Finite Group Databasebeta

← #28617087

Subgroups — #28617087

Order 15104.

1058 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837507C211yesmaximal, characteristic, complemented
2C2×C4×#11745672C211yesmaximal, characteristic, complemented
3#21426778C211yesmaximal, characteristic
4#21425431C211yesmaximal, characteristic, complemented
5#21425339C211yesmaximal, characteristic, complemented
6#21425296C211yesmaximal, characteristic
7#21425289C211yesmaximal, characteristic
8#21425244C211yesmaximal, characteristic, complemented
9#21425196C211yesmaximal, characteristic, complemented
10#21425104C211yesmaximal, characteristic
11#21425104C211yesmaximal, characteristic
12#21423926C211yesmaximal, characteristic, complemented
13C4×#14273651C211yesmaximal, characteristic, complemented
14#21423862C211yesmaximal, characteristic
15C2×C59×#541C211yesmaximal, characteristic
16C22×#11745672C2211yescharacteristic
17C22×#11745672C2211yescharacteristic
18C2×#14273706C2211yescharacteristic
19C2×C4×Dic118C2211yescharacteristic
20#16837507—24no—
21C4×#11745672—24no—
22C2×#14273660C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×#14273651C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273650C2211yescharacteristic
31C2×#14273650C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×#14273638C2211yescharacteristic
35C2×C4×C59⋊C8C2211yescharacteristic
36#16837308C2211yescharacteristic
37#16837300C2211yescharacteristic
38#16837297—21no—
39#16837296—21no—
40#16837290—21no—
41#16837283—21no—
42#16837262C2211yescharacteristic
43C4×C4⋊Dic59C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C59×#541—24no—
51C59×#541—24no—
52C2×C4⋊Q8×C59C2211yescharacteristic
53C2×#126×C59—21no—
54C2×#126×C59—21no—
55C2×#125×C59—21no—
56C2×#125×C59—21no—
57C2×#125×C59C2211yescharacteristic
58C2×C22⋊Q8×C59C2211yescharacteristic
59C2×C22⋊Q8×C59C2211yescharacteristic
60C2×C4×Q8×C59C2211yescharacteristic
61C2×C4×Q8×C59C2211yescharacteristic
62C2×#117×C59C2211yescharacteristic
63C22×Dic118C2311yescharacteristic
64C2×#11745672—22no—
65C2×#11745672—22no—
66C2×#11745672—22no—
67C2×#11745672—22no—
68C2×#11745672—22no—
69C2×#11745672—22no—
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74#14273706—22no—
75#14273706—22no—
76C4×Dic118—22no—
77C4×Dic118—22no—
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×Dic59⋊C4—21no—
82C2×Dic59⋊C4—21no—
83C2×Dic59⋊C4—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C4×Dic59—21no—
87C2×C4×Dic59—21no—
88#14273660—22no—
89#14273658—22no—
90#14273651—22no—
91#14273651—22no—
92#14273651—22no—
93#14273651—22no—
94#14273651—22no—
95#14273651—22no—
96#14273650—22no—
97#14273650—22no—
98C22⋊(C59⋊C8)—22no—
99C22⋊(C59⋊C8)—22no—
100#14273638—22no—
101C4×C59⋊C8—22no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C22×Q8×C59C2311yescharacteristic
108C22×Q8×C59C2311yescharacteristic
109C23×C4×C59C2311yescharacteristic
110C4⋊Q8×C59—22no—
111C4⋊Q8×C59—22no—
112#126×C59—28no—
113#126×C59—28no—
114#125×C59—28no—
115#125×C59—28no—
116#125×C59—22no—
117#125×C59—22no—
118C22⋊Q8×C59—22no—
119C22⋊Q8×C59—22no—
120C22⋊Q8×C59—22no—
121C22⋊Q8×C59—22no—
122C4×Q8×C59—22no—
123C4×Q8×C59—22no—
124C4×Q8×C59D414yes—
125C4×Q8×C59D414yes—
126#117×C59—22no—
