Finite Group Databasebeta

← #28609460

Subgroups — #28609460

Order 15104.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837519C211yesmaximal, characteristic, complemented
2#21432823C211yesmaximal, characteristic, complemented
3C22×#14273654C211yesmaximal, characteristic, complemented
4#21432545C211yesmaximal, characteristic, complemented
5#21424985C211yesmaximal, characteristic, complemented
6#21424802C211yesmaximal, characteristic, complemented
7#21424746C211yesmaximal, characteristic, complemented
8#21424540C211yesmaximal, characteristic, complemented
9#21424425C211yesmaximal, characteristic, complemented
10#21424425C211yesmaximal, characteristic, complemented
11#21424373C211yesmaximal, characteristic, complemented
12#21424303C211yesmaximal, characteristic, complemented
13#21423936C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic59C211yesmaximal, characteristic, complemented
15C59×#3002C211yesmaximal, characteristic
16C2×#14273734C2211yescharacteristic
17C2×#14273734C2211yescharacteristic
18C2×#14273734C2211yescharacteristic, complemented
19C22×#11745664C2211yescharacteristic
20C22×C4×Dic59C2211yescharacteristic
21#16837519—24no—
22#16837480—21no—
23#16837474—21no—
24#16837474—21no—
25D4×C59⋊C8—21no—
26C2×#14273663C2211yescharacteristic, complemented
27C2×#14273663C2211yescharacteristic, complemented
28#16837429C2211yescharacteristic, complemented
29C2×#14273654—24no—
30C2×#14273654C2211yescharacteristic
31C2×#14273654C2211yescharacteristic
32C2×#14273654C2211yescharacteristic
33C2×#14273654C2211yescharacteristic
34C2×#14273654C2211yescharacteristic, complemented
35C2×#14273654C2211yescharacteristic, complemented
36#16837369—21no—
37#16837369—21no—
38#16837369C2211yescharacteristic
39#16837369C2211yescharacteristic
40#16837369C2211yescharacteristic, complemented
41#16837366—21no—
42#16837366C2211yescharacteristic
43C2×C22⋊(C59⋊C8)—21no—
44C2×C22⋊(C59⋊C8)C2211yescharacteristic
45#16837358C2211yescharacteristic, complemented
46C2×C8×Dic59C2211yescharacteristic, complemented
47C2×C8×Dic59C2211yescharacteristic, complemented
48#16837167C2211yescharacteristic, complemented
49#16837167C2211yescharacteristic, complemented
50#16837161C2211yescharacteristic, complemented
51#16837161C2211yescharacteristic, complemented
52#16837156C2211yescharacteristic, complemented
53#16837156C2211yescharacteristic, complemented
54C22×#41×C59C2211yescharacteristic
55C2×#135×C59C2211yescharacteristic
56C2×#135×C59C2211yescharacteristic
57C59×#525C2211yescharacteristic
58C59×#452C411yescharacteristic, complemented
59C59×#452C411yescharacteristic, complemented
60C59×#451C411yescharacteristic, complemented
61C59×#450C411yescharacteristic, complemented
62C59×#449C411yescharacteristic, complemented
63C59×#449C411yescharacteristic, complemented
64C59×#448C411yescharacteristic, complemented
65C59×#447C411yescharacteristic, complemented
66C59×#416C2211yescharacteristic
67C59×#416C2211yescharacteristic
68C2×C22⋊C8×C59C2211yescharacteristic
69C23×Dic59—21no—
70#14273734—22no—
71#14273734—22no—
