Finite Group Databasebeta

← C2×#21436128 #29465355

Subgroups — C2×#21436128 #29465355

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×#16838120C211yesmaximal, characteristic, complemented
2C2×#16838040C211yesmaximal, characteristic
3#21436128C2116yesmaximal, direct product factor
4C2×#16837763C211yesmaximal, characteristic, complemented
5C2×#16837741C211yesmaximal, characteristic, complemented
6C2×#16837726C211yesmaximal, characteristic, complemented
7C2×#16837690C211yesmaximal, characteristic, complemented
8C2×#16837659C211yesmaximal, characteristic, complemented
9C2×#16837631C211yesmaximal, characteristic, complemented
10C2×#16837627C211yesmaximal, characteristic, complemented
11C2×#16837564C211yesmaximal, characteristic, complemented
12C2×#16837554C211yesmaximal, characteristic, complemented
13C2×#16837499C211yesmaximal, characteristic, complemented
14C2×#16837473C211yesmaximal, characteristic, complemented
15C2×#16837405C211yesmaximal, characteristic, complemented
16C2×C59×#416C211yesmaximal, characteristic, complemented
17C22×D4×D59C2211yescharacteristic
18C22×#11745672C2211yescharacteristic, complemented
19C22×#11745660C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22#16838120—24no—
23#16838120C2218yescomplemented
24#16838040—24no—
25#16838040C2218yes—
26C2×#14273726C2211yescharacteristic, complemented
27C2×#14273721—21no—
28C2×#14273720—21no—
29C2×#14273716C2211yescharacteristic
30C2×#14273713—21no—
31C2×#14273710—21no—
32C2×#14273707C2211yescharacteristic
33C2×#14273706C2211yescharacteristic, complemented
34C2×#14273703C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36C2×#14273699—21no—
37C2×#14273695—21no—
38C2×C4×Dic118—21no—
39C2×#14273692C2211yescharacteristic, complemented
40C2×D4×Dic59C2211yescharacteristic
41C2×C4×C22⋊D59C2211yescharacteristic
42C2×#14273685C2211yescharacteristic
43C22×(C2×D59)⋊C4—21no—
44#16837763C2218yescomplemented
45#16837741C2218yescomplemented
46#16837726C2218yescomplemented
47#16837690C2218yescomplemented
48#16837659C2218yescomplemented
49#16837631C2218yescomplemented
50#16837627C2218yescomplemented
51#16837564C2218yescomplemented
52#16837554C2218yescomplemented
53#16837499C2218yescomplemented
54#16837473C2218yescomplemented
55C2×#14273660C2211yescharacteristic, complemented
56C2×#14273659C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×Dic59⋊C8C2211yescharacteristic, complemented
59#16837405C2218yescomplemented
60C2×#14273652C2211yescharacteristic, complemented
61C2×#14273651C2211yescharacteristic, complemented
62C2×#14273649C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic, complemented
69C22×#41×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic, complemented
71C2×#117×C59C2211yescharacteristic, complemented
72C59×#416C2218yescomplemented
73C2×#103×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C24×D59—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C22⋊D59D411yescharacteristic
84C2×D4×D59—24no—
85C2×D4×D59—22no—
86C2×D4×D59—42no—
87C2×D4×D59C2314yes—
88C23×Dic59—21no—
89C22×C4×D59C2311yescharacteristic
90C2×#11745672—42no—
91C2×#11745672C2314yescomplemented
92C2×#11745660—42no—
93C2×#11745660C2314yes—
94C2×#11745670—24no—
95C2×#11745670C2314yes—
96C2×#11745659—42no—
97C2×#11745659C2314yes—
98C22×C59⋊C8C2311yescharacteristic
99C22×C59⋊C8C2311yescharacteristic
100#14273726—22no—
101#14273726C2314yescomplemented
102#14273721—28no—
103#14273720—28no—
104#14273716—22no—
105#14273716C2314yes—
106#14273713—28no—
107#14273710—28no—
108#14273707—22no—
