Finite Group Databasebeta

← C2×#21434306 #29456948

Subgroups — C2×#21434306 #29456948

Order 15104.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838010C211yesmaximal, characteristic, complemented
2C2×#16837881C211yesmaximal, characteristic
3#21434306C2116yesmaximal, direct product factor
4C2×#16837736C211yesmaximal, characteristic, complemented
5C2×#16837734C211yesmaximal, characteristic, complemented
6C2×#16837712C211yesmaximal, characteristic, complemented
7C2×#16837700C211yesmaximal, characteristic, complemented
8C2×#16837611C211yesmaximal, characteristic, complemented
9C2×#16837605C211yesmaximal, characteristic, complemented
10C2×#16837565C211yesmaximal, characteristic
11C2×#16837561C211yesmaximal, characteristic
12C2×#16837507C211yesmaximal, characteristic, complemented
13C2×#16837502C211yesmaximal, characteristic, complemented
14C2×C4×Dic236C211yesmaximal, characteristic, complemented
15C2×#16837461C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C59C211yesmaximal, characteristic, complemented
17C22×#11745687C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21#16838010—24no—
22#16838010C2218yescomplemented
23C2×#14273725C2211yescharacteristic
24C2×#14273722—21no—
25C2×#14273721—21no—
26C2×#14273719—21no—
27C2×#14273718C2211yescharacteristic
28C2×#14273717—21no—
29C2×#14273707C2211yescharacteristic
30C2×#14273703C2211yescharacteristic
31#16837881—24no—
32#16837881C2218yes—
33C2×C4×Dic118C2211yescharacteristic
34C2×C4×Dic118C2211yescharacteristic
35C2×#14273692C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×(C22⋊D59)⋊C4—21no—
39C2×#14273684C2211yescharacteristic
40C2×#14273683—21no—
41C22×Dic59⋊C4—21no—
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837736C2218yescomplemented
44#16837734C2218yescomplemented
45#16837712C2218yescomplemented
46#16837700C2218yescomplemented
47#16837611C2218yescomplemented
48#16837605C2218yescomplemented
49#16837565C2218yes—
50#16837561C2218yes—
51#16837507C2218yescomplemented
52#16837502C2218yescomplemented
53C4×Dic236C2218yescomplemented
54#16837461C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273638C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C4×SD16×C59C2218yescomplemented
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C2×#11745687—24no—
78C2×#11745687—22no—
79C2×#11745687—24no—
80C2×#11745687C2314yes—
81C22×Dic118C2311yescharacteristic
82C22×Dic118C2311yescharacteristic
83C22×C22⋊D59—21no—
84C23×Dic59—21no—
85C23×Dic59—21no—
86C22×C4×D59—21no—
87C22×C4×D59C2311yescharacteristic
88C2×Dic236—24no—
89C2×Dic236C2314yes—
90C2×#11745672—24no—
91C2×#11745672C2314yes—
92C2×#11745670—24no—
93C2×#11745670C2314yes—
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96#14273725—22no—
97#14273725C2314yes—
98#14273722—28no—
99#14273721—28no—
100#14273719—28no—
101#14273718—22no—
102#14273718C2314yes—
103#14273717—28no—
104#14273707—22no—
105#14273707C2314yes—
106#14273703—22no—
107#14273703C2314yes—
108C4×Dic118—22no—
109C4×Dic118—22no—
110C4×Dic118C2314yes—
111C4×Dic118C2314yes—
112#14273692—22no—
113#14273692C2314yes—
