Finite Group Databasebeta

← #28604470

Subgroups — #28604470

Order 15104.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273752C211yesmaximal, characteristic
2C2×#16837500C211yesmaximal, characteristic, complemented
3C2×C4×#11745671C211yesmaximal, characteristic, complemented
4C22⋊C4×D236C211yesmaximal, characteristic, complemented
5#21424971C211yesmaximal, characteristic, complemented
6#21424961C211yesmaximal, characteristic, complemented
7#21424451C211yesmaximal, characteristic, complemented
8#21424451C211yesmaximal, characteristic, complemented
9#21424447C211yesmaximal, characteristic, complemented
10#21424447C211yesmaximal, characteristic, complemented
11#21424127C211yesmaximal, characteristic, complemented
12#21424036C211yesmaximal, characteristic, complemented
13#21424026C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#2341C211yesmaximal, characteristic, complemented
16C23×D236C2211yescharacteristic
17C2×#14273752—24no—
18C2×#14273752—24no—
19C2×#14273752C418yescomplemented
20C22×#11745671C2211yescharacteristic
21C22×#11745671C2211yescharacteristic
22C22×#11745669C2211yescharacteristic
23C22×#11745669C2211yescharacteristic
24C22×#11745664C2211yescharacteristic
25C2×C4×D236C2211yescharacteristic
26C2×C4×D236C2211yescharacteristic
27C2×C22⋊C4×D59—21no—
28#16837500—24no—
29C4×#11745671—24no—
30C2×#14273660C2211yescharacteristic, complemented
31C2×#14273658C2211yescharacteristic, complemented
32C2×#14273651C2211yescharacteristic, complemented
33C2×#14273651C2211yescharacteristic, complemented
34C2×#14273648C2211yescharacteristic, complemented
35C2×#14273648C2211yescharacteristic, complemented
36C2×#14273647C2211yescharacteristic
37C2×#14273647C2211yescharacteristic
38C2×#14273647C2211yescharacteristic
39C2×#14273647C2211yescharacteristic
40C2×C22⋊(C59⋊C8)C2211yescharacteristic
41C2×#14273638C2211yescharacteristic, complemented
42C2×C4×C59⋊C8C2211yescharacteristic, complemented
43#16837304C2211yescharacteristic
44#16837304C2211yescharacteristic
45#16837280—21no—
46#16837280—21no—
47#16837262C2211yescharacteristic
48#16837257—21no—
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837157C2211yescharacteristic, complemented
52#16837157C2211yescharacteristic, complemented
53C22×#41×C59C2211yescharacteristic
54C2×C4×Q8×C59C2211yescharacteristic, complemented
55C2×C4×Q8×C59C2211yescharacteristic, complemented
56C59×#390—21no—
57C59×#390—21no—
58C59×#390C2211yescharacteristic, complemented
59C59×#390C2211yescharacteristic, complemented
60C59×#380—21no—
61C59×#380C2211yescharacteristic
62C4×C22⋊C4×C59—21no—
63C4×C22⋊C4×C59C2211yescharacteristic
64C24×D59—21no—
65C22×D236—22no—
66C22×D236—22no—
67C22×D236—21no—
68C22×D236—22no—
69C22×D236—41no—
70C22×D236—41no—
71C22×D236C2×C414yes—
