Finite Group Databasebeta

← C131×#29747 #45715631

Subgroups — C131×#29747 #45715631

Order 33536.

1024 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C131C211yesmaximal, characteristic, complemented
2C2×#408×C131C211yesmaximal, characteristic, complemented
3#2616×C131C211yesmaximal, characteristic, complemented
4#2615×C131C211yesmaximal, characteristic
5#2076×C131C211yesmaximal, characteristic, complemented
6#2075×C131C211yesmaximal, characteristic, complemented
7#2036×C131C211yesmaximal, characteristic, complemented
8#2035×C131C211yesmaximal, characteristic, complemented
9#2034×C131C211yesmaximal, characteristic, complemented
10#2033×C131C211yesmaximal, characteristic, complemented
11#2000×C131C211yesmaximal, characteristic, complemented
12#2000×C131C211yesmaximal, characteristic, complemented
13#1893×C131C211yesmaximal, characteristic, complemented
14#1892×C131C211yesmaximal, characteristic, complemented
15#1809×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×SD16×C131C2211yescharacteristic
18C22×M16×C131C2211yescharacteristic
19C23×C8×C131C2211yescharacteristic
20C2×C22⋊Q8×C131C2211yescharacteristic
21C2×C22⋊Q8×C131C2211yescharacteristic
22C2×C22⋊Q8×C131C2211yescharacteristic
23C2×#121×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25C2×#121×C131C2211yescharacteristic
26#468×C131—24no—
27C2×#107×C131C2211yescharacteristic
28C2×#107×C131C2211yescharacteristic
29C2×#106×C131C2211yescharacteristic
30C2×#103×C131C2211yescharacteristic
31C2×#103×C131C2211yescharacteristic
32C2×#103×C131C2211yescharacteristic
33C2×#102×C131C2211yescharacteristic
34C2×#102×C131C2211yescharacteristic
35C2×#102×C131C2211yescharacteristic
36#408×C131—24no—
37C2×C22⋊C8×C131C2211yescharacteristic
38C2×C22⋊C8×C131C2211yescharacteristic
39C2×C22⋊C8×C131C2211yescharacteristic
40C2×C22⋊C8×C131C2211yescharacteristic
41#395×C131—21no—
42#394×C131—21no—
43#394×C131—21no—
44#394×C131—21no—
45#393×C131—21no—
46#392×C131—21no—
47#392×C131—21no—
48#392×C131—21no—
49#380×C131C2211yescharacteristic
50#380×C131C2211yescharacteristic
51#380×C131C2211yescharacteristic
52#380×C131C2211yescharacteristic
53#380×C131C2211yescharacteristic
54#380×C131C2211yescharacteristic
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic
60#340×C131C2211yescharacteristic
61C2×#41×C131—22no—
62C2×#41×C131—22no—
63C2×#41×C131—41no—
64C2×#41×C131—41no—
65C2×#41×C131—41no—
66C2×#41×C131—41no—
67C22×Q8×C131D411yescharacteristic
68C22×Q8×C131C2311yescharacteristic
69C22×D4×C131—21no—
70C22×D4×C131—21no—
71C22×D4×C131—21no—
72C22×D4×C131D411yescharacteristic
73C22×D4×C131D411yescharacteristic
74C22×D4×C131D411yescharacteristic
75C22×D4×C131C2311yescharacteristic
76C23×C4×C131C2311yescharacteristic
77C23×C4×C131C2311yescharacteristic
78C23×C4×C131C2311yescharacteristic
79C2×SD16×C131—22no—
80C2×SD16×C131—41no—
81C2×SD16×C131—41no—
82C2×M16×C131—41no—
83C2×M16×C131—41no—
84C2×M16×C131D414yescomplemented
85C22×C8×C131—22no—
86C22×C8×C131—41no—
87C22×C8×C131—41no—
88C22×C8×C131C2311yescharacteristic
89C22×C8×C131C2311yescharacteristic
90C22×C8×C131C2311yescharacteristic
91C22×C8×C131C2311yescharacteristic
92C22⋊Q8×C131—22no—
93C22⋊Q8×C131—22no—
94C22⋊Q8×C131—41no—
95C22⋊Q8×C131—41no—
96C22⋊Q8×C131—41no—
