Finite Group Databasebeta

← C2×#21436314 #29465504

Subgroups — C2×#21436314 #29465504

Order 15104.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838092C211yesmaximal, characteristic, complemented
2C2×#16838048C211yesmaximal, characteristic
3#21436314C2116yesmaximal, direct product factor
4C2×#16837757C211yesmaximal, characteristic, complemented
5C2×#16837721C211yesmaximal, characteristic, complemented
6C2×#16837744C211yesmaximal, characteristic, complemented
7C2×#16837703C211yesmaximal, characteristic, complemented
8C2×#16837660C211yesmaximal, characteristic, complemented
9C2×#16837648C211yesmaximal, characteristic, complemented
10C2×#16837625C211yesmaximal, characteristic, complemented
11C2×#16837566C211yesmaximal, characteristic, complemented
12C2×#16837555C211yesmaximal, characteristic, complemented
13C2×C4×#11745660C211yesmaximal, characteristic, complemented
14C2×#16837404C211yesmaximal, characteristic, complemented
15C2×#16837408C211yesmaximal, characteristic, complemented
16C2×C59×#436C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×D236C2211yescharacteristic
19C22×Dic236C2211yescharacteristic, complemented
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22#16838092—24no—
23#16838092C2218yescomplemented
24#16838048—24no—
25#16838048C2218yes—
26C2×#14273720—21no—
27C2×#14273719C2211yescharacteristic, complemented
28C2×#14273717—21no—
29C2×#14273715C2211yescharacteristic
30C2×#14273712—21no—
31C2×#14273708—21no—
32C2×#14273706C2211yescharacteristic
33C2×#14273706C2211yescharacteristic
34C2×#14273706C2211yescharacteristic, complemented
35C2×#14273701C2211yescharacteristic
36C2×#14273700—21no—
37C2×#14273695—21no—
38C2×C4×Dic118C2211yescharacteristic, complemented
39C2×C4×D236C2211yescharacteristic
40C2×#14273686C2211yescharacteristic
41C2×#14273683—21no—
42C22×C4⋊Dic59C2211yescharacteristic, complemented
43C2×C22⋊C4×D59—21no—
44#16837757C2218yescomplemented
45#16837744C2218yescomplemented
46#16837721C2218yescomplemented
47#16837703C2218yescomplemented
48#16837660C2218yescomplemented
49#16837648C2218yescomplemented
50#16837625C2218yescomplemented
51#16837566C2218yescomplemented
52#16837555C2218yescomplemented
53C4×#11745660C2218yescomplemented
54C2×#14273661C2211yescharacteristic, complemented
55C2×#14273659C2211yescharacteristic, complemented
56C2×#14273659C2211yescharacteristic, complemented
57#16837408C2218yescomplemented
58#16837404C2218yescomplemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273652C2211yescharacteristic, complemented
61C2×#14273652C2211yescharacteristic, complemented
62C2×#14273652C2211yescharacteristic, complemented
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic, complemented
71C2×C4×D4×C59C2211yescharacteristic
72C59×#436C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic, complemented
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic, complemented
76C2×C4×C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—22no—
79C2×#11745685—24no—
80C2×#11745685—42no—
81C2×#11745685C2314yes—
82C22×Dic118C2311yescharacteristic
