Finite Group Databasebeta

← C137×#26148 #46875534

Subgroups — C137×#26148 #46875534

Order 35072.

904 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C137C211yesmaximal, characteristic, complemented
2C2×#428×C137C211yesmaximal, characteristic, complemented
3#2415×C137C211yesmaximal, characteristic
4D4×C4⋊C4×C137C211yesmaximal, characteristic
5#2096×C137C211yesmaximal, characteristic, complemented
6#2083×C137C211yesmaximal, characteristic, complemented
7#2077×C137C211yesmaximal, characteristic, complemented
8#2036×C137C211yesmaximal, characteristic, complemented
9#1927×C137C211yesmaximal, characteristic, complemented
10#1918×C137C211yesmaximal, characteristic, complemented
11#1894×C137C211yesmaximal, characteristic, complemented
12#1872×C137C211yesmaximal, characteristic, complemented
13#1870×C137C211yesmaximal, characteristic
14#1854×C137C211yesmaximal, characteristic, complemented
15#1853×C137C211yesmaximal, characteristic, complemented
16C22×M16×C137C2211yescharacteristic
17C2×C22⋊Q8×C137C2211yescharacteristic
18C2×C22⋊Q8×C137C2211yescharacteristic
19C2×C4×D4×C137—21no—
20C2×C4×D4×C137C2211yescharacteristic
21C2×#117×C137C2211yescharacteristic
22C22×C4⋊C4×C137C2211yescharacteristic
23C22×C4⋊C4×C137C2211yescharacteristic
24#484×C137—24no—
25#428×C137—24no—
26C2×#107×C137C2211yescharacteristic
27C2×#107×C137C2211yescharacteristic
28C2×#107×C137C2211yescharacteristic
29C2×#106×C137C2211yescharacteristic
30C2×#106×C137C2211yescharacteristic
31C2×#106×C137C2211yescharacteristic
32C2×#103×C137C2211yescharacteristic
33C2×#103×C137C2211yescharacteristic
34C2×#103×C137C2211yescharacteristic
35C2×#103×C137C2211yescharacteristic
36C2×C22⋊C8×C137C2211yescharacteristic
37C2×C22⋊C8×C137C2211yescharacteristic
38C2×C22⋊C8×C137C2211yescharacteristic
39#397×C137—21no—
40#394×C137—21no—
41#391×C137C2211yescharacteristic
42#389×C137—21no—
43#389×C137—21no—
44#389×C137C2211yescharacteristic
45#388×C137—21no—
46#385×C137—21no—
47#385×C137—21no—
48#384×C137C2211yescharacteristic
49#380×C137C2211yescharacteristic
50#380×C137C2211yescharacteristic
51#380×C137C2211yescharacteristic
52C4×C4⋊C4×C137C2211yescharacteristic
53#340×C137C2211yescharacteristic
54#340×C137C2211yescharacteristic
55#340×C137C2211yescharacteristic
56#340×C137C2211yescharacteristic
57#340×C137C2211yescharacteristic
58#340×C137C2211yescharacteristic
59#336×C137C2211yescharacteristic
60#336×C137C2211yescharacteristic
61C22×Q8×C137C2311yescharacteristic
62C22×D4×C137D411yescharacteristic
63C23×C4×C137—21no—
64C23×C4×C137—21no—
65C23×C4×C137C2311yescharacteristic
66C23×C4×C137C2311yescharacteristic
67C2×M16×C137—22no—
68C2×M16×C137—22no—
69C2×M16×C137—22no—
70C22×C8×C137C2311yescharacteristic
71C22×C8×C137C2311yescharacteristic
72C22×C8×C137C2311yescharacteristic
73C22×C8×C137C2311yescharacteristic
74C22⋊Q8×C137—22no—
75C22⋊Q8×C137—22no—
76C22⋊Q8×C137—22no—
77C22⋊Q8×C137—41no—
78C4×D4×C137—22no—
79C4×D4×C137—22no—
80C4×D4×C137—44no—
81#117×C137—22no—
82#117×C137—41no—
83C2×C4⋊C4×C137—22no—
84C2×C4⋊C4×C137—22no—
85C2×C4⋊C4×C137—21no—
86C2×C4⋊C4×C137—21no—
87C2×C4⋊C4×C137—21no—
88C2×C4⋊C4×C137—21no—
89C2×C4⋊C4×C137—21no—
90C2×C4⋊C4×C137—21no—
