Finite Group Databasebeta

← C137×#24008 #46873394

Subgroups — C137×#24008 #46873394

Order 35072.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C137C211yesmaximal, characteristic
2C2×#485×C137C211yesmaximal, characteristic, complemented
3C2×#482×C137C211yesmaximal, characteristic, complemented
4#2280×C137C211yesmaximal, characteristic, complemented
5#2036×C137C211yesmaximal, characteristic, complemented
6#2035×C137C211yesmaximal, characteristic, complemented
7#2034×C137C211yesmaximal, characteristic, complemented
8#2033×C137C211yesmaximal, characteristic, complemented
9#1875×C137C211yesmaximal, characteristic, complemented
10#1873×C137C211yesmaximal, characteristic, complemented
11#1854×C137C211yesmaximal, characteristic, complemented
12#1854×C137C211yesmaximal, characteristic, complemented
13#1788×C137C211yesmaximal, characteristic, complemented
14#1788×C137C211yesmaximal, characteristic, complemented
15#1779×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C24×C4×C137C2211yescharacteristic
18#525×C137—24no—
19#525×C137—24no—
20C2×#123×C137—21no—
21C2×C22⋊Q8×C137C2211yescharacteristic
22C2×C22⋊Q8×C137C2211yescharacteristic
23C2×#121×C137C2211yescharacteristic
24C2×#121×C137C2211yescharacteristic
25C2×#120×C137—21no—
26C2×C4×D4×C137—21no—
27C2×C4×D4×C137—21no—
28C2×#117×C137C2211yescharacteristic
29C2×#117×C137C2211yescharacteristic
30C2×#117×C137C2211yescharacteristic
31#485×C137—24no—
32#482×C137—24no—
33C2×#107×C137C2211yescharacteristic, complemented
34C2×#107×C137C2211yescharacteristic, complemented
35C2×#106×C137C2211yescharacteristic, complemented
36C2×#106×C137C2211yescharacteristic, complemented
37C2×#103×C137C2211yescharacteristic, complemented
38C2×#103×C137C2211yescharacteristic, complemented
39C2×#103×C137C2211yescharacteristic, complemented
40C2×#103×C137C2211yescharacteristic, complemented
41C2×#102×C137C2211yescharacteristic, complemented
42C2×#102×C137C2211yescharacteristic, complemented
43C2×#102×C137C2211yescharacteristic, complemented
44C2×#102×C137C2211yescharacteristic, complemented
45C2×C22⋊C8×C137C2211yescharacteristic
46C2×C22⋊C8×C137C2211yescharacteristic
47C2×C22⋊C8×C137C2211yescharacteristic
48C2×C22⋊C8×C137C2211yescharacteristic
49C2×C22⋊C8×C137C2211yescharacteristic
50C2×C22⋊C8×C137C2211yescharacteristic
51#381×C137—21no—
52#380×C137C2211yescharacteristic
53#380×C137C2211yescharacteristic
54#380×C137C2211yescharacteristic
55#380×C137C2211yescharacteristic
56#379×C137—21no—
57C4×C22⋊C4×C137—21no—
58C4×C22⋊C4×C137—21no—
59#340×C137C2211yescharacteristic, complemented
60#340×C137C2211yescharacteristic, complemented
61#340×C137C2211yescharacteristic, complemented
62#340×C137C2211yescharacteristic, complemented
63C25×C137D411yescharacteristic
64C2×#41×C137—22no—
65C2×#41×C137—22no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—41no—
69C2×#41×C137—41no—
70C22×Q8×C137C2311yescharacteristic
71C22×D4×C137—21no—
72C22×D4×C137—21no—
73C22×D4×C137—21no—
74C22×D4×C137C2311yescharacteristic
75C23×C4×C137—21no—
76C23×C4×C137—22no—
77C23×C4×C137—22no—
78C23×C4×C137—22no—
79C23×C4×C137—22no—
80C23×C4×C137—41no—
81C23×C4×C137—41no—
82C23×C4×C137D411yescharacteristic
