Finite Group Databasebeta

← C131×#25156 #45711040

Subgroups — C131×#25156 #45711040

Order 33536.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C131C211yesmaximal, characteristic, complemented
2C2×#450×C131C211yesmaximal, characteristic
3C2×#450×C131C211yesmaximal, characteristic
4C2×C4×SD16×C131C211yesmaximal, characteristic, complemented
5#2429×C131C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C131C211yesmaximal, characteristic
7#2065×C131C211yesmaximal, characteristic, complemented
8#2035×C131C211yesmaximal, characteristic, complemented
9#2035×C131C211yesmaximal, characteristic, complemented
10#2013×C131C211yesmaximal, characteristic, complemented
11#1968×C131C211yesmaximal, characteristic, complemented
12#1923×C131C211yesmaximal, characteristic, complemented
13#1880×C131C211yesmaximal, characteristic, complemented
14#1877×C131C211yesmaximal, characteristic, complemented
15#1864×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×SD16×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic
19C22×SD16×C131C2211yescharacteristic
20C22×SD16×C131C2211yescharacteristic
21C2×C4⋊Q8×C131C2211yescharacteristic, complemented
22C2×C22⋊Q8×C131C2211yescharacteristic
23C2×C22⋊Q8×C131C2211yescharacteristic
24C2×C4×Q8×C131C2211yescharacteristic, complemented
25C2×C4×D4×C131C2211yescharacteristic
26C2×C4×D4×C131C2211yescharacteristic
27C22×C22⋊C4×C131—21no—
28#461×C131—24no—
29#450×C131—24no—
30#450×C131—24no—
31C4×SD16×C131—24no—
32C2×#106×C131C2211yescharacteristic, complemented
33C2×#106×C131C2211yescharacteristic, complemented
34C2×C4⋊C8×C131C2211yescharacteristic, complemented
35C2×#103×C131C2211yescharacteristic, complemented
36C2×#103×C131C2211yescharacteristic, complemented
37C2×#103×C131C2211yescharacteristic, complemented
38C2×#103×C131C2211yescharacteristic, complemented
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×C22⋊C8×C131C2211yescharacteristic
44C2×C22⋊C8×C131C2211yescharacteristic
45C2×C4×C8×C131C2211yescharacteristic, complemented
46#398×C131—21no—
47#396×C131—21no—
48#391×C131C2211yescharacteristic, complemented
49#390×C131C2211yescharacteristic
50#390×C131C2211yescharacteristic
51#389×C131—21no—
52#389×C131C2211yescharacteristic, complemented
53#388×C131—21no—
54#386×C131—21no—
55#386×C131—21no—
56#380×C131C2211yescharacteristic
57#379×C131—21no—
58C4×C22⋊C4×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#336×C131C2211yescharacteristic, complemented
62#336×C131C2211yescharacteristic, complemented
63C25×C131—21no—
64C22×Q8×C131C2311yescharacteristic
65C22×Q8×C131C2311yescharacteristic
66C22×D4×C131—22no—
67C22×D4×C131—22no—
68C22×D4×C131—22no—
69C22×D4×C131—22no—
70C22×D4×C131—21no—
71C22×D4×C131—41no—
72C22×D4×C131—41no—
73C22×D4×C131C2311yescharacteristic
74C22×D4×C131C2311yescharacteristic
75C23×C4×C131—21no—
76C23×C4×C131—21no—
77C23×C4×C131C2311yescharacteristic
78C2×SD16×C131—22no—
79C2×SD16×C131—22no—
80C2×SD16×C131—22no—
81C2×SD16×C131—22no—
82C2×SD16×C131—22no—
83C2×SD16×C131—22no—
84C2×SD16×C131—22no—
85C2×SD16×C131—22no—
86C2×SD16×C131—22no—
87C2×SD16×C131—41no—
