Finite Group Databasebeta

← C2×#21436224 #29465409

Subgroups — C2×#21436224 #29465409

Order 15104.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838092C211yesmaximal, characteristic, complemented
2C2×#16838073C211yesmaximal, characteristic
3#21436224C2116yesmaximal, direct product factor
4C2×#16837767C211yesmaximal, characteristic, complemented
5C2×#16837721C211yesmaximal, characteristic, complemented
6C2×#16837727C211yesmaximal, characteristic, complemented
7C2×#16837710C211yesmaximal, characteristic, complemented
8C2×#16837648C211yesmaximal, characteristic, complemented
9C2×#16837631C211yesmaximal, characteristic, complemented
10C2×#16837603C211yesmaximal, characteristic, complemented
11C2×#16837566C211yesmaximal, characteristic, complemented
12C2×#16837566C211yesmaximal, characteristic, complemented
13C2×#16837510C211yesmaximal, characteristic, complemented
14C2×#16837404C211yesmaximal, characteristic, complemented
15C2×#16837399C211yesmaximal, characteristic, complemented
16C2×C59×#435C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745685C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22#16838092—24no—
23#16838092C2218yescomplemented
24#16838073—24no—
25#16838073C2218yes—
26C2×#14273724C2211yescharacteristic
27C2×#14273723—21no—
28C2×#14273720—21no—
29C2×#14273719C2211yescharacteristic
30C2×#14273717—21no—
31C2×#14273708—21no—
32C2×#14273706C2211yescharacteristic
33C2×#14273706C2211yescharacteristic
34C2×#14273701C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36C2×#14273700—21no—
37C2×#14273700—21no—
38C2×C4×Dic118C2211yescharacteristic
39C2×C4×Dic118C2211yescharacteristic
40C2×#14273689—21no—
41C2×#14273686C2211yescharacteristic
42C2×#14273683—21no—
43C22×C4⋊Dic59C2211yescharacteristic
44#16837767C2218yescomplemented
45#16837727C2218yescomplemented
46#16837721C2218yescomplemented
47#16837710C2218yescomplemented
48#16837648C2218yescomplemented
49#16837631C2218yescomplemented
50#16837603C2218yescomplemented
51#16837566C2218yescomplemented
52#16837566C2218yescomplemented
53#16837510C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57#16837404C2218yescomplemented
58#16837399C2218yescomplemented
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#435C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—22no—
79C2×#11745685—24no—
80C2×#11745685—24no—
81C2×#11745685—42no—
82C2×#11745685—42no—
83C2×#11745685C2314yes—
84C2×#11745685C2314yes—
85C22×Dic118C2311yescharacteristic
86C22×Dic118C2311yescharacteristic
87C22×D236—21no—
88C22×D236—21no—
89C22×D236C2311yescharacteristic
90C22×D236C2311yescharacteristic
91C22×C22⋊D59—21no—
92C22×C22⋊D59—21no—
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C23×Dic59—21no—
96C22×C4×D59—21no—
97C22×C4×D59—21no—
98C2×Dic236—24no—
99C2×Dic236C2314yes—
100C2×#11745660—42no—
101C2×#11745660—42no—
102C2×#11745660C2314yes—
103C2×#11745660C2314yes—
