Finite Group Databasebeta

← #28481852

Subgroups — #28481852

Order 15104.

454 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433052C211yesmaximal, characteristic
2#21424117C211yesmaximal, characteristic
3#21424113C211yesmaximal, characteristic
4C4×#14273658C211yesmaximal, characteristic, complemented
5#21422851C211yesmaximal, characteristic, complemented
6#21421998C211yesmaximal, characteristic, complemented
7C59×#1303C211yesmaximal, characteristic, complemented
8C4×#11745685C2211yescharacteristic
9#16837526C411yescharacteristic, complemented
10#16837526C411yescharacteristic, complemented
11#16837467C411yescharacteristic, complemented
12#16837467C411yescharacteristic, complemented
13(C22⋊D59)⋊C8—21no—
14(C22⋊D59)⋊C8—21no—
15#16837453—21no—
16C2×#14273658—21no—
17#16837426C2211yescharacteristic
18C2×#14273655—21no—
19C2×#14273653—21no—
20C2×C4×C59⋊C8C2211yescharacteristic
21C4×C8×D59—21no—
22C4×C4⋊Dic59C2211yescharacteristic
23#16837164—21no—
24#16837163—21no—
25#16837162—21no—
26#16837152—21no—
27#16837152—21no—
28C59×#431C2211yescharacteristic
29C59×#423C2211yescharacteristic
30C4×C4⋊C4×C59C2211yescharacteristic
31C2×#11745685D411yescharacteristic
32C2×#11745664—21no—
33C22×C59⋊C8D411yescharacteristic
34C22×C59⋊C8D411yescharacteristic
35C2×C8×D59—21no—
36C2×C8×D59—21no—
37C4×Dic118C2×C411yescharacteristic
38C4×Dic118Q811yescharacteristic
39C4×D236C2×C411yescharacteristic
40C4×D236Q811yescharacteristic
41C4×C22⋊D59—21no—
42C4×C22⋊D59—21no—
43#14273686D411yescharacteristic
44#14273684—21no—
45C2×C4⋊Dic59—21no—
46C2×C4×Dic59—21no—
47C42×D59—21no—
48#14273658—24no—
49C4⋊(C59⋊C8)—21no—
50C4⋊(C59⋊C8)—21no—
51Dic59⋊C8—21no—
52Dic59⋊C8—21no—
53#14273655—42no—
54#14273653—42no—
55(C2×D59)⋊C8—21no—
56(C2×D59)⋊C8—21no—
57C4×C59⋊C8C2×C411yescharacteristic
58C4×C59⋊C8C2×C411yescharacteristic
59C4×C59⋊C8D411yescharacteristic
60C4×C59⋊C8D411yescharacteristic
61C8×Dic59—21no—
62C8×Dic59—21no—
63C59⋊#95—21no—
64C2×M16×C59—21no—
65C2×C4⋊C4×C59—21no—
66C2×C42×C59—21no—
67C2×C42×C59C2311yescharacteristic
68C4⋊C8×C59—21no—
69C4⋊C8×C59—21no—
70C4⋊C8×C59C2×C411yescharacteristic
71C4⋊C8×C59C2×C411yescharacteristic
72C22⋊C8×C59—21no—
73C4×C8×C59—21no—
74#95×C59—21no—
75C22×C4×C59—41no—
76C22×C4×C59C2×D411yescharacteristic
77C22×C4×C59C2×D411yescharacteristic
78C22×C4×C59#4111yescharacteristic
79C2×C22⋊D59—21no—
80C22×Dic59—41no—
81#11745685—21no—
82#11745685—21no—
83#11745685SD1612yes—
84#11745685SD1612yes—
85C2×D236C4⋊C411yescharacteristic
86C2×C4×D59—21no—
87C2×C4×D59—21no—
88C2×C4×D59—21no—
89C2×Dic118C4⋊C411yescharacteristic
90M16×C59—41no—
91M16×C59—41no—
92C2×C8×C59—21no—
93C2×C8×C59—21no—
94C2×C8×C59—41no—
95C4⋊C4×C59—22no—
96C4⋊C4×C59—41no—
97C42×C59—41no—
98C42×C59—41no—
99C42×C59C22×C411yescharacteristic
100C42×C59C2×D411yescharacteristic
101C42×C59C2×Q811yescharacteristic
102C42×C59#4111yescharacteristic
103C22⋊Dic59—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106C4⋊Dic59—22no—
107C4⋊Dic59—41no—
108C4⋊Dic59C4⋊C411yescharacteristic
109C4⋊Dic59C4⋊C411yescharacteristic
110Dic59⋊C4—21no—
111Dic59⋊C4—21no—
112C4×Dic59—21no—
113C4×Dic59—21no—
114C4×Dic59—21no—
115C4×Dic59—41no—
116C4×Dic59—41no—
117#11745664—41no—
118#11745664—41no—
119C2×C59⋊C8—22no—
120C2×C59⋊C8—41no—
121C2×C59⋊C8—41no—
