Finite Group Databasebeta

← C2×#21434970 #29459366

Subgroups — C2×#21434970 #29459366

Order 15104.

2314 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837978C211yesmaximal, characteristic, complemented
2C2×#16837968C211yesmaximal, characteristic
3#21434970C2116yesmaximal, direct product factor
4C2×#16837746C211yesmaximal, characteristic, complemented
5C2×#16837745C211yesmaximal, characteristic, complemented
6C2×#16837726C211yesmaximal, characteristic, complemented
7C2×#16837649C211yesmaximal, characteristic, complemented
8C2×#16837647C211yesmaximal, characteristic, complemented
9C2×#16837632C211yesmaximal, characteristic, complemented
10C2×#16837630C211yesmaximal, characteristic, complemented
11C2×#16837543C211yesmaximal, characteristic, complemented
12C2×#16837540C211yesmaximal, characteristic, complemented
13C2×#16837554C211yesmaximal, characteristic, complemented
14C2×#16837554C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×Dic118C2211yescharacteristic, complemented
19C22×D4×D59C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22C22×#11745670C2211yescharacteristic
23C22×#11745670C2211yescharacteristic
24C22×#11745659C2211yescharacteristic, complemented
25C22×C8×D59C2211yescharacteristic, complemented
26#16837978—24no—
27#16837978C2218yescomplemented
28#16837968—24no—
29#16837968C2218yes—
30C2×#14273727—21no—
31C2×#14273723—21no—
32C2×#14273715—21no—
33C2×#14273713—21no—
34C2×#14273711—21no—
35C2×#14273711—21no—
36C2×#14273707C2211yescharacteristic
37C2×#14273707C2211yescharacteristic
38C2×#14273707C2211yescharacteristic, complemented
39C2×#14273707C2211yescharacteristic, complemented
40C2×#14273702C2211yescharacteristic
41C2×#14273701C2211yescharacteristic
42C2×#14273698C2211yescharacteristic
43C2×#14273697—21no—
44C2×#14273695—21no—
45C2×#14273685C2211yescharacteristic
46#16837746C2218yescomplemented
47#16837745C2218yescomplemented
48#16837726C2218yescomplemented
49#16837649C2218yescomplemented
50#16837647C2218yescomplemented
51#16837632C2218yescomplemented
52#16837630C2218yescomplemented
53#16837554C2218yescomplemented
54#16837554C2218yescomplemented
55#16837543C2218yescomplemented
56#16837540C2218yescomplemented
57C2×#14273660C2211yescharacteristic, complemented
58C2×#14273658C2211yescharacteristic, complemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273652C2211yescharacteristic, complemented
61C2×#14273650C2211yescharacteristic, complemented
62C2×#14273650C2211yescharacteristic, complemented
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65#16837367C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic, complemented
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—42no—
79C2×#11745685—42no—
80C2×#11745685D414yes—
81C2×#11745685C2314yes—
82C22×Dic118—21no—
83C22×Dic118—22no—
84C22×Dic118—42no—
85C22×Dic118—42no—
86C22×Dic118D411yescharacteristic
87C22×Dic118C2311yescharacteristic