104#14273724—22no—
105#14273724C2314yes—
106#14273723—28no—
107#14273720—28no—
108#14273719—22no—
109#14273719C2314yes—
110#14273717—28no—
111#14273708—28no—
112#14273706—22no—
113#14273706—22no—
114#14273706C2314yes—
115#14273706C2314yes—
116#14273701—22no—
117#14273701—22no—
118#14273701C2314yes—
119#14273701C2314yes—
120#14273700—28no—
121#14273700—28no—
122C4×Dic118—22no—
123C4×Dic118—22no—
124C4×Dic118C2314yes—
125C4×Dic118C2314yes—
126#14273689—28no—
127#14273686—22no—
128#14273686C2314yes—
129#14273683—28no—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59—22no—
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×C4⋊Dic59C2311yescharacteristic
135C2×C4⋊Dic59C2311yescharacteristic
136C2×C4⋊Dic59C2314yes—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C2×Dic59⋊C4—21no—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×C22⋊Dic59—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×C4×Dic59—21no—
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151#14273661C2314yes—
152#14273659C2314yes—
153#14273659C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158#14273649C2314yes—
159#14273649C2314yes—
160#14273649C2314yes—
161#14273649C2314yes—
162#14273649C2314yes—
163#14273649C2314yes—
164C22×D4×C59D411yescharacteristic
165C23×C4×C59C2311yescharacteristic
166C23×C4×C59C2311yescharacteristic
167C2×M16×C59—42no—
168C2×M16×C59C2314yes—
169C22×C8×C59—42no—
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2314yes—
175C4×D4×C59D414yes—
176C4×D4×C59C2314yes—
177C2×C4⋊C4×C59D411yescharacteristic
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C22⋊C4×C59D411yescharacteristic
180C2×C42×C59C2311yescharacteristic
181C4⋊C8×C59C2314yes—
182C22⋊C8×C59C2314yes—
183C22⋊C8×C59C2314yes—
184#97×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C24×C59C2×D411yescharacteristic
187C23×D59—21no—
188C23×D59—21no—
189C2×D4×C59—42no—
190C2×D4×C59C2×D414yes—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59—22no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2412yes—
203C22×C4×C59C2411yescharacteristic
204C2×C22⋊D59—24no—
205C2×C22⋊D59—24no—
206C2×C22⋊D59—24no—
207C2×C22⋊D59—24no—
208C2×C22⋊D59—44no—
209C2×C22⋊D59—44no—
210C2×C22⋊D59—82no—
211C2×C22⋊D59—82no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—24no—
219C22×Dic59—44no—
220#11745685—28no—
221#11745685—28no—
222#11745685—44no—
223#11745685—44no—
224#11745685—48no—
225#11745685—48no—
226C2×D236—22no—
227C2×D236—22no—
228C2×D236—22no—
229C2×D236—22no—
230C2×D236—24no—
231C2×D236—21no—
232C2×D236—21no—
233C2×D236—24no—
234C2×D236—44no—
235C2×D236—82no—
236C2×D236C2412yes—
237C2×D236C2412yes—
238C2×C4×D59—24no—
239C2×C4×D59—24no—
240C2×C4×D59—44no—
241C2×C4×D59—44no—
242C2×Dic118—21no—
243C2×Dic118—22no—
244C2×Dic118—22no—
245C2×Dic118—22no—
246C2×Dic118—21no—
247C2×Dic118#4114yes—
248C2×Dic118C2412yes—
249C2×Dic118C2412yes—
250M16×C59—44no—
