Finite Group Databasebeta

← C2×#21436182 #29465220

Subgroups — C2×#21436182 #29465220

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×#16838112C211yesmaximal, characteristic, complemented
2C2×#16838047C211yesmaximal, characteristic
3#21436182C2116yesmaximal, direct product factor
4C2×#16837762C211yesmaximal, characteristic, complemented
5C2×#16837739C211yesmaximal, characteristic, complemented
6C2×#16837717C211yesmaximal, characteristic, complemented
7C2×#16837682C211yesmaximal, characteristic, complemented
8C2×#16837651C211yesmaximal, characteristic, complemented
9C2×#16837642C211yesmaximal, characteristic, complemented
10C2×#16837624C211yesmaximal, characteristic, complemented
11C2×#16837561C211yesmaximal, characteristic, complemented
12C2×#16837551C211yesmaximal, characteristic, complemented
13C2×#16837475C211yesmaximal, characteristic, complemented
14C2×#16837400C211yesmaximal, characteristic, complemented
15C2×#102×D59C211yesmaximal, characteristic, complemented
16C2×C59×#440C211yesmaximal, characteristic, complemented
17C22×#11745687C2211yescharacteristic
18C22×D4×D59C2211yescharacteristic
19C22×#11745672C2211yescharacteristic, complemented
20C22×#11745671C2211yescharacteristic
21C22×#11745659C2211yescharacteristic, complemented
22C22×C8×D59C2211yescharacteristic
23#16838112—24no—
24#16838112C2218yescomplemented
25#16838047—24no—
26#16838047C2218yes—
27C2×#14273727C2211yescharacteristic, complemented
28C2×#14273719—21no—
29C2×#14273715C2211yescharacteristic
30C2×#14273711—21no—
31C2×#14273707C2211yescharacteristic
32C2×#14273705—21no—
33C2×#14273705—21no—
34C2×#14273703C2211yescharacteristic
35C2×#14273703C2211yescharacteristic, complemented
36C2×#14273702C2211yescharacteristic
37C2×#14273701—21no—
38C2×#14273697—21no—
39C2×C4×D236—21no—
40C2×C4×D236C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic, complemented
43C22×(C2×D59)⋊C4—21no—
44#16837762C2218yescomplemented
45#16837739C2218yescomplemented
46#16837717C2218yescomplemented
47#16837682C2218yescomplemented
48#16837651C2218yescomplemented
49#16837642C2218yescomplemented
50#16837624C2218yescomplemented
51#16837561C2218yescomplemented
52#16837551C2218yescomplemented
53#16837475C2218yescomplemented
54C2×#14273660C2211yescharacteristic, complemented
55C2×#14273660C2211yescharacteristic, complemented
56C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
57#16837400C2218yescomplemented
58C2×#14273652C2211yescharacteristic, complemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273650C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66#102×D59C2218yescomplemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic, complemented
71C2×C4×D4×C59C2211yescharacteristic
72C59×#440C2218yescomplemented
73C2×#107×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745687—24no—
79C2×#11745687—22no—
80C2×#11745687—42no—
81C2×#11745687C2314yes—
82C22×Dic118—21no—
83C22×Dic118C2311yescharacteristic
84C22×D236—21no—
85C22×D236D411yescharacteristic
86C22×D236C2311yescharacteristic
87C22×C22⋊D59—21no—
88C22×C22⋊D59—21no—
89C2×D4×D59—24no—
90C2×D4×D59—22no—
91C2×D4×D59—42no—
92C2×D4×D59C2314yes—
93C23×Dic59—21no—
