Finite Group Databasebeta

← #28482048

Subgroups — #28482048

Order 15104.

540 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426500C211yesmaximal, characteristic
2#21424073C211yesmaximal, characteristic
3C4×(C2×D59)⋊C8C211yesmaximal, characteristic
4#21421937C211yesmaximal, characteristic, complemented
5#21421936C211yesmaximal, characteristic, complemented
6#21421935C211yesmaximal, characteristic, complemented
7C59×#1279C211yesmaximal, characteristic, complemented
8C2×#14273684—21no—
9C2×C42×D59C2211yescharacteristic
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×(C2×D59)⋊C8—21no—
12C2×(C2×D59)⋊C8—21no—
13C2×C4×C59⋊C8C2211yescharacteristic
14#16837271C411yescharacteristic
15#16837271C411yescharacteristic
16#16837266—21no—
17#16837261—21no—
18#16837259C411yescharacteristic
19#16837259C411yescharacteristic
20C4×Dic59⋊C4—21no—
21C4×C4⋊Dic59C2211yescharacteristic
22#16837156—21no—
23#16837156—21no—
24C2×C4⋊C8×C59C2211yescharacteristic
25C2×C4×C8×C59C2211yescharacteristic
26C4×C4⋊C4×C59C2211yescharacteristic
27C22×C4×D59C2×C411yescharacteristic
28C22×C4×D59D411yescharacteristic
29C22×C4×D59D411yescharacteristic
30C22×C59⋊C8—21no—
31C22×C59⋊C8—21no—
32#14273684—42no—
33#14273684—42no—
34C2×C4⋊Dic59C2×C411yescharacteristic
35C2×C4⋊Dic59C2×C411yescharacteristic
36C2×Dic59⋊C4—21no—
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×Dic59⋊C4—21no—
40C2×(C2×D59)⋊C4—21no—
41C2×(C2×D59)⋊C4—21no—
42C2×C4×Dic59—21no—
43C2×C4×Dic59C2×C411yescharacteristic
44C2×C4×Dic59D411yescharacteristic
45C2×C4×Dic59D411yescharacteristic
46C42×D59—21no—
47C42×D59—21no—
48C42×D59—21no—
49C42×D59—21no—
50C4⋊(C59⋊C8)—21no—
51C4⋊(C59⋊C8)—21no—
52(C2×D59)⋊C8—24no—
53(C2×D59)⋊C8—42no—
54C4×C59⋊C8—21no—
55C4×C59⋊C8—21no—
56C59⋊#95—21no—
57C59⋊#95—21no—
58C59⋊#95—21no—
59C22×C8×C59—21no—
60C22×C8×C59—21no—
61C2×C4⋊C4×C59C2×C411yescharacteristic
62C2×C4⋊C4×C59C2×C411yescharacteristic
63C2×C42×C59—21no—
64C2×C42×C59C2311yescharacteristic
65C4⋊C8×C59—21no—
66C4⋊C8×C59—21no—
67C4×C8×C59—21no—
68C4×C8×C59—21no—
69#95×C59—21no—
70C23×D59C22⋊C411yescharacteristic
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59C22×C411yescharacteristic
74C22×C4×C59C2×D411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×Dic59—21no—
77C22×Dic59—21no—
78C22×Dic59C22⋊C411yescharacteristic
79C22×Dic59C22⋊C411yescharacteristic
80C22×Dic59C22⋊C411yescharacteristic
81C2×C4×D59—21no—
82C2×C4×D59—21no—
83C2×C4×D59—21no—
84C2×C4×D59—21no—
85C2×C4×D59—21no—
86C2×C4×D59—21no—
87C2×C4×D59—21no—
88C2×C4×D59—21no—
89C2×C4×D59—21no—
90C2×C4×D59—21no—
91C2×C4×D59—21no—
92C2×C4×D59—21no—
93C2×C4×D59—22no—
94C2×C4×D59—41no—
95C2×C4×D59D812yes—
96C2×C4×D59SD1612yes—
97C2×C8×C59—22no—
98C2×C8×C59—41no—
99C2×C8×C59—41no—
100C2×C8×C59—41no—
101C2×C8×C59—41no—
