Finite Group Databasebeta

← C2×#2424×C131 #45720534

Subgroups — C2×#2424×C131 #45720534

Order 33536.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C131C211yesmaximal, characteristic, complemented
2C22×#121×C131C211yesmaximal, characteristic, complemented
3C22×#120×C131C211yesmaximal, characteristic, complemented
4C22×#120×C131C211yesmaximal, characteristic, complemented
5C22×C4×D4×C131C211yesmaximal, characteristic, complemented
6C23×C22⋊C4×C131C211yesmaximal, characteristic, complemented
7#2424×C131C2116yesmaximal, direct product factor
8C2×#396×C131C211yesmaximal, characteristic, complemented
9C2×#394×C131C211yesmaximal, characteristic, complemented
10C2×#394×C131C211yesmaximal, characteristic, complemented
11C2×#392×C131C211yesmaximal, characteristic, complemented
12C2×#390×C131C211yesmaximal, characteristic, complemented
13C2×#388×C131C211yesmaximal, characteristic, complemented
14C2×#386×C131C211yesmaximal, characteristic, complemented
15C2×#386×C131C211yesmaximal, characteristic, complemented
16C2×#385×C131C211yesmaximal, characteristic, complemented
17C26×C131C2211yescharacteristic
18C23×D4×C131C2211yescharacteristic
19C23×D4×C131C2211yescharacteristic
20C23×D4×C131C2211yescharacteristic
21C23×D4×C131C2211yescharacteristic
22C23×D4×C131C2211yescharacteristic
23C23×D4×C131C2211yescharacteristic
24C23×D4×C131C2211yescharacteristic, complemented
25C24×C4×C131C2211yescharacteristic
26C24×C4×C131C2211yescharacteristic
27C24×C4×C131C2211yescharacteristic, complemented
28C2×#121×C131—28no—
29C2×#121×C131—28no—
30C2×#121×C131C2218yescomplemented
31C2×#121×C131C2218yescomplemented
32C2×#120×C131—28no—
33C2×#120×C131—28no—
34C2×#120×C131C2218yescomplemented
35C2×#120×C131C2218yescomplemented
36C2×C4×D4×C131—28no—
37C2×C4×D4×C131C2218yescomplemented
38C22×C4⋊C4×C131C2211yescharacteristic, complemented
39C22×C4⋊C4×C131C2211yescharacteristic, complemented
40C22×C4⋊C4×C131C2211yescharacteristic, complemented
41C22×C4⋊C4×C131C2211yescharacteristic, complemented
42C22×C22⋊C4×C131—28no—
43C22×C22⋊C4×C131C2211yescharacteristic
44C22×C22⋊C4×C131C2211yescharacteristic
45C22×C22⋊C4×C131C2211yescharacteristic
46C22×C22⋊C4×C131C2211yescharacteristic
47C22×C22⋊C4×C131C2211yescharacteristic
48C22×C22⋊C4×C131C2211yescharacteristic
49C22×C22⋊C4×C131C2211yescharacteristic
50C22×C22⋊C4×C131C2211yescharacteristic
51C22×C22⋊C4×C131C2211yescharacteristic
52C22×C22⋊C4×C131C2211yescharacteristic
53C22×C22⋊C4×C131C2218yescomplemented
54C22×C22⋊C4×C131C2211yescharacteristic, complemented
55C22×C22⋊C4×C131C2211yescharacteristic, complemented
56C22×C22⋊C4×C131C2211yescharacteristic, complemented
57C22×C22⋊C4×C131C2211yescharacteristic, complemented
58C22×C22⋊C4×C131C2211yescharacteristic, complemented
59C22×C42×C131C2211yescharacteristic, complemented
60#396×C131C2218yescomplemented
61#394×C131C2218yescomplemented
62#394×C131C2218yescomplemented
63#392×C131C2218yescomplemented
64#390×C131C2218yescomplemented
65#388×C131C2218yescomplemented
66#386×C131C2218yescomplemented
67#386×C131C2218yescomplemented
68#385×C131C2218yescomplemented
69C2×#95×C131C2211yescharacteristic, complemented
70C2×#95×C131C2211yescharacteristic, complemented
71C2×#95×C131C2211yescharacteristic, complemented
72C2×#95×C131C2211yescharacteristic, complemented
73C25×C131—24no—
74C25×C131—24no—
75C25×C131—24no—
76C25×C131—24no—
77C25×C131—24no—
78C25×C131—42no—
79C25×C131—42no—
80C25×C131C2311yescharacteristic
81C25×C131C2311yescharacteristic
82C25×C131C2311yescharacteristic
83C25×C131C2311yescharacteristic
