Finite Group Databasebeta

← #28615186

Subgroups — #28615186

Order 15104.

758 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21425037C211yesmaximal, characteristic, complemented
2#21425033C211yesmaximal, characteristic, complemented
3#21424711C211yesmaximal, characteristic, complemented
4#21424711C211yesmaximal, characteristic, complemented
5#21424704C211yesmaximal, characteristic, complemented
6#21424704C211yesmaximal, characteristic, complemented
7#21424394C211yesmaximal, characteristic
8#21424389C211yesmaximal, characteristic
9#21424281C211yesmaximal, characteristic, complemented
10#21424281C211yesmaximal, characteristic, complemented
11#21424276C211yesmaximal, characteristic, complemented
12#21424276C211yesmaximal, characteristic, complemented
13#21424213C211yesmaximal, characteristic, complemented
14#21424213C211yesmaximal, characteristic, complemented
15C4×#124×C59C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×C4⋊(C59⋊C8)C2211yescharacteristic
19C2×C4⋊(C59⋊C8)C2211yescharacteristic
20C2×C4⋊(C59⋊C8)C2211yescharacteristic
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×C4⋊(C59⋊C8)C2211yescharacteristic
23C2×C4⋊(C59⋊C8)C2211yescharacteristic
24C2×C22⋊(C59⋊C8)C2211yescharacteristic
25C2×C22⋊(C59⋊C8)C2211yescharacteristic
26C2×C22⋊(C59⋊C8)C2211yescharacteristic
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×C22⋊(C59⋊C8)C2211yescharacteristic
29C2×C22⋊(C59⋊C8)C2211yescharacteristic
30C2×#14273638C2211yescharacteristic
31C2×C4×C59⋊C8C2211yescharacteristic
32#16837157C2211yescharacteristic
33#16837157C2211yescharacteristic
34#16837157C2211yescharacteristic
35#16837157C2211yescharacteristic
36#16837157C2211yescharacteristic
37#16837157C2211yescharacteristic
38#16837157C2211yescharacteristic
39#16837157C2211yescharacteristic
40#16837157C2211yescharacteristic
41#16837157C2211yescharacteristic
42#16837157C2211yescharacteristic
43#16837157C2211yescharacteristic
44C2×#124×C59C411yescharacteristic
45C2×C4×Q8×C59C2211yescharacteristic
46C2×C4×D4×C59C2211yescharacteristic
47C59×#391C411yescharacteristic
48C59×#390C411yescharacteristic
49C59×#388C411yescharacteristic
50C59×#388C411yescharacteristic
51C59×#388C411yescharacteristic
52C59×#388C411yescharacteristic
53C59×#382C411yescharacteristic
54C4×C22⋊C4×C59C2211yescharacteristic
55C4×C22⋊C4×C59C2211yescharacteristic
56C4×C22⋊C4×C59C2211yescharacteristic
57C4×C22⋊C4×C59C2211yescharacteristic
58C43×C59C2211yescharacteristic
59C2×#11745664—41no—
60C2×#11745664—41no—
61C2×#11745664—41no—
62C22×C59⋊C8—41no—
63C22×C59⋊C8—41no—
64C22×C59⋊C8—41no—
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C4⋊(C59⋊C8)—41no—
74C4⋊(C59⋊C8)—41no—
75C4⋊(C59⋊C8)—41no—
76C4⋊(C59⋊C8)—41no—
77C4⋊(C59⋊C8)—41no—
78C4⋊(C59⋊C8)—41no—
79C22⋊(C59⋊C8)—41no—
80C22⋊(C59⋊C8)—41no—
81C22⋊(C59⋊C8)—41no—
82C22⋊(C59⋊C8)—41no—
83C22⋊(C59⋊C8)—41no—
84C22⋊(C59⋊C8)—41no—
85#14273638—41no—
86C4×C59⋊C8—41no—
87C22×Q8×C59C2×C411yescharacteristic
88C22×D4×C59C2×C411yescharacteristic
89C23×C4×C59C2311yescharacteristic