72#14273734—22no—
73#14273734—41no—
74#14273734—41no—
75#14273734—41no—
76C2×#11745664—21no—
77C2×#11745664—21no—
78C2×#11745664—21no—
79C2×#11745664—21no—
80C2×#11745664—22no—
81C2×#11745664—41no—
82C2×#11745664C2311yescharacteristic
83C2×#11745664C2311yescharacteristic
84C2×#11745664C2311yescharacteristic
85C2×#11745664C2311yescharacteristic
86C22×C59⋊C8—21no—
87C22×C59⋊C8—21no—
88C22×C59⋊C8—21no—
89C22×C59⋊C8—21no—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C2×C4×Dic59—22no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59—41no—
95C2×C4×Dic59C2311yescharacteristic
96C2×C4×Dic59C2311yescharacteristic
97#14273663—22no—
98#14273663—41no—
99C4⋊(C59⋊C8)—21no—
100C4⋊(C59⋊C8)—21no—
101#14273654—22no—
102#14273654—22no—
103#14273654—22no—
104#14273654—22no—
105#14273654—41no—
106#14273654D414yescomplemented
107C22⋊(C59⋊C8)—21no—
108C22⋊(C59⋊C8)—21no—
109C22⋊(C59⋊C8)—21no—
110C22⋊(C59⋊C8)—21no—
111C22⋊(C59⋊C8)—21no—
112C22⋊(C59⋊C8)—21no—
113C22⋊(C59⋊C8)—21no—
114C22⋊(C59⋊C8)—21no—
115C22⋊(C59⋊C8)D411yescharacteristic
116C22⋊(C59⋊C8)D411yescharacteristic
117C22⋊(C59⋊C8)D411yescharacteristic
118C22⋊(C59⋊C8)D411yescharacteristic
119#14273638—21no—
120C4×C59⋊C8—21no—
121C8×Dic59—22no—
122C8×Dic59—41no—
123C2×#41×C59—21no—
124C2×#41×C59—21no—
125C2×#41×C59—22no—
126C2×#41×C59—22no—
127C2×#41×C59—41no—
128C2×#41×C59—41no—
129C2×#41×C59C2×C411yescharacteristic
130C2×#41×C59C2×C411yescharacteristic
131C2×#41×C59C2311yescharacteristic
132C2×#41×C59C2311yescharacteristic
133C2×#41×C59C2311yescharacteristic
134C22×Q8×C59C2×C411yescharacteristic
135C22×D4×C59—21no—
136C22×D4×C59C2×C411yescharacteristic
137C23×C4×C59—21no—
138C23×C4×C59C2311yescharacteristic
139#135×C59—22no—
140#135×C59—22no—
141#135×C59—41no—
142#135×C59—41no—
143C2×Q16×C59C2×C411yescharacteristic, complemented
144C2×Q16×C59C2×C411yescharacteristic, complemented
145C2×SD16×C59C2×C411yescharacteristic, complemented
146C2×SD16×C59C2×C411yescharacteristic, complemented
147C2×SD16×C59C2×C411yescharacteristic, complemented
148C2×SD16×C59C2×C411yescharacteristic, complemented
149C2×D8×C59C2×C411yescharacteristic, complemented
150C2×D8×C59C2×C411yescharacteristic, complemented
151C22×C8×C59C2311yescharacteristic
152C22×C8×C59C2311yescharacteristic
153#123×C59—21no—
154C22⋊Q8×C59C2×C411yescharacteristic
155C22⋊Q8×C59C2×C411yescharacteristic
156#121×C59C2×C411yescharacteristic
157#121×C59C2×C411yescharacteristic
158#120×C59—21no—
159C4×D4×C59—21no—
160C4×D4×C59—21no—
161#117×C59C2311yescharacteristic
162#103×C59C2×C411yescharacteristic, complemented
163#103×C59C2×C411yescharacteristic, complemented
164#103×C59C2×C411yescharacteristic, complemented
165#103×C59C2×C411yescharacteristic, complemented
166#102×C59C2×C411yescharacteristic, complemented
167#102×C59C2×C411yescharacteristic, complemented
168#102×C59C2×C411yescharacteristic, complemented
169#102×C59C2×C411yescharacteristic, complemented
170C22⋊C8×C59C2×C411yescharacteristic
171C22⋊C8×C59C2×C411yescharacteristic
172C22⋊C8×C59C2×C411yescharacteristic
