Finite Group Databasebeta

← C131×#16290 #45702174

Subgroups — C131×#16290 #45702174

Order 33536.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C131C211yesmaximal, characteristic, complemented
2C2×#396×C131C211yesmaximal, characteristic, complemented
3C2×#394×C131C211yesmaximal, characteristic, complemented
4C2×#394×C131C211yesmaximal, characteristic, complemented
5C2×#394×C131C211yesmaximal, characteristic, complemented
6C2×#392×C131C211yesmaximal, characteristic
7C2×#390×C131C211yesmaximal, characteristic, complemented
8C2×#388×C131C211yesmaximal, characteristic, complemented
9#1444×C131C211yesmaximal, characteristic, complemented
10#1439×C131C211yesmaximal, characteristic, complemented
11#1439×C131C211yesmaximal, characteristic, complemented
12#1439×C131C211yesmaximal, characteristic, complemented
13#1438×C131C211yesmaximal, characteristic, complemented
14#1438×C131C211yesmaximal, characteristic, complemented
15#1436×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C23×D4×C131C2211yescharacteristic
19C22×C4⋊C4×C131C2211yescharacteristic
20C22×C4⋊C4×C131C2211yescharacteristic
21C22×C4⋊C4×C131C2211yescharacteristic
22C22×C4⋊C4×C131C2211yescharacteristic
23C22×C4⋊C4×C131C2211yescharacteristic
24C22×C4⋊C4×C131C2211yescharacteristic
25C22×C22⋊C4×C131C2211yescharacteristic
26C22×C22⋊C4×C131C2211yescharacteristic
27C22×C22⋊C4×C131C2211yescharacteristic
28C22×C22⋊C4×C131C2211yescharacteristic
29C22×C22⋊C4×C131C2211yescharacteristic
30C22×C22⋊C4×C131C2211yescharacteristic
31C22×C22⋊C4×C131C2211yescharacteristic
32C22×C22⋊C4×C131C2211yescharacteristic
33C22×C22⋊C4×C131C2211yescharacteristic
34C22×C22⋊C4×C131C2211yescharacteristic
35C22×C22⋊C4×C131C2211yescharacteristic
36C22×C22⋊C4×C131C2211yescharacteristic
37C22×C22⋊C4×C131C2211yescharacteristic
38C22×C22⋊C4×C131C2211yescharacteristic
39C22×C22⋊C4×C131C2211yescharacteristic
40C22×C42×C131C2211yescharacteristic
41#396×C131—24no—
42#396×C131—24no—
43#394×C131—24no—
44#394×C131—24no—
45#394×C131—24no—
46#392×C131—24no—
47#390×C131—24no—
48#388×C131—24no—
49C2×#95×C131C2211yescharacteristic
50C2×#95×C131C2211yescharacteristic
51C2×#95×C131C2211yescharacteristic
52C2×#95×C131C2211yescharacteristic
53C2×#95×C131C2211yescharacteristic
54C2×#95×C131C2211yescharacteristic
55C2×#95×C131C2211yescharacteristic
56C2×#95×C131C2211yescharacteristic
57C2×#95×C131C2211yescharacteristic
58C2×#95×C131C2211yescharacteristic
59C25×C131C2311yescharacteristic
60C25×C131C2311yescharacteristic
61C25×C131C2311yescharacteristic
62C22×D4×C131—22no—
63C22×D4×C131—22no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—22no—
67C22×D4×C131—22no—
68C22×D4×C131—22no—
69C22×D4×C131—22no—
70C22×D4×C131—22no—
71C22×D4×C131—22no—
72C22×D4×C131—22no—
73C22×D4×C131—41no—
74C22×D4×C131—41no—
75C22×D4×C131—41no—
76C22×D4×C131—41no—
77C22×D4×C131—41no—
78C22×D4×C131—41no—
79C22×D4×C131—41no—
80C22×D4×C131—41no—
81C22×D4×C131—41no—
82C22×D4×C131—41no—
83C23×C4×C131C2311yescharacteristic
