Finite Group Databasebeta

← #28485241

Subgroups — #28485241

Order 15104.

492 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
1#21435034C211yesmaximal, characteristic
2#21424936C211yesmaximal, characteristic
3#21422786C211yesmaximal, characteristic, complemented
4C2×#16837145C211yesmaximal, characteristic
5#21421993C211yesmaximal, characteristic, complemented
6#21421947C211yesmaximal, characteristic, complemented
7C59×#2962C211yesmaximal, characteristic, complemented
8C2×#14273724C2211yescharacteristic
9#16837776—21no—
10#16837750—21no—
11#16837602—22no—
12#16837552C414yes—
13#16837455C2211yescharacteristic
14#16837426C2211yescharacteristic
15C2×C4⋊(C59⋊C8)C2211yescharacteristic
16C2×#14273643—21no—
17C2×#14273643—21no—
18#16837151—21no—
19#16837148—21no—
20#16837145—21no—
21#16837145—21no—
22C59×#533C2211yescharacteristic
23C59×#446—22no—
24C59×#446—21no—
25C8×Q8×C59—21no—
26C59×#424—21no—
27C2×C4⋊C8×C59C2211yescharacteristic
28C59×#405—21no—
29C4×M16×C59C2211yescharacteristic
30C22×D236—21no—
31C22×D236—21no—
32C22×D236C2×C412yes—
33C2×#11745671—24no—
34C2×#11745664—21no—
35C22×C59⋊C8—21no—
36#14273724—21no—
37#14273724—21no—
38#14273724—21no—
39#14273724—21no—
40C4⋊(C59⋊C8)—21no—
41C4⋊(C59⋊C8)—21no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)—21no—
44C4⋊(C59⋊C8)—21no—
45#14273647—24no—
46#14273643—42no—
47#14273643—42no—
48C22⋊(C59⋊C8)C2×C412yes—
49C4×C59⋊C8—21no—
50C2×M16×C59D411yescharacteristic
51C2×M16×C59D411yescharacteristic
52C22×C8×C59—21no—
53C4⋊Q8×C59D411yescharacteristic
54C4⋊Q8×C59D411yescharacteristic
55#125×C59—21no—
56C22⋊Q8×C59—21no—
57C22⋊Q8×C59C2×C412yes—
58C4×Q8×C59—21no—
59C4×Q8×C59D412yes—
60#117×C59—21no—
61C2×C42×C59C2311yescharacteristic
62C4⋊C8×C59—22no—
63C4⋊C8×C59—22no—
64C4⋊C8×C59—21no—
65C4⋊C8×C59D411yescharacteristic
66C4⋊C8×C59D411yescharacteristic
67#97×C59—22no—
68#97×C59—21no—
69C4×C8×C59—22no—
70C4×C8×C59—21no—
71C23×D59—22no—
72C2×Q8×C59—21no—
73C2×Q8×C59C22⋊C412yes—
74C22×C4×C59C22×C411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×C4×C59#4111yescharacteristic
77C2×D236—22no—
78C2×D236—22no—
79C2×D236—41no—
80C2×D236—41no—
81C2×D236—41no—
82C2×D236—41no—
83C2×D236—41no—
84C2×D236—41no—
85C2×D236—41no—
86C2×D236—41no—
87C2×D236—82no—
88C2×D236—81no—
89C2×D236—81no—
90M16×C59—21no—
91M16×C59—21no—
92M16×C59—21no—
93M16×C59SD1612yescomplemented
94C2×C8×C59—21no—
95C2×C8×C59—21no—
96C2×C8×C59—21no—
97C2×C8×C59—21no—
98C2×C8×C59—41no—
99C2×C8×C59—41no—
100C4⋊C4×C59—22no—
101C4⋊C4×C59—21no—
102C4⋊C4×C59—21no—
103C4⋊C4×C59—21no—
104C4⋊C4×C59—22no—
105C4⋊C4×C59C22⋊C412yes—
106C22⋊C4×C59—22no—
107C42×C59—22no—
108C42×C59C2×D411yescharacteristic
109C42×C59C2×D411yescharacteristic
110C42×C59C2×D411yescharacteristic
111C42×C59#4111yescharacteristic
112#11745671—84no—
113#11745664—41no—
114#11745664—41no—
115C2×C59⋊C8—22no—
116C2×C59⋊C8—41no—
117C2×C59⋊C8—41no—
118C2×C59⋊C8—81no—
119C23×C59C4×D411yescharacteristic
