Finite Group Databasebeta

← C131×#14363 #45700247

Subgroups — C131×#14363 #45700247

Order 33536.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C131C211yesmaximal, characteristic
2C2×#390×C131C211yesmaximal, characteristic, complemented
3C2×#386×C131C211yesmaximal, characteristic, complemented
4C2×#386×C131C211yesmaximal, characteristic, complemented
5C2×#381×C131C211yesmaximal, characteristic, complemented
6#1441×C131C211yesmaximal, characteristic, complemented
7#1440×C131C211yesmaximal, characteristic, complemented
8#1439×C131C211yesmaximal, characteristic, complemented
9#1438×C131C211yesmaximal, characteristic, complemented
10#1438×C131C211yesmaximal, characteristic, complemented
11#1438×C131C211yesmaximal, characteristic, complemented
12#1437×C131C211yesmaximal, characteristic, complemented
13#1436×C131C211yesmaximal, characteristic, complemented
14C22⋊#95×C131C211yesmaximal, characteristic, complemented
15C22⋊#95×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C23×D4×C131C2211yescharacteristic
19C24×C4×C131C2211yescharacteristic
20C24×C4×C131C2211yescharacteristic
21C2×#121×C131—24no—
22C2×#121×C131—24no—
23C2×#121×C131C418yescomplemented
24C22×C4⋊C4×C131C2211yescharacteristic
25C22×C4⋊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×C42×C131C2211yescharacteristic
40#390×C131—24no—
41#386×C131—24no—
42#386×C131—24no—
43#381×C131—24no—
44C2×#95×C131C2211yescharacteristic
45C2×#95×C131C2211yescharacteristic
46C2×#95×C131C2211yescharacteristic
47C2×#95×C131C2211yescharacteristic
48C2×#95×C131C2211yescharacteristic
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
58C25×C131C2311yescharacteristic
59C25×C131C2311yescharacteristic
60C25×C131C2311yescharacteristic
61C22×D4×C131—22no—
62C22×D4×C131—22no—
63C22×D4×C131—22no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—22no—
67C22×D4×C131—41no—
68C22×D4×C131—41no—
69C22×D4×C131—41no—
70C22×D4×C131—41no—
71C22×D4×C131—41no—
72C22×D4×C131—41no—
73C22×D4×C131—41no—
74C22×D4×C131—41no—
75C22×D4×C131—41no—
76C22×D4×C131—41no—
77C22×D4×C131C2×C414yes—
78C22×D4×C131C2×C414yes—
79C22×D4×C131C2×C414yescomplemented
80C22×D4×C131D414yes—
81C22×D4×C131D414yes—
82C23×C4×C131—22no—
83C23×C4×C131—22no—
84C23×C4×C131—22no—
85C23×C4×C131—22no—
86C23×C4×C131—22no—
87C23×C4×C131—22no—
88C23×C4×C131—22no—
89C23×C4×C131—41no—
90C23×C4×C131—41no—
91C23×C4×C131—41no—
92C23×C4×C131—41no—
93C23×C4×C131—41no—
94C23×C4×C131—41no—
95C23×C4×C131C2×C414yescomplemented
96C23×C4×C131C2311yescharacteristic
97C23×C4×C131C2311yescharacteristic
98C23×C4×C131C2311yescharacteristic
99C23×C4×C131C2311yescharacteristic
100C23×C4×C131C2311yescharacteristic
101C23×C4×C131C2311yescharacteristic
102C23×C4×C131C2311yescharacteristic
103C23×C4×C131C2311yescharacteristic
104C23×C4×C131C2311yescharacteristic
105C23×C4×C131C2311yescharacteristic
106C23×C4×C131C2311yescharacteristic
107C23×C4×C131C2311yescharacteristic
108#121×C131—232no—
109C2×C4⋊C4×C131—22no—
110C2×C4⋊C4×C131—22no—
111C2×C4⋊C4×C131—22no—
112C2×C4⋊C4×C131—41no—
113C2×C4⋊C4×C131—41no—
114C2×C4⋊C4×C131C2×C414yescomplemented
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—41no—
137C2×C22⋊C4×C131—41no—