83C23×C4×C137D411yescharacteristic
84C23×C4×C137D411yescharacteristic
85C23×C4×C137C2311yescharacteristic
86C23×C4×C137C2311yescharacteristic
87C23×C4×C137C2311yescharacteristic
88C22×C8×C137C2311yescharacteristic
89C22×C8×C137C2311yescharacteristic
90C22×C8×C137C2311yescharacteristic
91C22×C8×C137C2311yescharacteristic
92#123×C137—28no—
93C22⋊Q8×C137—22no—
94C22⋊Q8×C137—22no—
95C22⋊Q8×C137—22no—
96C22⋊Q8×C137D414yes—
97#121×C137—22no—
98#121×C137—22no—
99#121×C137—22no—
100#121×C137D414yes—
101#120×C137—28no—
102C4×D4×C137—28no—
103C4×D4×C137—28no—
104#117×C137—22no—
105#117×C137—22no—
106#117×C137—22no—
107#117×C137—22no—
108#117×C137—41no—
109#117×C137—41no—
110C2×C4⋊C4×C137—21no—
111C2×C4⋊C4×C137—21no—
112C2×C4⋊C4×C137C2311yescharacteristic
113C2×C4⋊C4×C137C2311yescharacteristic
114C2×C4⋊C4×C137C2311yescharacteristic
115C2×C4⋊C4×C137C2311yescharacteristic
116C2×C4⋊C4×C137C2311yescharacteristic
117C2×C4⋊C4×C137C2311yescharacteristic
118C2×C22⋊C4×C137—21no—
119C2×C22⋊C4×C137—21no—
120C2×C22⋊C4×C137—21no—
121C2×C22⋊C4×C137—21no—
122C2×C22⋊C4×C137—21no—
123C2×C22⋊C4×C137—21no—
124C2×C22⋊C4×C137—21no—
125C2×C22⋊C4×C137—21no—
126C2×C22⋊C4×C137—21no—
127C2×C22⋊C4×C137—21no—
128C2×C22⋊C4×C137—21no—
129C2×C42×C137—21no—
130C2×C42×C137—21no—
131C2×C42×C137—21no—
132#107×C137—22no—
133#107×C137—22no—
134#106×C137—22no—
135#106×C137—22no—
136#103×C137—22no—
137#103×C137—22no—
138#103×C137—41no—
139#103×C137—41no—
140#102×C137—22no—
141#102×C137—22no—
142#102×C137—41no—
143#102×C137—41no—
144C22⋊C8×C137—22no—
145C22⋊C8×C137—22no—
146C22⋊C8×C137—22no—
147C22⋊C8×C137—22no—
148C22⋊C8×C137—41no—
149C22⋊C8×C137—41no—
150#95×C137—21no—
151#95×C137—21no—
152#95×C137—21no—
153#95×C137—21no—
154C24×C137—22no—
155C24×C137—22no—
156C24×C137—22no—
157C24×C137—21no—
158C24×C137—41no—
159C24×C137—41no—
160C24×C137—41no—
161C24×C137—41no—
162C24×C137C2×D411yescharacteristic
163C24×C137C2×D411yescharacteristic
164C24×C137C2×D411yescharacteristic
165#41×C137—44no—
166#41×C137—44no—
167#41×C137—44no—
168#41×C137—44no—
169C2×Q8×C137—21no—
170C2×Q8×C137—21no—
171C2×Q8×C137—21no—
172C2×Q8×C137—21no—
173C2×Q8×C137—21no—
174C2×Q8×C137C2×D412yes—
175C2×D4×C137—24no—
176C2×D4×C137—24no—
177C2×D4×C137—24no—
178C2×D4×C137—21no—
179C2×D4×C137—21no—
180C2×D4×C137—21no—
181C2×D4×C137—21no—
182C2×D4×C137—21no—
183C2×D4×C137—42no—
184C2×D4×C137—42no—
185C2×D4×C137—42no—
186C2×D4×C137—42no—
187C2×D4×C137—42no—
188C2×D4×C137—42no—
189C2×D4×C137C2×D412yes—
190C22×C4×C137—21no—
191C22×C4×C137—21no—
192C22×C4×C137—21no—
193C22×C4×C137—21no—
194C22×C4×C137—21no—
195C22×C4×C137—21no—
196C22×C4×C137—21no—
197C22×C4×C137—21no—
198C22×C4×C137—24no—
199C22×C4×C137—22no—
200C22×C4×C137—22no—
201C22×C4×C137—21no—
202C22×C4×C137—21no—
203C22×C4×C137—21no—
204C22×C4×C137—22no—
205C22×C4×C137—22no—
206C22×C4×C137—22no—
207C22×C4×C137—22no—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—21no—
211C22×C4×C137—21no—
212C22×C4×C137—21no—
213C22×C4×C137—21no—
214C22×C4×C137—21no—
215C22×C4×C137—21no—
216C22×C4×C137—21no—
217C22×C4×C137—21no—
218C22×C4×C137—41no—
219C22×C4×C137—41no—
220C22×C4×C137—41no—
221C22×C4×C137—44no—
222C22×C4×C137—44no—
223C22×C4×C137—44no—
224C22×C4×C137—44no—