114D4×Dic59—22no—
115D4×Dic59C2314yes—
116C4×C22⋊D59—28no—
117(C22⋊D59)⋊C4—28no—
118#14273684D414yes—
119#14273684C2314yes—
120#14273683—28no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—28no—
134C2×Dic59⋊C4D411yescharacteristic
135C2×Dic59⋊C4D411yescharacteristic
136C4⋊C4×D59—22no—
137C4⋊C4×D59C2314yes—
138C2×C22⋊Dic59—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×(C2×D59)⋊C4D411yescharacteristic
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273660C2314yes—
149#14273658C2314yes—
150Dic59⋊C8C2314yes—
151Dic59⋊C8C2314yes—
152#14273652C2314yes—
153#14273652C2314yes—
154#14273651C2314yes—
155#14273650C2314yes—
156#14273650C2314yes—
157#14273648C2314yes—
158(C2×D59)⋊C8C2314yes—
159(C2×D59)⋊C8C2314yes—
160#14273638C2314yes—
161C22×Q8×C59C2311yescharacteristic
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C2×SD16×C59—24no—
165C2×SD16×C59C2314yes—
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C4×Q8×C59—22no—
169C4×Q8×C59C2314yes—
170C4×D4×C59—22no—
171C4×D4×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C42×C59—21no—
177C2×C42×C59C2311yescharacteristic
178#106×C59C2314yes—
179#103×C59C2314yes—
180#102×C59C2314yes—
181C4×C8×C59C2314yes—
182C24×C59—21no—
183C23×D59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2412yes—
188C2×D4×C59—21no—
189C2×D4×C59—22no—
190C2×D4×C59#4114yes—
191C2×D4×C59C2412yes—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—24no—
196C22×C4×C59—82no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2411yescharacteristic
200C2×C22⋊D59—28no—
201C2×C22⋊D59—24no—
202C22×Dic59—28no—
203C22×Dic59—21no—
204C22×Dic59—24no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—24no—
209C22×Dic59—82no—
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213#11745687—216no—
214#11745687—28no—
215#11745687—28no—
216C2×C4×D59—22no—
217C2×C4×D59—22no—
218C2×C4×D59—24no—
219C2×C4×D59—82no—
220C2×C4×D59C2×D412yes—
221C2×C4×D59C2412yes—
222C2×Dic118—21no—
223C2×Dic118—22no—
224C2×Dic118—22no—
225C2×Dic118—22no—
226C2×Dic118—21no—
227C2×Dic118#4114yes—
228C2×Dic118C2412yes—
229C2×Dic118C2412yes—
230SD16×C59—28no—
231C2×C8×C59—22no—
232C2×C8×C59—22no—
233C2×C8×C59C2412yes—
234C2×C8×C59C2412yes—
235C4⋊C4×C59—24no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59C2412yes—
239C4⋊C4×C59C2412yes—
240C22⋊C4×C59—24no—
241C42×C59—24no—
242C42×C59C2×D412yes—
243C42×C59C2412yes—
244C22⋊Dic59—24no—
245#11745672—28no—
246#11745670—28no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4C2×D414yes—
250(C2×D59)⋊C4C2×D414yes—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—24no—
254C4⋊Dic59—24no—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4C2×D414yes—
266Dic59⋊C4C2×D414yes—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59—24no—
270C4×Dic59C2×D412yes—
271C4×Dic59C2412yes—
272C2×C59⋊C8—22no—
273C2×C59⋊C8—22no—
274C2×C59⋊C8C2412yes—
275C2×C59⋊C8C2412yes—
276Dic236—28no—
277C23×C59—24no—
278C23×C59—22no—
279C23×C59—42no—
280C23×C59—42no—
281C23×C59C22×D411yescharacteristic
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59C22×D412yes—
286Q8×C59—22no—