138C2×C22⋊C4×C131—41no—
139C2×C22⋊C4×C131—41no—
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×C131C2×C414yes—
153C2×C22⋊C4×C131C2×C414yescomplemented
154C2×C42×C131—22no—
155C2×C42×C131—41no—
156C2×C42×C131—41no—
157#95×C131—22no—
158#95×C131—22no—
159#95×C131—22no—
160#95×C131—22no—
161#95×C131—22no—
162#95×C131—22no—
163#95×C131—22no—
164#95×C131—41no—
165#95×C131—41no—
166#95×C131—41no—
167#95×C131—41no—
168#95×C131—41no—
169#95×C131—41no—
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×C131C22×C412yes—
210C24×C131C22×C412yes—
211C24×C131C22×C412yes—
212C24×C131C2×D412yes—
213C24×C131C2×D412yes—
214C24×C131C2×D412yes—
215C24×C131C2×D412yes—
216C24×C131C2411yescharacteristic
217C2×D4×C131—28no—
218C2×D4×C131—28no—
219C2×D4×C131—28no—
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×C131C22⋊C4116yescomplemented
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—28no—
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—28no—
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×C131—21no—
311C22×C4×C131—21no—
312C22×C4×C131—44no—
313C22×C4×C131—44no—
314C22×C4×C131—44no—
315C22×C4×C131—44no—
316C22×C4×C131—44no—
317C22×C4×C131—44no—
318C22×C4×C131—44no—
319C22×C4×C131—44no—
320C22×C4×C131—44no—
321C22×C4×C131—44no—
322C22×C4×C131—44no—
323C22×C4×C131—44no—
324C22×C4×C131C22×C412yes—
325C22×C4×C131C22×C412yes—
326C22×C4×C131C22×C412yes—
327C22×C4×C131C22×C412yes—
328C22×C4×C131C2×D412yes—
329C22×C4×C131C2×D412yes—
330C22×C4×C131C2×D412yes—
331C22×C4×C131C2×D412yes—
332C22×C4×C131C2×D412yes—
333C22×C4×C131#4112yes—
334C22×C4×C131#4112yes—
335C22×C4×C131#4112yes—
336C4⋊C4×C131—28no—
337C4⋊C4×C131—44no—
338C22⋊C4×C131—28no—
339C22⋊C4×C131—28no—
340C22⋊C4×C131—44no—
341C22⋊C4×C131—44no—
342C22⋊C4×C131—44no—
343C22⋊C4×C131—44no—
344C22⋊C4×C131—44no—
345C22⋊C4×C131—44no—
346C22⋊C4×C131—44no—
347C22⋊C4×C131—44no—
348C22⋊C4×C131—44no—
349C22⋊C4×C131—44no—
350C22⋊C4×C131—44no—
351C42×C131—44no—
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—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—22no—
387C23×C131—22no—
388C23×C131—22no—
389C23×C131—22no—
390C23×C131—22no—
391C23×C131—22no—
392C23×C131—22no—
393C23×C131—22no—
394C23×C131—22no—
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×C131—41no—
450C23×C131—41no—
451C23×C131—41no—
452C23×C131—41no—
453C23×C131—41no—
454C23×C131—41no—
455C23×C131C2×C22⋊C414yes—
456C23×C131C2×C22⋊C414yes—
457C23×C131C23×C411yescharacteristic
458C23×C131C22×D411yescharacteristic
459C23×C131C22×D411yescharacteristic
460C23×C131C22×D411yescharacteristic
461C23×C131C2×#4111yescharacteristic
462C23×C131C2×#4111yescharacteristic
463C23×C131C2×#4111yescharacteristic
464C23×C131H(5,𝔽2)11yescharacteristic
465C23×C131H(5,𝔽2)11yescharacteristic
466C23×C131H(5,𝔽2)11yescharacteristic
467C23×C131H(5,𝔽2)11yescharacteristic
468C23×C131H(5,𝔽2)11yescharacteristic
469C23×C131H(5,𝔽2)11yescharacteristic
470C23×C131H(5,𝔽2)11yescharacteristic
471C23×C1312−1+411yescharacteristic
472D4×C131—416no—
473D4×C131—416no—
474D4×C131—416no—
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—22no—
501C2×C4×C131—22no—
502C2×C4×C131—22no—
503C2×C4×C131—22no—
