Finite Group Databasebeta

← #28610805

Subgroups — #28610805

Order 15104.

1084 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837476C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D59C211yesmaximal, characteristic, complemented
3C2×#16837425C211yesmaximal, characteristic, complemented
4C4×#14273699C211yesmaximal, characteristic
5#21424888C211yesmaximal, characteristic, complemented
6#21424811C211yesmaximal, characteristic, complemented
7#21424709C211yesmaximal, characteristic, complemented
8#21424706C211yesmaximal, characteristic, complemented
9#21424394C211yesmaximal, characteristic, complemented
10#21424393C211yesmaximal, characteristic, complemented
11#21424274C211yesmaximal, characteristic, complemented
12#21424272C211yesmaximal, characteristic, complemented
13#21423964C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic59C211yesmaximal, characteristic, complemented
15C2×C59×#435C211yesmaximal, characteristic, complemented
16C22×#11745664C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18C2×#14273699C411yescharacteristic
19C2×C4×C22⋊D59C2211yescharacteristic
20C2×C4×C22⋊D59C2211yescharacteristic
21C22×C4×Dic59C2211yescharacteristic
22#16837476—24no—
23C8×C22⋊D59—24no—
24#16837425—24no—
25C2×Dic59⋊C8C2211yescharacteristic
26C2×Dic59⋊C8C2211yescharacteristic
27C2×Dic59⋊C8C2211yescharacteristic
28C2×Dic59⋊C8C2211yescharacteristic
29C2×Dic59⋊C8C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×(C2×D59)⋊C8C2211yescharacteristic
34C2×(C2×D59)⋊C8C2211yescharacteristic
35C2×(C2×D59)⋊C8C2211yescharacteristic
36C2×#14273637C2211yescharacteristic
37C2×C8×Dic59C2211yescharacteristic
38C2×C8×Dic59C2211yescharacteristic
39#16837302C411yescharacteristic
40#16837297C411yescharacteristic
41#16837296C411yescharacteristic
42#16837292C411yescharacteristic
43#16837282C411yescharacteristic
44#16837279C411yescharacteristic
45#16837260C411yescharacteristic
46C4×Dic59⋊C4C2211yescharacteristic
47C4×(C2×D59)⋊C4C2211yescharacteristic
48C4×C22⋊Dic59C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51#16837156C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54#16837156C2211yescharacteristic
55C22×M16×C59C2211yescharacteristic
56C23×C8×C59C2211yescharacteristic
57C2×C4×D4×C59C2211yescharacteristic
58C59×#435—24no—
59C2×C4⋊C8×C59C2211yescharacteristic
60C2×C22⋊C8×C59C2211yescharacteristic
61C2×C22⋊C8×C59C2211yescharacteristic
62C2×#97×C59C2211yescharacteristic
63C22×C22⋊D59C2×C411yescharacteristic
64C22×C22⋊D59C2×C411yescharacteristic
65C23×Dic59C2×C411yescharacteristic
66C23×Dic59C2×C411yescharacteristic
67C22×C4×D59C2311yescharacteristic
68C2×#11745664—22no—
69C2×#11745664—22no—
70C2×#11745664—41no—
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C2×C8×D59—22no—
76C2×C8×D59—22no—
77C2×C8×D59—41no—
78#14273699—24no—
79C4×C22⋊D59—22no—
80C4×C22⋊D59—22no—
81C4×C22⋊D59—22no—
82C4×C22⋊D59—22no—
83C2×Dic59⋊C4C2×C411yescharacteristic
84C2×Dic59⋊C4C2×C411yescharacteristic
85C2×Dic59⋊C4C2×C411yescharacteristic
86C2×Dic59⋊C4C2×C411yescharacteristic
87C2×C22⋊Dic59C2×C411yescharacteristic
88C2×C22⋊Dic59C2×C411yescharacteristic
89C2×C22⋊Dic59C2×C411yescharacteristic
90C2×C22⋊Dic59C2×C411yescharacteristic
91C2×(C2×D59)⋊C4C2×C411yescharacteristic
92C2×(C2×D59)⋊C4C2×C411yescharacteristic
93C2×(C2×D59)⋊C4C2×C411yescharacteristic
