Finite Group Databasebeta

← #28504749

Subgroups — #28504749

Order 15104.

422 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432867C211yesmaximal, characteristic
2C2×Dic59⋊C16C211yesmaximal, characteristic, complemented
3C2×#16837210C211yesmaximal, characteristic
4C2×#16837208C211yesmaximal, characteristic
5#21424266C211yesmaximal, characteristic, complemented
6#21422191C211yesmaximal, characteristic, complemented
7C59×#1382C211yesmaximal, characteristic, complemented
8C2×#14273749C2211yescharacteristic
9#16837870—21no—
10C22×C59⋊C16C2211yescharacteristic
11#16837496C411yescharacteristic
12#16837496C411yescharacteristic
13#16837489—21no—
14#16837489—21no—
15#16837484C411yescharacteristic
16#16837484C411yescharacteristic
17C2×#14273663C2211yescharacteristic
18C2×#14273662—21no—
19#16837425—21no—
20#16837396—21no—
21C2×C8×Dic59C2211yescharacteristic
22Dic59⋊C16—21no—
23Dic59⋊C16—21no—
24#16837210—22no—
25#16837208—22no—
26C22×C16×C59C2211yescharacteristic
27C2×#108×C59C2211yescharacteristic
28C59×#427C2211yescharacteristic
29C2×#11745685—21no—
30#14273749—21no—
31#14273749—21no—
32#14273749D412yes—
33#14273749Q812yes—
34C2×Dic236C2×C411yescharacteristic
35C2×#11745660—21no—
36C2×D472C2×C411yescharacteristic
37C2×#11745664—21no—
38C22×C59⋊C8D411yescharacteristic
39#14273692—21no—
40#14273692—21no—
41#14273689—21no—
42#14273689—21no—
43(C22⋊D59)⋊C4—41no—
44(C22⋊D59)⋊C4—41no—
45#14273684—41no—
46C2×C4×Dic59D411yescharacteristic
47C42×D59—41no—
48C2×C59⋊C16—21no—
49C2×C59⋊C16—21no—
50C2×C59⋊C16—21no—
51#14273663—21no—
52#14273663—21no—
53#14273662—42no—
54Dic59⋊C8—41no—
55Dic59⋊C8—41no—
56#14273650—21no—
57#14273650—21no—
58#14273647—21no—
59#14273647—21no—
60C8×Dic59C2×C411yescharacteristic
61C8×Dic59C2×C411yescharacteristic
62C8×Dic59D411yescharacteristic
63C8×Dic59D411yescharacteristic
64C2×M16×C59—21no—
65C22×C8×C59C2311yescharacteristic
66#117×C59—21no—
67C2×C16×C59—21no—
68C2×C16×C59—21no—
69C2×C16×C59—21no—
70#108×C59—21no—
71#108×C59—21no—
72#107×C59C2×C411yescharacteristic
73#107×C59C2×C411yescharacteristic
74#106×C59—21no—
75C22×C4×C59C2×D411yescharacteristic
76C2×C22⋊D59—41no—
77C22×Dic59SD1611yescharacteristic
78C22×Dic59SD1611yescharacteristic
79#11745685—22no—
80#11745685—22no—
81#11745685—41no—
82#11745685—41no—
83C2×D236—21no—
84C2×C4×D59—41no—
85C2×C4×D59—41no—
86C2×C4×D59—41no—
87C2×Dic118—21no—
88M16×C59—41no—
89M16×C59—41no—
90C2×C8×C59—41no—
91C2×C8×C59C22×C411yescharacteristic
92C2×C8×C59C2×D411yescharacteristic
93C2×C8×C59C2×D411yescharacteristic
94C2×C8×C59C2×Q811yescharacteristic
95C2×C8×C59#4111yescharacteristic
96C2×C8×C59#4111yescharacteristic
97C4⋊C4×C59—21no—
98C4⋊C4×C59—21no—
99C22⋊C4×C59—41no—
100C42×C59—41no—
101(C2×D59)⋊C4—41no—
102(C2×D59)⋊C4—41no—
103Dic59⋊C4—41no—
104Dic59⋊C4—41no—
105C4×Dic59—41no—
106C4×Dic59—41no—
107C4×Dic59C22⋊C411yescharacteristic
108C4×Dic59C22⋊C411yescharacteristic
109C4×Dic59D811yescharacteristic
110C4×Dic59D811yescharacteristic
111#11745664—41no—
112#11745664—41no—
113C2×C59⋊C8—21no—
114C2×C59⋊C8—21no—
