Finite Group Databasebeta

← #28499210

Subgroups — #28499210

Order 15104.

488 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16837171C211yesmaximal, characteristic, complemented
2#21422426C211yesmaximal, characteristic, complemented
3#21422123C212yesmaximal, complemented
4#21422099C212yesmaximal, complemented
5C59×#2591C211yesmaximal, characteristic
6C22×#11745664—21no—
7#16837366—21no—
8#16837171—21no—
9#16837171C2212yes—
10#16837128—21no—
11#16837128C2212yes—
12C2×#121×C59C411yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C59×#400C411yescharacteristic
15C59×#400C2211yescharacteristic
16C59×#394C411yescharacteristic
17C59×#394C2211yescharacteristic
18C59×#388—21no—
19C59×#388—21no—
20C59×#386—21no—
21C59×#386—21no—
22C4×C22⋊C4×C59C411yescharacteristic
23C2×#11745664—24no—
24C2×#11745664—22no—
25C2×#11745664—41no—
26C2×#11745664—42no—
27C2×#11745664—41no—
28C22×C59⋊C8—41no—
29C22⋊(C59⋊C8)—22no—
30C22⋊(C59⋊C8)—41no—
31C22×D4×C59—21no—
32C22×D4×C59C2×C411yescharacteristic
33C23×C4×C59C2×C411yescharacteristic
34C23×C4×C59D411yescharacteristic
35C23×C4×C59D411yescharacteristic
36#121×C59—41no—
37#121×C59—41no—
38C2×C4⋊C4×C59—41no—
39C2×C4⋊C4×C59—41no—
40C2×C4⋊C4×C59C2×C411yescharacteristic
41C2×C4⋊C4×C59C2×C411yescharacteristic
42C2×C4⋊C4×C59D411yescharacteristic
43C2×C4⋊C4×C59D411yescharacteristic
44C2×C4⋊C4×C59C2311yescharacteristic
45C2×C22⋊C4×C59—21no—
46C2×C22⋊C4×C59—21no—
47C2×C22⋊C4×C59—21no—
48C2×C22⋊C4×C59—21no—
49C2×C22⋊C4×C59—21no—
50C2×C22⋊C4×C59—21no—
51C2×C42×C59—21no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59—21no—
55#95×C59—21no—
56#95×C59C2×C411yescharacteristic
57#95×C59C2×C411yescharacteristic
58C24×C59—21no—
59C24×C59C22⋊C411yescharacteristic
60C2×D4×C59—41no—
61C2×D4×C59—42no—
62C2×D4×C59—42no—
63C2×D4×C59—41no—
64C2×D4×C59—41no—
65C2×D4×C59—81no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—22no—
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×C59—21no—
76C22×C4×C59—21no—
77C22×C4×C59—21no—
78C22×C4×C59—81no—
79C22×C4×C59—81no—
80C22×C4×C59C22⋊C411yescharacteristic
81C22×C4×C59C22⋊C411yescharacteristic
82C22×C4×C59C22⋊C411yescharacteristic
83C22×C4×C59C22×C411yescharacteristic
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59C2×D411yescharacteristic
86C4⋊C4×C59—41no—
87C4⋊C4×C59—41no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C22⋊C4×C59—42no—
92C22⋊C4×C59—42no—
93C22⋊C4×C59—42no—
94C22⋊C4×C59—41no—
95C22⋊C4×C59—41no—
96C22⋊C4×C59—81no—
97C22⋊C4×C59—81no—
98C42×C59—81no—
99#11745664—24no—
100#11745664—44no—
101#11745664—42no—
102#11745664—82no—
103C2×C59⋊C8—44no—
104C2×C59⋊C8—42no—
105C2×C59⋊C8—42no—
106C23×C59—22no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—41no—
110C23×C59—41no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59—41no—
114C23×C59—41no—
115C23×C59—41no—
116C23×C59—41no—
117C23×C59#9911yescharacteristic
118C23×C59#9911yescharacteristic
119C23×C59C2×C22⋊C411yescharacteristic
120D4×C59—82no—
121D4×C59—82no—
122D4×C59—82no—
123C2×C4×C59—22no—
124C2×C4×C59—22no—
125C2×C4×C59—22no—
126C2×C4×C59—22no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—42no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59—41no—
140C2×C4×C59—41no—
141C2×C4×C59—41no—
142C2×C4×C59—41no—
143C2×C4×C59—41no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—81no—
150C2×C4×C59—81no—
151C2×C4×C59—81no—
152C2×C4×C59#10412yes—
153C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C59#13711yescharacteristic
155C59⋊C8—44no—
156C59⋊C8—82no—
157#11766—591nomaximal, Sylow
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—42no—
166C22×C59—42no—
167C22×C59—81no—
168C22×C59—81no—
169C22×C59—81no—
170C22×C59—81no—
171C22×C59—81no—
172C22×C59—81no—
173C22×C59—81no—
174C22×C59#35512yes—
