Finite Group Databasebeta

← C2×#21434458 #29457934

Subgroups — C2×#21434458 #29457934

Order 15104.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838029C211yesmaximal, characteristic, complemented
2C2×#16837972C211yesmaximal, characteristic
3#21434458C2116yesmaximal, direct product factor
4C2×#16837771C211yesmaximal, characteristic, complemented
5C2×#16837769C211yesmaximal, characteristic, complemented
6C2×#16837760C211yesmaximal, characteristic, complemented
7C2×#16837756C211yesmaximal, characteristic, complemented
8C2×#16837755C211yesmaximal, characteristic, complemented
9C2×#16837754C211yesmaximal, characteristic, complemented
10C2×#16837751C211yesmaximal, characteristic, complemented
11C2×#16837400C211yesmaximal, characteristic
12C2×#16837409C211yesmaximal, characteristic, complemented
13C2×#16837395C211yesmaximal, characteristic
14C2×#103×D59C211yesmaximal, characteristic, complemented
15C2×#16837359C211yesmaximal, characteristic, complemented
16C2×C59×#489C211yesmaximal, characteristic, complemented
17C22×#11745687C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16838029—24no—
22#16838029C2218yescomplemented
23#16837972—24no—
24#16837972C2218yes—
25C2×#14273727C2211yescharacteristic
26C2×#14273726C2211yescharacteristic
27C2×#14273725—21no—
28C2×#14273725C2211yescharacteristic
29C2×#14273719C2211yescharacteristic
30C2×#14273718C2211yescharacteristic
31C2×#14273717—21no—
32C2×#14273714C2211yescharacteristic
33C2×#14273709—21no—
34C2×#14273709—21no—
35C2×#14273705—21no—
36C2×#14273704—21no—
37C2×#14273704—21no—
38C2×#14273703—21no—
39C2×#14273685C2211yescharacteristic
40C2×#14273684C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837771C2218yescomplemented
43#16837769C2218yescomplemented
44#16837760C2218yescomplemented
45#16837756C2218yescomplemented
46#16837755C2218yescomplemented
47#16837754C2218yescomplemented
48#16837751C2218yescomplemented
49#16837409C2218yescomplemented
50#16837400C2218yes—
51#16837395C2218yes—
52C2×#14273652C2211yescharacteristic
53C2×#14273652C2211yescharacteristic
54C2×#14273652C2211yescharacteristic
55C2×#14273652C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273651C2211yescharacteristic
58C2×#14273650C2211yescharacteristic
59C2×#14273650C2211yescharacteristic
60C2×#14273650C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62#103×D59C2218yescomplemented
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65#16837359C2218yescomplemented
66C2×#14273637C2211yescharacteristic
67C2×C4×C59⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×C4⋊Q8×C59C2211yescharacteristic
70C2×#124×C59C2211yescharacteristic
71C59×#489C2218yescomplemented
72C2×#103×C59C2211yescharacteristic
73C2×#103×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C2×#11745687—22no—
78C2×#11745687—24no—
79C2×#11745687—24no—
80C2×#11745687C2314yes—
81C22×Dic118—21no—
82C22×Dic118—21no—
83C22×Dic118C2311yescharacteristic
84C22×Dic118C2311yescharacteristic
85C2×Q8×D59—22no—
86C2×Q8×D59—24no—
87C2×Q8×D59—24no—
88C2×Q8×D59C2314yes—
89C22×C22⋊D59—21no—
90C23×Dic59—21no—
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59C2311yescharacteristic
94C2×#11745659—24no—
95C2×#11745659C2314yes—
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98C2×C8×D59—24no—
