Finite Group Databasebeta

← C31×#17650 #21474409

Subgroups — C31×#17650 #21474409

Order 7936.

1070 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C211yesmaximal, characteristic
2C2×C31×#432C211yesmaximal, characteristic, complemented
3C2×C4×M16×C31C211yesmaximal, characteristic, complemented
4C31×#1532C214yesmaximal, complemented
5C31×#1528C212yesmaximal, complemented
6C31×#1527C212yesmaximal, complemented
7C31×#1524C214yesmaximal, complemented
8C22×M16×C31—21no—
9C31×#529—21no—
10C31×#529—21no—
11C31×#529—21no—
12C31×#529—21no—
13C31×#529C412yes—
14C31×#529C412yes—
15C31×#529C2212yes—
16C31×#529C2212yes—
17C2×C31×#126—21no—
18C2×C31×#125C2211yescharacteristic
19C2×C31×#124C2211yescharacteristic
20C2×C31×#123—21no—
21C2×C31×C22⋊Q8C411yescharacteristic
22C2×C31×#121C411yescharacteristic
23C2×C4×Q8×C31C411yescharacteristic
24C2×C4×D4×C31—21no—
25C2×C4×D4×C31C411yescharacteristic
26C2×C31×#117—21no—
27C22×C42×C31C2211yescharacteristic
28C31×#432—21no—
29C31×#432—21no—
30C31×#432C2212yes—
31C31×#432C2212yescomplemented
32C2×C31×C4⋊C8—21no—
33C2×C31×C22⋊C8—21no—
34C4×M16×C31—21no—
35C4×M16×C31—21no—
36C4×M16×C31C2212yes—
37C4×M16×C31C2212yescomplemented
38C2×C31×#97C2212yescomplemented
39C2×C31×#97C2212yescomplemented
40C2×C4×C8×C31—21no—
41C31×#330C2218yescomplemented
42C31×#329C2218yescomplemented
43C22×Q8×C31C2×C411yescharacteristic
44C22×D4×C31—21no—
45C22×D4×C31C2×C411yescharacteristic
46C23×C4×C31—21no—
47C23×C4×C31C2×C411yescharacteristic
48C23×C4×C31D411yescharacteristic
49C23×C4×C31D411yescharacteristic
50C2×M16×C31—28no—
51C2×M16×C31—22no—
52C2×M16×C31—22no—
53C22×C8×C31—22no—
54C22×C8×C31—22no—
55C31×#126—22no—
56C31×#126—22no—
57C31×#126—22no—
58C31×#126—22no—
59C31×#125—21no—
60C31×#125—21no—
61C31×#125C2×C412yes—
62C31×#125C2312yes—
63C31×#124—21no—
64C31×#124—21no—
65C31×#124C2×C412yes—
66C31×#124C2312yes—
67C31×#123—22no—
68C31×#123—22no—
69C31×#123—22no—
70C31×#123—22no—
71C31×C22⋊Q8—21no—
72C31×C22⋊Q8—21no—
73C31×C22⋊Q8C2×C412yes—
74C31×C22⋊Q8C2×C412yes—
75C31×#121—21no—
76C31×#121—21no—
77C31×#121C2×C412yes—
78C31×#121C2×C412yes—
79C4×Q8×C31—21no—
80C4×Q8×C31—21no—
81C4×Q8×C31C2×C412yes—
82C4×Q8×C31C2×C412yes—
83C4×D4×C31—22no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C4×D4×C31—21no—
88C4×D4×C31—21no—
89C4×D4×C31C2×C412yes—
90C4×D4×C31C2×C412yes—
91C31×#117—22no—
92C31×#117—22no—
93C31×#117—22no—
94C31×#117—22no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31C2×C411yescharacteristic
100C2×C4⋊C4×C31C2×C411yescharacteristic
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31C2×C411yescharacteristic
108C2×C42×C31C2×C411yescharacteristic
109C2×C42×C31C2×C411yescharacteristic
110C2×C42×C31D411yescharacteristic
111C2×C42×C31D411yescharacteristic
112C2×C42×C31D411yescharacteristic
113C2×C42×C31D411yescharacteristic
114C2×C42×C31D411yescharacteristic
115C2×C42×C31D411yescharacteristic
