Finite Group Databasebeta

← #28606338

Subgroups — #28606338

Order 15104.

822 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D59C211yesmaximal, characteristic
2#21426972C211yesmaximal, characteristic
3#21426969C211yesmaximal, characteristic
4#21424828C211yesmaximal, characteristic, complemented
5#21424826C211yesmaximal, characteristic, complemented
6#21424690C211yesmaximal, characteristic, complemented
7#21424689C211yesmaximal, characteristic, complemented
8#21424687C211yesmaximal, characteristic, complemented
9#21424185C211yesmaximal, characteristic
10#21424185C211yesmaximal, characteristic
11#21424124C211yesmaximal, characteristic
12C4×#14273660C211yesmaximal, characteristic, complemented
13#21423988C211yesmaximal, characteristic, complemented
14#21423866C211yesmaximal, characteristic
15C59×#1921C211yesmaximal, characteristic, complemented
16C22×C8×D59C2211yescharacteristic
17C2×C4⋊C4×D59C2211yescharacteristic
18C2×C4⋊C4×D59C2211yescharacteristic
19C2×#14273661C2211yescharacteristic
20C2×#14273660C2211yescharacteristic
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273660C2211yescharacteristic
24#107×D59C418yescomplemented
25C2×(C2×D59)⋊C8C2211yescharacteristic
26C2×C4×C59⋊C8C2211yescharacteristic
27C2×C8×Dic59C2211yescharacteristic
28#16837301C2211yescharacteristic
29#16837300C2211yescharacteristic
30#16837298C2211yescharacteristic
31#16837289—21no—
32#16837286—21no—
33#16837284—21no—
34#16837283—21no—
35#16837261—21no—
36#16837259—21no—
37#16837259C2211yescharacteristic
38#16837259C2211yescharacteristic
39C4⋊C4×Dic59C2211yescharacteristic
40C4⋊C4×Dic59C2211yescharacteristic
41C4×C4⋊Dic59C2211yescharacteristic
42C4×(C2×D59)⋊C4—21no—
43C4×(C2×D59)⋊C4C2211yescharacteristic
44#16837249—21no—
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837156C2211yescharacteristic
53C2×#107×C59C2211yescharacteristic
54C59×#389C2211yescharacteristic
55C4×C4⋊C4×C59C2211yescharacteristic
56C59×#340C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#336C2211yescharacteristic
60C22×C4×D59—21no—
61C22×C4×D59—21no—
62C22×C4×D59C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C2×C8×D59—22no—
66C2×C8×D59—22no—
67C2×C8×D59C2×C414yes—
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—
77C4⋊C4×D59—22no—
78C4⋊C4×D59—22no—
79C4⋊C4×D59C2×C414yes—
80C4⋊C4×D59C2×C414yes—
81C2×(C2×D59)⋊C4—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×(C2×D59)⋊C4D411yescharacteristic
84C2×(C2×D59)⋊C4D411yescharacteristic
85C2×C4×Dic59—21no—
86C2×C4×Dic59—21no—
87C2×C4×Dic59—21no—
88C2×C4×Dic59C2311yescharacteristic
89#14273661C2×C414yes—
90#14273660—22no—
91#14273660—22no—
92#14273660C2×C414yes—
93#14273660C2×C414yes—
94(C2×D59)⋊C8—22no—
95C4×C59⋊C8—22no—
96C8×Dic59—22no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95D411yescharacteristic
106C59⋊#95D411yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109C2×C4⋊C4×C59—21no—
110C2×C4⋊C4×C59C2311yescharacteristic
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C4⋊C4×C59C2311yescharacteristic
114C2×C42×C59—21no—
115C2×C42×C59C2311yescharacteristic
116#107×C59C2×C414yes—
117#95×C59—21no—
118#95×C59—21no—
119C23×D59C2×D411yescharacteristic
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59C2×D411yescharacteristic
