Finite Group Databasebeta

← C137×#13996 #46863382

Subgroups — C137×#13996 #46863382

Order 35072.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C137C211yesmaximal, characteristic
2C2×#386×C137C211yesmaximal, characteristic
3C2×#386×C137C211yesmaximal, characteristic
4C2×#385×C137C211yesmaximal, characteristic, complemented
5C2×#381×C137C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C137C211yesmaximal, characteristic, complemented
7C22×#95×C137C211yesmaximal, characteristic, complemented
8#1445×C137C212yesmaximal, complemented
9#1439×C137C212yesmaximal, complemented
10#1437×C137C212yesmaximal, complemented
11C4⋊#95×C137C212yesmaximal, complemented
12C23×D4×C137C2211yescharacteristic
13C24×C4×C137C2211yescharacteristic
14C24×C4×C137C2211yescharacteristic
15C24×C4×C137C2211yescharacteristic
16C2×#123×C137—24no—
17C2×#123×C137—24no—
18C2×#123×C137C418yescomplemented
19C22×C4⋊C4×C137C2212yes—
20C22×C4⋊C4×C137C2212yes—
21C22×C22⋊C4×C137C2211yescharacteristic
22C22×C22⋊C4×C137C2211yescharacteristic
23C22×C22⋊C4×C137C2212yes—
24C22×C22⋊C4×C137C2212yes—
25C22×C22⋊C4×C137C2211yescharacteristic
26C22×C22⋊C4×C137C2211yescharacteristic
27C22×C22⋊C4×C137C2211yescharacteristic
28C22×C42×C137C2212yes—
29#386×C137—24no—
30#386×C137—24no—
31#385×C137—24no—
32#381×C137—24no—
33C4×C22⋊C4×C137—24no—
34C2×#95×C137—24no—
35C2×#95×C137C2212yes—
36C2×#95×C137C2212yes—
37C2×#95×C137C2212yes—
38C2×#95×C137C2211yescharacteristic
39C2×#95×C137C2212yes—
40C2×#95×C137C2211yescharacteristic
41C2×#95×C137C2212yes—
42C2×#95×C137C2212yes—
43C2×#95×C137C2212yes—
44C25×C137C2311yescharacteristic
45C25×C137C2311yescharacteristic
46C22×D4×C137—22no—
47C22×D4×C137—22no—
48C22×D4×C137—22no—
49C22×D4×C137—22no—
50C22×D4×C137—22no—
51C22×D4×C137—22no—
52C22×D4×C137C2×C414yes—
53C23×C4×C137—22no—
54C23×C4×C137—22no—
55C23×C4×C137—22no—
56C23×C4×C137—22no—
57C23×C4×C137—22no—
58C23×C4×C137—22no—
59C23×C4×C137—22no—
60C23×C4×C137—22no—
61C23×C4×C137—22no—
62C23×C4×C137—24no—
63C23×C4×C137—24no—
64C23×C4×C137—22no—
65C23×C4×C137—22no—
66C23×C4×C137—42no—
67C23×C4×C137—42no—
68C23×C4×C137C2×C414yes—
69C23×C4×C137D414yes—
70C23×C4×C137C2311yescharacteristic
71C23×C4×C137C2311yescharacteristic
72C23×C4×C137C2312yes—
73C23×C4×C137C2311yescharacteristic
74C23×C4×C137C2311yescharacteristic
75C23×C4×C137C2312yes—
76C23×C4×C137C2312yes—
77C23×C4×C137C2312yes—
78C23×C4×C137C2311yescharacteristic
79#123×C137—232no—
80C2×C4⋊C4×C137—24no—
81C2×C4⋊C4×C137—24no—
82C2×C4⋊C4×C137—24no—
83C2×C4⋊C4×C137—24no—
84C2×C4⋊C4×C137—42no—
85C2×C4⋊C4×C137C2×C418yescomplemented
86C2×C22⋊C4×C137—22no—
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—22no—
93C2×C22⋊C4×C137—24no—
94C2×C22⋊C4×C137—22no—
95C2×C22⋊C4×C137—22no—
96C2×C22⋊C4×C137—24no—
97C2×C22⋊C4×C137—24no—
98C2×C22⋊C4×C137—42no—
99C2×C22⋊C4×C137—42no—
100C2×C22⋊C4×C137C2×C414yes—
101C2×C22⋊C4×C137C2×C418yescomplemented
102C2×C22⋊C4×C137D414yes—
103C2×C22⋊C4×C137D414yes—
104C2×C22⋊C4×C137D414yes—
105C2×C42×C137—24no—
106C2×C42×C137—24no—
107C2×C42×C137—42no—
108#95×C137—24no—
109#95×C137—24no—
110#95×C137—24no—
111#95×C137—24no—
112#95×C137—24no—