116C2×C42×C31C2311yescharacteristic
117C2×C42×C31C2311yescharacteristic
118C2×C42×C31C2311yescharacteristic
119C31×C4⋊C8—22no—
120C31×C4⋊C8—22no—
121C31×C22⋊C8—22no—
122C31×C22⋊C8—22no—
123C31×#97—22no—
124C31×#97—22no—
125C31×#97C2314yes—
126C31×#97C2314yes—
127C4×C8×C31—22no—
128C4×C8×C31—22no—
129C24×C31—21no—
130C24×C31C22⋊C411yescharacteristic
131C2×Q8×C31—21no—
132C2×Q8×C31—42no—
133C2×Q8×C31C22×C412yes—
134C2×D4×C31—22no—
135C2×D4×C31—22no—
136C2×D4×C31—21no—
137C2×D4×C31—42no—
138C2×D4×C31—44no—
139C2×D4×C31C22×C412yes—
140C22×C4×C31—24no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—42no—
147C22×C4×C31—42no—
148C22×C4×C31—44no—
149C22×C4×C31C22⋊C411yescharacteristic
150C22×C4×C31C22⋊C411yescharacteristic
151C22×C4×C31C22⋊C411yescharacteristic
152C22×C4×C31C22⋊C411yescharacteristic
153C22×C4×C31C22⋊C411yescharacteristic
154C22×C4×C31C22⋊C411yescharacteristic
155C22×C4×C31C22⋊C411yescharacteristic
156C22×C4×C31C22⋊C411yescharacteristic
157C22×C4×C31C22⋊C411yescharacteristic
158C22×C4×C31C22×C411yescharacteristic
159C22×C4×C31C22×C411yescharacteristic
160C22×C4×C31C22×C411yescharacteristic
161C22×C4×C31C2×D411yescharacteristic
162C22×C4×C31C2×D411yescharacteristic
163C22×C4×C31C2×D411yescharacteristic
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167M16×C31—28no—
168M16×C31—28no—
169C2×C8×C31—28no—
170C2×C8×C31—24no—
171C2×C8×C31—24no—
172C2×C8×C31—44no—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—22no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—21no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—22no—
183C4⋊C4×C31C22×C412yes—
184C4⋊C4×C31C22×C412yes—
185C22⋊C4×C31—22no—
186C22⋊C4×C31—22no—
187C22⋊C4×C31—22no—
188C22⋊C4×C31—22no—
189C22⋊C4×C31—22no—
190C22⋊C4×C31—22no—
191C22⋊C4×C31—22no—
192C22⋊C4×C31—22no—
193C22⋊C4×C31—22no—
194C22⋊C4×C31—22no—
195C42×C31—22no—
196C42×C31—22no—
197C42×C31C22⋊C411yescharacteristic
198C42×C31C22⋊C411yescharacteristic
199C42×C31C22⋊C411yescharacteristic
200C42×C31C22⋊C411yescharacteristic
201C42×C31C22⋊C411yescharacteristic
202C42×C31C22⋊C411yescharacteristic
203C42×C31C22×C411yescharacteristic
204C42×C31C22×C411yescharacteristic
205C42×C31C22×C411yescharacteristic
206C42×C31C2×D411yescharacteristic
207C42×C31C2×D411yescharacteristic
208C42×C31C2×D411yescharacteristic
209C42×C31C2×D411yescharacteristic
210C42×C31C2×D411yescharacteristic
211C42×C31C2×D411yescharacteristic
212C42×C31C2411yescharacteristic
213#17650C3111yesmaximal, characteristic, direct product factor, Sylow
214C23×C31—22no—
215C23×C31—41no—
216C23×C31—41no—
217C23×C31—42no—
218C23×C31—42no—
219C23×C31—42no—
220C23×C31#10414yes—
221C23×C31C2×C22⋊C411yescharacteristic
222C23×C31C2×C22⋊C411yescharacteristic
223C23×C31C2×C22⋊C411yescharacteristic
224Q8×C31—42no—
225Q8×C31—42no—
226D4×C31—42no—
227D4×C31—44no—
228D4×C31—44no—
229D4×C31—42no—
230C2×C4×C31—22no—
231C2×C4×C31—22no—
