Finite Group Databasebeta

← #28483041

Subgroups — #28483041

Order 15104.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1M16×Dic118C211yesmaximal, characteristic
2#21424871C211yesmaximal, characteristic
3#21422852C211yesmaximal, characteristic
4#21422526C211yesmaximal, characteristic
5C2×#16837134C211yesmaximal, characteristic
6#21421992C211yesmaximal, characteristic
7C59×#1278C211yesmaximal, characteristic
8C2×C4×Dic118C2211yescharacteristic
9#16837532—21no—
10#16837530—22no—
11C8×Dic118—21no—
12C2×#14273662—21no—
13#16837426C2211yescharacteristic
14#16837426C2211yescharacteristic
15#16837425—21no—
16C2×C4⋊(C59⋊C8)C2211yescharacteristic
17M16×Dic59—21no—
18#16837166—21no—
19#16837153—22no—
20#16837134—21no—
21#16837134—21no—
22#16837134C411yescharacteristic
23#16837134C411yescharacteristic
24#16837134C411yescharacteristic
25#16837134C411yescharacteristic
26C59×#431C2211yescharacteristic
27C4×M16×C59C2211yescharacteristic
28C2×C4×C8×C59C2211yescharacteristic
29C22×Dic118Q811yescharacteristic
30C2×#11745664—21no—
31C2×#11745664—21no—
32C22×C59⋊C8—21no—
33C4×Dic118—21no—
34C4×Dic118—21no—
35C4×Dic118C2×C411yescharacteristic
36C4×Dic118C2×C411yescharacteristic
37C4×Dic118D411yescharacteristic
38C4×Dic118D411yescharacteristic
39C2×C4⋊Dic59Q811yescharacteristic
40C2×Dic59⋊C4—21no—
41C2×C4×Dic59—21no—
42#14273662—42no—
43C4⋊(C59⋊C8)—21no—
44C4⋊(C59⋊C8)—21no—
45C4⋊(C59⋊C8)—21no—
46C4⋊(C59⋊C8)—21no—
47C4⋊(C59⋊C8)C2×C411yescharacteristic
48C4⋊(C59⋊C8)C2×C411yescharacteristic
49C4⋊(C59⋊C8)D412yes—
50Dic59⋊C8—22no—
51Dic59⋊C8—22no—
52#14273637—22no—
53C8×Dic59—22no—
54C2×M16×C59D411yescharacteristic
55C2×M16×C59D411yescharacteristic
56C22×C8×C59—21no—
57C2×C42×C59C2311yescharacteristic
58C4⋊C8×C59—21no—
59C22⋊C8×C59—21no—
60#97×C59—21no—
61C4×C8×C59—21no—
62C4×C8×C59—21no—
63C4×C8×C59—21no—
64C4×C8×C59C2×C411yescharacteristic
65C4×C8×C59C2×C411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59C2×Q811yescharacteristic
68C22×C4×C59#4111yescharacteristic
69C22×Dic59—21no—
70C22×Dic59—21no—
71C2×Dic118—22no—
72C2×Dic118—21no—
73C2×Dic118—41no—
74C2×Dic118C4⋊C411yescharacteristic
75C2×Dic118C4⋊C411yescharacteristic
76M16×C59—21no—
77M16×C59—21no—
78M16×C59—21no—
79M16×C59SD1612yes—
80C2×C8×C59—21no—
81C2×C8×C59—21no—
82C2×C8×C59—21no—
83C2×C8×C59—21no—
84C2×C8×C59—42no—
85C2×C8×C59—41no—
86C42×C59C22×C411yescharacteristic
87C42×C59C2×D411yescharacteristic
88C42×C59C2×D411yescharacteristic
89C42×C59#4111yescharacteristic
90C4⋊Dic59—21no—
91C4⋊Dic59C4⋊C411yescharacteristic
92C4⋊Dic59C4⋊C411yescharacteristic
93Dic59⋊C4—21no—
94Dic59⋊C4—21no—
95Dic59⋊C4—21no—
96Dic59⋊C4—21no—
97C4×Dic59—21no—
98C4×Dic59—21no—
99C4×Dic59—21no—
100C4×Dic59—21no—
101#11745664—41no—
102#11745664—41no—
103#11745664—41no—
104#11745664—41no—
105C2×C59⋊C8—21no—
106C2×C59⋊C8—21no—
107C2×C59⋊C8—22no—
108C2×C59⋊C8—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8—41no—
111C23×C59C22⋊Q811yescharacteristic
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—41no—
115C2×C4×C59C2×C4⋊C411yescharacteristic
116C2×C4×C59C4×D411yescharacteristic
117C2×C4×C59C4×D411yescharacteristic
118C2×C4×C59#12011yescharacteristic
119C2×C4×C59C22⋊Q811yescharacteristic
120C2×C4×C59#12311yescharacteristic
121C2×C4×C59C2×SD1611yescharacteristic
122C2×C4×C59#13511yescharacteristic
123C2×C4×C59#13711yescharacteristic
124C2×C4×C59#13711yescharacteristic
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—42no—
130C2×Dic59—81no—
131Dic118—21no—
132Dic118—21no—
133Dic118—21no—
134Dic118—42no—
135Dic118#10812yescomplemented
136C8×C59—22no—
137C8×C59—22no—
138C8×C59—41no—
139C8×C59—41no—
140C8×C59—81no—
141C59⋊C8—41no—
142C59⋊C8—41no—
143C59⋊C8—42no—
144C59⋊C8—81no—
145#8909—591nomaximal, Sylow
146C22×C59—21no—
147C22×C59—21no—
148C22×C59#38511yescharacteristic
149C22×C59#47511yescharacteristic
150C22×C59#47911yescharacteristic
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59C2×#10811yescharacteristic
155C4×C59#43011yescharacteristic
156C4×C59C4×SD1611yescharacteristic
157C4×C59#44111yescharacteristic
158C4×C59#44811yescharacteristic