83C22×Dic118C2311yescharacteristic
84C22×D236—24no—
85C22×D236—21no—
86C22×D236—22no—
87C22×D236—42no—
88C22×D236C2311yescharacteristic
89C22×D236C2314yes—
90C22×D236C2311yescharacteristic
91C22×C22⋊D59—21no—
92C22×C22⋊D59—21no—
93C23×Dic59—21no—
94C22×C4×D59—21no—
95C22×C4×D59—21no—
96C2×Dic236—42no—
97C2×Dic236C2314yescomplemented
98C2×#11745660—24no—
99C2×#11745660—42no—
100C2×#11745660C2314yes—
101C2×#11745660C2314yes—
102#14273720—28no—
103#14273719—22no—
104#14273719C2314yescomplemented
105#14273717—28no—
106#14273715—22no—
107#14273715C2314yes—
108#14273712—28no—
109#14273708—28no—
110#14273706—22no—
111#14273706—22no—
112#14273706—22no—
113#14273706C2314yes—
114#14273706C2314yes—
115#14273706C2314yescomplemented
116#14273701—22no—
117#14273701C2314yes—
118#14273700—28no—
119#14273695—28no—
120C4×Dic118—22no—
121C4×Dic118C2314yescomplemented
122C4×D236—22no—
123C4×D236C2314yes—
124#14273686—22no—
125#14273686C2314yes—
126#14273683—28no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—22no—
129C2×C4⋊Dic59C2311yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2314yescomplemented
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59—21no—
142C2×C22⋊Dic59—21no—
143C2×C22⋊Dic59—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C22⋊C4×D59—28no—
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151#14273661C2314yescomplemented
152#14273659C2314yescomplemented
153#14273659C2314yescomplemented
154#14273652C2314yescomplemented
155#14273652C2314yescomplemented
156#14273652C2314yescomplemented
157#14273652C2314yescomplemented
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×C59—42no—
169C2×M16×C59C2314yes—
170C2×M16×C59C2314yescomplemented
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2311yescharacteristic
175C4×D4×C59D414yes—
176C4×D4×C59C2314yes—
177C2×C4⋊C4×C59D411yescharacteristic
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C22⋊C4×C59D411yescharacteristic
180C2×C42×C59C2311yescharacteristic
181C4⋊C8×C59C2314yescomplemented
182C22⋊C8×C59C2314yes—
183C22⋊C8×C59C2314yescomplemented
184C4×C8×C59C2314yescomplemented
185C24×C59C2×D411yescharacteristic
186C24×C59C2×D411yescharacteristic
187C23×D59—21no—
188C23×D59—21no—
189C23×D59—24no—
190C23×D59—44no—
191C23×D59—44no—
192C23×D59—82no—
193C2×D4×C59—42no—
194C2×D4×C59C2×D414yes—
195C22×C4×C59—22no—
196C22×C4×C59—22no—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D412yes—
204C22×C4×C59C2×D412yes—
205C22×C4×C59C2412yes—
206C22×C4×C59C2412yes—
207C22×C4×C59C2411yescharacteristic
208C2×C22⋊D59—24no—
209C2×C22⋊D59—24no—
210C2×C22⋊D59—44no—
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—44no—
222#11745685—48no—
223C2×D236—21no—
224C2×D236—22no—
225C2×D236—22no—
226C2×D236—22no—
227C2×D236—28no—
228C2×D236—24no—
229C2×D236—21no—
230C2×D236—44no—
231C2×D236—48no—
232C2×D236—44no—
233C2×D236#4114yes—
234C2×D236C2412yes—
235C2×D236C2412yes—
236C2×C4×D59—24no—
237C2×C4×D59—24no—
238C2×C4×D59—44no—
239C2×C4×D59—82no—
240C2×Dic118—22no—
241C2×Dic118—22no—
242C2×Dic118—22no—
243C2×Dic118—22no—
244C2×Dic118—21no—