232C2×C4×C31—22no—
233C2×C4×C31—22no—
234C2×C4×C31—22no—
235C2×C4×C31—22no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—22no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—22no—
245C2×C4×C31—41no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—41no—
250C2×C4×C31—41no—
251C2×C4×C31—44no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—42no—
255C2×C4×C31—44no—
256C2×C4×C31C2×C22⋊C411yescharacteristic
257C2×C4×C31C2×C22⋊C411yescharacteristic
258C2×C4×C31C2×C22⋊C411yescharacteristic
259C2×C4×C31C2×C22⋊C411yescharacteristic
260C2×C4×C31C2×C22⋊C411yescharacteristic
261C2×C4×C31C2×C22⋊C411yescharacteristic
262C2×C4×C31C2×C22⋊C411yescharacteristic
263C2×C4×C31C2×C22⋊C411yescharacteristic
264C2×C4×C31C2×C22⋊C411yescharacteristic
265C2×C4×C31C23×C411yescharacteristic
266C2×C4×C31C22×D411yescharacteristic
267C2×C4×C31C22×D411yescharacteristic
268C8×C31—28no—
269C8×C31—44no—
270C2×#529C2×C3111yescharacteristic
271C2×#432C2×C3111yescharacteristic, complemented
272C2×C4×M16C2×C3111yescharacteristic, complemented
273#1532C2×C3114yescomplemented
274#1528C2×C3112yescomplemented
275#1527C2×C3112yescomplemented
276#1524C2×C3114yescomplemented
277C22×C31—21no—
278C22×C31—21no—
279C22×C31—21no—
280C22×C31—21no—
281C22×C31—21no—
282C22×C31—21no—
283C22×C31—44no—
284C22×C31—42no—
285C22×C31—42no—
286C22×C31—42no—
287C22×C31—84no—
288C22×C31C2×#10412yes—
289C22×C31C2×#10412yes—
290C22×C31C2×#10412yes—
291C22×C31C22×C22⋊C411yescharacteristic
292C4×C31—21no—
293C4×C31—21no—
294C4×C31—21no—
295C4×C31—21no—
296C4×C31—21no—
297C4×C31—21no—
298C4×C31—21no—
299C4×C31—21no—
300C4×C31—21no—
301C4×C31—21no—
302C4×C31—42no—
303C4×C31—42no—
304C4×C31—42no—
305C4×C31#41312yes—
306C4×C31#42112yes—
307C22×M16—21no—
308#529—21no—
309#529—21no—
310#529—21no—
311#529—21no—
312#529C4×C3112yes—
313#529C4×C3112yes—
314#529C22×C3112yes—
315#529C22×C3112yes—
316C2×#126—21no—
317C2×#125C22×C3111yescharacteristic
318C2×#124C22×C3111yescharacteristic
319C2×#123—21no—
320C2×C22⋊Q8C4×C3111yescharacteristic
321C2×#121C4×C3111yescharacteristic
322C2×C4×Q8C4×C3111yescharacteristic
323C2×C4×D4—21no—
324C2×C4×D4C4×C3111yescharacteristic
325C2×#117—21no—
326C22×C42C22×C3111yescharacteristic
327#432—21no—
328#432—21no—
329#432C22×C3112yes—
330#432C22×C3112yescomplemented
331C2×C4⋊C8—21no—
332C2×C22⋊C8—21no—
333C4×M16—21no—
334C4×M16—21no—
335C4×M16C22×C3112yes—
336C4×M16C22×C3112yescomplemented
337C2×#97C22×C3112yescomplemented
338C2×#97C22×C3112yescomplemented
339C2×C4×C8—21no—
340#330C22×C3118yescomplemented
341#329C22×C3118yescomplemented
342C2×C31—22no—
343C2×C31—22no—
344C2×C31—22no—
345C2×C31—82no—
346C2×C31C2×#41311yescharacteristic
347C2×C31C22×#10411yescharacteristic
348C2×C31C2×#42111yescharacteristic
349C22×Q8C2×C4×C3111yescharacteristic
350C22×D4—21no—
351C22×D4C2×C4×C3111yescharacteristic
352C23×C4—21no—
353C23×C4C2×C4×C3111yescharacteristic
