Finite Group Databasebeta

← #28482587

Subgroups — #28482587

Order 15104.

440 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433209C211yesmaximal, characteristic
2#21424248C211yesmaximal, characteristic, complemented
3C4×#14273655C211yesmaximal, characteristic
4#21422849C211yesmaximal, characteristic, complemented
5#21422484C211yesmaximal, characteristic
6#21421945C211yesmaximal, characteristic, complemented
7C59×#1276C211yesmaximal, characteristic, complemented
8C4×#11745685C2211yescharacteristic
9#16837532—21no—
10#16837481—21no—
11#16837470—22no—
12#16837458—21no—
13#16837424—21no—
14C2×C4⋊(C59⋊C8)—22no—
15C2×C4⋊(C59⋊C8)C2211yescharacteristic
16C2×C4⋊(C59⋊C8)C2211yescharacteristic
17C2×#14273655C411yescharacteristic
18C2×#14273655C411yescharacteristic
19C4×#11745664C2211yescharacteristic
20#16837162C411yescharacteristic
21#16837162C411yescharacteristic
22#16837154—21no—
23#16837152—21no—
24#16837134—21no—
25#16837131—21no—
26C59×#431C2211yescharacteristic
27C59×#431C2211yescharacteristic
28C43×C59C2211yescharacteristic
29C2×#11745685C2×C411yescharacteristic
30C2×#11745664C2×C411yescharacteristic
31C2×#11745664C2×C411yescharacteristic
32C2×#11745659—22no—
33C22×C59⋊C8—21no—
34C22×C59⋊C8D412yes—
35C4×Dic118D411yescharacteristic
36C4×Dic118Q811yescharacteristic
37C4×D236D411yescharacteristic
38C4×D236Q811yescharacteristic
39C4×C22⋊D59—21no—
40C4×C22⋊D59—21no—
41#14273686C2×C411yescharacteristic
42#14273684—21no—
43C42×D59—21no—
44C4⋊(C59⋊C8)—21no—
45C4⋊(C59⋊C8)—21no—
46C4⋊(C59⋊C8)—21no—
47C4⋊(C59⋊C8)—21no—
48C4⋊(C59⋊C8)—44no—
49Dic59⋊C8—22no—
50#14273655—22no—
51#14273655—22no—
52(C2×D59)⋊C8—22no—
53#14273638—21no—
54#14273637—22no—
55C4×C59⋊C8—21no—
56C2×C42×C59—21no—
57C2×C42×C59—21no—
58C2×C42×C59C2×C411yescharacteristic
59C2×C42×C59C2×C411yescharacteristic
60C2×C42×C59C2311yescharacteristic
61C4⋊C8×C59—21no—
62C4⋊C8×C59D411yescharacteristic
63C4⋊C8×C59D411yescharacteristic
64C22⋊C8×C59—21no—
65C22⋊C8×C59—21no—
66C4×C8×C59—21no—
67C4×C8×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59C22×C411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59#4111yescharacteristic
73C2×C22⋊D59—21no—
74#11745685—21no—
75#11745685—21no—
76#11745685—21no—
77#11745685—21no—
78C2×D236C4⋊C411yescharacteristic
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×Dic118C4⋊C411yescharacteristic
83C2×C8×C59—21no—
84C2×C8×C59—21no—
85C2×C8×C59—41no—
86C42×C59—22no—
87C42×C59—22no—
88C42×C59—21no—
89C42×C59—21no—
90C42×C59—21no—
91C42×C59—42no—
92C42×C59M1612yescomplemented
93C42×C59C2×D411yescharacteristic
94C42×C59C2×D411yescharacteristic
95C42×C59C2×Q811yescharacteristic
96C42×C59#4111yescharacteristic
97C22⋊Dic59—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59C4⋊C411yescharacteristic
101C4⋊Dic59C4⋊C411yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59—21no—
107#11745664—21no—
108#11745664—21no—
109#11745664—21no—
110#11745664M1612yescomplemented
111C2×C59⋊C8—21no—
112C2×C59⋊C8—21no—
113C2×C59⋊C8—22no—
114C2×C59⋊C8—42no—
115C2×C59⋊C8—42no—