102C2×C8×C59—41no—
103C4⋊C4×C59—21no—
104C4⋊C4×C59—21no—
105C4⋊C4×C59—21no—
106C4⋊C4×C59—21no—
107C42×C59—41no—
108C42×C59—41no—
109C42×C59#4111yescharacteristic
110C42×C59#4111yescharacteristic
111C42×C59#4111yescharacteristic
112C42×C59#4111yescharacteristic
113(C2×D59)⋊C4—42no—
114(C2×D59)⋊C4—42no—
115C4⋊Dic59—21no—
116C4⋊Dic59—21no—
117C4⋊Dic59—21no—
118C4⋊Dic59—21no—
119Dic59⋊C4—42no—
120Dic59⋊C4—42no—
121Dic59⋊C4—42no—
122Dic59⋊C4—42no—
123C4×Dic59—21no—
124C4×Dic59—21no—
125C4×Dic59—21no—
126C4×Dic59—21no—
127C4×Dic59—21no—
128C4×Dic59—21no—
129C4×Dic59—41no—
130C4×Dic59—41no—
131C2×C59⋊C8—22no—
132C2×C59⋊C8—41no—
133C2×C59⋊C8—41no—
134C2×C59⋊C8—41no—
135C2×C59⋊C8—41no—
136C2×C59⋊C8—41no—
137C23×C59C2×C22⋊C411yescharacteristic
138C22×D59—21no—
139C22×D59—21no—
140C22×D59—21no—
141C22×D59—21no—
142C22×D59—21no—
143C22×D59—21no—
144C22×D59#10212yes—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59#11711yescharacteristic
154C2×C4×C59#11711yescharacteristic
155C2×C4×C59#12311yescharacteristic
156C2×C4×C59#12311yescharacteristic
157C2×C4×C59#12311yescharacteristic
158C2×C4×C59#12311yescharacteristic
159C2×C4×C59#13111yescharacteristic
160C2×C4×C59#13111yescharacteristic
161C2×C4×C59#13111yescharacteristic
162C2×C4×C59#13111yescharacteristic
163C2×C4×C59C2×D811yescharacteristic
164C2×C4×C59C2×SD1611yescharacteristic
165C2×C4×C59#13711yescharacteristic
166C2×C4×C59#13711yescharacteristic
167C2×Dic59—21no—
168C2×Dic59—21no—
169C2×Dic59—21no—
170C2×Dic59—21no—
171C2×Dic59—21no—
172C2×Dic59—21no—
173C2×Dic59—21no—
174C2×Dic59—41no—
175C2×Dic59—41no—
176C2×Dic59—41no—
177C2×Dic59—41no—
178C2×Dic59—41no—
179C2×Dic59—41no—
180C2×Dic59#10212yes—
181C2×Dic59#10412yes—
182C4×D59—22no—
183C4×D59—22no—
184C4×D59—22no—
185C4×D59—22no—
186C4×D59—42no—
187C4×D59—42no—
188C4×D59—41no—
189C4×D59—41no—
190C4×D59—41no—
191C4×D59—41no—
192C8×C59—42no—
193C8×C59—81no—
194C59⋊C8—42no—
195C59⋊C8—81no—
196#8709—591nomaximal, Sylow
197C22×C59#38111yescharacteristic
198C22×C59#40811yescharacteristic
199C22×C59#40811yescharacteristic
200C22×C59C2×#10211yescharacteristic
201C22×C59#41911yescharacteristic
202C22×C59C2×#10411yescharacteristic
203C22×C59#42111yescharacteristic
204C2×D59—22no—
205C2×D59—22no—
206C2×D59—22no—
207C2×D59—41no—
208C2×D59—41no—
209C2×D59—41no—
210C2×D59—41no—
211C4×C59—21no—
212C4×C59—21no—
213C4×C59—81no—
214C4×C59—81no—
215C4×C59#43311yescharacteristic
216C4×C59#43311yescharacteristic
217C4×C59#43311yescharacteristic
218C4×C59#43311yescharacteristic
219C4×C59#48011yescharacteristic
220C4×C59#48011yescharacteristic
221C4×C59#48311yescharacteristic
222C4×C59#48311yescharacteristic
223Dic59—22no—
224Dic59—22no—
225Dic59—41no—
226Dic59—81no—
227Dic59—81no—
228#2285—591no—
229#1797—591no—
