Finite Group Databasebeta

← C137×#9790 #46859176

Subgroups — C137×#9790 #46859176

Order 35072.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#488×C137C211yesmaximal, characteristic
2#1568×C137C211yesmaximal, characteristic, complemented
3#1528×C137C211yesmaximal, characteristic, complemented
4#1527×C137C211yesmaximal, characteristic
5#1470×C137C211yesmaximal, characteristic, complemented
6#1469×C137C211yesmaximal, characteristic
7#1451×C137C211yesmaximal, characteristic, complemented
8C2×#125×C137C2211yescharacteristic
9C2×#124×C137C2211yescharacteristic
10#488×C137—21no—
11#488×C137—21no—
12#488×C137—21no—
13#488×C137—21no—
14#432×C137C2211yescharacteristic
15#432×C137C2211yescharacteristic
16#431×C137C2211yescharacteristic
17C2×#103×C137C411yescharacteristic
18C2×#103×C137C411yescharacteristic
19C2×#102×C137C411yescharacteristic
20C2×#102×C137C411yescharacteristic
21C4×M16×C137C2211yescharacteristic
22C2×C4×C8×C137C2211yescharacteristic
23#335×C137—21no—
24#334×C137—21no—
25#330×C137—22no—
26#329×C137—22no—
27#324×C137—22no—
28#323×C137—22no—
29#322×C137—21no—
30#322×C137—21no—
31C22×Q8×C137C2×C411yescharacteristic
32C22×D4×C137C2×C411yescharacteristic
33C2×M16×C137—21no—
34C22×C8×C137C2×C411yescharacteristic
35C22×C8×C137C2×C411yescharacteristic
36#125×C137—21no—
37#125×C137—21no—
38#125×C137—21no—
39#125×C137—21no—
40#124×C137—21no—
41#124×C137—21no—
42#124×C137—21no—
43#124×C137—21no—
44C2×C4⋊C4×C137—21no—
45C2×C4⋊C4×C137—21no—
46C2×C4⋊C4×C137C2×C411yescharacteristic
47C2×C4⋊C4×C137C2×C411yescharacteristic
48C2×C22⋊C4×C137—21no—
49C2×C22⋊C4×C137—21no—
50C2×C42×C137C2311yescharacteristic
51C4⋊C8×C137—21no—
52C4⋊C8×C137—21no—
53C4⋊C8×C137—21no—
54#103×C137—21no—
55#103×C137—21no—
56#103×C137—21no—
57#103×C137—21no—
58#102×C137—21no—
59#102×C137—21no—
60#102×C137—21no—
61#102×C137—21no—
62C22⋊C8×C137—21no—
63C22⋊C8×C137—21no—
64C22⋊C8×C137D412yes—
65#97×C137—21no—
66#97×C137—21no—
67#97×C137D412yes—
68C4×C8×C137—21no—
69C4×C8×C137—21no—
70C4×C8×C137D411yescharacteristic
71C4×C8×C137D411yescharacteristic
72C4×C8×C137D411yescharacteristic
73C4×C8×C137D411yescharacteristic
74C24×C137—21no—
75C2×Q8×C137—21no—
76C2×Q8×C137—21no—
77C2×Q8×C137—41no—
78C2×Q8×C137—41no—
79C2×D4×C137—21no—
80C2×D4×C137—21no—
81C2×D4×C137—41no—
82C2×D4×C137—41no—
83C22×C4×C137—21no—
84C22×C4×C137—21no—
85C22×C4×C137—21no—
86C22×C4×C137C22×C411yescharacteristic
87C22×C4×C137C2×D411yescharacteristic
88C22×C4×C137#4111yescharacteristic
89M16×C137—42no—
90C2×C8×C137—22no—
91C2×C8×C137—22no—
92C2×C8×C137—41no—
93C2×C8×C137—41no—
94C2×C8×C137—41no—
95C2×C8×C137—41no—
96C2×C8×C137C22⋊C411yescharacteristic
97C2×C8×C137C22⋊C411yescharacteristic
98C2×C8×C137C22⋊C411yescharacteristic
99C2×C8×C137C22⋊C411yescharacteristic
100C4⋊C4×C137—21no—
101C4⋊C4×C137—21no—
102C4⋊C4×C137—21no—
103C4⋊C4×C137—21no—
104C4⋊C4×C137—41no—
105C4⋊C4×C137—41no—
106C4⋊C4×C137—41no—
107C4⋊C4×C137—41no—
108C22⋊C4×C137—41no—
109C22⋊C4×C137—41no—
110C22⋊C4×C137—41no—
111C22⋊C4×C137—41no—
112C42×C137C2×D411yescharacteristic
113C42×C137C2×D411yescharacteristic
114C42×C137C2×D411yescharacteristic
115C42×C137#4111yescharacteristic
116C23×C137—41no—
117C23×C137—42no—
118C23×C137—81no—
119C23×C137—81no—
120C23×C137C4×D411yescharacteristic
121Q8×C137—41no—
122Q8×C137—41no—
123Q8×C137—81no—
124D4×C137—41no—
125D4×C137—41no—
126D4×C137—81no—
127C2×C4×C137—22no—
128C2×C4×C137—21no—
129C2×C4×C137—21no—
130C2×C4×C137—41no—
131C2×C4×C137—41no—
132C2×C4×C137—41no—
133C2×C4×C137—41no—
134C2×C4×C137—42no—
135C2×C4×C137—81no—
136C2×C4×C137—81no—
137C2×C4×C137C2×C22⋊C411yescharacteristic
138C2×C4×C137C4×D411yescharacteristic
139C2×C4×C137#12111yescharacteristic
140C2×C4×C137#12111yescharacteristic
141C2×C4×C137#12411yescharacteristic
142C2×C4×C137#12711yescharacteristic
143C8×C137—21no—
144C8×C137—21no—
145C8×C137—21no—
146C8×C137—21no—
147C8×C137—42no—
148C8×C137—42no—
149C8×C137—81no—
150C8×C137—81no—
151C22×C137—21no—
152C22×C137—21no—
153C22×C137—81no—
154C22×C137—81no—
155C22×C137—81no—
156C22×C137—162no—
157C22×C137#39011yescharacteristic
158C22×C137#44412yes—
159C4×C137—21no—
160C4×C137—21no—
161C4×C137—21no—
162C4×C137—21no—
163C4×C137—21no—
164C4×C137—81no—
165C4×C137—81no—
166C4×C137—81no—
