Finite Group Databasebeta

← #28512490

Subgroups — #28512490

Order 15104.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273704C211yesmaximal, characteristic
2C2×#16837306C211yesmaximal, characteristic, complemented
3C2×#16837274C211yesmaximal, characteristic
4C2×C4×C22⋊Dic59C211yesmaximal, characteristic
5C22×C59⋊#95C211yesmaximal, characteristic
6#21422366C211yesmaximal, characteristic, complemented
7#21422362C211yesmaximal, characteristic, complemented
8#21422348C211yesmaximal, characteristic, complemented
9#21422347C211yesmaximal, characteristic, complemented
10#21422330C211yesmaximal, characteristic, complemented
11#21422327C211yesmaximal, characteristic, complemented
12Dic59⋊#95C211yesmaximal, characteristic, complemented
13#21422318C211yesmaximal, characteristic
14#21422318C211yesmaximal, characteristic
15C59×C22⋊#95C211yesmaximal, characteristic
16C23×Dic118C2211yescharacteristic
17C24×Dic59C2211yescharacteristic
18C24×Dic59C2211yescharacteristic
19C2×#14273704—24no—
20C2×#14273704—24no—
21C2×#14273704C418yescomplemented
22C22×C4⋊Dic59C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31#16837306—24no—
32#16837274—24no—
33C4×C22⋊Dic59—24no—
34C2×C59⋊#95—24no—
35C2×C59⋊#95C2211yescharacteristic
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C24×C4×C59C2211yescharacteristic
52C22×C22⋊C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C22×Dic118—22no—
59C22×Dic118—22no—
60C22×Dic118—22no—
61C22×Dic118—22no—
62C22×Dic118—41no—
63C22×Dic118—41no—
64C22×Dic118C2×C414yescomplemented
65C23×Dic59—22no—
66C23×Dic59—22no—
67C23×Dic59—22no—
68C23×Dic59—22no—
69C23×Dic59—22no—
70C23×Dic59—22no—
71C23×Dic59—22no—
72C23×Dic59—22no—
73C23×Dic59—22no—
74C23×Dic59—41no—
75C23×Dic59—41no—
76C23×Dic59—41no—
77C23×Dic59—41no—
78C23×Dic59C2×C414yes—
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C23×Dic59C2311yescharacteristic
85C23×Dic59C2311yescharacteristic
86C23×Dic59C2311yescharacteristic
87#14273704—232no—
88C2×C4⋊Dic59—22no—
89C2×C4⋊Dic59—22no—
90C2×C4⋊Dic59C2×C414yescomplemented
91C2×Dic59⋊C4—22no—
92C2×Dic59⋊C4—22no—
93C2×Dic59⋊C4—22no—
94C2×Dic59⋊C4—22no—
95C2×Dic59⋊C4—22no—
96C2×Dic59⋊C4—22no—
97C2×Dic59⋊C4—22no—
98C2×Dic59⋊C4—22no—
99C2×Dic59⋊C4—41no—
100C2×Dic59⋊C4—41no—
101C2×Dic59⋊C4C2×C414yescomplemented
102C2×Dic59⋊C4C2×C414yescomplemented
103C2×C22⋊Dic59—22no—
104C2×C22⋊Dic59—22no—
105C2×C22⋊Dic59C2×C414yes—
106C2×C22⋊Dic59D414yes—
107C2×C22⋊Dic59D414yes—
108C2×C22⋊Dic59Q814yescomplemented
109C2×C4×Dic59—22no—
110C2×C4×Dic59—22no—
111C2×C4×Dic59—22no—
112C2×C4×Dic59—22no—
113C2×C4×Dic59—41no—
114C2×C4×Dic59—41no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—22no—
119C59⋊#95—22no—
120C59⋊#95—22no—
121C59⋊#95—22no—
122C59⋊#95—22no—
123C59⋊#95—22no—
124C59⋊#95—22no—
125C59⋊#95—22no—
126C59⋊#95—41no—
127C59⋊#95—41no—
128C59⋊#95—41no—
129C59⋊#95—41no—
130C59⋊#95D414yes—