99C2×C8×D59C2314yes—
100#14273727—22no—
101#14273727C2314yes—
102#14273726—22no—
103#14273726C2314yes—
104#14273725—28no—
105#14273725—22no—
106#14273725C2314yes—
107#14273719—22no—
108#14273719C2314yes—
109#14273718—22no—
110#14273718C2314yes—
111#14273717—28no—
112#14273714—22no—
113#14273714C2314yes—
114#14273709—28no—
115#14273709—28no—
116#14273705—28no—
117#14273704—28no—
118#14273704—28no—
119#14273703—28no—
120#14273685—22no—
121#14273685C2314yes—
122#14273684D414yes—
123#14273684C2314yes—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×Dic59⋊C4—21no—
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⋊C4D411yescharacteristic
137C2×Dic59⋊C4D411yescharacteristic
138C4⋊C4×D59—22no—
139C4⋊C4×D59C2314yes—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4D411yescharacteristic
144C2×(C2×D59)⋊C4D411yescharacteristic
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273652C2314yes—
148#14273652C2314yes—
149#14273652C2314yes—
150#14273652C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273650C2314yes—
154#14273650C2314yes—
155#14273650C2314yes—
156#14273650C2314yes—
157#14273648C2314yes—
158#14273648C2314yes—
159#14273637C2314yes—
160C4×C59⋊C8C2314yes—
161C8×Dic59C2314yes—
162C22×Q8×C59—21no—
163C22×Q8×C59C2311yescharacteristic
164C22×D4×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C4⋊Q8×C59—22no—
168C4⋊Q8×C59C2314yes—
169#124×C59—22no—
170#124×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C42×C59C2311yescharacteristic
177#103×C59C2314yes—
178#103×C59C2314yes—
179#102×C59C2314yes—
180#102×C59C2314yes—
181#97×C59C2314yes—
182C24×C59—21no—
183C23×D59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—24no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59—82no—
189C2×Q8×C59C2412yes—
190C2×D4×C59—21no—
191C2×D4×C59—22no—
192C2×D4×C59—22no—
193C2×D4×C59C2412yes—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2411yescharacteristic
200C2×C22⋊D59—24no—
201C2×C22⋊D59—44no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—24no—
207C22×Dic59—44no—
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211Q8×D59—28no—
212Q8×D59—28no—
213Q8×D59—48no—
214#11745687—28no—
215#11745687—28no—
216#11745687—48no—
217C2×C4×D59—24no—
218C2×C4×D59—24no—
219C2×C4×D59—44no—
220C2×C4×D59—82no—
221C2×C4×D59C2×D412yes—
222C2×C4×D59#4114yes—
223C2×C4×D59#4114yes—
224C2×C4×D59C2412yes—
225C2×Dic118—22no—
226C2×Dic118—22no—
227C2×Dic118—22no—
228C2×Dic118—22no—
229C2×Dic118—21no—
230C2×Dic118—21no—
231C2×Dic118—24no—
232C2×Dic118—24no—
233C2×Dic118—44no—
234C2×Dic118—82no—
235C2×Dic118C2412yes—
236C2×Dic118C2412yes—
237C2×C8×C59—22no—
238C2×C8×C59—22no—
239C2×C8×C59C2412yes—
240C2×C8×C59C2412yes—
241C4⋊C4×C59—24no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59C2412yes—
245C4⋊C4×C59C2412yes—
246C22⋊C4×C59—24no—
247C22⋊C4×C59—24no—
248C42×C59C2×D412yes—
249C42×C59C2412yes—
250C22⋊Dic59—24no—
251C22⋊Dic59—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4C2×D414yes—
254(C2×D59)⋊C4C2×D414yes—
255C4⋊Dic59—21no—
256C4⋊Dic59—24no—
257C4⋊Dic59—24no—
258C4⋊Dic59—21no—
259C4⋊Dic59—24no—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4—24no—
268Dic59⋊C4—24no—
269Dic59⋊C4C2×D414yes—
270Dic59⋊C4C2×D414yes—
271C4×Dic59—24no—
272C4×Dic59C2×D412yes—
