Finite Group Databasebeta

← C137×#12095 #46861481

Subgroups — C137×#12095 #46861481

Order 35072.

458 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 74 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#2817×C137C211yesmaximal, characteristic, complemented
2#2022×C137C211yesmaximal, characteristic
3#1607×C137C212yesmaximal
4#1344×C137C212yesmaximal, complemented
5#1317×C137C211yesmaximal, characteristic, complemented
6#534×C137C2211yescharacteristic
7C2×#123×C137—21no—
8C2×C22⋊Q8×C137—21no—
9#480×C137—22no—
10C2×#99×C137—21no—
11#400×C137—22no—
12#397×C137—21no—
13#397×C137C2212yes—
14#395×C137—22no—
15#381×C137C2211yescharacteristic
16#342×C137C2211yescharacteristic
17#327×C137—22no—
18#323×C137C2212yes—
19C22×Q8×C137—21no—
20C22×D4×C137—21no—
21C23×C4×C137D411yescharacteristic
22#123×C137—42no—
23#123×C137—41no—
24#123×C137—42no—
25C22⋊Q8×C137—42no—
26C22⋊Q8×C137—42no—
27#121×C137—22no—
28#120×C137—41no—
29C2×C4⋊C4×C137—22no—
30C2×C4⋊C4×C137—21no—
31C2×C4⋊C4×C137—21no—
32C2×C4⋊C4×C137—41no—
33C2×C4⋊C4×C137D412yes—
34C2×C22⋊C4×C137—21no—
35C2×C22⋊C4×C137—22no—
36C2×C22⋊C4×C137—41no—
37C2×C22⋊C4×C137D411yescharacteristic
38C2×C22⋊C4×C137C2311yescharacteristic
39#107×C137—42no—
40#102×C137—42no—
41#99×C137—42no—
42C22⋊C8×C137—22no—
43#95×C137—22no—
44#95×C137—21no—
45#95×C137—22no—
46#95×C137—22no—
47#95×C137D412yes—
48C24×C137—21no—
49C24×C137C2×D411yescharacteristic
50C2×Q8×C137—42no—
51C2×Q8×C137—81no—
52C2×Q8×C137—81no—
53C2×D4×C137—22no—
54C2×D4×C137—41no—
55C2×D4×C137—41no—
56C2×D4×C137—41no—
57C2×D4×C137—41no—
58C2×D4×C137—41no—
59C2×D4×C137—41no—
60C22×C4×C137—21no—
61C22×C4×C137—21no—
62C22×C4×C137—21no—
63C22×C4×C137—21no—
64C22×C4×C137—22no—
65C22×C4×C137—22no—
66C22×C4×C137—41no—
67C22×C4×C137—41no—
68C22×C4×C137—41no—
69C22×C4×C137D812yes—
70C22×C4×C137C2×D412yes—
71C2×C8×C137—42no—
72C4⋊C4×C137—22no—
73C4⋊C4×C137—42no—
74C4⋊C4×C137—42no—
75C4⋊C4×C137—44no—
76C4⋊C4×C137—44no—
77C4⋊C4×C137—81no—
78C22⋊C4×C137—22no—
79C22⋊C4×C137—41no—
80C22⋊C4×C137—42no—
81C22⋊C4×C137—44no—
82C22⋊C4×C137—42no—
83C22⋊C4×C137—41no—
84C22⋊C4×C137—42no—
85C22⋊C4×C137—41no—
86C23×C137—21no—
87C23×C137—21no—
88C23×C137—42no—
89C23×C137—41no—
90C23×C137—41no—
91C23×C137—41no—
92C23×C137—82no—
93C23×C137#12011yescharacteristic
94C23×C137C2×D811yescharacteristic
95C23×C137AGL(1,ℤ/8)11yescharacteristic
96Q8×C137—84no—
97D4×C137—82no—
98D4×C137—81no—
99D4×C137—81no—
100D4×C137—81no—
101D4×C137—81no—
102C2×C4×C137—22no—
103C2×C4×C137—22no—
104C2×C4×C137—41no—
105C2×C4×C137—41no—
106C2×C4×C137—42no—
107C2×C4×C137—42no—
108C2×C4×C137—42no—
109C2×C4×C137—41no—
110C2×C4×C137—42no—
111C2×C4×C137—44no—
112C2×C4×C137—41no—
113C2×C4×C137—42no—
114C2×C4×C137—42no—
115C2×C4×C137—41no—
116C2×C4×C137—42no—
117C2×C4×C137—41no—
118C2×C4×C137—42no—
119C2×C4×C137—81no—
120C2×C4×C137—82no—
121C8×C137—82no—
122C22×C137—22no—
123C22×C137—21no—
124C22×C137—21no—
125C22×C137—41no—
126C22×C137—41no—
127C22×C137—42no—
128C22×C137—81no—
129C22×C137—82no—
130C22×C137—81no—
131C22×C137—82no—
132C22×C137—161no—
133C22×C137#44711yescharacteristic
134C22×C137#45311yescharacteristic
135C22×C137B(4,𝔽2)11yescharacteristic
136C4×C137—42no—
137C4×C137—42no—
138C4×C137—82no—
