Finite Group Databasebeta

← #28646292

Subgroups — #28646292

Order 15104.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21427792C211yesmaximal, characteristic
2#21426965C211yesmaximal, characteristic
3#21425657C211yesmaximal, characteristic, complemented
4#21425588C211yesmaximal, characteristic, complemented
5#21425586C211yesmaximal, characteristic, complemented
6#21425423C211yesmaximal, characteristic, complemented
7#21425046C211yesmaximal, characteristic, complemented
8#21424853C211yesmaximal, characteristic, complemented
9#21424670C211yesmaximal, characteristic, complemented
10#21424666C211yesmaximal, characteristic, complemented
11#21424284C211yesmaximal, characteristic
12#21424274C211yesmaximal, characteristic
13#21424182C211yesmaximal, characteristic
14#21424125C211yesmaximal, characteristic
15C2×C59×#340C211yesmaximal, characteristic
16C2×#14273726C2211yescharacteristic
17C2×#14273706—21no—
18C2×#14273686—21no—
19C2×#14273661C2211yescharacteristic
20C2×#14273661C2211yescharacteristic
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×Dic59⋊C8C2211yescharacteristic
24C2×Dic59⋊C8C2211yescharacteristic
25C2×C22⋊(C59⋊C8)C2211yescharacteristic
26#16837335—21no—
27#16837322—21no—
28#16837301C2211yescharacteristic
29#16837301C2211yescharacteristic
30#16837301C2211yescharacteristic
31#16837298C2211yescharacteristic
32#16837288—21no—
33#16837288—21no—
34#16837275—21no—
35#16837271C2211yescharacteristic
36#16837265—21no—
37#16837262C2211yescharacteristic
38#16837262C2211yescharacteristic
39C4⋊C4×Dic59C2211yescharacteristic
40C4⋊C4×Dic59C2211yescharacteristic
41C4×C22⋊Dic59C2211yescharacteristic
42#16837165C2211yescharacteristic
43#16837165C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C23×C8×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C22×C4⋊C4×C59C2211yescharacteristic
55C59×#340C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C22×Dic118—21no—
60C22×C59⋊C8C2311yescharacteristic
61C22×C59⋊C8C2311yescharacteristic
62#14273726—22no—
63#14273726—41no—
64#14273706—44no—
65#14273686—44no—
66C2×C4⋊Dic59—21no—
67C2×C4⋊Dic59—21no—
68C2×C4⋊Dic59—21no—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×Dic59⋊C4—21no—
76C2×Dic59⋊C4—21no—
77C2×C22⋊Dic59—21no—
78C2×C22⋊Dic59—21no—
79C2×C22⋊Dic59D411yescharacteristic
80C2×C22⋊Dic59D411yescharacteristic
81C2×C4×Dic59—21no—
82C2×C4×Dic59—21no—
83C2×C4×Dic59C2311yescharacteristic
84C2×C4×Dic59C2311yescharacteristic
85#14273661—22no—
86#14273661—41no—
87#14273660—22no—
88#14273660—41no—
89Dic59⋊C8—22no—
90Dic59⋊C8—41no—
91C22⋊(C59⋊C8)—22no—
92C59⋊#95—21no—
93C59⋊#95—21no—
94C59⋊#95—21no—
95C59⋊#95—21no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95D411yescharacteristic
101C59⋊#95D411yescharacteristic
102C23×C4×C59—21no—
103C23×C4×C59—21no—
104C23×C4×C59C2311yescharacteristic
105C22×C8×C59—22no—
106C22×C8×C59—22no—
107C22×C8×C59—41no—
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C2×C4⋊C4×C59—21no—
111C2×C4⋊C4×C59—22no—
112C2×C4⋊C4×C59—22no—
113C2×C4⋊C4×C59—21no—
114C2×C4⋊C4×C59—41no—
115C2×C4⋊C4×C59Q814yescomplemented
116C2×C4⋊C4×C59C2311yescharacteristic
117C2×C4⋊C4×C59C2311yescharacteristic
118C2×C4⋊C4×C59C2311yescharacteristic
119C2×C4⋊C4×C59C2311yescharacteristic
120C24×C59C2×D411yescharacteristic