287Q8×C59—22no—
288Q8×C59—42no—
289D4×C59—24no—
290D4×C59—22no—
291D4×C59C2×#4114yes—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—84no—
301C2×C4×C59C22×D412yes—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D411yescharacteristic
304C2×C4×C59C2×#4112yes—
305C2×C4×C59C2×#4112yes—
306C2×C4×C59C2511yescharacteristic
307C22⋊D59—216no—
308C2×Dic59—216no—
309C2×Dic59—24no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—42no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—84no—
321C2×Dic59C22×D412yes—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324C4×D59—24no—
325C4×D59—22no—
326C4×D59—22no—
327C4×D59—84no—
328Dic118—24no—
329Dic118—22no—
330Dic118—22no—
331Dic118—22no—
332Dic118—42no—
333Dic118C2×#4114yes—
334C8×C59—22no—
335C8×C59—22no—
336C59⋊C8—22no—
337C59⋊C8—22no—
338C2×#3120—591nomaximal, Sylow
339C22×C59—24no—
340C22×C59—48no—
341C22×C59—42no—
342C22×C59—42no—
343C22×C59#52512yes—
344C22×C59#57712yes—
345C22×C59#57812yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—22no—
348C2×D59—22no—
349C2×D59—22no—
350C2×D59—44no—
351C4×C59—22no—
352C4×C59—22no—
353C4×C59—42no—
354C4×C59—42no—
355C4×C59—42no—
356C4×C59#52512yes—
357C4×C59C22×#4111yescharacteristic
358C4×C59C22×#4111yescharacteristic
359Dic59—24no—
360Dic59—22no—
361Dic59—22no—
362Dic59—22no—
363Dic59—42no—
364Dic59—42no—
365Dic59—42no—
366C2×#541—591no—
367C2×#520—591no—
368#3120—5916no—
369C2×#484—591no—
370C2×#483—591no—
371C2×#479—591no—
372C2×#478—591no—
373C2×#462—591no—
374C2×#461—591no—
375C2×#452—591no—
376C2×#452—591no—
377C2×#441—591no—
378C2×#440—591no—
379C2×C4×Q16—591no—
380C2×C4×SD16D5911yescharacteristic, complemented
381C2×#433—591no—
382C2×C59—44no—
383C2×C59#312014yescomplemented
384C2×C59C2×#52511yescharacteristic
385C2×C59C2×#57711yescharacteristic
386C2×C59C2×#57811yescharacteristic
387D59—42no—
388C22×#41—591no—
389C22×Q16—591no—
390C22×Q16—591no—
391C22×SD16—591no—
392C22×SD16C2×D5911yescharacteristic
393#541—598no—
394#541—1184no—
395C2×C4⋊Q8—591no—
396C2×#126—1181no—
397C2×#126—1181no—
398C2×#125—591no—
399C2×#125—1181no—
400C2×#125—1181no—
401C2×C22⋊Q8—591no—
402C2×C22⋊Q8—591no—
403#520—598no—
404#520—1184no—
405C2×C4×Q8—591no—
406C2×C4×Q8—591no—
407C2×C4×Q8—591no—
408C2×C4×Q8C2×D5911yescharacteristic
409C2×C4×D4—591no—
410C2×C4×D4—1181no—
411C2×C4×D4—1181no—
412C2×C4×D4C2×D5911yescharacteristic
413C2×#117—591no—
414C2×#117—1181no—
415C22×C4⋊C4—591no—
416C22×C4⋊C4—1181no—
417#484—598no—
418#483—598no—
419#479—598no—
420#478—598no—
421#462—598no—
422#461—598no—
423#452—598no—
424#452—598no—
425#441—598no—
426#440—598no—
427C4×Q16—598no—
428C4×SD16C2×D5918yescomplemented
429#433—598no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#106—591no—
433C2×#106C2×D5911yescharacteristic
434C2×C4⋊C8—591no—
435C2×C4⋊C8—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#103—591no—
439C2×#103—591no—
440C2×#103—591no—
441C2×#103C2×D5911yescharacteristic
442C2×#102—591no—
443C2×#102C2×D5911yescharacteristic
444C2×C22⋊C8—591no—
445C2×C22⋊C8—591no—
446C2×#97—591no—
447C2×C4×C8C2×D5911yescharacteristic
