Finite Group Databasebeta

← C2×#21436175 #29465213

Subgroups — C2×#21436175 #29465213

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×#16838107C211yesmaximal, characteristic, complemented
2C2×#16838043C211yesmaximal, characteristic
3#21436175C2116yesmaximal, direct product factor
4C2×#16837763C211yesmaximal, characteristic, complemented
5C2×#16837717C211yesmaximal, characteristic, complemented
6C2×#16837681C211yesmaximal, characteristic, complemented
7C2×#16837649C211yesmaximal, characteristic, complemented
8C2×#16837641C211yesmaximal, characteristic, complemented
9C2×#16837627C211yesmaximal, characteristic, complemented
10C2×#16837567C211yesmaximal, characteristic, complemented
11C2×#16837555C211yesmaximal, characteristic, complemented
12C2×#16837501C211yesmaximal, characteristic, complemented
13C2×#16837470C211yesmaximal, characteristic, complemented
14C2×#16837402C211yesmaximal, characteristic, complemented
15C22×#14273647C211yesmaximal, characteristic, complemented
16C2×C59×#484C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C23×D236C2211yescharacteristic
19C22×#11745672C2211yescharacteristic, complemented
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22C22×#11745659C2211yescharacteristic, complemented
23C23×C59⋊C8C2211yescharacteristic
24#16838107—24no—
25#16838107C2218yescomplemented
26#16838043—24no—
27#16838043C2218yes—
28C2×#14273726C2211yescharacteristic, complemented
29C2×#14273717—21no—
30C2×#14273716C2211yescharacteristic
31C2×#14273712—21no—
32C2×#14273707C2211yescharacteristic, complemented
33C2×#14273706—21no—
34C2×#14273706C2211yescharacteristic
35C2×#14273705—21no—
36C2×#14273702—21no—
37C2×#14273702C2211yescharacteristic
38C2×#14273697—21no—
39C2×#14273692C2211yescharacteristic, complemented
40C2×#14273689C2211yescharacteristic
41C2×C4×C22⋊D59—21no—
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×C4⋊C4×D59C2211yescharacteristic, complemented
44C2×C22⋊C4×D59—21no—
45#16837763C2218yescomplemented
46#16837717C2218yescomplemented
47#16837681C2218yescomplemented
48#16837649C2218yescomplemented
49#16837641C2218yescomplemented
50#16837627C2218yescomplemented
51#16837567C2218yescomplemented
52#16837555C2218yescomplemented
53#16837501C2218yescomplemented
54#16837470C2218yescomplemented
55C2×#14273660C2211yescharacteristic, complemented
56C2×Dic59⋊C8C2211yescharacteristic, complemented
57#16837402C2218yescomplemented
58C2×#14273651C2211yescharacteristic, complemented
59C2×#14273650C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×#14273647C2218yescomplemented
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×#14273637C2211yescharacteristic, complemented
69C2×C22⋊Q8×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#484C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#107×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#103×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic
77C24×D59—21no—
78C2×#11745689—22no—
79C2×#11745689—24no—
80C2×#11745689—42no—
81C2×#11745689C2314yes—
82C22×Dic118—21no—
83C22×Dic118C2311yescharacteristic
84C22×D236—24no—
85C22×D236—21no—
86C22×D236—21no—
87C22×D236—22no—
88C22×D236—21no—
89C22×D236—42no—
90C22×D236C2311yescharacteristic
91C22×D236C2314yes—
92C22×D236C2311yescharacteristic
93C22×C22⋊D59D411yescharacteristic
94C22×C4×D59—21no—
95C22×C4×D59—21no—
96C22×C4×D59—21no—
97C22×C4×D59C2311yescharacteristic
98C2×#11745672—42no—
99C2×#11745672C2314yescomplemented
100C2×#11745660—24no—
101C2×#11745660—42no—
102C2×#11745660C2314yes—
103C2×#11745660C2314yes—