91C2×C4⋊C4×C137—21no—
92C2×C4⋊C4×C137—41no—
93C2×C4⋊C4×C137—41no—
94C2×C4⋊C4×C137D411yescharacteristic
95C2×C4⋊C4×C137C2311yescharacteristic
96C2×C4⋊C4×C137C2311yescharacteristic
97C2×C4⋊C4×C137C2311yescharacteristic
98C2×C4⋊C4×C137C2311yescharacteristic
99C2×C4⋊C4×C137C2311yescharacteristic
100C2×C4⋊C4×C137C2311yescharacteristic
101C2×C4⋊C4×C137C2311yescharacteristic
102C2×C22⋊C4×C137—21no—
103C2×C22⋊C4×C137—21no—
104C2×C22⋊C4×C137—21no—
105C2×C22⋊C4×C137—21no—
106C2×C22⋊C4×C137—21no—
107C2×C22⋊C4×C137—21no—
108C2×C22⋊C4×C137D411yescharacteristic
109C2×C22⋊C4×C137D411yescharacteristic
110C2×C42×C137—21no—
111C2×C42×C137—21no—
112C2×C42×C137C2311yescharacteristic
113#107×C137—22no—
114#107×C137—22no—
115#107×C137D414yescomplemented
116#106×C137—22no—
117#106×C137—22no—
118#106×C137—41no—
119#103×C137—22no—
120#103×C137—22no—
121#103×C137—22no—
122#103×C137—41no—
123C22⋊C8×C137—22no—
124C22⋊C8×C137—22no—
125C22⋊C8×C137—22no—
126#95×C137—21no—
127#95×C137—21no—
128#95×C137—21no—
129#95×C137—21no—
130#95×C137—21no—
131#95×C137—21no—
132#95×C137—21no—
133C24×C137C2×D411yescharacteristic
134C24×C137C2×D411yescharacteristic
135C2×Q8×C137—21no—
136C2×Q8×C137—21no—
137C2×Q8×C137—21no—
138C2×Q8×C137—21no—
139C2×Q8×C137—21no—
140C2×Q8×C137—21no—
141C2×D4×C137—22no—
142C2×D4×C137—22no—
143C2×D4×C137—22no—
144C22×C4×C137—21no—
145C22×C4×C137—21no—
146C22×C4×C137—21no—
147C22×C4×C137—21no—
148C22×C4×C137—21no—
149C22×C4×C137—21no—
150C22×C4×C137—21no—
151C22×C4×C137—21no—
152C22×C4×C137—21no—
153C22×C4×C137—21no—
154C22×C4×C137—21no—
155C22×C4×C137—21no—
156C22×C4×C137—21no—
157C22×C4×C137—21no—
158C22×C4×C137—21no—
159C22×C4×C137—21no—
160C22×C4×C137—21no—
161C22×C4×C137—21no—
162C22×C4×C137—42no—
163C22×C4×C137—42no—
164C22×C4×C137—42no—
165C22×C4×C137—42no—
166C22×C4×C137—81no—
167C22×C4×C137—81no—
168C22×C4×C137C2×D411yescharacteristic
169C22×C4×C137C2×D411yescharacteristic
170C22×C4×C137C2×D411yescharacteristic
171C22×C4×C137C2×D411yescharacteristic
172C22×C4×C137#4112yes—
173C22×C4×C137#4112yes—
174C22×C4×C137C2411yescharacteristic
175M16×C137—28no—
176C2×C8×C137—21no—
177C2×C8×C137—21no—
178C2×C8×C137—21no—
179C2×C8×C137—21no—
180C2×C8×C137—21no—
181C2×C8×C137—21no—
182C2×C8×C137—21no—
183C2×C8×C137—21no—
184C2×C8×C137—21no—
185C2×C8×C137—21no—
186C2×C8×C137C2×D412yes—
187C2×C8×C137#4112yes—
188C4⋊C4×C137—22no—
189C4⋊C4×C137—21no—
190C4⋊C4×C137—21no—
191C4⋊C4×C137—21no—
192C4⋊C4×C137—21no—
193C4⋊C4×C137—21no—
194C4⋊C4×C137—21no—
195C4⋊C4×C137—21no—
196C4⋊C4×C137—21no—
197C4⋊C4×C137—21no—
198C4⋊C4×C137—21no—
199C4⋊C4×C137—21no—
200C4⋊C4×C137—21no—
201C4⋊C4×C137—42no—
202C4⋊C4×C137—42no—
203C4⋊C4×C137—42no—
204C4⋊C4×C137—42no—
205C4⋊C4×C137—42no—
206C4⋊C4×C137—42no—
207C4⋊C4×C137—81no—
208C4⋊C4×C137C2×D412yes—
209C4⋊C4×C137C2×D412yes—
210C22⋊C4×C137—22no—
211C22⋊C4×C137—22no—
212C22⋊C4×C137—42no—
213C22⋊C4×C137—42no—
214C22⋊C4×C137—42no—
215C22⋊C4×C137—42no—
216C22⋊C4×C137—42no—
217C22⋊C4×C137—42no—
218C42×C137—21no—
219C42×C137—21no—
220C42×C137—42no—
221C42×C137—42no—
222C23×C137—21no—
223C23×C137—21no—
224C23×C137—21no—
225C23×C137—21no—
226C23×C137—21no—
227C23×C137—21no—
228C23×C137—21no—
229C23×C137—21no—