84C25×C131C2314yes—
85C25×C131C2311yescharacteristic
86C22×D4×C131—24no—
87C22×D4×C131—24no—
88C22×D4×C131—24no—
89C22×D4×C131—24no—
90C22×D4×C131—24no—
91C22×D4×C131—24no—
92C22×D4×C131—24no—
93C22×D4×C131—24no—
94C22×D4×C131—24no—
95C22×D4×C131—24no—
96C22×D4×C131—24no—
97C22×D4×C131—24no—
98C22×D4×C131—24no—
99C22×D4×C131—24no—
100C22×D4×C131—24no—
101C22×D4×C131—42no—
102C22×D4×C131—42no—
103C22×D4×C131—42no—
104C22×D4×C131—42no—
105C22×D4×C131—42no—
106C22×D4×C131D418yescomplemented
107C22×D4×C131C2314yes—
108C22×D4×C131C2314yes—
109C22×D4×C131C2314yes—
110C22×D4×C131C2314yes—
111C22×D4×C131C2314yes—
112C22×D4×C131C2314yes—
113C22×D4×C131C2314yescomplemented
114C23×C4×C131—24no—
115C23×C4×C131—24no—
116C23×C4×C131—24no—
117C23×C4×C131—24no—
118C23×C4×C131—24no—
119C23×C4×C131—24no—
120C23×C4×C131—42no—
121C23×C4×C131—42no—
122C23×C4×C131—42no—
123C23×C4×C131C2311yescharacteristic
124C23×C4×C131C2311yescharacteristic
125C23×C4×C131C2311yescharacteristic
126C23×C4×C131C2311yescharacteristic
127C23×C4×C131C2311yescharacteristic
128C23×C4×C131C2314yes—
129C23×C4×C131C2314yes—
130C23×C4×C131C2311yescharacteristic
131C23×C4×C131C2311yescharacteristic
132C23×C4×C131C2311yescharacteristic
133C23×C4×C131C2311yescharacteristic
134C23×C4×C131C2311yescharacteristic
135C23×C4×C131C2314yescomplemented
136#121×C131—232no—
137#121×C131—232no—
138#120×C131—232no—
139#120×C131—232no—
140C4×D4×C131—232no—
141C2×C4⋊C4×C131—24no—
142C2×C4⋊C4×C131—24no—
143C2×C4⋊C4×C131—24no—
144C2×C4⋊C4×C131—42no—
145C2×C4⋊C4×C131C2314yescomplemented
146C2×C4⋊C4×C131C2314yescomplemented
147C2×C4⋊C4×C131C2314yescomplemented
148C2×C4⋊C4×C131C2314yescomplemented
149C2×C22⋊C4×C131—24no—
150C2×C22⋊C4×C131—24no—
151C2×C22⋊C4×C131—24no—
152C2×C22⋊C4×C131—24no—
153C2×C22⋊C4×C131—24no—
154C2×C22⋊C4×C131—24no—
155C2×C22⋊C4×C131—24no—
156C2×C22⋊C4×C131—24no—
157C2×C22⋊C4×C131—24no—
158C2×C22⋊C4×C131—24no—
159C2×C22⋊C4×C131—24no—
160C2×C22⋊C4×C131—24no—
161C2×C22⋊C4×C131—232no—
162C2×C22⋊C4×C131—42no—
163C2×C22⋊C4×C131D418yescomplemented
164C2×C22⋊C4×C131D418yescomplemented
165C2×C22⋊C4×C131C2314yes—
166C2×C22⋊C4×C131C2314yes—
167C2×C22⋊C4×C131C2314yes—
168C2×C22⋊C4×C131C2314yes—
169C2×C22⋊C4×C131C2314yes—
170C2×C22⋊C4×C131C2314yes—
171C2×C22⋊C4×C131C2314yes—
172C2×C22⋊C4×C131C2314yes—
173C2×C22⋊C4×C131C2314yes—
174C2×C22⋊C4×C131C2314yes—
175C2×C22⋊C4×C131C2314yescomplemented
176C2×C22⋊C4×C131C2314yescomplemented
177C2×C22⋊C4×C131C2314yescomplemented
178C2×C22⋊C4×C131C2314yescomplemented
179C2×C22⋊C4×C131C2314yescomplemented
180C2×C42×C131—24no—
181C2×C42×C131C2314yescomplemented
182#95×C131C2314yescomplemented
183#95×C131C2314yescomplemented
184#95×C131C2314yescomplemented
185#95×C131C2314yescomplemented
186C24×C131—22no—
187C24×C131—22no—
188C24×C131—22no—
189C24×C131—22no—
190C24×C131—232no—
191C24×C131—28no—
192C24×C131—22no—
193C24×C131—22no—
194C24×C131—22no—
195C24×C131—22no—
196C24×C131—22no—
197C24×C131—22no—
198C24×C131—22no—
199C24×C131—22no—
200C24×C131—22no—
201C24×C131—28no—
202C24×C131—28no—
203C24×C131—22no—
204C24×C131—22no—
205C24×C131—22no—
206C24×C131—22no—
207C24×C131—22no—
208C24×C131—22no—
209C24×C131—22no—
210C24×C131—22no—
211C24×C131—22no—
212C24×C131—22no—
213C24×C131—22no—
214C24×C131—28no—
215C24×C131—28no—
216C24×C131—22no—
217C24×C131—22no—
218C24×C131—22no—
219C24×C131—22no—
220C24×C131—22no—
221C24×C131—44no—
222C24×C131—44no—
223C24×C131—416no—
224C24×C131—416no—
225C24×C131—416no—
226C24×C131—416no—
227C24×C131—416no—
228C24×C131—416no—
229C24×C131C2×D414yes—
