Finite Group Databasebeta

← C137×#13995 #46863381

Subgroups — C137×#13995 #46863381

Order 35072.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C137C211yesmaximal, characteristic
2C23×C22⋊C4×C137C211yesmaximal, characteristic, complemented
3C2×#390×C137C212yesmaximal, complemented
4C2×#386×C137C211yesmaximal, characteristic, complemented
5C2×#386×C137C211yesmaximal, characteristic, complemented
6C2×#385×C137C211yesmaximal, characteristic, complemented
7C2×#379×C137C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C137C211yesmaximal, characteristic, complemented
9#1439×C137C212yesmaximal, complemented
10#1438×C137C212yesmaximal, complemented
11#1437×C137C212yesmaximal, complemented
12C26×C137C2211yescharacteristic
13C23×D4×C137C2211yescharacteristic
14C23×D4×C137C2212yes—
15C24×C4×C137C2211yescharacteristic
16C24×C4×C137C2211yescharacteristic
17C2×#120×C137—24no—
18C2×#120×C137—24no—
19C2×#120×C137C418yescomplemented
20C22×C4⋊C4×C137C2212yescomplemented
21C22×C22⋊C4×C137—24no—
22C22×C22⋊C4×C137—28no—
23C22×C22⋊C4×C137C2211yescharacteristic
24C22×C22⋊C4×C137C2212yes—
25C22×C22⋊C4×C137C2212yes—
26C22×C22⋊C4×C137C2212yes—
27C22×C22⋊C4×C137C2212yes—
28C22×C22⋊C4×C137C2211yescharacteristic
29C22×C22⋊C4×C137C2212yes—
30C22×C22⋊C4×C137C2211yescharacteristic
31C22×C22⋊C4×C137C2211yescharacteristic, complemented
32C22×C22⋊C4×C137C2212yescomplemented
33C22×C22⋊C4×C137C2211yescharacteristic, complemented
34C22×C42×C137C2212yescomplemented
35#390×C137—28no—
36#386×C137—24no—
37#386×C137—24no—
38#385×C137—24no—
39#379×C137—24no—
40C4×C22⋊C4×C137—24no—
41C2×#95×C137C2212yescomplemented
42C2×#95×C137C2211yescharacteristic, complemented
43C2×#95×C137C2212yescomplemented
44C2×#95×C137C2211yescharacteristic, complemented
45C2×#95×C137C2212yescomplemented
46C25×C137—24no—
47C25×C137—22no—
48C25×C137—24no—
49C25×C137—22no—
50C25×C137—22no—
51C25×C137—22no—
52C25×C137—22no—
53C25×C137—22no—
54C25×C137—42no—
55C25×C137—42no—
56C25×C137C2×C414yes—
57C25×C137C2311yescharacteristic
58C25×C137C2312yes—
59C25×C137C2311yescharacteristic
60C22×D4×C137—22no—
61C22×D4×C137—22no—
62C22×D4×C137—24no—
63C22×D4×C137—22no—
64C22×D4×C137—22no—
65C22×D4×C137—24no—
66C22×D4×C137—22no—
67C22×D4×C137—22no—
68C22×D4×C137—24no—
69C22×D4×C137—24no—
70C22×D4×C137—42no—
71C22×D4×C137—42no—
72C22×D4×C137C2×C414yes—
73C22×D4×C137C2×C418yescomplemented
74C23×C4×C137—22no—
75C23×C4×C137—22no—
76C23×C4×C137—22no—
77C23×C4×C137—24no—
78C23×C4×C137—24no—
79C23×C4×C137—22no—
80C23×C4×C137—22no—
81C23×C4×C137—42no—
82C23×C4×C137—42no—
83C23×C4×C137D414yescomplemented
84C23×C4×C137C2311yescharacteristic
85C23×C4×C137C2311yescharacteristic
86C23×C4×C137C2311yescharacteristic
87C23×C4×C137C2311yescharacteristic
88C23×C4×C137C2312yes—
89C23×C4×C137C2312yes—
90C23×C4×C137C2312yes—
91C23×C4×C137C2311yescharacteristic
92#120×C137—232no—
93C2×C4⋊C4×C137—24no—
94C2×C4⋊C4×C137—24no—
