Finite Group Databasebeta

← C137×#25827 #46875213

Subgroups — C137×#25827 #46875213

Order 35072.

910 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3502×C137C211yesmaximal, characteristic
2#3166×C137C212yesmaximal
3#2565×C137C211yesmaximal, characteristic
4#2061×C137C212yesmaximal
5#2060×C137C212yesmaximal
6#1986×C137C212yesmaximal
7#1857×C137C212yesmaximal
8#1857×C137C212yesmaximal
9C4×#101×C137C211yesmaximal, characteristic
10Q82×C137—22no—
11#557×C137—22no—
12#557×C137—24no—
13#544×C137—22no—
14#544×C137C2212yes—
15#533×C137—22no—
16#533×C137C2212yes—
17C2×#125×C137C2211yescharacteristic
18#519×C137C2212yes—
19C2×C4×Q8×C137C2211yescharacteristic
20#501×C137—22no—
21#501×C137—22no—
22#499×C137—24no—
23#428×C137C2214yes—
24#428×C137C2214yes—
25C2×#101×C137C2212yes—
26C4×M16×C137C2212yes—
27#398×C137—22no—
28#391×C137C2211yescharacteristic
29#391×C137C2211yescharacteristic
30#387×C137—22no—
31#384×C137C2211yescharacteristic
32#382×C137C2211yescharacteristic
33C4×C4⋊C4×C137C2211yescharacteristic
34#343×C137C2212yes—
35#339×C137C2214yes—
36#339×C137C2214yes—
37C22×Q8×C137C2311yescharacteristic
38C2×M16×C137C2314yes—
39C4⋊Q8×C137—22no—
40C4⋊Q8×C137—22no—
41C4⋊Q8×C137—28no—
42C4⋊Q8×C137—24no—
43C4⋊Q8×C137D412yes—
44C4⋊Q8×C137D412yes—
45#125×C137—24no—
46#125×C137—28no—
47#125×C137—24no—
48#125×C137—22no—
49#125×C137—22no—
50#125×C137D414yes—
51C22⋊Q8×C137—22no—
52C22⋊Q8×C137—24no—
53C22⋊Q8×C137—22no—
54C4×Q8×C137—24no—
55C4×Q8×C137—24no—
56C4×Q8×C137—24no—
57C4×Q8×C137—24no—
58C4×Q8×C137—22no—
59C4×Q8×C137—22no—
60C4×Q8×C137—22no—
61C4×Q8×C137—22no—
62#117×C137—24no—
63#117×C137C2314yes—
64C2×C4⋊C4×C137—21no—
65C2×C4⋊C4×C137—22no—
66C2×C4⋊C4×C137—21no—
67C2×C4⋊C4×C137—21no—
68C2×C4⋊C4×C137D412yes—
69C2×C4⋊C4×C137C2311yescharacteristic
70C2×C4⋊C4×C137C2311yescharacteristic
71C2×C4⋊C4×C137C2311yescharacteristic
72C2×C42×C137D412yes—
73C2×C42×C137C2311yescharacteristic
74C2×C42×C137C2311yescharacteristic
75C2×C42×C137C2311yescharacteristic
76#107×C137—24no—
77#107×C137—24no—
78#106×C137—24no—
79#106×C137—24no—
80#101×C137Q818yescomplemented
81#97×C137—22no—
82C4×C8×C137—22no—
83#95×C137—21no—
84#95×C137—22no—
85#95×C137—22no—
86#95×C137—22no—
87C2×Q8×C137—24no—
88C2×Q8×C137—22no—
89C2×Q8×C137—22no—
90C2×Q8×C137—22no—
91C2×Q8×C137—22no—
92C2×Q8×C137C2×Q814yes—
93C22×C4×C137—21no—
94C22×C4×C137—21no—
95C22×C4×C137—21no—
96C22×C4×C137—21no—
97C22×C4×C137C2×D412yes—
98C22×C4×C137C2×D412yes—
99C22×C4×C137C2×D411yescharacteristic
100C22×C4×C137C2×D411yescharacteristic
101C22×C4×C137C2411yescharacteristic
102M16×C137—24no—
103M16×C137C2×Q818yes—
104C2×C8×C137—24no—
105C4⋊C4×C137—24no—
106C4⋊C4×C137—24no—
107C4⋊C4×C137—24no—
108C4⋊C4×C137—28no—
109C4⋊C4×C137—24no—
110C4⋊C4×C137—24no—
111C4⋊C4×C137—22no—
