Finite Group Databasebeta

← #28520605

Subgroups — #28520605

Order 15104.

2242 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273704C211yesmaximal, characteristic
2C2×#16837323C211yesmaximal, characteristic, complemented
3C2×#16837277C211yesmaximal, characteristic
4C2×#16837262C211yesmaximal, characteristic
5C2×#16837260C211yesmaximal, characteristic
6C22×C59⋊#95C211yesmaximal, characteristic
7#21422366C211yesmaximal, characteristic, complemented
8#21422361C211yesmaximal, characteristic, complemented
9#21422360C211yesmaximal, characteristic, complemented
10#21422360C211yesmaximal, characteristic, complemented
11#21422350C211yesmaximal, characteristic, complemented
12#21422348C211yesmaximal, characteristic, complemented
13#21422348C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic
15C59×C22⋊#95C211yesmaximal, characteristic
16C23×Dic118C2211yescharacteristic
17C24×Dic59C2211yescharacteristic
18C24×Dic59C2211yescharacteristic
19C2×#14273704—24no—
20C2×#14273704—24no—
21C2×#14273704—24no—
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×C4⋊Dic59C2211yescharacteristic
26C22×C4⋊Dic59C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×C22⋊Dic59C2211yescharacteristic
32C22×C22⋊Dic59C2211yescharacteristic
33#16837323—24no—
34#16837277—24no—
35#16837262—24no—
36#16837260—24no—
37C2×C59⋊#95—24no—
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
51C2×C59⋊#95C2211yescharacteristic
52C24×C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C22×C22⋊C4×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C2×#95×C59C2211yescharacteristic
59C22×Dic118—22no—
60C22×Dic118—22no—
61C22×Dic118—22no—
62C22×Dic118—22no—
63C22×Dic118—22no—
64C22×Dic118—41no—
65C22×Dic118—41no—
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×Dic59D414yes—
79C23×Dic59Q814yescomplemented
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C23×Dic59C2311yescharacteristic
85C23×Dic59C2311yescharacteristic
86C23×Dic59C2311yescharacteristic
87C23×Dic59C2311yescharacteristic
88#14273704—232no—
89C2×C4⋊Dic59—22no—
90C2×C4⋊Dic59—22no—
91C2×C4⋊Dic59—22no—
92C2×C4⋊Dic59—22no—
93C2×C4⋊Dic59—22no—
94C2×C4⋊Dic59—22no—
95C2×C4⋊Dic59—22no—
96C2×C4⋊Dic59—22no—
97C2×C4⋊Dic59—22no—
98C2×C4⋊Dic59—22no—
99C2×C4⋊Dic59—22no—
100C2×C4⋊Dic59—41no—
101C2×C4⋊Dic59—41no—
102C2×C4⋊Dic59—41no—
103C2×C4⋊Dic59—41no—
104C2×Dic59⋊C4—22no—
105C2×Dic59⋊C4—22no—
106C2×Dic59⋊C4—22no—
107C2×Dic59⋊C4—22no—
108C2×Dic59⋊C4—22no—
109C2×Dic59⋊C4—22no—
110C2×Dic59⋊C4—22no—
111C2×Dic59⋊C4—22no—
112C2×Dic59⋊C4—22no—
113C2×Dic59⋊C4—22no—
114C2×Dic59⋊C4—41no—
115C2×Dic59⋊C4—41no—
116C2×C22⋊Dic59—22no—
117C2×C22⋊Dic59—22no—
118C2×C22⋊Dic59—22no—
119C2×C22⋊Dic59—22no—
120C2×C22⋊Dic59—22no—
121C2×C22⋊Dic59D414yes—
122C59⋊#95—22no—
123C59⋊#95—22no—
124C59⋊#95—22no—
125C59⋊#95—22no—
126C59⋊#95—22no—
127C59⋊#95—22no—
128C59⋊#95—22no—
129C59⋊#95—22no—
130C59⋊#95—22no—
131C59⋊#95—22no—
132C59⋊#95—22no—
133C59⋊#95—41no—
134C59⋊#95—41no—
135C59⋊#95D414yes—
136C25×C59C2311yescharacteristic
137C23×C4×C59—22no—
138C23×C4×C59—22no—
139C23×C4×C59—22no—
140C23×C4×C59—22no—
141C23×C4×C59—41no—
142C23×C4×C59—41no—
143C23×C4×C59Q814yescomplemented