245C2×Dic118—21no—
246C2×Dic118C2412yes—
247C2×Dic118C2412yes—
248M16×C59—44no—
249M16×C59—44no—
250C2×C8×C59—22no—
251C2×C8×C59—22no—
252C2×C8×C59—22no—
253C2×C8×C59—22no—
254C2×C8×C59C2412yes—
255C2×C8×C59C2412yes—
256C2×C8×C59C2412yes—
257C2×C8×C59C2412yes—
258C4⋊C4×C59C2×D414yes—
259C22⋊C4×C59C2×D414yes—
260C22⋊C4×C59C2×D414yes—
261C42×C59C2×D412yes—
262C42×C59C2412yes—
263C22⋊Dic59—24no—
264C22⋊Dic59—24no—
265C22⋊Dic59—24no—
266C22⋊Dic59—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271C4⋊Dic59—21no—
272C4⋊Dic59—21no—
273C4⋊Dic59—24no—
274C4⋊Dic59—21no—
275C4⋊Dic59—21no—
276C4⋊Dic59C2412yes—
277C4⋊Dic59C2412yes—
278C4⋊Dic59C2412yes—
279C4⋊Dic59C2412yes—
280Dic59⋊C4—24no—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283Dic59⋊C4—24no—
284Dic59⋊C4—24no—
285Dic59⋊C4—24no—
286C4×Dic59—24no—
287C4×Dic59—24no—
288Dic236—44no—
289#11745660—28no—
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—24no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—48no—
304C22×D59—42no—
305C22×D59—42no—
306C22×D59—48no—
307C22×D59—42no—
308C22×D59—42no—
309C22×D59—42no—
310C22×D59—84no—
311C22×D59—816no—
312D4×C59—44no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—24no—
318C2×C4×C59—24no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59C22×D412yes—
324C2×C4×C59C22×D412yes—
325C2×C4×C59C22×D412yes—
326C2×C4×C59C22×D412yes—
327C2×C4×C59C22×D411yescharacteristic
328C2×C4×C59C2×#4112yes—
329C2×C4×C59H(5,𝔽2)12yes—
330C2×C4×C59C2511yescharacteristic
331C22⋊D59—48no—
332C22⋊D59—84no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—48no—
340C2×Dic59—42no—
341C2×Dic59—42no—
342C2×Dic59—42no—
343C2×Dic59—42no—
344C2×Dic59—42no—
345C2×Dic59—42no—
346D236—24no—
347D236—22no—
348D236—22no—
349D236—22no—
350D236—48no—
351D236—42no—
352D236C2×#4114yes—
353C4×D59—48no—
354C4×D59—84no—
355Dic118—22no—
356Dic118—22no—
357Dic118—22no—
358Dic118—22no—
359Dic118—42no—
360Dic118—42no—
361C8×C59—22no—
362C8×C59—22no—
363C8×C59—22no—
364C8×C59—22no—
365C2×#3323—591nomaximal, Sylow
366C22×C59—22no—
367C22×C59—22no—
368C22×C59—22no—
369C22×C59—22no—
370C22×C59—22no—
371C22×C59—22no—
372C22×C59—44no—
373C22×C59—44no—
374C22×C59#54612yes—
375C22×C59#57512yes—
376C22×C59#57712yes—
377C22×C59C23×D411yescharacteristic
378C2×D59—24no—
379C2×D59—48no—
380C2×D59—42no—
381C2×D59—42no—
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—816no—
386C2×D59—84no—
387C4×C59—22no—
388C4×C59—22no—
389C4×C59—22no—
390C4×C59—22no—
391C4×C59#54612yes—
392C4×C59C22×#4111yescharacteristic
393C4×C59C2×H(5,𝔽2)11yescharacteristic
394Dic59—42no—
395Dic59—42no—
396Dic59—42no—
397Dic59—42no—
398Dic59—42no—
399Dic59—42no—
400C2×#552—591no—
401C2×#546—591no—
402#3323—5916no—
403C2×#488—591no—
404C2×#481—591no—
405C2×#485—591no—
406C2×#478—591no—
407C2×#470—591no—
408C2×#468—591no—
409C2×#464—591no—
410C2×#452—591no—
411C2×#450—591no—
412C2×C4×SD16—591no—
413C2×#436D5911yescharacteristic, complemented
414C2×#417—591no—
415C2×#418—591no—
416C2×C59—42no—
417C2×C59—42no—
418C2×C59#332314yescomplemented