120C22×D59—42no—
121C22×D59—42no—
122C22×D59—42no—
123C22×D59—82no—
124C22×D59—82no—
125Q8×C59—42no—
126Q8×C59—41no—
127Q8×C59—41no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—22no—
131C2×C4×C59—22no—
132C2×C4×C59—41no—
133C2×C4×C59C2×C22⋊C411yescharacteristic
134C2×C4×C59C4×D411yescharacteristic
135C2×C4×C59#12011yescharacteristic
136C2×C4×C59#12111yescharacteristic
137C2×C4×C59#12111yescharacteristic
138C2×C4×C59#12311yescharacteristic
139C2×C4×C59C2×SD1611yescharacteristic
140C2×C4×C59#13511yescharacteristic
141C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C59#13711yescharacteristic
143D236—44no—
144D236—82no—
145D236—82no—
146D236—81no—
147D236—81no—
148D236—81no—
149D236—81no—
150D236—81no—
151D236—81no—
152C8×C59—22no—
153C8×C59—41no—
154C8×C59—41no—
155C8×C59—41no—
156C59⋊C8—42no—
157C59⋊C8—81no—
158C59⋊C8—81no—
159#9274—591nomaximal, Sylow
160C22×C59—21no—
161C22×C59—21no—
162C22×C59#38611yescharacteristic
163C22×C59C4×SD1611yescharacteristic
164C22×C59#44011yescharacteristic
165C2×D59—82no—
166C2×D59—82no—
167C2×D59—82no—
168C2×D59—162no—
169C2×D59—162no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—42no—
174C4×C59—42no—
175C4×C59#44811yescharacteristic
176C4×C59#44911yescharacteristic
177C4×C59#46011yescharacteristic
178C4×C59#46411yescharacteristic
179C4×C59#47111yescharacteristic
180C4×C59#47211yescharacteristic
181#3208—591no—
182#2962D5911yescharacteristic, complemented
183#1965—591no—
184#1550—591no—
185C2×#331—591no—
186#1301—591no—
187#1283—591no—
188C2×C59—21no—
189C2×C59—21no—
190C2×C59#188011yescharacteristic
191C2×C59#190711yescharacteristic
192C2×C59#191411yescharacteristic
193D59—162no—
194#533C2×D5911yescharacteristic
195C2×#127—591no—
196#492—1181no—
197#486—1181no—
198#460—1182no—
199#450—594no—
200#446—22no—
201#446—21no—
202C8×Q8—21no—
203#431—591no—
204#424—21no—
205#423—591no—
206C2×C4⋊C8—591no—
207C2×C4⋊C8C2×D5911yescharacteristic
208C2×#100—1181no—
209C2×#100—1181no—
210#405—21no—
211C4×M16C2×D5911yescharacteristic
212#333—1181no—
213#332—1181no—
214#331—1181no—
215#331—1181no—
216C59#927411yescharacteristic, complemented, Sylow
217C22×D4—592no—
218C22×D4—1181no—
219C22×D4—1181no—
220C2×SD16—1184no—
221C2×M16—1181no—
222C2×M16C22⋊D5911yescharacteristic
223C2×M16C22⋊D5911yescharacteristic
224C22×C8—21no—
225C22×C8—1181no—
226C4⋊Q8D23611yescharacteristic
227C4⋊Q8D23611yescharacteristic
228#127—1181no—
229#127—1181no—
230#127—1181no—
231#127—1181no—
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8C4×D5912yes—
235C4×Q8—21no—
236C4×Q8C22⋊D5912yes—
237#117—21no—
238C2×C42C22×D5911yescharacteristic
239C4⋊C8—22no—
240C4⋊C8—22no—
241C4⋊C8—21no—
242C4⋊C8—1181no—
243C4⋊C8—1181no—
244C4⋊C8—1181no—
245C4⋊C8—1181no—
246C4⋊C8—1181no—
247C4⋊C8C22⋊D5911yescharacteristic
248C4⋊C8C22⋊D5911yescharacteristic
249#102—1184no—
250#100—2362no—
251#100—2362no—
252C22⋊C8—592no—
253#97—22no—
254#97—21no—
