Finite Group Databasebeta

← C2×#21434350 #29456995

Subgroups — C2×#21434350 #29456995

Order 15104.

2210 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×#16838015C211yesmaximal, characteristic, complemented
2C2×#16837874C211yesmaximal, characteristic
3#21434350C2116yesmaximal, direct product factor
4C2×#16837746C211yesmaximal, characteristic, complemented
5C2×#16837745C211yesmaximal, characteristic, complemented
6C2×#16837699C211yesmaximal, characteristic, complemented
7C2×#16837608C211yesmaximal, characteristic, complemented
8C2×#16837607C211yesmaximal, characteristic, complemented
9C2×#16837554C211yesmaximal, characteristic
10C2×#16837554C211yesmaximal, characteristic
11C2×#16837501C211yesmaximal, characteristic, complemented
12C2×#16837499C211yesmaximal, characteristic, complemented
13C2×#16837493C211yesmaximal, characteristic, complemented
14C2×#16837489C211yesmaximal, characteristic, complemented
15C2×#16837462C211yesmaximal, characteristic, complemented
16C2×C59×#478C211yesmaximal, characteristic, complemented
17C22×D4×D59C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×#11745670C2211yescharacteristic
22#16838015—24no—
23#16838015C2218yescomplemented
24C2×#14273727C2211yescharacteristic, complemented
25C2×#14273722—21no—
26C2×#14273722—21no—
27C2×#14273718—21no—
28C2×#14273718—21no—
29C2×#14273707C2211yescharacteristic
30C2×#14273707C2211yescharacteristic
31#16837874—24no—
32#16837874C2218yes—
33C2×#14273692C2211yescharacteristic, complemented
34C2×#14273692C2211yescharacteristic, complemented
35C2×C4×D236C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×(C22⋊D59)⋊C4—21no—
40C2×#14273685C2211yescharacteristic
41C2×#14273684C2211yescharacteristic
42C22×(C2×D59)⋊C4—21no—
43C2×C22⋊C4×D59—21no—
44#16837746C2218yescomplemented
45#16837745C2218yescomplemented
46#16837699C2218yescomplemented
47#16837608C2218yescomplemented
48#16837607C2218yescomplemented
49#16837554C2218yes—
50#16837554C2218yes—
51#16837501C2218yescomplemented
52#16837499C2218yescomplemented
53#16837493C2218yescomplemented
54#16837489C2218yescomplemented
55#16837462C2218yescomplemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273652C2211yescharacteristic, complemented
61C2×#14273650C2211yescharacteristic, complemented
62C2×#14273650C2211yescharacteristic, complemented
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×(C2×D59)⋊C8C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×#14273637C2211yescharacteristic, complemented
68C2×C8×Dic59C2211yescharacteristic, complemented
69C2×#125×C59C2211yescharacteristic, complemented
70C2×C4×D4×C59C2211yescharacteristic
71C59×#478C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×C4⋊C8×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C24×D59—21no—
78C22×Dic118C2311yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C2×D4×D59—24no—
83C2×D4×D59—24no—
84C2×D4×D59—22no—
85C2×D4×D59C2314yes—
86C23×Dic59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59C2311yescharacteristic
90C2×#11745660—24no—
91C2×#11745660—24no—
