Finite Group Databasebeta

← C2×#21434305 #29456947

Subgroups — C2×#21434305 #29456947

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×#16838012C211yesmaximal, characteristic, complemented
2C2×#16837883C211yesmaximal, characteristic
3#21434305C2116yesmaximal, direct product factor
4C2×#16837732C211yesmaximal, characteristic, complemented
5C2×#16837708C211yesmaximal, characteristic, complemented
6C2×#16837705C211yesmaximal, characteristic, complemented
7C2×#16837611C211yesmaximal, characteristic, complemented
8C2×#16837606C211yesmaximal, characteristic, complemented
9C2×#16837566C211yesmaximal, characteristic
10C2×#16837562C211yesmaximal, characteristic
11C2×#16837506C211yesmaximal, characteristic, complemented
12C2×#16837501C211yesmaximal, characteristic, complemented
13C2×#16837496C211yesmaximal, characteristic, complemented
14C2×#16837487C211yesmaximal, characteristic, complemented
15C2×#16837460C211yesmaximal, characteristic, complemented
16C2×C59×#484C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745671C2211yescharacteristic
22#16838012—24no—
23#16838012C2218yescomplemented
24C2×#14273725C2211yescharacteristic
25C2×#14273720—21no—
26C2×#14273720—21no—
27C2×#14273718—21no—
28C2×#14273718C2211yescharacteristic
29C2×#14273717—21no—
30C2×#14273706C2211yescharacteristic
31#16837883—24no—
32#16837883C2218yes—
33C2×Q8×Dic59C2211yescharacteristic
34C2×#14273692C2211yescharacteristic
35C2×#14273692C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×C4×C22⋊D59—21no—
40C2×C4×C22⋊D59—21no—
41C2×#14273686C2211yescharacteristic
42C2×#14273685—21no—
43C2×C4⋊C4×D59—21no—
44#16837732C2218yescomplemented
45#16837708C2218yescomplemented
46#16837705C2218yescomplemented
47#16837611C2218yescomplemented
48#16837606C2218yescomplemented
49#16837566C2218yes—
50#16837562C2218yes—
51#16837506C2218yescomplemented
52#16837501C2218yescomplemented
53#16837496C2218yescomplemented
54#16837487C2218yescomplemented
55#16837460C2218yescomplemented
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×C22⋊Q8×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#484C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—24no—
79C2×#11745685—24no—
80C2×#11745685C2314yes—
81C22×Dic118C2311yescharacteristic
82C22×Dic118C2311yescharacteristic
83C22×D236C2311yescharacteristic
84C22×C22⋊D59—21no—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C2×Dic236—24no—
89C2×Dic236C2314yes—
90C2×#11745672—24no—
91C2×#11745672C2314yes—
92C2×#11745660—24no—
93C2×#11745660C2314yes—
94C2×#11745671—24no—
95C2×#11745671C2314yes—
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98#14273725—22no—
99#14273725C2314yes—
100#14273720—28no—
101#14273720—28no—
102#14273718—28no—
103#14273718—22no—
104#14273718C2314yes—
105#14273717—28no—
106#14273706—22no—
107#14273706C2314yes—
108Q8×Dic59—22no—
109Q8×Dic59C2314yes—
110#14273692—22no—
111#14273692—22no—
112#14273692—22no—
113#14273692C2314yes—
114#14273692C2314yes—
115#14273692C2314yes—
116#14273689—22no—
117#14273689—22no—
118#14273689C2314yes—
119#14273689C2314yes—
120C4×C22⋊D59—28no—
121C4×C22⋊D59—28no—
122#14273686D414yes—
123#14273686C2314yes—
124#14273685—28no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59D411yescharacteristic
128C2×C4⋊Dic59D411yescharacteristic
129C2×C4⋊Dic59C2311yescharacteristic
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C4⋊C4×D59—28no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59D411yescharacteristic
140C2×C22⋊Dic59D411yescharacteristic