94C22×C4×D59—21no—
95C22×C4×D59—21no—
96C22×C4×D59C2311yescharacteristic
97C22×C4×D59C2311yescharacteristic
98C2×#11745672—42no—
99C2×#11745672C2314yescomplemented
100C2×#11745671—42no—
101C2×#11745671C2314yes—
102C2×#11745659—42no—
103C2×#11745659C2314yescomplemented
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106C2×C8×D59—42no—
107C2×C8×D59C2314yes—
108#14273727—22no—
109#14273727C2314yescomplemented
110#14273719—28no—
111#14273715—22no—
112#14273715C2314yes—
113#14273711—28no—
114#14273707—22no—
115#14273707C2314yes—
116#14273705—28no—
117#14273705—28no—
118#14273703—22no—
119#14273703—22no—
120#14273703C2314yes—
121#14273703C2314yescomplemented
122#14273702—22no—
123#14273702C2314yes—
124#14273701—28no—
125#14273697—28no—
126C4×D236—28no—
127C4×D236D414yes—
128C4×D236C2314yes—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59D411yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C4⋊C4×D59—22no—
139C4⋊C4×D59—22no—
140C4⋊C4×D59C2314yes—
141C4⋊C4×D59C2314yescomplemented
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—28no—
149C2×(C2×D59)⋊C4D411yescharacteristic
150C2×(C2×D59)⋊C4D411yescharacteristic
151#14273660C2314yescomplemented
152#14273660C2314yescomplemented
153C4⋊(C59⋊C8)C2314yescomplemented
154#14273652C2314yescomplemented
155#14273652C2314yescomplemented
156#14273650C2314yescomplemented
157#14273649C2314yes—
158#14273649C2314yes—
159#14273648C2314yes—
160#14273648C2314yes—
161#14273647C2314yes—
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yescomplemented
164C22×Q8×C59C2311yescharacteristic
165C22×D4×C59C2311yescharacteristic
166C23×C4×C59—21no—
167C2×SD16×C59—24no—
168C2×SD16×C59C2314yes—
169C22×C8×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171C4×Q8×C59—22no—
172C4×Q8×C59C2314yescomplemented
173C4×D4×C59—22no—
174C4×D4×C59C2314yes—
175C2×C4⋊C4×C59—21no—
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C22⋊C4×C59—21no—
179C2×C42×C59—21no—
180C2×C42×C59C2311yescharacteristic
181#107×C59C2314yescomplemented
182#103×C59C2314yescomplemented
183#102×C59C2314yes—
184#97×C59C2314yescomplemented
185C24×C59—21no—
186C23×D59—21no—
187C23×D59—24no—
188C23×D59—44no—
189C23×D59—44no—
190C23×D59—82no—
191C23×D59C2×D411yescharacteristic
192C23×D59C2×D411yescharacteristic
193C2×Q8×C59—21no—
194C2×Q8×C59—22no—
195C2×Q8×C59—22no—
196C2×Q8×C59C2412yes—
197C2×D4×C59—21no—
198C2×D4×C59—22no—
199C2×D4×C59#4114yes—
200C2×D4×C59C2412yes—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—24no—
205C22×C4×C59—82no—
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2411yescharacteristic
209C2×C22⋊D59—24no—
210C2×C22⋊D59—24no—
211C2×C22⋊D59—44no—
212C2×C22⋊D59—44no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—24no—
217C22×Dic59—44no—
218C22×Dic59C2×D411yescharacteristic
219C22×Dic59C2×D411yescharacteristic
220#11745687—28no—
221#11745687—44no—
222#11745687—48no—
223D4×D59—28no—
224D4×D59—44no—
225D4×D59—48no—
226C2×D236—24no—
227C2×D236—22no—
228C2×D236—22no—
229C2×D236—21no—
230C2×D236—24no—
231C2×D236—82no—
232C2×D236C2×D414yes—
233C2×D236C2412yes—
234C2×C4×D59—22no—
235C2×C4×D59—22no—
236C2×C4×D59—22no—
237C2×C4×D59—22no—