90C23×C4×C59C2311yescharacteristic
91#124×C59—24no—
92C4×Q8×C59—41no—
93C4×Q8×C59—41no—
94C4×D4×C59—41no—
95C4×D4×C59—41no—
96C2×C4⋊C4×C59C2×C411yescharacteristic
97C2×C4⋊C4×C59C2×C411yescharacteristic
98C2×C4⋊C4×C59C2×C411yescharacteristic
99C2×C4⋊C4×C59C2×C411yescharacteristic
100C2×C22⋊C4×C59C2×C411yescharacteristic
101C2×C22⋊C4×C59C2×C411yescharacteristic
102C2×C22⋊C4×C59C2×C411yescharacteristic
103C2×C22⋊C4×C59C2×C411yescharacteristic
104C2×C22⋊C4×C59C2×C411yescharacteristic
105C2×C22⋊C4×C59C2×C411yescharacteristic
106C2×C22⋊C4×C59C2×C411yescharacteristic
107C2×C22⋊C4×C59C2×C411yescharacteristic
108C2×C22⋊C4×C59C2×C411yescharacteristic
109C2×C22⋊C4×C59C2×C411yescharacteristic
110C2×C42×C59C2×C411yescharacteristic
111C2×C42×C59C2×C411yescharacteristic
112C2×C42×C59C2×C411yescharacteristic
113C2×C42×C59C2×C411yescharacteristic
114C2×C42×C59C2311yescharacteristic
115C2×C42×C59C2311yescharacteristic
116C2×C42×C59C2311yescharacteristic
117C2×C42×C59C2311yescharacteristic
118C2×C42×C59C2311yescharacteristic
119#95×C59C2×C411yescharacteristic
120#95×C59C2×C411yescharacteristic
121#95×C59C2×C411yescharacteristic
122#95×C59C2×C411yescharacteristic
123#95×C59C2×C411yescharacteristic
124#95×C59C2×C411yescharacteristic
125#95×C59C2×C411yescharacteristic
126#95×C59C2×C411yescharacteristic
127C24×C59C22×C411yescharacteristic
128C24×C59C22×C411yescharacteristic
129C2×Q8×C59—22no—
130C2×Q8×C59—22no—
131C2×Q8×C59—41no—
132C2×D4×C59—22no—
133C2×D4×C59—22no—
134C2×D4×C59—41no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59C22×C411yescharacteristic
148C22×C4×C59C22×C411yescharacteristic
149C22×C4×C59C22×C411yescharacteristic
150C22×C4×C59C22×C411yescharacteristic
151C22×C4×C59C22×C411yescharacteristic
152C22×C4×C59C22×C411yescharacteristic
153C22×C4×C59C22×C411yescharacteristic
154C22×C4×C59C22×C411yescharacteristic
155C22×C4×C59C22×C411yescharacteristic
156C22×C4×C59C22×C411yescharacteristic
157C22×C4×C59C22×C411yescharacteristic
158C22×C4×C59C22×C411yescharacteristic
159C22×C4×C59C2411yescharacteristic
160C4⋊C4×C59—41no—
161C4⋊C4×C59—41no—
162C4⋊C4×C59—41no—
163C4⋊C4×C59—41no—
164C22⋊C4×C59—22no—
165C22⋊C4×C59—22no—
166C22⋊C4×C59—22no—
167C22⋊C4×C59—22no—
168C22⋊C4×C59—22no—
169C22⋊C4×C59—41no—
170C22⋊C4×C59—41no—
171C22⋊C4×C59—41no—
172C22⋊C4×C59—41no—
173C22⋊C4×C59M1614yescomplemented
174C42×C59—22no—
175C42×C59—22no—
176C42×C59—22no—
177C42×C59—21no—
178C42×C59—21no—
179C42×C59—21no—
180C42×C59—21no—
181C42×C59—21no—
182C42×C59—21no—
183C42×C59—21no—
184C42×C59—21no—
185C42×C59—21no—
186C42×C59—21no—
187C42×C59—41no—
188#11745664—44no—
189C2×C59⋊C8—21no—
190C2×C59⋊C8—21no—
191C2×C59⋊C8—21no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C2×C59⋊C8—21no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8—21no—
199C2×C59⋊C8—21no—
200C2×C59⋊C8—21no—
201C2×C59⋊C8—21no—
202C2×C59⋊C8—21no—
203C2×C59⋊C8—21no—
204C2×C59⋊C8—21no—
205C2×C59⋊C8—21no—
206C2×C59⋊C8—21no—
207C2×C59⋊C8—21no—
208C2×C59⋊C8—21no—
209C2×C59⋊C8—21no—