173C22⋊C8×C59C2×C411yescharacteristic
174C24×C59—21no—
175C24×C59#4111yescharacteristic
176#41×C59—21no—
177#41×C59—21no—
178#41×C59—22no—
179#41×C59—22no—
180#41×C59—21no—
181#41×C59—21no—
182#41×C59—21no—
183#41×C59—21no—
184#41×C59—21no—
185#41×C59—21no—
186#41×C59—21no—
187#41×C59—21no—
188#41×C59—42no—
189#41×C59—42no—
190#41×C59—41no—
191#41×C59—41no—
192#41×C59—42no—
193#41×C59—42no—
194#41×C59C2×D412yes—
195#41×C59#4112yes—
196C2×Q8×C59—21no—
197C2×Q8×C59—22no—
198C2×Q8×C59—41no—
199C2×Q8×C59C22×C411yescharacteristic
200C2×Q8×C59C22×C411yescharacteristic
201C2×Q8×C59C22×C411yescharacteristic
202C2×D4×C59—21no—
203C2×D4×C59—22no—
204C2×D4×C59—21no—
205C2×D4×C59—21no—
206C2×D4×C59—21no—
207C2×D4×C59—21no—
208C2×D4×C59—21no—
209C2×D4×C59—21no—
210C2×D4×C59—21no—
211C2×D4×C59—41no—
212C2×D4×C59—42no—
213C2×D4×C59—42no—
214C2×D4×C59C22×C411yescharacteristic
215C2×D4×C59C22×C411yescharacteristic
216C2×D4×C59C22×C411yescharacteristic
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—21no—
227C22×C4×C59—42no—
228C22×C4×C59—42no—
229C22×C4×C59C22×C411yescharacteristic
230C22×C4×C59C22×C411yescharacteristic
231C22×C4×C59C2×D411yescharacteristic
232C22×C4×C59C2×D411yescharacteristic
233C22×C4×C59#4111yescharacteristic
234C22×C4×C59C2411yescharacteristic
235C22×Dic59—21no—
236C22×Dic59—24no—
237C22×Dic59—21no—
238C22×Dic59—42no—
239C22×Dic59—42no—
240Q16×C59—22no—
241Q16×C59—41no—
242SD16×C59—22no—
243SD16×C59—22no—
244SD16×C59—41no—
245SD16×C59—41no—
246D8×C59—22no—
247D8×C59—41no—
248C2×C8×C59—21no—
249C2×C8×C59—21no—
250C2×C8×C59—21no—
251C2×C8×C59—21no—
252C2×C8×C59C22×C411yescharacteristic
253C2×C8×C59C22×C411yescharacteristic
254C2×C8×C59C22×C411yescharacteristic
255C2×C8×C59C22×C411yescharacteristic
256C4⋊C4×C59—21no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59C22×C411yescharacteristic
259C4⋊C4×C59C22×C411yescharacteristic
260C22⋊C4×C59—21no—
261C22⋊C4×C59—21no—
262C22⋊C4×C59—21no—
263C22⋊C4×C59—21no—
264C22⋊C4×C59—21no—
265C42×C59—21no—
266C4×Dic59—21no—
267C4×Dic59—21no—
268C4×Dic59—21no—
269C4×Dic59—42no—
270C4×Dic59C2×D412yes—
271#11745664—21no—
272#11745664—21no—
273#11745664—21no—
274#11745664—21no—
275#11745664—21no—
276#11745664—21no—
277#11745664—21no—
278#11745664—42no—
279#11745664—42no—
280#11745664—42no—
281#11745664—42no—
282#11745664C2×D412yes—
283C2×C59⋊C8—21no—
284C2×C59⋊C8—21no—
285C2×C59⋊C8—21no—
286C2×C59⋊C8—21no—
287C2×C59⋊C8—21no—
288C2×C59⋊C8—21no—
289C2×C59⋊C8—21no—
290C2×C59⋊C8—21no—
291C2×C59⋊C8—42no—
292C2×C59⋊C8—42no—
293C2×C59⋊C8—42no—
294C2×C59⋊C8—42no—
295C2×C59⋊C8C2×D411yescharacteristic
296C2×C59⋊C8C2×D411yescharacteristic
297C2×C59⋊C8C2×D411yescharacteristic
298C2×C59⋊C8C2×D411yescharacteristic
299C23×C59—21no—
300C23×C59—21no—
301C23×C59—21no—
302C23×C59—22no—
303C23×C59—21no—
304C23×C59—21no—
305C23×C59—41no—
306C23×C59—42no—
307C23×C59—42no—
308C23×C59—81no—
309C23×C59C4×D411yescharacteristic
310C23×C59C4×D411yescharacteristic
311C23×C59C2×#4111yescharacteristic
312Q8×C59—21no—
313Q8×C59—21no—
314Q8×C59—21no—
315Q8×C59—21no—
