Finite Group Databasebeta

← C2×#21436649 #29467360

Subgroups — C2×#21436649 #29467360

Order 15104.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838104C211yesmaximal, characteristic
2C2×#16838091C211yesmaximal, characteristic, complemented
3#21436649C2116yesmaximal, direct product factor
4C2×#16837802C211yesmaximal, characteristic, complemented
5C2×#16837719C211yesmaximal, characteristic, complemented
6C2×#16837746C211yesmaximal, characteristic, complemented
7C2×#16837733C211yesmaximal, characteristic, complemented
8C2×#16837708C211yesmaximal, characteristic, complemented
9C2×#16837704C211yesmaximal, characteristic, complemented
10C2×#16837647C211yesmaximal, characteristic, complemented
11C2×#16837646C211yesmaximal, characteristic, complemented
12C2×#16837493C211yesmaximal, characteristic, complemented
13C2×#16837477C211yesmaximal, characteristic, complemented
14C2×#16837445C211yesmaximal, characteristic, complemented
15C2×#16837443C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C22×#11745670C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20#16838104—24no—
21#16838104C2218yes—
22#16838091—24no—
23#16838091C2218yescomplemented
24C2×#14273720—21no—
25C2×#14273720—21no—
26C2×#14273719—21no—
27C2×#14273718C2211yescharacteristic
28C2×#14273718C2211yescharacteristic
29C2×#14273711—21no—
30C2×#14273709—21no—
31C2×#14273707C2211yescharacteristic
32C2×#14273706C2211yescharacteristic
33C2×#14273699—21no—
34C2×#14273698C2211yescharacteristic
35C2×#14273692C2211yescharacteristic
36C2×D4×Dic59—21no—
37C2×D4×Dic59C2211yescharacteristic
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×#14273685C2211yescharacteristic
40C2×#14273684—21no—
41C22×C4⋊Dic59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837802C2218yescomplemented
44#16837746C2218yescomplemented
45#16837733C2218yescomplemented
46#16837719C2218yescomplemented
47#16837708C2218yescomplemented
48#16837704C2218yescomplemented
49#16837647C2218yescomplemented
50#16837646C2218yescomplemented
51#16837493C2218yescomplemented
52#16837477C2218yescomplemented
53#16837445C2218yescomplemented
54#16837443C2218yescomplemented
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273658C2211yescharacteristic
61C2×#14273658C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118C2311yescharacteristic
78C22×C22⋊D59—21no—
79C22×C22⋊D59D411yescharacteristic
80C23×Dic59—21no—
81C23×Dic59—21no—
82C22×C4×D59—21no—
83C22×C4×D59C2311yescharacteristic
84C2×#11745670—24no—
85C2×#11745670C2314yes—
86C2×#11745664—24no—
87C2×#11745664C2314yes—
88C2×#11745659—24no—
89C2×#11745659C2314yes—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92#14273720—28no—
93#14273720—28no—
94#14273719—28no—
95#14273718—22no—
96#14273718—22no—
97#14273718C2314yes—
98#14273718C2314yes—
99#14273711—28no—
100#14273709—28no—
101#14273707—22no—
102#14273707C2314yes—
103#14273706—22no—
104#14273706C2314yes—
105#14273699—28no—
106#14273698—22no—
107#14273698C2314yes—
108#14273692—22no—
109#14273692C2314yes—
110D4×Dic59—28no—
111D4×Dic59—22no—
112D4×Dic59C2314yes—
113C4×C22⋊D59D414yes—
114C4×C22⋊D59C2314yes—
115#14273685—22no—
116#14273685C2314yes—
117#14273684—28no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—22no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2314yes—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4D411yescharacteristic
133C4⋊C4×D59—22no—
134C4⋊C4×D59C2314yes—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59D411yescharacteristic
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59C2311yescharacteristic
145#14273660C2314yes—
146#14273660C2314yes—
147#14273660C2314yes—
148#14273659C2314yes—
149#14273659C2314yes—
150#14273658C2314yes—
151#14273658C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273650C2314yes—
156#14273648C2314yes—
