Finite Group Databasebeta

← C2×#21436183 #29465221

Subgroups — C2×#21436183 #29465221

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×#16838110C211yesmaximal, characteristic, complemented
2C2×#16838043C211yesmaximal, characteristic
3#21436183C2116yesmaximal, direct product factor
4C2×#16837763C211yesmaximal, characteristic, complemented
5C2×#16837735C211yesmaximal, characteristic, complemented
6C2×#16837717C211yesmaximal, characteristic, complemented
7C2×#16837681C211yesmaximal, characteristic, complemented
8C2×#16837651C211yesmaximal, characteristic, complemented
9C2×#16837626C211yesmaximal, characteristic, complemented
10C2×#16837563C211yesmaximal, characteristic, complemented
11C2×#16837552C211yesmaximal, characteristic, complemented
12C2×#16837505C211yesmaximal, characteristic, complemented
13C2×#16837473C211yesmaximal, characteristic, complemented
14C2×#16837402C211yesmaximal, characteristic, complemented
15C22×#14273649C211yesmaximal, characteristic, complemented
16C2×C59×#467C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C23×D236C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×#11745659C2211yescharacteristic, complemented
22#16838110—24no—
23#16838110C2218yescomplemented
24#16838043—24no—
25#16838043C2218yes—
26C2×#14273726C2211yescharacteristic, complemented
27C2×#14273717—21no—
28C2×#14273716C2211yescharacteristic
29C2×#14273712—21no—
30C2×#14273707—21no—
31C2×#14273704—21no—
32C2×#14273703C2211yescharacteristic, complemented
33C2×#14273702—21no—
34C2×#14273702C2211yescharacteristic
35C2×#14273697—21no—
36C2×Q8×Dic59C2211yescharacteristic, complemented
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×(C22⋊D59)⋊C4—21no—
40C22×C4⋊Dic59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic, complemented
42C2×C22⋊C4×D59—21no—
43#16837763C2218yescomplemented
44#16837735C2218yescomplemented
45#16837717C2218yescomplemented
46#16837681C2218yescomplemented
47#16837651C2218yescomplemented
48#16837626C2218yescomplemented
49#16837563C2218yescomplemented
50#16837552C2218yescomplemented
51#16837505C2218yescomplemented
52#16837473C2218yescomplemented
53C2×#14273660C2211yescharacteristic, complemented
54C2×#14273660C2211yescharacteristic, complemented
55C2×Dic59⋊C8C2211yescharacteristic, complemented
56#16837402C2218yescomplemented
57C2×#14273651C2211yescharacteristic, complemented
58C2×#14273651C2211yescharacteristic, complemented
59C2×#14273649C2211yescharacteristic
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2218yescomplemented
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×#14273637C2211yescharacteristic, complemented
69C22×Q16×C59C2211yescharacteristic, complemented
70C23×C8×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#467C2218yescomplemented
74C2×#107×C59C2211yescharacteristic, complemented
75C2×#103×C59C2211yescharacteristic, complemented
76C2×#103×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745689—22no—
79C2×#11745689—24no—
80C2×#11745689—42no—
81C2×#11745689C2314yes—
82C22×Dic118—21no—
83C22×D236—24no—
84C22×D236—21no—
85C22×D236—21no—
86C22×D236—22no—
87C22×D236—21no—
88C22×D236—42no—
89C22×D236C2311yescharacteristic
90C22×D236C2314yes—
91C22×D236C2311yescharacteristic
92C22×C22⋊D59D411yescharacteristic
93C23×Dic59—21no—
94C22×C4×D59—21no—
95C22×C4×D59—21no—
96C22×C4×D59—21no—
97C22×C4×D59C2311yescharacteristic
98C2×#11745671—24no—
99C2×#11745671—42no—
100C2×#11745671C2314yes—
101C2×#11745671C2314yes—
102C2×#11745659—42no—
103C2×#11745659C2314yescomplemented
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106#14273726—22no—
107#14273726C2314yescomplemented
108#14273717—28no—
109#14273716—22no—
110#14273716C2314yes—
111#14273712—28no—
112#14273707—28no—
113#14273704—28no—
114#14273703—22no—
115#14273703C2314yescomplemented
116#14273702—22no—
117#14273702—28no—