113#95×C137—24no—
114#95×C137—24no—
115#95×C137—22no—
116#95×C137—22no—
117C24×C137—22no—
118C24×C137—22no—
119C24×C137—22no—
120C24×C137—22no—
121C24×C137—21no—
122C24×C137—21no—
123C24×C137—21no—
124C24×C137—21no—
125C24×C137—22no—
126C24×C137—22no—
127C24×C137—21no—
128C24×C137—21no—
129C24×C137—22no—
130C24×C137—22no—
131C24×C137C22×C412yes—
132C24×C137C22×C412yes—
133C24×C137C2×D412yes—
134C24×C137C2×D412yes—
135C24×C137C2×D412yes—
136C24×C137C2×D412yes—
137C24×C137#4112yes—
138C24×C137#4112yes—
139C24×C137C2411yescharacteristic
140C2×D4×C137—28no—
141C2×D4×C137—28no—
142C2×D4×C137—28no—
143C2×D4×C137—44no—
144C2×D4×C137—44no—
145C2×D4×C137—44no—
146C2×D4×C137—44no—
147C22×C4×C137—21no—
148C22×C4×C137—22no—
149C22×C4×C137—22no—
150C22×C4×C137—21no—
151C22×C4×C137—22no—
152C22×C4×C137—22no—
153C22×C4×C137—22no—
154C22×C4×C137—28no—
155C22×C4×C137—28no—
156C22×C4×C137—28no—
157C22×C4×C137—28no—
158C22×C4×C137—28no—
159C22×C4×C137—22no—
160C22×C4×C137—22no—
161C22×C4×C137—21no—
162C22×C4×C137—22no—
163C22×C4×C137—21no—
164C22×C4×C137—21no—
165C22×C4×C137—22no—
166C22×C4×C137—22no—
167C22×C4×C137—22no—
168C22×C4×C137—22no—
169C22×C4×C137—22no—
170C22×C4×C137—21no—
171C22×C4×C137—21no—
172C22×C4×C137—22no—
173C22×C4×C137—22no—
174C22×C4×C137—22no—
175C22×C4×C137—22no—
176C22×C4×C137—22no—
177C22×C4×C137—21no—
178C22×C4×C137—22no—
179C22×C4×C137—22no—
180C22×C4×C137—21no—
181C22×C4×C137—21no—
182C22×C4×C137—22no—
183C22×C4×C137—22no—
184C22×C4×C137—22no—
185C22×C4×C137—22no—
186C22×C4×C137—22no—
187C22×C4×C137—28no—
188C22×C4×C137—21no—
189C22×C4×C137—21no—
190C22×C4×C137—21no—
191C22×C4×C137—21no—
192C22×C4×C137—21no—
193C22×C4×C137—21no—
194C22×C4×C137—22no—
195C22×C4×C137—22no—
196C22×C4×C137—22no—
197C22×C4×C137—22no—
198C22×C4×C137—44no—
199C22×C4×C137—48no—
200C22×C4×C137—48no—
201C22×C4×C137—48no—
202C22×C4×C137—48no—
203C22×C4×C137—44no—
204C22×C4×C137—44no—
205C22×C4×C137—44no—
206C22×C4×C137—44no—
207C22×C4×C137—44no—
208C22×C4×C137—44no—
209C22×C4×C137C22×C414yes—
210C22×C4×C137C22×C412yes—
211C22×C4×C137C22×C414yes—
212C22×C4×C137C2×D414yes—
213C22×C4×C137C2×D412yes—
214C22×C4×C137C2×D414yes—
215C22×C4×C137C2×D414yes—
216C22×C4×C137C2×D412yes—
217C22×C4×C137#4114yes—
218C22×C4×C137#4114yes—
219C4⋊C4×C137—216no—
220C4⋊C4×C137—48no—
221C22⋊C4×C137—28no—
222C22⋊C4×C137—216no—
223C22⋊C4×C137—48no—
224C22⋊C4×C137—44no—
225C22⋊C4×C137—44no—
226C22⋊C4×C137—44no—
227C22⋊C4×C137C22⋊C4116yescomplemented
228C42×C137—48no—
229C23×C137—24no—
230C23×C137—24no—
231C23×C137—22no—
232C23×C137—22no—
233C23×C137—24no—
234C23×C137—22no—
235C23×C137—22no—
236C23×C137—24no—
237C23×C137—24no—
238C23×C137—24no—
239C23×C137—24no—
240C23×C137—24no—
241C23×C137—24no—
242C23×C137—24no—
243C23×C137—24no—
244C23×C137—24no—
245C23×C137—22no—
246C23×C137—22no—
247C23×C137—22no—
248C23×C137—24no—
249C23×C137—24no—
250C23×C137—41no—
251C23×C137—41no—
252C23×C137—41no—
253C23×C137—41no—
254C23×C137—41no—
255C23×C137—42no—
256C23×C137—41no—
257C23×C137—41no—
258C23×C137—41no—
259C23×C137—42no—
260C23×C137—42no—
261C23×C137—42no—
262C23×C137—42no—
263C23×C137—42no—
