Finite Group Databasebeta

← #28483227

Subgroups — #28483227

Order 15104.

604 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837458C211yesmaximal, characteristic
2C4×#14273703C211yesmaximal, characteristic
3C4×(C2×D59)⋊C8C211yesmaximal, characteristic
4C2×Q8⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
5#21421936C211yesmaximal, characteristic, complemented
6#21421935C211yesmaximal, characteristic, complemented
7C2×C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#14273703C411yescharacteristic
9C2×C42×D59C2211yescharacteristic
10#16837458—22no—
11#16837458—22no—
12C2×C4⋊(C59⋊C8)C2211yescharacteristic
13C2×(C2×D59)⋊C8—21no—
14C2×(C2×D59)⋊C8—21no—
15C2×#14273637—21no—
16C2×C4×C59⋊C8C2211yescharacteristic
17#16837309C411yescharacteristic
18#16837298C411yescharacteristic
19#16837283—21no—
20#16837273—21no—
21#16837259C411yescharacteristic
22C4×Dic59⋊C4—21no—
23C4×C4⋊Dic59C2211yescharacteristic
24C4×(C2×D59)⋊C4—21no—
25#16837156—21no—
26Q8⋊(C59⋊C8)—22no—
27C2×C4×Q8×C59C2211yescharacteristic
28C2×C4⋊C8×C59C2211yescharacteristic
29C2×C4×C8×C59C2211yescharacteristic
30C59×Q8⋊C8—22no—
31C22×C4×D59C2×C411yescharacteristic
32C22×C4×D59D411yescharacteristic
33C22×C4×D59D411yescharacteristic
34C22×C59⋊C8—21no—
35C22×C59⋊C8—21no—
36#14273703—22no—
37#14273703—22no—
38C2×C4⋊Dic59C2×C411yescharacteristic
39C2×C4⋊Dic59C2×C411yescharacteristic
40C2×Dic59⋊C4—21no—
41C2×Dic59⋊C4—21no—
42C2×(C2×D59)⋊C4—21no—
43C2×(C2×D59)⋊C4—21no—
44C2×C4×Dic59—21no—
45C2×C4×Dic59C2×C411yescharacteristic
46C2×C4×Dic59D411yescharacteristic
47C2×C4×Dic59D411yescharacteristic
48C42×D59—21no—
49C42×D59—21no—
50C42×D59—21no—
51C42×D59—21no—
52C4⋊(C59⋊C8)—21no—
53C4⋊(C59⋊C8)D412yes—
54(C2×D59)⋊C8—24no—
55(C2×D59)⋊C8—24no—
56#14273637—24no—
57C4×C59⋊C8—21no—
58C4×C59⋊C8—21no—
59C59⋊#95—21no—
60C59⋊#95—21no—
61C59⋊#95—21no—
62C59⋊#95—21no—
63C59⋊#95—21no—
64C22×Q8×C59C2×C411yescharacteristic
65C22×C8×C59—21no—
66C22×C8×C59—21no—
67C4×Q8×C59—21no—
68C4×Q8×C59—21no—
69C4×Q8×C59—21no—
70C4×Q8×C59—21no—
71C2×C4⋊C4×C59—21no—
72C2×C4⋊C4×C59C2×C411yescharacteristic
73C2×C42×C59—21no—
74C2×C42×C59C2311yescharacteristic
75C4⋊C8×C59—21no—
76C4⋊C8×C59D412yes—
77C4×C8×C59—21no—
78C4×C8×C59—21no—
79C23×D59C22⋊C411yescharacteristic
80C2×Q8×C59—21no—
81C2×Q8×C59—21no—
82C2×Q8×C59—21no—
83C2×Q8×C59—21no—
84C2×Q8×C59—21no—
85C2×Q8×C59M1612yes—
86C22×C4×C59—21no—
87C22×C4×C59—21no—
88C22×C4×C59C22×C411yescharacteristic
89C22×C4×C59C2×D411yescharacteristic
90C22×C4×C59C2×D411yescharacteristic
91C22×Dic59—21no—
92C22×Dic59—21no—
93C22×Dic59C22⋊C411yescharacteristic
94C22×Dic59C22⋊C411yescharacteristic
95C22×Dic59C22⋊C411yescharacteristic
96C2×C4×D59—22no—
97C2×C4×D59—21no—
98C2×C4×D59—21no—
99C2×C4×D59—21no—
100C2×C4×D59—21no—
101C2×C4×D59—21no—
102C2×C4×D59—21no—
103C2×C4×D59—21no—
104C2×C4×D59—21no—
105C2×C4×D59—21no—
106C2×C4×D59—21no—
107C2×C4×D59—21no—
108C2×C4×D59—21no—
109C2×C4×D59—21no—