72C22×D236C2311yescharacteristic
73C22×D236C2311yescharacteristic
74C22×C4×D59—21no—
75C22×C4×D59—21no—
76#14273752—232no—
77C2×#11745671—22no—
78C2×#11745671—22no—
79C2×#11745671C2×C414yes—
80C2×#11745671C2×C414yescomplemented
81C2×#11745671D414yes—
82C2×#11745671D414yes—
83C2×#11745669—22no—
84C2×#11745669—22no—
85C2×#11745669—22no—
86C2×#11745669—22no—
87C2×#11745669C2×C414yes—
88C2×#11745669C2×C414yescomplemented
89C2×#11745664—22no—
90C2×#11745664—22no—
91C2×#11745664C2×C414yescomplemented
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96C4×D236—22no—
97C4×D236—22no—
98C4×D236—41no—
99C4×D236—41no—
100C2×C4⋊Dic59C2311yescharacteristic
101C2×C4⋊Dic59C2311yescharacteristic
102C2×C22⋊Dic59—21no—
103C2×(C2×D59)⋊C4—21no—
104C2×(C2×D59)⋊C4—21no—
105C2×(C2×D59)⋊C4—21no—
106C2×(C2×D59)⋊C4—21no—
107C2×(C2×D59)⋊C4—21no—
108C2×(C2×D59)⋊C4—21no—
109C22⋊C4×D59—44no—
110#14273660—22no—
111#14273658—22no—
112#14273651—22no—
113#14273651—22no—
114#14273648—41no—
115#14273648—41no—
116#14273647—22no—
117#14273647—22no—
118#14273647—41no—
119#14273647—41no—
120C22⋊(C59⋊C8)—22no—
121#14273638—22no—
122C4×C59⋊C8—22no—
123C59⋊#95—21no—
124C2×#41×C59—22no—
125C2×#41×C59—22no—
126C2×#41×C59—22no—
127C2×#41×C59—41no—
128C2×#41×C59—41no—
129C2×#41×C59C2×C414yescomplemented
130C22×Q8×C59C2311yescharacteristic
131C22×D4×C59—21no—
132C22×D4×C59C2311yescharacteristic
133C23×C4×C59—21no—
134C23×C4×C59C2311yescharacteristic
135C4×Q8×C59—22no—
136C4×Q8×C59—22no—
137C4×Q8×C59—41no—
138C4×Q8×C59—41no—
139C2×C4⋊C4×C59—21no—
140C2×C4⋊C4×C59—21no—
141C2×C4⋊C4×C59C2311yescharacteristic
142C2×C4⋊C4×C59C2311yescharacteristic
143C2×C22⋊C4×C59—21no—
144C2×C22⋊C4×C59—21no—
145C2×C22⋊C4×C59—21no—
146C2×C22⋊C4×C59—21no—
147C2×C22⋊C4×C59—21no—
148C2×C22⋊C4×C59D411yescharacteristic
149C2×C22⋊C4×C59D411yescharacteristic
150C2×C42×C59—21no—
151C2×C42×C59—21no—
152C2×C42×C59C2311yescharacteristic
153C2×C42×C59C2311yescharacteristic
154#95×C59—21no—
155#95×C59D411yescharacteristic
156#95×C59D411yescharacteristic
157C24×C59—21no—
158C24×C59C2×D411yescharacteristic
159C23×D59—21no—
160C23×D59—21no—
161C23×D59—24no—
162C23×D59—42no—
163C23×D59—42no—
164C23×D59—42no—
165C23×D59—42no—
166C23×D59—81no—
167C23×D59—81no—
168#41×C59—28no—
169#41×C59—44no—
170#41×C59—44no—
171#41×C59—44no—
172C2×Q8×C59—21no—
173C2×Q8×C59—21no—
174C2×Q8×C59—21no—
175C2×Q8×C59C22×C412yes—
176C2×Q8×C59C2×D412yes—
177C2×Q8×C59C2×D412yes—
178C2×D4×C59—24no—
179C2×D4×C59—21no—
180C2×D4×C59—21no—
181C2×D4×C59—21no—
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—42no—
185C2×D4×C59—42no—
186C2×D4×C59C22×C412yes—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—24no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—42no—
196C22×C4×C59—42no—
197C22×C4×C59C22×C412yes—