122C2×C59⋊C8C22⋊C411yescharacteristic
123C2×C59⋊C8C22⋊C411yescharacteristic
124C2×C59⋊C8C22⋊C411yescharacteristic
125C2×C59⋊C8C22⋊C411yescharacteristic
126C8×D59—42no—
127C8×D59—42no—
128C23×C59#12111yescharacteristic
129C22×D59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—41no—
133C2×C4×C59—42no—
134C2×C4×C59—81no—
135C2×C4×C59—81no—
136C2×C4×C59C2×C22⋊C411yescharacteristic
137C2×C4×C59C2×C4⋊C411yescharacteristic
138C2×C4×C59#11711yescharacteristic
139C2×C4×C59#12111yescharacteristic
140C2×C4×C59C22⋊Q811yescharacteristic
141C2×C4×C59C22⋊Q811yescharacteristic
142C2×C4×C59C2×SD1611yescharacteristic
143C2×C4×C59C2×SD1611yescharacteristic
144C2×C4×C59#13511yescharacteristic
145C2×C4×C59#13511yescharacteristic
146C22⋊D59—22no—
147C22⋊D59—22no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—42no—
152C2×Dic59—81no—
153C2×Dic59—81no—
154D236—21no—
155D236#10612yescomplemented
156C4×D59—22no—
157C4×D59—22no—
158C4×D59—42no—
159C4×D59—41no—
160C4×D59—41no—
161Dic118—21no—
162Dic118#10612yescomplemented
163C8×C59—41no—
164C8×C59—41no—
165C8×C59—81no—
166C59⋊C8—21no—
167C59⋊C8—21no—
168C59⋊C8—21no—
169C59⋊C8—81no—
170C59⋊C8#10412yescomplemented
171#8666—591nomaximal, Sylow
172C22×C59—21no—
173C22×C59—21no—
174C22×C59#38011yescharacteristic
175C22×C59#46511yescharacteristic
176C22×C59#46511yescharacteristic
177C2×D59—22no—
178C2×D59—41no—
179C2×D59—41no—
180C4×C59—21no—
181C4×C59—21no—
182C4×C59—21no—
183C4×C59—82no—
184C4×C59C2×#10411yescharacteristic
185C4×C59#42111yescharacteristic
186C4×C59C2×#10611yescharacteristic
187C4×C59#42711yescharacteristic
188C4×C59#46511yescharacteristic
189C4×C59#46511yescharacteristic
190Dic59—22no—
191Dic59—41no—
192Dic59—41no—
193Dic59—82no—
194C8×#41—591no—
195#1806—591no—
196#1806—591no—
197C4×#106—591no—
198#1566—591no—
199#1303—591no—
200#1303D5911yescharacteristic, complemented
201C2×C59—21no—
202C2×C59—21no—
203C2×C59#180611yescharacteristic
204C2×C59#180711yescharacteristic
205C2×C59#181411yescharacteristic
206D59—42no—
207C4×#41—591no—
208C8×Q8—591no—
209C8×Q8—591no—
210C8×D4—591no—
211C8×D4—591no—
212C8×D4—1181no—
213C8×D4—1181no—
214#431—1181no—
215#431C2×D5911yescharacteristic
216C2×#106—1181no—
217#423—591no—
218#423C2×D5911yescharacteristic
219C2×#104—1181no—
220C2×#104—1181no—
221C2×C4×C8—591no—
222C2×C4×C8—1181no—
223C4×C4⋊C4—591no—
224C4×C4⋊C4C2×D5911yescharacteristic
225#340—1181no—
226#339—1181no—
227#339—1181no—
228#334—1181no—
229#334—1181no—
230C59#866611yescharacteristic, complemented, Sylow
231C2×#41—591no—
232C2×M16—21no—
233C2×M16—1181no—
234C22×C8—591no—
235C22×C8—591no—
236C22×C8—1181no—
237C22×C8—1181no—
238C4×Q8—591no—
239C4×Q8—591no—
240C4×D4—591no—
241C4×D4—591no—
242C4×D4—1181no—
243C4×D4—1181no—
244#117—591no—
245#117—1181no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—1181no—
248C2×C42—21no—
249C2×C42—1181no—
250C2×C42—1181no—
251C2×C42C22×D5911yescharacteristic
252#106—1184no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—1181no—
256C4⋊C8—1181no—
257C4⋊C8—1181no—
258C4⋊C8—1181no—
259C4⋊C8C4×D5911yescharacteristic
260C4⋊C8C4×D5911yescharacteristic
261#104—2362no—
262#104—2362no—
263C22⋊C8—21no—
264C22⋊C8—1181no—
265C22⋊C8—1181no—
266C4×C8—21no—
267C4×C8—591no—
268C4×C8—591no—
269C4×C8—591no—
270C4×C8—591no—
271C4×C8—1181no—
