Finite Group Databasebeta

← C137×#15179 #46864565

Subgroups — C137×#15179 #46864565

Order 35072.

1946 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C137C211yesmaximal, characteristic
2C2×#391×C137C211yesmaximal, characteristic, complemented
3C2×#391×C137C211yesmaximal, characteristic, complemented
4C2×#389×C137C211yesmaximal, characteristic, complemented
5C2×#380×C137C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C137C211yesmaximal, characteristic
7#1442×C137C212yesmaximal, complemented
8#1441×C137C212yesmaximal, complemented
9#1440×C137C212yesmaximal
10#1439×C137C212yesmaximal
11C4⋊#95×C137C211yesmaximal, characteristic, complemented
12C23×Q8×C137C2211yescharacteristic
13C24×C4×C137C2211yescharacteristic
14C2×C22⋊Q8×C137—24no—
15C2×C22⋊Q8×C137—24no—
16C2×C22⋊Q8×C137—24no—
17C22×C4⋊C4×C137C2211yescharacteristic
18C22×C4⋊C4×C137C2212yes—
19C22×C4⋊C4×C137C2212yes—
20C22×C4⋊C4×C137C2211yescharacteristic
21C22×C4⋊C4×C137C2211yescharacteristic
22C22×C22⋊C4×C137C2212yes—
23C22×C22⋊C4×C137C2211yescharacteristic
24C22×C22⋊C4×C137C2212yes—
25C22×C22⋊C4×C137C2211yescharacteristic
26C22×C42×C137C2211yescharacteristic
27C22×C42×C137C2211yescharacteristic
28#391×C137—24no—
29#391×C137—24no—
30#389×C137—24no—
31#380×C137—24no—
32C4×C22⋊C4×C137—24no—
33C2×#95×C137C2212yes—
34C2×#95×C137C2212yes—
35C2×#95×C137C2212yes—
36C2×#95×C137C2212yes—
37C2×#95×C137C2212yes—
38C2×#95×C137C2212yes—
39C2×#95×C137C2212yes—
40C2×#95×C137C2211yescharacteristic
41C2×#95×C137C2211yescharacteristic
42C2×#95×C137C2212yes—
43C25×C137C2311yescharacteristic
44C22×Q8×C137—22no—
45C22×Q8×C137—22no—
46C22×Q8×C137—22no—
47C22×Q8×C137—22no—
48C22×Q8×C137—22no—
49C22×Q8×C137—22no—
50C22×Q8×C137D414yes—
51C23×C4×C137—22no—
52C23×C4×C137—22no—
53C23×C4×C137—22no—
54C23×C4×C137—22no—
55C23×C4×C137—22no—
56C23×C4×C137—22no—
57C23×C4×C137D414yes—
58C23×C4×C137C2312yes—
59C23×C4×C137C2312yes—
60C23×C4×C137C2312yes—
61C23×C4×C137C2311yescharacteristic
62C23×C4×C137C2312yes—
63C23×C4×C137C2311yescharacteristic
64C23×C4×C137C2311yescharacteristic
65C23×C4×C137C2311yescharacteristic
66C23×C4×C137C2311yescharacteristic
67C23×C4×C137C2311yescharacteristic
68C22⋊Q8×C137—232no—
69C2×C4⋊C4×C137—22no—
70C2×C4⋊C4×C137—24no—
71C2×C4⋊C4×C137—24no—
72C2×C4⋊C4×C137—24no—
73C2×C4⋊C4×C137—22no—
74C2×C4⋊C4×C137—22no—
75C2×C4⋊C4×C137—22no—
76C2×C4⋊C4×C137—22no—
77C2×C4⋊C4×C137—24no—
78C2×C4⋊C4×C137—22no—
79C2×C4⋊C4×C137—24no—
80C2×C4⋊C4×C137—22no—
81C2×C4⋊C4×C137—42no—
82C2×C4⋊C4×C137D414yes—
83C2×C4⋊C4×C137D414yes—
84C2×C22⋊C4×C137—22no—
85C2×C22⋊C4×C137—22no—
86C2×C22⋊C4×C137—24no—
87C2×C22⋊C4×C137—22no—
88C2×C22⋊C4×C137—24no—
89C2×C22⋊C4×C137—24no—
90C2×C22⋊C4×C137—22no—
91C2×C22⋊C4×C137—22no—
92C2×C22⋊C4×C137—24no—
93C2×C22⋊C4×C137—24no—
94C2×C22⋊C4×C137—42no—
95C2×C22⋊C4×C137Q814yescomplemented
96C2×C42×C137—22no—
97C2×C42×C137—22no—