159C4×C59#45211yescharacteristic
160Dic59—22no—
161Dic59—41no—
162Dic59—41no—
163Dic59—41no—
164Q8×M16—591no—
165#1950—591no—
166#1566—591no—
167#1487—591no—
168C2×Q8⋊C8—591no—
169#1301—591no—
170#1278D5911yescharacteristic
171C2×C59—21no—
172C2×C59—21no—
173C2×C59#185511yescharacteristic
174C2×C59#186111yescharacteristic
175C2×C59#186511yescharacteristic
176C2×C4×Q8—591no—
177#446—1181no—
178#446—1182no—
179C8×Q8—1181no—
180#431C2×D5911yescharacteristic
181C2×#108—1181no—
182#423—591no—
183#423—591no—
184#423—1181no—
185C2×C4⋊C8—591no—
186C4×M16—1181no—
187C4×M16C2×D5911yescharacteristic
188C2×C4×C8C2×D5911yescharacteristic
189#341—1181no—
190#334—1182no—
191Q8⋊C8—591no—
192Q8⋊C8—591no—
193Q8⋊C8—591no—
194Q8⋊C8—591no—
195Q8⋊C8—1181no—
196Q8⋊C8—1181no—
197C59#890911yescharacteristic, complemented, Sylow
198C22×Q8—591no—
199C2×M16—1181no—
200C2×M16—1181no—
201C2×M16D23611yescharacteristic
202C2×M16D23611yescharacteristic
203C22×C8—21no—
204C22×C8—1181no—
205C4×Q8—591no—
206C4×Q8—591no—
207C4×Q8—591no—
208C4×Q8—591no—
209C4×Q8—1181no—
210C4×Q8—1181no—
211C2×C4⋊C4—591no—
212C2×C4⋊C4—1181no—
213C2×C42—1181no—
214C2×C42C22×D5911yescharacteristic
215#108—2362no—
216C4⋊C8—21no—
217C4⋊C8—591no—
218C4⋊C8—591no—
219C4⋊C8—592no—
220C4⋊C8—1182no—
221C4⋊C8—1182no—
222C4⋊C8—1181no—
223C4⋊C8—1181no—
224C4⋊C8—1181no—
225C4⋊C8—1181no—
226C22⋊C8—21no—
227#97—21no—
228#97—1182no—
229C4×C8—21no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—1182no—
233C4×C8C4×D5911yescharacteristic
234C4×C8C4×D5911yescharacteristic
235C2×Q8—591no—
236C2×Q8—591no—
237C2×Q8—1182no—
238C2×Q8—1181no—
239C2×Q8—2361no—
240C22×C4—1181no—
241C22×C4—1181no—
242C22×C4C2×D23611yescharacteristic
243C22×C4#1174568711yescharacteristic
244C22×C4Q8×D5911yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—2361no—
249M16—2361no—
250M16—2361no—
251M16—2361no—
252M16#1174566012yes—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—1181no—
260C2×C8—1181no—
261C2×C8—1182no—
262C2×C8—2361no—
263C2×C8—2361no—
264C2×C8—2361no—
265C4⋊C4—591no—
266C4⋊C4—591no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C42—1181no—
273C42—1181no—
274C42—1181no—
275C42—1181no—
276C42C2×C4×D5911yescharacteristic
277C42#1174568511yescharacteristic
278C42D4×D5911yescharacteristic
279C42D4×D5911yescharacteristic
280C23#1427370711yescharacteristic
281Q8—592no—
282Q8—1181no—
283Q8—1181no—
284Q8—1181no—
285Q8—2362no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—1181no—
290C2×C4—1181no—
291C2×C4—1181no—
292C2×C4—1181no—
293C2×C4—4721no—
294C2×C4—2362no—
295C2×C4C4⋊C4×D5911yescharacteristic
296C2×C4(C22⋊D59)⋊C411yescharacteristic
297C2×C4C4×D23611yescharacteristic
298C2×C4#1427369711yescharacteristic
299C2×C4#1427370511yescharacteristic
300C2×C4#1427370911yescharacteristic
301C2×C4C2×#1174566011yescharacteristic
302C2×C4#1427374911yescharacteristic
303C2×C4#1427376011yescharacteristic
304C2×C4#1427376011yescharacteristic
305C8—22no—
306C8—22no—
307C8—41no—
308C8—41no—
309C8—81no—
310C8—4721no—
311C8—2361no—
312C8—2361no—
313C8—2362no—
314C22—21no—
315C22—21no—
316C22#1683727611yescharacteristic
317C22#1683768811yescharacteristic
318C22#1683771011yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—1182no—
323C4—2361no—
324C4—2361no—
325C4—2361no—
326C4#108×D5911yescharacteristic
327C4#1683744911yescharacteristic
328C4C4×#1174566011yescharacteristic
329C4#1683751011yescharacteristic
330C4#1683754311yescharacteristic
331C4#1683756611yescharacteristic
332C2—21no—
333C2—21no—
334C2#2142430211yescharacteristic
335C2#2142433711yescharacteristic
336C2#2142436711yescharacteristic
subgroupG/H
centerC2×C4#14273697
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1278C2
socleC22×C59#385
prime radicalC23×C59C22⋊Q8
cosocleC2×C42×C59C23
hypercenter#1278D59
hypocenterC59#8909
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
135. Dic118#108semidirect
197. C59#8909semidirect

Maximal subgroups

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

subgroupindex
M16×Dic1182
#214248712
#214228522
#214225262
C2×#168371342
#214219922
C59×#12782
#890959