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59—24no—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—42no—
131C22×C4×C59—42no—
132C22×C4×C59—42no—
133C22×C4×C59—42no—
134C22×C4×C59—81no—
135C22×C4×C59C2×D411yescharacteristic
136C22×C4×C59C2×Q812yes—
137C22×C4×C59#4112yes—
138C22×C4×C59C2411yescharacteristic
139C22×Dic59—21no—
140C22×Dic59—21no—
141C22×Dic59—21no—
142C22×Dic59—21no—
143C22×Dic59C2×D411yescharacteristic
144C22×Dic59C2×D411yescharacteristic
145C22×Dic59C2×D411yescharacteristic
146C22×Dic59C2×D411yescharacteristic
147C2×Dic118—42no—
148C2×Dic118—42no—
149C2×Dic118—81no—
150C2×C8×C59—21no—
151C2×C8×C59—21no—
152C2×C8×C59—21no—
153C2×C8×C59—21no—
154C2×C8×C59—21no—
155C2×C8×C59—44no—
156C2×C8×C59#4112yes—
157C4⋊C4×C59—24no—
158C4⋊C4×C59—21no—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—42no—
164C4⋊C4×C59C2×Q812yes—
165C4⋊C4×C59C2×Q812yes—
166C4⋊C4×C59#4112yes—
167C22⋊Dic59—22no—
168C22⋊Dic59—42no—
169C22⋊Dic59—42no—
170C22⋊Dic59D814yes—
171C4⋊Dic59—21no—
172C4⋊Dic59—21no—
173C4⋊Dic59—21no—
174C4⋊Dic59—21no—
175C4⋊Dic59—21no—
176C4⋊Dic59—21no—
177C4⋊Dic59—21no—
178C4⋊Dic59—21no—
179C4⋊Dic59—42no—
180C4⋊Dic59—42no—
181C4⋊Dic59—42no—
182Dic59⋊C4—42no—
183Dic59⋊C4—42no—
184Dic59⋊C4—42no—
185Dic59⋊C4—81no—
186C4×Dic59—21no—
187C4×Dic59—21no—
188C4×Dic59—21no—
189C4×Dic59—21no—
190C4×Dic59—42no—
191C4×Dic59—42no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C2×C59⋊C8—21no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8—21no—
198C23×C59—21no—
199C23×C59—21no—
200C23×C59—21no—
201C23×C59—21no—
202C23×C59C22⋊Q812yes—
203C23×C59C2×D812yes—
204C23×C59#13712yes—
205C23×C59C22×D411yescharacteristic
206C2×C4×C59—21no—
207C2×C4×C59—21no—
208C2×C4×C59—22no—
209C2×C4×C59—22no—
210C2×C4×C59—22no—
211C2×C4×C59—22no—
212C2×C4×C59—22no—
213C2×C4×C59—22no—
214C2×C4×C59—22no—
215C2×C4×C59—41no—
216C2×C4×C59—41no—
217C2×C4×C59—41no—
218C2×C4×C59—41no—
219C2×C4×C59—41no—
220C2×C4×C59—41no—
221C2×C4×C59—48no—
222C2×C4×C59—41no—
223C2×C4×C59—41no—
224C2×C4×C59—41no—
225C2×C4×C59—84no—
226C2×C4×C59C22⋊Q812yes—
227C2×C4×C59C22×Q811yescharacteristic
228C2×C4×C59C2×#4111yescharacteristic
229C2×C4×C59C2×#4111yescharacteristic
230C2×C4×C59C2×#4111yescharacteristic
231C2×C4×C59H(5,𝔽2)11yescharacteristic
232C2×C4×C592−1+411yescharacteristic
233C2×Dic59—21no—
234C2×Dic59—21no—
235C2×Dic59—21no—
236C2×Dic59—21no—
237C2×Dic59—21no—
238C2×Dic59—21no—
239C2×Dic59—21no—
240C2×Dic59—21no—
241C2×Dic59—21no—
242C2×Dic59—21no—
243C2×Dic59—41no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59—41no—
247C2×Dic59—41no—
248C2×Dic59—41no—
249C2×Dic59—41no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254C2×Dic59—41no—
255C2×Dic59C2×D812yes—
256C2×Dic59C2×D812yes—
257Dic118—84no—
258C8×C59—22no—
259C8×C59—41no—
260C59⋊C8—41no—
261C59⋊C8—41no—
262#25988—591nomaximal, Sylow
263C22×C59—22no—
264C22×C59—22no—
265C22×C59—22no—
266C22×C59—22no—
267C22×C59—22no—
268C22×C59—22no—
269C22×C59#47414yes—
270C22×C59C2×C22⋊Q811yescharacteristic
271C22×C59#54611yescharacteristic
272C22×C59#54711yescharacteristic
273C22×C59C22×D811yescharacteristic
274C22×C59C2×#13711yescharacteristic
275C22×C59#57711yescharacteristic
276C22×C59#57811yescharacteristic
277C4×C59—22no—
278C4×C59—42no—
279C4×C59—42no—
280C4×C59—42no—
281C4×C59—81no—
282C4×C59#53311yescharacteristic