316Q8×C59—21no—
317Q8×C59—42no—
318Q8×C59C4×D412yes—
319D4×C59—22no—
320D4×C59—22no—
321D4×C59—21no—
322D4×C59—21no—
323D4×C59—21no—
324D4×C59—21no—
325D4×C59—21no—
326D4×C59—42no—
327D4×C59—42no—
328D4×C59—42no—
329D4×C59—41no—
330D4×C59—41no—
331D4×C59—41no—
332D4×C59—41no—
333D4×C59—42no—
334D4×C59—81no—
335D4×C59C4×D412yes—
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—22no—
345C2×C4×C59—21no—
346C2×C4×C59—22no—
347C2×C4×C59—21no—
348C2×C4×C59—21no—
349C2×C4×C59—21no—
350C2×C4×C59—21no—
351C2×C4×C59—21no—
352C2×C4×C59—21no—
353C2×C4×C59—42no—
354C2×C4×C59—42no—
355C2×C4×C59—42no—
356C2×C4×C59—41no—
357C2×C4×C59—41no—
358C2×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59C4×D411yescharacteristic
361C2×C4×C59C4×D411yescharacteristic
362C2×C4×C59C23×C411yescharacteristic
363C2×C4×C59C22×D411yescharacteristic
364C2×C4×C59C22×D411yescharacteristic
365C2×C4×C59C2×#4111yescharacteristic
366C2×C4×C59H(5,𝔽2)11yescharacteristic
367C2×C4×C59H(5,𝔽2)11yescharacteristic
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—22no—
372C2×Dic59—48no—
373C2×Dic59—41no—
374C2×Dic59—41no—
375C8×C59—21no—
376C8×C59—21no—
377C8×C59—21no—
378C8×C59—21no—
379C59⋊C8—21no—
380C59⋊C8—21no—
381C59⋊C8—22no—
382C59⋊C8—21no—
383C59⋊C8—21no—
384C59⋊C8—41no—
385C59⋊C8—41no—
386C59⋊C8—41no—
387#22888—591nomaximal, Sylow
388C22×C59—21no—
389C22×C59—21no—
390C22×C59—21no—
391C22×C59—21no—
392C22×C59—21no—
393C22×C59—22no—
394C22×C59—21no—
395C22×C59—21no—
396C22×C59—42no—
397C22×C59—42no—
398C22×C59—41no—
399C22×C59—41no—
400C22×C59—41no—
401C22×C59—41no—
402C22×C59—41no—
403C22×C59—41no—
404C22×C59—41no—
405C22×C59—41no—
406C22×C59—84no—
407C22×C59#44312yescomplemented
408C22×C59C2×C4×D411yescharacteristic
409C22×C59#54611yescharacteristic
410C22×C59#55111yescharacteristic
411C4×C59—21no—
412C4×C59—21no—
413C4×C59—22no—
414C4×C59—41no—
415C4×C59—41no—
416C4×C59—41no—
417C4×C59—41no—
418C4×C59C2×C4×D411yescharacteristic
419C4×C59#51811yescharacteristic
420C4×C59D4211yescharacteristic
421C4×C59#54611yescharacteristic
422Dic59—24no—
423Dic59—42no—
424#3002D5911yescharacteristic
425C2×#443—591no—
426#2933—591no—
427C22×#104—591no—
428#2880—591no—
429#1974—591no—
430#1937—591no—
431#1929—591no—
432#1896—591no—
433#1876—591no—
434#1876—591no—
435#1866—591no—
436#1855—591no—
437#1764—591no—
438C4×C22⋊C8—591no—
439C2×C59—21no—
440C2×C59—22no—
441C2×C59—21no—
442C2×C59—41no—
443C2×C59—42no—
444C2×C59—81no—
445C2×C59—81no—
446C2×C59#235811yescharacteristic
447C2×C59C2×#44311yescharacteristic
448C2×C59#295611yescharacteristic
449C22×#41C2×D5911yescharacteristic
450C2×#135C2×D5911yescharacteristic
451C2×#135C2×D5911yescharacteristic
452C2×#131—591no—
453C2×#131—591no—
454C2×#131—591no—
455C22×M16—591no—
456#525C2×D5911yescharacteristic
457C22×C42—591no—
458#452Dic5911yescharacteristic, complemented
459#452Dic5911yescharacteristic, complemented
460#451Dic5911yescharacteristic, complemented
461#450Dic5911yescharacteristic, complemented
462#449Dic5911yescharacteristic, complemented
463#449Dic5911yescharacteristic, complemented