98C2×C42×C137—22no—
99C2×C42×C137—22no—
100C2×C42×C137—22no—
101C2×C42×C137—22no—
102#95×C137—22no—
103#95×C137—22no—
104#95×C137—24no—
105#95×C137—24no—
106#95×C137—24no—
107#95×C137—24no—
108#95×C137—24no—
109#95×C137—24no—
110#95×C137—24no—
111#95×C137—42no—
112C24×C137—21no—
113C24×C137—21no—
114C24×C137—21no—
115C24×C137—21no—
116C24×C137—21no—
117C24×C137—21no—
118C24×C137—21no—
119C24×C137—21no—
120C24×C137—21no—
121C24×C137—21no—
122C24×C137—21no—
123C24×C137—21no—
124C24×C137C2×D412yes—
125C24×C137C2×Q812yes—
126C24×C137#4112yes—
127C24×C137C2411yescharacteristic
128C2×Q8×C137—28no—
129C2×Q8×C137—28no—
130C2×Q8×C137—28no—
131C2×Q8×C137—44no—
132C2×Q8×C137—44no—
133C2×Q8×C137—44no—
134C2×Q8×C137—44no—
135C22×C4×C137—21no—
136C22×C4×C137—21no—
137C22×C4×C137—21no—
138C22×C4×C137—21no—
139C22×C4×C137—21no—
140C22×C4×C137—21no—
141C22×C4×C137—22no—
142C22×C4×C137—21no—
143C22×C4×C137—21no—
144C22×C4×C137—21no—
145C22×C4×C137—21no—
146C22×C4×C137—22no—
147C22×C4×C137—21no—
148C22×C4×C137—22no—
149C22×C4×C137—22no—
150C22×C4×C137—22no—
151C22×C4×C137—22no—
152C22×C4×C137—21no—
153C22×C4×C137—21no—
154C22×C4×C137—22no—
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—22no—
162C22×C4×C137—22no—
163C22×C4×C137—22no—
164C22×C4×C137—22no—
165C22×C4×C137—21no—
166C22×C4×C137—21no—
167C22×C4×C137—21no—
168C22×C4×C137—22no—
169C22×C4×C137—22no—
170C22×C4×C137—22no—
171C22×C4×C137—21no—
172C22×C4×C137—22no—
173C22×C4×C137—22no—
174C22×C4×C137—21no—
175C22×C4×C137—22no—
176C22×C4×C137—22no—
177C22×C4×C137—21no—
178C22×C4×C137—21no—
179C22×C4×C137—21no—
180C22×C4×C137—21no—
181C22×C4×C137—21no—
182C22×C4×C137—21no—
183C22×C4×C137—28no—
184C22×C4×C137—28no—
185C22×C4×C137—28no—
186C22×C4×C137—22no—
187C22×C4×C137—22no—
188C22×C4×C137—22no—
189C22×C4×C137—22no—
190C22×C4×C137—22no—
191C22×C4×C137—22no—
192C22×C4×C137—22no—
193C22×C4×C137—44no—
194C22×C4×C137—44no—
195C22×C4×C137—44no—
196C22×C4×C137—44no—
197C22×C4×C137C2×D414yes—
198C22×C4×C137C2×D414yes—
199C22×C4×C137C2×D412yes—
200C22×C4×C137C2×D414yes—
201C22×C4×C137C2×D412yes—
202C22×C4×C137C2×D412yes—
203C22×C4×C137C2×D412yes—
204C22×C4×C137C2×D412yes—
205C22×C4×C137C2×Q812yes—
206C22×C4×C137C2×Q812yes—
207C22×C4×C137#4112yes—
208C22×C4×C137#4112yes—
209C22×C4×C137#4112yes—
210C22×C4×C137#4112yes—
211C22×C4×C137#4112yes—
212C4⋊C4×C137—216no—
213C4⋊C4×C137—28no—
214C4⋊C4×C137—28no—
215C4⋊C4×C137—48no—
216C4⋊C4×C137—44no—
217C22⋊C4×C137—28no—
218C22⋊C4×C137—216no—
219C22⋊C4×C137—28no—
220C22⋊C4×C137—48no—
221C42×C137—44no—
222C42×C137—44no—
223C23×C137—22no—
224C23×C137—22no—
225C23×C137—22no—
226C23×C137—22no—
227C23×C137—22no—
228C23×C137—22no—
229C23×C137—22no—
230C23×C137—22no—
231C23×C137—22no—
232C23×C137—22no—
233C23×C137—22no—
234C23×C137—22no—
235C23×C137—22no—
236C23×C137—22no—
237C23×C137—22no—
238C23×C137—22no—
239C23×C137—22no—