95C2×C4⋊C4×C137—42no—
96C2×C22⋊C4×C137—232no—
97C2×C22⋊C4×C137—22no—
98C2×C22⋊C4×C137—24no—
99C2×C22⋊C4×C137—22no—
100C2×C22⋊C4×C137—24no—
101C2×C22⋊C4×C137—24no—
102C2×C22⋊C4×C137—24no—
103C2×C22⋊C4×C137—24no—
104C2×C22⋊C4×C137—24no—
105C2×C22⋊C4×C137—24no—
106C2×C22⋊C4×C137—22no—
107C2×C22⋊C4×C137—22no—
108C2×C22⋊C4×C137—22no—
109C2×C22⋊C4×C137—24no—
110C2×C22⋊C4×C137—24no—
111C2×C22⋊C4×C137—24no—
112C2×C22⋊C4×C137—24no—
113C2×C22⋊C4×C137—24no—
114C2×C22⋊C4×C137—22no—
115C2×C22⋊C4×C137—22no—
116C2×C22⋊C4×C137—24no—
117C2×C22⋊C4×C137—24no—
118C2×C22⋊C4×C137—42no—
119C2×C22⋊C4×C137—42no—
120C2×C22⋊C4×C137—42no—
121C2×C22⋊C4×C137—42no—
122C2×C22⋊C4×C137C2×C414yes—
123C2×C22⋊C4×C137C2×C418yescomplemented
124C2×C22⋊C4×C137D414yes—
125C2×C22⋊C4×C137D414yes—
126C2×C22⋊C4×C137D414yescomplemented
127C2×C22⋊C4×C137D418yescomplemented
128C2×C42×C137—24no—
129C2×C42×C137—24no—
130C2×C42×C137—42no—
131#95×C137—24no—
132#95×C137—24no—
133#95×C137—24no—
134#95×C137—22no—
135#95×C137—22no—
136C24×C137—22no—
137C24×C137—22no—
138C24×C137—22no—
139C24×C137—22no—
140C24×C137—28no—
141C24×C137—28no—
142C24×C137—216no—
143C24×C137—216no—
144C24×C137—28no—
145C24×C137—22no—
146C24×C137—22no—
147C24×C137—22no—
148C24×C137—22no—
149C24×C137—22no—
150C24×C137—22no—
151C24×C137—22no—
152C24×C137—22no—
153C24×C137—22no—
154C24×C137—22no—
155C24×C137—22no—
156C24×C137—22no—
157C24×C137—28no—
158C24×C137—28no—
159C24×C137—21no—
160C24×C137—22no—
161C24×C137—21no—
162C24×C137—21no—
163C24×C137—21no—
164C24×C137—21no—
165C24×C137—21no—
166C24×C137—22no—
167C24×C137—22no—
168C24×C137—22no—
169C24×C137—48no—
170C24×C137—48no—
171C24×C137—48no—
172C24×C137—48no—
173C24×C137—48no—
174C24×C137—48no—
175C24×C137—48no—
176C24×C137—48no—
177C24×C137—48no—
178C24×C137—44no—
179C24×C137—44no—
180C24×C137—48no—
181C24×C137—44no—
182C24×C137—44no—
183C24×C137—44no—
184C24×C137—44no—
185C24×C137C22×C412yes—
186C24×C137C22×C414yes—
187C24×C137C22×C412yes—
188C24×C137C2×D414yes—
189C24×C137C2×D412yes—
190C24×C137C2×D412yes—
191C24×C137C2×D412yes—
192C24×C137C2×D412yes—
193C24×C137#4114yes—
194C24×C137#4112yes—
195C24×C137#4112yes—
196C24×C137C2411yescharacteristic
197C2×D4×C137—28no—
198C2×D4×C137—28no—
199C2×D4×C137—28no—
200C2×D4×C137—216no—
201C2×D4×C137—216no—
202C2×D4×C137—48no—
203C2×D4×C137—48no—
204C2×D4×C137—48no—
205C2×D4×C137—48no—
206C2×D4×C137—48no—
207C2×D4×C137—44no—
208C2×D4×C137—44no—
209C2×D4×C137—44no—
210C2×D4×C137—44no—
211C22×C4×C137—21no—
212C22×C4×C137—22no—
213C22×C4×C137—21no—
214C22×C4×C137—22no—
215C22×C4×C137—22no—
216C22×C4×C137—22no—
217C22×C4×C137—22no—
218C22×C4×C137—28no—
219C22×C4×C137—28no—
220C22×C4×C137—21no—
221C22×C4×C137—21no—
222C22×C4×C137—21no—
223C22×C4×C137—22no—
224C22×C4×C137—22no—
225C22×C4×C137—22no—
226C22×C4×C137—22no—
227C22×C4×C137—22no—
228C22×C4×C137—22no—
229C22×C4×C137—22no—
230C22×C4×C137—21no—
231C22×C4×C137—21no—