419C2×C59C2×#54611yescharacteristic
420C2×C59C2×#57511yescharacteristic
421C2×C59C2×#57711yescharacteristic
422D59—44no—
423D59—82no—
424C22×#41—591no—
425C23×D4—591no—
426C22×Q16—591no—
427C22×SD16—591no—
428C22×SD16—591no—
429C22×M16C2×D5911yescharacteristic
430C22×M16C2×D5911yescharacteristic, complemented
431#552—598no—
432#552—1184no—
433#546—598no—
434#546—1184no—
435C2×#126—1181no—
436C2×#125—591no—
437C2×#125—1181no—
438C2×#124—591no—
439C2×#123—1181no—
440C2×#123—1181no—
441C2×C22⋊Q8—591no—
442C2×C22⋊Q8—591no—
443C2×C22⋊Q8—591no—
444C2×#121—591no—
445C2×#121—1181no—
446C2×#120—1181no—
447C2×C4×Q8—591no—
448C2×C4×D4—591no—
449C2×C4×D4C2×D5911yescharacteristic
450C2×#117—591no—
451C2×#117—1181no—
452C22×C4⋊C4—591no—
453C22×C22⋊C4—1181no—
454#488—598no—
455#485—598no—
456#481—598no—
457#478—598no—
458#470—598no—
459#468—598no—
460#464—598no—
461#452—598no—
462#450—598no—
463C4×SD16—598no—
464#436C2×D5918yescomplemented
465C2×#107—591no—
466C2×#106—591no—
467C2×#106—591no—
468C2×C4⋊C8C2×D5911yescharacteristic, complemented
469#418—598no—
470#417—598no—
471C2×#103—591no—
472C2×#103—591no—
473C2×#103—591no—
474C2×#103—591no—
475C2×#102—591no—
476C2×#102—591no—
477C2×#102—591no—
478C2×#102—591no—
479C2×#102—591no—
480C2×#102—591no—
481C2×C22⋊C8C2×D5911yescharacteristic
482C2×C22⋊C8C2×D5911yescharacteristic, complemented
483C2×C4×C8C2×D5911yescharacteristic, complemented
484C59C2×#332311yescharacteristic, complemented, Sylow
485C25—1181no—
486C2×#41—594no—
487C2×#41—1184no—
488C2×#41—1182no—
489C2×#41—2362no—
490C22×Q8—591no—
491C22×Q8—591no—
492C22×D4—591no—
493C22×D4—591no—
494C22×D4—594no—
495C22×D4—1184no—
496C22×D4—1181no—
497C22×D4—1181no—
498C22×D4—1181no—
499C22×D4—1182no—
500C22×D4—2362no—
501C22×D4D23611yescharacteristic
502C23×C4—1181no—
503C23×C4—1181no—
504C23×C4—1181no—
505C23×C4C22×D5911yescharacteristic
506C23×C4C22×D5911yescharacteristic
507C2×Q16—594no—
508C2×Q16—2362no—
509C2×SD16—594no—
510C2×SD16—594no—
511C2×SD16—1184no—
512C2×SD16—2362no—
513C2×M16—42no—
514C2×M16—42no—
515C2×M16C22×D5914yes—
516C2×M16C22×D5914yescomplemented
517C22×C8C22×D5911yescharacteristic
518C22×C8C22×D5911yescharacteristic
519C22×C8C22×D5911yescharacteristic
520C22×C8C22×D5911yescharacteristic
521#126—1188no—
522#125—594no—
523#125—1188no—
524#125—1182no—
525#124—594no—
526#124—1182no—
527#123—1188no—
528#123—1188no—
529C22⋊Q8—594no—
530C22⋊Q8—594no—
531C22⋊Q8—594no—
532C22⋊Q8—1182no—
533C22⋊Q8—1182no—
534C22⋊Q8—1182no—
535#121—594no—
536#121—1182no—
537#121—1188no—
538#120—1188no—
539C4×Q8—594no—
540C4×Q8—1182no—
541C4×D4—594no—
542C4×D4—1182no—
543C4×D4D23614yes—
544C4×D4C22×D5914yes—
545#117—594no—
546#117—1182no—
547#117—1188no—
548C2×C4⋊C4—591no—
549C2×C4⋊C4—591no—
550C2×C4⋊C4—594no—
551C2×C4⋊C4—591no—
552C2×C4⋊C4—591no—
553C2×C4⋊C4—1181no—
554C2×C4⋊C4—1182no—
555C2×C4⋊C4—1181no—
556C2×C4⋊C4—1181no—
557C2×C4⋊C4—1181no—
558C2×C4⋊C4—1181no—
559C2×C4⋊C4—1181no—
560C2×C4⋊C4—1181no—
561C2×C4⋊C4D23611yescharacteristic
562C2×C22⋊C4—1181no—
563C2×C22⋊C4—1181no—
564C2×C22⋊C4—1181no—
565C2×C22⋊C4—1181no—