354C23×C4D4×C3111yescharacteristic
355C23×C4D4×C3111yescharacteristic
356C2×M16—28no—
357C2×M16—22no—
358C2×M16—22no—
359C22×C8—22no—
360C22×C8—22no—
361#126—22no—
362#126—22no—
363#126—22no—
364#126—22no—
365#125—21no—
366#125—21no—
367#125C2×C4×C3112yes—
368#125C23×C3112yes—
369#124—21no—
370#124—21no—
371#124C2×C4×C3112yes—
372#124C23×C3112yes—
373#123—22no—
374#123—22no—
375#123—22no—
376#123—22no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8C2×C4×C3112yes—
380C22⋊Q8C2×C4×C3112yes—
381#121—21no—
382#121—21no—
383#121C2×C4×C3112yes—
384#121C2×C4×C3112yes—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8C2×C4×C3112yes—
388C4×Q8C2×C4×C3112yes—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4C2×C4×C3112yes—
396C4×D4C2×C4×C3112yes—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4C2×C4×C3111yescharacteristic
406C2×C4⋊C4C2×C4×C3111yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C42—21no—
413C2×C42C2×C4×C3111yescharacteristic
414C2×C42C2×C4×C3111yescharacteristic
415C2×C42C2×C4×C3111yescharacteristic
416C2×C42D4×C3111yescharacteristic
417C2×C42D4×C3111yescharacteristic
418C2×C42D4×C3111yescharacteristic
419C2×C42D4×C3111yescharacteristic
420C2×C42D4×C3111yescharacteristic
421C2×C42D4×C3111yescharacteristic
422C2×C42C23×C3111yescharacteristic
423C2×C42C23×C3111yescharacteristic
424C2×C42C23×C3111yescharacteristic
425C4⋊C8—22no—
426C4⋊C8—22no—
427C22⋊C8—22no—
428C22⋊C8—22no—
429#97—22no—
430#97—22no—
431#97C23×C3114yes—
432#97C23×C3114yes—
433C4×C8—22no—
434C4×C8—22no—
435C31#1765011yescharacteristic, direct product factor, Sylow
436C24—21no—
437C24C22⋊C4×C3111yescharacteristic
438C2×Q8—21no—
439C2×Q8—42no—
440C2×Q8C22×C4×C3112yes—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—44no—
446C2×D4C22×C4×C3112yes—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—44no—
456C22×C4C22⋊C4×C3111yescharacteristic
457C22×C4C22⋊C4×C3111yescharacteristic
458C22×C4C22⋊C4×C3111yescharacteristic
459C22×C4C22⋊C4×C3111yescharacteristic
460C22×C4C22⋊C4×C3111yescharacteristic
461C22×C4C22⋊C4×C3111yescharacteristic
462C22×C4C22⋊C4×C3111yescharacteristic
463C22×C4C22⋊C4×C3111yescharacteristic
464C22×C4C22⋊C4×C3111yescharacteristic
465C22×C4C22×C4×C3111yescharacteristic
466C22×C4C22×C4×C3111yescharacteristic
467C22×C4C22×C4×C3111yescharacteristic
468C22×C4C2×D4×C3111yescharacteristic
469C22×C4C2×D4×C3111yescharacteristic
470C22×C4C2×D4×C3111yescharacteristic
471C22×C4C2×D4×C3111yescharacteristic
472C22×C4C2×D4×C3111yescharacteristic
473C22×C4C2×D4×C3111yescharacteristic
474M16—28no—
475M16—28no—
476C2×C8—28no—
477C2×C8—24no—
478C2×C8—24no—
479C2×C8—44no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4C22×C4×C3112yes—
491C4⋊C4C22×C4×C3112yes—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C42—22no—
503C42—22no—
504C42C22⋊C4×C3111yescharacteristic
505C42C22⋊C4×C3111yescharacteristic
506C42C22⋊C4×C3111yescharacteristic