238C2×C4×D59—24no—
239C2×C4×D59—24no—
240C2×C4×D59—82no—
241C2×C4×D59—82no—
242C2×C4×D59C2×D412yes—
243C2×C4×D59C2×D412yes—
244C2×C4×D59C2412yes—
245C2×C4×D59C2412yes—
246C2×Dic118—22no—
247C2×Dic118—22no—
248C2×Dic118—21no—
249C2×Dic118—24no—
250C2×Dic118—82no—
251C2×Dic118C2412yes—
252SD16×C59—28no—
253C2×C8×C59—22no—
254C2×C8×C59—22no—
255C2×C8×C59C2412yes—
256C2×C8×C59C2412yes—
257C4⋊C4×C59—24no—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59C2412yes—
261C4⋊C4×C59C2412yes—
262C22⋊C4×C59—24no—
263C42×C59—24no—
264C42×C59C2×D412yes—
265C42×C59C2412yes—
266#11745672—44no—
267#11745671—44no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4—24no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4—24no—
274(C2×D59)⋊C4C2×D414yes—
275(C2×D59)⋊C4C2×D414yes—
276C4⋊Dic59—21no—
277C4⋊Dic59—21no—
278C4⋊Dic59—24no—
279C4⋊Dic59—24no—
280C4⋊Dic59C2×D414yes—
281C4⋊Dic59C2412yes—
282C4⋊Dic59C2412yes—
283Dic59⋊C4—24no—
284Dic59⋊C4—24no—
285Dic59⋊C4—24no—
286Dic59⋊C4—24no—
287C2×C59⋊C8—22no—
288C2×C59⋊C8—22no—
289C2×C59⋊C8C2412yes—
290C2×C59⋊C8C2412yes—
291#11745659—44no—
292C8×D59—44no—
293C23×C59—24no—
294C23×C59—22no—
295C23×C59—42no—
296C23×C59—42no—
297C23×C59C22×D411yescharacteristic
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
304C22×D59—48no—
305C22×D59—42no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—48no—
309C22×D59—84no—
310C22×D59—816no—
311C22×D59#13714yes—
312C22×D59C22×D412yes—
313C22×D59C22×D412yes—
314Q8×C59—22no—
315Q8×C59—22no—
316Q8×C59—42no—
317D4×C59—24no—
318D4×C59—22no—
319D4×C59C2×#4114yes—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—42no—
326C2×C4×C59—42no—
327C2×C4×C59—42no—
328C2×C4×C59—84no—
329C2×C4×C59C22×D412yes—
330C2×C4×C59C22×D412yes—
331C2×C4×C59C22×D411yescharacteristic
332C2×C4×C59C2×#4112yes—
333C2×C4×C59H(5,𝔽2)12yes—
334C2×C4×C59C2511yescharacteristic
335C22⋊D59—48no—
336C22⋊D59—48no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—48no—
343C2×Dic59—42no—
344C2×Dic59—42no—
345C2×Dic59—42no—
346C2×Dic59C22×D412yes—
347C2×Dic59C22×D412yes—
348D236—28no—
349D236—22no—
350D236—22no—
351D236—42no—
352D236—84no—
353C4×D59—24no—
354C4×D59—24no—
355C4×D59—22no—
356C4×D59—22no—
357C4×D59—22no—
358C4×D59—22no—
359C4×D59—84no—
360C4×D59—84no—
361Dic118—22no—
362Dic118—22no—
363Dic118—42no—
364Dic118—84no—
365C8×C59—22no—
366C8×C59—22no—
367C59⋊C8—22no—
368C59⋊C8—22no—
369C2×#3314—591nomaximal, Sylow
370C22×C59—24no—
371C22×C59—48no—
372C22×C59—42no—
373C22×C59—42no—
374C22×C59#54612yes—
375C22×C59C2×#13712yes—
376C22×C59#57612yes—
377C22×C59C23×D411yescharacteristic
378C2×D59—22no—
379C2×D59—28no—
380C2×D59—22no—
381C2×D59—22no—
382C2×D59—22no—
383C2×D59—22no—
384C2×D59—44no—
385C2×D59—42no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—816no—
389C2×D59—84no—
390C2×D59C2×#13714yes—
391C4×C59—22no—
392C4×C59—22no—
393C4×C59—42no—
394C4×C59—42no—
395C4×C59—42no—
396C4×C59#54612yes—
397C4×C59C22×#4111yescharacteristic
398C4×C59C2×H(5,𝔽2)11yescharacteristic
399Dic59—22no—
400Dic59—22no—
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×#440D5911yescharacteristic, complemented
417C2×#435—591no—
418C2×#417—591no—
