Finite Group Databasebeta

← #28594769

Subgroups — #28594769

Order 15104.

1096 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×#16837477C211yesmaximal, characteristic, complemented
2C2×#16837476C211yesmaximal, characteristic, complemented
3C2×#16837472C211yesmaximal, characteristic, complemented
4C2×C4×#11745664C211yesmaximal, characteristic, complemented
5C4×#14273701C211yesmaximal, characteristic
6#21424893C211yesmaximal, characteristic, complemented
7#21424817C211yesmaximal, characteristic, complemented
8#21424700C211yesmaximal, characteristic, complemented
9#21424700C211yesmaximal, characteristic, complemented
10#21424391C211yesmaximal, characteristic, complemented
11#21424391C211yesmaximal, characteristic, complemented
12#21423973C211yesmaximal, characteristic, complemented
13#21423876C211yesmaximal, characteristic, complemented
14#21423866C211yesmaximal, characteristic, complemented
15C59×#1797C211yesmaximal, characteristic, complemented
16C22×#11745664C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20C2×#14273701C411yescharacteristic
21C2×C4×D236C2211yescharacteristic
22C2×C4×C22⋊D59C2211yescharacteristic
23C2×C4×C22⋊D59C2211yescharacteristic
24#16837477—24no—
25#16837476—24no—
26#16837472—24no—
27C2×Dic59⋊C8C2211yescharacteristic
28C2×Dic59⋊C8C2211yescharacteristic
29C2×(C2×D59)⋊C8C2211yescharacteristic
30C2×(C2×D59)⋊C8C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×(C2×D59)⋊C8C2211yescharacteristic
33C2×(C2×D59)⋊C8C2211yescharacteristic
34C2×(C2×D59)⋊C8C2211yescharacteristic
35C4×#11745664—24no—
36C2×#14273638C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38C2×#14273637C2211yescharacteristic
39C2×C4×C59⋊C8C2211yescharacteristic
40C2×C4×C59⋊C8C2211yescharacteristic
41C2×C8×Dic59C2211yescharacteristic
42#16837304C411yescharacteristic
43#16837300C411yescharacteristic
44#16837293C411yescharacteristic
45#16837293C411yescharacteristic
46#16837281C411yescharacteristic
47#16837281C411yescharacteristic
48#16837262C411yescharacteristic
49C4×C4⋊Dic59C2211yescharacteristic
50C4×(C2×D59)⋊C4C2211yescharacteristic
51C4×(C2×D59)⋊C4C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54#16837156C2211yescharacteristic
55#16837156C2211yescharacteristic
56C22×C42×C59C2211yescharacteristic
57C2×C4⋊C8×C59C2211yescharacteristic
58C2×C4⋊C8×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C2×C22⋊C8×C59C2211yescharacteristic
61C59×#336C2211yescharacteristic
62C59×#336C2211yescharacteristic
63C22×D236C2×C411yescharacteristic
64C22×C22⋊D59C2×C411yescharacteristic
65C22×C22⋊D59C2×C411yescharacteristic
66C22×C4×D59C2311yescharacteristic
67C22×C4×D59C2311yescharacteristic
68C2×#11745664—22no—
69C2×#11745664—22no—
70C2×#11745664—22no—
71C2×#11745664—22no—
72C2×#11745664—22no—
73C2×#11745664D414yescomplemented
74C2×#11745659—22no—
75C2×#11745659—22no—
76C2×#11745659—22no—
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81C2×C8×D59—22no—
82C2×C8×D59—22no—
83C2×C8×D59—22no—
84#14273701—24no—
85C4×D236—22no—
86C4×D236—22no—
87C4×C22⋊D59—22no—
88C4×C22⋊D59—22no—
89C4×C22⋊D59—22no—
90C4×C22⋊D59—22no—
91C2×C4⋊Dic59C2×C411yescharacteristic
92C2×C4⋊Dic59C2×C411yescharacteristic
93C2×C4⋊Dic59C2×C411yescharacteristic
94C2×Dic59⋊C4C2×C411yescharacteristic
