Finite Group Databasebeta

← C137×#9353 #46858739

Subgroups — C137×#9353 #46858739

Order 35072.

472 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3039×C137C211yesmaximal, characteristic
2#2990×C137C211yesmaximal, characteristic
3#1997×C137C211yesmaximal, characteristic, complemented
4#1548×C137C211yesmaximal, characteristic, complemented
5#1489×C137C211yesmaximal, characteristic
6#1309×C137C211yesmaximal, characteristic, complemented
7#1299×C137C211yesmaximal, characteristic, complemented
8C2×#137×C137C412yes—
9C2×C4⋊Q8×C137C2211yescharacteristic
10C4×#41×C137C2211yescharacteristic
11#462×C137—21no—
12#462×C137—21no—
13#461×C137—21no—
14#461×C137—21no—
15#446×C137—21no—
16#435×C137—22no—
17C8×D4×C137—21no—
18#432×C137—21no—
19#431×C137C2211yescharacteristic
20#423×C137C2211yescharacteristic
21#423×C137C2211yescharacteristic
22#423×C137C2211yescharacteristic
23C2×C4⋊C8×C137—21no—
24#419×C137C412yes—
25C4×M16×C137C2211yescharacteristic
26#343×C137—22no—
27#333×C137—21no—
28#333×C137—21no—
29Q8⋊C8×C137—21no—
30D4⋊C8×C137—21no—
31C2×#41×C137C2×C411yescharacteristic
32C22×Q8×C137C2×C412yes—
33#137×C137—44no—
34C2×Q16×C137—22no—
35C2×SD16×C137—22no—
36C2×M16×C137—21no—
37C2×M16×C137—21no—
38C2×M16×C137C2×C412yes—
39C2×M16×C137D412yes—
40C22×C8×C137—22no—
41C4⋊Q8×C137—21no—
42C4⋊Q8×C137—21no—
43C4⋊Q8×C137—21no—
44C4⋊Q8×C137—21no—
45C4×Q8×C137D411yescharacteristic
46C4×Q8×C137D411yescharacteristic
47C4×D4×C137—21no—
48C4×D4×C137—21no—
49C4×D4×C137D411yescharacteristic
50C4×D4×C137D411yescharacteristic
51#117×C137—21no—
52#117×C137C2×C411yescharacteristic
53C2×C4⋊C4×C137—21no—
54C2×C4⋊C4×C137—21no—
55C2×C42×C137—21no—
56C2×C42×C137C2311yescharacteristic
57C4⋊C8×C137—22no—
58C4⋊C8×C137—21no—
59C4⋊C8×C137—21no—
60C4⋊C8×C137—21no—
61C4⋊C8×C137—21no—
62C4⋊C8×C137—21no—
63C4⋊C8×C137—21no—
64C4⋊C8×C137D411yescharacteristic
65C4⋊C8×C137D411yescharacteristic
66#103×C137—22no—
67#103×C137—22no—
68C22⋊C8×C137—22no—
69C22⋊C8×C137—21no—
70#97×C137—22no—
71#97×C137—21no—
72C4×C8×C137—21no—
73C4×C8×C137—21no—
74#41×C137—22no—
75#41×C137—41no—
76C2×Q8×C137—22no—
77C2×Q8×C137—22no—
78C2×Q8×C137—42no—
79C2×Q8×C137—42no—
80C2×Q8×C137C22⋊C411yescharacteristic
81C2×D4×C137—21no—
82C2×D4×C137C22⋊C411yescharacteristic
83C22×C4×C137—21no—
84C22×C4×C137—21no—
85C22×C4×C137—21no—
86C22×C4×C137—22no—
87C22×C4×C137C22×C411yescharacteristic
88C22×C4×C137C2×D411yescharacteristic
89C22×C4×C137#4111yescharacteristic
90Q16×C137—44no—
91SD16×C137—44no—
92M16×C137—22no—
93M16×C137—41no—
94M16×C137—42no—
95M16×C137—42no—
96M16×C137—81no—
97C2×C8×C137—22no—
98C2×C8×C137—21no—
99C2×C8×C137—21no—
100C2×C8×C137—22no—
101C2×C8×C137—41no—
102C2×C8×C137—41no—
103C2×C8×C137—82no—
104C4⋊C4×C137—21no—
105C4⋊C4×C137—21no—
106C4⋊C4×C137—41no—
107C4⋊C4×C137—41no—
108C4⋊C4×C137—41no—
109C4⋊C4×C137—41no—
110C4⋊C4×C137C22⋊C411yescharacteristic
111C4⋊C4×C137C22⋊C411yescharacteristic