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59#4112yes—
204C22×C4×C59C2411yescharacteristic
205C22×Dic59—21no—
206C22×Dic59—21no—
207C2×D236—21no—
208C2×D236—21no—
209C2×D236—21no—
210C2×D236—21no—
211C2×D236—21no—
212C2×D236—21no—
213C2×D236—21no—
214C2×D236—28no—
215C2×D236—24no—
216C2×D236—21no—
217C2×D236—44no—
218C2×D236—44no—
219C2×D236—44no—
220C2×D236—42no—
221C2×D236—42no—
222C2×D236C22×C412yes—
223C2×D236C22×C412yes—
224C2×D236C2×D412yes—
225C2×D236C2×D412yes—
226C2×C4×D59—42no—
227C2×C4×D59—42no—
228C2×C4×D59—42no—
229C2×C4×D59—42no—
230C2×C4×D59—81no—
231C2×C4×D59—81no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59—42no—
237C4⋊C4×C59—42no—
238C22⋊C4×C59—22no—
239C22⋊C4×C59—41no—
240C22⋊C4×C59—42no—
241C22⋊C4×C59—42no—
242C22⋊C4×C59—81no—
243C22⋊C4×C59—81no—
244C22⋊C4×C59—81no—
245C42×C59—21no—
246C42×C59—21no—
247C42×C59—21no—
248C42×C59—21no—
249C42×C59—42no—
250C42×C59—42no—
251C22⋊Dic59—42no—
252#11745671—28no—
253#11745671C22⋊C4116yescomplemented
254#11745669—28no—
255#11745669—28no—
256(C2×D59)⋊C4—42no—
257(C2×D59)⋊C4—42no—
258(C2×D59)⋊C4—42no—
259(C2×D59)⋊C4—42no—
260(C2×D59)⋊C4—81no—
261(C2×D59)⋊C4—81no—
262C4⋊Dic59—21no—
263C4⋊Dic59—21no—
264C4⋊Dic59—21no—
265C4⋊Dic59—21no—
266#11745664—28no—
267C2×C59⋊C8—21no—
268C2×C59⋊C8—21no—
269C2×C59⋊C8—21no—
270C2×C59⋊C8—21no—
271C2×C59⋊C8—21no—
272C2×C59⋊C8—21no—
273C2×C59⋊C8—21no—
274C2×C59⋊C8—21no—
275C2×C59⋊C8C22×C412yes—
276C2×C59⋊C8C22×C412yes—
277C2×C59⋊C8C2×D412yes—
278C2×C59⋊C8C2×D412yes—
279C23×C59—21no—
280C23×C59—21no—
281C23×C59—21no—
282C23×C59—21no—
283C23×C59—21no—
284C23×C59—21no—
285C23×C59—22no—
286C23×C59—41no—
287C23×C59—41no—
288C23×C59—41no—
289C23×C59—41no—
290C23×C59—41no—
291C23×C59—41no—
292C23×C59C4×D412yes—
293C23×C59C22×D411yescharacteristic
294C22×D59—22no—
295C22×D59—22no—
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—48no—
299C22×D59—41no—
300C22×D59—41no—
301C22×D59—41no—
302C22×D59—41no—
303C22×D59—48no—
304C22×D59—41no—
305C22×D59—41no—
306C22×D59—41no—
307C22×D59—41no—
308C22×D59—41no—
309C22×D59—41no—
310C22×D59—84no—
311C22×D59—84no—
312C22×D59—84no—
313C22×D59—84no—
314C22×D59—84no—
315Q8×C59—22no—
316Q8×C59—22no—
317Q8×C59—22no—
318Q8×C59C2×C22⋊C414yescomplemented
319D4×C59—22no—
320D4×C59—22no—
321D4×C59—48no—
322D4×C59—41no—
323D4×C59—41no—
324C2×C4×C59—22no—
325C2×C4×C59—21no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—21no—
329C2×C4×C59—21no—
330C2×C4×C59—21no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—21no—
336C2×C4×C59—21no—
337C2×C4×C59—21no—
338C2×C4×C59—21no—
339C2×C4×C59—21no—
340C2×C4×C59—21no—
341C2×C4×C59—21no—
342C2×C4×C59—21no—
343C2×C4×C59—21no—
344C2×C4×C59—48no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—41no—
351C2×C4×C59C4×D412yes—