115C2×C59⋊C8—41no—
116C2×C59⋊C8C22⋊C411yescharacteristic
117C2×C59⋊C8C22⋊C411yescharacteristic
118Dic236—21no—
119Dic236C4⋊C412yes—
120D472—21no—
121D472C4⋊C412yes—
122#11745660—22no—
123#11745660—22no—
124C16×C59—41no—
125C59⋊C16—41no—
126C23×C59C2×SD1611yescharacteristic
127C22×D59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59C2×C22⋊C411yescharacteristic
131C2×C4×C59#12111yescharacteristic
132C2×C4×C59C22⋊Q811yescharacteristic
133C2×C4×C59C2×D811yescharacteristic
134C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C59#13711yescharacteristic
136C22⋊D59—42no—
137C22⋊D59—42no—
138C2×Dic59—22no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59#10211yescharacteristic
142C2×Dic59#10211yescharacteristic
143C2×Dic59#10211yescharacteristic
144C2×Dic59#10211yescharacteristic
145D236—22no—
146D236—41no—
147C4×D59—42no—
148C4×D59—42no—
149C4×D59—82no—
150C4×D59—82no—
151Dic118—22no—
152Dic118—41no—
153C8×C59—81no—
154C8×C59C2×C4⋊C411yescharacteristic
155C8×C59#11711yescharacteristic
156C8×C59#12111yescharacteristic
157C8×C59C22⋊Q811yescharacteristic
158C59⋊C8—21no—
159C59⋊C8—21no—
160C59⋊C8—81no—
161#12815—591nomaximal, Sylow
162C22×C59—21no—
163C22×C59—21no—
164C22×C59C2×#10211yescharacteristic
165C22×C59#46111yescharacteristic
166C22×C59#47611yescharacteristic
167C2×D59—42no—
168C2×D59—81no—
169C2×D59—81no—
170C4×C59—81no—
171C4×C59—81no—
172C4×C59#38011yescharacteristic
173C4×C59#41711yescharacteristic
174C4×C59#45911yescharacteristic
175C4×C59#47411yescharacteristic
176Dic59—21no—
177Dic59—21no—
178Dic59—21no—
179Dic59—42no—
180Dic59#35912yescomplemented
181C4×#135—591no—
182C2×C4⋊C16—591no—
183C2×#359—591no—
184C2×#359—591no—
185#1848—591no—
186#1382—591no—
187#1382D5911yescharacteristic, complemented
188C2×C59—21no—
189C2×C59—21no—
190C2×C59#180211yescharacteristic
191C2×C59C2×#35911yescharacteristic
192C2×C59#214311yescharacteristic
193D59—82no—
194C2×#135—591no—
195C4×#41—1181no—
196C22×C16—591no—
197C22×C16C2×D5911yescharacteristic
198C4×Q16—591no—
199C4×Q16—591no—
200C4×SD16—1181no—
201C4×SD16—1181no—
202C4×D8—591no—
203C4×D8—591no—
204C2×#108—591no—
205C2×#108—1181no—
206C2×#108C2×D5911yescharacteristic
207#427C2×D5911yescharacteristic
208#423—1181no—
209#416—1181no—
210C2×C4×C8—591no—
211C4⋊C16—1181no—
212C4⋊C16—1181no—
213#359—1182no—
214#359—1182no—
215C59#1281511yescharacteristic, complemented, Sylow
216C2×#41—1181no—
217#135—592no—
218#135—592no—
219#135—1181no—
220#135—1181no—
221C2×Q16—591no—
222C2×SD16—1181no—
223C2×D8—591no—
224C2×M16—21no—
225C2×M16—1181no—
226C22×C8—591no—
227C22×C8C22×D5911yescharacteristic
228C4×Q8—1181no—
229C4×Q8—1181no—
230C4×D4—1181no—
231C4×D4—1181no—
232C4×D4—2361no—
233C4×D4—2361no—
234#117—21no—
235#117—2361no—
236C2×C42—591no—
237C2×C42—2361no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—1181no—
242C2×C16—1181no—
243C2×C16—1181no—
244#108—21no—
245#108—21no—
246#108—1181no—
247#108—1181no—
248#108—2362no—
249#107C4×D5911yescharacteristic
250#107C4×D5911yescharacteristic
251#106—21no—
