Finite Group Databasebeta

← C131×#21772 #45707656

Subgroups — C131×#21772 #45707656

Order 33536.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C131C211yesmaximal, characteristic
2C2×#408×C131C211yesmaximal, characteristic, complemented
3#2311×C131C211yesmaximal, characteristic, complemented
4#1895×C131C211yesmaximal, characteristic, complemented
5#1894×C131C211yesmaximal, characteristic, complemented
6#1893×C131C211yesmaximal, characteristic, complemented
7#1892×C131C211yesmaximal, characteristic, complemented
8#1875×C131C211yesmaximal, characteristic, complemented
9#1874×C131C211yesmaximal, characteristic, complemented
10#1873×C131C211yesmaximal, characteristic, complemented
11#1872×C131C211yesmaximal, characteristic, complemented
12#1824×C131C211yesmaximal, characteristic, complemented
13#1823×C131C211yesmaximal, characteristic, complemented
14#1788×C131C211yesmaximal, characteristic, complemented
15#1788×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×#41×C131C2211yescharacteristic
18C22×M16×C131C2211yescharacteristic
19C23×C8×C131C2211yescharacteristic
20#537×C131—24no—
21#537×C131C418yescomplemented
22C2×C22⋊Q8×C131—21no—
23C2×C22⋊Q8×C131C2211yescharacteristic
24C2×C22⋊Q8×C131C2211yescharacteristic
25C2×#121×C131—21no—
26C2×#121×C131—21no—
27C2×#121×C131—21no—
28C2×#121×C131C2211yescharacteristic
29C2×#121×C131C2211yescharacteristic
30C2×#117×C131C2211yescharacteristic
31C22×C4⋊C4×C131C2211yescharacteristic
32C22×C4⋊C4×C131C2211yescharacteristic
33C2×#103×C131C2211yescharacteristic
34C2×#103×C131C2211yescharacteristic
35C2×#103×C131C2211yescharacteristic
36C2×#103×C131C2211yescharacteristic
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41#408×C131—24no—
42C2×C22⋊C8×C131C2211yescharacteristic
43C2×C22⋊C8×C131C2211yescharacteristic
44C2×C22⋊C8×C131C2211yescharacteristic
45C2×C22⋊C8×C131C2211yescharacteristic
46#391×C131—21no—
47#390×C131—21no—
48#386×C131—21no—
49#386×C131—21no—
50#380×C131C2211yescharacteristic
51#380×C131C2211yescharacteristic
52#380×C131C2211yescharacteristic
53#380×C131C2211yescharacteristic
54#340×C131C2211yescharacteristic
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic
60#340×C131C2211yescharacteristic
61#340×C131C2211yescharacteristic
62C2×#41×C131—22no—
63C2×#41×C131—41no—
64C2×#41×C131—41no—
65C2×#41×C131—41no—
66C2×#41×C131—41no—
67C2×#41×C131—41no—
68C2×#41×C131—41no—
69C2×#41×C131—41no—
70C2×#41×C131—41no—
71C2×#41×C131C2×C414yes—
72C2×#41×C131C2×C414yescomplemented
73C2×#41×C131D414yes—
74C22×Q8×C131D411yescharacteristic
75C22×Q8×C131C2311yescharacteristic
76C22×D4×C131—21no—
77C22×D4×C131—21no—
78C22×D4×C131—21no—
79C22×D4×C131D411yescharacteristic
80C22×D4×C131D411yescharacteristic
81C22×D4×C131D411yescharacteristic
82C22×D4×C131C2311yescharacteristic
83C23×C4×C131—21no—
84C23×C4×C131—21no—
85C23×C4×C131—21no—
86C23×C4×C131C2311yescharacteristic
87C23×C4×C131C2311yescharacteristic
88C23×C4×C131C2311yescharacteristic
