Finite Group Databasebeta

← C2×#21436584 #29467271

Subgroups — C2×#21436584 #29467271

Order 15104.

1942 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×#16838107C211yesmaximal, characteristic, complemented
2C2×#16838099C211yesmaximal, characteristic
3#21436584C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837739C211yesmaximal, characteristic, complemented
6C2×#16837719C211yesmaximal, characteristic, complemented
7C2×#16837744C211yesmaximal, characteristic, complemented
8C2×#16837708C211yesmaximal, characteristic, complemented
9C2×#16837680C211yesmaximal, characteristic, complemented
10C2×#16837646C211yesmaximal, characteristic, complemented
11C2×#16837630C211yesmaximal, characteristic, complemented
12C2×#16837499C211yesmaximal, characteristic, complemented
13C2×#16837476C211yesmaximal, characteristic, complemented
14C2×#16837442C211yesmaximal, characteristic, complemented
15C2×#107×D59C211yesmaximal, characteristic, complemented
16C2×C59×#480C211yesmaximal, characteristic, complemented
17C22×#11745670C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838107—24no—
21#16838107C2218yescomplemented
22#16838099—24no—
23#16838099C2218yes—
24C2×#14273726C2211yescharacteristic
25C2×#14273720—21no—
26C2×#14273718C2211yescharacteristic
27C2×#14273717—21no—
28C2×#14273708—21no—
29C2×#14273707C2211yescharacteristic
30C2×#14273706—21no—
31C2×#14273706C2211yescharacteristic
32C2×#14273705—21no—
33C2×#14273698—21no—
34C2×#14273698C2211yescharacteristic
35C2×#14273692C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×(C22⋊D59)⋊C4—21no—
40C2×#14273686C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837810C2218yescomplemented
44#16837744C2218yescomplemented
45#16837739C2218yescomplemented
46#16837719C2218yescomplemented
47#16837708C2218yescomplemented
48#16837680C2218yescomplemented
49#16837646C2218yescomplemented
50#16837630C2218yescomplemented
51#16837499C2218yescomplemented
52#16837476C2218yescomplemented
53#16837442C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58#107×D59C2218yescomplemented
59C2×#14273659C2211yescharacteristic
60C2×#14273658C2211yescharacteristic
61C2×#14273658C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#480C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×C22⋊D59—21no—
80C22×C22⋊D59D411yescharacteristic
81C23×Dic59—21no—
82C22×C4×D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59C2311yescharacteristic
85C2×#11745670—24no—
86C2×#11745670C2314yes—
87C2×#11745664—24no—
88C2×#11745664C2314yes—
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C2×C8×D59—24no—
92C2×C8×D59C2314yes—
93#14273726—22no—
94#14273726C2314yes—
95#14273720—28no—
96#14273718—22no—
97#14273718C2314yes—
98#14273717—28no—
99#14273708—28no—
100#14273707—22no—
101#14273707C2314yes—
102#14273706—22no—
103#14273706—28no—
104#14273706C2314yes—
105#14273705—28no—
106#14273698—28no—
107#14273698—22no—
108#14273698C2314yes—
109#14273692—22no—
110#14273692C2314yes—
111D4×Dic59—22no—
112D4×Dic59C2314yes—
113C4×C22⋊D59—28no—
114C4×C22⋊D59D414yes—
115C4×C22⋊D59C2314yes—
116(C22⋊D59)⋊C4—28no—
117#14273686—22no—
118#14273686C2314yes—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4D411yescharacteristic
131C4⋊C4×D59—22no—
132C4⋊C4×D59—22no—
133C4⋊C4×D59C2314yes—
134C4⋊C4×D59C2314yes—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59D411yescharacteristic
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59C2311yescharacteristic
145#14273661C2314yes—
146#14273660C2314yes—
147#14273660C2314yes—
148#14273660C2314yes—
149#14273659C2314yes—
150#14273658C2314yes—
151#14273658C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273650C2314yes—
156#14273648C2314yes—
157(C2×D59)⋊C8C2314yes—
158#14273637C2314yes—
159C22×D4×C59—21no—
