Finite Group Databasebeta

← C137×#9011 #46858397

Subgroups — C137×#9011 #46858397

Order 35072.

560 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2973×C137C211yesmaximal, characteristic
2#2395×C137C211yesmaximal, characteristic
3#1826×C137C212yesmaximal, complemented
4C4×#99×C137C211yesmaximal, characteristic
5#1297×C137C212yesmaximal, complemented
6C2×C4×D4×C137C2211yescharacteristic
7C2×#117×C137C2211yescharacteristic
8#435×C137—24no—
9#432×C137—21no—
10C2×#99×C137—21no—
11#407×C137C2212yes—
12C2×C22⋊C8×C137—21no—
13#400×C137C411yescharacteristic, complemented
14#399×C137C411yescharacteristic, complemented
15#398×C137C411yescharacteristic, complemented
16#397×C137—21no—
17#397×C137C411yescharacteristic, complemented
18#394×C137—21no—
19C4×C4⋊C4×C137—21no—
20C4×C22⋊C4×C137—21no—
21C4×C22⋊C4×C137C2212yes—
22C4×C22⋊C4×C137C2211yescharacteristic
23#342×C137—21no—
24#339×C137—24no—
25C22×D4×C137D411yescharacteristic
26C23×C4×C137D411yescharacteristic
27C23×C4×C137C2311yescharacteristic
28C2×M16×C137D414yes—
29C22×C8×C137—22no—
30C4×D4×C137—22no—
31C4×D4×C137—22no—
32#117×C137—22no—
33#117×C137—22no—
34C2×C4⋊C4×C137—21no—
35C2×C4⋊C4×C137—21no—
36C2×C4⋊C4×C137C2×C411yescharacteristic
37C2×C4⋊C4×C137C2×C411yescharacteristic
38C2×C4⋊C4×C137C2×C411yescharacteristic
39C2×C22⋊C4×C137—22no—
40C2×C22⋊C4×C137—21no—
41C2×C22⋊C4×C137—21no—
42C2×C22⋊C4×C137—21no—
43C2×C22⋊C4×C137—21no—
44C2×C22⋊C4×C137C2×C411yescharacteristic
45C2×C22⋊C4×C137D411yescharacteristic
46C2×C42×C137—21no—
47C2×C42×C137—21no—
48C2×C42×C137—22no—
49C2×C42×C137D411yescharacteristic
50C4⋊C8×C137—22no—
51#99×C137—24no—
52C22⋊C8×C137—22no—
53C22⋊C8×C137—22no—
54C22⋊C8×C137—22no—
55#97×C137—22no—
56#95×C137—21no—
57#95×C137—21no—
58#95×C137—21no—
59#95×C137—21no—
60#95×C137—22no—
61#95×C137C2×C411yescharacteristic
62#95×C137C2×C411yescharacteristic
63C24×C137C22⋊C411yescharacteristic
64C24×C137C2×D411yescharacteristic
65C2×D4×C137—22no—
66C2×D4×C137—22no—
67C2×D4×C137—41no—
68C22×C4×C137—21no—
69C22×C4×C137—21no—
70C22×C4×C137—21no—
71C22×C4×C137—21no—
72C22×C4×C137—21no—
73C22×C4×C137—21no—
74C22×C4×C137—42no—
75C22×C4×C137—42no—
76C22×C4×C137—42no—
77C22×C4×C137C22⋊C411yescharacteristic
78C22×C4×C137C22⋊C411yescharacteristic
79C22×C4×C137C22⋊C411yescharacteristic
80C22×C4×C137C22×C411yescharacteristic
81C22×C4×C137C2×D412yes—
82C22×C4×C137C2×D411yescharacteristic
83C22×C4×C137#4112yes—
84M16×C137—44no—
85C2×C8×C137—24no—
86C2×C8×C137—82no—
87C4⋊C4×C137—22no—
88C4⋊C4×C137—22no—
89C4⋊C4×C137—22no—
90C4⋊C4×C137—42no—
91C4⋊C4×C137—42no—
92C22⋊C4×C137—22no—
93C22⋊C4×C137—22no—
94C22⋊C4×C137—24no—
95C22⋊C4×C137—42no—
96C22⋊C4×C137—42no—
97C22⋊C4×C137—42no—
98C22⋊C4×C137—42no—
99C22⋊C4×C137—42no—
100C42×C137—21no—
101C42×C137—21no—
102C42×C137—42no—
103C42×C137—44no—
104C42×C137—41no—
105C42×C137—41no—
106C23×C137—21no—
107C23×C137—21no—
108C23×C137—21no—
109C23×C137—21no—
110C23×C137—41no—
111C23×C137—41no—
112C23×C137—41no—
113C23×C137—41no—
114C23×C137#10412yes—
115C23×C137C2×C22⋊C411yescharacteristic
116C23×C137#12112yes—
117D4×C137—44no—
118C2×C4×C137—24no—
119C2×C4×C137—22no—
120C2×C4×C137—22no—
121C2×C4×C137—21no—
122C2×C4×C137—21no—
123C2×C4×C137—21no—
124C2×C4×C137—21no—
125C2×C4×C137—21no—
126C2×C4×C137—41no—
127C2×C4×C137—42no—
128C2×C4×C137—41no—
129C2×C4×C137—41no—
130C2×C4×C137—42no—
131C2×C4×C137—41no—
132C2×C4×C137—41no—
133C2×C4×C137—41no—
134C2×C4×C137—44no—
135C2×C4×C137—41no—
136C2×C4×C137—41no—
137C2×C4×C137—41no—
138C2×C4×C137—41no—
139C2×C4×C137—41no—
140C2×C4×C137—41no—
141C2×C4×C137—41no—
142C2×C4×C137—41no—
143C2×C4×C137—81no—
144C2×C4×C137—82no—
145C2×C4×C137—82no—
146C2×C4×C137C4×D412yes—
147C2×C4×C137#12011yescharacteristic
148C2×C4×C137#12311yescharacteristic
149C8×C137—44no—
150C22×C137—21no—
151C22×C137—21no—
152C22×C137—22no—
153C22×C137—22no—
154C22×C137—22no—
155C22×C137—22no—
156C22×C137—42no—
157C22×C137—41no—
158C22×C137—41no—
159C22×C137—81no—
160C22×C137—81no—
161C22×C137—81no—
162C22×C137#38611yescharacteristic
163C22×C137C2×#10411yescharacteristic
164C22×C137#42111yescharacteristic
165C4×C137—21no—
166C4×C137—22no—