88C2×SD16×C131—41no—
89C2×SD16×C131D414yes—
90C22×C8×C131C2311yescharacteristic
91C22×C8×C131C2311yescharacteristic
92C22×C8×C131C2311yescharacteristic
93C22×C8×C131C2311yescharacteristic
94C4⋊Q8×C131—22no—
95C4⋊Q8×C131—41no—
96C22⋊Q8×C131—22no—
97C22⋊Q8×C131—22no—
98C22⋊Q8×C131—41no—
99C22⋊Q8×C131—41no—
100C4×Q8×C131—22no—
101C4×Q8×C131—41no—
102C4×D4×C131—22no—
103C4×D4×C131—22no—
104C4×D4×C131—41no—
105C4×D4×C131—41no—
106C2×C4⋊C4×C131—21no—
107C2×C4⋊C4×C131—21no—
108C2×C4⋊C4×C131—21no—
109C2×C4⋊C4×C131—21no—
110C2×C4⋊C4×C131—21no—
111C2×C4⋊C4×C131—21no—
112C2×C4⋊C4×C131C2311yescharacteristic
113C2×C4⋊C4×C131C2311yescharacteristic
114C2×C4⋊C4×C131C2311yescharacteristic
115C2×C4⋊C4×C131C2311yescharacteristic
116C2×C22⋊C4×C131—21no—
117C2×C22⋊C4×C131—21no—
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131—21no—
122C2×C22⋊C4×C131—21no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—44no—
126C2×C22⋊C4×C131D411yescharacteristic
127C2×C22⋊C4×C131D411yescharacteristic
128C2×C42×C131—21no—
129C2×C42×C131C2311yescharacteristic
130C2×C42×C131C2311yescharacteristic
131#106×C131—22no—
132#106×C131—41no—
133C4⋊C8×C131—22no—
134#103×C131—22no—
135#103×C131—22no—
136#103×C131—22no—
137#103×C131—41no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141#102×C131D414yes—
142C22⋊C8×C131—22no—
143C22⋊C8×C131—22no—
144C4×C8×C131—22no—
145#95×C131—21no—
146#95×C131—21no—
147#95×C131—21no—
148#95×C131—21no—
149#95×C131D411yescharacteristic
150#95×C131D411yescharacteristic
151C24×C131—21no—
152C24×C131—24no—
153C24×C131—21no—
154C24×C131—42no—
155C24×C131—42no—
156C24×C131—42no—
157C24×C131—42no—
158C24×C131—81no—
159C24×C131—81no—
160C24×C131C2×D411yescharacteristic
161C2×Q8×C131—21no—
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131—21no—
165C2×Q8×C131—21no—
166C2×Q8×C131—21no—
167C2×Q8×C131—21no—
168C2×Q8×C131—21no—
169C2×Q8×C131—21no—
170C2×Q8×C131—21no—
171C2×Q8×C131—21no—
172C2×Q8×C131C2×D412yes—
173C2×D4×C131—24no—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—21no—
180C2×D4×C131—21no—
181C2×D4×C131—21no—
182C2×D4×C131—42no—
183C2×D4×C131—42no—
184C2×D4×C131—44no—
185C2×D4×C131—44no—
186C2×D4×C131—44no—
187C2×D4×C131—44no—
188C2×D4×C131C2×D412yes—
189C2×D4×C131C2×D412yes—
190C2×D4×C131#4112yes—
191C2×D4×C131#4112yes—
192C22×C4×C131—21no—
193C22×C4×C131—21no—
194C22×C4×C131—21no—
195C22×C4×C131—21no—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
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—42no—
205C22×C4×C131—42no—
206C22×C4×C131—42no—
207C22×C4×C131—42no—
208C22×C4×C131—81no—
209C22×C4×C131—81no—
210C22×C4×C131C2×D411yescharacteristic
211C22×C4×C131C2×D411yescharacteristic
212C22×C4×C131C2×D411yescharacteristic
213C22×C4×C131C2×D411yescharacteristic
214C22×C4×C131C2×D411yescharacteristic
215C22×C4×C131C2411yescharacteristic
216SD16×C131—28no—
217SD16×C131—44no—
218SD16×C131—44no—
219SD16×C131—44no—
220C2×C8×C131—21no—
221C2×C8×C131—21no—
222C2×C8×C131—21no—
223C2×C8×C131—21no—
224C2×C8×C131—21no—
225C2×C8×C131—21no—
226C2×C8×C131—21no—
227C2×C8×C131—21no—
228C2×C8×C131—21no—