232C22×C4×C137—22no—
233C22×C4×C137—22no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—21no—
237C22×C4×C137—22no—
238C22×C4×C137—22no—
239C22×C4×C137—22no—
240C22×C4×C137—22no—
241C22×C4×C137—22no—
242C22×C4×C137—28no—
243C22×C4×C137—21no—
244C22×C4×C137—21no—
245C22×C4×C137—21no—
246C22×C4×C137—21no—
247C22×C4×C137—21no—
248C22×C4×C137—22no—
249C22×C4×C137—21no—
250C22×C4×C137—22no—
251C22×C4×C137—22no—
252C22×C4×C137—22no—
253C22×C4×C137—44no—
254C22×C4×C137—48no—
255C22×C4×C137—48no—
256C22×C4×C137—48no—
257C22×C4×C137—48no—
258C22×C4×C137—44no—
259C22×C4×C137—44no—
260C22×C4×C137C22×C412yes—
261C22×C4×C137C22×C414yes—
262C22×C4×C137C2×D414yes—
263C22×C4×C137C2×D412yes—
264C22×C4×C137C2×D414yes—
265C22×C4×C137C2×D414yes—
266C22×C4×C137C2×D414yes—
267C22×C4×C137C2×D412yes—
268C22×C4×C137C2×D414yes—
269C4⋊C4×C137—48no—
270C22⋊C4×C137—216no—
271C22⋊C4×C137—28no—
272C22⋊C4×C137—216no—
273C22⋊C4×C137—216no—
274C22⋊C4×C137—48no—
275C22⋊C4×C137—48no—
276C22⋊C4×C137—48no—
277C22⋊C4×C137—44no—
278C22⋊C4×C137—44no—
279C22⋊C4×C137—44no—
280C22⋊C4×C137C22⋊C4116yescomplemented
281C42×C137—48no—
282C23×C137—24no—
283C23×C137—24no—
284C23×C137—22no—
285C23×C137—22no—
286C23×C137—24no—
287C23×C137—22no—
288C23×C137—22no—
289C23×C137—24no—
290C23×C137—24no—
291C23×C137—24no—
292C23×C137—24no—
293C23×C137—24no—
294C23×C137—24no—
295C23×C137—24no—
296C23×C137—24no—
297C23×C137—24no—
298C23×C137—232no—
299C23×C137—24no—
300C23×C137—24no—
301C23×C137—24no—
302C23×C137—24no—
303C23×C137—24no—
304C23×C137—24no—
305C23×C137—24no—
306C23×C137—24no—
307C23×C137—24no—
308C23×C137—24no—
309C23×C137—24no—
310C23×C137—24no—
311C23×C137—24no—
312C23×C137—24no—
313C23×C137—24no—
314C23×C137—24no—
315C23×C137—24no—
316C23×C137—24no—
317C23×C137—22no—
318C23×C137—22no—
319C23×C137—24no—
320C23×C137—22no—
321C23×C137—24no—
322C23×C137—432no—
323C23×C137—432no—
324C23×C137—416no—
325C23×C137—416no—
326C23×C137—416no—
327C23×C137—432no—
328C23×C137—416no—
329C23×C137—432no—
330C23×C137—416no—
331C23×C137—42no—
332C23×C137—42no—
333C23×C137—42no—
334C23×C137—42no—
335C23×C137—42no—
336C23×C137—42no—
337C23×C137—42no—
338C23×C137—42no—
339C23×C137—42no—
340C23×C137—42no—
341C23×C137—42no—
342C23×C137—42no—
343C23×C137—42no—
344C23×C137—42no—
345C23×C137—42no—
346C23×C137—42no—
347C23×C137—416no—
348C23×C137—41no—
349C23×C137—41no—
350C23×C137—41no—
351C23×C137—41no—
352C23×C137—42no—
353C23×C137—41no—
354C23×C137—41no—
355C23×C137—41no—
356C23×C137—41no—
357C23×C137—42no—
358C23×C137—42no—
359C23×C137—42no—
360C23×C137—42no—
361C23×C137—42no—
362C23×C137—42no—
363C23×C137—42no—
364C23×C137—42no—
365C23×C137—42no—
366C23×C137C2×C22⋊C414yes—
367C23×C137C4×D418yes—
368C23×C137C4×D414yes—
369C23×C137C4×D414yes—
370C23×C137#12114yes—
371C23×C137#12114yes—
372C23×C137#12414yes—
373C23×C137#12714yes—
374C23×C137C23×C411yescharacteristic
375C23×C137C22×D411yescharacteristic
