Finite Group Databasebeta

← C137×#13463 #46862849

Subgroups — C137×#13463 #46862849

Order 35072.

484 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 98 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#2804×C137C211yesmaximal, characteristic
2#1867×C137C212yesmaximal
3#1856×C137C211yesmaximal, characteristic
4#1393×C137C211yesmaximal, characteristic
5#1390×C137C212yesmaximal
6#518×C137C2211yescharacteristic
7#428×C137—21no—
8C2×#100×C137C2211yescharacteristic
9C2×#99×C137C2212yes—
10#400×C137—21no—
11#393×C137—22no—
12#391×C137—21no—
13#390×C137C2211yescharacteristic
14#386×C137C2212yes—
15#385×C137—22no—
16#385×C137—22no—
17#342×C137—22no—
18#339×C137—21no—
19C22×Q8×C137—21no—
20C22×D4×C137C2311yescharacteristic
21C23×C4×C137D412yes—
22C2×M16×C137—21no—
23C4×D4×C137—41no—
24C4×D4×C137—41no—
25#117×C137—21no—
26C2×C4⋊C4×C137—21no—
27C2×C4⋊C4×C137—21no—
28C2×C4⋊C4×C137—42no—
29C2×C4⋊C4×C137D411yescharacteristic
30C2×C22⋊C4×C137—22no—
31C2×C22⋊C4×C137—22no—
32C2×C22⋊C4×C137—22no—
33C2×C22⋊C4×C137—22no—
34C2×C22⋊C4×C137D412yes—
35C2×C42×C137D411yescharacteristic
36#107×C137—41no—
37#106×C137—41no—
38#100×C137—21no—
39#100×C137Q812yescomplemented
40#99×C137—22no—
41#99×C137Q814yescomplemented
42#95×C137—22no—
43#95×C137—22no—
44#95×C137—21no—
45#95×C137—22no—
46#95×C137—42no—
47C24×C137C2×D412yes—
48C2×Q8×C137—42no—
49C2×Q8×C137—81no—
50C2×Q8×C137—81no—
51C2×D4×C137—41no—
52C2×D4×C137—41no—
53C2×D4×C137C2×Q811yescharacteristic
54C2×D4×C137C2×Q812yes—
55C2×D4×C137#4111yescharacteristic
56C22×C4×C137—21no—
57C22×C4×C137—22no—
58C22×C4×C137—21no—
59C22×C4×C137—22no—
60C22×C4×C137—22no—
61C22×C4×C137—22no—
62C22×C4×C137—42no—
63C22×C4×C137—42no—
64C22×C4×C137—82no—
65C22×C4×C137C2×D411yescharacteristic
66M16×C137—22no—
67M16×C137—41no—
68C2×C8×C137—41no—
69C4⋊C4×C137—21no—
70C4⋊C4×C137—21no—
71C4⋊C4×C137—41no—
72C4⋊C4×C137—81no—
73C4⋊C4×C137—81no—
74C4⋊C4×C137—84no—
75C22⋊C4×C137—24no—
76C22⋊C4×C137—44no—
77C22⋊C4×C137—42no—
78C22⋊C4×C137—42no—
79C22⋊C4×C137—41no—
80C22⋊C4×C137—42no—
81C22⋊C4×C137—82no—
82C42×C137—41no—
83C42×C137—41no—
84C23×C137—22no—
85C23×C137—22no—
86C23×C137—42no—
87C23×C137—42no—
88C23×C137#12011yescharacteristic
89C23×C137C22⋊Q812yes—
90C23×C137C4⋊Q812yes—
91Q8×C137—84no—
92D4×C137—41no—
93D4×C137—42no—
94D4×C137—41no—
95C2×C4×C137—21no—
96C2×C4×C137—21no—
97C2×C4×C137—22no—
98C2×C4×C137—41no—
99C2×C4×C137—41no—
100C2×C4×C137—44no—
101C2×C4×C137—42no—
102C2×C4×C137—42no—
103C2×C4×C137—42no—
104C2×C4×C137—42no—
105C2×C4×C137—42no—
106C2×C4×C137—44no—
107C2×C4×C137—41no—
108C2×C4×C137—41no—
109C2×C4×C137—41no—
110C2×C4×C137—42no—
111C2×C4×C137—42no—
112C2×C4×C137—82no—
113C2×C4×C137—82no—
114C2×C4×C137—82no—
115C2×C4×C137—82no—
116C2×C4×C137—82no—
117C2×C4×C137C22⋊Q811yescharacteristic
118C2×C4×C137C4⋊Q811yescharacteristic
119C8×C137—42no—
120C22×C137—21no—
121C22×C137—21no—
122C22×C137—22no—
123C22×C137—22no—
124C22×C137—42no—
125C22×C137—42no—
126C22×C137—42no—
127C22×C137—42no—
128C22×C137—82no—
129C22×C137#39511yescharacteristic
130C22×C137B(4,𝔽2)11yescharacteristic
131C22×C137#45811yescharacteristic
132C4×C137—21no—
133C4×C137—21no—
134C4×C137—42no—
135C4×C137—82no—
136C4×C137—84no—