229C2×C8×C131—21no—
230C2×C8×C131C2×D412yes—
231C2×C8×C131C2×D412yes—
232C4⋊C4×C131—21no—
233C4⋊C4×C131—21no—
234C4⋊C4×C131—21no—
235C4⋊C4×C131—21no—
236C4⋊C4×C131—21no—
237C4⋊C4×C131—21no—
238C4⋊C4×C131—21no—
239C4⋊C4×C131—42no—
240C4⋊C4×C131—42no—
241C4⋊C4×C131—42no—
242C4⋊C4×C131—42no—
243C4⋊C4×C131—42no—
244C4⋊C4×C131—42no—
245C4⋊C4×C131C2×D412yes—
246C22⋊C4×C131—41no—
247C22⋊C4×C131—42no—
248C22⋊C4×C131—42no—
249C22⋊C4×C131—42no—
250C22⋊C4×C131—42no—
251C22⋊C4×C131—42no—
252C22⋊C4×C131—42no—
253C22⋊C4×C131—42no—
254C22⋊C4×C131—81no—
255C22⋊C4×C131—81no—
256C22⋊C4×C131SD1614yescomplemented
257C42×C131—21no—
258C42×C131—21no—
259C42×C131—21no—
260C42×C131—21no—
261C42×C131—42no—
262C23×C131—21no—
263C23×C131—22no—
264C23×C131—21no—
265C23×C131—21no—
266C23×C131—22no—
267C23×C131—22no—
268C23×C131—21no—
269C23×C131—21no—
270C23×C131—21no—
271C23×C131—22no—
272C23×C131—48no—
273C23×C131—48no—
274C23×C131—41no—
275C23×C131—41no—
276C23×C131—41no—
277C23×C131—41no—
278C23×C131—41no—
279C23×C131—41no—
280C23×C131—41no—
281C23×C131—41no—
282C23×C131—41no—
283C23×C131—41no—
284C23×C131—84no—
285C23×C131—84no—
286C23×C131—84no—
287C23×C131—84no—
288C23×C131—84no—
289C23×C131C2×SD1612yes—
290C23×C131C22×D411yescharacteristic
291Q8×C131—22no—
292Q8×C131—22no—
293Q8×C131—41no—
294Q8×C131—41no—
295Q8×C131—41no—
296Q8×C131—41no—
297Q8×C131—41no—
298Q8×C131—41no—
299D4×C131—22no—
300D4×C131—22no—
301D4×C131—22no—
302D4×C131—22no—
303D4×C131—22no—
304D4×C131—48no—
305D4×C131—41no—
306D4×C131—41no—
307D4×C131#12114yes—
308C2×C4×C131—21no—
309C2×C4×C131—21no—
310C2×C4×C131—21no—
311C2×C4×C131—21no—
312C2×C4×C131—21no—
313C2×C4×C131—21no—
314C2×C4×C131—21no—
315C2×C4×C131—22no—
316C2×C4×C131—22no—
317C2×C4×C131—21no—
318C2×C4×C131—21no—
319C2×C4×C131—21no—
320C2×C4×C131—21no—
321C2×C4×C131—21no—
322C2×C4×C131—21no—
323C2×C4×C131—41no—
324C2×C4×C131—41no—
325C2×C4×C131—41no—
326C2×C4×C131—41no—
327C2×C4×C131—41no—
328C2×C4×C131—41no—
329C2×C4×C131—41no—
330C2×C4×C131—41no—
331C2×C4×C131—41no—
332C2×C4×C131—41no—
333C2×C4×C131—41no—
334C2×C4×C131—41no—
335C2×C4×C131—41no—
336C2×C4×C131—41no—
337C2×C4×C131—41no—
338C2×C4×C131—41no—
339C2×C4×C131—41no—
340C2×C4×C131—41no—
341C2×C4×C131—41no—
342C2×C4×C131—41no—
343C2×C4×C131—84no—
344C2×C4×C131—84no—
345C2×C4×C131C2×SD1612yes—
346C2×C4×C131C2×SD1612yes—
347C2×C4×C131C22×D411yescharacteristic
348C2×C4×C131C22×D411yescharacteristic
349C2×C4×C131C2×#4111yescharacteristic
350C2×C4×C131C2×#4111yescharacteristic
351C2×C4×C131H(5,𝔽2)11yescharacteristic
352C2×C4×C131H(5,𝔽2)11yescharacteristic
353C8×C131—22no—
354C8×C131—22no—
355C8×C131—41no—
356C8×C131—41no—
357C22×C131—22no—
358C22×C131—24no—
359C22×C131—22no—
360C22×C131—22no—
361C22×C131—42no—
362C22×C131—41no—
363C22×C131—42no—
364C22×C131—41no—
365C22×C131—41no—
366C22×C131—42no—
367C22×C131—41no—
368C22×C131—42no—
369C22×C131—42no—
370C22×C131—42no—
371C22×C131—42no—
372C22×C131—42no—
373C22×C131—42no—
374C22×C131—816no—
375C22×C131—81no—
376C22×C131—81no—
377C22×C131—81no—
378C22×C131—81no—
379C22×C131#52511yescharacteristic