167C4×C137—42no—
168C4×C137—41no—
169C4×C137—41no—
170C4×C137—41no—
171C4×C137—81no—
172C4×C137—84no—
173C4×C137—81no—
174C4×C137—81no—
175C4×C137#45812yes—
176C2×C137—21no—
177C2×C137—21no—
178C2×C137—42no—
179C2×C137—42no—
180C2×C137#187111yescharacteristic
181C2×C137#188411yescharacteristic
182C2×C137#189011yescharacteristic
183#9011C13711yesmaximal, characteristic, direct product factor, Sylow
184C137#901111yescharacteristic, direct product factor, Sylow
185#2973C2×C13711yescharacteristic
186#2395C2×C13711yescharacteristic
187#1826C2×C13712yescomplemented
188C4×#99C2×C13711yescharacteristic
189#1297C2×C13712yescomplemented
190C2×C4×D4C22×C13711yescharacteristic
191C2×#117C22×C13711yescharacteristic
192#435—24no—
193#432—21no—
194C2×#99—21no—
195#407C22×C13712yes—
196C2×C22⋊C8—21no—
197#400C4×C13711yescharacteristic, complemented
198#399C4×C13711yescharacteristic, complemented
199#398C4×C13711yescharacteristic, complemented
200#397—21no—
201#397C4×C13711yescharacteristic, complemented
202#394—21no—
203C4×C4⋊C4—21no—
204C4×C22⋊C4—21no—
205C4×C22⋊C4C22×C13712yes—
206C4×C22⋊C4C22×C13711yescharacteristic
207#342—21no—
208#339—24no—
209C22×D4D4×C13711yescharacteristic
210C23×C4D4×C13711yescharacteristic
211C23×C4C23×C13711yescharacteristic
212C2×M16D4×C13714yes—
213C22×C8—22no—
214C4×D4—22no—
215C4×D4—22no—
216#117—22no—
217#117—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×C4×C13711yescharacteristic
221C2×C4⋊C4C2×C4×C13711yescharacteristic
222C2×C4⋊C4C2×C4×C13711yescharacteristic
223C2×C22⋊C4—22no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4C2×C4×C13711yescharacteristic
229C2×C22⋊C4D4×C13711yescharacteristic
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—22no—
233C2×C42D4×C13711yescharacteristic
234C4⋊C8—22no—
235#99—24no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239#97—22no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—22no—
245#95C2×C4×C13711yescharacteristic
246#95C2×C4×C13711yescharacteristic
247C24C22⋊C4×C13711yescharacteristic
248C24C2×D4×C13711yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4C22⋊C4×C13711yescharacteristic
262C22×C4C22⋊C4×C13711yescharacteristic
263C22×C4C22⋊C4×C13711yescharacteristic
264C22×C4C22×C4×C13711yescharacteristic
265C22×C4C2×D4×C13712yes—
266C22×C4C2×D4×C13711yescharacteristic
267C22×C4#41×C13712yes—
268M16—44no—
269C2×C8—24no—
270C2×C8—82no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—24no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C42—21no—
285C42—21no—
286C42—42no—
287C42—44no—
288C42—41no—
289C42—41no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23#104×C13712yes—
299C23C2×C22⋊C4×C13711yescharacteristic
300C23#121×C13712yes—
301D4—44no—
302C2×C4—24no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—44no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4C4×D4×C13712yes—
331C2×C4#120×C13711yescharacteristic
332C2×C4#123×C13711yescharacteristic
333C8—44no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#386×C13711yescharacteristic
347C22C2×#104×C13711yescharacteristic
348C22#421×C13711yescharacteristic
349C4—21no—
350C4—22no—
351C4—42no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—84no—
357C4—81no—
358C4—81no—
359C4#458×C13712yes—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—42no—
364C2#1871×C13711yescharacteristic
365C2#1884×C13711yescharacteristic
366C2#1890×C13711yescharacteristic
subgroupG/H
centerC2×C4×C137#120
commutatorC22×C4C22×C4×C137
Frattini, cosocleC23×C4C23×C137
socleC22×C137#386
prime radicalC22×D4×C137D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1826×C137C2semidirect
5. #1297×C137C2semidirect
13. #400×C137C4semidirect
14. #399×C137C4semidirect
15. #398×C137C4semidirect
17. #397×C137C4semidirect
183. #9011C137direct (N × H)
184. C137#9011direct (N × H)
187. #1826C2×C137semidirect
189. #1297C2×C137semidirect
197. #400C4×C137semidirect
198. #399C4×C137semidirect
199. #398C4×C137semidirect
201. #397C4×C137semidirect

Maximal subgroups

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

subgroupindex
#2973×C1372
#2395×C1372
#1826×C1372
C4×#99×C1372
#1297×C1372
#9011137