230C23×C137—21no—
231C23×C137—21no—
232C23×C137—21no—
233C23×C137—21no—
234C23×C137#12312yes—
235C23×C137#13712yes—
236C23×C137C22×D411yescharacteristic
237Q8×C137—41no—
238Q8×C137—41no—
239Q8×C137—41no—
240Q8×C137—41no—
241D4×C137—28no—
242C2×C4×C137—21no—
243C2×C4×C137—21no—
244C2×C4×C137—21no—
245C2×C4×C137—21no—
246C2×C4×C137—22no—
247C2×C4×C137—22no—
248C2×C4×C137—22no—
249C2×C4×C137—22no—
250C2×C4×C137—21no—
251C2×C4×C137—21no—
252C2×C4×C137—22no—
253C2×C4×C137—22no—
254C2×C4×C137—21no—
255C2×C4×C137—21no—
256C2×C4×C137—21no—
257C2×C4×C137—21no—
258C2×C4×C137—41no—
259C2×C4×C137—41no—
260C2×C4×C137—41no—
261C2×C4×C137—41no—
262C2×C4×C137—41no—
263C2×C4×C137—41no—
264C2×C4×C137—41no—
265C2×C4×C137—41no—
266C2×C4×C137—41no—
267C2×C4×C137—41no—
268C2×C4×C137—41no—
269C2×C4×C137—41no—
270C2×C4×C137—41no—
271C2×C4×C137—41no—
272C2×C4×C137—41no—
273C2×C4×C137—41no—
274C2×C4×C137—41no—
275C2×C4×C137—41no—
276C2×C4×C137—41no—
277C2×C4×C137—41no—
278C2×C4×C137—41no—
279C2×C4×C137—41no—
280C2×C4×C137—41no—
281C2×C4×C137—41no—
282C2×C4×C137—41no—
283C2×C4×C137—41no—
284C2×C4×C137—84no—
285C2×C4×C137—84no—
286C2×C4×C137#12312yes—
287C2×C4×C137AGL(1,ℤ/8)12yes—
288C2×C4×C137C22×D411yescharacteristic
289C2×C4×C137C2×#4111yescharacteristic
290C2×C4×C137C2×#4111yescharacteristic
291C2×C4×C137C2×#4111yescharacteristic
292C2×C4×C137H(5,𝔽2)11yescharacteristic
293C2×C4×C1372−1+411yescharacteristic
294C8×C137—22no—
295C8×C137—22no—
296C8×C137—41no—
297C8×C137—41no—
298C22×C137—22no—
299C22×C137—22no—
300C22×C137—22no—
301C22×C137—22no—
302C22×C137—22no—
303C22×C137—22no—
304C22×C137—41no—
305C22×C137—41no—
306C22×C137—41no—
307C22×C137—41no—
308C22×C137—41no—
309C22×C137—41no—
310C22×C137—41no—
311C22×C137—41no—
312C22×C137C2×#12311yescharacteristic
313C22×C137D4211yescharacteristic
314C22×C137#54711yescharacteristic
315C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C137C2×#13711yescharacteristic
317C22×C137#57711yescharacteristic
318C22×C137#57811yescharacteristic
319C4×C137—22no—
320C4×C137—22no—
321C4×C137—41no—
322C4×C137—41no—
323C4×C137—42no—
324C4×C137—42no—
325C4×C137—81no—
326C4×C137—81no—
327C4×C137—81no—
328C4×C137—81no—
329C4×C137—81no—
330C4×C137—81no—
331C4×C137#52511yescharacteristic
332C4×C137#53911yescharacteristic
333C4×C137#54811yescharacteristic
334C4×C137#55311yescharacteristic
335C2×C137—42no—
336C2×C137—42no—
337C2×C137#244311yescharacteristic
338C2×C137#309211yescharacteristic
339C2×C137#309711yescharacteristic
340C2×C137#327011yescharacteristic
341C2×C137#327211yescharacteristic
342C2×C137#334411yescharacteristic
343C2×C137#335311yescharacteristic
344#26148C13711yesmaximal, characteristic, direct product factor, Sylow
345C137#2614811yescharacteristic, direct product factor, Sylow
346C2×#484C2×C13711yescharacteristic, complemented
347C2×#428C2×C13711yescharacteristic, complemented
348#2415C2×C13711yescharacteristic
349D4×C4⋊C4C2×C13711yescharacteristic
350#2096C2×C13711yescharacteristic, complemented
351#2083C2×C13711yescharacteristic, complemented
352#2077C2×C13711yescharacteristic, complemented
353#2036C2×C13711yescharacteristic, complemented
354#1927C2×C13711yescharacteristic, complemented