230C4×C22⋊C8—591no—
231#1279—591no—
232#1279—591no—
233#1279—591no—
234#1279D5911yescharacteristic, complemented
235C2×C59#148011yescharacteristic
236C2×C59#148511yescharacteristic
237C2×C59#149211yescharacteristic
238C2×C59#149711yescharacteristic
239C2×C59#181811yescharacteristic
240C2×C59#182311yescharacteristic
241C2×C59#182611yescharacteristic
242D59—42no—
243C2×#117—1181no—
244C22×C42—591no—
245C2×C4⋊C8—591no—
246C2×C4⋊C8C2×D5911yescharacteristic
247C2×C22⋊C8—1181no—
248C2×C22⋊C8—1181no—
249C2×C4×C8—591no—
250C2×C4×C8C2×D5911yescharacteristic
251#384—591no—
252#384—591no—
253#382—1181no—
254#380—591no—
255#380—591no—
256#380—1181no—
257C4×C4⋊C4—591no—
258C4×C4⋊C4—1181no—
259C4×C4⋊C4C2×D5911yescharacteristic
260#336—1181no—
261#336—1181no—
262C59#870911yescharacteristic, complemented, Sylow
263C23×C4—591no—
264C23×C4—591no—
265C23×C4—591no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—1181no—
269C22×C8—1181no—
270#117—2362no—
271#117—2362no—
272C2×C4⋊C4—591no—
273C2×C4⋊C4—591no—
274C2×C4⋊C4—1181no—
275C2×C4⋊C4—1181no—
276C2×C4⋊C4—1181no—
277C2×C4⋊C4—1181no—
278C2×C4⋊C4C4×D5911yescharacteristic
279C2×C4⋊C4C4×D5911yescharacteristic
280C2×C22⋊C4—1181no—
281C2×C22⋊C4—1181no—
282C2×C42—21no—
283C2×C42—591no—
284C2×C42—591no—
285C2×C42—591no—
286C2×C42—1181no—
287C2×C42—1181no—
288C2×C42—1181no—
289C2×C42—1181no—
290C2×C42—1181no—
291C2×C42C22×D5911yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—1181no—
295C4⋊C8—1181no—
296C22⋊C8—1184no—
297C22⋊C8—2362no—
298C4×C8—21no—
299C4×C8—21no—
300C4×C8—1181no—
301C4×C8—1181no—
302#95—21no—
303#95—1181no—
304#95—1181no—
305#95—1181no—
306C24—591no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—591no—
310C22×C4—591no—
311C22×C4—592no—
312C22×C4—592no—
313C22×C4—591no—
314C22×C4—1182no—
315C22×C4—1181no—
316C22×C4—1181no—
317C22×C4—1181no—
318C22×C4—1181no—
319C22×C4—1181no—
320C22×C4—1181no—
321C22×C4—1181no—
322C22×C4—1181no—
323C22×C4—1181no—
324C22×C4—1181no—
325C22×C4—1181no—
326C22×C4—1181no—
327C22×C4—1181no—
328C22×C4—1181no—
329C22×C4—2361no—
330C22×C4C2×C4×D5911yescharacteristic
331C22×C4D4×D5911yescharacteristic
332C22×C4D4×D5911yescharacteristic
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—1182no—
340C2×C8—2361no—
341C2×C8—2361no—
342C2×C8—2361no—
343C2×C8—2361no—
344C2×C8—2361no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—1181no—
350C4⋊C4—1181no—
351C4⋊C4—1181no—
352C4⋊C4—1181no—
353C4⋊C4—2362no—
354C4⋊C4—2362no—
355C4⋊C4—2362no—
356C4⋊C4—2362no—
357C22⋊C4—2362no—
358C22⋊C4—2362no—
359C42—41no—
360C42—41no—
361C42—1181no—
362C42—1181no—
363C42—1181no—
364C42—1181no—
365C42—1181no—
366C42—1181no—
367C42—2361no—
368C42—2361no—
369C42#1174568511yescharacteristic
370C42#1174568511yescharacteristic
371C42#1174568711yescharacteristic
