Finite Group Databasebeta

← #28483756

Subgroups — #28483756

Order 15104.

534 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 103 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
1#21433125C211yesmaximal, characteristic
2#21427380C211yesmaximal, characteristic
3#21422544C212yesmaximal, complemented
4#21421990C212yesmaximal, complemented
5C4×#100×C59C211yesmaximal, characteristic
6C2×C4×Dic118C2211yescharacteristic
7#16837474—24no—
8#16837459C2212yes—
9#16837366—21no—
10C2×C22⋊(C59⋊C8)—21no—
11#16837340—21no—
12#16837327C411yescharacteristic
13#16837327C411yescharacteristic
14#16837316—21no—
15#16837314C411yescharacteristic
16#16837314C411yescharacteristic
17C4×C22⋊Dic59—21no—
18C4×C22⋊Dic59—21no—
19#16837248C2211yescharacteristic
20#16837134—24no—
21C2×C4×D4×C59C2211yescharacteristic
22C2×#100×C59—21no—
23C4×M16×C59C2212yes—
24C59×#343—21no—
25C22×Dic118C2×C411yescharacteristic
26C2×#11745664—22no—
27C22×C59⋊C8—22no—
28C4×Dic118—22no—
29C4×Dic118—22no—
30C2×C4⋊Dic59C2×C411yescharacteristic
31C2×Dic59⋊C4—21no—
32C2×C22⋊Dic59—21no—
33C2×C22⋊Dic59—21no—
34C2×C22⋊Dic59—21no—
35C2×C22⋊Dic59—21no—
36C2×C4×Dic59—21no—
37C2×C4×Dic59—21no—
38C4⋊(C59⋊C8)D414yes—
39C22⋊(C59⋊C8)—22no—
40C22⋊(C59⋊C8)—22no—
41C22⋊(C59⋊C8)—22no—
42#14273638—22no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95C2×C411yescharacteristic
49C59⋊#95C2×C411yescharacteristic
50C22×D4×C59D411yescharacteristic
51C23×C4×C59D411yescharacteristic
52C23×C4×C59D411yescharacteristic
53C2×M16×C59—22no—
54C4×D4×C59—22no—
55C4×D4×C59—22no—
56C2×C4⋊C4×C59D411yescharacteristic
57C2×C22⋊C4×C59C2×C411yescharacteristic
58C2×C22⋊C4×C59C2×C411yescharacteristic
59C2×C42×C59C2311yescharacteristic
60#100×C59—24no—
61#97×C59—22no—
62C4×C8×C59—22no—
63C24×C59C22⋊C411yescharacteristic
64C24×C59C22⋊C411yescharacteristic
65C2×D4×C59—22no—
66C2×D4×C59—22no—
67C2×D4×C59—41no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—42no—
73C22×C4×C59—42no—
74C22×C4×C59C22⋊C411yescharacteristic
75C22×C4×C59C22⋊C411yescharacteristic
76C22×C4×C59C22×C411yescharacteristic
77C22×C4×C59C2×D411yescharacteristic
78C22×C4×C59C2×D411yescharacteristic
79C22×Dic59—21no—
80C22×Dic59—21no—
81C22×Dic59—21no—
82C22×Dic59—21no—
83C2×Dic118—22no—
84C2×Dic118—42no—
85M16×C59—24no—
86M16×C59—42no—
87C2×C8×C59—42no—
88C4⋊C4×C59—22no—
89C22⋊C4×C59—22no—
90C22⋊C4×C59—22no—
91C42×C59C2×D412yes—
92C42×C59#4112yes—
93C22⋊Dic59—42no—
94C22⋊Dic59—42no—
95C22⋊Dic59—42no—
96C22⋊Dic59—42no—
97C4⋊Dic59—22no—
98Dic59⋊C4—42no—
99C4×Dic59—42no—
100C4×Dic59—41no—
101C4×Dic59—41no—
102#11745664—82no—
103C2×C59⋊C8—24no—
104C2×C59⋊C8—82no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—41no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59—41no—
114C23×C59#10412yes—
115C23×C59C2×C22⋊C411yescharacteristic
116D4×C59—44no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—22no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—41no—
123C2×C4×C59—42no—
124C2×C4×C59—42no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—81no—
128C2×C4×C59—81no—
129C2×C4×C59C4×D412yes—
130C2×C4×C59#12011yescharacteristic
131C2×C4×C59#12112yes—
132C2×C4×C59#12311yescharacteristic
133C2×Dic59—22no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145Dic118—24no—
146Dic118—42no—
147C8×C59—44no—
148C59⋊C8—44no—
149#9029—591nomaximal, Sylow
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—22no—
153C22×C59—42no—
154C22×C59—42no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—81no—
161C22×C59—81no—
162C22×C59#38611yescharacteristic
163C22×C59C2×#10411yescharacteristic
164C22×C59#42111yescharacteristic
165C4×C59—22no—
166C4×C59—21no—
167C4×C59—22no—
168C4×C59—41no—
169C4×C59—41no—