94C2×(C2×D59)⋊C4C2×C411yescharacteristic
95C2×C4×Dic59—22no—
96C2×C4×Dic59—22no—
97C2×C4×Dic59C2×C411yescharacteristic
98C2×C4×Dic59C2×C411yescharacteristic
99C2×C4×Dic59C2311yescharacteristic
100C2×C4×Dic59C2311yescharacteristic
101C2×C4×Dic59C2311yescharacteristic
102Dic59⋊C8—22no—
103Dic59⋊C8—22no—
104Dic59⋊C8—22no—
105Dic59⋊C8—22no—
106Dic59⋊C8D414yescomplemented
107C22⋊(C59⋊C8)—22no—
108C22⋊(C59⋊C8)—22no—
109C22⋊(C59⋊C8)—41no—
110(C2×D59)⋊C8—22no—
111(C2×D59)⋊C8—22no—
112(C2×D59)⋊C8—41no—
113#14273637—22no—
114C8×Dic59—22no—
115C8×Dic59—22no—
116C59⋊#95C2×C411yescharacteristic
117C59⋊#95C2×C411yescharacteristic
118C59⋊#95C2×C411yescharacteristic
119C59⋊#95C2×C411yescharacteristic
120C59⋊#95C2×C411yescharacteristic
121C59⋊#95C2×C411yescharacteristic
122C22×D4×C59C2×C411yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C2×M16×C59—22no—
126C2×M16×C59—22no—
127C2×M16×C59—41no—
128C22×C8×C59—22no—
129C22×C8×C59—22no—
130C22×C8×C59—41no—
131C22×C8×C59C2311yescharacteristic
132C22×C8×C59C2311yescharacteristic
133C22×C8×C59C2311yescharacteristic
134C22×C8×C59C2311yescharacteristic
135C4×D4×C59—22no—
136C4×D4×C59—22no—
137C2×C4⋊C4×C59C2×C411yescharacteristic
138C2×C22⋊C4×C59C2×C411yescharacteristic
139C2×C22⋊C4×C59C2×C411yescharacteristic
140C2×C42×C59C2311yescharacteristic
141C4⋊C8×C59—22no—
142C22⋊C8×C59—22no—
143C22⋊C8×C59D414yescomplemented
144#97×C59—22no—
145C24×C59C22×C411yescharacteristic
146C24×C59C22×C411yescharacteristic
147C23×D59C22×C411yescharacteristic
148C2×D4×C59—22no—
149C2×D4×C59—22no—
150C2×D4×C59—41no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59C22×C411yescharacteristic
162C22×C4×C59C22×C411yescharacteristic
163C22×C4×C59C22×C411yescharacteristic
164C22×C4×C59C22×C411yescharacteristic
165C22×C4×C59C2×D412yes—
166C22×C4×C59#4112yes—
167C22×C4×C59C2411yescharacteristic
168C2×C22⋊D59—22no—
169C2×C22⋊D59—22no—
170C2×C22⋊D59—22no—
171C2×C22⋊D59—22no—
172C2×C22⋊D59—41no—
173C2×C22⋊D59M1614yescomplemented
174C22×Dic59—22no—
175C22×Dic59—22no—
176C22×Dic59—22no—
177C22×Dic59—22no—
178C22×Dic59—22no—
179C22×Dic59—41no—
180C22×Dic59C22×C411yescharacteristic
181C22×Dic59C22×C411yescharacteristic
182C22×Dic59C22×C411yescharacteristic
183C22×Dic59C22×C411yescharacteristic
184C22×Dic59C22×C411yescharacteristic
185C22×Dic59C22×C411yescharacteristic
186C22×Dic59C22×C411yescharacteristic
187C2×C4×D59—21no—
188C2×C4×D59—21no—
189C2×C4×D59—21no—
190C2×C4×D59—21no—
191C2×C4×D59—21no—
192C2×C4×D59—21no—
193M16×C59—44no—
194C2×C8×C59—21no—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—21no—
199C2×C8×C59—21no—
200C2×C8×C59—21no—
201C2×C8×C59—21no—
202C2×C8×C59—21no—
203C2×C8×C59—44no—
204C2×C8×C59C2×D412yes—
205C2×C8×C59C2×D412yes—
206C2×C8×C59C2×D412yes—
207C4⋊C4×C59—22no—
208C22⋊C4×C59—22no—
209C22⋊C4×C59—22no—
210C42×C59—21no—
211C42×C59—21no—
212C22⋊Dic59—22no—
213C22⋊Dic59—22no—
214C22⋊Dic59—22no—
215C22⋊Dic59—22no—
216(C2×D59)⋊C4—22no—
217(C2×D59)⋊C4—22no—
218(C2×D59)⋊C4—22no—
219(C2×D59)⋊C4—22no—
220Dic59⋊C4—22no—
221Dic59⋊C4—22no—
222Dic59⋊C4—22no—
223Dic59⋊C4—22no—
224C4×Dic59—21no—
225C4×Dic59—21no—
226C4×Dic59—21no—
227C4×Dic59—21no—
228C4×Dic59—22no—
229C4×Dic59—22no—
230C4×Dic59C2×D412yes—
231C4×Dic59#4112yes—
232#11745664—44no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8C2×D412yes—