225C22×C4×C137—42no—
226C22×C4×C137—42no—
227C22×C4×C137C2×D411yescharacteristic
228C22×C4×C137C2×D411yescharacteristic
229C22×C4×C137C2×D412yes—
230C22×C4×C137C2×D412yes—
231C22×C4×C137C2×D411yescharacteristic
232C22×C4×C137#4112yes—
233C22×C4×C137#4112yes—
234C22×C4×C137C2411yescharacteristic
235C2×C8×C137—21no—
236C2×C8×C137—21no—
237C2×C8×C137—21no—
238C2×C8×C137—21no—
239C2×C8×C137—21no—
240C2×C8×C137—21no—
241C2×C8×C137—21no—
242C2×C8×C137—21no—
243C2×C8×C137—21no—
244C2×C8×C137—21no—
245C2×C8×C137—21no—
246C2×C8×C137—21no—
247C4⋊C4×C137—24no—
248C4⋊C4×C137—24no—
249C4⋊C4×C137—21no—
250C4⋊C4×C137—21no—
251C4⋊C4×C137—21no—
252C4⋊C4×C137—21no—
253C4⋊C4×C137—21no—
254C4⋊C4×C137—21no—
255C4⋊C4×C137—21no—
256C4⋊C4×C137—21no—
257C4⋊C4×C137—21no—
258C4⋊C4×C137—21no—
259C4⋊C4×C137C2×D412yes—
260C4⋊C4×C137C2×D412yes—
261C22⋊C4×C137—24no—
262C22⋊C4×C137—24no—
263C22⋊C4×C137—24no—
264C22⋊C4×C137—24no—
265C22⋊C4×C137—24no—
266C22⋊C4×C137—42no—
267C22⋊C4×C137—42no—
268C22⋊C4×C137—42no—
269C22⋊C4×C137—42no—
270C22⋊C4×C137—42no—
271C22⋊C4×C137—42no—
272C42×C137—24no—
273C42×C137—42no—
274C42×C137—42no—
275C23×C137—21no—
276C23×C137—21no—
277C23×C137—21no—
278C23×C137—21no—
279C23×C137—21no—
280C23×C137—21no—
281C23×C137—21no—
282C23×C137—21no—
283C23×C137—21no—
284C23×C137—21no—
285C23×C137—21no—
286C23×C137—21no—
287C23×C137—21no—
288C23×C137—21no—
289C23×C137—21no—
290C23×C137—21no—
291C23×C137—21no—
292C23×C137—21no—
293C23×C137—22no—
294C23×C137—44no—
295C23×C137—44no—
296C23×C137—44no—
297C23×C137—44no—
298C23×C137—44no—
299C23×C137—44no—
300C23×C137—44no—
301C23×C137—41no—
302C23×C137—41no—
303C23×C137—41no—
304C23×C137—41no—
305C23×C137—41no—
306C23×C137—41no—
307C23×C137#12012yes—
308C23×C137#12312yes—
309C23×C137#13512yes—
310C23×C137C22×D411yescharacteristic
311Q8×C137—22no—
312Q8×C137—22no—
313Q8×C137—41no—
314Q8×C137—41no—
315D4×C137—22no—
316D4×C137—22no—
317D4×C137—48no—
318D4×C137—48no—
319D4×C137—48no—
320D4×C137—41no—
321D4×C137—41no—
322C2×C4×C137—21no—
323C2×C4×C137—21no—
324C2×C4×C137—21no—
325C2×C4×C137—21no—
326C2×C4×C137—22no—
327C2×C4×C137—22no—
328C2×C4×C137—22no—
329C2×C4×C137—22no—
330C2×C4×C137—22no—
331C2×C4×C137—22no—
332C2×C4×C137—22no—
333C2×C4×C137—22no—
334C2×C4×C137—22no—
335C2×C4×C137—22no—
336C2×C4×C137—21no—
337C2×C4×C137—22no—
338C2×C4×C137—21no—
339C2×C4×C137—21no—
340C2×C4×C137—44no—
341C2×C4×C137—44no—
342C2×C4×C137—44no—
343C2×C4×C137—48no—
344C2×C4×C137—41no—
345C2×C4×C137—41no—
346C2×C4×C137—41no—
347C2×C4×C137—41no—
348C2×C4×C137—41no—
349C2×C4×C137—41no—
350C2×C4×C137—41no—
351C2×C4×C137—41no—
352C2×C4×C137—41no—
353C2×C4×C137—41no—
354C2×C4×C137—41no—
355C2×C4×C137—41no—
356C2×C4×C137—41no—
357C2×C4×C137—41no—
358C2×C4×C137—41no—
359C2×C4×C137—41no—
360C2×C4×C137—41no—
361C2×C4×C137—41no—
362C2×C4×C137—41no—
363C2×C4×C137—41no—
364C2×C4×C137—41no—
365C2×C4×C137—41no—
366C2×C4×C137#12012yes—
367C2×C4×C137#12312yes—
368C2×C4×C137C22×D411yescharacteristic
369C2×C4×C137C22×D411yescharacteristic
370C2×C4×C137C2×#4111yescharacteristic
371C2×C4×C137C2×#4111yescharacteristic
372C2×C4×C137H(5,𝔽2)11yescharacteristic
373C2×C4×C137H(5,𝔽2)11yescharacteristic
374C8×C137—41no—