95C2×Dic59⋊C4C2×C411yescharacteristic
96C2×C22⋊Dic59C2×C411yescharacteristic
97C2×C22⋊Dic59C2×C411yescharacteristic
98C2×(C2×D59)⋊C4C2×C411yescharacteristic
99C2×(C2×D59)⋊C4C2×C411yescharacteristic
100C2×(C2×D59)⋊C4C2×C411yescharacteristic
101C2×(C2×D59)⋊C4C2×C411yescharacteristic
102C2×(C2×D59)⋊C4C2×C411yescharacteristic
103C2×(C2×D59)⋊C4C2×C411yescharacteristic
104C2×(C2×D59)⋊C4C2×C411yescharacteristic
105C2×(C2×D59)⋊C4C2×C411yescharacteristic
106C2×C4×Dic59C2311yescharacteristic
107C2×C4×Dic59C2311yescharacteristic
108Dic59⋊C8—22no—
109Dic59⋊C8—22no—
110(C2×D59)⋊C8—22no—
111(C2×D59)⋊C8—22no—
112(C2×D59)⋊C8—22no—
113(C2×D59)⋊C8—22no—
114(C2×D59)⋊C8—22no—
115(C2×D59)⋊C8—22no—
116#14273638—22no—
117#14273638D414yescomplemented
118#14273637—22no—
119C4×C59⋊C8—22no—
120C4×C59⋊C8—22no—
121C8×Dic59—22no—
122C59⋊#95C2×C411yescharacteristic
123C59⋊#95C2×C411yescharacteristic
124C59⋊#95C2×C411yescharacteristic
125C59⋊#95C2×C411yescharacteristic
126C59⋊#95C2×C411yescharacteristic
127C59⋊#95C2×C411yescharacteristic
128C23×C4×C59C2×C411yescharacteristic
129C23×C4×C59C2×C411yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C22×C8×C59C2311yescharacteristic
132C22×C8×C59C2311yescharacteristic
133C22×C8×C59C2311yescharacteristic
134C22×C8×C59C2311yescharacteristic
135C2×C42×C59—22no—
136C2×C42×C59—22no—
137C2×C42×C59C2×C411yescharacteristic
138C2×C42×C59C2×C411yescharacteristic
139C2×C42×C59C2311yescharacteristic
140C2×C42×C59C2311yescharacteristic
141C4⋊C8×C59—22no—
142C4⋊C8×C59—22no—
143C22⋊C8×C59—22no—
144C22⋊C8×C59—22no—
145C24×C59C22×C411yescharacteristic
146C23×D59C22×C411yescharacteristic
147C23×D59C22×C411yescharacteristic
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—41no—
157C22×C4×C59—41no—
158C22×C4×C59C22×C411yescharacteristic
159C22×C4×C59C22×C411yescharacteristic
160C22×C4×C59C22×C411yescharacteristic
161C22×C4×C59C22×C411yescharacteristic
162C22×C4×C59C22×C411yescharacteristic
163C22×C4×C59C2×D412yes—
164C22×C4×C59#4112yes—
165C22×C4×C59C2411yescharacteristic
166C2×C22⋊D59—22no—
167C2×C22⋊D59—22no—
168C2×C22⋊D59—22no—
169C2×C22⋊D59—22no—
170C2×C22⋊D59—41no—
171C2×C22⋊D59—41no—
172C22×Dic59C22×C411yescharacteristic
173C22×Dic59C22×C411yescharacteristic
174C22×Dic59C22×C411yescharacteristic
175C22×Dic59C22×C411yescharacteristic
176C22×Dic59C22×C411yescharacteristic
177C22×Dic59C22×C411yescharacteristic
178C2×D236—22no—
179C2×D236—22no—
180C2×D236—41no—
181C2×C4×D59—21no—
182C2×C4×D59—21no—
183C2×C4×D59—21no—
184C2×C4×D59—21no—
185C2×C4×D59—21no—
186C2×C4×D59—21no—
187C2×C4×D59—21no—
188C2×C4×D59—21no—
189C2×C4×D59—21no—
190C2×C4×D59—21no—
191C2×C4×D59—21no—
192C2×C4×D59—21no—
193C2×C8×C59—21no—
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—21no—
204C2×C8×C59—21no—
205C42×C59—22no—
206C42×C59—22no—
207C42×C59—21no—
208C42×C59—21no—
209C42×C59C2×D412yes—
210C42×C59#4112yes—
211C22⋊Dic59—22no—
212C22⋊Dic59—22no—
213(C2×D59)⋊C4—22no—
214(C2×D59)⋊C4—22no—
215(C2×D59)⋊C4—22no—
216(C2×D59)⋊C4—22no—
217(C2×D59)⋊C4—22no—
218(C2×D59)⋊C4—22no—
219(C2×D59)⋊C4—22no—
220(C2×D59)⋊C4M1614yescomplemented
221C4⋊Dic59—22no—
222C4⋊Dic59—22no—
223C4⋊Dic59—41no—
224Dic59⋊C4—22no—
225Dic59⋊C4—22no—
226C4×Dic59—21no—
227C4×Dic59—21no—
