Finite Group Databasebeta

← #28505774

Subgroups — #28505774

Order 15104.

462 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837832C211yesmaximal, characteristic
2#21425832C211yesmaximal, characteristic, complemented
3#21425823C211yesmaximal, characteristic, complemented
4#21424994C211yesmaximal, characteristic, complemented
5#21422193C211yesmaximal, characteristic, complemented
6#21422185C211yesmaximal, characteristic, complemented
7C59×#2957C211yesmaximal, characteristic, complemented
8C2×#14273749C2211yescharacteristic
9#16837832—22no—
10#16837832—22no—
11C2×#14273673C411yescharacteristic, complemented
12C2×#14273671C411yescharacteristic, complemented
13C2×#14273670C411yescharacteristic, complemented
14C2×#14273668C411yescharacteristic, complemented
15C2×#14273667C2211yescharacteristic
16C22×C59⋊C16C2211yescharacteristic
17#16837440C2211yescharacteristic
18#16837418—21no—
19#16837375—21no—
20#16837212—22no—
21#16837208—22no—
22C2×#135×C59C2211yescharacteristic
23C59×#568—21no—
24C59×#444—22no—
25C59×#443—22no—
26C2×#108×C59C2211yescharacteristic
27C59×#421—21no—
28C59×#405C2211yescharacteristic
29C2×#11745685—21no—
30#14273749—21no—
31#14273749—21no—
32#14273749—21no—
33#14273749—21no—
34C2×Dic236C2×C411yescharacteristic
35C2×#11745660—21no—
36C2×D472C2×C411yescharacteristic
37#14273686—21no—
38#14273673—22no—
39#14273671—22no—
40#14273670—22no—
41#14273668—22no—
42#14273667—21no—
43#14273667—21no—
44C2×C59⋊C16—21no—
45C2×C59⋊C16—21no—
46C2×C59⋊C16—21no—
47C2×C59⋊C16C2×C411yescharacteristic
48C2×C59⋊C16C2×C411yescharacteristic
49#14273661—21no—
50#14273659—21no—
51#14273653—42no—
52#14273641—42no—
53C2×#41×C59—21no—
54#135×C59—21no—
55#135×C59—21no—
56#135×C59D412yes—
57#135×C59D412yes—
58C2×Q16×C59C2×C411yescharacteristic
59C2×SD16×C59—21no—
60C2×D8×C59C2×C411yescharacteristic
61#131×C59—24no—
62#131×C59—42no—
63C2×M16×C59—21no—
64C2×M16×C59—42no—
65C2×M16×C59D411yescharacteristic
66C22×C8×C59C2311yescharacteristic
67#117×C59D411yescharacteristic
68#108×C59—21no—
69#108×C59D412yes—
70#104×C59—24no—
71#97×C59—21no—
72C4×C8×C59—21no—
73#41×C59—22no—
74#41×C59—22no—
75#41×C59—41no—
76#41×C59—41no—
77C2×Q8×C59—21no—
78C2×D4×C59—21no—
79C2×D4×C59—41no—
80C22×C4×C59—41no—
81C22×C4×C59C2×D411yescharacteristic
82C2×C22⋊D59—41no—
83#11745685—41no—
84#11745685—41no—
85#11745685—41no—
86#11745685—41no—
87C2×D236—21no—
88C2×C4×D59—41no—
89C2×Dic118—21no—
90Q16×C59—21no—
91Q16×C59C22⋊C412yes—
92SD16×C59—22no—
93SD16×C59—22no—
94D8×C59—21no—
95D8×C59C22⋊C412yes—
96M16×C59—21no—
97M16×C59—22no—
98M16×C59—44no—
99M16×C59—41no—
100M16×C59D812yes—
101C2×C8×C59—21no—
102C2×C8×C59—44no—
103C2×C8×C59—41no—
104C2×C8×C59C22×C411yescharacteristic
105C2×C8×C59C2×D411yescharacteristic
106C2×C8×C59C2×D411yescharacteristic
107C2×C8×C59C2×D411yescharacteristic
108C2×C8×C59#4111yescharacteristic
109C2×C8×C59#4111yescharacteristic
110C4⋊C4×C59—21no—
111C22⋊C4×C59—21no—
112C42×C59—21no—