230C24×C131C2×D414yes—
231C24×C131C2×D414yes—
232C24×C131C2×D414yes—
233C24×C131#4114yes—
234C24×C131#4114yes—
235C24×C131C2412yes—
236C24×C131C2412yes—
237C24×C131C2412yes—
238C24×C131C2412yes—
239C24×C131C2412yes—
240C24×C131C2411yescharacteristic
241C2×D4×C131—232no—
242C2×D4×C131—28no—
243C2×D4×C131—28no—
244C2×D4×C131—28no—
245C2×D4×C131—28no—
246C2×D4×C131—28no—
247C2×D4×C131—28no—
248C2×D4×C131—28no—
249C2×D4×C131—28no—
250C2×D4×C131—28no—
251C2×D4×C131—28no—
252C2×D4×C131—28no—
253C2×D4×C131—28no—
254C2×D4×C131—28no—
255C2×D4×C131—28no—
256C2×D4×C131—28no—
257C2×D4×C131—44no—
258C2×D4×C131—44no—
259C2×D4×C131—44no—
260C2×D4×C131—44no—
261C2×D4×C131—44no—
262C2×D4×C131—416no—
263C2×D4×C131—416no—
264C2×D4×C131—416no—
265C2×D4×C131—416no—
266C2×D4×C131—416no—
267C2×D4×C131—416no—
268C2×D4×C131C2×D4116yescomplemented
269C22×C4×C131—22no—
270C22×C4×C131—22no—
271C22×C4×C131—22no—
272C22×C4×C131—22no—
273C22×C4×C131—22no—
274C22×C4×C131—22no—
275C22×C4×C131—22no—
276C22×C4×C131—22no—
277C22×C4×C131—22no—
278C22×C4×C131—22no—
279C22×C4×C131—22no—
280C22×C4×C131—22no—
281C22×C4×C131—22no—
282C22×C4×C131—22no—
283C22×C4×C131—22no—
284C22×C4×C131—22no—
285C22×C4×C131—22no—
286C22×C4×C131—22no—
287C22×C4×C131—22no—
288C22×C4×C131—28no—
289C22×C4×C131—28no—
290C22×C4×C131—22no—
291C22×C4×C131—22no—
292C22×C4×C131—22no—
293C22×C4×C131—22no—
294C22×C4×C131—22no—
295C22×C4×C131—22no—
296C22×C4×C131—28no—
297C22×C4×C131—28no—
298C22×C4×C131—28no—
299C22×C4×C131—28no—
300C22×C4×C131—44no—
301C22×C4×C131—44no—
302C22×C4×C131—44no—
303C22×C4×C131—416no—
304C22×C4×C131—416no—
305C22×C4×C131—416no—
306C22×C4×C131C2×D414yes—
307C22×C4×C131C2×D414yes—
308C22×C4×C131C2×D414yes—
309C22×C4×C131C2×D414yes—
310C22×C4×C131C2×D414yes—
311C22×C4×C131C2412yes—
312C22×C4×C131C2412yes—
313C22×C4×C131C2412yes—
314C22×C4×C131C2412yes—
315C22×C4×C131C2412yes—
316C22×C4×C131C2412yes—
317C22×C4×C131C2412yes—
318C22×C4×C131C2412yes—
319C22×C4×C131C2412yes—
320C22×C4×C131C2412yes—
321C4⋊C4×C131—28no—
322C4⋊C4×C131—28no—
323C4⋊C4×C131—28no—
324C4⋊C4×C131—44no—
325C22⋊C4×C131—28no—
326C22⋊C4×C131—28no—
327C22⋊C4×C131—28no—
328C22⋊C4×C131—28no—
329C22⋊C4×C131—28no—
330C22⋊C4×C131—28no—
331C22⋊C4×C131—28no—
332C22⋊C4×C131—28no—
333C22⋊C4×C131—28no—
334C22⋊C4×C131—28no—
335C22⋊C4×C131—28no—
336C22⋊C4×C131—28no—
337C22⋊C4×C131—44no—
338C22⋊C4×C131C2×D4116yescomplemented
339C22⋊C4×C131C2×D4116yescomplemented
340C42×C131—28no—
341C23×C131—28no—
342C23×C131—28no—
343C23×C131—28no—
344C23×C131—28no—
345C23×C131—28no—
346C23×C131—28no—
347C23×C131—22no—
348C23×C131—22no—
349C23×C131—22no—
350C23×C131—22no—
351C23×C131—232no—
352C23×C131—28no—
353C23×C131—28no—
354C23×C131—28no—
355C23×C131—28no—
356C23×C131—28no—
357C23×C131—28no—
358C23×C131—28no—
359C23×C131—28no—
360C23×C131—28no—
361C23×C131—22no—
362C23×C131—22no—
363C23×C131—22no—
364C23×C131—22no—
365C23×C131—22no—
366C23×C131—22no—
367C23×C131—22no—
368C23×C131—22no—
369C23×C131—22no—
370C23×C131—22no—
371C23×C131—22no—
372C23×C131—22no—
373C23×C131—22no—
374C23×C131—22no—
375C23×C131—22no—
376C23×C131—22no—
377C23×C131—22no—
378C23×C131—22no—
379C23×C131—22no—
380C23×C131—22no—
381C23×C131—22no—
382C23×C131—22no—
383C23×C131—22no—
384C23×C131—22no—
385C23×C131—22no—
386C23×C131—416no—
387C23×C131—416no—
388C23×C131—416no—
389C23×C131—416no—
390C23×C131—4128no—
391C23×C131—416no—
392C23×C131—44no—
393C23×C131—44no—
394C23×C131—416no—
395C23×C131—44no—
396C23×C131—44no—
397C23×C131—44no—
398C23×C131—44no—
399C23×C131—44no—
400C23×C131—44no—