127#117×C59—22no—
128C2×C4⋊C4×C59—21no—
129C2×C4⋊C4×C59—21no—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—21no—
134C2×C4⋊C4×C59—21no—
135C2×C4⋊C4×C59—21no—
136C2×C4⋊C4×C59D411yescharacteristic
137C2×C4⋊C4×C59D411yescharacteristic
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
140C2×C22⋊C4×C59—21no—
141C2×C22⋊C4×C59—21no—
142C2×C22⋊C4×C59D411yescharacteristic
143C2×C22⋊C4×C59D411yescharacteristic
144C2×C42×C59—21no—
145C2×C42×C59—21no—
146C2×C42×C59C2311yescharacteristic
147C2×C42×C59C2311yescharacteristic
148C24×C59C2×D411yescharacteristic
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59—21no—
157C2×Q8×C59—21no—
158C2×Q8×C59—21no—
159C2×Q8×C59C2×D412yes—
160C2×Q8×C59C2×D412yes—
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×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2411yescharacteristic
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—21no—
180C22×Dic59—21no—
181C2×Dic118—21no—
182C2×Dic118—21no—
183C2×Dic118—21no—
184C2×Dic118—21no—
185C2×Dic118—21no—
186C2×Dic118#4112yes—
187C4⋊C4×C59—24no—
188C4⋊C4×C59—24no—
189C4⋊C4×C59—24no—
190C4⋊C4×C59—24no—
191C4⋊C4×C59—24no—
192C4⋊C4×C59—24no—
193C4⋊C4×C59—24no—
194C4⋊C4×C59—24no—
195C4⋊C4×C59—22no—
196C4⋊C4×C59—22no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59C2×D412yes—
200C4⋊C4×C59C2×D412yes—
201C22⋊C4×C59—24no—
202C22⋊C4×C59—24no—
203C22⋊C4×C59—22no—
204C22⋊C4×C59—22no—
205C42×C59—24no—
206C42×C59—24no—
207C42×C59—21no—
208C42×C59—21no—
209C42×C59C2×D412yes—
210C42×C59C2×D412yes—
211C22⋊Dic59—24no—
212C22⋊Dic59—81no—
213#11745672—28no—
214#11745672—28no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59#4112yes—
221Dic59⋊C4—24no—
222Dic59⋊C4—42no—
223Dic59⋊C4—81no—
224C4×Dic59—42no—
225C4×Dic59—81no—
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#4112yes—
237C2×C59⋊C8#4112yes—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59C22×D411yescharacteristic
246Q8×C59—22no—
247Q8×C59—22no—
248Q8×C59—22no—
249Q8×C59—22no—
250Q8×C59—41no—
251Q8×C59—41no—
252Q8×C59—41no—
253Q8×C59—41no—
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—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59#12012yes—
284C2×C4×C59#12012yes—
285C2×C4×C59C22×D411yescharacteristic
286C2×C4×C59C22×D411yescharacteristic
287C2×C4×C59C2×#4111yescharacteristic
288C2×C4×C59C2×#4111yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59C2×#4111yescharacteristic
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303Dic118—22no—
304Dic118—22no—
305Dic118—41no—
306Dic118—41no—
307C59⋊C8—22no—
308C59⋊C8—22no—
309C59⋊C8—41no—
310C59⋊C8—41no—
311#23586—591nomaximal, Sylow
312C22×C59—41no—
313C22×C59—41no—
314C22×C59—41no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59C2×#12011yescharacteristic
320C22×C59#52511yescharacteristic
321C22×C59#53211yescharacteristic
322C22×C59#57711yescharacteristic
323C22×C59#57811yescharacteristic
324C22×C59#57811yescharacteristic
325C22×C59#57811yescharacteristic
326C4×C59—22no—
327C4×C59—22no—
328C4×C59—41no—
329C4×C59—42no—
330C4×C59—42no—
331C4×C59—41no—
332C4×C59—42no—
333C4×C59—41no—
334C4×C59—42no—
335C4×C59#52511yescharacteristic
336C4×C59#52511yescharacteristic
337C4×C59#53211yescharacteristic
338C4×C59#53211yescharacteristic
