Finite Group Databasebeta

← C137×#10404 #46859790

Subgroups — C137×#10404 #46859790

Order 35072.

602 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2639×C137C211yesmaximal, characteristic
2#1874×C137C211yesmaximal, characteristic
3#1872×C137C211yesmaximal, characteristic, complemented
4C2×#328×C137C211yesmaximal, characteristic, complemented
5C2×#327×C137C211yesmaximal, characteristic
6#1442×C137C211yesmaximal, characteristic, complemented
7#1280×C137C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C137C2211yescharacteristic
9C2×#121×C137C2211yescharacteristic
10C22×C4⋊C4×C137C2211yescharacteristic
11C2×#103×C137—21no—
12C2×#102×C137—21no—
13C2×C22⋊C8×C137C2211yescharacteristic
14C2×C22⋊C8×C137C2211yescharacteristic
15#400×C137—21no—
16#397×C137—21no—
17#394×C137—21no—
18#393×C137—21no—
19#386×C137—21no—
20#386×C137—21no—
21C2×#95×C137—21no—
22C2×#95×C137—21no—
23C2×#95×C137C2211yescharacteristic
24C2×#95×C137C2211yescharacteristic
25#340×C137—21no—
26#340×C137—21no—
27#328×C137—22no—
28#327×C137—22no—
29C22×Q8×C137D411yescharacteristic
30C22×D4×C137—21no—
31C22×D4×C137D411yescharacteristic
32C23×C4×C137—21no—
33C23×C4×C137—21no—
34C23×C4×C137D411yescharacteristic
35C23×C4×C137D411yescharacteristic
36C23×C4×C137C2311yescharacteristic
37C22×C8×C137—21no—
38C22×C8×C137—21no—
39C22⋊Q8×C137—21no—
40C22⋊Q8×C137—21no—
41C22⋊Q8×C137—21no—
42C22⋊Q8×C137—21no—
43#121×C137—21no—
44#121×C137—21no—
45#121×C137—21no—
46#121×C137—21no—
47C2×C4⋊C4×C137—21no—
48C2×C4⋊C4×C137—21no—
49C2×C4⋊C4×C137—21no—
50C2×C4⋊C4×C137—42no—
51C2×C4⋊C4×C137D411yescharacteristic
52C2×C4⋊C4×C137D411yescharacteristic
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×C137—21no—
59#103×C137—42no—
60#102×C137—42no—
61C22⋊C8×C137—21no—
62C22⋊C8×C137—21no—
63C22⋊C8×C137—21no—
64C22⋊C8×C137—21no—
65#95×C137—21no—
66#95×C137—21no—
67#95×C137—21no—
68#95×C137—21no—
69#95×C137—21no—
70#95×C137—21no—
71#95×C137—21no—
72#95×C137—42no—
73#95×C137—42no—
74#95×C137D412yes—
75C24×C137—21no—
76C24×C137C2×D411yescharacteristic
77C2×Q8×C137—21no—
78C2×Q8×C137—21no—
79C2×Q8×C137—41no—
80C2×Q8×C137—41no—
81C2×D4×C137—21no—
82C2×D4×C137—21no—
83C2×D4×C137—41no—
84C2×D4×C137—41no—
85C2×D4×C137—41no—
86C2×D4×C137—41no—
87C2×D4×C137—41no—
88C2×D4×C137—41no—
89C2×D4×C137—41no—
90C2×D4×C137—41no—
91C22×C4×C137—22no—
92C22×C4×C137—21no—
93C22×C4×C137—21no—
94C22×C4×C137—21no—
95C22×C4×C137—21no—
96C22×C4×C137—21no—
97C22×C4×C137—22no—
98C22×C4×C137—21no—
99C22×C4×C137—21no—
100C22×C4×C137—21no—
101C22×C4×C137—21no—
102C22×C4×C137—41no—
103C22×C4×C137—41no—
104C22×C4×C137—41no—
105C22×C4×C137—41no—
106C22×C4×C137—41no—
107C22×C4×C137—41no—
108C22×C4×C137—41no—
109C22×C4×C137—41no—
110C22×C4×C137—41no—
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—41no—
120C22×C4×C137C2×D411yescharacteristic
121C22×C4×C137C2×D411yescharacteristic
122C22×C4×C137C2×D411yescharacteristic
123C22×C4×C137#4111yescharacteristic
124C22×C4×C137#4111yescharacteristic
125C22×C4×C137#4111yescharacteristic
126C2×C8×C137—41no—
127C2×C8×C137—41no—
128C2×C8×C137—41no—
129C2×C8×C137—41no—
130C2×C8×C137—41no—
131C2×C8×C137—41no—
132C4⋊C4×C137—22no—
133C4⋊C4×C137—22no—
134C4⋊C4×C137—21no—
135C4⋊C4×C137—21no—
136C4⋊C4×C137—21no—
137C4⋊C4×C137—21no—
138C4⋊C4×C137—41no—
139C4⋊C4×C137—41no—
140C4⋊C4×C137—41no—
141C4⋊C4×C137—41no—
142C22⋊C4×C137—41no—
143C22⋊C4×C137—41no—
144C22⋊C4×C137—41no—
