Finite Group Databasebeta

← C137×#7807 #46857193

Subgroups — C137×#7807 #46857193

Order 35072.

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

normal subgroups only

This group has 366 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#2805×C137C211yesmaximal, characteristic
2#2096×C137C211yesmaximal, characteristic
3#2084×C137C211yesmaximal, characteristic
4#2083×C137C211yesmaximal, characteristic
5#1272×C137C211yesmaximal, characteristic
6#1271×C137C211yesmaximal, characteristic
7#1271×C137C211yesmaximal, characteristic
8C2×#107×C137—21no—
9C2×#106×C137—21no—
10C2×#106×C137—21no—
11C2×#103×C137—21no—
12#400×C137—21no—
13#400×C137—21no—
14#395×C137—21no—
15#391×C137C2211yescharacteristic
16#389×C137—21no—
17#389×C137C2211yescharacteristic
18#389×C137C2211yescharacteristic
19#387×C137—21no—
20#387×C137—21no—
21#384×C137C2211yescharacteristic
22#340×C137—21no—
23#340×C137—21no—
24#336×C137C2211yescharacteristic
25#336×C137C2211yescharacteristic
26#336×C137C2211yescharacteristic
27C22×Q8×C137D411yescharacteristic
28C22×C8×C137—21no—
29C22×C8×C137—21no—
30C22×C8×C137—21no—
31C2×C4⋊C4×C137—21no—
32C2×C4⋊C4×C137—21no—
33C2×C4⋊C4×C137—21no—
34C2×C4⋊C4×C137—21no—
35C2×C4⋊C4×C137—21no—
36C2×C4⋊C4×C137—21no—
37C2×C4⋊C4×C137—21no—
38C2×C4⋊C4×C137D411yescharacteristic
39C2×C4⋊C4×C137D411yescharacteristic
40C2×C4⋊C4×C137D411yescharacteristic
41C2×C4⋊C4×C137D411yescharacteristic
42C2×C4⋊C4×C137D411yescharacteristic
43C2×C42×C137—21no—
44C2×C42×C137C2311yescharacteristic
45#107×C137—42no—
46#106×C137—42no—
47#106×C137—42no—
48#103×C137—42no—
49#95×C137—21no—
50#95×C137—21no—
51#95×C137—21no—
52#95×C137—21no—
53#95×C137—21no—
54#95×C137—21no—
55#95×C137—21no—
56#95×C137—21no—
57#95×C137—21no—
58C2×Q8×C137—21no—
59C2×Q8×C137—21no—
60C2×Q8×C137—41no—
61C2×Q8×C137—41no—
62C22×C4×C137—21no—
63C22×C4×C137—21no—
64C22×C4×C137—21no—
65C22×C4×C137—21no—
66C22×C4×C137—21no—
67C22×C4×C137—21no—
68C22×C4×C137—41no—
69C22×C4×C137C2×D411yescharacteristic
70C22×C4×C137C2×D411yescharacteristic
71C22×C4×C137C2×D411yescharacteristic
72C2×C8×C137—22no—
73C2×C8×C137—22no—
74C2×C8×C137—22no—
75C2×C8×C137—41no—
76C2×C8×C137—41no—
77C2×C8×C137—41no—
78C2×C8×C137—41no—
79C2×C8×C137—41no—
80C2×C8×C137—41no—
81C4⋊C4×C137—21no—
82C4⋊C4×C137—21no—
83C4⋊C4×C137—21no—
84C4⋊C4×C137—41no—
85C4⋊C4×C137—41no—
86C4⋊C4×C137—41no—
87C4⋊C4×C137—41no—
88C4⋊C4×C137—41no—
89C4⋊C4×C137—41no—
90C4⋊C4×C137—41no—
91C4⋊C4×C137—41no—
92C4⋊C4×C137—41no—
93C4⋊C4×C137—41no—
94C4⋊C4×C137—41no—
95C4⋊C4×C137—41no—
96C4⋊C4×C137—41no—
97C4⋊C4×C137—81no—
98C4⋊C4×C137—81no—
99C4⋊C4×C137SD1612yes—
100C42×C137—41no—
101C42×C137—81no—
102C23×C137#12011yescharacteristic
103Q8×C137—42no—
104Q8×C137—81no—
105C2×C4×C137—21no—
106C2×C4×C137—21no—
107C2×C4×C137—21no—
108C2×C4×C137—21no—
109C2×C4×C137—21no—
110C2×C4×C137—21no—
111C2×C4×C137—22no—
112C2×C4×C137—41no—
113C2×C4×C137—41no—
114C2×C4×C137—41no—
115C2×C4×C137—41no—
116C2×C4×C137—41no—
117C2×C4×C137—41no—
118C2×C4×C137—41no—
119C2×C4×C137—41no—
120C2×C4×C137—41no—
121C2×C4×C137—41no—
122C2×C4×C137—41no—
123C2×C4×C137—41no—
124C2×C4×C137—41no—
125C2×C4×C137—41no—
126C2×C4×C137—41no—
127C2×C4×C137—41no—
128C2×C4×C137—41no—
129C2×C4×C137—81no—
130C2×C4×C137—81no—
131C2×C4×C137—81no—
132C2×C4×C137C2×SD1611yescharacteristic
133C2×C4×C137#13511yescharacteristic
134C2×C4×C137#13511yescharacteristic
135C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C137#13711yescharacteristic
137C2×C4×C137#13711yescharacteristic