116C2×C59⋊C8—41no—
117#11745659—82no—
118C23×C59C4×D411yescharacteristic
119C22×D59—21no—
120C2×C4×C59—22no—
121C2×C4×C59—22no—
122C2×C4×C59—22no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—22no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59C2×C4⋊C411yescharacteristic
130C2×C4×C59C4×D411yescharacteristic
131C2×C4×C59#12011yescharacteristic
132C2×C4×C59C22⋊Q811yescharacteristic
133C2×C4×C59C22⋊Q811yescharacteristic
134C2×C4×C59#12311yescharacteristic
135C2×C4×C59C2×M1611yescharacteristic
136C2×C4×C59C2×M1611yescharacteristic
137C2×C4×C59#13111yescharacteristic
138C2×C4×C59#13111yescharacteristic
139C22⋊D59—41no—
140C22⋊D59—41no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144D236—21no—
145D236—21no—
146C4×D59—41no—
147C4×D59—41no—
148C4×D59—41no—
149C4×D59—41no—
150C4×D59—81no—
151Dic118—21no—
152Dic118—21no—
153C8×C59—41no—
154C8×C59—41no—
155C8×C59—81no—
156C59⋊C8—22no—
157C59⋊C8—41no—
158C59⋊C8—42no—
159C59⋊C8—81no—
160#8841—591nomaximal, Sylow
161C22×C59—21no—
162C22×C59—21no—
163C22×C59#38511yescharacteristic
164C22×C59#43511yescharacteristic
165C22×C59#43611yescharacteristic
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C4×C59—24no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—42no—
174C4×C59#42311yescharacteristic
175C4×C59#42411yescharacteristic
176C4×C59#43511yescharacteristic
177C4×C59#43611yescharacteristic
178C4×C59#45311yescharacteristic
179C4×C59#45611yescharacteristic
180Dic59—41no—
181Dic59—41no—
182Dic59—41no—
183#2989—591no—
184#1842—591no—
185C4×#104—591no—
186#1565—591no—
187#1477—591no—
188#1283—591no—
189#1276D5911yescharacteristic, complemented
190C2×C59—21no—
191C2×C59—21no—
192C2×C59#185111yescharacteristic
193C2×C59#185911yescharacteristic
194C2×C59#186111yescharacteristic
195D59—81no—
196C4×#41—591no—
197#446—1181no—
198#436—1181no—
199#435—1182no—
200#432—1181no—
201#431C2×D5911yescharacteristic
202#431C2×D5911yescharacteristic
203#423—1181no—
204C2×C4⋊C8—591no—
205C2×C4⋊C8—591no—
206C2×C4⋊C8—1182no—
207C2×#104—591no—
208C2×#104—591no—
209C4×M16—591no—
210C43C2×D5911yescharacteristic
211#339—591no—
212#339—591no—
213#335—1181no—
214#334—1181no—
215Q8⋊C8—1181no—
216D4⋊C8—1181no—
217C59#884111yescharacteristic, complemented, Sylow
218C2×#41—591no—
219C2×M16—591no—
220C2×M16—591no—
221C2×M16—1182no—
222C22×C8—592no—
223C22×C8—1181no—
224C4×Q8—591no—
225C4×Q8—591no—
226C4×D4—591no—
227C4×D4—591no—
228C4×D4—1181no—
229C4×D4—1181no—
230#117—591no—
231#117—1181no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—1181no—
235C2×C42C4×D5911yescharacteristic
236C2×C42C4×D5911yescharacteristic
237C2×C42C22×D5911yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—1182no—
240C4⋊C8—1181no—
241C4⋊C8—1181no—
242C4⋊C8—1181no—
243C4⋊C8—1181no—
244C4⋊C8—2364no—
245C4⋊C8D23611yescharacteristic
246C4⋊C8D23611yescharacteristic
247#104—1182no—
248#104—1182no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—1182no—
252#97—1182no—
253#97—1181no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—1181no—
