Finite Group Databasebeta

← #28482590

Subgroups — #28482590

Order 15104.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433209C211yesmaximal, characteristic
2#21424212C211yesmaximal, characteristic, complemented
3C4×#14273653C211yesmaximal, characteristic
4#21422481C211yesmaximal, characteristic
5#21421947C211yesmaximal, characteristic, complemented
6#21421928C211yesmaximal, characteristic, complemented
7C59×#1565C211yesmaximal, characteristic, complemented
8C4×#11745685C2211yescharacteristic
9#16837532—21no—
10#16837481—21no—
11#16837470—22no—
12#16837458—21no—
13#16837455C2211yescharacteristic
14#16837424—21no—
15C2×C4⋊(C59⋊C8)C2211yescharacteristic
16C2×#14273653C411yescharacteristic
17C2×#14273653C411yescharacteristic
18C42×Dic59C2211yescharacteristic
19#16837163C411yescharacteristic
20#16837163C411yescharacteristic
21#16837156—22no—
22#16837132—21no—
23#16837129—21no—
24C59×#431C2211yescharacteristic
25C2×C4⋊C8×C59C2211yescharacteristic
26C4×M16×C59C2211yescharacteristic
27C59×#335—21no—
28C59×#334—21no—
29C2×#11745685C2×C411yescharacteristic
30C2×#11745659—22no—
31C22×C59⋊C8D412yes—
32C4×Dic118D411yescharacteristic
33C4×Dic118Q811yescharacteristic
34C4×D236D411yescharacteristic
35C4×D236Q811yescharacteristic
36C4×C22⋊D59—21no—
37C4×C22⋊D59—21no—
38#14273686C2×C411yescharacteristic
39#14273684—21no—
40C2×C4×Dic59—21no—
41C2×C4×Dic59—21no—
42C2×C4×Dic59C2×C411yescharacteristic
43C2×C4×Dic59C2×C411yescharacteristic
44C42×D59—21no—
45C4⋊(C59⋊C8)—21no—
46C4⋊(C59⋊C8)—21no—
47C4⋊(C59⋊C8)—21no—
48Dic59⋊C8—22no—
49#14273653—22no—
50#14273653—22no—
51C22⋊(C59⋊C8)—21no—
52(C2×D59)⋊C8—22no—
53#14273637—22no—
54C4×C59⋊C8—21no—
55C2×M16×C59C2×C411yescharacteristic
56C2×M16×C59C2×C411yescharacteristic
57C22×C8×C59—21no—
58C2×C42×C59C2311yescharacteristic
59C4⋊C8×C59—21no—
60C4⋊C8×C59—21no—
61C4⋊C8×C59D411yescharacteristic
62C4⋊C8×C59D411yescharacteristic
63C22⋊C8×C59—21no—
64#97×C59—21no—
65C4×C8×C59—21no—
66C4×C8×C59—21no—
67C22×C4×C59C22×C411yescharacteristic
68C22×C4×C59C2×D411yescharacteristic
69C22×C4×C59#4111yescharacteristic
70C2×C22⋊D59—21no—
71C22×Dic59—21no—
72C22×Dic59—21no—
73#11745685—21no—
74#11745685—21no—
75#11745685—21no—
76#11745685—21no—
77C2×D236C4⋊C411yescharacteristic
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×Dic118C4⋊C411yescharacteristic
82M16×C59—21no—
83M16×C59—21no—
84M16×C59—21no—
85M16×C59M1612yescomplemented
86C2×C8×C59—21no—
87C2×C8×C59—21no—
88C2×C8×C59—21no—
89C2×C8×C59—21no—
90C2×C8×C59—42no—
91C2×C8×C59—41no—
92C42×C59C2×D411yescharacteristic
93C42×C59C2×D411yescharacteristic
94C42×C59C2×Q811yescharacteristic
95C42×C59#4111yescharacteristic
96C22⋊Dic59—21no—
97(C2×D59)⋊C4—21no—
98(C2×D59)⋊C4—21no—
99C4⋊Dic59C4⋊C411yescharacteristic
100C4⋊Dic59C4⋊C411yescharacteristic
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59—21no—
107C4×Dic59—21no—
108C4×Dic59—21no—
109C4×Dic59—42no—
110C4×Dic59—41no—
111C4×Dic59—41no—
112C4×Dic59M1612yescomplemented
