Finite Group Databasebeta

← #28508036

Subgroups — #28508036

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×#16837787C211yesmaximal, characteristic
2C2×#16837206C211yesmaximal, characteristic, complemented
3C2×#16837204C211yesmaximal, characteristic
4C2×#16837202C211yesmaximal, characteristic
5#21424827C211yesmaximal, characteristic, complemented
6#21422173C211yesmaximal, characteristic, complemented
7C2×C59×#358C211yesmaximal, characteristic, complemented
8C22×#11745671—21no—
9C22×D472C2211yescharacteristic
10C2×#14273716—21no—
11C22×C59⋊C16C2211yescharacteristic
12#16837787—22no—
13#16837787—22no—
14C2×#14273661C2211yescharacteristic
15C2×C8×Dic59C2211yescharacteristic
16#16837298—21no—
17#16837206—22no—
18#16837204—22no—
19#16837202—22no—
20#16837164—21no—
21C22×Q16×C59C2211yescharacteristic
22C22×C16×C59C2211yescharacteristic
23C2×#107×C59C2211yescharacteristic
24C59×#358—22no—
25C22×D236—21no—
26C2×#11745671—24no—
27C2×#11745671—42no—
28C2×#11745671—42no—
29C2×D472—21no—
30C2×D472—21no—
31C2×D472—21no—
32C2×D472—21no—
33C2×D472—21no—
34C2×D472D412yes—
35C22×C59⋊C8D411yescharacteristic
36#14273716—24no—
37#14273716—42no—
38C2×C4⋊Dic59—21no—
39C2×Dic59⋊C4—41no—
40C2×(C2×D59)⋊C4—41no—
41C2×(C2×D59)⋊C4—41no—
42C2×C4×Dic59D411yescharacteristic
43C2×C59⋊C16—21no—
44C2×C59⋊C16—21no—
45C2×C59⋊C16—21no—
46#14273661—21no—
47#14273661D412yes—
48C8×Dic59—21no—
49C8×Dic59—21no—
50C59⋊#95—41no—
51C22×Q8×C59—21no—
52C2×Q16×C59—21no—
53C2×Q16×C59—21no—
54C2×Q16×C59—21no—
55C2×Q16×C59—21no—
56C2×Q16×C59—21no—
57C2×Q16×C59D412yes—
58C22×C8×C59C2311yescharacteristic
59C2×C4⋊C4×C59—21no—
60C2×C16×C59—21no—
61C2×C16×C59—21no—
62C2×C16×C59—21no—
63#107×C59—21no—
64#107×C59—21no—
65C23×D59—41no—
66C2×Q8×C59—22no—
67C2×Q8×C59—41no—
68C2×Q8×C59—41no—
69C2×Q8×C59—41no—
70C2×Q8×C59—41no—
71C2×Q8×C59—41no—
72C22×C4×C59—41no—
73C22×C4×C59—41no—
74C22×C4×C59C2×D411yescharacteristic
75C22×Dic59—41no—
76C22×Dic59D811yescharacteristic
77C22×Dic59D811yescharacteristic
78C2×D236—22no—
79C2×D236—41no—
80C2×D236—41no—
81C2×D236—41no—
82C2×D236—41no—
83C2×D236—41no—
84Q16×C59—22no—
85Q16×C59—22no—
86Q16×C59—41no—
87Q16×C59—41no—
88C2×C8×C59C2×D411yescharacteristic
89C2×C8×C59C2×D411yescharacteristic
90C2×C8×C59C2×D411yescharacteristic
91C2×C8×C59#4111yescharacteristic
92C2×C8×C59#4111yescharacteristic
93C2×C8×C59#4111yescharacteristic
94C4⋊C4×C59—41no—
95C4⋊C4×C59—41no—
96#11745671—48no—
97(C2×D59)⋊C4—44no—
98(C2×D59)⋊C4—44no—
99C4⋊Dic59—22no—
100C4⋊Dic59—41no—
101Dic59⋊C4—82no—
102C4×Dic59—21no—
103C4×Dic59—21no—
104C2×C59⋊C8—21no—
105C2×C59⋊C8—21no—
106C2×C59⋊C8SD1612yes—
107D472—22no—
108D472—22no—
109D472—41no—
110D472—41no—
111C16×C59—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—
121Q8×C59—42no—
122Q8×C59—42no—
123Q8×C59—81no—
124Q8×C59—81no—
125C2×C4×C59—42no—
126C2×C4×C59—81no—
127C2×C4×C59—81no—
128C2×C4×C59—81no—
129C2×C4×C59—81no—
130C2×C4×C59—81no—
131C2×C4×C59#12011yescharacteristic
132C2×C4×C59#12111yescharacteristic
133C2×C4×C59#12411yescharacteristic
134C2×C4×C59C2×SD1611yescharacteristic
135C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—42no—
144C2×Dic59—81no—
145C2×Dic59—81no—
146D236—42no—
147D236—42no—
148D236—81no—
149D236—81no—
150C8×C59#12111yescharacteristic
151C8×C59#12111yescharacteristic
152C8×C59#12311yescharacteristic
153C8×C59#12311yescharacteristic
154C59⋊C8—22no—
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—82no—
171C4×C59—161no—
172C4×C59#39411yescharacteristic
173C4×C59#45011yescharacteristic
174C4×C59#46011yescharacteristic
175C4×C59#49011yescharacteristic
176Dic59—41no—
177Dic59—41no—
178Dic59—82no—
179C2×#495—591no—
180C2×#358—591no—
181C2×#358D5911yescharacteristic, complemented
182C2×#357—591no—
183C2×#357—591no—
184#1942—591no—
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×Q16C2×D5911yescharacteristic