240C23×C137—22no—
241C23×C137—41no—
242C23×C137—41no—
243C23×C137—41no—
244C23×C137—41no—
245C23×C137—41no—
246C23×C137—41no—
247C23×C137—41no—
248C23×C137—41no—
249C23×C137—41no—
250C23×C137—41no—
251C23×C137—41no—
252C23×C137—41no—
253C23×C137—41no—
254C23×C137—41no—
255C23×C137—41no—
256C23×C137—41no—
257C23×C137C22⋊Q814yes—
258C23×C137C22×D411yescharacteristic
259C23×C137C22×D411yescharacteristic
260C23×C137C22×D411yescharacteristic
261C23×C137C22×D411yescharacteristic
262C23×C137C22×Q811yescharacteristic
263C23×C137C2×#4111yescharacteristic
264C23×C137C2×#4111yescharacteristic
265C23×C137C2×#4111yescharacteristic
266C23×C137C2×#4111yescharacteristic
267C23×C137C2×#4111yescharacteristic
268C23×C137C2×#4111yescharacteristic
269C23×C137H(5,𝔽2)11yescharacteristic
270C23×C1372−1+411yescharacteristic
271C23×C1372−1+411yescharacteristic
272C23×C1372−1+411yescharacteristic
273Q8×C137—416no—
274C2×C4×C137—24no—
275C2×C4×C137—24no—
276C2×C4×C137—22no—
277C2×C4×C137—24no—
278C2×C4×C137—22no—
279C2×C4×C137—24no—
280C2×C4×C137—22no—
281C2×C4×C137—22no—
282C2×C4×C137—22no—
283C2×C4×C137—24no—
284C2×C4×C137—22no—
285C2×C4×C137—22no—
286C2×C4×C137—24no—
287C2×C4×C137—22no—
288C2×C4×C137—24no—
289C2×C4×C137—24no—
290C2×C4×C137—24no—
291C2×C4×C137—22no—
292C2×C4×C137—22no—
293C2×C4×C137—22no—
294C2×C4×C137—22no—
295C2×C4×C137—22no—
296C2×C4×C137—22no—
297C2×C4×C137—22no—
298C2×C4×C137—41no—
299C2×C4×C137—41no—
300C2×C4×C137—41no—
301C2×C4×C137—41no—
302C2×C4×C137—41no—
303C2×C4×C137—41no—
304C2×C4×C137—42no—
305C2×C4×C137—42no—
306C2×C4×C137—41no—
307C2×C4×C137—42no—
308C2×C4×C137—42no—
309C2×C4×C137—41no—
310C2×C4×C137—42no—
311C2×C4×C137—42no—
312C2×C4×C137—41no—
313C2×C4×C137—41no—
314C2×C4×C137—41no—
315C2×C4×C137—42no—
316C2×C4×C137—41no—
317C2×C4×C137—42no—
318C2×C4×C137—42no—
319C2×C4×C137—41no—
320C2×C4×C137—41no—
321C2×C4×C137—41no—
322C2×C4×C137—42no—
323C2×C4×C137—41no—
324C2×C4×C137—41no—
325C2×C4×C137—42no—
326C2×C4×C137—41no—
327C2×C4×C137—42no—
328C2×C4×C137—41no—
329C2×C4×C137—41no—
330C2×C4×C137—416no—
331C2×C4×C137—42no—
332C2×C4×C137—42no—
333C2×C4×C137—42no—
334C2×C4×C137—42no—
335C2×C4×C137—42no—
336C2×C4×C137—42no—
337C2×C4×C137—42no—
338C2×C4×C137#12014yes—
339C2×C4×C137#12114yes—
340C2×C4×C137#12114yes—
341C2×C4×C137#12114yes—
342C2×C4×C137#12314yes—
343C2×C4×C137#12314yes—
344C2×C4×C137#12414yes—
345C22×C137—24no—
346C22×C137—24no—
347C22×C137—24no—
348C22×C137—42no—
349C22×C137—42no—
350C22×C137—42no—
351C22×C137—42no—
352C22×C137—42no—
353C22×C137—42no—
354C22×C137—42no—
355C22×C137—42no—
356C22×C137—42no—
357C22×C137—42no—
358C22×C137—42no—
359C22×C137—42no—
360C22×C137C2×#12011yescharacteristic
361C22×C137C2×#12111yescharacteristic
362C22×C137C2×#12111yescharacteristic
363C22×C137C2×#12111yescharacteristic
364C22×C137C2×C22⋊Q811yescharacteristic
365C22×C137C2×#12311yescharacteristic