131C25×C59C2311yescharacteristic
132C23×C4×C59—22no—
133C23×C4×C59—22no—
134C23×C4×C59—22no—
135C23×C4×C59—22no—
136C23×C4×C59—41no—
137C23×C4×C59—41no—
138C23×C4×C59Q814yescomplemented
139C23×C4×C59C2311yescharacteristic
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C2×C22⋊C4×C59—22no—
146C2×C22⋊C4×C59—22no—
147C2×C22⋊C4×C59—22no—
148C2×C22⋊C4×C59—22no—
149C2×C22⋊C4×C59—22no—
150C2×C22⋊C4×C59C2×C414yes—
151#95×C59—22no—
152#95×C59—22no—
153#95×C59—41no—
154#95×C59—41no—
155C24×C59—21no—
156C24×C59—21no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59C22×C412yes—
164C24×C59C2×D412yes—
165C24×C59C2×D412yes—
166C24×C59C2×Q812yes—
167C24×C59C2×Q812yes—
168C24×C59#4112yes—
169C24×C59#4112yes—
170C24×C59C2411yescharacteristic
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—28no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—28no—
195C22×C4×C59—21no—
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—21no—
208C22×C4×C59—21no—
209C22×C4×C59—44no—
210C22×C4×C59—44no—
211C22×C4×C59—44no—
212C22×C4×C59—44no—
213C22×C4×C59—44no—
214C22×C4×C59C22×C412yes—
215C22×C4×C59C22×C412yes—
216C22×C4×C59C2×D412yes—
217C22×C4×C59C2×Q812yes—
218C22×C4×C59C2×Q812yes—
219C22×C4×C59#4112yes—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—28no—
233C22×Dic59—28no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—28no—
265C22×Dic59—44no—
266C22×Dic59—44no—
267C22×Dic59—44no—
268C22×Dic59—44no—
269C22×Dic59—44no—
270C22×Dic59—44no—
271C22×Dic59—44no—
272C22×Dic59—44no—
273C22×Dic59—44no—
274C22×Dic59—44no—
275C22×Dic59—44no—
276C22×Dic59C22×C412yes—
277C22×Dic59C22×C412yes—
278C22×Dic59C22×C412yes—
279C22×Dic59C22×C412yes—
280C22×Dic59C2×D412yes—
281C22×Dic59C2×D412yes—
282C22×Dic59C2×D412yes—
283C22×Dic59C2×D412yes—
284C22×Dic59C2×D412yes—
285C22×Dic59C2×D412yes—
286C22×Dic59C2×Q812yes—
287C22×Dic59C2×Q812yes—
288C22×Dic59#4112yes—
289C22×Dic59#4112yes—
290C2×Dic118—28no—
291C2×Dic118—28no—
292C2×Dic118—44no—
293C2×Dic118—44no—
294C2×Dic118—44no—
295C2×Dic118—44no—
296C2×Dic118—44no—
297C22⋊C4×C59—28no—
298C22⋊C4×C59—44no—
299C22⋊Dic59—28no—
300C22⋊Dic59C22⋊C4116yes—
301C4⋊Dic59—28no—
302Dic59⋊C4—28no—
303Dic59⋊C4—28no—
304Dic59⋊C4—44no—
305Dic59⋊C4—44no—
306C4×Dic59—44no—
307C4×Dic59—44no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59—22no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—22no—
325C23×C59—22no—
326C23×C59—22no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—22no—
331C23×C59—22no—
332C23×C59—22no—
333C23×C59—22no—
334C23×C59—22no—
335C23×C59—22no—
336C23×C59C2×C22⋊C414yes—
337C23×C59C4×Q814yes—
338C23×C59C4×Q814yes—
339C23×C59C22⋊Q814yes—
340C23×C59C22⋊Q814yes—
341C23×C59#12414yes—
342C23×C59C4⋊Q814yes—
343C23×C59C23×C411yescharacteristic
344C23×C59C22×D411yescharacteristic
345C23×C59C22×D411yescharacteristic
346C23×C59C22×D411yescharacteristic