376C23×C137C22×D411yescharacteristic
377C23×C137C22×D411yescharacteristic
378C23×C137C22×D412yes—
379C23×C137C22×D411yescharacteristic
380C23×C137C2×#4111yescharacteristic
381C23×C137C2×#4111yescharacteristic
382C23×C137C2×#4112yes—
383C23×C137H(5,𝔽2)12yes—
384C23×C137H(5,𝔽2)12yes—
385D4×C137—432no—
386D4×C137—416no—
387C2×C4×C137—24no—
388C2×C4×C137—24no—
389C2×C4×C137—22no—
390C2×C4×C137—22no—
391C2×C4×C137—24no—
392C2×C4×C137—24no—
393C2×C4×C137—24no—
394C2×C4×C137—24no—
395C2×C4×C137—24no—
396C2×C4×C137—24no—
397C2×C4×C137—22no—
398C2×C4×C137—22no—
399C2×C4×C137—22no—
400C2×C4×C137—22no—
401C2×C4×C137—24no—
402C2×C4×C137—24no—
403C2×C4×C137—22no—
404C2×C4×C137—22no—
405C2×C4×C137—24no—
406C2×C4×C137—24no—
407C2×C4×C137—24no—
408C2×C4×C137—24no—
409C2×C4×C137—416no—
410C2×C4×C137—416no—
411C2×C4×C137—41no—
412C2×C4×C137—41no—
413C2×C4×C137—42no—
414C2×C4×C137—41no—
415C2×C4×C137—42no—
416C2×C4×C137—41no—
417C2×C4×C137—42no—
418C2×C4×C137—42no—
419C2×C4×C137—42no—
420C2×C4×C137—42no—
421C2×C4×C137—42no—
422C2×C4×C137—42no—
423C2×C4×C137—42no—
424C2×C4×C137—42no—
425C2×C4×C137—41no—
426C2×C4×C137—41no—
427C2×C4×C137—41no—
428C2×C4×C137—41no—
429C2×C4×C137—41no—
430C2×C4×C137—41no—
431C2×C4×C137—42no—
432C2×C4×C137—42no—
433C2×C4×C137—42no—
434C2×C4×C137—42no—
435C2×C4×C137C2×C22⋊C418yescomplemented
436C2×C4×C137#12014yescomplemented
437C22×C137—24no—
438C22×C137—28no—
439C22×C137—28no—
440C22×C137—24no—
441C22×C137—24no—
442C22×C137—28no—
443C22×C137—24no—
444C22×C137—28no—
445C22×C137—24no—
446C22×C137—24no—
447C22×C137—28no—
448C22×C137—28no—
449C22×C137—28no—
450C22×C137—464no—
451C22×C137—44no—
452C22×C137—44no—
453C22×C137—44no—
454C22×C137—44no—
455C22×C137—44no—
456C22×C137—44no—
457C22×C137—44no—
458C22×C137—44no—
459C22×C137—44no—
460C22×C137—44no—
461C22×C137—44no—
462C22×C137—44no—
463C22×C137—42no—
464C22×C137—44no—
465C22×C137—44no—
466C22×C137—42no—
467C22×C137—42no—
468C22×C137—81no—
469C22×C137—81no—
470C22×C137—82no—
471C22×C137—81no—
472C22×C137—82no—
473C22×C137—81no—
474C22×C137#39018yescomplemented
475C22×C137C22×C22⋊C411yescharacteristic
476C22×C137C2×C4×D411yescharacteristic
477C22×C137C2×C4×D412yes—
478C22×C137C2×C4×D411yescharacteristic
479C22×C137#51812yes—
480C22×C137C2×#12011yescharacteristic
481C22×C137C2×#12111yescharacteristic
482C22×C137C2×#12111yescharacteristic
483C22×C137#52511yescharacteristic
484C22×C137#52512yes—
485C22×C137C2×#12411yescharacteristic
486C22×C137C2×#12711yescharacteristic
487C22×C137#53411yescharacteristic
488C22×C137#53511yescharacteristic
489C22×C137#53812yes—
490C22×C137D4212yes—
491C22×C137D4212yes—
492C22×C137D4212yes—
493C22×C137#54612yes—
494C22×C137#54612yes—
495C22×C137#54612yes—
496C22×C137#54612yes—
497C22×C137#55112yes—
498C4×C137—28no—
499C4×C137—24no—
500C4×C137—42no—
501C4×C137—44no—
502C4×C137—44no—
503C4×C137—42no—
504C4×C137—81no—
505C4×C137—81no—
506C2×C137—28no—