118#14273702C2314yes—
119#14273697—28no—
120Q8×Dic59—22no—
121Q8×Dic59C2314yescomplemented
122#14273689—22no—
123#14273689C2314yes—
124C4×C22⋊D59D414yes—
125C4×C22⋊D59C2314yes—
126(C22⋊D59)⋊C4—28no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—22no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59C2311yescharacteristic
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2314yes—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4D411yescharacteristic
137C4⋊C4×D59—22no—
138C4⋊C4×D59C2314yescomplemented
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)⋊C4D411yescharacteristic
146C22⋊C4×D59—28no—
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yescomplemented
150#14273660C2314yescomplemented
151Dic59⋊C8C2314yescomplemented
152#14273651C2314yescomplemented
153#14273651C2314yescomplemented
154#14273649C2314yes—
155#14273649C2314yes—
156#14273649C2314yes—
157#14273649C2314yes—
158#14273647C2314yes—
159#14273647C2314yes—
160C22⋊(C59⋊C8)C2314yes—
161(C2×D59)⋊C8C2314yescomplemented
162#14273637C2314yescomplemented
163C22×Q8×C59C2311yescharacteristic
164C22×Q8×C59C2311yescharacteristic
165C23×C4×C59C2311yescharacteristic
166C2×Q16×C59—42no—
167C2×Q16×C59C2314yescomplemented
168C22×C8×C59—42no—
169C22×C8×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2314yes—
172C22⋊Q8×C59—22no—
173C22⋊Q8×C59—22no—
174C22⋊Q8×C59C2314yes—
175C22⋊Q8×C59C2314yes—
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59—21no—
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59—21no—
182#107×C59C2314yescomplemented
183#103×C59C2314yescomplemented
184#103×C59C2314yescomplemented
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—21no—
195C2×Q8×C59—22no—
196C2×Q8×C59—22no—
197C2×Q8×C59—22no—
198C2×Q8×C59—22no—
199C2×Q8×C59C2412yes—
200C2×Q8×C59C2412yes—
201C22×C4×C59—22no—
202C22×C4×C59—22no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D412yes—
209C22×C4×C59C2412yes—
210C22×C4×C59C2411yescharacteristic
211C2×C22⋊D59—24no—
212C2×C22⋊D59C2×D414yes—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—24no—
216C22×Dic59—82no—
217C22×Dic59C2×D411yescharacteristic
218C22×Dic59C2×D411yescharacteristic
219C22×Dic59C2×D411yescharacteristic
220#11745689—28no—
221#11745689—44no—
222#11745689—48no—
223C2×D236—21no—
224C2×D236—22no—
225C2×D236—22no—
226C2×D236—22no—
227C2×D236—28no—
228C2×D236—24no—
229C2×D236—24no—
230C2×D236—21no—
231C2×D236—24no—
232C2×D236—44no—
233C2×D236—48no—
234C2×D236—44no—
235C2×D236—44no—
236C2×D236—82no—
237C2×D236#4114yes—
238C2×D236C2412yes—
239C2×D236C2412yes—
240C2×C4×D59—22no—
241C2×C4×D59—22no—
242C2×C4×D59—24no—
243C2×C4×D59—24no—
244C2×C4×D59—24no—
245C2×C4×D59—44no—
246C2×C4×D59—82no—
247C2×C4×D59—82no—
248C2×C4×D59C2×D412yes—
249C2×C4×D59C2412yes—
250C2×Dic118—24no—
251C2×Dic118—82no—
252Q16×C59—44no—
253C2×C8×C59—22no—
254C2×C8×C59—22no—
255C2×C8×C59—44no—
256C2×C8×C59C2412yes—
257C2×C8×C59C2412yes—
258C4⋊C4×C59—24no—
259C4⋊C4×C59—24no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59—21no—
262C4⋊C4×C59C2412yes—
263C4⋊C4×C59C2412yes—
264C22⋊C4×C59—24no—
265C22⋊C4×C59—24no—
266C22⋊Dic59C2×D414yes—
267#11745671—28no—
268#11745671—44no—
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—
275C4⋊Dic59—21no—
276C4⋊Dic59—21no—
277C4⋊Dic59—24no—
278C4⋊Dic59—24no—
279C4⋊Dic59C2412yes—
280C4⋊Dic59C2412yes—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283Dic59⋊C4—24no—
284Dic59⋊C4C2×D414yes—
285C4×Dic59—24no—
286C4×Dic59C2×D412yes—
287C4×Dic59C2412yes—
288C2×C59⋊C8—22no—
289C2×C59⋊C8—22no—
290C2×C59⋊C8C2412yes—
291C2×C59⋊C8C2412yes—
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—22no—
317Q8×C59—22no—
318Q8×C59—42no—
319Q8×C59—42no—
320C2×C4×C59—22no—
321C2×C4×C59—24no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—42no—
329C2×C4×C59—42no—
330C2×C4×C59—42no—
331C2×C4×C59—42no—
