×C59#285711yescharacteristic
370C23×Q8—592no—
371C2×C4⋊Q8—1184no—
372C2×C4⋊Q8—1184no—
373C2×C4⋊Q8—1184no—
374C22×C4⋊C4—591no—
375C22×C4⋊C4—591no—
376C22×C4⋊C4—591no—
377C22×C4⋊C4—591no—
378C22×C4⋊C4—592no—
379C22×C4⋊C4—592no—
380C22×C4⋊C4C2×D5912yes—
381C22×C4⋊C4C2×D5911yescharacteristic
382C22×C4⋊C4C2×D5911yescharacteristic
383C22×C42—591no—
384C22×C42—591no—
385C22×C42C2×D5911yescharacteristic
386#395—1188no—
387#389—24no—
388#389—1184no—
389C4×C4⋊C4—1184no—
390C2×#95—592no—
391C2×#95—592no—
392C2×#95—592no—
393C2×#95—592no—
394C2×#95—592no—
395C2×#95—591no—
396C2×#95—591no—
397C2×#95—592no—
398C2×#95—592no—
399C2×#95C2×D5912yes—
400C59#1512811yescharacteristic, complemented, Sylow
401C22×Q8—1184no—
402C22×Q8—1184no—
403C22×Q8—1184no—
404C22×Q8—1184no—
405C22×Q8—1184no—
406C22×Q8—2362no—
407C22×Q8—2362no—
408C23×C4—591no—
409C23×C4—591no—
410C23×C4—591no—
411C23×C4—592no—
412C23×C4—592no—
413C23×C4—591no—
414C23×C4C22×D5912yes—
415C23×C4C22×D5911yescharacteristic
416C23×C4C22×D5911yescharacteristic
417C23×C4C22×D5912yes—
418C23×C4C22×D5911yescharacteristic
419C4⋊Q8—11832no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—594no—
428C2×C4⋊C4—594no—
429C2×C4⋊C4—594no—
430C2×C4⋊C4—594no—
431C2×C4⋊C4—1184no—
432C2×C4⋊C4—1184no—
433C2×C4⋊C4—1182no—
434C2×C4⋊C4—1182no—
435C2×C4⋊C4—1182no—
436C2×C4⋊C4—1182no—
437C2×C4⋊C4—1182no—
438C2×C4⋊C4—1182no—
439C2×C4⋊C4—1182no—
440C2×C4⋊C4—1184no—
441C2×C4⋊C4—1182no—
442C2×C4⋊C4—1184no—
443C2×C4⋊C4—1184no—
444C2×C4⋊C4—2362no—
445C2×C4⋊C4Dic11814yescomplemented
446C2×C4⋊C4C22⋊D5914yes—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—594no—
451C2×C42—594no—
452C2×C42—1182no—
453C2×C42—1182no—
454C2×C42—1182no—
455C2×C42—1182no—
456#95—24no—
457#95—1184no—
458#95—1182no—
459#95—1182no—
460#95—1184no—
461#95—1184no—
462#95—1184no—
463#95—1184no—
464#95—2362no—
465#95—2362no—
466C24C23×D5911yescharacteristic
467C2×Q8—11816no—
468C2×Q8—2368no—
469C2×Q8—2368no—
470C2×Q8—2368no—
471C2×Q8—2368no—
472C2×Q8—2368no—
473C2×Q8—2368no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—592no—
499C22×C4—592no—
500C22×C4—592no—
501C22×C4—592no—
502C22×C4—592no—
503C22×C4—592no—
504C22×C4—592no—
505C22×C4—592no—
506C22×C4—592no—
507C22×C4—594no—
508C22×C4—592no—
509C22×C4—594no—
510C22×C4—1181no—
511C22×C4—1181no—
512C22×C4—1181no—
513C22×C4—1181no—
514C22×C4—1181no—
515C22×C4—1181no—
516C22×C4—1181no—
517C22×C4—1181no—
518C22×C4—1181no—
519C22×C4—1181no—
520C22×C4—1181no—
521C22×C4—1181no—
522C22×C4—1181no—
523C22×C4—1182no—
524C22×C4—1182no—
525C22×C4—1182no—
526C22×C4—1182no—
527C22×C4—1182no—
528C22×C4—1182no—
529C22×C4—1182no—
530C22×C4—1181no—
531C22×C4—1182no—
532C22×C4—1181no—
533C22×C4—1182no—
534C22×C4—1181no—
535C22×C4—1182no—
536C22×C4—1182no—
537C22×C4—1181no—
538C22×C4—1181no—
539C22×C4—1182no—
540C22×C4C2×Dic11814yes—
541C22×C4C2×Dic11812yes—
542C22×C4#1174568512yes—
543C22×C4D4×D5912yes—
544C22×C4D4×D5912yes—
545C22×C4D4×D5912yes—
546C22×C4Q8×D5912yes—
547C22×C4Q8×D5912yes—
548C22×C4Q8×D5912yes—
549C22×C4C2×C22⋊D5914yes—
550C22×C4C2×C22⋊D5912yes—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—48no—
554C4⋊C4—1188no—
555C4⋊C4—1188no—
556C4⋊C4—11816no—
557C4⋊C4—1188no—
558C4⋊C4—1188no—
559C4⋊C4—2368no—
560C42—44no—
561C42—1188no—
562C42—1188no—
563C23C2×D4×D5911yescharacteristic
564C23C2×D4×D5911yescharacteristic
565C23C2×D4×D5911yescharacteristic
566C23C22×C22⋊D5911yescharacteristic
567C23C2×Q8×D5911yescharacteristic
568C23C2×Q8×D5911yescharacteristic
569C23C2×Q8×D5911yescharacteristic
570C23C22×Dic11811yescharacteristic
571C23#41×D5911yescharacteristic
572C23#41×D5911yescharacteristic
573C23C2×#1174568511yescharacteristic
574C23#1427377211yescharacteristic
