Finite Group Databasebeta

← C2×#21436178 #29465216

Subgroups — C2×#21436178 #29465216

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×#16838040C211yesmaximal, characteristic
3#21436178C2116yesmaximal, direct product factor
4C2×#16837763C211yesmaximal, characteristic, complemented
5C2×#16837736C211yesmaximal, characteristic, complemented
6C2×#16837715C211yesmaximal, characteristic, complemented
7C2×#16837680C211yesmaximal, characteristic, complemented
8C2×#16837648C211yesmaximal, characteristic, complemented
9C2×#16837642C211yesmaximal, characteristic, complemented
10C2×#16837627C211yesmaximal, characteristic, complemented
11C2×#16837564C211yesmaximal, characteristic, complemented
12C2×#16837554C211yesmaximal, characteristic, complemented
13C2×#16837499C211yesmaximal, characteristic, complemented
14C2×#16837471C211yesmaximal, characteristic, complemented
15C2×#102×D59C211yesmaximal, characteristic, complemented
16C2×C59×#417C211yesmaximal, characteristic, complemented
17C22×D4×D59C2211yescharacteristic
18C22×#11745672C2211yescharacteristic, complemented
19C22×#11745660C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×C8×D59C2211yescharacteristic
22#16838107—24no—
23#16838107C2218yescomplemented
24#16838040—24no—
25#16838040C2218yes—
26C2×#14273726C2211yescharacteristic, complemented
27C2×#14273717—21no—
28C2×#14273716C2211yescharacteristic
29C2×#14273710—21no—
30C2×#14273707C2211yescharacteristic
31C2×#14273706—21no—
32C2×#14273706C2211yescharacteristic, complemented
33C2×#14273705—21no—
34C2×#14273703C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36C2×#14273699—21no—
37C2×#14273695—21no—
38C2×#14273692C2211yescharacteristic, complemented
39C2×D4×Dic59C2211yescharacteristic
40C2×C4×C22⋊D59—21no—
41C2×C4×C22⋊D59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43C22×(C2×D59)⋊C4—21no—
44#16837763C2218yescomplemented
45#16837736C2218yescomplemented
46#16837715C2218yescomplemented
47#16837680C2218yescomplemented
48#16837648C2218yescomplemented
49#16837642C2218yescomplemented
50#16837627C2218yescomplemented
51#16837564C2218yescomplemented
52#16837554C2218yescomplemented
53#16837499C2218yescomplemented
54#16837471C2218yescomplemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273660C2211yescharacteristic, complemented
58C2×Dic59⋊C8C2211yescharacteristic, complemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273651C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic
62C2×#14273648C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65#102×D59C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic, complemented
69C22×#41×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic, complemented
71C22×C4⋊C4×C59C2211yescharacteristic, complemented
72C59×#417C2218yescomplemented
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×D59—21no—
90C22×C4×D59C2311yescharacteristic
91C2×#11745672—42no—
92C2×#11745672C2314yescomplemented
93C2×#11745660—42no—
94C2×#11745660C2314yes—
95C2×#11745670—24no—
96C2×#11745670C2314yes—
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99C2×C8×D59—42no—
100C2×C8×D59C2314yes—
101#14273726—22no—
102#14273726C2314yescomplemented
103#14273717—28no—
104#14273716—22no—
105#14273716C2314yes—
106#14273710—28no—
107#14273707—22no—
108#14273707C2314yes—
109#14273706—22no—
110#14273706—28no—
111#14273706C2314yescomplemented
112#14273705—28no—
113#14273703—22no—
114#14273703C2314yes—
115#14273701—22no—
116#14273701C2314yes—
117#14273699—28no—
118#14273695—28no—
119#14273692—22no—
120#14273692C2314yescomplemented
121D4×Dic59—22no—
122D4×Dic59C2314yes—
123C4×C22⋊D59—28no—
124C4×C22⋊D59D414yes—
125C4×C22⋊D59C2314yes—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4D411yescharacteristic
135C4⋊C4×D59—22no—
136C4⋊C4×D59C2314yes—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59D411yescharacteristic
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—28no—
