Finite Group Databasebeta

← #28483037

Subgroups — #28483037

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#21422851C211yesmaximal, characteristic
3#21422524C211yesmaximal, characteristic
4C2×#16837132C211yesmaximal, characteristic
5#21421993C211yesmaximal, characteristic
6#21421934C211yesmaximal, characteristic
7C59×#1950C211yesmaximal, characteristic
8C2×C4×Dic118C2211yescharacteristic
9#16837532—21no—
10#16837530—22no—
11C8×Dic118—21no—
12#16837455C2211yescharacteristic
13#16837426C2211yescharacteristic
14#16837425—21no—
15M16×Dic59—21no—
16C2×C4×C59⋊C8C2211yescharacteristic
17#16837152—22no—
18#16837132—21no—
19#16837132—21no—
20#16837132C411yescharacteristic
21#16837132C411yescharacteristic
22#16837132C411yescharacteristic
23#16837132C411yescharacteristic
24C2×#108×C59—21no—
25C59×#423C2211yescharacteristic
26C2×C4⋊C8×C59C2211yescharacteristic
27C4×M16×C59C2211yescharacteristic
28C59×#341—21no—
29C22×Dic118Q811yescharacteristic
30C2×#11745664—21no—
31C22×C59⋊C8—21no—
32C4×Dic118—21no—
33C4×Dic118—21no—
34C4×Dic118C2×C411yescharacteristic
35C4×Dic118C2×C411yescharacteristic
36C4×Dic118D411yescharacteristic
37C4×Dic118D411yescharacteristic
38C2×C4⋊Dic59Q811yescharacteristic
39C2×Dic59⋊C4—21no—
40C2×C4×Dic59—21no—
41C4⋊(C59⋊C8)—21no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)D412yes—
44Dic59⋊C8—22no—
45Dic59⋊C8—22no—
46C22⋊(C59⋊C8)—21no—
47#14273637—22no—
48C4×C59⋊C8—21no—
49C4×C59⋊C8—21no—
50C4×C59⋊C8C2×C411yescharacteristic
51C4×C59⋊C8C2×C411yescharacteristic
52C8×Dic59—22no—
53C2×M16×C59—21no—
54C2×M16×C59D411yescharacteristic
55C2×M16×C59D411yescharacteristic
56C22×C8×C59—21no—
57C2×C42×C59C2311yescharacteristic
58#108×C59—42no—
59C4⋊C8×C59—21no—
60C4⋊C8×C59—21no—
61C4⋊C8×C59—21no—
62C4⋊C8×C59C2×C411yescharacteristic
63C4⋊C8×C59C2×C411yescharacteristic
64#97×C59—21no—
65C4×C8×C59—21no—
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×C59—41no—
80M16×C59—41no—
81M16×C59SD1612yes—
82C2×C8×C59—21no—
83C2×C8×C59—21no—
84C2×C8×C59—21no—
85C2×C8×C59—21no—
86C2×C8×C59—41no—
87C2×C8×C59—41no—
88C2×C8×C59—41no—
89C42×C59C22×C411yescharacteristic
90C42×C59C2×D411yescharacteristic
91C42×C59C2×D411yescharacteristic
92C42×C59#4111yescharacteristic
93C4⋊Dic59—21no—
94C4⋊Dic59C4⋊C411yescharacteristic
95C4⋊Dic59C4⋊C411yescharacteristic
96Dic59⋊C4—21no—
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100C4×Dic59—21no—
101C4×Dic59—21no—
102C4×Dic59—21no—
103C4×Dic59—21no—
104#11745664—41no—
105#11745664—41no—
106C2×C59⋊C8—21no—
107C2×C59⋊C8—21no—
108C2×C59⋊C8—22no—
109C2×C59⋊C8—42no—
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—41no—
138C8×C59—41no—
139C8×C59—41no—
140C8×C59—81no—
141C59⋊C8—22no—
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#1950D5911yescharacteristic
166#1566—591no—
167#1487—591no—
168C2×Q8⋊C8—591no—
169#1301—591no—
170#1278—591no—
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#431—591no—
181C2×#108—21no—
182#423—591no—
183#423—1181no—
184#423C2×D5911yescharacteristic
185C2×C4⋊C8C2×D5911yescharacteristic
186C4×M16—1181no—
187C4×M16C2×D5911yescharacteristic
188C2×C4×C8—591no—
189#341—21no—
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—21no—
200C2×M16—1181no—
201C2×M16C22⋊D5911yescharacteristic
202C2×M16C22⋊D5911yescharacteristic
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—42no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—592no—
220C4⋊C8—1182no—
221C4⋊C8—1182no—
222C4⋊C8—1181no—
223C4⋊C8—1181no—
224C4⋊C8C4×D5911yescharacteristic
225C4⋊C8C4×D5911yescharacteristic
226C22⋊C8—1181no—
227#97—21no—
228#97—1182no—
229C4×C8—21no—
230C4×C8—591no—
231C4×C8—591no—
232C4×C8—1182no—
233C4×C8—1181no—
234C4×C8—1181no—
235C2×Q8—591no—
236C2×Q8—591no—
237C2×Q8—1182no—
238C2×Q8—1181no—
239C2×Q8—2361no—
240C22×C4—1181no—
241C22×C4—1181no—
242C22×C4Q8×D5911yescharacteristic
243C22×C4#1174568911yescharacteristic
244C22×C4C2×C22⋊D5911yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—41no—
249M16—41no—
250M16—2361no—
251M16—2361no—
252M16#1174567012yes—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—1181no—
261C2×C8—1181no—
262C2×C8—1182no—
263C2×C8—2362no—
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#1427370311yescharacteristic
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×C4C4×C22⋊D5911yescharacteristic
297C2×C4#1427368911yescharacteristic
298C2×C4#1427369511yescharacteristic
299C2×C4#1427370511yescharacteristic
300C2×C4#1427371211yescharacteristic
301C2×C4C2×#1174567011yescharacteristic
302C2×C4#1427374711yescharacteristic
303C2×C4#1427375711yescharacteristic
304C2×C4#1427375811yescharacteristic
305C8—22no—
306C8—41no—
307C8—41no—
308C8—41no—
309C8—81no—
310C8—1182no—
311C8—4721no—
312C8—2361no—
313C8—2362no—
314C22—21no—
315C22—21no—
316C22#1683727311yescharacteristic
317C22#1683768411yescharacteristic
318C22#1683770611yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—1182no—
323C4—2361no—
324C4—2361no—
325C4—2361no—
326C4#108×D5911yescharacteristic
327C4#1683744911yescharacteristic
328C4C4×#1174567011yescharacteristic
329C4#1683750711yescharacteristic
330C4#1683754011yescharacteristic
331C4#1683756211yescharacteristic
332C2—21no—
333C2—21no—
334C2#2142429911yescharacteristic
335C2#2142433311yescharacteristic
336C2#2142436311yescharacteristic
subgroupG/H
centerC2×C4#14273695
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1950C2
socleC22×C59#385
prime radicalC23×C59C22⋊Q8
cosocleC2×C42×C59C23
hypercenter#1950D59
hypocenterC59#8909
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

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
#214228512
#214225242
C2×#168371322
#214219932
#214219342
C59×#19502
#890959