419C22×#102—591no—
420C2×C59—44no—
421C2×C59#331414yescomplemented
422C2×C59C2×#54611yescharacteristic
423C2×C59C22×#13711yescharacteristic
424C2×C59C2×#57611yescharacteristic
425D59—24no—
426D59—42no—
427D59—82no—
428C22×#41—591no—
429C23×D4—591no—
430C22×Q16—591no—
431C22×SD16—591no—
432C22×SD16C2×D5911yescharacteristic
433C22×M16—591no—
434C23×C8—591no—
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×Q8C2×D5911yescharacteristic, complemented
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#440C2×D5918yescomplemented
468#435—598no—
469C2×#107—591no—
470C2×#107—591no—
471C2×#107C2×D5911yescharacteristic, complemented
472C2×C4⋊C8—591no—
473#417—598no—
474C2×#103—591no—
475C2×#103—591no—
476C2×#103—591no—
477C2×#103C2×D5911yescharacteristic, complemented
478C2×#102—591no—
479C2×#102—591no—
480C2×#102—591no—
481C2×#102—591no—
482C2×#102—591no—
483C2×#102—598no—
484C2×#102C2×D5911yescharacteristic
485C2×C22⋊C8—591no—
486C2×C22⋊C8—591no—
487C2×#97C2×D5911yescharacteristic, complemented
488C59C2×#331411yescharacteristic, complemented, Sylow
489C25—1181no—
490C2×#41—594no—
491C2×#41—1182no—
492C2×#41—1184no—
493C2×#41—2362no—
494C22×Q8—591no—
495C22×Q8—1181no—
496C22×Q8C22×D5911yescharacteristic
497C22×D4—594no—
498C22×D4—591no—
499C22×D4—591no—
500C22×D4—1181no—
501C22×D4—1182no—
502C22×D4—1181no—
503C22×D4—1184no—
504C22×D4—1181no—
505C22×D4—2362no—
506C22×D4C22×D5911yescharacteristic
507C23×C4—21no—
508C23×C4—591no—
509C23×C4—591no—
510C23×C4—1181no—
511C23×C4—1181no—
512C23×C4—1181no—
513C2×Q16—594no—
514C2×Q16—2362no—
515C2×SD16—24no—
516C2×SD16—594no—
517C2×SD16—2362no—
518C2×SD16C22×D5914yes—
519C2×M16—594no—
520C2×M16—2362no—
521C22×C8—591no—
522C22×C8—591no—
523C22×C8—594no—
524C22×C8—2362no—
525C22×C8C22×D5911yescharacteristic
526C22×C8C22×D5911yescharacteristic
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—1188no—
537C22⋊Q8—1188no—
538C22⋊Q8—1182no—
539C22⋊Q8—1182no—
540C22⋊Q8—1182no—
541#121—594no—
542#121—1188no—
543#121—1182no—
544#120—1188no—
545C4×Q8—22no—
546C4×Q8C22×D5914yescomplemented
547C4×D4—22no—
548C4×D4—594no—
549C4×D4—594no—
550C4×D4—1188no—
551C4×D4C22×D5914yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—591no—
554C2×C4⋊C4—591no—
555C2×C4⋊C4—591no—
556C2×C4⋊C4—594no—
557C2×C4⋊C4—594no—
558C2×C4⋊C4—1182no—
559C2×C4⋊C4—1182no—
560C2×C4⋊C4—1181no—
561C2×C4⋊C4—1181no—
562C2×C4⋊C4—1181no—
563C2×C4⋊C4—1181no—
564C2×C4⋊C4—1181no—
565C2×C4⋊C4—1181no—
566C2×C4⋊C4C22×D5911yescharacteristic
567C2×C4⋊C4C22×D5911yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—591no—
570C2×C22⋊C4—591no—
571C2×C22⋊C4—1188no—
572C2×C22⋊C4—1181no—
573C2×C22⋊C4—1181no—
574C2×C22⋊C4—1181no—
575C2×C22⋊C4—1181no—
576C2×C22⋊C4—1181no—
577C2×C22⋊C4—1181no—
578C2×C42—21no—
579C2×C42C22×D5911yescharacteristic
580#107—594no—
581#107—594no—
582#107C22×D5914yescomplemented
583C4⋊C8—594no—
584#103—594no—
585#103—594no—
586#103—594no—
587#103C22×D5914yescomplemented
588#102—594no—
589#102—594no—
590#102—594no—
591#102—594no—
592#102—594no—
593#102C22×D5914yes—
594C22⋊C8—594no—
595C22⋊C8—594no—
596#97C22×D5914yescomplemented
597C24—21no—
598C24—591no—
599C24—591no—