112C22⋊C4×C137—21no—
113C22⋊C4×C137—21no—
114C22⋊C4×C137—21no—
115C42×C137—21no—
116C42×C137—21no—
117C42×C137—21no—
118C42×C137C2×D411yescharacteristic
119C42×C137C2×D411yescharacteristic
120C42×C137C2×D411yescharacteristic
121C42×C137#4111yescharacteristic
122C23×C137—21no—
123C23×C137C4×D411yescharacteristic
124Q8×C137—21no—
125Q8×C137—21no—
126Q8×C137—42no—
127Q8×C137—42no—
128Q8×C137—82no—
129D4×C137—21no—
130D4×C137—42no—
131D4×C137#10012yes—
132C2×C4×C137—21no—
133C2×C4×C137—21no—
134C2×C4×C137—21no—
135C2×C4×C137—21no—
136C2×C4×C137—21no—
137C2×C4×C137—21no—
138C2×C4×C137—21no—
139C2×C4×C137—21no—
140C2×C4×C137—21no—
141C2×C4×C137—42no—
142C2×C4×C137—41no—
143C2×C4×C137—41no—
144C2×C4×C137—41no—
145C2×C4×C137—41no—
146C2×C4×C137—42no—
147C2×C4×C137—82no—
148C2×C4×C137C2×C22⋊C411yescharacteristic
149C2×C4×C137C4×D411yescharacteristic
150C2×C4×C137#12011yescharacteristic
151C2×C4×C137#12111yescharacteristic
152C2×C4×C137#12111yescharacteristic
153C2×C4×C137#12311yescharacteristic
154C8×C137—42no—
155C8×C137—42no—
156C8×C137—41no—
157C8×C137—42no—
158C8×C137—41no—
159C8×C137—81no—
160C22×C137—21no—
161C22×C137—21no—
162C22×C137—22no—
163C22×C137—21no—
164C22×C137—41no—
165C22×C137—41no—
166C22×C137#38611yescharacteristic
167C4×C137—21no—
168C4×C137—21no—
169C4×C137—21no—
170C4×C137—41no—
171C4×C137—41no—
172C4×C137—41no—
173C4×C137—82no—
174C4×C137C2×#10011yescharacteristic
175C4×C137#41311yescharacteristic
176C4×C137#45511yescharacteristic
177C4×C137#45611yescharacteristic
178C4×C137#47111yescharacteristic
179C4×C137#47311yescharacteristic
180C2×C137—41no—
181C2×C137—42no—
182C2×C137#188211yescharacteristic
183C2×C137#190011yescharacteristic
184C2×C137#190811yescharacteristic
185#9353C13711yesmaximal, characteristic, direct product factor, Sylow
186C137#935311yescharacteristic, direct product factor, Sylow
187#3039C2×C13711yescharacteristic
188#2990C2×C13711yescharacteristic
189#1997C2×C13711yescharacteristic, complemented
190#1548C2×C13711yescharacteristic, complemented
191#1489C2×C13711yescharacteristic
192#1309C2×C13711yescharacteristic, complemented
193#1299C2×C13711yescharacteristic, complemented
194C2×#137C4×C13712yes—
195C2×C4⋊Q8C22×C13711yescharacteristic
196C4×#41C22×C13711yescharacteristic
197#462—21no—
198#462—21no—
199#461—21no—
200#461—21no—
201#446—21no—
202#435—22no—
203C8×D4—21no—
204#432—21no—
205#431C22×C13711yescharacteristic
206#423C22×C13711yescharacteristic
207#423C22×C13711yescharacteristic
208#423C22×C13711yescharacteristic
209C2×C4⋊C8—21no—
210#419C4×C13712yes—
211C4×M16C22×C13711yescharacteristic
212#343—22no—
213#333—21no—
214#333—21no—
215Q8⋊C8—21no—
216D4⋊C8—21no—
217C2×#41C2×C4×C13711yescharacteristic
218C22×Q8C2×C4×C13712yes—
219#137—44no—
220C2×Q16—22no—
221C2×SD16—22no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16C2×C4×C13712yes—
225C2×M16D4×C13712yes—