92C2×#11745660C2314yes—
93C2×#11745660C2314yes—
94C2×#11745670—24no—
95C2×#11745670—24no—
96C2×#11745670C2314yes—
97C2×#11745670C2314yes—
98C22×C59⋊C8C2311yescharacteristic
99C22×C59⋊C8C2311yescharacteristic
100#14273727—22no—
101#14273727C2314yescomplemented
102#14273722—28no—
103#14273722—28no—
104#14273718—28no—
105#14273718—28no—
106#14273707—22no—
107#14273707—22no—
108#14273707C2314yes—
109#14273707C2314yes—
110#14273692—22no—
111#14273692—22no—
112#14273692C2314yescomplemented
113#14273692C2314yescomplemented
114C4×D236—22no—
115C4×D236C2314yes—
116D4×Dic59—22no—
117D4×Dic59C2314yes—
118#14273689—22no—
119#14273689C2314yes—
120C4×C22⋊D59—28no—
121(C22⋊D59)⋊C4—28no—
122#14273685—22no—
123#14273685C2314yes—
124#14273684D414yes—
125#14273684C2314yes—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59C2311yescharacteristic
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4D411yescharacteristic
134C2×Dic59⋊C4D411yescharacteristic
135C2×C22⋊Dic59—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—28no—
142C2×(C2×D59)⋊C4D411yescharacteristic
143C2×(C2×D59)⋊C4D411yescharacteristic
144C22⋊C4×D59—28no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yescomplemented
150#14273658C2314yescomplemented
151C4⋊(C59⋊C8)C2314yescomplemented
152#14273652C2314yescomplemented
153#14273652C2314yescomplemented
154#14273650C2314yescomplemented
155#14273650C2314yescomplemented
156#14273647C2314yes—
157#14273647C2314yes—
158(C2×D59)⋊C8C2314yes—
159(C2×D59)⋊C8C2314yes—
160#14273637C2314yescomplemented
161C8×Dic59C2314yescomplemented
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166#125×C59—22no—
167#125×C59C2314yescomplemented
168C4×D4×C59—22no—
169C4×D4×C59C2314yes—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C42×C59C2311yescharacteristic
177#107×C59C2314yescomplemented
178#106×C59C2314yescomplemented
179C4⋊C8×C59C2314yescomplemented
180#102×C59C2314yes—
181#102×C59C2314yes—
182C24×C59—21no—
183C23×D59—21no—
184C23×D59—28no—
185C23×D59—24no—
186C23×D59—82no—
187C23×D59—82no—
188C23×D59C2×D411yescharacteristic
189C2×D4×C59—21no—
190C2×D4×C59—22no—
191C2×D4×C59#4114yes—
192C2×D4×C59C2412yes—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—24no—
197C22×C4×C59—82no—
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2411yescharacteristic
201C2×C22⋊D59—28no—
202C2×C22⋊D59—24no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—24no—
207C22×Dic59—82no—
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211D4×D59—216no—
212D4×D59—28no—
213D4×D59—28no—
214C2×D236—21no—
215C2×D236—22no—
216C2×D236#4114yes—
217C2×D236C2412yes—
218C2×C4×D59—22no—
219C2×C4×D59—22no—
220C2×C4×D59—24no—
221C2×C4×D59—24no—
222C2×C4×D59—82no—
223C2×C4×D59—82no—
224C2×C4×D59C2×D412yes—
225C2×C4×D59C2412yes—
226C2×Dic118—22no—
227C2×Dic118—22no—
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—21no—
231C2×Dic118—21no—
232C2×Dic118C2412yes—
233C2×Dic118C2412yes—
234C2×C8×C59—22no—
235C2×C8×C59—22no—
236C2×C8×C59C2412yes—
237C2×C8×C59C2412yes—
238C4⋊C4×C59—24no—