109#14273707C2314yes—
110#14273706—22no—
111#14273706C2314yescomplemented
112#14273703—22no—
113#14273703C2314yes—
114#14273701—22no—
115#14273701C2314yes—
116#14273699—28no—
117#14273695—28no—
118C4×Dic118—28no—
119#14273692—22no—
120#14273692C2314yescomplemented
121D4×Dic59—22no—
122D4×Dic59C2314yes—
123C4×C22⋊D59D414yes—
124C4×C22⋊D59C2314yes—
125#14273685—22no—
126#14273685C2314yes—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2311yescharacteristic
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4D411yescharacteristic
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59D411yescharacteristic
138C2×(C2×D59)⋊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—28no—
145C2×(C2×D59)⋊C4D411yescharacteristic
146C2×C4×Dic59—21no—
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yescomplemented
150#14273659C2314yescomplemented
151#14273658C2314yescomplemented
152Dic59⋊C8C2314yescomplemented
153#14273652C2314yescomplemented
154#14273651C2314yescomplemented
155#14273649C2314yes—
156#14273648C2314yes—
157#14273647C2314yes—
158#14273647C2314yes—
159C22⋊(C59⋊C8)C2314yescomplemented
160(C2×D59)⋊C8C2314yes—
161#14273637C2314yescomplemented
162C2×#41×C59—22no—
163C2×#41×C59—24no—
164C2×#41×C59—42no—
165C2×#41×C59C2314yes—
166C22×Q8×C59C2311yescharacteristic
167C22×D4×C59—21no—
168C22×D4×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C23×C4×C59C2311yescharacteristic
171C22×C8×C59—42no—
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2314yescomplemented
175#117×C59—22no—
176#117×C59C2314yescomplemented
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C22⋊C4×C59—21no—
180C2×C42×C59—21no—
181#103×C59C2314yescomplemented
182#103×C59C2314yescomplemented
183#102×C59C2314yes—
184#102×C59C2314yes—
185C24×C59—21no—
186C24×C59C2×D411yescharacteristic
187C23×D59—21no—
188C23×D59—24no—
189C23×D59—44no—
190C23×D59—44no—
191C23×D59—82no—
192C23×D59C2×D411yescharacteristic
193#41×C59—28no—
194#41×C59—44no—
195#41×C59—48no—
196C2×Q8×C59—21no—
197C2×Q8×C59—22no—
198C2×Q8×C59—22no—
199C2×Q8×C59C2412yes—
200C2×D4×C59—24no—
201C2×D4×C59—21no—
202C2×D4×C59—22no—
203C2×D4×C59—44no—
204C2×D4×C59#4114yes—
205C2×D4×C59C2412yes—
206C22×C4×C59—22no—
207C22×C4×C59—22no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—24no—
212C22×C4×C59—44no—
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2×D412yes—
215C22×C4×C59C2412yes—
216C22×C4×C59C2411yescharacteristic
217C2×C22⋊D59—24no—
218C2×C22⋊D59—24no—
219C2×C22⋊D59—42no—
220C2×C22⋊D59—44no—
221C2×C22⋊D59—82no—
222C2×C22⋊D59C2×D414yes—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—24no—
227C22×Dic59—82no—
228C22×Dic59C2×D411yescharacteristic
229C22×Dic59C2×D411yescharacteristic
230C22×Dic59C2×D411yescharacteristic
231D4×D59—28no—
232D4×D59—44no—
233D4×D59—48no—
234C2×D236—22no—
235C2×D236—22no—
236C2×D236—21no—
237C2×D236C2412yes—
238C2×C4×D59—22no—
239C2×C4×D59—22no—
240C2×C4×D59C2×D412yes—
241C2×C4×D59C2412yes—
242C2×Dic118—22no—
243C2×Dic118—22no—
244C2×Dic118—21no—
245C2×Dic118—24no—
246C2×Dic118—44no—
247C2×Dic118C2412yes—
248C2×C8×C59—22no—
249C2×C8×C59—22no—
250C2×C8×C59—44no—
251C2×C8×C59C2412yes—
252C2×C8×C59C2412yes—
253C4⋊C4×C59—21no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59C2412yes—
256C4⋊C4×C59C2412yes—
257C22⋊C4×C59—24no—
258C42×C59—24no—
259C22⋊Dic59—24no—
260C22⋊Dic59—24no—
261C22⋊Dic59C2×D414yes—
262#11745672—44no—
263#11745670—28no—
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)⋊C4C2×D414yes—
271C4⋊Dic59—21no—
272C4⋊Dic59—21no—
273C4⋊Dic59—24no—