210C2×C59⋊C8—21no—
211C2×C59⋊C8—21no—
212C2×C59⋊C8—21no—
213C2×C59⋊C8—44no—
214C23×C59—21no—
215C23×C59—21no—
216C23×C59—21no—
217C23×C59—21no—
218C23×C59—21no—
219C23×C59—21no—
220C23×C59—21no—
221C23×C59—21no—
222C23×C59—21no—
223C23×C59—21no—
224C23×C59—21no—
225C23×C59—21no—
226C23×C59—21no—
227C23×C59C2×M1612yes—
228C23×C59C23×C411yescharacteristic
229Q8×C59—44no—
230D4×C59—44no—
231C2×C4×C59—21no—
232C2×C4×C59—21no—
233C2×C4×C59—21no—
234C2×C4×C59—21no—
235C2×C4×C59—21no—
236C2×C4×C59—21no—
237C2×C4×C59—21no—
238C2×C4×C59—21no—
239C2×C4×C59—21no—
240C2×C4×C59—21no—
241C2×C4×C59—21no—
242C2×C4×C59—21no—
243C2×C4×C59—21no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—21no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59C2×M1612yes—
272C2×C4×C59C2×M1612yes—
273C2×C4×C59#13112yes—
274C2×C4×C59#13112yes—
275C2×C4×C59H(5,𝔽2)11yescharacteristic
276C2×C4×C59H(5,𝔽2)11yescharacteristic
277C2×C4×C59H(5,𝔽2)11yescharacteristic
278C2×C4×C59H(5,𝔽2)11yescharacteristic
279C2×C4×C592−1+411yescharacteristic
280C2×C4×C592−1+411yescharacteristic
281C59⋊C8—41no—
282C59⋊C8—41no—
283C59⋊C8—41no—
284C59⋊C8—41no—
285C59⋊C8—41no—
286C59⋊C8—41no—
287C59⋊C8—41no—
288C59⋊C8—41no—
289#23349—591nomaximal, Sylow
290C22×C59—22no—
291C22×C59—22no—
292C22×C59—22no—
293C22×C59—41no—
294C22×C59—41no—
295C22×C59—41no—
296C22×C59—41no—
297C22×C59—41no—
298C22×C59—41no—
299C22×C59—41no—
300C22×C59—41no—
301C22×C59—41no—
302C22×C59—41no—
303C22×C59—41no—
304C22×C59#51811yescharacteristic
305C22×C59#52011yescharacteristic
306C22×C59#52011yescharacteristic
307C22×C59C22×M1611yescharacteristic
308C22×C59C2×#13111yescharacteristic
309C22×C59C2×#13111yescharacteristic
310C22×C59#56811yescharacteristic
311C4×C59—22no—
312C4×C59—22no—
313C4×C59—22no—
314C4×C59—22no—
315C4×C59—41no—
316C4×C59—41no—
317C4×C59—41no—
318C4×C59—41no—
319C4×C59—41no—
320C4×C59—41no—
321C4×C59—41no—
322C4×C59—41no—
323C4×C59H(3,𝔽4)11yescharacteristic
324C4×C59#56211yescharacteristic
325C4×C59#56211yescharacteristic
326C4×C59#56311yescharacteristic
327C4×#124D5911yescharacteristic
328#1985—591no—
329#1984—591no—
330#1924—591no—
331#1924—591no—
332#1923—591no—
333#1923—591no—
334#1870—591no—
335#1869—591no—
336#1851—591no—
337#1851—591no—
338#1850—591no—
339#1850—591no—
340#1831—591no—
341#1831—591no—
342C2×C59—42no—
343C2×C59—81no—
344C2×C59#237911yescharacteristic
345C2×C59#297411yescharacteristic
346C2×C59#298111yescharacteristic
347C2×C59#298911yescharacteristic
348C2×C59#299011yescharacteristic
349C2×C59#299311yescharacteristic
350C2×C59#299411yescharacteristic
351C22×M16—591no—
352C23×C8—591no—
353C2×#124Dic5911yescharacteristic
354C2×C4×Q8C2×D5911yescharacteristic
355C2×C4×D4C2×D5911yescharacteristic
356C2×C4⋊C8—591no—
357C2×C4⋊C8—591no—
358C2×C4⋊C8—591no—
359C2×C4⋊C8—591no—
360C2×C4⋊C8—591no—
361C2×C4⋊C8—591no—
362C2×C22⋊C8—591no—
363C2×C22⋊C8—591no—
364C2×C22⋊C8—591no—
365C2×C22⋊C8—591no—
366C2×C22⋊C8—591no—
367C2×C22⋊C8—591no—
368C2×#97—591no—
369C2×C4×C8—591no—