464#448Dic5911yescharacteristic, complemented
465#447Dic5911yescharacteristic, complemented
466#443—1184no—
467#436—1181no—
468#435—1181no—
469#435—1181no—
470C8×D4—1181no—
471C2×#108—591no—
472C2×#108—591no—
473#424—591no—
474C2×#104—591no—
475C2×#104—591no—
476C2×#104—591no—
477C2×#104—591no—
478C2×#104—591no—
479C2×#104—591no—
480C2×#104—1184no—
481#416C2×D5911yescharacteristic
482#416C2×D5911yescharacteristic
483#408—591no—
484#408—591no—
485#408—591no—
486#408—1181no—
487#408—1181no—
488#407—591no—
489#407—1181no—
490C2×C22⋊C8—591no—
491C2×C22⋊C8—1181no—
492C2×C22⋊C8C2×D5911yescharacteristic
493#405—591no—
494C2×C4×C8—591no—
495C2×C4×C8—591no—
496#341—591no—
497#341—591no—
498#339—591no—
499#339—591no—
500#336—591no—
501#336—591no—
502C59#2288811yescharacteristic, complemented, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×Dic5911yescharacteristic
510C2×#41C2×Dic5911yescharacteristic
511C2×#41C22×D5911yescharacteristic
512C2×#41C22×D5911yescharacteristic
513C2×#41C22×D5911yescharacteristic
514C22×Q8C2×Dic5911yescharacteristic
515C22×D4—21no—
516C22×D4C2×Dic5911yescharacteristic
517C23×C4—21no—
518C23×C4—1181no—
519C23×C4C22×D5911yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×Dic5911yescharacteristic, complemented
525C2×Q16C2×Dic5911yescharacteristic, complemented
526C2×SD16C2×Dic5911yescharacteristic, complemented
527C2×SD16C2×Dic5911yescharacteristic, complemented
528C2×SD16C2×Dic5911yescharacteristic, complemented
529C2×SD16C2×Dic5911yescharacteristic, complemented
530C2×D8C2×Dic5911yescharacteristic, complemented
531C2×D8C2×Dic5911yescharacteristic, complemented
532#131—1182no—
533#131—1182no—
534#131—1182no—
535#131—2361no—
536#131—2361no—
537#131—2361no—
538C2×M16—591no—
539C2×M16—591no—
540C2×M16—591no—
541C2×M16—591no—
542C2×M16—1181no—
543C2×M16—1181no—
544C2×M16—1181no—
545C2×M16—1181no—
546C2×M16—1182no—
547C2×M16—2361no—
548C22×C8—591no—
549C22×C8—591no—
550C22×C8—1181no—
551C22×C8—1181no—
552C22×C8—1181no—
553C22×C8—1181no—
554C22×C8C22×D5911yescharacteristic
555C22×C8C22×D5911yescharacteristic
556#123—21no—
557C22⋊Q8C2×Dic5911yescharacteristic
558C22⋊Q8C2×Dic5911yescharacteristic
559#121C2×Dic5911yescharacteristic
560#121C2×Dic5911yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D5911yescharacteristic
565C2×C42—591no—
566C2×C42—591no—
567C2×C42—1182no—
568C2×C42—1181no—
569C2×C42—2361no—
570#108—1182no—
571#108—2361no—
572C4⋊C8—1181no—
573C4⋊C8—1181no—
574#104—594no—
575#104—1182no—
576#104—1182no—
577#104—1182no—
578#104—1182no—
579#104—2361no—
580#103C2×Dic5911yescharacteristic, complemented
581#103C2×Dic5911yescharacteristic, complemented
582#103C2×Dic5911yescharacteristic, complemented
583#103C2×Dic5911yescharacteristic, complemented
584#102C2×Dic5911yescharacteristic, complemented
585#102C2×Dic5911yescharacteristic, complemented
586#102C2×Dic5911yescharacteristic, complemented
587#102C2×Dic5911yescharacteristic, complemented
588C22⋊C8—591no—
589C22⋊C8—591no—
590C22⋊C8—591no—
591C22⋊C8—591no—
592C22⋊C8—1181no—