264C23×C137—42no—
265C23×C137—42no—
266C23×C137—42no—
267C23×C137—42no—
268C23×C137C2×C22⋊C414yes—
269C23×C137C4×D414yes—
270C23×C137C4×D414yes—
271C23×C137#12114yes—
272C23×C137#12114yes—
273C23×C137#12414yes—
274C23×C137#12714yes—
275C23×C137C23×C411yescharacteristic
276C23×C137C22×D411yescharacteristic
277C23×C137C22×D411yescharacteristic
278C23×C137C22×D411yescharacteristic
279C23×C137C22×D411yescharacteristic
280C23×C137C2×#4111yescharacteristic
281C23×C137C2×#4111yescharacteristic
282C23×C137C2×#4112yes—
283C23×C137C2×#4112yes—
284C23×C137H(5,𝔽2)12yes—
285C23×C1372−1+412yes—
286D4×C137—416no—
287C2×C4×C137—24no—
288C2×C4×C137—24no—
289C2×C4×C137—22no—
290C2×C4×C137—22no—
291C2×C4×C137—24no—
292C2×C4×C137—24no—
293C2×C4×C137—24no—
294C2×C4×C137—24no—
295C2×C4×C137—24no—
296C2×C4×C137—24no—
297C2×C4×C137—24no—
298C2×C4×C137—22no—
299C2×C4×C137—24no—
300C2×C4×C137—24no—
301C2×C4×C137—22no—
302C2×C4×C137—22no—
303C2×C4×C137—24no—
304C2×C4×C137—22no—
305C2×C4×C137—22no—
306C2×C4×C137—24no—
307C2×C4×C137—22no—
308C2×C4×C137—24no—
309C2×C4×C137—24no—
310C2×C4×C137—24no—
311C2×C4×C137—24no—
312C2×C4×C137—416no—
313C2×C4×C137—416no—
314C2×C4×C137—42no—
315C2×C4×C137—42no—
316C2×C4×C137—41no—
317C2×C4×C137—41no—
318C2×C4×C137—42no—
319C2×C4×C137—41no—
320C2×C4×C137—42no—
321C2×C4×C137—42no—
322C2×C4×C137—42no—
323C2×C4×C137—41no—
324C2×C4×C137—42no—
325C2×C4×C137—42no—
326C2×C4×C137—42no—
327C2×C4×C137—42no—
328C2×C4×C137—42no—
329C2×C4×C137—42no—
330C2×C4×C137—42no—
331C2×C4×C137—42no—
332C2×C4×C137—416no—
333C2×C4×C137—41no—
334C2×C4×C137—41no—
335C2×C4×C137—41no—
336C2×C4×C137—41no—
337C2×C4×C137—41no—
338C2×C4×C137—41no—
339C2×C4×C137—42no—
340C2×C4×C137—42no—
341C2×C4×C137—42no—
342C2×C4×C137—42no—
343C2×C4×C137C2×C22⋊C418yes—
344C2×C4×C137#12314yescomplemented
345C22×C137—24no—
346C22×C137—28no—
347C22×C137—28no—
348C22×C137—24no—
349C22×C137—24no—
350C22×C137—28no—
351C22×C137—28no—
352C22×C137—24no—
353C22×C137—24no—
354C22×C137—24no—
355C22×C137—42no—
356C22×C137—44no—
357C22×C137—44no—
358C22×C137—42no—
359C22×C137—42no—
360C22×C137—81no—
361C22×C137—81no—
362C22×C137—82no—
363C22×C137—82no—
364C22×C137—81no—
365C22×C137—81no—
366C22×C137#39018yes—
367C22×C137C22×C22⋊C411yescharacteristic
368C22×C137C2×C4×D411yescharacteristic
369C22×C137C2×C4×D411yescharacteristic
370C22×C137C4×#4112yes—
371C22×C137#52012yes—
372C22×C137C2×#12111yescharacteristic
373C22×C137C2×#12111yescharacteristic
374C22×C137C2×#12311yescharacteristic
375C22×C137#52511yescharacteristic
376C22×C137C2×#12411yescharacteristic
377C22×C137#52912yes—
378C22×C137C2×#12711yescharacteristic
379C22×C137#53411yescharacteristic
380C22×C137#53611yescharacteristic
381C22×C137#53912yes—
382C22×C137#54612yes—
383C22×C137#54612yes—
384C22×C137#54612yes—
385C22×C137#54712yes—
386C22×C137#54712yes—
387C22×C137#54712yes—
388C22×C137#55112yes—
389C22×C137#55212yes—
390C4×C137—28no—
391C4×C137—24no—
392C4×C137—42no—
393C4×C137—44no—
394C4×C137—44no—
395C4×C137—44no—
396C4×C137—42no—
397C4×C137—81no—
398C4×C137—81no—
399C2×C137—28no—
400C2×C137—82no—
401C2×C137C2×#39011yescharacteristic
