Finite Group Databasebeta

← C137×#13425 #46862811

Subgroups — C137×#13425 #46862811

Order 35072.

508 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 90 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#2717×C137C211yesmaximal, characteristic
2C2×#354×C137C211yesmaximal, characteristic
3C2×#352×C137C211yesmaximal, characteristic
4#1890×C137C211yesmaximal, characteristic
5#1885×C137C211yesmaximal, characteristic
6#1867×C137C211yesmaximal, characteristic
7#1390×C137C211yesmaximal, characteristic
8C2×#124×C137C2211yescharacteristic
9C2×#123×C137C2211yescharacteristic
10#518×C137C2211yescharacteristic
11#419×C137—21no—
12C2×#100×C137C2211yescharacteristic
13C2×#99×C137C2211yescharacteristic
14C2×#99×C137C2211yescharacteristic
15#397×C137—21no—
16#397×C137—21no—
17#395×C137—21no—
18#387×C137—21no—
19#386×C137C2211yescharacteristic
20#385×C137—21no—
21#385×C137—21no—
22#381×C137—21no—
23#380×C137—21no—
24#354×C137—22no—
25#352×C137—22no—
26#342×C137—21no—
27#342×C137—21no—
28#339×C137—21no—
29C22×Q8×C137D411yescharacteristic
30C22×D4×C137C2311yescharacteristic
31C23×C4×C137D411yescharacteristic
32C23×C4×C137D411yescharacteristic
33C2×M16×C137—21no—
34#124×C137—21no—
35#124×C137—21no—
36#124×C137—21no—
37#124×C137—21no—
38#123×C137—21no—
39#123×C137—21no—
40#123×C137—21no—
41#123×C137—21no—
42C4×D4×C137—41no—
43C4×D4×C137—41no—
44#117×C137—21no—
45C2×C4⋊C4×C137—21no—
46C2×C4⋊C4×C137—21no—
47C2×C4⋊C4×C137—21no—
48C2×C4⋊C4×C137—21no—
49C2×C4⋊C4×C137—41no—
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×C22⋊C4×C137—21no—
56C2×C22⋊C4×C137—21no—
57C2×C22⋊C4×C137—21no—
58C2×C22⋊C4×C137D411yescharacteristic
59C2×C22⋊C4×C137D411yescharacteristic
60C2×C42×C137D411yescharacteristic
61#103×C137—41no—
62#103×C137—41no—
63#100×C137—21no—
64#100×C137—21no—
65#99×C137—21no—
66#99×C137—21no—
67#99×C137—21no—
68#99×C137D412yes—
69#95×C137—21no—
70#95×C137—21no—
71#95×C137—21no—
72#95×C137—21no—
73#95×C137—21no—
74#95×C137—21no—
75#95×C137—41no—
76#95×C137—41no—
77#95×C137—41no—
78C24×C137C2×D411yescharacteristic
79C24×C137C2×D411yescharacteristic
80C2×Q8×C137—21no—
81C2×Q8×C137—21no—
82C2×Q8×C137—41no—
83C2×Q8×C137—41no—
84C2×D4×C137—41no—
85C2×D4×C137—41no—
86C2×D4×C137C2×D411yescharacteristic
87C2×D4×C137#4111yescharacteristic
88C2×D4×C137#4111yescharacteristic
89C2×D4×C137#4111yescharacteristic
90C22×C4×C137—21no—
91C22×C4×C137—21no—
92C22×C4×C137—21no—
93C22×C4×C137—21no—
94C22×C4×C137—21no—
95C22×C4×C137—21no—
96C22×C4×C137—21no—
97C22×C4×C137—21no—
98C22×C4×C137—21no—
99C22×C4×C137—21no—
100C22×C4×C137—21no—
101C22×C4×C137—21no—
102C22×C4×C137—42no—
103C22×C4×C137—41no—
104C22×C4×C137—41no—
105C22×C4×C137—41no—
106C22×C4×C137—41no—
107C22×C4×C137—41no—
108C22×C4×C137C2×D411yescharacteristic
109M16×C137—41no—
110M16×C137—41no—
111C2×C8×C137—41no—
112C4⋊C4×C137—21no—
113C4⋊C4×C137—21no—
114C4⋊C4×C137—42no—
115C4⋊C4×C137—41no—
116C4⋊C4×C137—41no—
117C4⋊C4×C137—81no—
118C4⋊C4×C137—81no—
119C4⋊C4×C137—82no—
120C22⋊C4×C137—22no—