112C4⋊C4×C137—22no—
113C4⋊C4×C137—24no—
114C4⋊C4×C137—22no—
115C4⋊C4×C137—22no—
116C4⋊C4×C137—22no—
117C4⋊C4×C137—42no—
118C4⋊C4×C137—44no—
119C4⋊C4×C137—41no—
120C4⋊C4×C137—41no—
121C4⋊C4×C137—42no—
122C4⋊C4×C137C2×D414yes—
123C4⋊C4×C137C2×D414yes—
124C22⋊C4×C137—24no—
125C42×C137—28no—
126C42×C137—22no—
127C42×C137—22no—
128C42×C137—24no—
129C42×C137—22no—
130C42×C137—22no—
131C42×C137C2×D412yes—
132C42×C137C2×D412yes—
133C23×C137C22×D411yescharacteristic
134Q8×C137—28no—
135Q8×C137—44no—
136Q8×C137—82no—
137Q8×C137—84no—
138C2×C4×C137—22no—
139C2×C4×C137—22no—
140C2×C4×C137—22no—
141C2×C4×C137—24no—
142C2×C4×C137—24no—
143C2×C4×C137—22no—
144C2×C4×C137—41no—
145C2×C4×C137—41no—
146C2×C4×C137—41no—
147C2×C4×C137—41no—
148C2×C4×C137—42no—
149C2×C4×C137—41no—
150C2×C4×C137—42no—
151C2×C4×C137—41no—
152C2×C4×C137—42no—
153C2×C4×C137—41no—
154C2×C4×C137—41no—
155C2×C4×C137—41no—
156C2×C4×C137#12011yescharacteristic
157C2×C4×C137#12011yescharacteristic
158C2×C4×C137#12012yes—
159C2×C4×C137C4⋊Q814yes—
160C2×C4×C137C22×D412yes—
161C2×C4×C137C22×Q812yes—
162C2×C4×C1372−1+412yes—
163C8×C137—28no—
164C22×C137—21no—
165C22×C137—21no—
166C22×C137C2×#12011yescharacteristic
167C22×C137C2×C4⋊Q811yescharacteristic
168C22×C137#53611yescharacteristic
169C4×C137—24no—
170C4×C137—22no—
171C4×C137—21no—
172C4×C137—21no—
173C4×C137—42no—
174C4×C137—42no—
175C4×C137—44no—
176C4×C137—44no—
177C4×C137—81no—
178C4×C137—81no—
179C4×C137—81no—
180C4×C137D4×Q814yes—
181C2×C137—21no—
182C2×C137—21no—
183C2×C137#243411yescharacteristic
184C2×C137#301811yescharacteristic
185C2×C137#302011yescharacteristic
186#25827C13711yesmaximal, characteristic, direct product factor, Sylow
187C137#2582711yescharacteristic, direct product factor, Sylow
188#3502C2×C13711yescharacteristic
189#3166C2×C13712yes—
190#2565C2×C13711yescharacteristic
191#2061C2×C13712yes—
192#2060C2×C13712yes—
193#1986C2×C13712yes—
194#1857C2×C13712yes—
195#1857C2×C13712yes—
196C4×#101C2×C13711yescharacteristic
197Q82—22no—
198#557—22no—
199#557—24no—
200#544—22no—
201#544C22×C13712yes—
202#533—22no—
203#533C22×C13712yes—
204C2×#125C22×C13711yescharacteristic
205#519C22×C13712yes—
206C2×C4×Q8C22×C13711yescharacteristic
207#501—22no—
208#501—22no—
209#499—24no—
210#428C22×C13714yes—
211#428C22×C13714yes—
212C2×#101C22×C13712yes—
213C4×M16C22×C13712yes—
214#398—22no—
215#391C22×C13711yescharacteristic
216#391C22×C13711yescharacteristic
217#387—22no—
218#384C22×C13711yescharacteristic
219#382C22×C13711yescharacteristic
220C4×C4⋊C4C22×C13711yescharacteristic
221#343C22×C13712yes—
222#339C22×C13714yes—
223#339C22×C13714yes—
224C22×Q8C23×C13711yescharacteristic
225C2×M16C23×C13714yes—
226C4⋊Q8—22no—
227C4⋊Q8—22no—
228C4⋊Q8—28no—
229C4⋊Q8—24no—
230C4⋊Q8D4×C13712yes—
231C4⋊Q8D4×C13712yes—