89C2×M16×C131—22no—
90C2×M16×C131—41no—
91C2×M16×C131—41no—
92C22×C8×C131—22no—
93C22×C8×C131—41no—
94C22×C8×C131—41no—
95C22×C8×C131C2311yescharacteristic
96C22×C8×C131C2311yescharacteristic
97C22×C8×C131C2311yescharacteristic
98C22×C8×C131C2311yescharacteristic
99C22⋊Q8×C131—28no—
100C22⋊Q8×C131—22no—
101C22⋊Q8×C131—22no—
102C22⋊Q8×C131C2×C414yes—
103C22⋊Q8×C131C2×C414yescomplemented
104#121×C131—28no—
105#121×C131—28no—
106#121×C131—28no—
107#121×C131—22no—
108#121×C131—22no—
109#121×C131C2×C414yes—
110#121×C131C2×C414yescomplemented
111#117×C131—41no—
112#117×C131—41no—
113C2×C4⋊C4×C131—21no—
114C2×C4⋊C4×C131—22no—
115C2×C4⋊C4×C131—21no—
116C2×C4⋊C4×C131—21no—
117C2×C4⋊C4×C131—21no—
118C2×C4⋊C4×C131—41no—
119C2×C4⋊C4×C131—41no—
120C2×C4⋊C4×C131C2×C414yescomplemented
121C2×C4⋊C4×C131C2311yescharacteristic
122C2×C4⋊C4×C131C2311yescharacteristic
123C2×C4⋊C4×C131C2311yescharacteristic
124C2×C4⋊C4×C131C2311yescharacteristic
125C2×C4⋊C4×C131C2311yescharacteristic
126C2×C4⋊C4×C131C2311yescharacteristic
127C2×C22⋊C4×C131—21no—
128C2×C22⋊C4×C131—21no—
129C2×C22⋊C4×C131—21no—
130C2×C22⋊C4×C131—21no—
131C2×C22⋊C4×C131—21no—
132C2×C22⋊C4×C131—21no—
133C2×C22⋊C4×C131—21no—
134C2×C22⋊C4×C131—21no—
135C2×C22⋊C4×C131—21no—
136C2×C42×C131—21no—
137#103×C131—41no—
138#103×C131—41no—
139#103×C131—41no—
140#103×C131—41no—
141#102×C131—41no—
142#102×C131—41no—
143#102×C131—41no—
144#102×C131—41no—
145C22⋊C8×C131—22no—
146C22⋊C8×C131—22no—
147C22⋊C8×C131—22no—
148C22⋊C8×C131—22no—
149#95×C131—21no—
150#95×C131—21no—
151#95×C131—21no—
152#95×C131—21no—
153C24×C131—21no—
154C24×C131C2×D411yescharacteristic
155C24×C131C2×D411yescharacteristic
156C24×C131C2×D411yescharacteristic
157#41×C131—44no—
158#41×C131—44no—
159#41×C131—44no—
160#41×C131—44no—
161#41×C131—44no—
162#41×C131—44no—
163#41×C131—44no—
164#41×C131—44no—
165C2×Q8×C131—21no—
166C2×Q8×C131—21no—
167C2×Q8×C131—21no—
168C2×Q8×C131—21no—
169C2×Q8×C131—21no—
170C2×Q8×C131—41no—
171C2×Q8×C131—41no—
172C2×Q8×C131C22⋊C414yes—
173C2×Q8×C131C22×C412yes—
174C2×D4×C131—24no—
175C2×D4×C131—24no—
176C2×D4×C131—24no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—21no—
180C2×D4×C131—21no—
181C2×D4×C131—21no—
182C2×D4×C131—41no—
183C2×D4×C131—41no—
184C2×D4×C131—41no—
185C2×D4×C131—41no—
186C2×D4×C131—41no—
187C2×D4×C131—41no—
188C2×D4×C131—42no—
189C2×D4×C131—42no—
190C2×D4×C131—81no—
191C2×D4×C131—81no—
192C2×D4×C131—81no—
193C2×D4×C131—81no—
194C2×D4×C131C22⋊C414yes—
195C2×D4×C131C22⋊C414yes—
196C2×D4×C131C22⋊C414yes—
197C2×D4×C131C22×C412yes—
198C22×C4×C131—21no—
199C22×C4×C131—21no—
200C22×C4×C131—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—21no—
204C22×C4×C131—21no—
205C22×C4×C131—21no—
206C22×C4×C131—21no—
207C22×C4×C131—21no—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131—21no—
213C22×C4×C131—24no—
214C22×C4×C131—24no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—42no—
220C22×C4×C131—42no—
221C22×C4×C131—42no—
