Finite Group Databasebeta

← #28483774

Subgroups — #28483774

Order 15104.

516 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 111 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#21433181C211yesmaximal, characteristic, complemented
2C4×#14273646C211yesmaximal, characteristic, complemented
3#21422539C212yesmaximal
4#21421989C212yesmaximal, complemented
5C59×#2398C211yesmaximal, characteristic
6#16837533—24no—
7#16837459—21no—
8#16837459C2212yes—
9#16837455—21no—
10C2×#14273646—21no—
11C4×#11745664C2212yes—
12#16837171—21no—
13D4⋊(C59⋊C8)—24no—
14C2×C4×Q8×C59C2211yescharacteristic
15C2×C4×D4×C59C2211yescharacteristic
16C59×#400C411yescharacteristic
17C59×#400C411yescharacteristic
18C59×#397—21no—
19C59×#394C411yescharacteristic
20C59×#394C411yescharacteristic
21C59×#393—21no—
22C4×C22⋊C4×C59—21no—
23C4×C22⋊C4×C59—21no—
24C59×#376C2211yescharacteristic
25C2×#11745664—22no—
26C4⋊(C59⋊C8)—22no—
27C4⋊(C59⋊C8)—22no—
28C4⋊(C59⋊C8)D414yes—
29#14273646—24no—
30C22⋊(C59⋊C8)—22no—
31#14273638—22no—
32#14273638—22no—
33#14273638—22no—
34C4×C59⋊C8—22no—
35C4×C59⋊C8—22no—
36C22×Q8×C59D411yescharacteristic
37C22×D4×C59C2×C411yescharacteristic
38C23×C4×C59—21no—
39C4×Q8×C59—22no—
40C4×Q8×C59—22no—
41C4×D4×C59—22no—
42C4×D4×C59—22no—
43C2×C4⋊C4×C59C2×C411yescharacteristic
44C2×C4⋊C4×C59C2×C411yescharacteristic
45C2×C4⋊C4×C59C2×C411yescharacteristic
46C2×C4⋊C4×C59D411yescharacteristic
47C2×C22⋊C4×C59—21no—
48C2×C22⋊C4×C59—21no—
49C2×C22⋊C4×C59—21no—
50C2×C22⋊C4×C59—21no—
51C2×C22⋊C4×C59—21no—
52C2×C42×C59—21no—
53C2×C42×C59D411yescharacteristic
54C2×C42×C59D411yescharacteristic
55C2×C42×C59C2311yescharacteristic
56#95×C59—21no—
57#95×C59—21no—
58#95×C59—21no—
59#95×C59—21no—
60#95×C59—21no—
61#95×C59C2×C411yescharacteristic
62#95×C59C2×C411yescharacteristic
63C24×C59—21no—
64C2×Q8×C59—22no—
65C2×Q8×C59—22no—
66C2×Q8×C59—41no—
67C2×D4×C59—22no—
68C2×D4×C59—42no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—42no—
73C22×C4×C59—42no—
74C22×C4×C59—41no—
75C22×C4×C59—41no—
76C22×C4×C59C22⋊C411yescharacteristic
77C22×C4×C59C22⋊C411yescharacteristic
78C22×C4×C59C22⋊C411yescharacteristic
79C22×C4×C59C22⋊C411yescharacteristic
80C22×C4×C59C22×C411yescharacteristic
81C22×C4×C59C2×D411yescharacteristic
82C22×C4×C59C2×D411yescharacteristic
83C4⋊C4×C59—22no—
84C4⋊C4×C59—22no—
85C4⋊C4×C59—22no—
86C4⋊C4×C59—22no—
87C22⋊C4×C59—42no—
88C22⋊C4×C59—42no—
89C22⋊C4×C59—42no—
90C22⋊C4×C59—42no—
91C22⋊C4×C59—42no—
92C42×C59—21no—
93C42×C59—21no—
94C42×C59—21no—
95C42×C59—21no—
96C42×C59—42no—
97C42×C59C2×D412yes—
98C42×C59#4112yes—
99#11745664—24no—
100#11745664—42no—
101C2×C59⋊C8—24no—
102C2×C59⋊C8—42no—
103C23×C59—22no—
104C23×C59—41no—
105C23×C59—41no—
106C23×C59—41no—
107C23×C59—41no—
108C23×C59—41no—
109C23×C59—41no—
110C23×C59C2×C22⋊C411yescharacteristic
111Q8×C59—44no—
112D4×C59—24no—
113D4×C59—42no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—22no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—82no—
137C2×C4×C59—82no—
138C2×C4×C59#10412yes—
139C2×C4×C59C4×D412yes—
140C2×C4×C59#12011yescharacteristic
141C2×C4×C59#12112yes—
142C2×C4×C59#12311yescharacteristic
143C59⋊C8—44no—
144C59⋊C8—44no—
145#9032—591nomaximal, Sylow
146C22×C59—21no—
147C22×C59—21no—
148C22×C59—42no—
149C22×C59—42no—
150C22×C59—42no—
151C22×C59—81no—
152C22×C59—81no—
153C22×C59—81no—
154C22×C59—81no—
155C22×C59#38611yescharacteristic
156C22×C59C2×#10411yescharacteristic
157C22×C59#42111yescharacteristic
158C4×C59—22no—
