Finite Group Databasebeta

← #28482592

Subgroups — #28482592

Order 15104.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433214C211yesmaximal, characteristic
2C4×#14273655C211yesmaximal, characteristic
3#21422846C211yesmaximal, characteristic, complemented
4#21422481C211yesmaximal, characteristic
5#21421946C211yesmaximal, characteristic, complemented
6#21421929C211yesmaximal, characteristic, complemented
7C59×#1831C211yesmaximal, characteristic, complemented
8C4×#11745685C2211yescharacteristic
9#16837529—21no—
10#16837479—21no—
11#16837473—22no—
12#16837458—21no—
13#16837455C2211yescharacteristic
14#16837455C2211yescharacteristic
15#16837424—21no—
16C2×#14273655C411yescharacteristic
17C2×#14273655C411yescharacteristic
18C4×#11745664C2211yescharacteristic
19#16837162C411yescharacteristic
20#16837162C411yescharacteristic
21#16837154—21no—
22#16837152—21no—
23#16837132—21no—
24#16837129—21no—
25C2×C4⋊C8×C59C2211yescharacteristic
26C2×C4⋊C8×C59C2211yescharacteristic
27C43×C59C2211yescharacteristic
28C59×#336—22no—
29C2×#11745685C2×C411yescharacteristic
30C2×#11745664C2×C411yescharacteristic
31C2×#11745664C2×C411yescharacteristic
32C2×#11745659—22no—
33C4×Dic118D411yescharacteristic
34C4×Dic118Q811yescharacteristic
35C4×D236D411yescharacteristic
36C4×D236Q811yescharacteristic
37C4×C22⋊D59—21no—
38C4×C22⋊D59—21no—
39#14273686C2×C411yescharacteristic
40#14273684—21no—
41C42×D59—21no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)D411yescharacteristic
44C4⋊(C59⋊C8)D411yescharacteristic
45Dic59⋊C8—22no—
46#14273655—22no—
47#14273655—22no—
48C22⋊(C59⋊C8)—21no—
49C22⋊(C59⋊C8)—21no—
50(C2×D59)⋊C8—22no—
51#14273638—21no—
52#14273637—22no—
53C4×C59⋊C8—21no—
54C4×C59⋊C8—21no—
55C4×C59⋊C8—21no—
56C22×C8×C59—21no—
57C22×C8×C59D412yes—
58C2×C42×C59—21no—
59C2×C42×C59—21no—
60C2×C42×C59C2×C411yescharacteristic
61C2×C42×C59C2×C411yescharacteristic
62C2×C42×C59C2311yescharacteristic
63C4⋊C8×C59—21no—
64C4⋊C8×C59—21no—
65C4⋊C8×C59—21no—
66C4⋊C8×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59C22×C411yescharacteristic
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59#4111yescharacteristic
72C2×C22⋊D59—21no—
73#11745685—21no—
74#11745685—21no—
75#11745685—21no—
76#11745685—21no—
77C2×D236C4⋊C411yescharacteristic
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×Dic118C4⋊C411yescharacteristic
82C2×C8×C59—22no—
83C2×C8×C59—42no—
84C2×C8×C59—42no—
85C2×C8×C59—41no—
86C42×C59—21no—
87C42×C59—21no—
88C42×C59—21no—
89C42×C59—41no—
90C42×C59—41no—
91C42×C59—42no—
92C42×C59M1612yescomplemented
93C42×C59C2×D411yescharacteristic
94C42×C59C2×D411yescharacteristic
95C42×C59C2×Q811yescharacteristic
96C42×C59#4111yescharacteristic
97C22⋊Dic59—21no—
98(C2×D59)⋊C4—21no—
99(C2×D59)⋊C4—21no—
100C4⋊Dic59C4⋊C411yescharacteristic
101C4⋊Dic59C4⋊C411yescharacteristic
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C4×Dic59—21no—
107#11745664—21no—
108#11745664—21no—
109#11745664—21no—
110#11745664M1612yescomplemented
111C2×C59⋊C8—21no—
112C2×C59⋊C8—21no—
113C2×C59⋊C8—21no—
114C2×C59⋊C8—21no—
115C2×C59⋊C8—41no—
116#11745659—82no—
117C23×C59C4×D411yescharacteristic
118C22×D59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—22no—
122C2×C4×C59—22no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59C2×C4⋊C411yescharacteristic
129C2×C4×C59C4×D411yescharacteristic
130C2×C4×C59#12011yescharacteristic
131C2×C4×C59C22⋊Q811yescharacteristic
132C2×C4×C59C22⋊Q811yescharacteristic
133C2×C4×C59#12311yescharacteristic
134C2×C4×C59C2×M1611yescharacteristic
135C2×C4×C59C2×M1611yescharacteristic
136C2×C4×C59#13111yescharacteristic
137C2×C4×C59#13111yescharacteristic
138C22⋊D59—41no—
139C22⋊D59—41no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143D236—21no—
144D236—21no—
145C4×D59—41no—
146C4×D59—41no—
147C4×D59—41no—
148C4×D59—41no—
149C4×D59—81no—
150Dic118—21no—
151Dic118—21no—
152C8×C59—42no—
153C8×C59—81no—
154C59⋊C8—22no—
155C59⋊C8—41no—
156C59⋊C8—41no—
157C59⋊C8—41no—
158C59⋊C8—81no—
159#8842—591nomaximal, Sylow
160C22×C59—21no—
161C22×C59—21no—
162C22×C59#38511yescharacteristic
163C22×C59#43511yescharacteristic
164C22×C59#43611yescharacteristic
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—42no—
172C4×C59—42no—
173C4×C59#42311yescharacteristic
174C4×C59#42411yescharacteristic
175C4×C59#43511yescharacteristic
176C4×C59#43611yescharacteristic
177C4×C59#45411yescharacteristic
178C4×C59#45511yescharacteristic
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182#2989—591no—