448C59C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—594no—
450C2×#41—1182no—
451C2×#41—1184no—
452C2×#41—1184no—
453C22×Q8—591no—
454C22×Q8—591no—
455C22×Q8C22×D5911yescharacteristic
456C22×D4—1181no—
457C22×D4C22×D5911yescharacteristic
458C23×C4—21no—
459C23×C4—591no—
460C23×C4—1181no—
461C23×C4—1181no—
462C23×C4—1181no—
463C2×Q16—594no—
464C2×Q16—594no—
465C2×Q16—1184no—
466C2×Q16—1184no—
467C2×SD16—24no—
468C2×SD16—594no—
469C2×SD16—1184no—
470C2×SD16C22×D5914yes—
471C22×C8—591no—
472C22×C8—591no—
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C4⋊Q8—594no—
476C4⋊Q8—1182no—
477#126—1188no—
478#126—1188no—
479#125—594no—
480#125—1188no—
481#125—1182no—
482#125—1188no—
483C22⋊Q8—594no—
484C22⋊Q8—594no—
485C22⋊Q8—1182no—
486C22⋊Q8—1182no—
487C4×Q8—22no—
488C4×Q8—594no—
489C4×Q8—594no—
490C4×Q8—594no—
491C4×Q8—1182no—
492C4×Q8—1182no—
493C4×Q8—1182no—
494C4×Q8C22×D5914yes—
495C4×D4—22no—
496C4×D4—594no—
497C4×D4—1182no—
498C4×D4—1188no—
499C4×D4—1188no—
500C4×D4C22×D5914yes—
501#117—594no—
502#117—594no—
503#117—1188no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—594no—
510C2×C4⋊C4—1182no—
511C2×C4⋊C4—1188no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1181no—
522C2×C4⋊C4C22×D5911yescharacteristic
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—591no—
526C2×C22⋊C4—591no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C42—21no—
531C2×C42—591no—
532C2×C42—1181no—
533C2×C42—1181no—
534C2×C42—1181no—
535C2×C42C22×D5911yescharacteristic
536#107—594no—
537#107—594no—
538#106—594no—
539#106C22×D5914yes—
540C4⋊C8—594no—
541C4⋊C8—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#103—594no—
546#103—594no—
547#103C22×D5914yes—
548#102—594no—
549#102C22×D5914yes—
550C22⋊C8—594no—
551C22⋊C8—594no—
552#97—594no—
553C4×C8C22×D5914yes—
554C24—21no—
555C24—591no—
556#41—1188no—
557#41—11816no—
558#41—1188no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—594no—
563C2×Q8—592no—
564C2×Q8—592no—
565C2×Q8—1181no—
566C2×Q8—1181no—
567C2×Q8—1182no—
568C2×Q8—1182no—
569C2×Q8—1182no—
570C2×Q8C23×D5912yes—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—1184no—
574C2×D4—1188no—
575C2×D4#1174568514yes—
576C2×D4C23×D5912yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—82no—
582C22×C4—591no—
583C22×C4—591no—
584C22×C4—591no—
585C22×C4—592no—
586C22×C4—592no—
587C22×C4—1184no—
588C22×C4—1184no—
589C22×C4—1184no—
590C22×C4—1188no—
591C22×C4—1181no—
592C22×C4—1182no—
593C22×C4—1182no—
594C22×C4—1181no—
595C22×C4—1181no—
596C22×C4—1181no—
597C22×C4—4722no—
598C22×C4—4722no—
599C22×C4D4×D5911yescharacteristic
600C22×C4D4×D5911yescharacteristic
601C22×C4C23×D5911yescharacteristic
602Q16—1188no—
603Q16—1188no—
604SD16—28no—
605SD16—1188no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—592no—
609C2×C8—592no—
610C2×C8—1182no—
611C2×C8—1182no—
612C2×C8C23×D5912yes—
613C2×C8C23×D5912yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—594no—
618C4⋊C4—594no—
619C4⋊C4—592no—
620C4⋊C4—592no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1181no—
