Finite Group Databasebeta

← #28506898

Subgroups — #28506898

Order 15104.

420 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432799C211yesmaximal, characteristic
2#21425861C211yesmaximal, characteristic, complemented
3#21425725C211yesmaximal, characteristic, complemented
4#21425723C211yesmaximal, characteristic, complemented
5C2×#16837184C211yesmaximal, characteristic, complemented
6#21425700C211yesmaximal, characteristic, complemented
7C2×C59×#349C211yesmaximal, characteristic, complemented
8C2×#14273733C2211yescharacteristic
9#16837913C411yescharacteristic
10C2×#14273667C2211yescharacteristic
11C2×#14273667C2211yescharacteristic
12#16837478—22no—
13#16837471—22no—
14#16837428C411yescharacteristic
15#16837368C411yescharacteristic
16#16837366C411yescharacteristic
17#16837357C2211yescharacteristic
18#16837222—22no—
19#16837187—22no—
20#16837185—22no—
21#16837184—22no—
22#16837179—22no—
23C22×M16×C59C2211yescharacteristic
24C2×M32×C59C2211yescharacteristic
25C2×M32×C59C2211yescharacteristic
26C59×#349—22no—
27C2×#11745685C2×C411yescharacteristic
28#14273733—21no—
29#14273733—21no—
30#14273733—21no—
31#14273733—21no—
32C2×#11745664C2×C411yescharacteristic
33C2×#11745664C2×C411yescharacteristic
34C2×#11745659—21no—
35C2×C8×D59—21no—
36#14273710—21no—
37#14273706—21no—
38#14273701—21no—
39#14273696—21no—
40C4×C22⋊D59—22no—
41#14273686C2×C411yescharacteristic
42#14273667—21no—
43#14273667—21no—
44#14273667—21no—
45#14273667D412yescomplemented
46C2×C59⋊C16—21no—
47C2×C59⋊C16—21no—
48Dic59⋊C8—22no—
49C22⋊(C59⋊C8)—22no—
50(C2×D59)⋊C8—22no—
51#14273637D412yes—
52C8×Dic59D412yes—
53C23×C4×C59C2×C411yescharacteristic
54C2×M16×C59—21no—
55C2×M16×C59—21no—
56C2×M16×C59—21no—
57C2×M16×C59—21no—
58C2×M16×C59—21no—
59C2×M16×C59—21no—
60C22×C8×C59C2×C411yescharacteristic
61C22×C8×C59C2311yescharacteristic
62M32×C59—21no—
63M32×C59—21no—
64M32×C59—21no—
65M32×C59D412yescomplemented
66C2×C16×C59—21no—
67C2×C16×C59—21no—
68C24×C59M1611yescharacteristic
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59M1611yescharacteristic
76C22×C4×C59C22×C411yescharacteristic
77C2×C22⋊D59—21no—
78C2×C22⋊D59—22no—
79#11745685—21no—
80#11745685—21no—
81#11745685—21no—
82#11745685—21no—
83C2×D236M1611yescharacteristic
84C2×C4×D59—21no—
85C2×Dic118M1611yescharacteristic
86M16×C59—41no—
87M16×C59—41no—
88M16×C59—41no—
89M16×C59—41no—
90C2×C8×C59—21no—
91C2×C8×C59—21no—
92C2×C8×C59—21no—
93C2×C8×C59C2×D411yescharacteristic
94C2×C8×C59C2×D411yescharacteristic
95C2×C8×C59C2×D411yescharacteristic
96C2×C8×C59C2×D411yescharacteristic
97C2×C8×C59#4111yescharacteristic
98C2×C8×C59#4111yescharacteristic
99C22⋊Dic59—22no—
100C22⋊Dic59—21no—
101(C2×D59)⋊C4—22no—
102C4⋊Dic59—21no—
103Dic59⋊C4—22no—
104C4×Dic59C22⋊C412yes—
105#11745664—21no—
106#11745664—21no—
107#11745664—21no—
108#11745664—21no—
109C2×C59⋊C8—21no—
110C2×C59⋊C8C22⋊C412yes—
111#11745659—41no—
112#11745659—41no—
113C8×D59—41no—
114C8×D59—41no—
115C16×C59—22no—
116C16×C59—41no—
117C59⋊C16—22no—
118C59⋊C16—41no—
119C23×C59—21no—
120C23×C59—21no—
121C23×C59—21no—
122C23×C59—81no—
123C23×C59C2×M1611yescharacteristic
124C22×D59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59—41no—
132C2×C4×C59C2×C22⋊C411yescharacteristic
133C2×C4×C59C4×D411yescharacteristic
134C2×C4×C59C4×D411yescharacteristic
135C2×C4×C59C2×M1611yescharacteristic
136C2×C4×C59#13111yescharacteristic
137C2×C4×C59#13111yescharacteristic
138C22⋊D59—41no—
139C22⋊D59—41no—
140C22⋊D59—82no—
141C2×Dic59—22no—
142C2×Dic59—21no—
143D236—21no—
144D236—21no—
145C4×D59—41no—
146C4×D59—41no—
147Dic118—21no—
148Dic118—21no—
149C8×C59—41no—
150C8×C59#12111yescharacteristic
151C8×C59#12111yescharacteristic
152C8×C59#12411yescharacteristic
153C8×C59#12711yescharacteristic
154C59⋊C8—22no—
155C59⋊C8—41no—
156#13201—591nomaximal, Sylow
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—81no—
162C22×C59—81no—
163C22×C59#40711yescharacteristic
164C22×C59#43511yescharacteristic
165C22×C59#43511yescharacteristic
166C2×D59—42no—
167C2×D59—41no—
168C4×C59—41no—
169C4×C59#39011yescharacteristic
170C4×C59#40811yescharacteristic
171C4×C59#43511yescharacteristic
172C4×C59#43511yescharacteristic
173Dic59—42no—