347C23×C59C22×Q811yescharacteristic
348C23×C59C22×Q811yescharacteristic
349C23×C59C2×#4111yescharacteristic
350C23×C59C2×#4111yescharacteristic
351C23×C59C2×#4111yescharacteristic
352C23×C59C2×#4111yescharacteristic
353C23×C59C2×#4111yescharacteristic
354C23×C59H(5,𝔽2)11yescharacteristic
355C23×C59H(5,𝔽2)11yescharacteristic
356C23×C59H(5,𝔽2)11yescharacteristic
357C23×C592−1+411yescharacteristic
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—22no—
361C2×C4×C59—22no—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—22no—
365C2×C4×C59—22no—
366C2×C4×C59—22no—
367C2×C4×C59—22no—
368C2×C4×C59—22no—
369C2×C4×C59—22no—
370C2×C4×C59—22no—
371C2×C4×C59—22no—
372C2×C4×C59—22no—
373C2×C4×C59—416no—
374C2×C4×C59—41no—
375C2×C4×C59—41no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59C22⋊Q814yescomplemented
401C2×Dic59—22no—
402C2×Dic59—22no—
403C2×Dic59—22no—
404C2×Dic59—22no—
405C2×Dic59—22no—
406C2×Dic59—22no—
407C2×Dic59—22no—
408C2×Dic59—22no—
409C2×Dic59—22no—
410C2×Dic59—22no—
411C2×Dic59—22no—
412C2×Dic59—22no—
413C2×Dic59—22no—
414C2×Dic59—22no—
415C2×Dic59—22no—
416C2×Dic59—22no—
417C2×Dic59—22no—
418C2×Dic59—22no—
419C2×Dic59—22no—
420C2×Dic59—22no—
421C2×Dic59—22no—
422C2×Dic59—22no—
423C2×Dic59—22no—
424C2×Dic59—22no—
425C2×Dic59—22no—
426C2×Dic59—22no—
427C2×Dic59—22no—
428C2×Dic59—22no—
429C2×Dic59—22no—
430C2×Dic59—22no—
431C2×Dic59—22no—
432C2×Dic59—22no—
433C2×Dic59—22no—
434C2×Dic59—416no—
435C2×Dic59—416no—
436C2×Dic59—41no—
437C2×Dic59—41no—
438C2×Dic59—41no—
439C2×Dic59—41no—
440C2×Dic59—41no—
441C2×Dic59—41no—
442C2×Dic59—41no—
443C2×Dic59—41no—
444C2×Dic59—41no—
445C2×Dic59—41no—
446C2×Dic59—41no—
447C2×Dic59—41no—
448C2×Dic59—41no—
449C2×Dic59—41no—
450C2×Dic59—41no—
451C2×Dic59—41no—
452C2×Dic59—41no—
453C2×Dic59—41no—
454C2×Dic59—41no—
455C2×Dic59—41no—
456C2×Dic59C2×C22⋊C414yes—
457C2×Dic59C2×C22⋊C414yes—
458C2×Dic59C4×D414yes—
459Dic118—416no—
460#14052—591nomaximal, Sylow
461C22×C59—24no—
462C22×C59—24no—
463C22×C59—24no—
464C22×C59—24no—
465C22×C59—24no—
466C22×C59—24no—
467C22×C59—24no—
468C22×C59—24no—
469C22×C59—24no—
470C22×C59—24no—
471C22×C59—24no—
472C22×C59—24no—
473C22×C59—24no—
474C22×C59—24no—
475C22×C59#39118yescomplemented
476C22×C59C22×C22⋊C411yescharacteristic
477C22×C59C2×C4×D411yescharacteristic
478C22×C59C2×C4×Q811yescharacteristic
479C22×C59C2×C4×Q811yescharacteristic
480C22×C59C4×#4111yescharacteristic
481C22×C59#51811yescharacteristic
482C22×C59#52011yescharacteristic
483C22×C59C2×C22⋊Q811yescharacteristic
484C22×C59C2×C22⋊Q811yescharacteristic
485C22×C59C2×C22⋊Q811yescharacteristic
486C22×C59#52511yescharacteristic
487C22×C59C2×#12411yescharacteristic
488C22×C59#52911yescharacteristic
489C22×C59C2×C4⋊Q811yescharacteristic
490C22×C59#53311yescharacteristic
491C22×C59#53811yescharacteristic
492C22×C59#53911yescharacteristic