157(C2×D59)⋊C8C2314yes—
158C8×Dic59C2314yes—
159C22×D4×C59—21no—
160C22×D4×C59C2311yescharacteristic
161C23×C4×C59C2311yescharacteristic
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164#121×C59—22no—
165#121×C59C2314yes—
166#117×C59—22no—
167#117×C59C2314yes—
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C42×C59—21no—
174#107×C59C2314yes—
175#106×C59C2314yes—
176#102×C59C2314yes—
177#102×C59C2314yes—
178C22⋊C8×C59C2314yes—
179C24×C59—21no—
180C24×C59C2×D411yescharacteristic
181C23×D59C2×D411yescharacteristic
182C2×D4×C59—24no—
183C2×D4×C59—21no—
184C2×D4×C59—22no—
185C2×D4×C59—22no—
186C2×D4×C59—44no—
187C2×D4×C59C2412yes—
188C22×C4×C59—22no—
189C22×C4×C59—22no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2411yescharacteristic
197C2×C22⋊D59—24no—
198C2×C22⋊D59—42no—
199C2×C22⋊D59—82no—
200C2×C22⋊D59C2×D414yes—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—24no—
206C22×Dic59—24no—
207C22×Dic59—82no—
208C22×Dic59—82no—
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C2×C4×D59—22no—
213C2×C4×D59—22no—
214C2×C4×D59—24no—
215C2×C4×D59—44no—
216C2×C4×D59C2×D412yes—
217C2×C4×D59C2412yes—
218C2×Dic118—22no—
219C2×Dic118—22no—
220C2×Dic118—21no—
221C2×Dic118C2412yes—
222C2×C8×C59—22no—
223C2×C8×C59—22no—
224C2×C8×C59C2412yes—
225C2×C8×C59C2412yes—
226C4⋊C4×C59—21no—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59C2412yes—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C22⋊C4×C59—24no—
233C22⋊C4×C59—24no—
234C42×C59—24no—
235C22⋊Dic59—24no—
236C22⋊Dic59—24no—
237C22⋊Dic59—24no—
238C22⋊Dic59C2×D414yes—
239#11745670—28no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4C2×D414yes—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—24no—
247C4⋊Dic59—24no—
248C4⋊Dic59—24no—
249C4⋊Dic59—24no—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4C2×D414yes—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D412yes—
262C4×Dic59C2412yes—
263#11745664—28no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8#4114yes—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268#11745659—28no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—42no—
274C23×C59—42no—
275C23×C59—42no—
276C23×C59C22×D412yes—
277C23×C59C22×D411yescharacteristic
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59C22×D412yes—
282D4×C59—22no—
283D4×C59—22no—
284D4×C59—48no—
285D4×C59—42no—
286C2×C4×C59—22no—
287C2×C4×C59—24no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59—42no—
296C2×C4×C59C22×D412yes—
297C2×C4×C59C22×D411yescharacteristic
298C2×C4×C59C2×#4112yes—
299C2×C4×C592−1+412yes—
300C2×C4×C59C2511yescharacteristic
301C22⋊D59—44no—
302C22⋊D59—84no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—42no—
311C2×Dic59—42no—
312C2×Dic59—42no—
313C2×Dic59—42no—
314C2×Dic59—84no—
315C2×Dic59—84no—
316C2×Dic59C22×D412yes—
317C2×Dic59C22×D412yes—
318C2×Dic59C22×D412yes—
319C4×D59—24no—
320C4×D59—22no—
321C4×D59—22no—
322C4×D59—48no—
323Dic118—22no—
324Dic118—22no—
325Dic118—42no—
326C8×C59—22no—
327C8×C59—22no—
328C59⋊C8—22no—
329C59⋊C8C2×#4114yes—
330C2×#3351—591nomaximal, Sylow
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—44no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—42no—
338C22×C59—84no—
339C22×C59#54712yes—
340C22×C59#57512yes—
341C22×C59#57712yes—
342C22×C59C23×D411yescharacteristic
343C2×D59—22no—
344C2×D59—22no—
345C2×D59—22no—
346C2×D59—44no—
347C4×C59—22no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59#54712yes—
352C4×C59C22×#4111yescharacteristic
353C4×C59C2×2−1+411yescharacteristic
354Dic59—22no—
355Dic59—22no—
356Dic59—22no—
357Dic59—42no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361C2×#553—591no—
362C2×#552—591no—
363#3351—5916no—
364C2×#499—591no—
365C2×#481—591no—
366C2×#485—591no—
367C2×#482D5911yescharacteristic, complemented
368C2×#483—591no—