332C2×C4×C59C22×D412yes—
333C2×C4×C59C22×D411yescharacteristic
334C2×C4×C59C2×#4112yes—
335C2×C4×C59H(5,𝔽2)12yes—
336C2×C4×C59C2511yescharacteristic
337C22⋊D59—28no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59—42no—
344C2×Dic59—42no—
345C2×Dic59—84no—
346C2×Dic59C22×D412yes—
347C2×Dic59C22×D412yes—
348C2×Dic59C22×D412yes—
349D236—24no—
350D236—22no—
351D236—22no—
352D236—22no—
353D236—48no—
354D236—48no—
355D236—42no—
356D236—84no—
357D236C2×#4114yes—
358C4×D59—24no—
359C4×D59—22no—
360C4×D59—22no—
361C4×D59—48no—
362C4×D59—84no—
363C4×D59—84no—
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×#484—591no—
409C2×#480—591no—
410C2×#474—591no—
411C2×#468—591no—
412C2×#467D5911yescharacteristic, complemented
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×Q16C2×D5911yescharacteristic, complemented
431C22×SD16—591no—
432C22×SD16—591no—
433C22×M16—591no—
434C23×C8C2×D5911yescharacteristic
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—1181no—
445C2×C22⋊Q8—1181no—
446C2×C22⋊Q8C2×D5911yescharacteristic
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⋊C4—591no—
457C22×C22⋊C4—1181no—
458#489—598no—
459#484—598no—
460#480—598no—
461#474—598no—
462#468—598no—
463#467C2×D5918yescomplemented
464#464—598no—
465#452—598no—
466#450—598no—
467#440—598no—
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×#103C2×D5911yescharacteristic, complemented
477C2×#103C2×D5911yescharacteristic, complemented
478C2×#102—591no—
479C2×#102—591no—
480C2×#102—591no—
481C2×#102—591no—
482C2×#102—598no—
483C2×#102—591no—
484C2×#102—591no—
485C2×C22⋊C8—591no—
486C2×C22⋊C8—591no—
487C2×#97—591no—
488C59C2×#331411yescharacteristic, complemented, Sylow
489C25—1181no—
490C2×#41—594no—
491C2×#41—1182no—
492C2×#41—1184no—
493C2×#41—2362no—
494C22×Q8—1181no—
495C22×Q8C22×D5911yescharacteristic
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—591no—
508C23×C4—1181no—
509C23×C4—1181no—
510C23×C4—1181no—
511C23×C4—1181no—
512C23×C4C22×D5911yescharacteristic
513C2×Q16—42no—
514C2×Q16C22×D5914yescomplemented
515C2×SD16—594no—
516C2×SD16—594no—
517C2×SD16—1184no—
518C2×SD16—2362no—
519C2×M16—594no—
520C2×M16—2362no—
521C22×C8—42no—
522C22×C8—591no—
523C22×C8—591no—
524C22×C8C22×D5911yescharacteristic
525C22×C8C22×D5911yescharacteristic
526C22×C8C22×D5914yes—
527C4⋊Q8—594no—
528C4⋊Q8—1182no—
529#125—1188no—
530#124—594no—
531#124—1182no—
532#123—1188no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—594no—
536C22⋊Q8—1188no—
537C22⋊Q8—1188no—
538C22⋊Q8—1182no—
539C22⋊Q8C22×D5914yes—
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—21no—
554C2×C4⋊C4—591no—
555C2×C4⋊C4—591no—
556C2×C4⋊C4—591no—
557C2×C4⋊C4—594no—
558C2×C4⋊C4—594no—
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—1182no—
566C2×C4⋊C4C22×D5911yescharacteristic
567C2×C4⋊C4C22×D5911yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—591no—
571C2×C22⋊C4—591no—
572C2×C22⋊C4—1188no—
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#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⋊C8—594no—
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—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—1184no—
615C2×Q8—4722no—
616C2×Q8C23×D5912yes—
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—591no—
644C22×C4—591no—
645C22×C4—591no—
646C22×C4—592no—
647C22×C4—592no—
648C22×C4—1184no—
649C22×C4—1184no—
650C22×C4—1184no—
651C22×C4—1182no—
652C22×C4—1182no—
653C22×C4—1184no—
654C22×C4—1181no—
655C22×C4—1181no—
656C22×C4—4722no—
657C22×C4—4722no—
658C22×C4—4722no—
659C22×C4—2364no—
660C22×C4D4×D5912yes—
661C22×C4D4×D5911yescharacteristic
662C22×C4C23×D5912yes—
663C22×C4C23×D5911yescharacteristic
664Q16—44no—
665SD16—1188no—
666SD16—2364no—
667M16—2364no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—44no—
671C2×C8—592no—
672C2×C8—592no—
673C2×C8—1182no—
674C2×C8—1182no—