228C4×Dic59—21no—
229C4×Dic59—21no—
230#11745664—28no—
231#11745664—28no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8C2×D412yes—
239C2×C59⋊C8C2×D412yes—
240C2×C59⋊C8C2×D412yes—
241C2×C59⋊C8C2×D412yes—
242C2×C59⋊C8#4112yes—
243C2×C59⋊C8#4112yes—
244#11745659—44no—
245C8×D59—44no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59C4×D412yes—
253C23×C59C23×C411yescharacteristic
254C22×D59—21no—
255C22×D59—21no—
256C22×D59—21no—
257C22×D59—21no—
258C22×D59—21no—
259C22×D59—21no—
260C22×D59—21no—
261C22×D59—21no—
262C22×D59—21no—
263C22×D59—21no—
264C22×D59—21no—
265C22×D59—21no—
266C22×D59—21no—
267C22×D59C2×M1612yes—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—44no—
283C2×C4×C59—44no—
284C2×C4×C59C4×D412yes—
285C2×C4×C59C4×D412yes—
286C2×C4×C59C4×D412yes—
287C2×C4×C59C2×M1612yes—
288C2×C4×C59#13112yes—
289C2×C4×C59C22×D411yescharacteristic
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59C2×#4111yescharacteristic
295C22⋊D59—44no—
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—21no—
314C2×Dic59C2×M1612yes—
315D236—44no—
316C4×D59—41no—
317C4×D59—41no—
318C4×D59—41no—
319C4×D59—41no—
320C4×D59—41no—
321C4×D59—41no—
322C4×D59—41no—
323C4×D59—41no—
324C8×C59—41no—
325C8×C59—41no—
326C8×C59—41no—
327C8×C59—41no—
328C59⋊C8—22no—
329C59⋊C8—22no—
330C59⋊C8—22no—
331C59⋊C8#12114yescomplemented
332#21490—591nomaximal, Sylow
333C22×C59—22no—
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59—41no—
339C22×C59—41no—
340C22×C59C2×C4×D411yescharacteristic
341C22×C59C2×C4×D411yescharacteristic
342C22×C59C4×#4111yescharacteristic
343C22×C59C22×M1611yescharacteristic
344C22×C59C2×#13111yescharacteristic
345C22×C59#56811yescharacteristic
346C22×C59#56811yescharacteristic
347C2×D59—22no—
348C2×D59—22no—
349C2×D59—22no—
350C2×D59—41no—
351C2×D59—41no—
352C2×D59—41no—
353C2×D59—41no—
354C2×D59—41no—
355C2×D59—41no—
356C2×D59—41no—
357C2×D59—41no—
358C2×D59—41no—
359C2×D59—41no—
360C2×D59—41no—
361C4×C59—22no—
362C4×C59—22no—
363C4×C59—22no—
364C4×C59—22no—
365C4×C59—22no—
366C4×C59C2×#12111yescharacteristic
367C4×C59#52511yescharacteristic
368C4×C59#52911yescharacteristic
369C4×C59#53211yescharacteristic
370Dic59—22no—
371Dic59—41no—
372Dic59—41no—
373Dic59—41no—
374Dic59—41no—
375Dic59—41no—
376C2×#436—591no—
377C2×#435—591no—
378C2×#435—591no—
379C2×C4×M16—591no—
380C4×#121—591no—
381#1955—591no—
382#1940—591no—
383#1923—591no—
384#1923—591no—
385#1870—591no—
386#1870—591no—
387#1797D5911yescharacteristic, complemented
388#1771—591no—
389#1753—591no—
390C8×C22⋊C4—591no—
391C2×C59—42no—
392C2×C59C4×#12111yescharacteristic
393C2×C59#293311yescharacteristic
394C2×C59D4×M1611yescharacteristic
395C2×C59D4×M1611yescharacteristic
396C2×C59#293511yescharacteristic
397C2×C59#296511yescharacteristic
398C2×C59#296711yescharacteristic
399D59—42no—
400D59—81no—
401C22×M16—591no—
402C22×M16—591no—
403C22×M16—591no—
404C23×C8—591no—
405C2×#121—591no—
406C2×C4×D4—591no—
407C2×C4×D4—591no—
408C2×C4×D4—591no—
409C22×C42C2×D5911yescharacteristic
410#436—1184no—
411#435—1184no—
412#435—1184no—
413C2×C4⋊C8—591no—
414C2×C4⋊C8—591no—
415C2×C4⋊C8C2×D5911yescharacteristic
416C2×C4⋊C8C2×D5911yescharacteristic
417C2×C22⋊C8—591no—
418C2×C22⋊C8—591no—
419C2×C22⋊C8—591no—