274C4⋊Dic59C2412yes—
275C4⋊Dic59C2412yes—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279Dic59⋊C4—24no—
280Dic59⋊C4C2×D414yes—
281C4×Dic59—24no—
282C4×Dic59—24no—
283C4×Dic59C2×D412yes—
284C4×Dic59C2412yes—
285C2×C59⋊C8—22no—
286C2×C59⋊C8—22no—
287C2×C59⋊C8C2412yes—
288C2×C59⋊C8C2412yes—
289#11745660—44no—
290#11745659—44no—
291C23×C59—24no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—42no—
297C23×C59—42no—
298C23×C59C22×D412yes—
299C23×C59C22×D411yescharacteristic
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
304C22×D59—48no—
305C22×D59—48no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—42no—
309C22×D59—84no—
310C22×D59—816no—
311C22×D59C22×D412yes—
312Q8×C59—22no—
313Q8×C59—22no—
314Q8×C59—42no—
315D4×C59—24no—
316D4×C59—22no—
317D4×C59—48no—
318D4×C59C2×#4114yes—
319C2×C4×C59—22no—
320C2×C4×C59—24no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—48no—
327C2×C4×C59—42no—
328C2×C4×C59—42no—
329C2×C4×C59—42no—
330C2×C4×C59C22×D412yes—
331C2×C4×C59C22×D411yescharacteristic
332C2×C4×C59C2×#4112yes—
333C2×C4×C59H(5,𝔽2)12yes—
334C2×C4×C59C2511yescharacteristic
335C22⋊D59—44no—
336C22⋊D59—48no—
337C22⋊D59—84no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—42no—
345C2×Dic59—42no—
346C2×Dic59—42no—
347C2×Dic59—84no—
348C2×Dic59C22×D412yes—
349C2×Dic59C22×D412yes—
350C2×Dic59C22×D412yes—
351D236—22no—
352D236—22no—
353D236—42no—
354C4×D59—24no—
355C4×D59—22no—
356C4×D59—22no—
357Dic118—22no—
358Dic118—22no—
359Dic118—48no—
360Dic118—42no—
361C8×C59—22no—
362C8×C59—22no—
363C59⋊C8—22no—
364C59⋊C8—22no—
365C2×#3311—591nomaximal, Sylow
366C22×C59—24no—
367C22×C59—22no—
368C22×C59—22no—
369C22×C59—22no—
370C22×C59—48no—
371C22×C59—44no—
372C22×C59—42no—
373C22×C59—42no—
374C22×C59#54612yes—
375C22×C59#57512yes—
376C22×C59#57712yes—
377C22×C59C23×D411yescharacteristic
378C2×D59—22no—
379C2×D59—22no—
380C2×D59—22no—
381C2×D59—44no—
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—816no—
386C2×D59—84no—
387C4×C59—22no—
388C4×C59—42no—
389C4×C59—42no—
390C4×C59—42no—
391C4×C59#54612yes—
392C4×C59C22×#4111yescharacteristic
393C4×C59C2×H(5,𝔽2)11yescharacteristic
394Dic59—22no—
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×#476—591no—
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×#416D5911yescharacteristic, complemented
416C2×C59—44no—
417C2×C59—42no—
418C2×C59#331114yescomplemented
419C2×C59C2×#54611yescharacteristic
420C2×C59C2×#57511yescharacteristic
421C2×C59C2×#57711yescharacteristic
422D59—42no—
423D59—82no—
424C22×#41C2×D5911yescharacteristic
425C23×D4—591no—
426C22×Q16—591no—
427C22×SD16—591no—
428C22×SD16—591no—
429C22×M16—591no—
430C23×C8C2×D5911yescharacteristic, complemented
431#556—598no—
432#556—1184no—
433#546—598no—
434#546—1184no—
435C2×C4⋊Q8—591no—
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×D4—591no—
451C2×#117—591no—
452C2×#117C2×D5911yescharacteristic, complemented
453C22×C22⋊C4—1181no—
454#489—598no—
455#485—598no—
456#482—598no—
457#476—598no—
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×#106—591no—
467C2×#106—591no—
468C2×C4⋊C8—591no—
469#418—598no—
470#416C2×D5918yescomplemented
471C2×#103—591no—
472C2×#103—591no—
473C2×#103C2×D5911yescharacteristic, complemented
474C2×#103C2×D5911yescharacteristic, complemented
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—22no—
487C2×#41—24no—
488C2×#41—42no—
489C2×#41C22×D5914yes—
490C22×Q8—591no—
491C22×Q8—1181no—
492C22×Q8C22×D5911yescharacteristic
493C22×D4—21no—
494C22×D4—591no—
495C22×D4—594no—
