Finite Group Databasebeta

← #28609445

Subgroups — #28609445

Order 15104.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837524C211yesmaximal, characteristic, complemented
2#21432823C211yesmaximal, characteristic, complemented
3C2×#16837419C211yesmaximal, characteristic, complemented
4#21432545C211yesmaximal, characteristic, complemented
5#21424985C211yesmaximal, characteristic, complemented
6#21424809C211yesmaximal, characteristic, complemented
7#21424746C211yesmaximal, characteristic, complemented
8#21424545C211yesmaximal, characteristic, complemented
9#21424425C211yesmaximal, characteristic, complemented
10#21424425C211yesmaximal, characteristic, complemented
11#21424373C211yesmaximal, characteristic, complemented
12#21424303C211yesmaximal, characteristic, complemented
13#21423936C211yesmaximal, characteristic, complemented
14#21423864C211yesmaximal, characteristic, complemented
15C59×#3002C211yesmaximal, characteristic
16C2×#14273734C2211yescharacteristic
17C2×#14273734C2211yescharacteristic
18C2×#14273734C2211yescharacteristic, complemented
19C22×#11745664C2211yescharacteristic
20C2×#14273686C2211yescharacteristic
21#16837524—24no—
22#16837480—21no—
23#16837474—21no—
24#16837474—21no—
25D4×C59⋊C8—21no—
26C2×#14273663C2211yescharacteristic, complemented
27C2×#14273663C2211yescharacteristic, complemented
28#16837429C2211yescharacteristic, complemented
29#16837419—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×#14273637C2211yescharacteristic, 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
69#14273734—22no—
70#14273734—22no—
71#14273734—22no—
72#14273734—41no—
73#14273734—41no—
74#14273734—41no—
75C2×#11745664—21no—
76C2×#11745664—21no—
77C2×#11745664—21no—
78C2×#11745664—21no—
79C2×#11745664—22no—
80C2×#11745664—41no—
81C2×#11745664C2311yescharacteristic
82C2×#11745664C2311yescharacteristic
83C2×#11745664C2311yescharacteristic
84C2×#11745664C2311yescharacteristic
85C22×C59⋊C8—21no—
86C22×C59⋊C8—21no—
87C22×C59⋊C8—21no—
88C22×C59⋊C8—21no—
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91#14273686—22no—
92#14273686—41no—
93C2×C4⋊Dic59—21no—
94C2×C22⋊Dic59—21no—
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—
120#14273637—22no—
121C4×C59⋊C8—21no—
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
144C2×Q16×C59C2×C411yescharacteristic
145C2×SD16×C59C2×C411yescharacteristic
146C2×SD16×C59C2×C411yescharacteristic
147C2×SD16×C59C2×C411yescharacteristic
148C2×SD16×C59C2×C411yescharacteristic
149C2×D8×C59C2×C411yescharacteristic
150C2×D8×C59C2×C411yescharacteristic
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
163#103×C59C2×C411yescharacteristic
164#103×C59C2×C411yescharacteristic
165#103×C59C2×C411yescharacteristic
166#102×C59C2×C411yescharacteristic
167#102×C59C2×C411yescharacteristic
168#102×C59C2×C411yescharacteristic
169#102×C59C2×C411yescharacteristic
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—21no—
237Q16×C59—22no—
238Q16×C59—41no—
239SD16×C59—22no—