504C2×C4×C131—22no—
505C2×C4×C131—416no—
506C2×C4×C131—416no—
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—41no—
551C2×C4×C131—41no—
552C2×C4×C131—41no—
553C2×C4×C131—41no—
554C2×C4×C131—41no—
555C2×C4×C131—41no—
556C2×C4×C131—41no—
557C2×C4×C131—41no—
558C2×C4×C131—41no—
559C2×C4×C131C2×C22⋊C414yes—
560C2×C4×C131C4×D414yes—
561C22×C131—24no—
562C22×C131—24no—
563C22×C131—24no—
564C22×C131—24no—
565C22×C131—24no—
566C22×C131—24no—
567C22×C131—42no—
568C22×C131—42no—
569C22×C131—42no—
570C22×C131—42no—
571C22×C131—42no—
572C22×C131—42no—
573C22×C131—42no—
574C22×C131—42no—
575C22×C131—42no—
576C22×C131—42no—
577C22×C131—42no—
578C22×C131—42no—
579C22×C131—42no—
580C22×C131—42no—
581C22×C131—42no—
582C22×C131—42no—
583C22×C131—42no—
584C22×C131—42no—
585C22×C131—42no—
586C22×C131—42no—
587C22×C131—42no—
588C22×C131—42no—
589C22×C131—42no—
590C22×C131—42no—
591C22×C131—42no—
592C22×C131—42no—
593C22×C131—42no—
594C22×C131—42no—
595C22×C131—42no—
596C22×C131—42no—
597C22×C131—42no—
598C22×C131—81no—
599C22×C131—81no—
600C22×C131—81no—
601C22×C131—81no—
602C22×C131—81no—
603C22×C131—81no—
604C22×C131—81no—
605C22×C131—81no—
606C22×C131C22×C22⋊C411yescharacteristic
607C22×C131C2×C4×D411yescharacteristic
608C22×C131C4×#4111yescharacteristic
609C22×C131#51811yescharacteristic
610C22×C131#51811yescharacteristic
611C22×C131#51811yescharacteristic
612C22×C131#52011yescharacteristic
613C22×C131#53411yescharacteristic
614C22×C131#53411yescharacteristic
615C22×C131#53411yescharacteristic
616C22×C131#53411yescharacteristic
617C22×C131#53511yescharacteristic
618C22×C131#53711yescharacteristic
619C22×C131#53811yescharacteristic
620C22×C131#53811yescharacteristic
621C22×C131#54011yescharacteristic
622C22×C131#54011yescharacteristic
623C22×C131#54011yescharacteristic
624C22×C131#54211yescharacteristic
625C22×C131D4211yescharacteristic
626C22×C131D4211yescharacteristic
627C22×C131#54611yescharacteristic
628C22×C131#54611yescharacteristic
629C22×C131#54611yescharacteristic
630C22×C131#54611yescharacteristic
631C22×C131#54611yescharacteristic
632C22×C131#54711yescharacteristic
633C22×C131#54711yescharacteristic
634C22×C131#55011yescharacteristic
635C22×C131#55311yescharacteristic
636C22×C131#55511yescharacteristic
637C22×C131#56011yescharacteristic
638C22×C131#56011yescharacteristic
639C22×C131#56211yescharacteristic
640C22×C131#56211yescharacteristic
641C4×C131—24no—
642C4×C131—24no—
643C4×C131—42no—
644C4×C131—42no—
645C4×C131—42no—
646C4×C131—42no—
647C4×C131—42no—
648C4×C131—42no—
649C4×C131—81no—
650C4×C131—81no—
651C4×C131—81no—
652C4×C131—81no—
653C2×C131—44no—
654C2×C131—44no—
655C2×C131—82no—
656C2×C131#230811yescharacteristic
657C2×C131#232411yescharacteristic
658C2×C131#233311yescharacteristic
659C2×C131D4×C22⋊C411yescharacteristic
660C2×C131#233911yescharacteristic
661C2×C131#236311yescharacteristic
662C2×C131#237711yescharacteristic
663C2×C131#267111yescharacteristic
664C2×C131#267311yescharacteristic
665C2×C131#267811yescharacteristic
666C2×C131#268211yescharacteristic
667C2×C131#268611yescharacteristic
668C2×C131#268811yescharacteristic
669C2×C131#269911yescharacteristic
670C2×C131#270111yescharacteristic
