Finite Group Databasebeta

← C2×#21436179 #29465217

Subgroups — C2×#21436179 #29465217

Order 15104.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838109C211yesmaximal, characteristic, complemented
2C2×#16838048C211yesmaximal, characteristic
3#21436179C2116yesmaximal, direct product factor
4C2×#16837762C211yesmaximal, characteristic, complemented
5C2×#16837738C211yesmaximal, characteristic, complemented
6C2×#16837716C211yesmaximal, characteristic, complemented
7C2×#16837683C211yesmaximal, characteristic, complemented
8C2×#16837648C211yesmaximal, characteristic, complemented
9C2×#16837643C211yesmaximal, characteristic, complemented
10C2×#16837625C211yesmaximal, characteristic, complemented
11C2×#16837566C211yesmaximal, characteristic, complemented
12C2×#16837555C211yesmaximal, characteristic, complemented
13C2×#16837504C211yesmaximal, characteristic, complemented
14C2×#16837404C211yesmaximal, characteristic, complemented
15C22×#14273649C211yesmaximal, characteristic, complemented
16C2×C59×#435C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×D236C2211yescharacteristic
19C22×Dic236C2211yescharacteristic, complemented
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22#16838109—24no—
23#16838109C2218yescomplemented
24#16838048—24no—
25#16838048C2218yes—
26C2×#14273727C2211yescharacteristic, complemented
27C2×#14273718—21no—
28C2×#14273715C2211yescharacteristic
29C2×#14273712—21no—
30C2×#14273706C2211yescharacteristic
31C2×#14273706C2211yescharacteristic
32C2×#14273706C2211yescharacteristic, complemented
33C2×#14273704—21no—
34C2×#14273704—21no—
35C2×#14273701C2211yescharacteristic
36C2×#14273700—21no—
37C2×#14273695—21no—
38C2×C4×Dic118C2211yescharacteristic, complemented
39C2×C4×D236C2211yescharacteristic
40C2×D4×Dic59—21no—
41C22×C4⋊Dic59C2211yescharacteristic
42C22×C4⋊Dic59C2211yescharacteristic, complemented
43C2×C22⋊C4×D59—21no—
44#16837762C2218yescomplemented
45#16837738C2218yescomplemented
46#16837716C2218yescomplemented
47#16837683C2218yescomplemented
48#16837648C2218yescomplemented
49#16837643C2218yescomplemented
50#16837625C2218yescomplemented
51#16837566C2218yescomplemented
52#16837555C2218yescomplemented
53#16837504C2218yescomplemented
54C2×#14273661C2211yescharacteristic, complemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273661C2211yescharacteristic, complemented
57#16837404C2218yescomplemented
58C2×#14273652C2211yescharacteristic, complemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273652C2211yescharacteristic, complemented
61C2×#14273652C2211yescharacteristic, complemented
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2218yescomplemented
69C22×M16×C59C2211yescharacteristic, complemented
70C23×C8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#435C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic, complemented
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic, complemented
76C2×#97×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—22no—
79C2×#11745685—24no—
80C2×#11745685—42no—
81C2×#11745685C2314yes—
82C22×Dic118—21no—
83C22×Dic118C2311yescharacteristic
84C22×Dic118C2311yescharacteristic