566C2×C22⋊C4—1181no—
567C2×C22⋊C4—1181no—
568C2×C22⋊C4—1181no—
569C2×C22⋊C4—1181no—
570C2×C22⋊C4—1188no—
571C2×C22⋊C4D23611yescharacteristic
572C2×C22⋊C4D23611yescharacteristic
573C2×C42—1181no—
574C2×C42—1181no—
575C2×C42C22×D5911yescharacteristic
576#107—594no—
577#106—594no—
578#106—594no—
579C4⋊C8C22×D5914yescomplemented
580#103—594no—
581#103—594no—
582#103—594no—
583#103—594no—
584#102—594no—
585#102—594no—
586#102—594no—
587#102—594no—
588#102—594no—
589#102—594no—
590C22⋊C8C22×D5914yes—
591C22⋊C8C22×D5914yescomplemented
592C4×C8C22×D5914yescomplemented
593C24—1181no—
594C24—1184no—
595C24—1181no—
596C24—4722no—
597C24—2364no—
598C24—2364no—
599C24C2×D23611yescharacteristic
600C24C2×D23611yescharacteristic
601#41—1188no—
602#41—2364no—
603#41—2368no—
604C2×Q8—592no—
605C2×Q8—592no—
606C2×Q8—1181no—
607C2×Q8—1181no—
608C2×Q8—1182no—
609C2×Q8—1182no—
610C2×Q8—1182no—
611C2×Q8—1182no—
612C2×D4—42no—
613C2×D4—594no—
614C2×D4—592no—
615C2×D4—592no—
616C2×D4—1188no—
617C2×D4—1184no—
618C2×D4—1184no—
619C2×D4—1181no—
620C2×D4—1184no—
621C2×D4—1181no—
622C2×D4—1182no—
623C2×D4—1182no—
624C2×D4—1182no—
625C2×D4—4722no—
626C2×D4—2364no—
627C2×D4—2368no—
628C2×D4—2364no—
629C2×D4—2364no—
630C2×D4C2×D23614yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—1184no—
636C22×C4—1181no—
637C22×C4—1181no—
638C22×C4—1181no—
639C22×C4—1181no—
640C22×C4—1181no—
641C22×C4—1181no—
642C22×C4—1184no—
643C22×C4—1184no—
644C22×C4—4722no—
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—2364no—
657SD16—1188no—
658SD16—2364no—
659M16—44no—
660M16—44no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
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⋊C4—1184no—
691C22⋊C4—1184no—
692C22⋊C4—1184no—
693C22⋊C4C2×D23614yes—
694C22⋊C4C2×D23614yes—
695C42—1184no—
696C42—1184no—
697C42C2×D23612yes—
698C42C23×D5912yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—1182no—
706C23—1184no—
707C23—1182no—
708C23—4724no—
709C23—47216no—
710C23—2368no—
711C23—2368no—
712C23—2362no—
713C23—2362no—
714C23—2362no—
715C23—2362no—
716C23—2362no—
717C23C22×D23612yes—
718C23C22×D23612yes—
719C23C22×D23611yescharacteristic
720Q8—1182no—
721Q8—1182no—
722Q8—1182no—
723Q8—1182no—
724Q8—2362no—
725Q8—2362no—
726D4—44no—
727D4—594no—
728D4—1182no—
729D4—1182no—
730D4—1182no—
731D4—1184no—
732D4—4724no—
733D4—2368no—
734D4—2368no—
735D4—2362no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—1182no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—1182no—
750C2×C4—1182no—
751C2×C4—1182no—
752C2×C4—4724no—
753C2×C4—2368no—
754C2×C4—2368no—
755C2×C4—2362no—
756C2×C4—2362no—
757C2×C4—2362no—
758C2×C4—2362no—
759C2×C4—2362no—
760C2×C4—2362no—
761C2×C4C22×D23612yes—
762C2×C4C22×D23612yes—
763C2×C4C22×D23612yes—
764C2×C4C22×D23612yes—
765C2×C4C22×D23611yescharacteristic
766C2×C4#41×D5912yes—
767C2×C4#1427377212yes—
768C2×C4C24×D5911yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—1184no—
782C22—47216no—
783C22—4724no—
784C22—2362no—
785C22—2362no—
786C22—2362no—
787C22—2362no—
788C22—2362no—
789C22—2368no—