402C2×C137C4×#12311yescharacteristic
403C2×C137#232211yescharacteristic
404C2×C137#233912yes—
405C2×C137#235912yes—
406C2×C137#241211yescharacteristic
407C2×C137#241311yescharacteristic
408C2×C137#242512yes—
409C2×C137#248812yes—
410C2×C137#250111yescharacteristic
411C2×C137#253911yescharacteristic
412#13996C13711yesmaximal, characteristic, direct product factor, Sylow
413C137#1399611yescharacteristic, direct product factor, Sylow
414C22×#123C2×C13711yescharacteristic
415C2×#386C2×C13711yescharacteristic
416C2×#386C2×C13711yescharacteristic
417C2×#385C2×C13711yescharacteristic, complemented
418C2×#381C2×C13711yescharacteristic, complemented
419C2×C4×C22⋊C4C2×C13711yescharacteristic, complemented
420C22×#95C2×C13711yescharacteristic, complemented
421#1445C2×C13712yescomplemented
422#1439C2×C13712yescomplemented
423#1437C2×C13712yescomplemented
424C4⋊#95C2×C13712yescomplemented
425C23×D4C22×C13711yescharacteristic
426C24×C4C22×C13711yescharacteristic
427C24×C4C22×C13711yescharacteristic
428C24×C4C22×C13711yescharacteristic
429C2×#123—24no—
430C2×#123—24no—
431C2×#123C4×C13718yescomplemented
432C22×C4⋊C4C22×C13712yes—
433C22×C4⋊C4C22×C13712yes—
434C22×C22⋊C4C22×C13711yescharacteristic
435C22×C22⋊C4C22×C13711yescharacteristic
436C22×C22⋊C4C22×C13712yes—
437C22×C22⋊C4C22×C13712yes—
438C22×C22⋊C4C22×C13711yescharacteristic
439C22×C22⋊C4C22×C13711yescharacteristic
440C22×C22⋊C4C22×C13711yescharacteristic
441C22×C42C22×C13712yes—
442#386—24no—
443#386—24no—
444#385—24no—
445#381—24no—
446C4×C22⋊C4—24no—
447C2×#95—24no—
448C2×#95C22×C13711yescharacteristic
449C2×#95C22×C13712yes—
450C2×#95C22×C13712yes—
451C2×#95C22×C13712yes—
452C2×#95C22×C13712yes—
453C2×#95C22×C13712yes—
454C2×#95C22×C13712yes—
455C2×#95C22×C13712yes—
456C2×#95C22×C13711yescharacteristic
457C25C23×C13711yescharacteristic
458C25C23×C13711yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C13714yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4C2×C4×C13714yes—
482C23×C4D4×C13714yes—
483C23×C4C23×C13711yescharacteristic
484C23×C4C23×C13711yescharacteristic
485C23×C4C23×C13712yes—
486C23×C4C23×C13711yescharacteristic
487C23×C4C23×C13712yes—
488C23×C4C23×C13711yescharacteristic
489C23×C4C23×C13712yes—
490C23×C4C23×C13712yes—
491C23×C4C23×C13711yescharacteristic
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4C2×C4×C13718yescomplemented
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×C4×C13714yes—
514C2×C22⋊C4C2×C4×C13718yescomplemented
515C2×C22⋊C4D4×C13714yes—
516C2×C22⋊C4D4×C13714yes—
517C2×C22⋊C4D4×C13714yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C13712yes—
545C24C22×C4×C13712yes—
546C24C2×D4×C13712yes—
547C24C2×D4×C13712yes—
548C24C2×D4×C13712yes—
549C24C2×D4×C13712yes—
550C24#41×C13712yes—
551C24#41×C13712yes—
552C24C24×C13711yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C13714yes—
623C22×C4C22×C4×C13712yes—
624C22×C4C22×C4×C13714yes—
625C22×C4C2×D4×C13714yes—
626C22×C4C2×D4×C13712yes—
627C22×C4C2×D4×C13714yes—
628C22×C4C2×D4×C13714yes—
629C22×C4C2×D4×C13712yes—
630C22×C4#41×C13714yes—
631C22×C4#41×C13714yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C137116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊C4×C13714yes—