170C4×C59#45512yes—
171Dic59—42no—
172Dic59—81no—
173Dic59—81no—
174Dic59—81no—
175#2973—591no—
176#2398—591no—
177C4×#100D5911yescharacteristic
178#1491—592no—
179#1300—592no—
180C2×C59—21no—
181C2×C59—21no—
182C2×C59—42no—
183C2×C59—81no—
184C2×C59#187111yescharacteristic
185C2×C59#188511yescharacteristic
186C2×C59#189111yescharacteristic
187C2×C4×Q8—591no—
188C2×C4×D4C2×D5911yescharacteristic
189#435—1184no—
190#432—592no—
191C2×#100—21no—
192#407—1181no—
193C2×C22⋊C8—1181no—
194C4×M16C2×D5912yes—
195#400—1181no—
196#397—591no—
197#397—591no—
198#394—1181no—
199#393—591no—
200#393—591no—
201C4×C22⋊C4—1181no—
202C4×C22⋊C4—1181no—
203#376—591no—
204#343—21no—
205Q8⋊C8—1184no—
206C59#902911yescharacteristic, complemented, Sylow
207C22×Q8—591no—
208C22×D4C22⋊D5911yescharacteristic
209C23×C4D23611yescharacteristic
210C23×C4D23611yescharacteristic
211C2×M16—22no—
212C2×M16—1182no—
213C22×C8—1182no—
214C4×Q8—1182no—
215C4×Q8—1182no—
216C4×D4—22no—
217C4×D4—22no—
218C2×C4⋊C4—591no—
219C2×C4⋊C4—1181no—
220C2×C4⋊C4C22⋊D5911yescharacteristic
221C2×C22⋊C4—1181no—
222C2×C22⋊C4—1181no—
223C2×C22⋊C4—1181no—
224C2×C22⋊C4—1181no—
225C2×C22⋊C4C4×D5911yescharacteristic
226C2×C22⋊C4C4×D5911yescharacteristic
227C2×C42—1181no—
228C2×C42—1181no—
229C2×C42C22×D5911yescharacteristic
230C4⋊C8—594no—
231#100—24no—
232C22⋊C8—1182no—
233C22⋊C8—1182no—
234C22⋊C8—1182no—
235#97—22no—
236#97—1182no—
237C4×C8—22no—
238#95—591no—
239#95—591no—
240#95—1181no—
241#95—1181no—
242#95—1181no—
243#95—1181no—
244#95—1181no—
245C24(C2×D59)⋊C411yescharacteristic
246C24(C2×D59)⋊C411yescharacteristic
247C2×Q8—1182no—
248C2×Q8—2362no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4—1181no—
262C22×C4(C2×D59)⋊C411yescharacteristic
263C22×C4(C2×D59)⋊C411yescharacteristic
264C22×C4C2×C4×D5911yescharacteristic
265C22×C4C2×D23611yescharacteristic
266C22×C4C2×C22⋊D5911yescharacteristic
267M16—24no—
268M16—42no—
269M16—4722no—
270C2×C8—42no—
271C2×C8—1184no—
272C2×C8—4722no—
273C4⋊C4—22no—
274C4⋊C4—1182no—
275C4⋊C4—2362no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—2362no—
279C22⋊C4—2362no—
280C22⋊C4—2362no—
281C22⋊C4—2362no—
282C42—2362no—
283C42—2361no—
284C42—2361no—
285C42D4×D5912yes—
286C42#1174568712yes—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#1427365512yes—
297C23C2×(C2×D59)⋊C411yescharacteristic
298Q8—1184no—
299Q8—2362no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—1182no—
314C2×C4—2361no—
315C2×C4—2361no—
316C2×C4—2361no—
317C2×C4—2361no—
318C2×C4—2361no—
319C2×C4—2361no—
320C2×C4—2361no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4—2361no—
325C2×C4(C22⋊D59)⋊C412yes—
326C2×C4#1427369711yescharacteristic
327C2×C4#1427369912yes—
328C2×C4#1427371111yescharacteristic
329C8—44no—
330C8—2364no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22#1683727911yescharacteristic
344C22C2×#1427365511yescharacteristic
345C22#1683742011yescharacteristic
346C4—22no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—4721no—
352C4—4721no—
353C4—4721no—
354C4—2362no—
355C4#1683758212yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#2142439611yescharacteristic
361C2#2142448211yescharacteristic
362C2#2142451211yescharacteristic
subgroupG/H
centerC2×C4#14273697
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC4×#100×C59C2
socleC22×C59#386
prime radicalC22×D4×C59D4
cosocleC2×C42×C59C23
hypercenterC4×#100D59
hypocenterC59#9029
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
3. #21422544C2semidirect
4. #21421990C2semidirect
206. C59#9029semidirect

Maximal subgroups

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

subgroupindex
#214331252
#214273802
#214225442
#214219902
C4×#100×C592
#902959