239C4⋊C4×C59—24no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59C2412yes—
244C4⋊C4×C59C2412yes—
245C4⋊C4×C59C2412yes—
246C22⋊C4×C59—24no—
247C42×C59C2×D412yes—
248C42×C59C2412yes—
249C22⋊Dic59—24no—
250#11745670—28no—
251#11745670—28no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4—24no—
254(C2×D59)⋊C4—24no—
255(C2×D59)⋊C4—24no—
256(C2×D59)⋊C4—24no—
257(C2×D59)⋊C4C2×D414yes—
258(C2×D59)⋊C4C2×D414yes—
259C4⋊Dic59—24no—
260C4⋊Dic59—24no—
261C4⋊Dic59—21no—
262C4⋊Dic59—24no—
263C4⋊Dic59—24no—
264C4⋊Dic59C2412yes—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4C2×D414yes—
268Dic59⋊C4C2×D414yes—
269C4×Dic59—24no—
270C4×Dic59—24no—
271C4×Dic59—24no—
272C4×Dic59C2×D412yes—
273C4×Dic59C2412yes—
274C2×C59⋊C8—22no—
275C2×C59⋊C8—22no—
276C2×C59⋊C8C2412yes—
277C2×C59⋊C8C2412yes—
278#11745660—28no—
279#11745660—28no—
280C23×C59—24no—
281C23×C59—22no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59C22×D411yescharacteristic
285C22×D59—22no—
286C22×D59—24no—
287C22×D59—22no—
288C22×D59—22no—
289C22×D59—22no—
290C22×D59—216no—
291C22×D59—42no—
292C22×D59—42no—
293C22×D59—84no—
294C22×D59—84no—
295C22×D59—816no—
296C22×D59C22×D412yes—
297D4×C59—24no—
298D4×C59—22no—
299D4×C59C2×#4114yes—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59—42no—
308C2×C4×C59—84no—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D412yes—
311C2×C4×C59C22×D411yescharacteristic
312C2×C4×C59C2×#4112yes—
313C2×C4×C59C2×#4112yes—
314C2×C4×C59C2511yescharacteristic
315C22⋊D59—216no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59—84no—
326C2×Dic59C22×D412yes—
327C2×Dic59C22×D412yes—
328C2×Dic59C22×D412yes—
329D236—24no—
330D236—22no—
331D236C2×#4114yes—
332C4×D59—24no—
333C4×D59—22no—
334C4×D59—22no—
335C4×D59—84no—
336C4×D59—84no—
337Dic118—22no—
338Dic118—22no—
339Dic118—22no—
340Dic118—22no—
341Dic118—42no—
342Dic118—42no—
343C8×C59—22no—
344C8×C59—22no—
345C59⋊C8—22no—
346C59⋊C8—22no—
347C2×#3123—591nomaximal, Sylow
348C22×C59—24no—
349C22×C59—48no—
350C22×C59—42no—
351C22×C59—42no—
352C22×C59#52512yes—
353C22×C59#57712yes—
354C22×C59#57712yes—
355C22×C59C23×D411yescharacteristic
356C2×D59—22no—
357C2×D59—24no—
358C2×D59—22no—
359C2×D59—22no—
360C2×D59—44no—
361C2×D59—48no—
362C2×D59—42no—
363C2×D59—42no—
364C2×D59—816no—
365C4×C59—22no—
366C4×C59—22no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59—42no—
370C4×C59#52512yes—
371C4×C59C22×#4111yescharacteristic
372C4×C59C22×#4111yescharacteristic
373Dic59—22no—
374Dic59—22no—
375Dic59—22no—
376Dic59—42no—
377Dic59—42no—
378Dic59—42no—
379C2×#541—591no—
380C2×#518—591no—
381#3123—5916no—
382C2×#485—591no—
383C2×#485—591no—
384C2×#478—591no—
385C2×#478D5911yescharacteristic, complemented
386C2×#461—591no—
387C2×#461—591no—
388C2×#450—591no—
389C2×#450—591no—
390C2×#440—591no—
391C2×#440—591no—
392C2×C4×SD16—591no—
393C2×C4×SD16—591no—
394C2×#433—591no—
395C2×C59—44no—
396C2×C59#312314yescomplemented
397C2×C59C2×#52511yescharacteristic
398C2×C59C2×#57711yescharacteristic
399C2×C59C2×#57711yescharacteristic
