Finite Group Databasebeta

← C137×#11841 #46861227

Subgroups — C137×#11841 #46861227

Order 35072.

506 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2482×C137C211yesmaximal, characteristic
2#1819×C137C211yesmaximal, characteristic
3C2×#323×C137C211yesmaximal, characteristic
4#1352×C137C212yesmaximal, complemented
5#1344×C137C212yesmaximal, complemented
6C2×#117×C137C411yescharacteristic, complemented
7C22×C22⋊C4×C137C2211yescharacteristic
8C2×C22⋊C8×C137—21no—
9#399×C137C411yescharacteristic, complemented
10#399×C137C2211yescharacteristic
11#397×C137C411yescharacteristic, complemented
12#397×C137C2211yescharacteristic
13#388×C137—21no—
14#388×C137—21no—
15#385×C137—21no—
16#381×C137C411yescharacteristic, complemented
17#379×C137—21no—
18#379×C137—21no—
19#342×C137—21no—
20#342×C137C2212yes—
21#323×C137—21no—
22#323×C137C2212yes—
23C25×C137D411yescharacteristic
24C23×C4×C137C2×C411yescharacteristic
25C23×C4×C137D411yescharacteristic
26C22×C8×C137—41no—
27#117×C137—41no—
28#117×C137—41no—
29C2×C4⋊C4×C137—21no—
30C2×C4⋊C4×C137—21no—
31C2×C4⋊C4×C137C2×C411yescharacteristic
32C2×C4⋊C4×C137C2×C411yescharacteristic
33C2×C22⋊C4×C137—21no—
34C2×C22⋊C4×C137—21no—
35C2×C22⋊C4×C137—21no—
36C2×C22⋊C4×C137—21no—
37C2×C22⋊C4×C137—22no—
38C2×C22⋊C4×C137—21no—
39C2×C22⋊C4×C137—21no—
40C2×C22⋊C4×C137—41no—
41C2×C22⋊C4×C137—41no—
42C2×C22⋊C4×C137—41no—
43C2×C22⋊C4×C137—41no—
44C2×C22⋊C4×C137C2×C411yescharacteristic
45C2×C22⋊C4×C137D411yescharacteristic
46C2×C22⋊C4×C137D411yescharacteristic
47C2×C22⋊C4×C137C2311yescharacteristic
48C2×C42×C137—21no—
49C22⋊C8×C137—22no—
50C22⋊C8×C137—41no—
51#95×C137—21no—
52#95×C137—21no—
53#95×C137—21no—
54#95×C137C2×C411yescharacteristic
55#95×C137C2×C411yescharacteristic
56C24×C137—21no—
57C24×C137—21no—
58C24×C137—22no—
59C24×C137—41no—
60C24×C137—42no—
61C24×C137—81no—
62C24×C137C22⋊C411yescharacteristic
63C24×C137C22⋊C411yescharacteristic
64C24×C137C2×D411yescharacteristic
65C22×C4×C137—21no—
66C22×C4×C137—21no—
67C22×C4×C137—21no—
68C22×C4×C137—21no—
69C22×C4×C137—21no—
70C22×C4×C137—21no—
71C22×C4×C137—21no—
72C22×C4×C137—21no—
73C22×C4×C137—42no—
74C22×C4×C137—42no—
75C22×C4×C137—81no—
76C22×C4×C137C22⋊C411yescharacteristic
77C22×C4×C137C22⋊C411yescharacteristic
78C22×C4×C137C22×C411yescharacteristic
79C22×C4×C137C2×D411yescharacteristic
80C2×C8×C137—42no—
81C2×C8×C137—82no—
82C4⋊C4×C137—41no—
83C4⋊C4×C137—41no—
84C4⋊C4×C137—81no—
85C4⋊C4×C137—81no—
86C22⋊C4×C137—41no—
87C22⋊C4×C137—41no—
88C22⋊C4×C137—41no—
89C22⋊C4×C137—41no—
90C22⋊C4×C137—42no—
91C22⋊C4×C137—42no—
92C22⋊C4×C137—41no—
93C22⋊C4×C137—41no—
94C22⋊C4×C137—42no—
95C22⋊C4×C137—42no—
96C22⋊C4×C137—42no—
97C22⋊C4×C137—81no—
98C22⋊C4×C137—81no—
99C22⋊C4×C137—82no—
100C22⋊C4×C137—82no—
101C42×C137—42no—
102C23×C137—22no—
103C23×C137—21no—
104C23×C137—21no—
105C23×C137—21no—
106C23×C137—21no—
107C23×C137—21no—
108C23×C137—21no—
109C23×C137—21no—
110C23×C137—41no—
111C23×C137—42no—
112C23×C137—42no—
113C23×C137—41no—
114C23×C137—41no—
115C23×C137—41no—
116C23×C137—41no—
117C23×C137—42no—
118C23×C137—42no—
119C23×C137—81no—
120C23×C137—81no—
121C23×C137—84no—
122C23×C137—84no—
123C23×C137#9911yescharacteristic
124C23×C137#9911yescharacteristic
125C23×C137C2×C22⋊C411yescharacteristic
126C23×C137#13512yes—
127C2×C4×C137—21no—
128C2×C4×C137—21no—
129C2×C4×C137—21no—
130C2×C4×C137—21no—
131C2×C4×C137—42no—
132C2×C4×C137—42no—
133C2×C4×C137—42no—
134C2×C4×C137—41no—
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—41no—
144C2×C4×C137—41no—
145C2×C4×C137—41no—
146C2×C4×C137—41no—
147C2×C4×C137—41no—
148C2×C4×C137—41no—
149C2×C4×C137—41no—
150C2×C4×C137—81no—
151C2×C4×C137—82no—
152C2×C4×C137—82no—
153C2×C4×C137—82no—
154C8×C137—82no—
155C22×C137—21no—
156C22×C137—21no—
157C22×C137—21no—
158C22×C137—21no—
159C22×C137—21no—
160C22×C137—21no—
161C22×C137—22no—
162C22×C137—21no—
163C22×C137—42no—
164C22×C137—42no—
165C22×C137—42no—
166C22×C137—42no—
167C22×C137—41no—
168C22×C137—41no—
169C22×C137—41no—
170C22×C137—41no—
171C22×C137—41no—
172C22×C137—81no—
173C22×C137—84no—
174C22×C137—81no—