575C23#1427377311yescharacteristic
576C23#1427377411yescharacteristic
577C23#1427377511yescharacteristic
578Q8—23632no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—594no—
608C2×C4—594no—
609C2×C4—594no—
610C2×C4—1182no—
611C2×C4—1182no—
612C2×C4—1182no—
613C2×C4—1182no—
614C2×C4—1182no—
615C2×C4—1182no—
616C2×C4—1182no—
617C2×C4—1182no—
618C2×C4—1182no—
619C2×C4—1182no—
620C2×C4—1182no—
621C2×C4—1182no—
622C2×C4—1182no—
623C2×C4—1182no—
624C2×C4—1182no—
625C2×C4—1182no—
626C2×C4—1182no—
627C2×C4—1182no—
628C2×C4—1182no—
629C2×C4—1184no—
630C2×C4—1182no—
631C2×C4—1182no—
632C2×C4—1184no—
633C2×C4—1184no—
634C2×C4—1184no—
635C2×C4—1184no—
636C2×C4—1184no—
637C2×C4—2362no—
638C2×C4—2362no—
639C2×C4—2361no—
640C2×C4—2362no—
641C2×C4—2361no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4—2362no—
645C2×C4—2362no—
646C2×C4—2362no—
647C2×C4—2362no—
648C2×C4—2362no—
649C2×C4#1427369514yes—
650C2×C4#1427370514yes—
651C2×C4#1427370514yes—
652C2×C4#1427370614yes—
653C2×C4#1427372514yes—
654C2×C4#1427372614yes—
655C2×C4#1427372614yes—
656C22C2×#1427369511yescharacteristic
657C22#121×D5911yescharacteristic
658C22C22⋊Q8×D5911yescharacteristic
659C22C2×#1427370511yescharacteristic
660C22C2×#1427370511yescharacteristic
661C22C2×#1427370611yescharacteristic
662C22C4⋊Q8×D5911yescharacteristic
663C22C2×#1427372511yescharacteristic
664C22C2×#1427372611yescharacteristic
665C22C2×#1427372611yescharacteristic
666C22#1683794911yescharacteristic
667C22#1683795611yescharacteristic
668C22#1683795811yescharacteristic
669C22#1683796811yescharacteristic
670C22#1683797511yescharacteristic
671C22#1683801711yescharacteristic
672C22#1683802411yescharacteristic
673C22#1683802911yescharacteristic
674C22#1683803211yescharacteristic
675C22D4×C22⋊D5911yescharacteristic
676C22#1683803611yescharacteristic
677C22#1683804011yescharacteristic
678C22#1683804911yescharacteristic
679C22#1683805911yescharacteristic
680C22#1683806211yescharacteristic
681C22#1683806511yescharacteristic
682C22Q8×C22⋊D5911yescharacteristic
683C22#1683806711yescharacteristic
684C22D4×Dic11811yescharacteristic
685C22#1683810811yescharacteristic
686C22#1683811111yescharacteristic
687C22#1683812811yescharacteristic
688C22#1683812911yescharacteristic
689C22#1683813211yescharacteristic
690C22Q8×Dic11811yescharacteristic
691C4—42no—
692C4—44no—
693C4—44no—
694C4—42no—
695C4—1184no—
696C4—1184no—
697C4—1184no—
698C4—2362no—
699C4—2364no—
700C4—2364no—
701C4#1683732218yescomplemented
702C2C2×#1683732211yescharacteristic
703C2#2142744811yescharacteristic
704C2#2142745711yescharacteristic
705C2#2142792911yescharacteristic
706C2#2142793611yescharacteristic
707C2#2142794011yescharacteristic
708C2#2142794711yescharacteristic
709C2#2142908311yescharacteristic
710C2#2142911511yescharacteristic
711C2#2142912011yescharacteristic
712C2#2142912311yescharacteristic
713C2#2142912411yescharacteristic
714C2#2142930311yescharacteristic
715C2#2142992311yescharacteristic
716C2#2143244711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutator, socle, prime radical, cosocleC24×C59C24
FittingC2×C59×#389C2
hypercenterC2×#389D59
hypocenterC59#15128
LCSG ▷ C24×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
61. C2×C4⋊Dic59Q8semidirect
73. C2×Dic59⋊C4Q8semidirect
79. C2×C4×Dic59Q8semidirect
102. C2×C4⋊C4×C59Q8semidirect
295. C2×Dic59C4⋊Q8semidirect
337. C4×C59#395semidirect
400. C59#15128semidirect
445. C2×C4⋊C4Dic118semidirect
701. C4#16837322semidirect

Maximal subgroups

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

subgroupindex
C22×#142737262
C2×#168373222
C2×#168373002
C2×C4×Dic59⋊C42
#214223662
#214223592
#214223472
#214223252
C2×C59×#3892
#1512859