272C4×C8—1181no—
273#95—21no—
274#95—1181no—
275#41—592no—
276#41—592no—
277#41—1181no—
278#41—1181no—
279C2×Q8—591no—
280C2×D4—591no—
281C2×D4—1181no—
282C22×C4—41no—
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4—1181no—
286C22×C4—2361no—
287C22×C4#1174568511yescharacteristic
288C22×C4D4×D5911yescharacteristic
289C22×C4D4×D5911yescharacteristic
290M16—41no—
291M16—41no—
292M16—2361no—
293M16—2361no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—41no—
297C2×C8—591no—
298C2×C8—591no—
299C2×C8—591no—
300C2×C8—591no—
301C2×C8—1182no—
302C2×C8—2362no—
303C2×C8—2362no—
304C2×C8—2361no—
305C2×C8—2361no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—591no—
309C4⋊C4—591no—
310C4⋊C4—1182no—
311C4⋊C4—1181no—
312C4⋊C4—1181no—
313C4⋊C4—2361no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4—1181no—
317C42—41no—
318C42—41no—
319C42—1181no—
320C42—1181no—
321C42—1181no—
322C42—2361no—
323C42—2361no—
324C42C2×C4×D5911yescharacteristic
325C42#1174568511yescharacteristic
326C42D4×D5911yescharacteristic
327C42Q8×D5911yescharacteristic
328C23—1181no—
329C23#1427370011yescharacteristic
330Q8—592no—
331Q8—1181no—
332D4—592no—
333D4—1182no—
334D4—1182no—
335D4—1181no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—1181no—
343C2×C4—1182no—
344C2×C4—1182no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—4721no—
348C2×C4—4721no—
349C2×C4—2362no—
350C2×C4—2362no—
351C2×C4—2361no—
352C2×C4—2361no—
353C2×C4C22⋊C4×D5911yescharacteristic
354C2×C4C4⋊C4×D5911yescharacteristic
355C2×C4#1427368411yescharacteristic
356C2×C4#1427370011yescharacteristic
357C2×C4#1427370511yescharacteristic
358C2×C4#1427370511yescharacteristic
359C2×C4SD16×D5911yescharacteristic
360C2×C4SD16×D5911yescharacteristic
361C2×C4#1427374611yescharacteristic
362C2×C4#1427375011yescharacteristic
363C8—41no—
364C8—41no—
365C8—81no—
366C8—592no—
367C8—1181no—
368C8—1181no—
369C8—1181no—
370C8—4721no—
371C22—21no—
372C22—21no—
373C22—1182no—
374C22—2361no—
375C22—2361no—
376C22#1683726111yescharacteristic
377C22#1683763011yescharacteristic
378C22#1683763411yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—1182no—
384C4—4722no—
385C4—2361no—
386C4—2361no—
387C4#104×D5911yescharacteristic
388C4#1683741711yescharacteristic
389C4#106×D5911yescharacteristic
390C4#1683743911yescharacteristic
391C4#1683763011yescharacteristic
392C4#1683763411yescharacteristic
393C2—21no—
394C2—21no—
395C2—2362no—
396C2#2142411511yescharacteristic
397C2#2142412011yescharacteristic
398C2#2142414911yescharacteristic
subgroupG/H
centerC2×C4#14273700
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1303C2
socleC22×C59#380
prime radicalC2×#11745685D4
cosocleC2×C42×C59C23
hypercenter#1303D59
hypocenterC59#8666
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. C4×#14273658C2semidirect
5. #21422851C2semidirect
6. #21421998C2semidirect
7. C59×#1303C2semidirect
9. #16837526C4semidirect
10. #16837526C4semidirect
11. #16837467C4semidirect
12. #16837467C4semidirect
155. D236#106semidirect
162. Dic118#106semidirect
170. C59⋊C8#104semidirect
200. #1303D59semidirect
230. C59#8666semidirect

Maximal subgroups

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

subgroupindex
#214330522
#214241172
#214241132
C4×#142736582
#214228512
#214219982
C59×#13032
#866659