Finite Group Databasebeta

← C137×#13873 #46863259

Subgroups — C137×#13873 #46863259

Order 35072.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C137C211yesmaximal, characteristic
2C2×#388×C137C212yesmaximal, complemented
3C2×#380×C137C211yesmaximal, characteristic, complemented
4C2×#379×C137C211yesmaximal, characteristic
5C2×#379×C137C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C137C211yesmaximal, characteristic, complemented
7#1440×C137C212yesmaximal, complemented
8#1439×C137C212yesmaximal, complemented
9#1437×C137C212yesmaximal, complemented
10C22⋊#95×C137C211yesmaximal, characteristic, complemented
11C22⋊#95×C137C211yesmaximal, characteristic, complemented
12C26×C137C2211yescharacteristic
13C24×C4×C137C2211yescharacteristic
14C24×C4×C137C2211yescharacteristic
15C22×C4⋊C4×C137C2212yescomplemented
16C22×C22⋊C4×C137—28no—
17C22×C22⋊C4×C137C418yescomplemented
18C22×C22⋊C4×C137C2211yescharacteristic
19C22×C22⋊C4×C137C2211yescharacteristic
20C22×C22⋊C4×C137C2212yes—
21C22×C22⋊C4×C137C2212yes—
22C22×C22⋊C4×C137C2212yes—
23C22×C22⋊C4×C137C2212yes—
24C22×C22⋊C4×C137C2211yescharacteristic
25C22×C22⋊C4×C137C2211yescharacteristic
26C22×C22⋊C4×C137C2211yescharacteristic
27C22×C22⋊C4×C137C2211yescharacteristic
28C22×C22⋊C4×C137C2211yescharacteristic
29C22×C22⋊C4×C137C2211yescharacteristic
30C22×C42×C137C2212yescomplemented
31#388×C137—28no—
32#380×C137—24no—
33#379×C137—24no—
34#379×C137—24no—
35C4×C22⋊C4×C137—24no—
36C2×#95×C137C2212yescomplemented
37C2×#95×C137C2212yescomplemented
38C2×#95×C137C2212yescomplemented
39C2×#95×C137C2212yescomplemented
40C2×#95×C137C2212yescomplemented
41C2×#95×C137C2212yescomplemented
42C25×C137—24no—
43C25×C137—24no—
44C25×C137—22no—
45C25×C137—22no—
46C25×C137—22no—
47C25×C137—22no—
48C25×C137—22no—
49C25×C137—22no—
50C25×C137—42no—
51C25×C137—42no—
52C25×C137C2×C414yes—
53C25×C137C2311yescharacteristic
54C25×C137C2311yescharacteristic
55C25×C137C2311yescharacteristic
56C23×C4×C137—22no—
57C23×C4×C137—22no—
58C23×C4×C137—22no—
59C23×C4×C137—22no—
60C23×C4×C137—24no—
61C23×C4×C137—24no—
62C23×C4×C137—42no—
63C23×C4×C137—42no—
64C23×C4×C137C2×C414yes—
65C23×C4×C137C2×C414yes—
66C23×C4×C137C2312yes—
67C23×C4×C137C2312yes—
68C23×C4×C137C2311yescharacteristic
69C23×C4×C137C2311yescharacteristic
70C23×C4×C137C2312yes—
71C23×C4×C137C2312yes—
72C23×C4×C137C2311yescharacteristic
73C23×C4×C137C2311yescharacteristic
74C2×C4⋊C4×C137—24no—
75C2×C4⋊C4×C137—24no—
76C2×C4⋊C4×C137—42no—
77C2×C22⋊C4×C137—22no—
78C2×C22⋊C4×C137—24no—
79C2×C22⋊C4×C137—22no—
80C2×C22⋊C4×C137—22no—
81C2×C22⋊C4×C137—22no—
82C2×C22⋊C4×C137—24no—
83C2×C22⋊C4×C137—24no—
84C2×C22⋊C4×C137—232no—
85C2×C22⋊C4×C137—22no—
86C2×C22⋊C4×C137—22no—
87C2×C22⋊C4×C137—22no—
88C2×C22⋊C4×C137—24no—
89C2×C22⋊C4×C137—24no—
90C2×C22⋊C4×C137—24no—
91C2×C22⋊C4×C137—24no—
92C2×C22⋊C4×C137—22no—
93C2×C22⋊C4×C137—22no—
