Finite Group Databasebeta

← C2×#21436129 #29465356

Subgroups — C2×#21436129 #29465356

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×#16838126C211yesmaximal, characteristic, complemented
2C2×#16838047C211yesmaximal, characteristic
3#21436129C2116yesmaximal, direct product factor
4C2×#16837764C211yesmaximal, characteristic, complemented
5C2×#16837746C211yesmaximal, characteristic, complemented
6C2×#16837728C211yesmaximal, characteristic, complemented
7C2×#16837661C211yesmaximal, characteristic, complemented
8C2×#16837632C211yesmaximal, characteristic, complemented
9C2×#16837625C211yesmaximal, characteristic, complemented
10C2×#16837565C211yesmaximal, characteristic, complemented
11C2×#16837554C211yesmaximal, characteristic, complemented
12C2×#16837502C211yesmaximal, characteristic, complemented
13C2×#16837472C211yesmaximal, characteristic, complemented
14C2×#16837405C211yesmaximal, characteristic, complemented
15C2×#16837395C211yesmaximal, characteristic, complemented
16C2×C59×#476C211yesmaximal, characteristic, complemented
17C22×#11745687C2211yescharacteristic
18C22×D4×D59C2211yescharacteristic
19C22×Dic236C2211yescharacteristic, complemented
20C22×#11745660C2211yescharacteristic
21C22×#11745670C2211yescharacteristic
22C22×#11745659C2211yescharacteristic
23C22×C8×D59C2211yescharacteristic, complemented
24#16838126—24no—
25#16838126C2218yescomplemented
26#16838047—24no—
27#16838047C2218yes—
28C2×#14273722—21no—
29C2×#14273722—21no—
30C2×#14273716—21no—
31C2×#14273715C2211yescharacteristic
32C2×#14273711—21no—
33C2×#14273707C2211yescharacteristic
34C2×#14273707C2211yescharacteristic
35C2×#14273707C2211yescharacteristic, complemented
36C2×#14273702C2211yescharacteristic
37C2×#14273701—21no—
38C2×#14273697—21no—
39C2×Q8×Dic59—21no—
40C2×C4×Dic118C2211yescharacteristic, complemented
41C2×C4×D236C2211yescharacteristic
42C2×#14273685C2211yescharacteristic
43C2×#14273685C2211yescharacteristic, complemented
44C22×(C2×D59)⋊C4—21no—
45#16837764C2218yescomplemented
46#16837746C2218yescomplemented
47#16837728C2218yescomplemented
48#16837661C2218yescomplemented
49#16837632C2218yescomplemented
50#16837625C2218yescomplemented
51#16837565C2218yescomplemented
52#16837554C2218yescomplemented
53#16837502C2218yescomplemented
54#16837472C2218yescomplemented
55C2×#14273660C2211yescharacteristic, complemented
56#16837405C2218yescomplemented
57#16837395C2218yescomplemented
58C2×#14273652C2211yescharacteristic, complemented
59C2×#14273650C2211yescharacteristic, complemented
60C2×#14273650C2211yescharacteristic, complemented
61C2×#14273650C2211yescharacteristic, complemented
62C2×#14273649C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×#14273638C2211yescharacteristic, complemented
69C2×C4⋊Q8×C59C2211yescharacteristic, complemented
70C2×C4×D4×C59C2211yescharacteristic
71C59×#476C2218yescomplemented
72C2×#106×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×C4⋊C8×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C24×D59—21no—
78C2×#11745687—24no—
79C2×#11745687—22no—
80C2×#11745687—42no—
81C2×#11745687C2314yes—