110C2×C4×D59—21no—
111C2×C4×D59—41no—
112C2×C8×C59—22no—
113C2×C8×C59—22no—
114C2×C8×C59—41no—
115C2×C8×C59—41no—
116C2×C8×C59—41no—
117C2×C8×C59—41no—
118C4⋊C4×C59—21no—
119C4⋊C4×C59—21no—
120C4⋊C4×C59—41no—
121C4⋊C4×C59—41no—
122C42×C59—41no—
123C42×C59—41no—
124C42×C59C2×D411yescharacteristic
125C42×C59C2×D411yescharacteristic
126C42×C59#4111yescharacteristic
127C42×C59#4111yescharacteristic
128(C2×D59)⋊C4—24no—
129(C2×D59)⋊C4—42no—
130C4⋊Dic59—21no—
131C4⋊Dic59—21no—
132C4⋊Dic59—21no—
133C4⋊Dic59M1612yes—
134Dic59⋊C4—24no—
135Dic59⋊C4—42no—
136C4×Dic59—21no—
137C4×Dic59—21no—
138C4×Dic59—21no—
139C4×Dic59—21no—
140C4×Dic59—21no—
141C4×Dic59—21no—
142C4×Dic59—41no—
143C4×Dic59—41no—
144C2×C59⋊C8—22no—
145C2×C59⋊C8—22no—
146C2×C59⋊C8—41no—
147C2×C59⋊C8—41no—
148C2×C59⋊C8—41no—
149C2×C59⋊C8—41no—
150C23×C59C2×C22⋊C411yescharacteristic
151C22×D59—21no—
152C22×D59—21no—
153C22×D59—21no—
154C22×D59—21no—
155C22×D59—21no—
156C22×D59—21no—
157C22×D59#10412yes—
158Q8×C59—22no—
159Q8×C59—22no—
160Q8×C59—41no—
161Q8×C59—41no—
162C2×C4×C59—21no—
163C2×C4×C59—21no—
164C2×C4×C59—22no—
165C2×C4×C59—41no—
166C2×C4×C59—41no—
167C2×C4×C59—41no—
168C2×C4×C59—41no—
169C2×C4×C59—41no—
170C2×C4×C59C4×D411yescharacteristic
171C2×C4×C59C4×D411yescharacteristic
172C2×C4×C59#12011yescharacteristic
173C2×C4×C59#12111yescharacteristic
174C2×C4×C59#12111yescharacteristic
175C2×C4×C59#12311yescharacteristic
176C2×C4×C59C2×M1611yescharacteristic
177C2×C4×C59C2×M1611yescharacteristic
178C2×C4×C59#13111yescharacteristic
179C2×C4×C59#13111yescharacteristic
180C2×C4×C59#13511yescharacteristic
181C2×C4×C59#13511yescharacteristic
182C2×C4×C59#13711yescharacteristic
183C2×C4×C59#13711yescharacteristic
184C2×Dic59—21no—
185C2×Dic59—21no—
186C2×Dic59—21no—
187C2×Dic59—21no—
188C2×Dic59—22no—
189C2×Dic59—21no—
190C2×Dic59—21no—
191C2×Dic59—21no—
192C2×Dic59—21no—
193C2×Dic59—21no—
194C2×Dic59—41no—
195C2×Dic59—41no—
196C2×Dic59—41no—
197C2×Dic59—41no—
198C2×Dic59—41no—
199C4×D59—42no—
200C4×D59—42no—
201C4×D59—41no—
202C4×D59—41no—
203C4×D59—41no—
204C4×D59—41no—
205C4×D59—41no—
206C4×D59—41no—
207C4×D59—41no—
208C4×D59—41no—
209C8×C59—42no—
210C8×C59—42no—
211C59⋊C8—42no—
212C59⋊C8—42no—
213#8941—591nomaximal, Sylow
214C22×C59#38611yescharacteristic
215C22×C59#40711yescharacteristic
216C22×C59#40811yescharacteristic
217C22×C59#41611yescharacteristic
218C22×C59#41911yescharacteristic
219C22×C59C2×#10411yescharacteristic
220C22×C59#42111yescharacteristic
221C2×D59—22no—
222C2×D59—22no—
223C2×D59—22no—
224C2×D59—41no—
225C2×D59—41no—
226C2×D59—41no—
227C2×D59—41no—
228C4×C59—21no—
229C4×C59—21no—
230C4×C59—42no—
231C4×C59—81no—
232C4×C59#43511yescharacteristic
233C4×C59#43511yescharacteristic
234C4×C59#43611yescharacteristic
235C4×C59#43611yescharacteristic
236C4×C59#45211yescharacteristic
237C4×C59#45211yescharacteristic
238C4×C59#48511yescharacteristic
239C4×C59#48511yescharacteristic
240Dic59—41no—