160C22×D4×C59C2311yescharacteristic
161C23×C4×C59—21no—
162C23×C4×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165#121×C59—22no—
166#121×C59C2314yes—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—22no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2314yes—
173C2×C22⋊C4×C59—21no—
174#107×C59C2314yes—
175#107×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—82no—
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×C59—24no—
194C22×C4×C59—82no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2411yescharacteristic
199C2×C22⋊D59—24no—
200C2×C22⋊D59—24no—
201C2×C22⋊D59—44no—
202C2×C22⋊D59C2×D414yes—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—24no—
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—24no—
216C2×C4×D59—82no—
217C2×C4×D59—82no—
218C2×C4×D59C2×D412yes—
219C2×C4×D59C2412yes—
220C2×Dic118—22no—
221C2×Dic118—22no—
222C2×Dic118—21no—
223C2×Dic118—24no—
224C2×Dic118—82no—
225C2×Dic118C2412yes—
226C2×C8×C59—22no—
227C2×C8×C59—22no—
228C2×C8×C59C2412yes—
229C2×C8×C59C2412yes—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59C2412yes—
235C4⋊C4×C59C2412yes—
236C4⋊C4×C59C2412yes—
237C22⋊C4×C59—24no—
238C22⋊Dic59—24no—
239C22⋊Dic59—24no—
240C22⋊Dic59—24no—
241C22⋊Dic59—24no—
242C22⋊Dic59C2×D414yes—
243#11745670—28no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4C2×D414yes—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253C4⋊Dic59C2412yes—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4C2×D414yes—
261C4×Dic59—24no—
262C4×Dic59—24no—
263C4×Dic59C2×D412yes—
264C4×Dic59C2412yes—
265#11745664—28no—
266C2×C59⋊C8—22no—
267C2×C59⋊C8#4114yes—
268C2×C59⋊C8C2412yes—
269C2×C59⋊C8C2412yes—
270C8×D59—28no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—42no—
276C23×C59—42no—
277C23×C59—42no—
278C23×C59C22×D412yes—
279C23×C59C22×D411yescharacteristic
280C22×D59—22no—
281C22×D59—22no—
282C22×D59#13714yes—
283C22×D59C22×D412yes—
284D4×C59—22no—
285D4×C59—22no—
286D4×C59—42no—
287D4×C59—84no—
288C2×C4×C59—22no—
289C2×C4×C59—24no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—84no—
299C2×C4×C59C22×D412yes—
300C2×C4×C59C22×D411yescharacteristic
301C2×C4×C59C2×#4112yes—
302C2×C4×C592−1+412yes—
303C2×C4×C59C2511yescharacteristic
304C22⋊D59—28no—
305C22⋊D59—48no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—42no—
314C2×Dic59—42no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—84no—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321C4×D59—24no—
322C4×D59—22no—
323C4×D59—22no—
324C4×D59—84no—
325C4×D59—84no—
326Dic118—22no—
327Dic118—22no—
328Dic118—42no—
329Dic118—84no—
330C8×C59—22no—
331C8×C59—22no—
332C59⋊C8—22no—
333C59⋊C8C2×#4114yes—
334C2×#3346—591nomaximal, Sylow
335C22×C59—22no—
336C22×C59—22no—
337C22×C59—22no—
338C22×C59—44no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—42no—
342C22×C59—84no—
343C22×C59#54712yes—
344C22×C59C2×#13712yes—
345C22×C59#57612yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—28no—
348C2×D59—22no—
349C2×D59—22no—
350C2×D59C2×#13714yes—
351C4×C59—22no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59—42no—
355C4×C59#54712yes—
356C4×C59C22×#4111yescharacteristic
357C4×C59C2×2−1+411yescharacteristic
358Dic59—22no—
359Dic59—22no—
360Dic59—22no—
361Dic59—42no—
362Dic59—42no—
363Dic59—42no—
364Dic59—42no—
365C2×#554—591no—
366C2×#553—591no—
367#3346—5916no—
368C2×#501—591no—
369C2×#484—591no—
370C2×#481—591no—
371C2×#485—591no—
372C2×#480D5911yescharacteristic, complemented
373C2×#479—591no—
374C2×#474—591no—
375C2×#468—591no—
376C2×#465—591no—
377C2×#440—591no—
378C2×#435—591no—
379C2×#428—591no—
380C22×#107—591no—
381C2×C59—42no—
382C2×C59—82no—
383C2×C59#334614yescomplemented
384C2×C59C2×#54711yescharacteristic
385C2×C59C22×#13711yescharacteristic