355#1918C2×C13711yescharacteristic, complemented
356#1894C2×C13711yescharacteristic, complemented
357#1872C2×C13711yescharacteristic, complemented
358#1870C2×C13711yescharacteristic
359#1854C2×C13711yescharacteristic, complemented
360#1853C2×C13711yescharacteristic, complemented
361C22×M16C22×C13711yescharacteristic
362C2×C22⋊Q8C22×C13711yescharacteristic
363C2×C22⋊Q8C22×C13711yescharacteristic
364C2×C4×D4—21no—
365C2×C4×D4C22×C13711yescharacteristic
366C2×#117C22×C13711yescharacteristic
367C22×C4⋊C4C22×C13711yescharacteristic
368C22×C4⋊C4C22×C13711yescharacteristic
369#484—24no—
370#428—24no—
371C2×#107C22×C13711yescharacteristic
372C2×#107C22×C13711yescharacteristic
373C2×#107C22×C13711yescharacteristic
374C2×#106C22×C13711yescharacteristic
375C2×#106C22×C13711yescharacteristic
376C2×#106C22×C13711yescharacteristic
377C2×#103C22×C13711yescharacteristic
378C2×#103C22×C13711yescharacteristic
379C2×#103C22×C13711yescharacteristic
380C2×#103C22×C13711yescharacteristic
381C2×C22⋊C8C22×C13711yescharacteristic
382C2×C22⋊C8C22×C13711yescharacteristic
383C2×C22⋊C8C22×C13711yescharacteristic
384#397—21no—
385#394—21no—
386#391C22×C13711yescharacteristic
387#389—21no—
388#389—21no—
389#389C22×C13711yescharacteristic
390#388—21no—
391#385—21no—
392#385—21no—
393#384C22×C13711yescharacteristic
394#380C22×C13711yescharacteristic
395#380C22×C13711yescharacteristic
396#380C22×C13711yescharacteristic
397C4×C4⋊C4C22×C13711yescharacteristic
398#340C22×C13711yescharacteristic
399#340C22×C13711yescharacteristic
400#340C22×C13711yescharacteristic
401#340C22×C13711yescharacteristic
402#340C22×C13711yescharacteristic
403#340C22×C13711yescharacteristic
404#336C22×C13711yescharacteristic
405#336C22×C13711yescharacteristic
406C22×Q8C23×C13711yescharacteristic
407C22×D4D4×C13711yescharacteristic
408C23×C4—21no—
409C23×C4—21no—
410C23×C4C23×C13711yescharacteristic
411C23×C4C23×C13711yescharacteristic
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—22no—
415C22×C8C23×C13711yescharacteristic
416C22×C8C23×C13711yescharacteristic
417C22×C8C23×C13711yescharacteristic
418C22×C8C23×C13711yescharacteristic
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—41no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—44no—
426#117—22no—
427#117—41no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—41no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4D4×C13711yescharacteristic
440C2×C4⋊C4C23×C13711yescharacteristic
441C2×C4⋊C4C23×C13711yescharacteristic
442C2×C4⋊C4C23×C13711yescharacteristic
443C2×C4⋊C4C23×C13711yescharacteristic
444C2×C4⋊C4C23×C13711yescharacteristic
445C2×C4⋊C4C23×C13711yescharacteristic
446C2×C4⋊C4C23×C13711yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4D4×C13711yescharacteristic
454C2×C22⋊C4D4×C13711yescharacteristic
455C2×C42—21no—
456C2×C42—21no—
457C2×C42C23×C13711yescharacteristic
458#107—22no—
459#107—22no—
460#107D4×C13714yescomplemented
461#106—22no—
462#106—22no—
463#106—41no—
464#103—22no—
465#103—22no—
466#103—22no—
467#103—41no—
468C22⋊C8—22no—
469C22⋊C8—22no—
470C22⋊C8—22no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478C24C2×D4×C13711yescharacteristic