401C23×C131—44no—
402C23×C131—44no—
403C23×C131—44no—
404C23×C131—44no—
405C23×C131—44no—
406C23×C131—44no—
407C23×C131—44no—
408C23×C131—44no—
409C23×C131—44no—
410C23×C131—44no—
411C23×C131—44no—
412C23×C131#121116yescomplemented
413C23×C131C22×D414yes—
414C23×C131C22×D414yes—
415C23×C131C22×D414yes—
416C23×C131C22×D414yes—
417C23×C131C22×D412yes—
418C23×C131C22×D412yes—
419C23×C131C22×D412yes—
420C23×C131C2×#4114yes—
421C23×C131C2×#4114yes—
422C23×C131C2×#4112yes—
423C23×C131C2×#4112yes—
424C23×C131H(5,𝔽2)12yes—
425C23×C131H(5,𝔽2)12yes—
426C23×C131C2511yescharacteristic
427D4×C131—232no—
428D4×C131—416no—
429D4×C131—416no—
430D4×C131—416no—
431D4×C131—416no—
432D4×C131—416no—
433D4×C131—416no—
434C2×C4×C131—28no—
435C2×C4×C131—28no—
436C2×C4×C131—28no—
437C2×C4×C131—28no—
438C2×C4×C131—28no—
439C2×C4×C131—22no—
440C2×C4×C131—22no—
441C2×C4×C131—22no—
442C2×C4×C131—22no—
443C2×C4×C131—22no—
444C2×C4×C131—22no—
445C2×C4×C131—22no—
446C2×C4×C131—22no—
447C2×C4×C131—22no—
448C2×C4×C131—22no—
449C2×C4×C131—22no—
450C2×C4×C131—22no—
451C2×C4×C131—22no—
452C2×C4×C131—22no—
453C2×C4×C131—22no—
454C2×C4×C131—22no—
455C2×C4×C131—22no—
456C2×C4×C131—22no—
457C2×C4×C131—22no—
458C2×C4×C131—22no—
459C2×C4×C131—22no—
460C2×C4×C131—22no—
461C2×C4×C131—22no—
462C2×C4×C131—22no—
463C2×C4×C131—22no—
464C2×C4×C131—416no—
465C2×C4×C131—416no—
466C2×C4×C131—416no—
467C2×C4×C131—44no—
468C2×C4×C131—44no—
469C2×C4×C131—44no—
470C2×C4×C131—44no—
471C2×C4×C131—44no—
472C2×C4×C131C22×D414yes—
473C2×C4×C131C22×D414yes—
474C2×C4×C131C22×D414yes—
475C2×C4×C131C22×D414yes—
476C2×C4×C131C22×D414yes—
477C22×C131—24no—
478C22×C131—232no—
479C22×C131—24no—
480C22×C131—24no—
481C22×C131—24no—
482C22×C131—24no—
483C22×C131—24no—
484C22×C131—24no—
485C22×C131—24no—
486C22×C131—24no—
487C22×C131—24no—
488C22×C131—24no—
489C22×C131—24no—
490C22×C131—24no—
491C22×C131—24no—
492C22×C131—24no—
493C22×C131—464no—
494C22×C131—42no—
495C22×C131—42no—
496C22×C131—42no—
497C22×C131—416no—
498C22×C131—416no—
499C22×C131—416no—
500C22×C131—42no—
501C22×C131—42no—
502C22×C131—42no—
503C22×C131—42no—
504C22×C131—42no—
505C22×C131—42no—
506C22×C131—42no—
507C22×C131—42no—
508C22×C131—42no—
509C22×C131—42no—
510C22×C131—42no—
511C22×C131—42no—
512C22×C131—42no—
513C22×C131—42no—
514C22×C131—42no—
515C22×C131—42no—
516C22×C131—88no—
517C22×C131C2×#12114yes—
518C22×C131C2×#12118yescomplemented
519C22×C131#52514yes—
520C22×C131#53814yes—
521C22×C131D4214yes—
522C22×C131D4214yes—
523C22×C131#54614yes—
524C22×C131#54614yes—
525C22×C131C23×D411yescharacteristic
526C22×C131C23×D411yescharacteristic
527C22×C131C23×D411yescharacteristic
528C22×C131C22×#4111yescharacteristic
529C22×C131C22×#4111yescharacteristic
530C22×C131C2×H(5,𝔽2)11yescharacteristic
531C22×C131C2×H(5,𝔽2)11yescharacteristic
532C4×C131—24no—
533C4×C131—24no—
534C4×C131—24no—
535C4×C131—24no—
536C4×C131—24no—
537C4×C131—42no—
538C4×C131—42no—
539C4×C131—42no—
540C4×C131—42no—
541C4×C131—42no—
542C2×C131—28no—
543C2×C131—44no—
544C2×C131—44no—
545C2×C131—44no—
546C2×C131—82no—
547C2×C131#242418yesdirect product factor
548C2×C131C22×#12111yescharacteristic
549C2×C131C2×#52511yescharacteristic
550C2×C131C2×#53811yescharacteristic
551C2×C131C2×D4211yescharacteristic
552C2×C131C2×D4211yescharacteristic
553C2×C131C2×#54611yescharacteristic
554C2×C131C2×#54611yescharacteristic
555C2×#2424C13111yesmaximal, characteristic, direct product factor, Sylow
556C131C2×#242411yescharacteristic, direct product factor, Sylow
557C22×#121C2×C13111yescharacteristic, complemented