88C22×Dic118C2311yescharacteristic
89C22×Dic118C2314yescomplemented
90C22×D236—21no—
91C22×D236D411yescharacteristic
92C22×D236C2311yescharacteristic
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C22×C22⋊D59—21no—
96C22×C22⋊D59D411yescharacteristic
97C22×C22⋊D59D411yescharacteristic
98C2×D4×D59—22no—
99C2×D4×D59—42no—
100C2×D4×D59—42no—
101C2×D4×D59C2314yes—
102C23×Dic59—21no—
103C22×C4×D59C2311yescharacteristic
104C22×C4×D59C2311yescharacteristic
105C2×#11745660—42no—
106C2×#11745660—42no—
107C2×#11745660C2314yes—
108C2×#11745660C2314yes—
109C2×#11745670—42no—
110C2×#11745670—42no—
111C2×#11745670C2314yes—
112C2×#11745670C2314yes—
113C2×#11745659—42no—
114C2×#11745659C2314yescomplemented
115C22×C59⋊C8C2311yescharacteristic
116C22×C59⋊C8C2311yescharacteristic
117C2×C8×D59—42no—
118C2×C8×D59C2314yescomplemented
119#14273727—28no—
120#14273723—28no—
121#14273715—28no—
122#14273713—28no—
123#14273711—28no—
124#14273711—28no—
125#14273707—22no—
126#14273707—22no—
127#14273707—22no—
128#14273707—22no—
129#14273707C2314yes—
130#14273707C2314yes—
131#14273707C2314yescomplemented
132#14273707C2314yescomplemented
133#14273702—22no—
134#14273702C2314yes—
135#14273701—22no—
136#14273701C2314yes—
137#14273698—22no—
138#14273698C2314yes—
139#14273697—28no—
140#14273695—28no—
141#14273685—22no—
142#14273685C2314yes—
143C2×C4⋊Dic59—21no—
144C2×C4⋊Dic59—21no—
145C2×C4⋊Dic59—21no—
146C2×C4⋊Dic59—21no—
147C2×C4⋊Dic59C2311yescharacteristic
148C2×C22⋊Dic59—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4—21no—
152C2×(C2×D59)⋊C4—21no—
153C2×(C2×D59)⋊C4—21no—
154C2×(C2×D59)⋊C4—21no—
155C2×(C2×D59)⋊C4—21no—
156C2×C4×Dic59—21no—
157#14273660C2314yescomplemented
158#14273658C2314yescomplemented
159#14273652C2314yescomplemented
160#14273652C2314yescomplemented
161#14273650C2314yescomplemented
162#14273650C2314yescomplemented
163#14273647C2314yes—
164#14273647C2314yes—
165C22⋊(C59⋊C8)C2314yescomplemented
166(C2×D59)⋊C8C2314yes—
167(C2×D59)⋊C8C2314yes—
168C22×D4×C59—21no—
169C22×D4×C59C2311yescharacteristic
170C23×C4×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173#121×C59—22no—
174#121×C59C2314yes—
175#117×C59—22no—
176#117×C59C2314yescomplemented
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59—21no—
182C2×C42×C59—21no—
183#107×C59C2314yescomplemented
184#106×C59C2314yescomplemented
185#102×C59C2314yes—
186#102×C59C2314yes—
187C22⋊C8×C59C2314yescomplemented
188C24×C59—21no—
189C24×C59C2×D411yescharacteristic
190C23×D59—21no—
191C23×D59—24no—
192C23×D59—44no—
193C23×D59—82no—
194C23×D59—82no—
195C23×D59C2×D411yescharacteristic
196C23×D59C2×D411yescharacteristic
197C2×D4×C59—24no—
198C2×D4×C59—21no—
199C2×D4×C59—22no—
200C2×D4×C59—22no—
201C2×D4×C59—82no—
202C2×D4×C59C2412yes—
203C22×C4×C59—22no—
204C22×C4×C59—22no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C2×C22⋊D59—24no—
213C2×C22⋊D59—24no—
214C2×C22⋊D59—24no—