252C4⋊C8—2361no—
253C4⋊C8—2361no—
254#103—1181no—
255#103—1181no—
256#102—1181no—
257#102—1181no—
258C4×C8—591no—
259C4×C8—591no—
260C4×C8—591no—
261C4×C8—591no—
262#41—1182no—
263#41—1182no—
264#41—2361no—
265#41—2361no—
266C2×Q8—1181no—
267C2×D4—1181no—
268C2×D4—2361no—
269C22×C4—591no—
270C22×C4—591no—
271C22×C4—2361no—
272C22×C4—2361no—
273C22×C4—2361no—
274C22×C4D4×D5911yescharacteristic
275Q16—592no—
276Q16—1181no—
277SD16—1182no—
278SD16—1182no—
279D8—592no—
280D8—1181no—
281M16—41no—
282M16—41no—
283M16—2361no—
284M16—2361no—
285C2×C8—41no—
286C2×C8—591no—
287C2×C8—591no—
288C2×C8—1181no—
289C2×C8—1181no—
290C2×C8—2361no—
291C2×C8C2×C4×D5911yescharacteristic
292C2×C8#1174568511yescharacteristic
293C2×C8#1174568511yescharacteristic
294C2×C8D4×D5911yescharacteristic
295C2×C8D4×D5911yescharacteristic
296C2×C8Q8×D5911yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—2361no—
300C4⋊C4—2361no—
301C22⋊C4—41no—
302C22⋊C4—2361no—
303C22⋊C4—2361no—
304C42—41no—
305C42—591no—
306C42—591no—
307C42—591no—
308C42—591no—
309C42—2361no—
310C42—2361no—
311C16—41no—
312C16—2361no—
313C23—2361no—
314C23SD16×D5911yescharacteristic
315Q8—1182no—
316Q8—2361no—
317D4—1182no—
318D4—2362no—
319D4—2362no—
320D4—2361no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—591no—
324C2×C4—591no—
325C2×C4—591no—
326C2×C4—591no—
327C2×C4—1182no—
328C2×C4—4722no—
329C2×C4—4722no—
330C2×C4—2361no—
331C2×C4—2361no—
332C2×C4—2362no—
333C2×C4—2362no—
334C2×C4C22⋊C4×D5911yescharacteristic
335C2×C4#1427370011yescharacteristic
336C2×C4#1427370511yescharacteristic
337C2×C4D8×D5911yescharacteristic
338C2×C4#1427375411yescharacteristic
339C2×C4#1427375911yescharacteristic
340C8—81no—
341C8—1181no—
342C8—1181no—
343C8—4721no—
344C8C4⋊C4×D5911yescharacteristic
345C8#1427368411yescharacteristic
346C8#1427370011yescharacteristic
347C8#1427370511yescharacteristic
348C22—21no—
349C22—21no—
350C22—4721no—
351C22—4721no—
352C22—2362no—
353C22#102×D5911yescharacteristic
354C22#1683760611yescharacteristic
355C22#1683769111yescharacteristic
356C4—81no—
357C4—81no—
358C4—592no—
359C4—1181no—
360C4—1181no—
361C4—1181no—
362C4—2362no—
363C4#1683726111yescharacteristic
364C4#1683740211yescharacteristic
365C4#1683759611yescharacteristic
366C4#1683768111yescharacteristic
367C2—21no—
368C2—21no—
369C2—4722no—
370C2#2142409511yescharacteristic
371C2#359×D5911yescharacteristic
372C2#2142582211yescharacteristic
subgroupG/H
centerC2×C4D8×D59
commutatorC2×C8×C59C22×C4
FrattiniC22×C8C22×D59
FittingC59×#1382C2
socleC22×C59C2×#102
prime radicalC2×#14273749C22
cosocleC22×C8×C59C23
hypercenter#1382D59
hypocenterC59#12815
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
2. C2×Dic59⋊C16C2semidirect
5. #21424266C2semidirect
6. #21422191C2semidirect
7. C59×#1382C2semidirect
180. Dic59#359semidirect
187. #1382D59semidirect
215. C59#12815semidirect

Maximal subgroups

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

subgroupindex
#214328672
C2×Dic59⋊C162
C2×#168372102
C2×#168372082
#214242662
#214221912
C59×#13822
#1281559