493C22×C59#54311yescharacteristic
494C22×C59#54411yescharacteristic
495C22×C59D4211yescharacteristic
496C22×C59D4211yescharacteristic
497C22×C59#54611yescharacteristic
498C22×C59#54611yescharacteristic
499C22×C59#54611yescharacteristic
500C22×C59#54611yescharacteristic
501C22×C59#54611yescharacteristic
502C22×C59#54711yescharacteristic
503C22×C59#54711yescharacteristic
504C22×C59D4×Q811yescharacteristic
505C22×C59#55111yescharacteristic
506C22×C59#55111yescharacteristic
507C22×C59#55211yescharacteristic
508C22×C59#55411yescharacteristic
509C22×C59#55411yescharacteristic
510C22×C59#55411yescharacteristic
511C4×C59—24no—
512C4×C59—42no—
513C4×C59—42no—
514C4×C59—42no—
515C4×C59—81no—
516C4×C59—81no—
517Dic59—24no—
518Dic59—24no—
519Dic59—24no—
520Dic59—42no—
521Dic59—42no—
522Dic59—42no—
523Dic59—42no—
524Dic59—42no—
525C22×C22⋊Q8—591no—
526C2×#391—591no—
527C2×#385—591no—
528C2×C4×C22⋊C4—591no—
529C22×#95—591no—
530#1446—591no—
531#1445—591no—
532#1441—591no—
533#1441—591no—
534#1436—591no—
535#1436—591no—
536C4⋊#95—591no—
537C22⋊#95—591no—
538C22⋊#95—591no—
539C22⋊#95D5911yescharacteristic
540C2×C59—28no—
541C2×C59C2×#39111yescharacteristic
542C2×C59C4×C22⋊Q811yescharacteristic
543C2×C59#232911yescharacteristic
544C2×C59D4×C22⋊C411yescharacteristic
545C2×C59#233911yescharacteristic
546C2×C59#236011yescharacteristic
547C2×C59#236811yescharacteristic
548C2×C59#243711yescharacteristic
549C2×C59#243811yescharacteristic
550C2×C59#244011yescharacteristic
551C2×C59#244911yescharacteristic
552C2×C59#245011yescharacteristic
553C2×C59#247211yescharacteristic
554C2×C59#248811yescharacteristic
555C2×C59#254911yescharacteristic
556C23×Q8—591no—
557C24×C4—591no—
558C24×C4—591no—
559C24×C4C2×D5911yescharacteristic
560C2×C22⋊Q8—598no—
561C2×C22⋊Q8—1184no—
562C2×C22⋊Q8—1184no—
563C22×C4⋊C4—591no—
564C22×C4⋊C4—591no—
565C22×C4⋊C4—591no—
566C22×C4⋊C4—591no—
567C22×C4⋊C4—591no—
568C22×C22⋊C4—591no—
569C22×C22⋊C4—591no—
570C22×C22⋊C4C2×D5911yescharacteristic
571C22×C22⋊C4C2×D5911yescharacteristic
572C22×C42—591no—
573C22×C42—591no—
574#391—1184no—
575#385—1184no—
576C4×C22⋊C4—1184no—
577C2×#95—591no—
578C2×#95—591no—
579C2×#95—591no—
580C2×#95—591no—
581C2×#95—591no—
582C2×#95—591no—
583C2×#95—591no—
584C2×#95—591no—
585C2×#95—591no—
586C2×#95—591no—
587C2×#95—591no—
588C2×#95—591no—
589C2×#95—591no—
590C2×#95—591no—
591C2×#95—591no—
592C2×#95—591no—
593C2×#95—1184no—
594C2×#95C2×D5911yescharacteristic
595C2×#95C2×D5911yescharacteristic
596C2×#95C2×D5911yescharacteristic
597C2×#95C2×D5911yescharacteristic
598C59#1405211yescharacteristic, complemented, Sylow
599C25C22×D5911yescharacteristic
600C22×Q8—594no—
601C22×Q8—1182no—
602C22×Q8—1182no—
603C22×Q8—1182no—
604C22×Q8—1182no—
605C22×Q8—2361no—
606C22×Q8—2361no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—41no—
612C23×C4—41no—
613C23×C4—591no—
614C23×C4—591no—
615C23×C4—591no—