85C22×D236—24no—
86C22×D236—21no—
87C22×D236—22no—
88C22×D236—42no—
89C22×D236C2311yescharacteristic
90C22×D236C2314yes—
91C22×D236C2311yescharacteristic
92C22×C22⋊D59—21no—
93C22×C22⋊D59—21no—
94C23×Dic59—21no—
95C23×Dic59—21no—
96C22×C4×D59—21no—
97C22×C4×D59—21no—
98C2×Dic236—42no—
99C2×Dic236C2314yescomplemented
100C2×#11745660—24no—
101C2×#11745660—42no—
102C2×#11745660C2314yes—
103C2×#11745660C2314yes—
104#14273727—22no—
105#14273727C2314yescomplemented
106#14273718—28no—
107#14273715—22no—
108#14273715C2314yes—
109#14273712—28no—
110#14273706—22no—
111#14273706—22no—
112#14273706—22no—
113#14273706C2314yes—
114#14273706C2314yes—
115#14273706C2314yescomplemented
116#14273704—28no—
117#14273704—28no—
118#14273701—22no—
119#14273701C2314yes—
120#14273700—28no—
121#14273695—28no—
122C4×Dic118—22no—
123C4×Dic118C2314yescomplemented
124C4×D236—22no—
125C4×D236C2314yes—
126D4×Dic59—28no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59—22no—
131C2×C4⋊Dic59—22no—
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×C4⋊Dic59C2311yescharacteristic
135C2×C4⋊Dic59C2311yescharacteristic
136C2×C4⋊Dic59C2314yes—
137C2×C4⋊Dic59C2314yescomplemented
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C2×C22⋊Dic59—21no—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C22⋊C4×D59—28no—
150C2×C4×Dic59—21no—
151#14273661C2314yescomplemented
152#14273661C2314yescomplemented
153#14273661C2314yescomplemented
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×C59C2314yescomplemented
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×C59C2314yescomplemented
182C22⋊C8×C59C2314yes—
183C22⋊C8×C59C2314yescomplemented
184#97×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—24no—
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—24no—
220C22×Dic59—82no—
221C22×Dic59—82no—
222#11745685—28no—
223#11745685—44no—
224#11745685—48no—
225C2×D236—21no—
226C2×D236—22no—
227C2×D236—22no—
228C2×D236—22no—
229C2×D236—28no—
230C2×D236—24no—
231C2×D236—21no—
232C2×D236—44no—
233C2×D236—48no—
234C2×D236—44no—
235C2×D236#4114yes—
236C2×D236C2412yes—
237C2×D236C2412yes—
238C2×C4×D59—24no—
239C2×C4×D59—24no—
240C2×C4×D59—44no—
241C2×C4×D59—82no—
242C2×Dic118—22no—
243C2×Dic118—22no—
244C2×Dic118—22no—
245C2×Dic118—22no—
246C2×Dic118—21no—
247C2×Dic118—21no—
248C2×Dic118—24no—
249C2×Dic118—82no—
250C2×Dic118C2412yes—
251C2×Dic118C2412yes—
252M16×C59—44no—
253C2×C8×C59—22no—
254C2×C8×C59—22no—
255C2×C8×C59—22no—
256C2×C8×C59—22no—
257C2×C8×C59—44no—
258C2×C8×C59C2412yes—
259C2×C8×C59C2412yes—
260C2×C8×C59C2412yes—
261C2×C8×C59C2412yes—
262C4⋊C4×C59C2×D414yes—
263C22⋊C4×C59C2×D414yes—
264C22⋊C4×C59C2×D414yes—
265C42×C59C2×D412yes—
266C42×C59C2412yes—
267C22⋊Dic59—24no—
268C22⋊Dic59—24no—
269C22⋊Dic59—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4—24no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4—24no—
274C4⋊Dic59—21no—
275C4⋊Dic59—24no—
276C4⋊Dic59—21no—
277C4⋊Dic59—21no—
278C4⋊Dic59—24no—
279C4⋊Dic59—24no—
280C4⋊Dic59—21no—
281C4⋊Dic59C2412yes—
282C4⋊Dic59C2412yes—
283C4⋊Dic59C2412yes—
284C4⋊Dic59C2412yes—
285Dic59⋊C4—24no—
286Dic59⋊C4—24no—