283C4×C59#54411yescharacteristic
284C4×C59#55111yescharacteristic
285C4×C59#55211yescharacteristic
286Dic59—22no—
287Dic59—22no—
288Dic59—41no—
289Dic59—41no—
290Dic59—81no—
291Dic59—81no—
292Dic59—81no—
293Dic59—81no—
294#2440—591no—
295#2344—591no—
296#2099—591no—
297#2086—591no—
298#2086—591no—
299#2057—591no—
300#1988—591no—
301#1947—591no—
302#1918—591no—
303#1918—591no—
304#1852—591no—
305#1850—591no—
306#1823—591no—
307#1808—591no—
308C2×#340D5911yescharacteristic
309C2×C59—24no—
310C2×C59#243811yescharacteristic
311C2×C59C2×#47411yescharacteristic
312C2×C59#308211yescharacteristic
313C2×C59#329411yescharacteristic
314C2×C59#331211yescharacteristic
315C2×C59#333411yescharacteristic
316C2×C59#334411yescharacteristic
317C23×C8C2×D5911yescharacteristic
318C2×C4⋊Q8—591no—
319C2×C22⋊Q8—1181no—
320C2×#117—1181no—
321C22×C4⋊C4C2×D5911yescharacteristic
322C22×C4⋊C4C2×D5911yescharacteristic
323C2×#107—591no—
324C2×#107—591no—
325C2×#107—591no—
326C2×#107—591no—
327C2×C4⋊C8—591no—
328C2×C4⋊C8—591no—
329C2×C22⋊C8—591no—
330#398—1181no—
331#395—1181no—
332#389—591no—
333#389—591no—
334#389—591no—
335#389—591no—
336#387—1181no—
337#387—1181no—
338#385—1181no—
339#384—591no—
340#381—1181no—
341#380—591no—
342#380—591no—
343C4×C4⋊C4—591no—
344C4×C4⋊C4—591no—
345C4×C22⋊C4—591no—
346#340—591no—
347#340—591no—
348#340—591no—
349#340—591no—
350#340—591no—
351#340—591no—
352#340—591no—
353#340—591no—
354#340C2×D5911yescharacteristic
355#340C2×D5911yescharacteristic
356#340C2×D5911yescharacteristic
357#340C2×D5911yescharacteristic
358#336—591no—
359#336—591no—
360C59#2598811yescharacteristic, complemented, Sylow
361C22×Q8—1181no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4C22×D5911yescharacteristic
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—41no—
368C22×C8—591no—
369C22×C8—591no—
370C22×C8C22×D5911yescharacteristic
371C22×C8C22×D5911yescharacteristic
372C4⋊Q8—1182no—
373C4⋊Q8—2361no—
374C22⋊Q8—2364no—
375#117—2364no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—591no—
382C2×C4⋊C4—591no—
383C2×C4⋊C4—591no—
384C2×C4⋊C4—591no—
385C2×C4⋊C4—1181no—
386C2×C4⋊C4—1181no—
387C2×C4⋊C4—1181no—
388C2×C4⋊C4—1181no—
389C2×C4⋊C4—1181no—
390C2×C4⋊C4—1181no—
391C2×C4⋊C4—1181no—
392C2×C4⋊C4Dic11814yescomplemented
393C2×C4⋊C4C22×D5911yescharacteristic
394C2×C4⋊C4C22×D5911yescharacteristic
395C2×C4⋊C4C22×D5911yescharacteristic
396C2×C4⋊C4C22×D5911yescharacteristic
397C2×C22⋊C4—591no—
398C2×C22⋊C4—591no—
399C2×C22⋊C4—1181no—
400C2×C22⋊C4—1181no—
401C2×C42—591no—
402C2×C42—591no—
403C2×C42—1181no—
404C2×C42—1181no—
405#107—1182no—
406#107—1182no—
407#107—2361no—
408#107—2361no—
409C4⋊C8—1182no—
410C4⋊C8—2361no—
411C22⋊C8—1182no—
412#95—591no—
413#95—591no—
414#95—1181no—
415#95—1181no—
416#95—1181no—
417#95—1181no—
418#95—1181no—
419#95—1181no—
420#95—1181no—
421#95—1181no—
422C24D4×D5911yescharacteristic
423C2×Q8—4721no—
424C2×Q8—2362no—
425C2×Q8—2362no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—81no—
440C22×C4—591no—
441C22×C4—591no—
442C22×C4—591no—
443C22×C4—591no—
444C22×C4—1181no—
445C22×C4—1181no—
446C22×C4—1181no—
447C22×C4—1181no—
448C22×C4C2×Dic11812yes—
449C22×C4D4×D5911yescharacteristic
450C22×C4#1174568712yes—
451C22×C4C23×D5911yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—44no—
458C2×C8—1181no—
