Finite Group Databasebeta

← #28492411

Subgroups — #28492411

Order 15104.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#21422787C211yesmaximal, characteristic
4#21422552C211yesmaximal, characteristic
5C2×#16837134C211yesmaximal, characteristic
6#21421970C211yesmaximal, characteristic
7C59×#1566C211yesmaximal, characteristic
8#16837959C2211yescharacteristic
9C2×C4×Dic118C2211yescharacteristic
10#16837710—22no—
11#16837698—21no—
12#16837688—21no—
13#16837444—21no—
14#16837426C2211yescharacteristic
15C2×C4⋊(C59⋊C8)C2211yescharacteristic
16#16837412—21no—
17C2×#14273645—21no—
18#16837170—21no—
19#16837150—21no—
20#16837147—21no—
21#16837134—21no—
22#16837134—21no—
23#16837134—21no—
24#16837134—21no—
25C59×#423C2211yescharacteristic
26C59×#423C2211yescharacteristic
27C2×C4×C8×C59C2211yescharacteristic
28C59×#334—22no—
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—
51C4⋊(C59⋊C8)—21no—
52C4⋊(C59⋊C8)—21no—
53#14273652—22no—
54#14273652—22no—
55#14273645—42no—
56C2×M16×C59—21no—
57C2×M16×C59—21no—
58C22×C8×C59—21no—
59C2×C42×C59C2311yescharacteristic
60C4⋊C8×C59—21no—
61C4⋊C8×C59—21no—
62C4⋊C8×C59—21no—
63C4⋊C8×C59D412yes—
64C4×C8×C59—21no—
65C4×C8×C59D411yescharacteristic
66C4×C8×C59D411yescharacteristic
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×Dic118SD1612yes—
80M16×C59—41no—
81M16×C59—41no—
82M16×C59—41no—
83M16×C59—41no—
84C2×C8×C59—21no—
85C2×C8×C59—22no—
86C2×C8×C59—21no—
87C2×C8×C59—42no—
88C2×C8×C59—41no—
89C42×C59C2×D411yescharacteristic
90C42×C59C2×D411yescharacteristic
91C42×C59C2×D411yescharacteristic
92C42×C59#4111yescharacteristic
93C22⋊Dic59—41no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100Dic59⋊C4—41no—
101Dic59⋊C4—41no—
102Dic59⋊C4—41no—
103Dic59⋊C4—41no—
104C4×Dic59—41no—
105C4×Dic59—41no—
106C4×Dic59—41no—
107#11745664—41no—
108#11745664—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8—41no—
111C2×C59⋊C8—81no—
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×SD1611yescharacteristic
123C2×C4×C59#13511yescharacteristic
124C2×C4×C59#13711yescharacteristic
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—22no—
141C8×C59—41no—
142C8×C59—42no—
143C8×C59—81no—
144C59⋊C8—81no—
145C59⋊C8—81no—
146#10462—591nomaximal, Sylow
147C22×C59—21no—
148C22×C59—21no—
149C22×C59#39411yescharacteristic
150C22×C59#48311yescharacteristic
151C22×C59#48511yescharacteristic
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59#44811yescharacteristic
156C4×C59#45211yescharacteristic
157C4×C59#46511yescharacteristic
158C4×C59#47011yescharacteristic
159C4×C59#47111yescharacteristic
160C4×C59#47311yescharacteristic
161Dic59—42no—
162Dic59—81no—
163Dic59—81no—
164Dic59—81no—
165#3078—591no—
166#1801—591no—
167#1566D5911yescharacteristic
168#1550—591no—
169#1493—591no—
170C2×Q8⋊C8—591no—
171#1292—591no—
172C2×C59—21no—
173C2×C59—21no—
174C2×C59#203511yescharacteristic
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⋊C8—591no—
187#419—1181no—
188C2×#101—1181no—
189C2×C4×C8C2×D5911yescharacteristic
190#343—1181no—
191#334—22no—
192#333—1181no—
193#332—1181no—
194Q8⋊C8—1181no—
195Q8⋊C8—1181no—
196Q8⋊C8—1181no—
197Q8⋊C8—1181no—
198C59#1046211yescharacteristic, 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—1181no—
227C4⋊C8—1181no—
228C4⋊C8—1181no—
229C4⋊C8—1181no—
230C4⋊C8C22⋊D5912yes—
231#103—1182no—
232#103—1182no—
233#101—2362no—
234C4×C8—21no—
235C4×C8D23611yescharacteristic
236C4×C8D23611yescharacteristic
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—21no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—4721no—
262C2×C8—2361no—
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
279C42D4×D5911yescharacteristic
280C42#1174568911yescharacteristic
281C42C2×C22⋊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#1427369511yescharacteristic
301C2×C4#1427370111yescharacteristic
302C2×C4#1427370211yescharacteristic
303C2×C4#1427370211yescharacteristic
304C2×C4#1427371211yescharacteristic
305C2×C4#1427371611yescharacteristic
306C2×C4SD16×D5911yescharacteristic
307C2×C4#1427374811yescharacteristic
308C2×C4#1427375611yescharacteristic
309C2×C4#1427375611yescharacteristic
310C8—22no—
311C8—41no—
312C8—42no—
313C8—81no—
314C8—4721no—
315C8—4721no—
316C22—21no—
317C22—21no—
318C22#1683731911yescharacteristic
319C22#1683773411yescharacteristic
320C22#1683774611yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—4721no—
325C4—4721no—
326C4—4721no—
327C4—2362no—
328C4#1683753911yescharacteristic
329C4#1683756111yescharacteristic
330C4#1683763211yescharacteristic
331C4#1683766111yescharacteristic
332C4#1683766611yescharacteristic
333C4#1683767811yescharacteristic
334C2—21no—
335C2—21no—
336C2#2142529411yescharacteristic
337C2#2142538311yescharacteristic
338C2#2142539711yescharacteristic
subgroupG/H
centerC22#16837319
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1566C2
socleC22×C59#394
prime radicalC23×C59#123
hypercenter#1566D59
hypocenterC59#10462
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
198. C59#10462semidirect

Maximal subgroups

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

subgroupindex
#214339032
#214240892
#214227872
#214225522
C2×#168371342
#214219702
C59×#15662
#1046259