682C23C4×D4×C13714yes—
683C23C4×D4×C13714yes—
684C23#121×C13714yes—
685C23#121×C13714yes—
686C23#124×C13714yes—
687C23#127×C13714yes—
688C23C23×C4×C13711yescharacteristic
689C23C22×D4×C13711yescharacteristic
690C23C22×D4×C13711yescharacteristic
691C23C22×D4×C13711yescharacteristic
692C23C22×D4×C13711yescharacteristic
693C23C2×#41×C13711yescharacteristic
694C23C2×#41×C13711yescharacteristic
695C23C2×#41×C13712yes—
696C23C2×#41×C13712yes—
697C23H(5,𝔽2)×C13712yes—
698C232−1+4×C13712yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—416no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C22⋊C4×C13718yes—
757C2×C4#123×C13714yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—28no—
766C22—28no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—82no—
777C22—82no—
778C22—81no—
779C22#390×C13718yes—
780C22C22×C22⋊C4×C13711yescharacteristic
781C22C2×C4×D4×C13711yescharacteristic
782C22C2×C4×D4×C13711yescharacteristic
783C22C4×#41×C13712yes—
784C22#520×C13712yes—
785C22C2×#121×C13711yescharacteristic
786C22C2×#121×C13711yescharacteristic
787C22C2×#123×C13711yescharacteristic
788C22#525×C13711yescharacteristic
789C22C2×#124×C13711yescharacteristic
790C22#529×C13712yes—
791C22C2×#127×C13711yescharacteristic
792C22#534×C13711yescharacteristic
793C22#536×C13711yescharacteristic
794C22#539×C13712yes—
795C22#546×C13712yes—
796C22#546×C13712yes—
797C22#546×C13712yes—
798C22#547×C13712yes—
799C22#547×C13712yes—
800C22#547×C13712yes—
801C22#551×C13712yes—
802C22#552×C13712yes—
803C4—28no—
804C4—24no—
805C4—44no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×#390×C13711yescharacteristic
815C2C4×#123×C13711yescharacteristic
816C2#2322×C13711yescharacteristic
817C2#2339×C13712yes—
818C2#2359×C13712yes—
819C2#2412×C13711yescharacteristic
820C2#2413×C13711yescharacteristic
821C2#2425×C13712yes—
822C2#2488×C13712yes—
823C2#2501×C13711yescharacteristic
824C2#2539×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
prime radicalC23×D4×C137C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#385×C137C2semidirect
5. C2×#381×C137C2semidirect
6. C2×C4×C22⋊C4×C137C2semidirect
7. C22×#95×C137C2semidirect
8. #1445×C137C2semidirect
9. #1439×C137C2semidirect
10. #1437×C137C2semidirect
11. C4⋊#95×C137C2semidirect
18. C2×#123×C137C4semidirect
85. C2×C4⋊C4×C137C2×C4semidirect
101. C2×C22⋊C4×C137C2×C4semidirect
227. C22⋊C4×C137C22⋊C4semidirect
344. C2×C4×C137#123semidirect
412. #13996C137direct (N × H)
413. C137#13996direct (N × H)
417. C2×#385C2×C137semidirect
418. C2×#381C2×C137semidirect
419. C2×C4×C22⋊C4C2×C137semidirect
420. C22×#95C2×C137semidirect
421. #1445C2×C137semidirect
422. #1439C2×C137semidirect
423. #1437C2×C137semidirect
424. C4⋊#95C2×C137semidirect
431. C2×#123C4×C137semidirect
498. C2×C4⋊C4C2×C4×C137semidirect
514. C2×C22⋊C4C2×C4×C137semidirect
640. C22⋊C4C22⋊C4×C137semidirect
757. C2×C4#123×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1372
C2×#386×C1372
C2×#385×C1372
C2×#381×C1372
C2×C4×C22⋊C4×C1372
C22×#95×C1372
#1445×C1372
#1439×C1372
#1437×C1372
C4⋊#95×C1372
#13996137