352C2×C4×C59AGL(1,ℤ/8)12yescomplemented
353C2×C4×C59C23×C411yescharacteristic
354C2×C4×C59C22×D411yescharacteristic
355C2×C4×C59C22×D411yescharacteristic
356C2×C4×C59C2×#4111yescharacteristic
357C2×C4×C59H(5,𝔽2)11yescharacteristic
358C2×C4×C59H(5,𝔽2)11yescharacteristic
359C2×Dic59—41no—
360C2×Dic59—41no—
361C2×Dic59—41no—
362C2×Dic59—41no—
363C2×Dic59—41no—
364C2×Dic59—41no—
365D236—22no—
366D236—22no—
367D236—22no—
368D236—22no—
369D236—22no—
370D236—48no—
371D236—41no—
372D236—41no—
373D236C2×C22⋊C414yes—
374C4×D59—84no—
375C4×D59—84no—
376C59⋊C8—22no—
377C59⋊C8—41no—
378C59⋊C8—41no—
379C59⋊C8C2×C22⋊C414yescomplemented
380#22443—591nomaximal, Sylow
381C22×C59—22no—
382C22×C59—22no—
383C22×C59—22no—
384C22×C59—41no—
385C22×C59—41no—
386C22×C59—41no—
387C22×C59—41no—
388C22×C59—42no—
389C22×C59—42no—
390C22×C59—42no—
391C22×C59—81no—
392C22×C59—81no—
393C22×C59—81no—
394C22×C59—81no—
395C22×C59C2×C4×D411yescharacteristic
396C22×C59D4211yescharacteristic
397C22×C59D4211yescharacteristic
398C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C59#57511yescharacteristic
400C22×C59#57611yescharacteristic
401C22×C59#57711yescharacteristic
402C2×D59—24no—
403C2×D59—42no—
404C2×D59—42no—
405C2×D59—42no—
406C2×D59—42no—
407C2×D59—42no—
408C2×D59—42no—
409C2×D59—42no—
410C2×D59—42no—
411C2×D59—42no—
412C2×D59—816no—
413C2×D59—81no—
414C2×D59—81no—
415C2×D59—81no—
416C2×D59—81no—
417C4×C59—22no—
418C4×C59—24no—
419C4×C59—22no—
420C4×C59—41no—
421C4×C59—41no—
422C4×C59—41no—
423C4×C59—81no—
424C4×C59—81no—
425C4×C59C22×C22⋊C411yescharacteristic
426C4×C59#51811yescharacteristic
427C4×C59#54611yescharacteristic
428C4×C59#54611yescharacteristic
429Dic59—81no—
430Dic59—81no—
431C22×AGL(1,ℤ/8)—591no—
432C2×#440—591no—
433C2×C4×SD16—591no—
434#2341D5911yescharacteristic, complemented
435D4×C22⋊C4—591no—
436#1972—591no—
437#1970—591no—
438#1880—591no—
439#1880—591no—
440#1879—591no—
441#1879—591no—
442#1809—591no—
443#1788—591no—
444#1786—591no—
445#1753—591no—
446C2×C59—42no—
447C2×C59—82no—
448C2×C59D4×C22⋊C411yescharacteristic
449C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
450C2×C59#294611yescharacteristic
451C2×C59#326511yescharacteristic
452C2×C59#326811yescharacteristic
453C2×C59#327411yescharacteristic
454C2×C59#327511yescharacteristic
455D59—44no—
456D59—82no—
457C22×#41C2×D5911yescharacteristic
458C23×D4—591no—
459C2×AGL(1,ℤ/8)—598no—
460C2×AGL(1,ℤ/8)—1184no—
461C2×AGL(1,ℤ/8)—1184no—
462C22×SD16—591no—
463C22×SD16—591no—
464C22×D8—591no—
465C22×D8—591no—
466C22×M16—591no—
467C2×C4×Q8C2×D5911yescharacteristic, complemented
468C2×C4×Q8C2×D5911yescharacteristic, complemented
469C2×C4×D4—591no—
470C2×C4×D4—591no—
471C22×C22⋊C4—1181no—
472#440—1184no—
473C4×SD16—1184no—
474C2×#107—591no—
475C2×#106—591no—
476C2×#103—591no—