287Dic59⋊C4—24no—
288Dic59⋊C4—24no—
289C4×Dic59—24no—
290Dic236—44no—
291#11745660—28no—
292#11745660—44no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59#13714yes—
299C23×C59C22×D412yes—
300C23×C59C22×D412yes—
301C23×C59C22×D411yescharacteristic
302C22×D59—24no—
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—48no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—42no—
309C22×D59—48no—
310C22×D59—42no—
311C22×D59—42no—
312C22×D59—84no—
313C22×D59—816no—
314D4×C59—28no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—24no—
320C2×C4×C59—24no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59C22×D412yes—
326C2×C4×C59C22×D412yes—
327C2×C4×C59C22×D412yes—
328C2×C4×C59C22×D412yes—
329C2×C4×C59C22×D411yescharacteristic
330C2×C4×C59C2×#4112yes—
331C2×C4×C59H(5,𝔽2)12yes—
332C2×C4×C59C2511yescharacteristic
333C22⋊D59—48no—
334C22⋊D59—84no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—42no—
342C2×Dic59—42no—
343C2×Dic59—42no—
344C2×Dic59—42no—
345C2×Dic59—42no—
346C2×Dic59—42no—
347C2×Dic59—84no—
348C2×Dic59—84no—
349D236—24no—
350D236—22no—
351D236—22no—
352D236—22no—
353D236—48no—
354D236—42no—
355D236C2×#4114yes—
356C4×D59—48no—
357C4×D59—84no—
358Dic118—22no—
359Dic118—22no—
360Dic118—22no—
361Dic118—22no—
362Dic118—42no—
363Dic118—42no—
364Dic118—84no—
365C8×C59—22no—
366C8×C59—22no—
367C8×C59—22no—
368C8×C59—22no—
369C2×#3314—591nomaximal, Sylow
370C22×C59—22no—
371C22×C59—28no—
372C22×C59—22no—
373C22×C59—22no—
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—44no—
377C22×C59#54612yes—
378C22×C59C2×#13714yes—
379C22×C59C2×#13712yes—
380C22×C59#57612yes—
381C22×C59C23×D411yescharacteristic
382C2×D59—24no—
383C2×D59—48no—
384C2×D59—42no—
385C2×D59—42no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—42no—
389C2×D59—816no—
390C2×D59—84no—
391C4×C59—22no—
392C4×C59—22no—
393C4×C59—22no—
394C4×C59—22no—
395C4×C59#54612yes—
396C4×C59C22×#4111yescharacteristic
397C4×C59C2×H(5,𝔽2)11yescharacteristic
398Dic59—42no—
399Dic59—42no—
400Dic59—42no—
401Dic59—42no—
402Dic59—42no—
403Dic59—42no—
404C2×#554—591no—
405C2×#546—591no—
406#3314—5916no—
407C2×#489—591no—
408C2×#484—591no—
409C2×#480—591no—
410C2×#474—591no—
411C2×#468—591no—
412C2×#467—591no—
413C2×#464—591no—
414C2×#452—591no—
415C2×#450—591no—
416C2×#440—591no—
417C2×#435D5911yescharacteristic, complemented
418C2×#417—591no—
419C22×#102—591no—
420C2×C59—24no—
421C2×C59—42no—
422C2×C59#331414yescomplemented
423C2×C59C2×#54611yescharacteristic
424C2×C59C22×#13711yescharacteristic
425C2×C59C2×#57611yescharacteristic
426D59—44no—
427D59—82no—
428C22×#41—591no—
429C23×D4—591no—
430C22×Q16—591no—
431C22×SD16—591no—
432C22×SD16—591no—
433C22×M16C2×D5911yescharacteristic, complemented
434C23×C8C2×D5911yescharacteristic
435#554—598no—
436#554—1184no—
437#546—598no—
438#546—1184no—
439C2×C4⋊Q8—591no—
440C2×#125—1181no—
441C2×#124—591no—
442C2×#123—1181no—
443C2×C22⋊Q8—591no—
444C2×C22⋊Q8—591no—
445C2×C22⋊Q8—591no—
446C2×C22⋊Q8—1181no—
447C2×C22⋊Q8—1181no—
448C2×#121—591no—
449C2×#121—1181no—
450C2×#120—1181no—
451C2×C4×Q8—591no—
452C2×C4×D4—591no—
453C2×C4×D4—1181no—