675C2×C8C23×D5912yes—
676C2×C8C23×D5912yes—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—594no—
682C4⋊C4—592no—
683C4⋊C4—592no—
684C4⋊C4—1184no—
685C4⋊C4—1184no—
686C4⋊C4—1184no—
687C4⋊C4—1184no—
688C4⋊C4—1181no—
689C4⋊C4—1184no—
690C4⋊C4—1181no—
691C4⋊C4C23×D5912yes—
692C4⋊C4C23×D5912yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—594no—
696C22⋊C4—594no—
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—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—4724no—
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—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—4724no—
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#1427377212yes—
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#1683804112yes—
798C22C2×#1427375914yes—
799C22C2×#1427375912yes—
800C22#1683820412yes—
801C22C22×D4×D5911yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—1182no—
808C4—1182no—
809C4—1182no—
810C4—2362no—
811C4—2362no—
812C4#1683804112yes—
813C4C2×#41×D5911yescharacteristic
814C4C2×#1427377211yescharacteristic
815C2—24no—
816C2—4722no—
817C2—2362no—
818C2—2364no—
819C2#2143618314yesdirect product factor
820C2C2×#1683804111yescharacteristic
821C2C22×#1427375911yescharacteristic
822C2C2×#1683820411yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#467C2
socleC23×C59C22×D4
prime radicalC2×#16838043C2
hypercenterC2×#467D59
hypocenterC59C2×#3314
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#16838110C2semidirect
3. #21436183C2direct (N × H)
4. C2×#16837763C2semidirect
5. C2×#16837735C2semidirect
6. C2×#16837717C2semidirect
7. C2×#16837681C2semidirect
8. C2×#16837651C2semidirect
9. C2×#16837626C2semidirect
10. C2×#16837563C2semidirect
11. C2×#16837552C2semidirect
12. C2×#16837505C2semidirect
13. C2×#16837473C2semidirect
14. C2×#16837402C2semidirect
15. C22×#14273649C2semidirect
16. C2×C59×#467C2semidirect
21. C22×#11745659C22semidirect
23. #16838110C22semidirect
26. C2×#14273726C22semidirect
32. C2×#14273703C22semidirect
36. C2×Q8×Dic59C22semidirect
41. C2×C4⋊C4×D59C22semidirect
43. #16837763C22semidirect
44. #16837735C22semidirect
45. #16837717C22semidirect
46. #16837681C22semidirect
47. #16837651C22semidirect
48. #16837626C22semidirect
49. #16837563C22semidirect
50. #16837552C22semidirect
51. #16837505C22semidirect
52. #16837473C22semidirect
53. C2×#14273660C22semidirect
54. C2×#14273660C22semidirect
55. C2×Dic59⋊C8C22semidirect
56. #16837402C22semidirect
57. C2×#14273651C22semidirect
58. C2×#14273651C22semidirect
63. C2×#14273649C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×#14273637C22semidirect
69. C22×Q16×C59C22semidirect
73. C59×#467C22semidirect
74. C2×#107×C59C22semidirect
75. C2×#103×C59C22semidirect
76. C2×#103×C59C22semidirect
103. C2×#11745659C23semidirect
107. #14273726C23semidirect
115. #14273703C23semidirect
121. Q8×Dic59C23semidirect
138. C4⋊C4×D59C23semidirect
149. #14273660C23semidirect
150. #14273660C23semidirect
151. Dic59⋊C8C23semidirect
152. #14273651C23semidirect
153. #14273651C23semidirect
161. (C2×D59)⋊C8C23semidirect
162. #14273637C23semidirect
167. C2×Q16×C59C23semidirect
182. #107×C59C23semidirect
183. #103×C59C23semidirect
184. #103×C59C23semidirect
412. C2×#467D59semidirect
421. C2×C59#3314semidirect
430. C22×Q16C2×D59semidirect
463. #467C2×D59semidirect
471. C2×#107C2×D59semidirect
476. C2×#103C2×D59semidirect
477. C2×#103C2×D59semidirect
488. C59C2×#3314semidirect
514. C2×Q16C22×D59semidirect
582. #107C22×D59semidirect
586. #103C22×D59semidirect
587. #103C22×D59semidirect
819. C2#21436183direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381102
C2×#168380432
#214361832
C2×#168377632
C2×#168377352
C2×#168377172
C2×#168376812
C2×#168376512
C2×#168376262
C2×#168375632
C2×#168375522
C2×#168375052
C2×#168374732
C2×#168374022
C22×#142736492
C2×C59×#4672
C2×#331459