459C2×C8—1181no—
460C2×C8—1181no—
461C2×C8—1181no—
462C2×C8—1181no—
463C2×C8—1181no—
464C2×C8#1174568512yes—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—1181no—
473C4⋊C4—1181no—
474C4⋊C4—1181no—
475C4⋊C4—1181no—
476C4⋊C4—1181no—
477C4⋊C4—1181no—
478C4⋊C4—1181no—
479C4⋊C4—1181no—
480C4⋊C4—4721no—
481C4⋊C4—2362no—
482C4⋊C4—2362no—
483C4⋊C4—2362no—
484C4⋊C4—2362no—
485C4⋊C4—2362no—
486C4⋊C4—2362no—
487C4⋊C4C2×Dic11812yes—
488C4⋊C4C2×Dic11812yes—
489C4⋊C4#1174568512yes—
490C22⋊C4—594no—
491C22⋊C4—1182no—
492C22⋊C4—2362no—
493C22⋊C4—2362no—
494C42—1181no—
495C42—1181no—
496C42—1181no—
497C42—1181no—
498C42—2362no—
499C42—2362no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23#1427370412yes—
505C23D8×D5912yes—
506C23#1427375612yes—
507C23C2×D4×D5911yescharacteristic
508Q8—4724no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—48no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—84no—
529C2×C4—592no—
530C2×C4—592no—
531C2×C4—1181no—
532C2×C4—1181no—
533C2×C4—1181no—
534C2×C4—1181no—
535C2×C4—1181no—
536C2×C4—1181no—
537C2×C4—1181no—
538C2×C4—1181no—
539C2×C4—1181no—
540C2×C4—1181no—
541C2×C4—2361no—
542C2×C4—2361no—
543C2×C4—2361no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4—2361no—
547C2×C4—2361no—
548C2×C4—2361no—
549C2×C4—2361no—
550C2×C4—2361no—
551C2×C4—2361no—
552C2×C4—2361no—
553C2×C4#1427370412yes—
554C2×C4C22×Dic11811yescharacteristic
555C2×C4C2×#1174568711yescharacteristic
556C2×C4C2×#1174568511yescharacteristic
557C2×C4C2×#1174568511yescharacteristic
558C2×C4#1427377211yescharacteristic
559C2×C4#1427377511yescharacteristic
560C8—22no—
561C8—41no—
562C8—2361no—
563C8—2361no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22#1683768014yes—
571C22C2×#1427370411yescharacteristic
572C22#1683804211yescharacteristic
573C22#1683805311yescharacteristic
574C22C2×D8×D5911yescharacteristic
575C22C2×#1427375611yescharacteristic
576C22#1683820811yescharacteristic
577C22#1683821511yescharacteristic
578C4—22no—
579C4—42no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—1182no—
584C4—1182no—
585C4—4721no—
586C4—4721no—
587C4—4721no—
588C4—4721no—
589C4—2361no—
590C4—2361no—
591C4#1683795911yescharacteristic
592C4#1683803311yescharacteristic
593C4#1683807811yescharacteristic
594C4#1683808711yescharacteristic
595C2—24no—
596C2#2142777211yescharacteristic
597C2C2×#1683768011yescharacteristic
598C2#2143393411yescharacteristic
599C2#2143590511yescharacteristic
600C2#2143614311yescharacteristic
601C2#2143644111yescharacteristic
602C2#2143654711yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#340C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
hypercenterC2×#340D59
hypocenterC59#25988
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #21425657C2semidirect
4. #21425588C2semidirect
5. #21425586C2semidirect
6. #21425423C2semidirect
7. #21425046C2semidirect
8. #21424853C2semidirect
9. #21424670C2semidirect
10. #21424666C2semidirect
115. C2×C4⋊C4×C59Q8semidirect
360. C59#25988semidirect
392. C2×C4⋊C4Dic118semidirect

Maximal subgroups

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

subgroupindex
#214277922
#214269652
#214256572
#214255882
#214255862
#214254232
#214250462
#214248532
#214246702
#214246662
#214242842
#214242742
#214241822
#214241252
C2×C59×#3402
#2598859