215C2×C22⋊D59—42no—
216C2×C22⋊D59—42no—
217C2×C22⋊D59—44no—
218C2×C22⋊D59—82no—
219C2×C22⋊D59—82no—
220C2×C22⋊D59C2×D414yes—
221C2×C22⋊D59C2×D414yes—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—24no—
226C22×Dic59—44no—
227C22×Dic59C2×D411yescharacteristic
228C22×Dic59C2×D411yescharacteristic
229D4×D59—44no—
230D4×D59—44no—
231D4×D59—48no—
232#11745685—48no—
233#11745685—44no—
234#11745685—44no—
235C2×D236—22no—
236C2×D236—22no—
237C2×D236—21no—
238C2×D236—24no—
239C2×D236—42no—
240C2×D236—82no—
241C2×D236C2×D414yes—
242C2×D236C2412yes—
243C2×C4×D59—22no—
244C2×C4×D59—22no—
245C2×C4×D59—22no—
246C2×C4×D59—22no—
247C2×C4×D59C2×D412yes—
248C2×C4×D59C2×D412yes—
249C2×C4×D59C2412yes—
250C2×C4×D59C2412yes—
251C2×Dic118—22no—
252C2×Dic118—22no—
253C2×Dic118—22no—
254C2×Dic118—22no—
255C2×Dic118—21no—
256C2×Dic118—21no—
257C2×Dic118—24no—
258C2×Dic118—44no—
259C2×Dic118—44no—
260C2×Dic118—42no—
261C2×Dic118—44no—
262C2×Dic118—48no—
263C2×Dic118C2×D414yes—
264C2×Dic118C2412yes—
265C2×Dic118C2412yes—
266C2×C8×C59—22no—
267C2×C8×C59—22no—
268C2×C8×C59C2412yes—
269C2×C8×C59C2412yes—
270C4⋊C4×C59—21no—
271C4⋊C4×C59—21no—
272C4⋊C4×C59—21no—
273C4⋊C4×C59C2412yes—
274C4⋊C4×C59C2412yes—
275C4⋊C4×C59C2412yes—
276C22⋊C4×C59—24no—
277C22⋊C4×C59—24no—
278C42×C59—24no—
279C22⋊Dic59—24no—
280#11745670—44no—
281#11745670—44no—
282(C2×D59)⋊C4—24no—
283(C2×D59)⋊C4—24no—
284(C2×D59)⋊C4—24no—
285(C2×D59)⋊C4—24no—
286(C2×D59)⋊C4—24no—
287(C2×D59)⋊C4—24no—
288(C2×D59)⋊C4—24no—
289C4⋊Dic59—21no—
290C4⋊Dic59—24no—
291C4⋊Dic59—24no—
292C4⋊Dic59—24no—
293C4⋊Dic59—24no—
294C4⋊Dic59C2412yes—
295C4×Dic59—24no—
296C2×C59⋊C8—22no—
297C2×C59⋊C8—22no—
298C2×C59⋊C8C2412yes—
299C2×C59⋊C8C2412yes—
300#11745660—44no—
301#11745660—44no—
302#11745659—44no—
303C8×D59—44no—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—22no—
307C23×C59—22no—
308C23×C59—42no—
309C23×C59—42no—
310C23×C59—42no—
311C23×C59C22×D412yes—
312C23×C59C22×D411yescharacteristic
313C22×D59—22no—
314C22×D59—22no—
315C22×D59—22no—
316C22×D59—22no—
317C22×D59—22no—
318C22×D59—22no—
319C22×D59—22no—
320C22×D59—48no—
321C22×D59—42no—
322C22×D59—42no—
323C22×D59—42no—
324C22×D59—84no—
325C22×D59—84no—
326C22×D59—816no—
327C22×D59C22×D412yes—
328C22×D59C22×D412yes—
329D4×C59—22no—
330D4×C59—22no—
331D4×C59—42no—
332D4×C59—84no—
333C2×C4×C59—22no—
334C2×C4×C59—24no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—22no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—42no—
341C2×C4×C59—42no—
342C2×C4×C59—42no—
343C2×C4×C59C22×D412yes—
344C2×C4×C59C22×D411yescharacteristic
345C2×C4×C59H(5,𝔽2)12yes—
346C2×C4×C59H(5,𝔽2)12yes—
347C2×C4×C59C2511yescharacteristic
348C22⋊D59—44no—
349C22⋊D59—44no—
350C22⋊D59—48no—
351C22⋊D59—84no—
352C22⋊D59—84no—
353C2×Dic59—22no—
354C2×Dic59—22no—
355C2×Dic59—22no—
356C2×Dic59—22no—
357C2×Dic59—22no—
358C2×Dic59—48no—
359C2×Dic59—42no—