97C22⋊Q8×C131—41no—
98#121×C131—22no—
99#121×C131—22no—
100#121×C131—41no—
101#121×C131—41no—
102#121×C131—41no—
103#121×C131—41no—
104C2×C4⋊C4×C131—21no—
105C2×C4⋊C4×C131—21no—
106C2×C4⋊C4×C131—21no—
107C2×C4⋊C4×C131C2311yescharacteristic
108C2×C4⋊C4×C131C2311yescharacteristic
109C2×C4⋊C4×C131C2311yescharacteristic
110C2×C4⋊C4×C131C2311yescharacteristic
111C2×C4⋊C4×C131C2311yescharacteristic
112C2×C4⋊C4×C131C2311yescharacteristic
113C2×C22⋊C4×C131—21no—
114C2×C22⋊C4×C131—21no—
115C2×C22⋊C4×C131—21no—
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—
125#107×C131—22no—
126#107×C131—41no—
127#106×C131—41no—
128#103×C131—22no—
129#103×C131—41no—
130#103×C131—41no—
131#102×C131—22no—
132#102×C131—41no—
133#102×C131—41no—
134C22⋊C8×C131—22no—
135C22⋊C8×C131—22no—
136C22⋊C8×C131—22no—
137C22⋊C8×C131—22no—
138#95×C131—21no—
139#95×C131—21no—
140#95×C131—21no—
141#95×C131—21no—
142#95×C131—21no—
143#95×C131—21no—
144C24×C131—21no—
145C24×C131C2×D411yescharacteristic
146C24×C131C2×D411yescharacteristic
147C24×C131C2×D411yescharacteristic
148#41×C131—44no—
149#41×C131—44no—
150#41×C131—44no—
151#41×C131—44no—
152C2×Q8×C131—22no—
153C2×Q8×C131—21no—
154C2×Q8×C131—21no—
155C2×Q8×C131—21no—
156C2×Q8×C131—21no—
157C2×Q8×C131—21no—
158C2×Q8×C131—21no—
159C2×Q8×C131—41no—
160C2×Q8×C131—41no—
161C2×D4×C131—22no—
162C2×D4×C131—22no—
163C2×D4×C131—22no—
164C2×D4×C131—21no—
165C2×D4×C131—21no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—41no—
171C2×D4×C131—41no—
172C2×D4×C131—41no—
173C2×D4×C131—41no—
174C2×D4×C131—41no—
175C2×D4×C131—41no—
176C2×D4×C131—42no—
177C2×D4×C131—42no—
178C2×D4×C131—42no—
179C2×D4×C131—81no—
180C2×D4×C131—81no—
181C2×D4×C131—81no—
182C2×D4×C131—81no—
183C2×D4×C131—81no—
184C2×D4×C131—81no—
185C22×C4×C131—21no—
186C22×C4×C131—21no—
187C22×C4×C131—21no—
188C22×C4×C131—21no—
189C22×C4×C131—21no—
190C22×C4×C131—21no—
191C22×C4×C131—21no—
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—21no—
205C22×C4×C131—21no—
206C22×C4×C131—21no—
207C22×C4×C131—21no—
208C22×C4×C131C2×D411yescharacteristic
209C22×C4×C131C2×D411yescharacteristic
210C22×C4×C131C2×D411yescharacteristic
211C22×C4×C131C2×D412yes—
212C22×C4×C131#4112yes—
213C22×C4×C131C2411yescharacteristic
214SD16×C131—44no—
215M16×C131—44no—
216C2×C8×C131—21no—
217C2×C8×C131—21no—
218C2×C8×C131—21no—
219C2×C8×C131—21no—
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—44no—
227C2×C8×C131C2×D412yes—
228C2×C8×C131C2×D412yes—
229C4⋊C4×C131—21no—
230C4⋊C4×C131—21no—
231C4⋊C4×C131—21no—
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—21no—
240C4⋊C4×C131—21no—
241C4⋊C4×C131—42no—
242C4⋊C4×C131—42no—
243C4⋊C4×C131—42no—
244C22⋊C4×C131—42no—
245C22⋊C4×C131—42no—
246C22⋊C4×C131—42no—
247C22⋊C4×C131—42no—
248C22⋊C4×C131—42no—
249C22⋊C4×C131—42no—
250C22⋊C4×C131—81no—
251C22⋊C4×C131—81no—
252C22⋊C4×C131—81no—
253C22⋊C4×C131—81no—
254C22⋊C4×C131—81no—
255C22⋊C4×C131—81no—
256C23×C131—21no—
257C23×C131—21no—
258C23×C131—21no—
259C23×C131—21no—
260C23×C131—21no—
261C23×C131—21no—
262C23×C131—21no—
263C23×C131—21no—
264C23×C131—21no—
265C23×C131—21no—
266C23×C131—21no—
267C23×C131—21no—
268C23×C131—21no—
269C23×C131—21no—
270C23×C131—21no—
271C23×C131—21no—
272C23×C131—21no—