146C2×(C2×D59)⋊C4D411yescharacteristic
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273661C2314yescomplemented
150#14273660C2314yescomplemented
151#14273660C2314yescomplemented
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×C59—21no—
171C23×C4×C59C2311yescharacteristic
172C2×M16×C59—42no—
173C2×M16×C59C2314yescomplemented
174C22×C8×C59C2311yescharacteristic
175C22×C8×C59C2311yescharacteristic
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59—22no—
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C4⋊C4×C59C2314yescomplemented
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—24no—
213C22×C4×C59—44no—
214C22×C4×C59—82no—
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D412yes—
217C22×C4×C59C2412yes—
218C22×C4×C59C2411yescharacteristic
219C2×C22⋊D59—24no—
220C2×C22⋊D59—24no—
221C2×C22⋊D59—24no—
222C2×C22⋊D59—44no—
223C2×C22⋊D59—82no—
224C2×C22⋊D59C2×D414yes—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—24no—
229C22×Dic59—82no—
230C22×Dic59C2×D411yescharacteristic
231C22×Dic59C2×D411yescharacteristic
232C22×Dic59C2×D411yescharacteristic
233D4×D59—28no—
234D4×D59—44no—
235D4×D59—48no—
236C2×D236—22no—
237C2×D236—22no—
238C2×D236—21no—
239C2×D236C2412yes—
240C2×C4×D59—22no—
241C2×C4×D59—22no—
242C2×C4×D59—24no—
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—
252M16×C59—44no—
253C2×C8×C59—22no—
254C2×C8×C59—22no—
255C2×C8×C59C2412yes—
256C2×C8×C59C2412yes—
257C4⋊C4×C59—21no—
258C4⋊C4×C59—21no—
259C4⋊C4×C59—24no—
260C4⋊C4×C59C2412yes—
261C4⋊C4×C59C2412yes—
262C22⋊Dic59—24no—
263C22⋊Dic59—24no—
264C22⋊Dic59C2×D414yes—
265#11745672—44no—
266#11745670—28no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4—24no—
272(C2×D59)⋊C4C2×D414yes—
273C4⋊Dic59—21no—
274C4⋊Dic59—21no—
275C4⋊Dic59—24no—
276C4⋊Dic59C2412yes—
277C4⋊Dic59C2412yes—
278Dic59⋊C4—24no—
279Dic59⋊C4—24no—
280Dic59⋊C4—24no—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283Dic59⋊C4C2×D414yes—
284C4×Dic59—24no—
285C4×Dic59C2×D412yes—
286C4×Dic59C2412yes—
287C2×C59⋊C8—22no—
288C2×C59⋊C8—22no—
289C2×C59⋊C8C2412yes—
290C2×C59⋊C8C2412yes—
291#11745660—44no—
292C8×D59—44no—
293C23×C59—24no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—42no—
299C23×C59—42no—
300C23×C59C22×D412yes—
301C23×C59C22×D411yescharacteristic
302C22×D59—22no—
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—48no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—42no—
309C22×D59—48no—
310C22×D59—84no—
311C22×D59—816no—
312C22×D59#13714yes—
313C22×D59C22×D412yes—
314Q8×C59—22no—
315Q8×C59—22no—
316Q8×C59—42no—
317D4×C59—24no—
318D4×C59—22no—
319D4×C59—48no—
320D4×C59C2×#4114yes—
321C2×C4×C59—22no—
322C2×C4×C59—24no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—48no—
329C2×C4×C59—42no—
330C2×C4×C59—42no—
331C2×C4×C59—42no—
332C2×C4×C59—84no—
333C2×C4×C59C22×D412yes—
334C2×C4×C59C22×D411yescharacteristic
335C2×C4×C59C2×#4112yes—
336C2×C4×C59H(5,𝔽2)12yes—
337C2×C4×C59C2511yescharacteristic
338C22⋊D59—28no—
339C22⋊D59—48no—
340C22⋊D59—84no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—22no—
345C2×Dic59—22no—
346C2×Dic59—22no—
347C2×Dic59—42no—
348C2×Dic59—42no—
349C2×Dic59—42no—
350C2×Dic59—84no—
351C2×Dic59C22×D412yes—
352C2×Dic59C22×D412yes—
353C2×Dic59C22×D412yes—
354D236—22no—
355D236—22no—
356D236—42no—
357C4×D59—24no—
358C4×D59—22no—
359C4×D59—22no—
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—22no—
372C22×C59—22no—
373C22×C59—22no—
374C22×C59—48no—
375C22×C59—44no—
376C22×C59—42no—
377C22×C59—42no—
378C22×C59#54612yes—
379C22×C59C2×#13712yes—
380C22×C59#57612yes—
381C22×C59C23×D411yescharacteristic
382C2×D59—22no—
383C2×D59—28no—
384C2×D59—22no—
385C2×D59—42no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—816no—
389C2×D59—84no—
390C2×D59C2×#13714yes—
391C4×C59—22no—
392C4×C59—42no—
393C4×C59—42no—
394C4×C59—42no—
395C4×C59#54612yes—
396C4×C59C22×#4111yescharacteristic
397C4×C59C2×H(5,𝔽2)11yescharacteristic