593C22⋊C8—1181no—
594C22⋊C8—1181no—
595C22⋊C8—1181no—
596C22⋊C8—1181no—
597C22⋊C8—1181no—
598C22⋊C8—1181no—
599C22⋊C8—1181no—
600C22⋊C8C2×Dic5911yescharacteristic
601C22⋊C8C2×Dic5911yescharacteristic
602C22⋊C8C2×Dic5911yescharacteristic
603C22⋊C8C2×Dic5911yescharacteristic
604#97—1181no—
605C4×C8—1181no—
606C4×C8—1182no—
607C4×C8—2361no—
608C24—21no—
609C24#1174568711yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41D4×D5912yes—
629#41#1174568712yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×Dic5911yescharacteristic
634C2×Q8C22×Dic5911yescharacteristic
635C2×Q8C22×Dic5911yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×Dic5911yescharacteristic
649C2×D4C22×Dic5911yescharacteristic
650C2×D4C22×Dic5911yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—1181no—
664C22×C4—1184no—
665C22×C4—1181no—
666C22×C4—2362no—
667C22×C4—2362no—
668C22×C4D4×D5911yescharacteristic
669C22×C4D4×D5911yescharacteristic
670C22×C4#1174568711yescharacteristic
671C22×C4C22×Dic5911yescharacteristic
672C22×C4C22×Dic5911yescharacteristic
673C22×C4C23×D5911yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—592no—
683M16—1181no—
684M16—1181no—
685M16—1181no—
686M16—1181no—
687M16—1181no—
688M16—1181no—
689M16—1181no—
690M16—2362no—
691M16—2362no—
692M16—2362no—
693M16—2362no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—591no—
699C2×C8—591no—
700C2×C8—591no—
701C2×C8—591no—
702C2×C8—1181no—
703C2×C8—1181no—
704C2×C8—1181no—
705C2×C8—1181no—
706C2×C8—1181no—
707C2×C8—1181no—
708C2×C8—1181no—
709C2×C8—1181no—
710C2×C8—2362no—
711C2×C8—2362no—
712C2×C8—2362no—
713C2×C8—2362no—
714C2×C8C22×Dic5911yescharacteristic
715C2×C8C22×Dic5911yescharacteristic
716C2×C8C22×Dic5911yescharacteristic
717C2×C8C22×Dic5911yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×Dic5911yescharacteristic
721C4⋊C4C22×Dic5911yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—592no—
729C42—1181no—
730C42—1181no—
731C42—1181no—
732C42—2362no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23D4×Dic5911yescharacteristic
744C23D4×Dic5911yescharacteristic
745C23C2×#1174568711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8D4×Dic5912yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—81no—
769D4D4×Dic5912yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—1182no—
795C2×C4—1182no—
796C2×C4—1182no—
797C2×C4—1182no—
798C2×C4—2368no—
799C2×C4—2361no—
800C2×C4—2361no—
801C2×C4D4×Dic5911yescharacteristic
802C2×C4D4×Dic5911yescharacteristic
803C2×C4C23×Dic5911yescharacteristic
804C2×C4C2×D4×D5911yescharacteristic
805C2×C4C2×D4×D5911yescharacteristic
806C2×C4C2×#1174568711yescharacteristic
807C2×C4#1427377211yescharacteristic
808C2×C4#1427377211yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—1181no—
814C8—1181no—
815C8—1182no—
816C8—1181no—
817C8—1181no—
818C8—2361no—
819C8—2361no—
820C8—2361no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#1683751912yescomplemented
841C22C2×D4×Dic5911yescharacteristic
842C22#1683803911yescharacteristic
843C22#1683808311yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—1184no—
