Finite Group Databasebeta

← #28508295

Subgroups — #28508295

Order 15104.

410 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273673C211yesmaximal, characteristic
2C2×C4⋊(C59⋊C16)C211yesmaximal, characteristic
3C2×#16837206C211yesmaximal, characteristic
4C2×#16837205C211yesmaximal, characteristic
5#21424957C211yesmaximal, characteristic
6#21422187C211yesmaximal, characteristic
7C59×#1969C211yesmaximal, characteristic
8C22×Dic236C2211yescharacteristic
9C2×#14273673—22no—
10C2×#14273673—22no—
11C2×#14273673—22no—
12C22×C59⋊C16C2211yescharacteristic
13C22×C59⋊C16C2211yescharacteristic
14C2×#14273661C2211yescharacteristic
15C2×#14273652—21no—
16#16837308—21no—
17C4⋊(C59⋊C16)—22no—
18#16837206—22no—
19#16837205—22no—
20C22×Q16×C59C2211yescharacteristic
21C2×#107×C59C2211yescharacteristic
22C2×#103×C59—21no—
23C2×C4×C8×C59C2211yescharacteristic
24C59×#391—21no—
25C22×Dic118—21no—
26C2×Dic236—21no—
27C2×Dic236—21no—
28C2×Dic236—21no—
29C2×Dic236—21no—
30C2×Dic236—21no—
31C2×Dic236D412yes—
32C2×C4⋊Dic59—21no—
33#14273673—28no—
34C2×C59⋊C16—21no—
35C2×C59⋊C16—21no—
36C2×C59⋊C16—21no—
37C2×C59⋊C16—21no—
38C2×C59⋊C16—21no—
39C2×C59⋊C16D412yes—
40#14273661—21no—
41#14273661—21no—
42#14273652—42no—
43C59⋊#95—41no—
44C59⋊#95—41no—
45C22×Q8×C59—21no—
46C2×Q16×C59—21no—
47C2×Q16×C59—21no—
48C2×Q16×C59—21no—
49C2×Q16×C59—21no—
50C2×Q16×C59—21no—
51C2×Q16×C59D412yes—
52C22×C8×C59D411yescharacteristic
53C22×C8×C59C2311yescharacteristic
54C2×C4⋊C4×C59—21no—
55C2×C42×C59D411yescharacteristic
56#107×C59—21no—
57#107×C59—21no—
58#103×C59—42no—
59C4×C8×C59—21no—
60C4×C8×C59—21no—
61#95×C59—41no—
62#95×C59—41no—
63C2×Q8×C59—22no—
64C2×Q8×C59—41no—
65C2×Q8×C59—41no—
66C2×Q8×C59—41no—
67C2×Q8×C59—41no—
68C2×Q8×C59—41no—
69C22×C4×C59—41no—
70C22×C4×C59—41no—
71C22×C4×C59D811yescharacteristic
72C22×C4×C59D811yescharacteristic
73C22×C4×C59C2×D411yescharacteristic
74C22×Dic59—41no—
75C22×Dic59—41no—
76C2×Dic118—22no—
77C2×Dic118—41no—
78C2×Dic118—41no—
79C2×Dic118—41no—
80C2×Dic118—41no—
81C2×Dic118—41no—
82Q16×C59—22no—
83Q16×C59—22no—
84Q16×C59—41no—
85Q16×C59—41no—
86C2×C8×C59—21no—
87C2×C8×C59—21no—
88C2×C8×C59—21no—
89C2×C8×C59C2×D411yescharacteristic
90C2×C8×C59C2×D411yescharacteristic
91C2×C8×C59C2×D411yescharacteristic
92C2×C8×C59#4111yescharacteristic
93C2×C8×C59#4111yescharacteristic
94C2×C8×C59#4111yescharacteristic
95C4⋊C4×C59—41no—
96C4⋊C4×C59—41no—
97C42×C59—21no—
98C42×C59—21no—
99C4⋊Dic59—41no—
100C4⋊Dic59—41no—
101Dic236—22no—
102Dic236—22no—
103Dic236—41no—
104Dic236—41no—
105C59⋊C16—22no—
106C59⋊C16—41no—
107C23×C59C2×D811yescharacteristic
108Q8×C59—42no—
109Q8×C59—42no—
110Q8×C59—81no—
111Q8×C59—81no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—42no—
118C2×C4×C59—81no—
119C2×C4×C59—81no—
120C2×C4×C59—81no—
121C2×C4×C59—81no—
122C2×C4×C59—81no—
123C2×C4×C59Q3212yescomplemented
124C2×C4×C59#12111yescharacteristic
125C2×C4×C59#12111yescharacteristic
126C2×C4×C59#12111yescharacteristic
127C2×C4×C59#13511yescharacteristic
128C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
130C2×Dic59—42no—
131C2×Dic59—81no—
132C2×Dic59—81no—
133C2×Dic59—81no—
134C2×Dic59—81no—
135C2×Dic59—81no—
136Dic118—42no—
137Dic118—42no—
138Dic118—81no—
139Dic118—81no—
140C8×C59—41no—
141C8×C59#12011yescharacteristic
142C8×C59#12311yescharacteristic
143C8×C59#12311yescharacteristic
144C8×C59#12411yescharacteristic
145#13450—591nomaximal, Sylow
146C22×C59#45911yescharacteristic
147C22×C59#45911yescharacteristic
148C22×C59#46611yescharacteristic
149C22×C59C2×Q3211yescharacteristic
150C22×C59#50811yescharacteristic
151C22×C59#51011yescharacteristic
152C22×C59#51011yescharacteristic
153C4×C59—22no—
154C4×C59—41no—
155C4×C59—82no—
156C4×C59—161no—
157C4×C59#39411yescharacteristic
158C4×C59#46311yescharacteristic
159C4×C59#46311yescharacteristic
160C4×C59#46911yescharacteristic
161Dic59—82no—
162Dic59—161no—
163C22×Q32—591no—
164C2×C4⋊C16—591no—
165C2×#358—591no—
166C2×#358—591no—
167#1969—591no—
168#1969D5911yescharacteristic
169#1380—591no—
170C2×C59#205411yescharacteristic