558C22×#121C2×C13111yescharacteristic, complemented
559C22×#120C2×C13111yescharacteristic, complemented
560C22×#120C2×C13111yescharacteristic, complemented
561C22×C4×D4C2×C13111yescharacteristic, complemented
562C23×C22⋊C4C2×C13111yescharacteristic, complemented
563#2424C2×C131116yesdirect product factor
564C2×#396C2×C13111yescharacteristic, complemented
565C2×#394C2×C13111yescharacteristic, complemented
566C2×#394C2×C13111yescharacteristic, complemented
567C2×#392C2×C13111yescharacteristic, complemented
568C2×#390C2×C13111yescharacteristic, complemented
569C2×#388C2×C13111yescharacteristic, complemented
570C2×#386C2×C13111yescharacteristic, complemented
571C2×#386C2×C13111yescharacteristic, complemented
572C2×#385C2×C13111yescharacteristic, complemented
573C26C22×C13111yescharacteristic
574C23×D4C22×C13111yescharacteristic
575C23×D4C22×C13111yescharacteristic
576C23×D4C22×C13111yescharacteristic
577C23×D4C22×C13111yescharacteristic
578C23×D4C22×C13111yescharacteristic
579C23×D4C22×C13111yescharacteristic
580C23×D4C22×C13111yescharacteristic, complemented
581C24×C4C22×C13111yescharacteristic
582C24×C4C22×C13111yescharacteristic
583C24×C4C22×C13111yescharacteristic, complemented
584C2×#121—28no—
585C2×#121—28no—
586C2×#121C22×C13118yescomplemented
587C2×#121C22×C13118yescomplemented
588C2×#120—28no—
589C2×#120—28no—
590C2×#120C22×C13118yescomplemented
591C2×#120C22×C13118yescomplemented
592C2×C4×D4—28no—
593C2×C4×D4C22×C13118yescomplemented
594C22×C4⋊C4C22×C13111yescharacteristic, complemented
595C22×C4⋊C4C22×C13111yescharacteristic, complemented
596C22×C4⋊C4C22×C13111yescharacteristic, complemented
597C22×C4⋊C4C22×C13111yescharacteristic, complemented
598C22×C22⋊C4—28no—
599C22×C22⋊C4C22×C13111yescharacteristic
600C22×C22⋊C4C22×C13111yescharacteristic
601C22×C22⋊C4C22×C13111yescharacteristic
602C22×C22⋊C4C22×C13111yescharacteristic
603C22×C22⋊C4C22×C13111yescharacteristic
604C22×C22⋊C4C22×C13111yescharacteristic
605C22×C22⋊C4C22×C13111yescharacteristic
606C22×C22⋊C4C22×C13111yescharacteristic
607C22×C22⋊C4C22×C13111yescharacteristic
608C22×C22⋊C4C22×C13111yescharacteristic
609C22×C22⋊C4C22×C13118yescomplemented
610C22×C22⋊C4C22×C13111yescharacteristic, complemented
611C22×C22⋊C4C22×C13111yescharacteristic, complemented
612C22×C22⋊C4C22×C13111yescharacteristic, complemented
613C22×C22⋊C4C22×C13111yescharacteristic, complemented
614C22×C22⋊C4C22×C13111yescharacteristic, complemented
615C22×C42C22×C13111yescharacteristic, complemented
616#396C22×C13118yescomplemented
617#394C22×C13118yescomplemented
618#394C22×C13118yescomplemented
619#392C22×C13118yescomplemented
620#390C22×C13118yescomplemented
621#388C22×C13118yescomplemented
622#386C22×C13118yescomplemented
623#386C22×C13118yescomplemented
624#385C22×C13118yescomplemented
625C2×#95C22×C13111yescharacteristic, complemented
626C2×#95C22×C13111yescharacteristic, complemented
627C2×#95C22×C13111yescharacteristic, complemented
628C2×#95C22×C13111yescharacteristic, complemented
629C25—24no—
630C25—24no—
631C25—24no—
632C25—24no—
633C25—24no—
634C25—42no—
635C25—42no—
636C25C23×C13111yescharacteristic
637C25C23×C13111yescharacteristic
638C25C23×C13111yescharacteristic
639C25C23×C13111yescharacteristic
640C25C23×C13114yes—
641C25C23×C13111yescharacteristic
642C22×D4—24no—
643C22×D4—24no—
644C22×D4—24no—
645C22×D4—24no—
646C22×D4—24no—
647C22×D4—24no—
648C22×D4—24no—
649C22×D4—24no—
650C22×D4—24no—
651C22×D4—24no—
652C22×D4—24no—
653C22×D4—24no—
654C22×D4—24no—
655C22×D4—24no—
656C22×D4—24no—