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147C2×C4×Dic59C2311yescharacteristic
148C2×C4×Dic59C2311yescharacteristic
149#14273658C2314yes—
150#14273658C2314yes—
151Dic59⋊C8C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273650C2314yes—
155#14273650C2314yes—
156#14273650C2314yes—
157#14273649C2314yes—
158#14273647C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160#14273637C2314yes—
161C8×Dic59C2314yes—
162C22×Q8×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C23×C4×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C22⋊Q8×C59—22no—
168C22⋊Q8×C59C2314yes—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59—22no—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C4⋊C4×C59C2314yes—
176C2×C22⋊C4×C59—21no—
177#107×C59C2314yes—
178#107×C59C2314yes—
179#103×C59C2314yes—
180#103×C59C2314yes—
181C22⋊C8×C59C2314yes—
182C24×C59C2×D411yescharacteristic
183C23×D59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2412yes—
188C22×C4×C59—22no—
189C22×C4×C59—22no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—24no—
195C22×C4×C59—82no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D412yes—
198C22×C4×C59C2412yes—
199C22×C4×C59C2411yescharacteristic
200C2×C22⋊D59—28no—
201C2×C22⋊D59—24no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209#11745685—216no—
210#11745685—28no—
211#11745685—28no—
212C2×D236—21no—
213C2×D236—22no—
214C2×D236#4114yes—
215C2×D236C2412yes—
216C2×C4×D59—28no—
217C2×C4×D59—24no—
218C2×C4×D59—24no—
219C2×C4×D59—24no—
220C2×C4×D59—82no—
221C2×C4×D59—82no—
222C2×Dic118—21no—
223C2×Dic118—22no—
224C2×Dic118—22no—
225C2×Dic118—22no—
226C2×Dic118—21no—
227C2×Dic118#4114yes—
228C2×Dic118C2412yes—
229C2×Dic118C2412yes—
230C2×C8×C59—22no—
231C2×C8×C59—22no—
232C2×C8×C59C2412yes—
233C2×C8×C59C2412yes—
234C4⋊C4×C59—24no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—24no—
238C4⋊C4×C59—21no—
239C4⋊C4×C59C2412yes—
240C4⋊C4×C59C2412yes—
241C4⋊C4×C59C2412yes—
242C22⋊C4×C59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59C2×D414yes—
245C22⋊Dic59C2×D414yes—
246#11745672—28no—
247#11745671—28no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250C4⋊Dic59—21no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253C4⋊Dic59C2×D414yes—
254C4⋊Dic59C2×D414yes—
255C4⋊Dic59C2412yes—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263C4×Dic59—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C4×Dic59—24no—
267C4×Dic59C2×D412yes—
268C4×Dic59C2×D412yes—
269C4×Dic59C2412yes—
270C4×Dic59C2412yes—
271C2×C59⋊C8—22no—
272C2×C59⋊C8—22no—
273C2×C59⋊C8C2412yes—
274C2×C59⋊C8C2412yes—
275Dic236—28no—
276#11745660—28no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59C22×D412yes—
281C23×C59C22×D411yescharacteristic
282C22×D59—24no—
283C22×D59—22no—
284C22×D59—42no—
285C22×D59—42no—
286Q8×C59—22no—
287Q8×C59—22no—
288Q8×C59—42no—
289C2×C4×C59—22no—
290C2×C4×C59—24no—
291C2×C4×C59—22no—
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—42no—
301C2×C4×C59—84no—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D411yescharacteristic
304C2×C4×C59C2×#4112yes—
305C2×C4×C59C2×#4112yes—
306C2×C4×C59C2511yescharacteristic
307C22⋊D59—216no—
308C2×Dic59—24no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321C2×Dic59C22×D412yes—
322D236—24no—
323D236—22no—
324D236C2×#4114yes—
325C4×D59—216no—
326C4×D59—84no—
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—22no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—44no—
343C22×C59#52512yes—