400D59—42no—
401D59—44no—
402C23×D4—591no—
403C22×SD16—591no—
404C22×SD16—591no—
405C22×SD16—591no—
406C22×SD16—591no—
407#541—598no—
408#541—1184no—
409C2×C4⋊Q8—591no—
410C2×#126—1181no—
411C2×#126—1181no—
412C2×#125—1181no—
413C2×#125—1181no—
414C2×#125C2×D5911yescharacteristic, complemented
415C2×C22⋊Q8—591no—
416C2×C22⋊Q8—591no—
417#518—598no—
418#518—1184no—
419C2×C4×Q8—591no—
420C2×C4×Q8—591no—
421C2×C4×D4—591no—
422C2×C4×D4—591no—
423C2×C4×D4—591no—
424C2×C4×D4—1181no—
425C2×C4×D4—1181no—
426C2×C4×D4C2×D5911yescharacteristic
427C2×#117—591no—
428C2×#117—591no—
429C22×C22⋊C4—1181no—
430C22×C22⋊C4—1181no—
431#485—598no—
432#485—598no—
433#478—598no—
434#478C2×D5918yescomplemented
435#461—598no—
436#461—598no—
437#450—598no—
438#450—598no—
439#440—598no—
440#440—598no—
441C4×SD16—598no—
442C4×SD16—598no—
443#433—598no—
444C2×#107—591no—
445C2×#107C2×D5911yescharacteristic, complemented
446C2×#106—591no—
447C2×#106C2×D5911yescharacteristic, complemented
448C2×C4⋊C8—591no—
449C2×C4⋊C8C2×D5911yescharacteristic, complemented
450C2×#103—591no—
451C2×#103—591no—
452C2×#103—591no—
453C2×#103—591no—
454C2×#102—591no—
455C2×#102—591no—
456C2×#102C2×D5911yescharacteristic
457C2×#102C2×D5911yescharacteristic
458C2×C22⋊C8—591no—
459C2×C22⋊C8—591no—
460C2×#97—591no—
461C2×C4×C8—591no—
462C59C2×#312311yescharacteristic, complemented, Sylow
463C25—1181no—
464C22×Q8—591no—
465C22×Q8—591no—
466C22×D4—594no—
467C22×D4—591no—
468C22×D4—1182no—
469C22×D4—1181no—
470C22×D4—1184no—
471C22×D4—1184no—
472C22×D4C22×D5911yescharacteristic
473C23×C4—21no—
474C23×C4—591no—
475C23×C4—1181no—
476C23×C4—1181no—
477C23×C4—1181no—
478C2×SD16—594no—
479C2×SD16—594no—
480C2×SD16—594no—
481C2×SD16—594no—
482C2×SD16—1184no—
483C2×SD16—1184no—
484C2×SD16—1184no—
485C2×SD16—1184no—
486C22×C8—591no—
487C22×C8—591no—
488C22×C8C22×D5911yescharacteristic
489C22×C8C22×D5911yescharacteristic
490C4⋊Q8—594no—
491C4⋊Q8—1182no—
492#126—1188no—
493#126—1188no—
494#125—22no—
495#125—1188no—
496#125—1188no—
497#125C22×D5914yescomplemented
498C22⋊Q8—594no—
499C22⋊Q8—594no—
500C22⋊Q8—1182no—
501C22⋊Q8—1182no—
502C4×Q8—594no—
503C4×Q8—594no—
504C4×Q8—1182no—
505C4×Q8—1182no—
506C4×D4—22no—
507C4×D4—594no—
508C4×D4—594no—
509C4×D4—594no—
510C4×D4—1182no—
511C4×D4—1182no—
512C4×D4—1188no—
513C4×D4—1188no—
514C4×D4—1182no—
515C4×D4C22×D5914yes—
516#117—594no—
517#117—594no—
518#117—594no—
519#117—1182no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—591no—
524C2×C4⋊C4—591no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4C22×D5911yescharacteristic
532C2×C4⋊C4C22×D5911yescharacteristic
533C2×C4⋊C4C22×D5911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—591no—
536C2×C22⋊C4—591no—
537C2×C22⋊C4—1188no—
538C2×C22⋊C4—1188no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4—1181no—
541C2×C22⋊C4—1181no—
542C2×C22⋊C4—1181no—
543C2×C22⋊C4—1181no—
544C2×C22⋊C4—1181no—
545C2×C42—591no—
546C2×C42—1181no—
547C2×C42—1181no—
548C2×C42—1181no—
549C2×C42C22×D5911yescharacteristic
550#107—594no—