94C2×C22⋊C4×C137—22no—
95C2×C22⋊C4×C137—24no—
96C2×C22⋊C4×C137—24no—
97C2×C22⋊C4×C137—24no—
98C2×C22⋊C4×C137—24no—
99C2×C22⋊C4×C137—42no—
100C2×C22⋊C4×C137—42no—
101C2×C22⋊C4×C137—42no—
102C2×C22⋊C4×C137—42no—
103C2×C22⋊C4×C137C2×C414yes—
104C2×C22⋊C4×C137C2×C414yes—
105C2×C22⋊C4×C137C2×C414yes—
106C2×C22⋊C4×C137C2×C414yes—
107C2×C22⋊C4×C137D414yes—
108C2×C22⋊C4×C137D414yes—
109C2×C22⋊C4×C137D418yes—
110C2×C42×C137—24no—
111C2×C42×C137—24no—
112C2×C42×C137—42no—
113#95×C137—24no—
114#95×C137—24no—
115#95×C137—24no—
116#95×C137—24no—
117#95×C137—42no—
118#95×C137—42no—
119C24×C137—22no—
120C24×C137—22no—
121C24×C137—22no—
122C24×C137—22no—
123C24×C137—216no—
124C24×C137—216no—
125C24×C137—28no—
126C24×C137—28no—
127C24×C137—28no—
128C24×C137—22no—
129C24×C137—21no—
130C24×C137—21no—
131C24×C137—21no—
132C24×C137—21no—
133C24×C137—21no—
134C24×C137—21no—
135C24×C137—22no—
136C24×C137—21no—
137C24×C137—21no—
138C24×C137—21no—
139C24×C137—21no—
140C24×C137—21no—
141C24×C137—21no—
142C24×C137—22no—
143C24×C137—22no—
144C24×C137—22no—
145C24×C137—22no—
146C24×C137—28no—
147C24×C137—28no—
148C24×C137—44no—
149C24×C137—44no—
150C24×C137—48no—
151C24×C137—48no—
152C24×C137—48no—
153C24×C137—48no—
154C24×C137—48no—
155C24×C137—48no—
156C24×C137—48no—
157C24×C137—48no—
158C24×C137—48no—
159C24×C137—48no—
160C24×C137—44no—
161C24×C137—44no—
162C24×C137—44no—
163C24×C137—44no—
164C24×C137C22×C412yes—
165C24×C137C22×C412yes—
166C24×C137C22×C412yes—
167C24×C137C2×D414yes—
168C24×C137C2×D412yes—
169C24×C137C2×D412yes—
170C24×C137#4114yes—
171C24×C137#4112yes—
172C24×C137#4112yes—
173C24×C137#4112yes—
174C24×C137#4112yes—
175C24×C137C2411yescharacteristic
176C22×C4×C137—21no—
177C22×C4×C137—21no—
178C22×C4×C137—21no—
179C22×C4×C137—21no—
180C22×C4×C137—22no—
181C22×C4×C137—22no—
182C22×C4×C137—28no—
183C22×C4×C137—28no—
184C22×C4×C137—21no—
185C22×C4×C137—21no—
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—22no—
194C22×C4×C137—22no—
195C22×C4×C137—22no—
196C22×C4×C137—21no—
197C22×C4×C137—21no—
198C22×C4×C137—22no—
199C22×C4×C137—22no—
200C22×C4×C137—22no—
201C22×C4×C137—22no—
202C22×C4×C137—22no—
203C22×C4×C137—22no—
204C22×C4×C137—28no—
205C22×C4×C137—28no—
206C22×C4×C137—22no—
207C22×C4×C137—22no—
208C22×C4×C137—22no—
209C22×C4×C137—22no—
210C22×C4×C137—22no—
211C22×C4×C137—22no—
212C22×C4×C137—22no—
213C22×C4×C137—22no—
214C22×C4×C137—22no—
215C22×C4×C137—22no—
216C22×C4×C137—22no—
217C22×C4×C137—22no—
218C22×C4×C137—22no—
219C22×C4×C137—22no—
220C22×C4×C137—44no—
221C22×C4×C137—44no—
222C22×C4×C137—48no—
223C22×C4×C137—48no—
224C22×C4×C137—48no—
225C22×C4×C137—48no—
226C22×C4×C137C22×C412yes—
227C22×C4×C137C22×C412yes—
228C22×C4×C137C22×C412yes—
229C22×C4×C137C22×C412yes—
230C22×C4×C137C2×D414yes—
231C22×C4×C137C2×D414yes—
232C22×C4×C137C2×D414yes—
233C22×C4×C137C2×D414yes—