82C22×Dic118C2311yescharacteristic
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×D59C2311yescharacteristic
95C22×C4×D59C2311yescharacteristic
96C2×Dic236—42no—
97C2×Dic236C2314yescomplemented
98C2×#11745660—42no—
99C2×#11745660C2314yes—
100C2×#11745670—24no—
101C2×#11745670C2314yes—
102C2×#11745659—42no—
103C2×#11745659C2314yes—
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106C2×C8×D59—42no—
107C2×C8×D59C2314yescomplemented
108#14273722—28no—
109#14273722—28no—
110#14273716—28no—
111#14273715—22no—
112#14273715C2314yes—
113#14273711—28no—
114#14273707—22no—
115#14273707—22no—
116#14273707—22no—
117#14273707C2314yes—
118#14273707C2314yes—
119#14273707C2314yescomplemented
120#14273702—22no—
121#14273702C2314yes—
122#14273701—28no—
123#14273697—28no—
124Q8×Dic59—28no—
125C4×Dic118—22no—
126C4×Dic118C2314yescomplemented
127C4×D236D414yes—
128C4×D236C2314yes—
129#14273685—22no—
130#14273685—22no—
131#14273685C2314yes—
132#14273685C2314yescomplemented
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59—21no—
135C2×C4⋊Dic59—21no—
136C2×C4⋊Dic59D411yescharacteristic
137C2×C4⋊Dic59C2311yescharacteristic
138C2×Dic59⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
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—28no—
148C2×(C2×D59)⋊C4D411yescharacteristic
149C2×(C2×D59)⋊C4D411yescharacteristic
150C2×C4×Dic59—21no—
151C2×C4×Dic59—21no—
152C2×C4×Dic59—21no—
153#14273660C2314yescomplemented
154#14273652C2314yescomplemented
155#14273650C2314yescomplemented
156#14273650C2314yescomplemented
157#14273650C2314yescomplemented
158#14273649C2314yes—
159#14273648C2314yes—
160#14273647C2314yes—
161#14273647C2314yes—
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yescomplemented
164#14273638C2314yescomplemented
165C22×Q8×C59—21no—
166C22×D4×C59C2311yescharacteristic
167C23×C4×C59—21no—
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C4⋊Q8×C59—22no—
171C4⋊Q8×C59C2314yescomplemented
172C4×D4×C59—22no—
173C4×D4×C59C2314yes—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C22⋊C4×C59—21no—
179C2×C42×C59C2311yescharacteristic
180#106×C59C2314yescomplemented
181#106×C59C2314yescomplemented
182C4⋊C8×C59C2314yescomplemented
183#102×C59C2314yes—
184#102×C59C2314yes—
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—24no—
194C2×Q8×C59—44no—
195C2×D4×C59—21no—
196C2×D4×C59—22no—
197C2×D4×C59#4114yes—
198C2×D4×C59C2412yes—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—24no—
203C22×C4×C59—82no—
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2411yescharacteristic
207C2×C22⋊D59—24no—
208C2×C22⋊D59—24no—
209C2×C22⋊D59—44no—
210C2×C22⋊D59—44no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—24no—
215C22×Dic59—44no—
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218#11745687—28no—
219#11745687—44no—
220#11745687—48no—
221D4×D59—28no—
222D4×D59—44no—
223D4×D59—48no—
224C2×D236—22no—
225C2×D236—22no—
226C2×D236—21no—
227C2×D236—24no—
228C2×D236—42no—
229C2×D236—82no—
230C2×D236C2×D414yes—
231C2×D236C2412yes—
232C2×C4×D59—22no—
233C2×C4×D59—22no—
234C2×C4×D59—22no—
235C2×C4×D59—22no—
236C2×C4×D59C2×D412yes—
