Finite Group Databasebeta

← #28493285

Subgroups — #28493285

Order 15104.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21425022C211yesmaximal, characteristic
2#21424902C211yesmaximal, characteristic
3#21424860C211yesmaximal, characteristic, complemented
4#21424814C211yesmaximal, characteristic, complemented
5C2×#16837145C211yesmaximal, characteristic
6#21421980C211yesmaximal, characteristic, complemented
7C2×C59×#335C211yesmaximal, characteristic, complemented
8C2×#14273724C2211yescharacteristic
9C2×#14273659—21no—
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×Dic59⋊C8—21no—
12C2×#14273649—21no—
13C2×#14273649—21no—
14C2×#14273649—21no—
15C2×#14273649—21no—
16#16837272C2211yescharacteristic
17C4×C4⋊Dic59C2211yescharacteristic
18#16837165—21no—
19#16837156—21no—
20#16837145—22no—
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×C4×C8×C59C2211yescharacteristic
24C59×#335—22no—
25C22×D236—21no—
26C22×D236—21no—
27C22×D236—21no—
28C22×C59⋊C8—21no—
29#14273724—21no—
30#14273724—21no—
31#14273724—21no—
32#14273724Q812yes—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59—21no—
36C2×C4⋊Dic59D411yescharacteristic
37C2×C4⋊Dic59D411yescharacteristic
38C2×C4×Dic59—21no—
39#14273659—42no—
40C4⋊(C59⋊C8)—21no—
41C4⋊(C59⋊C8)—21no—
42Dic59⋊C8—42no—
43#14273649—42no—
44#14273649—42no—
45#14273649—42no—
46#14273649—42no—
47C59⋊#95—21no—
48C22×C8×C59—21no—
49C22×C8×C59—21no—
50C22×C8×C59D411yescharacteristic
51C22×C8×C59D411yescharacteristic
52C2×C42×C59C2311yescharacteristic
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59—21no—
56C4⋊C8×C59D412yes—
57C4×C8×C59—21no—
58C4×C8×C59—21no—
59C23×D59—41no—
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59#4111yescharacteristic
63C22×Dic59—21no—
64C22×Dic59—21no—
65C22×Dic59—41no—
66C2×D236—22no—
67C2×D236—22no—
68C2×D236—22no—
69C2×D236—41no—
70C2×D236—41no—
71C2×D236—41no—
72C2×D236—41no—
73C2×D236—41no—
74C2×D236—41no—
75C2×D236—41no—
76C2×D236—41no—
77C2×D236—41no—
78C2×D236—41no—
79C2×D236—41no—
80C2×D236—81no—
81C2×D236—81no—
82C2×C8×C59—21no—
83C2×C8×C59—21no—
84C2×C8×C59—21no—
85C2×C8×C59—22no—
86C2×C8×C59—21no—
87C2×C8×C59—21no—
88C2×C8×C59—41no—
89C2×C8×C59—41no—
90C2×C8×C59—41no—
91C2×C8×C59—41no—
92C2×C8×C59—41no—
93C2×C8×C59SD1612yes—
94C42×C59C2×D411yescharacteristic
95C42×C59C2×Q811yescharacteristic
96C42×C59#4111yescharacteristic
97C42×C59#4111yescharacteristic
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59—21no—
101C4⋊Dic59—41no—
102C4⋊Dic59—41no—
103C4⋊Dic59—41no—
104C4⋊Dic59—41no—
105C4⋊Dic59—81no—
106C4⋊Dic59D812yes—
107C4×Dic59—41no—
108C4×Dic59—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8—41no—
111C2×C59⋊C8—41no—
112C23×C59#12111yescharacteristic
113C22×D59—42no—
114C22×D59—81no—
115C22×D59—81no—
116C22×D59—81no—
117C22×D59—81no—
118C22×D59—81no—
119C22×D59—81no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59#12111yescharacteristic
123C2×C4×C59#12111yescharacteristic
124C2×C4×C59C22⋊Q811yescharacteristic
125C2×C4×C59C22⋊Q811yescharacteristic
126C2×C4×C59C22⋊Q811yescharacteristic
127C2×C4×C59#12611yescharacteristic