226C22×C8—22no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4×Q8D4×C13711yescharacteristic
232C4×Q8D4×C13711yescharacteristic
233C4×D4—21no—
234C4×D4—21no—
235C4×D4D4×C13711yescharacteristic
236C4×D4D4×C13711yescharacteristic
237#117—21no—
238#117C2×C4×C13711yescharacteristic
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C42—21no—
242C2×C42C23×C13711yescharacteristic
243C4⋊C8—22no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8D4×C13711yescharacteristic
251C4⋊C8D4×C13711yescharacteristic
252#103—22no—
253#103—22no—
254C22⋊C8—22no—
255C22⋊C8—21no—
256#97—22no—
257#97—21no—
258C4×C8—21no—
259C4×C8—21no—
260#41—22no—
261#41—41no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8C22⋊C4×C13711yescharacteristic
267C2×D4—21no—
268C2×D4C22⋊C4×C13711yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4C22×C4×C13711yescharacteristic
274C22×C4C2×D4×C13711yescharacteristic
275C22×C4#41×C13711yescharacteristic
276Q16—44no—
277SD16—44no—
278M16—22no—
279M16—41no—
280M16—42no—
281M16—42no—
282M16—81no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—82no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4C22⋊C4×C13711yescharacteristic
297C4⋊C4C22⋊C4×C13711yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42C2×D4×C13711yescharacteristic
305C42C2×D4×C13711yescharacteristic
306C42C2×D4×C13711yescharacteristic
307C42#41×C13711yescharacteristic
308C23—21no—
309C23C4×D4×C13711yescharacteristic
310Q8—21no—
311Q8—21no—
312Q8—42no—
313Q8—42no—
314Q8—82no—
315D4—21no—
316D4—42no—
317D4#100×C13712yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4C2×C22⋊C4×C13711yescharacteristic
335C2×C4C4×D4×C13711yescharacteristic
336C2×C4#120×C13711yescharacteristic
337C2×C4#121×C13711yescharacteristic
338C2×C4#121×C13711yescharacteristic
339C2×C4#123×C13711yescharacteristic
340C8—42no—
341C8—42no—
342C8—41no—
343C8—42no—
344C8—41no—
345C8—81no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22#386×C13711yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—82no—
360C4C2×#100×C13711yescharacteristic
361C4#413×C13711yescharacteristic
362C4#455×C13711yescharacteristic
363C4#456×C13711yescharacteristic
364C4#471×C13711yescharacteristic
365C4#473×C13711yescharacteristic
366C2—41no—
367C2—42no—
368C2#1882×C13711yescharacteristic
369C2#1900×C13711yescharacteristic
370C2#1908×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#386
commutatorC22×C4C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radicalC2×#41×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
3. #1997×C137C2semidirect
4. #1548×C137C2semidirect
6. #1309×C137C2semidirect
7. #1299×C137C2semidirect
185. #9353C137direct (N × H)
186. C137#9353direct (N × H)
189. #1997C2×C137semidirect
190. #1548C2×C137semidirect
192. #1309C2×C137semidirect
193. #1299C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3039×C1372
#2990×C1372
#1997×C1372
#1548×C1372
#1489×C1372
#1309×C1372
#1299×C1372
#9353137