Finite Group Databasebeta

← #28508040

Subgroups — #28508040

Order 15104.

482 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
1C2×#16837786C211yesmaximal, characteristic
2C2×#16837205C211yesmaximal, characteristic, complemented
3C2×#16837205C211yesmaximal, characteristic, complemented
4C2×#16837202C211yesmaximal, characteristic
5C2×#16837202C211yesmaximal, characteristic
6#21422174C211yesmaximal, characteristic, complemented
7C59×#1942C211yesmaximal, characteristic, complemented
8C22×Dic236C2211yescharacteristic
9C22×#11745660—21no—
10C22×D472C2211yescharacteristic
11C2×#14273715—21no—
12C22×C59⋊C16C2211yescharacteristic
13C22×C59⋊C16C2211yescharacteristic
14#16837786—22no—
15#16837786—22no—
16#16837205—22no—
17#16837205—22no—
18#16837202—22no—
19#16837202—22no—
20C2×#107×C59C2211yescharacteristic
21C2×#107×C59C2211yescharacteristic
22C2×C4×C8×C59C2211yescharacteristic
23C59×#389—21no—
24C59×#340—21no—
25C22×Dic118—21no—
26C22×D236—21no—
27C2×Dic236—21no—
28C2×Dic236—21no—
29C2×Dic236—21no—
30C2×Dic236—21no—
31C2×Dic236—21no—
32C2×Dic236D412yes—
33C2×#11745660—24no—
34C2×#11745660—42no—
35C2×#11745660—42no—
36C2×D472—21no—
37C2×D472—21no—
38C2×D472—21no—
39C2×D472—21no—
40C2×D472—21no—
41C2×D472D412yes—
42#14273715—24no—
43#14273715—42no—
44C2×(C2×D59)⋊C4—41no—
45C2×(C2×D59)⋊C4—41no—
46C2×C59⋊C16—21no—
47C2×C59⋊C16—21no—
48C2×C59⋊C16—21no—
49C2×C59⋊C16—21no—
50C2×C59⋊C16—21no—
51C2×C59⋊C16—21no—
52C22×C8×C59D411yescharacteristic
53C22×C8×C59C2311yescharacteristic
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59—41no—
57C2×C42×C59D411yescharacteristic
58#107×C59—21no—
59#107×C59—21no—
60#107×C59—21no—
61#107×C59D412yes—
62C4×C8×C59—21no—
63C4×C8×C59—21no—
64#95×C59—41no—
65C23×D59—41no—
66C22×C4×C59—41no—
67C22×C4×C59—41no—
68C22×C4×C59D811yescharacteristic
69C22×C4×C59D811yescharacteristic
70C22×C4×C59C2×D411yescharacteristic
71C22×Dic59—41no—
72C2×D236—22no—
73C2×D236—41no—
74C2×D236—41no—
75C2×D236—41no—
76C2×D236—41no—
77C2×D236—41no—
78C2×Dic118—22no—
79C2×Dic118—41no—
80C2×Dic118—41no—
81C2×Dic118—41no—
82C2×Dic118—41no—
83C2×Dic118—41no—
84C2×C8×C59—21no—
85C2×C8×C59—21no—
86C2×C8×C59SD1612yes—
87C2×C8×C59C2×D411yescharacteristic
88C2×C8×C59C2×D411yescharacteristic
89C2×C8×C59C2×D411yescharacteristic
90C2×C8×C59#4111yescharacteristic
91C2×C8×C59#4111yescharacteristic
92C2×C8×C59#4111yescharacteristic
93C4⋊C4×C59—22no—
94C4⋊C4×C59—41no—
95C4⋊C4×C59—41no—
96C4⋊C4×C59—41no—
97C4⋊C4×C59—82no—
98C42×C59—21no—
99C42×C59—21no—
100(C2×D59)⋊C4—44no—
101(C2×D59)⋊C4—44no—
102Dic236—22no—
103Dic236—22no—
104Dic236—41no—
105Dic236—41no—
106D472—22no—
107D472—22no—
108D472—41no—
109D472—41no—
110#11745660—48no—
111C59⋊C16—41no—
112C59⋊C16—41no—
113C23×C59C2×D811yescharacteristic
114C22×D59—42no—
115C22×D59—81no—
116C22×D59—81no—
117C22×D59—81no—
118C22×D59—81no—
119C22×D59—81no—
120C22×D59—81no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—42no—