104C2×#11745659—42no—
105C2×#11745659C2314yescomplemented
106C22×C59⋊C8—42no—
107C22×C59⋊C8C2311yescharacteristic
108C22×C59⋊C8C2311yescharacteristic
109C22×C59⋊C8C2314yes—
110#14273726—22no—
111#14273726C2314yescomplemented
112#14273717—28no—
113#14273716—22no—
114#14273716C2314yes—
115#14273712—28no—
116#14273707—22no—
117#14273707C2314yescomplemented
118#14273706—22no—
119#14273706—28no—
120#14273706C2314yes—
121#14273705—28no—
122#14273702—22no—
123#14273702—28no—
124#14273702C2314yes—
125#14273697—28no—
126#14273692—22no—
127#14273692C2314yescomplemented
128#14273689—22no—
129#14273689C2314yes—
130C4×C22⋊D59—28no—
131C4×C22⋊D59D414yes—
132C4×C22⋊D59C2314yes—
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59C2311yescharacteristic
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4D411yescharacteristic
140C4⋊C4×D59—22no—
141C4⋊C4×D59C2314yescomplemented
142C2×C22⋊Dic59—21no—
143C2×C22⋊Dic59D411yescharacteristic
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4D411yescharacteristic
150C22⋊C4×D59—28no—
151C2×C4×Dic59—21no—
152C2×C4×Dic59C2311yescharacteristic
153#14273660C2314yescomplemented
154Dic59⋊C8C2314yescomplemented
155#14273651C2314yescomplemented
156#14273650C2314yescomplemented
157#14273649C2314yes—
158#14273649C2314yes—
159#14273647C2314yes—
160#14273647C2314yes—
161#14273647C2314yes—
162#14273647C2314yes—
163(C2×D59)⋊C8C2314yescomplemented
164#14273637C2314yescomplemented
165C22×Q8×C59C2311yescharacteristic
166C23×C4×C59—21no—
167C23×C4×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C22⋊Q8×C59—22no—
171C22⋊Q8×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—22no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2314yes—
179C2×C22⋊C4×C59—21no—
180#107×C59C2314yescomplemented
181#107×C59C2314yescomplemented
182#103×C59C2314yescomplemented
183#103×C59C2314yescomplemented
184C22⋊C8×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C23×D59—21no—
187C23×D59—21no—
188C23×D59—24no—
189C23×D59—44no—
190C23×D59—44no—
191C23×D59—82no—
192C23×D59C2×D411yescharacteristic
193C2×Q8×C59—21no—
194C2×Q8×C59—22no—
195C2×Q8×C59—22no—
196C2×Q8×C59C2412yes—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—24no—
204C22×C4×C59—82no—
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D412yes—
207C22×C4×C59C2412yes—
208C22×C4×C59C2411yescharacteristic
209C2×C22⋊D59—24no—
210C2×C22⋊D59C2×D414yes—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216#11745689—28no—
217#11745689—44no—
218#11745689—48no—
219C2×D236—21no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—22no—
223C2×D236—28no—
224C2×D236—24no—
225C2×D236—24no—
226C2×D236—21no—
227C2×D236—24no—
228C2×D236—44no—
229C2×D236—48no—
230C2×D236—44no—
231C2×D236—44no—
232C2×D236—82no—
233C2×D236#4114yes—
234C2×D236C2412yes—
235C2×D236C2412yes—
236C2×C4×D59—22no—
237C2×C4×D59—22no—
238C2×C4×D59—24no—
239C2×C4×D59—24no—
240C2×C4×D59—24no—
241C2×C4×D59—44no—
242C2×C4×D59—82no—
243C2×C4×D59—82no—
244C2×C4×D59C2×D412yes—
245C2×C4×D59C2412yes—
246C2×Dic118—22no—
247C2×Dic118—22no—
248C2×Dic118—21no—
249C2×Dic118—24no—
250C2×Dic118—82no—
251C2×Dic118C2412yes—
252C2×C8×C59—22no—
253C2×C8×C59—22no—
254C2×C8×C59C2412yes—
255C2×C8×C59C2412yes—
256C4⋊C4×C59—21no—
257C4⋊C4×C59—24no—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—24no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59C2412yes—
262C4⋊C4×C59C2412yes—
263C4⋊C4×C59C2412yes—
264C22⋊C4×C59—24no—
265C22⋊Dic59—24no—
266C22⋊Dic59C2×D414yes—
267#11745672—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)⋊C4C2×D414yes—