273C23×C131—21no—
274C23×C131—21no—
275C23×C131—21no—
276C23×C131—41no—
277C23×C131—41no—
278C23×C131—41no—
279C23×C131—41no—
280C23×C131—41no—
281C23×C131—41no—
282C23×C131—41no—
283C23×C131#12112yes—
284C23×C131C22×D411yescharacteristic
285Q8×C131—44no—
286Q8×C131—41no—
287Q8×C131—41no—
288Q8×C131—41no—
289Q8×C131—41no—
290D4×C131—44no—
291D4×C131—44no—
292D4×C131—44no—
293D4×C131—41no—
294D4×C131—41no—
295D4×C131—41no—
296D4×C131—41no—
297D4×C131—84no—
298D4×C131—84no—
299D4×C131—84no—
300C2×C4×C131—21no—
301C2×C4×C131—21no—
302C2×C4×C131—22no—
303C2×C4×C131—22no—
304C2×C4×C131—22no—
305C2×C4×C131—22no—
306C2×C4×C131—21no—
307C2×C4×C131—21no—
308C2×C4×C131—21no—
309C2×C4×C131—21no—
310C2×C4×C131—21no—
311C2×C4×C131—21no—
312C2×C4×C131—41no—
313C2×C4×C131—41no—
314C2×C4×C131—41no—
315C2×C4×C131—41no—
316C2×C4×C131—41no—
317C2×C4×C131—41no—
318C2×C4×C131—41no—
319C2×C4×C131—41no—
320C2×C4×C131—41no—
321C2×C4×C131—41no—
322C2×C4×C131—41no—
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#12112yes—
342C2×C4×C131C22×D411yescharacteristic
343C2×C4×C131C2×#4111yescharacteristic
344C2×C4×C131H(5,𝔽2)11yescharacteristic
345C2×C4×C131H(5,𝔽2)11yescharacteristic
346C2×C4×C131H(5,𝔽2)11yescharacteristic
347C2×C4×C131H(5,𝔽2)11yescharacteristic
348C8×C131—22no—
349C8×C131—22no—
350C8×C131—41no—
351C8×C131—41no—
352C22×C131—22no—
353C22×C131—22no—
354C22×C131—22no—
355C22×C131—41no—
356C22×C131—41no—
357C22×C131—41no—
358C22×C131—41no—
359C22×C131—41no—
360C22×C131—41no—
361C22×C131—41no—
362C22×C131—41no—
363C22×C131—41no—
364C22×C131—41no—
365C22×C131—41no—
366C22×C131—41no—
367C22×C131—41no—
368C22×C131—41no—
369C22×C131—41no—
370C22×C131—41no—
371C22×C131—41no—
372C22×C131—41no—
373C22×C131—81no—
374C22×C131—81no—
375C22×C131—81no—
376C22×C131—81no—
377C22×C131—81no—
378C22×C131—81no—
379C22×C131—81no—
380C22×C131C2×#12111yescharacteristic
381C22×C131#53411yescharacteristic
382C22×C131#53411yescharacteristic
383C22×C131#57611yescharacteristic
384C22×C131#57711yescharacteristic
385C22×C131#57711yescharacteristic
386C22×C131#57811yescharacteristic
387C4×C131—22no—
388C4×C131—41no—
389C4×C131—41no—
390C4×C131—81no—
391C4×C131—81no—
392C4×C131—81no—
393C4×C131—81no—
394C4×C131—81no—
395C4×C131—81no—
396C4×C131—81no—
397C4×C131#53411yescharacteristic
398C4×C131#53511yescharacteristic
399C4×C131#53811yescharacteristic
400C4×C131#53811yescharacteristic
401C2×C131—42no—
402C2×C131—81no—
403C2×C131—81no—
404C2×C131—161no—
405C2×C131#261711yescharacteristic
406C2×C131#306211yescharacteristic
407C2×C131#306311yescharacteristic
408C2×C131#319811yescharacteristic
409C2×C131#320011yescharacteristic
410C2×C131#320111yescharacteristic
411C2×C131#320311yescharacteristic
412#29747C13111yesmaximal, characteristic, direct product factor, Sylow
413C131#2974711yescharacteristic, direct product factor, Sylow
414C2×#468C2×C13111yescharacteristic, complemented
415C2×#408C2×C13111yescharacteristic, complemented
416#2616C2×C13111yescharacteristic, complemented
417#2615C2×C13111yescharacteristic
418#2076C2×C13111yescharacteristic, complemented
419#2075C2×C13111yescharacteristic, complemented
420#2036C2×C13111yescharacteristic, complemented
421#2035C2×C13111yescharacteristic, complemented