121C22⋊C4×C137—21no—
122C22⋊C4×C137—21no—
123C22⋊C4×C137—42no—
124C22⋊C4×C137—41no—
125C22⋊C4×C137—41no—
126C22⋊C4×C137—41no—
127C22⋊C4×C137—41no—
128C22⋊C4×C137—41no—
129C22⋊C4×C137—41no—
130C22⋊C4×C137—41no—
131C22⋊C4×C137—41no—
132C22⋊C4×C137—41no—
133C22⋊C4×C137—41no—
134C22⋊C4×C137—41no—
135C22⋊C4×C137—41no—
136C22⋊C4×C137—41no—
137C42×C137—21no—
138C42×C137—21no—
139C42×C137—41no—
140C23×C137—21no—
141C23×C137—21no—
142C23×C137—21no—
143C23×C137—21no—
144C23×C137—41no—
145C23×C137—41no—
146C23×C137—41no—
147C23×C137—41no—
148C23×C137#12011yescharacteristic
149C23×C137#12111yescharacteristic
150C23×C137#12111yescharacteristic
151C23×C137#12311yescharacteristic
152C23×C137#12411yescharacteristic
153Q8×C137—42no—
154Q8×C137—81no—
155D4×C137—41no—
156D4×C137—41no—
157D4×C137—41no—
158D4×C137—41no—
159C2×C4×C137—21no—
160C2×C4×C137—21no—
161C2×C4×C137—22no—
162C2×C4×C137—41no—
163C2×C4×C137—41no—
164C2×C4×C137—42no—
165C2×C4×C137—42no—
166C2×C4×C137—41no—
167C2×C4×C137—41no—
168C2×C4×C137—41no—
169C2×C4×C137—41no—
170C2×C4×C137—41no—
171C2×C4×C137—41no—
172C2×C4×C137—42no—
173C2×C4×C137—41no—
174C2×C4×C137—41no—
175C2×C4×C137—41no—
176C2×C4×C137—41no—
177C2×C4×C137—41no—
178C2×C4×C137—41no—
179C2×C4×C137—41no—
180C2×C4×C137—41no—
181C2×C4×C137—41no—
182C2×C4×C137—41no—
183C2×C4×C137—41no—
184C2×C4×C137—81no—
185C2×C4×C137—81no—
186C2×C4×C137—81no—
187C2×C4×C137—81no—
188C2×C4×C137—81no—
189C2×C4×C137—81no—
190C2×C4×C137—81no—
191C2×C4×C137—81no—
192C2×C4×C137—81no—
193C2×C4×C137—81no—
194C2×C4×C137—81no—
195C2×C4×C137#12111yescharacteristic
196C2×C4×C137#12311yescharacteristic
197C8×C137—81no—
198C22×C137—21no—
199C22×C137—21no—
200C22×C137—21no—
201C22×C137—21no—
202C22×C137—21no—
203C22×C137—21no—
204C22×C137—41no—
205C22×C137—41no—
206C22×C137—41no—
207C22×C137—41no—
208C22×C137—41no—
209C22×C137—41no—
210C22×C137—41no—
211C22×C137—41no—
212C22×C137—81no—
213C22×C137—81no—
214C22×C137#39411yescharacteristic
215C22×C137B(4,𝔽2)11yescharacteristic
216C22×C137#45811yescharacteristic
217C4×C137—21no—
218C4×C137—21no—
219C4×C137—42no—
220C4×C137—81no—
221C4×C137—81no—
222C4×C137—81no—
223C4×C137—82no—
224C4×C137—81no—
225C4×C137—81no—
226C4×C137—81no—
227C4×C137—81no—
228C4×C137—161no—
229C2×C137—21no—
230C2×C137—21no—
231C2×C137—41no—
232C2×C137—41no—
233C2×C137—41no—
234C2×C137—41no—
235C2×C137#204411yescharacteristic
236C2×C137#219711yescharacteristic
237C2×C137#220111yescharacteristic
238#13425C13711yesmaximal, characteristic, direct product factor, Sylow
239C137#1342511yescharacteristic, direct product factor, Sylow
240#2717C2×C13711yescharacteristic
241C2×#354C2×C13711yescharacteristic
242C2×#352C2×C13711yescharacteristic
243#1890C2×C13711yescharacteristic
244#1885C2×C13711yescharacteristic
245#1867C2×C13711yescharacteristic
246#1390C2×C13711yescharacteristic
247C2×#124C22×C13711yescharacteristic
248C2×#123C22×C13711yescharacteristic
249#518C22×C13711yescharacteristic
250#419—21no—
251C2×#100C22×C13711yescharacteristic