852C4—2362no—
853C4C2×D4×Dic5911yescharacteristic
854C4#1683787711yescharacteristic
855C4#1683803411yescharacteristic
856C4#1683803911yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2#2142708011yescharacteristic
865C2C2×#1683751911yescharacteristic
866C2#2143300611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC59×#3002C2
socleC22×C59C2×C4×D4
cosocleC22×C4×C59C24
hypercenter#3002D59
hypocenterC59#22888
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#16837519C2semidirect
2. #21432823C2semidirect
3. C22×#14273654C2semidirect
4. #21432545C2semidirect
5. #21424985C2semidirect
6. #21424802C2semidirect
7. #21424746C2semidirect
8. #21424540C2semidirect
9. #21424425C2semidirect
10. #21424425C2semidirect
11. #21424373C2semidirect
12. #21424303C2semidirect
13. #21423936C2semidirect
14. C22⋊C8×Dic59C2semidirect
18. C2×#14273734C22semidirect
26. C2×#14273663C22semidirect
27. C2×#14273663C22semidirect
28. #16837429C22semidirect
34. C2×#14273654C22semidirect
35. C2×#14273654C22semidirect
40. #16837369C22semidirect
45. #16837358C22semidirect
46. C2×C8×Dic59C22semidirect
47. C2×C8×Dic59C22semidirect
48. #16837167C22semidirect
49. #16837167C22semidirect
50. #16837161C22semidirect
51. #16837161C22semidirect
52. #16837156C22semidirect
53. #16837156C22semidirect
58. C59×#452C4semidirect
59. C59×#452C4semidirect
60. C59×#451C4semidirect
61. C59×#450C4semidirect
62. C59×#449C4semidirect
63. C59×#449C4semidirect
64. C59×#448C4semidirect
65. C59×#447C4semidirect
106. #14273654D4semidirect
143. C2×Q16×C59C2×C4semidirect
144. C2×Q16×C59C2×C4semidirect
145. C2×SD16×C59C2×C4semidirect
146. C2×SD16×C59C2×C4semidirect
147. C2×SD16×C59C2×C4semidirect
148. C2×SD16×C59C2×C4semidirect
149. C2×D8×C59C2×C4semidirect
150. C2×D8×C59C2×C4semidirect
162. #103×C59C2×C4semidirect
163. #103×C59C2×C4semidirect
164. #103×C59C2×C4semidirect
165. #103×C59C2×C4semidirect
166. #102×C59C2×C4semidirect
167. #102×C59C2×C4semidirect
168. #102×C59C2×C4semidirect
169. #102×C59C2×C4semidirect
407. C22×C59#443semidirect
458. #452Dic59semidirect
459. #452Dic59semidirect
460. #451Dic59semidirect
461. #450Dic59semidirect
462. #449Dic59semidirect
463. #449Dic59semidirect
464. #448Dic59semidirect
465. #447Dic59semidirect
502. C59#22888semidirect
524. C2×Q16C2×Dic59semidirect
525. C2×Q16C2×Dic59semidirect
526. C2×SD16C2×Dic59semidirect
527. C2×SD16C2×Dic59semidirect
528. C2×SD16C2×Dic59semidirect
529. C2×SD16C2×Dic59semidirect
530. C2×D8C2×Dic59semidirect
531. C2×D8C2×Dic59semidirect
580. #103C2×Dic59semidirect
581. #103C2×Dic59semidirect
582. #103C2×Dic59semidirect
583. #103C2×Dic59semidirect
584. #102C2×Dic59semidirect
585. #102C2×Dic59semidirect
586. #102C2×Dic59semidirect
587. #102C2×Dic59semidirect
840. C22#16837519semidirect

Maximal subgroups

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

subgroupindex
C2×#168375192
#214328232
C22×#142736542
#214325452
#214249852
#214248022
#214247462
#214245402
#214244252
#214243732
#214243032
#214239362
C22⋊C8×Dic592
C59×#30022
#2288859