237C2×C4×D59C2×D412yes—
238C2×C4×D59C2412yes—
239C2×C4×D59C2412yes—
240C2×Dic118—22no—
241C2×Dic118—22no—
242C2×Dic118—22no—
243C2×Dic118—22no—
244C2×Dic118—21no—
245C2×Dic118—21no—
246C2×Dic118C2412yes—
247C2×Dic118C2412yes—
248C2×C8×C59—22no—
249C2×C8×C59—22no—
250C2×C8×C59C2412yes—
251C2×C8×C59C2412yes—
252C4⋊C4×C59—24no—
253C4⋊C4×C59—21no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59C2412yes—
257C4⋊C4×C59C2412yes—
258C4⋊C4×C59C2412yes—
259C22⋊C4×C59—24no—
260C42×C59C2×D412yes—
261C42×C59C2412yes—
262#11745670—28no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4C2×D414yes—
272(C2×D59)⋊C4C2×D414yes—
273C4⋊Dic59—21no—
274C4⋊Dic59—24no—
275C4⋊Dic59—24no—
276C4⋊Dic59—24no—
277C4⋊Dic59C2×D414yes—
278C4⋊Dic59C2412yes—
279Dic59⋊C4—24no—
280C4×Dic59—24no—
281C4×Dic59—24no—
282C4×Dic59—24no—
283C2×C59⋊C8—22no—
284C2×C59⋊C8—22no—
285C2×C59⋊C8C2412yes—
286C2×C59⋊C8C2412yes—
287Dic236—44no—
288#11745660—44no—
289#11745659—44no—
290C8×D59—44no—
291C23×C59—24no—
292C23×C59—22no—
293C23×C59—42no—
294C23×C59—42no—
295C23×C59C22×D411yescharacteristic
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—48no—
304C22×D59—48no—
305C22×D59—42no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—84no—
309C22×D59—816no—
310C22×D59C22×D412yes—
311C22×D59C22×D412yes—
312Q8×C59—48no—
313D4×C59—24no—
314D4×C59—22no—
315D4×C59C2×#4114yes—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—42no—
322C2×C4×C59—42no—
323C2×C4×C59—42no—
324C2×C4×C59—84no—
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—48no—
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×Dic59C22×D412yes—
343C2×Dic59C22×D412yes—
344D236—22no—
345D236—22no—
346D236—44no—
347D236—42no—
348D236—84no—
349C4×D59—24no—
350C4×D59—24no—
351C4×D59—22no—
352C4×D59—22no—
353C4×D59—22no—
354C4×D59—22no—
355Dic118—22no—
356Dic118—22no—
357Dic118—22no—
358Dic118—22no—
359Dic118—42no—
360Dic118—42no—
361C8×C59—22no—
362C8×C59—22no—
363C59⋊C8—22no—
364C59⋊C8—22no—
365C2×#3311—591nomaximal, Sylow
366C22×C59—24no—
367C22×C59—48no—
368C22×C59—42no—
369C22×C59—42no—
370C22×C59#54612yes—
371C22×C59#57512yes—
372C22×C59#57712yes—
373C22×C59C23×D411yescharacteristic
374C2×D59—22no—
375C2×D59—22no—
376C2×D59—22no—
377C2×D59—22no—
378C2×D59—22no—
379C2×D59—22no—
380C2×D59—44no—
381C2×D59—44no—
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—816no—
386C2×D59—84no—
387C4×C59—22no—
388C4×C59—22no—
389C4×C59—42no—
390C4×C59—42no—
391C4×C59—42no—
392C4×C59#54612yes—
393C4×C59C22×#4111yescharacteristic
394C4×C59C2×H(5,𝔽2)11yescharacteristic
395Dic59—22no—
396Dic59—22no—
397Dic59—42no—
398Dic59—42no—
399Dic59—42no—
400C2×#556—591no—
401C2×#546—591no—
402#3311—5916no—
403C2×#489—591no—
404C2×#485—591no—
405C2×#482—591no—
406C2×#476D5911yescharacteristic, complemented
407C2×#470—591no—
408C2×#465—591no—
409C2×#464—591no—
410C2×#452—591no—
411C2×#450—591no—
412C2×#440—591no—
413C2×#435—591no—
414C2×#418—591no—
415C2×#416—591no—
416C2×C59—44no—
417C2×C59#331114yescomplemented
418C2×C59C2×#54611yescharacteristic
419C2×C59C2×#57511yescharacteristic
420C2×C59C2×#57711yescharacteristic