360C2×Dic59—42no—
361C2×Dic59—42no—
362C2×Dic59C22×D412yes—
363C2×Dic59C22×D412yes—
364D236—22no—
365D236—22no—
366D236—44no—
367D236—42no—
368D236—84no—
369C4×D59—24no—
370C4×D59—24no—
371C4×D59—22no—
372C4×D59—22no—
373C4×D59—22no—
374C4×D59—22no—
375Dic118—22no—
376Dic118—22no—
377Dic118—22no—
378Dic118—22no—
379Dic118—44no—
380Dic118—48no—
381Dic118—42no—
382Dic118—42no—
383C8×C59—22no—
384C8×C59—22no—
385C59⋊C8—22no—
386C59⋊C8—22no—
387C2×#3200—591nomaximal, Sylow
388C22×C59—22no—
389C22×C59—22no—
390C22×C59—22no—
391C22×C59—44no—
392C22×C59—42no—
393C22×C59—42no—
394C22×C59—42no—
395C22×C59—84no—
396C22×C59#53412yes—
397C22×C59#57712yes—
398C22×C59#57712yes—
399C22×C59C23×D411yescharacteristic
400C2×D59—22no—
401C2×D59—22no—
402C2×D59—22no—
403C2×D59—22no—
404C2×D59—22no—
405C2×D59—22no—
406C2×D59—44no—
407C2×D59—44no—
408C2×D59—42no—
409C2×D59—42no—
410C2×D59—42no—
411C2×D59—816no—
412C2×D59—84no—
413C4×C59—22no—
414C4×C59—42no—
415C4×C59—42no—
416C4×C59—42no—
417C4×C59#53412yes—
418C4×C59C2×H(5,𝔽2)11yescharacteristic
419C4×C59C2×H(5,𝔽2)11yescharacteristic
420Dic59—22no—
421Dic59—22no—
422Dic59—42no—
423Dic59—42no—
424Dic59—42no—
425C2×#536—591no—
426C2×#535—591no—
427#3200—5916no—
428C2×#485—591no—
429C2×#485—591no—
430C2×#482—591no—
431C2×#482D5911yescharacteristic, complemented
432C2×#468—591no—
433C2×#468—591no—
434C2×#465—591no—
435C2×#465—591no—
436C2×#448—591no—
437C2×#448—591no—
438C2×#450—591no—
439C2×#450—591no—
440C2×#408—591no—
441C2×C59—42no—
442C2×C59—82no—
443C2×C59#320014yescomplemented
444C2×C59C2×#53411yescharacteristic
445C2×C59C2×#57711yescharacteristic
446C2×C59C2×#57711yescharacteristic
447D59—42no—
448D59—42no—
449D59—82no—
450C22×#41—591no—
451C23×Q8—591no—
452C23×D4—591no—
453C22×SD16—591no—
454C22×SD16—591no—
455C22×SD16—591no—
456C22×SD16—591no—
457C22×M16—591no—
458C23×C8—591no—
459#536—598no—
460#536—1184no—
461#535—598no—
462#535—1184no—
463C2×C4⋊Q8—1181no—
464C2×#127—1181no—
465C2×#124—1181no—
466C2×#124—1181no—
467C2×#123—1181no—
468C2×#123—1181no—
469C2×C22⋊Q8—591no—
470C2×C22⋊Q8—591no—
471C2×C22⋊Q8—591no—
472C2×C22⋊Q8—591no—
473C2×#121—591no—
474C2×#121—591no—
475C2×#121—591no—
476C2×#121C2×D5911yescharacteristic
477C2×#120—1181no—
478C2×#120—1181no—
479C2×#117—591no—
480C2×#117C2×D5911yescharacteristic, complemented
481#485—598no—
482#485—598no—
483#482—598no—
484#482C2×D5918yescomplemented
485#468—598no—
486#468—598no—
487#465—598no—
488#465—598no—
489#450—598no—
490#450—598no—
491#448—598no—
492#448—598no—
493C2×#107—591no—
494C2×#107C2×D5911yescharacteristic, complemented
495C2×#106—591no—
496C2×#106C2×D5911yescharacteristic, complemented
497C2×#103—591no—
498C2×#103—591no—
499C2×#103—591no—
500C2×#103—591no—
501C2×#102—591no—
502C2×#102—591no—
503C2×#102C2×D5911yescharacteristic
504C2×#102C2×D5911yescharacteristic
505#408—598no—
506C2×C22⋊C8—591no—
507C2×C22⋊C8—591no—
508C2×C22⋊C8—591no—