84C23×C4×C131C2311yescharacteristic
85C23×C4×C131C2311yescharacteristic
86C23×C4×C131C2311yescharacteristic
87C23×C4×C131C2311yescharacteristic
88C23×C4×C131C2311yescharacteristic
89C23×C4×C131C2311yescharacteristic
90C23×C4×C131C2311yescharacteristic
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C23×C4×C131C2311yescharacteristic
94C23×C4×C131C2311yescharacteristic
95C2×C4⋊C4×C131—22no—
96C2×C4⋊C4×C131—22no—
97C2×C4⋊C4×C131—22no—
98C2×C4⋊C4×C131—22no—
99C2×C4⋊C4×C131—22no—
100C2×C4⋊C4×C131—22no—
101C2×C4⋊C4×C131—22no—
102C2×C4⋊C4×C131—22no—
103C2×C4⋊C4×C131—22no—
104C2×C4⋊C4×C131—22no—
105C2×C4⋊C4×C131—22no—
106C2×C4⋊C4×C131—22no—
107C2×C4⋊C4×C131—41no—
108C2×C4⋊C4×C131—41no—
109C2×C4⋊C4×C131—41no—
110C2×C4⋊C4×C131—41no—
111C2×C4⋊C4×C131—41no—
112C2×C4⋊C4×C131—41no—
113C2×C22⋊C4×C131—22no—
114C2×C22⋊C4×C131—22no—
115C2×C22⋊C4×C131—22no—
116C2×C22⋊C4×C131—22no—
117C2×C22⋊C4×C131—22no—
118C2×C22⋊C4×C131—22no—
119C2×C22⋊C4×C131—22no—
120C2×C22⋊C4×C131—22no—
121C2×C22⋊C4×C131—22no—
122C2×C22⋊C4×C131—22no—
123C2×C22⋊C4×C131—22no—
124C2×C22⋊C4×C131—22no—
125C2×C22⋊C4×C131—22no—
126C2×C22⋊C4×C131—22no—
127C2×C22⋊C4×C131—22no—
128C2×C22⋊C4×C131—22no—
129C2×C22⋊C4×C131—22no—
130C2×C22⋊C4×C131—22no—
131C2×C22⋊C4×C131—22no—
132C2×C22⋊C4×C131—22no—
133C2×C22⋊C4×C131—22no—
134C2×C22⋊C4×C131—22no—
135C2×C22⋊C4×C131—22no—
136C2×C22⋊C4×C131—22no—
137C2×C22⋊C4×C131—22no—
138C2×C22⋊C4×C131—22no—
139C2×C22⋊C4×C131—22no—
140C2×C22⋊C4×C131—41no—
141C2×C22⋊C4×C131—41no—
142C2×C22⋊C4×C131—41no—
143C2×C22⋊C4×C131—41no—
144C2×C22⋊C4×C131—41no—
145C2×C22⋊C4×C131—41no—
146C2×C22⋊C4×C131—41no—
147C2×C22⋊C4×C131—41no—
148C2×C22⋊C4×C131—41no—
149C2×C22⋊C4×C131—41no—
150C2×C22⋊C4×C131—41no—
151C2×C22⋊C4×C131—41no—
152C2×C22⋊C4×C131—41no—
153C2×C22⋊C4×C131—41no—
154C2×C22⋊C4×C131—41no—
155C2×C22⋊C4×C131—41no—
156C2×C22⋊C4×C131D414yes—
157C2×C22⋊C4×C131D414yescomplemented
158C2×C42×C131—22no—
159C2×C42×C131—22no—
160C2×C42×C131—41no—
161#95×C131—22no—
162#95×C131—22no—
163#95×C131—22no—
164#95×C131—22no—
165#95×C131—22no—
166#95×C131—41no—
167#95×C131—41no—
168#95×C131—41no—
169#95×C131D414yescomplemented
170#95×C131D414yescomplemented
171C24×C131—21no—
172C24×C131—21no—
173C24×C131—21no—
174C24×C131—21no—
175C24×C131—21no—
176C24×C131—21no—
177C24×C131—21no—
178C24×C131—21no—
179C24×C131—21no—
180C24×C131—21no—
181C24×C131—21no—
182C24×C131—21no—
183C24×C131—21no—
184C24×C131—21no—
185C24×C131—21no—
186C24×C131—21no—
187C24×C131—21no—
188C24×C131—21no—
189C24×C131—21no—
190C24×C131—21no—
191C24×C131—21no—
192C24×C131—21no—
193C24×C131—21no—
194C24×C131—21no—
195C24×C131—21no—
196C24×C131—21no—
197C24×C131—21no—
198C24×C131—21no—
199C24×C131—21no—
200C24×C131—21no—
201C24×C131—21no—
202C24×C131—21no—
203C24×C131—21no—
204C24×C131—21no—
205C24×C131—21no—
206C24×C131—21no—
207C24×C131—21no—
208C24×C131—21no—
209C24×C131—21no—
210C24×C131—21no—
211C24×C131—21no—
212C24×C131—21no—
213C24×C131C2×D412yes—
214C24×C131C2×D412yes—