241Dic59—41no—
242Dic59—41no—
243Dic59—42no—
244Dic59—81no—
245C2×#432—591no—
246C4×C22⋊Q8—591no—
247C4×C22⋊C8—591no—
248C2×Q8⋊C8—591no—
249C2×Q8⋊C8D5911yescharacteristic, complemented
250#1279—591no—
251#1279—591no—
252C2×C59#148811yescharacteristic
253C2×C59#149111yescharacteristic
254C2×C59#149411yescharacteristic
255C2×C59#149711yescharacteristic
256C2×C59#187011yescharacteristic
257C2×C59#187111yescharacteristic
258C2×C59#187311yescharacteristic
259D59—42no—
260C2×C22⋊Q8—591no—
261C2×C4×Q8C2×D5911yescharacteristic
262C22×C42—591no—
263#432—1182no—
264#432—1182no—
265C2×C4⋊C8—591no—
266C2×C4⋊C8C2×D5911yescharacteristic
267C2×C22⋊C8—1181no—
268C2×C22⋊C8—1181no—
269C2×#97—1181no—
270C2×C4×C8—591no—
271C2×C4×C8C2×D5911yescharacteristic
272#391—591no—
273#389—591no—
274#387—1181no—
275#385—1181no—
276#380—591no—
277C4×C4⋊C4—591no—
278C4×C4⋊C4—1181no—
279C4×C22⋊C4—1181no—
280#336—1181no—
281Q8⋊C8—22no—
282Q8⋊C8—1182no—
283C59#894111yescharacteristic, complemented, Sylow
284C22×Q8C4×D5911yescharacteristic
285C23×C4—591no—
286C23×C4—591no—
287C23×C4—591no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—1181no—
291C22×C8—1181no—
292C22⋊Q8—1182no—
293C22⋊Q8—1182no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—591no—
300C2×C4⋊C4—591no—
301C2×C4⋊C4—1181no—
302C2×C4⋊C4—1181no—
303C2×C4⋊C4C4×D5911yescharacteristic
304C2×C22⋊C4—1181no—
305C2×C22⋊C4—1181no—
306C2×C42—21no—
307C2×C42—591no—
308C2×C42—591no—
309C2×C42—591no—
310C2×C42—1181no—
311C2×C42—1181no—
312C2×C42—1181no—
313C2×C42—1181no—
314C2×C42—1181no—
315C2×C42C22×D5911yescharacteristic
316C4⋊C8—21no—
317C4⋊C8—592no—
318C4⋊C8—1181no—
319C4⋊C8C22⋊D5912yes—
320C22⋊C8—1184no—
321C22⋊C8—1184no—
322#97—1184no—
323C4×C8—21no—
324C4×C8—21no—
325C4×C8—1181no—
326C4×C8—1181no—
327#95—1181no—
328#95—1181no—
329#95—1181no—
330#95—1181no—
331#95—1181no—
332C24—591no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8#1174565912yes—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—591no—
342C22×C4—591no—
343C22×C4—591no—
344C22×C4—1182no—
345C22×C4—1181no—
346C22×C4—1181no—
347C22×C4—1181no—
348C22×C4—1181no—
349C22×C4—1181no—
350C22×C4—1181no—
351C22×C4—1181no—
352C22×C4—1181no—
353C22×C4—1181no—
354C22×C4—1181no—
355C22×C4—1181no—
356C22×C4—1181no—
357C22×C4—1181no—
358C22×C4—1181no—
359C22×C4—1181no—
360C22×C4—1181no—
361C22×C4—2361no—
362C22×C4C2×C4×D5911yescharacteristic
363C22×C4D4×D5911yescharacteristic
364C22×C4D4×D5911yescharacteristic
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—1182no—
372C2×C8—1182no—
373C2×C8—2361no—
374C2×C8—2361no—
375C2×C8—2361no—
376C2×C8—2361no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—592no—
382C4⋊C4—1184no—
383C4⋊C4—1181no—
384C4⋊C4—1181no—
385C4⋊C4—1181no—
386C4⋊C4—2362no—
387C22⋊C4—1184no—
388C22⋊C4—2362no—
389C42—41no—
390C42—41no—
391C42—1181no—
392C42—1181no—
393C42—1181no—
394C42—1181no—
395C42—1181no—
396C42—1181no—
397C42—2361no—
398C42—2361no—