138C8×C137—42no—
139C8×C137—42no—
140C8×C137—42no—
141C22×C137#44811yescharacteristic
142C22×C137#44911yescharacteristic
143C22×C137#45211yescharacteristic
144C22×C137#45311yescharacteristic
145C22×C137#45611yescharacteristic
146C22×C137#45611yescharacteristic
147C22×C137#45811yescharacteristic
148C4×C137—21no—
149C4×C137—21no—
150C4×C137—21no—
151C4×C137—21no—
152C4×C137—21no—
153C4×C137—21no—
154C4×C137—42no—
155C4×C137—81no—
156C4×C137—81no—
157C4×C137—81no—
158C4×C137—81no—
159C4×C137—81no—
160C4×C137—161no—
161C2×C137#160911yescharacteristic
162C2×C137#161111yescharacteristic
163C2×C137#161811yescharacteristic
164C2×C137#162211yescharacteristic
165C2×C137#165011yescharacteristic
166C2×C137#165311yescharacteristic
167C2×C137#166011yescharacteristic
168#7807C13711yesmaximal, characteristic, direct product factor, Sylow
169C137#780711yescharacteristic, direct product factor, Sylow
170#2805C2×C13711yescharacteristic
171#2096C2×C13711yescharacteristic
172#2084C2×C13711yescharacteristic
173#2083C2×C13711yescharacteristic
174#1272C2×C13711yescharacteristic
175#1271C2×C13711yescharacteristic
176#1271C2×C13711yescharacteristic
177C2×#107—21no—
178C2×#106—21no—
179C2×#106—21no—
180C2×#103—21no—
181#400—21no—
182#400—21no—
183#395—21no—
184#391C22×C13711yescharacteristic
185#389—21no—
186#389C22×C13711yescharacteristic
187#389C22×C13711yescharacteristic
188#387—21no—
189#387—21no—
190#384C22×C13711yescharacteristic
191#340—21no—
192#340—21no—
193#336C22×C13711yescharacteristic
194#336C22×C13711yescharacteristic
195#336C22×C13711yescharacteristic
196C22×Q8D4×C13711yescharacteristic
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4D4×C13711yescharacteristic
208C2×C4⋊C4D4×C13711yescharacteristic
209C2×C4⋊C4D4×C13711yescharacteristic
210C2×C4⋊C4D4×C13711yescharacteristic
211C2×C4⋊C4D4×C13711yescharacteristic
212C2×C42—21no—
213C2×C42C23×C13711yescharacteristic
214#107—42no—
215#106—42no—
216#106—42no—
217#103—42no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4C2×D4×C13711yescharacteristic
239C22×C4C2×D4×C13711yescharacteristic
240C22×C4C2×D4×C13711yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4SD16×C13712yes—
269C42—41no—
270C42—81no—
271C23#120×C13711yescharacteristic
272Q8—42no—
273Q8—81no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4C2×SD16×C13711yescharacteristic
302C2×C4#135×C13711yescharacteristic
303C2×C4#135×C13711yescharacteristic
304C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
305C2×C4#137×C13711yescharacteristic
306C2×C4#137×C13711yescharacteristic
307C8—42no—
308C8—42no—
309C8—42no—
310C22#448×C13711yescharacteristic
311C22#449×C13711yescharacteristic
312C22#452×C13711yescharacteristic
313C22#453×C13711yescharacteristic
314C22#456×C13711yescharacteristic
315C22#456×C13711yescharacteristic
316C22#458×C13711yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—161no—
330C2#1609×C13711yescharacteristic
331C2#1611×C13711yescharacteristic
332C2#1618×C13711yescharacteristic
333C2#1622×C13711yescharacteristic
334C2#1650×C13711yescharacteristic
335C2#1653×C13711yescharacteristic
336C2#1660×C13711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C137#120
commutator, Frattini, cosocleC2×C42C23×C137
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
168. #7807C137direct (N × H)
169. C137#7807direct (N × H)

Maximal subgroups

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

subgroupindex
#2805×C1372
#2096×C1372
#2084×C1372
#2083×C1372
#1272×C1372
#1271×C1372
#7807137