370#391Dic5911yescharacteristic
371#390Dic5911yescharacteristic
372#388Dic5911yescharacteristic
373#388Dic5911yescharacteristic
374#388Dic5911yescharacteristic
375#388Dic5911yescharacteristic
376#382Dic5911yescharacteristic
377C4×C22⋊C4C2×D5911yescharacteristic
378C4×C22⋊C4C2×D5911yescharacteristic
379C4×C22⋊C4C2×D5911yescharacteristic
380C4×C22⋊C4C2×D5911yescharacteristic
381C43C2×D5911yescharacteristic
382#336—591no—
383#336—591no—
384#336—591no—
385#336—591no—
386#336—591no—
387#336—591no—
388#336—591no—
389#336—591no—
390#336—591no—
391#336—591no—
392#336—591no—
393#336—591no—
394C59#2334911yescharacteristic, complemented, Sylow
395C22×Q8C2×Dic5911yescharacteristic
396C22×D4C2×Dic5911yescharacteristic
397C23×C4C22×D5911yescharacteristic
398C23×C4C22×D5911yescharacteristic
399C2×M16—2361no—
400C2×M16—2361no—
401C2×M16—2361no—
402C22×C8—591no—
403C22×C8—591no—
404C22×C8—591no—
405C22×C8—591no—
406C22×C8—591no—
407C22×C8—591no—
408C22×C8—591no—
409C22×C8—591no—
410C22×C8—2361no—
411C22×C8—2361no—
412C22×C8—2361no—
413#124—24no—
414C4×Q8—41no—
415C4×Q8—41no—
416C4×D4—41no—
417C4×D4—41no—
418C2×C4⋊C4C2×Dic5911yescharacteristic
419C2×C4⋊C4C2×Dic5911yescharacteristic
420C2×C4⋊C4C2×Dic5911yescharacteristic
421C2×C4⋊C4C2×Dic5911yescharacteristic
422C2×C22⋊C4C2×Dic5911yescharacteristic
423C2×C22⋊C4C2×Dic5911yescharacteristic
424C2×C22⋊C4C2×Dic5911yescharacteristic
425C2×C22⋊C4C2×Dic5911yescharacteristic
426C2×C22⋊C4C2×Dic5911yescharacteristic
427C2×C22⋊C4C2×Dic5911yescharacteristic
428C2×C22⋊C4C2×Dic5911yescharacteristic
429C2×C22⋊C4C2×Dic5911yescharacteristic
430C2×C22⋊C4C2×Dic5911yescharacteristic
431C2×C22⋊C4C2×Dic5911yescharacteristic
432C2×C42C2×Dic5911yescharacteristic
433C2×C42C2×Dic5911yescharacteristic
434C2×C42C2×Dic5911yescharacteristic
435C2×C42C2×Dic5911yescharacteristic
436C2×C42C22×D5911yescharacteristic
437C2×C42C22×D5911yescharacteristic
438C2×C42C22×D5911yescharacteristic
439C2×C42C22×D5911yescharacteristic
440C2×C42C22×D5911yescharacteristic
441C4⋊C8—2361no—
442C4⋊C8—2361no—
443C4⋊C8—2361no—
444C4⋊C8—2361no—
445C4⋊C8—2361no—
446C4⋊C8—2361no—
447C22⋊C8—2361no—
448C22⋊C8—2361no—
449C22⋊C8—2361no—
450C22⋊C8—2361no—
451C22⋊C8—2361no—
452C22⋊C8—2361no—
453#97—2361no—
454C4×C8—2361no—
455#95C2×Dic5911yescharacteristic
456#95C2×Dic5911yescharacteristic
457#95C2×Dic5911yescharacteristic
458#95C2×Dic5911yescharacteristic
459#95C2×Dic5911yescharacteristic
460#95C2×Dic5911yescharacteristic
461#95C2×Dic5911yescharacteristic
462#95C2×Dic5911yescharacteristic
463C24C22×Dic5911yescharacteristic
464C24C22×Dic5911yescharacteristic
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—41no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—41no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4C22×Dic5911yescharacteristic
484C22×C4C22×Dic5911yescharacteristic
485C22×C4C22×Dic5911yescharacteristic
486C22×C4C22×Dic5911yescharacteristic
487C22×C4C22×Dic5911yescharacteristic
488C22×C4C22×Dic5911yescharacteristic
489C22×C4C22×Dic5911yescharacteristic