420C2×C22⋊C8—591no—
421C2×C22⋊C8—591no—
422C2×C22⋊C8—591no—
423C2×C22⋊C8C2×D5911yescharacteristic
424C2×C22⋊C8C2×D5911yescharacteristic
425C4×M16—1184no—
426C2×#97—591no—
427C2×#97—591no—
428C2×#97—591no—
429C2×C4×C8—591no—
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#336C2×D5911yescharacteristic
447#336C2×D5911yescharacteristic
448C59#2149011yescharacteristic, complemented, Sylow
449C22×D4—591no—
450C22×D4—591no—
451C22×D4—591no—
452C23×C4—591no—
453C23×C4—591no—
454C23×C4C4×D5911yescharacteristic
455C23×C4C4×D5911yescharacteristic
456C23×C4C22×D5911yescharacteristic
457C2×M16—594no—
458C2×M16—1182no—
459C2×M16—1182no—
460C2×M16—1182no—
461C2×M16—1182no—
462C2×M16—1182no—
463C2×M16—1182no—
464C2×M16—1182no—
465C2×M16—1182no—
466C22×C8—591no—
467C22×C8—591no—
468C22×C8—591no—
469C22×C8—591no—
470C22×C8—1182no—
471C22×C8—1182no—
472C22×C8—1182no—
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C22×C8C22×D5911yescharacteristic
476C22×C8C22×D5911yescharacteristic
477#121—1184no—
478C4×D4—1182no—
479C4×D4—1182no—
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⋊C4—591no—
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⋊C4—591no—
498C2×C22⋊C4—591no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—591no—
502C2×C42—591no—
503C2×C42C4×D5911yescharacteristic
504C2×C42C4×D5911yescharacteristic
505C2×C42C22×D5911yescharacteristic
506C2×C42C22×D5911yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—1182no—
510C4⋊C8—1182no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8—1182no—
514C22⋊C8—1182no—
515C22⋊C8—1182no—
516C22⋊C8—1182no—
517C22⋊C8—1182no—
518C22⋊C8—1182no—
519#97—594no—
520#97—1182no—
521#97—1182no—
522C4×C8—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—
532C24—591no—
533C24C2×C4×D5911yescharacteristic
534C2×D4—1182no—
535C2×D4—1182no—
536C2×D4—1182no—
537C2×D4—1182no—
538C2×D4—1182no—
539C2×D4—1182no—
540C2×D4—2361no—
541C2×D4—2361no—
542C2×D4—2361no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—591no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—591no—
557C22×C4—591no—
558C22×C4—591no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—1181no—
562C22×C4—1181no—
563C22×C4—1181no—
564C22×C4—1181no—
565C22×C4—1181no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4C2×C4×D5911yescharacteristic
572C22×C4C2×C4×D5911yescharacteristic
573C22×C4C2×C4×D5911yescharacteristic
574C22×C4C2×C4×D5911yescharacteristic
575C22×C4C2×C4×D5911yescharacteristic
576C22×C4D4×D5912yes—
577C22×C4#1174568912yes—
578C22×C4C23×D5911yescharacteristic
579M16—1188no—
580M16—1188no—
581M16—2364no—
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—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—592no—
595C2×C8—592no—
596C2×C8—592no—
597C2×C8—592no—
598C2×C8—592no—
599C2×C8—592no—
600C2×C8—1181no—
601C2×C8—1181no—
602C2×C8—1181no—
603C2×C8—1181no—
604C2×C8—1181no—
605C2×C8—1181no—
606C2×C8—2364no—
607C4⋊C4—1182no—
608C4⋊C4—1182no—
609C4⋊C4—1182no—
610C4⋊C4—1182no—
611C4⋊C4—2361no—
612C22⋊C4—594no—
613C22⋊C4—1182no—
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—22no—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—1181no—
627C42—1181no—
628C42—1181no—
629C42—1181no—
630C42D4×D5912yes—