234C4⋊C4×C137—48no—
235C22⋊C4×C137—28no—
236C22⋊C4×C137—28no—
237C22⋊C4×C137—28no—
238C22⋊C4×C137—28no—
239C22⋊C4×C137—28no—
240C22⋊C4×C137—48no—
241C22⋊C4×C137—48no—
242C22⋊C4×C137—48no—
243C22⋊C4×C137—48no—
244C22⋊C4×C137—44no—
245C22⋊C4×C137—44no—
246C22⋊C4×C137C22⋊C4116yescomplemented
247C42×C137—48no—
248C23×C137—22no—
249C23×C137—22no—
250C23×C137—22no—
251C23×C137—22no—
252C23×C137—24no—
253C23×C137—24no—
254C23×C137—24no—
255C23×C137—24no—
256C23×C137—24no—
257C23×C137—24no—
258C23×C137—24no—
259C23×C137—24no—
260C23×C137—24no—
261C23×C137—24no—
262C23×C137—24no—
263C23×C137—24no—
264C23×C137—232no—
265C23×C137—22no—
266C23×C137—22no—
267C23×C137—22no—
268C23×C137—22no—
269C23×C137—22no—
270C23×C137—22no—
271C23×C137—22no—
272C23×C137—22no—
273C23×C137—22no—
274C23×C137—22no—
275C23×C137—22no—
276C23×C137—22no—
277C23×C137—24no—
278C23×C137—24no—
279C23×C137—24no—
280C23×C137—24no—
281C23×C137—24no—
282C23×C137—24no—
283C23×C137—24no—
284C23×C137—24no—
285C23×C137—24no—
286C23×C137—24no—
287C23×C137—24no—
288C23×C137—24no—
289C23×C137—416no—
290C23×C137—416no—
291C23×C137—416no—
292C23×C137—416no—
293C23×C137—416no—
294C23×C137—432no—
295C23×C137—432no—
296C23×C137—432no—
297C23×C137—432no—
298C23×C137—41no—
299C23×C137—41no—
300C23×C137—41no—
301C23×C137—41no—
302C23×C137—41no—
303C23×C137—41no—
304C23×C137—41no—
305C23×C137—41no—
306C23×C137—42no—
307C23×C137—42no—
308C23×C137—42no—
309C23×C137—42no—
310C23×C137—42no—
311C23×C137—42no—
312C23×C137—42no—
313C23×C137—42no—
314C23×C137—42no—
315C23×C137—42no—
316C23×C137—42no—
317C23×C137—42no—
318C23×C137—416no—
319C23×C137C2×C22⋊C414yes—
320C23×C137#11714yes—
321C23×C137#11714yes—
322C23×C137C4×D414yes—
323C23×C137C4×D414yes—
324C23×C137#12114yes—
325C23×C137#12314yes—
326C23×C137#12414yes—
327C23×C137#12614yes—
328C23×C137C23×C411yescharacteristic
329C23×C137C22×D412yes—
330C23×C137C22×D411yescharacteristic
331C23×C137C22×D411yescharacteristic
332C23×C137C2×#4111yescharacteristic
333C23×C137C2×#4111yescharacteristic
334C23×C137C2×#4112yes—
335C23×C137C2×#4111yescharacteristic
336C23×C137C2×#4111yescharacteristic
337C23×C137H(5,𝔽2)12yes—
338C23×C137H(5,𝔽2)12yes—
339C2×C4×C137—22no—
340C2×C4×C137—22no—
341C2×C4×C137—22no—
342C2×C4×C137—22no—
343C2×C4×C137—24no—
344C2×C4×C137—24no—
345C2×C4×C137—24no—
346C2×C4×C137—24no—
347C2×C4×C137—22no—
348C2×C4×C137—22no—
349C2×C4×C137—22no—
350C2×C4×C137—22no—
351C2×C4×C137—22no—
352C2×C4×C137—22no—
353C2×C4×C137—24no—
354C2×C4×C137—24no—
355C2×C4×C137—24no—
356C2×C4×C137—24no—
357C2×C4×C137—24no—
358C2×C4×C137—24no—
359C2×C4×C137—416no—
360C2×C4×C137—416no—
361C2×C4×C137—42no—
362C2×C4×C137—42no—
363C2×C4×C137—42no—
364C2×C4×C137—42no—
365C2×C4×C137—42no—
366C2×C4×C137—42no—
367C2×C4×C137—42no—
368C2×C4×C137—42no—
369C2×C4×C137—42no—
370C2×C4×C137—42no—
371C2×C4×C137—42no—
372C2×C4×C137—42no—