251C2×C8×C59—22no—
252C2×C8×C59—22no—
253C2×C8×C59—22no—
254C2×C8×C59—22no—
255C2×C8×C59—44no—
256C2×C8×C59C2412yes—
257C2×C8×C59C2412yes—
258C2×C8×C59C2412yes—
259C2×C8×C59C2412yes—
260C4⋊C4×C59C2×D414yes—
261C22⋊C4×C59C2×D414yes—
262C22⋊C4×C59C2×D414yes—
263C42×C59C2×D412yes—
264C42×C59C2412yes—
265C22⋊Dic59—24no—
266C22⋊Dic59—24no—
267C22⋊Dic59—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270C4⋊Dic59—21no—
271C4⋊Dic59—21no—
272C4⋊Dic59—24no—
273C4⋊Dic59—21no—
274C4⋊Dic59—21no—
275C4⋊Dic59C2412yes—
276C4⋊Dic59C2412yes—
277C4⋊Dic59C2412yes—
278C4⋊Dic59C2412yes—
279Dic59⋊C4—24no—
280Dic59⋊C4—24no—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283Dic59⋊C4—24no—
284Dic59⋊C4—24no—
285C4×Dic59—24no—
286C4×Dic59—24no—
287C4×Dic59—24no—
288Dic236—28no—
289#11745660—44no—
290#11745660—44no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59C22×D412yes—
298C23×C59C22×D412yes—
299C23×C59C22×D411yescharacteristic
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—42no—
303C22×D59—42no—
304C22×D59—42no—
305C22×D59—42no—
306C22×D59—42no—
307C22×D59—42no—
308D4×C59—44no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—24no—
314C2×C4×C59—24no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59C22×D412yes—
320C2×C4×C59C22×D412yes—
321C2×C4×C59C22×D412yes—
322C2×C4×C59C22×D412yes—
323C2×C4×C59C22×D411yescharacteristic
324C2×C4×C59C2×#4112yes—
325C2×C4×C59H(5,𝔽2)12yes—
326C2×C4×C59C2511yescharacteristic
327C22⋊D59—48no—
328C22⋊D59—48no—
329C22⋊D59—84no—
330C22⋊D59—84no—
331C2×Dic59—24no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—48no—
339C2×Dic59—42no—
340C2×Dic59—42no—
341C2×Dic59—42no—
342C2×Dic59—42no—
343C2×Dic59—42no—
344D236—22no—
345D236—22no—
346D236—22no—
347D236—22no—
348D236—48no—
349D236—42no—
350D236—42no—
351D236—84no—
352C4×D59—48no—
353C4×D59—48no—
354Dic118—24no—
355Dic118—22no—
356Dic118—22no—
357Dic118—22no—
358Dic118—42no—
359Dic118C2×#4114yes—
360C8×C59—22no—
361C8×C59—22no—
362C8×C59—22no—
363C8×C59—22no—
364C2×#3317—591nomaximal, Sylow
365C22×C59—22no—
366C22×C59—22no—
367C22×C59—22no—
368C22×C59—22no—
369C22×C59—22no—
370C22×C59—22no—
371C22×C59—44no—
372C22×C59—44no—
373C22×C59#54612yes—
374C22×C59#57512yes—
375C22×C59#57712yes—
376C22×C59C23×D411yescharacteristic
377C2×D59—42no—
378C2×D59—42no—
379C2×D59—42no—
380C2×D59—42no—
381C2×D59—42no—
382C2×D59—42no—
383C2×D59—84no—
384C2×D59—84no—
385C4×C59—22no—
386C4×C59—22no—
387C4×C59—22no—
388C4×C59—22no—
389C4×C59#54612yes—
390C4×C59C22×#4111yescharacteristic
391C4×C59C2×H(5,𝔽2)11yescharacteristic
392Dic59—24no—
393Dic59—42no—
394Dic59—42no—
395Dic59—42no—
396Dic59—42no—
397Dic59—42no—
398C2×#552—591no—
399C2×#550—591no—
400#3317—5916no—
401C2×#490—591no—
402C2×#481—591no—
403C2×#482—591no—
404C2×#479—591no—
405C2×#468—591no—
406C2×#465—591no—
407C2×#460—591no—
408C2×#452—591no—
409C2×#452—591no—
410C2×#441—591no—