240SD16×C59—22no—
241SD16×C59—41no—
242SD16×C59—41no—
243D8×C59—22no—
244D8×C59—41no—
245C2×C8×C59—21no—
246C2×C8×C59—21no—
247C2×C8×C59—21no—
248C2×C8×C59—21no—
249C2×C8×C59C22×C411yescharacteristic
250C2×C8×C59C22×C411yescharacteristic
251C2×C8×C59C22×C411yescharacteristic
252C2×C8×C59C22×C411yescharacteristic
253C4⋊C4×C59—21no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59C22×C411yescharacteristic
256C4⋊C4×C59C22×C411yescharacteristic
257C22⋊C4×C59—21no—
258C22⋊C4×C59—21no—
259C22⋊C4×C59—21no—
260C22⋊C4×C59—21no—
261C22⋊C4×C59—21no—
262C42×C59—21no—
263C22⋊Dic59—42no—
264C4⋊Dic59—42no—
265C4×Dic59—21no—
266C4×Dic59—21no—
267C4×Dic59—21no—
268C4×Dic59C2×D412yes—
269#11745664—21no—
270#11745664—21no—
271#11745664—21no—
272#11745664—21no—
273#11745664—21no—
274#11745664—21no—
275#11745664—21no—
276#11745664—42no—
277#11745664—42no—
278#11745664—42no—
279#11745664—42no—
280#11745664C2×D412yes—
281C2×C59⋊C8—21no—
282C2×C59⋊C8—21no—
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—42no—
290C2×C59⋊C8—42no—
291C2×C59⋊C8—42no—
292C2×C59⋊C8—42no—
293C2×C59⋊C8C2×D411yescharacteristic
294C2×C59⋊C8C2×D411yescharacteristic
295C2×C59⋊C8C2×D411yescharacteristic
296C2×C59⋊C8C2×D411yescharacteristic
297C23×C59—21no—
298C23×C59—21no—
299C23×C59—21no—
300C23×C59—21no—
301C23×C59—21no—
302C23×C59—41no—
303C23×C59—41no—
304C23×C59—42no—
305C23×C59—42no—
306C23×C59—81no—
307C23×C59C4×D411yescharacteristic
308C23×C59C4×D411yescharacteristic
309C23×C59C2×#4111yescharacteristic
310Q8×C59—21no—
311Q8×C59—21no—
312Q8×C59—21no—
313Q8×C59—21no—
314Q8×C59—21no—
315Q8×C59—42no—
316Q8×C59C4×D412yes—
317D4×C59—22no—
318D4×C59—22no—
319D4×C59—21no—
320D4×C59—21no—
321D4×C59—21no—
322D4×C59—21no—
323D4×C59—21no—
324D4×C59—42no—
325D4×C59—42no—
326D4×C59—42no—
327D4×C59—42no—
328D4×C59—41no—
329D4×C59—41no—
330D4×C59—41no—
331D4×C59—41no—
332D4×C59—81no—
333D4×C59C4×D412yes—
334C2×C4×C59—21no—
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—22no—
343C2×C4×C59—21no—
344C2×C4×C59—22no—
345C2×C4×C59—21no—
346C2×C4×C59—21no—
347C2×C4×C59—21no—
348C2×C4×C59—21no—
349C2×C4×C59—21no—
350C2×C4×C59—21no—
351C2×C4×C59—42no—
352C2×C4×C59—42no—
353C2×C4×C59—42no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59—41no—
358C2×C4×C59C4×D411yescharacteristic
359C2×C4×C59C4×D411yescharacteristic
360C2×C4×C59C23×C411yescharacteristic
361C2×C4×C59C22×D411yescharacteristic
362C2×C4×C59C22×D411yescharacteristic
363C2×C4×C59C2×#4111yescharacteristic
364C2×C4×C59H(5,𝔽2)11yescharacteristic
365C2×C4×C59H(5,𝔽2)11yescharacteristic
366C2×Dic59—22no—
367C2×Dic59—41no—
368C2×Dic59—41no—
369C2×Dic59—41no—
370C2×Dic59—41no—
371C2×Dic59—41no—
372C8×C59—21no—
373C8×C59—21no—
374C8×C59—21no—
375C8×C59—21no—
376C59⋊C8—21no—
377C59⋊C8—21no—
378C59⋊C8—22no—
379C59⋊C8—21no—
380C59⋊C8—21no—
381C59⋊C8—41no—
382C59⋊C8—41no—
383C59⋊C8—41no—
384#22887—591nomaximal, Sylow
385C22×C59—21no—
386C22×C59—21no—
387C22×C59—21no—
388C22×C59—21no—
389C22×C59—22no—
390C22×C59—21no—