215C24×C131#4112yes—
216C24×C131C2411yescharacteristic
217C2×D4×C131—28no—
218C2×D4×C131—44no—
219C2×D4×C131—44no—
220C2×D4×C131—44no—
221C2×D4×C131—44no—
222C2×D4×C131—44no—
223C2×D4×C131—44no—
224C2×D4×C131—44no—
225C2×D4×C131—44no—
226C2×D4×C131—44no—
227C2×D4×C131—44no—
228C2×D4×C131—44no—
229C2×D4×C131—44no—
230C2×D4×C131—44no—
231C2×D4×C131—44no—
232C2×D4×C131—44no—
233C2×D4×C131—44no—
234C2×D4×C131—44no—
235C2×D4×C131—44no—
236C2×D4×C131—44no—
237C2×D4×C131—44no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—21no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—21no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—21no—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—21no—
253C22×C4×C131—21no—
254C22×C4×C131—21no—
255C22×C4×C131—21no—
256C22×C4×C131—21no—
257C22×C4×C131—21no—
258C22×C4×C131—21no—
259C22×C4×C131—21no—
260C22×C4×C131—21no—
261C22×C4×C131—21no—
262C22×C4×C131—21no—
263C22×C4×C131—21no—
264C22×C4×C131—21no—
265C22×C4×C131—21no—
266C22×C4×C131—21no—
267C22×C4×C131—21no—
268C22×C4×C131—21no—
269C22×C4×C131—21no—
270C22×C4×C131—21no—
271C22×C4×C131—21no—
272C22×C4×C131—21no—
273C22×C4×C131—21no—
274C22×C4×C131—21no—
275C22×C4×C131—21no—
276C22×C4×C131—21no—
277C22×C4×C131—21no—
278C22×C4×C131—21no—
279C22×C4×C131—21no—
280C22×C4×C131—21no—
281C22×C4×C131—21no—
282C22×C4×C131—21no—
283C22×C4×C131—21no—
284C22×C4×C131—21no—
285C22×C4×C131—21no—
286C22×C4×C131—21no—
287C22×C4×C131—21no—
288C22×C4×C131—21no—
289C22×C4×C131—21no—
290C22×C4×C131—21no—
291C22×C4×C131—21no—
292C22×C4×C131—21no—
293C22×C4×C131—21no—
294C22×C4×C131—21no—
295C22×C4×C131—21no—
296C22×C4×C131—21no—
297C22×C4×C131—21no—
298C22×C4×C131—21no—
299C22×C4×C131—21no—
300C22×C4×C131—21no—
301C22×C4×C131—21no—
302C22×C4×C131—21no—
303C22×C4×C131—21no—
304C22×C4×C131—21no—
305C22×C4×C131—21no—
306C22×C4×C131—21no—
307C22×C4×C131—21no—
308C22×C4×C131—21no—
309C22×C4×C131—21no—
310C22×C4×C131C2×D412yes—
311C22×C4×C131C2×D412yes—
312C22×C4×C131C2×D412yes—
313C22×C4×C131C2×D412yes—
314C22×C4×C131C2×D412yes—
315C22×C4×C131C2×D412yes—
316C22×C4×C131C2×D412yes—
317C22×C4×C131C2×D412yes—
318C22×C4×C131C2×D412yes—
319C22×C4×C131C2×D412yes—
320C22×C4×C131#4112yes—
321C22×C4×C131#4112yes—
322C4⋊C4×C131—44no—
323C4⋊C4×C131—44no—
324C4⋊C4×C131—44no—
325C4⋊C4×C131—44no—
326C4⋊C4×C131—44no—
327C4⋊C4×C131—44no—
328C22⋊C4×C131—28no—
329C22⋊C4×C131—44no—
330C22⋊C4×C131—44no—
331C22⋊C4×C131—44no—
332C22⋊C4×C131—44no—
333C22⋊C4×C131—44no—
334C22⋊C4×C131—44no—
335C22⋊C4×C131—44no—
336C22⋊C4×C131—44no—
337C22⋊C4×C131—44no—
338C22⋊C4×C131—44no—
339C22⋊C4×C131—44no—
340C22⋊C4×C131—44no—
341C22⋊C4×C131—44no—
342C22⋊C4×C131—44no—
343C42×C131—44no—
344C23×C131—22no—
345C23×C131—22no—
346C23×C131—22no—
347C23×C131—22no—
348C23×C131—22no—
349C23×C131—22no—
350C23×C131—22no—
351C23×C131—22no—
352C23×C131—22no—
353C23×C131—22no—
354C23×C131—22no—
355C23×C131—22no—
356C23×C131—22no—
357C23×C131—22no—
358C23×C131—22no—