257#41—1181no—
258#41—1181no—
259#41—1181no—
260#41—1181no—
261C2×Q8—591no—
262C2×D4—591no—
263C2×D4—1181no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—1181no—
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4C2×C4×D5911yescharacteristic
270C22×C4D4×D5911yescharacteristic
271C22×C4#1174568711yescharacteristic
272M16—592no—
273M16—1181no—
274M16—1181no—
275M16—1181no—
276M16—4722no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—41no—
280C2×C8—1181no—
281C2×C8—1181no—
282C2×C8—1182no—
283C2×C8—2362no—
284C2×C8—2361no—
285C2×C8—2362no—
286C4⋊C4—591no—
287C4⋊C4—591no—
288C4⋊C4—1181no—
289C4⋊C4—1181no—
290C22⋊C4—1181no—
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C42—22no—
294C42—22no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—42no—
299C42—1181no—
300C42—1181no—
301C42—1181no—
302C42#1174565912yescomplemented
303C42C2×D23611yescharacteristic
304C42#1174568511yescharacteristic
305C42D4×D5911yescharacteristic
306C42Q8×D5911yescharacteristic
307C23—1181no—
308C23(C22⋊D59)⋊C411yescharacteristic
309Q8—1181no—
310Q8—1181no—
311D4—1181no—
312D4—1181no—
313D4—2361no—
314D4—2361no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—4721no—
328C2×C4—2361no—
329C2×C4—2361no—
330C2×C4—2361no—
331C2×C4—2361no—
332C2×C4C4⋊C4×D5911yescharacteristic
333C2×C4C4×D23611yescharacteristic
334C2×C4#1427369711yescharacteristic
335C2×C4#1427370511yescharacteristic
336C2×C4#1427370711yescharacteristic
337C2×C4#1427370911yescharacteristic
338C2×C4M16×D5911yescharacteristic
339C2×C4C2×#1174565911yescharacteristic
340C2×C4#1427373311yescharacteristic
341C2×C4#1427373511yescharacteristic
342C8—41no—
343C8—41no—
344C8—81no—
345C8—1182no—
346C8—4721no—
347C8—2361no—
348C8—2362no—
349C22—21no—
350C22—21no—
351C22—2361no—
352C22—2361no—
353C22—2361no—
354C22#1683727611yescharacteristic
355C22#1683747011yescharacteristic
356C22#1683747711yescharacteristic
357C4—24no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—42no—
362C4—2361no—
363C4—2361no—
364C4—2361no—
365C4#1683742411yescharacteristic
366C4#1683742711yescharacteristic
367C4#1683747511yescharacteristic
368C4#1683748111yescharacteristic
369C4#1683757111yescharacteristic
370C4#1683758611yescharacteristic
371C2—21no—
372C2—21no—
373C2—4721no—
374C2#2142428011yescharacteristic
375C2#2142432311yescharacteristic
376C2#2142433711yescharacteristic
subgroupG/H
centerC2×C4#14273697
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1276C2
socleC22×C59#385
prime radicalC2×#11745685C2×C4
cosocleC2×C42×C59C23
hypercenter#1276D59
hypocenterC59#8841
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
2. #21424248C2semidirect
4. #21422849C2semidirect
6. #21421945C2semidirect
7. C59×#1276C2semidirect
92. C42×C59M16semidirect
110. #11745664M16semidirect
189. #1276D59semidirect
217. C59#8841semidirect
302. C42#11745659semidirect

Maximal subgroups

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

subgroupindex
#214332092
#214242482
C4×#142736552
#214228492
#214224842
#214219452
C59×#12762
#884159