479C24C2×D4×C13711yescharacteristic
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4C2×D4×C13711yescharacteristic
514C22×C4C2×D4×C13711yescharacteristic
515C22×C4C2×D4×C13711yescharacteristic
516C22×C4C2×D4×C13711yescharacteristic
517C22×C4#41×C13712yes—
518C22×C4#41×C13712yes—
519C22×C4C24×C13711yescharacteristic
520M16—28no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8C2×D4×C13712yes—
532C2×C8#41×C13712yes—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4C2×D4×C13712yes—
554C4⋊C4C2×D4×C13712yes—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—42no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23#123×C13712yes—
580C23#137×C13712yes—
581C23C22×D4×C13711yescharacteristic
582Q8—41no—
583Q8—41no—
584Q8—41no—
585Q8—41no—
586D4—28no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—84no—
630C2×C4—84no—
631C2×C4#123×C13712yes—
632C2×C4AGL(1,ℤ/8)×C13712yes—
633C2×C4C22×D4×C13711yescharacteristic
634C2×C4C2×#41×C13711yescharacteristic
635C2×C4C2×#41×C13711yescharacteristic
636C2×C4C2×#41×C13711yescharacteristic
637C2×C4H(5,𝔽2)×C13711yescharacteristic
638C2×C42−1+4×C13711yescharacteristic
639C8—22no—
640C8—22no—
641C8—41no—
642C8—41no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22C2×#123×C13711yescharacteristic
658C22D42×C13711yescharacteristic
659C22#547×C13711yescharacteristic
660C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
661C22C2×#137×C13711yescharacteristic
662C22#577×C13711yescharacteristic
663C22#578×C13711yescharacteristic
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—42no—
669C4—42no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4#525×C13711yescharacteristic
677C4#539×C13711yescharacteristic
678C4#548×C13711yescharacteristic
679C4#553×C13711yescharacteristic
680C2—42no—
681C2—42no—
682C2#2443×C13711yescharacteristic
683C2#3092×C13711yescharacteristic
684C2#3097×C13711yescharacteristic
685C2#3270×C13711yescharacteristic
686C2#3272×C13711yescharacteristic
687C2#3344×C13711yescharacteristic
688C2#3353×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC22×D4×C137D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C4×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#484×C137C2semidirect
2. C2×#428×C137C2semidirect
5. #2096×C137C2semidirect
6. #2083×C137C2semidirect
7. #2077×C137C2semidirect
8. #2036×C137C2semidirect
9. #1927×C137C2semidirect
10. #1918×C137C2semidirect
11. #1894×C137C2semidirect
12. #1872×C137C2semidirect
14. #1854×C137C2semidirect
15. #1853×C137C2semidirect
115. #107×C137D4semidirect
344. #26148C137direct (N × H)
345. C137#26148direct (N × H)
346. C2×#484C2×C137semidirect
347. C2×#428C2×C137semidirect
350. #2096C2×C137semidirect
351. #2083C2×C137semidirect
352. #2077C2×C137semidirect
353. #2036C2×C137semidirect
354. #1927C2×C137semidirect
355. #1918C2×C137semidirect
356. #1894C2×C137semidirect
357. #1872C2×C137semidirect
359. #1854C2×C137semidirect
360. #1853C2×C137semidirect
460. #107D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C1372
C2×#428×C1372
#2415×C1372
D4×C4⋊C4×C1372
#2096×C1372
#2083×C1372
#2077×C1372
#2036×C1372
#1927×C1372
#1918×C1372
#1894×C1372
#1872×C1372
#1870×C1372
#1854×C1372
#1853×C1372
#26148137