375C8×C137—41no—
376C8×C137—41no—
377C8×C137—41no—
378C22×C137—22no—
379C22×C137—22no—
380C22×C137—22no—
381C22×C137—22no—
382C22×C137—22no—
383C22×C137—22no—
384C22×C137—22no—
385C22×C137—22no—
386C22×C137—22no—
387C22×C137—416no—
388C22×C137—41no—
389C22×C137—41no—
390C22×C137—41no—
391C22×C137—41no—
392C22×C137—41no—
393C22×C137—41no—
394C22×C137—41no—
395C22×C137—41no—
396C22×C137—41no—
397C22×C137—41no—
398C22×C137—41no—
399C22×C137—41no—
400C22×C137—42no—
401C22×C137—42no—
402C22×C137—42no—
403C22×C137—81no—
404C22×C137—81no—
405C22×C137—81no—
406C22×C137—81no—
407C22×C137C2×#12011yescharacteristic
408C22×C137C2×#12311yescharacteristic
409C22×C137#53411yescharacteristic
410C22×C137C2×#13511yescharacteristic
411C22×C137#57511yescharacteristic
412C22×C137#57511yescharacteristic
413C22×C137#57511yescharacteristic
414C4×C137—22no—
415C4×C137—22no—
416C4×C137—41no—
417C4×C137—42no—
418C4×C137—42no—
419C4×C137—42no—
420C4×C137—81no—
421C4×C137—81no—
422C4×C137—81no—
423C4×C137—81no—
424C4×C137#54611yescharacteristic
425C4×C137#54611yescharacteristic
426C4×C137#54611yescharacteristic
427C4×C137#54611yescharacteristic
428C2×C137—42no—
429C2×C137—42no—
430C2×C137—42no—
431C2×C137—82no—
432C2×C137#240511yescharacteristic
433C2×C137#300211yescharacteristic
434C2×C137#300511yescharacteristic
435C2×C137#309111yescharacteristic
436C2×C137#309311yescharacteristic
437C2×C137#319111yescharacteristic
438C2×C137#319711yescharacteristic
439#24008C13711yesmaximal, characteristic, direct product factor, Sylow
440C137#2400811yescharacteristic, direct product factor, Sylow
441C2×#525C2×C13711yescharacteristic
442C2×#485C2×C13711yescharacteristic, complemented
443C2×#482C2×C13711yescharacteristic, complemented
444#2280C2×C13711yescharacteristic, complemented
445#2036C2×C13711yescharacteristic, complemented
446#2035C2×C13711yescharacteristic, complemented
447#2034C2×C13711yescharacteristic, complemented
448#2033C2×C13711yescharacteristic, complemented
449#1875C2×C13711yescharacteristic, complemented
450#1873C2×C13711yescharacteristic, complemented
451#1854C2×C13711yescharacteristic, complemented
452#1854C2×C13711yescharacteristic, complemented
453#1788C2×C13711yescharacteristic, complemented
454#1788C2×C13711yescharacteristic, complemented
455#1779C2×C13711yescharacteristic, complemented
456C22×#41C22×C13711yescharacteristic
457C24×C4C22×C13711yescharacteristic
458#525—24no—
459#525—24no—
460C2×#123—21no—
461C2×C22⋊Q8C22×C13711yescharacteristic
462C2×C22⋊Q8C22×C13711yescharacteristic
463C2×#121C22×C13711yescharacteristic
464C2×#121C22×C13711yescharacteristic
465C2×#120—21no—
466C2×C4×D4—21no—
467C2×C4×D4—21no—
468C2×#117C22×C13711yescharacteristic
469C2×#117C22×C13711yescharacteristic
470C2×#117C22×C13711yescharacteristic
471#485—24no—
472#482—24no—
473C2×#107C22×C13711yescharacteristic, complemented
474C2×#107C22×C13711yescharacteristic, complemented
475C2×#106C22×C13711yescharacteristic, complemented
476C2×#106C22×C13711yescharacteristic, complemented
477C2×#103C22×C13711yescharacteristic, complemented
478C2×#103C22×C13711yescharacteristic, complemented
479C2×#103C22×C13711yescharacteristic, complemented