128C2×C4×C59C2×D811yescharacteristic
129C2×C4×C59C2×SD1611yescharacteristic
130C2×C4×C59#13511yescharacteristic
131C2×C4×C59#13511yescharacteristic
132C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C59#13711yescharacteristic
136C2×Dic59—22no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—81no—
143C2×Dic59—81no—
144C2×Dic59—81no—
145D236—42no—
146D236—42no—
147D236—42no—
148D236—42no—
149D236—82no—
150D236—82no—
151D236—81no—
152D236—81no—
153D236—81no—
154D236—81no—
155C8×C59—22no—
156C8×C59—42no—
157C8×C59—41no—
158C8×C59—81no—
159C59⋊C8—81no—
160#10599—591nomaximal, Sylow
161C22×C59#39611yescharacteristic
162C22×C59#46011yescharacteristic
163C22×C59#46311yescharacteristic
164C22×C59#46611yescharacteristic
165C22×C59#46811yescharacteristic
166C22×C59#47111yescharacteristic
167C22×C59#47211yescharacteristic
168C2×D59—82no—
169C2×D59—82no—
170C2×D59—82no—
171C2×D59—161no—
172C2×D59—161no—
173C2×D59—161no—
174C2×D59—161no—
175C4×C59—21no—
176C4×C59—21no—
177C4×C59#45911yescharacteristic
178C4×C59#46411yescharacteristic
179C4×C59#46511yescharacteristic
180C4×C59#46911yescharacteristic
181C4×C59#47411yescharacteristic
182C4×C59#47611yescharacteristic
183C4×C59#47811yescharacteristic
184C4×C59#47811yescharacteristic
185Dic59—42no—
186Dic59—81no—
187Dic59—161no—
188#1982—591no—
189#1957—591no—
190#1948—591no—
191#1939—591no—
192C2×#335D5911yescharacteristic, complemented
193C2×#331—591no—
194#1296—591no—
195C2×C59#166811yescharacteristic
196C2×C59#168111yescharacteristic
197C2×C59#168611yescharacteristic
198C2×C59#169711yescharacteristic
199C2×C59#206311yescharacteristic
200C2×C59#206511yescharacteristic
201C2×C59#206711yescharacteristic
202D59—162no—
203C2×#127—591no—
204C2×#106—1181no—
205C2×C4⋊C8—591no—
206C2×C4⋊C8—1181no—
207C2×C4⋊C8C2×D5911yescharacteristic
208C2×C4⋊C8C2×D5911yescharacteristic
209C2×#102—1181no—
210C2×#102—1181no—
211C2×#102—1181no—
212C2×#102—1181no—
213C2×C4×C8C2×D5911yescharacteristic
214#384—591no—
215C4×C4⋊C4—591no—
216#340—1181no—
217#336—1181no—
218#335—22no—
219#331—1182no—
220C59#1059911yescharacteristic, complemented, Sylow
221C22×D4—1181no—
222C22×D4—1181no—
223C22×D4—1181no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—1181no—
227C22×C8D23611yescharacteristic
228C22×C8D23611yescharacteristic
229#127—592no—
230#127—1181no—
231#127—1181no—
232#127—1181no—
233C2×C4⋊C4—591no—
234C2×C4⋊C4—591no—
235C2×C4⋊C4—1181no—
236C2×C4⋊C4—1181no—
237C2×C4⋊C4—1181no—
238C2×C42—1181no—
239C2×C42C22×D5911yescharacteristic
240#106—2362no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—1181no—
245C4⋊C8—1181no—
246C4⋊C8—2362no—
247C4⋊C8C22⋊D5912yes—
248#102—2362no—
249#102—2362no—
250#102—2362no—
251#102—2362no—
252C4×C8—21no—
253C4×C8—21no—
254#95—1181no—
255C24—2361no—
256C2×D4—1182no—
257C2×D4—1182no—
258C2×D4—1182no—
259C2×D4—4721no—
260C2×D4—4721no—
261C2×D4—2361no—
262C2×D4—2361no—
263C2×D4—2361no—
264C2×D4—2361no—
265C2×D4—2361no—
266C2×D4—2361no—
267C2×D4—2361no—
268C2×D4—2361no—
269C2×D4—2361no—
270C2×D4—2361no—
271C2×D4—2361no—
272C22×C4—1181no—
273C22×C4—1181no—
274C22×C4—2361no—
275C22×C4C2×D23611yescharacteristic