477C2×#103—591no—
478C2×#102—591no—
479C2×#102—591no—
480C2×#102—591no—
481C2×#102—591no—
482C2×#102—591no—
483C2×#102—591no—
484C2×C22⋊C8—591no—
485C2×#97—591no—
486C2×C4×C8—591no—
487#390—21no—
488#390—21no—
489#390—591no—
490#390—591no—
491#390C2×D5911yescharacteristic, complemented
492#390C2×D5911yescharacteristic, complemented
493#386—1181no—
494#386—1181no—
495#380—21no—
496#380—591no—
497#380C2×D5911yescharacteristic
498#379—1181no—
499C4×C22⋊C4—21no—
500C4×C22⋊C4C2×D5911yescharacteristic
501#340—591no—
502#340—591no—
503#336—591no—
504#336—591no—
505C59#2244311yescharacteristic, complemented, Sylow
506C25—1181no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41C4×D5914yescomplemented
513C22×Q8C22×D5911yescharacteristic
514C22×D4—21no—
515C22×D4—594no—
516C22×D4—591no—
517C22×D4—591no—
518C22×D4—1182no—
519C22×D4—1182no—
520C22×D4—1182no—
521C22×D4—1181no—
522C22×D4—2361no—
523C22×D4—2361no—
524C22×D4C22×D5911yescharacteristic
525C23×C4—21no—
526C23×C4—1181no—
527C23×C4—1181no—
528C23×C4C22×D5911yescharacteristic
529AGL(1,ℤ/8)—11832no—
530C2×SD16—594no—
531C2×SD16—594no—
532C2×SD16—594no—
533C2×SD16—594no—
534C2×SD16—1182no—
535C2×SD16—1182no—
536C2×D8—594no—
537C2×D8—594no—
538C2×D8—1182no—
539C2×D8—1182no—
540C2×D8—1182no—
541C2×D8—1182no—
542C2×M16—594no—
543C2×M16—1182no—
544C2×M16—1182no—
545C22×C8—591no—
546C22×C8—591no—
547C22×C8—591no—
548C22×C8—591no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×D4—1182no—
554C4×D4—1182no—
555C4×D4—2361no—
556C4×D4—2361no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—591no—
560C2×C4⋊C4—591no—
561C2×C4⋊C4C22×D5911yescharacteristic
562C2×C4⋊C4C22×D5911yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—1181no—
569C2×C22⋊C4—1181no—
570C2×C22⋊C4—1181no—
571C2×C22⋊C4—1181no—
572C2×C22⋊C4—1181no—
573C2×C22⋊C4—1181no—
574C2×C22⋊C4—1181no—
575C2×C22⋊C4—2364no—
576C2×C22⋊C4C22⋊D5911yescharacteristic
577C2×C22⋊C4C22⋊D5911yescharacteristic
578C2×C42—21no—
579C2×C42—21no—
580C2×C42C22×D5911yescharacteristic
581C2×C42C22×D5911yescharacteristic
582#107—1182no—
583#106—1182no—
584#103—1182no—
585#103—1182no—
586#102—1182no—
587#102—1182no—
588#102—2361no—
589#102—2361no—
590#102—2361no—
591#102—2361no—
592C22⋊C8—1182no—
593#97—1182no—
594C4×C8—1182no—
595#95—21no—
596#95—1181no—
597#95C22⋊D5911yescharacteristic
598#95C22⋊D5911yescharacteristic
599C24—21no—
600C24—1181no—
601C24—1184no—
602C24—1181no—
603C24—4721no—
604C24—4721no—
605C24—2362no—
606C24—2362no—
607C24—2362no—
608C24—2362no—
609C24C2×C22⋊D5911yescharacteristic
610#41—28no—
611#41—44no—
612#41—44no—
613#41—44no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8C2×C4×D5912yes—
618C2×Q8D4×D5912yes—
619C2×Q8D4×D5912yes—
620C2×D4—24no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—592no—