359C23×C131—22no—
360C23×C131—22no—
361C23×C131—22no—
362C23×C131—22no—
363C23×C131—22no—
364C23×C131—22no—
365C23×C131—41no—
366C23×C131—41no—
367C23×C131—41no—
368C23×C131—41no—
369C23×C131—41no—
370C23×C131—41no—
371C23×C131—41no—
372C23×C131—41no—
373C23×C131—41no—
374C23×C131—41no—
375C23×C131—41no—
376C23×C131—41no—
377C23×C131—41no—
378C23×C131—41no—
379C23×C131—41no—
380C23×C131—41no—
381C23×C131—41no—
382C23×C131—41no—
383C23×C131—41no—
384C23×C131—41no—
385C23×C131—41no—
386C23×C131—41no—
387C23×C131—41no—
388C23×C131—41no—
389C23×C131—41no—
390C23×C131—41no—
391C23×C131—41no—
392C23×C131—41no—
393C23×C131—41no—
394C23×C131—41no—
395C23×C131—41no—
396C23×C131—41no—
397C23×C131—41no—
398C23×C131—41no—
399C23×C131—41no—
400C23×C131—41no—
401C23×C131—41no—
402C23×C131—41no—
403C23×C131—41no—
404C23×C131—41no—
405C23×C131—41no—
406C23×C131—41no—
407C23×C131—41no—
408C23×C131—41no—
409C23×C131—41no—
410C23×C131—41no—
411C23×C131—41no—
412C23×C131—41no—
413C23×C131—41no—
414C23×C131—41no—
415C23×C131—41no—
416C23×C131—41no—
417C23×C131—41no—
418C23×C131—41no—
419C23×C131—41no—
420C23×C131—41no—
421C23×C131—41no—
422C23×C131—41no—
423C23×C131—41no—
424C23×C131—41no—
425C23×C131—41no—
426C23×C131—41no—
427C23×C131—41no—
428C23×C131—41no—
429C23×C131—41no—
430C23×C131—41no—
431C23×C131—41no—
432C23×C131—41no—
433C23×C131—41no—
434C23×C131—41no—
435C23×C131—41no—
436C23×C131—41no—
437C23×C131—41no—
438C23×C131—41no—
439C23×C131—41no—
440C23×C131—41no—
441C23×C131—41no—
442C23×C131—41no—
443C23×C131—41no—
444C23×C131—41no—
445C23×C131—41no—
446C23×C131—41no—
447C23×C131—41no—
448C23×C131—41no—
449C23×C131C22×D411yescharacteristic
450C23×C131C22×D411yescharacteristic
451C23×C131C22×D411yescharacteristic
452C23×C131C22×D411yescharacteristic
453C23×C131C2×#4111yescharacteristic
454C23×C131C2×#4111yescharacteristic
455C23×C131C2×#4111yescharacteristic
456C23×C131H(5,𝔽2)11yescharacteristic
457C23×C131H(5,𝔽2)11yescharacteristic
458C23×C131H(5,𝔽2)11yescharacteristic
459C23×C131H(5,𝔽2)11yescharacteristic
460C23×C131H(5,𝔽2)11yescharacteristic
461C23×C131H(5,𝔽2)11yescharacteristic
462C23×C1312−1+411yescharacteristic
463C23×C1312−1+411yescharacteristic
464D4×C131—416no—
465D4×C131—416no—
466D4×C131—416no—
467C2×C4×C131—22no—
468C2×C4×C131—22no—
469C2×C4×C131—22no—
470C2×C4×C131—22no—
471C2×C4×C131—22no—
472C2×C4×C131—22no—
473C2×C4×C131—22no—
474C2×C4×C131—22no—
475C2×C4×C131—22no—
476C2×C4×C131—22no—
477C2×C4×C131—22no—
478C2×C4×C131—22no—
479C2×C4×C131—22no—
480C2×C4×C131—22no—
481C2×C4×C131—22no—
482C2×C4×C131—22no—
483C2×C4×C131—22no—
484C2×C4×C131—22no—
485C2×C4×C131—22no—
486C2×C4×C131—22no—
487C2×C4×C131—22no—
488C2×C4×C131—22no—
489C2×C4×C131—22no—
490C2×C4×C131—22no—
491C2×C4×C131—22no—
492C2×C4×C131—22no—
493C2×C4×C131—22no—
494C2×C4×C131—22no—
495C2×C4×C131—22no—
496C2×C4×C131—22no—
497C2×C4×C131—22no—
498C2×C4×C131—22no—
499C2×C4×C131—22no—
500C2×C4×C131—41no—
501C2×C4×C131—41no—
502C2×C4×C131—41no—