422#2034C2×C13111yescharacteristic, complemented
423#2033C2×C13111yescharacteristic, complemented
424#2000C2×C13111yescharacteristic, complemented
425#2000C2×C13111yescharacteristic, complemented
426#1893C2×C13111yescharacteristic, complemented
427#1892C2×C13111yescharacteristic, complemented
428#1809C2×C13111yescharacteristic, complemented
429C22×#41C22×C13111yescharacteristic
430C22×SD16C22×C13111yescharacteristic
431C22×M16C22×C13111yescharacteristic
432C23×C8C22×C13111yescharacteristic
433C2×C22⋊Q8C22×C13111yescharacteristic
434C2×C22⋊Q8C22×C13111yescharacteristic
435C2×C22⋊Q8C22×C13111yescharacteristic
436C2×#121C22×C13111yescharacteristic
437C2×#121C22×C13111yescharacteristic
438C2×#121C22×C13111yescharacteristic
439#468—24no—
440C2×#107C22×C13111yescharacteristic
441C2×#107C22×C13111yescharacteristic
442C2×#106C22×C13111yescharacteristic
443C2×#103C22×C13111yescharacteristic
444C2×#103C22×C13111yescharacteristic
445C2×#103C22×C13111yescharacteristic
446C2×#102C22×C13111yescharacteristic
447C2×#102C22×C13111yescharacteristic
448C2×#102C22×C13111yescharacteristic
449#408—24no—
450C2×C22⋊C8C22×C13111yescharacteristic
451C2×C22⋊C8C22×C13111yescharacteristic
452C2×C22⋊C8C22×C13111yescharacteristic
453C2×C22⋊C8C22×C13111yescharacteristic
454#395—21no—
455#394—21no—
456#394—21no—
457#394—21no—
458#393—21no—
459#392—21no—
460#392—21no—
461#392—21no—
462#380C22×C13111yescharacteristic
463#380C22×C13111yescharacteristic
464#380C22×C13111yescharacteristic
465#380C22×C13111yescharacteristic
466#380C22×C13111yescharacteristic
467#380C22×C13111yescharacteristic
468#340C22×C13111yescharacteristic
469#340C22×C13111yescharacteristic
470#340C22×C13111yescharacteristic
471#340C22×C13111yescharacteristic
472#340C22×C13111yescharacteristic
473#340C22×C13111yescharacteristic
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8D4×C13111yescharacteristic
481C22×Q8C23×C13111yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C13111yescharacteristic
486C22×D4D4×C13111yescharacteristic
487C22×D4D4×C13111yescharacteristic
488C22×D4C23×C13111yescharacteristic
489C23×C4C23×C13111yescharacteristic
490C23×C4C23×C13111yescharacteristic
491C23×C4C23×C13111yescharacteristic
492C2×SD16—22no—
493C2×SD16—41no—
494C2×SD16—41no—
495C2×M16—41no—
496C2×M16—41no—
497C2×M16D4×C13114yescomplemented
498C22×C8—22no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8C23×C13111yescharacteristic
502C22×C8C23×C13111yescharacteristic
503C22×C8C23×C13111yescharacteristic
504C22×C8C23×C13111yescharacteristic
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—41no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510C22⋊Q8—41no—
511#121—22no—
512#121—22no—
513#121—41no—
514#121—41no—
515#121—41no—
516#121—41no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4C23×C13111yescharacteristic
521C2×C4⋊C4C23×C13111yescharacteristic
522C2×C4⋊C4C23×C13111yescharacteristic
523C2×C4⋊C4C23×C13111yescharacteristic
524C2×C4⋊C4C23×C13111yescharacteristic
525C2×C4⋊C4C23×C13111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
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—21no—
538#107—22no—
539#107—41no—
540#106—41no—
541#103—22no—
542#103—41no—
