Finite Group Databasebeta

← #28490007

Subgroups — #28490007

Order 15104.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837812C211yesmaximal, characteristic
2C2×#16837772C211yesmaximal, characteristic
3#21425068C211yesmaximal, characteristic
4C2×#16837144C211yesmaximal, characteristic
5C2×#16837144C211yesmaximal, characteristic
6#21421977C211yesmaximal, characteristic
7C59×#2822C211yesmaximal, characteristic
8C2×#14273727C2211yescharacteristic
9#16837812—22no—
10#16837812—22no—
11#16837772—22no—
12#16837772—22no—
13C2×#14273660—21no—
14C2×#14273658—21no—
15C2×#14273650—21no—
16C2×#14273650—21no—
17C2×#14273638C2211yescharacteristic
18C2×#14273638C2211yescharacteristic
19C2×#14273638C2211yescharacteristic
20#16837164—22no—
21#16837144—22no—
22#16837144—22no—
23C2×#125×C59C2211yescharacteristic
24C2×#125×C59C2211yescharacteristic
25C59×#400—21no—
26C59×#400—21no—
27C59×#398—22no—
28C59×#398—21no—
29C59×#398—21no—
30C59×#382C2211yescharacteristic
31C22×Dic118—21no—
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34C22×C59⋊C8—21no—
35#14273727—21no—
36#14273727—21no—
37#14273727—21no—
38#14273727D412yes—
39C2×C4⋊Dic59—21no—
40C2×C4⋊Dic59—21no—
41#14273660—24no—
42#14273658—24no—
43#14273650—24no—
44#14273650—24no—
45#14273638—21no—
46#14273638—21no—
47#14273638—21no—
48#14273638—21no—
49#14273638D412yes—
50#14273638D412yes—
51#125×C59—21no—
52#125×C59—21no—
53#125×C59—21no—
54#125×C59—21no—
55#125×C59—21no—
56#125×C59—21no—
57#125×C59—21no—
58#125×C59—21no—
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59—21no—
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59—21no—
63C2×C4⋊C4×C59—22no—
64C2×C4⋊C4×C59D411yescharacteristic
65C2×C4⋊C4×C59D411yescharacteristic
66C2×C4⋊C4×C59D411yescharacteristic
67C2×C4⋊C4×C59D411yescharacteristic
68C2×C4⋊C4×C59D412yes—
69C2×C42×C59C2311yescharacteristic
70#95×C59—22no—
71#95×C59—22no—
72#95×C59—22no—
73#95×C59—21no—
74#95×C59—21no—
75C22×C4×C59—22no—
76C22×C4×C59—21no—
77C22×C4×C59—21no—
78C22×C4×C59—21no—
79C22×C4×C59—21no—
80C22×C4×C59C2×D411yescharacteristic
81C22×C4×C59C2×D411yescharacteristic
82C22×C4×C59C2×D411yescharacteristic
83C22×Dic59—41no—
84C2×Dic118—22no—
85C2×Dic118—44no—
86C2×Dic118—41no—
87C4⋊C4×C59—21no—
88C4⋊C4×C59—21no—
89C4⋊C4×C59—21no—
90C4⋊C4×C59—21no—
91C4⋊C4×C59—21no—
92C4⋊C4×C59—21no—
93C4⋊C4×C59—21no—
94C4⋊C4×C59—21no—
95C4⋊C4×C59—42no—
96C4⋊C4×C59—41no—
97C4⋊C4×C59—41no—
98C4⋊C4×C59—41no—
99C4⋊C4×C59—41no—
100C4⋊C4×C59—41no—
101C4⋊C4×C59—41no—
102C4⋊C4×C59—41no—
103C4⋊C4×C59—41no—
104C4⋊C4×C59—82no—
105C42×C59C2×D411yescharacteristic
106C42×C59C2×D411yescharacteristic
107C42×C59C2×D411yescharacteristic
108C42×C59#4111yescharacteristic
109C4⋊Dic59—22no—
110C4⋊Dic59—22no—
111C4⋊Dic59—41no—
112C4⋊Dic59—41no—
113C2×C59⋊C8—24no—
114C2×C59⋊C8—22no—
115C2×C59⋊C8—22no—
116C2×C59⋊C8—22no—
117C2×C59⋊C8—42no—
118C2×C59⋊C8—41no—
119C2×C59⋊C8—41no—
120C23×C59#12011yescharacteristic
121C2×C4×C59—22no—
122C2×C4×C59—21no—
123C2×C4×C59—22no—
124C2×C4×C59—21no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—42no—
130C2×C4×C59—42no—
131C2×C4×C59—42no—
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59—42no—
135C2×C4×C59—42no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59#12011yescharacteristic
139C2×C4×C59#12011yescharacteristic
140C2×C4×C59#12111yescharacteristic
141C2×C4×C59#12111yescharacteristic
142C2×C4×C59#12111yescharacteristic
143C2×C4×C59#12711yescharacteristic
144C2×Dic59—42no—
145C2×Dic59—82no—
146Dic118—44no—
147Dic118—82no—
148C59⋊C8—24no—
149C59⋊C8—42no—