421D59—42no—
422D59—42no—
423D59—82no—
424C22×#41—591no—
425C23×D4—591no—
426C22×Q16—591no—
427C22×SD16—591no—
428C22×SD16—591no—
429C22×M16—591no—
430C23×C8—591no—
431#556—598no—
432#556—1184no—
433#546—598no—
434#546—1184no—
435C2×C4⋊Q8C2×D5911yescharacteristic, complemented
436C2×#126—1181no—
437C2×#126—1181no—
438C2×#124—591no—
439C2×#124—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×Q8—1181no—
449C2×C4×D4—591no—
450C2×C4×D4C2×D5911yescharacteristic
451C2×#117—591no—
452C2×#117—591no—
453C22×C22⋊C4—1181no—
454#489—598no—
455#485—598no—
456#482—598no—
457#476C2×D5918yescomplemented
458#470—598no—
459#465—598no—
460#464—598no—
461#452—598no—
462#450—598no—
463#440—598no—
464#435—598no—
465C2×#107—591no—
466C2×#106C2×D5911yescharacteristic, complemented
467C2×#106C2×D5911yescharacteristic, complemented
468C2×C4⋊C8C2×D5911yescharacteristic, complemented
469#418—598no—
470#416—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×#102C2×D5911yescharacteristic
480C2×#102C2×D5911yescharacteristic
481C2×C22⋊C8—591no—
482C2×C22⋊C8—591no—
483C2×#97—591no—
484C59C2×#331111yescharacteristic, complemented, Sylow
485C25—1181no—
486C2×#41—594no—
487C2×#41—1182no—
488C2×#41—1184no—
489C2×#41—2362no—
490C22×Q8—21no—
491C22×Q8—591no—
492C22×Q8—591no—
493C22×D4—594no—
494C22×D4—591no—
495C22×D4—591no—
496C22×D4—1181no—
497C22×D4—1182no—
498C22×D4—1181no—
499C22×D4—1184no—
500C22×D4—1181no—
501C22×D4—2362no—
502C22×D4C22×D5911yescharacteristic
503C23×C4—21no—
504C23×C4—591no—
505C23×C4—591no—
506C23×C4—1181no—
507C2×Q16—594no—
508C2×Q16—2362no—
509C2×SD16—594no—
510C2×SD16—594no—
511C2×SD16—1184no—
512C2×SD16—2362no—
513C2×M16—594no—
514C2×M16—2362no—
515C22×C8—591no—
516C22×C8—591no—
517C22×C8—594no—
518C22×C8—2362no—
519C22×C8C22×D5911yescharacteristic
520C22×C8C22×D5911yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8C22×D5914yescomplemented
523#126—1188no—
524#126—1188no—
525#124—594no—
526#124—1188no—
527#124—1182no—
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—1188no—
537#121—1182no—
538#120—1188no—
539C4×Q8—594no—
540C4×Q8—1188no—
541C4×Q8—1182no—
542C4×D4—22no—
543C4×D4—594no—
544C4×D4—594no—
545C4×D4C22×D5914yes—
546#117—594no—
547#117—594no—
548#117—1182no—
549#117—1182no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—591no—
552C2×C4⋊C4—591no—
553C2×C4⋊C4—1181no—
554C2×C4⋊C4—1181no—
555C2×C4⋊C4—1181no—
556C2×C4⋊C4—1181no—
557C2×C4⋊C4C22×D5911yescharacteristic
558C2×C4⋊C4C22×D5911yescharacteristic
559C2×C4⋊C4C22×D5911yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—591no—
562C2×C22⋊C4—591no—
563C2×C22⋊C4—1188no—
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—1181no—
571C2×C22⋊C4—1181no—
572C2×C42—1181no—
573C2×C42—1181no—
574C2×C42—1181no—
575C2×C42C22×D5911yescharacteristic
576#107—594no—
577#106C22×D5914yescomplemented
578#106C22×D5914yescomplemented
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#102C22×D5914yes—
589#102C22×D5914yes—
590C22⋊C8—594no—
591C22⋊C8—594no—
592#97—594no—
593C24—21no—
594C24—591no—
595C24—591no—
596C24—1184no—
597C24—1181no—
598C24—4722no—
