Finite Group Databasebeta

← C137×#7594 #46856980

Subgroups — C137×#7594 #46856980

Order 35072.

482 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2293×C137C211yesmaximal, characteristic
2#1839×C137C211yesmaximal, characteristic, complemented
3#1831×C137C211yesmaximal, characteristic, complemented
4#1271×C137C212yesmaximal, complemented
5#1270×C137C212yesmaximal
6C2×C4×D4×C137C411yescharacteristic
7C2×#117×C137—21no—
8C2×C4⋊C8×C137—21no—
9#390×C137C411yescharacteristic
10#390×C137C2211yescharacteristic
11#389×C137C411yescharacteristic
12#389×C137C2211yescharacteristic
13#388×C137—21no—
14#388×C137—21no—
15C4×C4⋊C4×C137C411yescharacteristic
16C4×C22⋊C4×C137—21no—
17C43×C137C2211yescharacteristic
18#336×C137—21no—
19#336×C137—21no—
20#336×C137—21no—
21#336×C137C2212yes—
22#336×C137C2212yes—
23C22×D4×C137C2×C411yescharacteristic
24C23×C4×C137—21no—
25C22×C8×C137—22no—
26C22×C8×C137—22no—
27C4×D4×C137—22no—
28C4×D4×C137C814yescomplemented
29#117×C137—44no—
30C2×C4⋊C4×C137—21no—
31C2×C4⋊C4×C137—21no—
32C2×C4⋊C4×C137C2×C411yescharacteristic
33C2×C4⋊C4×C137C2×C411yescharacteristic
34C2×C4⋊C4×C137C2×C411yescharacteristic
35C2×C22⋊C4×C137—21no—
36C2×C22⋊C4×C137—21no—
37C2×C22⋊C4×C137—21no—
38C2×C22⋊C4×C137—21no—
39C2×C22⋊C4×C137—21no—
40C2×C42×C137—21no—
41C2×C42×C137C2×C411yescharacteristic
42C2×C42×C137C2×C411yescharacteristic
43C2×C42×C137D411yescharacteristic
44C2×C42×C137D411yescharacteristic
45C2×C42×C137D411yescharacteristic
46C2×C42×C137D411yescharacteristic
47C2×C42×C137C2311yescharacteristic
48C4⋊C8×C137—42no—
49#95×C137—21no—
50#95×C137—21no—
51#95×C137—21no—
52C24×C137—21no—
53C2×D4×C137—21no—
54C2×D4×C137—41no—
55C2×D4×C137—41no—
56C2×D4×C137C2×C812yes—
57C22×C4×C137—21no—
58C22×C4×C137—24no—
59C22×C4×C137—21no—
60C22×C4×C137—21no—
61C22×C4×C137—42no—
62C22×C4×C137—42no—
63C22×C4×C137C22⋊C411yescharacteristic
64C22×C4×C137C22⋊C411yescharacteristic
65C22×C4×C137C22⋊C411yescharacteristic
66C22×C4×C137C22⋊C411yescharacteristic
67C22×C4×C137C22×C411yescharacteristic
68C22×C4×C137C2×D411yescharacteristic
69C22×C4×C137C2×D411yescharacteristic
70C2×C8×C137—42no—
71C2×C8×C137—42no—
72C2×C8×C137—42no—
73C2×C8×C137—42no—
74C2×C8×C137—42no—
75C2×C8×C137—42no—
76C4⋊C4×C137—21no—
77C4⋊C4×C137—41no—
78C4⋊C4×C137—41no—
79C4⋊C4×C137—42no—
80C4⋊C4×C137—42no—
81C4⋊C4×C137C2×C812yes—
82C22⋊C4×C137—24no—
83C22⋊C4×C137—42no—
84C22⋊C4×C137—42no—
85C22⋊C4×C137—41no—
86C22⋊C4×C137—42no—
87C22⋊C4×C137—41no—
88C42×C137—21no—
89C42×C137—22no—
90C42×C137—21no—
91C42×C137—41no—
92C42×C137—41no—
93C42×C137—41no—
94C42×C137—41no—
95C42×C137—42no—
96C42×C137C2×C812yes—
97C42×C137M1612yes—
98C23×C137—22no—
99C23×C137—41no—
100C23×C137—41no—
101C23×C137—41no—
102C23×C137—41no—
103C23×C137—41no—
104C23×C137—41no—
105C23×C137C2×C22⋊C411yescharacteristic
106D4×C137—42no—
107D4×C137—42no—
108C2×C4×C137—21no—
109C2×C4×C137—21no—
110C2×C4×C137—21no—
111C2×C4×C137—21no—
112C2×C4×C137—21no—
113C2×C4×C137—21no—
114C2×C4×C137—21no—
115C2×C4×C137—21no—
116C2×C4×C137—21no—
117C2×C4×C137—21no—
118C2×C4×C137—22no—
119C2×C4×C137—21no—
120C2×C4×C137—21no—
121C2×C4×C137—21no—
122C2×C4×C137—21no—
123C2×C4×C137—21no—
124C2×C4×C137—21no—
125C2×C4×C137—48no—
126C2×C4×C137—41no—
127C2×C4×C137—41no—
128C2×C4×C137—41no—
129C2×C4×C137—41no—
130C2×C4×C137—41no—
131C2×C4×C137—41no—
132C2×C4×C137—41no—
133C2×C4×C137—41no—
134C2×C4×C137C22⋊C812yes—
135C2×C4×C137C22⋊C812yes—
136C2×C4×C137C22×C811yescharacteristic
137C2×C4×C137C2×M1611yescharacteristic
138C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C137AGL(1,ℤ/8)12yes—
140C2×C4×C137#13711yescharacteristic
141C8×C137—82no—
142C8×C137—82no—
143C22×C137—42no—
144C22×C137—42no—
145C22×C137—42no—
146C22×C137—81no—
147C22×C137—81no—
148C22×C137—81no—
149C22×C137—81no—
150C22×C137C2×C22⋊C811yescharacteristic
151C22×C137#41011yescharacteristic
152C22×C137#41311yescharacteristic
153C22×C137#41711yescharacteristic
154C22×C137#41811yescharacteristic
155C22×C137#42111yescharacteristic
156C22×C137#42111yescharacteristic
157C4×C137—21no—
158C4×C137—21no—
159C4×C137—22no—
160C4×C137—22no—
161C4×C137—21no—
162C4×C137—21no—
163C4×C137—22no—
164C4×C137—41no—
165C4×C137—42no—
166C4×C137—41no—
167C4×C137—81no—
168C4×C137—81no—
169C2×C137—82no—