128C2×C4×C59—81no—
129C2×C4×C59—81no—
130C2×C4×C59—81no—
131C2×C4×C59—81no—
132C2×C4×C59—81no—
133C2×C4×C59#12011yescharacteristic
134C2×C4×C59#12111yescharacteristic
135C2×C4×C59#12411yescharacteristic
136C2×C4×C59C2×SD1611yescharacteristic
137C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
139C2×Dic59—42no—
140C2×Dic59—81no—
141C2×Dic59—81no—
142D236—42no—
143D236—42no—
144D236—81no—
145D236—81no—
146Dic118—42no—
147Dic118—42no—
148Dic118—81no—
149Dic118—81no—
150C8×C59—22no—
151C8×C59#12111yescharacteristic
152C8×C59#12111yescharacteristic
153C8×C59#12311yescharacteristic
154C8×C59#12311yescharacteristic
155#13408—591nomaximal, Sylow
156C22×C59#44711yescharacteristic
157C22×C59#45911yescharacteristic
158C22×C59#48611yescharacteristic
159C22×C59#50811yescharacteristic
160C22×C59#50811yescharacteristic
161C22×C59#50911yescharacteristic
162C22×C59#51011yescharacteristic
163C2×D59—82no—
164C2×D59—82no—
165C2×D59—82no—
166C2×D59—161no—
167C2×D59—161no—
168C2×D59—161no—
169C2×D59—161no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59—82no—
173C4×C59—161no—
174C4×C59#39411yescharacteristic
175C4×C59#45011yescharacteristic
176C4×C59#46011yescharacteristic
177C4×C59#49011yescharacteristic
178Dic59—82no—
179C2×#495—591no—
180C2×#358—591no—
181C2×#358—591no—
182C2×#357—591no—
183C2×#357—591no—
184#1942D5911yescharacteristic, complemented
185#1374—591no—
186C2×C59#204111yescharacteristic
187C2×C59#218611yescharacteristic
188C2×C59#218911yescharacteristic
189C2×C59#221011yescharacteristic
190C2×C59#221111yescharacteristic
191C2×C59#224211yescharacteristic
192C2×C59#224311yescharacteristic
193D59—162no—
194C22×Q16—591no—
195C22×SD16—1181no—
196C22×D8—591no—
197C2×#124—1181no—
198C22×C16—591no—
199C22×C16—591no—
200#495—1182no—
201#495—1182no—
202C2×#107C2×D5911yescharacteristic
203C2×#107C2×D5911yescharacteristic
204C2×C4×C8C2×D5911yescharacteristic
205#389—21no—
206#358—1182no—
207#358—1182no—
208#357—1182no—
209#357—1182no—
210#340—21no—
211C59#1340811yescharacteristic, complemented, Sylow
212C22×Q8—1181no—
213C22×D4—1181no—
214C2×Q16—592no—
215C2×Q16—1181no—
216C2×Q16—1181no—
217C2×Q16—1181no—
218C2×Q16—1181no—
219C2×Q16—1181no—
220C2×SD16—1184no—
221C2×SD16—2362no—
222C2×SD16—2362no—
223C2×D8—592no—
224C2×D8—1181no—
225C2×D8—1181no—
226C2×D8—1181no—
227C2×D8—1181no—
228C2×D8—1181no—
229C22×C8C22⋊D5911yescharacteristic
230C22×C8C22×D5911yescharacteristic
231#124—1184no—
232#124—2362no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C22⋊C4—2361no—
237C2×C22⋊C4—2361no—
238C2×C42C22⋊D5911yescharacteristic
239C2×C16—1181no—
240C2×C16—1181no—
241C2×C16—1181no—
242C2×C16—1181no—
243C2×C16—1181no—
244C2×C16—1181no—
245#107—21no—
246#107—21no—
247#107—21no—
248#107D23612yes—
249C4×C8—21no—
250C4×C8—21no—
251#95—41no—
252C24—2361no—
253C2×Q8—1182no—
254C2×Q8—2361no—
255C2×Q8—2361no—
256C2×Q8—2361no—