369C2×#479—591no—
370C2×#478—591no—
371C2×#468—591no—
372C2×#468—591no—
373C2×C4×SD16—591no—
374C2×#436—591no—
375C2×#428—591no—
376C2×#428—591no—
377C2×C59—42no—
378C2×C59—82no—
379C2×C59#335114yescomplemented
380C2×C59C2×#54711yescharacteristic
381C2×C59C2×#57511yescharacteristic
382C2×C59C2×#57711yescharacteristic
383D59—42no—
384C22×SD16—591no—
385C22×M16—591no—
386C22×M16—591no—
387#553—598no—
388#553—1184no—
389#552—598no—
390#552—1184no—
391C2×#126—1181no—
392C2×#126—1181no—
393C2×#125—591no—
394C2×#125—591no—
395C2×#125—1181no—
396C2×#123—1181no—
397C2×#123—1181no—
398C2×C22⋊Q8—591no—
399C2×C22⋊Q8—591no—
400C2×#121—591no—
401C2×#121—1181no—
402C2×#121C2×D5911yescharacteristic
403C2×C4×Q8—591no—
404C2×C4×D4—591no—
405C2×C4×D4—591no—
406C2×C4×D4—1181no—
407C2×#117—591no—
408C2×#117—1181no—
409C2×#117C2×D5911yescharacteristic
410C22×C4⋊C4—591no—
411C22×C4⋊C4—591no—
412#499—598no—
413#485—598no—
414#483—598no—
415#482C2×D5918yescomplemented
416#481—598no—
417#479—598no—
418#478—598no—
419#468—598no—
420#468—598no—
421C4×SD16—598no—
422#436—598no—
423#428—598no—
424#428—598no—
425C2×#107—591no—
426C2×#107—591no—
427C2×#107—591no—
428C2×#107C2×D5911yescharacteristic
429C2×#106—591no—
430C2×#106—591no—
431C2×#106—591no—
432C2×#106—591no—
433C2×#106C2×D5911yescharacteristic
434C2×C4⋊C8—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#102—591no—
439C2×#102C2×D5911yescharacteristic
440C2×#102C2×D5911yescharacteristic
441C2×C22⋊C8—591no—
442C2×C22⋊C8C2×D5911yescharacteristic
443C2×C4×C8—591no—
444C59C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8—591no—
446C22×D4—21no—
447C22×D4—591no—
448C22×D4—1181no—
449C22×D4C22×D5911yescharacteristic
450C23×C4—591no—
451C23×C4—1181no—
452C23×C4—1181no—
453C23×C4—1181no—
454C23×C4C22×D5911yescharacteristic
455C2×SD16—594no—
456C2×SD16—1184no—
457C2×M16—594no—
458C2×M16—594no—
459C2×M16—1184no—
460C2×M16—1184no—
461C22×C8—591no—
462C22×C8—591no—
463C22×C8C22×D5911yescharacteristic
464C22×C8C22×D5911yescharacteristic
465#126—1188no—
466#126—1188no—
467#125—594no—
468#125—594no—
469#125—1188no—
470#125—1182no—
471#125—1182no—
472#123—1188no—
473#123—1188no—
474C22⋊Q8—594no—
475C22⋊Q8—594no—
476C22⋊Q8—1182no—
477C22⋊Q8—1182no—
478#121—22no—
479#121—594no—
480#121—1182no—
481#121—1188no—
482#121C22×D5914yes—
483C4×Q8—594no—
484C4×Q8—1182no—
485C4×D4—594no—
486C4×D4—594no—
487C4×D4—594no—
488C4×D4—1182no—
489C4×D4—1188no—
490#117—22no—
491#117—594no—
492#117—1188no—
493#117—1182no—
494#117C22×D5914yes—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—594no—
500C2×C4⋊C4—594no—
501C2×C4⋊C4—1182no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1182no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4C22×D5911yescharacteristic
513C2×C4⋊C4C22×D5911yescharacteristic
514C2×C4⋊C4C22×D5911yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—591no—
518C2×C22⋊C4—591no—
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4—1181no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C42—21no—
525C2×C42—591no—
526C2×C42—1181no—
527C2×C42—1181no—
528#107—594no—
529#107—594no—
530#107—594no—
531#107C22×D5914yes—
532#106—594no—
533#106—594no—
534#106—594no—
535#106—594no—
536#106C22×D5914yes—
537C4⋊C8—594no—
538#103—594no—
539#103—594no—
540#103—594no—
541#102—594no—
542#102C22×D5914yes—
543#102C22×D5914yes—
544C22⋊C8—594no—
545C22⋊C8C22×D5914yes—
546C4×C8—594no—
547C24—21no—
548C24—591no—
549C24D4×D5911yescharacteristic
550C2×Q8—592no—
551C2×Q8—1181no—
552C2×Q8—1182no—
553C2×Q8—1182no—
554C2×D4—24no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—44no—
559C2×D4—594no—
560C2×D4—1184no—
561C2×D4—4722no—
562C2×D4—2362no—
563C2×D4C23×D5912yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—591no—
570C22×C4—591no—
571C22×C4—591no—
572C22×C4—592no—
573C22×C4—592no—