380C22×C131D4211yescharacteristic
381C22×C131D4211yescharacteristic
382C22×C131C22×SD1611yescharacteristic
383C22×C131#57511yescharacteristic
384C22×C131#57711yescharacteristic
385C22×C131#57711yescharacteristic
386C4×C131—22no—
387C4×C131—22no—
388C4×C131—41no—
389C4×C131—42no—
390C4×C131—41no—
391C4×C131—42no—
392C4×C131—41no—
393C4×C131—81no—
394C4×C131—81no—
395C4×C131—81no—
396C4×C131—81no—
397C4×C131C2×#12111yescharacteristic
398C4×C131#53811yescharacteristic
399C4×C131#54611yescharacteristic
400C4×C131#54611yescharacteristic
401C2×C131—42no—
402C2×C131—44no—
403C2×C131—82no—
404C2×C131#242411yescharacteristic
405C2×C131#310111yescharacteristic
406C2×C131#312311yescharacteristic
407C2×C131#326711yescharacteristic
408C2×C131#327511yescharacteristic
409C2×C131D4×SD1611yescharacteristic
410C2×C131D4×SD1611yescharacteristic
411#25156C13111yesmaximal, characteristic, direct product factor, Sylow
412C131#2515611yescharacteristic, direct product factor, Sylow
413C2×#461C2×C13111yescharacteristic, complemented
414C2×#450C2×C13111yescharacteristic
415C2×#450C2×C13111yescharacteristic
416C2×C4×SD16C2×C13111yescharacteristic, complemented
417#2429C2×C13111yescharacteristic, complemented
418D4×C22⋊C4C2×C13111yescharacteristic
419#2065C2×C13111yescharacteristic, complemented
420#2035C2×C13111yescharacteristic, complemented
421#2035C2×C13111yescharacteristic, complemented
422#2013C2×C13111yescharacteristic, complemented
423#1968C2×C13111yescharacteristic, complemented
424#1923C2×C13111yescharacteristic, complemented
425#1880C2×C13111yescharacteristic, complemented
426#1877C2×C13111yescharacteristic, complemented
427#1864C2×C13111yescharacteristic, complemented
428C23×D4C22×C13111yescharacteristic
429C22×SD16C22×C13111yescharacteristic
430C22×SD16C22×C13111yescharacteristic
431C22×SD16C22×C13111yescharacteristic
432C22×SD16C22×C13111yescharacteristic
433C2×C4⋊Q8C22×C13111yescharacteristic, complemented
434C2×C22⋊Q8C22×C13111yescharacteristic
435C2×C22⋊Q8C22×C13111yescharacteristic
436C2×C4×Q8C22×C13111yescharacteristic, complemented
437C2×C4×D4C22×C13111yescharacteristic
438C2×C4×D4C22×C13111yescharacteristic
439C22×C22⋊C4—21no—
440#461—24no—
441#450—24no—
442#450—24no—
443C4×SD16—24no—
444C2×#106C22×C13111yescharacteristic, complemented
445C2×#106C22×C13111yescharacteristic, complemented
446C2×C4⋊C8C22×C13111yescharacteristic, complemented
447C2×#103C22×C13111yescharacteristic, complemented
448C2×#103C22×C13111yescharacteristic, complemented
449C2×#103C22×C13111yescharacteristic, complemented
450C2×#103C22×C13111yescharacteristic, complemented
451C2×#102C22×C13111yescharacteristic
452C2×#102C22×C13111yescharacteristic
453C2×#102C22×C13111yescharacteristic
454C2×#102C22×C13111yescharacteristic
455C2×C22⋊C8C22×C13111yescharacteristic
456C2×C22⋊C8C22×C13111yescharacteristic
457C2×C4×C8C22×C13111yescharacteristic, complemented
458#398—21no—
459#396—21no—
460#391C22×C13111yescharacteristic, complemented
461#390C22×C13111yescharacteristic
462#390C22×C13111yescharacteristic
463#389—21no—
464#389C22×C13111yescharacteristic, complemented
