Finite Group Databasebeta

← #28610918

Subgroups — #28610918

Order 15104.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837480C211yesmaximal, characteristic, complemented
2C2×#16837480C211yesmaximal, characteristic, complemented
3C2×#16837474C211yesmaximal, characteristic, complemented
4C2×#16837429C211yesmaximal, characteristic, complemented
5#21424895C211yesmaximal, characteristic, complemented
6#21424815C211yesmaximal, characteristic, complemented
7#21424711C211yesmaximal, characteristic, complemented
8#21424704C211yesmaximal, characteristic, complemented
9#21424394C211yesmaximal, characteristic, complemented
10#21424389C211yesmaximal, characteristic, complemented
11#21424281C211yesmaximal, characteristic, complemented
12#21424281C211yesmaximal, characteristic, complemented
13#21423971C211yesmaximal, characteristic, complemented
14#21423862C211yesmaximal, characteristic, complemented
15C59×#2392C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20#16837480—24no—
21#16837480—24no—
22#16837474—24no—
23#16837429—24no—
24C2×C4⋊(C59⋊C8)C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27C2×C4⋊(C59⋊C8)C2211yescharacteristic
28C2×C4⋊(C59⋊C8)C2211yescharacteristic
29C2×C4⋊(C59⋊C8)C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic
38C2×#14273638C2211yescharacteristic
39C2×#14273638C2211yescharacteristic
40C2×C4×C59⋊C8C2211yescharacteristic
41C2×C4×C59⋊C8C2211yescharacteristic
42#16837157C2211yescharacteristic
43#16837157C2211yescharacteristic
44#16837157C2211yescharacteristic
45#16837157C2211yescharacteristic
46#16837157C2211yescharacteristic
47#16837157C2211yescharacteristic
48C2×C4×D4×C59C2211yescharacteristic
49C2×C4×D4×C59C2211yescharacteristic
50C2×C4×D4×C59C2211yescharacteristic
51C2×#117×C59C2211yescharacteristic
52C59×#398C411yescharacteristic
53C59×#397C411yescharacteristic
54C59×#396C411yescharacteristic
55C59×#396C411yescharacteristic
56C59×#394C411yescharacteristic
57C59×#394C411yescharacteristic
58C59×#394C411yescharacteristic
59C59×#392C411yescharacteristic
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C22⋊C4×C59C2211yescharacteristic
62C4×C22⋊C4×C59C2211yescharacteristic
63C2×#11745664—22no—
64C2×#11745664—22no—
65C2×#11745664—22no—
66C2×#11745664—22no—
67C2×#11745664—22no—
68C2×#11745664—22no—
69C2×#11745664—41no—
70C2×#11745664—41no—
71C2×#11745664—41no—
72C22×C59⋊C8—22no—
73C22×C59⋊C8—22no—
74C22×C59⋊C8—41no—
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C4⋊(C59⋊C8)—22no—
84C4⋊(C59⋊C8)—22no—
85C4⋊(C59⋊C8)—22no—
86C4⋊(C59⋊C8)—22no—
87C4⋊(C59⋊C8)—22no—
88C4⋊(C59⋊C8)D414yescomplemented
89C22⋊(C59⋊C8)—22no—
90C22⋊(C59⋊C8)—22no—
91C22⋊(C59⋊C8)—22no—
92C22⋊(C59⋊C8)—22no—
93C22⋊(C59⋊C8)—22no—
94C22⋊(C59⋊C8)—41no—
95C22⋊(C59⋊C8)—41no—
96C22⋊(C59⋊C8)D414yescomplemented
97#14273638—22no—
98#14273638—22no—
99C4×C59⋊C8—22no—
100C4×C59⋊C8—22no—
101C22×D4×C59C2×C411yescharacteristic
102C22×D4×C59C2×C411yescharacteristic
103C22×D4×C59C2×C411yescharacteristic
104C23×C4×C59C2311yescharacteristic
105C23×C4×C59C2311yescharacteristic
