Finite Group Databasebeta

← C137×#7795 #46857181

Subgroups — C137×#7795 #46857181

Order 35072.

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

normal subgroups only

This group has 500 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#2682×C137C211yesmaximal, characteristic
2#2099×C137C211yesmaximal, characteristic, complemented
3#2071×C137C211yesmaximal, characteristic, complemented
4#2071×C137C211yesmaximal, characteristic, complemented
5#1271×C137C211yesmaximal, characteristic, complemented
6#1270×C137C211yesmaximal, characteristic, complemented
7#1270×C137C211yesmaximal, characteristic, complemented
8C2×#123×C137—21no—
9C2×#121×C137—21no—
10C2×#102×C137—21no—
11C2×#102×C137—21no—
12#396×C137—21no—
13#394×C137—21no—
14#392×C137—21no—
15#390×C137C2211yescharacteristic
16#390×C137C2211yescharacteristic
17#389×C137C2211yescharacteristic
18#385×C137—21no—
19#384×C137C2211yescharacteristic
20#340×C137—21no—
21#340×C137—21no—
22#340×C137—21no—
23#340×C137—21no—
24#336×C137C2211yescharacteristic
25#336×C137C2211yescharacteristic
26#336×C137C2211yescharacteristic
27C22×D4×C137—21no—
28C22×D4×C137—21no—
29C22×D4×C137D411yescharacteristic
30C22×D4×C137D411yescharacteristic
31C23×C4×C137—21no—
32C22×C8×C137—21no—
33C22×C8×C137—21no—
34C22×C8×C137—21no—
35#123×C137—42no—
36#123×C137—42no—
37#121×C137—42no—
38#121×C137—42no—
39C2×C4⋊C4×C137—21no—
40C2×C4⋊C4×C137—21no—
41C2×C4⋊C4×C137—21no—
42C2×C4⋊C4×C137—21no—
43C2×C4⋊C4×C137—21no—
44C2×C4⋊C4×C137D411yescharacteristic
45C2×C4⋊C4×C137D411yescharacteristic
46C2×C4⋊C4×C137D411yescharacteristic
47C2×C4⋊C4×C137D411yescharacteristic
48C2×C22⋊C4×C137—21no—
49C2×C22⋊C4×C137—21no—
50C2×C22⋊C4×C137—21no—
51C2×C22⋊C4×C137—21no—
52C2×C22⋊C4×C137—21no—
53C2×C22⋊C4×C137—21no—
54C2×C22⋊C4×C137—21no—
55C2×C42×C137C2311yescharacteristic
56#102×C137—42no—
57#102×C137—42no—
58#95×C137—21no—
59#95×C137—21no—
60C24×C137—21no—
61C24×C137—21no—
62C2×D4×C137—21no—
63C2×D4×C137—21no—
64C2×D4×C137—21no—
65C2×D4×C137—41no—
66C2×D4×C137—41no—
67C2×D4×C137—41no—
68C2×D4×C137—41no—
69C2×D4×C137—42no—
70C2×D4×C137—42no—
71C2×D4×C137—42no—
72C2×D4×C137—81no—
73C2×D4×C137—81no—
74C2×D4×C137—81no—
75C2×D4×C137D812yes—
76C22×C4×C137—21no—
77C22×C4×C137—21no—
78C22×C4×C137—21no—
79C22×C4×C137—21no—
80C22×C4×C137—42no—
81C22×C4×C137—42no—
82C22×C4×C137—41no—
83C22×C4×C137—81no—
84C22×C4×C137C2×D411yescharacteristic
85C22×C4×C137C2×D411yescharacteristic
86C22×C4×C137C2×D411yescharacteristic
87C2×C8×C137—41no—
88C2×C8×C137—41no—
89C2×C8×C137—41no—
90C2×C8×C137—41no—
91C2×C8×C137—41no—
92C2×C8×C137—41no—
93C2×C8×C137—41no—
94C2×C8×C137—41no—
95C2×C8×C137—41no—
96C4⋊C4×C137—21no—
97C4⋊C4×C137—41no—
98C4⋊C4×C137—41no—
99C4⋊C4×C137—41no—
100C4⋊C4×C137—42no—
101C4⋊C4×C137—42no—
102C4⋊C4×C137—41no—
103C4⋊C4×C137—41no—
104C4⋊C4×C137—41no—
105C4⋊C4×C137—41no—
106C4⋊C4×C137—41no—
107C4⋊C4×C137—41no—
108C4⋊C4×C137SD1612yes—
109C22⋊C4×C137—42no—
110C22⋊C4×C137—42no—
111C22⋊C4×C137—41no—
112C22⋊C4×C137—41no—