386C2×C59C2×#57611yescharacteristic
387D59—24no—
388C22×SD16—591no—
389C22×M16—591no—
390C23×C8—591no—
391#554—598no—
392#554—1184no—
393#553—598no—
394#553—1184no—
395C2×C4⋊Q8—591no—
396C2×#126—1181no—
397C2×#125—591no—
398C2×#125—1181no—
399C2×#123—1181no—
400C2×C22⋊Q8—591no—
401C2×C22⋊Q8—591no—
402C2×C22⋊Q8—1181no—
403C2×C22⋊Q8—1181no—
404C2×#121—591no—
405C2×#121—1181no—
406C2×#121C2×D5911yescharacteristic
407C2×C4×Q8—591no—
408C2×C4×D4—591no—
409C2×C4×D4—591no—
410C2×C4×D4—1181no—
411C2×C4×D4—1181no—
412C2×#117—591no—
413C22×C4⋊C4—591no—
414C22×C4⋊C4—591no—
415C22×C4⋊C4C2×D5911yescharacteristic
416#501—598no—
417#485—598no—
418#484—598no—
419#481—598no—
420#480C2×D5918yescomplemented
421#479—598no—
422#474—598no—
423#468—598no—
424#465—598no—
425#440—598no—
426#435—598no—
427#428—598no—
428C2×#107—591no—
429C2×#107—591no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#107—598no—
433C2×#107C2×D5911yescharacteristic
434C2×#107C2×D5911yescharacteristic
435C2×#106—591no—
436C2×#106—591no—
437C2×#106—591no—
438C2×C4⋊C8—591no—
439C2×#103—591no—
440C2×#103—591no—
441C2×#103—591no—
442C2×#102—591no—
443C2×#102C2×D5911yescharacteristic
444C2×#102C2×D5911yescharacteristic
445C2×C22⋊C8—591no—
446C2×C22⋊C8C2×D5911yescharacteristic
447C2×#97—591no—
448C59C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—591no—
450C22×Q8—1181no—
451C22×D4—21no—
452C22×D4—591no—
453C22×D4—1181no—
454C22×D4C22×D5911yescharacteristic
455C23×C4—21no—
456C23×C4—591no—
457C23×C4—1181no—
458C23×C4—1181no—
459C23×C4—1181no—
460C23×C4C22×D5911yescharacteristic
461C2×SD16—594no—
462C2×SD16—1184no—
463C2×M16—594no—
464C2×M16—1184no—
465C22×C8—591no—
466C22×C8—591no—
467C22×C8—594no—
468C22×C8—1184no—
469C22×C8C22×D5911yescharacteristic
470C22×C8C22×D5911yescharacteristic
471C4⋊Q8—594no—
472C4⋊Q8—1182no—
473#126—1188no—
474#125—594no—
475#125—1182no—
476#125—1188no—
477#123—1188no—
478C22⋊Q8—594no—
479C22⋊Q8—594no—
480C22⋊Q8—1188no—
481C22⋊Q8—1188no—
482C22⋊Q8—1182no—
483C22⋊Q8—1182no—
484#121—22no—
485#121—594no—
486#121—1182no—
487#121—1188no—
488#121C22×D5914yes—
489C4×Q8—594no—
490C4×Q8—1182no—
491C4×D4—594no—
492C4×D4—594no—
493C4×D4—594no—
494C4×D4—1182no—
495C4×D4—1188no—
496C4×D4—1188no—
497#117—594no—
498#117—1182no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—594no—
506C2×C4⋊C4—594no—
507C2×C4⋊C4—1182no—
508C2×C4⋊C4—1182no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
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⋊C4C22×D5911yescharacteristic
518C2×C4⋊C4C22×D5911yescharacteristic
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C4⋊C4C22×D5914yes—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—591no—
523C2×C22⋊C4—591no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C42—591no—
530C2×C42—1181no—
531C2×C42—1181no—
532#107—594no—
533#107—594no—
534#107—594no—
535#107—594no—
536#107C22×D5914yes—
537#107C22×D5914yes—
538#106—594no—
539#106—594no—
540#106—594no—
541C4⋊C8—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#102—594no—
546#102C22×D5914yes—
547#102C22×D5914yes—
548C22⋊C8—594no—
549C22⋊C8C22×D5914yes—
550#97—594no—
551C24—21no—
552C24—591no—
553C24D4×D5911yescharacteristic
554C2×Q8—592no—
555C2×Q8—1184no—
556C2×Q8—1181no—
557C2×Q8—1182no—
558C2×Q8—1182no—
559C2×Q8—4722no—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—82no—
565C2×D4—594no—
566C2×D4—1184no—
567C2×D4—1184no—
568C2×D4—2364no—
569C2×D4C23×D5912yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—82no—
577C22×C4—591no—
578C22×C4—591no—
579C22×C4—591no—
580C22×C4—592no—
581C22×C4—592no—
582C22×C4—1184no—
583C22×C4—1184no—
584C22×C4—1184no—
585C22×C4—1182no—
586C22×C4—1182no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—4722no—