339Dic59—42no—
340Dic59—42no—
341Dic59—81no—
342Dic59—81no—
343C2×#541D5911yescharacteristic
344C2×#441—591no—
345C2×C4×Q16—591no—
346#2323—591no—
347#2059—591no—
348#2043—591no—
349#2036—591no—
350#2035—591no—
351#2026—591no—
352#2016—591no—
353#2001—591no—
354#2001—591no—
355#1763—591no—
356C4×#103—591no—
357#1750—591no—
358C2×C59—81no—
359C2×C59#238811yescharacteristic
360C2×C59#301111yescharacteristic
361C2×C59#301311yescharacteristic
362C2×C59#312011yescharacteristic
363C2×C59#312711yescharacteristic
364C2×C59#317711yescharacteristic
365C2×C59#317811yescharacteristic
366C22×Q16—591no—
367C22×Q16—591no—
368#541—24no—
369#541—24no—
370C2×C4⋊Q8C2×D5911yescharacteristic
371C2×#126—21no—
372C2×#126—21no—
373C2×#125—21no—
374C2×#125—21no—
375C2×#125C2×D5911yescharacteristic
376C2×C22⋊Q8—591no—
377C2×C22⋊Q8C2×D5911yescharacteristic
378C2×C22⋊Q8C2×D5911yescharacteristic
379C2×C4×Q8—591no—
380C2×C4×Q8C2×D5911yescharacteristic
381C2×C4×Q8C2×D5911yescharacteristic
382C2×#117C2×D5911yescharacteristic
383#441—1184no—
384C4×Q16—1184no—
385C2×#107—591no—
386C2×#106—591no—
387C2×#103—591no—
388C2×#103—591no—
389C2×#103—591no—
390C2×#103—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×#103—591no—
394C2×#103—591no—
395C2×C22⋊C8—591no—
396C2×C22⋊C8—591no—
397C2×#97—591no—
398C2×C4×C8—591no—
399#391—591no—
400#389—591no—
401#389—1181no—
402#388—1181no—
403#388—1181no—
404#387—1181no—
405#380—591no—
406C4×C4⋊C4—591no—
407#340—591no—
408#340—591no—
409#340—591no—
410#340—591no—
411#336—591no—
412#336—591no—
413C59#2358611yescharacteristic, complemented, Sylow
414C22×Q8—591no—
415C22×Q8C22×D5911yescharacteristic
416C22×Q8C22×D5911yescharacteristic
417C23×C4C22×D5911yescharacteristic
418C2×Q16—1182no—
419C2×Q16—1182no—
420C2×Q16—1182no—
421C2×Q16—1182no—
422C2×Q16—1182no—
423C2×Q16—1182no—
424C22×C8—591no—
425C22×C8—591no—
426C22×C8—591no—
427C22×C8—591no—
428C4⋊Q8—22no—
429C4⋊Q8—22no—
430#126—28no—
431#126—28no—
432#125—28no—
433#125—28no—
434#125—22no—
435#125—22no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8—1182no—
441C22⋊Q8—1182no—
442C4×Q8—22no—
443C4×Q8—22no—
444C4×Q8—1182no—
445C4×Q8—1182no—
446C4×Q8C22⋊D5914yes—
447C4×Q8C22⋊D5914yes—
448#117—22no—
449#117—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—591no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—591no—
461C2×C4⋊C4—1181no—
462C2×C4⋊C4—1181no—
463C2×C4⋊C4—1181no—
464C2×C4⋊C4C22⋊D5911yescharacteristic
465C2×C4⋊C4C22⋊D5911yescharacteristic
466C2×C4⋊C4C22×D5911yescharacteristic
467C2×C4⋊C4C22×D5911yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1181no—
471C2×C22⋊C4—1181no—
472C2×C22⋊C4C22⋊D5911yescharacteristic
473C2×C22⋊C4C22⋊D5911yescharacteristic
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—1181no—
477C2×C42—1181no—
478C2×C42C22×D5911yescharacteristic
479C2×C42C22×D5911yescharacteristic
480#107—1182no—
481#106—1182no—
482#103—1182no—
483#103—1182no—
484#103—1182no—
485#103—1182no—
486#103—1182no—
487#103—1182no—
488#103—1182no—
489#103—1182no—
490C22⋊C8—1182no—
491C22⋊C8—1182no—
492#97—1182no—
493C4×C8—1182no—
494#95—1181no—
495#95—1181no—
496#95—1181no—
497#95—1181no—
498#95—1181no—
499C24C2×C22⋊D5911yescharacteristic