454C2×C4×D4C2×D5911yescharacteristic
455C22×C4⋊C4—591no—
456C22×C4⋊C4—591no—
457C22×C22⋊C4—1181no—
458#489—598no—
459#484—598no—
460#480—598no—
461#474—598no—
462#468—598no—
463#467—598no—
464#464—598no—
465#452—598no—
466#450—598no—
467#440—598no—
468#435C2×D5918yescomplemented
469C2×#107—591no—
470C2×#107—591no—
471C2×#107—591no—
472C2×C4⋊C8C2×D5911yescharacteristic, complemented
473#417—598no—
474C2×#103—591no—
475C2×#103—591no—
476C2×#103—591no—
477C2×#103—591no—
478C2×#102—591no—
479C2×#102—591no—
480C2×#102—591no—
481C2×#102—591no—
482C2×#102—591no—
483C2×#102—591no—
484C2×#102—598no—
485C2×C22⋊C8C2×D5911yescharacteristic
486C2×C22⋊C8C2×D5911yescharacteristic, complemented
487C2×#97C2×D5911yescharacteristic, complemented
488C59C2×#331411yescharacteristic, complemented, Sylow
489C25—1181no—
490C2×#41—594no—
491C2×#41—1184no—
492C2×#41—1182no—
493C2×#41—2362no—
494C22×Q8—591no—
495C22×Q8—591no—
496C22×Q8—1181no—
497C22×D4—591no—
498C22×D4—591no—
499C22×D4—594no—
500C22×D4—1184no—
501C22×D4—1181no—
502C22×D4—1181no—
503C22×D4—1181no—
504C22×D4—1182no—
505C22×D4—2362no—
506C22×D4D23611yescharacteristic
507C23×C4—1181no—
508C23×C4—1181no—
509C23×C4—1181no—
510C23×C4—1181no—
511C23×C4C22×D5911yescharacteristic
512C23×C4C22×D5911yescharacteristic
513C2×Q16—594no—
514C2×Q16—2362no—
515C2×SD16—594no—
516C2×SD16—594no—
517C2×SD16—1184no—
518C2×SD16—2362no—
519C2×M16—42no—
520C2×M16C22×D5914yescomplemented
521C22×C8—42no—
522C22×C8C22×D5911yescharacteristic
523C22×C8C22×D5911yescharacteristic
524C22×C8C22×D5911yescharacteristic
525C22×C8C22×D5911yescharacteristic
526C22×C8C22×D5914yes—
527C4⋊Q8—594no—
528C4⋊Q8—1182no—
529#125—1188no—
530#124—594no—
531#124—1182no—
532#123—1188no—
533C22⋊Q8—594no—
534C22⋊Q8—594no—
535C22⋊Q8—594no—
536C22⋊Q8—1182no—
537C22⋊Q8—1182no—
538C22⋊Q8—1182no—
539C22⋊Q8—1188no—
540C22⋊Q8—1188no—
541#121—594no—
542#121—1182no—
543#121—1188no—
544#120—1188no—
545C4×Q8—594no—
546C4×Q8—1182no—
547C4×D4—594no—
548C4×D4—1188no—
549C4×D4—1182no—
550C4×D4D23614yes—
551C4×D4C22×D5914yes—
552C2×C4⋊C4—591no—
553C2×C4⋊C4—591no—
554C2×C4⋊C4—591no—
555C2×C4⋊C4—594no—
556C2×C4⋊C4—594no—
557C2×C4⋊C4—591no—
558C2×C4⋊C4—1181no—
559C2×C4⋊C4—1181no—
560C2×C4⋊C4—1182no—
561C2×C4⋊C4—1182no—
562C2×C4⋊C4—1181no—
563C2×C4⋊C4—1181no—
564C2×C4⋊C4—1181no—
565C2×C4⋊C4—1181no—
566C2×C4⋊C4—1181no—
567C2×C4⋊C4D23611yescharacteristic
568C2×C22⋊C4—1181no—
569C2×C22⋊C4—1181no—
570C2×C22⋊C4—1181no—
571C2×C22⋊C4—1181no—
572C2×C22⋊C4—1181no—
573C2×C22⋊C4—1181no—
574C2×C22⋊C4—1181no—
575C2×C22⋊C4—1188no—
576C2×C22⋊C4D23611yescharacteristic
577C2×C22⋊C4D23611yescharacteristic
578C2×C42—1181no—
579C2×C42C22×D5911yescharacteristic
580#107—594no—
581#107—594no—
582#107—594no—
583C4⋊C8C22×D5914yescomplemented
584#103—594no—
585#103—594no—
586#103—594no—
587#103—594no—
588#102—594no—
589#102—594no—
590#102—594no—
591#102—594no—
592#102—594no—
593#102—594no—
594C22⋊C8C22×D5914yes—
595C22⋊C8C22×D5914yescomplemented
596#97C22×D5914yescomplemented
597C24—1181no—
598C24—1184no—
599C24—1181no—
600C24—4722no—
601C24—2364no—
602C24—2364no—
603C24C2×D23611yescharacteristic
604C24C2×D23611yescharacteristic