490C22×C4C22×Dic5911yescharacteristic
491C22×C4C22×Dic5911yescharacteristic
492C22×C4C22×Dic5911yescharacteristic
493C22×C4C22×Dic5911yescharacteristic
494C22×C4C22×Dic5911yescharacteristic
495C22×C4C23×D5911yescharacteristic
496M16—2364no—
497C2×C8—1181no—
498C2×C8—1181no—
499C2×C8—1181no—
500C2×C8—1181no—
501C2×C8—1181no—
502C2×C8—1181no—
503C2×C8—1181no—
504C2×C8—1181no—
505C2×C8—1181no—
506C2×C8—1181no—
507C2×C8—1181no—
508C2×C8—1181no—
509C2×C8—1181no—
510C2×C8—1181no—
511C2×C8—1181no—
512C2×C8—1181no—
513C2×C8—1181no—
514C2×C8—1181no—
515C2×C8—1181no—
516C2×C8—1181no—
517C2×C8—1181no—
518C2×C8—1181no—
519C2×C8—1181no—
520C2×C8—1181no—
521C2×C8—2364no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4#1174566414yescomplemented
536C42—22no—
537C42—22no—
538C42—22no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—41no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23C2×#1174566412yes—
564C23C23×Dic5911yescharacteristic
565Q8—44no—
566D4—44no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4C2×#1174566412yes—
608C2×C4C2×#1174566412yes—
609C2×C4#1427373412yes—
610C2×C4#1427373412yes—
611C2×C4#1427377211yescharacteristic
612C2×C4#1427377211yescharacteristic
613C2×C4#1427377311yescharacteristic
614C2×C4#1427377311yescharacteristic
615C2×C4#1427377411yescharacteristic
616C2×C4#1427377411yescharacteristic
617C8—2361no—
618C8—2361no—
619C8—2361no—
620C8—2361no—
621C8—2361no—
622C8—2361no—
623C8—2361no—
624C8—2361no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22#1683787711yescharacteristic
640C22#1683788511yescharacteristic
641C22#1683788511yescharacteristic
642C22C22×#1174566411yescharacteristic
643C22C2×#1427373411yescharacteristic
644C22C2×#1427373411yescharacteristic
645C22#1683816911yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4#1683814411yescharacteristic
659C4#1683814611yescharacteristic
660C4#1683814611yescharacteristic
661C4#1683815211yescharacteristic
662C2—42no—
663C2—81no—
664C2#2142727011yescharacteristic
665C2#2143313111yescharacteristic
666C2#2143317211yescharacteristic
667C2#2143321311yescharacteristic
668C2#2143322111yescharacteristic
669C2#2143324511yescharacteristic
670C2#2143325611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC4×#124×C59C2
prime radicalC22×D4×C59C2×C4
cosocleC22×C4×C59C24
hypercenterC4×#124D59
hypocenterC59#23349
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #21425037C2semidirect
2. #21425033C2semidirect
3. #21424711C2semidirect
4. #21424711C2semidirect
5. #21424704C2semidirect
6. #21424704C2semidirect
9. #21424281C2semidirect
10. #21424281C2semidirect
11. #21424276C2semidirect
12. #21424276C2semidirect
13. #21424213C2semidirect
14. #21424213C2semidirect
173. C22⋊C4×C59M16semidirect
394. C59#23349semidirect
535. C22⋊C4#11745664semidirect

Maximal subgroups

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

subgroupindex
#214250372
#214250332
#214247112
#214247042
#214243942
#214243892
#214242812
#214242762
#214242132
C4×#124×C592
#2334959