551#107C22×D5914yescomplemented
552#106—594no—
553#106C22×D5914yescomplemented
554C4⋊C8—594no—
555C4⋊C8C22×D5914yescomplemented
556#103—594no—
557#103—594no—
558#103—594no—
559#103—594no—
560#102—594no—
561#102—594no—
562#102C22×D5914yes—
563#102C22×D5914yes—
564C22⋊C8—594no—
565C22⋊C8—594no—
566#97—594no—
567C4×C8—594no—
568C24—21no—
569C24—591no—
570C24—1184no—
571C24—1188no—
572C24—1181no—
573C24—4722no—
574C24—4722no—
575C2×Q8—592no—
576C2×Q8—592no—
577C2×Q8—1181no—
578C2×Q8—1181no—
579C2×Q8—1182no—
580C2×Q8—1182no—
581C2×Q8—1182no—
582C2×Q8—1182no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—594no—
586C2×D4—592no—
587C2×D4—1184no—
588C2×D4—1188no—
589C2×D4—11816no—
590C2×D4—1188no—
591C2×D4—1188no—
592C2×D4—1181no—
593C2×D4—1182no—
594C2×D4#1174568914yes—
595C2×D4C23×D5912yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—591no—
602C22×C4—591no—
603C22×C4—591no—
604C22×C4—592no—
605C22×C4—592no—
606C22×C4—1184no—
607C22×C4—1184no—
608C22×C4—1182no—
609C22×C4—1182no—
610C22×C4—1181no—
611C22×C4—1181no—
612C22×C4—1181no—
613C22×C4—1184no—
614C22×C4—4722no—
615C22×C4—4722no—
616C22×C4—4722no—
617C22×C4D4×D5911yescharacteristic
618C22×C4D4×D5911yescharacteristic
619C22×C4C23×D5911yescharacteristic
620SD16—1188no—
621SD16—1188no—
622SD16—1188no—
623SD16—1188no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—592no—
627C2×C8—592no—
628C2×C8—1182no—
629C2×C8—1182no—
630C2×C8C23×D5912yes—
631C2×C8C23×D5912yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—594no—
638C4⋊C4—594no—
639C4⋊C4—592no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4—1184no—
643C4⋊C4—1184no—
644C4⋊C4—1181no—
645C4⋊C4—1184no—
646C4⋊C4—1184no—
647C4⋊C4C23×D5912yes—
648C4⋊C4C23×D5912yes—
649C4⋊C4C23×D5912yes—
650C22⋊C4—24no—
651C22⋊C4—594no—
652C22⋊C4—594no—
653C22⋊C4—1184no—
654C22⋊C4—1184no—
655C22⋊C4—1184no—
656C22⋊C4—1184no—
657C22⋊C4—1184no—
658C22⋊C4—1184no—
659C42—592no—
660C42—592no—
661C42—1184no—
662C42—1184no—
663C42—1184no—
664C42D4×D5912yes—
665C42C23×D5912yes—
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—592no—
671C23—11816no—
672C23—1182no—
673C23—1184no—
674C23—1182no—
675C23—1182no—
676C23—1182no—
677C23—4724no—
678C23—4724no—
679C23—47216no—
680C23—2362no—
681C23—2362no—
682C23C2×D4×D5911yescharacteristic
683Q8—1182no—
684Q8—1182no—
685Q8—1182no—
686Q8—1182no—
687Q8—2362no—
688Q8—2362no—
689D4—24no—
690D4—22no—
691D4—594no—
692D4—11816no—
693D4—1184no—
694D4—1182no—
695D4C2×#1174568914yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—592no—
706C2×C4—592no—
707C2×C4—592no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1184no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—4724no—
718C2×C4—4724no—
719C2×C4—4724no—
720C2×C4—2362no—
721C2×C4—2362no—
722C2×C4—2362no—
723C2×C4C2×D4×D5912yes—
724C2×C4C2×D4×D5912yes—
725C2×C4C2×D4×D5911yescharacteristic
726C2×C4#41×D5912yes—
727C2×C4C2×#1174568912yes—
728C2×C4C24×D5911yescharacteristic
729C8—22no—
730C8—22no—
731C8—1182no—
732C8—1182no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—48no—