106C23×C4×C59C2311yescharacteristic
107C4×D4×C59—22no—
108C4×D4×C59—22no—
109C4×D4×C59—22no—
110C4×D4×C59—22no—
111C4×D4×C59—22no—
112C4×D4×C59—22no—
113#117×C59—22no—
114#117×C59—22no—
115C2×C4⋊C4×C59C2×C411yescharacteristic
116C2×C4⋊C4×C59C2×C411yescharacteristic
117C2×C4⋊C4×C59C2×C411yescharacteristic
118C2×C4⋊C4×C59C2×C411yescharacteristic
119C2×C4⋊C4×C59C2×C411yescharacteristic
120C2×C4⋊C4×C59C2×C411yescharacteristic
121C2×C4⋊C4×C59C2×C411yescharacteristic
122C2×C22⋊C4×C59C2×C411yescharacteristic
123C2×C22⋊C4×C59C2×C411yescharacteristic
124C2×C22⋊C4×C59C2×C411yescharacteristic
125C2×C22⋊C4×C59C2×C411yescharacteristic
126C2×C22⋊C4×C59C2×C411yescharacteristic
127C2×C22⋊C4×C59C2×C411yescharacteristic
128C2×C22⋊C4×C59C2×C411yescharacteristic
129C2×C22⋊C4×C59C2×C411yescharacteristic
130C2×C22⋊C4×C59C2×C411yescharacteristic
131C2×C22⋊C4×C59C2×C411yescharacteristic
132C2×C22⋊C4×C59C2×C411yescharacteristic
133C2×C22⋊C4×C59C2×C411yescharacteristic
134C2×C42×C59C2311yescharacteristic
135C2×C42×C59C2311yescharacteristic
136C2×C42×C59C2311yescharacteristic
137C2×C42×C59C2311yescharacteristic
138#95×C59C2×C411yescharacteristic
139#95×C59C2×C411yescharacteristic
140#95×C59C2×C411yescharacteristic
141#95×C59C2×C411yescharacteristic
142#95×C59C2×C411yescharacteristic
143#95×C59C2×C411yescharacteristic
144C24×C59C22×C411yescharacteristic
145C24×C59C22×C411yescharacteristic
146C24×C59C22×C411yescharacteristic
147C2×D4×C59—22no—
148C2×D4×C59—22no—
149C2×D4×C59—22no—
150C2×D4×C59—22no—
151C2×D4×C59—41no—
152C2×D4×C59—41no—
153C2×D4×C59—41no—
154C2×D4×C59—41no—
155C2×D4×C59—41no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59C22×C411yescharacteristic
173C22×C4×C59C22×C411yescharacteristic
174C22×C4×C59C22×C411yescharacteristic
175C22×C4×C59C22×C411yescharacteristic
176C22×C4×C59C22×C411yescharacteristic
177C22×C4×C59C22×C411yescharacteristic
178C22×C4×C59C22×C411yescharacteristic
179C22×C4×C59C22×C411yescharacteristic
180C22×C4×C59C22×C411yescharacteristic
181C22×C4×C59C22×C411yescharacteristic
182C22×C4×C59C22×C411yescharacteristic
183C22×C4×C59C2×D412yes—
184C22×C4×C59#4112yes—
185C22×C4×C59C2411yescharacteristic
186C4⋊C4×C59—22no—
187C4⋊C4×C59—22no—
188C4⋊C4×C59—22no—
189C4⋊C4×C59—22no—
190C4⋊C4×C59—22no—
191C4⋊C4×C59—22no—
192C4⋊C4×C59—41no—
193C22⋊C4×C59—22no—
194C22⋊C4×C59—22no—
195C22⋊C4×C59—22no—
196C22⋊C4×C59—22no—
197C22⋊C4×C59—22no—
198C22⋊C4×C59—22no—
199C22⋊C4×C59—22no—
200C22⋊C4×C59—22no—
201C22⋊C4×C59—22no—
202C22⋊C4×C59—41no—
203C22⋊C4×C59—41no—
204C22⋊C4×C59—41no—
205C42×C59—21no—
206C42×C59—21no—
207C42×C59—21no—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59C2×D412yes—
212C42×C59#4112yes—
213#11745664—44no—
214#11745664—44no—
215#11745664—44no—
216C2×C59⋊C8—21no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—44no—
237C2×C59⋊C8C2×D412yes—
238C2×C59⋊C8C2×D412yes—
239C2×C59⋊C8C2×D412yes—
240C2×C59⋊C8C2×D412yes—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
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×C59—21no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59C4×D412yes—