671#14363C13111yesmaximal, characteristic, direct product factor, Sylow
672C131#1436311yescharacteristic, direct product factor, Sylow
673C22×#121C2×C13111yescharacteristic
674C2×#390C2×C13111yescharacteristic, complemented
675C2×#386C2×C13111yescharacteristic, complemented
676C2×#386C2×C13111yescharacteristic, complemented
677C2×#381C2×C13111yescharacteristic, complemented
678#1441C2×C13111yescharacteristic, complemented
679#1440C2×C13111yescharacteristic, complemented
680#1439C2×C13111yescharacteristic, complemented
681#1438C2×C13111yescharacteristic, complemented
682#1438C2×C13111yescharacteristic, complemented
683#1438C2×C13111yescharacteristic, complemented
684#1437C2×C13111yescharacteristic, complemented
685#1436C2×C13111yescharacteristic, complemented
686C22⋊#95C2×C13111yescharacteristic, complemented
687C22⋊#95C2×C13111yescharacteristic, complemented
688C23×D4C22×C13111yescharacteristic
689C23×D4C22×C13111yescharacteristic
690C23×D4C22×C13111yescharacteristic
691C24×C4C22×C13111yescharacteristic
692C24×C4C22×C13111yescharacteristic
693C2×#121—24no—
694C2×#121—24no—
695C2×#121C4×C13118yescomplemented
696C22×C4⋊C4C22×C13111yescharacteristic
697C22×C4⋊C4C22×C13111yescharacteristic
698C22×C22⋊C4C22×C13111yescharacteristic
699C22×C22⋊C4C22×C13111yescharacteristic
700C22×C22⋊C4C22×C13111yescharacteristic
701C22×C22⋊C4C22×C13111yescharacteristic
702C22×C22⋊C4C22×C13111yescharacteristic
703C22×C22⋊C4C22×C13111yescharacteristic
704C22×C22⋊C4C22×C13111yescharacteristic
705C22×C22⋊C4C22×C13111yescharacteristic
706C22×C22⋊C4C22×C13111yescharacteristic
707C22×C22⋊C4C22×C13111yescharacteristic
708C22×C22⋊C4C22×C13111yescharacteristic
709C22×C22⋊C4C22×C13111yescharacteristic
710C22×C22⋊C4C22×C13111yescharacteristic
711C22×C42C22×C13111yescharacteristic
712#390—24no—
713#386—24no—
714#386—24no—
715#381—24no—
716C2×#95C22×C13111yescharacteristic
717C2×#95C22×C13111yescharacteristic
718C2×#95C22×C13111yescharacteristic
719C2×#95C22×C13111yescharacteristic
720C2×#95C22×C13111yescharacteristic
721C2×#95C22×C13111yescharacteristic
722C2×#95C22×C13111yescharacteristic
723C2×#95C22×C13111yescharacteristic
724C2×#95C22×C13111yescharacteristic
725C2×#95C22×C13111yescharacteristic
726C2×#95C22×C13111yescharacteristic
727C2×#95C22×C13111yescharacteristic
728C2×#95C22×C13111yescharacteristic
729C2×#95C22×C13111yescharacteristic
730C25C23×C13111yescharacteristic
731C25C23×C13111yescharacteristic
732C25C23×C13111yescharacteristic
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4C2×C4×C13114yes—
750C22×D4C2×C4×C13114yes—
751C22×D4C2×C4×C13114yescomplemented
752C22×D4D4×C13114yes—
753C22×D4D4×C13114yes—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—41no—
762C23×C4—41no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4C2×C4×C13114yescomplemented
768C23×C4C23×C13111yescharacteristic
769C23×C4C23×C13111yescharacteristic
770C23×C4C23×C13111yescharacteristic
771C23×C4C23×C13111yescharacteristic
772C23×C4C23×C13111yescharacteristic
773C23×C4C23×C13111yescharacteristic
774C23×C4C23×C13111yescharacteristic
775C23×C4C23×C13111yescharacteristic
776C23×C4C23×C13111yescharacteristic
777C23×C4C23×C13111yescharacteristic