145C22⋊C4×C137—41no—
146C22⋊C4×C137—81no—
147C22⋊C4×C137—81no—
148C22⋊C4×C137—81no—
149C22⋊C4×C137—81no—
150C23×C137—21no—
151C23×C137—21no—
152C23×C137—21no—
153C23×C137—21no—
154C23×C137—41no—
155C23×C137—41no—
156C23×C137—41no—
157C23×C137—41no—
158C23×C137—41no—
159C23×C137—41no—
160C23×C137—41no—
161C23×C137#12011yescharacteristic
162C23×C137#12111yescharacteristic
163C23×C137#12411yescharacteristic
164C23×C137#13511yescharacteristic
165C23×C137#13511yescharacteristic
166C23×C137AGL(1,ℤ/8)11yescharacteristic
167C23×C137#13711yescharacteristic
168Q8×C137—42no—
169Q8×C137—81no—
170D4×C137—42no—
171D4×C137—81no—
172D4×C137—81no—
173D4×C137—81no—
174D4×C137—81no—
175D4×C137—81no—
176C2×C4×C137—21no—
177C2×C4×C137—21no—
178C2×C4×C137—21no—
179C2×C4×C137—21no—
180C2×C4×C137—41no—
181C2×C4×C137—41no—
182C2×C4×C137—41no—
183C2×C4×C137—41no—
184C2×C4×C137—42no—
185C2×C4×C137—42no—
186C2×C4×C137—42no—
187C2×C4×C137—42no—
188C2×C4×C137—42no—
189C2×C4×C137—42no—
190C2×C4×C137—41no—
191C2×C4×C137—41no—
192C2×C4×C137—41no—
193C2×C4×C137—41no—
194C2×C4×C137—41no—
195C2×C4×C137—41no—
196C2×C4×C137—41no—
197C2×C4×C137—41no—
198C2×C4×C137—41no—
199C2×C4×C137—41no—
200C2×C4×C137—41no—
201C2×C4×C137—41no—
202C2×C4×C137—41no—
203C2×C4×C137—42no—
204C2×C4×C137—41no—
205C2×C4×C137—41no—
206C2×C4×C137—42no—
207C2×C4×C137—81no—
208C2×C4×C137—81no—
209C2×C4×C137—81no—
210C2×C4×C137—81no—
211C2×C4×C137—81no—
212C2×C4×C137—81no—
213C2×C4×C137—81no—
214C2×C4×C137—81no—
215C2×C4×C137—81no—
216C2×C4×C137—81no—
217C2×C4×C137#12111yescharacteristic
218C2×C4×C137#12111yescharacteristic
219C2×C4×C137#12311yescharacteristic
220C2×C4×C137#12311yescharacteristic
221C8×C137—81no—
222C8×C137—81no—
223C22×C137—21no—
224C22×C137—21no—
225C22×C137—21no—
226C22×C137—21no—
227C22×C137—21no—
228C22×C137—21no—
229C22×C137—21no—
230C22×C137—21no—
231C22×C137—21no—
232C22×C137—21no—
233C22×C137—21no—
234C22×C137—21no—
235C22×C137—81no—
236C22×C137—81no—
237C22×C137—81no—
238C22×C137—81no—
239C22×C137—81no—
240C22×C137—81no—
241C22×C137—81no—
242C22×C137#39411yescharacteristic
243C22×C137#44911yescharacteristic
244C22×C137#45211yescharacteristic
245C22×C137#45411yescharacteristic
246C22×C137#45511yescharacteristic
247C22×C137B(4,𝔽2)11yescharacteristic
248C22×C137#45811yescharacteristic
249C22×C137#46311yescharacteristic
250C22×C137#46411yescharacteristic
251C22×C137#48811yescharacteristic
252C22×C137#48911yescharacteristic
253C4×C137—21no—
254C4×C137—21no—
255C4×C137—21no—
256C4×C137—21no—
257C4×C137—82no—
258C4×C137—82no—
259C4×C137—81no—
260C4×C137—81no—
261C4×C137—81no—
262C4×C137—81no—
263C4×C137—81no—
264C2×C137—21no—
265C2×C137—21no—
266C2×C137—21no—
267C2×C137—21no—
268C2×C137—161no—
269C2×C137#159711yescharacteristic
270C2×C137#160611yescharacteristic
271C2×C137#161211yescharacteristic
272C2×C137#161511yescharacteristic
273C2×C137#204011yescharacteristic
274C2×C137#204211yescharacteristic
275C2×C137#204411yescharacteristic
276#10404C13711yesmaximal, characteristic, direct product factor, Sylow
277C137#1040411yescharacteristic, direct product factor, Sylow
278#2639C2×C13711yescharacteristic
279#1874C2×C13711yescharacteristic
280#1872C2×C13711yescharacteristic, complemented
281C2×#328C2×C13711yescharacteristic, complemented
282C2×#327C2×C13711yescharacteristic
283#1442C2×C13711yescharacteristic, complemented
284#1280C2×C13711yescharacteristic, complemented