252C2×#99C22×C13711yescharacteristic
253C2×#99C22×C13711yescharacteristic
254#397—21no—
255#397—21no—
256#395—21no—
257#387—21no—
258#386C22×C13711yescharacteristic
259#385—21no—
260#385—21no—
261#381—21no—
262#380—21no—
263#354—22no—
264#352—22no—
265#342—21no—
266#342—21no—
267#339—21no—
268C22×Q8D4×C13711yescharacteristic
269C22×D4C23×C13711yescharacteristic
270C23×C4D4×C13711yescharacteristic
271C23×C4D4×C13711yescharacteristic
272C2×M16—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281C4×D4—41no—
282C4×D4—41no—
283#117—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—41no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4D4×C13711yescharacteristic
298C2×C22⋊C4D4×C13711yescharacteristic
299C2×C42D4×C13711yescharacteristic
300#103—41no—
301#103—41no—
302#100—21no—
303#100—21no—
304#99—21no—
305#99—21no—
306#99—21no—
307#99D4×C13712yes—
308#95—21no—
309#95—21no—
310#95—21no—
311#95—21no—
312#95—21no—
313#95—21no—
314#95—41no—
315#95—41no—
316#95—41no—
317C24C2×D4×C13711yescharacteristic
318C24C2×D4×C13711yescharacteristic
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4C2×D4×C13711yescharacteristic
326C2×D4#41×C13711yescharacteristic
327C2×D4#41×C13711yescharacteristic
328C2×D4#41×C13711yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4C2×D4×C13711yescharacteristic
348M16—41no—
349M16—41no—
350C2×C8—41no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—42no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—81no—
357C4⋊C4—81no—
358C4⋊C4—82no—
359C22⋊C4—22no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—42no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C42—21no—
377C42—21no—
378C42—41no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23#120×C13711yescharacteristic
388C23#121×C13711yescharacteristic
389C23#121×C13711yescharacteristic
390C23#123×C13711yescharacteristic
391C23#124×C13711yescharacteristic
392Q8—42no—
393Q8—81no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4#121×C13711yescharacteristic
435C2×C4#123×C13711yescharacteristic
436C8—81no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—81no—
452C22—81no—
453C22#394×C13711yescharacteristic
454C22B(4,𝔽2)×C13711yescharacteristic
455C22#458×C13711yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—82no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—161no—
468C2—21no—
469C2—21no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—41no—
474C2#2044×C13711yescharacteristic
475C2#2197×C13711yescharacteristic
476C2#2201×C13711yescharacteristic
subgroupG/H
center, socleC22×C137B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C137
prime radicalC22×D4×C137C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C137 ◁ C22×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
238. #13425C137direct (N × H)
239. C137#13425direct (N × H)

Maximal subgroups

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

subgroupindex
#2717×C1372
C2×#354×C1372
C2×#352×C1372
#1890×C1372
#1885×C1372
#1867×C1372
#1390×C1372
#13425137