273C4×Dic59C2412yes—
274C2×C59⋊C8—22no—
275C2×C59⋊C8—22no—
276C2×C59⋊C8C2412yes—
277C2×C59⋊C8C2412yes—
278#11745659—28no—
279C8×D59—28no—
280C23×C59—22no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59C22×D411yescharacteristic
285C22×D59—22no—
286C22×D59—22no—
287C22×D59#12414yes—
288C22×D59C22×D412yes—
289Q8×C59—22no—
290Q8×C59—22no—
291Q8×C59—42no—
292Q8×C59—84no—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—42no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59—42no—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D412yes—
306C2×C4×C59C22×D411yescharacteristic
307C2×C4×C59C2×#4112yes—
308C2×C4×C59C2×#4112yes—
309C2×C4×C59C2511yescharacteristic
310C22⋊D59—48no—
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—42no—
321C2×Dic59—48no—
322C2×Dic59#12414yes—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325C2×Dic59C22×D412yes—
326C4×D59—48no—
327C4×D59—84no—
328C4×D59#12418yes—
329C4×D59C2×#4114yes—
330C4×D59C2×#4114yes—
331Dic118—22no—
332Dic118—22no—
333Dic118—22no—
334Dic118—22no—
335Dic118—42no—
336Dic118—42no—
337Dic118—48no—
338Dic118—84no—
339C8×C59—22no—
340C8×C59—22no—
341C59⋊C8—22no—
342C59⋊C8—22no—
343C2×#3137—591nomaximal, Sylow
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—84no—
348C22×C59C2×#12412yes—
349C22×C59#57712yes—
350C22×C59#57812yes—
351C22×C59C23×D411yescharacteristic
352C2×D59—28no—
353C2×D59—22no—
354C2×D59—22no—
355C2×D59C2×#12414yes—
356C4×C59—22no—
357C4×C59—22no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59—42no—
361C4×C59C2×#12412yes—
362C4×C59C22×#4111yescharacteristic
363C4×C59C22×#4111yescharacteristic
364Dic59—22no—
365Dic59—22no—
366Dic59—42no—
367Dic59—42no—
368Dic59—42no—
369Dic59—42no—
370Dic59C2×#12414yes—
371C2×#544—591no—
372C2×#536—591no—
373#3137—5916no—
374C2×#491—591no—
375C2×#491—591no—
376C2×#489—591no—
377C2×#489D5911yescharacteristic, complemented
378C2×#488—591no—
379C2×#488—591no—
380C2×#487—591no—
381C2×#487—591no—
382C2×#417—591no—
383C2×#419—591no—
384C2×#416—591no—
385C22×#103—591no—
386C2×#405—591no—
387C2×C59—82no—
388C2×C59#313714yescomplemented
389C2×C59C22×#12411yescharacteristic
390C2×C59C2×#57711yescharacteristic
391C2×C59C2×#57811yescharacteristic
392D59—24no—
393C22×#41—591no—
394C23×Q8—591no—
395C22×M16—591no—
396C23×C8—591no—
397#544—598no—
398#544—1184no—
399#536—598no—
400#536—1184no—
401C2×C4⋊Q8—591no—
402C2×C4⋊Q8—591no—
403C2×C4⋊Q8—591no—
404C2×C4⋊Q8—1181no—
405C2×C4⋊Q8C2×D5911yescharacteristic
406C2×#125—591no—
407C2×#125—591no—
408C2×#125—1181no—
409C2×#124—591no—
410C2×#124C2×D5911yescharacteristic
411C2×#123—1181no—
412C2×#123—1181no—
413C2×C22⋊Q8—1181no—
414C2×C22⋊Q8—1181no—
415C2×C22⋊Q8—1181no—
416C2×C22⋊Q8—1181no—
417C2×#117—591no—
418C2×#117—591no—
419C22×C4⋊C4—591no—
420#491—598no—
421#491—598no—
422#489—598no—
423#489C2×D5918yescomplemented
424#488—598no—
425#488—598no—
426#487—598no—
427#487—598no—
428#419—598no—
429#417—598no—
430#416—598no—
431C2×#103—591no—
432C2×#103—591no—
433C2×#103—591no—
434C2×#103—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#103—591no—
439C2×#103—591no—
440C2×#103—591no—
441C2×#103—598no—
442C2×#103C2×D5911yescharacteristic
443C2×#103C2×D5911yescharacteristic
444C2×#102—591no—
445C2×#102—591no—
446C2×#102C2×D5911yescharacteristic