366C22×C137C2×#12311yescharacteristic
367C22×C137#52511yescharacteristic
368C22×C137C2×#12411yescharacteristic
369C22×C137#52911yescharacteristic
370C22×C137#52911yescharacteristic
371C22×C137#53311yescharacteristic
372C22×C137#53311yescharacteristic
373C22×C137#53611yescharacteristic
374C22×C137#53711yescharacteristic
375C22×C137#54111yescharacteristic
376C22×C137#54111yescharacteristic
377C22×C137#54211yescharacteristic
378C22×C137#54211yescharacteristic
379C22×C137#54611yescharacteristic
380C22×C137#54611yescharacteristic
381C22×C137#54711yescharacteristic
382C22×C137#54711yescharacteristic
383C22×C137#54811yescharacteristic
384C22×C137#54811yescharacteristic
385C22×C137#54811yescharacteristic
386C22×C137#54811yescharacteristic
387C22×C137D4×Q811yescharacteristic
388C22×C137D4×Q811yescharacteristic
389C22×C137D4×Q811yescharacteristic
390C22×C137#55011yescharacteristic
391C22×C137#55211yescharacteristic
392C22×C137#55211yescharacteristic
393C22×C137#55411yescharacteristic
394C22×C137#55611yescharacteristic
395C4×C137—42no—
396C4×C137—44no—
397C4×C137—44no—
398C4×C137—42no—
399C4×C137—42no—
400C4×C137—42no—
401C4×C137—42no—
402C4×C137—44no—
403C4×C137—82no—
404C4×C137#39418yes—
405C2×C137—44no—
406C2×C137C2×#39411yescharacteristic
407C2×C137#240711yescharacteristic
408C2×C137#240911yescharacteristic
409C2×C137#241511yescharacteristic
410C2×C137#241711yescharacteristic
411C2×C137#242111yescharacteristic
412C2×C137#242311yescharacteristic
413C2×C137#242611yescharacteristic
414C2×C137#242711yescharacteristic
415C2×C137#242911yescharacteristic
416C2×C137#242911yescharacteristic
417C2×C137#248911yescharacteristic
418C2×C137#249211yescharacteristic
419C2×C137#262511yescharacteristic
420C2×C137#285511yescharacteristic
421#15179C13711yesmaximal, characteristic, direct product factor, Sylow
422C137#1517911yescharacteristic, direct product factor, Sylow
423C22×C22⋊Q8C2×C13711yescharacteristic
424C2×#391C2×C13711yescharacteristic, complemented
425C2×#391C2×C13711yescharacteristic, complemented
426C2×#389C2×C13711yescharacteristic, complemented
427C2×#380C2×C13711yescharacteristic
428C2×C4×C22⋊C4C2×C13711yescharacteristic
429#1442C2×C13712yescomplemented
430#1441C2×C13712yescomplemented
431#1440C2×C13712yes—
432#1439C2×C13712yes—
433C4⋊#95C2×C13711yescharacteristic, complemented
434C23×Q8C22×C13711yescharacteristic
435C24×C4C22×C13711yescharacteristic
436C2×C22⋊Q8—24no—
437C2×C22⋊Q8—24no—
438C2×C22⋊Q8—24no—
439C22×C4⋊C4C22×C13712yes—
440C22×C4⋊C4C22×C13711yescharacteristic
441C22×C4⋊C4C22×C13712yes—
442C22×C4⋊C4C22×C13711yescharacteristic
443C22×C4⋊C4C22×C13711yescharacteristic
444C22×C22⋊C4C22×C13712yes—
445C22×C22⋊C4C22×C13711yescharacteristic
446C22×C22⋊C4C22×C13712yes—
447C22×C22⋊C4C22×C13711yescharacteristic
448C22×C42C22×C13711yescharacteristic
449C22×C42C22×C13711yescharacteristic
450#391—24no—