509C2×C22⋊C8C2×D5911yescharacteristic, complemented
510C59C2×#320011yescharacteristic, complemented, Sylow
511C25—1181no—
512C2×#41—594no—
513C2×#41—594no—
514C2×#41—2362no—
515C2×#41—2362no—
516C22×Q8—591no—
517C22×Q8—591no—
518C22×Q8—591no—
519C22×Q8—594no—
520C22×Q8—1181no—
521C22×Q8—1182no—
522C22×Q8—2362no—
523C22×Q8—2362no—
524C22×D4—21no—
525C22×D4—591no—
526C22×D4—591no—
527C22×D4—594no—
528C22×D4—591no—
529C22×D4—591no—
530C22×D4—1181no—
531C22×D4—1182no—
532C22×D4—1181no—
533C22×D4—1181no—
534C22×D4—1181no—
535C22×D4—2362no—
536C22×D4—2362no—
537C22×D4C22×D5911yescharacteristic
538C23×C4—591no—
539C23×C4—591no—
540C23×C4—1181no—
541C23×C4C22×D5911yescharacteristic
542C2×SD16—594no—
543C2×SD16—594no—
544C2×SD16—594no—
545C2×SD16—594no—
546C2×SD16—2362no—
547C2×SD16—2362no—
548C2×SD16—2362no—
549C2×SD16—2362no—
550C2×M16—594no—
551C2×M16—2362no—
552C22×C8—591no—
553C22×C8—591no—
554C22×C8—594no—
555C22×C8—2362no—
556C22×C8C22×D5911yescharacteristic
557C22×C8C22×D5911yescharacteristic
558C4⋊Q8—1188no—
559#127—1188no—
560#124—1188no—
561#124—1188no—
562#123—1188no—
563#123—1188no—
564C22⋊Q8—594no—
565C22⋊Q8—594no—
566C22⋊Q8—594no—
567C22⋊Q8—594no—
568C22⋊Q8—1182no—
569C22⋊Q8—1182no—
570C22⋊Q8—1182no—
571C22⋊Q8—1182no—
572#121—22no—
573#121—594no—
574#121—594no—
575#121—594no—
576#121—1182no—
577#121—1182no—
578#121—1182no—
579#121C22×D5914yes—
580#120—1188no—
581#120—1188no—
582#117—22no—
583#117—594no—
584#117—1182no—
585#117C22×D5914yescomplemented
586C2×C4⋊C4—591no—
587C2×C4⋊C4—1181no—
588C2×C4⋊C4—1181no—
589C2×C4⋊C4—1181no—
590C2×C4⋊C4—1181no—
591C2×C4⋊C4C22×D5911yescharacteristic
592C2×C4⋊C4C22×D5911yescharacteristic
593C2×C4⋊C4C22×D5911yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—1181no—
597C2×C22⋊C4—1181no—
598C2×C22⋊C4—1181no—
599C2×C22⋊C4—1181no—
600C2×C22⋊C4—1181no—
601C2×C22⋊C4—1181no—
602C2×C22⋊C4—1181no—
603C2×C22⋊C4—1181no—
604C2×C42—21no—
605C2×C42—1181no—
606#107—594no—
607#107C22×D5914yescomplemented
608#106—594no—
609#106C22×D5914yescomplemented
610#103—594no—
611#103—594no—
612#103—594no—
613#103—594no—
614#102—594no—
615#102—594no—
616#102C22×D5914yes—
617#102C22×D5914yes—
618C22⋊C8—594no—
619C22⋊C8—594no—
620C22⋊C8—594no—
621C22⋊C8C22×D5914yescomplemented
622C24—21no—
623C24—591no—
624C24—591no—
625C24—1184no—
626C24—1181no—
627C24—4722no—
628C24—4722no—
629C24—2364no—
630C24D4×D5911yescharacteristic
631#41—2368no—
632#41—2364no—
633#41—2364no—
634C2×Q8—594no—
635C2×Q8—592no—
636C2×Q8—592no—
637C2×Q8—1181no—
638C2×Q8—1181no—
639C2×Q8—1184no—
640C2×Q8—1182no—
641C2×Q8—1182no—
642C2×Q8—1182no—
643C2×Q8—1182no—
644C2×Q8—2362no—
645C2×Q8—2364no—
646C2×Q8—2364no—
647C2×Q8—2364no—
648C2×Q8—2368no—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—82no—
654C2×D4—594no—
655C2×D4—594no—
656C2×D4—594no—
657C2×D4—592no—
658C2×D4—1184no—
659C2×D4—1184no—
660C2×D4—1184no—
661C2×D4—1184no—