411C2×#435D5911yescharacteristic, complemented
412C2×#417—591no—
413C2×#416—591no—
414C2×C59—42no—
415C2×C59—42no—
416C2×C59#331714yescomplemented
417C2×C59C2×#54611yescharacteristic
418C2×C59C2×#57511yescharacteristic
419C2×C59C2×#57711yescharacteristic
420D59—82no—
421D59—82no—
422C22×#41—591no—
423C22×#41—591no—
424C22×Q16—591no—
425C22×SD16—591no—
426C22×SD16—591no—
427C22×M16C2×D5911yescharacteristic
428C23×C8C2×D5911yescharacteristic
429#552—598no—
430#552—1184no—
431#550—598no—
432#550—1184no—
433C2×#127—591no—
434C2×#127—1181no—
435C2×#126—1181no—
436C2×#125—591no—
437C2×#125—1181no—
438C2×#123—1181no—
439C2×C22⋊Q8—591no—
440C2×C22⋊Q8—591no—
441C2×#121—591no—
442C2×#121—591no—
443C2×#121—1181no—
444C2×#121—1181no—
445C2×C4×Q8—591no—
446C2×C4×Q8—591no—
447C2×C4×D4—1181no—
448C2×C4×D4C2×D5911yescharacteristic
449C2×#117—591no—
450C2×#117—1181no—
451C22×C4⋊C4—591no—
452#490—598no—
453#482—598no—
454#481—598no—
455#479—598no—
456#468—598no—
457#465—598no—
458#460—598no—
459#452—598no—
460#452—598no—
461#441—598no—
462#435C2×D5918yescomplemented
463C2×#107—591no—
464C2×#106—591no—
465C2×#106—591no—
466C2×C4⋊C8C2×D5911yescharacteristic
467#417—598no—
468#416—598no—
469C2×#103—591no—
470C2×#103—591no—
471C2×#103—591no—
472C2×#103—591no—
473C2×#102—591no—
474C2×#102—591no—
475C2×#102—591no—
476C2×#102—591no—
477C2×#102—591no—
478C2×#102—591no—
479C2×C22⋊C8C2×D5911yescharacteristic
480C2×C22⋊C8C2×D5911yescharacteristic
481C2×#97C2×D5911yescharacteristic
482C59C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—594no—
484C2×#41—594no—
485C2×#41—1184no—
486C2×#41—1184no—
487C2×#41—1182no—
488C2×#41—1182no—
489C2×#41—2362no—
490C2×#41—2362no—
491C22×Q8—591no—
492C22×Q8—591no—
493C22×D4—591no—
494C22×D4—591no—
495C22×D4—1181no—
496C22×D4—1181no—
497C22×D4—1181no—
498C22×D4—1181no—
499C22×D4—1181no—
500C22×D4—1181no—
501C22×D4D23611yescharacteristic
502C23×C4—1181no—
503C23×C4—1181no—
504C23×C4—1181no—
505C23×C4C22×D5911yescharacteristic
506C23×C4C22×D5911yescharacteristic
507C2×Q16—594no—
508C2×Q16—1184no—
509C2×SD16—594no—
510C2×SD16—594no—
511C2×SD16—2362no—
512C2×SD16—2362no—
513C2×M16—42no—
514C2×M16C22×D5914yes—
515C22×C8—42no—
516C22×C8C22×D5911yescharacteristic
517C22×C8C22×D5911yescharacteristic
518C22×C8C22×D5911yescharacteristic
519C22×C8C22×D5911yescharacteristic
520C22×C8C22×D5914yes—
521#127—594no—
522#127—1188no—
523#127—1182no—
524#126—1188no—
525#125—594no—
526#125—1188no—
527#125—1182no—
528#123—1188no—
529C22⋊Q8—594no—
530C22⋊Q8—594no—
531C22⋊Q8—1182no—
532C22⋊Q8—1182no—
533#121—594no—
534#121—594no—
535#121—1182no—
536#121—1182no—
537#121—1188no—
538#121—1188no—
539C4×Q8—594no—
540C4×Q8—594no—
541C4×Q8—1182no—
542C4×Q8—1182no—
543C4×D4—1188no—
544C4×D4D23614yes—
545C4×D4C22×D5914yes—
546#117—594no—
547#117—1182no—
548#117—1188no—
549C2×C4⋊C4—591no—
550C2×C4⋊C4—591no—
551C2×C4⋊C4—594no—
552C2×C4⋊C4—591no—
553C2×C4⋊C4—591no—