592C22×C4—4722no—
593C22×C4—4722no—
594C22×C4D4×D5912yes—
595C22×C4D4×D5911yescharacteristic
596C22×C4C23×D5912yes—
597C22×C4C23×D5911yescharacteristic
598SD16—1188no—
599M16—1188no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—594no—
603C2×C8—592no—
604C2×C8—592no—
605C2×C8—1188no—
606C2×C8—1182no—
607C2×C8C23×D5912yes—
608C2×C8C23×D5912yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—594no—
614C4⋊C4—592no—
615C4⋊C4—592no—
616C4⋊C4—592no—
617C4⋊C4—1184no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4—1184no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1181no—
625C4⋊C4—1181no—
626C4⋊C4—1181no—
627C4⋊C4—1184no—
628C4⋊C4C23×D5912yes—
629C4⋊C4C23×D5912yes—
630C4⋊C4C23×D5912yes—
631C22⋊C4—24no—
632C22⋊C4—594no—
633C22⋊C4—594no—
634C22⋊C4—1184no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C22⋊C4—1184no—
639C42—592no—
640C42—592no—
641C42—1184no—
642C42—1184no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—594no—
651C23—592no—
652C23—1182no—
653C23—1182no—
654C23C2×D4×D5912yes—
655C23C2×D4×D5911yescharacteristic
656Q8—1182no—
657Q8—1182no—
658Q8—4724no—
659Q8—2362no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664D4—1188no—
665D4—2368no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—84no—
677C2×C4—592no—
678C2×C4—592no—
679C2×C4—592no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1184no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—4724no—
691C2×C4—4724no—
692C2×C4—4724no—
693C2×C4—2362no—
694C2×C4—2362no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4C2×D4×D5912yes—
698C2×C4C2×D4×D5911yescharacteristic
699C2×C4#41×D5912yes—
700C2×C4#1427377412yes—
701C2×C4C24×D5911yescharacteristic
702C8—22no—
703C8—22no—
704C8—594no—
705C8—1182no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—594no—
715C22—1182no—
716C22—1182no—
717C22—1188no—
718C22#1683805012yes—
719C22#137×D5912yes—
720C22#1683820312yes—
721C22C22×D4×D5911yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—1182no—
727C4—1182no—
728C4—1182no—
729C4—2362no—
730C4—2362no—
731C4—2362no—
732C4—2362no—
733C4#1683805012yes—
734C4C2×#41×D5911yescharacteristic
735C4C2×#1427377411yescharacteristic
736C2—42no—
737C2—82no—
738C2—1184no—
739C2#2143658414yesdirect product factor
740C2C2×#1683805011yescharacteristic
741C2C2×#137×D5911yescharacteristic
742C2C2×#1683820311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#480C2
socleC23×C59C22×D4
prime radicalC2×#16838099C2
hypercenterC2×#480D59
hypocenterC59C2×#3346
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16838107C2semidirect
3. #21436584C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837739C2semidirect
6. C2×#16837719C2semidirect
7. C2×#16837744C2semidirect
8. C2×#16837708C2semidirect
9. C2×#16837680C2semidirect
10. C2×#16837646C2semidirect
11. C2×#16837630C2semidirect
12. C2×#16837499C2semidirect
13. C2×#16837476C2semidirect
14. C2×#16837442C2semidirect
15. C2×#107×D59C2semidirect
16. C2×C59×#480C2semidirect
21. #16838107C22semidirect
43. #16837810C22semidirect
44. #16837744C22semidirect
45. #16837739C22semidirect
46. #16837719C22semidirect
47. #16837708C22semidirect
48. #16837680C22semidirect
49. #16837646C22semidirect
50. #16837630C22semidirect
51. #16837499C22semidirect
52. #16837476C22semidirect
53. #16837442C22semidirect
58. #107×D59C22semidirect
71. C59×#480C22semidirect
372. C2×#480D59semidirect
383. C2×C59#3346semidirect
420. #480C2×D59semidirect
448. C59C2×#3346semidirect
739. C2#21436584direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381072
C2×#168380992
#214365842
C2×#168378102
C2×#168377392
C2×#168377192
C2×#168377442
C2×#168377082
C2×#168376802
C2×#168376462
C2×#168376302
C2×#168374992
C2×#168374762
C2×#168374422
C2×#107×D592
C2×C59×#4802
C2×#334659