662C2×D4—1181no—
663C2×D4—1182no—
664C2×D4—1182no—
665C2×D4—4722no—
666C2×D4—4722no—
667C2×D4—4722no—
668C2×D4—2362no—
669C2×D4—2364no—
670C2×D4—2364no—
671C2×D4—2368no—
672C2×D4—2362no—
673C2×D4—2362no—
674C2×D4—2364no—
675C2×D4C23×D5912yes—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—591no—
682C22×C4—591no—
683C22×C4—592no—
684C22×C4—592no—
685C22×C4—592no—
686C22×C4—592no—
687C22×C4—1182no—
688C22×C4—1182no—
689C22×C4—1182no—
690C22×C4—1182no—
691C22×C4—1184no—
692C22×C4—1181no—
693C22×C4—1181no—
694C22×C4—1181no—
695C22×C4—2364no—
696C22×C4D4×D5912yes—
697C22×C4D4×D5911yescharacteristic
698C22×C4C23×D5912yes—
699C22×C4C23×D5911yescharacteristic
700SD16—2364no—
701SD16—2364no—
702SD16—2364no—
703SD16—2364no—
704M16—2364no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—592no—
708C2×C8—592no—
709C2×C8—1182no—
710C2×C8—1182no—
711C2×C8—2364no—
712C2×C8C23×D5912yes—
713C2×C8C23×D5912yes—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—592no—
718C4⋊C4—1184no—
719C4⋊C4—1184no—
720C4⋊C4—1184no—
721C4⋊C4—1184no—
722C4⋊C4—1181no—
723C4⋊C4C23×D5912yes—
724C4⋊C4C23×D5912yes—
725C4⋊C4C23×D5912yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—1184no—
729C22⋊C4—1184no—
730C22⋊C4—1184no—
731C22⋊C4—1184no—
732C22⋊C4—1184no—
733C22⋊C4—1184no—
734C22⋊C4—1184no—
735C22⋊C4—1184no—
736C42—24no—
737C42—1184no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—592no—
746C23—592no—
747C23—1182no—
748C23—1182no—
749C23—1182no—
750C23—1182no—
751C23—1182no—
752C23—1182no—
753C23—1182no—
754C23—4724no—
755C23—4724no—
756C23—47216no—
757C23—2368no—
758C23—2362no—
759C23—2362no—
760C23—2362no—
761C23C2×D4×D5912yes—
762C23C2×D4×D5911yescharacteristic
763Q8—1182no—
764Q8—1182no—
765Q8—1182no—
766Q8—1182no—
767Q8—2364no—
768Q8—2368no—
769Q8—2362no—
770Q8—2362no—
771D4—22no—
772D4—22no—
773D4—42no—
774D4—84no—
775D4—1182no—
776D4—1182no—
777D4—4724no—
778D4—4724no—
779D4—4724no—
780D4—2364no—
781D4—2364no—
782D4—2364no—
783D4—2368no—
784D4—2362no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—592no—
796C2×C4—592no—
797C2×C4—1182no—
798C2×C4—1182no—
799C2×C4—1184no—
800C2×C4—1184no—
801C2×C4—1182no—
802C2×C4—1182no—
803C2×C4—1182no—
804C2×C4—1182no—
805C2×C4—1182no—
806C2×C4—1182no—
807C2×C4—1182no—
808C2×C4—2368no—
809C2×C4—2362no—
810C2×C4—2362no—
811C2×C4—2362no—
812C2×C4C2×D4×D5912yes—
813C2×C4C2×D4×D5911yescharacteristic
814C2×C4#1427377312yes—
815C2×C4#1427377312yes—
816C2×C4C24×D5911yescharacteristic
817C8—22no—
818C8—22no—
819C8—1182no—
820C8—1182no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—1182no—
830C22—1182no—
831C22—1182no—
832C22—1182no—
833C22—1182no—
834C22—1182no—
835C22—47216no—
836C22—4724no—
837C22—2362no—
838C22—2362no—
839C22—2362no—
840C22—2364no—
841C22—2364no—
842C22#1683796312yes—
843C22#1683820912yes—
844C22#1683821212yes—
845C22C22×D4×D5911yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—1182no—