167C4×C137#41311yescharacteristic
168C4×C137#41311yescharacteristic
169C2×C137—22no—
170C2×C137—161no—
171C2×C137#196711yescharacteristic
172C2×C137#197511yescharacteristic
173C2×C137#197611yescharacteristic
174#9790C13711yesmaximal, characteristic, direct product factor, Sylow
175C137#979011yescharacteristic, direct product factor, Sylow
176C2×#488C2×C13711yescharacteristic
177#1568C2×C13711yescharacteristic, complemented
178#1528C2×C13711yescharacteristic, complemented
179#1527C2×C13711yescharacteristic
180#1470C2×C13711yescharacteristic, complemented
181#1469C2×C13711yescharacteristic
182#1451C2×C13711yescharacteristic, complemented
183C2×#125C22×C13711yescharacteristic
184C2×#124C22×C13711yescharacteristic
185#488—21no—
186#488—21no—
187#488—21no—
188#488—21no—
189#432C22×C13711yescharacteristic
190#432C22×C13711yescharacteristic
191#431C22×C13711yescharacteristic
192C2×#103C4×C13711yescharacteristic
193C2×#103C4×C13711yescharacteristic
194C2×#102C4×C13711yescharacteristic
195C2×#102C4×C13711yescharacteristic
196C4×M16C22×C13711yescharacteristic
197C2×C4×C8C22×C13711yescharacteristic
198#335—21no—
199#334—21no—
200#330—22no—
201#329—22no—
202#324—22no—
203#323—22no—
204#322—21no—
205#322—21no—
206C22×Q8C2×C4×C13711yescharacteristic
207C22×D4C2×C4×C13711yescharacteristic
208C2×M16—21no—
209C22×C8C2×C4×C13711yescharacteristic
210C22×C8C2×C4×C13711yescharacteristic
211#125—21no—
212#125—21no—
213#125—21no—
214#125—21no—
215#124—21no—
216#124—21no—
217#124—21no—
218#124—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×C4×C13711yescharacteristic
222C2×C4⋊C4C2×C4×C13711yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42C23×C13711yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229#103—21no—
230#103—21no—
231#103—21no—
232#103—21no—
233#102—21no—
234#102—21no—
235#102—21no—
236#102—21no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239C22⋊C8D4×C13712yes—
240#97—21no—
241#97—21no—
242#97D4×C13712yes—
243C4×C8—21no—
244C4×C8—21no—
245C4×C8D4×C13711yescharacteristic
246C4×C8D4×C13711yescharacteristic
247C4×C8D4×C13711yescharacteristic
248C4×C8D4×C13711yescharacteristic
249C24—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C2×D4—41no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C22×C4×C13711yescharacteristic
262C22×C4C2×D4×C13711yescharacteristic
263C22×C4#41×C13711yescharacteristic
264M16—42no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8C22⋊C4×C13711yescharacteristic
272C2×C8C22⋊C4×C13711yescharacteristic
273C2×C8C22⋊C4×C13711yescharacteristic
274C2×C8C22⋊C4×C13711yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42C2×D4×C13711yescharacteristic
288C42C2×D4×C13711yescharacteristic
289C42C2×D4×C13711yescharacteristic
290C42#41×C13711yescharacteristic
291C23—41no—
292C23—42no—
293C23—81no—
294C23—81no—
295C23C4×D4×C13711yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—81no—
299D4—41no—
300D4—41no—
301D4—81no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4C2×C22⋊C4×C13711yescharacteristic
313C2×C4C4×D4×C13711yescharacteristic
314C2×C4#121×C13711yescharacteristic
315C2×C4#121×C13711yescharacteristic
316C2×C4#124×C13711yescharacteristic
317C2×C4#127×C13711yescharacteristic
318C8—21no—
319C8—21no—
320C8—21no—
321C8—21no—
322C8—42no—
323C8—42no—
324C8—81no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—162no—
332C22#390×C13711yescharacteristic
333C22#444×C13712yes—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4#413×C13711yescharacteristic
343C4#413×C13711yescharacteristic
344C2—22no—
345C2—161no—
346C2#1967×C13711yescharacteristic
347C2#1975×C13711yescharacteristic
348C2#1976×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#390
commutatorC22×C4C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radicalC22×D4×C137C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1568×C137C2semidirect
3. #1528×C137C2semidirect
5. #1470×C137C2semidirect
7. #1451×C137C2semidirect
174. #9790C137direct (N × H)
175. C137#9790direct (N × H)
177. #1568C2×C137semidirect
178. #1528C2×C137semidirect
180. #1470C2×C137semidirect
182. #1451C2×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#488×C1372
#1568×C1372
#1528×C1372
#1527×C1372
#1470×C1372
#1469×C1372
#1451×C1372
#9790137