113C22⋊C4×C137—41no—
114C22⋊C4×C137—41no—
115C22⋊C4×C137—41no—
116C22⋊C4×C137—41no—
117C22⋊C4×C137—41no—
118C22⋊C4×C137—41no—
119C22⋊C4×C137—81no—
120C42×C137—41no—
121C23×C137—22no—
122C23×C137—41no—
123C23×C137—41no—
124C23×C137—41no—
125C23×C137—41no—
126C23×C137—41no—
127C23×C137—41no—
128C23×C137—41no—
129C23×C137—41no—
130C23×C137—41no—
131C23×C137—41no—
132C23×C137—41no—
133C23×C137—41no—
134C23×C137—41no—
135C23×C137#12011yescharacteristic
136D4×C137—42no—
137D4×C137—42no—
138D4×C137—81no—
139D4×C137—81no—
140D4×C137—84no—
141D4×C137—84no—
142C2×C4×C137—21no—
143C2×C4×C137—21no—
144C2×C4×C137—21no—
145C2×C4×C137—21no—
146C2×C4×C137—21no—
147C2×C4×C137—21no—
148C2×C4×C137—22no—
149C2×C4×C137—41no—
150C2×C4×C137—41no—
151C2×C4×C137—41no—
152C2×C4×C137—41no—
153C2×C4×C137—41no—
154C2×C4×C137—41no—
155C2×C4×C137—41no—
156C2×C4×C137—41no—
157C2×C4×C137—41no—
158C2×C4×C137—41no—
159C2×C4×C137—41no—
160C2×C4×C137—84no—
161C2×C4×C137—81no—
162C2×C4×C137—81no—
163C2×C4×C137—81no—
164C2×C4×C137C2×D811yescharacteristic
165C2×C4×C137C2×SD1611yescharacteristic
166C2×C4×C137#13511yescharacteristic
167C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
170C8×C137—81no—
171C8×C137—81no—
172C8×C137—81no—
173C22×C137—42no—
174C22×C137—42no—
175C22×C137—42no—
176C22×C137—81no—
177C22×C137—81no—
178C22×C137—81no—
179C22×C137—81no—
180C22×C137—81no—
181C22×C137—81no—
182C22×C137—81no—
183C22×C137—81no—
184C22×C137—81no—
185C22×C137—81no—
186C22×C137—81no—
187C22×C137#44711yescharacteristic
188C22×C137#44911yescharacteristic
189C22×C137#45011yescharacteristic
190C22×C137#45411yescharacteristic
191C22×C137#45511yescharacteristic
192C22×C137#45511yescharacteristic
193C22×C137#45811yescharacteristic
194C4×C137—21no—
195C4×C137—21no—
196C4×C137—21no—
197C4×C137—21no—
198C4×C137—21no—
199C4×C137—21no—
200C4×C137—42no—
201C4×C137—81no—
202C4×C137—81no—
203C4×C137—81no—
204C4×C137—161no—
205C2×C137—82no—
206C2×C137—161no—
207C2×C137#160711yescharacteristic
208C2×C137#161211yescharacteristic
209C2×C137#161611yescharacteristic
210C2×C137#162511yescharacteristic
211C2×C137#163911yescharacteristic
212C2×C137#164211yescharacteristic
213C2×C137#166211yescharacteristic
214#7795C13711yesmaximal, characteristic, direct product factor, Sylow
215C137#779511yescharacteristic, direct product factor, Sylow
216#2682C2×C13711yescharacteristic
217#2099C2×C13711yescharacteristic, complemented
218#2071C2×C13711yescharacteristic, complemented
219#2071C2×C13711yescharacteristic, complemented
220#1271C2×C13711yescharacteristic, complemented
221#1270C2×C13711yescharacteristic, complemented
222#1270C2×C13711yescharacteristic, complemented
223C2×#123—21no—
224C2×#121—21no—
225C2×#102—21no—
226C2×#102—21no—
227#396—21no—
228#394—21no—
229#392—21no—
230#390C22×C13711yescharacteristic
231#390C22×C13711yescharacteristic
232#389C22×C13711yescharacteristic
233#385—21no—
234#384C22×C13711yescharacteristic
235#340—21no—
236#340—21no—
237#340—21no—
238#340—21no—