113C2×C59⋊C8—22no—
114C2×C59⋊C8—42no—
115C2×C59⋊C8—41no—
116#11745659—82no—
117C23×C59C4×D411yescharacteristic
118C22×D59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—41no—
122C2×C4×C59C2×C4⋊C411yescharacteristic
123C2×C4×C59C4×D411yescharacteristic
124C2×C4×C59#12011yescharacteristic
125C2×C4×C59C22⋊Q811yescharacteristic
126C2×C4×C59C22⋊Q811yescharacteristic
127C2×C4×C59#12311yescharacteristic
128C2×C4×C59C2×M1611yescharacteristic
129C2×C4×C59C2×M1611yescharacteristic
130C2×C4×C59#13111yescharacteristic
131C2×C4×C59#13111yescharacteristic
132C22⋊D59—41no—
133C22⋊D59—41no—
134C2×Dic59—22no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—22no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143D236—21no—
144D236—21no—
145C4×D59—41no—
146C4×D59—41no—
147C4×D59—41no—
148C4×D59—41no—
149C4×D59—81no—
150Dic118—21no—
151Dic118—21no—
152C8×C59—22no—
153C8×C59—41no—
154C8×C59—41no—
155C8×C59—41no—
156C8×C59—81no—
157C59⋊C8—42no—
158C59⋊C8—81no—
159#8842—591nomaximal, Sylow
160C22×C59—21no—
161C22×C59—21no—
162C22×C59#38511yescharacteristic
163C22×C59#43511yescharacteristic
164C22×C59#43611yescharacteristic
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59#42311yescharacteristic
172C4×C59#42411yescharacteristic
173C4×C59#43511yescharacteristic
174C4×C59#43611yescharacteristic
175C4×C59#45411yescharacteristic
176C4×C59#45511yescharacteristic
177Dic59—42no—
178Dic59—42no—
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182#2989—591no—
183#1831—591no—
184C4×#104—591no—
185#1565D5911yescharacteristic, complemented
186#1477—591no—
187#1283—591no—
188#1276—591no—
189C2×C59—21no—
190C2×C59—21no—
191C2×C59#185111yescharacteristic
192C2×C59#186011yescharacteristic
193C2×C59#186111yescharacteristic
194D59—81no—
195C4×#41—591no—
196#446—1181no—
197#436—1181no—
198#435—1182no—
199#432—1181no—
200#431—591no—
201#431C2×D5911yescharacteristic
202#423—1181no—
203C2×C4⋊C8—591no—
204C2×C4⋊C8C2×D5911yescharacteristic
205C2×#104—591no—
206C2×#104—591no—
207C4×M16C2×D5911yescharacteristic
208C43—591no—
209#339—591no—
210#339—591no—
211#336—1182no—
212#335—21no—
213#334—21no—
214Q8⋊C8—1181no—
215D4⋊C8—1181no—
216C59#884211yescharacteristic, complemented, Sylow
217C2×#41—591no—
218C2×M16—1182no—
219C2×M16C4×D5911yescharacteristic
220C2×M16C4×D5911yescharacteristic
221C22×C8—21no—
222C22×C8—592no—
223C4×Q8—591no—
224C4×Q8—591no—
225C4×D4—591no—
226C4×D4—591no—
227C4×D4—1181no—
228C4×D4—1181no—
229#117—591no—
230#117—1181no—
231C2×C42—591no—
232C2×C42—591no—
233C2×C42—1181no—
234C2×C42—1181no—
235C2×C42—1181no—
236C2×C42C22×D5911yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—1182no—
240C4⋊C8—1181no—
241C4⋊C8—1181no—
242C4⋊C8—1181no—
243C4⋊C8C22⋊D5911yescharacteristic
244C4⋊C8C22⋊D5911yescharacteristic
245#104—1182no—
246#104—1182no—
247C22⋊C8—21no—
248C22⋊C8—1182no—
249C22⋊C8—1181no—
250#97—21no—
251#97—1182no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—1181no—
255#41—1181no—
256#41—1181no—
257#41—1181no—