257C2×Q8—2361no—
258C2×Q8—2361no—
259C2×D4—1182no—
260C2×D4—2361no—
261C2×D4—2361no—
262C2×D4—2361no—
263C2×D4—2361no—
264C2×D4—2361no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—2361no—
268C22×C4#1174566911yescharacteristic
269C22×C4#1174566911yescharacteristic
270C22×C4C2×C22⋊D5911yescharacteristic
271Q16—1182no—
272Q16—1182no—
273Q16—2361no—
274Q16—2361no—
275SD16—2368no—
276D8—1182no—
277D8—1182no—
278D8—2361no—
279D8—2361no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8#1174567112yes—
283C2×C8C2×D23611yescharacteristic
284C2×C8#1174568511yescharacteristic
285C2×C8D4×D5911yescharacteristic
286C2×C8D4×D5911yescharacteristic
287C2×C8#1174568911yescharacteristic
288C2×C8#1174568911yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—82no—
294C22⋊C4—2364no—
295C22⋊C4—2364no—
296C42—21no—
297C42—21no—
298C16—2361no—
299C16—2361no—
300C23—4721no—
301C23—4721no—
302C23—4721no—
303C23—4721no—
304C23—4721no—
305C23—4721no—
306C23—2362no—
307C23C2×#1174566911yescharacteristic
308Q8—4721no—
309Q8—4721no—
310Q8—2362no—
311Q8—2362no—
312D4—4721no—
313D4—4721no—
314D4—2362no—
315D4—2362no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—4721no—
329C2×C4—4721no—
330C2×C4—2362no—
331C2×C4#1427369511yescharacteristic
332C2×C4#1427370111yescharacteristic
333C2×C4#1427371611yescharacteristic
334C2×C4C2×#1174567111yescharacteristic
335C2×C4#1427375211yescharacteristic
336C2×C4#1427375211yescharacteristic
337C8—22no—
338C8#1427370211yescharacteristic
339C8#1427370211yescharacteristic
340C8#1427371211yescharacteristic
341C8#1427371211yescharacteristic
342C22—9441no—
343C22—9441no—
344C22—9441no—
345C22—9441no—
346C22—4722no—
347C22—4722no—
348C22—4722no—
349C22#1683753511yescharacteristic
350C22#1683759711yescharacteristic
351C22#1683775011yescharacteristic
352C22#1683783211yescharacteristic
353C22#1683783211yescharacteristic
354C22#1683783811yescharacteristic
355C22#1683784311yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—161no—
360C4—4722no—
361C4#1683731911yescharacteristic
362C4#1683755211yescharacteristic
363C4#1683760211yescharacteristic
364C4#1683776811yescharacteristic
365C2—9442no—
366C2#2142533011yescharacteristic
367C2#2142601711yescharacteristic
368C2#2142603411yescharacteristic
369C2#2142615111yescharacteristic
370C2#2142615811yescharacteristic
371C2#2142633011yescharacteristic
372C2#2142633511yescharacteristic
subgroupG/H
centerC23C2×#11745669
commutator, cosocleC22×C8×C59C23
FrattiniC22×C8C22×D59
FittingC59×#1942C2
socleC23×C59C2×D8
prime radicalC22×D472C22
hypercenter#1942D59
hypocenterC59#13408
LCSG ▷ C22×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. C2×#16837205C2semidirect
3. C2×#16837205C2semidirect
6. #21422174C2semidirect
7. C59×#1942C2semidirect
184. #1942D59semidirect
211. C59#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#168377862
C2×#168372052
C2×#168372022
#214221742
C59×#19422
#1340859