391C22×C59—21no—
392C22×C59—21no—
393C22×C59—21no—
394C22×C59—41no—
395C22×C59—41no—
396C22×C59—41no—
397C22×C59—41no—
398C22×C59—41no—
399C22×C59—41no—
400C22×C59—41no—
401C22×C59—41no—
402C22×C59—81no—
403C22×C59—81no—
404C22×C59—84no—
405C22×C59C2×C4×D411yescharacteristic
406C22×C59#54611yescharacteristic
407C22×C59#55111yescharacteristic
408C4×C59—21no—
409C4×C59—21no—
410C4×C59—22no—
411C4×C59—41no—
412C4×C59—41no—
413C4×C59—41no—
414C4×C59—41no—
415C4×C59C2×C4×D411yescharacteristic
416C4×C59#51811yescharacteristic
417C4×C59D4211yescharacteristic
418C4×C59#54611yescharacteristic
419Dic59—42no—
420Dic59—81no—
421#3002D5911yescharacteristic
422C2×#444—591no—
423#2933—591no—
424C2×#421—591no—
425#2880—591no—
426#1974—591no—
427#1938—591no—
428#1929—591no—
429#1897—591no—
430#1876—591no—
431#1876—591no—
432#1866—591no—
433#1855—591no—
434#1764—591no—
435#1750—591no—
436C2×C59—21no—
437C2×C59—21no—
438C2×C59—41no—
439C2×C59—41no—
440C2×C59—42no—
441C2×C59—81no—
442C2×C59—81no—
443C2×C59#235811yescharacteristic
444C2×C59#295511yescharacteristic
445C2×C59#295711yescharacteristic
446C22×#41C2×D5911yescharacteristic
447C2×#135C2×D5911yescharacteristic
448C2×#135C2×D5911yescharacteristic
449C2×#131—591no—
450C2×#131—591no—
451C2×#131—591no—
452C22×M16—591no—
453#525C2×D5911yescharacteristic
454C2×#117—591no—
455#452Dic5911yescharacteristic, complemented
456#452Dic5911yescharacteristic, complemented
457#451Dic5911yescharacteristic, complemented
458#450Dic5911yescharacteristic, complemented
459#449Dic5911yescharacteristic, complemented
460#449Dic5911yescharacteristic, complemented
461#448Dic5911yescharacteristic, complemented
462#447Dic5911yescharacteristic, complemented
463#444—1184no—
464#436—1181no—
465#435—1181no—
466#435—1181no—
467C8×D4—1181no—
468C2×#108—591no—
469C2×#108—591no—
470#424—591no—
471#421—1184no—
472C2×#104—591no—
473C2×#104—591no—
474C2×#104—591no—
475C2×#104—591no—
476C2×#104—591no—
477C2×#104—591no—
478#416C2×D5911yescharacteristic
479#416C2×D5911yescharacteristic
480#408—591no—
481#408—591no—
482#408—591no—
483#408—1181no—
484#408—1181no—
485#407—591no—
486#407—1181no—
487C2×C22⋊C8—591no—
488C2×C22⋊C8—1181no—
489C2×C22⋊C8C2×D5911yescharacteristic
490#405—591no—
491C2×#97—591no—
492C2×C4×C8—591no—
493#341—591no—
494#341—591no—
495#339—591no—
496#339—591no—
497#336—591no—
498#336—591no—
499C59#2288711yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×Dic5911yescharacteristic
507C2×#41C2×Dic5911yescharacteristic
508C2×#41C22×D5911yescharacteristic
509C2×#41C22×D5911yescharacteristic
510C2×#41C22×D5911yescharacteristic
511C22×Q8C2×Dic5911yescharacteristic
512C22×D4—21no—
513C22×D4C2×Dic5911yescharacteristic
514C23×C4—21no—
515C23×C4C22×D5911yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×Dic5911yescharacteristic
521C2×Q16C2×Dic5911yescharacteristic
522C2×SD16C2×Dic5911yescharacteristic
523C2×SD16C2×Dic5911yescharacteristic
524C2×SD16C2×Dic5911yescharacteristic
525C2×SD16C2×Dic5911yescharacteristic