285C2×C22⋊Q8C22×C13711yescharacteristic
286C2×#121C22×C13711yescharacteristic
287C22×C4⋊C4C22×C13711yescharacteristic
288C2×#103—21no—
289C2×#102—21no—
290C2×C22⋊C8C22×C13711yescharacteristic
291C2×C22⋊C8C22×C13711yescharacteristic
292#400—21no—
293#397—21no—
294#394—21no—
295#393—21no—
296#386—21no—
297#386—21no—
298C2×#95—21no—
299C2×#95—21no—
300C2×#95C22×C13711yescharacteristic
301C2×#95C22×C13711yescharacteristic
302#340—21no—
303#340—21no—
304#328—22no—
305#327—22no—
306C22×Q8D4×C13711yescharacteristic
307C22×D4—21no—
308C22×D4D4×C13711yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4D4×C13711yescharacteristic
312C23×C4D4×C13711yescharacteristic
313C23×C4C23×C13711yescharacteristic
314C22×C8—21no—
315C22×C8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4D4×C13711yescharacteristic
329C2×C4⋊C4D4×C13711yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336#103—42no—
337#102—42no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—42no—
350#95—42no—
351#95D4×C13712yes—
352C24—21no—
353C24C2×D4×C13711yescharacteristic
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4C2×D4×C13711yescharacteristic
398C22×C4C2×D4×C13711yescharacteristic
399C22×C4C2×D4×C13711yescharacteristic
400C22×C4#41×C13711yescharacteristic
401C22×C4#41×C13711yescharacteristic
402C22×C4#41×C13711yescharacteristic
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—41no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23#120×C13711yescharacteristic
439C23#121×C13711yescharacteristic
440C23#124×C13711yescharacteristic
441C23#135×C13711yescharacteristic
442C23#135×C13711yescharacteristic
443C23AGL(1,ℤ/8)×C13711yescharacteristic
444C23#137×C13711yescharacteristic
445Q8—42no—
446Q8—81no—
447D4—42no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4#121×C13711yescharacteristic
495C2×C4#121×C13711yescharacteristic
496C2×C4#123×C13711yescharacteristic
497C2×C4#123×C13711yescharacteristic
498C8—81no—
499C8—81no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22#394×C13711yescharacteristic
520C22#449×C13711yescharacteristic
521C22#452×C13711yescharacteristic
522C22#454×C13711yescharacteristic
523C22#455×C13711yescharacteristic
524C22B(4,𝔽2)×C13711yescharacteristic
525C22#458×C13711yescharacteristic
526C22#463×C13711yescharacteristic
527C22#464×C13711yescharacteristic
528C22#488×C13711yescharacteristic
529C22#489×C13711yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—82no—
539C4—81no—
540C4—81no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—161no—
546C2#1597×C13711yescharacteristic
547C2#1606×C13711yescharacteristic
548C2#1612×C13711yescharacteristic
549C2#1615×C13711yescharacteristic
550C2#2040×C13711yescharacteristic
551C2#2042×C13711yescharacteristic
552C2#2044×C13711yescharacteristic
subgroupG/H
center, socleC23×C137#120
commutator, Frattini, cosocleC23×C4C23×C137
prime radicalC2×#121×C137C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1872×C137C2semidirect
4. C2×#328×C137C2semidirect
6. #1442×C137C2semidirect
7. #1280×C137C2semidirect
276. #10404C137direct (N × H)
277. C137#10404direct (N × H)
280. #1872C2×C137semidirect
281. C2×#328C2×C137semidirect
283. #1442C2×C137semidirect
284. #1280C2×C137semidirect

Maximal subgroups

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

subgroupindex
#2639×C1372
#1874×C1372
#1872×C1372
C2×#328×C1372
C2×#327×C1372
#1442×C1372
#1280×C1372
#10404137