195C22×SD16—1181no—
196C22×D8—591no—
197C2×#124—1181no—
198C22×C16—591no—
199C22×C16C2×D5911yescharacteristic
200#495—1182no—
201#495—1182no—
202C2×#107—591no—
203C2×#107C2×D5911yescharacteristic
204C2×C4×C8—591no—
205#389—1181no—
206#358—22no—
207#358—1182no—
208#357—1182no—
209#357—1182no—
210#340—1181no—
211C59#1340811yescharacteristic, complemented, Sylow
212C22×Q8—21no—
213C22×D4—1181no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16C22⋊D5912yes—
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×C8—591no—
230C22×C8C22×D5911yescharacteristic
231#124—1184no—
232#124—2362no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—1181no—
235C2×C4⋊C4—2361no—
236C2×C22⋊C4—2361no—
237C2×C22⋊C4—2361no—
238C2×C42—591no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—1181no—
243C2×C16—1181no—
244C2×C16—1181no—
245#107—21no—
246#107—21no—
247#107—592no—
248#107—1181no—
249C4×C8—1181no—
250C4×C8—1181no—
251#95—2361no—
252C24—2361no—
253C2×Q8—22no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
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—591no—
268C22×C4—591no—
269C22×C4—2361no—
270C22×C4D4×D5911yescharacteristic
271Q16—22no—
272Q16—22no—
273Q16—41no—
274Q16—41no—
275SD16—2368no—
276D8—1182no—
277D8—1182no—
278D8—2361no—
279D8—2361no—
280C2×C8—592no—
281C2×C8—1181no—
282C2×C8—1181no—
283C2×C8#1174568511yescharacteristic
284C2×C8#1174568511yescharacteristic
285C2×C8D4×D5911yescharacteristic
286C2×C8D4×D5911yescharacteristic
287C2×C8#1174568711yescharacteristic
288C2×C8C2×C22⋊D5911yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—1182no—
292C4⋊C4—4722no—
293C4⋊C4—2361no—
294C22⋊C4—2364no—
295C22⋊C4—2364no—
296C42—1181no—
297C42—1181no—
298C16—41no—
299C16—2361no—
300C23—4721no—
301C23—4721no—
302C23—4721no—
303C23—4721no—
304C23—4721no—
305C23—4721no—
306C23—2362no—
307C23D8×D5911yescharacteristic
308Q8—42no—
309Q8—42no—
310Q8—81no—
311Q8—81no—
312D4—4721no—
313D4—4721no—
314D4—2362no—
315D4—2362no—
316C2×C4—42no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—1181no—
328C2×C4—4721no—
329C2×C4—4721no—
330C2×C4—2362no—
331C2×C4#1427369511yescharacteristic
332C2×C4#1427370011yescharacteristic
333C2×C4#1427371311yescharacteristic
334C2×C4SD16×D5911yescharacteristic
335C2×C4#1427375111yescharacteristic
336C2×C4#1427375411yescharacteristic
337C8—1182no—
338C8#1427369911yescharacteristic
339C8#1427370011yescharacteristic
340C8#1427370911yescharacteristic
341C8#1427371011yescharacteristic
342C22—9441no—
343C22—9441no—
344C22—9441no—
345C22—9441no—
346C22—4722no—
347C22—4722no—
348C22—4722no—
349C22#1683753411yescharacteristic
350C22#1683759611yescharacteristic
351C22#1683774711yescharacteristic
352C22#1683783311yescharacteristic
353C22#1683783511yescharacteristic
354C22#1683783911yescharacteristic
355C22#1683784411yescharacteristic
356C4—82no—
357C4—161no—
358C4—4722no—
359C4—2361no—
360C4—2361no—
361C4#1683731711yescharacteristic
362C4#1683755111yescharacteristic
363C4#1683760111yescharacteristic
364C4#1683776511yescharacteristic
365C2—9442no—
366C2#2142532811yescharacteristic
367C2#2142601811yescharacteristic
368C2#2142603511yescharacteristic
369C2#2142615411yescharacteristic
370C2#2142616111yescharacteristic
371C2#2142632911yescharacteristic
372C2#2142633411yescharacteristic
subgroupG/H
centerC23D8×D59
commutator, cosocleC22×C8×C59C23
FrattiniC22×C8C22×D59
FittingC2×C59×#358C2
socleC23×C59C2×D8
prime radicalC22×D472C22
hypercenterC2×#358D59
hypocenterC59#13408
LCSG ▷ C22×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#16837206C2semidirect
5. #21424827C2semidirect
6. #21422173C2semidirect
7. C2×C59×#358C2semidirect
181. C2×#358D59semidirect
211. C59#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#168377872
C2×#168372062
C2×#168372042
C2×#168372022
#214248272
#214221732
C2×C59×#3582
#1340859