262C23×C59C23×C411yescharacteristic
263D4×C59—44no—
264D4×C59—44no—
265D4×C59—44no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
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—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
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—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—21no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—21no—
298C2×C4×C59—21no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59C4×D412yes—
308C2×C4×C59C4×D412yes—
309C2×C4×C59C4×D412yes—
310C2×C4×C59#13112yes—
311C2×C4×C59C22×D411yescharacteristic
312C2×C4×C59C22×D411yescharacteristic
313C2×C4×C59C2×#4111yescharacteristic
314C2×C4×C59C2×#4111yescharacteristic
315C2×C4×C59H(5,𝔽2)11yescharacteristic
316C2×C4×C592−1+411yescharacteristic
317C59⋊C8—22no—
318C59⋊C8—22no—
319C59⋊C8—22no—
320C59⋊C8—22no—
321C59⋊C8—41no—
322C59⋊C8—41no—
323C59⋊C8—41no—
324C59⋊C8—41no—
325#22994—591nomaximal, Sylow
326C22×C59—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—41no—
330C22×C59—41no—
331C22×C59—41no—
332C22×C59—41no—
333C22×C59—41no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59—41no—
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×C59C2×#13111yescharacteristic
351C22×C59#56811yescharacteristic
352C22×C59#56811yescharacteristic
353C22×C59#56811yescharacteristic
354C4×C59—22no—
355C4×C59—22no—
356C4×C59—22no—
357C4×C59—22no—
358C4×C59—41no—
359C4×C59—41no—
360C4×C59—41no—
361C4×C59—41no—
362C4×C59—41no—
363C4×C59—41no—
364C4×C59—41no—
365C4×C59D4211yescharacteristic
366C4×C59#54711yescharacteristic
367C4×C59#54811yescharacteristic
368C4×C59#55311yescharacteristic
369C2×#436—591no—
370C2×#436—591no—
371C2×#435—591no—
372C2×#424—591no—
373#2392D5911yescharacteristic
374#1955—591no—
375#1939—591no—
376#1924—591no—
377#1923—591no—
378#1870—591no—
379#1869—591no—
380#1851—591no—
381#1851—591no—
382#1771—591no—
383#1750—591no—
384C2×C59—42no—
385C2×C59—81no—
386C2×C59—81no—
387C2×C59#236111yescharacteristic
388C2×C59#293011yescharacteristic
389C2×C59#293011yescharacteristic
390C2×C59#293311yescharacteristic
391C2×C59#293511yescharacteristic
392C2×C59#299311yescharacteristic
393C2×C59#299511yescharacteristic
394C22×M16—591no—
395C22×M16—591no—
396C22×M16—591no—
397C23×C8—591no—
398C2×C4×D4C2×D5911yescharacteristic
399C2×C4×D4C2×D5911yescharacteristic
400C2×C4×D4C2×D5911yescharacteristic
401C2×#117C2×D5911yescharacteristic
402#436—1184no—
403#436—1184no—
404#435—1184no—
405#424—1184no—
406C2×C4⋊C8—591no—
407C2×C4⋊C8—591no—
408C2×C4⋊C8—591no—
409C2×C4⋊C8—591no—
410C2×C4⋊C8—591no—
411C2×C4⋊C8—591no—
412C2×C22⋊C8—591no—
413C2×C22⋊C8—591no—
414C2×C22⋊C8—591no—
415C2×C22⋊C8—591no—
416C2×C22⋊C8—591no—
417C2×C22⋊C8—591no—
418C2×C22⋊C8—591no—
419C2×C22⋊C8—591no—
420C2×#97—591no—
421C2×#97—591no—
422C2×C4×C8—591no—
423C2×C4×C8—591no—
424#398Dic5911yescharacteristic
425#397Dic5911yescharacteristic
426#396Dic5911yescharacteristic
427#396Dic5911yescharacteristic
428#394Dic5911yescharacteristic