526C2×D8C2×Dic5911yescharacteristic
527C2×D8C2×Dic5911yescharacteristic
528#131—1182no—
529#131—1182no—
530#131—1182no—
531#131—2361no—
532#131—2361no—
533#131—2361no—
534C2×M16—591no—
535C2×M16—591no—
536C2×M16—591no—
537C2×M16—591no—
538C2×M16—1181no—
539C2×M16—1181no—
540C2×M16—1181no—
541C2×M16—1181no—
542C2×M16—1182no—
543C2×M16—2361no—
544C22×C8—591no—
545C22×C8—591no—
546C22×C8—1181no—
547C22×C8—1181no—
548C22×C8—1181no—
549C22×C8—1181no—
550C22×C8C22×D5911yescharacteristic
551C22×C8C22×D5911yescharacteristic
552#123—21no—
553C22⋊Q8C2×Dic5911yescharacteristic
554C22⋊Q8C2×Dic5911yescharacteristic
555#121C2×Dic5911yescharacteristic
556#121C2×Dic5911yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—1182no—
561#117—2361no—
562#117C22×D5911yescharacteristic
563C2×C4⋊C4—1181no—
564C2×C22⋊C4—1181no—
565C2×C42—591no—
566C2×C42—591no—
567#108—1182no—
568#108—2361no—
569C4⋊C8—1181no—
570C4⋊C8—1181no—
571#104—594no—
572#104—1182no—
573#104—1182no—
574#104—1182no—
575#104—1182no—
576#104—2361no—
577#103C2×Dic5911yescharacteristic
578#103C2×Dic5911yescharacteristic
579#103C2×Dic5911yescharacteristic
580#103C2×Dic5911yescharacteristic
581#102C2×Dic5911yescharacteristic
582#102C2×Dic5911yescharacteristic
583#102C2×Dic5911yescharacteristic
584#102C2×Dic5911yescharacteristic
585C22⋊C8—591no—
586C22⋊C8—591no—
587C22⋊C8—591no—
588C22⋊C8—591no—
589C22⋊C8—1181no—
590C22⋊C8—1181no—
591C22⋊C8—1181no—
592C22⋊C8—1181no—
593C22⋊C8—1181no—
594C22⋊C8—1181no—
595C22⋊C8—1181no—
596C22⋊C8—1181no—
597C22⋊C8C2×Dic5911yescharacteristic
598C22⋊C8C2×Dic5911yescharacteristic
599C22⋊C8C2×Dic5911yescharacteristic
600C22⋊C8C2×Dic5911yescharacteristic
601#97—1181no—
602#97—1182no—
603C4×C8—1181no—
604C4×C8—2361no—
605C24—21no—
606C24#1174568711yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41D4×D5912yes—
626#41#1174568712yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×Dic5911yescharacteristic
631C2×Q8C22×Dic5911yescharacteristic
632C2×Q8C22×Dic5911yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×Dic5911yescharacteristic
646C2×D4C22×Dic5911yescharacteristic
647C2×D4C22×Dic5911yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—1181no—
661C22×C4—1181no—
662C22×C4D4×D5911yescharacteristic
663C22×C4D4×D5911yescharacteristic
664C22×C4#1174568711yescharacteristic
665C22×C4C22×Dic5911yescharacteristic
666C22×C4C22×Dic5911yescharacteristic
667C22×C4C23×D5911yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—592no—
677M16—1181no—
678M16—1181no—
679M16—1181no—
680M16—1181no—
681M16—1181no—
682M16—1181no—
683M16—1181no—
684M16—2362no—
685M16—2362no—
686M16—2362no—
687M16—2362no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—591no—
693C2×C8—591no—
694C2×C8—591no—
695C2×C8—591no—
696C2×C8—1181no—
697C2×C8—1181no—
698C2×C8—1181no—
699C2×C8—1181no—
700C2×C8—1181no—
701C2×C8—1181no—
702C2×C8—1181no—
703C2×C8—1181no—
704C2×C8—2362no—
705C2×C8—2362no—
706C2×C8—2362no—
707C2×C8—2362no—
708C2×C8C22×Dic5911yescharacteristic