274C4⋊Dic59—21no—
275C4⋊Dic59—24no—
276C4⋊Dic59C2412yes—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279Dic59⋊C4—24no—
280Dic59⋊C4—24no—
281Dic59⋊C4C2×D414yes—
282C4×Dic59—24no—
283C4×Dic59C2×D412yes—
284C4×Dic59C2412yes—
285C2×C59⋊C8—22no—
286C2×C59⋊C8—22no—
287C2×C59⋊C8—44no—
288C2×C59⋊C8C2412yes—
289C2×C59⋊C8C2412yes—
290#11745660—28no—
291#11745660—44no—
292#11745659—44no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59#13714yes—
296C23×C59C22×D412yes—
297C23×C59C22×D411yescharacteristic
298C22×D59—22no—
299C22×D59—24no—
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—42no—
310C22×D59—42no—
311C22×D59—84no—
312C22×D59—816no—
313C22×D59C22×D412yes—
314Q8×C59—22no—
315Q8×C59—22no—
316Q8×C59—42no—
317C2×C4×C59—22no—
318C2×C4×C59—24no—
319C2×C4×C59—22no—
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—42no—
329C2×C4×C59—84no—
330C2×C4×C59C22×D412yes—
331C2×C4×C59C22×D411yescharacteristic
332C2×C4×C59C2×#4112yes—
333C2×C4×C59H(5,𝔽2)12yes—
334C2×C4×C59C2511yescharacteristic
335C22⋊D59—28no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—42no—
342C2×Dic59—42no—
343C2×Dic59C22×D412yes—
344C2×Dic59C22×D412yes—
345C2×Dic59C22×D412yes—
346D236—24no—
347D236—22no—
348D236—22no—
349D236—22no—
350D236—48no—
351D236—48no—
352D236—42no—
353D236—84no—
354D236C2×#4114yes—
355C4×D59—24no—
356C4×D59—22no—
357C4×D59—22no—
358C4×D59—48no—
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—22no—
371C22×C59—28no—
372C22×C59—22no—
373C22×C59#54612yes—
374C22×C59C2×#13714yes—
375C22×C59C2×#13712yes—
376C22×C59#57612yes—
377C22×C59C23×D411yescharacteristic
378C2×D59—22no—
379C2×D59—24no—
380C2×D59—22no—
381C2×D59—22no—
382C2×D59—44no—
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—42no—
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—22no—
402Dic59—42no—
403Dic59—42no—
404C2×#554—591no—
405C2×#546—591no—
406#3314—5916no—
407C2×#489—591no—
408C2×#484D5911yescharacteristic, complemented
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×#435—591no—
418C2×#417—591no—
419C22×#102—591no—
420C2×C59—24no—
421C2×C59#331414yescomplemented
422C2×C59C2×#54611yescharacteristic
423C2×C59C22×#13711yescharacteristic
424C2×C59C2×#57611yescharacteristic
425D59—42no—
426D59—44no—
427D59—82no—
428C22×#41—591no—
429C23×D4—591no—
430C22×Q16—591no—
431C22×SD16—591no—
432C22×SD16—591no—
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—1181no—
446C2×C22⋊Q8—1181no—
447C2×C22⋊Q8C2×D5911yescharacteristic
448C2×#121—591no—
449C2×#121—1181no—
450C2×#120—1181no—
451C2×C4×Q8—591no—
452C2×C4×D4—591no—
453C2×C4×D4—591no—
454C2×C4×D4—1181no—
455C22×C4⋊C4—591no—
456C22×C4⋊C4C2×D5911yescharacteristic
457C22×C22⋊C4—1181no—
458#489—598no—
459#484C2×D5918yescomplemented
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#435—598no—
469C2×#107—591no—
470C2×#107C2×D5911yescharacteristic, complemented
471C2×#107C2×D5911yescharacteristic, complemented
472C2×C4⋊C8—591no—
473#417—598no—
474C2×#103—591no—
475C2×#103—591no—
476C2×#103C2×D5911yescharacteristic, complemented
477C2×#103C2×D5911yescharacteristic, complemented
478C2×#102—591no—
479C2×#102—591no—
480C2×#102—591no—
481C2×#102—591no—
482C2×#102—591no—
483C2×#102—591no—
484C2×#102—598no—
485C2×C22⋊C8—591no—
486C2×C22⋊C8C2×D5911yescharacteristic
487C2×#97—591no—
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—591no—
498C22×D4—591no—
499C22×D4—591no—
500C22×D4—594no—
501C22×D4—1184no—
502C22×D4—1181no—
503C22×D4—1181no—
504C22×D4—1181no—
505C22×D4—1182no—