373C2×C4×C137—42no—
374C2×C4×C137—42no—
375C2×C4×C137—42no—
376C2×C4×C137—42no—
377C2×C4×C137—42no—
378C2×C4×C137—42no—
379C2×C4×C137—42no—
380C2×C4×C137—42no—
381C2×C4×C137—42no—
382C2×C4×C137—42no—
383C2×C4×C137—42no—
384C2×C4×C137—42no—
385C2×C4×C137—42no—
386C2×C4×C137—42no—
387C2×C4×C137C2×C22⋊C414yes—
388C2×C4×C137C2×C22⋊C414yes—
389C22×C137—24no—
390C22×C137—24no—
391C22×C137—24no—
392C22×C137—24no—
393C22×C137—24no—
394C22×C137—28no—
395C22×C137—28no—
396C22×C137—28no—
397C22×C137—28no—
398C22×C137—24no—
399C22×C137—24no—
400C22×C137—24no—
401C22×C137—24no—
402C22×C137—24no—
403C22×C137—24no—
404C22×C137—24no—
405C22×C137—464no—
406C22×C137—42no—
407C22×C137—42no—
408C22×C137—42no—
409C22×C137—42no—
410C22×C137—42no—
411C22×C137—42no—
412C22×C137—44no—
413C22×C137—44no—
414C22×C137—44no—
415C22×C137—44no—
416C22×C137—44no—
417C22×C137—44no—
418C22×C137—44no—
419C22×C137—44no—
420C22×C137—42no—
421C22×C137—42no—
422C22×C137#38818yescomplemented
423C22×C137C22×C22⋊C411yescharacteristic
424C22×C137C2×#11711yescharacteristic
425C22×C137C2×#11711yescharacteristic
426C22×C137C2×C4×D411yescharacteristic
427C22×C137C2×C4×D411yescharacteristic
428C22×C137#51811yescharacteristic
429C22×C137#51811yescharacteristic
430C22×C137C2×#12111yescharacteristic
431C22×C137C2×#12311yescharacteristic
432C22×C137#52512yes—
433C22×C137#52512yes—
434C22×C137C2×#12411yescharacteristic
435C22×C137C2×#12611yescharacteristic
436C22×C137#53812yes—
437C22×C137#53812yes—
438C22×C137D4212yes—
439C22×C137D4212yes—
440C22×C137#54612yes—
441C22×C137#54612yes—
442C22×C137#54612yes—
443C22×C137#54612yes—
444C22×C137#55112yes—
445C22×C137#55112yes—
446C4×C137—24no—
447C4×C137—24no—
448C4×C137—42no—
449C4×C137—42no—
450C4×C137—44no—
451C4×C137—44no—
452C4×C137—82no—
453C4×C137—82no—
454C2×C137—28no—
455C2×C137—44no—
456C2×C137—44no—
457C2×C137#228011yescharacteristic
458C2×C137C2×#38811yescharacteristic
459C2×C137#231211yescharacteristic
460C2×C137D4×C22⋊C411yescharacteristic
461C2×C137D4×C22⋊C411yescharacteristic
462C2×C137#234211yescharacteristic
463C2×C137#234211yescharacteristic
464C2×C137#241812yes—
465C2×C137#242412yes—
466C2×C137#247212yes—
467C2×C137#248012yes—
468#13873C13711yesmaximal, characteristic, direct product factor, Sylow
469C137#1387311yescharacteristic, direct product factor, Sylow
470C23×C22⋊C4C2×C13711yescharacteristic
471C2×#388C2×C13712yescomplemented
472C2×#380C2×C13711yescharacteristic, complemented
473C2×#379C2×C13711yescharacteristic
474C2×#379C2×C13711yescharacteristic
475C2×C4×C22⋊C4C2×C13711yescharacteristic, complemented
476#1440C2×C13712yescomplemented
477#1439C2×C13712yescomplemented
478#1437C2×C13712yescomplemented
479C22⋊#95C2×C13711yescharacteristic, complemented
480C22⋊#95C2×C13711yescharacteristic, complemented
481C26C22×C13711yescharacteristic
482C24×C4C22×C13711yescharacteristic