258#41—1181no—
259C2×Q8—591no—
260C2×D4—591no—
261C2×D4—1181no—
262C22×C4—1181no—
263C22×C4—1181no—
264C22×C4—1181no—
265C22×C4—1181no—
266C22×C4—1181no—
267C22×C4C2×C4×D5911yescharacteristic
268C22×C4D4×D5911yescharacteristic
269C22×C4#1174568911yescharacteristic
270M16—21no—
271M16—21no—
272M16—21no—
273M16—4722no—
274M16#1174565912yescomplemented
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—42no—
280C2×C8—41no—
281C2×C8—1182no—
282C2×C8—2361no—
283C2×C8—2362no—
284C4⋊C4—591no—
285C4⋊C4—591no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C42—592no—
292C42—1181no—
293C42—1181no—
294C42—1181no—
295C42—1181no—
296C42—1181no—
297C42—1181no—
298C42—2361no—
299C42—2361no—
300C42—2362no—
301C42#1174568511yescharacteristic
302C42D4×D5911yescharacteristic
303C42Q8×D5911yescharacteristic
304C42C2×C22⋊D5911yescharacteristic
305C23—1181no—
306C23#1427368911yescharacteristic
307Q8—1181no—
308Q8—1181no—
309D4—1181no—
310D4—1181no—
311D4—2361no—
312D4—2361no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—1182no—
317C2×C4—1182no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—4721no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4—2361no—
328C2×C4—2361no—
329C2×C4—2361no—
330C2×C4C4⋊C4×D5911yescharacteristic
331C2×C4C4×C22⋊D5911yescharacteristic
332C2×C4#1427369511yescharacteristic
333C2×C4#1427370311yescharacteristic
334C2×C4#1427370511yescharacteristic
335C2×C4#1427371211yescharacteristic
336C2×C4M16×D5911yescharacteristic
337C2×C4C2×#1174565911yescharacteristic
338C2×C4#1427373311yescharacteristic
339C2×C4#1427373511yescharacteristic
340C8—22no—
341C8—41no—
342C8—41no—
343C8—41no—
344C8—81no—
345C8—4721no—
346C8—2362no—
347C22—21no—
348C22—21no—
349C22—2361no—
350C22—2361no—
351C22—2361no—
352C22#1683727311yescharacteristic
353C22#1683747211yescharacteristic
354C22#1683747911yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—2362no—
359C4—2362no—
360C4—2361no—
361C4—2361no—
362C4—2361no—
363C4#1683742411yescharacteristic
364C4#1683742711yescharacteristic
365C4#1683747311yescharacteristic
366C4#1683747811yescharacteristic
367C4#1683757311yescharacteristic
368C4#1683757811yescharacteristic
369C2—21no—
370C2—21no—
371C2—4721no—
372C2#2142427711yescharacteristic
373C2#2142432611yescharacteristic
374C2#2142433311yescharacteristic
subgroupG/H
centerC2×C4#14273695
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1565C2
socleC22×C59#385
prime radicalC2×#11745685C2×C4
cosocleC2×C42×C59C23
hypercenter#1565D59
hypocenterC59#8842
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
2. #21424212C2semidirect
5. #21421947C2semidirect
6. #21421928C2semidirect
7. C59×#1565C2semidirect
85. M16×C59M16semidirect
112. C4×Dic59M16semidirect
185. #1565D59semidirect
216. C59#8842semidirect
274. M16#11745659semidirect

Maximal subgroups

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

subgroupindex
#214332092
#214242122
C4×#142736532
#214224812
#214219472
#214219282
C59×#15652
#884259