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59C2411yescharacteristic
127C22×Dic59—21no—
128C22×Dic59—21no—
129C22×Dic59—21no—
130C22×Dic59—21no—
131C22×Dic59C2×D411yescharacteristic
132C22×Dic59C2×D411yescharacteristic
133C22×Dic59C2×D411yescharacteristic
134C2×C4×D59—21no—
135C2×C4×D59—21no—
136C2×C4×D59—21no—
137C2×C4×D59—21no—
138C2×C4×D59—24no—
139C2×C4×D59—24no—
140C2×C4×D59—81no—
141C2×C4×D59—81no—
142C2×C4×D59—81no—
143C2×C4×D59—81no—
144C2×C4×D59C22×C412yes—
145C2×C4×D59#4112yes—
146C2×C8×C59—21no—
147C2×C8×C59—21no—
148C2×C8×C59—21no—
149C2×C8×C59—21no—
150C2×C8×C59—21no—
151C2×C8×C59C22×C412yes—
152C4⋊C4×C59—21no—
153C4⋊C4×C59—21no—
154C4⋊C4×C59—21no—
155C4⋊C4×C59—21no—
156C4⋊C4×C59—21no—
157C4⋊C4×C59—21no—
158C4⋊C4×C59—81no—
159C4⋊C4×C59C22×C412yes—
160C4⋊C4×C59C22×C412yes—
161C42×C59—21no—
162C42×C59—21no—
163C42×C59—81no—
164(C2×D59)⋊C4—22no—
165(C2×D59)⋊C4—42no—
166(C2×D59)⋊C4—42no—
167(C2×D59)⋊C4Q1614yes—
168C4⋊Dic59—21no—
169C4⋊Dic59—21no—
170C4⋊Dic59—21no—
171C4⋊Dic59—21no—
172C4⋊Dic59—21no—
173C4⋊Dic59—21no—
174C4⋊Dic59—81no—
175C4⋊Dic59C22×C412yes—
176C4⋊Dic59C22×C412yes—
177Dic59⋊C4—24no—
178Dic59⋊C4—24no—
179Dic59⋊C4—81no—
180Dic59⋊C4—81no—
181C4×Dic59—21no—
182C4×Dic59—21no—
183C4×Dic59—81no—
184C4×Dic59—81no—
185C4×Dic59—81no—
186C2×C59⋊C8—21no—
187C2×C59⋊C8—21no—
188C2×C59⋊C8—21no—
189C2×C59⋊C8C22×C412yes—
190C2×C59⋊C8#4112yes—
191C2×C59⋊C8#4112yes—
192C8×D59—28no—
193C23×C59C22×D411yescharacteristic
194C22×D59—21no—
195C22×D59—21no—
196C22×D59—21no—
197C22×D59—21no—
198C22×D59C4×D412yes—
199C22×D59C2×Q1612yes—
200C22×D59#13512yes—
201C2×C4×C59—21no—
202C2×C4×C59—21no—
203C2×C4×C59—22no—
204C2×C4×C59—22no—
205C2×C4×C59—21no—
206C2×C4×C59—21no—
207C2×C4×C59—21no—
208C2×C4×C59—41no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—41no—
212C2×C4×C59—41no—
213C2×C4×C59—41no—
214C2×C4×C59—41no—
215C2×C4×C59—41no—
216C2×C4×C59—41no—
217C2×C4×C59—41no—
218C2×C4×C59C2×Q1612yes—
219C2×C4×C59C23×C411yescharacteristic
220C2×C4×C59C2×#4111yescharacteristic
221C2×C4×C59C2×#4111yescharacteristic
222C2×C4×C59C2×#4111yescharacteristic
223C2×C4×C592−1+411yescharacteristic
224C2×C4×C592−1+411yescharacteristic
225C2×Dic59—21no—
226C2×Dic59—21no—
227C2×Dic59—21no—
228C2×Dic59—21no—
229C2×Dic59—22no—
230C2×Dic59—22no—
231C2×Dic59—21no—
232C2×Dic59—21no—
233C2×Dic59—21no—
234C2×Dic59—41no—
235C2×Dic59—41no—
236C2×Dic59—41no—
237C2×Dic59—41no—
238C2×Dic59—41no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59C4×D412yes—
245C2×Dic59C2×Q1612yes—
246C4×D59—22no—
247C4×D59—22no—
248C4×D59—22no—
249C4×D59—22no—
250C4×D59—84no—
251C4×D59—84no—
252C8×C59—22no—
253C8×C59—41no—
254C59⋊C8—41no—
255C59⋊C8#11714yes—
256#22612—591nomaximal, Sylow
257C22×C59C2×C4×D411yescharacteristic
258C22×C59#54711yescharacteristic
259C22×C59#54711yescharacteristic
260C22×C59C22×Q1611yescharacteristic
261C22×C59C2×#13511yescharacteristic
262C22×C59#57611yescharacteristic
263C22×C59#57611yescharacteristic
264C2×D59—22no—
265C2×D59—22no—
266C2×D59—22no—
267C2×D59—22no—
268C2×D59—22no—
269C2×D59—22no—
270C2×D59C4×Q1614yes—
271C4×C59—22no—
272C4×C59—41no—
273C4×C59—42no—
274C4×C59—42no—
275C4×C59—81no—
276C4×C59—81no—
277C4×C59C2×#11711yescharacteristic
278C4×C59#51911yescharacteristic
