Finite Group Databasebeta

← #28486056

Subgroups — #28486056

Order 15104.

506 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 117 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#21433176C211yesmaximal, characteristic
2#21429085C211yesmaximal, characteristic
3#21424089C211yesmaximal, characteristic
4#21422768C211yesmaximal, characteristic
5#21421998C211yesmaximal, characteristic
6#21421997C211yesmaximal, characteristic
7C59×#1546C211yesmaximal, characteristic
8C2×#14273725—21no—
9C2×C4×Dic118C2211yescharacteristic
10C8×Dic118—22no—
11#16837526—22no—
12#16837455C2211yescharacteristic
13#16837452—22no—
14#16837426C2211yescharacteristic
15C2×#14273645—21no—
16#16837333C414yes—
17#16837309—21no—
18#16837298—22no—
19C4×C4⋊Dic59C2211yescharacteristic
20#16837170—21no—
21#16837148—22no—
22C2×C4⋊Q8×C59C2211yescharacteristic
23C59×#431C2211yescharacteristic
24C59×#423C2211yescharacteristic
25C59×#332—22no—
26C22×Dic118D411yescharacteristic
27C2×#11745664—21no—
28#14273725—42no—
29#14273725—42no—
30C4×Dic118—21no—
31C4×Dic118—21no—
32C4×Dic118—21no—
33C4×Dic118—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59D411yescharacteristic
36C2×Dic59⋊C4—24no—
37C2×Dic59⋊C4C2×C412yes—
38C2×C4×Dic59—21no—
39C2×C4×Dic59D412yes—
40C4⋊(C59⋊C8)—21no—
41C4⋊(C59⋊C8)—21no—
42C4⋊(C59⋊C8)D412yes—
43Dic59⋊C8—24no—
44#14273645—42no—
45C22⋊(C59⋊C8)—21no—
46C4×C59⋊C8—21no—
47C8×Dic59—24no—
48C59⋊#95—24no—
49C59⋊#95C2×C412yes—
50C22×Q8×C59—21no—
51C2×M16×C59—21no—
52C4⋊Q8×C59—21no—
53C4⋊Q8×C59—21no—
54C4⋊Q8×C59—21no—
55C4⋊Q8×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59C2×C412yes—
58C2×C42×C59C2311yescharacteristic
59C4⋊C8×C59—21no—
60C4⋊C8×C59—21no—
61C4⋊C8×C59D412yes—
62C22⋊C8×C59—21no—
63C4×C8×C59—21no—
64C2×Q8×C59—41no—
65C2×Q8×C59—41no—
66C2×Q8×C59—41no—
67C2×Q8×C59—41no—
68C2×Q8×C59—41no—
69C2×Q8×C59—41no—
70C22×C4×C59—22no—
71C22×C4×C59C22×C411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×C4×C59C2×D411yescharacteristic
74C22×Dic59—22no—
75C22×Dic59C22⋊C412yes—
76C22×Dic59C22⋊C412yes—
77C2×Dic118—21no—
78C2×Dic118—21no—
79C2×Dic118—21no—
80C2×Dic118—21no—
81C2×Dic118D812yes—
82C2×Dic118SD1612yes—
83M16×C59—41no—
84M16×C59—41no—
85C2×C8×C59—22no—
86C2×C8×C59—41no—
87C4⋊C4×C59—22no—
88C4⋊C4×C59—22no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C42×C59C2×D411yescharacteristic
92C42×C59C2×D411yescharacteristic
93C42×C59#4111yescharacteristic
94C42×C59#4111yescharacteristic
95C4⋊Dic59—24no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98Dic59⋊C4—22no—
99Dic59⋊C4—22no—
100Dic59⋊C4—48no—
101C4×Dic59—22no—
102C4×Dic59—22no—
103C4×Dic59—41no—
104C4×Dic59—41no—
105#11745664—41no—
106#11745664—41no—
107C2×C59⋊C8—22no—
108C2×C59⋊C8—41no—
109C23×C59C2×C22⋊C411yescharacteristic
110Q8×C59—81no—
111Q8×C59—81no—
112Q8×C59—81no—
113Q8×C59—81no—
114C2×C4×C59—22no—
115C2×C4×C59—41no—
116C2×C4×C59—42no—
117C2×C4×C59—42no—
118C2×C4×C59—42no—
119C2×C4×C59C4×D411yescharacteristic
120C2×C4×C59C4×D411yescharacteristic
121C2×C4×C59#12011yescharacteristic
122C2×C4×C59#12111yescharacteristic
123C2×C4×C59#12111yescharacteristic
124C2×C4×C59#12311yescharacteristic
125C2×C4×C59C2×D811yescharacteristic
126C2×C4×C59C2×SD1611yescharacteristic
127C2×C4×C59#13511yescharacteristic
128C2×C4×C59#13511yescharacteristic
129C2×Dic59—22no—
130C2×Dic59—22no—
131C2×Dic59—24no—
132C2×Dic59—22no—
133C2×Dic59—42no—
134C2×Dic59—42no—
135C2×Dic59—42no—
136C2×Dic59#10214yes—
137Dic118—22no—
138Dic118—22no—
139Dic118—22no—
140Dic118—22no—
141C8×C59—42no—
142C8×C59—81no—
143C59⋊C8—42no—
144C59⋊C8—81no—
145#9394—591nomaximal, Sylow
146C22×C59—21no—
147C22×C59—21no—
148C22×C59#38611yescharacteristic
149C22×C59C2×#10211yescharacteristic
150C22×C59#41611yescharacteristic
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—82no—
155C4×C59#45612yes—
156C4×C59#46511yescharacteristic
157C4×C59#46511yescharacteristic
158C4×C59#46611yescharacteristic