851C4—1182no—
852C4—2362no—
853C4—2362no—
854C4—2362no—
855C4#1683796312yes—
856C4C2×#1427377311yescharacteristic
857C4C2×#1427377311yescharacteristic
858C2—42no—
859C2—82no—
860C2—4722no—
861C2—2362no—
862C2—2362no—
863C2#2143497014yesdirect product factor
864C2C2×#1683796311yescharacteristic
865C2C2×#1683820911yescharacteristic
866C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
prime radicalC2×#16837968C2
hypercenterC2×#482D59
hypocenterC59C2×#3200
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16837978C2semidirect
3. #21434970C2direct (N × H)
4. C2×#16837746C2semidirect
5. C2×#16837745C2semidirect
6. C2×#16837726C2semidirect
7. C2×#16837649C2semidirect
8. C2×#16837647C2semidirect
9. C2×#16837632C2semidirect
10. C2×#16837630C2semidirect
11. C2×#16837543C2semidirect
12. C2×#16837540C2semidirect
13. C2×#16837554C2semidirect
14. C2×#16837554C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#482C2semidirect
18. C23×Dic118C22semidirect
24. C22×#11745659C22semidirect
25. C22×C8×D59C22semidirect
27. #16837978C22semidirect
38. C2×#14273707C22semidirect
39. C2×#14273707C22semidirect
46. #16837746C22semidirect
47. #16837745C22semidirect
48. #16837726C22semidirect
49. #16837649C22semidirect
50. #16837647C22semidirect
51. #16837632C22semidirect
52. #16837630C22semidirect
53. #16837554C22semidirect
54. #16837554C22semidirect
55. #16837543C22semidirect
56. #16837540C22semidirect
57. C2×#14273660C22semidirect
58. C2×#14273658C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273652C22semidirect
61. C2×#14273650C22semidirect
62. C2×#14273650C22semidirect
65. #16837367C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
70. C2×#117×C59C22semidirect
71. C59×#482C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
76. C2×C22⋊C8×C59C22semidirect
89. C22×Dic118C23semidirect
114. C2×#11745659C23semidirect
118. C2×C8×D59C23semidirect
131. #14273707C23semidirect
132. #14273707C23semidirect
157. #14273660C23semidirect
158. #14273658C23semidirect
159. #14273652C23semidirect
160. #14273652C23semidirect
161. #14273650C23semidirect
162. #14273650C23semidirect
165. C22⋊(C59⋊C8)C23semidirect
176. #117×C59C23semidirect
183. #107×C59C23semidirect
184. #106×C59C23semidirect
187. C22⋊C8×C59C23semidirect
431. C2×#482D59semidirect
443. C2×C59#3200semidirect
480. C2×#117C2×D59semidirect
484. #482C2×D59semidirect
494. C2×#107C2×D59semidirect
496. C2×#106C2×D59semidirect
509. C2×C22⋊C8C2×D59semidirect
510. C59C2×#3200semidirect
585. #117C22×D59semidirect
607. #107C22×D59semidirect
609. #106C22×D59semidirect
621. C22⋊C8C22×D59semidirect
863. C2#21434970direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379782
C2×#168379682
#214349702
C2×#168377462
C2×#168377452
C2×#168377262
C2×#168376492
C2×#168376472
C2×#168376322
C2×#168376302
C2×#168375432
C2×#168375402
C2×#168375542
C2×#168373672
C2×C59×#4822
C2×#320059