616C23×C4—591no—
617C23×C4—591no—
618C23×C4—591no—
619C23×C4—591no—
620C23×C4—591no—
621C23×C4—594no—
622C23×C4—1182no—
623C23×C4—1182no—
624C23×C4—1182no—
625C23×C4—1182no—
626C23×C4—1182no—
627C23×C4—1182no—
628C23×C4—1182no—
629C23×C4—1182no—
630C23×C4—1182no—
631C23×C4—2361no—
632C23×C4—2361no—
633C23×C4—2361no—
634C23×C4—2361no—
635C23×C4Dic11814yescomplemented
636C23×C4C22×D5911yescharacteristic
637C23×C4C22×D5911yescharacteristic
638C23×C4C22×D5911yescharacteristic
639C23×C4C22×D5911yescharacteristic
640C23×C4C22×D5911yescharacteristic
641C23×C4C22×D5911yescharacteristic
642C22⋊Q8—11832no—
643C2×C4⋊C4—594no—
644C2×C4⋊C4—594no—
645C2×C4⋊C4—594no—
646C2×C4⋊C4—1182no—
647C2×C4⋊C4—1182no—
648C2×C4⋊C4—1182no—
649C2×C4⋊C4—1182no—
650C2×C4⋊C4—1182no—
651C2×C4⋊C4—1182no—
652C2×C4⋊C4—1182no—
653C2×C4⋊C4—1182no—
654C2×C4⋊C4—1182no—
655C2×C4⋊C4—1182no—
656C2×C4⋊C4—2361no—
657C2×C4⋊C4—2361no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—594no—
664C2×C22⋊C4—594no—
665C2×C22⋊C4—594no—
666C2×C22⋊C4—594no—
667C2×C22⋊C4—1182no—
668C2×C22⋊C4—1182no—
669C2×C22⋊C4C4×D5914yes—
670C2×C42—1182no—
671C2×C42—1182no—
672C2×C42—1182no—
673C2×C42—1182no—
674C2×C42—2361no—
675C2×C42—2361no—
676#95—22no—
677#95—22no—
678#95—41no—
679#95—41no—
680#95—594no—
681#95—1182no—
682#95—1182no—
683#95—1182no—
684#95—1182no—
685#95—1182no—
686#95—1182no—
687#95—1182no—
688#95—1182no—
689#95—1182no—
690#95—1182no—
691#95—1182no—
692#95—2361no—
693#95—2361no—
694#95—2361no—
695#95—2361no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24C2×Dic11812yes—
705C24C2×C4×D5912yes—
706C24#1174568512yes—
707C24D4×D5912yes—
708C24D4×D5912yes—
709C24#1174568712yes—
710C24Q8×D5912yes—
711C24C23×D5911yescharacteristic
712C2×Q8—1188no—
713C2×Q8—1188no—
714C2×Q8—2364no—
715C2×Q8—2364no—
716C2×Q8—2364no—
717C2×Q8—2364no—
718C2×Q8—2364no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—28no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—28no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—592no—
763C22×C4—592no—
764C22×C4—592no—
765C22×C4—592no—
766C22×C4—592no—
767C22×C4—592no—
768C22×C4—592no—
769C22×C4—592no—
770C22×C4—592no—
771C22×C4—592no—
772C22×C4—592no—
773C22×C4—592no—
774C22×C4—592no—
775C22×C4—592no—
776C22×C4—1188no—
777C22×C4—1181no—
778C22×C4—1181no—
779C22×C4—1181no—
780C22×C4—1181no—
781C22×C4—1181no—
782C22×C4—1181no—
783C22×C4—1181no—
784C22×C4—1181no—
785C22×C4—1181no—
786C22×C4—1181no—
787C22×C4—1181no—
788C22×C4—1181no—
789C22×C4—1188no—
790C22×C4—1188no—
791C22×C4—1181no—
792C22×C4—1181no—
793C22×C4—1181no—
794C22×C4—1181no—
795C22×C4—1181no—
796C22×C4—1181no—
797C22×C4—1181no—
798C22×C4—1181no—
799C22×C4—1181no—
800C22×C4—1181no—
801C22×C4—1181no—
802C22×C4—1181no—
803C22×C4—1181no—
804C22×C4—1181no—
805C22×C4—1181no—
806C22×C4—1181no—
807C22×C4—1181no—
808C22×C4—1181no—
809C22×C4—1181no—