554C2×C4⋊C4—1181no—
555C2×C4⋊C4—1182no—
556C2×C4⋊C4—1181no—
557C2×C4⋊C4—1181no—
558C2×C4⋊C4—1181no—
559C2×C4⋊C4—1181no—
560C2×C4⋊C4—1181no—
561C2×C4⋊C4—1181no—
562C2×C4⋊C4D23611yescharacteristic
563C2×C22⋊C4—1181no—
564C2×C22⋊C4—1181no—
565C2×C22⋊C4—1181no—
566C2×C22⋊C4—1181no—
567C2×C22⋊C4—1181no—
568C2×C22⋊C4D23611yescharacteristic
569C2×C22⋊C4D23611yescharacteristic
570C2×C42—1181no—
571C2×C42—1181no—
572C2×C42—1181no—
573C2×C42C22×D5911yescharacteristic
574#107—594no—
575#106—594no—
576#106—594no—
577C4⋊C8C22×D5914yes—
578#103—594no—
579#103—594no—
580#103—594no—
581#103—594no—
582#102—594no—
583#102—594no—
584#102—594no—
585#102—594no—
586#102—594no—
587#102—594no—
588C22⋊C8C22×D5914yes—
589C22⋊C8C22×D5914yes—
590#97C22×D5914yes—
591C24—1181no—
592C24—1181no—
593C24C2×D23611yescharacteristic
594C24C2×D23611yescharacteristic
595#41—1188no—
596#41—1188no—
597#41—2364no—
598#41—2364no—
599#41—2368no—
600#41—2368no—
601C2×Q8—594no—
602C2×Q8—592no—
603C2×Q8—592no—
604C2×Q8—1181no—
605C2×Q8—1181no—
606C2×Q8—1182no—
607C2×Q8—1182no—
608C2×Q8—1182no—
609C2×D4—42no—
610C2×D4—592no—
611C2×D4—592no—
612C2×D4—1184no—
613C2×D4—1184no—
614C2×D4—1184no—
615C2×D4—1184no—
616C2×D4—1184no—
617C2×D4—1184no—
618C2×D4—1181no—
619C2×D4—1181no—
620C2×D4—1182no—
621C2×D4—1182no—
622C2×D4—1182no—
623C2×D4—1182no—
624C2×D4—4722no—
625C2×D4—4722no—
626C2×D4—4722no—
627C2×D4—2364no—
628C2×D4—2364no—
629C2×D4—2364no—
630C2×D4C2×D23614yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—1181no—
636C22×C4—1184no—
637C22×C4—1181no—
638C22×C4—1181no—
639C22×C4—1181no—
640C22×C4—1181no—
641C22×C4—1181no—
642C22×C4—1184no—
643C22×C4—1184no—
644C22×C4—2364no—
645C22×C4—2364no—
646C22×C4—2364no—
647C22×C4C2×D23612yes—
648C22×C4C2×D23612yes—
649C22×C4C2×D23611yescharacteristic
650C22×C4C2×D23611yescharacteristic
651C22×C4C2×D23611yescharacteristic
652C22×C4C2×D23611yescharacteristic
653C22×C4C23×D5912yes—
654C22×C4C23×D5912yes—
655C22×C4C23×D5911yescharacteristic
656Q16—1188no—
657SD16—2364no—
658SD16—2364no—
659M16—44no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—44no—
665C2×C8C23×D5912yes—
666C2×C8C23×D5912yes—
667C2×C8C23×D5912yes—
668C2×C8C23×D5912yes—
669C4⋊C4—592no—
670C4⋊C4—592no—
671C4⋊C4—592no—
672C4⋊C4—592no—
673C4⋊C4—1181no—
674C4⋊C4—1181no—
675C4⋊C4—1184no—
676C4⋊C4—1181no—
677C4⋊C4—1181no—
678C4⋊C4—1184no—
679C4⋊C4—1184no—
680C4⋊C4—1184no—
681C4⋊C4—1184no—
682C4⋊C4—1184no—
683C4⋊C4—1184no—
684C4⋊C4C2×D23614yes—
685C22⋊C4—1184no—
686C22⋊C4—1184no—
687C22⋊C4—1184no—
688C22⋊C4—1184no—
689C22⋊C4—1184no—
690C22⋊C4C2×D23614yes—
691C22⋊C4C2×D23614yes—
692C42—1184no—
693C42—1184no—
694C42—1184no—
695C42C2×D23612yes—
696C42C23×D5912yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—1182no—
704C23—1182no—
705C23—2362no—
706C23—2362no—
707C23—2362no—
708C23—2362no—
709C23—2362no—
710C23—2362no—
711C23C22×D23612yes—
712C23C22×D23612yes—