503C2×C4×C131—41no—
504C2×C4×C131—41no—
505C2×C4×C131—41no—
506C2×C4×C131—41no—
507C2×C4×C131—41no—
508C2×C4×C131—41no—
509C2×C4×C131—41no—
510C2×C4×C131—41no—
511C2×C4×C131—41no—
512C2×C4×C131—41no—
513C2×C4×C131—41no—
514C2×C4×C131—41no—
515C2×C4×C131—41no—
516C2×C4×C131—41no—
517C2×C4×C131—41no—
518C2×C4×C131—41no—
519C2×C4×C131—41no—
520C2×C4×C131—41no—
521C2×C4×C131—41no—
522C2×C4×C131—41no—
523C2×C4×C131—41no—
524C2×C4×C131—41no—
525C2×C4×C131—41no—
526C2×C4×C131—41no—
527C2×C4×C131—41no—
528C2×C4×C131—41no—
529C2×C4×C131—41no—
530C2×C4×C131—41no—
531C2×C4×C131—41no—
532C2×C4×C131—41no—
533C2×C4×C131—41no—
534C2×C4×C131—41no—
535C2×C4×C131—41no—
536C2×C4×C131—41no—
537C2×C4×C131—41no—
538C2×C4×C131—41no—
539C2×C4×C131—41no—
540C2×C4×C131—41no—
541C2×C4×C131—41no—
542C2×C4×C131—41no—
543C2×C4×C131—41no—
544C2×C4×C131—41no—
545C2×C4×C131—41no—
546C2×C4×C131—41no—
547C2×C4×C131—41no—
548C2×C4×C131—41no—
549C2×C4×C131—41no—
550C2×C4×C131#12114yes—
551C22×C131—42no—
552C22×C131—42no—
553C22×C131—42no—
554C22×C131—42no—
555C22×C131—42no—
556C22×C131—42no—
557C22×C131—42no—
558C22×C131—42no—
559C22×C131—42no—
560C22×C131—42no—
561C22×C131—42no—
562C22×C131—42no—
563C22×C131—42no—
564C22×C131—42no—
565C22×C131—42no—
566C22×C131—42no—
567C22×C131—42no—
568C22×C131—42no—
569C22×C131—42no—
570C22×C131—42no—
571C22×C131—42no—
572C22×C131—81no—
573C22×C131—81no—
574C22×C131—81no—
575C22×C131—81no—
576C22×C131—81no—
577C22×C131—81no—
578C22×C131—81no—
579C22×C131—81no—
580C22×C131—81no—
581C22×C131—81no—
582C22×C131—81no—
583C22×C131—81no—
584C22×C131—81no—
585C22×C131—81no—
586C22×C131—81no—
587C22×C131—81no—
588C22×C131—81no—
589C22×C131—81no—
590C22×C131—81no—
591C22×C131—81no—
592C22×C131—81no—
593C22×C131—81no—
594C22×C131—81no—
595C22×C131—81no—
596C22×C131C2×#12111yescharacteristic
597C22×C131#52511yescharacteristic
598C22×C131#53211yescharacteristic
599C22×C131#53411yescharacteristic
600C22×C131#53511yescharacteristic
601C22×C131#53511yescharacteristic
602C22×C131#53611yescharacteristic
603C22×C131#53711yescharacteristic
604C22×C131#53711yescharacteristic
605C22×C131#53711yescharacteristic
606C22×C131#53711yescharacteristic
607C22×C131#53811yescharacteristic
608C22×C131#53811yescharacteristic
609C22×C131#53811yescharacteristic
610C22×C131#53911yescharacteristic
611C22×C131#54011yescharacteristic
612C22×C131#54211yescharacteristic
613C22×C131#54211yescharacteristic
614C22×C131#54211yescharacteristic
615C22×C131D4211yescharacteristic
616C22×C131D4211yescharacteristic
617C22×C131D4211yescharacteristic
618C22×C131D4211yescharacteristic
619C22×C131D4211yescharacteristic
620C22×C131#54611yescharacteristic
621C22×C131#54611yescharacteristic
622C22×C131#54611yescharacteristic
623C22×C131#54711yescharacteristic
624C22×C131#54811yescharacteristic
625C22×C131#55011yescharacteristic
626C22×C131#55111yescharacteristic
627C22×C131#56011yescharacteristic
628C22×C131#56011yescharacteristic
629C22×C131#56211yescharacteristic