507C2×C137—48no—
508C2×C137—82no—
509C2×C137C2×#39011yescharacteristic
510C2×C137C4×#12011yescharacteristic
511C2×C137#232111yescharacteristic
512C2×C137D4×C22⋊C412yes—
513C2×C137#235812yes—
514C2×C137#241011yescharacteristic
515C2×C137#241111yescharacteristic
516C2×C137#242412yes—
517C2×C137#243311yescharacteristic
518C2×C137#247212yes—
519C2×C137#253911yescharacteristic
520#13995C13711yesmaximal, characteristic, direct product factor, Sylow
521C137#1399511yescharacteristic, direct product factor, Sylow
522C22×#120C2×C13711yescharacteristic
523C23×C22⋊C4C2×C13711yescharacteristic, complemented
524C2×#390C2×C13712yescomplemented
525C2×#386C2×C13711yescharacteristic, complemented
526C2×#386C2×C13711yescharacteristic, complemented
527C2×#385C2×C13711yescharacteristic, complemented
528C2×#379C2×C13711yescharacteristic, complemented
529C2×C4×C22⋊C4C2×C13711yescharacteristic, complemented
530#1439C2×C13712yescomplemented
531#1438C2×C13712yescomplemented
532#1437C2×C13712yescomplemented
533C26C22×C13711yescharacteristic
534C23×D4C22×C13711yescharacteristic
535C23×D4C22×C13712yes—
536C24×C4C22×C13711yescharacteristic
537C24×C4C22×C13711yescharacteristic
538C2×#120—24no—
539C2×#120—24no—
540C2×#120C4×C13718yescomplemented
541C22×C4⋊C4C22×C13712yescomplemented
542C22×C22⋊C4—24no—
543C22×C22⋊C4—28no—
544C22×C22⋊C4C22×C13712yes—
545C22×C22⋊C4C22×C13711yescharacteristic
546C22×C22⋊C4C22×C13712yes—
547C22×C22⋊C4C22×C13712yes—
548C22×C22⋊C4C22×C13712yes—
549C22×C22⋊C4C22×C13712yes—
550C22×C22⋊C4C22×C13711yescharacteristic
551C22×C22⋊C4C22×C13711yescharacteristic
552C22×C22⋊C4C22×C13711yescharacteristic, complemented
553C22×C22⋊C4C22×C13712yescomplemented
554C22×C22⋊C4C22×C13711yescharacteristic, complemented
555C22×C42C22×C13712yescomplemented
556#390—28no—
557#386—24no—
558#386—24no—
559#385—24no—
560#379—24no—
561C4×C22⋊C4—24no—
562C2×#95C22×C13711yescharacteristic, complemented
563C2×#95C22×C13712yescomplemented
564C2×#95C22×C13712yescomplemented
565C2×#95C22×C13712yescomplemented
566C2×#95C22×C13711yescharacteristic, complemented
567C25—24no—
568C25—22no—
569C25—24no—
570C25—22no—
571C25—22no—
572C25—22no—
573C25—22no—
574C25—22no—
575C25—42no—
576C25—42no—
577C25C2×C4×C13714yes—
578C25C23×C13711yescharacteristic
579C25C23×C13712yes—
580C25C23×C13711yescharacteristic
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4C2×C4×C13714yes—
594C22×D4C2×C4×C13718yescomplemented
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—42no—
603C23×C4—42no—
604C23×C4D4×C13714yescomplemented
605C23×C4C23×C13711yescharacteristic
606C23×C4C23×C13711yescharacteristic
607C23×C4C23×C13711yescharacteristic
608C23×C4C23×C13712yes—
609C23×C4C23×C13712yes—
610C23×C4C23×C13711yescharacteristic
611C23×C4C23×C13712yes—
612C23×C4C23×C13711yescharacteristic
613#120—232no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—42no—