605#41—1188no—
606#41—2364no—
607#41—2368no—
608C2×Q8—592no—
609C2×Q8—592no—
610C2×Q8—1184no—
611C2×Q8—1181no—
612C2×Q8—1181no—
613C2×Q8—1182no—
614C2×Q8—1182no—
615C2×Q8—1182no—
616C2×Q8—1182no—
617C2×Q8—4722no—
618C2×D4—24no—
619C2×D4—594no—
620C2×D4—592no—
621C2×D4—592no—
622C2×D4—1188no—
623C2×D4—1184no—
624C2×D4—1184no—
625C2×D4—1181no—
626C2×D4—1184no—
627C2×D4—1181no—
628C2×D4—1182no—
629C2×D4—1182no—
630C2×D4—1182no—
631C2×D4—4722no—
632C2×D4—2364no—
633C2×D4—2368no—
634C2×D4—2364no—
635C2×D4—2364no—
636C2×D4C2×D23614yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—1184no—
642C22×C4—1184no—
643C22×C4—1181no—
644C22×C4—1181no—
645C22×C4—1181no—
646C22×C4—1181no—
647C22×C4—1181no—
648C22×C4—1181no—
649C22×C4—1184no—
650C22×C4—1184no—
651C22×C4—4722no—
652C22×C4—4722no—
653C22×C4—4722no—
654C22×C4—2364no—
655C22×C4C2×D23612yes—
656C22×C4C2×D23612yes—
657C22×C4C2×D23611yescharacteristic
658C22×C4C2×D23611yescharacteristic
659C22×C4C2×D23611yescharacteristic
660C22×C4C2×D23611yescharacteristic
661C22×C4C23×D5912yes—
662C22×C4C23×D5912yes—
663C22×C4C23×D5911yescharacteristic
664Q16—2364no—
665SD16—1188no—
666SD16—2364no—
667M16—44no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—44no—
673C2×C8C23×D5912yes—
674C2×C8C23×D5912yes—
675C2×C8C23×D5912yes—
676C2×C8C23×D5912yes—
677C4⋊C4—592no—
678C4⋊C4—592no—
679C4⋊C4—592no—
680C4⋊C4—592no—
681C4⋊C4—1181no—
682C4⋊C4—1184no—
683C4⋊C4—1184no—
684C4⋊C4—1181no—
685C4⋊C4—1181no—
686C4⋊C4—1181no—
687C4⋊C4—1184no—
688C4⋊C4—1184no—
689C4⋊C4—1184no—
690C4⋊C4—1184no—
691C4⋊C4—1184no—
692C4⋊C4C2×D23614yes—
693C22⋊C4—1184no—
694C22⋊C4—1184no—
695C22⋊C4—1184no—
696C22⋊C4—1184no—
697C22⋊C4—1184no—
698C22⋊C4—1184no—
699C22⋊C4—1184no—
700C22⋊C4C2×D23614yes—
701C22⋊C4C2×D23614yes—
702C42—1184no—
703C42C2×D23612yes—
704C42C23×D5912yes—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—1182no—
711C23—1184no—
712C23—1182no—
713C23—47216no—
714C23—4724no—
715C23—2368no—
716C23—2368no—
717C23—2362no—
718C23—2362no—
719C23—2362no—
720C23—2362no—
721C23—2362no—
722C23#1427376014yes—
723C23C22×D23612yes—
724C23C22×D23612yes—
725C23C22×D23611yescharacteristic
726Q8—1182no—
727Q8—1182no—
728Q8—1182no—
729Q8—1182no—
730Q8—4724no—
731Q8—2362no—
732Q8—2362no—
733D4—28no—
734D4—594no—
735D4—1182no—
736D4—1182no—
737D4—1182no—
738D4—1184no—
739D4—4724no—
740D4—2368no—
741D4—2368no—
742D4—2362no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—1182no—
754C2×C4—1182no—
755C2×C4—1182no—
756C2×C4—1182no—
757C2×C4—1182no—
758C2×C4—1182no—
759C2×C4—4724no—
760C2×C4—4724no—
761C2×C4—4724no—
762C2×C4—2368no—
763C2×C4—2362no—
764C2×C4—2362no—
765C2×C4—2362no—
766C2×C4—2362no—
767C2×C4—2362no—
768C2×C4—2362no—
769C2×C4C22×D23612yes—
770C2×C4C22×D23612yes—
771C2×C4C22×D23612yes—
772C2×C4C22×D23612yes—
773C2×C4C22×D23611yescharacteristic
774C2×C4#41×D5912yes—
775C2×C4#1427377212yes—
776C2×C4C24×D5911yescharacteristic
777C8—22no—
778C8—22no—
779C8—22no—
780C8—22no—
781C22—28no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—44no—
788C22—1184no—
789C22—47216no—
790C22—4724no—
791C22—2362no—
792C22—2362no—
793C22—2362no—