630C22×C131#56211yescharacteristic
631C4×C131—24no—
632C4×C131—42no—
633C4×C131—42no—
634C4×C131—42no—
635C4×C131—42no—
636C4×C131—42no—
637C4×C131—42no—
638C4×C131—42no—
639C4×C131—42no—
640C4×C131—42no—
641C4×C131—81no—
642C4×C131—81no—
643C2×C131—82no—
644C2×C131—82no—
645C2×C131—82no—
646C2×C131#242411yescharacteristic
647C2×C131#242811yescharacteristic
648C2×C131#246111yescharacteristic
649C2×C131#262011yescharacteristic
650C2×C131#263011yescharacteristic
651C2×C131#266211yescharacteristic
652C2×C131#266911yescharacteristic
653C2×C131#267211yescharacteristic
654C2×C131#267511yescharacteristic
655C2×C131#267611yescharacteristic
656C2×C131#268111yescharacteristic
657C2×C131#268211yescharacteristic
658C2×C131#268511yescharacteristic
659C2×C131#270511yescharacteristic
660C2×C131#282911yescharacteristic
661#16290C13111yesmaximal, characteristic, direct product factor, Sylow
662C131#1629011yescharacteristic, direct product factor, Sylow
663C2×#396C2×C13111yescharacteristic, complemented
664C2×#396C2×C13111yescharacteristic, complemented
665C2×#394C2×C13111yescharacteristic, complemented
666C2×#394C2×C13111yescharacteristic, complemented
667C2×#394C2×C13111yescharacteristic, complemented
668C2×#392C2×C13111yescharacteristic
669C2×#390C2×C13111yescharacteristic, complemented
670C2×#388C2×C13111yescharacteristic, complemented
671#1444C2×C13111yescharacteristic, complemented
672#1439C2×C13111yescharacteristic, complemented
673#1439C2×C13111yescharacteristic, complemented
674#1439C2×C13111yescharacteristic, complemented
675#1438C2×C13111yescharacteristic, complemented
676#1438C2×C13111yescharacteristic, complemented
677#1436C2×C13111yescharacteristic, complemented
678C23×D4C22×C13111yescharacteristic
679C23×D4C22×C13111yescharacteristic
680C23×D4C22×C13111yescharacteristic
681C22×C4⋊C4C22×C13111yescharacteristic
682C22×C4⋊C4C22×C13111yescharacteristic
683C22×C4⋊C4C22×C13111yescharacteristic
684C22×C4⋊C4C22×C13111yescharacteristic
685C22×C4⋊C4C22×C13111yescharacteristic
686C22×C4⋊C4C22×C13111yescharacteristic
687C22×C22⋊C4C22×C13111yescharacteristic
688C22×C22⋊C4C22×C13111yescharacteristic
689C22×C22⋊C4C22×C13111yescharacteristic
690C22×C22⋊C4C22×C13111yescharacteristic
691C22×C22⋊C4C22×C13111yescharacteristic
692C22×C22⋊C4C22×C13111yescharacteristic
693C22×C22⋊C4C22×C13111yescharacteristic
694C22×C22⋊C4C22×C13111yescharacteristic
695C22×C22⋊C4C22×C13111yescharacteristic
696C22×C22⋊C4C22×C13111yescharacteristic
697C22×C22⋊C4C22×C13111yescharacteristic
698C22×C22⋊C4C22×C13111yescharacteristic
699C22×C22⋊C4C22×C13111yescharacteristic
700C22×C22⋊C4C22×C13111yescharacteristic
701C22×C22⋊C4C22×C13111yescharacteristic
702C22×C42C22×C13111yescharacteristic
703#396—24no—
704#396—24no—
705#394—24no—
706#394—24no—
707#394—24no—
708#392—24no—
709#390—24no—
710#388—24no—
711C2×#95C22×C13111yescharacteristic
712C2×#95C22×C13111yescharacteristic
713C2×#95C22×C13111yescharacteristic
714C2×#95C22×C13111yescharacteristic