279C4×C59#55211yescharacteristic
280C4×C59#55211yescharacteristic
281Dic59—22no—
282Dic59—22no—
283Dic59—41no—
284Dic59—42no—
285Dic59—42no—
286Dic59—81no—
287Dic59—81no—
288C22×#107—591no—
289#2345—591no—
290#2345—591no—
291#1942—591no—
292#1942—591no—
293#1921—591no—
294#1921—591no—
295#1921—591no—
296#1921D5911yescharacteristic, complemented
297#1824—591no—
298#1824—591no—
299#1808—591no—
300C4×#107—591no—
301C4×#107—591no—
302C8×C22⋊C4—591no—
303C2×C59#234411yescharacteristic
304C2×C59C2×C4×Q1611yescharacteristic
305C2×C59#294811yescharacteristic
306C2×C59#333811yescharacteristic
307C2×C59#333811yescharacteristic
308C2×C59#333911yescharacteristic
309C2×C59#333911yescharacteristic
310D59—24no—
311C23×C8—591no—
312C22×C4⋊C4—591no—
313C22×C4⋊C4—591no—
314C2×#107—591no—
315C2×#107—591no—
316C2×#107—591no—
317C2×#107—598no—
318C2×#107—591no—
319C2×#107—591no—
320C2×#107C2×D5911yescharacteristic
321C2×C22⋊C8—591no—
322C2×C4×C8—591no—
323C2×C4×C8—591no—
324#389—591no—
325#389—591no—
326#389—591no—
327#389C2×D5911yescharacteristic
328#387—1181no—
329#387—1181no—
330#387—1181no—
331#387—1181no—
332#380—591no—
333#380—591no—
334#380—1181no—
335#380—1181no—
336C4×C4⋊C4—591no—
337C4×C4⋊C4—591no—
338C4×C4⋊C4—591no—
339C4×C4⋊C4C2×D5911yescharacteristic
340C4×C22⋊C4—591no—
341C4×C22⋊C4—1181no—
342C4×C22⋊C4—1181no—
343#340—591no—
344#340—591no—
345#340—591no—
346#340—591no—
347#340—591no—
348#340—591no—
349#340—591no—
350#340C2×D5911yescharacteristic
351#340C2×D5911yescharacteristic
352#340C2×D5911yescharacteristic
353#336—591no—
354#336C2×D5911yescharacteristic
355C59#2261211yescharacteristic, complemented, Sylow
356C23×C4—591no—
357C23×C4—1181no—
358C23×C4—1181no—
359C22×C8—591no—
360C22×C8—594no—
361C22×C8—591no—
362C22×C8—1182no—
363C22×C8—1182no—
364C22×C8C22×D5911yescharacteristic
365C22×C8C22×D5911yescharacteristic
366C2×C4⋊C4—21no—
367C2×C4⋊C4—591no—
368C2×C4⋊C4—591no—
369C2×C4⋊C4—594no—
370C2×C4⋊C4—594no—
371C2×C4⋊C4—591no—
372C2×C4⋊C4—591no—
373C2×C4⋊C4—1182no—
374C2×C4⋊C4—1182no—
375C2×C4⋊C4—1181no—
376C2×C4⋊C4—1181no—
377C2×C4⋊C4—1181no—
378C2×C4⋊C4—1181no—
379C2×C4⋊C4—1181no—
380C2×C4⋊C4C22×D5911yescharacteristic
381C2×C4⋊C4C22×D5911yescharacteristic
382C2×C4⋊C4C22×D5911yescharacteristic
383C2×C4⋊C4C22×D5911yescharacteristic
384C2×C22⋊C4—591no—
385C2×C22⋊C4—591no—
386C2×C22⋊C4—1181no—
387C2×C22⋊C4—1181no—
388C2×C42—21no—
389C2×C42—591no—
390C2×C42—1181no—
391C2×C42—1181no—
392C2×C42—1181no—
393C2×C42C22×D5911yescharacteristic
394#107—594no—
395#107—594no—
396#107—594no—
397#107—1182no—
398#107—1182no—
399#107C4×D5914yes—
400C22⋊C8—1182no—
401C4×C8—1182no—
402C4×C8—1182no—
403#95—21no—
404#95—21no—
405#95—591no—
406#95—591no—
407#95—1181no—
408#95—1181no—
409#95—1181no—
410#95—1181no—
411#95—1181no—
412#95—1181no—
413#95—1181no—
414#95—1181no—
415C24—591no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—591no—
421C22×C4—591no—
422C22×C4—592no—
423C22×C4—592no—
424C22×C4—591no—
425C22×C4—1184no—
426C22×C4—1184no—
427C22×C4—1181no—
428C22×C4—1181no—
429C22×C4—1181no—
430C22×C4—1181no—
431C22×C4—1181no—
432C22×C4—1181no—
433C22×C4—1181no—
434C22×C4—1181no—
435C22×C4—4721no—
436C22×C4—4721no—
437C22×C4—4721no—
438C22×C4—4721no—
439C22×C4D4×D5911yescharacteristic
440C22×C4D4×D5911yescharacteristic