399C42#1174568511yescharacteristic
400C42D4×D5911yescharacteristic
401C42#1174568711yescharacteristic
402C42C2×C22⋊D5911yescharacteristic
403C23—592no—
404C23—1181no—
405C23—1181no—
406C23—1181no—
407C23—1181no—
408C23—1181no—
409C23—1181no—
410C23C22⋊C4×D5911yescharacteristic
411Q8—22no—
412Q8—22no—
413Q8—41no—
414Q8—41no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—1181no—
424C2×C4—1181no—
425C2×C4—1181no—
426C2×C4—1181no—
427C2×C4—1181no—
428C2×C4—1181no—
429C2×C4—1181no—
430C2×C4—1182no—
431C2×C4—1181no—
432C2×C4—1181no—
433C2×C4—2362no—
434C2×C4—2362no—
435C2×C4—2361no—
436C2×C4—2361no—
437C2×C4—2361no—
438C2×C4—2361no—
439C2×C4—2361no—
440C2×C4—2361no—
441C2×C4—2361no—
442C2×C4—2361no—
443C2×C4—2361no—
444C2×C4—2361no—
445C2×C4—2361no—
446C2×C4—2361no—
447C2×C4—2361no—
448C2×C4(C22⋊D59)⋊C411yescharacteristic
449C2×C4C4×C22⋊D5911yescharacteristic
450C2×C4#1427369511yescharacteristic
451C2×C4#1427369811yescharacteristic
452C2×C4#1427370011yescharacteristic
453C2×C4#1427370911yescharacteristic
454C2×C4M16×D5911yescharacteristic
455C2×C4C2×#1174565911yescharacteristic
456C2×C4#1427373311yescharacteristic
457C2×C4#1427373511yescharacteristic
458C2×C4#1427374811yescharacteristic
459C2×C4#1427375011yescharacteristic
460C2×C4#1427375611yescharacteristic
461C2×C4#1427375911yescharacteristic
462C8—42no—
463C8—42no—
464C8—2362no—
465C8—2362no—
466C22—1182no—
467C22—1182no—
468C22—1182no—
469C22—2361no—
470C22—2361no—
471C22—2361no—
472C22—2361no—
473C22#1683727811yescharacteristic
474C22#1683736411yescharacteristic
475C22#1683736711yescharacteristic
476C22#1683739711yescharacteristic
477C22#1683740911yescharacteristic
478C22#104×D5911yescharacteristic
479C22#1683741711yescharacteristic
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—4721no—
485C4—2361no—
486C4—2361no—
487C4—2361no—
488C4—2362no—
489C4#1683747011yescharacteristic
490C4#1683747311yescharacteristic
491C4#1683747711yescharacteristic
492C4#1683747811yescharacteristic
493C4#1683756111yescharacteristic
494C4#1683756311yescharacteristic
495C4#1683774111yescharacteristic
496C4#1683774211yescharacteristic
497C2—2362no—
498C2#2142252911yescharacteristic
499C2#2142254111yescharacteristic
500C2#2142255511yescharacteristic
501C2#2142256711yescharacteristic
502C2#2142439011yescharacteristic
503C2#2142439511yescharacteristic
504C2#2142440511yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC2×C59×Q8⋊C8C2
socleC23×C59C2×C22⋊C4
prime radicalC23×D59C22⋊C4
cosocleC2×C42×C59C23
hypercenterC2×Q8⋊C8D59
hypocenterC59#8941
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊(C59⋊C8)C2semidirect
5. #21421936C2semidirect
6. #21421935C2semidirect
7. C2×C59×Q8⋊C8C2semidirect
249. C2×Q8⋊C8D59semidirect
283. C59#8941semidirect

Maximal subgroups

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

subgroupindex
C2×#168374582
C4×#142737032
C4×(C2×D59)⋊C82
C2×Q8⋊(C59⋊C8)2
#214219362
#214219352
C2×C59×Q8⋊C82
#894159