715C2×#95C22×C13111yescharacteristic
716C2×#95C22×C13111yescharacteristic
717C2×#95C22×C13111yescharacteristic
718C2×#95C22×C13111yescharacteristic
719C2×#95C22×C13111yescharacteristic
720C2×#95C22×C13111yescharacteristic
721C25C23×C13111yescharacteristic
722C25C23×C13111yescharacteristic
723C25C23×C13111yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C23×C4C23×C13111yescharacteristic
746C23×C4C23×C13111yescharacteristic
747C23×C4C23×C13111yescharacteristic
748C23×C4C23×C13111yescharacteristic
749C23×C4C23×C13111yescharacteristic
750C23×C4C23×C13111yescharacteristic
751C23×C4C23×C13111yescharacteristic
752C23×C4C23×C13111yescharacteristic
753C23×C4C23×C13111yescharacteristic
754C23×C4C23×C13111yescharacteristic
755C23×C4C23×C13111yescharacteristic
756C23×C4C23×C13111yescharacteristic
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—41no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4—41no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4D4×C13114yes—
819C2×C22⋊C4D4×C13114yescomplemented
820C2×C42—22no—
821C2×C42—22no—
822C2×C42—41no—
823#95—22no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—41no—
829#95—41no—
830#95—41no—
831#95D4×C13114yescomplemented
832#95D4×C13114yescomplemented
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24C2×D4×C13112yes—
876C24C2×D4×C13112yes—
877C24#41×C13112yes—
878C24C24×C13111yescharacteristic
879C2×D4—28no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4C2×D4×C13112yes—
973C22×C4C2×D4×C13112yes—
974C22×C4C2×D4×C13112yes—
975C22×C4C2×D4×C13112yes—
976C22×C4C2×D4×C13112yes—
977C22×C4C2×D4×C13112yes—
978C22×C4C2×D4×C13112yes—
979C22×C4C2×D4×C13112yes—
980C22×C4C2×D4×C13112yes—
981C22×C4C2×D4×C13112yes—
982C22×C4#41×C13112yes—
983C22×C4#41×C13112yes—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C22⋊C4—28no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C42—44no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23C22×D4×C13111yescharacteristic
1112C23C22×D4×C13111yescharacteristic
1113C23C22×D4×C13111yescharacteristic
1114C23C22×D4×C13111yescharacteristic
1115C23C2×#41×C13111yescharacteristic
1116C23C2×#41×C13111yescharacteristic
1117C23C2×#41×C13111yescharacteristic
1118C23H(5,𝔽2)×C13111yescharacteristic
1119C23H(5,𝔽2)×C13111yescharacteristic
1120C23H(5,𝔽2)×C13111yescharacteristic
1121C23H(5,𝔽2)×C13111yescharacteristic
1122C23H(5,𝔽2)×C13111yescharacteristic
1123C23H(5,𝔽2)×C13111yescharacteristic
1124C232−1+4×C13111yescharacteristic
1125C232−1+4×C13111yescharacteristic
1126D4—416no—
1127D4—416no—
1128D4—416no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4#121×C13114yes—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22C2×#121×C13111yescharacteristic
1259C22#525×C13111yescharacteristic
1260C22#532×C13111yescharacteristic
1261C22#534×C13111yescharacteristic
1262C22#535×C13111yescharacteristic
1263C22#535×C13111yescharacteristic
1264C22#536×C13111yescharacteristic
1265C22#537×C13111yescharacteristic