398Dic59—22no—
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×#440—591no—
417C2×#435—591no—
418C2×#417D5911yescharacteristic, complemented
419C22×#102—591no—
420C2×C59—44no—
421C2×C59—42no—
422C2×C59#331414yescomplemented
423C2×C59C2×#54611yescharacteristic
424C2×C59C22×#13711yescharacteristic
425C2×C59C2×#57611yescharacteristic
426D59—24no—
427D59—82no—
428C22×#41C2×D5911yescharacteristic
429C23×D4—591no—
430C22×Q16—591no—
431C22×SD16—591no—
432C22×SD16—591no—
433C22×M16C2×D5911yescharacteristic, complemented
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×Q8—591no—
452C2×C4×D4—591no—
453C2×C4×D4—591no—
454C2×C4×D4—1181no—
455C22×C4⋊C4—591no—
456C22×C4⋊C4C2×D5911yescharacteristic, complemented
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#435—598no—
469C2×#107—591no—
470C2×#107—591no—
471C2×#107—591no—
472C2×C4⋊C8—591no—
473#417C2×D5918yescomplemented
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—598no—
483C2×#102C2×D5911yescharacteristic
484C2×#102C2×D5911yescharacteristic
485C2×C22⋊C8—591no—
486C2×C22⋊C8—591no—
487C2×#97—591no—
488C59C2×#331411yescharacteristic, complemented, Sylow
489C25—1181no—
490C2×#41—22no—
491C2×#41—24no—
492C2×#41—42no—
493C2×#41C22×D5914yes—
494C22×Q8—591no—
495C22×Q8—1181no—
496C22×Q8C22×D5911yescharacteristic
497C22×D4—21no—
498C22×D4—591no—
499C22×D4—594no—
500C22×D4—591no—
501C22×D4—1182no—
502C22×D4—1181no—
503C22×D4—1184no—
504C22×D4—1181no—
505C22×D4—2362no—
506C22×D4C22×D5911yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—591no—
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—42no—
520C2×M16C22×D5914yescomplemented
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—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—591no—
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⋊C4—1181no—
565C2×C4⋊C4C22×D5911yescharacteristic
566C2×C4⋊C4C22×D5911yescharacteristic
567C2×C4⋊C4C22×D5914yescomplemented
568C2×C22⋊C4—591no—
569C2×C22⋊C4—591no—
570C2×C22⋊C4—1188no—
571C2×C22⋊C4—1181no—
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#107—594no—
582#107—594no—
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#102C22×D5914yes—
593#102C22×D5914yes—
594C22⋊C8—594no—
595C22⋊C8—594no—
596#97—594no—
597C24—21no—
598C24—591no—
599C24—1184no—
600C24—1181no—
601C24—4722no—
602C24—2364no—
603C24—2364no—
604C24D4×D5911yescharacteristic
605#41—28no—
606#41—44no—
607#41—48no—
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—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—594no—
623C2×D4—592no—
624C2×D4—1184no—
625C2×D4—1184no—
626C2×D4—1188no—
627C2×D4—1184no—
628C2×D4—1181no—
629C2×D4—1182no—
630C2×D4—1182no—
631C2×D4—4722no—
632C2×D4—2364no—
633C2×D4—2368no—
634C2×D4—2364no—
635C2×D4#1174568514yes—
636C2×D4C23×D5912yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4—591no—
647C22×C4—591no—
648C22×C4—591no—
649C22×C4—592no—
650C22×C4—592no—
651C22×C4—1184no—
652C22×C4—1184no—
653C22×C4—1182no—
654C22×C4—1182no—
655C22×C4—1181no—
656C22×C4—1181no—
657C22×C4—1181no—
658C22×C4—4722no—
659C22×C4—4722no—
660C22×C4D4×D5912yes—
661C22×C4D4×D5911yescharacteristic
662C22×C4C23×D5912yes—
663C22×C4C23×D5911yescharacteristic
664Q16—2364no—
665SD16—1188no—
666SD16—2364no—
667M16—44no—
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—21no—
679C4⋊C4—24no—
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—594no—
694C22⋊C4—594no—
695C22⋊C4—1184no—
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—22no—
708C23—22no—
709C23—24no—
710C23—42no—
711C23—42no—
712C23—594no—
713C23—592no—
714C23—1182no—
715C23—1182no—
716C23—1182no—
717C23—47216no—
718C23—4724no—
719C23—2368no—
720C23—2368no—
721C23—2362no—
722C23—2362no—
723C23—2362no—
724C23C2×D4×D5912yes—
725C23C2×D4×D5911yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—1182no—
730Q8—1182no—
731Q8—4724no—
732Q8—2362no—
733D4—22no—
734D4—24no—
735D4—48no—
736D4—1188no—
737D4—1182no—