483C24×C4C22×C13711yescharacteristic
484C22×C4⋊C4C22×C13712yescomplemented
485C22×C22⋊C4—28no—
486C22×C22⋊C4C4×C13718yescomplemented
487C22×C22⋊C4C22×C13711yescharacteristic
488C22×C22⋊C4C22×C13711yescharacteristic
489C22×C22⋊C4C22×C13712yes—
490C22×C22⋊C4C22×C13712yes—
491C22×C22⋊C4C22×C13712yes—
492C22×C22⋊C4C22×C13712yes—
493C22×C22⋊C4C22×C13711yescharacteristic
494C22×C22⋊C4C22×C13711yescharacteristic
495C22×C22⋊C4C22×C13711yescharacteristic
496C22×C22⋊C4C22×C13711yescharacteristic
497C22×C22⋊C4C22×C13711yescharacteristic
498C22×C22⋊C4C22×C13711yescharacteristic
499C22×C42C22×C13712yescomplemented
500#388—28no—
501#380—24no—
502#379—24no—
503#379—24no—
504C4×C22⋊C4—24no—
505C2×#95C22×C13712yescomplemented
506C2×#95C22×C13712yescomplemented
507C2×#95C22×C13712yescomplemented
508C2×#95C22×C13712yescomplemented
509C2×#95C22×C13712yescomplemented
510C2×#95C22×C13712yescomplemented
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C13714yes—
522C25C23×C13711yescharacteristic
523C25C23×C13711yescharacteristic
524C25C23×C13711yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C13714yes—
534C23×C4C2×C4×C13714yes—
535C23×C4C23×C13712yes—
536C23×C4C23×C13712yes—
537C23×C4C23×C13711yescharacteristic
538C23×C4C23×C13711yescharacteristic
539C23×C4C23×C13712yes—
540C23×C4C23×C13712yes—
541C23×C4C23×C13711yescharacteristic
542C23×C4C23×C13711yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C13714yes—
573C2×C22⋊C4C2×C4×C13714yes—
574C2×C22⋊C4C2×C4×C13714yes—
575C2×C22⋊C4C2×C4×C13714yes—
576C2×C22⋊C4D4×C13714yes—
577C2×C22⋊C4D4×C13714yes—
578C2×C22⋊C4D4×C13718yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C13712yes—
634C24C22×C4×C13712yes—
635C24C22×C4×C13712yes—
636C24C2×D4×C13714yes—
637C24C2×D4×C13712yes—
638C24C2×D4×C13712yes—
639C24#41×C13714yes—
640C24#41×C13712yes—
641C24#41×C13712yes—
642C24#41×C13712yes—
643C24#41×C13712yes—
644C24C24×C13711yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C13712yes—
696C22×C4C22×C4×C13712yes—
697C22×C4C22×C4×C13712yes—
698C22×C4C22×C4×C13712yes—
699C22×C4C2×D4×C13714yes—
700C22×C4C2×D4×C13714yes—
701C22×C4C2×D4×C13714yes—
702C22×C4C2×D4×C13714yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C137116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—416no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23C2×C22⋊C4×C13714yes—
789C23#117×C13714yes—
790C23#117×C13714yes—
791C23C4×D4×C13714yes—
792C23C4×D4×C13714yes—
793C23#121×C13714yes—
794C23#123×C13714yes—
795C23#124×C13714yes—
796C23#126×C13714yes—
797C23C23×C4×C13711yescharacteristic
798C23C22×D4×C13712yes—
799C23C22×D4×C13711yescharacteristic
800C23C22×D4×C13711yescharacteristic
801C23C2×#41×C13711yescharacteristic
802C23C2×#41×C13711yescharacteristic
803C23C2×#41×C13712yes—
804C23C2×#41×C13711yescharacteristic
805C23C2×#41×C13711yescharacteristic
806C23H(5,𝔽2)×C13712yes—