113C22⋊Dic59—41no—
114C4⋊Dic59—41no—
115C4×Dic59—41no—
116Dic236—21no—
117Dic236—21no—
118D472—21no—
119D472—21no—
120#11745660—41no—
121#11745660—41no—
122C59⋊C16—21no—
123C59⋊C16—21no—
124C59⋊C16—41no—
125C23×C59—41no—
126C23×C59AGL(1,ℤ/8)11yescharacteristic
127C22×D59—41no—
128Q8×C59—22no—
129Q8×C59—41no—
130D4×C59—22no—
131D4×C59—42no—
132D4×C59—42no—
133D4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—42no—
136C2×C4×C59—42no—
137C2×C4×C59—41no—
138C2×C4×C59C4×D411yescharacteristic
139C2×C4×C59#12011yescharacteristic
140C2×C4×C59#12111yescharacteristic
141C2×C4×C59C2×D811yescharacteristic
142C2×C4×C59#13511yescharacteristic
143C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
144C22⋊D59—81no—
145C22⋊D59—81no—
146C2×Dic59—41no—
147C2×Dic59—81no—
148D236—41no—
149D236—41no—
150C4×D59—81no—
151C4×D59—81no—
152Dic118—41no—
153Dic118—41no—
154C8×C59—22no—
155C8×C59—42no—
156C8×C59C2×C22⋊C411yescharacteristic
157C8×C59C4×D411yescharacteristic
158C8×C59#12111yescharacteristic
159C8×C59#12311yescharacteristic
160#13016—591nomaximal, Sylow
161C22×C59—41no—
162C22×C59—42no—
163C22×C59—161no—
164C22×C59#44211yescharacteristic
165C22×C59#44911yescharacteristic
166C22×C59#45911yescharacteristic
167C2×D59—81no—
168C2×D59—161no—
169C4×C59—42no—
170C4×C59—81no—
171C4×C59#38611yescharacteristic
172C4×C59C4×D811yescharacteristic
173C4×C59#44711yescharacteristic
174C4×C59#46311yescharacteristic
175Dic59—81no—
176Dic59—161no—
177C2×#508—591no—
178#2957D5911yescharacteristic, complemented
179#2145—591no—
180#2143—591no—
181#1976—591no—
182#1382—591no—
183#1379—591no—
184C2×C59—21no—
185C2×C59—21no—
186C2×C59—21no—
187C2×C59—82no—
188C2×C59#187911yescharacteristic
189D59—161no—
190C2×#135—591no—
191C2×#135C2×D5911yescharacteristic
192#568—21no—
193#508—1182no—
194#508—1182no—
195C2×Q32—591no—
196C2×SD32—591no—
197C2×SD32—591no—
198C2×D16—591no—
199C2×M32—591no—
200C22×C16—591no—
201#444—22no—
202#443—22no—
203C2×#108C2×D5911yescharacteristic
204#427—591no—
205#421—21no—
206#421—1181no—
207#410—1181no—
208#405C2×D5911yescharacteristic
209#360—1182no—
210#359—1182no—
211C59#1301611yescharacteristic, complemented, Sylow
212C2×#41—21no—
213C2×#41—1181no—
214#135—21no—
215#135—21no—
216#135—1181no—
217#135—1181no—
218#135—1181no—
219#135—1181no—
220#135D23612yes—
221#135C22⋊D5912yes—
222C2×Q16—591no—
223C2×Q16C4×D5911yescharacteristic
224C2×SD16—21no—
225C2×SD16—1181no—
226C2×D8—591no—
227C2×D8C4×D5911yescharacteristic
228#131—24no—
229#131—42no—
230C2×M16—21no—
231C2×M16—42no—
232C2×M16C22⋊D5911yescharacteristic
233C22×C8C22×D5911yescharacteristic
234#117—1181no—
235#117C22⋊D5911yescharacteristic
236Q32—1182no—
237SD32—1182no—
238SD32—1182no—
239D16—1182no—
240M32—1181no—
241M32—1181no—
242C2×C16—591no—
243C2×C16—591no—
244C2×C16—1181no—
245C2×C16—1181no—
246C2×C16—1181no—
247#108—21no—
248#108C22⋊D5912yes—
249#107—1181no—
250#106—1181no—
251#104—24no—
252#104—2362no—
253#99—2362no—
