Finite Group Databasebeta

← #28492419

Subgroups — #28492419

Order 15104.

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

normal subgroups only

This group has 374 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
1#21433903C211yesmaximal, characteristic
2#21424089C211yesmaximal, characteristic
3#21422854C211yesmaximal, characteristic
4#21422784C211yesmaximal, characteristic
5#21422550C211yesmaximal, characteristic
6C2×#16837132C211yesmaximal, characteristic
7C59×#1292C211yesmaximal, characteristic
8#16837959C2211yescharacteristic
9C2×C4×Dic118C2211yescharacteristic
10#16837710—22no—
11#16837698—21no—
12#16837688—21no—
13#16837444—21no—
14#16837426C2211yescharacteristic
15#16837412—21no—
16C2×#14273645—21no—
17C2×C4×C59⋊C8C2211yescharacteristic
18#16837170—21no—
19#16837154—22no—
20#16837150—21no—
21#16837149—21no—
22#16837132—21no—
23#16837132—21no—
24#16837132—21no—
25#16837132—21no—
26C59×#423C2211yescharacteristic
27C59×#423C2211yescharacteristic
28C2×C4⋊C8×C59C2211yescharacteristic
29C22×Dic118D411yescharacteristic
30C2×#11745664—21no—
31C22×C59⋊C8—21no—
32#14273727D411yescharacteristic
33#14273727D411yescharacteristic
34#14273719—21no—
35#14273706—21no—
36#14273706—21no—
37C4×Dic118—21no—
38C4×Dic118—21no—
39C4×Dic118—21no—
40C4×Dic118—21no—
41C4×Dic118—21no—
42C4×Dic118—21no—
43#14273686—21no—
44C2×C4⋊Dic59D411yescharacteristic
45C2×Dic59⋊C4—21no—
46C2×C4×Dic59—21no—
47#14273661—22no—
48#14273659—22no—
49C4⋊(C59⋊C8)—21no—
50C4⋊(C59⋊C8)—21no—
51#14273652—22no—
52#14273652—22no—
53#14273645—42no—
54C4×C59⋊C8—21no—
55C4×C59⋊C8D411yescharacteristic
56C4×C59⋊C8D411yescharacteristic
57C2×M16×C59—21no—
58C2×M16×C59—21no—
59C22×C8×C59—21no—
60C2×C42×C59C2311yescharacteristic
61C4⋊C8×C59—21no—
62C4⋊C8×C59—21no—
63C4⋊C8×C59—21no—
64C4⋊C8×C59—21no—
65C4⋊C8×C59—21no—
66C4⋊C8×C59D412yes—
67C22×C4×C59C2×D411yescharacteristic
68C22×C4×C59#4111yescharacteristic
69C22×C4×C59#4111yescharacteristic
70C22×Dic59—21no—
71C22×Dic59—21no—
72C2×Dic118—21no—
73C2×Dic118—21no—
74C2×Dic118—21no—
75C2×Dic118—21no—
76C2×Dic118—21no—
77C2×Dic118—21no—
78C2×Dic118—21no—
79C2×Dic118Q1612yes—
80M16×C59—41no—
81M16×C59—41no—
82M16×C59—41no—
83M16×C59—41no—
84C2×C8×C59—22no—
85C2×C8×C59—41no—
86C2×C8×C59—41no—
87C2×C8×C59—81no—
88C42×C59C2×D411yescharacteristic
89C42×C59C2×D411yescharacteristic
90C42×C59C2×D411yescharacteristic
91C42×C59#4111yescharacteristic
92C22⋊Dic59—41no—
93C4⋊Dic59—21no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99Dic59⋊C4—41no—
100Dic59⋊C4—41no—
101Dic59⋊C4—41no—
102Dic59⋊C4—41no—
103C4×Dic59—41no—
104C4×Dic59—41no—
105C4×Dic59—41no—
106#11745664—41no—
107#11745664—41no—
108C2×C59⋊C8—21no—
109C2×C59⋊C8—21no—
110C2×C59⋊C8—42no—
111C2×C59⋊C8—41no—
112C23×C59#12311yescharacteristic
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—41no—
116C2×C4×C59#12011yescharacteristic
117C2×C4×C59#12111yescharacteristic
118C2×C4×C59#12111yescharacteristic
119C2×C4×C59#12111yescharacteristic
120C2×C4×C59#12311yescharacteristic
121C2×C4×C59#12411yescharacteristic
122C2×C4×C59C2×Q1611yescharacteristic
123C2×C4×C59#13511yescharacteristic
124C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C59#13711yescharacteristic
126C2×Dic59—22no—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—81no—
133Dic118—22no—
134Dic118—22no—
135Dic118—41no—
136Dic118—41no—
137Dic118—41no—
138Dic118—41no—
139Dic118—81no—
140C8×C59—42no—
141C8×C59—81no—
142C8×C59—81no—
143C59⋊C8—22no—
144C59⋊C8—41no—
145C59⋊C8—81no—
146#10463—591nomaximal, Sylow
147C22×C59—21no—
148C22×C59—21no—
149C22×C59#39411yescharacteristic
150C22×C59#48411yescharacteristic
151C22×C59#48511yescharacteristic
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59#44911yescharacteristic
156C4×C59#45111yescharacteristic
157C4×C59#46711yescharacteristic
158C4×C59#46811yescharacteristic
159C4×C59#47111yescharacteristic
160C4×C59#47311yescharacteristic
161Dic59—42no—
162Dic59—81no—