807C23H(5,𝔽2)×C13712yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C13714yes—
857C2×C4C2×C22⋊C4×C13714yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—28no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22#388×C13718yescomplemented
892C22C22×C22⋊C4×C13711yescharacteristic
893C22C2×#117×C13711yescharacteristic
894C22C2×#117×C13711yescharacteristic
895C22C2×C4×D4×C13711yescharacteristic
896C22C2×C4×D4×C13711yescharacteristic
897C22#518×C13711yescharacteristic
898C22#518×C13711yescharacteristic
899C22C2×#121×C13711yescharacteristic
900C22C2×#123×C13711yescharacteristic
901C22#525×C13712yes—
902C22#525×C13712yes—
903C22C2×#124×C13711yescharacteristic
904C22C2×#126×C13711yescharacteristic
905C22#538×C13712yes—
906C22#538×C13712yes—
907C22D42×C13712yes—
908C22D42×C13712yes—
909C22#546×C13712yes—
910C22#546×C13712yes—
911C22#546×C13712yes—
912C22#546×C13712yes—
913C22#551×C13712yes—
914C22#551×C13712yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2#2280×C13711yescharacteristic
927C2C2×#388×C13711yescharacteristic
928C2#2312×C13711yescharacteristic
929C2D4×C22⋊C4×C13711yescharacteristic
930C2D4×C22⋊C4×C13711yescharacteristic
931C2#2342×C13711yescharacteristic
932C2#2342×C13711yescharacteristic
933C2#2418×C13712yes—
934C2#2424×C13712yes—
935C2#2472×C13712yes—
936C2#2480×C13712yes—
subgroupG/H
center, socleC24×C137C24
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
prime radicalC26×C137C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C137C2semidirect
3. C2×#380×C137C2semidirect
6. C2×C4×C22⋊C4×C137C2semidirect
7. #1440×C137C2semidirect
8. #1439×C137C2semidirect
9. #1437×C137C2semidirect
10. C22⋊#95×C137C2semidirect
11. C22⋊#95×C137C2semidirect
15. C22×C4⋊C4×C137C22semidirect
17. C22×C22⋊C4×C137C4semidirect
30. C22×C42×C137C22semidirect
36. C2×#95×C137C22semidirect
37. C2×#95×C137C22semidirect
38. C2×#95×C137C22semidirect
39. C2×#95×C137C22semidirect
40. C2×#95×C137C22semidirect
41. C2×#95×C137C22semidirect
246. C22⋊C4×C137C22⋊C4semidirect
422. C22×C137#388semidirect
468. #13873C137direct (N × H)
469. C137#13873direct (N × H)
471. C2×#388C2×C137semidirect
472. C2×#380C2×C137semidirect
475. C2×C4×C22⋊C4C2×C137semidirect
476. #1440C2×C137semidirect
477. #1439C2×C137semidirect
478. #1437C2×C137semidirect
479. C22⋊#95C2×C137semidirect
480. C22⋊#95C2×C137semidirect
484. C22×C4⋊C4C22×C137semidirect
486. C22×C22⋊C4C4×C137semidirect
499. C22×C42C22×C137semidirect
505. C2×#95C22×C137semidirect
506. C2×#95C22×C137semidirect
507. C2×#95C22×C137semidirect
508. C2×#95C22×C137semidirect
509. C2×#95C22×C137semidirect
510. C2×#95C22×C137semidirect
715. C22⋊C4C22⋊C4×C137semidirect
891. C22#388×C137semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1372
C2×#388×C1372
C2×#380×C1372
C2×#379×C1372
C2×C4×C22⋊C4×C1372
#1440×C1372
#1439×C1372
#1437×C1372
C22⋊#95×C1372
#13873137