222C22×C4×C131—81no—
223C22×C4×C131—81no—
224C22×C4×C131—81no—
225C22×C4×C131—81no—
226C22×C4×C131C22×C412yes—
227C22×C4×C131C22×C412yes—
228C22×C4×C131C22×C412yes—
229C22×C4×C131C2×D411yescharacteristic
230C22×C4×C131C2×D411yescharacteristic
231C22×C4×C131C2×D411yescharacteristic
232C22×C4×C131C2×D412yes—
233C22×C4×C131C2×D412yes—
234C22×C4×C131C2×D412yes—
235C22×C4×C131C2411yescharacteristic
236M16×C131—44no—
237C2×C8×C131—21no—
238C2×C8×C131—21no—
239C2×C8×C131—21no—
240C2×C8×C131—21no—
241C2×C8×C131—21no—
242C2×C8×C131—21no—
243C2×C8×C131—21no—
244C2×C8×C131—21no—
245C2×C8×C131—21no—
246C2×C8×C131—21no—
247C2×C8×C131—21no—
248C2×C8×C131—21no—
249C2×C8×C131—44no—
250C4⋊C4×C131—24no—
251C4⋊C4×C131—24no—
252C4⋊C4×C131—24no—
253C4⋊C4×C131—21no—
254C4⋊C4×C131—21no—
255C4⋊C4×C131—21no—
256C4⋊C4×C131—21no—
257C4⋊C4×C131—21no—
258C4⋊C4×C131—21no—
259C4⋊C4×C131—21no—
260C4⋊C4×C131—21no—
261C4⋊C4×C131—21no—
262C4⋊C4×C131—21no—
263C4⋊C4×C131—42no—
264C4⋊C4×C131C22×C412yes—
265C4⋊C4×C131C22×C412yes—
266C22⋊C4×C131—24no—
267C22⋊C4×C131—24no—
268C22⋊C4×C131—24no—
269C22⋊C4×C131—24no—
270C22⋊C4×C131—42no—
271C22⋊C4×C131—81no—
272C22⋊C4×C131—81no—
273C22⋊C4×C131—81no—
274C22⋊C4×C131—81no—
275C42×C131—42no—
276C23×C131—21no—
277C23×C131—21no—
278C23×C131—21no—
279C23×C131—21no—
280C23×C131—21no—
281C23×C131—21no—
282C23×C131—21no—
283C23×C131—21no—
284C23×C131—21no—
285C23×C131—21no—
286C23×C131—21no—
287C23×C131—21no—
288C23×C131—21no—
289C23×C131—21no—
290C23×C131—21no—
291C23×C131—21no—
292C23×C131—21no—
293C23×C131—21no—
294C23×C131—22no—
295C23×C131—41no—
296C23×C131—41no—
297C23×C131—41no—
298C23×C131—41no—
299C23×C131—41no—
300C23×C131—41no—
301C23×C131C2×C22⋊C412yes—
302C23×C131C2×C22⋊C412yes—
303C23×C131C2×C22⋊C412yes—
304C23×C131C22×D411yescharacteristic
305Q8×C131—22no—
306Q8×C131—22no—
307Q8×C131—44no—
308Q8×C131—41no—
309Q8×C131—41no—
310D4×C131—22no—
311D4×C131—22no—
312D4×C131—44no—
313D4×C131—44no—
314D4×C131—44no—
315D4×C131—48no—
316D4×C131—41no—
317D4×C131—41no—
318D4×C131—84no—
319D4×C131—84no—
320C2×C4×C131—21no—
321C2×C4×C131—21no—
322C2×C4×C131—21no—
323C2×C4×C131—21no—
324C2×C4×C131—21no—
325C2×C4×C131—21no—
326C2×C4×C131—22no—
327C2×C4×C131—22no—
328C2×C4×C131—22no—
329C2×C4×C131—22no—
330C2×C4×C131—22no—
331C2×C4×C131—22no—
332C2×C4×C131—22no—
333C2×C4×C131—22no—
334C2×C4×C131—22no—
335C2×C4×C131—22no—
336C2×C4×C131—22no—
337C2×C4×C131—22no—
338C2×C4×C131—22no—
339C2×C4×C131—22no—
340C2×C4×C131—22no—
341C2×C4×C131—48no—
342C2×C4×C131—41no—
343C2×C4×C131—41no—
344C2×C4×C131—41no—
345C2×C4×C131—41no—
346C2×C4×C131—41no—
347C2×C4×C131—41no—
348C2×C4×C131—41no—
349C2×C4×C131—41no—
350C2×C4×C131—41no—
351C2×C4×C131—41no—
352C2×C4×C131—41no—
353C2×C4×C131—41no—
354C2×C4×C131—41no—
355C2×C4×C131—41no—
356C2×C4×C131—41no—
357C2×C4×C131—41no—
358C2×C4×C131—41no—
359C2×C4×C131—41no—
360C2×C4×C131—84no—
361C2×C4×C131—84no—
362C2×C4×C131C2×C22⋊C412yes—
363C2×C4×C131C2×C22⋊C412yes—