372C42#1174568911yescharacteristic
373C23—592no—
374C23—1181no—
375C23—1181no—
376C23—1181no—
377C23—1181no—
378C23—1181no—
379C23—1181no—
380C23C22⋊C4×D5911yescharacteristic
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—592no—
390C2×C4—592no—
391C2×C4—1181no—
392C2×C4—1181no—
393C2×C4—1181no—
394C2×C4—1181no—
395C2×C4—1182no—
396C2×C4—1182no—
397C2×C4—1182no—
398C2×C4—1182no—
399C2×C4—1181no—
400C2×C4—1181no—
401C2×C4—1181no—
402C2×C4—2362no—
403C2×C4—2362no—
404C2×C4—2361no—
405C2×C4—2361no—
406C2×C4—2361no—
407C2×C4—2361no—
408C2×C4—2361no—
409C2×C4—2361no—
410C2×C4—2361no—
411C2×C4—2361no—
412C2×C4—2361no—
413C2×C4—2361no—
414C2×C4#1427368411yescharacteristic
415C2×C4#1427368511yescharacteristic
416C2×C4#1427370911yescharacteristic
417C2×C4#1427370911yescharacteristic
418C2×C4#1427371211yescharacteristic
419C2×C4#1427371211yescharacteristic
420C2×C4#1427373311yescharacteristic
421C2×C4#1427373311yescharacteristic
422C2×C4#1427373511yescharacteristic
423C2×C4#1427373511yescharacteristic
424C2×C4D8×D5911yescharacteristic
425C2×C4SD16×D5911yescharacteristic
426C2×C4#1427375611yescharacteristic
427C2×C4#1427375911yescharacteristic
428C8—42no—
429C8—81no—
430C8—4721no—
431C8—2362no—
432C22—1182no—
433C22—1182no—
434C22—1182no—
435C22—2361no—
436C22—2361no—
437C22—2361no—
438C22—2361no—
439C22#1683726411yescharacteristic
440C22#1683736711yescharacteristic
441C22#1683736711yescharacteristic
442C22#102×D5911yescharacteristic
443C22#1683740911yescharacteristic
444C22#104×D5911yescharacteristic
445C22#1683741711yescharacteristic
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—1182no—
451C4—1182no—
452C4—4721no—
453C4—4721no—
454C4—2361no—
455C4#1683746111yescharacteristic
456C4#1683746211yescharacteristic
457C4#1683746211yescharacteristic
458C4#1683746411yescharacteristic
459C4#1683771411yescharacteristic
460C4#1683771711yescharacteristic
461C4#1683773111yescharacteristic
462C4#1683773411yescharacteristic
463C2—2362no—
464C2#2142249311yescharacteristic
465C2#2142251511yescharacteristic
466C2#2142254511yescharacteristic
467C2#2142256711yescharacteristic
468C2#2142416611yescharacteristic
469C2#2142418111yescharacteristic
470C2#2142419411yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1279C2
socleC23×C59C2×C22⋊C4
prime radicalC23×D59C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1279D59
hypocenterC59#8709
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #21421937C2semidirect
5. #21421936C2semidirect
6. #21421935C2semidirect
7. C59×#1279C2semidirect
234. #1279D59semidirect
262. C59#8709semidirect

Maximal subgroups

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

subgroupindex
#214265002
#214240732
C4×(C2×D59)⋊C82
#214219372
#214219362
#214219352
C59×#12792
#870959