778C23×C4C23×C13111yescharacteristic
779C23×C4C23×C13111yescharacteristic
780#121—232no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—41no—
785C2×C4⋊C4—41no—
786C2×C4⋊C4C2×C4×C13114yescomplemented
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—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
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⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4C2×C4×C13114yes—
825C2×C22⋊C4C2×C4×C13114yescomplemented
826C2×C42—22no—
827C2×C42—41no—
828C2×C42—41no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95—41no—
840#95—41no—
841#95—41no—
842#95D4×C13114yescomplemented
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—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24C22×C4×C13112yes—
882C24C22×C4×C13112yes—
883C24C22×C4×C13112yes—
884C24C2×D4×C13112yes—
885C24C2×D4×C13112yes—
886C24C2×D4×C13112yes—
887C24C2×D4×C13112yes—
888C24C24×C13111yescharacteristic
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4C22⋊C4×C131116yescomplemented
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—28no—
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—28no—
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×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4C22×C4×C13112yes—
997C22×C4C22×C4×C13112yes—
998C22×C4C22×C4×C13112yes—
999C22×C4C22×C4×C13112yes—
1000C22×C4C2×D4×C13112yes—
1001C22×C4C2×D4×C13112yes—
1002C22×C4C2×D4×C13112yes—
1003C22×C4C2×D4×C13112yes—
1004C22×C4C2×D4×C13112yes—
1005C22×C4#41×C13112yes—
1006C22×C4#41×C13112yes—
1007C22×C4#41×C13112yes—
1008C4⋊C4—28no—
1009C4⋊C4—44no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C42—44no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
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—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23C2×C22⋊C4×C13114yes—
1128C23C2×C22⋊C4×C13114yes—
1129C23C23×C4×C13111yescharacteristic
1130C23C22×D4×C13111yescharacteristic
1131C23C22×D4×C13111yescharacteristic
1132C23C22×D4×C13111yescharacteristic
1133C23C2×#41×C13111yescharacteristic
1134C23C2×#41×C13111yescharacteristic
1135C23C2×#41×C13111yescharacteristic
1136C23H(5,𝔽2)×C13111yescharacteristic
1137C23H(5,𝔽2)×C13111yescharacteristic
1138C23H(5,𝔽2)×C13111yescharacteristic
1139C23H(5,𝔽2)×C13111yescharacteristic
1140C23H(5,𝔽2)×C13111yescharacteristic
1141C23H(5,𝔽2)×C13111yescharacteristic
1142C23H(5,𝔽2)×C13111yescharacteristic
1143C232−1+4×C13111yescharacteristic
1144D4—416no—
1145D4—416no—
1146D4—416no—
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—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—416no—
1178C2×C4—416no—
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—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4C2×C22⋊C4×C13114yes—
1232C2×C4C4×D4×C13114yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22C22×C22⋊C4×C13111yescharacteristic
1279C22C2×C4×D4×C13111yescharacteristic
1280C22C4×#41×C13111yescharacteristic
1281C22#518×C13111yescharacteristic
1282C22#518×C13111yescharacteristic
1283C22#518×C13111yescharacteristic
1284C22#520×C13111yescharacteristic
1285C22#534×C13111yescharacteristic
1286C22#534×C13111yescharacteristic