657C22×D4—42no—
658C22×D4—42no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4—42no—
662C22×D4D4×C13118yescomplemented
663C22×D4C23×C13114yes—
664C22×D4C23×C13114yes—
665C22×D4C23×C13114yes—
666C22×D4C23×C13114yes—
667C22×D4C23×C13114yes—
668C22×D4C23×C13114yes—
669C22×D4C23×C13114yescomplemented
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—24no—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—42no—
677C23×C4—42no—
678C23×C4—42no—
679C23×C4C23×C13111yescharacteristic
680C23×C4C23×C13111yescharacteristic
681C23×C4C23×C13111yescharacteristic
682C23×C4C23×C13111yescharacteristic
683C23×C4C23×C13111yescharacteristic
684C23×C4C23×C13114yes—
685C23×C4C23×C13114yes—
686C23×C4C23×C13111yescharacteristic
687C23×C4C23×C13111yescharacteristic
688C23×C4C23×C13111yescharacteristic
689C23×C4C23×C13111yescharacteristic
690C23×C4C23×C13111yescharacteristic
691C23×C4C23×C13114yescomplemented
692#121—232no—
693#121—232no—
694#120—232no—
695#120—232no—
696C4×D4—232no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—42no—
701C2×C4⋊C4C23×C13114yescomplemented
702C2×C4⋊C4C23×C13114yescomplemented
703C2×C4⋊C4C23×C13114yescomplemented
704C2×C4⋊C4C23×C13114yescomplemented
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—232no—
718C2×C22⋊C4—42no—
719C2×C22⋊C4D4×C13118yescomplemented
720C2×C22⋊C4D4×C13118yescomplemented
721C2×C22⋊C4C23×C13114yes—
722C2×C22⋊C4C23×C13114yes—
723C2×C22⋊C4C23×C13114yes—
724C2×C22⋊C4C23×C13114yes—
725C2×C22⋊C4C23×C13114yes—
726C2×C22⋊C4C23×C13114yes—
727C2×C22⋊C4C23×C13114yes—
728C2×C22⋊C4C23×C13114yes—
729C2×C22⋊C4C23×C13114yes—
730C2×C22⋊C4C23×C13114yes—
731C2×C22⋊C4C23×C13114yescomplemented
732C2×C22⋊C4C23×C13114yescomplemented
733C2×C22⋊C4C23×C13114yescomplemented
734C2×C22⋊C4C23×C13114yescomplemented
735C2×C22⋊C4C23×C13114yescomplemented
736C2×C42—24no—
737C2×C42C23×C13114yescomplemented
738#95C23×C13114yescomplemented
739#95C23×C13114yescomplemented
740#95C23×C13114yescomplemented
741#95C23×C13114yescomplemented
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—232no—
747C24—28no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—28no—
758C24—28no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—22no—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—22no—
770C24—28no—
771C24—28no—
772C24—22no—
773C24—22no—
774C24—22no—
775C24—22no—
776C24—22no—
777C24—44no—
778C24—44no—
779C24—416no—
780C24—416no—
781C24—416no—
782C24—416no—
783C24—416no—
784C24—416no—
785C24C2×D4×C13114yes—
786C24C2×D4×C13114yes—
787C24C2×D4×C13114yes—
788C24C2×D4×C13114yes—
789C24#41×C13114yes—
790C24#41×C13114yes—
791C24C24×C13112yes—
792C24C24×C13112yes—
793C24C24×C13112yes—
794C24C24×C13112yes—
795C24C24×C13112yes—
796C24C24×C13111yescharacteristic
797C2×D4—232no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—416no—
819C2×D4—416no—
820C2×D4—416no—
821C2×D4—416no—
822C2×D4—416no—
823C2×D4—416no—
824C2×D4C2×D4×C131116yescomplemented
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—416no—
860C22×C4—416no—
861C22×C4—416no—
862C22×C4C2×D4×C13114yes—
863C22×C4C2×D4×C13114yes—
864C22×C4C2×D4×C13114yes—
865C22×C4C2×D4×C13114yes—
866C22×C4C2×D4×C13114yes—
867C22×C4C24×C13112yes—
868C22×C4C24×C13112yes—
869C22×C4C24×C13112yes—
870C22×C4C24×C13112yes—
871C22×C4C24×C13112yes—
872C22×C4C24×C13112yes—
873C22×C4C24×C13112yes—
874C22×C4C24×C13112yes—
875C22×C4C24×C13112yes—
876C22×C4C24×C13112yes—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—44no—
894C22⋊C4C2×D4×C131116yescomplemented
895C22⋊C4C2×D4×C131116yescomplemented