344C22×C59#57712yes—
345C22×C59#57812yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—24no—
348C2×D59—48no—
349C2×D59—42no—
350C2×D59—42no—
351C4×C59—22no—
352C4×C59—42no—
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—22no—
364Dic59—42no—
365Dic59—42no—
366C2×#541—591no—
367C2×#520—591no—
368#3120—5916no—
369C2×#484D5911yescharacteristic, complemented
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×SD16—591no—
381C2×#433—591no—
382C2×C59—42no—
383C2×C59#312014yescomplemented
384C2×C59C2×#52511yescharacteristic
385C2×C59C2×#57711yescharacteristic
386C2×C59C2×#57811yescharacteristic
387D59—44no—
388C22×#41—591no—
389C22×Q16—591no—
390C22×Q16—591no—
391C22×SD16—591no—
392C22×SD16—591no—
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⋊Q8C2×D5911yescharacteristic
403#520—598no—
404#520—1184no—
405C2×C4×Q8—591no—
406C2×C4×Q8—591no—
407C2×C4×Q8—591no—
408C2×C4×Q8—591no—
409C2×C4×D4—591no—
410C2×C4×D4—591no—
411C2×C4×D4—1181no—
412C2×C4×D4—1181no—
413C2×#117—591no—
414C2×#117—1181no—
415C22×C4⋊C4—1181no—
416C22×C4⋊C4C2×D5911yescharacteristic
417#484C2×D5918yescomplemented
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×SD16—598no—
429#433—598no—
430C2×#107C2×D5911yescharacteristic
431C2×#107C2×D5911yescharacteristic
432C2×#106—591no—
433C2×#106—591no—
434C2×C4⋊C8—591no—
435C2×C4⋊C8—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#103—591no—
439C2×#103—591no—
440C2×#103C2×D5911yescharacteristic
441C2×#103C2×D5911yescharacteristic
442C2×#102—591no—
443C2×#102—591no—
444C2×C22⋊C8—591no—
445C2×C22⋊C8C2×D5911yescharacteristic
446C2×#97—591no—
447C2×C4×C8—591no—
448C59C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—594no—
450C2×#41—1184no—
451C2×#41—1184no—
452C2×#41—1182no—
453C22×Q8—591no—
454C22×Q8—591no—
455C22×Q8C22×D5911yescharacteristic
456C22×D4—591no—
457C22×D4—1181no—
458C23×C4—21no—
459C23×C4—1181no—
460C23×C4—1181no—
461C23×C4—1181no—
462C23×C4C22×D5911yescharacteristic
463C2×Q16—594no—
464C2×Q16—594no—
465C2×Q16—1184no—
466C2×Q16—1184no—
467C2×SD16—594no—
468C2×SD16—594no—
469C2×SD16—1184no—
470C2×SD16—1184no—
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—1182no—
481#125—1188no—
482#125—1188no—
483C22⋊Q8—22no—
484C22⋊Q8—594no—
485C22⋊Q8—1182no—
486C22⋊Q8C22×D5914yes—
487C4×Q8—594no—
488C4×Q8—594no—
489C4×Q8—594no—
490C4×Q8—594no—
491C4×Q8—1182no—
492C4×Q8—1182no—
493C4×Q8—1182no—
494C4×Q8—1182no—
495C4×D4—594no—
496C4×D4—594no—
497C4×D4—1182no—
498C4×D4—1182no—
499C4×D4—1188no—
500C4×D4—1188no—
501#117—594no—
502#117—594no—
503#117—1188no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—1188no—
511C2×C4⋊C4—1181no—
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⋊C4C22×D5911yescharacteristic
521C2×C4⋊C4C22×D5911yescharacteristic
522C2×C4⋊C4C22×D5914yes—
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—591no—
531C2×C42—591no—
532C2×C42—1181no—
533C2×C42—1181no—
534C2×C42—1181no—
535C2×C42—1181no—
536#107C22×D5914yes—
537#107C22×D5914yes—
538#106—594no—
539#106—594no—
540C4⋊C8—594no—
541C4⋊C8—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#103—594no—
546#103C22×D5914yes—
547#103C22×D5914yes—
548#102—594no—
549#102—594no—
550C22⋊C8—594no—
551C22⋊C8C22×D5914yes—
552#97—594no—
553C4×C8—594no—
554C24—1181no—
555C24D4×D5911yescharacteristic
556#41—1188no—
557#41—1188no—
558#41—11816no—
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—594no—
572C2×D4—592no—
573C2×D4—1188no—
574C2×D4—1184no—
575C2×D4—1181no—