447C2×#102C2×D5911yescharacteristic
448#405—598no—
449C2×#97—591no—
450C2×#97C2×D5911yescharacteristic
451C2×C4×C8—591no—
452C2×C4×C8—591no—
453C59C2×#313711yescharacteristic, complemented, Sylow
454C2×#41—594no—
455C2×#41—1182no—
456C2×#41—1184no—
457C2×#41—1184no—
458C22×Q8—21no—
459C22×Q8—594no—
460C22×Q8—591no—
461C22×Q8—591no—
462C22×Q8—1181no—
463C22×Q8—1181no—
464C22×Q8—1182no—
465C22×Q8—1184no—
466C22×Q8—1184no—
467C22×Q8C22×D5911yescharacteristic
468C22×D4—1181no—
469C22×D4C22×D5911yescharacteristic
470C23×C4—591no—
471C23×C4—1181no—
472C23×C4—1181no—
473C23×C4—1181no—
474C2×M16—594no—
475C2×M16—1184no—
476C22×C8—591no—
477C22×C8—591no—
478C22×C8—594no—
479C22×C8—1184no—
480C22×C8C22×D5911yescharacteristic
481C22×C8C22×D5911yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—594no—
484C4⋊Q8—594no—
485C4⋊Q8—594no—
486C4⋊Q8—1182no—
487C4⋊Q8—1182no—
488C4⋊Q8—1188no—
489C4⋊Q8—1182no—
490C4⋊Q8C22×D5914yes—
491#125—594no—
492#125—594no—
493#125—1182no—
494#125—1188no—
495#125—1182no—
496#124—22no—
497#124—594no—
498#124—1182no—
499#124C22×D5914yes—
500#123—1188no—
501#123—1188no—
502C22⋊Q8—1188no—
503C22⋊Q8—1188no—
504C22⋊Q8—1188no—
505C22⋊Q8—1188no—
506#117—594no—
507#117—594no—
508#117—594no—
509#117—1182no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—591no—
514C2×C4⋊C4—591no—
515C2×C4⋊C4—594no—
516C2×C4⋊C4—1182no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1181no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4C22×D5911yescharacteristic
528C2×C4⋊C4C22×D5911yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—591no—
532C2×C22⋊C4—591no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C42—591no—
537C2×C42—1181no—
538C2×C42C22×D5911yescharacteristic
539#103—594no—
540#103—594no—
541#103—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#103—594no—
546#103—594no—
547#103—594no—
548#103—594no—
549#103C22×D5914yes—
550#103C22×D5914yes—
551#102—594no—
552#102—594no—
553#102C22×D5914yes—
554#102C22×D5914yes—
555#97—594no—
556#97C22×D5914yes—
557C4×C8—594no—
558C4×C8—594no—
559C24—21no—
560C24—591no—
561#41—1188no—
562#41—1188no—
563#41—2368no—
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—592no—
570C2×Q8—592no—
571C2×Q8—1184no—
572C2×Q8—1184no—
573C2×Q8—1188no—
574C2×Q8—1188no—
575C2×Q8—1181no—
576C2×Q8—1181no—
577C2×Q8—1182no—
578C2×Q8—1182no—
579C2×Q8—1182no—
580C2×Q8—1182no—
581C2×Q8—4722no—
582C2×Q8—2364no—
583C2×Q8—2368no—
584C2×Q8C23×D5912yes—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—1184no—
589C2×D4—2364no—
590C2×D4C23×D5912yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—591no—
595C22×C4—592no—
596C22×C4—594no—
597C22×C4—594no—
598C22×C4—592no—
599C22×C4—591no—
600C22×C4—591no—
601C22×C4—1184no—
602C22×C4—1184no—
603C22×C4—1184no—
604C22×C4—1181no—
605C22×C4—1181no—
606C22×C4—1181no—
607C22×C4—1181no—
608C22×C4—4722no—
609C22×C4—2364no—
610C22×C4—2364no—
611C22×C4D4×D5911yescharacteristic
612C22×C4D4×D5911yescharacteristic
613C22×C4C23×D5911yescharacteristic
614M16—1188no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—592no—
618C2×C8—592no—
619C2×C8—1188no—
620C2×C8—1182no—
621C2×C8—1182no—
622C2×C8C23×D5912yes—
623C2×C8C23×D5912yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—594no—