629C2×D4—592no—
630C2×D4—592no—
631C2×D4—592no—
632C2×D4—1188no—
633C2×D4—1184no—
634C2×D4—1181no—
635C2×D4—1181no—
636C2×D4—1181no—
637C2×D4—1181no—
638C2×D4—1181no—
639C2×D4—1181no—
640C2×D4—1181no—
641C2×D4—1181no—
642C2×D4—2364no—
643C2×D4—2364no—
644C2×D4—2364no—
645C2×D4—2362no—
646C2×D4—2362no—
647C2×D4C2×C4×D5912yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—1181no—
659C22×C4—1181no—
660C22×C4—4721no—
661C22×C4—4721no—
662C22×C4—2362no—
663C22×C4—2362no—
664C22×C4—2362no—
665C22×C4—2362no—
666C22×C4C2×C4×D5912yes—
667C22×C4#1174568512yes—
668C22×C4C2×C22⋊D5911yescharacteristic
669C22×C4C2×C22⋊D5911yescharacteristic
670C22×C4C2×C22⋊D5911yescharacteristic
671C22×C4C2×C22⋊D5911yescharacteristic
672C22×C4C2×C22⋊D5911yescharacteristic
673C22×C4C23×D5911yescharacteristic
674SD16—5916no—
675SD16—1188no—
676D8—1188no—
677D8—1188no—
678M16—1188no—
679C2×C8—592no—
680C2×C8—592no—
681C2×C8—592no—
682C2×C8—592no—
683C2×C8—1181no—
684C2×C8—1181no—
685C2×C8—1181no—
686C2×C8—1181no—
687C2×C8—1181no—
688C2×C8—1181no—
689C2×C8—1181no—
690C2×C8—1181no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—1181no—
698C4⋊C4—1181no—
699C4⋊C4—1181no—
700C4⋊C4—1181no—
701C22⋊C4—22no—
702C22⋊C4—41no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—4721no—
709C22⋊C4—4721no—
710C22⋊C4—2362no—
711C22⋊C4—2362no—
712C22⋊C4—2362no—
713C22⋊C4—2362no—
714C22⋊C4—2362no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—42no—
720C42—42no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—1182no—
735C23—1182no—
736C23—1182no—
737C23—1182no—
738C23—4724no—
739C23—4724no—
740C23—4724no—
741C23—4724no—
742C23—4724no—
743C23—2368no—
744C23—2368no—
745C23—2361no—
746C23—2361no—
747C23—2361no—
748C23—2361no—
749C23—2361no—
750C23—2361no—
751C23—2361no—
752C23—2361no—
753C23—2361no—
754C23—2361no—
755C23C4×C22⋊D5912yes—
756C23C22×C22⋊D5911yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C22⋊C4×D5914yescomplemented
761D4—22no—
762D4—22no—
763D4—48no—
764D4—41no—
765D4—41no—
766D4—594no—
767D4—1182no—
768D4—1182no—
769D4—1182no—
770D4—1182no—
771D4—1182no—
772D4—2368no—
773D4—2361no—
774D4—2361no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—4724no—
803C2×C4—4724no—
804C2×C4—2361no—
805C2×C4—2361no—
806C2×C4—2361no—
807C2×C4—2361no—
808C2×C4—2361no—
809C2×C4—2361no—
810C2×C4C4×C22⋊D5912yes—
811C2×C4#1427375212yescomplemented
812C2×C4C22×C4×D5911yescharacteristic
813C2×C4C2×D4×D5911yescharacteristic
814C2×C4C2×D4×D5911yescharacteristic
815C2×C4C2×#1174568511yescharacteristic
816C2×C4#1427377211yescharacteristic
817C2×C4#1427377211yescharacteristic
818C8—594no—
819C8—1182no—
820C8—2361no—
821C8—2361no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—1184no—
837C22—47216no—
838C22—4721no—
839C22—4721no—
840C22—4721no—