599C24—2364no—
600C24—2364no—
601#41—1188no—
602#41—2364no—
603#41—2368no—
604C2×Q8—24no—
605C2×Q8—44no—
606C2×Q8—592no—
607C2×Q8—592no—
608C2×Q8—1181no—
609C2×Q8—1181no—
610C2×Q8—1182no—
611C2×Q8—1182no—
612C2×Q8—1182no—
613C2×Q8—1182no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—594no—
617C2×D4—592no—
618C2×D4—1184no—
619C2×D4—1184no—
620C2×D4—1188no—
621C2×D4—1184no—
622C2×D4—1181no—
623C2×D4—1182no—
624C2×D4—1182no—
625C2×D4—4722no—
626C2×D4—2362no—
627C2×D4—2364no—
628C2×D4—2368no—
629C2×D4—2364no—
630C2×D4—2364no—
631C2×D4#1174568914yes—
632C2×D4C23×D5912yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—82no—
638C22×C4—591no—
639C22×C4—591no—
640C22×C4—592no—
641C22×C4—592no—
642C22×C4—592no—
643C22×C4—592no—
644C22×C4—1184no—
645C22×C4—1182no—
646C22×C4—1182no—
647C22×C4—1182no—
648C22×C4—1182no—
649C22×C4—1181no—
650C22×C4—1181no—
651C22×C4—1181no—
652C22×C4—2364no—
653C22×C4D4×D5911yescharacteristic
654C22×C4D4×D5911yescharacteristic
655C22×C4C23×D5911yescharacteristic
656Q16—2364no—
657SD16—1188no—
658SD16—2364no—
659M16—2364no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—592no—
663C2×C8—592no—
664C2×C8—1182no—
665C2×C8—1182no—
666C2×C8—2364no—
667C2×C8C23×D5912yes—
668C2×C8C23×D5912yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—594no—
674C4⋊C4—592no—
675C4⋊C4—1184no—
676C4⋊C4—1184no—
677C4⋊C4—1184no—
678C4⋊C4—1181no—
679C4⋊C4—1184no—
680C4⋊C4C23×D5912yes—
681C4⋊C4C23×D5912yes—
682C4⋊C4C23×D5912yes—
683C22⋊C4—24no—
684C22⋊C4—594no—
685C22⋊C4—594no—
686C22⋊C4—1184no—
687C22⋊C4—1184no—
688C22⋊C4—1184no—
689C22⋊C4—1184no—
690C22⋊C4—1184no—
691C22⋊C4—1184no—
692C22⋊C4—1184no—
693C22⋊C4—1184no—
694C42—1184no—
695C42—1184no—
696C42—1184no—
697C42D4×D5912yes—
698C42C23×D5912yes—
699C23—22no—
700C23—24no—
701C23—42no—
702C23—42no—
703C23—592no—
704C23—592no—
705C23—1182no—
706C23—1182no—
707C23—1182no—
708C23—1182no—
709C23—1182no—
710C23—1182no—
711C23—1182no—
712C23—4724no—
713C23—47216no—
714C23—2368no—
715C23—2368no—
716C23—2362no—
717C23—2362no—
718C23—2362no—
719C23C2×D4×D5911yescharacteristic
720Q8—48no—
721Q8—1182no—
722Q8—1182no—
723Q8—1182no—
724Q8—1182no—
725Q8—2362no—
726Q8—2362no—
727D4—22no—
728D4—24no—
729D4—1182no—
730D4—1182no—
731D4—4724no—
732D4—2364no—
733D4—2368no—
734D4—2368no—
735D4—2362no—
736D4C2×#1174568914yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—84no—
746C2×C4—592no—
747C2×C4—592no—
748C2×C4—1182no—
749C2×C4—1182no—
750C2×C4—1182no—
751C2×C4—1182no—
752C2×C4—1182no—
753C2×C4—1182no—
754C2×C4—1184no—
755C2×C4—1184no—
756C2×C4—1182no—
757C2×C4—1182no—
758C2×C4—1182no—
759C2×C4—2368no—
760C2×C4—2362no—
761C2×C4—2362no—
762C2×C4—2362no—
763C2×C4C2×D4×D5912yes—
764C2×C4C2×D4×D5912yes—
765C2×C4C2×D4×D5911yescharacteristic
766C2×C4C2×#1174568912yes—
767C2×C4#1427377312yes—
768C2×C4C24×D5911yescharacteristic
769C8—22no—
770C8—22no—
771C8—1182no—
772C8—1182no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—1182no—
778C22—1182no—
779C22—1182no—
780C22—1182no—
781C22—1182no—
782C22—1182no—
783C22—47216no—
784C22—4724no—
785C22—2362no—
786C22—2362no—