480C2×#103C22×C13711yescharacteristic, complemented
481C2×#102C22×C13711yescharacteristic, complemented
482C2×#102C22×C13711yescharacteristic, complemented
483C2×#102C22×C13711yescharacteristic, complemented
484C2×#102C22×C13711yescharacteristic, complemented
485C2×C22⋊C8C22×C13711yescharacteristic
486C2×C22⋊C8C22×C13711yescharacteristic
487C2×C22⋊C8C22×C13711yescharacteristic
488C2×C22⋊C8C22×C13711yescharacteristic
489C2×C22⋊C8C22×C13711yescharacteristic
490C2×C22⋊C8C22×C13711yescharacteristic
491#381—21no—
492#380C22×C13711yescharacteristic
493#380C22×C13711yescharacteristic
494#380C22×C13711yescharacteristic
495#380C22×C13711yescharacteristic
496#379—21no—
497C4×C22⋊C4—21no—
498C4×C22⋊C4—21no—
499#340C22×C13711yescharacteristic, complemented
500#340C22×C13711yescharacteristic, complemented
501#340C22×C13711yescharacteristic, complemented
502#340C22×C13711yescharacteristic, complemented
503C25D4×C13711yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C23×C13711yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C23×C13711yescharacteristic
515C23×C4—21no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4D4×C13711yescharacteristic
523C23×C4D4×C13711yescharacteristic
524C23×C4D4×C13711yescharacteristic
525C23×C4C23×C13711yescharacteristic
526C23×C4C23×C13711yescharacteristic
527C23×C4C23×C13711yescharacteristic
528C22×C8C23×C13711yescharacteristic
529C22×C8C23×C13711yescharacteristic
530C22×C8C23×C13711yescharacteristic
531C22×C8C23×C13711yescharacteristic
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8D4×C13714yes—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C13714yes—
541#120—28no—
542C4×D4—28no—
543C4×D4—28no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—41no—
549#117—41no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4C23×C13711yescharacteristic
553C2×C4⋊C4C23×C13711yescharacteristic
554C2×C4⋊C4C23×C13711yescharacteristic
555C2×C4⋊C4C23×C13711yescharacteristic
556C2×C4⋊C4C23×C13711yescharacteristic
557C2×C4⋊C4C23×C13711yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572#107—22no—
573#107—22no—
574#106—22no—
575#106—22no—
576#103—22no—
577#103—22no—
578#103—41no—
579#103—41no—
580#102—22no—
581#102—22no—
582#102—41no—
583#102—41no—
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C22⋊C8—22no—
588C22⋊C8—41no—
589C22⋊C8—41no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C2×D4×C13711yescharacteristic
603C24C2×D4×C13711yescharacteristic
604C24C2×D4×C13711yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×D4×C13712yes—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×D4×C13712yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C13711yescharacteristic
668C22×C4C2×D4×C13711yescharacteristic
669C22×C4C2×D4×C13712yes—
670C22×C4C2×D4×C13712yes—
671C22×C4C2×D4×C13711yescharacteristic
672C22×C4#41×C13712yes—
673C22×C4#41×C13712yes—
674C22×C4C24×C13711yescharacteristic
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4C2×D4×C13712yes—
700C4⋊C4C2×D4×C13712yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C42—24no—
713C42—42no—
714C42—42no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23#120×C13712yes—
748C23#123×C13712yes—
749C23#135×C13712yes—