429#394Dic5911yescharacteristic
430#394Dic5911yescharacteristic
431#392Dic5911yescharacteristic
432C4×C4⋊C4C2×D5911yescharacteristic
433C4×C22⋊C4C2×D5911yescharacteristic
434C4×C22⋊C4C2×D5911yescharacteristic
435#336—591no—
436#336—591no—
437#336—591no—
438#336—591no—
439#336—591no—
440#336—591no—
441C59#2299411yescharacteristic, complemented, Sylow
442C22×D4C2×Dic5911yescharacteristic
443C22×D4C2×Dic5911yescharacteristic
444C22×D4C2×Dic5911yescharacteristic
445C23×C4C22×D5911yescharacteristic
446C23×C4C22×D5911yescharacteristic
447C23×C4C22×D5911yescharacteristic
448C2×M16—1182no—
449C2×M16—1182no—
450C2×M16—1182no—
451C2×M16—1182no—
452C2×M16—1182no—
453C2×M16—1182no—
454C2×M16—2361no—
455C2×M16—2361no—
456C2×M16—2361no—
457C22×C8—591no—
458C22×C8—591no—
459C22×C8—591no—
460C22×C8—591no—
461C22×C8—591no—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8—591no—
465C22×C8—1182no—
466C22×C8—1182no—
467C22×C8—2361no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4C2×Dic5911yescharacteristic
477C2×C4⋊C4C2×Dic5911yescharacteristic
478C2×C4⋊C4C2×Dic5911yescharacteristic
479C2×C4⋊C4C2×Dic5911yescharacteristic
480C2×C4⋊C4C2×Dic5911yescharacteristic
481C2×C4⋊C4C2×Dic5911yescharacteristic
482C2×C4⋊C4C2×Dic5911yescharacteristic
483C2×C22⋊C4C2×Dic5911yescharacteristic
484C2×C22⋊C4C2×Dic5911yescharacteristic
485C2×C22⋊C4C2×Dic5911yescharacteristic
486C2×C22⋊C4C2×Dic5911yescharacteristic
487C2×C22⋊C4C2×Dic5911yescharacteristic
488C2×C22⋊C4C2×Dic5911yescharacteristic
489C2×C22⋊C4C2×Dic5911yescharacteristic
490C2×C22⋊C4C2×Dic5911yescharacteristic
491C2×C22⋊C4C2×Dic5911yescharacteristic
492C2×C22⋊C4C2×Dic5911yescharacteristic
493C2×C22⋊C4C2×Dic5911yescharacteristic
494C2×C22⋊C4C2×Dic5911yescharacteristic
495C2×C42C22×D5911yescharacteristic
496C2×C42C22×D5911yescharacteristic
497C2×C42C22×D5911yescharacteristic
498C2×C42C22×D5911yescharacteristic
499C4⋊C8—594no—
500C4⋊C8—1182no—
501C4⋊C8—1182no—
502C4⋊C8—1182no—
503C4⋊C8—1182no—
504C4⋊C8—1182no—
505C22⋊C8—594no—
506C22⋊C8—1182no—
507C22⋊C8—1182no—
508C22⋊C8—1182no—
509C22⋊C8—1182no—
510C22⋊C8—1182no—
511C22⋊C8—2361no—
512C22⋊C8—2361no—
513#97—1182no—
514#97—1182no—
515C4×C8—1182no—
516C4×C8—1182no—
517#95C2×Dic5911yescharacteristic
518#95C2×Dic5911yescharacteristic
519#95C2×Dic5911yescharacteristic
520#95C2×Dic5911yescharacteristic
521#95C2×Dic5911yescharacteristic
522#95C2×Dic5911yescharacteristic
523C24C22×Dic5911yescharacteristic
524C24C22×Dic5911yescharacteristic
525C24C22×Dic5911yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
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×C4D4×D5912yes—
552C22×C4#1174568712yes—
553C22×C4C22×Dic5911yescharacteristic
554C22×C4C22×Dic5911yescharacteristic
555C22×C4C22×Dic5911yescharacteristic
556C22×C4C22×Dic5911yescharacteristic
557C22×C4C22×Dic5911yescharacteristic
558C22×C4C22×Dic5911yescharacteristic
559C22×C4C22×Dic5911yescharacteristic
560C22×C4C22×Dic5911yescharacteristic
561C22×C4C22×Dic5911yescharacteristic
562C22×C4C22×Dic5911yescharacteristic