600C24—1184no—
601C24—1181no—
602C24—4722no—
603C24—2364no—
604C24—2364no—
605#41—1188no—
606#41—2364no—
607#41—2368no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—592no—
612C2×Q8—1184no—
613C2×Q8—1181no—
614C2×Q8—1182no—
615C2×Q8—1182no—
616C2×Q8—4722no—
617C2×Q8C23×D5912yes—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—594no—
621C2×D4—592no—
622C2×D4—1184no—
623C2×D4—1184no—
624C2×D4—1184no—
625C2×D4—1188no—
626C2×D4—1184no—
627C2×D4—1181no—
628C2×D4—1182no—
629C2×D4—1182no—
630C2×D4—4722no—
631C2×D4—2364no—
632C2×D4—2368no—
633C2×D4—2364no—
634C2×D4—2364no—
635C2×D4#1174568514yes—
636C2×D4C23×D5912yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—82no—
642C22×C4—591no—
643C22×C4—591no—
644C22×C4—592no—
645C22×C4—592no—
646C22×C4—592no—
647C22×C4—592no—
648C22×C4—1184no—
649C22×C4—1184no—
650C22×C4—1184no—
651C22×C4—1182no—
652C22×C4—1182no—
653C22×C4—1182no—
654C22×C4—1182no—
655C22×C4—1181no—
656C22×C4—1181no—
657C22×C4—1181no—
658C22×C4—4722no—
659C22×C4—4722no—
660C22×C4—2364no—
661C22×C4D4×D5911yescharacteristic
662C22×C4D4×D5911yescharacteristic
663C22×C4C23×D5911yescharacteristic
664Q16—2364no—
665SD16—28no—
666SD16—2364no—
667M16—2364no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—592no—
671C2×C8—592no—
672C2×C8—1182no—
673C2×C8—1182no—
674C2×C8—2364no—
675C2×C8C23×D5912yes—
676C2×C8C23×D5912yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—594no—
681C4⋊C4—592no—
682C4⋊C4—592no—
683C4⋊C4—1184no—
684C4⋊C4—1184no—
685C4⋊C4—1184no—
686C4⋊C4—1184no—
687C4⋊C4—1184no—
688C4⋊C4—1181no—
689C4⋊C4—1181no—
690C4⋊C4—1184no—
691C4⋊C4C23×D5912yes—
692C4⋊C4C23×D5912yes—
693C22⋊C4—24no—
694C22⋊C4—594no—
695C22⋊C4—594no—
696C22⋊C4—1184no—
697C22⋊C4—1184no—
698C22⋊C4—1184no—
699C22⋊C4—1184no—
700C22⋊C4—1184no—
701C22⋊C4—1184no—
702C42—24no—
703C42D4×D5912yes—
704C42C23×D5912yes—
705C23—22no—
706C23—24no—
707C23—42no—
708C23—42no—
709C23—594no—
710C23—592no—
711C23—592no—
712C23—1182no—
713C23—1182no—
714C23—1182no—
715C23—1182no—
716C23—1182no—
717C23—1182no—
718C23—47216no—
719C23—4724no—
720C23—2368no—
721C23—2368no—
722C23—2362no—
723C23—2362no—
724C23—2362no—
725C23C2×D4×D5911yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—1182no—
730Q8—1182no—
731Q8—4724no—
732Q8—2362no—
733D4—22no—
734D4—24no—
735D4—1188no—
736D4—1182no—
737D4—1182no—
738D4—4724no—
739D4—2368no—
740D4—2368no—
741D4—2362no—
742D4C2×#1174568514yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—592no—
753C2×C4—592no—
754C2×C4—1182no—
755C2×C4—1182no—
756C2×C4—1182no—
757C2×C4—1182no—
758C2×C4—1182no—
759C2×C4—1182no—
760C2×C4—1184no—
761C2×C4—1184no—
762C2×C4—1182no—
763C2×C4—1182no—
764C2×C4—1182no—
765C2×C4—4724no—
766C2×C4—4724no—
767C2×C4—2368no—
768C2×C4—2362no—
769C2×C4—2362no—
770C2×C4—2362no—
771C2×C4C2×D4×D5912yes—
772C2×C4C2×D4×D5912yes—
773C2×C4C2×D4×D5911yescharacteristic
774C2×C4C2×#1174568512yes—
775C2×C4#1427377312yes—
776C2×C4C24×D5911yescharacteristic
777C8—22no—
778C8—22no—
779C8—1182no—
780C8—1182no—
781C22—24no—
782C22—48no—
783C22—42no—
784C22—42no—
785C22—594no—
786C22—1188no—
787C22—1182no—
788C22—1182no—
789C22—1182no—
790C22—1182no—
791C22—1182no—