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C23×C4×C59C2311yescharacteristic
149C23×C4×C59C2311yescharacteristic
150C2×C22⋊C4×C59—22no—
151C2×C22⋊C4×C59—22no—
152C2×C22⋊C4×C59—22no—
153C2×C22⋊C4×C59—22no—
154C2×C22⋊C4×C59D414yes—
155C2×C22⋊C4×C59Q814yescomplemented
156#95×C59—22no—
157#95×C59—22no—
158#95×C59—41no—
159#95×C59—41no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59C2×D412yes—
169C24×C59C2×D412yes—
170C24×C59C2×D412yes—
171C24×C59C2×Q812yes—
172C24×C59C2×Q812yes—
173C24×C59C2×Q812yes—
174C24×C59#4112yes—
175C24×C59C2411yescharacteristic
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—28no—
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—21no—
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—21no—
210C22×C4×C59—21no—
211C22×C4×C59—28no—
212C22×C4×C59—44no—
213C22×C4×C59—44no—
214C22×C4×C59—44no—
215C22×C4×C59—44no—
216C22×C4×C59—44no—
217C22×C4×C59C2×D412yes—
218C22×C4×C59C2×D412yes—
219C22×C4×C59C2×D412yes—
220C22×C4×C59C2×Q812yes—
221C22×C4×C59C2×Q812yes—
222C22×C4×C59C2×Q812yes—
223C22×C4×C59C2×Q812yes—
224C22×C4×C59#4112yes—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—28no—
234C22×Dic59—28no—
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—28no—
260C22×Dic59—28no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59—21no—
267C22×Dic59—21no—
268C22×Dic59—21no—
269C22×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—44no—
276C22×Dic59—44no—
277C22×Dic59—44no—
278C22×Dic59—44no—
279C22×Dic59—44no—
280C22×Dic59—44no—
281C22×Dic59—44no—
282C22×Dic59—44no—
283C22×Dic59—44no—
284C22×Dic59—44no—
285C22×Dic59C2×D412yes—
286C22×Dic59C2×D412yes—
287C22×Dic59C2×D412yes—
288C22×Dic59C2×D412yes—
289C22×Dic59C2×D412yes—
290C22×Dic59C2×D412yes—
291C22×Dic59C2×Q812yes—
292C22×Dic59C2×Q812yes—
293C22×Dic59#4112yes—
294C22×Dic59#4112yes—
295C2×Dic118—28no—
296C2×Dic118—44no—
297C2×Dic118—44no—
298C2×Dic118—44no—
299C2×Dic118—44no—
300C2×Dic118—44no—
301C2×Dic118—44no—
302C22⋊C4×C59—28no—
303C22⋊C4×C59—28no—
304C22⋊Dic59—28no—
305C22⋊Dic59—44no—
306C4⋊Dic59—28no—
307C4⋊Dic59—44no—
308C4⋊Dic59—44no—
309C4⋊Dic59—44no—
310C4⋊Dic59—44no—
311Dic59⋊C4—28no—
312Dic59⋊C4—28no—
313Dic59⋊C4—44no—
314Dic59⋊C4—44no—
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×C59—22no—
337C23×C59—22no—
338C23×C59—22no—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—22no—
343C23×C59#12014yes—
344C23×C59C22⋊Q814yes—
345C23×C59C22⋊Q814yes—
346C23×C59C22⋊Q814yes—
347C23×C59C4⋊Q814yes—
348C23×C59C4⋊Q814yes—
349C23×C59C4⋊Q814yes—
350C23×C59C22×D411yescharacteristic
351C23×C59C22×D411yescharacteristic
352C23×C59C22×D411yescharacteristic
353C23×C59C22×D411yescharacteristic
354C23×C59C22×Q811yescharacteristic
355C23×C59C22×Q811yescharacteristic
356C23×C59C22×Q811yescharacteristic
357C23×C59C2×#4111yescharacteristic
358C23×C59C2×#4111yescharacteristic
359C23×C59C2×#4111yescharacteristic
360C23×C59C2×#4111yescharacteristic
361C23×C59H(5,𝔽2)11yescharacteristic
362C23×C59H(5,𝔽2)11yescharacteristic
363C23×C59H(5,𝔽2)11yescharacteristic
364C23×C592−1+411yescharacteristic
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—22no—
374C2×C4×C59—22no—
375C2×C4×C59—22no—
376C2×C4×C59—22no—
377C2×C4×C59—22no—