137C4×C137—81no—
138C4×C137—81no—
139C4×C137—82no—
140C4×C137—81no—
141C2×C137—21no—
142C2×C137—21no—
143C2×C137—42no—
144C2×C137—42no—
145C2×C137#206211yescharacteristic
146C2×C137#219811yescharacteristic
147C2×C137#219911yescharacteristic
148#13463C13711yesmaximal, characteristic, direct product factor, Sylow
149C137#1346311yescharacteristic, direct product factor, Sylow
150#2804C2×C13711yescharacteristic
151#1867C2×C13712yes—
152#1856C2×C13711yescharacteristic
153#1393C2×C13711yescharacteristic
154#1390C2×C13712yes—
155#518C22×C13711yescharacteristic
156#428—21no—
157C2×#100C22×C13711yescharacteristic
158C2×#99C22×C13712yes—
159#400—21no—
160#393—22no—
161#391—21no—
162#390C22×C13711yescharacteristic
163#386C22×C13712yes—
164#385—22no—
165#385—22no—
166#342—22no—
167#339—21no—
168C22×Q8—21no—
169C22×D4C23×C13711yescharacteristic
170C23×C4D4×C13712yes—
171C2×M16—21no—
172C4×D4—41no—
173C4×D4—41no—
174#117—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4D4×C13711yescharacteristic
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4D4×C13712yes—
184C2×C42D4×C13711yescharacteristic
185#107—41no—
186#106—41no—
187#100—21no—
188#100Q8×C13712yescomplemented
189#99—22no—
190#99Q8×C13714yescomplemented
191#95—22no—
192#95—22no—
193#95—21no—
194#95—22no—
195#95—42no—
196C24C2×D4×C13712yes—
197C2×Q8—42no—
198C2×Q8—81no—
199C2×Q8—81no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4C2×Q8×C13711yescharacteristic
203C2×D4C2×Q8×C13712yes—
204C2×D4#41×C13711yescharacteristic
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—82no—
214C22×C4C2×D4×C13711yescharacteristic
215M16—22no—
216M16—41no—
217C2×C8—41no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—41no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C4⋊C4—84no—
224C22⋊C4—24no—
225C22⋊C4—44no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—41no—
229C22⋊C4—42no—
230C22⋊C4—82no—
231C42—41no—
232C42—41no—
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23#120×C13711yescharacteristic
238C23C22⋊Q8×C13712yes—
239C23C4⋊Q8×C13712yes—
240Q8—84no—
241D4—41no—
242D4—42no—
243D4—41no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4C22⋊Q8×C13711yescharacteristic
267C2×C4C4⋊Q8×C13711yescharacteristic
268C8—42no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22#395×C13711yescharacteristic
279C22B(4,𝔽2)×C13711yescharacteristic
280C22#458×C13711yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—82no—
285C4—84no—
286C4—81no—
287C4—81no—
288C4—82no—
289C4—81no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2#2062×C13711yescharacteristic
295C2#2198×C13711yescharacteristic
296C2#2199×C13711yescharacteristic
subgroupG/H
center, socleC22×C137B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C137
prime radicalC22×D4×C137C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C137 ◁ C22×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
39. #100×C137Q8semidirect
41. #99×C137Q8semidirect
148. #13463C137direct (N × H)
149. C137#13463direct (N × H)
188. #100Q8×C137semidirect
190. #99Q8×C137semidirect

Maximal subgroups

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

subgroupindex
#2804×C1372
#1867×C1372
#1856×C1372
#1393×C1372
#1390×C1372
#13463137