183#1831D5911yescharacteristic, complemented
184C4×#104—591no—
185#1565—591no—
186#1477—591no—
187#1283—591no—
188#1276—591no—
189C2×C59—21no—
190C2×C59—21no—
191C2×C59#185111yescharacteristic
192C2×C59#186011yescharacteristic
193C2×C59#186111yescharacteristic
194D59—81no—
195C4×#41—591no—
196#446—1181no—
197#436—1181no—
198#435—1182no—
199#432—1181no—
200#431—591no—
201#431—591no—
202#423—1181no—
203C2×C4⋊C8C2×D5911yescharacteristic
204C2×C4⋊C8C2×D5911yescharacteristic
205C2×#104—591no—
206C2×#104—591no—
207C4×M16—591no—
208C43C2×D5911yescharacteristic
209#339—591no—
210#339—591no—
211#336—22no—
212#335—1181no—
213#334—1181no—
214Q8⋊C8—1181no—
215D4⋊C8—1181no—
216C59#884211yescharacteristic, complemented, Sylow
217C2×#41—591no—
218C2×M16—591no—
219C2×M16—591no—
220C2×M16—1182no—
221C22×C8—21no—
222C22×C8C22⋊D5912yes—
223C4×Q8—591no—
224C4×Q8—591no—
225C4×D4—591no—
226C4×D4—591no—
227C4×D4—1181no—
228C4×D4—1181no—
229#117—591no—
230#117—1181no—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42—1181no—
234C2×C42C4×D5911yescharacteristic
235C2×C42C4×D5911yescharacteristic
236C2×C42C22×D5911yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—591no—
242C4⋊C8—591no—
243C4⋊C8—1182no—
244C4⋊C8—1181no—
245#104—1182no—
246#104—1182no—
247C22⋊C8—1182no—
248C22⋊C8—1181no—
249C22⋊C8—1181no—
250#97—1182no—
251#97—1181no—
252C4×C8—1181no—
253C4×C8—1181no—
254C4×C8—1181no—
255#41—1181no—
256#41—1181no—
257#41—1181no—
258#41—1181no—
259C2×Q8—591no—
260C2×D4—591no—
261C2×D4—1181no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—1181no—
265C22×C4—1181no—
266C22×C4—1181no—
267C22×C4C2×C4×D5911yescharacteristic
268C22×C4#1174568511yescharacteristic
269C22×C4C2×C22⋊D5911yescharacteristic
270M16—592no—
271M16—1181no—
272M16—1181no—
273M16—1181no—
274M16—4722no—
275C2×C8—22no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—41no—
279C2×C8—1181no—
280C2×C8—1181no—
281C2×C8—1181no—
282C2×C8—1181no—
283C2×C8—2361no—
284C4⋊C4—591no—
285C4⋊C4—591no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4—1181no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—41no—
295C42—41no—
296C42—42no—
297C42—1181no—
298C42—1181no—
299C42—1181no—
300C42#1174565912yescomplemented
301C42D4×D5911yescharacteristic
302C42D4×D5911yescharacteristic
303C42Q8×D5911yescharacteristic
304C42#1174568911yescharacteristic
305C23—1181no—
306C23C4×C22⋊D5911yescharacteristic
307Q8—1181no—
308Q8—1181no—
309D4—1181no—
310D4—1181no—
311D4—2361no—
312D4—2361no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—1181no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—4721no—
326C2×C4—2361no—
327C2×C4—2361no—
328C2×C4—2361no—
329C2×C4—2361no—
330C2×C4C4⋊C4×D5911yescharacteristic
331C2×C4#1427368911yescharacteristic
332C2×C4#1427369511yescharacteristic
333C2×C4#1427370311yescharacteristic
334C2×C4#1427370511yescharacteristic
335C2×C4#1427371211yescharacteristic
336C2×C4M16×D5911yescharacteristic
337C2×C4C2×#1174565911yescharacteristic
338C2×C4#1427373311yescharacteristic
339C2×C4#1427373511yescharacteristic
340C8—42no—
341C8—81no—
342C8—1182no—
343C8—4721no—
344C8—2361no—
345C8—2361no—
346C8—2361no—
347C22—21no—
348C22—21no—
349C22—2361no—
350C22—2361no—
351C22—2361no—
352C22#1683727311yescharacteristic
353C22#1683747311yescharacteristic
354C22#1683747811yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—42no—
360C4—2361no—
361C4—2361no—
362C4—2361no—
363C4#1683742411yescharacteristic
364C4#1683742711yescharacteristic
365C4#1683747211yescharacteristic
366C4#1683747911yescharacteristic
367C4#1683757411yescharacteristic
368C4#1683757911yescharacteristic
369C2—21no—
370C2—21no—
371C2—4721no—
372C2#2142427711yescharacteristic
373C2#2142432811yescharacteristic
374C2#2142433511yescharacteristic
subgroupG/H
centerC2×C4#14273695
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1831C2
socleC22×C59#385
prime radicalC2×#11745685C2×C4
cosocleC2×C42×C59C23
hypercenter#1831D59
hypocenterC59#8842
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1831

Complements

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

NH ≅ G/Ntype
3. #21422846C2semidirect
5. #21421946C2semidirect
6. #21421929C2semidirect
7. C59×#1831C2semidirect
92. C42×C59M16semidirect
110. #11745664M16semidirect
183. #1831D59semidirect
216. C59#8842semidirect
300. C42#11745659semidirect

Maximal subgroups

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

subgroupindex
#214332142
C4×#142736552
#214228462
#214224812
#214219462
#214219292
C59×#18312
#884259