810C22×C4—1181no—
811C22×C4—1181no—
812C22×C4—1181no—
813C22×C4—1181no—
814C22×C4—1181no—
815C22×C4—1181no—
816C22×C4—1181no—
817C22×C4—1181no—
818C22×C4—1181no—
819C22×C4—1181no—
820C22×C4—1181no—
821C22×C4—2364no—
822C22×C4—2364no—
823C22×C4—2364no—
824C22×C4—2364no—
825C22×C4—2364no—
826C22×C4—2364no—
827C22×C4—2364no—
828C22×C4—2364no—
829C22×C4—2364no—
830C22×C4—2364no—
831C22×C4—2364no—
832C22×C4C2×Dic11812yes—
833C22×C4C2×Dic11812yes—
834C22×C4C2×C4×D5912yes—
835C22×C4C2×C4×D5912yes—
836C22×C4D4×D5912yes—
837C22×C4#1174568712yes—
838C4⋊C4—1188no—
839C4⋊C4—1188no—
840C4⋊C4—1188no—
841C4⋊C4—2364no—
842C4⋊C4—2364no—
843C22⋊C4—28no—
844C22⋊C4—44no—
845C22⋊C4—5916no—
846C22⋊C4—1188no—
847C42—2364no—
848C42—2364no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23C22⋊C4×D5914yes—
878C23#1427369214yes—
879C23C4×Dic11814yes—
880C23#1427370414yes—
881C23#1427370514yes—
882C23#1427371314yes—
883C23#1427372614yes—
884C23C22×C4×D5911yescharacteristic
885C23C2×D4×D5911yescharacteristic
886C23C2×D4×D5911yescharacteristic
887C23C2×D4×D5911yescharacteristic
888C23C2×Q8×D5911yescharacteristic
889C23C22×Dic11811yescharacteristic
890C23#41×D5911yescharacteristic
891C23#41×D5911yescharacteristic
892C23C2×#1174568711yescharacteristic
893C23C2×#1174568711yescharacteristic
894C23C2×#1174568511yescharacteristic
895C23#1427377211yescharacteristic
896C23#1427377211yescharacteristic
897C23#1427377311yescharacteristic
898C23#1427377411yescharacteristic
899Q8—23616no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—594no—
943C2×C4—594no—
944C2×C4—594no—
945C2×C4—1182no—
946C2×C4—1182no—
947C2×C4—1182no—
948C2×C4—1182no—
949C2×C4—1182no—
950C2×C4—1182no—
951C2×C4—1182no—
952C2×C4—1182no—
953C2×C4—1182no—
954C2×C4—1182no—
955C2×C4—1182no—
956C2×C4—1182no—
957C2×C4—1182no—
958C2×C4—1182no—
959C2×C4—1182no—
960C2×C4—1182no—
961C2×C4—1182no—
962C2×C4—1182no—
963C2×C4—1182no—
964C2×C4—1182no—
965C2×C4—1182no—
966C2×C4—1182no—
967C2×C4—1182no—
968C2×C4—1182no—
969C2×C4—1182no—
970C2×C4—1182no—
971C2×C4—1182no—
972C2×C4—1182no—
973C2×C4—1182no—
974C2×C4—1182no—
975C2×C4—1182no—
976C2×C4—1182no—
977C2×C4—1182no—
978C2×C4—23616no—
979C2×C4—23616no—
980C2×C4—2361no—
981C2×C4—2361no—
982C2×C4—2361no—
983C2×C4—2361no—
984C2×C4—2361no—
985C2×C4—2361no—
986C2×C4—2361no—
987C2×C4—2361no—
988C2×C4—2361no—
989C2×C4—2361no—
990C2×C4—2361no—
991C2×C4—2361no—
992C2×C4—2361no—
993C2×C4—2361no—
994C2×C4—2361no—
995C2×C4—2361no—
996C2×C4—2361no—
997C2×C4—2361no—
998C2×C4—2361no—
999C2×C4—2361no—
1000C2×C4#1427370414yescomplemented
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22#1683730618yescomplemented
1016C22C2×C22⋊C4×D5911yescharacteristic
1017C22C4×D4×D5911yescharacteristic
1018C22C2×#1427369211yescharacteristic
1019C22C2×C4×Dic11811yescharacteristic
1020C22C4×#1174568711yescharacteristic
1021C22#1683787411yescharacteristic