276C22×C4D4×D5911yescharacteristic
277C22×C4#1174568911yescharacteristic
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—2361no—
290C2×C8—2361no—
291C2×C8—2361no—
292C2×C8#1174566012yes—
293C4⋊C4—592no—
294C4⋊C4—1181no—
295C4⋊C4—1181no—
296C4⋊C4—1181no—
297C4⋊C4—4721no—
298C4⋊C4—2361no—
299C4⋊C4—2361no—
300C4⋊C4—2361no—
301C4⋊C4—2361no—
302C42—2361no—
303C42—2361no—
304C42#1174568511yescharacteristic
305C42#1174568711yescharacteristic
306C42Q8×D5911yescharacteristic
307C42C2×C22⋊D5911yescharacteristic
308C23—4721no—
309C23—4721no—
310C23—4721no—
311C23—4721no—
312C23—4721no—
313C23—4721no—
314C23—2362no—
315C23#1427370211yescharacteristic
316D4—4722no—
317D4—4722no—
318D4—4721no—
319D4—4721no—
320D4—4721no—
321D4—4721no—
322D4—2362no—
323D4—2362no—
324D4—2362no—
325D4—2362no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—1182no—
329C2×C4—4721no—
330C2×C4—4721no—
331C2×C4—4721no—
332C2×C4—2361no—
333C2×C4—2361no—
334C2×C4—2361no—
335C2×C4—2361no—
336C2×C4—2361no—
337C2×C4#1427369911yescharacteristic
338C2×C4#1427370111yescharacteristic
339C2×C4#1427370311yescharacteristic
340C2×C4#1427370511yescharacteristic
341C2×C4#1427370711yescharacteristic
342C2×C4#1427372211yescharacteristic
343C2×C4D8×D5911yescharacteristic
344C2×C4C2×#1174566011yescharacteristic
345C2×C4#1427374911yescharacteristic
346C2×C4#1427375011yescharacteristic
347C2×C4#1427375111yescharacteristic
348C2×C4#1427375511yescharacteristic
349C2×C4#1427375511yescharacteristic
350C2×C4#1427375911yescharacteristic
351C8—22no—
352C8—41no—
353C8—42no—
354C8—81no—
355C8—4721no—
356C22—9441no—
357C22—9441no—
358C22—9441no—
359C22—9441no—
360C22—4722no—
361C22—4722no—
362C22—4722no—
363C22#1683732411yescharacteristic
364C22#1683760311yescharacteristic
365C22#1683761811yescharacteristic
366C22#1683763911yescharacteristic
367C22#1683764911yescharacteristic
368C22#1683766611yescharacteristic
369C22#1683767311yescharacteristic
370C4—21no—
371C4—21no—
372C4—9441no—
373C4—4721no—
374C4—2362no—
375C4#1683759511yescharacteristic
376C4#1683762611yescharacteristic
377C4#1683763111yescharacteristic
378C4#1683765511yescharacteristic
379C4#1683768111yescharacteristic
380C4#1683769311yescharacteristic
381C4#1683770311yescharacteristic
382C4#1683770511yescharacteristic
383C2—9442no—
384C2#2142345711yescharacteristic
385C2#2142353411yescharacteristic
386C2#2142356911yescharacteristic
387C2#2142363011yescharacteristic
388C2#2142545111yescharacteristic
389C2#2142546911yescharacteristic
390C2#2142547911yescharacteristic
subgroupG/H
centerC23#14273702
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC2×C59×#335C2
socleC23×C59#121
prime radicalC2×#14273724C22
hypercenterC2×#335D59
hypocenterC59#10599
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
3. #21424860C2semidirect
4. #21424814C2semidirect
6. #21421980C2semidirect
7. C2×C59×#335C2semidirect
192. C2×#335D59semidirect
220. C59#10599semidirect

Maximal subgroups

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

subgroupindex
#214250222
#214249022
#214248602
#214248142
C2×#168371452
#214219802
C2×C59×#3352
#1059959