378C2×C4×C59—22no—
379C2×C4×C59—22no—
380C2×C4×C59—22no—
381C2×C4×C59—22no—
382C2×C4×C59—22no—
383C2×C4×C59—22no—
384C2×C4×C59—22no—
385C2×C4×C59—22no—
386C2×C4×C59—416no—
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×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59C22⋊Q814yescomplemented
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—416no—
433C2×Dic59—416no—
434C2×Dic59—41no—
435C2×Dic59—41no—
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×Dic59—41no—
457C2×Dic59—41no—
458C2×Dic59—41no—
459C2×Dic59—41no—
460C2×Dic59—41no—
461C2×Dic59—41no—
462C2×Dic59—41no—
463C2×Dic59—41no—
464C2×Dic59#12114yes—
465C2×Dic59C22⋊Q814yescomplemented
466Dic118—416no—
467#14758—591nomaximal, Sylow
468C22×C59—24no—
469C22×C59—24no—
470C22×C59—24no—
471C22×C59—24no—
472C22×C59—24no—
473C22×C59—24no—
474C22×C59—24no—
475C22×C59—24no—
476C22×C59—24no—
477C22×C59—24no—
478C22×C59—24no—
479C22×C59—24no—
480C22×C59—24no—
481C22×C59—24no—
482C22×C59#39518yescomplemented
483C22×C59C2×#12011yescharacteristic
484C22×C59C2×#12111yescharacteristic
485C22×C59C2×C22⋊Q811yescharacteristic
486C22×C59C2×C22⋊Q811yescharacteristic
487C22×C59C2×C22⋊Q811yescharacteristic
488C22×C59C2×C22⋊Q811yescharacteristic
489C22×C59C2×C22⋊Q811yescharacteristic
490C22×C59C2×C4⋊Q811yescharacteristic
491C22×C59C2×C4⋊Q811yescharacteristic
492C22×C59C2×C4⋊Q811yescharacteristic
493C22×C59#53211yescharacteristic
494C22×C59#53311yescharacteristic
495C22×C59#53311yescharacteristic
496C22×C59#53411yescharacteristic
497C22×C59#53711yescharacteristic
498C22×C59#54311yescharacteristic
499C22×C59#54311yescharacteristic
500C22×C59#54411yescharacteristic
501C22×C59#54411yescharacteristic
502C22×C59D4211yescharacteristic
503C22×C59D4211yescharacteristic
504C22×C59#54611yescharacteristic
505C22×C59#54611yescharacteristic
506C22×C59#54611yescharacteristic
507C22×C59#54611yescharacteristic
508C22×C59#54611yescharacteristic
509C22×C59#54711yescharacteristic
510C22×C59#54711yescharacteristic
511C22×C59D4×Q811yescharacteristic
512C22×C59#55111yescharacteristic
513C22×C59#55111yescharacteristic
514C22×C59#55211yescharacteristic
515C22×C59#55411yescharacteristic
516C22×C59#55411yescharacteristic
517C22×C59#55411yescharacteristic
518C4×C59—24no—
519C4×C59—42no—
520C4×C59—42no—
521C4×C59—42no—
522C4×C59—42no—
523C4×C59—42no—
524Dic59—24no—
525Dic59—24no—
526Dic59—42no—
527Dic59—42no—
528Dic59—42no—
529Dic59—42no—
530Dic59—81no—
531Dic59—81no—
532C22×C22⋊Q8—591no—
533C2×#395—591no—
534C2×#385—591no—
535C2×#380—591no—
536C2×#380—591no—
537C22×#95—591no—
538#1446—591no—
539#1444—591no—
540#1444—591no—
541#1444—591no—
542#1441—591no—
543#1441—591no—
544#1441—591no—
545C22⋊#95—591no—
546C22⋊#95D5911yescharacteristic
547C2×C59—28no—
548C2×C59C2×#39511yescharacteristic
549C2×C59#241011yescharacteristic
550C2×C59#241711yescharacteristic
551C2×C59#243011yescharacteristic
552C2×C59#243711yescharacteristic
553C2×C59#243711yescharacteristic
554C2×C59#243811yescharacteristic
555C2×C59#243811yescharacteristic
556C2×C59#244011yescharacteristic
557C2×C59#244011yescharacteristic
558C2×C59#254911yescharacteristic
559C2×C59#254911yescharacteristic
560C2×C59#256411yescharacteristic