787C22—2362no—
788C22—2364no—
789C22—2364no—
790C22#1683804312yes—
791C22#1683819812yes—
792C22#1683820812yes—
793C22C22×D4×D5911yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—1182no—
800C4—1182no—
801C4—2362no—
802C4—2362no—
803C4—2362no—
804C4#1683804312yes—
805C4C22×#1174568911yescharacteristic
806C4C2×#1427377311yescharacteristic
807C2—44no—
808C2—4722no—
809C2—2362no—
810C2—2362no—
811C2#2143612914yesdirect product factor
812C2C2×#1683804311yescharacteristic
813C2C2×#1683819811yescharacteristic
814C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#476C2
socleC23×C59C22×D4
prime radicalC2×#16838047C2
hypercenterC2×#476D59
hypocenterC59C2×#3311
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16838126C2semidirect
3. #21436129C2direct (N × H)
4. C2×#16837764C2semidirect
5. C2×#16837746C2semidirect
6. C2×#16837728C2semidirect
7. C2×#16837661C2semidirect
8. C2×#16837632C2semidirect
9. C2×#16837625C2semidirect
10. C2×#16837565C2semidirect
11. C2×#16837554C2semidirect
12. C2×#16837502C2semidirect
13. C2×#16837472C2semidirect
14. C2×#16837405C2semidirect
15. C2×#16837395C2semidirect
16. C2×C59×#476C2semidirect
19. C22×Dic236C22semidirect
23. C22×C8×D59C22semidirect
25. #16838126C22semidirect
35. C2×#14273707C22semidirect
40. C2×C4×Dic118C22semidirect
43. C2×#14273685C22semidirect
45. #16837764C22semidirect
46. #16837746C22semidirect
47. #16837728C22semidirect
48. #16837661C22semidirect
49. #16837632C22semidirect
50. #16837625C22semidirect
51. #16837565C22semidirect
52. #16837554C22semidirect
53. #16837502C22semidirect
54. #16837472C22semidirect
55. C2×#14273660C22semidirect
56. #16837405C22semidirect
57. #16837395C22semidirect
58. C2×#14273652C22semidirect
59. C2×#14273650C22semidirect
60. C2×#14273650C22semidirect
61. C2×#14273650C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×#14273638C22semidirect
69. C2×C4⋊Q8×C59C22semidirect
71. C59×#476C22semidirect
72. C2×#106×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×C4⋊C8×C59C22semidirect
97. C2×Dic236C23semidirect
107. C2×C8×D59C23semidirect
119. #14273707C23semidirect
126. C4×Dic118C23semidirect
132. #14273685C23semidirect
153. #14273660C23semidirect
154. #14273652C23semidirect
155. #14273650C23semidirect
156. #14273650C23semidirect
157. #14273650C23semidirect
163. (C2×D59)⋊C8C23semidirect
164. #14273638C23semidirect
171. C4⋊Q8×C59C23semidirect
180. #106×C59C23semidirect
181. #106×C59C23semidirect
182. C4⋊C8×C59C23semidirect
406. C2×#476D59semidirect
417. C2×C59#3311semidirect
435. C2×C4⋊Q8C2×D59semidirect
457. #476C2×D59semidirect
466. C2×#106C2×D59semidirect
467. C2×#106C2×D59semidirect
468. C2×C4⋊C8C2×D59semidirect
484. C59C2×#3311semidirect
522. C4⋊Q8C22×D59semidirect
577. #106C22×D59semidirect
578. #106C22×D59semidirect
579. C4⋊C8C22×D59semidirect
811. C2#21436129direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381262
C2×#168380472
#214361292
C2×#168377642
C2×#168377462
C2×#168377282
C2×#168376612
C2×#168376322
C2×#168376252
C2×#168375652
C2×#168375542
C2×#168375022
C2×#168374722
C2×#168374052
C2×#168373952
C2×C59×#4762
C2×#331159