150C59⋊C8—42no—
151#10084—591nomaximal, Sylow
152C22×C59#39211yescharacteristic
153C22×C59#45412yes—
154C22×C59#45511yescharacteristic
155C22×C59#45611yescharacteristic
156C22×C59#45612yes—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—82no—
164C4×C59—81no—
165C4×C59—81no—
166C4×C59—81no—
167C4×C59—81no—
168Dic59—82no—
169C2×#501—591no—
170C2×#491—591no—
171#2822D5911yescharacteristic
172#1993—591no—
173C2×#330—591no—
174C2×#330—591no—
175#1295—591no—
176C2×C59#166312yes—
177C2×C59#166412yes—
178C2×C59#200311yescharacteristic
179C2×C59#200511yescharacteristic
180C2×C59#200711yescharacteristic
181C2×C4⋊Q8—591no—
182C2×#125C2×D5911yescharacteristic
183C2×#125C2×D5911yescharacteristic
184#501—1182no—
185#501—1182no—
186#491—1182no—
187#491—1182no—
188C2×#107—1181no—
189C2×#106—1181no—
190C2×#103—1181no—
191C2×#103—1181no—
192C2×#97—591no—
193C2×#97—591no—
194C2×#97—591no—
195#400—21no—
196#400—21no—
197#398—22no—
198#398—21no—
199#398—21no—
200#382C2×D5911yescharacteristic
201#340—1182no—
202#330—1182no—
203#330—1182no—
204C59#1008411yescharacteristic, complemented, Sylow
205C22×Q8—1181no—
206C22×C8—1181no—
207C22×C8—1181no—
208C22×C8—1181no—
209C4⋊Q8—592no—
210C4⋊Q8—1181no—
211C4⋊Q8—1181no—
212C4⋊Q8—1181no—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#125—21no—
219#125—21no—
220#125—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—1181no—
227C2×C4⋊C4—1181no—
228C2×C4⋊C4C22⋊D5911yescharacteristic
229C2×C4⋊C4C22⋊D5911yescharacteristic
230C2×C4⋊C4C22⋊D5911yescharacteristic
231C2×C4⋊C4C22⋊D5911yescharacteristic
232C2×C4⋊C4C22⋊D5912yes—
233C2×C42C22×D5911yescharacteristic
234#107—1184no—
235#106—1184no—
236#103—1184no—
237#103—1184no—
238#97—592no—
239#97—592no—
240#97—1181no—
241#97—1181no—
242#97—1181no—
243#97—1181no—
244#95—22no—
245#95—22no—
246#95—22no—
247#95—21no—
248#95—21no—
249C2×Q8—1182no—
250C2×Q8—2364no—
251C2×Q8—2361no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—2361no—
258C22×C4C2×C22⋊D5911yescharacteristic
259C22×C4C2×C22⋊D5911yescharacteristic
260C22×C4C2×C22⋊D5911yescharacteristic
261C2×C8—1184no—
262C2×C8—1182no—
263C2×C8—1182no—
264C2×C8—1182no—
265C2×C8—2362no—
266C2×C8—2361no—
267C2×C8—2361no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—82no—
286C4⋊C4—1182no—
287C4⋊C4—1182no—
288C4⋊C4—2361no—
289C4⋊C4—2361no—
290C42D4×D5911yescharacteristic
291C42D4×D5911yescharacteristic
292C42D4×D5911yescharacteristic
293C42#1174568711yescharacteristic
294C23#1427369611yescharacteristic
295Q8—4722no—
296Q8—2364no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—4722no—
315C2×C4—2362no—
316C2×C4#1427369511yescharacteristic
317C2×C4#1427369511yescharacteristic
318C2×C4#1427369811yescharacteristic
319C2×C4#1427369911yescharacteristic
320C2×C4#1427369911yescharacteristic
321C2×C4#1427372311yescharacteristic
322C8—1184no—
323C8—2362no—
324C8—2362no—
325C22#1683731011yescharacteristic
326C22#1683757512yes—
327C22#1683758011yescharacteristic
328C22#1683758511yescharacteristic
329C22#1683758512yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—4722no—
342C2#2142342412yes—
343C2#2142343012yes—
344C2#2142511611yescharacteristic
345C2#2142513011yescharacteristic
346C2#2142514311yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2822C2
socle, prime radicalC23×C59#120
hypercenter#2822D59
hypocenterC59#10084
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
204. C59#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#168378122
C2×#168377722
#214250682
C2×#168371442
#214219772
C59×#28222
#1008459