496C22×D4—591no—
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—1181no—
506C23×C4C22×D5911yescharacteristic
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—42no—
516C22×C8—591no—
517C22×C8—591no—
518C22×C8C22×D5911yescharacteristic
519C22×C8C22×D5911yescharacteristic
520C22×C8C22×D5914yescomplemented
521C4⋊Q8—594no—
522C4⋊Q8—1182no—
523#126—1188no—
524#126—1188no—
525#124—594no—
526#124—1182no—
527#124—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—1188no—
537#121—1182no—
538#120—1188no—
539C4×Q8—594no—
540C4×Q8—1188no—
541C4×Q8—1182no—
542C4×D4—594no—
543C4×D4—594no—
544C4×D4—594no—
545C4×D4—1182no—
546#117—22no—
547#117—594no—
548#117—1182no—
549#117C22×D5914yescomplemented
550C2×C4⋊C4—591no—
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⋊C4—1181no—
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—21no—
573C2×C42—591no—
574C2×C42—1181no—
575C2×C42—1181no—
576#107—594no—
577#106—594no—
578#106—594no—
579C4⋊C8—594no—
580#103—594no—
581#103—594no—
582#103C22×D5914yescomplemented
583#103C22×D5914yescomplemented
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—1184no—
596C24—1181no—
597C24—4722no—
598C24—2364no—
599C24—2364no—
600C24D4×D5911yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—592no—
608C2×Q8—1184no—
609C2×Q8—1181no—
610C2×Q8—1182no—
611C2×Q8—1182no—
612C2×Q8—2364no—
613C2×Q8C23×D5912yes—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—594no—
619C2×D4—592no—
620C2×D4—1184no—
621C2×D4—1188no—
622C2×D4—1184no—
623C2×D4—1181no—
624C2×D4—1182no—
625C2×D4—1182no—
626C2×D4—4722no—
627C2×D4—2364no—
628C2×D4—2368no—
629C2×D4—2362no—
630C2×D4—2364no—
631C2×D4#1174568514yes—
632C2×D4C23×D5912yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—44no—
640C22×C4—591no—
641C22×C4—591no—
642C22×C4—591no—
643C22×C4—592no—
644C22×C4—592no—
645C22×C4—1184no—
646C22×C4—1182no—
647C22×C4—1182no—
648C22×C4—1181no—
649C22×C4—1181no—
650C22×C4—1181no—
651C22×C4—4722no—
652C22×C4D4×D5912yes—
653C22×C4D4×D5911yescharacteristic
654C22×C4C23×D5912yes—
655C22×C4C23×D5911yescharacteristic
656Q16—2364no—
657SD16—1188no—
658SD16—2364no—
659M16—2364no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—44no—
663C2×C8—592no—
664C2×C8—592no—
665C2×C8—1182no—
666C2×C8—1182no—
667C2×C8C23×D5912yes—
668C2×C8C23×D5912yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—594no—
672C4⋊C4—592no—
673C4⋊C4—592no—
674C4⋊C4—1184no—
675C4⋊C4—1184no—
676C4⋊C4—1184no—
677C4⋊C4—1184no—
678C4⋊C4—1181no—
679C4⋊C4—1181no—
680C4⋊C4—1184no—
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—24no—
695C42—592no—
696C42—592no—
697C42—1184no—
698C42—1184no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—42no—
705C23—42no—
706C23—592no—
707C23—1182no—
708C23—1182no—
709C23—1182no—
710C23—1182no—
711C23—4724no—
712C23—47216no—
713C23—2368no—
714C23—2368no—
715C23—2362no—
716C23—2362no—
717C23—2362no—
718C23C2×D4×D5912yes—
719C23C2×D4×D5911yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—1182no—
724Q8—1182no—
725Q8—2368no—
726Q8—2362no—
727D4—22no—
728D4—24no—
729D4—48no—
730D4—1182no—
731D4—1182no—
732D4—4724no—
733D4—2364no—
734D4—2368no—
735D4—2362no—
736D4C2×#1174568514yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—48no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—592no—
749C2×C4—592no—
750C2×C4—592no—
751C2×C4—1182no—
752C2×C4—1182no—
753C2×C4—1182no—
754C2×C4—1182no—
755C2×C4—1182no—
756C2×C4—1184no—
757C2×C4—1182no—
758C2×C4—1182no—
759C2×C4—1182no—
760C2×C4—4724no—
761C2×C4—2362no—
762C2×C4—2362no—
763C2×C4—2362no—