630C4⋊C4—1181no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4C23×D5912yes—
634C4⋊C4C23×D5912yes—
635C22⋊C4—24no—
636C22⋊C4—594no—
637C22⋊C4—594no—
638C22⋊C4—1184no—
639C22⋊C4—1184no—
640C22⋊C4—1184no—
641C42—24no—
642C42—592no—
643C42—592no—
644C42—1184no—
645C42—1184no—
646C42—1184no—
647C42D4×D5912yes—
648C42C23×D5912yes—
649C23—24no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—592no—
654C23—1182no—
655C23—1182no—
656C23—1182no—
657C23C2×D4×D5911yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—594no—
662Q8—1184no—
663Q8—1182no—
664Q8—1182no—
665Q8—1182no—
666Q8—2362no—
667D4—24no—
668D4—22no—
669D4—11816no—
670D4C2×#1174568514yes—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—592no—
681C2×C4—592no—
682C2×C4—592no—
683C2×C4—11816no—
684C2×C4—1182no—
685C2×C4—1184no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1184no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—4724no—
696C2×C4—4724no—
697C2×C4—2362no—
698C2×C4—2362no—
699C2×C4—2362no—
700C2×C4C2×D4×D5912yes—
701C2×C4C2×D4×D5912yes—
702C2×C4C2×D4×D5911yescharacteristic
703C2×C4#41×D5912yes—
704C2×C4C2×#1174568512yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1182no—
709C8—1182no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—1182no—
715C22—1182no—
716C22—1182no—
717C22—2364no—
718C22#1683791112yes—
719C22#1683820812yes—
720C22#1683821612yes—
721C22C22×D4×D5911yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1182no—
728C4—1182no—
729C4—1182no—
730C4—1184no—
731C4—2362no—
732C4—2362no—
733C4—2362no—
734C4#1683791112yes—
735C4C2×#41×D5911yescharacteristic
736C4C22×#1174568511yescharacteristic
737C2—44no—
738C2—2362no—
739C2#2143430614yesdirect product factor
740C2C2×#1683791111yescharacteristic
741C2C2×#1683820811yescharacteristic
742C2C2×#1683821611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×SD16×C59C2
socleC23×C59C22×D4
prime radicalC22×#11745687C22
hypercenterC2×C4×SD16D59
hypocenterC59C2×#3120
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16838010C2semidirect
3. #21434306C2direct (N × H)
4. C2×#16837736C2semidirect
5. C2×#16837734C2semidirect
6. C2×#16837712C2semidirect
7. C2×#16837700C2semidirect
8. C2×#16837611C2semidirect
9. C2×#16837605C2semidirect
12. C2×#16837507C2semidirect
13. C2×#16837502C2semidirect
14. C2×C4×Dic236C2semidirect
15. C2×#16837461C2semidirect
16. C2×C4×SD16×C59C2semidirect
22. #16838010C22semidirect
43. #16837736C22semidirect
44. #16837734C22semidirect
45. #16837712C22semidirect
46. #16837700C22semidirect
47. #16837611C22semidirect
48. #16837605C22semidirect
51. #16837507C22semidirect
52. #16837502C22semidirect
53. C4×Dic236C22semidirect
54. #16837461C22semidirect
72. C4×SD16×C59C22semidirect
380. C2×C4×SD16D59semidirect
383. C2×C59#3120semidirect
428. C4×SD16C2×D59semidirect
448. C59C2×#3120semidirect
739. C2#21434306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380102
C2×#168378812
#214343062
C2×#168377362
C2×#168377342
C2×#168377122
C2×#168377002
C2×#168376112
C2×#168376052
C2×#168375652
C2×#168375612
C2×#168375072
C2×#168375022
C2×C4×Dic2362
C2×#168374612
C2×C4×SD16×C592
C2×#312059