794C22—2368no—
795C22—2362no—
796C22—2362no—
797C22#1683804712yes—
798C22C2×#1427376014yes—
799C22C2×#1427376012yes—
800C22#1683820712yes—
801C22C23×D23611yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—2362no—
807C4—2362no—
808C4—2362no—
809C4—2362no—
810C4—2362no—
811C4—2362no—
812C4#1683804712yes—
813C4C2×#41×D5911yescharacteristic
814C4C2×#1427377211yescharacteristic
815C2—24no—
816C2—42no—
817C2—4722no—
818C2—2364no—
819C2#2143617914yesdirect product factor
820C2C2×#1683804711yescharacteristic
821C2C22×#1427376011yescharacteristic
822C2C2×#1683820711yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C22×D4
prime radicalC2×#16838048C2
hypercenterC2×#435D59
hypocenterC59C2×#3314
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×#16838109C2semidirect
3. #21436179C2direct (N × H)
4. C2×#16837762C2semidirect
5. C2×#16837738C2semidirect
6. C2×#16837716C2semidirect
7. C2×#16837683C2semidirect
8. C2×#16837648C2semidirect
9. C2×#16837643C2semidirect
10. C2×#16837625C2semidirect
11. C2×#16837566C2semidirect
12. C2×#16837555C2semidirect
13. C2×#16837504C2semidirect
14. C2×#16837404C2semidirect
15. C22×#14273649C2semidirect
16. C2×C59×#435C2semidirect
19. C22×Dic236C22semidirect
23. #16838109C22semidirect
26. C2×#14273727C22semidirect
32. C2×#14273706C22semidirect
38. C2×C4×Dic118C22semidirect
42. C22×C4⋊Dic59C22semidirect
44. #16837762C22semidirect
45. #16837738C22semidirect
46. #16837716C22semidirect
47. #16837683C22semidirect
48. #16837648C22semidirect
49. #16837643C22semidirect
50. #16837625C22semidirect
51. #16837566C22semidirect
52. #16837555C22semidirect
53. #16837504C22semidirect
54. C2×#14273661C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273661C22semidirect
57. #16837404C22semidirect
58. C2×#14273652C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273652C22semidirect
61. C2×#14273652C22semidirect
68. C2×#14273649C22semidirect
69. C22×M16×C59C22semidirect
72. C59×#435C22semidirect
73. C2×C4⋊C8×C59C22semidirect
75. C2×C22⋊C8×C59C22semidirect
76. C2×#97×C59C22semidirect
99. C2×Dic236C23semidirect
105. #14273727C23semidirect
115. #14273706C23semidirect
123. C4×Dic118C23semidirect
137. C2×C4⋊Dic59C23semidirect
151. #14273661C23semidirect
152. #14273661C23semidirect
153. #14273661C23semidirect
154. #14273652C23semidirect
155. #14273652C23semidirect
156. #14273652C23semidirect
157. #14273652C23semidirect
168. C2×M16×C59C23semidirect
181. C4⋊C8×C59C23semidirect
183. C22⋊C8×C59C23semidirect
184. #97×C59C23semidirect
417. C2×#435D59semidirect
422. C2×C59#3314semidirect
433. C22×M16C2×D59semidirect
468. #435C2×D59semidirect
472. C2×C4⋊C8C2×D59semidirect
486. C2×C22⋊C8C2×D59semidirect
487. C2×#97C2×D59semidirect
488. C59C2×#3314semidirect
520. C2×M16C22×D59semidirect
583. C4⋊C8C22×D59semidirect
595. C22⋊C8C22×D59semidirect
596. #97C22×D59semidirect
819. C2#21436179direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381092
C2×#168380482
#214361792
C2×#168377622
C2×#168377382
C2×#168377162
C2×#168376832
C2×#168376482
C2×#168376432
C2×#168376252
C2×#168375662
C2×#168375552
C2×#168375042
C2×#168374042
C22×#142736492
C2×C59×#4352
C2×#331459