451#391—24no—
452#389—24no—
453#380—24no—
454C4×C22⋊C4—24no—
455C2×#95C22×C13712yes—
456C2×#95C22×C13712yes—
457C2×#95C22×C13712yes—
458C2×#95C22×C13712yes—
459C2×#95C22×C13712yes—
460C2×#95C22×C13712yes—
461C2×#95C22×C13711yescharacteristic
462C2×#95C22×C13712yes—
463C2×#95C22×C13711yescharacteristic
464C2×#95C22×C13712yes—
465C25C23×C13711yescharacteristic
466C22×Q8—22no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—22no—
470C22×Q8—22no—
471C22×Q8—22no—
472C22×Q8D4×C13714yes—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4D4×C13714yes—
480C23×C4C23×C13712yes—
481C23×C4C23×C13712yes—
482C23×C4C23×C13712yes—
483C23×C4C23×C13712yes—
484C23×C4C23×C13711yescharacteristic
485C23×C4C23×C13711yescharacteristic
486C23×C4C23×C13711yescharacteristic
487C23×C4C23×C13711yescharacteristic
488C23×C4C23×C13711yescharacteristic
489C23×C4C23×C13711yescharacteristic
490C22⋊Q8—232no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—42no—
504C2×C4⋊C4D4×C13714yes—
505C2×C4⋊C4D4×C13714yes—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4Q8×C13714yescomplemented
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524#95—22no—
525#95—22no—
526#95—24no—
527#95—24no—
528#95—24no—
529#95—24no—
530#95—24no—
531#95—24no—
532#95—24no—
533#95—42no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24C2×D4×C13712yes—
547C24C2×Q8×C13712yes—
548C24#41×C13712yes—
549C24C24×C13711yescharacteristic
550C2×Q8—28no—
551C2×Q8—28no—
552C2×Q8—28no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4C2×D4×C13714yes—
620C22×C4C2×D4×C13714yes—
621C22×C4C2×D4×C13712yes—
622C22×C4C2×D4×C13714yes—
623C22×C4C2×D4×C13712yes—
624C22×C4C2×D4×C13712yes—
625C22×C4C2×D4×C13712yes—
626C22×C4C2×D4×C13712yes—
627C22×C4C2×Q8×C13712yes—
628C22×C4C2×Q8×C13712yes—
629C22×C4#41×C13712yes—
630C22×C4#41×C13712yes—
631C22×C4#41×C13712yes—
632C22×C4#41×C13712yes—
633C22×C4#41×C13712yes—
634C4⋊C4—216no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C22⋊C4—28no—
640C22⋊C4—216no—
641C22⋊C4—28no—
642C22⋊C4—48no—
643C42—44no—
644C42—44no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23C22⋊Q8×C13714yes—
680C23C22×D4×C13711yescharacteristic
681C23C22×D4×C13711yescharacteristic
682C23C22×D4×C13711yescharacteristic
683C23C22×D4×C13711yescharacteristic
684C23C22×Q8×C13711yescharacteristic
685C23C2×#41×C13711yescharacteristic
686C23C2×#41×C13711yescharacteristic
687C23C2×#41×C13711yescharacteristic
688C23C2×#41×C13711yescharacteristic
689C23C2×#41×C13711yescharacteristic
690C23C2×#41×C13711yescharacteristic
691C23H(5,𝔽2)×C13711yescharacteristic
692C232−1+4×C13711yescharacteristic
693C232−1+4×C13711yescharacteristic
694C232−1+4×C13711yescharacteristic
695Q8—416no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—416no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4#120×C13714yes—
761C2×C4#121×C13714yes—
762C2×C4#121×C13714yes—