737C22—1182no—
738C22—1182no—
739C22—1182no—
740C22—1184no—
741C22—47216no—
742C22—2362no—
743C22—2362no—
744C22—2364no—
745C22—2368no—
746C22#1683791512yes—
747C22#1683820912yes—
748C22#1683821212yes—
749C22C22×D4×D5911yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1182no—
756C4—1182no—
757C4—1182no—
758C4—2362no—
759C4—2362no—
760C4—2362no—
761C4#1683791512yes—
762C4C2×#41×D5911yescharacteristic
763C4C22×#1174568911yescharacteristic
764C2—44no—
765C2—2362no—
766C2—2364no—
767C2#2143435014yesdirect product factor
768C2C2×#1683791511yescharacteristic
769C2C2×#1683820911yescharacteristic
770C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#478C2
socleC23×C59C22×D4
prime radicalC22×D4×D59C22
hypercenterC2×#478D59
hypocenterC59C2×#3123
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16838015C2semidirect
3. #21434350C2direct (N × H)
4. C2×#16837746C2semidirect
5. C2×#16837745C2semidirect
6. C2×#16837699C2semidirect
7. C2×#16837608C2semidirect
8. C2×#16837607C2semidirect
11. C2×#16837501C2semidirect
12. C2×#16837499C2semidirect
13. C2×#16837493C2semidirect
14. C2×#16837489C2semidirect
15. C2×#16837462C2semidirect
16. C2×C59×#478C2semidirect
23. #16838015C22semidirect
24. C2×#14273727C22semidirect
33. C2×#14273692C22semidirect
34. C2×#14273692C22semidirect
44. #16837746C22semidirect
45. #16837745C22semidirect
46. #16837699C22semidirect
47. #16837608C22semidirect
48. #16837607C22semidirect
51. #16837501C22semidirect
52. #16837499C22semidirect
53. #16837493C22semidirect
54. #16837489C22semidirect
55. #16837462C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273658C22semidirect
58. C2×C4⋊(C59⋊C8)C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273652C22semidirect
61. C2×#14273650C22semidirect
62. C2×#14273650C22semidirect
67. C2×#14273637C22semidirect
68. C2×C8×Dic59C22semidirect
69. C2×#125×C59C22semidirect
71. C59×#478C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×C4⋊C8×C59C22semidirect
101. #14273727C23semidirect
112. #14273692C23semidirect
113. #14273692C23semidirect
149. #14273660C23semidirect
150. #14273658C23semidirect
151. C4⋊(C59⋊C8)C23semidirect
152. #14273652C23semidirect
153. #14273652C23semidirect
154. #14273650C23semidirect
155. #14273650C23semidirect
160. #14273637C23semidirect
161. C8×Dic59C23semidirect
167. #125×C59C23semidirect
177. #107×C59C23semidirect
178. #106×C59C23semidirect
179. C4⋊C8×C59C23semidirect
385. C2×#478D59semidirect
396. C2×C59#3123semidirect
414. C2×#125C2×D59semidirect
434. #478C2×D59semidirect
445. C2×#107C2×D59semidirect
447. C2×#106C2×D59semidirect
449. C2×C4⋊C8C2×D59semidirect
462. C59C2×#3123semidirect
497. #125C22×D59semidirect
551. #107C22×D59semidirect
553. #106C22×D59semidirect
555. C4⋊C8C22×D59semidirect
767. C2#21434350direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380152
C2×#168378742
#214343502
C2×#168377462
C2×#168377452
C2×#168376992
C2×#168376082
C2×#168376072
C2×#168375542
C2×#168375012
C2×#168374992
C2×#168374932
C2×#168374892
C2×#168374622
C2×C59×#4782
C2×#312359