175C22×C137—84no—
176C22×C137#35212yes—
177C22×C137C2×#9911yescharacteristic
178C22×C137#41611yescharacteristic
179C22×C137#42111yescharacteristic
180C4×C137—41no—
181C4×C137—41no—
182C4×C137—41no—
183C4×C137—41no—
184C4×C137—81no—
185C4×C137—81no—
186C4×C137—81no—
187C4×C137—81no—
188C4×C137—162no—
189C2×C137—21no—
190C2×C137—21no—
191C2×C137—22no—
192C2×C137—42no—
193C2×C137—41no—
194C2×C137—81no—
195C2×C137#151611yescharacteristic
196C2×C137C2×#35211yescharacteristic
197C2×C137#212711yescharacteristic
198#11841C13711yesmaximal, characteristic, direct product factor, Sylow
199C137#1184111yescharacteristic, direct product factor, Sylow
200#2482C2×C13711yescharacteristic
201#1819C2×C13711yescharacteristic
202C2×#323C2×C13711yescharacteristic
203#1352C2×C13712yescomplemented
204#1344C2×C13712yescomplemented
205C2×#117C4×C13711yescharacteristic, complemented
206C22×C22⋊C4C22×C13711yescharacteristic
207C2×C22⋊C8—21no—
208#399C4×C13711yescharacteristic, complemented
209#399C22×C13711yescharacteristic
210#397C4×C13711yescharacteristic, complemented
211#397C22×C13711yescharacteristic
212#388—21no—
213#388—21no—
214#385—21no—
215#381C4×C13711yescharacteristic, complemented
216#379—21no—
217#379—21no—
218#342—21no—
219#342C22×C13712yes—
220#323—21no—
221#323C22×C13712yes—
222C25D4×C13711yescharacteristic
223C23×C4C2×C4×C13711yescharacteristic
224C23×C4D4×C13711yescharacteristic
225C22×C8—41no—
226#117—41no—
227#117—41no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C2×C4×C13711yescharacteristic
231C2×C4⋊C4C2×C4×C13711yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—41no—
242C2×C22⋊C4—41no—
243C2×C22⋊C4C2×C4×C13711yescharacteristic
244C2×C22⋊C4D4×C13711yescharacteristic
245C2×C22⋊C4D4×C13711yescharacteristic
246C2×C22⋊C4C23×C13711yescharacteristic
247C2×C42—21no—
248C22⋊C8—22no—
249C22⋊C8—41no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95C2×C4×C13711yescharacteristic
254#95C2×C4×C13711yescharacteristic
255C24—21no—
256C24—21no—
257C24—22no—
258C24—41no—
259C24—42no—
260C24—81no—
261C24C22⋊C4×C13711yescharacteristic
262C24C22⋊C4×C13711yescharacteristic
263C24C2×D4×C13711yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—81no—
275C22×C4C22⋊C4×C13711yescharacteristic
276C22×C4C22⋊C4×C13711yescharacteristic
277C22×C4C22×C4×C13711yescharacteristic
278C22×C4C2×D4×C13711yescharacteristic
279C2×C8—42no—
280C2×C8—82no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—81no—
297C22⋊C4—81no—
298C22⋊C4—82no—
299C22⋊C4—82no—
300C42—42no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—22no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—81no—
320C23—84no—
321C23—84no—
322C23#99×C13711yescharacteristic
323C23#99×C13711yescharacteristic
324C23C2×C22⋊C4×C13711yescharacteristic
325C23#135×C13712yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C8—82no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—84no—
373C22—81no—
374C22—84no—
375C22#352×C13712yes—
376C22C2×#99×C13711yescharacteristic
377C22#416×C13711yescharacteristic
378C22#421×C13711yescharacteristic
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—162no—
388C2—21no—
389C2—21no—
390C2—22no—
391C2—42no—
392C2—41no—
393C2—81no—
394C2#1516×C13711yescharacteristic
395C2C2×#352×C13711yescharacteristic
396C2#2127×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#99
commutatorC22×C4C22×C4×C137
Frattini, cosocleC2×C22⋊C4C23×C137
prime radicalC25×C137D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C24×C137 ◁ C22×C22⋊C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1352×C137C2semidirect
5. #1344×C137C2semidirect
6. C2×#117×C137C4semidirect
9. #399×C137C4semidirect
11. #397×C137C4semidirect
16. #381×C137C4semidirect
198. #11841C137direct (N × H)
199. C137#11841direct (N × H)
203. #1352C2×C137semidirect
204. #1344C2×C137semidirect
205. C2×#117C4×C137semidirect
208. #399C4×C137semidirect
210. #397C4×C137semidirect
215. #381C4×C137semidirect

Maximal subgroups

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

subgroupindex
#2482×C1372
#1819×C1372
C2×#323×C1372
#1352×C1372
#1344×C1372
#11841137