617C2×C22⋊C4—232no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—24no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4C2×C4×C13714yes—
644C2×C22⋊C4C2×C4×C13718yescomplemented
645C2×C22⋊C4D4×C13714yes—
646C2×C22⋊C4D4×C13714yes—
647C2×C22⋊C4D4×C13718yescomplemented
648C2×C22⋊C4D4×C13714yescomplemented
649C2×C42—24no—
650C2×C42—24no—
651C2×C42—42no—
652#95—24no—
653#95—24no—
654#95—24no—
655#95—22no—
656#95—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—28no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28no—
679C24—28no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24C22×C4×C13712yes—
707C24C22×C4×C13714yes—
708C24C22×C4×C13712yes—
709C24C2×D4×C13714yes—
710C24C2×D4×C13712yes—
711C24C2×D4×C13712yes—
712C24C2×D4×C13712yes—
713C24C2×D4×C13712yes—
714C24#41×C13714yes—
715C24#41×C13712yes—
716C24#41×C13712yes—
717C24C24×C13711yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C13712yes—
782C22×C4C22×C4×C13714yes—
783C22×C4C2×D4×C13714yes—
784C22×C4C2×D4×C13712yes—
785C22×C4C2×D4×C13714yes—
786C22×C4C2×D4×C13714yes—
787C22×C4C2×D4×C13714yes—
788C22×C4C2×D4×C13712yes—
789C22×C4C2×D4×C13714yes—
790C4⋊C4—48no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—216no—
794C22⋊C4—216no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4C22⋊C4×C137116yescomplemented
802C42—48no—
803C23—24no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—416no—
849C23—432no—
850C23—416no—
851C23—432no—
852C23—416no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23C2×C22⋊C4×C13714yes—
888C23C4×D4×C13718yes—
889C23C4×D4×C13714yes—
890C23C4×D4×C13714yes—
891C23#121×C13714yes—
892C23#121×C13714yes—
893C23#124×C13714yes—
894C23#127×C13714yes—
895C23C23×C4×C13711yescharacteristic
896C23C22×D4×C13711yescharacteristic
897C23C22×D4×C13711yescharacteristic
898C23C22×D4×C13711yescharacteristic
899C23C22×D4×C13712yes—
900C23C22×D4×C13711yescharacteristic
901C23C2×#41×C13711yescharacteristic
902C23C2×#41×C13711yescharacteristic
903C23C2×#41×C13712yes—
904C23H(5,𝔽2)×C13712yes—
905C23H(5,𝔽2)×C13712yes—
906D4—432no—
907D4—416no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4C2×C22⋊C4×C13718yescomplemented
957C2×C4#120×C13714yescomplemented
958C22—24no—
959C22—24no—
960C22—24no—
961C22—28no—
962C22—28no—
963C22—24no—
964C22—24no—
965C22—28no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—44no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—82no—
993C22—81no—
994C22—82no—
995C22#390×C13718yescomplemented
996C22C22×C22⋊C4×C13711yescharacteristic
997C22C2×C4×D4×C13711yescharacteristic
998C22C2×C4×D4×C13711yescharacteristic
999C22C2×C4×D4×C13712yes—
1000C22#518×C13712yes—
1001C22C2×#120×C13711yescharacteristic
1002C22C2×#121×C13711yescharacteristic
1003C22C2×#121×C13711yescharacteristic
1004C22#525×C13711yescharacteristic
1005C22#525×C13712yes—
1006C22C2×#124×C13711yescharacteristic
1007C22C2×#127×C13711yescharacteristic
1008C22#534×C13711yescharacteristic