631C42#1174568712yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—592no—
639C23—1181no—
640C23—1181no—
641C23—1181no—
642C23—1181no—
643C23—1181no—
644C23—1181no—
645C23—1181no—
646C23—1181no—
647C23—1181no—
648C23—1181no—
649C23—1181no—
650C23—1181no—
651C23—1181no—
652C23#1427368912yes—
653C23C22×C4×D5911yescharacteristic
654D4—2364no—
655D4—2364no—
656D4—2364no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—592no—
674C2×C4—1181no—
675C2×C4—1181no—
676C2×C4—1181no—
677C2×C4—1181no—
678C2×C4—1181no—
679C2×C4—1181no—
680C2×C4—1181no—
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—2361no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4—2361no—
695C2×C4—2361no—
696C2×C4—2361no—
697C2×C4—2361no—
698C2×C4—2361no—
699C2×C4(C22⋊D59)⋊C412yes—
700C2×C4(C22⋊D59)⋊C412yes—
701C2×C4#1427368912yes—
702C2×C4M16×D5912yes—
703C2×C4#1427373312yes—
704C2×C4C2×D4×D5911yescharacteristic
705C2×C4C2×D4×D5911yescharacteristic
706C2×C4#41×D5911yescharacteristic
707C2×C4#41×D5911yescharacteristic
708C2×C4C2×#1174568711yescharacteristic
709C2×C4C2×#1174568911yescharacteristic
710C8—41no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—594no—
715C8—1182no—
716C8—1182no—
717C8—1182no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—1182no—
726C22—1182no—
727C22—1182no—
728C22—2361no—
729C22—2361no—
730C22—2361no—
731C22—2361no—
732C22—2361no—
733C22—2361no—
734C22—2361no—
735C22—2361no—
736C22—2361no—
737C22—2361no—
738C22—2361no—
739C22C2×(C22⋊D59)⋊C411yescharacteristic
740C22C2×#1427368911yescharacteristic
741C22#1683787011yescharacteristic
742C22C2×M16×D5911yescharacteristic
743C22C2×#1427373311yescharacteristic
744C22#1683816811yescharacteristic
745C22#1683816811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—1182no—
752C4—2361no—
753C4—2361no—
754C4—2361no—
755C4—2361no—
756C4—2361no—
757C4#121×D5911yescharacteristic
758C4#1683791511yescharacteristic
759C4#1683793811yescharacteristic
760C4#1683794711yescharacteristic
761C2—42no—
762C2—4721no—
763C2—2362no—
764C2#2142660211yescharacteristic
765C2#2143281711yescharacteristic
766C2#2143282811yescharacteristic
767C2#2143283111yescharacteristic
768C2#2143283911yescharacteristic
769C2#2143306011yescharacteristic
770C2#2143307611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1797C2
prime radicalC2×#14273701C4
cosocleC22×C4×C59C24
hypercenter#1797D59
hypocenterC59#21490
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
1. C2×#16837477C2semidirect
2. C2×#16837476C2semidirect
3. C2×#16837472C2semidirect
4. C2×C4×#11745664C2semidirect
6. #21424893C2semidirect
7. #21424817C2semidirect
8. #21424700C2semidirect
9. #21424700C2semidirect
10. #21424391C2semidirect
11. #21424391C2semidirect
12. #21423973C2semidirect
13. #21423876C2semidirect
14. #21423866C2semidirect
15. C59×#1797C2semidirect
73. C2×#11745664D4semidirect
117. #14273638D4semidirect
220. (C2×D59)⋊C4M16semidirect
331. C59⋊C8#121semidirect
387. #1797D59semidirect
448. C59#21490semidirect

Maximal subgroups

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

subgroupindex
C2×#168374772
C2×#168374762
C2×#168374722
C2×C4×#117456642
C4×#142737012
#214248932
#214248172
#214247002
#214243912
#214239732
#214238762
#214238662
C59×#17972
#2149059