364C2×C4×C131C2×C22⋊C412yes—
365C2×C4×C131C23×C411yescharacteristic
366C2×C4×C131C22×D411yescharacteristic
367C2×C4×C131H(5,𝔽2)11yescharacteristic
368C2×C4×C131H(5,𝔽2)11yescharacteristic
369C2×C4×C131H(5,𝔽2)11yescharacteristic
370C2×C4×C131H(5,𝔽2)11yescharacteristic
371C8×C131—41no—
372C8×C131—41no—
373C8×C131—41no—
374C8×C131—41no—
375C22×C131—22no—
376C22×C131—22no—
377C22×C131—22no—
378C22×C131—22no—
379C22×C131—22no—
380C22×C131—22no—
381C22×C131—22no—
382C22×C131—22no—
383C22×C131—22no—
384C22×C131—41no—
385C22×C131—41no—
386C22×C131—41no—
387C22×C131—41no—
388C22×C131—41no—
389C22×C131—41no—
390C22×C131—41no—
391C22×C131—41no—
392C22×C131—41no—
393C22×C131—41no—
394C22×C131—41no—
395C22×C131—41no—
396C22×C131—42no—
397C22×C131—42no—
398C22×C131—42no—
399C22×C131—81no—
400C22×C131—81no—
401C22×C131—81no—
402C22×C131—81no—
403C22×C131C22×C22⋊C411yescharacteristic
404C22×C131#53411yescharacteristic
405C22×C131#53411yescharacteristic
406C22×C131#57611yescharacteristic
407C22×C131#57711yescharacteristic
408C22×C131#57711yescharacteristic
409C22×C131#57811yescharacteristic
410C4×C131—22no—
411C4×C131—22no—
412C4×C131—22no—
413C4×C131—42no—
414C4×C131—42no—
415C4×C131—42no—
416C4×C131—81no—
417C4×C131—81no—
418C4×C131—81no—
419C4×C131—81no—
420C4×C131#51811yescharacteristic
421C4×C131#51811yescharacteristic
422C4×C131#53411yescharacteristic
423C4×C131#53411yescharacteristic
424C2×C131—42no—
425C2×C131—42no—
426C2×C131—42no—
427C2×C131—82no—
428C2×C131#230811yescharacteristic
429C2×C131#289711yescharacteristic
430C2×C131#289811yescharacteristic
431C2×C131#319811yescharacteristic
432C2×C131#320111yescharacteristic
433C2×C131#320311yescharacteristic
434C2×C131#320411yescharacteristic
435#21772C13111yesmaximal, characteristic, direct product factor, Sylow
436C131#2177211yescharacteristic, direct product factor, Sylow
437C2×#537C2×C13111yescharacteristic
438C2×#408C2×C13111yescharacteristic, complemented
439#2311C2×C13111yescharacteristic, complemented
440#1895C2×C13111yescharacteristic, complemented
441#1894C2×C13111yescharacteristic, complemented
442#1893C2×C13111yescharacteristic, complemented
443#1892C2×C13111yescharacteristic, complemented
444#1875C2×C13111yescharacteristic, complemented
445#1874C2×C13111yescharacteristic, complemented
446#1873C2×C13111yescharacteristic, complemented
447#1872C2×C13111yescharacteristic, complemented
448#1824C2×C13111yescharacteristic, complemented
449#1823C2×C13111yescharacteristic, complemented
450#1788C2×C13111yescharacteristic, complemented
451#1788C2×C13111yescharacteristic, complemented
452C22×#41C22×C13111yescharacteristic
453C22×#41C22×C13111yescharacteristic
454C22×M16C22×C13111yescharacteristic
455C23×C8C22×C13111yescharacteristic
456#537—24no—
457#537C4×C13118yescomplemented
458C2×C22⋊Q8—21no—
459C2×C22⋊Q8C22×C13111yescharacteristic
460C2×C22⋊Q8C22×C13111yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C22×C13111yescharacteristic