159C4×C59—22no—
160C4×C59—21no—
161C4×C59—22no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—81no—
166C4×C59—81no—
167C4×C59—81no—
168C4×C59#45412yes—
169#2983—591no—
170#2398D5911yescharacteristic
171C4×#101—591no—
172#1490—592no—
173#1300—592no—
174C2×C59—21no—
175C2×C59—21no—
176C2×C59—82no—
177C2×C59#187111yescharacteristic
178C2×C59#188811yescharacteristic
179C2×C59#189111yescharacteristic
180C2×C4×Q8C2×D5911yescharacteristic
181C2×C4×D4C2×D5911yescharacteristic
182#446—1184no—
183#432—592no—
184#432—1181no—
185#431—1181no—
186C2×#101—1181no—
187C4×M16—592no—
188#400Dic5911yescharacteristic
189#400Dic5911yescharacteristic
190#397—21no—
191#394Dic5911yescharacteristic
192#394Dic5911yescharacteristic
193#393—21no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196#376C2×D5911yescharacteristic
197#343—1181no—
198D4⋊C8—1184no—
199C59#903211yescharacteristic, complemented, Sylow
200C22×Q8C22⋊D5911yescharacteristic
201C22×D4C2×Dic5911yescharacteristic
202C23×C4—21no—
203C2×M16—1182no—
204C4×Q8—22no—
205C4×Q8—22no—
206C4×D4—22no—
207C4×D4—22no—
208C2×C4⋊C4C2×Dic5911yescharacteristic
209C2×C4⋊C4C2×Dic5911yescharacteristic
210C2×C4⋊C4C2×Dic5911yescharacteristic
211C2×C4⋊C4C22⋊D5911yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C42—21no—
218C2×C42C22⋊D5911yescharacteristic
219C2×C42C22⋊D5911yescharacteristic
220C2×C42C22×D5911yescharacteristic
221C4⋊C8—594no—
222C4⋊C8—1182no—
223C4⋊C8—1182no—
224#101—1184no—
225C22⋊C8—1182no—
226#97—1182no—
227#97—1182no—
228#97—1182no—
229C4×C8—1182no—
230C4×C8—1182no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95C2×Dic5911yescharacteristic
237#95C2×Dic5911yescharacteristic
238C24—21no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×D4—22no—
243C2×D4—42no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C22⋊Dic5911yescharacteristic
252C22×C4C22⋊Dic5911yescharacteristic
253C22×C4C22⋊Dic5911yescharacteristic
254C22×C4C22⋊Dic5911yescharacteristic
255C22×C4C22×Dic5911yescharacteristic
256C22×C4C2×C22⋊D5911yescharacteristic
257C22×C4C2×C22⋊D5911yescharacteristic
258M16—1184no—
259M16—2362no—
260C2×C8—1184no—
261C2×C8—2362no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—42no—
276C42D4×D5912yes—
277C42#1174568712yes—
278C23—22no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23C2×C22⋊Dic5911yescharacteristic
286Q8—44no—
287D4—24no—
288D4—42no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4#1427365412yes—
314C2×C4D4×Dic5912yes—
315C2×C4#1427369511yescharacteristic
316C2×C4#1427369912yes—
317C2×C4#1427370811yescharacteristic
318C8—2364no—
319C8—2364no—
320C22—21no—
321C22—21no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#1683728211yescharacteristic
330C22C2×#1427365411yescharacteristic
331C22#1683741911yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4#1683757412yes—
343C2—21no—
344C2—21no—
345C2—82no—
346C2#2142439911yescharacteristic
347C2#2142450011yescharacteristic
348C2#2142451511yescharacteristic
subgroupG/H
centerC2×C4#14273695
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2398C2
socleC22×C59#386
prime radicalC22×D4×C59C2×C4
cosocleC2×C42×C59C23
hypercenter#2398D59
hypocenterC59#9032
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. #21433181C2semidirect
2. C4×#14273646C2semidirect
4. #21421989C2semidirect
199. C59#9032semidirect

Maximal subgroups

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

subgroupindex
#214331812
C4×#142736462
#214225392
#214219892
C59×#23982
#903259