232#125—24no—
233#125—28no—
234#125—24no—
235#125—22no—
236#125—22no—
237#125D4×C13714yes—
238C22⋊Q8—22no—
239C22⋊Q8—24no—
240C22⋊Q8—22no—
241C4×Q8—24no—
242C4×Q8—24no—
243C4×Q8—24no—
244C4×Q8—24no—
245C4×Q8—22no—
246C4×Q8—22no—
247C4×Q8—22no—
248C4×Q8—22no—
249#117—24no—
250#117C23×C13714yes—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4D4×C13712yes—
256C2×C4⋊C4C23×C13711yescharacteristic
257C2×C4⋊C4C23×C13711yescharacteristic
258C2×C4⋊C4C23×C13711yescharacteristic
259C2×C42D4×C13712yes—
260C2×C42C23×C13711yescharacteristic
261C2×C42C23×C13711yescharacteristic
262C2×C42C23×C13711yescharacteristic
263#107—24no—
264#107—24no—
265#106—24no—
266#106—24no—
267#101Q8×C13718yescomplemented
268#97—22no—
269C4×C8—22no—
270#95—21no—
271#95—22no—
272#95—22no—
273#95—22no—
274C2×Q8—24no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8C2×Q8×C13714yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4C2×D4×C13712yes—
285C22×C4C2×D4×C13712yes—
286C22×C4C2×D4×C13711yescharacteristic
287C22×C4C2×D4×C13711yescharacteristic
288C22×C4C24×C13711yescharacteristic
289M16—24no—
290M16C2×Q8×C13718yes—
291C2×C8—24no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—24no—
295C4⋊C4—28no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—24no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—42no—
305C4⋊C4—44no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—42no—
309C4⋊C4C2×D4×C13714yes—
310C4⋊C4C2×D4×C13714yes—
311C22⋊C4—24no—
312C42—28no—
313C42—22no—
314C42—22no—
315C42—24no—
316C42—22no—
317C42—22no—
318C42C2×D4×C13712yes—
319C42C2×D4×C13712yes—
320C23C22×D4×C13711yescharacteristic
321Q8—28no—
322Q8—44no—
323Q8—82no—
324Q8—84no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4#120×C13711yescharacteristic
344C2×C4#120×C13711yescharacteristic
345C2×C4#120×C13712yes—
346C2×C4C4⋊Q8×C13714yes—
347C2×C4C22×D4×C13712yes—
348C2×C4C22×Q8×C13712yes—
349C2×C42−1+4×C13712yes—
350C8—28no—
351C22—21no—
352C22—21no—
353C22C2×#120×C13711yescharacteristic
354C22C2×C4⋊Q8×C13711yescharacteristic
355C22#536×C13711yescharacteristic
356C4—24no—
357C4—22no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—42no—
362C4—44no—
363C4—44no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4D4×Q8×C13714yes—
368C2—21no—
369C2—21no—
370C2#2434×C13711yescharacteristic
371C2#3018×C13711yescharacteristic
372C2#3020×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC23×C137C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
80. #101×C137Q8semidirect
186. #25827C137direct (N × H)
187. C137#25827direct (N × H)
267. #101Q8×C137semidirect

Maximal subgroups

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

subgroupindex
#3502×C1372
#3166×C1372
#2565×C1372
#2061×C1372
#2060×C1372
#1986×C1372
#1857×C1372
C4×#101×C1372
#25827137