709C2×C8C22×Dic5911yescharacteristic
710C2×C8C22×Dic5911yescharacteristic
711C2×C8C22×Dic5911yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—2362no—
715C4⋊C4C22×Dic5911yescharacteristic
716C4⋊C4C22×Dic5911yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—2362no—
723C42—21no—
724C42—592no—
725C42—1181no—
726C42—1181no—
727C42—1181no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23D4×Dic5911yescharacteristic
739C23D4×Dic5911yescharacteristic
740C23C2×#1174568711yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8D4×Dic5912yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4D4×Dic5912yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—1182no—
790C2×C4—2361no—
791C2×C4—2361no—
792C2×C4—2361no—
793C2×C4—2361no—
794C2×C4—2361no—
795C2×C4D4×Dic5911yescharacteristic
796C2×C4D4×Dic5911yescharacteristic
797C2×C4C23×Dic5911yescharacteristic
798C2×C4C2×D4×D5911yescharacteristic
799C2×C4C2×D4×D5911yescharacteristic
800C2×C4C2×#1174568711yescharacteristic
801C2×C4#1427377211yescharacteristic
802C2×C4#1427377211yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—1181no—
808C8—1181no—
809C8—1182no—
810C8—1181no—
811C8—1181no—
812C8—2361no—
813C8—2361no—
814C8—2361no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×D4×Dic5911yescharacteristic
836C22#1683803911yescharacteristic
837C22#1683808311yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—4721no—
846C4—2362no—
847C4C2×D4×Dic5911yescharacteristic
848C4#1683787711yescharacteristic
849C4#1683803411yescharacteristic
850C4#1683803911yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#2142708011yescharacteristic
859C2#2143299911yescharacteristic
860C2#2143301311yescharacteristic
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#22887
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×#16837524C2semidirect
2. #21432823C2semidirect
3. C2×#16837419C2semidirect
4. #21432545C2semidirect
5. #21424985C2semidirect
6. #21424809C2semidirect
7. #21424746C2semidirect
8. #21424545C2semidirect
9. #21424425C2semidirect
10. #21424425C2semidirect
11. #21424373C2semidirect
12. #21424303C2semidirect
13. #21423936C2semidirect
14. #21423864C2semidirect
18. C2×#14273734C22semidirect
26. C2×#14273663C22semidirect
27. C2×#14273663C22semidirect
28. #16837429C22semidirect
34. C2×#14273654C22semidirect
35. C2×#14273654C22semidirect
40. #16837369C22semidirect
45. #16837358C22semidirect
46. C2×#14273637C22semidirect
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
455. #452Dic59semidirect
456. #452Dic59semidirect
457. #451Dic59semidirect
458. #450Dic59semidirect
459. #449Dic59semidirect
460. #449Dic59semidirect
461. #448Dic59semidirect
462. #447Dic59semidirect
499. C59#22887semidirect

Maximal subgroups

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

subgroupindex
C2×#168375242
#214328232
C2×#168374192
#214325452
#214249852
#214248092
#214247462
#214245452
#214244252
#214243732
#214243032
#214239362
#214238642
C59×#30022
#2288759