254#97—21no—
255C4×C8—21no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260#41—2361no—
261#41—2361no—
262#41—2361no—
263#41—2361no—
264C2×Q8—21no—
265C2×Q8—1181no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—1181no—
269C2×D4—2361no—
270C22×C4—41no—
271C22×C4—2361no—
272C22×C4C2×C22⋊D5911yescharacteristic
273Q16—21no—
274Q16—1181no—
275Q16—1181no—
276Q16(C2×D59)⋊C412yes—
277SD16—22no—
278SD16—22no—
279SD16—2361no—
280SD16—2361no—
281D8—21no—
282D8—1181no—
283D8—1181no—
284D8(C2×D59)⋊C412yes—
285M16—21no—
286M16—22no—
287M16—44no—
288M16—41no—
289M16#1174566912yes—
290C2×C8—21no—
291C2×C8—44no—
292C2×C8—41no—
293C2×C8C2×C4×D5911yescharacteristic
294C2×C8C2×D23611yescharacteristic
295C2×C8#1174568511yescharacteristic
296C2×C8#1174568511yescharacteristic
297C2×C8C2×C22⋊D5911yescharacteristic
298C2×C8C2×C22⋊D5911yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—2361no—
301C22⋊C4—21no—
302C22⋊C4—2361no—
303C42—21no—
304C42—2361no—
305C16—1181no—
306C16—1181no—
307C16—2361no—
308C23—41no—
309C23—2361no—
310C23#1427375211yescharacteristic
311Q8—22no—
312Q8—41no—
313Q8—2361no—
314Q8—2361no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—4721no—
320D4—4721no—
321D4—2361no—
322D4—2361no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—4721no—
328C2×C4—4721no—
329C2×C4—4721no—
330C2×C4—2361no—
331C2×C4C4×C22⋊D5911yescharacteristic
332C2×C4#1427369611yescharacteristic
333C2×C4#1427370111yescharacteristic
334C2×C4C2×#1174566911yescharacteristic
335C2×C4#1427374711yescharacteristic
336C2×C4#1427375311yescharacteristic
337C8—22no—
338C8—42no—
339C8C2×(C2×D59)⋊C411yescharacteristic
340C8C4×C22⋊D5911yescharacteristic
341C8#1427370111yescharacteristic
342C8#1427371011yescharacteristic
343C22—41no—
344C22—42no—
345C22—161no—
346C22—9441no—
347C22—4721no—
348C22#1683751211yescharacteristic
349C22#1683754711yescharacteristic
350C22#1683759711yescharacteristic
351C4—42no—
352C4—81no—
353C4—9441no—
354C4—4721no—
355C4#1683728111yescharacteristic
356C4C4×#1174566911yescharacteristic
357C4#1683753611yescharacteristic
358C4#1683761711yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—9441no—
364C2#2142444411yescharacteristic
subgroupG/H
centerC4#16837536
commutatorC2×C8×C59C22×C4
FrattiniC22×C8C22×D59
FittingC59×#2957C2
socleC2×C59#1879
prime radicalC2×#16837832C2
cosocleC22×C8×C59C23
hypercenter#2957D59
hypocenterC59#13016
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #21425832C2semidirect
3. #21425823C2semidirect
4. #21424994C2semidirect
5. #21422193C2semidirect
6. #21422185C2semidirect
7. C59×#2957C2semidirect
11. C2×#14273673C4semidirect
12. C2×#14273671C4semidirect
13. C2×#14273670C4semidirect
14. C2×#14273668C4semidirect
178. #2957D59semidirect
211. C59#13016semidirect

Maximal subgroups

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

subgroupindex
C2×#168378322
#214258322
#214258232
#214249942
#214221932
#214221852
C59×#29572
#1301659