Finite Group Databasebeta

← C137×#9302 #46858688

Subgroups — C137×#9302 #46858688

Order 35072.

480 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3227×C137C211yesmaximal, characteristic
2#2331×C137C211yesmaximal, characteristic, complemented
3#1963×C137C211yesmaximal, characteristic
4#1549×C137C211yesmaximal, characteristic, complemented
5#1517×C137C211yesmaximal, characteristic
6#1286×C137C211yesmaximal, characteristic, complemented
7#1274×C137C211yesmaximal, characteristic, complemented
8#532×C137C2211yescharacteristic
9C2×C4⋊Q8×C137C2211yescharacteristic
10#498×C137C412yescomplemented
11#486×C137C412yescomplemented
12#481×C137—22no—
13#476×C137—22no—
14#431×C137C2211yescharacteristic
15#431×C137C2211yescharacteristic
16#423×C137C2211yescharacteristic
17C2×#104×C137—21no—
18C2×#104×C137—21no—
19#391×C137—22no—
20#389×C137—21no—
21#387×C137—22no—
22#382×C137C2211yescharacteristic
23C4×C4⋊C4×C137—21no—
24#376×C137C2211yescharacteristic
25#332×C137—22no—
26#327×C137—22no—
27C2×#41×C137—21no—
28C22×Q8×C137—21no—
29C2×M16×C137—21no—
30C4⋊Q8×C137—21no—
31C4⋊Q8×C137—21no—
32C4⋊Q8×C137C2×C411yescharacteristic
33C4⋊Q8×C137C2×C412yes—
34C4⋊Q8×C137D412yes—
35#127×C137C2×C411yescharacteristic
36#124×C137—21no—
37#121×C137—21no—
38#121×C137—21no—
39C4×D4×C137—21no—
40C4×D4×C137—21no—
41C2×C4⋊C4×C137—21no—
42C2×C4⋊C4×C137—21no—
43C2×C4⋊C4×C137—22no—
44C2×C4⋊C4×C137D412yes—
45C2×C42×C137—22no—
46C2×C42×C137D411yescharacteristic
47C2×C42×C137D411yescharacteristic
48C2×C42×C137C2311yescharacteristic
49#106×C137—24no—
50C4⋊C8×C137—21no—
51C4⋊C8×C137—21no—
52C4⋊C8×C137—21no—
53C4⋊C8×C137—21no—
54#104×C137—42no—
55#104×C137—42no—
56#102×C137—24no—
57C22⋊C8×C137—21no—
58C22⋊C8×C137—21no—
59C4×C8×C137—21no—
60C4×C8×C137C2×C412yes—
61#95×C137—22no—
62#95×C137—22no—
63#95×C137—21no—
64#95×C137—21no—
65#95×C137—21no—
66#95×C137D412yes—
67#41×C137—41no—
68#41×C137—41no—
69#41×C137—41no—
70#41×C137—41no—
71C2×Q8×C137—22no—
72C2×Q8×C137—22no—
73C2×Q8×C137—21no—
74C2×Q8×C137—82no—
75C2×D4×C137—21no—
76C2×D4×C137—21no—
77C2×D4×C137—21no—
78C2×D4×C137—41no—
79C22×C4×C137—21no—
80C22×C4×C137—22no—
81C22×C4×C137—21no—
82C22×C4×C137—22no—
83C22×C4×C137—41no—
84C22×C4×C137C2×D411yescharacteristic
85C22×C4×C137C2×D411yescharacteristic
86C22×C4×C137C2×D411yescharacteristic
87M16×C137—41no—
88M16×C137—41no—
89C2×C8×C137—22no—
90C2×C8×C137—41no—
91C2×C8×C137—41no—
92C4⋊C4×C137—22no—
93C4⋊C4×C137—22no—
94C4⋊C4×C137—22no—
95C4⋊C4×C137—21no—
96C4⋊C4×C137—21no—
97C4⋊C4×C137—41no—
98C4⋊C4×C137—41no—
99C4⋊C4×C137—82no—
100C4⋊C4×C137C22⋊C414yes—
101C22⋊C4×C137—41no—
102C22⋊C4×C137—41no—
103C42×C137—21no—
104C42×C137—21no—
105C42×C137—21no—
106C42×C137—82no—
107C42×C137SD1612yes—
108C42×C137C22×C411yescharacteristic
109C42×C137C2×D411yescharacteristic
110C42×C137#4111yescharacteristic
111C42×C137#4111yescharacteristic
112C23×C137—41no—
113C23×C137#12011yescharacteristic
114Q8×C137—41no—
115Q8×C137—41no—
116Q8×C137—82no—
117Q8×C137—82no—
118D4×C137—42no—
119D4×C137—41no—
120D4×C137—41no—
121D4×C137—81no—
122D4×C137—81no—
123D4×C137—81no—
124C2×C4×C137—24no—
125C2×C4×C137—22no—
126C2×C4×C137—41no—
127C2×C4×C137—41no—
128C2×C4×C137—41no—
129C2×C4×C137—42no—
130C2×C4×C137—42no—
131C2×C4×C137—41no—
132C2×C4×C137—42no—
133C2×C4×C137—41no—
134C2×C4×C137—41no—
135C2×C4×C137—42no—
136C2×C4×C137—41no—
137C2×C4×C137—41no—
138C2×C4×C137—42no—
139C2×C4×C137—81no—
140C2×C4×C137—81no—
141C2×C4×C137C2×C22⋊C411yescharacteristic
142C2×C4×C137C4×D411yescharacteristic
143C2×C4×C137C4×D411yescharacteristic
144C2×C4×C137#12111yescharacteristic
145C2×C4×C137#12111yescharacteristic
146C2×C4×C137#12311yescharacteristic
147C2×C4×C137C2×SD1611yescharacteristic
148C2×C4×C137#13511yescharacteristic
149C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C137#13711yescharacteristic
151C8×C137—42no—
152C8×C137—81no—
153C8×C137—81no—
154C22×C137—21no—
155C22×C137—21no—
156C22×C137—81no—
157C22×C137—81no—
158C22×C137—81no—
159C22×C137#38611yescharacteristic
160C22×C137#44811yescharacteristic
161C22×C137#44911yescharacteristic
162C4×C137—21no—
163C4×C137—21no—
164C4×C137—21no—
165C4×C137—21no—
166C4×C137—42no—
167C4×C137—44no—
168C4×C137—82no—
169C4×C137—81no—
170C4×C137—81no—
171C4×C137C4×SD1611yescharacteristic
172C4×C137#44011yescharacteristic
173C4×C137#46011yescharacteristic
174C4×C137#46411yescharacteristic
175C2×C137—21no—