1266C22#537×C13111yescharacteristic
1267C22#537×C13111yescharacteristic
1268C22#537×C13111yescharacteristic
1269C22#538×C13111yescharacteristic
1270C22#538×C13111yescharacteristic
1271C22#538×C13111yescharacteristic
1272C22#539×C13111yescharacteristic
1273C22#540×C13111yescharacteristic
1274C22#542×C13111yescharacteristic
1275C22#542×C13111yescharacteristic
1276C22#542×C13111yescharacteristic
1277C22D42×C13111yescharacteristic
1278C22D42×C13111yescharacteristic
1279C22D42×C13111yescharacteristic
1280C22D42×C13111yescharacteristic
1281C22D42×C13111yescharacteristic
1282C22#546×C13111yescharacteristic
1283C22#546×C13111yescharacteristic
1284C22#546×C13111yescharacteristic
1285C22#547×C13111yescharacteristic
1286C22#548×C13111yescharacteristic
1287C22#550×C13111yescharacteristic
1288C22#551×C13111yescharacteristic
1289C22#560×C13111yescharacteristic
1290C22#560×C13111yescharacteristic
1291C22#562×C13111yescharacteristic
1292C22#562×C13111yescharacteristic
1293C4—24no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—81no—
1304C4—81no—
1305C2—82no—
1306C2—82no—
1307C2—82no—
1308C2#2424×C13111yescharacteristic
1309C2#2428×C13111yescharacteristic
1310C2#2461×C13111yescharacteristic
1311C2#2620×C13111yescharacteristic
1312C2#2630×C13111yescharacteristic
1313C2#2662×C13111yescharacteristic
1314C2#2669×C13111yescharacteristic
1315C2#2672×C13111yescharacteristic
1316C2#2675×C13111yescharacteristic
1317C2#2676×C13111yescharacteristic
1318C2#2681×C13111yescharacteristic
1319C2#2682×C13111yescharacteristic
1320C2#2685×C13111yescharacteristic
1321C2#2705×C13111yescharacteristic
1322C2#2829×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutator, Frattini, cosocleC24C24×C131
prime radicalC2×#392×C131C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#396×C131C2semidirect
2. C2×#396×C131C2semidirect
3. C2×#394×C131C2semidirect
4. C2×#394×C131C2semidirect
5. C2×#394×C131C2semidirect
7. C2×#390×C131C2semidirect
8. C2×#388×C131C2semidirect
9. #1444×C131C2semidirect
10. #1439×C131C2semidirect
11. #1439×C131C2semidirect
12. #1439×C131C2semidirect
13. #1438×C131C2semidirect
14. #1438×C131C2semidirect
15. #1436×C131C2semidirect
157. C2×C22⋊C4×C131D4semidirect
169. #95×C131D4semidirect
170. #95×C131D4semidirect
661. #16290C131direct (N × H)
662. C131#16290direct (N × H)
663. C2×#396C2×C131semidirect
664. C2×#396C2×C131semidirect
665. C2×#394C2×C131semidirect
666. C2×#394C2×C131semidirect
667. C2×#394C2×C131semidirect
669. C2×#390C2×C131semidirect
670. C2×#388C2×C131semidirect
671. #1444C2×C131semidirect
672. #1439C2×C131semidirect
673. #1439C2×C131semidirect
674. #1439C2×C131semidirect
675. #1438C2×C131semidirect
676. #1438C2×C131semidirect
677. #1436C2×C131semidirect
819. C2×C22⋊C4D4×C131semidirect
831. #95D4×C131semidirect
832. #95D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C1312
C2×#394×C1312
C2×#392×C1312
C2×#390×C1312
C2×#388×C1312
#1444×C1312
#1439×C1312
#1438×C1312
#1436×C1312
#16290131