563C22×C4C22×Dic5911yescharacteristic
564C22×C4C23×D5911yescharacteristic
565M16—2364no—
566M16—2364no—
567M16—2364no—
568C2×C8—592no—
569C2×C8—592no—
570C2×C8—592no—
571C2×C8—592no—
572C2×C8—1181no—
573C2×C8—1181no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8—1181no—
578C2×C8—1181no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8—1181no—
582C2×C8—1181no—
583C2×C8—1181no—
584C2×C8—1181no—
585C2×C8—1181no—
586C2×C8—1181no—
587C2×C8—1181no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—1181no—
591C2×C8—1181no—
592C2×C8—2364no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—41no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42D4×D5912yes—
619C42#1174568712yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23D4×Dic5912yes—
641C23C23×Dic5911yescharacteristic
642D4—44no—
643D4—44no—
644D4—44no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
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—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4D4×Dic5912yes—
687C2×C4D4×Dic5912yes—
688C2×C4D4×Dic5912yes—
689C2×C4#1427373412yes—
690C2×C4C2×D4×D5911yescharacteristic
691C2×C4C2×D4×D5911yescharacteristic
692C2×C4C2×#1174568711yescharacteristic
693C2×C4C2×#1174568711yescharacteristic
694C2×C4#1427377311yescharacteristic
695C2×C4#1427377411yescharacteristic
696C8—1182no—
697C8—1182no—
698C8—1182no—
699C8—1182no—
700C8—2361no—
701C8—2361no—
702C8—2361no—
703C8—2361no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22C2×D4×Dic5911yescharacteristic
726C22C2×D4×Dic5911yescharacteristic
727C22#1683788511yescharacteristic
728C22C2×#1427373411yescharacteristic
729C22#1683816911yescharacteristic
730C22#1683816911yescharacteristic
731C22#1683816911yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4#1683803611yescharacteristic
744C4#1683805211yescharacteristic
745C4#1683805811yescharacteristic
746C4#1683810411yescharacteristic
747C2—42no—
748C2—81no—
749C2—81no—
750C2#2142711611yescharacteristic
751C2#2143280011yescharacteristic
752C2#2143280011yescharacteristic
753C2#2143282311yescharacteristic
754C2#2143284011yescharacteristic
755C2#2143324511yescharacteristic
756C2#2143326611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#2392C2
prime radicalC59×#392C4
cosocleC22×C4×C59C24
hypercenter#2392D59
hypocenterC59#22994
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. C2×#16837480C2semidirect
2. C2×#16837480C2semidirect
3. C2×#16837474C2semidirect
4. C2×#16837429C2semidirect
5. #21424895C2semidirect
6. #21424815C2semidirect
7. #21424711C2semidirect
8. #21424704C2semidirect
9. #21424394C2semidirect
10. #21424389C2semidirect
11. #21424281C2semidirect
12. #21424281C2semidirect
13. #21423971C2semidirect
14. #21423862C2semidirect
88. C4⋊(C59⋊C8)D4semidirect
96. C22⋊(C59⋊C8)D4semidirect
441. C59#22994semidirect

Maximal subgroups

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

subgroupindex
C2×#168374802
C2×#168374742
C2×#168374292
#214248952
#214248152
#214247112
#214247042
#214243942
#214243892
#214242812
#214239712
#214238622
C59×#23922
#2299459