465C2×#121C22×C13111yescharacteristic
466C2×#117C22×C13111yescharacteristic
467C22×C4⋊C4C22×C13111yescharacteristic
468C22×C4⋊C4C22×C13111yescharacteristic
469C2×#103C22×C13111yescharacteristic
470C2×#103C22×C13111yescharacteristic
471C2×#103C22×C13111yescharacteristic
472C2×#103C22×C13111yescharacteristic
473C2×#102C22×C13111yescharacteristic
474C2×#102C22×C13111yescharacteristic
475C2×#102C22×C13111yescharacteristic
476C2×#102C22×C13111yescharacteristic
477#408—24no—
478C2×C22⋊C8C22×C13111yescharacteristic
479C2×C22⋊C8C22×C13111yescharacteristic
480C2×C22⋊C8C22×C13111yescharacteristic
481C2×C22⋊C8C22×C13111yescharacteristic
482#391—21no—
483#390—21no—
484#386—21no—
485#386—21no—
486#380C22×C13111yescharacteristic
487#380C22×C13111yescharacteristic
488#380C22×C13111yescharacteristic
489#380C22×C13111yescharacteristic
490#340C22×C13111yescharacteristic
491#340C22×C13111yescharacteristic
492#340C22×C13111yescharacteristic
493#340C22×C13111yescharacteristic
494#340C22×C13111yescharacteristic
495#340C22×C13111yescharacteristic
496#340C22×C13111yescharacteristic
497#340C22×C13111yescharacteristic
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×C4×C13114yes—
508C2×#41C2×C4×C13114yescomplemented
509C2×#41D4×C13114yes—
510C22×Q8D4×C13111yescharacteristic
511C22×Q8C23×C13111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C13111yescharacteristic
516C22×D4D4×C13111yescharacteristic
517C22×D4D4×C13111yescharacteristic
518C22×D4C23×C13111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C13111yescharacteristic
523C23×C4C23×C13111yescharacteristic
524C23×C4C23×C13111yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C23×C13111yescharacteristic
532C22×C8C23×C13111yescharacteristic
533C22×C8C23×C13111yescharacteristic
534C22×C8C23×C13111yescharacteristic
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×C4×C13114yes—
539C22⋊Q8C2×C4×C13114yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×C4×C13114yes—
546#121C2×C4×C13114yescomplemented
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4C2×C4×C13114yescomplemented
557C2×C4⋊C4C23×C13111yescharacteristic
558C2×C4⋊C4C23×C13111yescharacteristic
559C2×C4⋊C4C23×C13111yescharacteristic
560C2×C4⋊C4C23×C13111yescharacteristic
561C2×C4⋊C4C23×C13111yescharacteristic
562C2×C4⋊C4C23×C13111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C42—21no—
573#103—41no—
574#103—41no—
575#103—41no—
576#103—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C13111yescharacteristic
591C24C2×D4×C13111yescharacteristic
592C24C2×D4×C13111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C13114yes—
609C2×Q8C22×C4×C13112yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C13114yes—
631C2×D4C22⋊C4×C13114yes—
632C2×D4C22⋊C4×C13114yes—
633C2×D4C22×C4×C13112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C13112yes—
663C22×C4C22×C4×C13112yes—
664C22×C4C22×C4×C13112yes—
665C22×C4C2×D4×C13111yescharacteristic
666C22×C4C2×D4×C13111yescharacteristic