896C42—28no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—232no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—28no—
915C23—28no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—416no—
943C23—416no—
944C23—416no—
945C23—416no—
946C23—4128no—
947C23—416no—
948C23—44no—
949C23—44no—
950C23—416no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—44no—
956C23—44no—
957C23—44no—
958C23—44no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23#121×C131116yescomplemented
969C23C22×D4×C13114yes—
970C23C22×D4×C13114yes—
971C23C22×D4×C13114yes—
972C23C22×D4×C13114yes—
973C23C22×D4×C13112yes—
974C23C22×D4×C13112yes—
975C23C22×D4×C13112yes—
976C23C2×#41×C13114yes—
977C23C2×#41×C13114yes—
978C23C2×#41×C13112yes—
979C23C2×#41×C13112yes—
980C23H(5,𝔽2)×C13112yes—
981C23H(5,𝔽2)×C13112yes—
982C23C25×C13111yescharacteristic
983D4—232no—
984D4—416no—
985D4—416no—
986D4—416no—
987D4—416no—
988D4—416no—
989D4—416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—416no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4C22×D4×C13114yes—
1029C2×C4C22×D4×C13114yes—
1030C2×C4C22×D4×C13114yes—
1031C2×C4C22×D4×C13114yes—
1032C2×C4C22×D4×C13114yes—
1033C22—24no—
1034C22—232no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—464no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—416no—
1054C22—416no—
1055C22—416no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—88no—
1073C22C2×#121×C13114yes—
1074C22C2×#121×C13118yescomplemented
1075C22#525×C13114yes—
1076C22#538×C13114yes—
1077C22D42×C13114yes—
1078C22D42×C13114yes—
1079C22#546×C13114yes—
1080C22#546×C13114yes—
1081C22C23×D4×C13111yescharacteristic
1082C22C23×D4×C13111yescharacteristic
1083C22C23×D4×C13111yescharacteristic
1084C22C22×#41×C13111yescharacteristic
1085C22C22×#41×C13111yescharacteristic
1086C22C2×H(5,𝔽2)×C13111yescharacteristic
1087C22C2×H(5,𝔽2)×C13111yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C2—28no—
1099C2—44no—
1100C2—44no—
1101C2—44no—
1102C2—82no—
1103C2#2424×C13118yesdirect product factor
1104C2C22×#121×C13111yescharacteristic
1105C2C2×#525×C13111yescharacteristic
1106C2C2×#538×C13111yescharacteristic
1107C2C2×D42×C13111yescharacteristic
1108C2C2×D42×C13111yescharacteristic
1109C2C2×#546×C13111yescharacteristic
1110C2C2×#546×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutator, Frattini, cosocleC23C25×C131
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C131C2semidirect
2. C22×#121×C131C2semidirect
3. C22×#120×C131C2semidirect
4. C22×#120×C131C2semidirect
5. C22×C4×D4×C131C2semidirect
6. C23×C22⋊C4×C131C2semidirect
7. #2424×C131C2direct (N × H)
8. C2×#396×C131C2semidirect
9. C2×#394×C131C2semidirect
10. C2×#394×C131C2semidirect
11. C2×#392×C131C2semidirect
12. C2×#390×C131C2semidirect
13. C2×#388×C131C2semidirect
14. C2×#386×C131C2semidirect
15. C2×#386×C131C2semidirect
16. C2×#385×C131C2semidirect
24. C23×D4×C131C22semidirect
27. C24×C4×C131C22semidirect
30. C2×#121×C131C22semidirect
31. C2×#121×C131C22semidirect
34. C2×#120×C131C22semidirect
35. C2×#120×C131C22semidirect
37. C2×C4×D4×C131C22semidirect
38. C22×C4⋊C4×C131C22semidirect
39. C22×C4⋊C4×C131C22semidirect
40. C22×C4⋊C4×C131C22semidirect
41. C22×C4⋊C4×C131C22semidirect
53. C22×C22⋊C4×C131C22semidirect
54. C22×C22⋊C4×C131C22semidirect
55. C22×C22⋊C4×C131C22semidirect
56. C22×C22⋊C4×C131C22semidirect
57. C22×C22⋊C4×C131C22semidirect
58. C22×C22⋊C4×C131C22semidirect
59. C22×C42×C131C22semidirect
60. #396×C131C22semidirect
61. #394×C131C22semidirect
62. #394×C131C22semidirect
63. #392×C131C22semidirect