738D4—1182no—
739D4—4724no—
740D4—2368no—
741D4—2362no—
742D4C2×#1174568514yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—84no—
755C2×C4—592no—
756C2×C4—592no—
757C2×C4—592no—
758C2×C4—1182no—
759C2×C4—1182no—
760C2×C4—1182no—
761C2×C4—1182no—
762C2×C4—1182no—
763C2×C4—1184no—
764C2×C4—1182no—
765C2×C4—1182no—
766C2×C4—1182no—
767C2×C4—4724no—
768C2×C4—4724no—
769C2×C4—2362no—
770C2×C4—2362no—
771C2×C4—2362no—
772C2×C4C2×D4×D5912yes—
773C2×C4C2×D4×D5911yescharacteristic
774C2×C4C2×#1174568512yes—
775C2×C4#1427377212yes—
776C2×C4C24×D5911yescharacteristic
777C8—22no—
778C8—22no—
779C8—1182no—
780C8—1182no—
781C22—22no—
782C22—24no—
783C22—22no—
784C22—22no—
785C22—44no—
786C22—48no—
787C22—42no—
788C22—42no—
789C22—594no—
790C22—1188no—
791C22—1182no—
792C22—1182no—
793C22—47216no—
794C22—4724no—
795C22—2362no—
796C22—2362no—
797C22—2362no—
798C22#1683804212yes—
799C22#137×D5912yes—
800C22#1683820612yes—
801C22C22×D4×D5911yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—1182no—
807C4—1182no—
808C4—1182no—
809C4—2362no—
810C4—2362no—
811C4—2362no—
812C4#1683804212yes—
813C4C22×#1174568511yescharacteristic
814C4C2×#1427377211yescharacteristic
815C2—42no—
816C2—44no—
817C2—1184no—
818C2—4722no—
819C2#2143617814yesdirect product factor
820C2C2×#1683804211yescharacteristic
821C2C2×#137×D5911yescharacteristic
822C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#417C2
socleC23×C59C22×D4
prime radicalC2×#16838040C2
hypercenterC2×#417D59
hypocenterC59C2×#3314
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16838107C2semidirect
3. #21436178C2direct (N × H)
4. C2×#16837763C2semidirect
5. C2×#16837736C2semidirect
6. C2×#16837715C2semidirect
7. C2×#16837680C2semidirect
8. C2×#16837648C2semidirect
9. C2×#16837642C2semidirect
10. C2×#16837627C2semidirect
11. C2×#16837564C2semidirect
12. C2×#16837554C2semidirect
13. C2×#16837499C2semidirect
14. C2×#16837471C2semidirect
15. C2×#102×D59C2semidirect
16. C2×C59×#417C2semidirect
18. C22×#11745672C22semidirect
23. #16838107C22semidirect
26. C2×#14273726C22semidirect
32. C2×#14273706C22semidirect
38. C2×#14273692C22semidirect
44. #16837763C22semidirect
45. #16837736C22semidirect
46. #16837715C22semidirect
47. #16837680C22semidirect
48. #16837648C22semidirect
49. #16837642C22semidirect
50. #16837627C22semidirect
51. #16837564C22semidirect
52. #16837554C22semidirect
53. #16837499C22semidirect
54. #16837471C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273660C22semidirect
58. C2×Dic59⋊C8C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273651C22semidirect
65. #102×D59C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
68. C2×#14273637C22semidirect
70. C22×M16×C59C22semidirect
71. C22×C4⋊C4×C59C22semidirect
72. C59×#417C22semidirect
73. C2×#103×C59C22semidirect
74. C2×#103×C59C22semidirect
92. C2×#11745672C23semidirect
102. #14273726C23semidirect
111. #14273706C23semidirect
120. #14273692C23semidirect
149. #14273661C23semidirect
150. #14273660C23semidirect
151. #14273660C23semidirect
152. Dic59⋊C8C23semidirect
153. #14273652C23semidirect
154. #14273651C23semidirect
159. C22⋊(C59⋊C8)C23semidirect
161. #14273637C23semidirect
173. C2×M16×C59C23semidirect
180. C2×C4⋊C4×C59C23semidirect
181. #103×C59C23semidirect
182. #103×C59C23semidirect
418. C2×#417D59semidirect
422. C2×C59#3314semidirect
433. C22×M16C2×D59semidirect
456. C22×C4⋊C4C2×D59semidirect
473. #417C2×D59semidirect
476. C2×#103C2×D59semidirect
477. C2×#103C2×D59semidirect
488. C59C2×#3314semidirect
520. C2×M16C22×D59semidirect
567. C2×C4⋊C4C22×D59semidirect
586. #103C22×D59semidirect
587. #103C22×D59semidirect
819. C2#21436178direct (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×#168380402
#214361782
C2×#168377632
C2×#168377362
C2×#168377152
C2×#168376802
C2×#168376482
C2×#168376422
C2×#168376272
C2×#168375642
C2×#168375542
C2×#168374992
C2×#168374712
C2×#102×D592
C2×C59×#4172
C2×#331459