465#388—21no—
466#386—21no—
467#386—21no—
468#380C22×C13111yescharacteristic
469#379—21no—
470C4×C22⋊C4C22×C13111yescharacteristic
471#340C22×C13111yescharacteristic, complemented
472#340C22×C13111yescharacteristic, complemented
473#336C22×C13111yescharacteristic, complemented
474#336C22×C13111yescharacteristic, complemented
475C25—21no—
476C22×Q8C23×C13111yescharacteristic
477C22×Q8C23×C13111yescharacteristic
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4C23×C13111yescharacteristic
486C22×D4C23×C13111yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C23×C13111yescharacteristic
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16D4×C13114yes—
502C22×C8C23×C13111yescharacteristic
503C22×C8C23×C13111yescharacteristic
504C22×C8C23×C13111yescharacteristic
505C22×C8C23×C13111yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—41no—
511C22⋊Q8—41no—
512C4×Q8—22no—
513C4×Q8—41no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—41no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4C23×C13111yescharacteristic
525C2×C4⋊C4C23×C13111yescharacteristic
526C2×C4⋊C4C23×C13111yescharacteristic
527C2×C4⋊C4C23×C13111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—44no—
538C2×C22⋊C4D4×C13111yescharacteristic
539C2×C22⋊C4D4×C13111yescharacteristic
540C2×C42—21no—
541C2×C42C23×C13111yescharacteristic
542C2×C42C23×C13111yescharacteristic
543#106—22no—
544#106—41no—
545C4⋊C8—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#103—41no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102D4×C13114yes—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C4×C8—22no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95D4×C13111yescharacteristic
562#95D4×C13111yescharacteristic
563C24—21no—
564C24—24no—
565C24—21no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24C2×D4×C13111yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×D4×C13112yes—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4C2×D4×C13112yes—
601C2×D4C2×D4×C13112yes—
602C2×D4#41×C13112yes—
603C2×D4#41×C13112yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C13111yescharacteristic
623C22×C4C2×D4×C13111yescharacteristic
624C22×C4C2×D4×C13111yescharacteristic
625C22×C4C2×D4×C13111yescharacteristic
626C22×C4C2×D4×C13111yescharacteristic
627C22×C4C24×C13111yescharacteristic
628SD16—28no—
629SD16—44no—
630SD16—44no—
631SD16—44no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8C2×D4×C13112yes—
643C2×C8C2×D4×C13112yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C13112yes—
658C22⋊C4—41no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4SD16×C13114yescomplemented
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—42no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—48no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C2×SD16×C13112yes—
702C23C22×D4×C13111yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4#121×C13114yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4C2×SD16×C13112yes—
758C2×C4C2×SD16×C13112yes—
759C2×C4C22×D4×C13111yescharacteristic
760C2×C4C22×D4×C13111yescharacteristic