1287C22#534×C13111yescharacteristic
1288C22#534×C13111yescharacteristic
1289C22#535×C13111yescharacteristic
1290C22#537×C13111yescharacteristic
1291C22#538×C13111yescharacteristic
1292C22#538×C13111yescharacteristic
1293C22#540×C13111yescharacteristic
1294C22#540×C13111yescharacteristic
1295C22#540×C13111yescharacteristic
1296C22#542×C13111yescharacteristic
1297C22D42×C13111yescharacteristic
1298C22D42×C13111yescharacteristic
1299C22#546×C13111yescharacteristic
1300C22#546×C13111yescharacteristic
1301C22#546×C13111yescharacteristic
1302C22#546×C13111yescharacteristic
1303C22#546×C13111yescharacteristic
1304C22#547×C13111yescharacteristic
1305C22#547×C13111yescharacteristic
1306C22#550×C13111yescharacteristic
1307C22#553×C13111yescharacteristic
1308C22#555×C13111yescharacteristic
1309C22#560×C13111yescharacteristic
1310C22#560×C13111yescharacteristic
1311C22#562×C13111yescharacteristic
1312C22#562×C13111yescharacteristic
1313C4—24no—
1314C4—24no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C2—44no—
1326C2—44no—
1327C2—82no—
1328C2#2308×C13111yescharacteristic
1329C2#2324×C13111yescharacteristic
1330C2#2333×C13111yescharacteristic
1331C2D4×C22⋊C4×C13111yescharacteristic
1332C2#2339×C13111yescharacteristic
1333C2#2363×C13111yescharacteristic
1334C2#2377×C13111yescharacteristic
1335C2#2671×C13111yescharacteristic
1336C2#2673×C13111yescharacteristic
1337C2#2678×C13111yescharacteristic
1338C2#2682×C13111yescharacteristic
1339C2#2686×C13111yescharacteristic
1340C2#2688×C13111yescharacteristic
1341C2#2699×C13111yescharacteristic
1342C2#2701×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC22×#121×C131C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#390×C131C2semidirect
3. C2×#386×C131C2semidirect
4. C2×#386×C131C2semidirect
5. C2×#381×C131C2semidirect
6. #1441×C131C2semidirect
7. #1440×C131C2semidirect
8. #1439×C131C2semidirect
9. #1438×C131C2semidirect
10. #1438×C131C2semidirect
11. #1438×C131C2semidirect
12. #1437×C131C2semidirect
13. #1436×C131C2semidirect
14. C22⋊#95×C131C2semidirect
15. C22⋊#95×C131C2semidirect
23. C2×#121×C131C4semidirect
79. C22×D4×C131C2×C4semidirect
95. C23×C4×C131C2×C4semidirect
114. C2×C4⋊C4×C131C2×C4semidirect
153. C2×C22⋊C4×C131C2×C4semidirect
170. #95×C131D4semidirect
237. C2×D4×C131C22⋊C4semidirect
671. #14363C131direct (N × H)
672. C131#14363direct (N × H)
674. C2×#390C2×C131semidirect
675. C2×#386C2×C131semidirect
676. C2×#386C2×C131semidirect
677. C2×#381C2×C131semidirect
678. #1441C2×C131semidirect
679. #1440C2×C131semidirect
680. #1439C2×C131semidirect
681. #1438C2×C131semidirect
682. #1438C2×C131semidirect
683. #1438C2×C131semidirect
684. #1437C2×C131semidirect
685. #1436C2×C131semidirect
686. C22⋊#95C2×C131semidirect
687. C22⋊#95C2×C131semidirect
695. C2×#121C4×C131semidirect
751. C22×D4C2×C4×C131semidirect
767. C23×C4C2×C4×C131semidirect
786. C2×C4⋊C4C2×C4×C131semidirect
825. C2×C22⋊C4C2×C4×C131semidirect
842. #95D4×C131semidirect
909. C2×D4C22⋊C4×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1312
C2×#390×C1312
C2×#386×C1312
C2×#381×C1312
#1441×C1312
#1440×C1312
#1439×C1312
#1438×C1312
#1437×C1312
#1436×C1312
C22⋊#95×C1312
#14363131