139C4×C137—81no—
140C4×C137—82no—
141C4×C137—81no—
142C4×C137—82no—
143C2×C137—21no—
144C2×C137—21no—
145C2×C137—41no—
146C2×C137—41no—
147C2×C137—161no—
148C2×C137#159511yescharacteristic
149C2×C137#220112yes—
150#12095C13711yesmaximal, characteristic, direct product factor, Sylow
151C137#1209511yescharacteristic, direct product factor, Sylow
152#2817C2×C13711yescharacteristic, complemented
153#2022C2×C13711yescharacteristic
154#1607C2×C13712yes—
155#1344C2×C13712yescomplemented
156#1317C2×C13711yescharacteristic, complemented
157#534C22×C13711yescharacteristic
158C2×#123—21no—
159C2×C22⋊Q8—21no—
160#480—22no—
161C2×#99—21no—
162#400—22no—
163#397—21no—
164#397C22×C13712yes—
165#395—22no—
166#381C22×C13711yescharacteristic
167#342C22×C13711yescharacteristic
168#327—22no—
169#323C22×C13712yes—
170C22×Q8—21no—
171C22×D4—21no—
172C23×C4D4×C13711yescharacteristic
173#123—42no—
174#123—41no—
175#123—42no—
176C22⋊Q8—42no—
177C22⋊Q8—42no—
178#121—22no—
179#120—41no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4D4×C13712yes—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4D4×C13711yescharacteristic
189C2×C22⋊C4C23×C13711yescharacteristic
190#107—42no—
191#102—42no—
192#99—42no—
193C22⋊C8—22no—
194#95—22no—
195#95—21no—
196#95—22no—
197#95—22no—
198#95D4×C13712yes—
199C24—21no—
200C24C2×D4×C13711yescharacteristic
201C2×Q8—42no—
202C2×Q8—81no—
203C2×Q8—81no—
204C2×D4—22no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—41no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4D8×C13712yes—
221C22×C4C2×D4×C13712yes—
222C2×C8—42no—
223C4⋊C4—22no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—44no—
227C4⋊C4—44no—
228C4⋊C4—81no—
229C22⋊C4—22no—
230C22⋊C4—41no—
231C22⋊C4—42no—
232C22⋊C4—44no—
233C22⋊C4—42no—
234C22⋊C4—41no—
235C22⋊C4—42no—
236C22⋊C4—41no—
237C23—21no—
238C23—21no—
239C23—42no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—82no—
244C23#120×C13711yescharacteristic
245C23C2×D8×C13711yescharacteristic
246C23AGL(1,ℤ/8)×C13711yescharacteristic
247Q8—84no—
248D4—82no—
249D4—81no—
250D4—81no—
251D4—81no—
252D4—81no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—81no—
271C2×C4—82no—
272C8—82no—
273C22—22no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—81no—
280C22—82no—
281C22—81no—
282C22—82no—
283C22—161no—
284C22#447×C13711yescharacteristic
285C22#453×C13711yescharacteristic
286C22B(4,𝔽2)×C13711yescharacteristic
287C4—42no—
288C4—42no—
289C4—82no—
290C4—81no—
291C4—82no—
292C4—81no—
293C4—82no—
294C2—21no—
295C2—21no—
296C2—41no—
297C2—41no—
298C2—161no—
299C2#1595×C13711yescharacteristic
300C2#2201×C13712yes—
subgroupG/H
center, socleC22×C137B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C137
prime radical#534×C137C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C137 ◁ C2×C22⋊C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2817×C137C2semidirect
4. #1344×C137C2semidirect
5. #1317×C137C2semidirect
150. #12095C137direct (N × H)
151. C137#12095direct (N × H)
152. #2817C2×C137semidirect
155. #1344C2×C137semidirect
156. #1317C2×C137semidirect

Maximal subgroups

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

subgroupindex
#2817×C1372
#2022×C1372
#1607×C1372
#1344×C1372
#1317×C1372
#12095137