159C4×C59#46611yescharacteristic
160Dic59—24no—
161Dic59—44no—
162Dic59—42no—
163#2982—591no—
164#2546—591no—
165#1801—591no—
166#1546—591no—
167#1546D5911yescharacteristic
168#1303—591no—
169#1303—591no—
170C2×C59—21no—
171C2×C59—21no—
172C2×C59#188611yescharacteristic
173C2×C59#189311yescharacteristic
174C2×C59#191511yescharacteristic
175C2×C4⋊Q8—1181no—
176C2×C4⋊Q8C2×D5911yescharacteristic
177C2×C4×Q8—591no—
178C8×Q8—1182no—
179C8×Q8—1182no—
180#431—591no—
181#431—1182no—
182#431C2×D5911yescharacteristic
183#423—591no—
184#423C2×D5911yescharacteristic
185C2×#101—1181no—
186#398—594no—
187#391—1181no—
188#389—1182no—
189C4×C4⋊C4—591no—
190#343—1181no—
191#332—22no—
192#332—1182no—
193C59#939411yescharacteristic, complemented, Sylow
194C22×Q8—21no—
195C22×Q8—591no—
196C2×M16—21no—
197C2×M16—1181no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—2362no—
203C4⋊Q8—2362no—
204C4×Q8—1181no—
205C4×Q8—1181no—
206C4×Q8—1181no—
207C4×Q8—1181no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—592no—
210C2×C4⋊C4—591no—
211C2×C4⋊C4—1181no—
212C2×C4⋊C4—1184no—
213C2×C4⋊C4C4×D5912yes—
214C2×C42—592no—
215C2×C42—1181no—
216C2×C42C22×D5911yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—592no—
220C4⋊C8—1184no—
221C4⋊C8—1181no—
222C4⋊C8—1181no—
223C4⋊C8C22⋊D5912yes—
224#101—2362no—
225C22⋊C8—21no—
226C22⋊C8—1181no—
227C4×C8—21no—
228C4×C8—1184no—
229C4×C8—1181no—
230#95—592no—
231#95—1184no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—592no—
239C2×Q8—592no—
240C2×Q8—1181no—
241C2×Q8—1181no—
242C2×Q8—1181no—
243C2×Q8—1181no—
244C22×C4—22no—
245C22×C4—592no—
246C22×C4—592no—
247C22×C4—1182no—
248C22×C4C2×C4×D5911yescharacteristic
249C22×C4D4×D5911yescharacteristic
250C22×C4D4×D5911yescharacteristic
251M16—41no—
252M16—41no—
253M16—2361no—
254M16—2361no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—1182no—
258C2×C8—2361no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—1184no—
264C4⋊C4—1182no—
265C4⋊C4—1182no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4—2368no—
269C42—1182no—
270C42—1182no—
271C42—2361no—
272C42—2361no—
273C42#1174568511yescharacteristic
274C42D4×D5911yescharacteristic
275C42#1174568711yescharacteristic
276C42C2×C22⋊D5911yescharacteristic
277C23C22⋊C4×D5911yescharacteristic
278Q8—81no—
279Q8—81no—
280Q8—81no—
281Q8—81no—
282Q8—1182no—
283Q8—1182no—
284Q8—1182no—
285Q8—1182no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—594no—
292C2×C4—1182no—
293C2×C4—1182no—
294C2×C4—1184no—
295C2×C4—1182no—
296C2×C4—2362no—
297C2×C4—2362no—
298C2×C4—2362no—
299C2×C4(C22⋊D59)⋊C411yescharacteristic
300C2×C4C4×C22⋊D5911yescharacteristic
301C2×C4#1427369511yescharacteristic
302C2×C4#1427369811yescharacteristic
303C2×C4#1427370011yescharacteristic
304C2×C4#1427370911yescharacteristic
305C2×C4D8×D5911yescharacteristic
306C2×C4SD16×D5911yescharacteristic
307C2×C4#1427374611yescharacteristic
308C2×C4#1427374811yescharacteristic
309C8—42no—
310C8—81no—
311C8—4721no—
312C8—2362no—
313C22—21no—
314C22—21no—
315C22#1683727811yescharacteristic
316C22#102×D5911yescharacteristic
317C22#1683739511yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—1184no—
323C4—2364no—
324C4—2362no—
325C4#1683758312yes—
326C4#1683762811yescharacteristic
327C4#1683763011yescharacteristic
328C4#1683763511yescharacteristic
329C4#1683763711yescharacteristic
330C2—21no—
331C2—21no—
332C2#2142448611yescharacteristic
333C2#2142452111yescharacteristic
334C2#2142464511yescharacteristic
subgroupG/H
centerC22#16837278
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1546C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1546D59
hypocenterC59#9394
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
193. C59#9394semidirect

Maximal subgroups

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

subgroupindex
#214331762
#214290852
#214240892
#214227682
#214219982
#214219972
C59×#15462
#939459