576C2×D4—1182no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—591no—
586C22×C4—591no—
587C22×C4—591no—
588C22×C4—591no—
589C22×C4—1184no—
590C22×C4—1184no—
591C22×C4—1188no—
592C22×C4—1181no—
593C22×C4—1184no—
594C22×C4—1181no—
595C22×C4—1181no—
596C22×C4—4722no—
597C22×C4—4722no—
598C22×C4D4×D5912yes—
599C22×C4D4×D5911yescharacteristic
600C22×C4C23×D5912yes—
601C22×C4C23×D5911yescharacteristic
602Q16—1188no—
603Q16—1188no—
604SD16—1188no—
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—24no—
618C4⋊C4—21no—
619C4⋊C4—594no—
620C4⋊C4—594no—
621C4⋊C4—592no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1181no—
631C4⋊C4—1184no—
632C4⋊C4C23×D5912yes—
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—592no—
642C42—592no—
643C42—592no—
644C42—592no—
645C42—1184no—
646C42—1184no—
647C42—1184no—
648C42—1184no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1184no—
653C23—1182no—
654C23—2362no—
655C23—2362no—
656C23C2×D4×D5912yes—
657C23C2×D4×D5911yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—594no—
662Q8—1184no—
663Q8—1182no—
664Q8—1182no—
665Q8—1182no—
666Q8—2362no—
667D4—594no—
668D4—11816no—
669D4—1184no—
670D4—1182no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—84no—
684C2×C4—592no—
685C2×C4—592no—
686C2×C4—592no—
687C2×C4—592no—
688C2×C4—11816no—
689C2×C4—1184no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—4724no—
698C2×C4—4724no—
699C2×C4—2362no—
700C2×C4—2362no—
701C2×C4C2×D4×D5912yes—
702C2×C4C2×D4×D5911yescharacteristic
703C2×C4#41×D5912yes—
704C2×C4#41×D5912yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1182no—
709C8—1182no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—1184no—
715C22—2362no—
716C22—2362no—
717C22—2368no—
718C22#1683791012yes—
719C22#1683821212yes—
720C22#1683821512yes—
721C22C22×D4×D5911yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1182no—
728C4—1182no—
729C4—1182no—
730C4—1182no—
731C4—1184no—
732C4—2362no—
733C4—2362no—
734C4#1683791012yes—
735C4C2×#41×D5911yescharacteristic
736C4C2×#41×D5911yescharacteristic
737C2—42no—
738C2—2364no—
739C2#2143430514yesdirect product factor
740C2C2×#1683791011yescharacteristic
741C2C2×#1683821211yescharacteristic
742C2C2×#1683821511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#484C2
socleC23×C59C22×D4
prime radicalC22×#11745685C22
hypercenterC2×#484D59
hypocenterC59C2×#3120
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#16838012C2semidirect
3. #21434305C2direct (N × H)
4. C2×#16837732C2semidirect
5. C2×#16837708C2semidirect
6. C2×#16837705C2semidirect
7. C2×#16837611C2semidirect
8. C2×#16837606C2semidirect
11. C2×#16837506C2semidirect
12. C2×#16837501C2semidirect
13. C2×#16837496C2semidirect
14. C2×#16837487C2semidirect
15. C2×#16837460C2semidirect
16. C2×C59×#484C2semidirect
23. #16838012C22semidirect
44. #16837732C22semidirect
45. #16837708C22semidirect
46. #16837705C22semidirect
47. #16837611C22semidirect
48. #16837606C22semidirect
51. #16837506C22semidirect
52. #16837501C22semidirect
53. #16837496C22semidirect
54. #16837487C22semidirect
55. #16837460C22semidirect
71. C59×#484C22semidirect
369. C2×#484D59semidirect
383. C2×C59#3120semidirect
417. #484C2×D59semidirect
448. C59C2×#3120semidirect
739. C2#21434305direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380122
C2×#168378832
#214343052
C2×#168377322
C2×#168377082
C2×#168377052
C2×#168376112
C2×#168376062
C2×#168375662
C2×#168375622
C2×#168375062
C2×#168375012
C2×#168374962
C2×#168374872
C2×#168374602
C2×C59×#4842
C2×#312059