667C22×C4C2×D4×C13111yescharacteristic
668C22×C4C2×D4×C13112yes—
669C22×C4C2×D4×C13112yes—
670C22×C4C2×D4×C13112yes—
671C22×C4C24×C13111yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C22×C4×C13112yes—
701C4⋊C4C22×C4×C13112yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C13112yes—
738C23C2×C22⋊C4×C13112yes—
739C23C2×C22⋊C4×C13112yes—
740C23C22×D4×C13111yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C13112yes—
799C2×C4C2×C22⋊C4×C13112yes—
800C2×C4C2×C22⋊C4×C13112yes—
801C2×C4C23×C4×C13111yescharacteristic
802C2×C4C22×D4×C13111yescharacteristic
803C2×C4H(5,𝔽2)×C13111yescharacteristic
804C2×C4H(5,𝔽2)×C13111yescharacteristic
805C2×C4H(5,𝔽2)×C13111yescharacteristic
806C2×C4H(5,𝔽2)×C13111yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C13111yescharacteristic
840C22#534×C13111yescharacteristic
841C22#534×C13111yescharacteristic
842C22#576×C13111yescharacteristic
843C22#577×C13111yescharacteristic
844C22#577×C13111yescharacteristic
845C22#578×C13111yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4#518×C13111yescharacteristic
857C4#518×C13111yescharacteristic
858C4#534×C13111yescharacteristic
859C4#534×C13111yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2#2308×C13111yescharacteristic
865C2#2897×C13111yescharacteristic
866C2#2898×C13111yescharacteristic
867C2#3198×C13111yescharacteristic
868C2#3201×C13111yescharacteristic
869C2#3203×C13111yescharacteristic
870C2#3204×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutatorC2×C4C23×C4×C131
Frattini, cosocleC22×C4C24×C131
prime radicalC2×#537×C131C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#408×C131C2semidirect
3. #2311×C131C2semidirect
4. #1895×C131C2semidirect
5. #1894×C131C2semidirect
6. #1893×C131C2semidirect
7. #1892×C131C2semidirect
8. #1875×C131C2semidirect
9. #1874×C131C2semidirect
10. #1873×C131C2semidirect
11. #1872×C131C2semidirect
12. #1824×C131C2semidirect
13. #1823×C131C2semidirect
14. #1788×C131C2semidirect
15. #1788×C131C2semidirect
21. #537×C131C4semidirect
72. C2×#41×C131C2×C4semidirect
103. C22⋊Q8×C131C2×C4semidirect
110. #121×C131C2×C4semidirect
120. C2×C4⋊C4×C131C2×C4semidirect
435. #21772C131direct (N × H)
436. C131#21772direct (N × H)
438. C2×#408C2×C131semidirect
439. #2311C2×C131semidirect
440. #1895C2×C131semidirect
441. #1894C2×C131semidirect
442. #1893C2×C131semidirect
443. #1892C2×C131semidirect
444. #1875C2×C131semidirect
445. #1874C2×C131semidirect
446. #1873C2×C131semidirect
447. #1872C2×C131semidirect
448. #1824C2×C131semidirect
449. #1823C2×C131semidirect
450. #1788C2×C131semidirect
451. #1788C2×C131semidirect
457. #537C4×C131semidirect
508. C2×#41C2×C4×C131semidirect
539. C22⋊Q8C2×C4×C131semidirect
546. #121C2×C4×C131semidirect
556. C2×C4⋊C4C2×C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1312
C2×#408×C1312
#2311×C1312
#1895×C1312
#1894×C1312
#1893×C1312
#1892×C1312
#1875×C1312
#1874×C1312
#1873×C1312
#1872×C1312
#1824×C1312
#1823×C1312
#1788×C1312
#21772131