713C23C22×D23611yescharacteristic
714Q8—594no—
715Q8—1182no—
716Q8—1184no—
717Q8—1182no—
718Q8—1182no—
719Q8—2362no—
720D4—44no—
721D4—1182no—
722D4—1182no—
723D4—1182no—
724D4—1182no—
725D4—4724no—
726D4—4724no—
727D4—4724no—
728D4—2368no—
729D4—2368no—
730D4—2368no—
731D4—2362no—
732D4—2362no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—1182no—
744C2×C4—1184no—
745C2×C4—1182no—
746C2×C4—1182no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—1182no—
750C2×C4—2368no—
751C2×C4—2368no—
752C2×C4—2368no—
753C2×C4—2362no—
754C2×C4—2362no—
755C2×C4—2362no—
756C2×C4—2362no—
757C2×C4—2362no—
758C2×C4C22×D23612yes—
759C2×C4C22×D23612yes—
760C2×C4C22×D23612yes—
761C2×C4C22×D23612yes—
762C2×C4C22×D23611yescharacteristic
763C2×C4#41×D5912yes—
764C2×C4#1427377212yes—
765C2×C4C24×D5911yescharacteristic
766C8—22no—
767C8—22no—
768C8—22no—
769C8—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—4724no—
779C22—4724no—
780C22—2362no—
781C22—2362no—
782C22—2362no—
783C22—2362no—
784C22—2362no—
785C22—2362no—
786C22#1683804712yes—
787C22#1683820212yes—
788C22#1683821412yes—
789C22C23×D23611yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—1184no—
795C4—2362no—
796C4—2362no—
797C4—2362no—
798C4—2362no—
799C4—2362no—
800C4#1683804712yes—
801C4C2×#41×D5911yescharacteristic
802C4C2×#1427377211yescharacteristic
803C2—42no—
804C2—42no—
805C2—4722no—
806C2—4722no—
807C2#2143622414yesdirect product factor
808C2C2×#1683804711yescharacteristic
809C2C2×#1683820211yescharacteristic
810C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C22×D4
prime radicalC2×#16838073C2
hypercenterC2×#435D59
hypocenterC59C2×#3317
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16838092C2semidirect
3. #21436224C2direct (N × H)
4. C2×#16837767C2semidirect
5. C2×#16837721C2semidirect
6. C2×#16837727C2semidirect
7. C2×#16837710C2semidirect
8. C2×#16837648C2semidirect
9. C2×#16837631C2semidirect
10. C2×#16837603C2semidirect
11. C2×#16837566C2semidirect
12. C2×#16837566C2semidirect
13. C2×#16837510C2semidirect
14. C2×#16837404C2semidirect
15. C2×#16837399C2semidirect
16. C2×C59×#435C2semidirect
23. #16838092C22semidirect
44. #16837767C22semidirect
45. #16837727C22semidirect
46. #16837721C22semidirect
47. #16837710C22semidirect
48. #16837648C22semidirect
49. #16837631C22semidirect
50. #16837603C22semidirect
51. #16837566C22semidirect
52. #16837566C22semidirect
53. #16837510C22semidirect
57. #16837404C22semidirect
58. #16837399C22semidirect
72. C59×#435C22semidirect
411. C2×#435D59semidirect
416. C2×C59#3317semidirect
462. #435C2×D59semidirect
482. C59C2×#3317semidirect
807. C2#21436224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380922
C2×#168380732
#214362242
C2×#168377672
C2×#168377212
C2×#168377272
C2×#168377102
C2×#168376482
C2×#168376312
C2×#168376032
C2×#168375662
C2×#168375102
C2×#168374042
C2×#168373992
C2×C59×#4352
C2×#331759