764C2×C4C2×D4×D5912yes—
765C2×C4C2×D4×D5911yescharacteristic
766C2×C4C2×#1174568512yes—
767C2×C4#1427377212yes—
768C2×C4C24×D5911yescharacteristic
769C8—22no—
770C8—22no—
771C8—1182no—
772C8—1182no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—22no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—48no—
781C22—1182no—
782C22—1182no—
783C22—1182no—
784C22—47216no—
785C22—4724no—
786C22—2362no—
787C22—2362no—
788C22—2362no—
789C22—2364no—
790C22#1683804212yes—
791C22#1683819912yes—
792C22#1683820912yes—
793C22C22×D4×D5911yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—1182no—
799C4—1182no—
800C4—1182no—
801C4—2362no—
802C4—2362no—
803C4—2362no—
804C4#1683804212yes—
805C4C22×#1174568511yescharacteristic
806C4C2×#1427377211yescharacteristic
807C2—42no—
808C2—44no—
809C2—4722no—
810C2—2362no—
811C2#2143612814yesdirect product factor
812C2C2×#1683804211yescharacteristic
813C2C2×#1683819911yescharacteristic
814C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#416C2
socleC23×C59C22×D4
prime radicalC2×#16838040C2
hypercenterC2×#416D59
hypocenterC59C2×#3311
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16838120C2semidirect
3. #21436128C2direct (N × H)
4. C2×#16837763C2semidirect
5. C2×#16837741C2semidirect
6. C2×#16837726C2semidirect
7. C2×#16837690C2semidirect
8. C2×#16837659C2semidirect
9. C2×#16837631C2semidirect
10. C2×#16837627C2semidirect
11. C2×#16837564C2semidirect
12. C2×#16837554C2semidirect
13. C2×#16837499C2semidirect
14. C2×#16837473C2semidirect
15. C2×#16837405C2semidirect
16. C2×C59×#416C2semidirect
18. C22×#11745672C22semidirect
23. #16838120C22semidirect
26. C2×#14273726C22semidirect
33. C2×#14273706C22semidirect
39. C2×#14273692C22semidirect
44. #16837763C22semidirect
45. #16837741C22semidirect
46. #16837726C22semidirect
47. #16837690C22semidirect
48. #16837659C22semidirect
49. #16837631C22semidirect
50. #16837627C22semidirect
51. #16837564C22semidirect
52. #16837554C22semidirect
53. #16837499C22semidirect
54. #16837473C22semidirect
55. C2×#14273660C22semidirect
56. C2×#14273659C22semidirect
57. C2×#14273658C22semidirect
58. C2×Dic59⋊C8C22semidirect
59. #16837405C22semidirect
60. C2×#14273652C22semidirect
61. C2×#14273651C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
68. C2×#14273637C22semidirect
70. C23×C8×C59C22semidirect
71. C2×#117×C59C22semidirect
72. C59×#416C22semidirect
73. C2×#103×C59C22semidirect
74. C2×#103×C59C22semidirect
91. C2×#11745672C23semidirect
101. #14273726C23semidirect
111. #14273706C23semidirect
120. #14273692C23semidirect
149. #14273660C23semidirect
150. #14273659C23semidirect
151. #14273658C23semidirect
152. Dic59⋊C8C23semidirect
153. #14273652C23semidirect
154. #14273651C23semidirect
159. C22⋊(C59⋊C8)C23semidirect
161. #14273637C23semidirect
174. C22×C8×C59C23semidirect
176. #117×C59C23semidirect
181. #103×C59C23semidirect
182. #103×C59C23semidirect
415. C2×#416D59semidirect
418. C2×C59#3311semidirect
430. C23×C8C2×D59semidirect
452. C2×#117C2×D59semidirect
470. #416C2×D59semidirect
473. C2×#103C2×D59semidirect
474. C2×#103C2×D59semidirect
484. C59C2×#3311semidirect
520. C22×C8C22×D59semidirect
549. #117C22×D59semidirect
582. #103C22×D59semidirect
583. #103C22×D59semidirect
811. C2#21436128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381202
C2×#168380402
#214361282
C2×#168377632
C2×#168377412
C2×#168377262
C2×#168376902
C2×#168376592
C2×#168376312
C2×#168376272
C2×#168375642
C2×#168375542
C2×#168374992
C2×#168374732
C2×#168374052
C2×C59×#4162
C2×#331159