792C22—47216no—
793C22—4724no—
794C22—2362no—
795C22—2362no—
796C22—2362no—
797C22—2364no—
798C22#1683804812yes—
799C22#137×D5912yes—
800C22#1683820612yes—
801C22C22×D4×D5911yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—1182no—
808C4—1182no—
809C4—2362no—
810C4—2362no—
811C4—2362no—
812C4#1683804812yes—
813C4C22×#1174568511yescharacteristic
814C4C2×#1427377311yescharacteristic
815C2—44no—
816C2—1184no—
817C2—4722no—
818C2—2362no—
819C2#2143618214yesdirect product factor
820C2C2×#1683804811yescharacteristic
821C2C2×#137×D5911yescharacteristic
822C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#440C2
socleC23×C59C22×D4
prime radicalC2×#16838047C2
hypercenterC2×#440D59
hypocenterC59C2×#3314
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16838112C2semidirect
3. #21436182C2direct (N × H)
4. C2×#16837762C2semidirect
5. C2×#16837739C2semidirect
6. C2×#16837717C2semidirect
7. C2×#16837682C2semidirect
8. C2×#16837651C2semidirect
9. C2×#16837642C2semidirect
10. C2×#16837624C2semidirect
11. C2×#16837561C2semidirect
12. C2×#16837551C2semidirect
13. C2×#16837475C2semidirect
14. C2×#16837400C2semidirect
15. C2×#102×D59C2semidirect
16. C2×C59×#440C2semidirect
19. C22×#11745672C22semidirect
21. C22×#11745659C22semidirect
24. #16838112C22semidirect
27. C2×#14273727C22semidirect
35. C2×#14273703C22semidirect
42. C2×C4⋊C4×D59C22semidirect
44. #16837762C22semidirect
45. #16837739C22semidirect
46. #16837717C22semidirect
47. #16837682C22semidirect
48. #16837651C22semidirect
49. #16837642C22semidirect
50. #16837624C22semidirect
51. #16837561C22semidirect
52. #16837551C22semidirect
53. #16837475C22semidirect
54. C2×#14273660C22semidirect
55. C2×#14273660C22semidirect
56. C2×C4⋊(C59⋊C8)C22semidirect
57. #16837400C22semidirect
58. C2×#14273652C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273650C22semidirect
66. #102×D59C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
70. C2×C4×Q8×C59C22semidirect
72. C59×#440C22semidirect
73. C2×#107×C59C22semidirect
74. C2×#103×C59C22semidirect
76. C2×#97×C59C22semidirect
99. C2×#11745672C23semidirect
103. C2×#11745659C23semidirect
109. #14273727C23semidirect
121. #14273703C23semidirect
141. C4⋊C4×D59C23semidirect
151. #14273660C23semidirect
152. #14273660C23semidirect
153. C4⋊(C59⋊C8)C23semidirect
154. #14273652C23semidirect
155. #14273652C23semidirect
156. #14273650C23semidirect
163. (C2×D59)⋊C8C23semidirect
172. C4×Q8×C59C23semidirect
181. #107×C59C23semidirect
182. #103×C59C23semidirect
184. #97×C59C23semidirect
416. C2×#440D59semidirect
421. C2×C59#3314semidirect
451. C2×C4×Q8C2×D59semidirect
467. #440C2×D59semidirect
471. C2×#107C2×D59semidirect
477. C2×#103C2×D59semidirect
487. C2×#97C2×D59semidirect
488. C59C2×#3314semidirect
546. C4×Q8C22×D59semidirect
582. #107C22×D59semidirect
587. #103C22×D59semidirect
596. #97C22×D59semidirect
819. C2#21436182direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381122
C2×#168380472
#214361822
C2×#168377622
C2×#168377392
C2×#168377172
C2×#168376822
C2×#168376512
C2×#168376422
C2×#168376242
C2×#168375612
C2×#168375512
C2×#168374752
C2×#168374002
C2×#102×D592
C2×C59×#4402
C2×#331459