170C2×C137#145811yescharacteristic
171C2×C137#147711yescharacteristic
172C2×C137#147811yescharacteristic
173C2×C137#151211yescharacteristic
174C2×C137#151411yescharacteristic
175C2×C137#153511yescharacteristic
176C2×C137#155711yescharacteristic
177#7594C13711yesmaximal, characteristic, direct product factor, Sylow
178C137#759411yescharacteristic, direct product factor, Sylow
179#2293C2×C13711yescharacteristic
180#1839C2×C13711yescharacteristic, complemented
181#1831C2×C13711yescharacteristic, complemented
182#1271C2×C13712yescomplemented
183#1270C2×C13712yes—
184C2×C4×D4C4×C13711yescharacteristic
185C2×#117—21no—
186C2×C4⋊C8—21no—
187#390C4×C13711yescharacteristic
188#390C22×C13711yescharacteristic
189#389C4×C13711yescharacteristic
190#389C22×C13711yescharacteristic
191#388—21no—
192#388—21no—
193C4×C4⋊C4C4×C13711yescharacteristic
194C4×C22⋊C4—21no—
195C43C22×C13711yescharacteristic
196#336—21no—
197#336—21no—
198#336—21no—
199#336C22×C13712yes—
200#336C22×C13712yes—
201C22×D4C2×C4×C13711yescharacteristic
202C23×C4—21no—
203C22×C8—22no—
204C22×C8—22no—
205C4×D4—22no—
206C4×D4C8×C13714yescomplemented
207#117—44no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×C4×C13711yescharacteristic
211C2×C4⋊C4C2×C4×C13711yescharacteristic
212C2×C4⋊C4C2×C4×C13711yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C42—21no—
219C2×C42C2×C4×C13711yescharacteristic
220C2×C42C2×C4×C13711yescharacteristic
221C2×C42D4×C13711yescharacteristic
222C2×C42D4×C13711yescharacteristic
223C2×C42D4×C13711yescharacteristic
224C2×C42D4×C13711yescharacteristic
225C2×C42C23×C13711yescharacteristic
226C4⋊C8—42no—
227#95—21no—
228#95—21no—
229#95—21no—
230C24—21no—
231C2×D4—21no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4C2×C8×C13712yes—
235C22×C4—21no—
236C22×C4—24no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4C22⋊C4×C13711yescharacteristic
242C22×C4C22⋊C4×C13711yescharacteristic
243C22×C4C22⋊C4×C13711yescharacteristic
244C22×C4C22⋊C4×C13711yescharacteristic
245C22×C4C22×C4×C13711yescharacteristic
246C22×C4C2×D4×C13711yescharacteristic
247C22×C4C2×D4×C13711yescharacteristic
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4C2×C8×C13712yes—
260C22⋊C4—24no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—41no—
264C22⋊C4—42no—
265C22⋊C4—41no—
266C42—21no—
267C42—22no—
268C42—21no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42—41no—
273C42—42no—
274C42C2×C8×C13712yes—
275C42M16×C13712yes—
276C23—22no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×C22⋊C4×C13711yescharacteristic
284D4—42no—
285D4—42no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—48no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4C22⋊C8×C13712yes—
313C2×C4C22⋊C8×C13712yes—
314C2×C4C22×C8×C13711yescharacteristic
315C2×C4C2×M16×C13711yescharacteristic
316C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
317C2×C4AGL(1,ℤ/8)×C13712yes—
318C2×C4#137×C13711yescharacteristic
319C8—82no—
320C8—82no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22C2×C22⋊C8×C13711yescharacteristic
329C22#410×C13711yescharacteristic
330C22#413×C13711yescharacteristic
331C22#417×C13711yescharacteristic
332C22#418×C13711yescharacteristic
333C22#421×C13711yescharacteristic
334C22#421×C13711yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—42no—
345C4—81no—
346C4—81no—
347C2—82no—
348C2#1458×C13711yescharacteristic
349C2#1477×C13711yescharacteristic
350C2#1478×C13711yescharacteristic
351C2#1512×C13711yescharacteristic
352C2#1514×C13711yescharacteristic
353C2#1535×C13711yescharacteristic
354C2#1557×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C2×C22⋊C4
commutatorC2×C4C22×C8×C137
Frattini, cosocleC2×C42C23×C137
prime radicalC22×D4×C137C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ C43×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1839×C137C2semidirect
3. #1831×C137C2semidirect
4. #1271×C137C2semidirect
28. C4×D4×C137C8semidirect
177. #7594C137direct (N × H)
178. C137#7594direct (N × H)
180. #1839C2×C137semidirect
181. #1831C2×C137semidirect
182. #1271C2×C137semidirect
206. C4×D4C8×C137semidirect

Maximal subgroups

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

subgroupindex
#2293×C1372
#1839×C1372
#1831×C1372
#1271×C1372
#1270×C1372
#7594137