1022C22#1683788111yescharacteristic
1023C22C2×#1427370411yescharacteristic
1024C22C2×#1427370411yescharacteristic
1025C22C2×#1427370511yescharacteristic
1026C22#1683791111yescharacteristic
1027C22C2×#1427371311yescharacteristic
1028C22#1683793211yescharacteristic
1029C22C2×#1427372611yescharacteristic
1030C22#1683795511yescharacteristic
1031C22#1683798511yescharacteristic
1032C22#1683799411yescharacteristic
1033C22#1683802811yescharacteristic
1034C22#1683803011yescharacteristic
1035C22#1683803411yescharacteristic
1036C22#1683803611yescharacteristic
1037C22#1683803911yescharacteristic
1038C22#1683803911yescharacteristic
1039C22#1683804111yescharacteristic
1040C22#1683804111yescharacteristic
1041C22#1683804411yescharacteristic
1042C22#1683805011yescharacteristic
1043C22#1683805211yescharacteristic
1044C22#1683806511yescharacteristic
1045C22#1683807511yescharacteristic
1046C22#1683808311yescharacteristic
1047C22#1683808911yescharacteristic
1048C22#1683810611yescharacteristic
1049C22#1683810611yescharacteristic
1050C22#1683811011yescharacteristic
1051C4—24no—
1052C4—42no—
1053C4—42no—
1054C4—42no—
1055C4—81no—
1056C4—81no—
1057C4—1184no—
1058C4—1184no—
1059C4—1184no—
1060C4—2362no—
1061C4—2362no—
1062C4—2362no—
1063C4—2362no—
1064C4—2362no—
1065C2—28no—
1066C2C2×#1683730611yescharacteristic
1067C2C4×#1427370411yescharacteristic
1068C2#2142682411yescharacteristic
1069C2#2142691411yescharacteristic
1070C2#2142692211yescharacteristic
1071C2#2142709611yescharacteristic
1072C2#2142717711yescharacteristic
1073C2#2142776211yescharacteristic
1074C2#2142777411yescharacteristic
1075C2#2142779911yescharacteristic
1076C2#2142790711yescharacteristic
1077C2#2142792211yescharacteristic
1078C2#2142822411yescharacteristic
1079C2#2142842411yescharacteristic
1080C2#2142910811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×C22⋊#95C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenterC22⋊#95D59
hypocenterC59#14052
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16837306C2semidirect
6. #21422366C2semidirect
7. #21422362C2semidirect
8. #21422348C2semidirect
9. #21422347C2semidirect
10. #21422330C2semidirect
11. #21422327C2semidirect
12. Dic59⋊#95C2semidirect
21. C2×#14273704C4semidirect
64. C22×Dic118C2×C4semidirect
90. C2×C4⋊Dic59C2×C4semidirect
101. C2×Dic59⋊C4C2×C4semidirect
102. C2×Dic59⋊C4C2×C4semidirect
108. C2×C22⋊Dic59Q8semidirect
138. C23×C4×C59Q8semidirect
400. C2×C4×C59C22⋊Q8semidirect
475. C22×C59#391semidirect
598. C59#14052semidirect
635. C23×C4Dic118semidirect
1000. C2×C4#14273704semidirect
1015. C22#16837306semidirect

Maximal subgroups

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

subgroupindex
C22×#142737042
C2×#168373062
C2×#168372742
C2×C4×C22⋊Dic592
C22×C59⋊#952
#214223662
#214223622
#214223482
#214223472
#214223302
#214223272
Dic59⋊#952
#214223182
C59×C22⋊#952
#1405259