255C4×C8—22no—
256C4×C8—21no—
257C4×C8—1181no—
258C24—1182no—
259C2×Q8—21no—
260C2×Q8(C2×D59)⋊C412yes—
261C2×D4—1182no—
262C2×D4—1182no—
263C2×D4—4721no—
264C2×D4—4721no—
265C2×D4—4722no—
266C2×D4—2361no—
267C2×D4—2361no—
268C2×D4—2361no—
269C2×D4—2361no—
270C2×D4—2361no—
271C2×D4—2361no—
272C2×D4—2361no—
273C2×D4—2361no—
274C22×C4C2×C4×D5911yescharacteristic
275C22×C4#1174568511yescharacteristic
276C22×C4C2×C22⋊D5911yescharacteristic
277SD16—4724no—
278M16—21no—
279M16—21no—
280M16—21no—
281M16—2361no—
282M16—2361no—
283M16#1174567112yescomplemented
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—1182no—
291C2×C8—4721no—
292C2×C8—2361no—
293C2×C8—2361no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4(C2×D59)⋊C412yes—
300C22⋊C4—22no—
301C42—22no—
302C42C2×D23611yescharacteristic
303C42#1174568511yescharacteristic
304C42C2×C22⋊D5911yescharacteristic
305C42C2×C22⋊D5911yescharacteristic
306C23—4722no—
307C23—4722no—
308C23—2362no—
309C23—2362no—
310C23—2362no—
311C23C4×C22⋊D5911yescharacteristic
312Q8—42no—
313Q8—41no—
314Q8—41no—
315D4—4722no—
316D4—4722no—
317D4—4721no—
318D4—4721no—
319D4—4721no—
320D4—4721no—
321D4—4721no—
322D4—4721no—
323D4—2364no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4C2×(C2×D59)⋊C411yescharacteristic
330C2×C4C4×C22⋊D5911yescharacteristic
331C2×C4#1427369611yescharacteristic
332C2×C4#1427370111yescharacteristic
333C2×C4#1427370111yescharacteristic
334C2×C4#1427371011yescharacteristic
335C2×C4C2×#1174567111yescharacteristic
336C2×C4#1427374711yescharacteristic
337C2×C4#1427375211yescharacteristic
338C2×C4#1427375811yescharacteristic
339C8—22no—
340C8—41no—
341C8—41no—
342C8—41no—
343C8—4721no—
344C8—4721no—
345C8—2362no—
346C22—21no—
347C22—21no—
348C22—9442no—
349C22—9442no—
350C22—4722no—
351C22—4722no—
352C22—4722no—
353C22#1683728111yescharacteristic
354C22C4×#1174567111yescharacteristic
355C22#1683750011yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4#1683754111yescharacteristic
362C4#1683754711yescharacteristic
363C4#1683760211yescharacteristic
364C4#1683762411yescharacteristic
365C4#1683766511yescharacteristic
366C4#1683767211yescharacteristic
367C2—21no—
368C2—21no—
369C2—9442no—
370C2#2142445111yescharacteristic
371C2#2142460411yescharacteristic
372C2#2142464311yescharacteristic
subgroupG/H
centerC22#16837281
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2962C2
socleC22×C59#386
prime radicalC2×#14273724C22
cosocleC2×C42×C59C23
hypercenter#2962D59
hypocenterC59#9274
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #21422786C2semidirect
5. #21421993C2semidirect
6. #21421947C2semidirect
7. C59×#2962C2semidirect
93. M16×C59SD16semidirect
182. #2962D59semidirect
216. C59#9274semidirect
283. M16#11745671semidirect

Maximal subgroups

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

subgroupindex
#214350342
#214249362
#214227862
C2×#168371452
#214219932
#214219472
C59×#29622
#927459