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—592no—
511C2×Q8—1181no—
512C2×Q8—1181no—
513C2×Q8—1181no—
514C2×Q8—1181no—
515C2×Q8—1181no—
516C2×Q8C2×C22⋊D5912yes—
517C2×Q8C2×C22⋊D5912yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—1181no—
529C22×C4—1181no—
530C22×C4—1181no—
531C22×C4—1181no—
532C22×C4C2×C22⋊D5911yescharacteristic
533C22×C4C2×C22⋊D5911yescharacteristic
534C22×C4C2×C22⋊D5911yescharacteristic
535C22×C4C2×C22⋊D5911yescharacteristic
536C22×C4C2×C22⋊D5911yescharacteristic
537C22×C4C23×D5911yescharacteristic
538Q16—1188no—
539Q16—1188no—
540C2×C8—592no—
541C2×C8—592no—
542C2×C8—1181no—
543C2×C8—1181no—
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—592no—
565C4⋊C4—1184no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4—4721no—
572C4⋊C4—2362no—
573C4⋊C4C2×C22⋊D5912yes—
574C4⋊C4C2×C22⋊D5912yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—1184no—
580C22⋊C4—4721no—
581C42—24no—
582C42—24no—
583C42—21no—
584C42—21no—
585C42—4721no—
586C42—2362no—
587C42C2×C22⋊D5912yes—
588C42C2×C22⋊D5912yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23C22×C22⋊D5911yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—1182no—
606Q8—1182no—
607Q8—2361no—
608Q8—2361no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—1182no—
639C2×C4—1182no—
640C2×C4—2361no—
641C2×C4—2361no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4#1427369612yes—
651C2×C4#1427369612yes—
652C2×C4C22×C22⋊D5911yescharacteristic
653C2×C4C22×C22⋊D5911yescharacteristic
654C2×C4#41×D5911yescharacteristic
655C2×C4#41×D5911yescharacteristic
656C2×C4#41×D5911yescharacteristic
657C2×C4#41×D5911yescharacteristic
658C8—1182no—
659C8—1182no—
660C8—2361no—
661C8—2361no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22C2×#1427369611yescharacteristic
670C22#1683790911yescharacteristic
671C22#1683794811yescharacteristic
672C22#1683821011yescharacteristic
673C22#1683821711yescharacteristic
674C22#1683821711yescharacteristic
675C22#1683821711yescharacteristic
676C4—22no—
677C4—22no—
678C4—41no—
679C4—42no—
680C4—41no—
681C4—42no—
682C4—41no—
683C4—42no—
684C4—42no—
685C4—4721no—
686C4—4721no—
687C4—2362no—
688C4—2362no—
689C4#1683790911yescharacteristic
690C4#1683790911yescharacteristic
691C4#1683794811yescharacteristic
692C4#1683794811yescharacteristic
693C2—81no—
694C2#2142730911yescharacteristic
695C2#2143339111yescharacteristic
696C2#2143341111yescharacteristic
697C2#2143430411yescharacteristic
698C2#2143439111yescharacteristic
699C2#2143474911yescharacteristic
700C2#2143476611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#541C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
hypercenterC2×#541D59
hypocenterC59#23586
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×#16837507C2semidirect
2. C2×C4×#11745672C2semidirect
4. #21425431C2semidirect
5. #21425339C2semidirect
8. #21425244C2semidirect
9. #21425196C2semidirect
12. #21423926C2semidirect
13. C4×#14273651C2semidirect
413. C59#23586semidirect

Maximal subgroups

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

subgroupindex
C2×#168375072
C2×C4×#117456722
#214267782
#214254312
#214253392
#214252962
#214252892
#214252442
#214251962
#214251042
#214239262
C4×#142736512
#214238622
C2×C59×#5412
#2358659