507C42C22⋊C4×C3111yescharacteristic
508C42C22⋊C4×C3111yescharacteristic
509C42C22⋊C4×C3111yescharacteristic
510C42C22×C4×C3111yescharacteristic
511C42C22×C4×C3111yescharacteristic
512C42C22×C4×C3111yescharacteristic
513C42C2×D4×C3111yescharacteristic
514C42C2×D4×C3111yescharacteristic
515C42C2×D4×C3111yescharacteristic
516C42C2×D4×C3111yescharacteristic
517C42C2×D4×C3111yescharacteristic
518C42C2×D4×C3111yescharacteristic
519C42C24×C3111yescharacteristic
520C23—22no—
521C23—41no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23C31×#10414yes—
527C23C2×C22⋊C4×C3111yescharacteristic
528C23C2×C22⋊C4×C3111yescharacteristic
529C23C2×C22⋊C4×C3111yescharacteristic
530Q8—42no—
531Q8—42no—
532D4—42no—
533D4—44no—
534D4—44no—
535D4—42no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—44no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4C2×C22⋊C4×C3111yescharacteristic
563C2×C4C2×C22⋊C4×C3111yescharacteristic
564C2×C4C2×C22⋊C4×C3111yescharacteristic
565C2×C4C2×C22⋊C4×C3111yescharacteristic
566C2×C4C2×C22⋊C4×C3111yescharacteristic
567C2×C4C2×C22⋊C4×C3111yescharacteristic
568C2×C4C2×C22⋊C4×C3111yescharacteristic
569C2×C4C2×C22⋊C4×C3111yescharacteristic
570C2×C4C2×C22⋊C4×C3111yescharacteristic
571C2×C4C23×C4×C3111yescharacteristic
572C2×C4C22×D4×C3111yescharacteristic
573C2×C4C22×D4×C3111yescharacteristic
574C8—28no—
575C8—44no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—44no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—84no—
587C22C2×C31×#10412yes—
588C22C2×C31×#10412yes—
589C22C2×C31×#10412yes—
590C22C22×C22⋊C4×C3111yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—42no—
602C4—42no—
603C4—42no—
604C4C31×#41312yes—
605C4C31×#42112yes—
606C2—22no—
607C2—22no—
608C2—22no—
609C2—82no—
610C2C2×C31×#41311yescharacteristic
611C2C22×C31×#10411yescharacteristic
612C2C2×C31×#42111yescharacteristic
subgroupG/H
centerC2×C4×C31C2×C22⋊C4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC42C24×C31
socleC22×C31C22×C22⋊C4
prime radicalC2×C31×#121C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#432C2semidirect
3. C2×C4×M16×C31C2semidirect
4. C31×#1532C2semidirect
5. C31×#1528C2semidirect
6. C31×#1527C2semidirect
7. C31×#1524C2semidirect
31. C31×#432C22semidirect
37. C4×M16×C31C22semidirect
38. C2×C31×#97C22semidirect
39. C2×C31×#97C22semidirect
41. C31×#330C22semidirect
42. C31×#329C22semidirect
213. #17650C31direct (N × H)
271. C2×#432C2×C31semidirect
272. C2×C4×M16C2×C31semidirect
273. #1532C2×C31semidirect
274. #1528C2×C31semidirect
275. #1527C2×C31semidirect
276. #1524C2×C31semidirect
330. #432C22×C31semidirect
336. C4×M16C22×C31semidirect
337. C2×#97C22×C31semidirect
338. C2×#97C22×C31semidirect
340. #330C22×C31semidirect
341. #329C22×C31semidirect
435. C31#17650direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5292
C2×C31×#4322
C2×C4×M16×C312
C31×#15322
C31×#15282
C31×#15272
C31×#15242
#1765031