790C22#1683804712yes—
791C22#1683820212yes—
792C22#1683821412yes—
793C22C23×D23611yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—2362no—
799C4—2362no—
800C4—2362no—
801C4—2362no—
802C4—2362no—
803C4—2362no—
804C4#1683804712yes—
805C4C2×#41×D5911yescharacteristic
806C4C2×#1427377211yescharacteristic
807C2—42no—
808C2—42no—
809C2—4722no—
810C2—2364no—
811C2#2143631414yesdirect product factor
812C2C2×#1683804711yescharacteristic
813C2C2×#1683820211yescharacteristic
814C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#436C2
socleC23×C59C22×D4
prime radicalC2×#16838048C2
hypercenterC2×#436D59
hypocenterC59C2×#3323
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#16838092C2semidirect
3. #21436314C2direct (N × H)
4. C2×#16837757C2semidirect
5. C2×#16837721C2semidirect
6. C2×#16837744C2semidirect
7. C2×#16837703C2semidirect
8. C2×#16837660C2semidirect
9. C2×#16837648C2semidirect
10. C2×#16837625C2semidirect
11. C2×#16837566C2semidirect
12. C2×#16837555C2semidirect
13. C2×C4×#11745660C2semidirect
14. C2×#16837404C2semidirect
15. C2×#16837408C2semidirect
16. C2×C59×#436C2semidirect
19. C22×Dic236C22semidirect
23. #16838092C22semidirect
27. C2×#14273719C22semidirect
34. C2×#14273706C22semidirect
38. C2×C4×Dic118C22semidirect
42. C22×C4⋊Dic59C22semidirect
44. #16837757C22semidirect
45. #16837744C22semidirect
46. #16837721C22semidirect
47. #16837703C22semidirect
48. #16837660C22semidirect
49. #16837648C22semidirect
50. #16837625C22semidirect
51. #16837566C22semidirect
52. #16837555C22semidirect
53. C4×#11745660C22semidirect
54. C2×#14273661C22semidirect
55. C2×#14273659C22semidirect
56. C2×#14273659C22semidirect
57. #16837408C22semidirect
58. #16837404C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273652C22semidirect
61. C2×#14273652C22semidirect
62. C2×#14273652C22semidirect
70. C22×M16×C59C22semidirect
72. C59×#436C22semidirect
73. C2×C4⋊C8×C59C22semidirect
75. C2×C22⋊C8×C59C22semidirect
76. C2×C4×C8×C59C22semidirect
97. C2×Dic236C23semidirect
104. #14273719C23semidirect
115. #14273706C23semidirect
121. C4×Dic118C23semidirect
133. C2×C4⋊Dic59C23semidirect
151. #14273661C23semidirect
152. #14273659C23semidirect
153. #14273659C23semidirect
154. #14273652C23semidirect
155. #14273652C23semidirect
156. #14273652C23semidirect
157. #14273652C23semidirect
170. C2×M16×C59C23semidirect
181. C4⋊C8×C59C23semidirect
183. C22⋊C8×C59C23semidirect
184. C4×C8×C59C23semidirect
413. C2×#436D59semidirect
418. C2×C59#3323semidirect
430. C22×M16C2×D59semidirect
464. #436C2×D59semidirect
468. C2×C4⋊C8C2×D59semidirect
482. C2×C22⋊C8C2×D59semidirect
483. C2×C4×C8C2×D59semidirect
484. C59C2×#3323semidirect
516. C2×M16C22×D59semidirect
579. C4⋊C8C22×D59semidirect
591. C22⋊C8C22×D59semidirect
592. C4×C8C22×D59semidirect
811. C2#21436314direct (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×#168380482
#214363142
C2×#168377572
C2×#168377212
C2×#168377442
C2×#168377032
C2×#168376602
C2×#168376482
C2×#168376252
C2×#168375662
C2×#168375552
C2×C4×#117456602
C2×#168374042
C2×#168374082
C2×C59×#4362
C2×#332359