561C2×C59#265911yescharacteristic
562C2×C59#285711yescharacteristic
563C23×Q8—591no—
564C24×C4—591no—
565C24×C4—591no—
566C24×C4C2×D5911yescharacteristic
567C2×C22⋊Q8—1184no—
568C2×C22⋊Q8—1184no—
569C2×C22⋊Q8—1184no—
570C22×C4⋊C4—591no—
571C22×C4⋊C4—591no—
572C22×C4⋊C4—591no—
573C22×C4⋊C4—591no—
574C22×C4⋊C4—591no—
575C22×C4⋊C4—591no—
576C22×C4⋊C4—591no—
577C22×C4⋊C4—591no—
578C22×C4⋊C4—591no—
579C22×C22⋊C4—591no—
580C22×C22⋊C4—591no—
581C22×C22⋊C4C2×D5911yescharacteristic
582C22×C22⋊C4C2×D5911yescharacteristic
583#395—1184no—
584#385—1184no—
585#380—1184no—
586#380—1184no—
587C2×#95—591no—
588C2×#95—591no—
589C2×#95—591no—
590C2×#95—591no—
591C2×#95—591no—
592C2×#95—591no—
593C2×#95—591no—
594C2×#95—591no—
595C2×#95—591no—
596C2×#95—591no—
597C2×#95—591no—
598C2×#95—591no—
599C2×#95—591no—
600C2×#95—591no—
601C2×#95—1184no—
602C2×#95C2×D5911yescharacteristic
603C2×#95C2×D5911yescharacteristic
604C2×#95C2×D5911yescharacteristic
605C2×#95C2×D5911yescharacteristic
606C59#1475811yescharacteristic, complemented, Sylow
607C25C22×D5911yescharacteristic
608C22×Q8—1182no—
609C22×Q8—1182no—
610C22×Q8—1182no—
611C22×Q8—1182no—
612C22×Q8—1182no—
613C22×Q8—2361no—
614C22×Q8—2361no—
615C23×C4—22no—
616C23×C4—22no—
617C23×C4—22no—
618C23×C4—22no—
619C23×C4—41no—
620C23×C4—41no—
621C23×C4—591no—
622C23×C4—591no—
623C23×C4—591no—
624C23×C4—591no—
625C23×C4—591no—
626C23×C4—591no—
627C23×C4—594no—
628C23×C4—594no—
629C23×C4—591no—
630C23×C4—591no—
631C23×C4—1182no—
632C23×C4—1182no—
633C23×C4—1182no—
634C23×C4—1182no—
635C23×C4—1182no—
636C23×C4—1182no—
637C23×C4—1182no—
638C23×C4—1182no—
639C23×C4—2361no—
640C23×C4—2361no—
641C23×C4—2361no—
642C23×C4—2361no—
643C23×C4Dic11814yescomplemented
644C23×C4C22×D5911yescharacteristic
645C23×C4C22×D5911yescharacteristic
646C23×C4C22×D5911yescharacteristic
647C23×C4C22×D5911yescharacteristic
648C23×C4C22×D5911yescharacteristic
649C23×C4C22×D5911yescharacteristic
650C22⋊Q8—11832no—
651C2×C4⋊C4—1182no—
652C2×C4⋊C4—1182no—
653C2×C4⋊C4—1182no—
654C2×C4⋊C4—1182no—
655C2×C4⋊C4—1182no—
656C2×C4⋊C4—1182no—
657C2×C4⋊C4—1182no—
658C2×C4⋊C4—1182no—
659C2×C4⋊C4—1182no—
660C2×C4⋊C4—1182no—
661C2×C4⋊C4—1182no—
662C2×C4⋊C4—1182no—
663C2×C4⋊C4—1182no—
664C2×C4⋊C4—1182no—
665C2×C4⋊C4—1182no—
666C2×C4⋊C4—1182no—
667C2×C4⋊C4—1182no—
668C2×C4⋊C4—1182no—
669C2×C4⋊C4—1182no—
670C2×C4⋊C4—1182no—
671C2×C4⋊C4—1182no—
672C2×C4⋊C4—2361no—
673C2×C4⋊C4—2361no—
674C2×C4⋊C4—2361no—
675C2×C4⋊C4—2361no—
676C2×C4⋊C4—2361no—
677C2×C4⋊C4—2361no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—594no—
683C2×C22⋊C4—1182no—
684C2×C22⋊C4—1182no—
685C2×C22⋊C4—1182no—
686C2×C22⋊C4—1182no—
687C2×C22⋊C4—1182no—
688C2×C22⋊C4Dic11814yescomplemented
689C2×C22⋊C4D23614yes—
690#95—22no—
691#95—22no—
692#95—41no—
693#95—41no—
694#95—594no—
695#95—1182no—
696#95—1182no—
697#95—1182no—
698#95—1182no—
699#95—1182no—
700#95—1182no—
701#95—1182no—
702#95—1182no—
703#95—1182no—
704#95—1182no—
705#95—1182no—
706#95—2361no—
707#95—2361no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24C2×Dic11812yes—
717C24C2×Dic11812yes—
718C24C2×D23612yes—
719C24D4×D5912yes—
720C24D4×D5912yes—
721C24#1174568712yes—
722C24Q8×D5912yes—