174Dic59—41no—
175#2930—591no—
176#2153—591no—
177#2117—591no—
178#2117—591no—
179C2×#349—591no—
180C2×#349D5911yescharacteristic, complemented
181#2110—591no—
182C2×C59—21no—
183C2×C59—21no—
184C2×C59—21no—
185C2×C59—81no—
186C2×C59#195511yescharacteristic
187D59—81no—
188C2×#131—591no—
189C22×M16C2×D5911yescharacteristic
190#525—591no—
191C2×M32—591no—
192C2×M32—591no—
193C2×M32C2×D5911yescharacteristic
194C2×M32C2×D5911yescharacteristic
195#436—1182no—
196#435—1182no—
197#424—591no—
198#408—591no—
199#407—591no—
200#405—591no—
201#364—1182no—
202#350—1182no—
203#350—1182no—
204#349—22no—
205#349—1182no—
206#347—1182no—
207C59#1320111yescharacteristic, complemented, Sylow
208C2×#41—591no—
209C23×C4C4×D5911yescharacteristic
210#131—1181no—
211#131—1181no—
212#131—1181no—
213#131—1181no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—591no—
221C2×M16—591no—
222C2×M16—1181no—
223C22×C8—1181no—
224C22×C8C4×D5911yescharacteristic
225C22×C8C22×D5911yescharacteristic
226#123—1181no—
227C22⋊Q8—1181no—
228#121—1181no—
229#120—1181no—
230C4×D4—1182no—
231#117—591no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32—592no—
236M32—1181no—
237M32—1181no—
238M32—1181no—
239M32C22⋊D5912yescomplemented
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—1181no—
243C2×C16—1181no—
244C4⋊C8—1182no—
245C22⋊C8—1182no—
246C22⋊C8—1182no—
247#97—592no—
248C4×C8—592no—
249C24#1174565911yescharacteristic
250#41—1181no—
251#41—1181no—
252#41—1181no—
253#41—1181no—
254C2×Q8—591no—
255C2×D4—591no—
256C2×D4—1182no—
257C2×D4—1181no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—1181no—
265C22×C4#1174565911yescharacteristic
266C22×C4C2×C4×D5911yescharacteristic
267M16—41no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—1181no—
272M16—1181no—
273M16—1181no—
274M16—1181no—
275M16—2361no—
276M16—2361no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—592no—
281C2×C8—1181no—
282C2×C8—2361no—
283C2×C8—2361no—
284C2×C8#1174568511yescharacteristic
285C2×C8D4×D5911yescharacteristic
286C2×C8D4×D5911yescharacteristic
287C2×C8D4×D5911yescharacteristic
288C2×C8#1174568711yescharacteristic
289C2×C8C2×C22⋊D5911yescharacteristic
290C4⋊C4—1182no—
291C4⋊C4—1181no—
292C22⋊C4—1182no—
293C22⋊C4—1182no—
294C22⋊C4—1181no—
295C42—592no—
296C16—22no—
297C16—41no—
298C16—1182no—
299C16—2361no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—81no—
304C23—1181no—
305C23C2×#1174565911yescharacteristic
306Q8—1181no—
307Q8—1181no—
308D4—1181no—
309D4—1181no—
310D4—4722no—
311D4—2361no—
312D4—2361no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—1182no—
321C2×C4—1181no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4C22⋊C4×D5911yescharacteristic
325C2×C4(C22⋊D59)⋊C411yescharacteristic
326C2×C4C4×C22⋊D5911yescharacteristic
327C2×C4M16×D5911yescharacteristic
328C2×C4#1427373311yescharacteristic
329C2×C4#1427373511yescharacteristic
330C8—41no—
331C8—1182no—
332C8—2361no—
333C8#1427369911yescharacteristic
334C8#1427370011yescharacteristic
335C8#1427371311yescharacteristic
336C8#1427372311yescharacteristic
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22—2362no—
344C22—2361no—
345C22#1683736411yescharacteristic
346C22#1683747011yescharacteristic
347C22#1683747311yescharacteristic
348C4—41no—
349C4—2362no—
350C4—2361no—
351C4#1683730211yescharacteristic
352C4#1683736711yescharacteristic
353C4#1683747111yescharacteristic
354C4#1683747611yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—81no—
359C2—4721no—
360C2#2142489211yescharacteristic
subgroupG/H
centerC4#16837302
commutatorC22×C4×C59C22×C4
FrattiniC22×C8C22×D59
FittingC2×C59×#349C2
socleC2×C59#1955
prime radical#16837913C4
cosocleC22×C8×C59C23
hypercenterC2×#349D59
hypocenterC59#13201
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. #21425861C2semidirect
3. #21425725C2semidirect
4. #21425723C2semidirect
5. C2×#16837184C2semidirect
6. #21425700C2semidirect
7. C2×C59×#349C2semidirect
45. #14273667D4semidirect
65. M32×C59D4semidirect
180. C2×#349D59semidirect
207. C59#13201semidirect
239. M32C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
#214327992
#214258612
#214257252
#214257232
C2×#168371842
#214257002
C2×C59×#3492
#1320159