176C2×C137—21no—
177C2×C137—161no—
178C2×C137#188011yescharacteristic
179C2×C137#190411yescharacteristic
180C2×C137#191211yescharacteristic
181#9302C13711yesmaximal, characteristic, direct product factor, Sylow
182C137#930211yescharacteristic, direct product factor, Sylow
183#3227C2×C13711yescharacteristic
184#2331C2×C13711yescharacteristic, complemented
185#1963C2×C13711yescharacteristic
186#1549C2×C13711yescharacteristic, complemented
187#1517C2×C13711yescharacteristic
188#1286C2×C13711yescharacteristic, complemented
189#1274C2×C13711yescharacteristic, complemented
190#532C22×C13711yescharacteristic
191C2×C4⋊Q8C22×C13711yescharacteristic
192#498C4×C13712yescomplemented
193#486C4×C13712yescomplemented
194#481—22no—
195#476—22no—
196#431C22×C13711yescharacteristic
197#431C22×C13711yescharacteristic
198#423C22×C13711yescharacteristic
199C2×#104—21no—
200C2×#104—21no—
201#391—22no—
202#389—21no—
203#387—22no—
204#382C22×C13711yescharacteristic
205C4×C4⋊C4—21no—
206#376C22×C13711yescharacteristic
207#332—22no—
208#327—22no—
209C2×#41—21no—
210C22×Q8—21no—
211C2×M16—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8C2×C4×C13711yescharacteristic
215C4⋊Q8C2×C4×C13712yes—
216C4⋊Q8D4×C13712yes—
217#127C2×C4×C13711yescharacteristic
218#124—21no—
219#121—21no—
220#121—21no—
221C4×D4—21no—
222C4×D4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4D4×C13712yes—
227C2×C42—22no—
228C2×C42D4×C13711yescharacteristic
229C2×C42D4×C13711yescharacteristic
230C2×C42C23×C13711yescharacteristic
231#106—24no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236#104—42no—
237#104—42no—
238#102—24no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241C4×C8—21no—
242C4×C8C2×C4×C13712yes—
243#95—22no—
244#95—22no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95D4×C13712yes—
249#41—41no—
250#41—41no—
251#41—41no—
252#41—41no—
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8—21no—
256C2×Q8—82no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4C2×D4×C13711yescharacteristic
267C22×C4C2×D4×C13711yescharacteristic
268C22×C4C2×D4×C13711yescharacteristic
269M16—41no—
270M16—41no—
271C2×C8—22no—
272C2×C8—41no—
273C2×C8—41no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—82no—
282C4⋊C4C22⋊C4×C13714yes—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C42—21no—
286C42—21no—
287C42—21no—
288C42—82no—
289C42SD16×C13712yes—
290C42C22×C4×C13711yescharacteristic
291C42C2×D4×C13711yescharacteristic
292C42#41×C13711yescharacteristic
293C42#41×C13711yescharacteristic
294C23—41no—
295C23#120×C13711yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—82no—
299Q8—82no—
300D4—42no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×C22⋊C4×C13711yescharacteristic
324C2×C4C4×D4×C13711yescharacteristic
325C2×C4C4×D4×C13711yescharacteristic
326C2×C4#121×C13711yescharacteristic
327C2×C4#121×C13711yescharacteristic
328C2×C4#123×C13711yescharacteristic
329C2×C4C2×SD16×C13711yescharacteristic
330C2×C4#135×C13711yescharacteristic
331C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
332C2×C4#137×C13711yescharacteristic
333C8—42no—
334C8—81no—
335C8—81no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#386×C13711yescharacteristic
342C22#448×C13711yescharacteristic
343C22#449×C13711yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—44no—
350C4—82no—
351C4—81no—
352C4—81no—
353C4C4×SD16×C13711yescharacteristic
354C4#440×C13711yescharacteristic
355C4#460×C13711yescharacteristic
356C4#464×C13711yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2#1880×C13711yescharacteristic
361C2#1904×C13711yescharacteristic
362C2#1912×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#386
commutatorC42C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radical#532×C137C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2331×C137C2semidirect
4. #1549×C137C2semidirect
6. #1286×C137C2semidirect
7. #1274×C137C2semidirect
10. #498×C137C4semidirect
11. #486×C137C4semidirect
181. #9302C137direct (N × H)
182. C137#9302direct (N × H)
184. #2331C2×C137semidirect
186. #1549C2×C137semidirect
188. #1286C2×C137semidirect
189. #1274C2×C137semidirect
192. #498C4×C137semidirect
193. #486C4×C137semidirect

Maximal subgroups

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

subgroupindex
#3227×C1372
#2331×C1372
#1963×C1372
#1549×C1372
#1517×C1372
#1286×C1372
#1274×C1372
#9302137