171C2×C59#220911yescharacteristic
172C2×C59#220911yescharacteristic
173C2×C59#221111yescharacteristic
174C2×C59#221111yescharacteristic
175C2×C59#221611yescharacteristic
176C2×C59#221911yescharacteristic
177C22×Q16—591no—
178C22×Q16C2×D5911yescharacteristic
179C2×Q32—1182no—
180C2×Q32—1182no—
181C2×Q32—1182no—
182C22×C16—591no—
183C22×C16—591no—
184C2×#107—591no—
185C2×#107C2×D5911yescharacteristic
186C2×#103—21no—
187C2×#103—1181no—
188C2×C4×C8C2×D5911yescharacteristic
189#391—21no—
190#391—1181no—
191C4⋊C16—1182no—
192#358—1182no—
193#358—1182no—
194C59#1345011yescharacteristic, complemented, Sylow
195C22×Q8—21no—
196C22×Q8—1181no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—592no—
203C2×Q16—1181no—
204C2×Q16—1181no—
205C2×Q16—1181no—
206C2×Q16—1181no—
207C2×Q16—1181no—
208C2×Q16D23612yes—
209C22×C8C22⋊D5911yescharacteristic
210C22×C8C22×D5911yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4—1181no—
213C2×C42C22⋊D5911yescharacteristic
214Q32—1188no—
215C2×C16—592no—
216C2×C16—1181no—
217C2×C16—1181no—
218C2×C16—1181no—
219C2×C16—1181no—
220C2×C16—1181no—
221#107—21no—
222#107—21no—
223#107—1181no—
224#107—1181no—
225#103—42no—
226#103—2362no—
227C4×C8—21no—
228C4×C8—21no—
229#95—41no—
230#95—41no—
231#95—2361no—
232#95—2361no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—1182no—
240C2×Q8—2361no—
241C2×Q8—2361no—
242C2×Q8—2361no—
243C2×Q8—2361no—
244C2×Q8—2361no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—2361no—
248C22×C4—2361no—
249C22×C4#1174566911yescharacteristic
250C22×C4#1174566911yescharacteristic
251C22×C4C2×C22⋊D5911yescharacteristic
252Q16—22no—
253Q16—22no—
254Q16—41no—
255Q16—41no—
256Q16—1182no—
257Q16—1182no—
258Q16—2361no—
259Q16—2361no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8C2×D23611yescharacteristic
264C2×C8#1174568511yescharacteristic
265C2×C8D4×D5911yescharacteristic
266C2×C8D4×D5911yescharacteristic
267C2×C8#1174568711yescharacteristic
268C2×C8#1174568711yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—2361no—
272C4⋊C4—2361no—
273C42—21no—
274C42—21no—
275C16—1182no—
276C16—2361no—
277C23C2×#1174566911yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282Q8—4721no—
283Q8—4721no—
284Q8—2362no—
285Q8—2362no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—4721no—
298C2×C4—4721no—
299C2×C4—4721no—
300C2×C4—4721no—
301C2×C4—4721no—
302C2×C4—2362no—
303C2×C4#1427367312yescomplemented
304C2×C4#1427369811yescharacteristic
305C2×C4#1427369911yescharacteristic
306C2×C4#1427370111yescharacteristic
307C2×C4#1427374711yescharacteristic
308C2×C4#1427375211yescharacteristic
309C2×C4#1427375311yescharacteristic
310C8—41no—
311C8#1427369711yescharacteristic
312C8#1427370911yescharacteristic
313C8#1427371111yescharacteristic
314C8#1427371311yescharacteristic
315C22#1683759411yescharacteristic
316C22#1683759711yescharacteristic
317C22#1683763611yescharacteristic
318C22C2×#1427367311yescharacteristic
319C22#1683783211yescharacteristic
320C22#1683784211yescharacteristic
321C22#1683784311yescharacteristic
322C4—22no—
323C4—41no—
324C4—82no—
325C4—161no—
326C4—9441no—
327C4—4722no—
328C4#1683731811yescharacteristic
329C4#1683761411yescharacteristic
330C4#1683761711yescharacteristic
331C4#1683765311yescharacteristic
332C2#2142540611yescharacteristic
333C2#2142614311yescharacteristic
334C2#2142614611yescharacteristic
335C2#2142615511yescharacteristic
336C2#2142615811yescharacteristic
337C2#2142618511yescharacteristic
338C2#2142620211yescharacteristic
subgroupG/H
centerC23C2×#11745669
commutator, cosocleC22×C8×C59C23
FrattiniC22×C8C22×D59
FittingC59×#1969C2
socle, prime radicalC23×C59C2×D8
hypercenter#1969D59
hypocenterC59#13450
LCSG ▷ C22×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

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

NH ≅ G/Ntype
123. C2×C4×C59Q32semidirect
194. C59#13450semidirect
303. C2×C4#14273673semidirect

Maximal subgroups

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

subgroupindex
C22×#142736732
C2×C4⋊(C59⋊C16)2
C2×#168372062
C2×#168372052
#214249572
#214221872
C59×#19692
#1345059