239#336C22×C13711yescharacteristic
240#336C22×C13711yescharacteristic
241#336C22×C13711yescharacteristic
242C22×D4—21no—
243C22×D4—21no—
244C22×D4D4×C13711yescharacteristic
245C22×D4D4×C13711yescharacteristic
246C23×C4—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250#123—42no—
251#123—42no—
252#121—42no—
253#121—42no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4D4×C13711yescharacteristic
260C2×C4⋊C4D4×C13711yescharacteristic
261C2×C4⋊C4D4×C13711yescharacteristic
262C2×C4⋊C4D4×C13711yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42C23×C13711yescharacteristic
271#102—42no—
272#102—42no—
273#95—21no—
274#95—21no—
275C24—21no—
276C24—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—81no—
288C2×D4—81no—
289C2×D4—81no—
290C2×D4D8×C13712yes—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—81no—
299C22×C4C2×D4×C13711yescharacteristic
300C22×C4C2×D4×C13711yescharacteristic
301C22×C4C2×D4×C13711yescharacteristic
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4SD16×C13712yes—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—81no—
335C42—41no—
336C23—22no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23#120×C13711yescharacteristic
351D4—42no—
352D4—42no—
353D4—81no—
354D4—81no—
355D4—84no—
356D4—84no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—84no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4C2×D8×C13711yescharacteristic
380C2×C4C2×SD16×C13711yescharacteristic
381C2×C4#135×C13711yescharacteristic
382C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
383C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
384C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
385C8—81no—
386C8—81no—
387C8—81no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22#447×C13711yescharacteristic
403C22#449×C13711yescharacteristic
404C22#450×C13711yescharacteristic
405C22#454×C13711yescharacteristic
406C22#455×C13711yescharacteristic
407C22#455×C13711yescharacteristic
408C22#458×C13711yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4—161no—
420C2—82no—
421C2—161no—
422C2#1607×C13711yescharacteristic
423C2#1612×C13711yescharacteristic
424C2#1616×C13711yescharacteristic
425C2#1625×C13711yescharacteristic
426C2#1639×C13711yescharacteristic
427C2#1642×C13711yescharacteristic
428C2#1662×C13711yescharacteristic
subgroupG/H
center, socleC23×C137#120
commutator, Frattini, cosocleC2×C42C23×C137
prime radical#2682×C137C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2099×C137C2semidirect
3. #2071×C137C2semidirect
4. #2071×C137C2semidirect
5. #1271×C137C2semidirect
6. #1270×C137C2semidirect
7. #1270×C137C2semidirect
214. #7795C137direct (N × H)
215. C137#7795direct (N × H)
217. #2099C2×C137semidirect
218. #2071C2×C137semidirect
219. #2071C2×C137semidirect
220. #1271C2×C137semidirect
221. #1270C2×C137semidirect
222. #1270C2×C137semidirect

Maximal subgroups

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

subgroupindex
#2682×C1372
#2099×C1372
#2071×C1372
#1271×C1372
#1270×C1372
#7795137