441C22×C4C23×D5911yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—592no—
448C2×C8—592no—
449C2×C8—592no—
450C2×C8—1188no—
451C2×C8—1181no—
452C2×C8—1181no—
453C2×C8—1181no—
454C2×C8C2×C4×D5912yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—592no—
463C4⋊C4—592no—
464C4⋊C4—1184no—
465C4⋊C4—1184no—
466C4⋊C4—1181no—
467C4⋊C4—1181no—
468C4⋊C4—1181no—
469C4⋊C4—1181no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4—4721no—
473C4⋊C4—4721no—
474C4⋊C4—4721no—
475C4⋊C4C2×C4×D5912yes—
476C4⋊C4C2×C4×D5912yes—
477C22⋊C4—594no—
478C22⋊C4—1182no—
479C22⋊C4—2362no—
480C22⋊C4—2362no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—1181no—
485C42—1181no—
486C42—4721no—
487C42—4721no—
488C42—4721no—
489C23—592no—
490C23—592no—
491C23—592no—
492C23—1181no—
493C23—1181no—
494C23—1181no—
495C23—1181no—
496C23C2×D4×D5911yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—592no—
515C2×C4—592no—
516C2×C4—1181no—
517C2×C4—1181no—
518C2×C4—1181no—
519C2×C4—1181no—
520C2×C4—1182no—
521C2×C4—1182no—
522C2×C4—1182no—
523C2×C4—1182no—
524C2×C4—1181no—
525C2×C4—1181no—
526C2×C4—1181no—
527C2×C4—1182no—
528C2×C4—1182no—
529C2×C4—4724no—
530C2×C4—4724no—
531C2×C4—2361no—
532C2×C4—2361no—
533C2×C4—2361no—
534C2×C4—2361no—
535C2×C4—2361no—
536C2×C4—2361no—
537C2×C4—2361no—
538C2×C4—2361no—
539C2×C4—2361no—
540C2×C4—2361no—
541C2×C4Q16×D5912yes—
542C2×C4C22×C4×D5911yescharacteristic
543C2×C4#41×D5911yescharacteristic
544C2×C4#41×D5911yescharacteristic
545C2×C4#41×D5911yescharacteristic
546C2×C4#1427377411yescharacteristic
547C2×C4#1427377511yescharacteristic
548C8—22no—
549C8—41no—
550C8—594no—
551C8—2361no—
552C22—594no—
553C22—1182no—
554C22—1182no—
555C22—1182no—
556C22—1182no—
557C22—1182no—
558C22—1182no—
559C22C4×D4×D5911yescharacteristic
560C22#1683805011yescharacteristic
561C22#1683805411yescharacteristic
562C22C2×Q16×D5911yescharacteristic
563C22#135×D5911yescharacteristic
564C22#1683820611yescharacteristic
565C22#1683820611yescharacteristic
566C4—22no—
567C4—41no—
568C4—42no—
569C4—42no—
570C4—81no—
571C4—81no—
572C4—1182no—
573C4—1182no—
574C4—4721no—
575C4—4721no—
576C4—2361no—
577C4—2362no—
578C4—2362no—
579C4#117×D5911yescharacteristic
580C4#1683787811yescharacteristic
581C4#1683808411yescharacteristic
582C4#1683808811yescharacteristic
583C2—1184no—
584C2#2142696211yescharacteristic
585C2C4×Q16×D5911yescharacteristic
586C2#2143294511yescharacteristic
587C2#2143648311yescharacteristic
588C2#2143648711yescharacteristic
589C2#2143649111yescharacteristic
590C2#2143649511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1921C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
cosocleC22×C4×C59C24
hypercenter#1921D59
hypocenterC59#22612
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. #21424828C2semidirect
5. #21424826C2semidirect
6. #21424690C2semidirect
7. #21424689C2semidirect
8. #21424687C2semidirect
12. C4×#14273660C2semidirect
13. #21423988C2semidirect
15. C59×#1921C2semidirect
24. #107×D59C4semidirect
296. #1921D59semidirect
355. C59#22612semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D592
#214269722
#214269692
#214248282
#214248262
#214246902
#214246892
#214246872
#214241852
#214241242
C4×#142736602
#214239882
#214238662
C59×#19212
#2261259