175C22×C59C2×#9911yescharacteristic
176C22×C59#41711yescharacteristic
177C22×C59C2×#10411yescharacteristic
178C4×C59—21no—
179C4×C59—22no—
180C4×C59—21no—
181C4×C59—41no—
182C4×C59—41no—
183C4×C59—41no—
184C4×C59—41no—
185C4×C59—81no—
186C4×C59—81no—
187C4×C59—81no—
188#2591D5911yescharacteristic
189C2×#343—591no—
190#1463—591no—
191#1353—592no—
192#1345—592no—
193C2×C59—21no—
194C2×C59—21no—
195C2×C59—22no—
196C2×C59—41no—
197C2×C59—161no—
198C2×C59#150411yescharacteristic
199C2×C59#212111yescharacteristic
200C2×C59C2×#35511yescharacteristic
201C22×M16—1181no—
202C2×#121Dic5911yescharacteristic
203C22×C4⋊C4C2×D5911yescharacteristic
204#407—1181no—
205#400Dic5911yescharacteristic
206#400C2×D5911yescharacteristic
207#394Dic5911yescharacteristic
208#394C2×D5911yescharacteristic
209#388—21no—
210#388—21no—
211#386—21no—
212#386—21no—
213C4×C22⋊C4Dic5911yescharacteristic
214#343—592no—
215#343—1181no—
216#324—592no—
217#324—1181no—
218C59#1176611yescharacteristic, complemented, Sylow
219C22×D4—21no—
220C22×D4C2×Dic5911yescharacteristic
221C23×C4C2×Dic5911yescharacteristic
222C23×C4C22⋊D5911yescharacteristic
223C23×C4C22⋊D5911yescharacteristic
224C2×M16—1184no—
225C2×M16—1182no—
226C2×M16—2361no—
227C2×M16—2361no—
228C2×M16—2362no—
229C22×C8—2361no—
230#121—41no—
231#121—41no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4C2×Dic5911yescharacteristic
235C2×C4⋊C4C2×Dic5911yescharacteristic
236C2×C4⋊C4C22⋊D5911yescharacteristic
237C2×C4⋊C4C22⋊D5911yescharacteristic
238C2×C4⋊C4C22×D5911yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C42—21no—
246C22⋊C8—1182no—
247C22⋊C8—2361no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95C2×Dic5911yescharacteristic
253#95C2×Dic5911yescharacteristic
254C24—21no—
255C24C22⋊Dic5911yescharacteristic
256C2×D4—41no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—81no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—81no—
275C22×C4—81no—
276C22×C4C22⋊Dic5911yescharacteristic
277C22×C4C22⋊Dic5911yescharacteristic
278C22×C4C22⋊Dic5911yescharacteristic
279C22×C4C22×Dic5911yescharacteristic
280C22×C4C2×C22⋊D5911yescharacteristic
281C22×C4C2×C22⋊D5911yescharacteristic
282M16—1184no—
283M16—4722no—
284M16—2364no—
285M16—2362no—
286C2×C8—2362no—
287C2×C8—2364no—
288C2×C8—2362no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C42—81no—
302C23—21no—
303C23—21no—
304C23—22no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#1427364211yescharacteristic
314C23#1427364211yescharacteristic
315C23C2×C22⋊Dic5911yescharacteristic
316D4—82no—
317D4—82no—
318D4—82no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4#1427365412yes—
349C2×C4#1427375211yescharacteristic
350C2×C4#1427375711yescharacteristic
351C8—4722no—
352C8—2364no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22#1683719912yes—
370C22C2×#1427364211yescharacteristic
371C22#1683740311yescharacteristic
372C22C2×#1427365411yescharacteristic
373C4—21no—
374C4—22no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—81no—
381C4—81no—
382C4—81no—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—41no—
387C2—161no—
388C2#2142260011yescharacteristic
389C2#2142574211yescharacteristic
390C2C2×#1683719911yescharacteristic
subgroupG/H
centerC22C2×#14273642
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#2591C2
socleC22×C59C2×#99
prime radicalC2×#121×C59C4
cosocleC2×C4⋊C4×C59C23
hypercenter#2591D59
hypocenterC59#11766
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
1. C2×#16837171C2semidirect
2. #21422426C2semidirect
3. #21422123C2semidirect
4. #21422099C2semidirect
218. C59#11766semidirect

Maximal subgroups

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

subgroupindex
C2×#168371712
#214224262
#214221232
#214220992
C59×#25912
#1176659