64. #390×C131C22semidirect
65. #388×C131C22semidirect
66. #386×C131C22semidirect
67. #386×C131C22semidirect
68. #385×C131C22semidirect
69. C2×#95×C131C22semidirect
70. C2×#95×C131C22semidirect
71. C2×#95×C131C22semidirect
72. C2×#95×C131C22semidirect
106. C22×D4×C131D4semidirect
113. C22×D4×C131C23semidirect
135. C23×C4×C131C23semidirect
145. C2×C4⋊C4×C131C23semidirect
146. C2×C4⋊C4×C131C23semidirect
147. C2×C4⋊C4×C131C23semidirect
148. C2×C4⋊C4×C131C23semidirect
163. C2×C22⋊C4×C131D4semidirect
164. C2×C22⋊C4×C131D4semidirect
175. C2×C22⋊C4×C131C23semidirect
176. C2×C22⋊C4×C131C23semidirect
177. C2×C22⋊C4×C131C23semidirect
178. C2×C22⋊C4×C131C23semidirect
179. C2×C22⋊C4×C131C23semidirect
181. C2×C42×C131C23semidirect
182. #95×C131C23semidirect
183. #95×C131C23semidirect
184. #95×C131C23semidirect
185. #95×C131C23semidirect
268. C2×D4×C131C2×D4semidirect
338. C22⋊C4×C131C2×D4semidirect
339. C22⋊C4×C131C2×D4semidirect
412. C23×C131#121semidirect
518. C22×C131C2×#121semidirect
547. C2×C131#2424direct (N × H)
555. C2×#2424C131direct (N × H)
556. C131C2×#2424direct (N × H)
557. C22×#121C2×C131semidirect
558. C22×#121C2×C131semidirect
559. C22×#120C2×C131semidirect
560. C22×#120C2×C131semidirect
561. C22×C4×D4C2×C131semidirect
562. C23×C22⋊C4C2×C131semidirect
563. #2424C2×C131direct (N × H)
564. C2×#396C2×C131semidirect
565. C2×#394C2×C131semidirect
566. C2×#394C2×C131semidirect
567. C2×#392C2×C131semidirect
568. C2×#390C2×C131semidirect
569. C2×#388C2×C131semidirect
570. C2×#386C2×C131semidirect
571. C2×#386C2×C131semidirect
572. C2×#385C2×C131semidirect
580. C23×D4C22×C131semidirect
583. C24×C4C22×C131semidirect
586. C2×#121C22×C131semidirect
587. C2×#121C22×C131semidirect
590. C2×#120C22×C131semidirect
591. C2×#120C22×C131semidirect
593. C2×C4×D4C22×C131semidirect
594. C22×C4⋊C4C22×C131semidirect
595. C22×C4⋊C4C22×C131semidirect
596. C22×C4⋊C4C22×C131semidirect
597. C22×C4⋊C4C22×C131semidirect
609. C22×C22⋊C4C22×C131semidirect
610. C22×C22⋊C4C22×C131semidirect
611. C22×C22⋊C4C22×C131semidirect
612. C22×C22⋊C4C22×C131semidirect
613. C22×C22⋊C4C22×C131semidirect
614. C22×C22⋊C4C22×C131semidirect
615. C22×C42C22×C131semidirect
616. #396C22×C131semidirect
617. #394C22×C131semidirect
618. #394C22×C131semidirect
619. #392C22×C131semidirect
620. #390C22×C131semidirect
621. #388C22×C131semidirect
622. #386C22×C131semidirect
623. #386C22×C131semidirect
624. #385C22×C131semidirect
625. C2×#95C22×C131semidirect
626. C2×#95C22×C131semidirect
627. C2×#95C22×C131semidirect
628. C2×#95C22×C131semidirect
662. C22×D4D4×C131semidirect
669. C22×D4C23×C131semidirect
691. C23×C4C23×C131semidirect
701. C2×C4⋊C4C23×C131semidirect
702. C2×C4⋊C4C23×C131semidirect
703. C2×C4⋊C4C23×C131semidirect
704. C2×C4⋊C4C23×C131semidirect
719. C2×C22⋊C4D4×C131semidirect
720. C2×C22⋊C4D4×C131semidirect
731. C2×C22⋊C4C23×C131semidirect
732. C2×C22⋊C4C23×C131semidirect
733. C2×C22⋊C4C23×C131semidirect
734. C2×C22⋊C4C23×C131semidirect
735. C2×C22⋊C4C23×C131semidirect
737. C2×C42C23×C131semidirect
738. #95C23×C131semidirect
739. #95C23×C131semidirect
740. #95C23×C131semidirect
741. #95C23×C131semidirect
824. C2×D4C2×D4×C131semidirect
894. C22⋊C4C2×D4×C131semidirect
895. C22⋊C4C2×D4×C131semidirect
968. C23#121×C131semidirect
1074. C22C2×#121×C131semidirect
1103. C2#2424×C131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#121×C1312
C22×#120×C1312
C22×C4×D4×C1312
C23×C22⋊C4×C1312
#2424×C1312
C2×#396×C1312
C2×#394×C1312
C2×#392×C1312
C2×#390×C1312
C2×#388×C1312
C2×#386×C1312
C2×#385×C1312
C2×#2424131