245C8×D59—44no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59C4×D412yes—
259C23×C59C2×M1612yes—
260C23×C59C23×C411yescharacteristic
261C22×D59—21no—
262C22×D59—21no—
263C22×D59—21no—
264C22×D59—21no—
265C22×D59—21no—
266C22×D59—21no—
267C22×D59C2×M1612yes—
268D4×C59—44no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59C4×D412yes—
289C2×C4×C59C22×D411yescharacteristic
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C2×C4×C59H(5,𝔽2)11yescharacteristic
294C2×C4×C592−1+411yescharacteristic
295C22⋊D59—28no—
296C22⋊D59—44no—
297C2×Dic59—21no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—21no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—21no—
307C2×Dic59—21no—
308C2×Dic59—21no—
309C2×Dic59—21no—
310C2×Dic59—21no—
311C2×Dic59—21no—
312C2×Dic59—21no—
313C2×Dic59—44no—
314C2×Dic59—44no—
315C2×Dic59C4×D412yes—
316C2×Dic59C4×D412yes—
317C2×Dic59C2×M1612yes—
318C2×Dic59#13112yes—
319C2×Dic59#13112yes—
320C4×D59—41no—
321C4×D59—41no—
322C4×D59—41no—
323C4×D59—41no—
324C8×C59—22no—
325C8×C59—22no—
326C8×C59—22no—
327C8×C59—41no—
328C59⋊C8—22no—
329C59⋊C8—41no—
330C59⋊C8—41no—
331C59⋊C8—41no—
332#22986—591nomaximal, Sylow
333C22×C59—22no—
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—22no—
337C22×C59—22no—
338C22×C59—22no—
339C22×C59—41no—
340C22×C59—41no—
341C22×C59—41no—
342C22×C59—41no—
343C22×C59—41no—
344C22×C59—41no—
345C22×C59—41no—
346C22×C59—41no—
347C22×C59C2×C4×D411yescharacteristic
348C22×C59C2×C4×D411yescharacteristic
349C22×C59#52011yescharacteristic
350C22×C59C22×M1611yescharacteristic
351C22×C59C2×#13111yescharacteristic
352C22×C59C2×#13111yescharacteristic
353C22×C59#56811yescharacteristic
354C2×D59—22no—
355C2×D59—22no—
356C2×D59—22no—
357C2×D59—41no—
358C2×D59—41no—
359C2×D59—41no—
360C2×D59—41no—
361C4×C59—22no—
362C4×C59—41no—
363C4×C59—41no—
364C4×C59—41no—
365C4×C59D4211yescharacteristic
366C4×C59#54711yescharacteristic
367C4×C59#54811yescharacteristic
368C4×C59#55311yescharacteristic
369Dic59—22no—
370Dic59—22no—
371Dic59—41no—
372Dic59—41no—
373Dic59—41no—
374Dic59—41no—
375Dic59#43514yescomplemented
376C2×#435—591no—
377C2×#435D5911yescharacteristic, complemented
378C2×C8×D4—591no—
379C2×#423—591no—
380C4×#121—591no—
381#1954—591no—
382#1939—591no—
383#1924—591no—
384#1924—591no—
385#1870—591no—
386#1870—591no—
387#1850—591no—
388#1850—591no—
389#1770—591no—
390C4×C22⋊C8—591no—
391C2×C59—42no—
392C2×C59—42no—
393C2×C59#236111yescharacteristic
394C2×C59C2×#43511yescharacteristic
395C2×C59#293111yescharacteristic
396C2×C59#293311yescharacteristic
397C2×C59D4×M1611yescharacteristic
398C2×C59#299011yescharacteristic
399C2×C59#299311yescharacteristic
400D59—42no—
401C22×M16—591no—
402C22×M16C2×D5911yescharacteristic
403C23×C8—591no—
404C23×C8C2×D5911yescharacteristic
405C2×#121—591no—
406C2×C4×D4—591no—
407C2×C4×D4—591no—
408C2×C4×D4C2×D5911yescharacteristic
409C22×C42—591no—
410#435—24no—
411#435—1184no—
412C8×D4—1184no—
413#423—1184no—
414C2×C4⋊C8—591no—
415C2×C4⋊C8—591no—
416C2×C4⋊C8—591no—
417C2×C4⋊C8—591no—
418C2×C4⋊C8—591no—
419C2×C4⋊C8C2×D5911yescharacteristic
420C2×C22⋊C8—591no—
421C2×C22⋊C8—591no—
422C2×C22⋊C8—591no—
423C2×C22⋊C8—591no—
424C2×C22⋊C8—591no—
425C2×C22⋊C8—591no—
426C2×C22⋊C8C2×D5911yescharacteristic
427C2×C22⋊C8C2×D5911yescharacteristic
428C2×#97—591no—
429C2×#97C2×D5911yescharacteristic