723C24C23×D5911yescharacteristic
724C2×Q8—1188no—
725C2×Q8—2364no—
726C2×Q8—2364no—
727C2×Q8—2364no—
728C2×Q8—2364no—
729C2×Q8—2364no—
730C2×Q8—2364no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—28no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
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—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—28no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—592no—
773C22×C4—592no—
774C22×C4—592no—
775C22×C4—592no—
776C22×C4—592no—
777C22×C4—592no—
778C22×C4—592no—
779C22×C4—592no—
780C22×C4—592no—
781C22×C4—592no—
782C22×C4—1188no—
783C22×C4—1188no—
784C22×C4—1181no—
785C22×C4—1181no—
786C22×C4—1181no—
787C22×C4—1181no—
788C22×C4—1181no—
789C22×C4—1181no—
790C22×C4—1181no—
791C22×C4—1181no—
792C22×C4—1188no—
793C22×C4—1188no—
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—1181no—
822C22×C4—1181no—
823C22×C4—1181no—
824C22×C4—1181no—
825C22×C4—1181no—
826C22×C4—1181no—
827C22×C4—1181no—
828C22×C4—1181no—
829C22×C4—1181no—
830C22×C4—1181no—
831C22×C4—1181no—
832C22×C4—2364no—
833C22×C4—2364no—
834C22×C4—2364no—
835C22×C4—2364no—
836C22×C4—2364no—
837C22×C4—2364no—
838C22×C4—2364no—
839C22×C4—2364no—
840C22×C4—2364no—
841C22×C4—2364no—
842C22×C4C2×Dic11812yes—
843C22×C4C2×Dic11812yes—
844C22×C4C2×Dic11812yes—
845C22×C4C2×Dic11812yes—
846C22×C4C2×D23612yes—
847C22×C4C2×D23612yes—
848C22×C4D4×D5912yes—
849C22×C4#1174568712yes—
850C4⋊C4—1188no—
851C4⋊C4—1188no—
852C4⋊C4—1188no—
853C4⋊C4—2364no—
854C4⋊C4—2364no—
855C4⋊C4—2364no—
856C4⋊C4—2364no—
857C4⋊C4—2364no—
858C4⋊C4—2364no—
859C22⋊C4—28no—
860C22⋊C4—28no—
861C22⋊C4—1188no—
862C22⋊C4—2364no—
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—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23#1427369714yes—
892C23#1427370414yes—
893C23#1427370414yes—
894C23#1427370714yes—
895C23#1427372614yes—
896C23#1427372614yes—
897C23#1427372714yes—
898C23C2×D4×D5911yescharacteristic
899C23C2×D4×D5911yescharacteristic
900C23C2×D4×D5911yescharacteristic
901C23C22×D23611yescharacteristic
902C23C2×Q8×D5911yescharacteristic
903C23C22×Dic11811yescharacteristic
904C23C22×Dic11811yescharacteristic
905C23#41×D5911yescharacteristic
906C23#41×D5911yescharacteristic
907C23C2×#1174568711yescharacteristic
908C23C2×#1174568711yescharacteristic
909C23#1427377211yescharacteristic
910C23#1427377211yescharacteristic
911C23#1427377311yescharacteristic
912C23#1427377411yescharacteristic
913Q8—23616no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—416no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—594no—
957C2×C4—594no—
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—1182no—
979C2×C4—1182no—
980C2×C4—1182no—
981C2×C4—1182no—
982C2×C4—23616no—
983C2×C4—23616no—
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—2361no—
1001C2×C4—2361no—
1002C2×C4—2361no—
1003C2×C4—2361no—
1004C2×C4—2361no—
1005C2×C4—2361no—
1006C2×C4—2361no—
1007C2×C4—2361no—
1008C2×C4—2361no—
1009C2×C4—2361no—
1010C2×C4—2361no—
1011C2×C4—2361no—
1012C2×C4—2361no—
1013C2×C4—2361no—
1014C2×C4#1427370414yescomplemented
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—24no—
1019C22—24no—
1020C22—24no—
1021C22—24no—