1009C22#535×C13711yescharacteristic
1010C22#538×C13712yes—
1011C22D42×C13712yes—
1012C22D42×C13712yes—
1013C22D42×C13712yes—
1014C22#546×C13712yes—
1015C22#546×C13712yes—
1016C22#546×C13712yes—
1017C22#546×C13712yes—
1018C22#551×C13712yes—
1019C4—28no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—44no—
1024C4—44no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×#390×C13711yescharacteristic
1031C2C4×#120×C13711yescharacteristic
1032C2#2321×C13711yescharacteristic
1033C2D4×C22⋊C4×C13712yes—
1034C2#2358×C13712yes—
1035C2#2410×C13711yescharacteristic
1036C2#2411×C13711yescharacteristic
1037C2#2424×C13712yes—
1038C2#2433×C13711yescharacteristic
1039C2#2472×C13712yes—
1040C2#2539×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
prime radicalC22×#120×C137C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C137C2semidirect
3. C2×#390×C137C2semidirect
4. C2×#386×C137C2semidirect
5. C2×#386×C137C2semidirect
6. C2×#385×C137C2semidirect
7. C2×#379×C137C2semidirect
8. C2×C4×C22⋊C4×C137C2semidirect
9. #1439×C137C2semidirect
10. #1438×C137C2semidirect
11. #1437×C137C2semidirect
19. C2×#120×C137C4semidirect
20. C22×C4⋊C4×C137C22semidirect
31. C22×C22⋊C4×C137C22semidirect
32. C22×C22⋊C4×C137C22semidirect
33. C22×C22⋊C4×C137C22semidirect
34. C22×C42×C137C22semidirect
41. C2×#95×C137C22semidirect
42. C2×#95×C137C22semidirect
43. C2×#95×C137C22semidirect
44. C2×#95×C137C22semidirect
45. C2×#95×C137C22semidirect
73. C22×D4×C137C2×C4semidirect
83. C23×C4×C137D4semidirect
123. C2×C22⋊C4×C137C2×C4semidirect
126. C2×C22⋊C4×C137D4semidirect
127. C2×C22⋊C4×C137D4semidirect
280. C22⋊C4×C137C22⋊C4semidirect
435. C2×C4×C137C2×C22⋊C4semidirect
436. C2×C4×C137#120semidirect
474. C22×C137#390semidirect
520. #13995C137direct (N × H)
521. C137#13995direct (N × H)
523. C23×C22⋊C4C2×C137semidirect
524. C2×#390C2×C137semidirect
525. C2×#386C2×C137semidirect
526. C2×#386C2×C137semidirect
527. C2×#385C2×C137semidirect
528. C2×#379C2×C137semidirect
529. C2×C4×C22⋊C4C2×C137semidirect
530. #1439C2×C137semidirect
531. #1438C2×C137semidirect
532. #1437C2×C137semidirect
540. C2×#120C4×C137semidirect
541. C22×C4⋊C4C22×C137semidirect
552. C22×C22⋊C4C22×C137semidirect
553. C22×C22⋊C4C22×C137semidirect
554. C22×C22⋊C4C22×C137semidirect
555. C22×C42C22×C137semidirect
562. C2×#95C22×C137semidirect
563. C2×#95C22×C137semidirect
564. C2×#95C22×C137semidirect
565. C2×#95C22×C137semidirect
566. C2×#95C22×C137semidirect
594. C22×D4C2×C4×C137semidirect
604. C23×C4D4×C137semidirect
644. C2×C22⋊C4C2×C4×C137semidirect
647. C2×C22⋊C4D4×C137semidirect
648. C2×C22⋊C4D4×C137semidirect
801. C22⋊C4C22⋊C4×C137semidirect
956. C2×C4C2×C22⋊C4×C137semidirect
957. C2×C4#120×C137semidirect
995. C22#390×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1372
C23×C22⋊C4×C1372
C2×#390×C1372
C2×#386×C1372
C2×#385×C1372
C2×#379×C1372
C2×C4×C22⋊C4×C1372
#1439×C1372
#1438×C1372
#1437×C1372
#13995137