543#103—41no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24C2×D4×C13111yescharacteristic
559C24C2×D4×C13111yescharacteristic
560C24C2×D4×C13111yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—41no—
573C2×Q8—41no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
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—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4C2×D4×C13111yescharacteristic
622C22×C4C2×D4×C13111yescharacteristic
623C22×C4C2×D4×C13111yescharacteristic
624C22×C4C2×D4×C13112yes—
625C22×C4#41×C13112yes—
626C22×C4C24×C13111yescharacteristic
627SD16—44no—
628M16—44no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—44no—
640C2×C8C2×D4×C13112yes—
641C2×C8C2×D4×C13112yes—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23#121×C13112yes—
697C23C22×D4×C13111yescharacteristic
698Q8—44no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703D4—44no—
704D4—44no—
705D4—44no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
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#121×C13112yes—
755C2×C4C22×D4×C13111yescharacteristic
756C2×C4C2×#41×C13111yescharacteristic
757C2×C4H(5,𝔽2)×C13111yescharacteristic
758C2×C4H(5,𝔽2)×C13111yescharacteristic
759C2×C4H(5,𝔽2)×C13111yescharacteristic
760C2×C4H(5,𝔽2)×C13111yescharacteristic
761C8—22no—
762C8—22no—
763C8—41no—
764C8—41no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22C2×#121×C13111yescharacteristic
794C22#534×C13111yescharacteristic
795C22#534×C13111yescharacteristic
796C22#576×C13111yescharacteristic
797C22#577×C13111yescharacteristic
798C22#577×C13111yescharacteristic
799C22#578×C13111yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4#534×C13111yescharacteristic
811C4#535×C13111yescharacteristic
812C4#538×C13111yescharacteristic
813C4#538×C13111yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—161no—
818C2#2617×C13111yescharacteristic
819C2#3062×C13111yescharacteristic
820C2#3063×C13111yescharacteristic
821C2#3198×C13111yescharacteristic
822C2#3200×C13111yescharacteristic
823C2#3201×C13111yescharacteristic
824C2#3203×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#2615×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C131C2semidirect
2. C2×#408×C131C2semidirect
3. #2616×C131C2semidirect
5. #2076×C131C2semidirect
6. #2075×C131C2semidirect
7. #2036×C131C2semidirect
8. #2035×C131C2semidirect
9. #2034×C131C2semidirect
10. #2033×C131C2semidirect
11. #2000×C131C2semidirect
12. #2000×C131C2semidirect
13. #1893×C131C2semidirect
14. #1892×C131C2semidirect
15. #1809×C131C2semidirect
84. C2×M16×C131D4semidirect
412. #29747C131direct (N × H)
413. C131#29747direct (N × H)
414. C2×#468C2×C131semidirect
415. C2×#408C2×C131semidirect
416. #2616C2×C131semidirect
418. #2076C2×C131semidirect
419. #2075C2×C131semidirect
420. #2036C2×C131semidirect
421. #2035C2×C131semidirect
422. #2034C2×C131semidirect
423. #2033C2×C131semidirect
424. #2000C2×C131semidirect
425. #2000C2×C131semidirect
426. #1893C2×C131semidirect
427. #1892C2×C131semidirect
428. #1809C2×C131semidirect
497. C2×M16D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1312
C2×#408×C1312
#2616×C1312
#2615×C1312
#2076×C1312
#2075×C1312
#2036×C1312
#2035×C1312
#2034×C1312
#2033×C1312
#2000×C1312
#1893×C1312
#1892×C1312
#1809×C1312
#29747131