628C4⋊C4—594no—
629C4⋊C4—592no—
630C4⋊C4—592no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1184no—
635C4⋊C4—1184no—
636C4⋊C4—1184no—
637C4⋊C4—1181no—
638C4⋊C4—1181no—
639C4⋊C4—1184no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4—1184no—
643C4⋊C4C23×D5912yes—
644C4⋊C4C23×D5912yes—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—594no—
648C22⋊C4—594no—
649C22⋊C4—1184no—
650C22⋊C4—1184no—
651C22⋊C4—1184no—
652C42—592no—
653C42—592no—
654C42—1184no—
655C42D4×D5912yes—
656C42C23×D5912yes—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—594no—
662C23—592no—
663C23—1182no—
664C23—1182no—
665C23C2×D4×D5911yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—84no—
670Q8—1182no—
671Q8—1182no—
672Q8—1182no—
673Q8—1182no—
674Q8—4724no—
675Q8—2368no—
676Q8—2362no—
677Q8—2362no—
678D4—22no—
679D4—22no—
680D4—42no—
681D4—2368no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—594no—
691C2×C4—592no—
692C2×C4—598no—
693C2×C4—594no—
694C2×C4—594no—
695C2×C4—592no—
696C2×C4—592no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—4724no—
704C2×C4—2368no—
705C2×C4—2368no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4—2362no—
710C2×C4C2×D4×D5912yes—
711C2×C4C2×D4×D5912yes—
712C2×C4C2×D4×D5911yescharacteristic
713C2×C4#41×D5912yes—
714C2×C4#41×D5912yes—
715C2×C4C24×D5911yescharacteristic
716C8—22no—
717C8—22no—
718C8—1182no—
719C8—1182no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—594no—
725C22—1188no—
726C22—1182no—
727C22—1182no—
728C22#124×D5912yes—
729C22#1683821212yes—
730C22#1683821812yes—
731C22C22×D4×D5911yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—594no—
738C4—1182no—
739C4—1182no—
740C4—2362no—
741C4—2362no—
742C4—2362no—
743C4—2362no—
744C4#124×D5912yes—
745C4C2×#41×D5911yescharacteristic
746C4C2×#41×D5911yescharacteristic
747C2—82no—
748C2—1184no—
749C2#2143445814yesdirect product factor
750C2C2×#124×D5911yescharacteristic
751C2C2×#1683821211yescharacteristic
752C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#489C2
socleC23×C59C22×D4
prime radicalC22×#11745687C22
hypercenterC2×#489D59
hypocenterC59C2×#3137
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#16838029C2semidirect
3. #21434458C2direct (N × H)
4. C2×#16837771C2semidirect
5. C2×#16837769C2semidirect
6. C2×#16837760C2semidirect
7. C2×#16837756C2semidirect
8. C2×#16837755C2semidirect
9. C2×#16837754C2semidirect
10. C2×#16837751C2semidirect
12. C2×#16837409C2semidirect
14. C2×#103×D59C2semidirect
15. C2×#16837359C2semidirect
16. C2×C59×#489C2semidirect
22. #16838029C22semidirect
42. #16837771C22semidirect
43. #16837769C22semidirect
44. #16837760C22semidirect
45. #16837756C22semidirect
46. #16837755C22semidirect
47. #16837754C22semidirect
48. #16837751C22semidirect
49. #16837409C22semidirect
62. #103×D59C22semidirect
65. #16837359C22semidirect
71. C59×#489C22semidirect
377. C2×#489D59semidirect
388. C2×C59#3137semidirect
423. #489C2×D59semidirect
453. C59C2×#3137semidirect
749. C2#21434458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380292
C2×#168379722
#214344582
C2×#168377712
C2×#168377692
C2×#168377602
C2×#168377562
C2×#168377552
C2×#168377542
C2×#168377512
C2×#168374002
C2×#168374092
C2×#168373952
C2×#103×D592
C2×#168373592
C2×C59×#4892
C2×#313759