163Dic59—81no—
164Dic59—81no—
165#3078—591no—
166#1801—591no—
167#1567—591no—
168#1550—591no—
169#1493—591no—
170C2×Q8⋊C8—591no—
171#1292D5911yescharacteristic
172C2×C59—21no—
173C2×C59—21no—
174C2×C59#203611yescharacteristic
175C2×C59#205011yescharacteristic
176C2×C59#205211yescharacteristic
177#533—591no—
178C2×C4×Q8—591no—
179#479—1182no—
180#477—1181no—
181#475—1181no—
182#428—1181no—
183#423—591no—
184#423C2×D5911yescharacteristic
185#423C2×D5911yescharacteristic
186C2×C4⋊C8C2×D5911yescharacteristic
187#419—1181no—
188C2×#101—1181no—
189C2×C4×C8—591no—
190#343—1181no—
191#335—1182no—
192#333—1181no—
193#332—1181no—
194Q8⋊C8—1181no—
195Q8⋊C8—1181no—
196Q8⋊C8—1181no—
197Q8⋊C8—1181no—
198C59#1046311yescharacteristic, complemented, Sylow
199C22×Q8—591no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—1181no—
203C22×C8—21no—
204C22×C8—1181no—
205C4⋊Q8—591no—
206C4⋊Q8—591no—
207#125—1181no—
208C22⋊Q8—1181no—
209C22⋊Q8—1181no—
210C4×Q8—1181no—
211C4×Q8—1181no—
212C4×Q8—1181no—
213C4×Q8—1181no—
214C4×Q8—1181no—
215C4×Q8—1181no—
216#117—1181no—
217C2×C4⋊C4—591no—
218C2×C4⋊C4—1181no—
219C2×C42—1181no—
220C2×C42C22×D5911yescharacteristic
221#107—1182no—
222#106—1182no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—1181no—
229C4⋊C8—1181no—
230C4⋊C8D23612yes—
231#103—1182no—
232#103—1182no—
233#101—2362no—
234C4×C8—591no—
235C4×C8—591no—
236C4×C8—1181no—
237C2×Q8—592no—
238C2×Q8—1181no—
239C2×Q8—1181no—
240C2×Q8—1181no—
241C2×Q8—1181no—
242C2×Q8—1181no—
243C2×Q8—1181no—
244C2×Q8—1181no—
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4#1174568511yescharacteristic
248C22×C4D4×D5911yescharacteristic
249C22×C4#1174568911yescharacteristic
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—2361no—
255M16—2361no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—81no—
260C2×C8—1181no—
261C2×C8—1181no—
262C2×C8—2362no—
263C2×C8—2361no—
264C4⋊C4—1181no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—2361no—
271C4⋊C4—2361no—
272C4⋊C4—2361no—
273C4⋊C4—2361no—
274C22⋊C4—2361no—
275C42—2361no—
276C42—2361no—
277C42—2361no—
278C42C2×D23611yescharacteristic
279C42#1174568511yescharacteristic
280C42D4×D5911yescharacteristic
281C42D4×D5911yescharacteristic
282C23#1427371211yescharacteristic
283Q8—1182no—
284Q8—1182no—
285Q8—4721no—
286Q8—2361no—
287Q8—2361no—
288Q8—2361no—
289Q8—2361no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—1182no—
294C2×C4—4721no—
295C2×C4—2361no—
296C2×C4—2361no—
297C2×C4—2361no—
298C2×C4—2361no—
299C2×C4—2361no—
300C2×C4#1427369711yescharacteristic
301C2×C4#1427370011yescharacteristic
302C2×C4#1427370011yescharacteristic
303C2×C4#1427370211yescharacteristic
304C2×C4#1427371211yescharacteristic
305C2×C4#1427371511yescharacteristic
306C2×C4Q16×D5911yescharacteristic
307C2×C4#1427374811yescharacteristic
308C2×C4#1427375111yescharacteristic
309C2×C4#1427375611yescharacteristic
310C8—42no—
311C8—81no—
312C8—81no—
313C8—1182no—
314C8—4721no—
315C8—2361no—
316C22—21no—
317C22—21no—
318C22#1683732011yescharacteristic
319C22#1683773911yescharacteristic
320C22#1683774611yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—4721no—
325C4—4721no—
326C4—4721no—
327C4—2362no—
328C4#1683754811yescharacteristic
329C4#1683755911yescharacteristic
330C4#1683764211yescharacteristic
331C4#1683764711yescharacteristic
332C4#1683766411yescharacteristic
333C4#1683767611yescharacteristic
334C2—21no—
335C2—21no—
336C2#2142530211yescharacteristic
337C2#2142538411yescharacteristic
338C2#2142539811yescharacteristic
subgroupG/H
centerC22#16837320
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1292C2
socleC22×C59#394
prime radicalC23×C59#123
hypercenter#1292D59
hypocenterC59#10463
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
198. C59#10463semidirect

Maximal subgroups

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

subgroupindex
#214339032
#214240892
#214228542
#214227842
#214225502
C2×#168371322
C59×#12922
#1046359