506C22×D4—2362no—
507C23×C4—21no—
508C23×C4—591no—
509C23×C4—1181no—
510C23×C4—1181no—
511C23×C4—1181no—
512C23×C4C22×D5911yescharacteristic
513C2×Q16—594no—
514C2×Q16—2362no—
515C2×SD16—594no—
516C2×SD16—594no—
517C2×SD16—1184no—
518C2×SD16—2362no—
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—22no—
534C22⋊Q8—594no—
535C22⋊Q8—594no—
536C22⋊Q8—1188no—
537C22⋊Q8—1188no—
538C22⋊Q8—1182no—
539C22⋊Q8—1182no—
540C22⋊Q8C22×D5914yes—
541#121—594no—
542#121—1188no—
543#121—1182no—
544#120—1188no—
545C4×Q8—594no—
546C4×Q8—1182no—
547C4×D4—594no—
548C4×D4—594no—
549C4×D4—594no—
550C4×D4—1182no—
551C4×D4—1188no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—591no—
556C2×C4⋊C4—591no—
557C2×C4⋊C4—594no—
558C2×C4⋊C4—1182no—
559C2×C4⋊C4—1181no—
560C2×C4⋊C4—1181no—
561C2×C4⋊C4—1181no—
562C2×C4⋊C4—1181no—
563C2×C4⋊C4—1181no—
564C2×C4⋊C4C22×D5911yescharacteristic
565C2×C4⋊C4C22×D5911yescharacteristic
566C2×C4⋊C4C22×D5914yes—
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—591no—
579C2×C42—1181no—
580#107—594no—
581#107C22×D5914yescomplemented
582#107C22×D5914yescomplemented
583C4⋊C8—594no—
584#103—594no—
585#103—594no—
586#103C22×D5914yescomplemented
587#103C22×D5914yescomplemented
588#102—594no—
589#102—594no—
590#102—594no—
591#102—594no—
592#102—594no—
593#102—594no—
594C22⋊C8—594no—
595C22⋊C8C22×D5914yes—
596#97—594no—
597C24—591no—
598C24—1181no—
599C24—1184no—
600C24—1181no—
601C24—4722no—
602C24—2364no—
603C24—2364no—
604C24D4×D5911yescharacteristic
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—594no—
619C2×D4—594no—
620C2×D4—592no—
621C2×D4—592no—
622C2×D4—1188no—
623C2×D4—1184no—
624C2×D4—1184no—
625C2×D4—1184no—
626C2×D4—1181no—
627C2×D4—1184no—
628C2×D4—1181no—
629C2×D4—1182no—
630C2×D4—1182no—
631C2×D4—1182no—
632C2×D4—4722no—
633C2×D4—2364no—
634C2×D4—2368no—
635C2×D4—2364no—
636C2×D4—2364no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—82no—
645C22×C4—591no—
646C22×C4—591no—
647C22×C4—591no—
648C22×C4—592no—
649C22×C4—592no—
650C22×C4—1184no—
651C22×C4—1184no—
652C22×C4—1184no—
653C22×C4—1182no—
654C22×C4—1182no—
655C22×C4—1181no—
656C22×C4—1181no—
657C22×C4—4722no—
658C22×C4—4722no—
659C22×C4—2364no—
660C22×C4D4×D5912yes—
661C22×C4D4×D5911yescharacteristic
662C22×C4C23×D5912yes—
663C22×C4C23×D5911yescharacteristic
664Q16—2364no—
665SD16—1188no—
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—21no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—594no—
683C4⋊C4—592no—
684C4⋊C4—1184no—
685C4⋊C4—1184no—
686C4⋊C4—1184no—
687C4⋊C4—1184no—
688C4⋊C4—1181no—
689C4⋊C4—1184no—
690C4⋊C4C23×D5912yes—
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—592no—
703C42—592no—
704C42—1184no—
705C23—22no—
706C23—22no—
707C23—592no—
708C23—1182no—
709C23—1182no—
710C23—1182no—
711C23—1182no—
712C23—1184no—
713C23—1182no—
714C23—47216no—
715C23—4724no—
716C23—2368no—
717C23—2368no—
718C23—2362no—
719C23—2362no—
720C23—2362no—
721C23—2362no—
722C23—2362no—
723C23#1427375914yes—
724C23C2×D4×D5912yes—
725C23C2×D4×D5911yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—1182no—
730Q8—1182no—
731Q8—4724no—
732Q8—2362no—
733D4—594no—
734D4—1188no—
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—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—84no—
756C2×C4—592no—
757C2×C4—592no—
758C2×C4—592no—
759C2×C4—1182no—
760C2×C4—1182no—
761C2×C4—1182no—
762C2×C4—1182no—
763C2×C4—1182no—
764C2×C4—1184no—
765C2×C4—1182no—
766C2×C4—1182no—
767C2×C4—4724no—
768C2×C4—4724no—
769C2×C4—2368no—
770C2×C4—2362no—
771C2×C4—2362no—