574C22×C4—1184no—
575C22×C4—1184no—
576C22×C4—1182no—
577C22×C4—1182no—
578C22×C4—1184no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—4722no—
584C22×C4—4722no—
585C22×C4—2364no—
586C22×C4D4×D5912yes—
587C22×C4D4×D5911yescharacteristic
588C22×C4C23×D5912yes—
589C22×C4C23×D5911yescharacteristic
590SD16—1188no—
591M16—1188no—
592M16—1188no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—594no—
596C2×C8—592no—
597C2×C8—592no—
598C2×C8—1182no—
599C2×C8C23×D5912yes—
600C2×C8C23×D5912yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—594no—
605C4⋊C4—592no—
606C4⋊C4—592no—
607C4⋊C4—592no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1181no—
616C4⋊C4—1181no—
617C4⋊C4—1181no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4C23×D5912yes—
621C4⋊C4C23×D5912yes—
622C4⋊C4C23×D5912yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—594no—
626C22⋊C4—594no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C22⋊C4—1184no—
632C42—24no—
633C42—592no—
634C42—592no—
635C42—1184no—
636C42—1184no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—592no—
645C23—1182no—
646C23—1182no—
647C23—1182no—
648C23C2×D4×D5912yes—
649C23C2×D4×D5911yescharacteristic
650Q8—1182no—
651Q8—1182no—
652Q8—2362no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—4724no—
658D4—2364no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—592no—
670C2×C4—592no—
671C2×C4—592no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1184no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—4724no—
683C2×C4—4724no—
684C2×C4—2368no—
685C2×C4—2362no—
686C2×C4—2362no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4C2×D4×D5912yes—
690C2×C4C2×D4×D5911yescharacteristic
691C2×C4#41×D5912yes—
692C2×C4#1427377412yes—
693C2×C4C24×D5911yescharacteristic
694C8—22no—
695C8—22no—
696C8—594no—
697C8—1182no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—1182no—
707C22—1182no—
708C22—1182no—
709C22—2364no—
710C22#1683805012yes—
711C22#1683819812yes—
712C22#1683820912yes—
713C22C22×D4×D5911yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—1182no—
719C4—1182no—
720C4—1182no—
721C4—2362no—
722C4—2362no—
723C4—2362no—
724C4—2362no—
725C4#1683805012yes—
726C4C2×#41×D5911yescharacteristic
727C4C2×#1427377411yescharacteristic
728C2—42no—
729C2—82no—
730C2—2362no—
731C2#2143664914yesdirect product factor
732C2C2×#1683805011yescharacteristic
733C2C2×#1683819811yescharacteristic
734C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
prime radicalC2×#16838104C2
hypercenterC2×#482D59
hypocenterC59C2×#3351
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
2. C2×#16838091C2semidirect
3. #21436649C2direct (N × H)
4. C2×#16837802C2semidirect
5. C2×#16837719C2semidirect
6. C2×#16837746C2semidirect
7. C2×#16837733C2semidirect
8. C2×#16837708C2semidirect
9. C2×#16837704C2semidirect
10. C2×#16837647C2semidirect
11. C2×#16837646C2semidirect
12. C2×#16837493C2semidirect
13. C2×#16837477C2semidirect
14. C2×#16837445C2semidirect
15. C2×#16837443C2semidirect
16. C2×C59×#482C2semidirect
23. #16838091C22semidirect
43. #16837802C22semidirect
44. #16837746C22semidirect
45. #16837733C22semidirect
46. #16837719C22semidirect
47. #16837708C22semidirect
48. #16837704C22semidirect
49. #16837647C22semidirect
50. #16837646C22semidirect
51. #16837493C22semidirect
52. #16837477C22semidirect
53. #16837445C22semidirect
54. #16837443C22semidirect
71. C59×#482C22semidirect
367. C2×#482D59semidirect
379. C2×C59#3351semidirect
415. #482C2×D59semidirect
444. C59C2×#3351semidirect
731. C2#21436649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381042
C2×#168380912
#214366492
C2×#168378022
C2×#168377192
C2×#168377462
C2×#168377332
C2×#168377082
C2×#168377042
C2×#168376472
C2×#168376462
C2×#168374932
C2×#168374772
C2×#168374452
C2×#168374432
C2×C59×#4822
C2×#335159