430C2×C4×C8—591no—
431C2×C4×C8—591no—
432#390—591no—
433#389—591no—
434#388—591no—
435#388—591no—
436#386—591no—
437#386—591no—
438#380—591no—
439C4×C4⋊C4—591no—
440C4×C22⋊C4—591no—
441C4×C22⋊C4—591no—
442#336—591no—
443#336—591no—
444#336—591no—
445#336—591no—
446#336—591no—
447#336—591no—
448C59#2298611yescharacteristic, complemented, Sylow
449C22×D4—591no—
450C22×D4—591no—
451C22×D4C4×D5911yescharacteristic
452C23×C4—591no—
453C23×C4—591no—
454C23×C4—591no—
455C23×C4C22×D5911yescharacteristic
456C23×C4C22×D5911yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—41no—
460C2×M16—1182no—
461C2×M16—1182no—
462C2×M16—2361no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8—591no—
467C22×C8—591no—
468C22×C8—591no—
469C22×C8—591no—
470C22×C8—1182no—
471C22×C8—1182no—
472C22×C8—2361no—
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C22×C8C22×D5911yescharacteristic
476C22×C8C22×D5911yescharacteristic
477#121—1184no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—1182no—
481C4×D4—1182no—
482C4×D4—1182no—
483C4×D4—1182no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4C4×D5911yescharacteristic
489C2×C22⋊C4—591no—
490C2×C22⋊C4—591no—
491C2×C22⋊C4—591no—
492C2×C22⋊C4—591no—
493C2×C22⋊C4—591no—
494C2×C22⋊C4—591no—
495C2×C22⋊C4—591no—
496C2×C22⋊C4—591no—
497C2×C22⋊C4C4×D5911yescharacteristic
498C2×C22⋊C4C4×D5911yescharacteristic
499C2×C42—591no—
500C2×C42—591no—
501C2×C42—591no—
502C2×C42—591no—
503C2×C42—591no—
504C2×C42—1182no—
505C2×C42—1182no—
506C2×C42C22×D5911yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—594no—
509C4⋊C8—1182no—
510C4⋊C8—1182no—
511C4⋊C8—1182no—
512C4⋊C8—1182no—
513C22⋊C8—22no—
514C22⋊C8—1182no—
515C22⋊C8—1182no—
516C22⋊C8—1182no—
517C22⋊C8—1182no—
518C22⋊C8—2361no—
519C22⋊C8—2361no—
520C22⋊C8C22⋊D5914yescomplemented
521#97—22no—
522#97—1182no—
523C4×C8—1182no—
524C4×C8—1182no—
525#95—591no—
526#95—591no—
527#95—591no—
528#95—591no—
529#95—591no—
530#95—591no—
531C24—591no—
532C24C2×C4×D5911yescharacteristic
533C24C2×C4×D5911yescharacteristic
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—594no—
538C2×D4—1182no—
539C2×D4—1182no—
540C2×D4—1182no—
541C2×D4—1182no—
542C2×D4—2361no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—591no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—591no—
557C22×C4—591no—
558C22×C4—591no—
559C22×C4—591no—
560C22×C4—1182no—
561C22×C4—1182no—
562C22×C4—1182no—
563C22×C4—1182no—
564C22×C4—1182no—
565C22×C4—1181no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—2361no—
572C22×C4C2×C4×D5911yescharacteristic
573C22×C4C2×C4×D5911yescharacteristic
574C22×C4C2×C4×D5911yescharacteristic
575C22×C4C2×C4×D5911yescharacteristic
576C22×C4#1174568512yes—
577C22×C4C2×C22⋊D5912yes—
578C22×C4C23×D5911yescharacteristic
579M16—44no—
580M16—2364no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8—592no—
592C2×C8—1181no—
593C2×C8—1181no—
594C2×C8—1181no—
595C2×C8—1181no—
596C2×C8—1181no—
597C2×C8—1181no—
598C2×C8—1181no—
599C2×C8—1181no—
600C2×C8—1181no—
601C2×C8—1181no—
602C2×C8—1181no—
603C2×C8—2364no—
604C2×C8D4×D5912yes—
605C2×C8C2×C22⋊D5912yes—
606C2×C8C2×C22⋊D5912yes—
607C4⋊C4—22no—
608C4⋊C4—1182no—
609C4⋊C4—1182no—
610C4⋊C4—1182no—
611C4⋊C4—1182no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—1182no—
615C22⋊C4—1182no—
616C22⋊C4—1182no—