750C23C22×D4×C13711yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4#120×C13712yes—
807C2×C4#123×C13712yes—
808C2×C4C22×D4×C13711yescharacteristic
809C2×C4C22×D4×C13711yescharacteristic
810C2×C4C2×#41×C13711yescharacteristic
811C2×C4C2×#41×C13711yescharacteristic
812C2×C4H(5,𝔽2)×C13711yescharacteristic
813C2×C4H(5,𝔽2)×C13711yescharacteristic
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×#120×C13711yescharacteristic
848C22C2×#123×C13711yescharacteristic
849C22#534×C13711yescharacteristic
850C22C2×#135×C13711yescharacteristic
851C22#575×C13711yescharacteristic
852C22#575×C13711yescharacteristic
853C22#575×C13711yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4#546×C13711yescharacteristic
865C4#546×C13711yescharacteristic
866C4#546×C13711yescharacteristic
867C4#546×C13711yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2#2405×C13711yescharacteristic
873C2#3002×C13711yescharacteristic
874C2#3005×C13711yescharacteristic
875C2#3091×C13711yescharacteristic
876C2#3093×C13711yescharacteristic
877C2#3191×C13711yescharacteristic
878C2#3197×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC2×#525×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C24×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C137C2semidirect
3. C2×#482×C137C2semidirect
4. #2280×C137C2semidirect
5. #2036×C137C2semidirect
6. #2035×C137C2semidirect
7. #2034×C137C2semidirect
8. #2033×C137C2semidirect
9. #1875×C137C2semidirect
10. #1873×C137C2semidirect
11. #1854×C137C2semidirect
12. #1854×C137C2semidirect
13. #1788×C137C2semidirect
14. #1788×C137C2semidirect
15. #1779×C137C2semidirect
33. C2×#107×C137C22semidirect
34. C2×#107×C137C22semidirect
35. C2×#106×C137C22semidirect
36. C2×#106×C137C22semidirect
37. C2×#103×C137C22semidirect
38. C2×#103×C137C22semidirect
39. C2×#103×C137C22semidirect
40. C2×#103×C137C22semidirect
41. C2×#102×C137C22semidirect
42. C2×#102×C137C22semidirect
43. C2×#102×C137C22semidirect
44. C2×#102×C137C22semidirect
59. #340×C137C22semidirect
60. #340×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
439. #24008C137direct (N × H)
440. C137#24008direct (N × H)
442. C2×#485C2×C137semidirect
443. C2×#482C2×C137semidirect
444. #2280C2×C137semidirect
445. #2036C2×C137semidirect
446. #2035C2×C137semidirect
447. #2034C2×C137semidirect
448. #2033C2×C137semidirect
449. #1875C2×C137semidirect
450. #1873C2×C137semidirect
451. #1854C2×C137semidirect
452. #1854C2×C137semidirect
453. #1788C2×C137semidirect
454. #1788C2×C137semidirect
455. #1779C2×C137semidirect
473. C2×#107C22×C137semidirect
474. C2×#107C22×C137semidirect
475. C2×#106C22×C137semidirect
476. C2×#106C22×C137semidirect
477. C2×#103C22×C137semidirect
478. C2×#103C22×C137semidirect
479. C2×#103C22×C137semidirect
480. C2×#103C22×C137semidirect
481. C2×#102C22×C137semidirect
482. C2×#102C22×C137semidirect
483. C2×#102C22×C137semidirect
484. C2×#102C22×C137semidirect
499. #340C22×C137semidirect
500. #340C22×C137semidirect
501. #340C22×C137semidirect
502. #340C22×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1372
C2×#485×C1372
C2×#482×C1372
#2280×C1372
#2036×C1372
#2035×C1372
#2034×C1372
#2033×C1372
#1875×C1372
#1873×C1372
#1854×C1372
#1788×C1372
#1779×C1372
#24008137