1022C22—24no—
1023C22—24no—
1024C22—24no—
1025C22—24no—
1026C22—24no—
1027C22—24no—
1028C22—24no—
1029C22#1683732318yescomplemented
1030C22C2×#1427369711yescharacteristic
1031C22#121×D5911yescharacteristic
1032C22C22⋊Q8×D5911yescharacteristic
1033C22C2×#1427370411yescharacteristic
1034C22C2×#1427370411yescharacteristic
1035C22C2×#1427370411yescharacteristic
1036C22C2×#1427370711yescharacteristic
1037C22C2×#1427372611yescharacteristic
1038C22C2×#1427372611yescharacteristic
1039C22C2×#1427372711yescharacteristic
1040C22#1683794711yescharacteristic
1041C22#1683795411yescharacteristic
1042C22#1683795511yescharacteristic
1043C22#1683796011yescharacteristic
1044C22#1683797911yescharacteristic
1045C22#1683802711yescharacteristic
1046C22#1683802811yescharacteristic
1047C22#1683803011yescharacteristic
1048C22#1683803111yescharacteristic
1049C22#1683803411yescharacteristic
1050C22D4×D23611yescharacteristic
1051C22#1683803911yescharacteristic
1052C22#1683803911yescharacteristic
1053C22#1683804411yescharacteristic
1054C22#1683804711yescharacteristic
1055C22#1683804711yescharacteristic
1056C22#1683805011yescharacteristic
1057C22#1683805611yescharacteristic
1058C22D4×Dic11811yescharacteristic
1059C22#1683807511yescharacteristic
1060C22#1683808311yescharacteristic
1061C22#1683808911yescharacteristic
1062C22#1683810911yescharacteristic
1063C22#1683811111yescharacteristic
1064C22#1683811111yescharacteristic
1065C4—24no—
1066C4—42no—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4—42no—
1071C4—1184no—
1072C4—1184no—
1073C4—4721no—
1074C4—4721no—
1075C4—2362no—
1076C4—2362no—
1077C4—2362no—
1078C4—2362no—
1079C2—28no—
1080C2C2×#1683732311yescharacteristic
1081C2#2142746911yescharacteristic
1082C2#2142754411yescharacteristic
1083C2#2142770411yescharacteristic
1084C2#2142776011yescharacteristic
1085C2#2142776211yescharacteristic
1086C2#2142777011yescharacteristic
1087C2#2142777411yescharacteristic
1088C2#2142779711yescharacteristic
1089C2#2142779811yescharacteristic
1090C2#2142910211yescharacteristic
1091C2#2142910911yescharacteristic
1092C2#2142928011yescharacteristic
1093C2#2143021311yescharacteristic
1094C2#2143244611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutator, socle, cosocleC24×C59C24
FittingC59×C22⋊#95C2
prime radicalC25×C59C23
hypercenterC22⋊#95D59
hypocenterC59#14758
LCSG ▷ C24×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16837323C2semidirect
7. #21422366C2semidirect
8. #21422361C2semidirect
9. #21422360C2semidirect
10. #21422360C2semidirect
11. #21422350C2semidirect
12. #21422348C2semidirect
13. #21422348C2semidirect
79. C23×Dic59Q8semidirect
143. C23×C4×C59Q8semidirect
155. C2×C22⋊C4×C59Q8semidirect
407. C2×C4×C59C22⋊Q8semidirect
465. C2×Dic59C22⋊Q8semidirect
482. C22×C59#395semidirect
606. C59#14758semidirect
643. C23×C4Dic118semidirect
688. C2×C22⋊C4Dic118semidirect
1014. C2×C4#14273704semidirect
1029. C22#16837323semidirect

Maximal subgroups

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

subgroupindex
C22×#142737042
C2×#168373232
C2×#168372772
C2×#168372622
C2×#168372602
C22×C59⋊#952
#214223662
#214223612
#214223602
#214223502
#214223482
#214223182
C59×C22⋊#952
#1475859