772C2×C4C2×D4×D5912yes—
773C2×C4C2×D4×D5911yescharacteristic
774C2×C4#41×D5912yes—
775C2×C4#1427377312yes—
776C2×C4C24×D5911yescharacteristic
777C8—22no—
778C8—22no—
779C8—1182no—
780C8—1182no—
781C22—28no—
782C22—22no—
783C22—22no—
784C22—1182no—
785C22—1184no—
786C22—1182no—
787C22—1182no—
788C22—47216no—
789C22—4724no—
790C22—2362no—
791C22—2362no—
792C22—2362no—
793C22—2364no—
794C22—2368no—
795C22—2362no—
796C22—2362no—
797C22#1683804412yes—
798C22C2×#1427375914yes—
799C22C2×#1427375912yes—
800C22#1683820612yes—
801C22C22×D4×D5911yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—1182no—
808C4—1182no—
809C4—1182no—
810C4—2362no—
811C4—2362no—
812C4#1683804412yes—
813C4C2×#41×D5911yescharacteristic
814C4C2×#1427377311yescharacteristic
815C2—24no—
816C2—4722no—
817C2—2362no—
818C2—2364no—
819C2#2143617514yesdirect product factor
820C2C2×#1683804411yescharacteristic
821C2C22×#1427375911yescharacteristic
822C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#484C2
socleC23×C59C22×D4
prime radicalC2×#16838043C2
hypercenterC2×#484D59
hypocenterC59C2×#3314
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#16838107C2semidirect
3. #21436175C2direct (N × H)
4. C2×#16837763C2semidirect
5. C2×#16837717C2semidirect
6. C2×#16837681C2semidirect
7. C2×#16837649C2semidirect
8. C2×#16837641C2semidirect
9. C2×#16837627C2semidirect
10. C2×#16837567C2semidirect
11. C2×#16837555C2semidirect
12. C2×#16837501C2semidirect
13. C2×#16837470C2semidirect
14. C2×#16837402C2semidirect
15. C22×#14273647C2semidirect
16. C2×C59×#484C2semidirect
19. C22×#11745672C22semidirect
22. C22×#11745659C22semidirect
25. #16838107C22semidirect
28. C2×#14273726C22semidirect
32. C2×#14273707C22semidirect
39. C2×#14273692C22semidirect
43. C2×C4⋊C4×D59C22semidirect
45. #16837763C22semidirect
46. #16837717C22semidirect
47. #16837681C22semidirect
48. #16837649C22semidirect
49. #16837641C22semidirect
50. #16837627C22semidirect
51. #16837567C22semidirect
52. #16837555C22semidirect
53. #16837501C22semidirect
54. #16837470C22semidirect
55. C2×#14273660C22semidirect
56. C2×Dic59⋊C8C22semidirect
57. #16837402C22semidirect
58. C2×#14273651C22semidirect
59. C2×#14273650C22semidirect
66. C2×#14273647C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×#14273637C22semidirect
71. C59×#484C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#107×C59C22semidirect
74. C2×#103×C59C22semidirect
75. C2×#103×C59C22semidirect
99. C2×#11745672C23semidirect
105. C2×#11745659C23semidirect
111. #14273726C23semidirect
117. #14273707C23semidirect
127. #14273692C23semidirect
141. C4⋊C4×D59C23semidirect
153. #14273660C23semidirect
154. Dic59⋊C8C23semidirect
155. #14273651C23semidirect
156. #14273650C23semidirect
163. (C2×D59)⋊C8C23semidirect
164. #14273637C23semidirect
180. #107×C59C23semidirect
181. #107×C59C23semidirect
182. #103×C59C23semidirect
183. #103×C59C23semidirect
408. C2×#484D59semidirect
421. C2×C59#3314semidirect
459. #484C2×D59semidirect
470. C2×#107C2×D59semidirect
471. C2×#107C2×D59semidirect
476. C2×#103C2×D59semidirect
477. C2×#103C2×D59semidirect
488. C59C2×#3314semidirect
581. #107C22×D59semidirect
582. #107C22×D59semidirect
586. #103C22×D59semidirect
587. #103C22×D59semidirect
819. C2#21436175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381072
C2×#168380432
#214361752
C2×#168377632
C2×#168377172
C2×#168376812
C2×#168376492
C2×#168376412
C2×#168376272
C2×#168375672
C2×#168375552
C2×#168375012
C2×#168374702
C2×#168374022
C22×#142736472
C2×C59×#4842
C2×#331459