763C2×C4#121×C13714yes—
764C2×C4#123×C13714yes—
765C2×C4#123×C13714yes—
766C2×C4#124×C13714yes—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22C2×#120×C13711yescharacteristic
783C22C2×#121×C13711yescharacteristic
784C22C2×#121×C13711yescharacteristic
785C22C2×#121×C13711yescharacteristic
786C22C2×C22⋊Q8×C13711yescharacteristic
787C22C2×#123×C13711yescharacteristic
788C22C2×#123×C13711yescharacteristic
789C22#525×C13711yescharacteristic
790C22C2×#124×C13711yescharacteristic
791C22#529×C13711yescharacteristic
792C22#529×C13711yescharacteristic
793C22#533×C13711yescharacteristic
794C22#533×C13711yescharacteristic
795C22#536×C13711yescharacteristic
796C22#537×C13711yescharacteristic
797C22#541×C13711yescharacteristic
798C22#541×C13711yescharacteristic
799C22#542×C13711yescharacteristic
800C22#542×C13711yescharacteristic
801C22#546×C13711yescharacteristic
802C22#546×C13711yescharacteristic
803C22#547×C13711yescharacteristic
804C22#547×C13711yescharacteristic
805C22#548×C13711yescharacteristic
806C22#548×C13711yescharacteristic
807C22#548×C13711yescharacteristic
808C22#548×C13711yescharacteristic
809C22D4×Q8×C13711yescharacteristic
810C22D4×Q8×C13711yescharacteristic
811C22D4×Q8×C13711yescharacteristic
812C22#550×C13711yescharacteristic
813C22#552×C13711yescharacteristic
814C22#552×C13711yescharacteristic
815C22#554×C13711yescharacteristic
816C22#556×C13711yescharacteristic
817C4—42no—
818C4—44no—
819C4—44no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—44no—
825C4—82no—
826C4#394×C13718yes—
827C2—44no—
828C2C2×#394×C13711yescharacteristic
829C2#2407×C13711yescharacteristic
830C2#2409×C13711yescharacteristic
831C2#2415×C13711yescharacteristic
832C2#2417×C13711yescharacteristic
833C2#2421×C13711yescharacteristic
834C2#2423×C13711yescharacteristic
835C2#2426×C13711yescharacteristic
836C2#2427×C13711yescharacteristic
837C2#2429×C13711yescharacteristic
838C2#2429×C13711yescharacteristic
839C2#2489×C13711yescharacteristic
840C2#2492×C13711yescharacteristic
841C2#2625×C13711yescharacteristic
842C2#2855×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutator, Frattini, cosocleC24C24×C137
prime radicalC25×C137C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#391×C137C2semidirect
3. C2×#391×C137C2semidirect
4. C2×#389×C137C2semidirect
7. #1442×C137C2semidirect
8. #1441×C137C2semidirect
11. C4⋊#95×C137C2semidirect
95. C2×C22⋊C4×C137Q8semidirect
421. #15179C137direct (N × H)
422. C137#15179direct (N × H)
424. C2×#391C2×C137semidirect
425. C2×#391C2×C137semidirect
426. C2×#389C2×C137semidirect
429. #1442C2×C137semidirect
430. #1441C2×C137semidirect
433. C4⋊#95C2×C137semidirect
517. C2×C22⋊C4Q8×C137semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1372
C2×#391×C1372
C2×#389×C1372
C2×#380×C1372
C2×C4×C22⋊C4×C1372
#1442×C1372
#1441×C1372
#1440×C1372
#1439×C1372
C4⋊#95×C1372
#15179137