841C22—4721no—
842C22—2362no—
843C22—2362no—
844C22—2362no—
845C22—2362no—
846C22—2362no—
847C22—2362no—
848C22—2362no—
849C22—2362no—
850C22—2362no—
851C22C2×C4×C22⋊D5911yescharacteristic
852C22D4×C22⋊D5911yescharacteristic
853C22D4×C22⋊D5911yescharacteristic
854C22C2×#1427375211yescharacteristic
855C22#1683820011yescharacteristic
856C22#1683820511yescharacteristic
857C22#1683821011yescharacteristic
858C4—22no—
859C4—22no—
860C4—24no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—4721no—
867C4—4721no—
868C4C2×C22⋊C4×D5911yescharacteristic
869C4#1683787511yescharacteristic
870C4#1683804211yescharacteristic
871C4#1683804211yescharacteristic
872C2—42no—
873C2—82no—
874C2—4722no—
875C2—2364no—
876C2C22⋊C4×C22⋊D5911yescharacteristic
877C2C4×#1427375211yescharacteristic
878C2#2143292411yescharacteristic
879C2#2143559211yescharacteristic
880C2#2143563711yescharacteristic
881C2#2143571611yescharacteristic
882C2#2143572811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2341C2
socleC23×C59C22×D4
prime radicalC22×#14273752C2
cosocleC22×C4×C59C24
hypercenter#2341D59
hypocenterC59#22443
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#16837500C2semidirect
3. C2×C4×#11745671C2semidirect
4. C22⋊C4×D236C2semidirect
5. #21424971C2semidirect
6. #21424961C2semidirect
7. #21424451C2semidirect
8. #21424451C2semidirect
9. #21424447C2semidirect
10. #21424447C2semidirect
11. #21424127C2semidirect
12. #21424036C2semidirect
13. #21424026C2semidirect
14. #21423880C2semidirect
15. C59×#2341C2semidirect
19. C2×#14273752C4semidirect
30. C2×#14273660C22semidirect
31. C2×#14273658C22semidirect
32. C2×#14273651C22semidirect
33. C2×#14273651C22semidirect
34. C2×#14273648C22semidirect
35. C2×#14273648C22semidirect
41. C2×#14273638C22semidirect
42. C2×C4×C59⋊C8C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
51. #16837157C22semidirect
52. #16837157C22semidirect
54. C2×C4×Q8×C59C22semidirect
55. C2×C4×Q8×C59C22semidirect
58. C59×#390C22semidirect
59. C59×#390C22semidirect
80. C2×#11745671C2×C4semidirect
88. C2×#11745669C2×C4semidirect
91. C2×#11745664C2×C4semidirect
129. C2×#41×C59C2×C4semidirect
253. #11745671C22⋊C4semidirect
318. Q8×C59C2×C22⋊C4semidirect
352. C2×C4×C59AGL(1,ℤ/8)semidirect
379. C59⋊C8C2×C22⋊C4semidirect
434. #2341D59semidirect
467. C2×C4×Q8C2×D59semidirect
468. C2×C4×Q8C2×D59semidirect
491. #390C2×D59semidirect
492. #390C2×D59semidirect
505. C59#22443semidirect
512. C2×#41C4×D59semidirect
760. Q8C22⋊C4×D59semidirect
811. C2×C4#14273752semidirect

Maximal subgroups

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

subgroupindex
C22×#142737522
C2×#168375002
C2×C4×#117456712
C22⋊C4×D2362
#214249712
#214249612
#214244512
#214244472
#214241272
#214240362
#214240262
#214238802
C59×#23412
#2244359