617C22⋊C4—1182no—
618C22⋊C4—1182no—
619C22⋊C4—1182no—
620C22⋊C4—1182no—
621C22⋊C4—1182no—
622C42—21no—
623C42—21no—
624C42—592no—
625C42—592no—
626C42—1182no—
627C42—1182no—
628C42—1181no—
629C42—1181no—
630C42—1181no—
631C42—1181no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—592no—
645C23—1181no—
646C23—1181no—
647C23—1181no—
648C23—1181no—
649C23—1181no—
650C23—1181no—
651C23C4×C22⋊D5912yes—
652C23M16×D5912yes—
653C23C22×C4×D5911yescharacteristic
654D4—44no—
655D4—1188no—
656D4—2364no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—592no—
677C2×C4—592no—
678C2×C4—592no—
679C2×C4—592no—
680C2×C4—592no—
681C2×C4—1181no—
682C2×C4—1181no—
683C2×C4—1181no—
684C2×C4—1181no—
685C2×C4—1181no—
686C2×C4—1181no—
687C2×C4—1181no—
688C2×C4—1181no—
689C2×C4—1181no—
690C2×C4—1181no—
691C2×C4—1181no—
692C2×C4—1181no—
693C2×C4—1181no—
694C2×C4—1181no—
695C2×C4—1181no—
696C2×C4—1181no—
697C2×C4—2364no—
698C2×C4—2364no—
699C2×C4—2361no—
700C2×C4—2361no—
701C2×C4—2361no—
702C2×C4—2361no—
703C2×C4C4×C22⋊D5912yes—
704C2×C4C2×D4×D5911yescharacteristic
705C2×C4C22×C22⋊D5911yescharacteristic
706C2×C4#41×D5911yescharacteristic
707C2×C4C2×#1174568511yescharacteristic
708C2×C4#1427377211yescharacteristic
709C2×C4#1427377411yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—41no—
714C8—1182no—
715C8—2361no—
716C8—2361no—
717C8—2361no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—1182no—
733C22—1182no—
734C22—1182no—
735C22—2361no—
736C22—2361no—
737C22—2361no—
738C22—2361no—
739C22C4×D4×D5911yescharacteristic
740C22C2×C4×C22⋊D5911yescharacteristic
741C22#1683788111yescharacteristic
742C22C2×M16×D5911yescharacteristic
743C22#131×D5911yescharacteristic
744C22#131×D5911yescharacteristic
745C22#1683816811yescharacteristic
746C4—22no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—594no—
751C4—1182no—
752C4—1182no—
753C4—2361no—
754C4—2361no—
755C4—2361no—
756C4—2361no—
757C4D4×C22⋊D5911yescharacteristic
758C4#1683805111yescharacteristic
759C4#1683806111yescharacteristic
760C4#1683810111yescharacteristic
761C2—42no—
762C2—42no—
763C2—2362no—
764C2#2142711311yescharacteristic
765C2#435×D5911yescharacteristic
766C2#2143280611yescharacteristic
767C2#2143281911yescharacteristic
768C2M16×C22⋊D5911yescharacteristic
769C2#2143321611yescharacteristic
770C2#2143323811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC2×C59×#435C2
prime radicalC2×#14273699C4
cosocleC22×C4×C59C24
hypercenterC2×#435D59
hypocenterC59#22986
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16837476C2semidirect
2. C2×C8×C22⋊D59C2semidirect
3. C2×#16837425C2semidirect
5. #21424888C2semidirect
6. #21424811C2semidirect
7. #21424709C2semidirect
8. #21424706C2semidirect
9. #21424394C2semidirect
10. #21424393C2semidirect
11. #21424274C2semidirect
12. #21424272C2semidirect
13. #21423964C2semidirect
14. C22⋊C8×Dic59C2semidirect
15. C2×C59×#435C2semidirect
106. Dic59⋊C8D4semidirect
143. C22⋊C8×C59D4semidirect
173. C2×C22⋊D59M16semidirect
375. Dic59#435semidirect
377. C2×#435D59semidirect
448. C59#22986semidirect
520. C22⋊C8C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168374762
C2×C8×C22⋊D592
C2×#168374252
C4×#142736992
#214248882
#214248112
#214247092
#214247062
#214243942
#214243932
#214242742
#214242722
#214239642
C22⋊C8×Dic592
C2×C59×#4352
#2298659