761C2×C4C2×#41×C13111yescharacteristic
762C2×C4C2×#41×C13111yescharacteristic
763C2×C4H(5,𝔽2)×C13111yescharacteristic
764C2×C4H(5,𝔽2)×C13111yescharacteristic
765C8—22no—
766C8—22no—
767C8—41no—
768C8—41no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—24no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22#525×C13111yescharacteristic
792C22D42×C13111yescharacteristic
793C22D42×C13111yescharacteristic
794C22C22×SD16×C13111yescharacteristic
795C22#575×C13111yescharacteristic
796C22#577×C13111yescharacteristic
797C22#577×C13111yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—41no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×#121×C13111yescharacteristic
810C4#538×C13111yescharacteristic
811C4#546×C13111yescharacteristic
812C4#546×C13111yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2#2424×C13111yescharacteristic
817C2#3101×C13111yescharacteristic
818C2#3123×C13111yescharacteristic
819C2#3267×C13111yescharacteristic
820C2#3275×C13111yescharacteristic
821C2D4×SD16×C13111yescharacteristic
822C2D4×SD16×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC23×D4×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#461×C131C2semidirect
4. C2×C4×SD16×C131C2semidirect
5. #2429×C131C2semidirect
7. #2065×C131C2semidirect
8. #2035×C131C2semidirect
9. #2035×C131C2semidirect
10. #2013×C131C2semidirect
11. #1968×C131C2semidirect
12. #1923×C131C2semidirect
13. #1880×C131C2semidirect
14. #1877×C131C2semidirect
15. #1864×C131C2semidirect
21. C2×C4⋊Q8×C131C22semidirect
24. C2×C4×Q8×C131C22semidirect
32. C2×#106×C131C22semidirect
33. C2×#106×C131C22semidirect
34. C2×C4⋊C8×C131C22semidirect
35. C2×#103×C131C22semidirect
36. C2×#103×C131C22semidirect
37. C2×#103×C131C22semidirect
38. C2×#103×C131C22semidirect
45. C2×C4×C8×C131C22semidirect
48. #391×C131C22semidirect
52. #389×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #336×C131C22semidirect
62. #336×C131C22semidirect
256. C22⋊C4×C131SD16semidirect
411. #25156C131direct (N × H)
412. C131#25156direct (N × H)
413. C2×#461C2×C131semidirect
416. C2×C4×SD16C2×C131semidirect
417. #2429C2×C131semidirect
419. #2065C2×C131semidirect
420. #2035C2×C131semidirect
421. #2035C2×C131semidirect
422. #2013C2×C131semidirect
423. #1968C2×C131semidirect
424. #1923C2×C131semidirect
425. #1880C2×C131semidirect
426. #1877C2×C131semidirect
427. #1864C2×C131semidirect
433. C2×C4⋊Q8C22×C131semidirect
436. C2×C4×Q8C22×C131semidirect
444. C2×#106C22×C131semidirect
445. C2×#106C22×C131semidirect
446. C2×C4⋊C8C22×C131semidirect
447. C2×#103C22×C131semidirect
448. C2×#103C22×C131semidirect
449. C2×#103C22×C131semidirect
450. C2×#103C22×C131semidirect
457. C2×C4×C8C22×C131semidirect
460. #391C22×C131semidirect
464. #389C22×C131semidirect
471. #340C22×C131semidirect
472. #340C22×C131semidirect
473. #336C22×C131semidirect
474. #336C22×C131semidirect
668. C22⋊C4SD16×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1312
C2×#450×C1312
C2×C4×SD16×C1312
#2429×C1312
D4×C22⋊C4×C1312
#2065×C1312
#2035×C1312
#2013×C1312
#1968×C1312
#1923×C1312
#1880×C1312
#1877×C1312
#1864×C1312
#25156131